diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/0RuesRQixLY.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/0RuesRQixLY.srt new file mode 100644 index 0000000000000000000000000000000000000000..dbc44ee5c181517d2a48fe521cc641e903bc621b --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/0RuesRQixLY.srt @@ -0,0 +1,3377 @@ +1 +00:00:21,740 --> 00:00:25,520 +كل واحد يفتح لي على رسمة الـ trigonometric + +2 +00:00:25,520 --> 00:00:30,920 +functions اللي رسمناها المرة الماضية، مينحاول نستفيد + +3 +00:00:30,920 --> 00:00:35,120 +أو نطلع من خلال الرسم بعض الشغلات الأساسية + +4 +00:00:35,120 --> 00:00:39,620 +المتعلقة بالـ trigonometric functions، طلع لي في + +5 +00:00:39,620 --> 00:00:46,340 +الرسمة كويس، طلع لي في رسمة cos X و sec X في الأول + +6 +00:00:47,740 --> 00:00:57,020 +كوكوساين الـ X وكذلك مقلوبها سيك الـ X، شو رأيك في رسمة + +7 +00:00:57,020 --> 00:01:02,060 +كوكوساين الـ X؟ هل هي متماثلة بالنسبة لمحور Y؟ يعني هل + +8 +00:01:02,060 --> 00:01:06,180 +الرسم اللي على يمين محور Y زي الرسم اللي على شمال + +9 +00:01:06,180 --> 00:01:11,900 +محور Y؟ بالضبط، يعني طيب ممتاز، لو كان المنحنى متماثل + +10 +00:01:11,900 --> 00:01:17,290 +بالنسبة لمحور Y، يبقى دالة بنسميها even function + +11 +00:01:17,290 --> 00:01:23,910 +بناء عليه cosine الـ X is an even function، طلع لي + +12 +00:01:23,910 --> 00:01:29,530 +لسيك X اللي هي مقلوب الـ cosine، برضه الرسمة اللي على + +13 +00:01:29,530 --> 00:01:36,300 +يمين محور Y زي الرسمة اللي على شمال محور Y، يبقى + +14 +00:01:36,300 --> 00:01:42,720 +بناء عليه كذلك سيك الـ X is even function، تمام تمام. + +15 +00:01:42,720 --> 00:01:48,220 +اللي هنضايق مع مين عندنا؟ الأربع نسب الأخرى اللي هي + +16 +00:01:48,220 --> 00:01:55,470 +مين؟ ساين الـ X، تان الـ X، كوتان الـ X، كوسيكانت الـ X. + +17 +00:01:55,470 --> 00:01:59,630 +الأربع نسب الأخرى، فالله عليك في الرسمات تبعتهم شوف + +18 +00:01:59,630 --> 00:02:05,050 +ليهم، هل هي متماثلة بالنسبة لنقطة الأصل أم لا؟ بمعنى + +19 +00:02:05,050 --> 00:02:11,510 +لو رسمت أي خط يمر بنقطة الأصل بيكون بعد أي نقطة + +20 +00:02:11,510 --> 00:02:15,170 +على الناحية دي ازاي البعد من الناحية الثانية أم + +21 +00:02:15,170 --> 00:02:20,250 +لا؟ مين + +22 +00:02:20,250 --> 00:02:21,530 +اللي بتعترض عليها؟ + +23 +00:02:28,180 --> 00:02:33,740 +آخر واحدة، مظبوط؟ ارسم أي خط يمر بنقطة الأصل، خط + +24 +00:02:33,740 --> 00:02:39,720 +اللي عجبك، وشوفها متماثلة بالنسبة له ولا لأ، أي نقطة + +25 +00:02:39,720 --> 00:02:43,020 +على منحنى الـ cosecant من الناحية دي، وأي نقطة + +26 +00:02:43,020 --> 00:02:47,060 +على منحنى ال cosecant من الناحية المناظرة لها، نفس + +27 +00:02:47,060 --> 00:02:52,610 +البعد ولا لأ؟ يبقى عندك الأربع نسب أو الأربع نسب + +28 +00:02:52,610 --> 00:02:58,610 +الأخرى كلها are odd functions، تمام؟ يبقى النسب + +29 +00:02:58,610 --> 00:03:04,790 +المثلثية الستة، اثنين منهم even وأربعة odd، الكلام + +30 +00:03:04,790 --> 00:03:09,070 +اللي بنقوله بدنا نسجله ونشوف ما هو المعنى الرياضي + +31 +00:03:09,070 --> 00:03:12,610 +له، يبقى باجي بقول from the graph of the + +32 +00:03:12,610 --> 00:03:17,370 +trigonometric functions we have، النقطة الأولى + +33 +00:03:17,370 --> 00:03:28,090 +cosine الـ X and Sec X، أو + +34 +00:03:28,090 --> 00:03:35,870 +graph is symmetric about + +35 +00:03:35,870 --> 00:03:40,970 +the Y axis. + +36 +00:03:44,770 --> 00:03:51,990 +أي أن لما تبقى الـ cosine even يبقى cosine لسالب x + +37 +00:03:51,990 --> 00:03:58,990 +شو بده تساوي؟ تعريف الـ even function، cosine الـ x + +38 +00:03:58,990 --> 00:04:03,790 +and second لسالب x + +39 +00:04:22,840 --> 00:04:26,700 +هذه النقطة الأولى، النقطة الثانية + +40 +00:04:29,520 --> 00:04:33,900 +الشيء اللي قلناه هو symmetric about the y-axis، + +41 +00:04:33,900 --> 00:04:43,580 +يعني هذا بدي أعطيك إنه cosine الـ x and sec الـ x + +42 +00:04:43,580 --> 00:04:51,420 +are even functions، يبقى هدول دوال زوجية، الآن بدنا + +43 +00:04:51,420 --> 00:05:00,400 +نيجي لقدام لـ sign الـ X وكذلك تان الـ X وكذلك كتان + +44 +00:05:00,400 --> 00:05:12,620 +الـ X and cosecant الـ X are symmetric about + +45 +00:05:12,620 --> 00:05:14,760 +the origin. + +46 +00:05:23,180 --> 00:05:29,120 +يبقى هدول symmetric about the origin، that is، ساين + +47 +00:05:29,120 --> 00:05:39,720 +الـ X وتان الـ X وكوتان الـ X and ال cosecant X are + +48 +00:05:39,720 --> 00:05:47,040 +odd functions، هذا شو بده يعطيك؟ هذا بده يعطيك + +49 +00:05:47,040 --> 00:05:57,120 +معناها ساين لسالب x بده يساوي سالب ساين الـ x، تان لسالب x + +50 +00:05:57,120 --> 00:06:07,500 +بده يساوي سالب تان الـ x، كوتان لسالب x يساوي سالب كوتان الـ x and + +51 +00:06:07,500 --> 00:06:14,100 +كوسيكانت لسالب x يساوي سالب كوسيكانت الـ x. + +52 +00:06:19,080 --> 00:06:27,660 +ساين الاكس يساوي سالب سين الاكس، وتان الاكس يساوي + +53 +00:06:27,660 --> 00:06:36,780 +سالب تان الاكس، وكوتان لسالب اكس يساوي سالب كوتان + +54 +00:06:36,780 --> 00:06:43,260 +الاكس، وكوسيكانت لسالب اكس يساوي سالب كوسيكانت الاكس. + +55 +00:06:43,260 --> 00:06:50,030 +هذا معناه الـ odd function، يبقى النسب المثلثية ستة، + +56 +00:06:50,030 --> 00:06:57,470 +اثنين even وأربعة odd، يبقى كوساين لسالب X هو كوساين X، + +57 +00:06:57,470 --> 00:07:05,090 +سكند لسالب X هي سكند X، ساين لسالب X بسالب ساين X، + +58 +00:07:05,090 --> 00:07:10,870 +تان لسالب X هو سالب تان X، كوتان لسالب X هو سالب + +59 +00:07:10,870 --> 00:07:18,020 +كوتان X، كوسيكانت لسالب X هو سالب كوسيكانت X، الآن + +60 +00:07:18,020 --> 00:07:22,820 +بدنا نربط القديم بالجديد، يعني بدنا نعطي أمثلة على + +61 +00:07:22,820 --> 00:07:27,400 +المثال اللي وقتاش بتكون الدالة even ووقتاش بتكون + +62 +00:07:27,400 --> 00:07:32,600 +الدالة odd وبدنا ندخل فيها النسب المثلثية اللي + +63 +00:07:32,600 --> 00:07:36,880 +عندنا، يبقى بدنا نعطي مثال توضيحي على ذلك، يبقى + +64 +00:07:36,880 --> 00:07:44,000 +example، المثال + +65 +00:07:44,000 --> 00:07:53,190 +بيقول ما يأتي، determine whether + +66 +00:07:53,190 --> 00:08:02,010 +the following functions + +67 +00:08:02,010 --> 00:08:11,130 +are even, odd or neither. + +68 +00:08:13,690 --> 00:08:20,350 +هل هي even ولا odd والله لا even ولا odd، نمرة a + +69 +00:08:20,350 --> 00:08:31,690 +بدنا ناخد الدالة f of x يساوي x تربيع cosine 2x، + +70 +00:08:33,710 --> 00:08:38,610 +مشان نحكم على هذه الـ function يبقى بنيجي بنشيل كل + +71 +00:08:38,610 --> 00:08:43,910 +X وبنحط مكانها مين؟ سالب X، يبقى بنا نيجي ناخد F + +72 +00:08:43,910 --> 00:08:52,850 +of سالب X، يبقى هذه سالب X الكل تربيع، Cos 2 في سالب + +73 +00:08:52,850 --> 00:09:02,870 +X، هذه بدها تساوي X تربيع itself، وهذه كوساين لثلاث + +74 +00:09:02,870 --> 00:09:09,450 +اتنين X، الآن الـ cosine even يبقى ثالث بالزاوية + +75 +00:09:09,450 --> 00:09:14,670 +وهذه تطير وتبقى باسم الزاوية، يبقى هذا الكلام + +76 +00:09:14,670 --> 00:09:20,600 +يعطينا X تربيع في كوساين 2X، الآن الـ cosine + +77 +00:09:20,600 --> 00:09:31,700 +هي عبارة + +78 +00:09:31,700 --> 00:09:36,740 +عن رأس المسألة اللي عندنا، يبقى هذا بده يساوي الـ F + +79 +00:09:36,740 --> 00:09:41,940 +of X itself، يبقى معناه هذا الكلام إن الدالة هذه + +80 +00:09:41,940 --> 00:09:49,700 +معناها is even function، الـ F of X يساوي X تربيع + +81 +00:09:49,700 --> 00:10:01,820 +فيه Cos 2X is an even function، طيب نيجي ناخد كمان + +82 +00:10:01,820 --> 00:10:09,600 +function أخرى نمرة بيه، الـ F of X يساوي، يساوي مين؟ + +83 +00:10:09,860 --> 00:10:17,380 +absolute value لـ X زائد ساين square X، كله مقسومًا + +84 +00:10:17,380 --> 00:10:20,760 +على الجذر الثالث لـ X + +85 +00:10:26,010 --> 00:10:35,370 +هذه بدها تساوي أو بدي اخذ الـ F of سالب X، يبقى سالب + +86 +00:10:35,370 --> 00:10:42,230 +اللي هو الـ X كله كـ absolute value، زائد sin تربيع + +87 +00:10:42,230 --> 00:10:48,450 +لسالب X على الجذر الثالث لسالب X + +88 +00:10:51,370 --> 00:10:56,370 +هذا الكلام بده يساوي، أظن من خلاص الـ absolute value + +89 +00:10:56,370 --> 00:11:02,430 +هذا بتعطينا absolute value لـ X كما هي، هذه باجي + +90 +00:11:02,430 --> 00:11:11,090 +بقول هيك، يطلع لي كويس، لما أقول sin²x، أليست هي sin + +91 +00:11:11,090 --> 00:11:19,390 +x الكل square؟ تمام تمام، يبقى هذه الـ sin odd، يبقى + +92 +00:11:19,390 --> 00:11:28,180 +لما أقول sin لسالب x الكل تربيع، يبقى سالب sin x + +93 +00:11:28,180 --> 00:11:35,840 +الكل تربيع، إذا هذه مربعها شو بدي يعطيني؟ sin تربيع + +94 +00:11:35,840 --> 00:11:44,260 +الـ x، يبقى هذه زائد سالب ساين X الكل تربيع على هذه + +95 +00:11:44,260 --> 00:11:50,860 +الجذر الثالث، السالب واحد، هذه أليست هي السالب واحد + +96 +00:11:50,860 --> 00:11:52,880 +الكل تكعيب X + +97 +00:11:56,270 --> 00:12:03,030 +سكت الشعب مش شايف بالضبط، بس هذا مين؟ الجذر الثالث + +98 +00:12:03,030 --> 00:12:08,210 +طب كتبت هيك ليش؟ كتبت عشان بس بدي أوضح لك إن السالب + +99 +00:12:08,210 --> 00:12:13,610 +هذه تبقى كما هي، طيب هذا الكلام بده يساوي absolute + +100 +00:12:13,610 --> 00:12:19,090 +value لـ X، هذه لما ربيعها بيطير السالب بيصير sine + +101 +00:12:19,090 --> 00:12:26,860 +square X، هذه يساوي السالب الجذر الثالث لـ X، سالب + +102 +00:12:26,860 --> 00:12:31,200 +واحد الكل تكعيب، طلعها برا الجذر، تطلع السالب برا الجذر + +103 +00:12:31,200 --> 00:12:38,600 +بظل الجذر الثالث لمين؟ لـ X، ممكن أخد هذه السالب عامل + +104 +00:12:38,600 --> 00:12:43,200 +مشترك من الكل، ويبقى عندي في الداخل absolute value + +105 +00:12:43,200 --> 00:12:52,070 +لـ X، ساين تربيع الـ X، وهنا الجذر الثالث لـ X، سؤال هو + +106 +00:12:52,070 --> 00:12:56,850 +المقدار بين القوسين مش هو عبارة عن أصل المثل اللي + +107 +00:12:56,850 --> 00:13:02,150 +فوق؟ يبقى بده أشيله وأحط بداله F of X، وشرط السالب + +108 +00:13:02,150 --> 00:13:09,190 +هي ضرورة، يبقى سالب F of X، يبقى بناء عليه F of سالب X + +109 +00:13:09,190 --> 00:13:13,590 +صار تانية مية سالب F of X، معناه هذا الكلام إن الدالة + +110 +00:13:13,590 --> 00:13:19,690 +F معناها odd function، يبقى سؤال F is M + +111 +00:13:22,880 --> 00:13:36,320 +F of X يساوي واحد زائد تان X زائد 2 باي على + +112 +00:13:36,320 --> 00:13:48,940 +مين؟ على سك الـ X ناقص 2 باي، مش عارف + +113 +00:13:48,940 --> 00:13:55,560 +اكتب الدالة بشكل ألطف من الشكل اللي قدامنا، باجي بقول + +114 +00:13:55,560 --> 00:14:02,360 +هذه عبارة عن واحد زائد هذه X زائد 2 باي، قداش + +115 +00:14:02,360 --> 00:14:08,080 +الـ period تبعت التان باي، طيب يبقى بقدر احذف باي + +116 +00:14:08,080 --> 00:14:13,300 +ومضاعفات 2 باي و 3 باي و 10 باي كله بقدر + +117 +00:14:13,300 --> 00:14:17,030 +احذفه، ما عنديش مشكلة إن هذه الـ period تبعتي التان. + +118 +00:14:17,030 --> 00:14:23,530 +إذا هذه بالضبط هي واحد زائد تان الـ X على الـ + +119 +00:14:23,530 --> 00:14:29,770 +period لسك كده؟ 2 باي، يبقى احذف والله أضف لن + +120 +00:14:29,770 --> 00:14:34,150 +تغير في القيمة، إذا هذه لو أضفت لها 2 باي كده + +121 +00:14:34,150 --> 00:14:41,080 +ستبقى ال... سك X فقط، لغير يبقى هذه صارت سك X، يبقى + +122 +00:14:41,080 --> 00:14:46,040 +صارت مسألتي بالشكل قدامنا هذا، يبقى أنا لسه الخطوة + +123 +00:14:46,040 --> 00:14:52,440 +الأولى حطيت المسألة في شكل جديد مكافئ للشكل الأول، + +124 +00:14:52,440 --> 00:15:01,140 +بروح أخذ f of سالب x يساوي واحد زائد تان لسالب x + +125 +00:15:01,140 --> 00:15:08,800 +على سكند لسالب x، ويساوي واحد، التان قد والله even، + +126 +00:15:11,220 --> 00:15:17,920 +يعني السالب هذا ماله؟ يطلع برة، يبقى هنا سالب تان + +127 +00:15:17,920 --> 00:15:19,580 +الـ X، السك + +128 +00:15:23,470 --> 00:15:33,650 +يبقى هذا لا + +129 +00:15:33,650 --> 00:15:36,530 +يساوي f of x، + +130 +00:15:58,370 --> 00:16:04,070 +بأخذ إشارة سالب من البسط عامل مشترك، يبقى لو أخذت + +131 +00:16:04,070 --> 00:16:10,010 +إشارة سالب من البسط عامل مشترك، بضل ناقص واحد زائد + +132 +00:16:10,010 --> 00:16:17,420 +تان الـ X على المقام اللي هو سك X كما هو، يبقى هل + +133 +00:16:17,420 --> 00:16:22,600 +المقدار بين القوسين هو الدالة الأصلية اللي هناك؟ لأ، + +134 +00:16:22,600 --> 00:16:29,520 +برضه ما هو شهوة، يبقى كمان لا يساوي سالب F of X، + +135 +00:16:29,520 --> 00:16:35,920 +يبقى الدالة ما لها not، odd، بناء عليه الدالة هذه is + +136 +00:16:35,920 --> 00:16:45,690 +neither even nor odd، يبقى سواء الـ F is neither even + +137 +00:16:45,690 --> 00:16:52,390 +nor odd، يبقى لا هذا ولا ذاك. + +138 +00:17:13,450 --> 00:17:18,890 +الآن بدنا نيجي لآخر نقطة في هذا الـ section واللي + +139 +00:17:18,890 --> 00:17:26,910 +هي عبارة عن الـ trigonometric identities. + +140 +00:17:32,870 --> 00:17:37,730 +المتطابقات المثلثية، وهذه غالبكم كانوا بيتضايقوا + +141 +00:17:37,730 --> 00:17:42,610 +منها وهم في المرحلة الثانوية، وهنعرضها لك إن شاء + +142 +00:17:42,610 --> 00:17:48,170 +الله بطريقة سهلة ومبسطة ويسيرة، خلي بالك، معناه + +143 +00:17:48,910 --> 00:17:55,030 +يبقى باجي لأول متطابقة من هذه المتطابقات، أظن فش + +144 +00:17:55,030 --> 00:18:00,950 +واحد يكون بجهلها، زائد كوساين تربيع الـ X بواحد، كله + +145 +00:18:00,950 --> 00:18:05,750 +بعرفها، هذه مظلوم، فش واحد بعرفهاش، طيب يبقى لو جيت + +146 +00:18:05,750 --> 00:18:12,510 +للمتطابقة الأولى، كوساين تربيع الـ X زائد ساين تربيع + +147 +00:18:12,510 --> 00:18:18,650 +الـ X يساوي واحد، مش رأيك هذه هطلع منها متطابقتين + +148 +00:18:18,650 --> 00:18:25,390 +أخرى منها، مرة بدي أقسم عليكم ساين تربيع ومرة + +149 +00:18:25,390 --> 00:18:29,110 +بده أقسم علي ساين تربيع بطلعتين تانية، يبقى + +150 +00:18:29,110 --> 00:18:32,840 +بيصيروا جداش؟ ثلاث، لكن ثلاث هو في الحقيقة هما + +151 +00:18:32,840 --> 00:18:37,640 +واحدة في الشريحة تمام، إذا لو قسمت على كوساين تربيع + +152 +00:18:37,640 --> 00:18:41,860 +جداش؟ بيطلع عندي هنا واحد، ساين تربيع على كوساين + +153 +00:18:41,860 --> 00:18:47,380 +تربيع ليهم، مين؟ تان تربيع الـ X، واحد على كوساين تربيع + +154 +00:18:47,380 --> 00:18:53,800 +دي مقلوب السيك يبقى سك تربيع الـ X، تمام، ما حدا + +155 +00:18:53,800 --> 00:18:57,520 +أحسن من حدا، زي ما قسمت على كوساين تربيع بدك تروح + +156 +00:18:57,520 --> 00:19:01,520 +تقسم على الـ ساين تربيع بيصير الـ كوساين تربيع على الـ ساين + +157 +00:19:01,520 --> 00:19:09,740 +تربيع بكوتان تربيع الـ X زائد واحد سواء على الـ ساين + +158 +00:19:09,740 --> 00:19:15,700 +تربيع اللي بكوسيكانت تربيع الـ X، يبقى هي عندي صار عندي + +159 +00:19:15,700 --> 00:19:21,180 +ثلاث متطابقات مثلثية، لكن في الحقيقة هذه واحدة بس + +160 +00:19:21,180 --> 00:19:24,780 +بتنتهي إن بجيبهم بسهولة، الباقية اقسم إن اجت معاك + +161 +00:19:24,780 --> 00:19:34,990 +دغري، طيب، ننتقل إلى المتطابقة الثانية كنت زمان أعلمكم + +162 +00:19:34,990 --> 00:19:41,210 +ما هو جاء ألف زائد باء، جاء ألف زائد باء، جاء ألف + +163 +00:19:41,210 --> 00:19:46,570 +جابا زائد جتا ألف جابا، نبدأ بجاء وجتا، وبعد كده + +164 +00:19:46,570 --> 00:19:50,150 +نقلب، اللي كانت جتا بنخليها جتا، واللي كانت جتا + +165 +00:19:50,150 --> 00:19:54,670 +بنخليها جا، مش هيك كنت أعلمكم؟ احنا نفس القصة، بس هنقول + +166 +00:19:54,670 --> 00:20:01,020 +ساين وكوساين، يبقى بالداخل ميم لساين + +167 +00:20:02,220 --> 00:20:10,620 +الـ X زائد الـ Y يساوي ساين الأولى كوساين التانية + +168 +00:20:10,620 --> 00:20:18,120 +يبقى هي ساين X في كوساين Y، الشارع هذه الزائد اللي + + +201 +00:24:03,060 --> 00:24:08,400 +الشباب إنه بيفهم هذه فهما جامدا كيف يعني فهما + +202 +00:24:08,400 --> 00:24:12,220 +جامدا يعني بقول لك هذا أنا مش حافظ غيره لكن هذا أنا + +203 +00:24:12,220 --> 00:24:17,240 +بقدر أطوعه حسب المثل اللي عندي ازاي ما بدي فمثلا + +204 +00:24:17,240 --> 00:24:26,980 +لو كانت هذه Sin 6X ستة اكس مش اثنين اكس طلع اثنين + +205 +00:24:26,980 --> 00:24:30,540 +هذا القاعدة بتاعت القانون والزاوية اللي جوا هنا + +206 +00:24:30,540 --> 00:24:35,600 +نصف الزاوية اللي برا يعني لو كانت هذه ال sign ستة + +207 +00:24:35,600 --> 00:24:42,180 +اكس بقول له اثنين sin ثلاثة اكس cosine ثلاثة اكس عادي + +208 +00:24:42,180 --> 00:24:51,600 +جدا، لو كان sin 10x، يبقى بقول له 2sin 5x cos 5x، طب + +209 +00:24:51,600 --> 00:25:01,100 +لو كانت هذه sin X فقط، يبقى بصير 2 زي ما هي sin X + +210 +00:25:01,100 --> 00:25:07,020 +على 2 cos X على 2، يعني sin نصف ال X في cos نصف ال X، + +211 +00:25:07,020 --> 00:25:09,980 +الزاوية اللي جوا، نصف في الزاوية اللي برا، تفضل + +212 +00:25:14,480 --> 00:25:21,780 +ما لها؟ هذه زائد + +213 +00:25:21,780 --> 00:25:28,760 +يبقى هذه زائد اللي تحت ناقص هذه ناقص يبقى هنا ناقص + +214 +00:25:28,760 --> 00:25:33,640 +هذه زائدة عكسها تماما ال cos زي بعضه المقام مخالف + +215 +00:25:33,640 --> 00:25:39,560 +في الإشارة تمام طيب أروح نكمل باقي شغلنا يبقى أنا + +216 +00:25:39,560 --> 00:25:46,280 +بدي أستخدم هذا القانون أو هذه القاعدة متى لازم + +217 +00:25:46,280 --> 00:25:51,820 +الأمر يعني حسب طبيعة المثل اللي عندي بدي أحور هذا + +218 +00:25:51,820 --> 00:25:56,670 +زي ما بدي حسب نوع المثل اللي موجودة عنه مش هذا + +219 +00:25:56,670 --> 00:26:00,650 +جامد ما لهش ليونة لابد ليونة زي ما بدك حسب طبيعة + +220 +00:26:00,650 --> 00:26:06,930 +المثل يبقى هذه النقطة اللي هي sin 2x بدنا نروح + +221 +00:26:06,930 --> 00:26:13,350 +لـ cos 2x يعني لو ال X ساوي ال Y يبقى ايش بيصير عندي + +222 +00:26:13,350 --> 00:26:21,830 +هنا cos 2x شوف ايش بيصير بصير cosine x cosine ال y + +223 +00:26:21,830 --> 00:26:26,510 +يعني cosine x في cosine ال x يعني cosine تربيع ال + +224 +00:26:26,510 --> 00:26:32,690 +x sine x sine x يبقى sine تربيع ال x إذا نهديها + +225 +00:26:32,690 --> 00:26:41,130 +بصير cosine تربيع ال x ناقص sine تربيع ال x تمام + +226 +00:26:41,130 --> 00:26:48,440 +أصلًا صبر شوية راجع يبقى الآن الصيغة الأولى لـ cos 2x + +227 +00:26:48,440 --> 00:26:53,980 +باجي على الصيغة لأن هذه بشيل كل y و بحط مكانها x + +228 +00:26:53,980 --> 00:26:57,820 +بصير cos تربيع ناقص sin تربيع ال x + +229 +00:27:04,000 --> 00:27:13,220 +هشام إسماعيل ياغي ياغي ياغي ياغي ياغي ياغي + +230 +00:27:13,220 --> 00:27:19,820 +ياغي ياغي ياغي ياغي ياغي ياغي ياغي + +231 +00:27:19,930 --> 00:27:25,410 +بقول لك يا إبراهيم قال ال sign تربيع هذه بدي آجي من فوق و + +232 +00:27:25,410 --> 00:27:29,470 +أكتبها بدلالة ال cosine إذا أنا بقدر أشيل ال sign + +233 +00:27:29,470 --> 00:27:34,430 +تربيع و أكتب بدلالة واحد ناقص cosine تربيع طيب هي + +234 +00:27:34,430 --> 00:27:40,770 +مسبوقة بناقص بصير cosine تربيع بالموجب والواحد + +235 +00:27:40,770 --> 00:27:46,310 +بالسالب إذا بصير هذه اثنين cosine تربيع ال X ناقص + +236 +00:27:46,310 --> 00:27:52,470 +واحد يبقى هذه بصير اثنين cosine تربيع ال X ناقص + +237 +00:27:52,470 --> 00:27:57,950 +واحد من وين جبتها هذا from واحد من الأولى هذا from + +238 +00:28:05,220 --> 00:28:10,740 +بس اصبر علينا شوية واحدة واحدة احنا جايين يبقى + +239 +00:28:10,740 --> 00:28:16,340 +الآن هذه صارت cosine اثنين X لها صيغتان الصيغة + +240 +00:28:16,340 --> 00:28:19,440 +الأولى cosine تربيع ال X ناقص sine تربيع ال X + +241 +00:28:19,440 --> 00:28:24,240 +الصيغة الثانية اثنين cosine تربيع ال X ناقص واحد + +242 +00:28:24,240 --> 00:28:32,050 +اجى صاحبنا هذا المستعجل أقول شو اسمك أنت؟ آدم زايد + +243 +00:28:32,050 --> 00:28:50,670 +زايد زايد زايد زايد زايد زايد زايد زايد زايد زايد + +244 +00:28:50,850 --> 00:28:56,350 +بيقول لي هذه يستوي، قل لي بالله على ال cosine تربيع + +245 +00:28:56,350 --> 00:29:03,210 +هذه و أخلص منها بقول له بيكتب واحد ناقص sin + +246 +00:29:03,210 --> 00:29:08,550 +تربيع ال X بيصير ناقص sin تربيع و ناقص sin تربيع + +247 +00:29:08,550 --> 00:29:14,690 +بناقص اثنين sided يعني بيصير هذه واحد ناقص اثنين + +248 +00:29:14,690 --> 00:29:21,730 +sin تربيع ال X يبقى أسعار cosine 2x لها ثلاث صيغ + +249 +00:29:21,730 --> 00:29:26,970 +الصيغة الأولى cosine تربيع ال X نقص sin تربيع ال X + +250 +00:29:26,970 --> 00:29:30,470 +الصيغة الثانية اثنين cosine تربيع ال X نقص واحد + +251 +00:29:30,470 --> 00:29:38,580 +الصيغة الثالثة واحد نقص اثنين sin تربيع ال X يبقى + +252 +00:29:38,580 --> 00:29:43,860 +ياغي و زايد قالوا لنا فيه صيغتين غير الصيغة الأولى + +253 +00:29:43,860 --> 00:29:49,060 +قلنا ماشي تمام و كتبنا الصيغة الثلاث بدنا قانون واحد + +254 +00:29:49,060 --> 00:29:54,200 +ثالث غير اثنين ويقترح علينا اقتراح آخر في حد بده + +255 +00:29:54,200 --> 00:30:00,900 +يقترح أيوة فارق من المفضل أيوة طبعًا فارق من المفضل + +256 +00:30:00,900 --> 00:30:04,440 +يعني بصير جذر اثنين cosine ال X ناقص واحد جذر + +257 +00:30:04,440 --> 00:30:09,130 +اثنين cosine X زائد واحد لأ بنأتي بجديد أنا بدي جديد + +258 +00:30:09,130 --> 00:30:14,350 +أستعمله و أنا بشتغل فيه؟ إذا ما فيش أنا بأجيب ها + +259 +00:30:14,350 --> 00:30:21,390 +أيوه هاي احنا الساعة بهاي الدول يا رجل ما وصلناش ال 10 + +260 +00:30:21,390 --> 00:30:25,930 +فيها ها دي أنا بحكي ها + +261 +00:30:25,930 --> 00:30:31,290 +ماهي فيه + +262 +00:30:31,290 --> 00:30:37,400 +جديد؟ طيب أنا من هدول بدي أطلع لك شغلة جديدة و اسميها + +263 +00:30:37,400 --> 00:30:45,760 +رقم أربعة رقم أربعة شوف يا سيد أطلع لي في هذه + +264 +00:30:45,760 --> 00:30:51,860 +cosine اثنين اكس وهذه شايف فاهم؟ بدي أوصل واحد على + +265 +00:30:51,860 --> 00:30:56,540 +الشغلة الثانية ايش بيصير؟ واحد زائد cosine اثنين اكس + +266 +00:30:56,540 --> 00:31:03,260 +بدي أقسم كله على اثنين بصينا عند مين؟ cosine تربيع + +267 +00:31:03,260 --> 00:31:10,520 +ال X يساوي النص في واحد زائد cosine اثنين X يعني + +268 +00:31:10,520 --> 00:31:16,320 +جبت مربع النسبة المثلثية بواسطة النسبة المثلثية بس + +269 +00:31:16,320 --> 00:31:20,400 +ضعف الزاوية الزاوية اللي جوا جد الزاوية اللي برا + +270 +00:31:20,400 --> 00:31:25,440 +ما لها مرتين بعكس ال sign كانت ال sign الزاوية اللي + +271 +00:31:25,440 --> 00:31:30,600 +برا جد اللي جوا مرتين تمام هذه اللي جوا جد اللي + +272 +00:31:30,600 --> 00:31:36,320 +برا مرتين على عكسها تماما طيب كويس ما حدش أحسن من + +273 +00:31:36,320 --> 00:31:40,160 +حد زي ما جبت هذه جبنا ثانية زي ما جبنا cosine + +274 +00:31:40,160 --> 00:31:47,300 +تربيع ال X يبقى بدنا نروح نجيب sin تربيع ال X يبقى + +275 +00:31:47,300 --> 00:31:48,920 +نصف في واحد + +276 +00:32:02,420 --> 00:32:09,730 +لغاية هنا هذول أهم المتطابقات المثلثية في Calculus + +277 +00:32:09,730 --> 00:32:14,150 +A و Calculus B و Calculus C و المعادلة التفاضلية و + +278 +00:32:14,150 --> 00:32:18,550 +الفيزياء و اللي مش عارف ايه كل الشغلة تتعلق + +279 +00:32:18,550 --> 00:32:24,090 +بالرياضيات هدول هم الأساس طبعًا في أخريات طبعًا لكن + +280 +00:32:24,090 --> 00:32:31,710 +هدول أهم حاجة بتقابلنا أثناء الشغل طب نكمل ها بدنا + +281 +00:32:31,710 --> 00:32:40,510 +نروح نيجي لمن لتان جيت sin2x و cos2x بدنا tan + +282 +00:32:40,510 --> 00:32:45,190 +اثنين اكس رغم أنها نادرة الاستعمال عندنا في ال + +283 +00:32:45,190 --> 00:32:48,550 +calculus أهم حاجة مين اللي هي ال sin و ال cos لكن + +284 +00:32:48,550 --> 00:32:54,910 +بدنا نقولها إذا لو جيت هنا خمسة و روحت قلت بدي + +285 +00:32:54,910 --> 00:33:02,790 +tan اثنين اكس يساوي يبقى شيلنا واي وحطينا مكان X + +286 +00:33:02,790 --> 00:33:09,330 +بيصير tan اثنين X بيصير tan X زائد tan ال X باثنين + +287 +00:33:09,330 --> 00:33:17,230 +tan ال X يبقى باثنين tan ال X على واحد ناقص tan + +288 +00:33:17,230 --> 00:33:22,350 +تربيع ال X مش ده تهمية كتير ماهياش مهمة عندنا كتير + +289 +00:33:23,200 --> 00:33:29,320 +هذه خمسة ابني جي الستة ستة شباب في إن حاجة اسمها + +290 +00:33:29,320 --> 00:33:37,660 +قاعدة جيوب التمام ال law of cosine يبقى ال law of + +291 +00:33:37,660 --> 00:33:43,800 +cosine ايش قاعدة جيوب التمام قاعدة جيوب التمام + +292 +00:33:43,800 --> 00:33:49,760 +تقول لو عندك ثلاث أضلاع المثلث و بدك تجيب ثلاث زوايا + +293 +00:33:50,890 --> 00:33:54,170 +أنت ما عندكش لا طول، من خلال الأطوال بقدر أجيب + +294 +00:33:54,170 --> 00:33:57,830 +الزوايا، الزوايا هي هذه القاعدة اللي بيسميها قاعدة + +295 +00:33:57,830 --> 00:34:02,750 +جيب تملة، لو كان عندك أي مثلث شو ما يكون شكله + +296 +00:34:08,300 --> 00:34:15,700 +هذا مثلث سمت الضلع هذا A سمت الضلع هذا B سمت الضلع + +297 +00:34:15,700 --> 00:34:22,860 +هذا C ونفترض أن هذا محور X وهذا محور Y وهذه نقطة + +298 +00:34:22,860 --> 00:34:29,930 +الأصل اللي هي Zero أخذنا الضلعين A و B حصروني بينهم + +299 +00:34:29,930 --> 00:34:35,130 +زاوية زاوية هذه سميتها ايش؟ ثيتا، لو بدي أعرف كده + +300 +00:34:35,130 --> 00:34:39,470 +الزاوية ثيتا، بقول له هذه القاعدة بتقول لي cosine + +301 +00:34:39,470 --> 00:34:44,930 +ثيتا يساوي، بدي أعلمك الطريقة و بتصير بعد هيك فارغة + +302 +00:34:44,930 --> 00:34:50,770 +بسيطة ولا حاجة، أين الزاوية ثيتا هي؟ أين ضلعيها؟ A + +303 +00:34:50,770 --> 00:34:57,120 +و B مش هنجيب كوساين الجيب تمام بقول مربع الضلع + +304 +00:34:57,120 --> 00:35:02,880 +الأول للزاوية زائد مربع الضلع الثاني للزاوية ناقص + +305 +00:35:02,880 --> 00:35:06,900 +مربع الضلع الثالث اللي هو قبل الزاوية على اثنين + +306 +00:35:06,900 --> 00:35:13,760 +حاصل ضرب ضلعيها يعني ايش باجي بقول A تربيع زي B + +307 +00:35:13,760 --> 00:35:22,450 +تربيع ناقص C تربيع على اثنين B بس سبع يبقى جيب + +308 +00:35:22,450 --> 00:35:26,470 +تمام أي زاوية باطل على الضلعين اللي يتكونوا + +309 +00:35:26,470 --> 00:35:31,530 +للزاوية مربع الأول زائد مربع الثاني ناقص مربع الضلع + +310 +00:35:31,530 --> 00:35:35,790 +الثالث اللي بيقفل المثلث اللي بيقفل المثلث على + +311 +00:35:35,790 --> 00:35:41,530 +اثنين حاصل ضرب ضلعيها بناء عليه لو بدي أجيب جيب + +312 +00:35:41,530 --> 00:35:47,370 +تمام الزاوية اللي فوق بقول له A تربيع زائد C تربيع + +313 +00:35:47,370 --> 00:35:52,210 +ناقص B تربيع على اثنين AC لو بدي أجيب جيب تمام + +314 +00:35:52,210 --> 00:35:57,430 +الزوايا هذه بقول B تربيع زائد C تربيع ناقص A تربيع + +315 +00:35:57,430 --> 00:36:01,770 +على اثنين BC وبالتالي بأجيب تسموه في التنمية حل + +316 +00:36:01,770 --> 00:36:06,850 +المثلث بيعطيك ثلاث معلومات والله معلومتين وبدك + +317 +00:36:06,850 --> 00:36:09,750 +تجيب باقي المعلومات تبع المثلث يعني بدنا نجيب + +318 +00:36:09,750 --> 00:36:14,230 +الأضلاع كلها وبدنا نجيب الزوايا كلها ده اسمه بجيب + +319 +00:36:14,230 --> 00:36:22,000 +تسموه حل المثلث تمام؟ طب لو حصل أن الزاوية هذه كانت + +320 +00:36:22,000 --> 00:36:28,160 +تسعين درجة تسعين درجة بيصير جتا تسعين بجدل صفر + +321 +00:36:28,160 --> 00:36:33,080 +بيصير هذا بصفر اه لأن في المثلثة القائمة الزاوية + +322 +00:36:33,080 --> 00:36:36,740 +مربع الضلع هذا زائد مربع الضلع هذا بيساوي مربع + +323 +00:36:36,740 --> 00:36:41,540 +الضلع الثالث فيه ثورة إذا بيصير بصفر جدل صفر على + +324 +00:36:41,540 --> 00:36:46,220 +أي رقم يساوي صفر كلام صحيح يبقى سواء كان قائم ولا + +325 +00:36:46,220 --> 00:36:51,280 +حاد ولا منفرج ما عندنا مشكلة في هذه الحالة طيب هذا + +326 +00:36:51,280 --> 00:36:55,140 +كله كان موجود في الطبعات من الطبعة الأولى وحتى + +327 +00:36:55,140 --> 00:37:00,060 +الطبعة الحادية عشرة اجى في الطبعة الثانية عشرة + +328 +00:37:00,060 --> 00:37:06,460 +اللي بين ايدينا و حطينا الخاصية رقم سبعة الخاصية رقم + +329 +00:37:06,460 --> 00:37:13,400 +سبعة بتقول ما يأتي بتقول for any + +330 +00:37:14,550 --> 00:37:23,170 +أنقل theta لأي زاوية theta major مقاسة + +331 +00:37:23,170 --> 00:37:32,590 +بالتقدير الدائري major in radians بالتقدير + +332 +00:37:32,590 --> 00:37:34,570 +الدائري we have + +333 +00:37:37,520 --> 00:37:39,020 +النقطة الأولى + +334 +00:38:07,610 --> 00:38:11,410 +و الكلام هذا رايح مثل و تقن باريه هنا في صفحة + +335 +00:38:11,410 --> 00:38:15,590 +الثمانية و عشرين بدك البرهان مر عليه في الكتاب، + +336 +00:38:15,590 --> 00:38:20,770 +بدكش بلاش، لكن هل لها استعمالات خلال الأسئلة أو + +337 +00:38:20,770 --> 00:38:25,670 +خلال الشغل من شغله؟ ما ألاقش استعمالات بالمرة، أهم + +338 +00:38:25,670 --> 00:38:32,050 +حاجة قلت لك لحد هنا، من الأول لحد هنا، هذا أهم ما + +339 +00:38:32,050 --> 00:38:35,640 +يأتي طبعًا في بعض المعلومات الأخرى عن حساب المثلثة مش + +340 +00:38:35,640 --> 00:38:40,340 +كده بس بتلزمناش زي قاعدة الجيم ألف شرط على جه ألف + +341 +00:38:40,340 --> 00:38:43,800 +يساوي بقى شرط على جه باقي يساوي جيم شرطة على جه جيم + +342 +00:38:43,800 --> 00:38:49,860 +في أي مثلث تلزمنا في شغلنا؟ ما تلزمناش احنا يبقى احنا + +343 +00:38:49,860 --> 00:38:56,510 +هذه أهم حاجة بتمر علينا في قواعد حساب المثلث الآن + +344 +00:38:56,510 --> 00:39:02,990 +بدنا نأخذ أمثلة على كل ما سمعته عندنا بدل المثال + +345 +00:39:02,990 --> 00:39:08,570 +أربعة أمثلة و بدنا نيجي نشوف هذه الأمثلة قبل ما + +346 +00:39:08,570 --> 00:39:14,910 +نشوف، حد بيحب يسأله يتساءل هنا؟ أيوه؟ كيف؟ ما لهاش + +347 +00:39:14,910 --> 00:39:18,370 +استخدامات عندنا حاليًا، بعد ما تتطور إن شاء الله + +348 +00:39:18,370 --> 00:39:28,420 +بصير الاستخدامات ثانية، هذا، اهتلتها في ال T نقص + +349 +00:39:28,420 --> 00:39:33,760 +هذه الإشارة بالزائد يبقى هذه بالزائد اللي تحت + +350 +00:39:33,760 --> 00:39:38,780 +بالناقص بيدك هي بالناقص تصير ناقص و اللي تحت زائد + +351 +00:39:38,780 --> 00:39:40,640 +مخالفة على طول الخط + +352 +00:39:43,420 --> 00:39:48,180 +كيف؟ كيف استنتجها يعني؟ احنا هذا كله مراجعة اللي + +353 +00:39:48,180 --> 00:39:51,620 +أنت اخذته في الثانوية، هم لازم تستنتج من جديد هذا + +354 +00:39:51,620 --> 00:39:56,260 +كله من الأول و ده راح أرسم لك دائرة و أقول لك هي + +355 +00:39:56,260 --> 00:40:00,400 +المحاور و آخذ نقطة على محيط الدائرة و أقول لك هذا X + +356 +00:40:00,400 --> 00:40:04,200 +و هذا Y و هذا نصف القطر و يلا اربع ال cosine و ال + +357 +00:40:04,200 --> 00:40:08,230 +sine بيطلع عندك جداش، ما بديش هذا الكلام فانا ما + +358 +00:40:08,230 --> 00:40:11,510 +بضيع وقتي في معلومات عتيجة أو بيتة بالنسبة لك، أنا + +359 +00:40:11,510 --> 00:40:20,850 +كل بذاكرك هي تذكير، اه، ايش لازمان؟ كده؟ بسيطة، + +360 +00:40:20,850 --> 00:40:28,850 +لسه مش بقول، نمرا ورا أحد، نمرا اثنين، غريب جدا، + +361 +00:40:28,850 --> 00:40:32,230 +اه، أيوة، مالها؟ + +362 +00:40:49,460 --> 00:40:51,620 +خلاص؟ أيوه + +363 +00:40:55,650 --> 00:40:59,870 +سؤال وجيه جدًا، بيقول افترض هذه أندا كانت cosine + +364 +00:40:59,870 --> 00:41:05,650 +أربعة X بيصير cosine تربيع اثنين X ناقص sine تربيع + +365 +00:41:05,650 --> 00:41:11,070 +اثنين X ويساوي اثنين cosine تربيع اثنين X ناقص + +366 +00:41:11,070 --> 00:41:15,430 +واحد واحد ناقص اثنين sine تربيع اثنين X و هكذا + +367 +00:41:15,430 --> 00:41:20,090 +يعني أنت بتقدر تشتغل بالقاعدة هذه زي ما بدها طيب + +368 +00:41:20,090 --> 00:41:28,690 +نبدأ نأخذ أمثلة على كل ما سبق و + +369 +00:41:28,690 --> + +401 +00:45:10,940 --> 00:45:16,140 +لواحد والله هذا خلى في بالي يترقى في بالي سؤال هذا + +402 +00:45:16,140 --> 00:45:19,580 +السؤال جبناه أعتقد العام الماضي أو اللي جابله + +403 +00:45:19,580 --> 00:45:25,140 +السؤال بيقول بدي الـ period لـ absolute value لـ + +404 +00:45:25,140 --> 00:45:31,280 +cosine الـ X اللي بيعرف يرفع يده فوق خليني أعرفه في + +405 +00:45:31,280 --> 00:45:35,520 +المحاضرة الماضية في المحاضرة بدي قداش الـ period لـ + +406 +00:45:35,520 --> 00:45:38,740 +هذه الدالة أيوة + +407 +00:45:40,080 --> 00:45:50,700 +باي على اثنين يعني نص باي وجهة نظر باي + +408 +00:45:50,700 --> 00:46:02,720 +و نص باي باي و نص على الوسط أو كما قال أيوة اللي + +409 +00:46:02,720 --> 00:46:08,160 +بقى عاوز يرفع أيضا فوق أيوة أيضا في الآخر كده إيش؟ + +410 +00:46:08,160 --> 00:46:18,490 +مش سامع أي عدد على اثنين؟ أي عدد سالب تردي؟ يعني + +411 +00:46:18,490 --> 00:46:21,870 +ثلاثة باي على اثنين أو خمسة باي على اثنين؟ يعني + +412 +00:46:21,870 --> 00:46:24,970 +الـ period هذه بتم غطي زي ما بدي؟ والله الـ period + +413 +00:46:24,970 --> 00:46:30,810 +قيمة ثابتة دائما أنا بسأل الـ period بتم غطي هذي كل + +414 +00:46:30,810 --> 00:46:36,010 +يوم تبقى في لون؟ والله لون واحد يبقى يا صاحبي إجابتك + +415 +00:46:36,010 --> 00:46:46,680 +هذه لما حللها من عشوة اسمك أنت؟ مش سامع مهندس يبقى + +416 +00:46:46,680 --> 00:46:52,620 +الـ period لـ الـ cosine باي فقط لغير رسمة الـ cosine + +417 +00:46:52,620 --> 00:46:56,640 +اللي عندك لما نأخذ له الـ absolute value كل اللي + +418 +00:46:56,640 --> 00:47:02,300 +كانت تحت تنجلي بيصير فوق وبالتالي الـ cosine بيصير + +419 +00:47:02,300 --> 00:47:08,410 +كله فوق ما عنديش رسومات تحت طبعا يبقى الـ period بيصير + +420 +00:47:08,410 --> 00:47:14,970 +قداش باي فقط زي ما قال هشام ياغي هذا طبعا و زي ما + +421 +00:47:14,970 --> 00:47:20,310 +قال صاحبنا هناك يبقى الـ period تبقى هيو ساوي باي + +422 +00:47:20,310 --> 00:47:25,870 +فقط بحط بكل امتحان جبت أجابة باي على اثنين و باي + +423 +00:47:25,870 --> 00:47:30,450 +و ثلاثة باي على اثنين و اثنين باي أو باي على + +424 +00:47:30,450 --> 00:47:34,950 +اثنين و باي و اثنين باي و none of the above و + +425 +00:47:34,950 --> 00:47:39,830 +اللي حط لخط تحت الإجابة الصحيحة يبقى دير بالك من + +426 +00:47:39,830 --> 00:47:45,450 +هذا الكلام هذا يدل على الذكاء و على الفهم اه مش + +427 +00:47:45,450 --> 00:47:47,890 +ليه يقول الـ cosine خلاص ما احنا عارفين هاتنين باي + +428 +00:47:47,890 --> 00:47:52,090 +يبقى اثنين باي ويمشي طيب هذا كلام خاطر نجل و نمر + +429 +00:47:52,090 --> 00:48:01,420 +بيهنمر بيه بدي الـ domain لدالة F سؤال هو هل هناك + +430 +00:48:01,420 --> 00:48:10,060 +قيمة دالة هذه ما هي غير معرفة عندها في نهاية طيب يبقى + +431 +00:48:10,060 --> 00:48:16,440 +هذه من سالب infinity إلى infinity واحد مهندس يعني + +432 +00:48:16,440 --> 00:48:21,420 +مخنضي فكر وقال لي أنا بدي أطلع الإجابة هذه بقولك + +433 +00:48:21,420 --> 00:48:27,150 +يعني قال له هذا الواحد يعتبر function ثابتة قلت له + +434 +00:48:27,150 --> 00:48:32,350 +صحيح الـ domain تبعها من وين لوين كل الـ real line و + +435 +00:48:32,350 --> 00:48:36,730 +هذه الـ cosine الـ domain تبعها منين كل الـ real line + +436 +00:48:36,730 --> 00:48:41,730 +والدلتين هدول مطروحتين من بعض بطريقة واحنا أخذنا أن + +437 +00:48:41,730 --> 00:48:45,230 +الـ domain الفرق بين دلتين هو domain المجموعة بين + +438 +00:48:45,230 --> 00:48:49,350 +دلتين هو domain حاصل ضرب دلتين وهو الـ intersection + +439 +00:48:49,350 --> 00:48:54,650 +between two domains مظبوط يبقى من سالب infinity + +440 +00:48:54,650 --> 00:48:57,890 +لإنفنتي تقاطع مع سالب infinity لإنفنتي هيبقى 200 + +441 +00:48:57,890 --> 00:49:02,730 +سالب infinity لإنفنتي اللي احنا قلنا عليها يبقى + +442 +00:49:02,730 --> 00:49:06,830 +ما عندي مشكلة واحد فكر زي هيك بطريقة ثانية بتدهش + +443 +00:49:06,830 --> 00:49:13,890 +أقوله بدي الـ range لدالة F يساوي يبقى بدنا الواحد + +444 +00:49:13,890 --> 00:49:20,130 +ناقص cosine الـ X قداش الـ range من وين لوين من صفر + +445 +00:49:20,130 --> 00:49:24,630 +لإثنين متأكدين طب الـ cosine تأخذ قيمة سالم + +446 +00:49:29,820 --> 00:49:35,860 +لو cosine أخدت أقل قيمة لها قداش سالب واحد مع + +447 +00:49:35,860 --> 00:49:41,660 +السالب مش بيصير موجب واحد واحد نام لو أخدت أقصى + +448 +00:49:41,660 --> 00:49:45,900 +قيمة لها قداش واحد بيصير واحد وأقصى واحد بظل باقي + +449 +00:49:45,900 --> 00:49:50,600 +القيم كلها تتأرجح ما بين الـ 0 و 2 يبقى الـ range من + +450 +00:49:50,600 --> 00:49:57,380 +عند الـ 0 لغاية من الـ 2 بدنا نيجي لنمرة C بدنا + +451 +00:49:57,380 --> 00:50:03,620 +domain الدالة F ويساوي في قيمة هنا الدالة ما هي غير + +452 +00:50:03,620 --> 00:50:12,560 +معرفة عندها؟ في؟ اللي هي مين؟ ممتاز يبقى .. يبقى + +453 +00:50:12,560 --> 00:50:17,560 +خليني أطرح السؤال بطريقة أخرى هل domain الـ tan + +454 +00:50:17,560 --> 00:50:25,860 +تربيع يختلف عن domain الـ tan؟ في اختلاف؟ لا يوجد + +455 +00:50:25,860 --> 00:50:29,000 +اختلاف في المرة الـ domain أنا لا أتكلم عن الـ + +456 +00:50:29,000 --> 00:50:33,100 +range أنا أتكلم عن الـ domain domain الـ tan هو + +457 +00:50:33,100 --> 00:50:37,960 +domain الـ tan تربيع لأن tan تربيع تعني domain الـ + +458 +00:50:37,960 --> 00:50:42,440 +tan تقاطع domain الـ tan حصل ضرب دلتين يبقى + +459 +00:50:42,440 --> 00:50:44,940 +domain تبع الـ intersection ما بين الاتنين يعني الـ + +460 +00:50:44,940 --> 00:50:48,960 +domain الـ intersection مع نفسه يبقى نفسه تمام؟ طيب + +461 +00:50:48,960 --> 00:50:52,540 +جبنا domain الـ tan و احنا عندنا كمان واحد الواحد من + +462 +00:50:52,540 --> 00:50:56,330 +سالب infinity لـ infinity دومين الثاني احنا عارفين + +463 +00:50:56,330 --> 00:50:59,510 +أخذناه قبل هيك أنت رستريكشن من حياطيني دومين + +464 +00:50:59,510 --> 00:51:04,850 +الثاني يبقى هذا بتعطيني كل الـ real line ما عدا in + +465 +00:51:04,850 --> 00:51:11,000 +by على اثنين حيث أن odd مش شكل أخذناها من هناك يبقى + +466 +00:51:11,000 --> 00:51:17,060 +هذا بدي يعطيني كل الـ real line بدي أشيل منه زائد + +467 +00:51:17,060 --> 00:51:24,780 +أو ناقص in by على اثنين و الـ in is odd الشكل اللي + +468 +00:51:24,780 --> 00:51:31,360 +عندنا هنا طيب هذا من هذا الـ domain بدي الـ range + +469 +00:51:31,360 --> 00:51:33,640 +بتابع الدالة F + +470 +00:51:36,460 --> 00:51:42,600 +ممكن يأخذ قيمة سالبة range الدالة هذه؟ ممكن في يوم + +471 +00:51:42,600 --> 00:51:48,080 +الأيام يأخذ سالب؟ لأنه tan تربيع زائد واحد + +472 +00:51:48,080 --> 00:51:51,740 +يقول عمره ما هياخد قيمة سالبة طب الـ tan تربيع يعني + +473 +00:51:51,740 --> 00:51:57,680 +بياخد صفر؟ tan تربيع بياخد زيرو؟ اه بياخد زيرو + +474 +00:51:57,680 --> 00:52:02,380 +المنحنى الثانية مربع نقطة أصل مربع زيرو بزيرو زائد + +475 +00:52:02,380 --> 00:52:07,060 +واحد يبقى فيها واحد يبقى أقل قيمة تأخذها الدالة دي + +476 +00:52:07,060 --> 00:52:14,500 +قداش واحد و أكبر قيمة لأن الـ tan تربيع بتأخذ كل + +477 +00:52:14,500 --> 00:52:18,940 +الـ tan بتأخذ من سالب infinity إلى infinity لما + +478 +00:52:18,940 --> 00:52:24,280 +تربعها بتبطر تصير سالب بيصير كل موجب من zero إلى + +479 +00:52:24,280 --> 00:52:29,860 +infinity زائد واحد بيصير من واحد إلى infinity يبقى + +480 +00:52:29,860 --> 00:52:34,920 +هذا الـ range بده يصير من عند الواحد closed و لغاية + +481 +00:52:34,920 --> 00:52:38,840 +infinity مش زي الثلاثية الأولتين من zero لا اثنين وإنما من واحد لغاية infinity هذا هو + +482 +00:52:38,840 --> 00:52:44,370 +zero لا اثنين وإنما من واحد لغاية infinity هذا هو + +483 +00:52:44,370 --> 00:52:52,230 +المثال الأول بدنا نيجي للمثال رقم اثنين الشكل اللي + +484 +00:52:52,230 --> 00:52:58,950 +قلناه شوفوا يا سيدي المثال رقم اثنين بيقول ما يأتي + +485 +00:52:58,950 --> 00:53:06,190 +write the following write the following + +486 +00:53:12,090 --> 00:53:24,850 +functions in terms of in terms of sign الـ X and + +487 +00:53:24,850 --> 00:53:30,010 +cosine الـ X اكتب لي الدالة اللي التالية بدلالة الـ + +488 +00:53:30,010 --> 00:53:37,930 +sign و الـ cosine نمرة A بدنا sign + +489 +00:53:39,620 --> 00:53:47,580 +لثلاثة باي على اثنين نقطة sin X إذا + +490 +00:53:47,580 --> 00:53:52,120 +بتقدر تكتبها بدالة sin X لحالها ما عندنا مشكلة cosine X + +491 +00:53:52,120 --> 00:53:55,400 +لحالها ما عندنا مشكلة بدالة sin و الـ cosine مع بعض برضه + +492 +00:53:55,400 --> 00:54:00,460 +ما في مشكلة هاللي تقدر عليه اكتب لي هذه الدالة إيه + +493 +00:54:00,460 --> 00:54:03,860 +بقى ماجي بقول مولاك واسم ثلاثة باي على اثنين هذي + +494 +00:54:03,860 --> 00:54:08,920 +270 يعني أقل من الـ period بتاعة الـ sign + +495 +00:54:08,920 --> 00:54:15,920 +مظبوط أقل منها بقوله بسيطة إذا هذه بقدر أفكها دوري + +496 +00:54:15,920 --> 00:54:22,760 +و أجي و أقوله الـ sign ثلاثة by على اثنين cosine الـ + +497 +00:54:22,760 --> 00:54:29,340 +X لشيء عادي بالناقص يبقى بالناقص cosine ثلاثة by + +498 +00:54:29,340 --> 00:54:37,770 +على اثنين في sign الـ X هذا الكلام يساوي قداش جيب الـ + +499 +00:54:37,770 --> 00:54:45,030 +270 سالب واحد في cosine الـ X يبقى سالب cosine الـ X + +500 +00:54:45,030 --> 00:54:52,170 +جبت الـ 270 بـ Zero يبقى راحة يبقى ضلي الجواب بس سالب + +501 +00:54:52,170 --> 00:54:55,650 +cosine الـ X نمرة B + +502 +00:54:59,260 --> 00:55:08,880 +بنضله cosine ثلاثة باي زائد X بقول له الـ period لـ + +503 +00:55:08,880 --> 00:55:13,580 +الـ cosine قداش يبقى أنا بقدر أشيل اثنين باي من + +504 +00:55:13,580 --> 00:55:18,520 +مسألتي بالمرة بقدر أتخلص منها يبقى هذه عمليا هي + +505 +00:55:18,520 --> 00:55:25,410 +cosine باي زائد X السبب إن الـ period للـ cosine اثنين + +506 +00:55:25,410 --> 00:55:29,090 +باي يبقى أهمل الـ period هذه اللي هي الاثنين باي + +507 +00:55:29,090 --> 00:55:34,690 +بضال عندي بس باي بقول هذه بفكها زي اللي فوق يبقى + +508 +00:55:34,690 --> 00:55:43,030 +cosine باي cosine الـ X ناقص sin باي في الـ sin الـ X + +509 +00:55:43,030 --> 00:55:48,210 +واحد وسبع cosine مية و ثمانين هذه بقداش سالب واحد + +510 +00:55:48,210 --> 00:55:54,330 +في cosine الـ X بسالب cosine الـ X sin المية و ثمانين + +511 +00:55:54,330 --> 00:56:00,390 +بزيرو يبقى طار الـ zero طلع الإجابتين هذا مالهم زي + +512 +00:56:00,390 --> 00:56:06,370 +بعض كان بإمكاني أعصير السؤالين بسؤال واحد و أقول + +513 +00:56:06,370 --> 00:56:11,330 +لك show that إن الـ sin ثلاثة بي عتنين ناقص X + +514 +00:56:11,330 --> 00:56:14,510 +يساوي الـ cosine ثلاثة بي زائد X + +515 +00:56:24,080 --> 00:56:29,260 +الإشارة اللي هنا في حالة الـ cosine عكس الإشارة + +516 +00:56:29,260 --> 00:56:33,420 +اللي هنا بالضبط تمام في الـ sine زي بعض طالع عندك + +517 +00:56:33,420 --> 00:56:38,340 +كتبناها قبل قليل تمام يبقى النتيجة يسمي سالب + +518 +00:56:38,340 --> 00:56:47,900 +cosine الـ X نجي لنمر الـ C نمر الـ C بدنا واحد على + +519 +00:56:47,900 --> 00:56:57,260 +tan الـ X زائد cotan الـ X عشان نعرف كم تساوي بدلالة + +520 +00:56:57,260 --> 00:57:03,840 +main الـ sine و الـ cosine يبقى + +521 +00:57:03,840 --> 00:57:13,000 +هذه تساوي واحد على sine الـ X على cosine الـ X زائد + +522 +00:57:13,000 --> 00:57:21,940 +cosine الـ X على sine الـ X هذا واحد على بدا واحدة + +523 +00:57:21,940 --> 00:57:29,820 +لها المقامات يبقى بالصيرة sin X في cos X على هذه + +524 +00:57:29,820 --> 00:57:39,240 +بيبقى sin في sin بـ sin تربيع X زائد هذه على هذه + +525 +00:57:39,240 --> 00:57:46,800 +بيبقى cos بـ cos تربيع X تمام يبقى هذه لو قلبتها إيش + +526 +00:57:46,800 --> 00:57:53,440 +بيصير؟ sin الـ X في cosine الـ X sin تربيع زائد cosine + +527 +00:57:53,440 --> 00:58:01,280 +تربيع لـ قداش بواحد يبقى النتيجة sin الـ X في cosine + +528 +00:58:01,280 --> 00:58:07,140 +الـ X هيها كتبتها بدلالة الـ sin و الـ cosine واحد قال + +529 +00:58:07,140 --> 00:58:11,420 +لي أنا بدأ أكتب بدلالة مش sin X sin اثنين X بقوله + +530 +00:58:11,420 --> 00:58:15,560 +ما فيش مشكلة أضرب في اثنين و أقسم على اثنين يبقى + +531 +00:58:15,560 --> 00:58:20,880 +بصير نص اثنين sin x cos x اللي بصير اثنين x يبقى + +532 +00:58:20,880 --> 00:58:24,420 +نص sin اثنين x بس مش هذا المطلوب المطلوب جالي + +533 +00:58:24,420 --> 00:58:27,480 +اكتبها بدلالة مين الـ sign و الـ cosine يبقى + +534 +00:58:27,480 --> 00:58:33,940 +بيخليها زي ما هي بالضبط تماما طيب هذا نمرة c بدا أجي + +535 +00:58:33,940 --> 00:58:41,640 +لنمرة d يبقى نمرة d بيقول لي cosine تربيع x على + +536 +00:58:41,640 --> 00:58:49,190 +اثنين يعني أنا بدي أتخلص من مين من الـ X على 2 و + +537 +00:58:49,190 --> 00:58:53,430 +اكتبها بدلالة من cosine الـ X أو sine الـ X اللي + +538 +00:58:53,430 --> 00:59:00,650 +تقدر عليه اللي تشوفه بقوله هذا الكلام يساوي يطلع لي + +539 +00:59:00,650 --> 00:59:06,750 +في نمرة 4 عندك من المتطابقات قبل شوية يبقى هذه + +540 +00:59:06,750 --> 00:59:14,370 +بقدر أكتب عليها نص في واحد زائد cosine جد هذه + +541 +00:59:14,370 --> 00:59:22,310 +مرتين يبقى اثنين في X على اثنين تمام يبقى هذه + +542 +00:59:22,310 --> 00:59:29,790 +صارت نص في واحد زائد cosine الـ X يبقى هاي كتبناها + +543 +00:59:29,790 --> 00:59:39,570 +بدلالة اثنين cosine الـ X طيب نمرة E بيقول ليه sin + +544 +00:59:39,570 --> 00:59:42,250 +لثلاثة X + +545 +00:59:45,060 --> 00:59:51,620 +sin لثلاثة X احنا قلنا بنا نكتبها بدالة sin X و cos + +546 +00:59:51,620 --> 01:00:01,200 +X مظبوط يبقى هذي فكر كويس باجي بقوله هذي sin X + +547 +01:00:01,200 --> 01:00:08,760 +زائد اثنين X مظبوط وبعد هيك صارت هذي sin لمجموع + +548 +01:00:08,760 --> 01:00:14,150 +قيمتين يبقى بقدر أفكها باستخدام الـ sin يبقى هذه + +549 +01:00:14,150 --> 01:00:28,490 +الـ sin X في cos 2X زائد cos x في sin 2x لماذا أنا + +550 +01:00:28,490 --> 01:00:33,590 +بدي أوصلها إلى cos x و sin x يعني بدي أشوف في + +551 +01:00:33,590 --> 01:00:38,450 +المثلة خلقت 2x بالمرة ووصلها إن شاء الله توصلها الـ + +552 +01:00:38,450 --> 01:00:41,630 +sin تربيع و cos تربيع ما عنديش مشكلة يبقى باجي + +553 +01:00:41,630 --> 01:00:48,330 +بقوله هذا الكلام يساوي sin x مطلوبة بس cosine اثنين + +554 +01:00:48,330 --> 01:00:54,010 +x هذه معلها مش مطلوبة إذا cosine اثنين x لها + +555 +01:00:54,010 --> 01:01:02,170 +بدل الصيغة تلصيح حط الصيغة اللي تعجبك بقوله كويس + +556 +01:01:02,170 --> 01:01:08,130 +و الصيغة بديها بدلالة cosine X و sine X أو أي + +557 +01:01:08,130 --> 01:01:12,250 +واحدة فيهم سيانة بتفرقش عندنا يبقى باجي بقول له + +558 +01:01:12,250 --> 01:01:17,130 +هاي cos و cosine 2X مين الصيغة اللي بدكيها؟ + +559 +01:01:19,350 --> 01:01:26,310 +اثنين cosine تربيع الـ X ناقص واحد هاي معناها cosine + +560 +01:01:26,310 --> 01:01:33,170 +اثنين X طيب نيجي يدي الزائد cosine الـ X في يدي + +561 +01:01:33,170 --> 01:01:40,930 +اثنين sin الـ X في cosine الـ X هاي خلصتها كل ابداع + +562 +01:01:40,930 --> 01:01:46,270 +الـ cosine بس بدي عملية ترتيب و تهذيب يبقى هذا الكلام + +563 +01:01:46,270 --> 01:01:47,290 +بده يساوي + +564 +01:02:05,650 --> 01:02:16,740 +طيب إيش رأيك هذه؟ و هذه في بينهم sin X cos X و 2 + +565 +01:02:16,740 --> 01:02:27,500 +عامل مش هي يبقى 4 صح؟ يبقى بيظل عندي 4 sin X cos X + +566 +01:02:27,500 --> 01:02:38,100 +ناقص sin X ممكن تحويلها بدل الـ sin الواحد ناقص sin + +567 +01:02:38,100 --> 01:02:41,620 +تربيع الـ X وبالتالي كلها بتصير بدل الـ اثنين sin + +568 +01:02:41,620 --> 01:02:42,900 +خلها زمان + +569 +01:02 + +601 +01:06:19,250 --> 01:06:23,430 +في الـ interval هادي لإن هذه الزاوية سالب باي على ستة + +602 +01:06:23,430 --> 01:06:27,870 +موجة بقى سالبة و هنا عندنا زاوية موجة بقوله بسيطة + +603 +01:06:27,870 --> 01:06:32,390 +جدا هات الزاوية اللي بتكملها 360 بتكون + +604 +01:06:32,390 --> 01:06:36,000 +هي الزاوية المطلوبة في الربع الرابع يبقى لما أقول + +605 +01:06:36,000 --> 01:06:39,600 +30 شو اللي بيكملها 330 يعني + +606 +01:06:39,600 --> 01:06:44,880 +11 باي على 6 باي على 6 بـ 30 في 11 + +607 +01:06:44,880 --> 01:06:48,980 +بـ 330 درجة يبقى الزاوية الأخرى هي + +608 +01:06:48,980 --> 01:06:58,780 +11 باي على 6 و θ تساوي 11 باي على 6 + +609 +01:06:58,780 --> 01:07:01,580 +هذا حل المسألة نمرى + +610 +01:07:04,220 --> 01:07:09,220 +لربالك، لو كانت الإشارة هذه بالسالب، لأصبح الحل في + +611 +01:07:09,220 --> 01:07:12,860 +الربع الثاني والربع الثالث، يعني إزاي بتطلع في + +612 +01:07:12,860 --> 01:07:18,190 +الربع الثاني والربع الثالث؟ طيب، نمرى بيه؟نمرى بيه + +613 +01:07:18,190 --> 01:07:22,350 +بيقول ساين 2 θ ناقص كوزاين اه الزاوية هذه + +614 +01:07:22,350 --> 01:07:27,050 +غير الزاوية هذه مظبوط إذًا يبدأ أخلي الزاوية كلهم + +615 +01:07:27,050 --> 01:07:31,730 +بدلالة 2 θ يبدأ أخلي الزاوية كلهم بدلالة + +616 +01:07:31,730 --> 01:07:36,370 +θ يبقى الأسهل إن أخليها بدلالة 2 بدلالة + +617 +01:07:36,370 --> 01:07:41,390 +θ إذا ساين 2 θ اللي هي 2 ساين θ + +618 +01:07:41,390 --> 01:07:48,520 +كوزاين θ ناقص كوزاين θ يساوي قداش يساوي Zero في + +619 +01:07:48,520 --> 01:07:54,580 +عمل مشترك اللي هو Cos θ بيظل 2 Sin θ + +620 +01:07:54,580 --> 01:08:01,340 +ناقص 1 يساوي Zero هذا معناه إنه Cos θ بده + +621 +01:08:01,340 --> 01:08:07,100 +يساوي Zero و 2 Sin θ ناقص 1 يساوي Zero + +622 +01:08:07,100 --> 01:08:14,240 +أو إن شئتم فقولوا Cos θ يساوي Zero و Sin θ + +623 +01:08:14,240 --> 01:08:22,730 +يساوي نصف يبقى θ تساوي. الآن بدي أدور مين الزاوية + +624 +01:08:22,730 --> 01:08:27,410 +اللي جيب تمامها يساوي الصفر والزاوية موجودة من صفر + +625 +01:08:27,410 --> 01:08:29,370 +لـ 2 باي. + +626 +01:08:33,040 --> 01:08:38,540 +كوزاين صفر بصفر لا بواحد يبقى هذا كلام مش صحيح يبقى + +627 +01:08:38,540 --> 01:08:43,840 +مين الزاوية اللي جيبها تماما يساوي صفر تساعد يبقى θ + +628 +01:08:43,840 --> 01:08:50,360 +تساوي باي على 2 وكذلك θ تساوي قداش 3 + +629 +01:08:50,360 --> 01:08:54,500 +باي سهل جدا لو قلبت هالرسم بتلاقي كلامنا صحيح + +630 +01:08:54,500 --> 01:08:59,590 +بدون حسابات ولا تحسب على Calculator ولا غيره نجي + +631 +01:08:59,590 --> 01:09:04,090 +للتاني هو θ تساوي من الزاوية اللي جيبها يساوي نصف + +632 +01:09:04,090 --> 01:09:11,230 +30 يعني باي على 6 و θ تساوي استنى شوية الـ + +633 +01:09:11,230 --> 01:09:16,110 +جيب موجب يعني في الربع الأول والربع الرابع بقوله + +634 +01:09:16,110 --> 01:09:22,170 +بسيطة هذه باي على 6 مكملتها 180 بتكون + +635 +01:09:22,170 --> 01:09:26,190 +هي اللي باي على 6 لإن جيب أي زاوية قادة يساوي + +636 +01:09:26,190 --> 01:09:31,990 +جيب الزاوية المكملة لأ مش المتممة، المتممة بتكون + +637 +01:09:31,990 --> 01:09:38,270 +90 مكملة بتكون 180 يبقى θ تساوي 180 + +638 +01:09:38,270 --> 01:09:45,880 +و 50 درجة اللي هو 5 باي على 6 يبقى كل قيمة + +639 +01:09:45,880 --> 01:09:52,700 +منهم أو كل معادلة منهم إلها حلين يبقى مسألتنا هذه + +640 +01:09:52,700 --> 01:09:58,520 +إلها أربعة حلول زي ما أنت شايف وليس حلين بعض + +641 +01:09:58,520 --> 01:10:03,360 +الشباب بيحط على الكمبيوتر تطلع الزاوية الحادة بيحطها + +642 +01:10:03,360 --> 01:10:09,630 +و بيجي ماشي وبالتالي بيضيع نصف السؤال هذا هو المثال + +643 +01:10:09,630 --> 01:10:15,690 +رقم 3 بدنا نروح للمثال رقم 4 وما أدرك + +644 +01:10:15,690 --> 01:10:24,470 +مالمثال رقم 4 بيقول لي Show that بيلي إنه نمر + +645 +01:10:24,470 --> 01:10:35,740 +ايه؟ ساين θ زائد كوزاين 2 θ ناقص 1 + +646 +01:10:35,740 --> 01:10:44,740 +على مين؟ على كوزاين θ ناقص ساين 2 θ يساوي + +647 +01:10:44,740 --> 01:10:50,640 +تان الزاوية θ نقولها Solution + +648 +01:10:56,130 --> 01:10:59,230 +في مثل هذا النوع من المسائل اللي بقيت سموها + +649 +01:10:59,230 --> 01:11:04,330 +المتطابقات المثلثية بقيت كثير من الشباب من حد يطلع + +650 +01:11:04,330 --> 01:11:09,160 +في المسألة بسيطة النبض يرفع عنده اهتمام؟ خاصة في + +651 +01:11:09,160 --> 01:11:13,260 +المرحلة الثانوية، ليش؟ لإنّه مش عارف يدير القوانين + +652 +01:11:13,260 --> 01:11:17,080 +اللي أخذها بها تخدمه في المثلة، تا قبل قليل لما + +653 +01:11:17,080 --> 01:11:22,000 +شرحنا القوانين قولنا بدك تقبل أنت الشاطر وتحرك + +654 +01:11:22,000 --> 01:11:25,960 +القوانين يمين وشمال بحيث تتناسب طبيعة المثلة اللي + +655 +01:11:25,960 --> 01:11:30,980 +عندك بعدين أنا بسأل بقول تان θ صعبة فاكفكها + +656 +01:11:30,980 --> 01:11:36,660 +ووصلها للشكل هذه لكن هذه بقدر أشتغل فيها وربما تصل + +657 +01:11:36,660 --> 01:11:42,000 +إلى مين؟ الطرف اليمين إذا لو جيت مسكت الطرف الشمال + +658 +01:11:42,000 --> 01:11:46,760 +يبقى بالدايجي أقول له هاي ساين θ زائد كوزاين + +659 +01:11:46,760 --> 01:11:52,220 +2 θ ناقص 1 على كوزاين θ ناقص ساين + +660 +01:11:52,220 --> 01:11:58,750 +2 θ يساوي طيب ايش يساوي ساين θ أنا بديها + +661 +01:11:58,750 --> 01:12:03,790 +لإن تان تعني ساين على كوزاين يبقى هذه خليها ما عندي + +662 +01:12:03,790 --> 01:12:09,770 +مشكلة فيها إذا مشكلتي تكمن في وين؟ في كوزاين 2 + +663 +01:12:09,770 --> 01:12:15,970 +θ ناقص 1 في عندي أكثر من مقترح المقترح الأول + +664 +01:12:15,970 --> 01:12:18,990 +أنه أخد إشارة سالب عام المشترك + +665 +01:12:25,980 --> 01:12:30,760 +مظبوط؟ هذا المقترح الأول المقترح الثاني كوزاين + +666 +01:12:30,760 --> 01:12:36,280 +2 θ هذه إلها ثلاث صيغ أشيلها وأحط الصيغة + +667 +01:12:36,280 --> 01:12:41,320 +اللتي تعجبني من الثلاث بقول لها بده احط صيغة طيّر + +668 +01:12:41,320 --> 01:12:48,680 +لمين؟ سالب 1 يعني بده يخلي اللي 1 ناقص ناقص + +669 +01:12:48,680 --> 01:12:55,280 +ايش؟ 2 ساين تربيع θ يعني المقترح هذا أنا + +670 +01:12:55,280 --> 01:13:01,200 +ما بديش اه ساين θ هي هذه بدي أقول زائد 1 ناقص + +671 +01:13:01,200 --> 01:13:05,580 +2 ساين تربيع θ ناقص 1 + +672 +01:13:14,130 --> 01:13:19,090 +لكن أول ما يجي في بالك مش ما يجي تفكيري الأولاني و + +673 +01:13:19,090 --> 01:13:22,370 +أول ما يجي تفكيري الثاني إن أشيل كوزاين 2 θ + +674 +01:13:22,370 --> 01:13:27,050 +وأحط إحدى القيم الثلاث هذا أول ما سيطرق على من؟ + +675 +01:13:27,050 --> 01:13:32,300 +على ذهنك هيبدأ جهدك كوزاين θ ما عنديش فيها مشكلة + +676 +01:13:32,300 --> 01:13:37,260 +ناقص هذه مالهاش اللاصقة واحدة يبقى أنا مجبر عليها + +677 +01:13:37,260 --> 01:13:42,380 +2 ساين θ كوزاين θ يبقى بقل يصير عندي في + +678 +01:13:42,380 --> 01:13:47,830 +البسط والمقام 2 θ كله بدلالة 8 بدلالة θ هذا + +679 +01:13:47,830 --> 01:13:53,550 +الكلام يساوي ناقص 1 وزايد 1 مع السلامة وبقدر + +680 +01:13:53,550 --> 01:14:00,990 +أخد ساين θ عامل مشترك من الكل بيظل 1 ناقص 2 + +681 +01:14:00,990 --> 01:14:06,620 +ساين الزاوية θ على هنا كمان بقدر أخد كوزاين + +682 +01:14:06,620 --> 01:14:11,540 +θ عام المشترك يبقى هي كوزاين θ عام المشترك + +683 +01:14:11,540 --> 01:14:17,480 +1 ناقص 2 ساين θ هذا ما هذا الله سهل عليه + +684 +01:14:17,480 --> 01:14:22,980 +يبقى صار عندي ساين θ على كوزاين θ اليومين + +685 +01:14:28,710 --> 01:14:36,190 +بسيط جدا طيب هذا يعتبر سؤال سهل Very easy أنت قلت + +686 +01:14:36,190 --> 01:14:41,050 +شوية تضحكوا ليش أنا حاطط بس قيمة الـ كوزاين والـ + +687 +01:14:41,050 --> 01:14:46,230 +ساين نتيجة وبس وبقى كله لعاله راح طبيعي مدوش + +688 +01:14:46,230 --> 01:14:54,120 +تفكير طيب نيجي ناخد كمان سؤال 1 ناقص كوزاين θ + +689 +01:14:54,120 --> 01:15:04,840 +على ساين θ يساوي ساين θ على 1 زائد كوزاين θ يساوي + +690 +01:15:04,840 --> 01:15:07,600 +تان θ على 2 + +691 +01:15:09,990 --> 01:15:14,350 +هذا قصة طويلة، هذول ثلاث شغلات مش شغلتين كمان، + +692 +01:15:14,350 --> 01:15:23,170 +مظبوط؟ يبقى بنيجي للحل، Solution يلا فاكر لي كويس + +693 +01:15:23,170 --> 01:15:28,990 +كيف التفكير الأول اللي بنخلي بس أول Two terms + +694 +01:15:28,990 --> 01:15:35,050 +يساووا بعض، وبعدين بنفهم على باقي المسألة اللي + +695 +01:15:35,050 --> 01:15:36,050 +يبقى + +696 +01:15:42,700 --> 01:15:48,480 +فتح كويس عينك وخليك دقيق النظر أنا عندي بدي أثبت + +697 +01:15:48,480 --> 01:15:52,360 +إن الـ term هذا يساوي الـ term هذا لاحظ الـ ساين كانت + +698 +01:15:52,360 --> 01:15:56,560 +في المقام صارت في البسط 1 ناقص كوزاين صارت تحت + +699 +01:15:56,560 --> 01:16:02,060 +1 زائد كوزاين بمعنى لو جيت أخدت الطرف الشمال + +700 +01:16:02,060 --> 01:16:06,900 +1 ناقص كوزاين θ على الـ ساين θ بتقدر + +701 +01:16:06,900 --> 01:16:11,140 +تخلق في المثلة 1 زائد كوزاين θ + +702 +01:16:13,630 --> 01:16:17,610 +اللي هو المنافسة صحيح ولا لأ؟ يبقى أنا لو ضربت في + +703 +01:16:17,610 --> 01:16:22,530 +المرافق معناته ضربت في 1 صحيح معناته خلقت في + +704 +01:16:22,530 --> 01:16:26,410 +المقام 1 زي الـ pusatita اللي هي مطلوبة عندي و + +705 +01:16:26,410 --> 01:16:30,820 +بعدين الله بفرجها يا أخي زي الليش يبقى باجي بقوله + +706 +01:16:30,820 --> 01:16:37,260 +بدي أروح أضرب هذه 1 زائد كوزاين θ على 1 زائد + +707 +01:16:37,260 --> 01:16:42,940 +كوزاين θ هذه اعتمدت عندك على مين؟ على دقة النظر + +708 +01:16:42,940 --> 01:16:47,080 +أنا عندي هذا term بده أوصل لـ term هذا 1 زائد + +709 +01:16:47,080 --> 01:16:50,540 +كوزاين θ هو المرافق لـ 1 ناقص كوزاين θ فعلا + +710 +01:16:50,540 --> 01:16:55,020 +هيُوصر في المقام يبقى انتهيته بعد هيك نتحاسب مش + +711 +01:16:55,020 --> 01:16:59,560 +مش مشكلة وبنشوف وين متوصل بقوله كويس هذا الكلام بده + +712 +01:16:59,560 --> 01:17:06,720 +يساوي ايش رأيك في الـ براصنة؟ فرق بين المربعين؟ بدي + +713 +01:17:06,720 --> 01:17:10,480 +أرجعه إلى الأصل اللي ابتدى به يبقى الأصل اللي ابتدى به + +714 +01:17:10,480 --> 01:17:17,740 +هو 1 ناقص كوزاين تربيع θ على ساين θ في + +715 +01:17:17,740 --> 01:17:23,120 +1 زائد كوزاين الزاوية θ واحد يقول بدي أحلل + +716 +01:17:23,120 --> 01:17:28,640 +هذه وأختصر وبقوله رجعت لرأس المسس لا ممتاز اه + +717 +01:17:28,640 --> 01:17:33,600 +1 ناقص كوزاين تربيع θ من أول متطاقم مثل هذه + +718 +01:17:33,600 --> 01:17:40,860 +ساين تربيع يبقى هذا بيصير ساين تربيع θ على ساين + +719 +01:17:40,860 --> 01:17:46,320 +θ في 1 زائد كوزاين الزاوية θ ابن اختصر + +720 +01:17:46,320 --> 01:17:52,570 +التربيع مع الـ ساين بيظل ساين θ على 1 زائد + +721 +01:17:52,570 --> 01:17:58,270 +كوزاين هه غير هو طلعت لحالها بسهولة، مظبوط؟ يبقى + +722 +01:17:58,270 --> 01:18:02,370 +ولا في .. بس ضربت في المرافق غير هو طلعت يعني أنت + +723 +01:18:02,370 --> 01:18:06,850 +بتحيط بمفاتيحه كويس بتلاقي أجت معاك فكل المتطابقات + +724 +01:18:06,850 --> 01:18:10,770 +اللي كانت بتزهجكوا في الثانوية وبتستنوا المدرس + +725 +01:18:10,770 --> 01:18:14,590 +يحلها اللي كنت تنسخه من ورا بسيطة بتشغل مخك حاجة + +726 +01:18:14,590 --> 01:18:18,570 +بسيطة مش كتير، بنعشه عميق في تفكيري، بس تفكير + +727 +01:18:18,570 --> 01:18:23,440 +بسيط، طيب ما دام هيك تعال نفكر أنا وصلت الـ term + +728 +01:18:23,440 --> 01:18:28,180 +الأول الى term الثاني إذا وصلت الـ term الأول إلى + +729 +01:18:28,180 --> 01:18:31,840 +الثالث أو الثاني الى الثالث ابنك بحلنا الإشكالية + +730 +01:18:31,840 --> 01:18:35,820 +صحيح ولا لأ؟ طب تعالى أفكر كده إذا وصل الـ term + +731 +01:18:35,820 --> 01:18:40,280 +الثاني إلى الثالث بقولك بس طلع كويس في المثلة + +732 +01:18:40,280 --> 01:18:46,440 +الطرف الشمال هذا كله بدلالة مين؟ θ الجواب هنا + +733 +01:18:46,440 --> 01:18:51,150 +بدلالة مين؟ حول مثلث بدلالة θ على 2 تبقى حلية + +734 +01:18:51,150 --> 01:18:56,710 +الإشكالية ولا حاجة بيصير بس حول المثلة كلها بدلالة + +735 +01:18:56,710 --> 01:19:01,070 +θ على 2 بقوله والله كويس يبقى باجي بقوله And + +736 +01:19:01,070 --> 01:19:09,290 +هذا ساين θ على 1 زائد كوزاين θ يسمى بدي أحول + +737 +01:19:09,290 --> 01:19:14,290 +البسط والمقام كله بدلالة θ على 2 يبقى ساين θ + +738 +01:19:14,290 --> 01:19:15,350 +بـ قداش + +739 +01:19:34,190 --> 01:19:42,760 +نجي لـ 1 زائد كوزاين الزاوية θ هذه لو كانت لو + +740 +01:19:42,760 --> 01:19:48,120 +كانت 1 زائد كوزاين 2 θ كان قلنا له هذه + +741 +01:19:48,120 --> 01:19:53,600 +2 كوزاين تربيع θ صح ولا لا؟ يبقى أنا عندي في + +742 +01:19:53,600 --> 01:19:58,380 +القانون هيك بفكر في الهامش بقول أنا عندي كوزاين + +743 +01:19:58,380 --> 01:20:04,960 +تربيع θ يساوي النصف في 1 زائد كوزاين 2 + +744 +01:20:04,960 --> 01:20:05,460 +θ + +745 +01:20:08,960 --> 01:20:16,120 +بقول له تمام يبقى هذه لو قلت لك كوزاين تربيع θ + +746 +01:20:16,120 --> 01:20:21,000 +على 2 ايش بدك تقوله؟ نصف في 1 زائد كوزاين جد + +747 +01:20:21,000 --> 01:20:26,340 +هذه مرتين اليمين θ هي و 1 زائد كوساين θ + +748 +01:20:26,340 --> 01:20:30,740 +اللي بدنا ياها هي موجودة يبقى اش اعمل؟ بس أضرب في + +749 +01:20:30,740 --> 01:20:35,040 +2 يبقى خلصت القصة هذه يبقى لو ضربتها في 2 + +750 +01:20:35,040 --> 01:20:40,460 +بيصير 2 كوساين تربيع θ على 2 يساوي 1 + +751 +01:20:40,460 --> 01:20:45,640 +زائد كوساين الزاوية θ تمام؟ إذا في الهامش هذا + +752 +01:20:45,640 --> 01:20:51,080 +اللي اشتغلته بعدين بشيل 1 ذات cos θ و بحط قيمته + +753 +01:20:51,080 --> 01:20:54,220 +طبعا أنا اشتغلت في الـ end وسينما حالي مش عارف بس أنا + +754 +01:20:54,220 --> 01:20:58,040 +قادر احطها لكم وأمشي دوري لكن جبت لك من وين كيف + +755 +01:20:58,040 --> 01:21:02,160 +فكرت فيها إذا بقدر أشيلها وأكثر بدالها 2 + +756 +01:21:02,160 --> 01:21:08,900 +كوساين تربيع θ على 2 يبقى هاي حولت مسألتي + +757 +01:21:08,900 --> 01:21:13,620 +كلها بدالت الزاوية θ على 2 أظن بقدر أقول + +758 +01:21:13,620 --> 01:21:21,110 +2 مع 2 و cos مع التربيع بيظل قداش عندي ساين + +759 +01:21:21,110 --> 01:21:32,370 +θ على 2 على cos θ على 2 قداش هذا بيعطيني تان θ على + +760 +01:21:32,370 --> 01:21:37,570 +2 إذا وهو المطلوب خلصنا ايوه + +761 +01:21:43,600 --> 01:21:50,680 +مش مشكلة عادي جدا حول زي ما بدك بالطريقة التي + +762 +01:21:50,680 --> 01:21:55,900 +تراها مناسبة لحد هنا Stop انتهى الـ section إليكم + +763 +01:21:55,900 --> 01:22:01,500 +أرقام المسائل المطلوبة من هذا الـ section هذا + +764 +01:22:01,500 --> 01:22:06,680 +section 1 3 مش هيك يبقى هنا ما أقولكوا + +765 +01:22:06,680 --> 01:22:10,760 +هاكتب لكوا فوق مش هي الكل يشوفها يبقى Exercises + +766 +01:22:10,760 --> 01:22:16,600 +1 3 المسائل التالية من 1 لـ 25 + +767 +01:22:16,600 --> 01:22:23,930 +الـ odd 1 لـ 25 الـ odd من 1 و 31 + +768 +01:22:23,930 --> 01: + +801 +01:26:41,730 --> 01:26:46,130 +الفترة الزمنية وأنت في الصف السابع أعتقد بيقولوا + +802 +01:26:46,130 --> 01:26:50,490 +السرعة المتوسطة تساوي المسافة على الزمن تمام؟ هي + +803 +01:26:50,490 --> 01:26:55,250 +هذه المسافة على الزمن يعني المسافة المقطوعة على + +804 +01:26:55,250 --> 01:27:01,850 +الزمن المستغرق في قطع هذه المسافة طبعًا هنا الحركة + +805 +01:27:01,850 --> 01:27:07,010 +without acceleration بدون عجلة هي السرعة المتوسطة + +806 +01:27:07,010 --> 01:27:18,300 +تمام؟ طيب لازم أنسى الموضوع المعادل للتغير هو + +807 +01:27:18,300 --> 01:27:21,260 +متوسط معدل التغير + +808 +01:27:32,270 --> 01:27:35,750 +The average rate of change متوسط معدل التغير + +809 +01:27:35,750 --> 01:27:40,210 +الدالة Y تساوي F of X with respect to X يعني + +810 +01:27:40,210 --> 01:27:46,250 +بالنسبة للمتغير X over the interval على الفترة X1 + +811 +01:27:46,250 --> 01:27:53,490 +و X2 is Delta Y على Delta X وين Delta Y و Delta X + +812 +01:27:53,490 --> 01:27:58,350 +هذه خلي بالك معايا كويسًا الآن أنا لو جئت للمحاور + +813 +01:27:58,350 --> 01:28:04,470 +و روحت قلت هذا محور X وهذا محور Y وهذا نقطة الأصل + +814 +01:28:04,470 --> 01:28:10,890 +اللي هي Zero رسمنا منحنى لدالة F of X فكانت بقدر + +815 +01:28:10,890 --> 01:28:16,990 +الله الدالة بالشكل هذا هيك يبقى هذا منحنى الدالة + +816 +01:28:16,990 --> 01:28:26,900 +هيك Y تساوي F of X أخذنا نقطتين على المنحنى مثل + +817 +01:28:26,900 --> 01:28:34,040 +النقطة هذه و مثل النقطة اللي عندنا هذه أو النقطة + +818 +01:28:34,040 --> 01:28:38,840 +هذه والنقطة قريبة شوية النقطة هذه هذه النقطة جت + +819 +01:28:38,840 --> 01:28:46,200 +نازل رأسك اللي جت إحداثيها هو X1 ومن هنا جت نازل + +820 +01:28:46,200 --> 01:28:53,360 +عمود ثاني اللي جت هذا من X2 هذه النقطة سميتها P + +821 +01:28:53,360 --> 01:29:02,820 +اللي إحداثيها تبع X1 وF من X1 أو X1 وY1 النقطة هذه + +822 +01:29:02,820 --> 01:29:12,570 +سميتها Q X2 و F of X2 بالشكل اللي عندنا هذا بدي أشوف + +823 +01:29:12,570 --> 01:29:18,150 +قداش مقدار التغير في X و قداش مقدار التغير في Y + +824 +01:29:18,150 --> 01:29:24,750 +باجي بقول له البعد هذا هو عبارة عن مين؟ F of X1 ايه + +825 +01:29:24,750 --> 01:29:30,480 +الإحداثي؟ رقم Y بالنسبة لمين؟ للنقطة هذه بالدالة + +826 +01:29:30,480 --> 01:29:34,180 +للنقطة الثانية لأن هذه الخطة المنقطة اللي احنا + +827 +01:29:34,180 --> 01:29:41,540 +رسمناها كلها هو F of X اتنين يبقى كل هذا F of X + +828 +01:29:41,540 --> 01:29:49,180 +اتنين لو جئت من هنا رسمت خط أفقي موازي لمحور X + +829 +01:29:49,180 --> 01:29:55,170 +إذا هذا يعتبر الفرق ما بين الاتنين اللي هو F اكس + +830 +01:29:55,170 --> 01:30:03,850 +اتنين بدي أشيل منه F اكس واحد يبقى هذه F اكس + +831 +01:30:03,850 --> 01:30:10,690 +اتنين ناقص F اكس واحد هذه اللي بدي اسميها Delta Y + +832 +01:30:10,690 --> 01:30:18,870 +الفرق في ال Y يبقى Delta Y هذه F اكس اتنين ناقص F + +833 +01:30:18,870 --> 01:30:27,000 +اكس واحد على هذه كلها المسافة من هنا إلى هنا هي X2 + +834 +01:30:27,000 --> 01:30:35,380 +هذه لحالها كلها المسافة X1 يبقى الفرق بينهم X2-X1 + +835 +01:30:35,380 --> 01:30:44,360 +يعطينا المسافة X2-X1 المسافة من هنا إلى هنا يبقى + +836 +01:30:44,360 --> 01:30:48,660 +على X2-X1 + +837 +01:30:49,610 --> 01:30:55,310 +هذا الكلام يساوي، بدي أحاول أصيغ هذا الكلام بصياغة + +838 +01:30:55,310 --> 01:31:01,590 +أخرى، لو جئت المسافة هذه من هنا لهنا سميتها H، + +839 +01:31:01,590 --> 01:31:11,430 +يبقى هذه هي H يبقى x2 ناقص x1 هي h إذا صارت x2 هي + +840 +01:31:11,430 --> 01:31:18,670 +عبارة عن x1 زائد مين؟ زائد h إذا صارت x2 هذه x1 + +841 +01:31:18,670 --> 01:31:25,430 +زائد h إذا هذه ممكن أصيرها صياغة أخرى و أقول f of + +842 +01:31:25,430 --> 01:31:33,340 +x1 زائد h ناقص f of x1 على مين؟ على x واحد زائد h + +843 +01:31:33,340 --> 01:31:39,100 +ناقص x واحد يبقى بضال قداش h وبشرط أن ال h هذه + +844 +01:31:39,100 --> 01:31:44,920 +does not equal to zero لأن لو كانت هذه ب zero بصير + +845 +01:31:44,920 --> 01:31:50,880 +ما عنديش هنا المتوسط معدل التغير يبقى هذا اللي + +846 +01:31:50,880 --> 01:31:56,460 +كتبته هو متوسط معدل التغير خليني أسألكم السؤال + +847 +01:31:56,460 --> 01:32:02,220 +التالي هذه كلها اللي هي delta y وهذه كلها اللي هي + +848 +01:32:02,220 --> 01:32:09,440 +مين Delta X طب لما نقسم هذا على هذا أليس هو ميل + +849 +01:32:09,440 --> 01:32:15,760 +الخط المستقيم اللي عندنا هذا هيك صح ولا لأ يبقى + +850 +01:32:15,760 --> 01:32:21,180 +هذا ميل الخط المستقيم اللي عندنا هذا اللي بسميه + +851 +01:32:21,180 --> 01:32:27,760 +secant قاطع وليس مماس قاطع للمرحلة قطع في النقطتين + +852 +01:32:27,760 --> 01:32:36,160 +P و لQ يبقى هذا الكلام بالضبط بيساوي ال slope of + +853 +01:32:36,160 --> 01:32:46,160 +the secant اللي هو PQ يبقى هذا ميل القطع أو ميل + +854 +01:32:46,160 --> 01:32:52,380 +الخط المستقيم اللي هو line PQ طيب كويس احنا إن شاء + +855 +01:32:52,380 --> 01:32:56,430 +الله بعد شهر وشوية و تسير فيها عيد الأضحى + +856 +01:32:56,430 --> 01:33:00,870 +والناس بيروحوا يزوروا بعض و يسلموا على بعض حبت + +857 +01:33:00,870 --> 01:33:06,550 +النقطة Q هتروح تسلم على مين؟ على النقطة P تبدأ تمشي + +858 +01:33:06,550 --> 01:33:12,690 +في الطريق المرسوم إليها وهي المنحنى Y تساوي F of X + +859 +01:33:12,690 --> 01:33:21,130 +أجت كاسدر هك على المنحنى كل ما تقرب Q من P الـH + +860 +01:33:21,130 --> 01:33:28,710 +هذه بتكبر ولا بتصغر؟ يعني لما وصلت هنا صارت الـH + +861 +01:33:28,710 --> 01:33:34,870 +أصغر فلما نيكوتة كانت تقترب من P يبقى الـH وإن + +862 +01:33:34,870 --> 01:33:40,560 +بدها تروح بتروح لـ 0 يبقى في هذه الحالة القاطع ايش + +863 +01:33:40,560 --> 01:33:45,620 +بده يصبح؟ مماس، على طول القاطع يبقى بده يصبح أيش؟ + +864 +01:33:45,620 --> 01:33:51,160 +مماس، يبقى إذا اقتربت النقطة Q من النقطة P فإن ال + +865 +01:33:51,160 --> 01:33:55,640 +secant يصبح tangent واحنا الموضوع اللي كاتبينه + +866 +01:33:55,640 --> 01:34:00,020 +tangent to the curve يبقى القاطع للمنحنة بده يصير + +867 +01:34:00,020 --> 01:34:05,290 +مين؟ بده يصير مماس للمنحنة بدنا نكتب هالكلمة هذه + +868 +01:34:05,290 --> 01:34:13,450 +اللي حكيناها بالعربي فبروح بقول ما يأتي if + +869 +01:34:13,450 --> 01:34:22,230 +the point if the point Q approaches + +870 +01:34:27,720 --> 01:34:40,980 +إذا اقتربت أو approach إذا اقتربت the point P + +871 +01:34:40,980 --> 01:34:48,660 +إذا الـ Q اقتربت من P along the + +872 +01:34:48,660 --> 01:35:02,750 +curve على المنحنى Y تساوي F of X then the + +873 +01:35:02,750 --> 01:35:17,350 +secant PQ secant PQ becomes a tangent بده يصبح + +874 +01:35:17,350 --> 01:35:20,310 +مماس to the curve + +875 +01:35:23,480 --> 01:35:34,360 +يصبح مماس للمنحنى at the point P نصيح مماس لمنحنة + +876 +01:35:34,360 --> 01:35:45,380 +عند P هذا يعني أن ال slope of the curve + +877 +01:36:08,750 --> 01:36:15,720 +طيب فإجابه اقول ما يأتي لو النقطة Q Approach the + +878 +01:36:15,720 --> 01:36:21,700 +point P إذا النقطة Q اقتربت من النقطة P يعني صارت + +879 +01:36:21,700 --> 01:36:25,840 +المسافة بينهم ضئيلة جداً بس بتقترب مش عشوائيًا + +880 +01:36:25,840 --> 01:36:31,520 +ماشية على المنحنى Y تساوي F of X نازل على المنحنى + +881 +01:36:31,520 --> 01:36:37,340 +على P إذا اقتربت منها along the curve Y تساوي F of + +882 +01:36:37,340 --> 01:36:43,560 +X then the secant PQ يبقى القاطع هذا بيصبح ايه؟ + +883 +01:36:43,560 --> 01:36:51,900 +بيصبح مماس للمنحنى بهذا الشكل يبقى + +884 +01:36:51,900 --> 01:36:53,940 +هذا tangent + +885 +01:36:57,280 --> 01:37:06,160 +بنصبح مماس للمنحنى عند نقطة P عند نقطة P وفي هذه + +886 +01:37:06,160 --> 01:37:12,180 +الحالة ميل المنحنى عند نقطة P يساوي ميل المماس + +887 +01:37:12,180 --> 01:37:17,260 +للمنحنى عند نقطة P يبقى المنحنى ميله عند نقطة P هو + +888 +01:37:17,260 --> 01:37:23,780 +ميل المماس للمنحنى عند نفس النقطة تمامًا طب حد بيعرف + +889 +01:37:23,780 --> 01:37:30,010 +يقول لك كيف بدنا نوجد ده؟ لكل بساطة طبعًا هناخد ال + +890 +01:37:30,010 --> 01:37:34,990 +section الجاي بروح باخد ال limit لهذا المقدار لما + +891 +01:37:34,990 --> 01:37:39,770 +ال H بده يروح ل zero وهو اللي بسميه ايش؟ معدل + +892 +01:37:39,770 --> 01:37:45,070 +التغير يبقى معدل التغير هو ال limit لما ال H بده + +893 +01:37:45,070 --> 01:37:49,090 +يروح ل zero يعني لو ال H راحت ل zero بحصل على مين؟ + +894 +01:37:49,090 --> 01:37:55,870 +على معدل التغير أول مثال بسيط جدا على هذا الموضوع + +895 +01:37:55,870 --> 01:37:56,590 +example + +896 +01:38:01,020 --> 01:38:21,180 +بقول find the average rate of change of the + +897 +01:38:21,180 --> 01:38:30,170 +function f of θ يساوي الجذر التربيعي ل 4 θ + +898 +01:38:30,170 --> 01:38:42,610 +plus one over the interval على الفترة من عند ال + +899 +01:38:42,610 --> 01:38:50,210 +zero لغاية اتنين تحكي + +900 +01:38:50,210 --> 01:38:55,450 +أشيله خلي الجلم يحكي مدوش يسمع حكي + +901 +01:39:10,970 --> 01:39:16,190 +اللي هبقى بيقول لي هات لي قداش متوسط معدله تغير + +902 +01:39:16,190 --> 01:39:21,110 +للدالة هذه على الفترة هذه يبقى احنا نذهب نحسب له + +903 +01:39:21,110 --> 01:39:27,110 +قداش ال F of Zero يبقى الجذر التربيعي ل Zero زائد + +904 +01:39:27,110 --> 01:39:33,630 +واحد يساوي واحد بدنا كمان ال F of اتنين أول الفترة + +905 +01:39:33,630 --> 01:39:38,470 +و آخر يعني F of X اتنين و F of X واحد يبقى F of + +906 +01:39:38,470 --> 01:39:43,390 +اتنين يساوي الجذر التربيعي اللي 4 في 2 زائد + +907 +01:39:43,390 --> 01:39:48,790 +واحد يعني الجذر التسعة اللي هو بقداش 3 الآن ال + +908 +01:39:48,790 --> 01:39:54,990 +average rate of change اللي هو دلتا F على دلتا + +909 +01:39:54,990 --> 01:40:01,330 +ثيتا Delta Y على Delta X هنا دلتا F على دلتا ثيتا + +910 +01:40:01,330 --> 01:40:09,900 +بده يساوي مين F of اتنين ناقص f of zero على ال 2 + +911 +01:40:09,900 --> 01:40:17,220 +ناقص ال zero كلام من التعريف يبقى هذا الكلام بده + +912 +01:40:17,220 --> 01:40:24,620 +يساوي 3 ناقص 1 على 2 ويساوي كده 1 + +913 +01:40:24,620 --> 01:40:32,260 +صحيح مثال ثاني كمان وآخر بيقول ما يأتي example + +914 +01:40:32,260 --> 01:40:32,940 +two + +915 +01:40:38,010 --> 01:40:45,990 +consider the curve اعتبر + +916 +01:40:45,990 --> 01:40:55,510 +المنحنى y تساوي x تربيع ناقص 4 x المطلوب الأول + +917 +01:40:55,510 --> 01:41:05,430 +find the slope of + +918 +01:41:07,570 --> 01:41:20,710 +the curve للمنحنى at the point عند النقطة P (1, -3) + +919 +01:41:20,710 --> 01:41:33,950 +نمر بـ Find an equation بدنا معادلة of + +920 +01:41:35,380 --> 01:41:50,300 +the tangent line خط التماس at the point P (1, -3) + +921 +01:42:01,840 --> 01:42:07,720 +سؤال مرة ثانية اعتبر المنحنى f of x أو y يساوي x + +922 +01:42:07,720 --> 01:42:12,460 +تربيع ناقص 4x مطلوب أن يقول لي هاتي ال slope + +923 +01:42:12,460 --> 01:42:18,500 +للمنحنى عند النقطة وهاتي معادلة المماس للمنحنى عند + +924 +01:42:18,500 --> 01:42:22,800 +نفس النقطة يبقى أنا أقول ال slope لل curve بتساوي + +925 +01:42:22,800 --> 01:42:28,280 +ال slope تبع مين؟ تبع ال tangent بدنا نجيب لل slope + +926 +01:42:28,280 --> 01:42:32,920 +تبع مين؟ تبع ال curve يبقى بدنا نجيب للمثال اللي + +927 +01:42:32,920 --> 01:42:36,980 +عندنا ونشوف كيف بدنا نجيب ال slope ل ال curve + +928 +01:42:36,980 --> 01:42:42,960 +اللي عندنا يبقى كتبنا قبل أقل اللي هو delta Y على + +929 +01:42:42,960 --> 01:42:53,300 +delta X يساوي F of قداش X واحد عندي يعني f of x + +930 +01:42:53,300 --> 01:43:00,960 +واحد زائد ال h ناقص f of x واحد على h، مظبوط؟ يبقى + +931 +01:43:00,960 --> 01:43:04,960 +هذا الكلام بده يساوي، بده آجي على الدالة، بده أشيل + +932 +01:43:04,960 --> 01:43:09,940 +كل x وأحط مكانها x واحد زائد ال h ال x واحد عندي + +933 +01:43:09,940 --> 01:43:15,510 +بقداش اللي هو 1، يبقى بده أشيل بدي أشيل 1 + +934 +01:43:15,510 --> 01:43:21,010 +زائد h بدي أشيل كل X وأحط مكانها 1 زائد h + +935 +01:43:21,010 --> 01:43:27,550 +لكل تربيع ناقص 4 في 1 زائد h هذا لسه كل + +936 +01:43:27,550 --> 01:43:34,990 +ال term الأول ناقص F of X اللي عندنا هذا يبقى ناقص + +937 +01:43:34,990 --> 01:43:43,140 +F of واحد F of واحد اللي هي مين؟ 1 تربيع ناقص + +938 +01:43:43,140 --> 01:43:49,060 +4 في 1 كل هذا الكلام على كده؟ على H تمام + +939 +01:43:49,060 --> 01:43:55,060 +يبقى هذا الكلام بده يساوي 1 زائد 2 H زائد + +940 +01:43:55,060 --> 01:44:02,580 +ال H تربيع ناقص 4 ناقص 4 H طلع لي هذه سالب + +941 +01:44:02,580 --> 01:44:08,400 +4 وزائد 1 سالب 3 وعندك سالب يبقى موجبة + +942 +01:44:08,400 --> 01:44:14,480 +بتلاتة كله على h، 3 بالموجب و1 بالموجب + +943 +01:44:14,480 --> 01:44:20,680 +4 وسالب 4 مع السلامة، ضال عندي هنا h + +944 +01:44:20,680 --> 01:44:26,420 +تربيع، عندك 2 h وناقص 4 h بناقص 2 + +945 +01:44:26,420 --> 01:44:31,810 +h، كله على h لو أخذنا h عامل مشترك بيبقى + +946 +01:44:31,810 --> 01:44:37,650 +ال h ناقص 2 على h يساوي ال h ناقص 2 هذا + +947 +01:44:37,650 --> 01:44:43,970 +مين ال average rate of change هذا بده يساوي ال + +948 +01:44:43,970 --> 01:44:53,120 +average rate of change يعني مين؟ the slope of the + +949 +01:44:53,120 --> 01:44:59,660 +secant مظبوط احنا قلنا لما ال Q تيجي نازلة رايحة + +950 +01:44:59,660 --> 01:45:05,920 +على P إذا H بده تروح لوين؟ ل Zero إذا H راحت ل + +951 +01:45:05,920 --> 01:45:12,320 +Zero بيصبح ال secant معله tangent يبقى بصير مماس و + +952 +01:45:12,320 --> 01:45:18,300 +بصير ميل المماس هو ميل مين؟ ميل المنحنى يبقى بيجي + +953 +01:45:18,300 --> 01:45:30,270 +بيقول له هنا F h راحت لـ Zero get the slope of the + +954 +01:45:30,270 --> 01:45:37,030 +curve اللي هو المطلوب الأول من هنا نمرا a مطلوب + +955 +01:45:37,030 --> 01:45:42,570 +الأول تبع المثال يبقى لما ال H بده تروح لل zero we + +956 +01:45:42,570 --> 01:45:45,610 +get the slope of the curve اللي هو بده يساوي قداش + +957 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24379, "start": 224.77, "end": 243.79, "text": "اي ان لما تبقى ال cosine even يبقى cosine لسلب x شو بده تساوي تعريف ال even function cosine ال x and second لسلب x", "tokens": [47302, 16472, 5296, 15042, 6055, 3555, 4587, 7578, 2423, 23565, 754, 7251, 3555, 4587, 7578, 23565, 5296, 3794, 46152, 2031, 13412, 2407, 47525, 3224, 6055, 3794, 995, 45865, 37279, 16572, 5172, 2423, 754, 2445, 23565, 2423, 2031, 293, 1150, 5296, 3794, 46152, 2031], "avg_logprob": -0.2555042484944517, "compression_ratio": 1.3277310924369747, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 224.77, "end": 225.31, "word": "اي", "probability": 0.0977783203125}, {"start": 225.31, "end": 225.83, "word": " ان", "probability": 0.56201171875}, {"start": 225.83, "end": 227.77, "word": " لما", "probability": 0.6883544921875}, {"start": 227.77, "end": 228.23, "word": " تبقى", "probability": 0.961181640625}, {"start": 228.23, "end": 228.37, "word": " ال", "probability": 0.78515625}, {"start": 228.37, "end": 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هدول دوال زوجية الان بدنا نيجي لامام ل sign ال X و كذلك تان ال X و كذلك كتان ال X and cosecant ال X are symmetric about the origin", "tokens": [1829, 3555, 4587, 7578, 8032, 3215, 12610, 11778, 2407, 6027, 30767, 29245, 10632, 2423, 7649, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 10943, 10943, 5296, 1465, 2423, 1783, 4032, 9122, 8848, 23275, 6055, 7649, 2423, 1783, 4032, 9122, 8848, 23275, 9122, 2655, 7649, 2423, 1783, 293, 30261, 66, 394, 2423, 1783, 366, 32330, 466, 264, 4957], "avg_logprob": -0.18133223684210525, "compression_ratio": 1.455223880597015, "no_speech_prob": 0.0, "words": [{"start": 287.58, "end": 288.1, "word": "يبقى", "probability": 0.892822265625}, {"start": 288.1, "end": 288.48, "word": " هدول", "probability": 0.8751627604166666}, {"start": 288.48, "end": 289.12, "word": " دوال", "probability": 0.9412434895833334}, {"start": 289.12, "end": 290.08, "word": " زوجية", "probability": 0.9586588541666666}, {"start": 290.08, "end": 291.1, "word": " الان", "probability": 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356.5, "word": " لسلب", "probability": 0.9881184895833334}, {"start": 356.5, "end": 357.12, "word": " x", "probability": 0.98291015625}, {"start": 357.12, "end": 358.16, "word": " بده", "probability": 0.947509765625}, {"start": 358.16, "end": 358.56, "word": " يسوي", "probability": 0.9484049479166666}, {"start": 358.56, "end": 359.08, "word": " tan", "probability": 0.92578125}, {"start": 359.08, "end": 359.36, "word": " ال", "probability": 0.916015625}, {"start": 359.36, "end": 359.88, "word": " x", "probability": 0.92041015625}, {"start": 359.88, "end": 361.48, "word": " cotan", "probability": 0.743408203125}, {"start": 361.48, "end": 362.94, "word": " لسلب", "probability": 0.99169921875}, {"start": 362.94, "end": 363.54, "word": " x", "probability": 0.98291015625}, {"start": 363.54, "end": 364.78, "word": " يسوي", "probability": 0.8933919270833334}, {"start": 364.78, "end": 365.48, "word": " cotan", "probability": 0.9580078125}, {"start": 365.48, "end": 365.7, "word": " ال", "probability": 0.96923828125}, {"start": 365.7, "end": 366.18, "word": " x", "probability": 0.8994140625}, {"start": 366.18, "end": 367.5, "word": " and", "probability": 0.7734375}, {"start": 367.5, "end": 369.28, "word": " cosecant", "probability": 0.84814453125}, {"start": 369.28, "end": 370.46, "word": " لسلب", "probability": 0.99267578125}, {"start": 370.46, "end": 371.04, "word": " x", "probability": 0.94677734375}, {"start": 371.04, "end": 372.18, "word": " يسوي", "probability": 0.896484375}, {"start": 372.18, "end": 373.38, "word": " cosecant", "probability": 0.97314453125}, {"start": 373.38, "end": 373.76, "word": " ال", "probability": 0.92236328125}, {"start": 373.76, "end": 374.1, "word": " x", "probability": 0.8095703125}], "temperature": 1.0}, {"id": 15, "seek": 40682, "start": 379.08, "end": 406.82, "text": "سين الاكس يساوي سالب سين الاكس وتان الاكس يساوي سالب تان الاكس وكتان لسالب اكس يساوي سالب كتان الاكس وكسيكنت لسالب اكس يساوي سالب كسيكنت الاكس هذا معناه ال odd function", "tokens": [3794, 9957, 42963, 4117, 3794, 7251, 3794, 995, 45865, 8608, 6027, 3555, 8608, 9957, 42963, 4117, 3794, 34683, 7649, 42963, 4117, 3794, 7251, 3794, 995, 45865, 8608, 6027, 3555, 6055, 7649, 42963, 4117, 3794, 4032, 4117, 2655, 7649, 5296, 3794, 6027, 3555, 1975, 4117, 3794, 7251, 3794, 995, 45865, 8608, 6027, 3555, 9122, 2655, 7649, 42963, 4117, 3794, 4032, 4117, 3794, 1829, 19452, 2655, 5296, 3794, 6027, 3555, 1975, 4117, 3794, 7251, 3794, 995, 45865, 8608, 6027, 3555, 9122, 3794, 1829, 19452, 2655, 42963, 4117, 3794, 23758, 20449, 8315, 3224, 2423, 7401, 2445], "avg_logprob": -0.17270611448490875, "compression_ratio": 2.587719298245614, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 379.08000000000004, "end": 380.48, "word": "سين", "probability": 0.346527099609375}, {"start": 380.48, "end": 381.88, "word": " الاكس", "probability": 0.7445475260416666}, {"start": 381.88, "end": 382.76, "word": " يساوي", "probability": 0.8533935546875}, {"start": 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393.54, "end": 394.54, "word": " يساوي", "probability": 0.979736328125}, {"start": 394.54, "end": 396.26, "word": " سالب", "probability": 0.9798177083333334}, {"start": 396.26, "end": 396.78, "word": " كتان", "probability": 0.9943033854166666}, {"start": 396.78, "end": 397.26, "word": " الاكس", "probability": 0.9925130208333334}, {"start": 397.26, "end": 398.62, "word": " وكسيكنت", "probability": 0.647216796875}, {"start": 398.62, "end": 399.46, "word": " لسالب", "probability": 0.9901123046875}, {"start": 399.46, "end": 399.98, "word": " اكس", "probability": 0.9609375}, {"start": 399.98, "end": 400.94, "word": " يساوي", "probability": 0.97802734375}, {"start": 400.94, "end": 401.74, "word": " سالب", "probability": 0.9816080729166666}, {"start": 401.74, "end": 402.66, "word": " كسيكنت", "probability": 0.96953125}, {"start": 402.66, "end": 403.26, "word": " الاكس", "probability": 0.9913736979166666}, {"start": 403.26, "end": 403.98, "word": " هذا", "probability": 0.7763671875}, {"start": 403.98, "end": 404.5, "word": " معناه", "probability": 0.8160807291666666}, {"start": 404.5, "end": 404.92, "word": " ال", "probability": 0.2281494140625}, {"start": 404.92, "end": 406.08, "word": " odd", "probability": 0.1849365234375}, {"start": 406.08, "end": 406.82, "word": " function", "probability": 0.93115234375}], "temperature": 1.0}, {"id": 16, "seek": 43687, "start": 407.31, "end": 436.87, "text": "يبقى النسب المثلثية ستةين تان even وأربعة odd يبقى cosine لسلب X هو cosine X second لسلب X هي second X sin لسلب X بسالب sin X tan لسلب X هو سالب tan X cotan لسلب X هو سالب cotan X cosecant لسلب X هو سالب cosecant X", "tokens": [1829, 3555, 4587, 7578, 28239, 35457, 9673, 12984, 1211, 12984, 10632, 8608, 2655, 3660, 9957, 6055, 7649, 754, 36725, 25513, 27884, 7401, 7251, 3555, 4587, 7578, 23565, 5296, 3794, 46152, 1783, 31439, 23565, 1783, 1150, 5296, 3794, 46152, 1783, 39896, 1150, 1783, 3343, 5296, 3794, 46152, 1783, 4724, 3794, 6027, 3555, 3343, 1783, 7603, 5296, 3794, 46152, 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{"start": 413.23, "end": 414.37, "word": " يبقى", "probability": 0.947998046875}, {"start": 414.37, "end": 415.19, "word": " cosine", "probability": 0.6005859375}, {"start": 415.19, "end": 415.83, "word": " لسلب", "probability": 0.68798828125}, {"start": 415.83, "end": 416.09, "word": " X", "probability": 0.54443359375}, {"start": 416.09, "end": 416.33, "word": " هو", "probability": 0.8818359375}, {"start": 416.33, "end": 416.89, "word": " cosine", "probability": 0.81640625}, {"start": 416.89, "end": 417.47, "word": " X", "probability": 0.81689453125}, {"start": 417.47, "end": 418.27, "word": " second", "probability": 0.38037109375}, {"start": 418.27, "end": 419.27, "word": " لسلب", "probability": 0.9895833333333334}, {"start": 419.27, "end": 419.87, "word": " X", "probability": 0.9521484375}, {"start": 419.87, "end": 420.19, "word": " هي", "probability": 0.95068359375}, {"start": 420.19, "end": 420.71, "word": " second", "probability": 0.92431640625}, {"start": 420.71, "end": 421.27, 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{"start": 427.99, "end": 428.47, "word": " X", "probability": 0.98193359375}, {"start": 428.47, "end": 429.25, "word": " cotan", "probability": 0.772216796875}, {"start": 429.25, "end": 429.73, "word": " لسلب", "probability": 0.9874674479166666}, {"start": 429.73, "end": 430.11, "word": " X", "probability": 0.99658203125}, {"start": 430.11, "end": 430.37, "word": " هو", "probability": 0.9775390625}, {"start": 430.37, "end": 430.87, "word": " سالب", "probability": 0.9786783854166666}, {"start": 430.87, "end": 431.41, "word": " cotan", "probability": 0.810546875}, {"start": 431.41, "end": 431.93, "word": " X", "probability": 0.9931640625}, {"start": 431.93, "end": 432.83, "word": " cosecant", "probability": 0.8269856770833334}, {"start": 432.83, "end": 433.39, "word": " لسلب", "probability": 0.9912109375}, {"start": 433.39, "end": 433.75, "word": " X", "probability": 0.99609375}, {"start": 433.75, "end": 434.41, "word": " هو", "probability": 0.97705078125}, {"start": 434.41, "end": 435.39, "word": " سالب", "probability": 0.9480794270833334}, {"start": 435.39, "end": 436.49, "word": " cosecant", "probability": 0.98095703125}, {"start": 436.49, "end": 436.87, "word": " X", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 17, "seek": 46530, "start": 437.3, "end": 465.3, "text": "الان بدنا نربط القديم بالجديد، يعني بدنا نعطي أمثلة على المثائل اللي وقتاش بتكون الدالة even ووقتاش بتكون الدالة odd وبدنا ندخل فيها النسب المثلثية اللي عندنا، يبقى بدنا نعطي مثال توضيحي على ذلك، يبقى example المثال بيقول ما يأتي", "tokens": [6027, 7649, 47525, 8315, 8717, 25513, 9566, 25062, 16254, 2304, 20666, 7435, 16254, 3215, 12399, 37495, 22653, 47525, 8315, 8717, 3615, 9566, 1829, 5551, 2304, 12984, 37977, 15844, 9673, 12984, 16373, 1211, 13672, 1829, 4032, 38149, 33599, 39894, 30544, 32748, 6027, 3660, 754, 4032, 30543, 2655, 33599, 39894, 30544, 32748, 6027, 3660, 7401, 4032, 44510, 8315, 8717, 3215, 9778, 1211, 8978, 11296, 28239, 35457, 9673, 12984, 1211, 12984, 10632, 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441.84, "word": " نعطي", "probability": 0.9666748046875}, {"start": 441.84, "end": 442.48, "word": " أمثلة", "probability": 0.9432373046875}, {"start": 442.48, "end": 442.82, "word": " على", "probability": 0.8623046875}, {"start": 442.82, "end": 443.78, "word": " المثائل", "probability": 0.79327392578125}, {"start": 443.78, "end": 444.4, "word": " اللي", "probability": 0.82275390625}, {"start": 444.4, "end": 444.86, "word": " وقتاش", "probability": 0.5163167317708334}, {"start": 444.86, "end": 445.3, "word": " بتكون", "probability": 0.89404296875}, {"start": 445.3, "end": 445.86, "word": " الدالة", "probability": 0.84375}, {"start": 445.86, "end": 446.14, "word": " even", "probability": 0.67041015625}, {"start": 446.14, "end": 446.96, "word": " ووقتاش", "probability": 0.833984375}, {"start": 446.96, "end": 447.4, "word": " بتكون", "probability": 0.7744140625}, {"start": 447.4, "end": 448.0, "word": " الدالة", "probability": 0.9884440104166666}, {"start": 448.0, "end": 448.38, "word": " odd", "probability": 0.9599609375}, {"start": 448.38, "end": 449.1, "word": " وبدنا", "probability": 0.8076171875}, {"start": 449.1, "end": 449.6, "word": " ندخل", "probability": 0.993408203125}, {"start": 449.6, "end": 449.94, "word": " فيها", "probability": 0.991943359375}, {"start": 449.94, "end": 450.54, "word": " النسب", "probability": 0.930908203125}, {"start": 450.54, "end": 452.24, "word": " المثلثية", "probability": 0.95947265625}, {"start": 452.24, "end": 452.6, "word": " اللي", "probability": 0.927978515625}, {"start": 452.6, "end": 453.36, "word": " عندنا،", "probability": 0.7443033854166666}, {"start": 453.36, "end": 453.64, "word": " يبقى", "probability": 0.88427734375}, {"start": 453.64, "end": 453.9, "word": " بدنا", "probability": 0.8837890625}, {"start": 453.9, "end": 454.36, "word": " نعطي", "probability": 0.9949951171875}, {"start": 454.36, "end": 454.78, "word": " مثال", "probability": 0.99462890625}, {"start": 454.78, "end": 455.62, "word": " توضيحي", "probability": 0.97607421875}, {"start": 455.62, "end": 455.94, "word": " على", "probability": 0.9287109375}, {"start": 455.94, "end": 456.6, "word": " ذلك،", "probability": 0.8792317708333334}, {"start": 456.6, "end": 456.88, "word": " يبقى", "probability": 0.96923828125}, {"start": 456.88, "end": 457.7, "word": " example", "probability": 0.89697265625}, {"start": 457.7, "end": 464.0, "word": " المثال", "probability": 0.91552734375}, {"start": 464.0, "end": 464.46, "word": " بيقول", "probability": 0.98291015625}, {"start": 464.46, "end": 464.76, "word": " ما", "probability": 0.96826171875}, {"start": 464.76, "end": 465.3, "word": " يأتي", "probability": 0.8767903645833334}], "temperature": 1.0}, {"id": 18, "seek": 49113, "start": 466.15, "end": 491.13, "text": "determine whether the following functions are even, odd or neither", "tokens": [49136, 533, 1968, 264, 3480, 6828, 366, 754, 11, 7401, 420, 9662], "avg_logprob": -0.17938701923076922, "compression_ratio": 1.0153846153846153, 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ناخد الدالة f of x يساوي x تربيع cosine 2x", "tokens": [3224, 1211, 39896, 754, 49429, 7401, 4032, 21984, 20193, 754, 49429, 7401, 8717, 29973, 7578, 257, 47525, 8315, 8717, 47283, 3215, 32748, 6027, 3660, 283, 295, 2031, 7251, 3794, 995, 45865, 2031, 6055, 2288, 21292, 3615, 23565, 568, 87], "avg_logprob": -0.26171875074505807, "compression_ratio": 1.2589285714285714, "no_speech_prob": 0.0, "words": [{"start": 493.69, "end": 494.05, "word": "هل", "probability": 0.8583984375}, {"start": 494.05, "end": 494.25, "word": " هي", "probability": 0.888671875}, {"start": 494.25, "end": 494.73, "word": " even", "probability": 0.82080078125}, {"start": 494.73, "end": 495.57, "word": " ولا", "probability": 0.65771484375}, {"start": 495.57, "end": 496.11, "word": " odd", "probability": 0.89990234375}, {"start": 496.11, "end": 496.69, "word": " و", "probability": 0.233642578125}, {"start": 496.69, "end": 496.91, "word": " الله", "probability": 0.548828125}, {"start": 496.91, "end": 497.13, "word": " 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"text": "لأن الـ cosine هي عبارة عن رأس المسألة اللي عندنا يبقى هذا بده يساوي ال F of X itself يبقى معناه هذا الكلام ان الدالة هذه معناها is even function", "tokens": [1211, 33456, 2423, 39184, 23565, 39896, 6225, 3555, 9640, 3660, 18871, 12602, 10721, 3794, 9673, 3794, 10721, 37977, 13672, 1829, 43242, 8315, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 7251, 3794, 995, 45865, 2423, 479, 295, 1783, 2564, 7251, 3555, 4587, 7578, 20449, 8315, 3224, 23758, 2423, 28820, 10943, 16472, 32748, 6027, 3660, 29538, 20449, 8315, 11296, 307, 754, 2445], "avg_logprob": -0.41905737314067903, "compression_ratio": 1.4713375796178343, "no_speech_prob": 0.0, "words": [{"start": 559.66, "end": 560.06, "word": "لأن", "probability": 0.54248046875}, {"start": 560.06, "end": 560.26, "word": " الـ", "probability": 0.691650390625}, {"start": 560.26, "end": 560.6, "word": " cosine", "probability": 0.309326171875}, {"start": 560.6, "end": 561.2, "word": " هي", "probability": 0.2073974609375}, {"start": 561.2, 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الكل تربيع يبقى سالب sin x الكل تربيع اذا هذه مربعها شو بدي اعطيني sin تربيع ال x يبقى هذه زائد سالب", "tokens": [1211, 3794, 6027, 3555, 2031, 2423, 28820, 6055, 2288, 21292, 3615, 7251, 3555, 4587, 7578, 8608, 6027, 3555, 3343, 2031, 2423, 28820, 6055, 2288, 21292, 3615, 1975, 15730, 29538, 3714, 25513, 3615, 11296, 13412, 2407, 4724, 16254, 1975, 3615, 9566, 1829, 22653, 3343, 6055, 2288, 21292, 3615, 2423, 2031, 7251, 3555, 4587, 7578, 29538, 30767, 16373, 3215, 8608, 6027, 3555], "avg_logprob": -0.39549180718718985, "compression_ratio": 1.6283185840707965, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 681.92, "end": 683.18, "word": "لسالب", "probability": 0.4703369140625}, {"start": 683.18, "end": 683.62, "word": " x", "probability": 0.364990234375}, {"start": 683.62, "end": 684.32, "word": " الكل", "probability": 0.6688232421875}, {"start": 684.32, "end": 685.0, "word": " تربيع", "probability": 0.748046875}, {"start": 685.0, "end": 686.06, "word": " يبقى", 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"end": 2556.06, "word": " تربيع", "probability": 0.8472900390625}, {"start": 2556.06, "end": 2556.22, "word": " ال", "probability": 0.62548828125}, {"start": 2556.22, "end": 2556.7, "word": " X", "probability": 0.88330078125}, {"start": 2556.7, "end": 2557.96, "word": " نمر", "probability": 0.876708984375}, {"start": 2557.96, "end": 2558.56, "word": " B", "probability": 0.82275390625}, {"start": 2558.56, "end": 2561.72, "word": " F", "probability": 0.912109375}, {"start": 2561.72, "end": 2562.12, "word": " of", "probability": 0.95654296875}, {"start": 2562.12, "end": 2562.76, "word": " X", "probability": 0.9970703125}, {"start": 2562.76, "end": 2565.26, "word": " يساوي", "probability": 0.9422607421875}, {"start": 2565.26, "end": 2567.02, "word": " واحد", "probability": 0.974853515625}, {"start": 2567.02, "end": 2568.38, "word": " ناقص", "probability": 0.9549560546875}, {"start": 2568.38, "end": 2569.1, "word": " كوسين", "probability": 0.8763020833333334}, {"start": 2569.1, "end": 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قبل هيكل انت رستريكشن من حياطيني دومين الثاني يبقى هذا بتعطيني كل ال real line ماعدا in by على اتنين", "tokens": [3215, 20498, 9957, 6024, 104, 7649, 1829, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 4032, 47283, 3215, 8315, 3224, 12174, 36150, 39896, 28820, 16472, 2655, 12602, 14851, 16572, 4117, 8592, 1863, 9154, 11331, 1829, 41193, 9957, 1829, 11778, 20498, 9957, 6024, 104, 7649, 1829, 7251, 3555, 4587, 7578, 23758, 39894, 3615, 9566, 1829, 22653, 28242, 2423, 957, 1622, 19446, 3615, 28259, 294, 538, 15844, 1975, 2655, 1863, 9957], "avg_logprob": -0.4827898602554764, "compression_ratio": 1.5333333333333334, "no_speech_prob": 0.0, "words": [{"start": 3054.81, "end": 3055.35, "word": "دومين", "probability": 0.3929443359375}, {"start": 3055.35, "end": 3055.73, "word": " الثاني", "probability": 0.74310302734375}, {"start": 3055.73, "end": 3055.93, "word": " احنا", "probability": 0.5906982421875}, {"start": 3055.93, "end": 3056.33, "word": " عارفين", "probability": 0.864501953125}, 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"probability": 0.94970703125}, {"start": 5560.48, "end": 5561.9, "word": " PQ", "probability": 0.80322265625}, {"start": 5561.9, "end": 5564.22, "word": " يبقى", "probability": 0.9478759765625}, {"start": 5564.22, "end": 5564.5, "word": " هذا", "probability": 0.939453125}, {"start": 5564.5, "end": 5565.06, "word": " ميل", "probability": 0.4666748046875}, {"start": 5565.06, "end": 5565.72, "word": " القطع", "probability": 0.8214518229166666}, {"start": 5565.72, "end": 5565.94, "word": " او", "probability": 0.71630859375}, {"start": 5565.94, "end": 5566.16, "word": " ميل", "probability": 0.957763671875}, {"start": 5566.16, "end": 5566.7, "word": " الخط", "probability": 0.986572265625}, {"start": 5566.7, "end": 5567.38, "word": " المستقيم", "probability": 0.9674072265625}, {"start": 5567.38, "end": 5567.5, "word": " اللي", "probability": 0.931640625}, {"start": 5567.5, "end": 5567.64, "word": " هو", "probability": 0.87158203125}, {"start": 5567.64, "end": 5567.98, "word": " main", 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7605, 1975, 34268, 26890, 9673, 1863, 5016, 1863, 3660, 288, 6055, 3794, 995, 45865, 2031, 6055, 25513, 10632, 8717, 995, 4587, 9381, 5551, 25513, 27884, 2031, 9673, 9566, 1211, 37746, 16247, 12610, 915, 264, 13525, 295], "avg_logprob": -0.21269531026482583, "compression_ratio": 1.1428571428571428, "no_speech_prob": 0.0, "words": [{"start": 6038.01, "end": 6038.73, "word": "consider", "probability": 0.55609130859375}, {"start": 6038.73, "end": 6039.01, "word": " the", "probability": 0.84326171875}, {"start": 6039.01, "end": 6039.75, "word": " curve", "probability": 0.9560546875}, {"start": 6039.75, "end": 6045.99, "word": " اعتبر", "probability": 0.8566080729166666}, {"start": 6045.99, "end": 6047.25, "word": " المنحنة", "probability": 0.87705078125}, {"start": 6047.25, "end": 6048.33, "word": " y", "probability": 0.4912109375}, {"start": 6048.33, "end": 6049.25, "word": " تساوي", "probability": 0.752716064453125}, {"start": 6049.25, "end": 6049.77, "word": " x", "probability": 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نمر بـ Find an equation بدنا معادلة of", "tokens": [2278, 7605, 5296, 19528, 1863, 5016, 1863, 3660, 412, 264, 935, 43242, 28239, 47432, 3660, 430, 16, 46952, 46152, 6055, 1211, 2655, 3660, 8717, 29973, 4724, 39184, 11809, 364, 5367, 47525, 8315, 20449, 18513, 37977, 295], "avg_logprob": -0.32559120655059814, "compression_ratio": 1.0731707317073171, "no_speech_prob": 0.0, "words": [{"start": 6067.57, "end": 6067.95, "word": "The", "probability": 0.0897216796875}, {"start": 6067.95, "end": 6069.01, "word": " curve", "probability": 0.82373046875}, {"start": 6069.01, "end": 6071.47, "word": " للمنحنة", "probability": 0.859375}, {"start": 6071.47, "end": 6072.65, "word": " at", "probability": 0.81591796875}, {"start": 6072.65, "end": 6073.85, "word": " the", "probability": 0.8056640625}, {"start": 6073.85, "end": 6074.93, "word": " point", "probability": 0.9814453125}, {"start": 6074.93, "end": 6076.19, "word": " عند", "probability": 0.96337890625}, {"start": 6076.19, "end": 6077.83, 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ال second معله tangent يبقى بصير مماس و بصير ميل المماس هو ميل مين؟ ميل المنحنة يبقى بيجي بيقوله هنا F", "tokens": [40228, 22653, 3714, 9957, 22807, 264, 13525, 295, 264, 1150, 3714, 19913, 3555, 2407, 9566, 1975, 5016, 8315, 12174, 12610, 8315, 5296, 15042, 2423, 1249, 6055, 1829, 7435, 1829, 8717, 31377, 37977, 12602, 47302, 5016, 3660, 15844, 430, 11933, 15730, 389, 47525, 3224, 6055, 32887, 5016, 5296, 2407, 9957, 22807, 5296, 17182, 11933, 15730, 389, 12602, 39319, 2655, 5296, 17182, 4724, 1829, 9381, 49628, 2423, 1150, 20449, 43761, 27747, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 3714, 15042, 3794, 4032, 4724, 9381, 13546, 3714, 26895, 9673, 15042, 3794, 31439, 3714, 26895, 3714, 9957, 22807, 3714, 26895, 9673, 1863, 5016, 1863, 3660, 7251, 3555, 4587, 7578, 4724, 1829, 7435, 1829, 4724, 1829, 39648, 3224, 34105, 479], "avg_logprob": -0.23262392087229367, "compression_ratio": 1.766355140186916, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 6290.34, "end": 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"word": " Zero", "probability": 0.23583984375}, {"start": 6304.2, "end": 6304.92, "word": " إذا", "probability": 0.936767578125}, {"start": 6304.92, "end": 6305.16, "word": " H", "probability": 0.9248046875}, {"start": 6305.16, "end": 6305.74, "word": " راحت", "probability": 0.8111979166666666}, {"start": 6305.74, "end": 6305.92, "word": " ل", "probability": 0.93310546875}, {"start": 6305.92, "end": 6306.38, "word": " Zero", "probability": 0.9423828125}, {"start": 6306.38, "end": 6307.14, "word": " بيصبح", "probability": 0.8887939453125}, {"start": 6307.14, "end": 6307.38, "word": " ال", "probability": 0.8076171875}, {"start": 6307.38, "end": 6307.76, "word": " second", "probability": 0.8095703125}, {"start": 6307.76, "end": 6308.34, "word": " معله", "probability": 0.80859375}, {"start": 6308.34, "end": 6309.72, "word": " tangent", "probability": 0.298583984375}, {"start": 6309.72, "end": 6310.74, "word": " يبقى", "probability": 0.8822021484375}, {"start": 6310.74, "end": 6311.3, "word": " بصير", "probability": 0.9541015625}, {"start": 6311.3, "end": 6311.9, "word": " مماس", "probability": 0.8152669270833334}, {"start": 6311.9, "end": 6312.32, "word": " و", "probability": 0.5908203125}, {"start": 6312.32, "end": 6312.7, "word": " بصير", "probability": 0.8800455729166666}, {"start": 6312.7, "end": 6313.18, "word": " ميل", "probability": 0.669189453125}, {"start": 6313.18, "end": 6313.9, "word": " المماس", "probability": 0.8697916666666666}, {"start": 6313.9, "end": 6314.16, "word": " هو", "probability": 0.96435546875}, {"start": 6314.16, "end": 6314.5, "word": " ميل", "probability": 0.96337890625}, {"start": 6314.5, "end": 6315.56, "word": " مين؟", "probability": 0.8522135416666666}, {"start": 6315.56, "end": 6316.18, "word": " ميل", "probability": 0.955810546875}, {"start": 6316.18, "end": 6317.2, "word": " المنحنة", "probability": 0.9248046875}, {"start": 6317.2, "end": 6317.94, "word": " يبقى", "probability": 0.9732666015625}, {"start": 6317.94, "end": 6318.3, "word": " بيجي", "probability": 0.8060302734375}, {"start": 6318.3, "end": 6318.78, "word": " بيقوله", "probability": 0.747314453125}, {"start": 6318.78, "end": 6319.08, "word": " هنا", "probability": 0.96044921875}, {"start": 6319.08, "end": 6319.58, "word": " F", "probability": 0.92578125}], "temperature": 1.0}, {"id": 264, "seek": 632225, "start": 6320.01, "end": 6322.25, "text": "أتش راحت لـ Zero", "tokens": [10721, 2655, 8592, 12602, 39319, 2655, 5296, 39184, 17182], "avg_logprob": -0.6972656071186065, "compression_ratio": 0.6944444444444444, "no_speech_prob": 0.0, "words": [{"start": 6320.01, "end": 6320.67, "word": "أتش", "probability": 0.5653177897135416}, {"start": 6320.67, "end": 6321.53, "word": " راحت", "probability": 0.6735026041666666}, {"start": 6321.53, "end": 6321.87, "word": " لـ", "probability": 0.693603515625}, {"start": 6321.87, "end": 6322.25, "word": " Zero", "probability": 0.25634765625}], "temperature": 1.0}, {"id": 265, "seek": 635189, "start": 6323.87, "end": 6351.89, "text": "get the slope of the curve اللي هو المطلوب الأول من هنا نمرا a مطلوب الأول تبع المثلة يبقى لما ال H بده تروح لل zero we get the slope of the curve اللي هو بده ساوي قداش سالب اتنين سالب اتنين بالضبط هو الإسلوب", "tokens": [847, 264, 13525, 295, 264, 7605, 13672, 1829, 31439, 9673, 9566, 1211, 37746, 16247, 12610, 9154, 34105, 8717, 2304, 23557, 257, 3714, 9566, 1211, 37746, 16247, 12610, 6055, 3555, 3615, 9673, 12984, 37977, 7251, 3555, 4587, 7578, 5296, 15042, 2423, 389, 47525, 3224, 6055, 32887, 5016, 24976, 4018, 321, 483, 264, 13525, 295, 264, 7605, 13672, 1829, 31439, 47525, 3224, 8608, 995, 45865, 12174, 3215, 33599, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 20666, 11242, 3555, 9566, 31439, 33688, 3794, 1211, 37746], "avg_logprob": -0.22795138243171903, "compression_ratio": 1.8295454545454546, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 6323.87, "end": 6324.41, "word": "get", 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{"start": 6344.65, "end": 6345.61, "word": " قداش", "probability": 0.80908203125}, {"start": 6345.61, "end": 6346.91, "word": " سالب", "probability": 0.629638671875}, {"start": 6346.91, "end": 6347.41, "word": " اتنين", "probability": 0.8809814453125}, {"start": 6347.41, "end": 6348.31, "word": " سالب", "probability": 0.9124348958333334}, {"start": 6348.31, "end": 6348.81, "word": " اتنين", "probability": 0.98046875}, {"start": 6348.81, "end": 6349.97, "word": " بالضبط", "probability": 0.9893798828125}, {"start": 6349.97, "end": 6350.57, "word": " هو", "probability": 0.9912109375}, {"start": 6350.57, "end": 6351.89, "word": " الإسلوب", "probability": 0.72265625}], "temperature": 1.0}, {"id": 266, "seek": 637731, "start": 6353.33, "end": 6377.31, "text": "the tangent at main at P واحد مسالم تلاتة صحيح ولا لا؟ قال له ال اسلوب of the curve هو الاسلوب of main of the tangent قال له المطلوب التاني عندك بدي معادلة المماس المماس خط مستقيم", "tokens": [3322, 27747, 412, 2135, 412, 430, 36764, 24401, 47524, 45340, 6055, 1211, 9307, 3660, 20328, 5016, 1829, 5016, 49429, 20193, 22807, 50239, 46740, 2423, 24525, 1211, 37746, 295, 264, 7605, 31439, 2423, 32277, 1211, 37746, 295, 2135, 295, 264, 27747, 50239, 46740, 9673, 9566, 1211, 37746, 16712, 7649, 1829, 43242, 4117, 4724, 16254, 20449, 18513, 37977, 9673, 15042, 3794, 9673, 15042, 3794, 16490, 9566, 3714, 14851, 4587, 32640], "avg_logprob": -0.3405797118725984, "compression_ratio": 1.6369047619047619, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 6353.33, "end": 6353.89, "word": "the", "probability": 0.11236572265625}, {"start": 6353.89, "end": 6355.93, "word": " tangent", "probability": 0.923828125}, {"start": 6355.93, "end": 6357.65, "word": " at", "probability": 0.671875}, {"start": 6357.65, "end": 6358.27, "word": " main", "probability": 0.39111328125}, {"start": 6358.27, "end": 6359.07, "word": " at", "probability": 0.87890625}, {"start": 6359.07, "end": 6359.55, "word": " P", "probability": 0.6923828125}, {"start": 6359.55, "end": 6360.61, "word": " واحد", "probability": 0.542633056640625}, {"start": 6360.61, "end": 6361.21, "word": " مسالم", "probability": 0.459228515625}, {"start": 6361.21, "end": 6362.25, "word": " تلاتة", "probability": 0.731689453125}, {"start": 6362.25, "end": 6362.67, "word": " صحيح", "probability": 0.84228515625}, {"start": 6362.67, "end": 6362.83, "word": " ولا", "probability": 0.8701171875}, {"start": 6362.83, "end": 6363.63, "word": " لا؟", "probability": 0.5364990234375}, {"start": 6363.63, "end": 6364.81, "word": " قال", "probability": 0.2049560546875}, {"start": 6364.81, "end": 6364.97, "word": " له", "probability": 0.433349609375}, {"start": 6364.97, "end": 6365.07, "word": " ال", "probability": 0.6904296875}, {"start": 6365.07, "end": 6365.73, "word": " اسلوب", "probability": 0.6754557291666666}, {"start": 6365.73, "end": 6366.37, "word": " of", "probability": 0.716796875}, {"start": 6366.37, "end": 6367.01, "word": " the", "probability": 0.5498046875}, {"start": 6367.01, "end": 6367.51, "word": " curve", "probability": 0.8515625}, {"start": 6367.51, "end": 6367.83, "word": " هو", "probability": 0.9365234375}, {"start": 6367.83, "end": 6368.59, "word": " الاسلوب", "probability": 0.7955322265625}, {"start": 6368.59, "end": 6368.85, "word": " of", "probability": 0.7763671875}, {"start": 6368.85, "end": 6369.25, "word": " main", "probability": 0.8193359375}, {"start": 6369.25, "end": 6369.95, "word": " of", "probability": 0.95556640625}, {"start": 6369.95, "end": 6370.19, "word": " the", "probability": 0.87939453125}, {"start": 6370.19, "end": 6370.83, "word": " tangent", "probability": 0.8984375}, {"start": 6370.83, "end": 6371.73, "word": " قال", "probability": 0.59326171875}, {"start": 6371.73, "end": 6371.85, "word": " له", "probability": 0.65673828125}, {"start": 6371.85, "end": 6372.41, "word": " المطلوب", "probability": 0.96630859375}, {"start": 6372.41, "end": 6372.97, "word": " التاني", "probability": 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b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3CIXK0BIA2g_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..f892b82001a361e6d10e2ae76711ba6a2459730e --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3CIXK0BIA2g_raw.srt @@ -0,0 +1,3352 @@ +1 +00:00:22,290 --> 00:00:26,990 +بسم الله الرحمن الرحيم بقيت في section خمسة اربعة + +2 +00:00:26,990 --> 00:00:30,970 +من المرة الماضية اخر نقطة اللى قدامنا اللى هى ال + +3 +00:00:30,970 --> 00:00:38,530 +total area المساحة الكلية هنعطى تعريف فيه بان نحسب + +4 +00:00:38,530 --> 00:00:42,930 +المساحة الكلية يعني المساحة اللى موجودة بين منحنا + +5 +00:00:42,930 --> 00:00:50,070 +ومحور Xطبعا احنا سابقا اخدنا كيفية إيجاد هذه + +6 +00:00:50,070 --> 00:00:55,150 +المساحة إذا كان عنده الدالة دائما و أبدا non + +7 +00:00:55,150 --> 00:01:01,490 +negative يعني بتاخد قيمة موجبة دائما و أبدا لكنها + +8 +00:01:01,490 --> 00:01:06,270 +تاخد قيمة موجبة و قيمة سالبة هذه لم نتعرض لها قبل + +9 +00:01:06,270 --> 00:01:13,350 +ذلكبنتعرض لو كانت الدالة أعلى محور X أو أسفل محور + +10 +00:01:13,350 --> 00:01:17,370 +X كيف بنحسب المساحة اللي محصورة بينها و بينها محور + +11 +00:01:17,370 --> 00:01:22,030 +X طبعا إذا الدالة فوق محور X و بنحسب المساحة + +12 +00:01:22,030 --> 00:01:26,530 +المساحة بتطلع بقيمة موجبة إذا الدالة أسفل محور X + +13 +00:01:26,530 --> 00:01:30,030 +يبدأ المساحة اللي بينها و بينها محور X تطلع عندنا + +14 +00:01:30,030 --> 00:01:36,510 +بإشارة سالب كما سنرى بعد قليل ال remark بتقولي ما + +15 +00:01:36,510 --> 00:01:42,090 +يأتيمشان نجد الـ total area المساحة الكلية بين + +16 +00:01:42,090 --> 00:01:46,730 +الرسم البياني اللي اتدالة Y تساوي F of X ومحور X + +17 +00:01:46,730 --> 00:01:51,810 +على الفترة A وB بدنا نعمل الخطوات التالية We make + +18 +00:01:51,810 --> 00:01:56,070 +the following steps الخطوة الأولى We subdivide the + +19 +00:01:56,070 --> 00:02:02,260 +interval A وBAt the zeros of F يعني بدنا نيجي نقسم + +20 +00:02:02,260 --> 00:02:09,340 +الفترة من A إلى B حسب أصفار الدالة يبقى وين الدالة + +21 +00:02:09,340 --> 00:02:16,260 +بتاخد القيم اللي بتخلي الدالة تساوي صفر بدنا نجزئي + +22 +00:02:16,260 --> 00:02:21,860 +التكامل إلى مجموعة من التكاملات على هذه الفترات + +23 +00:02:22,420 --> 00:02:26,720 +النقطة الثانية بدى نحسب قيمة كل تكامل من هذه + +24 +00:02:26,720 --> 00:02:31,420 +التكاملات على الفترة الخاصة ابو يعني لو اتخيلنا ان + +25 +00:02:31,420 --> 00:02:34,600 +هذا الرسم اللى عندها هي رسم في المنعنى y تساوي f + +26 +00:02:34,600 --> 00:02:38,220 +of x نلاقي ان الدالة أخدت zero عند ال a و عند x + +27 +00:02:38,220 --> 00:02:43,040 +واحد و x اتنين و عند m و عند ال b إذا قسمنا الفترة + +28 +00:02:43,040 --> 00:02:48,460 +إلى ثلاث فتراتبدي اخد الفترة من a الى x1 ومن x1 + +29 +00:02:48,460 --> 00:02:54,400 +الى x2 ومن x2 الى b يبقى لو كاملت الدالة على + +30 +00:02:54,400 --> 00:03:00,260 +الفترة من a الى x1 بحصل على المساحة a1لو كملت على + +31 +00:03:00,260 --> 00:03:06,140 +الفترة من X1 إلى X2 بحصل المساحة A2 لو كملت من X2 + +32 +00:03:06,140 --> 00:03:12,840 +إلى B بحصل المساحة A3 موجبة موجبة سالبة هتطلع عنا + +33 +00:03:12,840 --> 00:03:17,240 +إذا انجلبت كامل على الفترات التلاتة اللي عندك أو + +34 +00:03:17,240 --> 00:03:21,200 +الأربعة أو الخمسة جد ما يكونوا حسب أصفر الدالة + +35 +00:03:21,200 --> 00:03:25,500 +بعدها بيقول بتجمع ال absolute values لل integrals + +36 +00:03:25,740 --> 00:03:29,740 +التكاملات نتيجة توقيتها قد يكون موجب وقد يكون سالم + +37 +00:03:29,740 --> 00:03:33,820 +إذا باخد ال absolute value لكل تكامل من التكاملات + +38 +00:03:33,820 --> 00:03:39,300 +التلتة بيصير كله موجب يبقى بجمع بكون جبت المساحة + +39 +00:03:39,300 --> 00:03:44,890 +الحقيقية اللي محصورة بين المنحنة ومحور Xيبقى هنا + +40 +00:03:44,890 --> 00:03:47,990 +الـ Total Area A يبقى سواء Absolute Value لـ A1 + +41 +00:03:47,990 --> 00:03:51,790 +زاد Absolute Value لـ A2 زاد Absolute Value لـ A3 + +42 +00:03:51,790 --> 00:03:57,930 +بيعطيني المساحة الحقيقية حيث A1 يتكامل من A ل X1 ل + +43 +00:03:57,930 --> 00:04:04,990 +F of X DX الـ A2 تكامل من X1 ل X2 ل F of X DX الـ + +44 +00:04:04,990 --> 00:04:12,570 +A3 تتكامل من X2 إلى B ل F of X DX و هكذا طب السؤال + +45 +00:04:12,570 --> 00:04:18,440 +هولو انا بقادرة لانسي تاخد ال absolute value و روح + +46 +00:04:18,440 --> 00:04:24,320 +جماعة التكاملات يمكن يطلع التكامل او المساحة تكون + +47 +00:04:24,320 --> 00:04:30,170 +صفر فهل هذا الكلام معقول؟ يعنيلو جاءت تخيلت ان + +48 +00:04:30,170 --> 00:04:35,090 +دوان دي رسمها وكانت المساحة a1 و a3 مجموعهم عدديًا + +49 +00:04:35,090 --> 00:04:41,830 +يسوى مجموع a2 يبقى a2 سلبه لفوق موجة بيجيبوا يطلع + +50 +00:04:41,830 --> 00:04:46,230 +النتج قد صفر هل يقل مساحة بالمنحنى وما هو ركزي + +51 +00:04:46,230 --> 00:04:50,470 +يسوى صفر؟ طبعًا لأ لو كانت المساحة اللي اتاحت أكبر + +52 +00:04:50,470 --> 00:04:55,490 +من مساحتي الاتنين عدديًاهيطلع تكامل سالبة ليعقل + +53 +00:04:55,490 --> 00:05:00,910 +مساحة تاخد قيمة سالبة؟ طبعا لا وهكذا إذا نضطر لاخذ + +54 +00:05:00,910 --> 00:05:05,050 +ال absolute value حتى نطلع جداش المساحة الحقيقية + +55 +00:05:05,050 --> 00:05:11,390 +اللي موجودة ما بين المنحنة ومحور Xنعطي الان مثال + +56 +00:05:11,390 --> 00:05:16,430 +عددي على كيفية حساب ال total area جاليهات لل total + +57 +00:05:16,430 --> 00:05:21,030 +area المساحة الموجودة ما بين محور X والرسم البياني + +58 +00:05:21,030 --> 00:05:25,270 +لدالي F of X يساوي X تكييم زي تلاتة X تربيه زي + +59 +00:05:25,270 --> 00:05:29,570 +اتنين X على الفترة من ولا و لامن سالب اتنين لغاية + +60 +00:05:29,570 --> 00:05:33,710 +اتنين لغاية اتنين يبقى انا بده اروح اطبق الخطوات + +61 +00:05:33,710 --> 00:05:38,570 +الثلاث اللي موجودة عندى ال sub divide the interval + +62 +00:05:38,570 --> 00:05:44,070 +of the zeros of F يبقى اول خطوة بده اروح اجيب أصفر + +63 +00:05:44,070 --> 00:05:47,950 +الدالة اللي عندها دي بده اجيب أصفر الدالة يبقى بده + +64 +00:05:47,950 --> 00:05:52,370 +اعمل الخطوة الأولى يبقى بده اخد ال F of Xاللي + +65 +00:05:52,370 --> 00:05:58,870 +عندنا اللي هي جداش X تكيب وهنا ناقص ثلاثة X تربيع + +66 +00:05:58,870 --> 00:06:04,890 +وهنا زائد اتنين X وروح أسويها بجداش بالزيرو بدي + +67 +00:06:04,890 --> 00:06:09,890 +أجيب أصفر الدليل بدي أروح أحلل هذه المعادلة يبقى + +68 +00:06:09,890 --> 00:06:15,730 +ممكن أخد X عامل مشترك بظل X تربيع ناقص ثلاثة X + +69 +00:06:15,730 --> 00:06:22,160 +زائد جداش اتنين يساوي Zeroهذا الكلام عبارة عن X في + +70 +00:06:22,160 --> 00:06:29,880 +غسين بده يساوي Zero يبقى هنا X هنا X هنا واحد هنا + +71 +00:06:29,880 --> 00:06:36,500 +اتنين هنا ناقص هنا ناقص يبقى ناقص X و ناقص اتنين X + +72 +00:06:36,500 --> 00:06:42,300 +بناقص ثلاثة X يبقى تحليلنا سليم يبقى أصفار الدالة + +73 +00:06:42,300 --> 00:06:48,100 +هي X يساوي Zero وال X يساوي واحد وال X يساوي كداش + +74 +00:07:00,980 --> 00:07:06,800 +بتجزء الفترة اللى عندك حسب أسفار الدلة يبقى انا + +75 +00:07:06,800 --> 00:07:15,920 +عندى من X2 لغاية Zero ومن Zero لغاية One لغاية + +76 +00:07:15,920 --> 00:07:21,000 +اتنين يبقى اي أسفار الدلةيبقى بناء عليه الـ total + +77 +00:07:21,000 --> 00:07:26,440 +area اللي أوي بدى التكامل أوي بدى أروحة كامل على + +78 +00:07:26,440 --> 00:07:32,300 +الفترة الأولى يبقى بدى A كامل من سالب 2 لغاية 0 لل + +79 +00:07:32,300 --> 00:07:39,760 +F of X DX لل X تكييب ناقص 3X تربيع زائد 2X كله + +80 +00:07:39,760 --> 00:07:47,540 +بالنسبة لميم الى DXيساوي بدا كامل يبقى x أص أربعة + +81 +00:07:47,540 --> 00:07:54,140 +على أربعة ناقص x تكييب على تلاتة بتروح مع التلاتة + +82 +00:07:54,140 --> 00:07:59,880 +زائد x تربيع على الإتنين بتروح مع الإتنين يبقى هذا + +83 +00:07:59,880 --> 00:08:05,600 +الكل من ناقص إتنين لغاية Zeroيبقى لو جيت اعوض + +84 +00:08:05,600 --> 00:08:09,740 +بالقيمة اللي فوق Zero ناقص Zero زائد Zero يبقى + +85 +00:08:09,740 --> 00:08:14,320 +Zero ناقص Zero زائد Zero هيعوض بالقيمة اللي فوق + +86 +00:08:14,320 --> 00:08:21,360 +ناقص افتح جزء بدا اشيل كل X و احط مكانها ناقص + +87 +00:08:21,360 --> 00:08:26,380 +اتنين يبقى ناقص اتنين اقص اربعة بقى داشر ستة عشرة + +88 +00:08:26,380 --> 00:08:34,380 +على أربعة اللي بعد هي ناقص اتنين تكيباللي هو ناقص + +89 +00:08:34,380 --> 00:08:40,640 +تمانية مع ناقص بصير زائد تمانية اللي بعدها ناقص + +90 +00:08:40,640 --> 00:08:48,510 +اتنين تربية زائد جداش زائد اربعة ويساوييبقى، لاحظة + +91 +00:08:48,510 --> 00:08:53,070 +القيمة اللي فوت ناقص القيمة ده، شلت كل X وحطيت + +92 +00:08:53,070 --> 00:08:58,430 +مكانها ناقص اتنين، يبقى هذه الستاشر على اربعة فضل + +93 +00:08:58,430 --> 00:09:03,210 +كده ايش؟ اربعة واربعة، تمانية و تمانية، ستاشر يبقى + +94 +00:09:03,210 --> 00:09:10,240 +النتيجة سالب ستاشربعد هيك هذه كلها تعتبر لمن؟ A1 + +95 +00:09:10,240 --> 00:09:16,580 +بدي أروح أجيب له A2 يبقى A2 تكامل من 0 إلى 1 + +96 +00:09:16,580 --> 00:09:23,180 +integration من 0 إلى 1 لل X تكيب ناقص 3X تربيع + +97 +00:09:23,180 --> 00:09:29,980 +زائد 2X كله في DX نتيجة التكامل هي X أقص 4 على 4 + +98 +00:09:30,390 --> 00:09:35,910 +نقص X تكيب زاد X تربية نفس النتيجة اللي فوق بس من + +99 +00:09:35,910 --> 00:09:40,990 +واحد لواحد من Zero لغاية واحد يبقى بتعود بالقيمة + +100 +00:09:40,990 --> 00:09:47,450 +اللي فوق يبقى ربع ناقص واحد زاد واحد ناقص Zero + +101 +00:09:47,450 --> 00:09:53,330 +Zero Zero كله ب Zero يبقى النتيجة كده؟ ربع فقط + +102 +00:09:53,330 --> 00:10:00,040 +لغيربتداجي للـ A تلاتة يبقى هو تكمل على الفترة + +103 +00:10:00,040 --> 00:10:05,220 +التالتة يبقى من واحد لغاية اتنين يبقى من واحد + +104 +00:10:05,220 --> 00:10:10,900 +لغاية اتنين لل X تكييب ناقص تلاتة X تربية زائد + +105 +00:10:10,900 --> 00:10:18,260 +اتنين X DX الشكل لأن هذا يبقى X أس أربعة على أربعة + +106 +00:10:18,260 --> 00:10:24,160 +ناقص X تكيب زائد X تربية كله من عند الواحد لغاية + +107 +00:10:24,160 --> 00:10:29,250 +اتنينلغاية اتنين يبقى هذا الكلام بده يساوي بده + +108 +00:10:29,250 --> 00:10:33,090 +يعود بالقيمة اللي فوق ناقص اللي تانية نقص ربع ليه؟ + +109 +00:10:33,090 --> 00:10:42,890 +ستاشر على أربع ناقص تمانية زائد أربع ناقص افتح جزء + +110 +00:10:42,890 --> 00:10:49,630 +بده يشيل كل اكس ويحط مكانها واحد يبقى هذا ربع وهنا + +111 +00:10:49,630 --> 00:10:56,610 +ناقص واحد زائد واحديبقى النتيجة هذه تساوي 16 على 4 + +112 +00:10:56,610 --> 00:11:06,130 +فيها 4 وهنا ناقص 8 وزائد 4 وهنا ناقص ربع زائد 1 + +113 +00:11:06,130 --> 00:11:13,980 +ناقص 1 أظن هلال بصفرتمام؟ ودولب صفر بيظل الجواب + +114 +00:11:13,980 --> 00:11:20,180 +قداش سالب رفع طب اطلعلي هنا طلعت قيمة واحدة موجبة + +115 +00:11:20,180 --> 00:11:24,640 +وتنتن بالسالم لو مااخدتش absolute value بيطلع + +116 +00:11:24,640 --> 00:11:29,760 +عليها كلها قيمة سالمة لكن احنا بنروح بنقول هنا + +117 +00:11:29,760 --> 00:11:37,670 +total areaبتعطيها الرمز A يساوي absolute value للـ + +118 +00:11:37,670 --> 00:11:44,010 +A1 absolute value للـ A2 absolute value للـ A3 + +119 +00:11:44,010 --> 00:11:50,650 +ويساوي absolute value لـ 16 absolute value لربع + +120 +00:11:50,650 --> 00:11:54,410 +absolute value لـ 4 + +121 +00:12:02,750 --> 00:12:13,270 +يساوي طبعا ستاشر زائد ربع زائد ربع يعني ستاشر زائد + +122 +00:12:13,270 --> 00:12:19,090 +نص ستاشر و نص يعني تلاتة و تلاتين على اتنين يبقى + +123 +00:12:19,090 --> 00:12:23,770 +النتيجة تلاتة و تلاتين على اتنين اللي هي المساحة + +124 +00:12:23,770 --> 00:12:27,840 +الكليةلكن لو مااخدناش absolute value واضح ان + +125 +00:12:27,840 --> 00:12:33,800 +المساعة تطلع جداش بيما سالم، هل ضروري نرسم؟ ليس + +126 +00:12:33,800 --> 00:12:37,300 +بالضرورة، انا سواء عرفت شكله من حد و الله عارف + +127 +00:12:37,300 --> 00:12:42,450 +بهمنيش، لكن بهمني أصفار الدالة أحددهم جداشوتقيد + +128 +00:12:42,450 --> 00:12:47,010 +بالفترة اللي بكون معطيها لي تمام؟ وبناء عليه بقدر + +129 +00:12:47,010 --> 00:12:52,250 +أعرف أكم جزء عندي أو أكم تكامل وبالتالي بروح باخد + +130 +00:12:52,250 --> 00:12:57,750 +ال absolute value لنتيجة هذه التكاملات بيعطيني ال + +131 +00:12:57,750 --> 00:13:03,550 +total area للمساحة المحصورة بين المنحنة ومحورك + +132 +00:13:03,550 --> 00:13:10,110 +سواء كانت هذه المساحات موجبة ام سالقةعليك انتهينا + +133 +00:13:10,110 --> 00:13:15,130 +من هذا ال section و إليكم أرقام المسائل ل + +134 +00:13:15,130 --> 00:13:21,410 +exercises خمسة أربعة يبقى خمسة أربعة من واحد لسبعة + +135 +00:13:21,410 --> 00:13:28,150 +وأربعين الأد يبقى exercises خمسة أربعة من واحد + +136 +00:13:28,150 --> 00:13:36,550 +لسبعة وأربعين الأدو من واحد و ستين لاربع و ستين و + +137 +00:13:36,550 --> 00:13:44,610 +من واحد و ستين لاربع و ستين كذلك الآن بنيجي ل + +138 +00:13:44,610 --> 00:13:51,810 +section خمسة خمسة section + +139 +00:13:51,810 --> 00:13:57,010 +خمسة خمسة اللي هو ال indefinite integrals + +140 +00:14:03,480 --> 00:14:09,300 +اندفينيات انتجرالز and the substitution method and + +141 +00:14:09,300 --> 00:14:17,720 +the substitution method + +142 +00:14:17,720 --> 00:14:24,440 +if + +143 +00:14:24,440 --> 00:14:28,220 +ال if is continuous + +144 +00:14:30,290 --> 00:14:39,210 +إذا كان الفرق مستمر فإن انترفل + +145 +00:14:39,210 --> 00:14:53,930 +I و N هو عدد + +146 +00:14:53,930 --> 00:14:54,890 +حقيقي + +147 +00:14:59,860 --> 00:15:08,380 +للـ F of X كله to the power N فالـ F prime of X DX + +148 +00:15:08,380 --> 00:15:19,660 +بده ساوي تكامل للـ UN DU و اللي هو بده ساوي U أس N + +149 +00:15:19,660 --> 00:15:28,850 +زائد واحد على N زائد واحد زائد constant CIn + +150 +00:15:28,850 --> 00:15:33,350 +general على + +151 +00:15:33,350 --> 00:15:44,350 +وجه العموم تكامل لل F of G of X في G prime of X DX + +152 +00:15:44,350 --> 00:15:49,390 +دو سوى تكامل F of U DU + +153 +00:16:16,500 --> 00:16:24,060 +خلّي براكة احنا رافعين عنوان انا وبنشوف شو هذا + +154 +00:16:24,060 --> 00:16:28,300 +العنوان وبنقل عليك كيف بنشتغلبقول in definite + +155 +00:16:28,300 --> 00:16:32,740 +integrals التكاملات غير المحدودة and the + +156 +00:16:32,740 --> 00:16:38,760 +substitution method وطريقة التعويض يعني كيف نستخدم + +157 +00:16:38,760 --> 00:16:45,540 +طريقة التعويض في التكاملات غير المحدودة بقول لو + +158 +00:16:45,540 --> 00:16:51,140 +كانت الدالة دالة متصلة على فترة مامتصل يعني قابل + +159 +00:16:51,140 --> 00:16:56,140 +للتكامل إذا يمكن تكاملها على هذه الفترة وكان ال N + +160 +00:16:56,140 --> 00:17:01,860 +عبارة عن عدد حقيقي سواء كسر موجب أو سلب مع أنه + +161 +00:17:01,860 --> 00:17:07,040 +مشكلة يبقاش بيقول تكامل لل F of X مرفوعة to the + +162 +00:17:07,040 --> 00:17:13,760 +power N مضروبة في مشتقة مداخل القوس DXبقدر أقول + +163 +00:17:13,760 --> 00:17:19,140 +هذه تكامل you to the power in the you وتضيف للأس + +164 +00:17:19,140 --> 00:17:24,540 +واحد و أقسم على الأس الجديد السؤال هو كيف هذه صارت + +165 +00:17:24,540 --> 00:17:32,520 +بهذا الشكل هذا السؤال قلب الكلب لو جيت أن المثل + +166 +00:17:32,520 --> 00:17:37,550 +عندي بهذا الشكلهذه الشكلة لو طلعتها عمليا بلاقيها + +167 +00:17:37,550 --> 00:17:41,690 +كالكعة كبيرة هيك أنا بدي أبسطها و أخليها بشكل + +168 +00:17:41,690 --> 00:17:48,230 +معقول وبشكل لطيف مثل هذا الشكل، السؤال كيف؟ باجي + +169 +00:17:48,230 --> 00:17:52,650 +بطلع في المثل هو مين المصعب المثل ال F prime ولا + +170 +00:17:52,650 --> 00:17:54,670 +ال F of X to the power N؟ + +171 +00:18:00,710 --> 00:18:06,710 +يبقى انا لو + +172 +00:18:06,710 --> 00:18:13,750 +حطيت ال U تساوي F of X كتعوضة ليس بالضرورة U ممكن + +173 +00:18:13,750 --> 00:18:24,620 +T ممكن V ممكنيجب ان اوضح الرمز الانجليزي يبقى + +174 +00:18:24,620 --> 00:18:31,880 +دي يو على دي اكس بده يساوي f prime of x او دي يو + +175 +00:18:31,880 --> 00:18:38,120 +بده يساوي f prime of x في دي اكس تمام؟ اذا بقدر + +176 +00:18:38,120 --> 00:18:41,360 +اشيل ال f prime of x دي اكس + +177 +00:18:47,920 --> 00:18:54,480 +يبقى بصير تكامل U to the power N DU يبقى اللي كان + +178 +00:18:54,480 --> 00:18:59,340 +شكلها غريب و صعب صارت سهل جدا إزاي تكامل X to the + +179 +00:18:59,340 --> 00:19:05,000 +power Nبشرط لأنه مستويش سالب واحد هو دي البلد يبقى + +180 +00:19:05,000 --> 00:19:08,700 +أشمع عليه اللي أضيف له الأس واحد و أقسم على الأس + +181 +00:19:08,700 --> 00:19:13,960 +الجديد وبعد ما خلص بشيل ال U و بحط بدلها مين F of + +182 +00:19:13,960 --> 00:19:17,950 +X بصير المثل أن انت جيتها بدلة ال Xزي ما بدأت + +183 +00:19:17,950 --> 00:19:20,930 +التكوين ودلت ال X فالجواب دلت ال X وبالتالي مكون + +184 +00:19:20,930 --> 00:19:25,690 +اه خلصت المشكلة هذه يبقى عشان أستخدم التعويض أول + +185 +00:19:25,690 --> 00:19:30,770 +ما بدور على الشغل اللي مخلي شكل المسألة صعب بحيث + +186 +00:19:30,770 --> 00:19:35,530 +هذا لو اشتقت ياطيني مين الدلة اللي فوق أو كنص في + +187 +00:19:35,530 --> 00:19:39,150 +الدلة اللي فوق مابتفرجش عندنا زي ما سنرى بعد قليل + +188 +00:19:39,150 --> 00:19:45,370 +يبقى ها بدي مشتقة اللي جوا تبقى مين هي اللي براأو + +189 +00:19:45,370 --> 00:19:49,310 +قريبة من قريبها على طول الخط من الدرجة الأولى، + +190 +00:19:49,310 --> 00:19:54,140 +أقارب من الدرجة الأولىهذا بالمثل بالشكل هذا يبقى + +191 +00:19:54,140 --> 00:19:58,180 +هي النتيجة قد لا تكون المثل بهذا الشكل قد تكون + +192 +00:19:58,180 --> 00:20:03,600 +composition function كيف؟ تكامل لل F of G of X في + +193 +00:20:03,600 --> 00:20:08,480 +G prime of X DX ممكن ما تكونش بالشكل اللي فوق ممكن + +194 +00:20:08,480 --> 00:20:12,520 +تكون بالشكل اللي عندنا هذا يبقى برضه لمصعب المثل + +195 +00:20:12,520 --> 00:20:16,420 +اللي هو الجزء الأول يبقى بروح لل G of X اللي هي + +196 +00:20:16,420 --> 00:20:23,850 +مخلية المثل غير طبيعيةو بروح بقوله حط ال U تساوي G + +197 +00:20:23,850 --> 00:20:31,190 +of X أو T تساوي G أو W أو أي رمز يعجبك طبعا يبقى + +198 +00:20:31,190 --> 00:20:39,100 +باشي بقوله يبقى DU بتساوي G prime of X في DXإذاً + +199 +00:20:39,100 --> 00:20:43,560 +بادر جي برايم اف اكس دي اكس كلها بحط بدل امين دي + +200 +00:20:43,560 --> 00:20:48,100 +يو والجي بحط بدي بيبقى صارت يتعمل F of U دي يو + +201 +00:20:48,100 --> 00:20:52,120 +يبقى بصير شكل المثل بدل ما يكون كلكا او غير شكل + +202 +00:20:52,120 --> 00:20:58,650 +اكس بصير شكل لطيف يمكن تكاملهالان الكلام اللى + +203 +00:20:58,650 --> 00:21:03,490 +بنقوله نظري بدنا نعطي عليه مجموعة لا بأس بيها من + +204 +00:21:03,490 --> 00:21:10,990 +الأمثلة يبقى باجي بقوله examples مجموعة من + +205 +00:21:10,990 --> 00:21:16,650 +التكاملة احسبلي evaluate + +206 +00:21:16,650 --> 00:21:23,410 +the following integrals + +207 +00:21:25,030 --> 00:21:31,670 +أحسب لي كل من التكاملات التالية تكامل الأول تكامل + +208 +00:21:31,670 --> 00:21:39,750 +اتنين X زائد تلاتة كله أس تمانية بالنسبة الى DX + +209 +00:21:39,750 --> 00:21:44,610 +قلبي + +210 +00:21:44,610 --> 00:21:49,980 +الكوينةهذه لو كانت X أس تمانية كما نقول نضيف لأس + +211 +00:21:49,980 --> 00:21:54,040 +واحد بنقسم على الأس اللي يتذكر لبنجوسين هذه هي + +212 +00:21:54,040 --> 00:21:58,260 +اللي كلكعت الدنيا يبقى هذه على مين على الحالة + +213 +00:21:58,260 --> 00:22:03,240 +الأولى والله أعلم مش عارفين احنا يبقى ال F of X هي + +214 +00:22:03,240 --> 00:22:08,980 +سبب الكلكعة طيب يعني هذه زي هذه اه زيها بس فارق + +215 +00:22:08,980 --> 00:22:14,140 +بسيط كيف؟ لو شيلت ال F of X وحطيت هذه بصير مشتقتها + +216 +00:22:14,140 --> 00:22:21,270 +جديش2DX يبقى ال F prime of X DX هي main DX إذا + +217 +00:22:21,270 --> 00:22:27,650 +باجي بشيل كل اللي بين قسينها دي و بحطه بأي متغير U + +218 +00:22:27,650 --> 00:22:32,510 +Y W الرمز اللي عاجبك قلتلك ليست أستا مقيد بالـU + +219 +00:22:32,510 --> 00:22:38,240 +وأنا لأ فضل إنك تحط Uحط اي رمز اخر ليش لان ال U + +220 +00:22:38,240 --> 00:22:41,480 +جينا في ال integration by parts في calculus بيه + +221 +00:22:41,480 --> 00:22:46,180 +انه يمكن يلخبك فتعود خلي جلب جيحط اي رمز ييجي في + +222 +00:22:46,180 --> 00:22:50,900 +بالك مش قرآن نزل من السماء لازم احط التعويض U تمام + +223 +00:22:50,900 --> 00:22:56,720 +يبقى بروح بده احط مثلا T احط ال T تساوي اتنين X + +224 +00:22:56,720 --> 00:23:03,750 +زائد تلاتةلو جيت أفاضلها يبقى بدأ أقوله دي تي + +225 +00:23:03,750 --> 00:23:09,290 +يساوي اتنين مالكش تاعة و تفاضل ال X يبقى داشر DX و + +226 +00:23:09,290 --> 00:23:14,070 +تفاضل التلاتة Zero مش واحد يقولي من وين هذه أجت + +227 +00:23:14,070 --> 00:23:17,870 +بدأ أخد دي تي على DX دي تي على DX اللي هو باتنين + +228 +00:23:17,870 --> 00:23:22,850 +أضرب كله في DX يبقى دي تي يساوي اتنينأنا ماعنديش + +229 +00:23:22,850 --> 00:23:28,250 +اتنين DX عندي DX لحالها يبقى من هذا الكلام لو جسمت + +230 +00:23:28,250 --> 00:23:34,930 +على اتنين بصير نص DT هو بدي يساوي جداش DX إذا هذا + +231 +00:23:34,930 --> 00:23:40,830 +التكامل بده يساوي هاي تكامل هذا حاطيته كله بجداش + +232 +00:23:40,830 --> 00:23:46,630 +الابنجسين T و هي أس تمانية زي ما هي و ال DX طلعت + +233 +00:23:46,630 --> 00:23:53,080 +عندي بجداش نص DTالان طبق اللي قواها دي التكامل + +234 +00:23:53,080 --> 00:24:01,600 +بقول يا نص خليك برا وهي تكامل T أس تمانية DT تمام؟ + +235 +00:24:01,600 --> 00:24:06,180 +يبقى هاي النص برا هذا أبدا جلب واضيف على الأس + +236 +00:24:06,180 --> 00:24:11,860 +واحدة بتقسم على الأس الجديد يبقى هذا بصير T أس + +237 +00:24:11,860 --> 00:24:20,680 +تسعة على تسعة زائد constant Cأو 1 على 18 و ال T + +238 +00:24:20,680 --> 00:24:24,580 +بقدر أشيله و أحط قيمته التعويضة اللي أنا حطيتها + +239 +00:24:24,580 --> 00:24:35,700 +حطيت ال T ب2X زائد 3 يبقى 2X زائد 3 كله أس 9 زائد + +240 +00:24:35,700 --> 00:24:41,100 +constant C طب تعالى اطلع في النتيجة أنا وياكيك + +241 +00:24:41,100 --> 00:24:48,460 +مباشرةأشوف هذا المثال وهي النتيجة اللى عندنا بقوله + +242 +00:24:48,460 --> 00:24:54,280 +كويس يبقى بكل بساطة انا شو اللى عملته اضفت للأس + +243 +00:24:54,280 --> 00:24:59,740 +واحد و جسمت على الأس اليسار عندي جداش تسع مظبوط في + +244 +00:24:59,740 --> 00:25:05,580 +المعامل في واحد على المعامل تبع من ال X إذا كانت + +245 +00:25:05,580 --> 00:25:09,820 +المعادلة من الدرجة الأولى الدرجة التانية بصير كلام + +246 +00:25:09,820 --> 00:25:14,620 +غلطيبقى إذا المعادلة بين جثين من الدرجة الأولى ما + +247 +00:25:14,620 --> 00:25:18,400 +عليك إلا تضيف للأسر واحد و تقسم على الأسر جديد + +248 +00:25:18,400 --> 00:25:23,740 +تضرب في المعامل تبع X فقط لغير بيكون هو النتيجة و + +249 +00:25:23,740 --> 00:25:27,320 +تقول إزاي تكون أصلا خايف تقلط يبقى يشتغل زي ما + +250 +00:25:27,320 --> 00:25:33,060 +اشتغلنا طبعا طيب هذا السؤال يعتبر من أبسط أنواع + +251 +00:25:33,060 --> 00:25:40,260 +الأمثلة المثال رقم اتنينيبقى بدنا تكامل لل X + +252 +00:25:40,260 --> 00:25:48,920 +تربيعي الجدري التربيعي لل 2X تكعيب زائد 3 كله في + +253 +00:25:48,920 --> 00:25:49,260 +DX + +254 +00:25:52,460 --> 00:25:57,760 +الحين لو جيت للدلة لبرا الجذر والدلة لتحت الجذر، + +255 +00:25:57,760 --> 00:26:01,760 +من مصعب المثل، الدلة تحت الجذر ولا اللي برا؟ تحت + +256 +00:26:01,760 --> 00:26:06,520 +الجذر، اتنين، مشتقت الدلة اللي تحت الجذر بقداش؟ + +257 +00:26:06,520 --> 00:26:12,960 +ستة اكس تربية في DX، يعني الدلة اللي برا هذه هي + +258 +00:26:12,960 --> 00:26:19,740 +مشتقتيعني اللي تحت الجدرد كان نجوس أس يبقى كأنه + +259 +00:26:19,740 --> 00:26:24,280 +نجوس مرفوع الأس واللي برا هو مشتقته من الدرجة + +260 +00:26:24,280 --> 00:26:28,300 +الأولى يبقى الفارجية تبسكه نصرا، مظبوط؟ إذن هذا + +261 +00:26:28,300 --> 00:26:31,820 +على النقطة الأولى مباشرة، طبعا إيش أسويه؟ بقوله + +262 +00:26:31,820 --> 00:26:38,010 +بسيطة جدا، بقوله putأحنا حاطين هنا جداش T بده أحط + +263 +00:26:38,010 --> 00:26:47,650 +هنا W تساوي اتنين X تكيب زائد تلاتة بدنا DW بستة X + +264 +00:26:47,650 --> 00:26:52,470 +تربية في DX و تفاضل التلاتة بجدار ب Zero ماعنديش + +265 +00:26:52,470 --> 00:26:59,020 +ستة بلاش X على ستة يبقى هذا معناه انه سُدسدي + +266 +00:26:59,020 --> 00:27:05,040 +دابليو بده يساوي ال X تربية دي X إذا بقدر أشيل ال + +267 +00:27:05,040 --> 00:27:11,160 +X تربية هذه كلها مع ال DX و أكتب بدلها قداش سُدس + +268 +00:27:11,160 --> 00:27:18,100 +دي دابليو يبقى صارة المثلة تكامل جذر ال W وهذا + +269 +00:27:18,100 --> 00:27:24,870 +سُدس وهذا دي دابليوو الـ SUDS هذا مقدار ثابت يبقى + +270 +00:27:24,870 --> 00:27:32,870 +مقدار ثابت خلّيك برا وهي تكامل وهنا W أُص نُص DW + +271 +00:27:32,870 --> 00:27:39,030 +يبقى المثل اللي كانت مكلقة هيك وشكلها غريب شوية + +272 +00:27:39,030 --> 00:27:44,390 +صارت very easy بسيطة جدا ولا حاجة يبقى دي سهل اضيف + +273 +00:27:44,390 --> 00:27:50,530 +للأُص واحد و اقسم على الأُص الجديد يبقى هذا SUDS + +274 +00:27:50,910 --> 00:27:57,570 +وهذا W أس ثلاثة على اتنين على ثلاثة على اتنين زائد + +275 +00:27:57,570 --> 00:28:03,070 +constant C بنضيف للأس واحد بنقسم على الأس الجديد + +276 +00:28:03,070 --> 00:28:10,010 +يبقى هذي بيصير اتنين على ستة مضروبة في تلاتة و ال + +277 +00:28:10,010 --> 00:28:16,330 +W مين هي اتنين X تكييب زائد تلاتة اتنين X تكييب + +278 +00:28:16,590 --> 00:28:22,630 +زائد تلاتة بالشكل اللي عندنا هذا أس قداش أس تلاتة + +279 +00:28:22,630 --> 00:28:27,950 +على اتنين تلاتة على اتنين زائد constant C نختصر + +280 +00:28:27,950 --> 00:28:33,530 +اتنين مع اتنين بيبقى التسعة في اتنين X تكعيب زائد + +281 +00:28:33,530 --> 00:28:39,850 +تلاتة كل أس تلاتة على اتنين زائد constant C يعني + +282 +00:28:39,850 --> 00:28:43,730 +بعد ما تخلص بترجع المسألة بدلالة ال variable + +283 +00:28:43,730 --> 00:28:45,550 +الأصلي + +284 +00:28:59,240 --> 00:29:07,440 +سؤال التالت بيقول اللي بده تكامل X الجذر التربيعي + +285 +00:29:07,440 --> 00:29:14,700 +لأربعة ناقص X DX يقول مصعب المثل المقدار اللي برا + +286 +00:29:14,700 --> 00:29:20,080 +ولا تحت الجذريبقى بدي أشيل اللي تحت الجدر و أحطه + +287 +00:29:20,080 --> 00:29:28,920 +بأي متغير حط لهنا put مثلا y يسوى أربعة ناقص x + +288 +00:29:28,920 --> 00:29:35,500 +يبقى dy تفاضل أربعة from zero بناقص dx أنا ماعنديش + +289 +00:29:35,500 --> 00:29:43,020 +ناقص dx يبقى سالف dy هي اللي بدي أتساوي من dx إذا + +290 +00:29:43,020 --> 00:29:49,250 +بصير المسألة تكاملبالـ dx هدا أعوض بها من هنا لو + +291 +00:29:49,250 --> 00:29:54,590 +جبت ال x هنا بصير أربعة ناقص إذا بقدر أشيل هذه و + +292 +00:29:54,590 --> 00:30:01,990 +كنت ببنالها أربعة ناقص y و هذه حاطيتها ب y و ال dx + +293 +00:30:01,990 --> 00:30:05,030 +هي بسالب dy + +294 +00:30:07,450 --> 00:30:13,550 +يعني كأن المسألة صارت تكامل السلب بده يدخل على + +295 +00:30:13,550 --> 00:30:21,570 +القصب يصير كده؟ Y ناقص أربعة وجذر ال Y تاني Y أص + +296 +00:30:21,570 --> 00:30:30,830 +نص في DYتمام؟ إذا بدي أفك الجثة هذا بصير تكامل ل Y + +297 +00:30:30,830 --> 00:30:38,110 +أس ثلاثة على اتنين ناقص أربعة Y أس نص كله في دي Y + +298 +00:30:38,110 --> 00:30:44,810 +يبقى ماضلش عليه اللي هي كامل يبقى هذه تكاملها بY + +299 +00:30:44,810 --> 00:30:51,640 +أس جديدخمسة على اتنين على خمسة على اتنين يعني اللي + +300 +00:30:51,640 --> 00:31:01,600 +هو جدات بخمسين ناقص اربع في Y أس تلاتة على اتنين + +301 +00:31:01,600 --> 00:31:11,060 +ضرب تلتين زاد كونستانسينعيد ترتيبها لما نعيد + +302 +00:31:11,060 --> 00:31:16,940 +ترتيبها يبقى هذه اتنين على خمسة تمام يبقى اتنين + +303 +00:31:16,940 --> 00:31:24,780 +على خمسة وهذه Y بداشي لو احط مقتل يجداش اربعة ناقص + +304 +00:31:24,780 --> 00:31:32,680 +X أس خمسة على اتنين ناقص تمانية على تلاتة تمانية + +305 +00:31:32,680 --> 00:31:40,020 +على تلاتةأربعة ناقص X أس تلاتة على اتنين زائد + +306 +00:31:40,020 --> 00:31:48,640 +constant C يعني لما تحط تعويضة بهذا الشكل بدك تغير + +307 +00:31:48,640 --> 00:31:53,360 +كل اللي جوا المتغير X و تحوله كله بدلالة المتغير + +308 +00:31:53,360 --> 00:31:58,140 +الجديد اللي هو مش تخلي إشي X و إشي Y من حد ما تحط + +309 +00:31:58,140 --> 00:32:02,920 +التعويض بتغير كل اللي في الداخل بدلالة مين المتغير + +310 +00:32:02,920 --> 00:32:11,650 +الجديدنعطي كمان مثال أربعة بيقول يبقى التكامل واحد + +311 +00:32:11,650 --> 00:32:19,870 +على جذر ال X في واحد زائد جذر ال X لكل تربية DX + +312 +00:32:40,060 --> 00:32:43,780 +طيب ما بدنا نيجي على المثلة تبعتنا هذه و نروح + +313 +00:32:43,780 --> 00:32:48,020 +نتطلع فيها، مين المصعب المثلة؟ هل جدراليكس ولا + +314 +00:32:48,020 --> 00:32:52,600 +واحث زي الجدراليكس؟ واحث زي الجدراليكس و كل تربية + +315 +00:32:52,600 --> 00:32:55,840 +يبقى الواحث زي الجدراليكس هو المصعب المثل، نهيك + +316 +00:32:55,840 --> 00:33:01,380 +على أنه لو اشتقت الواحث زي الجدراليكسبطلع واحد على + +317 +00:33:01,380 --> 00:33:06,200 +اتنين جذر ال X كلام مظبوط ميا ميا بروحش باخد جذر + +318 +00:33:06,200 --> 00:33:10,900 +ال X باخد ال واحد زائد جذر ال X بروح بحطها بأي + +319 +00:33:10,900 --> 00:33:18,680 +متغير اخر لو رحت حطيت مثلا Z تساوي واحد زائد جذر + +320 +00:33:18,680 --> 00:33:23,140 +ال X لحظة انا بحطلك رموز مختلفة مش هقولك بتقيدش + +321 +00:33:23,140 --> 00:33:28,480 +بال U هذه اي رمز حطه من هال 27 حرف اللي عندكطيب + +322 +00:33:28,480 --> 00:33:35,160 +بدي أروح أشتقه يبقى هذا بدي يعطيلك ان DZ يسوى واحد + +323 +00:33:35,160 --> 00:33:41,930 +على اتنين جذر ال X في DXتفضل 1 بـ0 تفضل جذر ال X + +324 +00:33:41,930 --> 00:33:47,250 +ب2 او 1 ع 2 جذر ال X ماعنديش 1 ع 2 جذر ال X عندي 1 + +325 +00:33:47,250 --> 00:33:51,490 +ع جذر ال X بروح بدرب في اتنين الطرفين يفجر لو + +326 +00:33:51,490 --> 00:33:59,370 +ضربنا في اتنين بصير 2DZ بده يساوي 1 ع جذر ال X في + +327 +00:33:59,370 --> 00:34:06,590 +DXأذا بدي ارجع للتكامل تبعي واحد على جذر ال X DX + +328 +00:34:06,590 --> 00:34:14,330 +هذا كله بدي اكتب داله كده ايش؟ 2DZ يبقى هذا الكلام + +329 +00:34:14,330 --> 00:34:22,750 +بدي يصير تكامل هذا واحد على Z تربيع وهذا اللي بقي + +330 +00:34:22,750 --> 00:34:33,600 +كله 2DZ فقط لغيبعد ما كانت جذور ومشالكة مو غير شكل + +331 +00:34:33,600 --> 00:34:38,560 +صارت بسيطة بقول يا اتنين برا يبقى هذا اتنين برا + +332 +00:34:38,560 --> 00:34:43,080 +وهذا ال z والسالب اتنين دي z + +333 +00:34:49,290 --> 00:34:58,830 +زاد كنستان سي يبقى نقص اتنين في واحد على زد زاد + +334 +00:34:58,830 --> 00:35:07,860 +كنستان سي يعني نقص اتنين علىبواحد زائد جذر ال X + +335 +00:35:07,860 --> 00:35:15,160 +يبقى واحد زائد جذر ال X زائد كونه صنسي وانتهينا من + +336 +00:35:15,160 --> 00:35:24,660 +المسألة اللي عندنا طيب السؤال الخامس بيقول يتكامل + +337 +00:35:24,660 --> 00:35:30,800 +ل cosine تلاتة X زائد أربعة كله بالنسبة إلى مين + +338 +00:35:30,800 --> 00:35:32,100 +إلى DX + +339 +00:35:35,260 --> 00:35:40,980 +من اللي وضع هغريب في المثالة الزاوية يبقى الزاوية + +340 +00:35:40,980 --> 00:35:46,060 +كل الشيء لو حطها بالمتغير اللي بدها هي يبقى انا لو + +341 +00:35:46,060 --> 00:35:52,920 +حطيت ثيتا تساوي تلاتة اكس زائد اربعة يبقى دي ثيتا + +342 +00:35:52,920 --> 00:35:59,340 +يساوي كداشت تلاتة في دي اكس او تلت دي ثيتا هو + +343 +00:35:59,340 --> 00:36:07,330 +المين بدي اكساذا هذه المثلة بيصير تكامل ل cos θ و + +344 +00:36:07,330 --> 00:36:14,430 +ال dx له تلت dθ التلت برا مالوش دعوة وهي تكامل ل + +345 +00:36:14,430 --> 00:36:25,360 +cos θ dθ وهذا تلت sin θ بدون سالب أفنديتفاضل + +346 +00:36:25,360 --> 00:36:31,300 +الـsin بـcos تكامل cos بـsin دوري زائد constant C + +347 +00:36:31,300 --> 00:36:36,360 +يبقى هذا التلت برا وهذا الـsin بشيل الـθيتا و + +348 +00:36:36,360 --> 00:36:44,800 +بكتبها 3x زائد 4 زائد constant C طب ايش بتلاحظ على + +349 +00:36:44,800 --> 00:36:46,380 +نتيجة التكامل؟ + +350 +00:36:50,730 --> 00:36:56,010 +الزاوية من الدرجة الأولى يبقى واحد على معامل X لكن + +351 +00:36:56,010 --> 00:36:59,010 +لو كانت من الدرجة التانية أو التالتة بصير كلامي + +352 +00:36:59,010 --> 00:37:05,250 +غلط تمام فقط إذا كان من الدرجة الأولى انسى خلاص حط + +353 +00:37:05,250 --> 00:37:09,530 +الزاوية إيش ما تكون تكون وفاضلها وحولها طيب نيجي + +354 +00:37:09,530 --> 00:37:12,370 +للسؤال السادس بدنا تكامل + +355 +00:37:14,990 --> 00:37:22,390 +سؤال السادس بدي تكامل لتلاتة X أُص خمسة في الجذر + +356 +00:37:22,390 --> 00:37:30,310 +التربيع إلى X تكيّب زائد واحد بالـDX لمصعب + +357 +00:37:30,310 --> 00:37:35,070 +مثلا من الكمية اللي تحت الجذر، شيلها وحطها + +358 +00:37:35,070 --> 00:37:41,400 +بالمتغيرة اللي بدكيهاحط لي T تساوي X تكييب زائد + +359 +00:37:41,400 --> 00:37:50,950 +واحد إذا ال DT بدي تساوي تلاتة X ترابيع DXتلاتة + +360 +00:37:50,950 --> 00:37:58,870 +موجودة بس هي DX والخمسة يبقى هذي بروح بحللها تلاتة + +361 +00:37:58,870 --> 00:38:05,010 +X تربيع X تكييب يبقى هذي تلاتة X والخمسة في الجذر + +362 +00:38:05,010 --> 00:38:11,070 +التربيعي لمين؟ ل X تكييب زائد واحد في DX ويساوي + +363 +00:38:11,720 --> 00:38:17,660 +الان تلاتة X تربية مع الـDX هذه كلها بحفظ بدالها + +364 +00:38:17,660 --> 00:38:24,560 +DT يبقى ماعنديش مشكلة الـX تكيب T ناقص واحد إذا + +365 +00:38:24,560 --> 00:38:29,740 +بقدر أشيل هذه و أكتب بدالها T ناقص واحد يبقى تكامل + +366 +00:38:29,740 --> 00:38:37,180 +الـT ناقص واحد هي من؟ بالـX تكيب وهذه جذري الـT + +367 +00:38:37,180 --> 00:38:45,120 +وضلش عندها إلا الباقي اللي همين DTيبقى هذا DT يبقى + +368 +00:38:45,120 --> 00:38:51,600 +مثلتنا صارت بسيطة جدا يبقى هذه تكامل T أس ثلاثة + +369 +00:38:51,600 --> 00:38:59,470 +على اتنين ناقص T أس نص DTيبقى خلاص، بالضبط أضيف + +370 +00:38:59,470 --> 00:39:04,750 +للأس واحد و أقسم على الأس الجديد يبقى هذه اتنين + +371 +00:39:04,750 --> 00:39:12,670 +على خمسة T أس خمسة على اتنين ناقص تلتين T أس تلاتة + +372 +00:39:12,670 --> 00:39:19,180 +على اتنين زائد constant Cبننشيل ال T ونحط بلاله X + +373 +00:39:19,180 --> 00:39:26,540 +تكيب زائد واحد يبقى هذه يسوى خمسين X تكيب زائد + +374 +00:39:26,540 --> 00:39:33,940 +واحد قص خمسة على اتنين ناقص تلتين X تكيب زائد واحد + +375 +00:39:33,940 --> 00:39:42,210 +قص تلاتة على اتنين زائد constant Cيعني أنت بدك + +376 +00:39:42,210 --> 00:39:47,430 +تتحيل على المثلة وبحيث تحورها بالطريقة اللي بدك + +377 +00:39:47,430 --> 00:39:53,850 +إياها بحيث تقدر تبسط المثلة ومن ثم تقوم بعملية + +378 +00:39:53,850 --> 00:40:01,750 +تكامل هذه المثلة طيب هذا كان المثال رقم ستة بدنا + +379 +00:40:01,750 --> 00:40:10,090 +نروح لمثال رقم سبعة يبقى مثال رقم سبعةبيقول لي + +380 +00:40:10,090 --> 00:40:18,490 +تكامل أحد أسئلة الكتاب واحد على X تربيع صين واحد + +381 +00:40:18,490 --> 00:40:24,550 +على X كوصين واحد على X في من؟ في DX + +382 +00:40:32,990 --> 00:40:37,890 +أنا أريد أسأل سؤال، مين اللي وضع مش طبيعي؟ واحد + +383 +00:40:37,890 --> 00:40:42,790 +على اكس الجزاوي، مش واحد على اكس تربية، اللي وضع + +384 +00:40:42,790 --> 00:40:45,290 +مش طبيعي واحد على اكس جزاوي، هم يقولوا ده من + +385 +00:40:45,290 --> 00:40:49,170 +الـsin X أو الـprofine X، إذا بقدر أشيل واحد على + +386 +00:40:49,170 --> 00:40:54,750 +اكس و أحطها بأي متغير جديدلو حطيت على سبيل المثال + +387 +00:40:54,750 --> 00:41:02,170 +θ بواحد على x يبقى هدا بده يعطيك d θ بسالب واحد + +388 +00:41:02,170 --> 00:41:10,320 +على x تربيه في dx أو سالب d θهو عبارة عالميا 1 على + +389 +00:41:10,320 --> 00:41:17,620 +x تربية dx إذا بقدر 1 على x تربية مع ال dx هذه + +390 +00:41:17,620 --> 00:41:23,160 +كلها أشيل و أكتب بدل السالب dθ يبقى هاي السالب برا + +391 +00:41:23,160 --> 00:41:28,980 +وهي تكاوم صين ثيتا كوصين ثيتا d ثيتا + +392 +00:41:32,100 --> 00:41:38,200 +الحين إلك الخيار هناك أكثر من طريقة للحل إحدى + +393 +00:41:38,200 --> 00:41:42,600 +الطرق ما هو الـ sine تفضلها مين؟ cosine إذا بقدر + +394 +00:41:42,600 --> 00:41:47,880 +أشيل sin θ و أحطها variable جديد لو حطيت على سبيل + +395 +00:41:47,880 --> 00:41:55,780 +المثال y تساوي sin θ هذا بدي أعطيك أن dy يساوي cos + +396 +00:41:55,780 --> 00:42:04,710 +θ dθإذا هذه كلها بصير تساوي سالب تكامل YD1 + +397 +00:42:07,690 --> 00:42:13,530 +يبقى هذا يبقى داشر سالب y تربيع على اتنين زائد + +398 +00:42:13,530 --> 00:42:20,650 +كونستان سي ال y ب sign ثيتا يبقى هذه ناقص نص sign + +399 +00:42:20,650 --> 00:42:26,850 +تربيع ثيتا زائد كونستان سي ثيتا يبقى داشر واحد على + +400 +00:42:26,850 --> 00:42:35,090 +اكس يبقى هنا سالب نص sign تربيع لواحد على اكس زائد + +401 +00:42:35,090 --> 00:42:42,390 +كونستان سيأجى واحد تانى اسمع شوية يا ابناى اجى + +402 +00:42:42,390 --> 00:42:47,710 +واحد تانى ماعجبهش الطريقة هذه قال انا عندي طريقة + +403 +00:42:47,710 --> 00:42:52,490 +غير الطريقة هذه بقوله كيف قاللي هذه ههه بعد ما + +404 +00:42:52,490 --> 00:42:58,610 +خلصنا احنا قاللي هذه بقدر اكتبها سالب نص تكامل + +405 +00:42:58,610 --> 00:43:06,440 +اتنين sin θ cos θ dθدرب في اتنين وجسم على اتنين + +406 +00:43:06,440 --> 00:43:12,060 +قلنا له والله كلامك مظبوط مية مية قال له هذه تساوي + +407 +00:43:12,060 --> 00:43:18,360 +سالب نص تكامل قال له هذه ال sign اتنين ثيتا دي + +408 +00:43:18,360 --> 00:43:23,720 +ثيتا قلت له برضه حساب مثلثات مظبوط بدنا نكامل + +409 +00:43:23,720 --> 00:43:30,180 +تكامل ال signسالب كوصين مقسم على تفاضل الزاوية + +410 +00:43:30,180 --> 00:43:38,100 +مظبوط يبقى هذا سالب نص برا وهذا سالب كوصين اتنين + +411 +00:43:38,100 --> 00:43:44,460 +ثيتا على اتنين زائد كونستان سي يبقى صارة النتيجة + +412 +00:43:44,460 --> 00:43:50,520 +سالب في سالب موجب رابع كوصين اتنين ثيتا زائد + +413 +00:43:50,520 --> 00:43:56,710 +كونستان سي هاي جواب يا شبابوهي جواب تاني وشكلا + +414 +00:43:56,710 --> 00:44:05,170 +مختلفا مصغوط لكن بقدر اوصل واحدتيهم للتاني مصغوط + +415 +00:44:05,640 --> 00:44:12,600 +بقدر اكتب هذه بدلالة ال cosine واحنا بنعرف انه sin + +416 +00:44:12,600 --> 00:44:18,000 +تربية ثيتا يسوى النص في واحد ناقص cosine اتنين + +417 +00:44:18,000 --> 00:44:23,920 +ثيتا مظبوط ولا لأ اذا بقدر اكتب هذه بدلالة ضيعة في + +418 +00:44:23,920 --> 00:44:24,200 +الزمن + +419 +00:44:36,250 --> 00:44:41,090 +زائد Constancy يعني اتنين في واحد على X لحد هنا مش + +420 +00:44:41,090 --> 00:44:44,990 +مطلوب انك تتحول لو ما بقى اتحول بدنا نحوله بحساب + +421 +00:44:44,990 --> 00:44:48,910 +المثلثات عادي جدا يبقى لو واحد طلع معاه الجواب هيك + +422 +00:44:48,910 --> 00:44:52,390 +ومش واحد يقوله والله جوابي غلط و جوابك صح لاتنين + +423 +00:44:52,390 --> 00:44:56,170 +صح مائة بالمائة ولا واحد بيقدر يعترض عليه كنت بدك + +424 +00:44:56,170 --> 00:44:59,850 +اتقول غير هذا الكلام؟ لو طلبنا تيتا تصين الواحد + +425 +00:44:59,850 --> 00:45:02,470 +على X طلبت تيتا تصين الواحد على X + +426 +00:45:08,550 --> 00:45:16,350 +لم تأتي بجديد كمان طيب طب اسمع شوية بقى انا بدي + +427 +00:45:16,350 --> 00:45:20,390 +اشتغل هالشغل وشوفوا ليه ايش رأيكم فيها كمان انا + +428 +00:45:20,390 --> 00:45:27,150 +عند المثل هذه هي سالب تكامل ل sine theta cosine + +429 +00:45:27,150 --> 00:45:33,810 +theta d theta فتحة كويسة هذا للي بعرف مستقلات + +430 +00:45:33,810 --> 00:45:41,760 +الدول المثلثين هو تفاضل الصين بقداشيعني بقدر اكتب + +431 +00:45:41,760 --> 00:45:46,600 +هذه يساوي + +432 +00:45:46,600 --> 00:45:56,760 +ناقص تكامل ل sin θ D sin θ ال D مش عبارة عن شر + +433 +00:45:56,760 --> 00:46:03,510 +التفاضل صح ولا لا؟يبقى كإني أنا كتبت ناقص sin θ + +434 +00:46:03,510 --> 00:46:12,010 +مشتقت sin θ يبقى + +435 +00:46:12,010 --> 00:46:15,310 +كإني أنا كتبت ناقص sin θ مشتقت sin θ يبقى كإني أنا + +436 +00:46:15,310 --> 00:46:17,950 +كتبت ناقص sin θ مشتقت sin θ يبقى كإني أنا كتبت + +437 +00:46:17,950 --> 00:46:19,650 +ناقص sin θ مشتقت sin θ + +438 +00:46:27,910 --> 00:46:35,630 +يبقى هذا الكلام يساوي ناقص sin تربيع ثيتا على + +439 +00:46:35,630 --> 00:46:43,770 +اتنين زائد constant Cيبقى بيرتلا لو سُحدّش أن بقلة + +440 +00:46:43,770 --> 00:46:49,510 +الصير ثيتا وإن مصر كأن المتغير كله هو main sin + +441 +00:46:49,510 --> 00:46:53,910 +ثيتا لإن بقدر أشيل ثيتا و أحط مكان واحد على x يبقى + +442 +00:46:53,910 --> 00:46:59,770 +هذا الكلام يساوي الناقص نص sin تربية واحد على x + +443 +00:46:59,770 --> 00:47:05,880 +زائد constant C هل اختلفت عن هذا؟اللي بيشتغل الشغل + +444 +00:47:05,880 --> 00:47:08,460 +هي دي صح، اللي بيشتغل هي دي صح، اللي بيشتغل هي دي + +445 +00:47:08,460 --> 00:47:11,300 +صح، ولا واحد بيقدر يعترض عليه، ايش بيكون بدك + +446 +00:47:11,300 --> 00:47:20,240 +تعترض؟ أبدا، + +447 +00:47:20,240 --> 00:47:24,240 +هي نفس الفكرة، يعني بعد ما أخد تاني ال sign هو أخد + +448 +00:47:24,240 --> 00:47:28,740 +ال cosine، ماعندي مشكلة عادية جدا، كله صحيح ولا + +449 +00:47:28,740 --> 00:47:30,340 +واحد بيقدر يعترض عليه + +450 +00:47:34,940 --> 00:47:42,440 +طيب نيجي للسؤال اللي بعده هذا السؤال رقم سبعة نيجي + +451 +00:47:42,440 --> 00:47:53,300 +للسؤال رقم تمانية تمانية بيقول يتكامل ل سك أس خمسة + +452 +00:47:53,300 --> 00:48:03,960 +X على تلاتة تان X على تلاتة كله في DX + +453 +00:48:12,650 --> 00:48:29,910 +تان اكسعة تلاتة DX تان + +454 +00:48:29,910 --> 00:48:38,210 +اكسعة تلاتة DX تان اكسعة تلاتة DXتساوي X ع تلاتة + +455 +00:48:38,210 --> 00:48:46,370 +يبقى Dθ بطولت DX يعني تلاتة D ثيتا بده يساوي DX + +456 +00:48:46,370 --> 00:48:53,950 +يعني أصبحت المسألة هي تلاتة تكامل سك أس خمسة ثيتا + +457 +00:48:53,950 --> 00:48:57,850 +تان ثيتا D ثيتا ما خلصناهش + +458 +00:49:03,920 --> 00:49:08,640 +سلامة كويسة يبقى قادي عشان انا لا أخلي برفق معاك + +459 +00:49:08,640 --> 00:49:13,740 +صاحبنا هذا بيقول السكوس خمسة بده يخليها السكوس + +460 +00:49:13,740 --> 00:49:20,720 +أربعة ثيتا في سك ثيتا في تان ثيتا في دي ثيتا قلت و + +461 +00:49:20,720 --> 00:49:24,890 +الله كلامك مظبوطالمكالكة في الدنيا هي six plus + +462 +00:49:24,890 --> 00:49:32,090 +أربعة يبقى باجي بقوله حط ال Y تساوي six ثيتا يبقى + +463 +00:49:32,090 --> 00:49:39,850 +DY ب six ثيتا تان ثيتا دي ثيتاصحيح؟ طب إيش رايكوا + +464 +00:49:39,850 --> 00:49:45,510 +أسوي هالشغل هادى؟ بدل ما قد أعوض و أسوي، لأ بجيبها + +465 +00:49:45,510 --> 00:49:50,770 +دغري، يبقى سويتك ولا سويتك سيان يعني أنا لو روحت + +466 +00:49:50,770 --> 00:49:58,650 +قولت كام ولا سك أص أربعة ثيتا مش تقل سك الثيتامش + +467 +00:49:58,650 --> 00:50:02,210 +تقّت الـsecθ التي هي تان ثيتا تان ثيتا دي ثيتا + +468 +00:50:02,210 --> 00:50:06,470 +يبقى هذه روحت كتبتها بالشكل هذا مظبوط هيك؟ في + +469 +00:50:06,470 --> 00:50:13,290 +مشكلة؟ كأن المسألة تكامل T أُس أربعة دي تي T أس + +470 +00:50:13,290 --> 00:50:17,230 +أربعة دي تي يعني بضع ضيف لأس واحد و أقسم على الأس + +471 +00:50:17,230 --> 00:50:23,430 +الجديد يبقى هي التلاتة برا وهذا سيك أس خمسة ثيتا + +472 +00:50:23,430 --> 00:50:30,030 +على خمسة زائد constant Cالان المشكلتنا في ثيتا بده + +473 +00:50:30,030 --> 00:50:38,030 +اشيلها واحط بدالها X على 3 يبقى 3 أخمس سك أس خمسة + +474 +00:50:38,030 --> 00:50:44,250 +لل X على 3 زائد كونس تنسيكا فالله المؤمنين + +475 +00:50:44,250 --> 00:50:53,870 +القادرين تمام؟ طيب بدنا نجي الآن لسؤال رقم 9 9 + +476 +00:50:53,870 --> 00:50:55,150 +بدنا تكامل + +477 +00:50:58,150 --> 00:51:08,550 +لـSin أُس خمسة برضه X على تلاتة Cos X على تلاتة DX + +478 +00:51:08,550 --> 00:51:18,030 +تسوي + +479 +00:51:18,030 --> 00:51:25,370 +زي اللي تو؟ طب أسوي هذا اللي فوق هذه؟ أسوي زيها؟ + +480 +00:51:38,750 --> 00:51:45,690 +هي تكامل لصين اص خمسة اكس على تلاتة + +481 +00:51:50,000 --> 00:51:58,040 +يبقى باجي بقول في دي لصين اكس على تلاتة بس هذه + +482 +00:51:58,040 --> 00:52:05,860 +مشتقتها جداش مشتقتها جداش لأ مشقة الصين بكوسين + +483 +00:52:05,860 --> 00:52:12,920 +كوسين اكس على تلاتة ضرب تلت مظبوط يبقى بصير الفرق + +484 +00:52:12,920 --> 00:52:15,380 +بين هذين بقول طب اضرب في تلاتة + +485 +00:52:18,580 --> 00:52:22,940 +بنفع ولا لا؟ يبقى تلف بتروح مع التلاتة بنعود زي ما + +486 +00:52:22,940 --> 00:52:27,950 +كناواضح؟ يبقى ماعنديش مشكلة في هذه الحالة يبقى على + +487 +00:52:27,950 --> 00:52:34,570 +طول الخط بقوله يا تلاتة خليك برا وهذه بيصير تكامل + +488 +00:52:34,570 --> 00:52:42,650 +ل sin أُس خمسة X على تلاتة مشتقة sin X على تلاتة + +489 +00:52:42,650 --> 00:52:48,910 +يبقى كأن احنا تكامل T أُس خمسة DT يبقى T أُس ستة + +490 +00:52:48,910 --> 00:52:56,500 +على ستة وفلسنايبقى هذه التلاتة اللي برا وهي sin 6x + +491 +00:52:56,500 --> 00:53:07,180 +على 3 على 6 زائد constant C يبقى هذه النصالـ 6X + +492 +00:53:07,180 --> 00:53:14,120 +على 3 زائد Constancy طب أنا عملتها بكل بساطة هيك + +493 +00:53:14,120 --> 00:53:20,420 +لكن أنا متأكد ان خمسين في المية منكوا لا يزالوا + +494 +00:53:20,420 --> 00:53:27,800 +مستغربين هالحركة هذه الجرعة طيب + +495 +00:53:27,800 --> 00:53:32,600 +بنعيدها كمان مرة صح صح اللي مستغرب وكان بيسأل + +496 +00:53:32,600 --> 00:53:39,110 +أزميله صح صح معايا كويسأحنا عندنا هذه المثلة بديش + +497 +00:53:39,110 --> 00:53:43,430 +أعمل خطواتين زي المثل اللي جابله أول حاجة أبدل ال + +498 +00:53:43,430 --> 00:53:48,390 +X على ثلاثة و بعدين أحط التعويض Y تساوي سكلالة بدي + +499 +00:53:48,390 --> 00:53:52,310 +أجيبها مرة واحدة بدل ما أعملها على خطواتين بدي + +500 +00:53:52,310 --> 00:53:56,690 +أعملها بخط واحدة بجيب أقول أه هذه المثلة مقطع فضل + +501 +00:53:56,690 --> 00:54:04,020 +الصين الزاوية بكسين الزاويةإذا هذه هي مشتقة هذه بس + +502 +00:54:04,020 --> 00:54:08,380 +بيفرقوا عن بعض بمقدار ثابت بقولكوا إذا هذه بدأ + +503 +00:54:08,380 --> 00:54:15,370 +اكتبها sign زي ما هي وهذه دي signطب لو جيت اشتقت + +504 +00:54:15,370 --> 00:54:21,410 +هذه ماشتقت هذه ب cosine ضرب تلت اذا بدها تفرق عن + +505 +00:54:21,410 --> 00:54:25,270 +هذه بقدرش بتلت يبقى مش هان اضيع هذا الفرق بقوم + +506 +00:54:25,270 --> 00:54:30,130 +اضرب في تلاتة اذا لو ضربت في تلاتة بصير تلاتة في + +507 +00:54:30,130 --> 00:54:35,570 +دي صعيبهذا لو يا شباب بصير cosine ضرب طول مع تلاتة + +508 +00:54:35,570 --> 00:54:40,050 +بتروح بضلش الا ال cosine x على تلاتة dx اللي هي + +509 +00:54:40,050 --> 00:54:45,610 +هذه يعني يا شباب هذه ههه تكافئ تماما المقدار بين + +510 +00:54:45,610 --> 00:54:51,630 +القوسينتكافى المقدار هذا بالضبط تماما كأنه شيلت + +511 +00:54:51,630 --> 00:54:56,370 +هذه و كتبت هذه بدلها طيب التلاتة هيبرة ال sign زي + +512 +00:54:56,370 --> 00:55:00,470 +ما هي و دي ال sign زي ما هي يبقى صارت المثلة كانها + +513 +00:55:00,470 --> 00:55:06,930 +تكامل T أس خمسة DT يبقى بضيف للأس واحد و بقسم على + +514 +00:55:06,930 --> 00:55:11,570 +الأس الجديد هيوضفنا و اختصرنا و كتبنا النتيجة حد + +515 +00:55:11,570 --> 00:55:18,250 +قالوا أي تساؤل هنا؟اذا ماعرفش بلاش بتروح تقولي put + +516 +00:55:18,250 --> 00:55:24,950 +اله cosine x ع تلاتة تساوي T واشتقها وضرب في تلاتة + +517 +00:55:24,950 --> 00:55:28,790 +و تعال عوّد ماعنديش مشكلة اذا عود اشتغل تاني يبقى + +518 +00:55:28,790 --> 00:55:33,510 +سوا اشتغلت هيك و الله هيك على كل الأمرين ستصل إلى + +519 +00:55:33,510 --> 00:55:39,750 +نفس النتيجةطيب هذا كان السؤال رقم تسعة سؤال رقم + +520 +00:55:39,750 --> 00:55:48,450 +عشرة بدنا تكامن لكوسين جذر الثيتا على الجذر + +521 +00:55:48,450 --> 00:55:57,470 +التربيعي لثيتا في صين تكيب جذر الثيتا في دي ثيتا + +522 +00:55:57,470 --> 00:56:05,970 +سؤال من الكتابوجئنا به في إحدى الامتحانات ذات مرة + +523 +00:56:05,970 --> 00:56:12,350 +زي ما هو هيك طيب القصة بسيطة جدا شو رأيك اوزع + +524 +00:56:12,350 --> 00:56:17,090 +الجدر على المقام هذا قبل ما أبدأ أشتغل يعني هذه + +525 +00:56:17,090 --> 00:56:24,710 +المثلة مش هي عبارة عن cosine جدر الثيتا على جدر + +526 +00:56:24,710 --> 00:56:32,770 +الثيتا الجدر التربيعي لصين تكييب جدر الثيتاخلّيني + +527 +00:56:32,770 --> 00:56:37,130 +أسألكم السؤال التالي، من المصعب المثل؟ هل الـ Cos + +528 +00:56:37,130 --> 00:56:42,050 +ولا الـ Sin؟ الـ Sin هو الممكن نهيك عن تفضلها بكون + +529 +00:56:42,050 --> 00:56:49,340 +البصرة اللي فوقمظبوط وزيادة شوية كمان عليك اذا انا + +530 +00:56:49,340 --> 00:56:53,520 +لو جيت الكمية اللي تحت اليد السين جادر مش مش تروح + +531 +00:56:53,520 --> 00:56:57,240 +تاخد السين تكيب لإن السين تكيب لو جيت اشتقى بيطلع + +532 +00:56:57,240 --> 00:57:00,660 +تلاتة سين تربيها في الكوسين يبقى تعويض تتماشي الله + +533 +00:57:00,660 --> 00:57:05,820 +عليها خربت الدنيا ومش صلعتها تمام يبقى بروح بقوله + +534 +00:57:05,820 --> 00:57:12,740 +حط ايه هه اللي هو ال X بدها ساوي مثلا سين + +535 +00:57:15,700 --> 00:57:22,300 +طيب بدنا دي اكس يبقى تفاضل الصين بكوصين جذر الثيتا + +536 +00:57:22,300 --> 00:57:28,760 +ضرب تفاضل الزاوية اتنين جذر ثيتا دي ثيتا بقوله + +537 +00:57:28,760 --> 00:57:32,920 +تمام ماعنديش اتنين الآن يبقى اضرب في اتنين يبقى لو + +538 +00:57:32,920 --> 00:57:38,420 +ضربت في اتنين بصير اتنين دي اكس بده يسوى كوصين جذر + +539 +00:57:38,420 --> 00:57:43,990 +الثيتا على جذر الثيتا في دي ثيتاأذا هذه الكلكة + +540 +00:57:43,990 --> 00:57:51,730 +التي لديها كلها بقدر أشيلها و أكتب درجة داشر نان + +541 +00:57:51,730 --> 00:57:55,690 +دي اكس والله هذه حلت المشكلة كلها شوفيش اللي أخدته + +542 +00:57:55,690 --> 00:57:58,490 +مش أخدت sign تكين لو أخدت sign تكين اللي صدرت + +543 +00:57:58,490 --> 00:58:03,550 +تلاتة sign تربية في ال cosine في تقريركان غير شكل + +544 +00:58:03,550 --> 00:58:07,270 +تمام يبقى التعويض اللى بدى تحطها بيبقى تبسط + +545 +00:58:07,270 --> 00:58:13,210 +المسألة مش تعجد المسألة دى بالك تمام يبقى بيصير + +546 +00:58:13,210 --> 00:58:19,930 +المسألة هذه تكامل هذا واحد على الجدر التربيعى هذه + +547 +00:58:19,930 --> 00:58:27,470 +حاطنها ب X بيصير X تكيب والباقي كله ب 2DX اتنين DX + +548 +00:58:27,470 --> 00:58:33,400 +يعني اتنين تكاملالجدر التربيه اللي يعني X أُس + +549 +00:58:33,400 --> 00:58:39,460 +تلاتة على اتنين لو طلعت غوض بصير السالب تلاتة على + +550 +00:58:39,460 --> 00:58:45,140 +اتنين دي يعني الكلكة الكبيرة صارت ولا حاجة صح؟ + +551 +00:58:45,140 --> 00:58:51,360 +يبقى هذه بسيطة جدا يبقى هذه اتنين خليك برا وهذه X + +552 +00:58:51,360 --> 00:58:57,540 +أضيف للأس واحد و أقسم على الأس الجديد و أقول له + +553 +00:58:57,540 --> 00:59:05,150 +زائد كونستانسيتمام يبقى هذا يصيب ناقص أربعة وال X + +554 +00:59:05,150 --> 00:59:13,830 +عندي يبقى كم بصين لجذري الثيتا وهذا كله أس كم سالب + +555 +00:59:13,830 --> 00:59:20,710 +نص زائد constant C بدك تنزلها تحت يبقى سالب أربعة + +556 +00:59:20,710 --> 00:59:26,890 +على الجذري التربيعي لصين جذري الثيتا زائد constant + +557 +00:59:26,890 --> 00:59:27,750 +C + +558 +00:59:29,900 --> 00:59:36,660 +من أسئلة الكتاب مش من برا طيب السؤال الحدي عشرة + +559 +00:59:36,660 --> 00:59:48,140 +بدنا تكامل الجذري التربيعي لل X تكييف ناقص ثلاثة + +560 +00:59:48,140 --> 00:59:54,480 +على ال X أس إحداشر في DX + +561 +00:59:59,550 --> 01:00:06,350 +X تكيب ناقص تلاتة على ال X كله تحت الجدر التربيعي + +562 +01:00:06,350 --> 01:00:13,550 +يلا شوف ايش تقترح علينا فكر كويس على الممسح اللوح + +563 +01:00:13,550 --> 01:00:17,690 +هذا برضه من الكتاب من أسئلة الكتاب + +564 +01:00:22,590 --> 01:00:27,370 +لو ازال المقام تبقى كسور كما هي واحد ع الاكس اكس + +565 +01:00:27,370 --> 01:00:31,870 +تمانية زائد تلات او ناقص تلات ع الاكس اكس احداش + +566 +01:00:37,380 --> 01:00:45,440 +أيوة كلام كويس تصير + +567 +01:00:45,440 --> 01:00:51,220 +اكسس أربعة صاحبنا + +568 +01:00:51,220 --> 01:00:58,480 +اقترح ما يأتيجالي هذه هي تكامل للجذر التربيعي ل X + +569 +01:00:58,480 --> 01:01:04,000 +تكييب ناقص ثلاثة على X أس تمانية في X تكييب في + +570 +01:01:04,000 --> 01:01:08,560 +الـDX قلنا له مظبوط جالي ال X أس تمانية بتطلعها + +571 +01:01:08,560 --> 01:01:14,880 +برا الجذر وجوه التكاملمش برها بقول له تمام قال لي + +572 +01:01:14,880 --> 01:01:20,040 +هذه يبقى تكامل واحد على X أُص أربعة و هذا الجدرى + +573 +01:01:20,040 --> 01:01:25,260 +التربية اللي X تكيب ناقص ثلاثة على X تكيب دي X + +574 +01:01:25,260 --> 01:01:29,940 +قولنا له تمام قال لي هذه تكامل واحد على X أُص + +575 +01:01:29,940 --> 01:01:34,620 +أربعة و هذا الجدرى التربية اللي واحد ناقص ثلاثة + +576 +01:01:34,620 --> 01:01:40,510 +على X تكيب دي X مش هي قصاد؟وانا بدي ازيد عليها و + +577 +01:01:40,510 --> 01:01:45,830 +اقولك كل اللي تحت الجدر هذا شيله و حطه بمتغير جديد + +578 +01:01:45,830 --> 01:01:52,170 +حط اي متغير يجي في بالك اذا لو حطيت ال W تساوي + +579 +01:01:52,170 --> 01:02:00,350 +واحد ناقص تلاتة على X تكعيب و بدنا نجيب ال W دي W + +580 +01:02:00,350 --> 01:02:08,990 +تمام ففضل واحد ب Zeroوهذه تصبح ناقص ثلاثة مالهاش + +581 +01:02:08,990 --> 01:02:17,090 +دعوة وهذه واحد عليك استكعيب الكل تربيع في من في + +582 +01:02:17,090 --> 01:02:22,090 +اللي له مشتقة تبعته او اريحك شويةقبل ان تذهب + +583 +01:02:22,090 --> 01:02:24,550 +للتفاضل بلاش بعضكوا يذهبوا يخططوا يخططوا يخططوا + +584 +01:02:24,550 --> 01:02:25,410 +يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا + +585 +01:02:25,410 --> 01:02:28,890 +يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا + +586 +01:02:28,890 --> 01:02:31,130 +يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا + +587 +01:02:31,130 --> 01:02:37,210 +يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا + +588 +01:02:37,210 --> 01:02:40,510 +يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا يخططوا + +589 +01:02:40,510 --> 01:02:48,710 +يخططوا يخططوا + +590 +01:02:48,710 --> 01:02:55,450 +يخمظبوط احنا + +591 +01:02:55,450 --> 01:03:02,730 +ايش سوينا هو اكس اه و سالب اربع صح استنى و سالب + +592 +01:03:02,730 --> 01:03:10,410 +اربع تمام يبقى واحد تسعة على اكس أس اربع تمام ناجس + +593 +01:03:10,410 --> 01:03:14,330 +عشان ما ناجس بتروح بالزاد ما هي ناقص و ناقص تمام + +594 +01:03:14,330 --> 01:03:17,910 +يبقى هذا تسعة + +595 +01:03:19,090 --> 01:03:27,450 +DW يساوي واحد على X أُص أربعة DX إذا الـ DX هذه مع + +596 +01:03:27,450 --> 01:03:32,530 +واحد على X أُص أربعة بدي أشيلها و أكتب لها تسعة DW + +597 +01:03:32,530 --> 01:03:40,970 +يبقى يا بصير هي التسعة برا وهي تكامل وجذر الـW DW + +598 +01:03:40,970 --> 01:03:44,250 +مظبوط + +599 +01:03:44,250 --> 01:03:52,800 +ايه؟ صارت كل حاجة بسيطة جدايبقى كل جدر ال W يبقى + +600 +01:03:52,800 --> 01:04:00,400 +هذا بيصير تسع و هذا W أس ثلاثة على اتنين على تلاتة + +601 +01:04:00,400 --> 01:04:07,380 +على اتنين زائد constant C يبقى هذا بيصير اتنين على + +602 +01:04:07,380 --> 01:04:09,220 +سبعة وعشرين + +603 +01:04:11,160 --> 01:04:17,560 +و ال W بده شيلها و حط قمتها اللي هو حد ناقص تلاتة + +604 +01:04:17,560 --> 01:04:30,180 +على X تعيب أس تلاتة على اتنين زائد constant C طب + +605 +01:04:30,180 --> 01:04:33,960 +لحد هنا انتهينا من هذا ال section و عليكم أرقام + +606 +01:04:33,960 --> 01:04:39,580 +المسائل يفجأة بنيجي هنا هيحطهم لك هنا exercises + +607 +01:04:41,270 --> 01:04:51,230 +خمسة خمسة exercises خمسة خمسة المسائل التالية من + +608 +01:04:51,230 --> 01:05:00,570 +واحد لتلاتة وخمسين من واحد لغاية تلاتة وخمسين القد + +609 +01:05:00,570 --> 01:05:05,590 +ومنضيف عليهم سؤال تلاتة وستين + +610 +01:05:10,480 --> 01:05:17,460 +لازلنا في ما يشبه هذا الموضوع وهو آخر section في + +611 +01:05:17,460 --> 01:05:23,560 +هذا ال chapter خمسة ستة خمسة ستة تقول لي + +612 +01:05:23,560 --> 01:05:28,400 +substitution substitution + +613 +01:05:28,400 --> 01:05:36,980 +and ال area between + +614 +01:05:36,980 --> 01:05:39,480 +curves + +615 +01:05:45,020 --> 01:05:52,480 +بناخد النقطة الأولى Substitution Indefinite + +616 +01:05:52,480 --> 01:06:02,560 +Integrals Indefinite + +617 +01:06:02,560 --> 01:06:13,980 +Integrals F G' is continuous function + +618 +01:06:15,980 --> 01:06:25,300 +إذا الـG' كانت continuous function on + +619 +01:06:25,300 --> 01:06:36,700 +the closed interval A وB and if الـF كذلك is + +620 +01:06:36,700 --> 01:06:39,380 +continuous + +621 +01:06:45,520 --> 01:06:58,740 +on the range of g على ال range of g then تكامل من + +622 +01:06:58,740 --> 01:07:09,020 +a إلى b لل f of g of x في ال g prime of x dx بده + +623 +01:07:09,020 --> 01:07:20,870 +يساوي تكامل لل g of aوهنا الـ G of B للـ F of U في + +624 +01:07:20,870 --> 01:07:21,350 +الـ DU + +625 +01:07:59,820 --> 01:08:04,780 +هذا شباب هو التكامل بالتعويض نفسه بس بدنا نغير + +626 +01:08:04,780 --> 01:08:09,800 +حدود التكامل طبقا للتعويضة الجديدة وبالتالي بدنا + +627 +01:08:09,800 --> 01:08:13,820 +ننتقل من ال indefinite ال integrals الى definite + +628 +01:08:13,820 --> 01:08:19,210 +integralsالتكاملات المحدودة فبجب ال substitution + +629 +01:08:19,210 --> 01:08:24,510 +and area between curves يبقى فيها موضوعين الموضوع + +630 +01:08:24,510 --> 01:08:28,190 +الأول هو ال substitution والثاني ال area between + +631 +01:08:28,190 --> 01:08:32,410 +curves اليوم بدي ناخد بس الموضوع الأول والثاني + +632 +01:08:32,410 --> 01:08:36,390 +للمحاضرة القادمة ان شاء الله يبقى بيجي للنقطة + +633 +01:08:36,390 --> 01:08:40,610 +الأولى substitution and infinite integrals التعويض + +634 +01:08:40,640 --> 01:08:44,860 +في التكاملات المحدودة الشغل اللي كنا بنشغله في ال + +635 +01:08:44,860 --> 01:08:48,920 +section و كله تكاملات غير محدود تعويض في تكاملات + +636 +01:08:48,920 --> 01:08:54,620 +غير محدودة بقول لو كان ال G prime ده المتصل على + +637 +01:08:54,620 --> 01:08:59,720 +الفترة A و B و ال F متصل على ال range بتابع الدالة + +638 +01:08:59,720 --> 01:09:04,540 +G then يعني انا عندي composition ما بين ال F و ال + +639 +01:09:04,540 --> 01:09:09,780 +G ال G element في domain من؟ في domain ال F + +640 +01:09:10,050 --> 01:09:15,970 +وبالتالي ال F of G of X صار Range صار Range لباليه + +641 +01:09:15,970 --> 01:09:19,510 +فعلى أي حال انسى ال domain و ال range بديك تعرف ما + +642 +01:09:19,510 --> 01:09:23,530 +ياتي لو كان عندى هك بدي اعمل تعويضة شو هذه + +643 +01:09:23,530 --> 01:09:30,390 +التعويضة بتروح احط ال U تساوي G of X يبقى DU + +644 +01:09:30,390 --> 01:09:37,210 +بتساوي G prime of X في DX مظبوط اذا هذي G prime of + +645 +01:09:37,210 --> 01:09:44,060 +X DX صارت مين؟د يو وال جي هيها يو هذه ال a و ال b + +646 +01:09:44,060 --> 01:09:49,810 +حدود لمين؟للمتغير X انت بقى اللي يصير عندك متغير X + +647 +01:09:49,810 --> 01:09:54,650 +للمتغير اللي يديه ال main U بدك تجيب الحدود + +648 +01:09:54,650 --> 01:09:59,130 +المناظرة لهذه الحدود بده تجيبها من وين بده تجيبها + +649 +01:09:59,130 --> 01:10:06,810 +من التعويضة لما تبقى X ب B بصير ال U تسوى G of B + +650 +01:10:06,810 --> 01:10:14,930 +لما تبقى ال X ب Aبتصير G of A يبقى صارت هذه G of A + +651 +01:10:14,930 --> 01:10:21,310 +و هكذا يعني قصدنا من ذلك انه لما تحط تعويضة تغير + +652 +01:10:21,310 --> 01:10:28,110 +حدود التكامل طبقا لهذه التعويضة الجديدة بنفع قبل + +653 +01:10:28,110 --> 01:10:31,650 +ان تقول هقولها لك بس مش الحين الآن عمليا عارف ايش + +654 +01:10:31,650 --> 01:10:36,410 +اللي بدك هيهالحد هنا انتهى الوزن النظر يتبع هذه + +655 +01:10:36,410 --> 01:10:41,450 +النقطة بدنا نبدأ ناخد أمثلة عليها يبقى example + +656 +01:10:41,450 --> 01:10:48,030 +احسبلي + +657 +01:10:48,030 --> 01:10:56,610 +التكاملات التالية the following integrals + +658 +01:11:01,040 --> 01:11:05,160 +أول تكامل من هذه التكاملات ال integration من سلب + +659 +01:11:05,160 --> 01:11:13,340 +واحد إلى واحد لل X تكيب في واحد زاد X أُص أربعة + +660 +01:11:13,340 --> 01:11:26,500 +زاد X أُص أربعة تكيب في DX خلّينا + +661 +01:11:26,500 --> 01:11:32,170 +نسأل السؤال التاليحد متوقع جداش تكون النتيجة هذه؟ + +662 +01:11:32,170 --> 01:11:39,590 +حد بيعرف جداش؟ انا عمري مش حسبت الحقيقة لكن بجرد + +663 +01:11:39,590 --> 01:11:46,600 +النظر ايوة Zero الهين هقولك ليش Zero تمام؟تعالى + +664 +01:11:46,600 --> 01:11:50,360 +احنا بنشتغل شغل لوميان زى اللى توقعتنا بنشتغل وانا + +665 +01:11:50,360 --> 01:11:53,920 +ماعرفش انها zero ولا غير zero بقى يبطل عليهم صعب + +666 +01:11:53,920 --> 01:11:58,600 +مثلا الاكستاكيب والله عزيزي اكسوس اربعة مشتقتها + +667 +01:11:58,600 --> 01:11:59,780 +بتجيبلي الاكستاكيب + +668 +01:12:02,650 --> 01:12:10,190 +الـ T تساوي واحد زائد X أُس أربعة يبقى الـ DT بدل + +669 +01:12:10,190 --> 01:12:18,890 +ساوية أربعة X تكييب في DX يبقى الرابع DT بدل ساوية + +670 +01:12:18,890 --> 01:12:26,030 +X تكييب DX إذا هشيل الـ X تكييب مع الـ DX هذه و + +671 +01:12:26,030 --> 01:12:31,470 +اكتب بدلها جداش رابع DT إذا صارت هذه هذا رابع + +672 +01:12:31,650 --> 01:12:41,050 +ويتكامل T تكيب DT هذه الحدود سالب واحد واحد هي + +673 +01:12:41,050 --> 01:12:47,610 +حدود لل X لكن المثل صارت بدلالة T إذا بدأتي تشوف + +674 +01:12:47,610 --> 01:12:54,920 +الحدود المناظرة لما تكبر X بواحد وT بقدرشبتنان + +675 +01:12:54,920 --> 01:12:57,840 +يبقى بيصير واحد اقصى اربعة اللي هو واحد واحد + +676 +01:12:57,840 --> 01:13:03,700 +باتنين يبقى هذا بيصير اتنين لما تبقى X بسالب واحد + +677 +01:13:03,700 --> 01:13:09,700 +بيصير سالب واحد اقصى اربعة اللي هو واحد واحد اتنين + +678 +01:13:09,700 --> 01:13:15,800 +تذلك إذا تساوى حدات تكمل فالنقيم تتكمل تساوي جداش + +679 +01:13:15,800 --> 01:13:24,870 +تساوي Zero على طول القطبعد ما خلص الأمثلة في شغلة + +680 +01:13:24,870 --> 01:13:29,750 +بدي أقولها لك، هذه الدالة، دالة فردية ولا زوجية؟ + +681 +01:13:35,930 --> 01:13:42,190 +الدالة الفردية يعني دالة فردية إذا كان حدود + +682 +01:13:42,190 --> 01:13:46,270 +التكتمل هما نفسهم الإتنين بس واحد سالب و واحد موجب + +683 +01:13:46,270 --> 01:13:50,830 +والدالة فردية فالنتيجة التكمل يساوي الصفر أما إذا + +684 +01:13:50,830 --> 01:13:56,810 +كانت الدالة زوجية فالنتيجة يساوي اتنينتتامل على نص + +685 +01:13:56,810 --> 01:14:01,330 +الفترة لهذه الدالة وهذا ما سنعطيه إليكم في + +686 +01:14:01,330 --> 01:14:05,010 +المحاضرة القادمة مش اليوم اليوم مش هنلعب بس خليا + +687 +01:14:05,010 --> 01:14:08,890 +في بالك هنرجع هنا يبقى النتيجة تساوي Zero على طول + +688 +01:14:08,890 --> 01:14:14,610 +الخط مثال رقم اتنينسؤال في الكتاب هذا دير بالك + +689 +01:14:14,610 --> 01:14:22,070 +تكامل من سالب واحد لغاية ال zero لل X تكييب على + +690 +01:14:22,070 --> 01:14:27,470 +الجدرى التربيعي ل X أُص أربعة زائد تسعة في DX + +691 +01:14:29,430 --> 01:14:33,670 +مشكلتنا كمان وين؟ من سالب واحد؟ اه من سالب واحد + +692 +01:14:33,670 --> 01:14:39,210 +يبقى مشكلتنا مع الكمية اللى تحت الجدر اذا لو حطيت + +693 +01:14:39,210 --> 01:14:46,430 +ال W يساوي X أُص أربعة زائد تسعة يبقى DW ساوي + +694 +01:14:46,430 --> 01:14:50,770 +أربعة X تكييب DX او ربع DW + +695 +01:14:59,270 --> 01:15:09,940 +الربع خلّيك برا وهي تكامل وهي DW وهذا جذر ال Wبقيت + +696 +01:15:09,940 --> 01:15:16,280 +حدود التكامل لما تبقى ال X ب Zero يبقى ال W بقداش + +697 +01:15:16,280 --> 01:15:22,120 +تسعة لما تبقى ال X ب سالب واحد يبقى ال W بقداش + +698 +01:15:22,120 --> 01:15:30,260 +عشرة يصير التكامل من عشرة إلى تسعة لمن لربا DW + +699 +01:15:30,260 --> 01:15:36,230 +تمام التمام شو رايك الرقم الكبير؟فوق والصغير .. + +700 +01:15:36,230 --> 01:15:39,670 +ولا العكس الكبير تحت والصغير فوق بيجيب انشقلب + +701 +01:15:39,670 --> 01:15:46,930 +وبيجيب إشارة مين سالم يبقى هذا بيصير سالم ربع وهي + +702 +01:15:46,930 --> 01:15:56,790 +تكمل من تسعة لغاية عشرة ل W أس ناقص نص DWتمام؟ + +703 +01:15:56,790 --> 01:16:05,270 +يبقى هذا الكلام ناقص ربع وهذا W أس نص على نص + +704 +01:16:05,270 --> 01:16:11,310 +والحكي هذا من تسعة لغاية يداش عشرة يبقى الجواب + +705 +01:16:11,310 --> 01:16:17,950 +يسوى ناقص نص الجدرى التربية لعشرة ناقص الجدرى + +706 +01:16:17,950 --> 01:16:26,450 +التربية لمن؟لتسعة أو إن شئتم فقولوا سالب نص جذر + +707 +01:16:26,450 --> 01:16:31,810 +العشرة ناقص تلاتة قد ما يطلع يطلع خليه زي ما هو + +708 +01:16:31,810 --> 01:16:42,090 +طيب سؤال التالتبيقول يتكامل من Zero لغاية واحد + +709 +01:16:42,090 --> 01:16:51,090 +للعشرة جذر ال X على واحد زاد X أُس تلاتة على + +710 +01:16:51,090 --> 01:16:56,310 +اتنين، الكل تربيع بالنسبة إلى DX + +711 +01:17:00,120 --> 01:17:04,680 +مين مصعب المثلة؟ المقدار بين القوسين، يبقى بشيل + +712 +01:17:04,680 --> 01:17:10,000 +المقدار بين القوسين دل كامل وبحق بدله متغير جديد + +713 +01:17:10,500 --> 01:17:16,000 +إذا لو حطيت ال Y يسوى واحد زائد X أص تلاتة على + +714 +01:17:16,000 --> 01:17:24,820 +اتنين يبقى DY يسوى تلاتة على اتنين X أص نص DX يعني + +715 +01:17:24,820 --> 01:17:33,540 +صار تلتين DY بده يسوى جذر ال X في DX + +716 +01:17:36,620 --> 01:17:42,020 +طيب لو روحت ضربت في عشرة بالمرة رايح او طلعت + +717 +01:17:42,020 --> 01:17:46,360 +العشرة برا سيام تفرقش علنا لو روحت ضربت في عشرة + +718 +01:17:46,360 --> 01:17:53,720 +بصيرة عشرين على تلاتة dy بيكون عشرة جذر ال x dx + +719 +01:17:54,460 --> 01:18:00,140 +يبقى هذا بده يساوي عشرين على تلاتة برة وهي تكامن + +720 +01:18:00,140 --> 01:18:05,040 +جال عشرة جدر ال X DX كلها بده اشيلها و اكتب بدالها + +721 +01:18:05,040 --> 01:18:10,480 +عشرين على تلاتة DY هي العشرين على تلاتة برة وهي ال + +722 +01:18:10,480 --> 01:18:18,200 +DY برة، ضال هذا كله في Y ترميبقيت حدود التكامل لما + +723 +01:18:18,200 --> 01:18:24,140 +تبقى X بواحد بصير Y بقداش باتنين و لما تبقى X + +724 +01:18:24,140 --> 01:18:30,150 +بالزيرو بصير Y بقداش بواحد بالشكل اللي أعنىيبقى + +725 +01:18:30,150 --> 01:18:36,710 +هذه بدها تساوي عشرين على تلاتة وهذا تكملها بسالب + +726 +01:18:36,710 --> 01:18:43,750 +واحد على Y من الواحد لغاية اتنين يبقى هذه السالب + +727 +01:18:43,750 --> 01:18:54,380 +عشرين على تلاتة وهنا النص ناقص واحديبقى هنا ناقص + +728 +01:18:54,380 --> 01:19:02,340 +عشرين على تلاتة في ناقص نص ناقص مع ناقص زائد ويبقى + +729 +01:19:02,340 --> 01:19:07,280 +فقط عشر عالمين على تلاتة + +730 +01:19:29,240 --> 01:19:39,800 +السؤال الرابع يقول التكامل من 0 لغاية 4 لل X + +731 +01:19:39,800 --> 01:19:49,440 +الجدرى التربية إلى 16 ناقص 3 X كله في DX من 0 ل4 + +732 +01:19:49,440 --> 01:19:54,790 +مصدرطبعا الكمية اللي تحت الددر هي اللي خلّى المثل + +733 +01:19:54,790 --> 01:20:01,290 +مشلقة مش طبيعية يبقى بدأ أشيل هذا و أضع بدله مثلا + +734 +01:20:01,290 --> 01:20:08,270 +w بساوية ستة عشر ناقص تلاتة x يبقى dw ناقص تلاتة + +735 +01:20:08,270 --> 01:20:15,360 +في dx أنا ماعنديش وإنما عندي بسDX لحالها يبغى بدرب + +736 +01:20:15,360 --> 01:20:21,920 +في سالب تلت لو ضربنا في سالب تلت بصير سالب تلت + +737 +01:20:21,920 --> 01:20:30,300 +سالب تلت DW بده يساوي مين DX إذا آلة المسألة إلى + +738 +01:20:30,300 --> 01:20:38,020 +تكامل أنا بده DX من هذه بقدر أقول إذاتلاتة X يسوى + +739 +01:20:38,020 --> 01:20:40,060 +ستاشر ناقص W + +740 +01:20:48,000 --> 01:20:55,160 +الـ x بدأ أشيل و أكتب بدلها تلت في ستة عشر ناقص w + +741 +01:20:55,160 --> 01:21:03,820 +وصلت للجدرد هذا حطيته كله مجدوش w ال dx بسالب تلت + +742 +01:21:03,820 --> 01:21:12,840 +dw يبقى هاي سالب تلت وهذا dwبقيت حدود التكامل لما + +743 +01:21:12,840 --> 01:21:18,900 +تبقى x بقداش اربعة اربعة في تلاتة باطناش ستاش ناقص + +744 +01:21:18,900 --> 01:21:25,240 +اتناش بيظل اربعة كما هي لم تتغير وهذه ستاش بيظل + +745 +01:21:25,240 --> 01:21:34,440 +Zeroلحظة عندك سالف وهنا مانطير من السالف مع تلت + +746 +01:21:34,440 --> 01:21:42,640 +شرف برا يبقى هذا تسعة وهذا تكامل من أربع لغاية + +747 +01:21:42,640 --> 01:21:52,820 +ستاشرواضال هدول بس مصبور يبقى هذا 16W أس نص ناقص W + +748 +01:21:52,820 --> 01:22:02,200 +أس تلاتة على الإتنين كله DWيبقى هذا التس و برة + +749 +01:22:02,200 --> 01:22:09,220 +مالوش دعوة بدنا نكامل يبقى هذا ست عشر W أس تلاتة + +750 +01:22:09,220 --> 01:22:16,140 +على اتنين على تلاتة على اتنين ناقص W أس خمسة على + +751 +01:22:16,140 --> 01:22:22,610 +اتنين على خمسة على اتنين والحكي هذامن أربعة لغاية + +752 +01:22:22,610 --> 01:22:29,870 +كم؟ ستة عشر يبقى هذا تسعة وهذا يصبح اتنين وتلاتين + +753 +01:22:29,870 --> 01:22:38,110 +على تلاتة وهنا ستة عشر أس تلاتة على اتنين ناقص + +754 +01:22:38,110 --> 01:22:45,050 +وهنا اتنين على خمسة ستة عشر أس خمسة على اتنين + +755 +01:22:45,050 --> 01:22:50,700 +يعوضنا بالقيمة اللي فوقنقص اتنين و تلاتين على + +756 +01:22:50,700 --> 01:22:59,080 +تلاتة فمين في اربعة از تلاتة على الاتنين نقص مع + +757 +01:22:59,080 --> 01:23:06,740 +نقص بالصير زائد اتنين على خمسة في اربعة از خمسة + +758 +01:23:06,740 --> 01:23:12,120 +على الاتنين بالشكل اللي عندنا ده مرة تانية شلت هذه + +759 +01:23:12,120 --> 01:23:16,420 +و حطيت ستاشر والاشارة السلب زي ما هياللي بعدها بده + +760 +01:23:16,420 --> 01:23:21,080 +أشيل هذه و أحط مكانها أربعة و بيصير هنا ناقص و هنا + +761 +01:23:21,080 --> 01:23:25,480 +ناقص ناقص و بيصير هنا زايد بالشكل اللي عندنا هذا + +762 +01:23:25,480 --> 01:23:30,820 +يبقى هذا الكلام بده يسوي هاي التسو أخليه برا هذه + +763 +01:23:30,820 --> 01:23:37,170 +يا شباب هو الجذر التربيةي لست عشر تكيينالجذر + +764 +01:23:37,170 --> 01:23:45,410 +التربيعى ل 16 ارتكب يعني 16 في 16 في 16 يعني 16 في + +765 +01:23:45,410 --> 01:23:56,370 +4 مظبوط ب 64 يبقى هذه بصير 32 في 64 على 3ناقص + +766 +01:23:56,370 --> 01:24:03,110 +اتنين على خمسة هذه الجدر التربية الى ستاشر في + +767 +01:24:03,110 --> 01:24:12,170 +الخمسة يعني ستاشر في ستاشر في أربعة يبقى هذه ستاشر + +768 +01:24:12,170 --> 01:24:20,830 +في ستاشر في هذين 256 في هذا اللي هو الجداش في + +769 +01:24:20,830 --> 01:24:28,810 +أربعة على خمسة ناقصأتنين وتلاتين على تلاتة هذا + +770 +01:24:28,810 --> 01:24:33,870 +الجدر التربيعي له أربعة تكييب يعني أربعة في أربعة + +771 +01:24:33,870 --> 01:24:37,610 +في أربعة تحت الجدر التربيعي يعني أربعة في اتنين له + +772 +01:24:37,610 --> 01:24:39,950 +بقداش تمانية + +773 +01:24:46,350 --> 01:24:54,590 +الجدر التربيعي لأربع أقص خمسة يبقى ست عشر في اتنين + +774 +01:24:54,590 --> 01:25:02,150 +يبقى اتنين و تلاتين بالشكل اللي عندنا تمام؟ يبقى + +775 +01:25:02,150 --> 01:25:08,640 +التسع اللي برا هذه المعهادلو أخدت اتنين و تلاتين + +776 +01:25:08,640 --> 01:25:14,160 +على تلاتة عام المشترك اتنين و تلاتين بيظل اربعة و + +777 +01:25:14,160 --> 01:25:18,800 +ستين بدي أشيل منهم جداش تمانية بصير جداش ستة و + +778 +01:25:18,800 --> 01:25:25,360 +خمسين يبقى ستة و خمسين خلصت من هذه و هذه نجل هذه + +779 +01:25:25,360 --> 01:25:33,780 +زائد اتنين على خمسة في اتنين و تلاتينتنين و تلاتين + +780 +01:25:33,780 --> 01:25:39,800 +هذه اللي بيظل ست عشر في اتنين هذه مضروبة في اربع + +781 +01:25:39,800 --> 01:25:45,080 +يعني ست عشر في ست عشر في اربع يبقى بتاخد اتنين و + +782 +01:25:45,080 --> 01:25:53,480 +تلاتين بيظل ست عشر في اتنين يبقى هذه بيظل اخدنا + +783 +01:25:53,480 --> 01:25:57,680 +اتنين على خمسة و ست عشر في اتنين بيظل اتنين و + +784 +01:25:57,680 --> 01:26:05,430 +تلاتينتنين و تلاتين وهذه اتنين على خمسة زائد واحد + +785 +01:26:05,430 --> 01:26:10,590 +طبعا اه استنى شوية هذه ناقص وهذه زائد لا لا استنى + +786 +01:26:10,590 --> 01:26:20,690 +شوية استنى شوية هذه أخدنا ناقص عام المشترك بظل + +787 +01:26:20,690 --> 01:26:27,350 +اتنين على خمسة وهذه في اتنين و تلاتين بظل اتنين و + +788 +01:26:27,350 --> 01:26:36,260 +تلاتينناقص واحد تمام؟ يبقى هي يقفلنا يبقى هذه + +789 +01:26:36,260 --> 01:26:45,060 +تساوي تسعة برة و هنا لو أخدنا اتنين و تلاتين عامل + +790 +01:26:45,060 --> 01:26:51,970 +مشتركمن الشجتين يبقى بصير اتنين و تلاتين عامل + +791 +01:26:51,970 --> 01:26:57,390 +مشترك في جوس بقى لدي ستة و خمسين على تلاتة يبقى + +792 +01:26:57,390 --> 01:27:07,630 +ستة و خمسين على تلاتة ناقص اتنين في واحد و تلاتين + +793 +01:27:07,630 --> 01:27:13,590 +على خمسةالشكل اللي عندنا هذا احسبه جد ما يطلع + +794 +01:27:13,590 --> 01:27:19,270 +الجواب عندك يطلع مش مشكلتنا هاي بساطنا هالك للاخر + +795 +01:27:19,270 --> 01:27:30,010 +أقل + +796 +01:27:30,010 --> 01:27:36,710 +من عشرة كل + +797 +01:27:36,710 --> 01:27:42,420 +شي أقل من عشرةطيب هذا كان المثال رقم اربع المثال + +798 +01:27:42,420 --> 01:27:50,820 +رقم خمسة تكامل من zero لغاية πاية على اتنين لصين + +799 +01:27:50,820 --> 01:28:00,160 +ال X على تلاتة زائد اتنين كوصين ال X الكل تربيع DX + +800 +01:28:00,160 --> 01:28:07,540 +خلونا ندرك هنا المشكلة وين؟ في الغصب ولا المقام + +801 +01:28:08,780 --> 01:28:15,420 +يبقى بدي أحط ال Y يسوى تلاتة زائد اتنين Cos X يبقى + +802 +01:28:15,420 --> 01:28:22,220 +Dy سالب اتنين Sin X في DX يبقى هذا الكلام بدي + +803 +01:28:22,220 --> 01:28:30,040 +أعطيك سالب نص Dy بدي أسوى Sin X في DX يبقى هذا + +804 +01:28:30,040 --> 01:28:38,460 +الكلام بدي أسوى سالب نص تكامل لمين لDY على Y تربية + +805 +01:28:39,050 --> 01:28:40,870 +ده قوة حدود التكامل + +806 +01:28:53,020 --> 01:28:58,500 +يبقى بضيع إشارة السلب و بغير حدود التكامل يبقى نص + +807 +01:28:58,500 --> 01:29:05,080 +تكامل من تلاتة إلى خمسة الى y اقص ناقص اتنين dy + +808 +01:29:05,080 --> 01:29:13,720 +يبقى هنا نص و هنا سلب واحد على y من تلاتة لغاية + +809 +01:29:13,720 --> 01:29:24,850 +كدهش خمسة يبقى هنا ناقص نص برةفي خمس ناقص طول هذا + +810 +01:29:24,850 --> 01:29:31,770 +الكلام كله بده يساوي ناقص نص كله على خمستاشر فيها + +811 +01:29:31,770 --> 01:29:41,190 +تلاتة ناقص خمسة يبقى ناقص نص في ناقص اتنين على + +812 +01:29:41,190 --> 01:29:50,570 +قداش على خمستاشر يبقى الجواب واحد على خمستاشرسؤال + +813 +01:29:50,570 --> 01:30:03,270 +للشادس بيقوللي تكامل من zero لغاية pi على ستة لكو + +814 +01:30:03,270 --> 01:30:12,010 +سايل و سالب تلاتة للي اتنين theta سايل اتنين theta + +815 +01:30:12,010 --> 01:30:14,410 +في دي theta + +816 +01:30:30,790 --> 01:30:35,590 +عشان اقص المشكلة فيها مش في الـSin لان مرفوع الأقص + +817 +01:30:35,590 --> 01:30:40,370 +سالب ثلاثة يعني سين اتنين ثيتا على كوسين تكييب + +818 +01:30:40,370 --> 01:30:44,090 +اتنين ثيتا اذا بدي اشيل كوسين واحطها باي variable + +819 +01:30:44,090 --> 01:30:52,960 +جديدلو حطيت ال T تساوي و لا بلاش T حط ال X المرة + +820 +01:30:52,960 --> 01:31:06,030 +هذه يساوي Cos 2θ يبقى DX بسالب 2Sin 2θ Dθتفارق + +821 +01:31:06,030 --> 01:31:12,290 +cosine بالسالب sin ده بتفادل الزاوية يبقى سالب نص + +822 +01:31:12,290 --> 01:31:19,030 +dx يبدو يساوي sin اتنين ثيتا في d + +823 +01:31:21,860 --> 01:31:26,480 +يبقى هذا الكلام كله بده يشيل وقته بداله سالب نص + +824 +01:31:26,480 --> 01:31:32,580 +يبقى سالب نص خلّيه برا وهي التكامل هذا حطينه بداله + +825 +01:31:32,580 --> 01:31:40,980 +X و سالب تلتة وهذا كله بده يجي بداله قداش DX بقيت + +826 +01:31:40,980 --> 01:31:48,720 +حدود التكامل بدي أحط θ ب 30 درجة 30 في 2 ب 60 جتة + +827 +01:31:48,720 --> 01:31:50,760 +60 له ب نص + +828 +01:31:57,940 --> 01:32:03,530 +الرقم الكبير تحت والصغيرفوق يبقى من شكل بحدود + +829 +01:32:03,530 --> 01:32:09,790 +التكامل وبنضيع الإشارة تبقى للخواص يبقى هذا نص + +830 +01:32:09,790 --> 01:32:17,970 +تكامل من نص لغاية واحد لل X أس ناقص ثلاثة في DX + +831 +01:32:17,970 --> 01:32:25,790 +يسوى نص مالكش داوة و X أس ناقص اتنين على ناقص + +832 +01:32:25,790 --> 01:32:31,190 +اتنين من عند النص لغاية مين لغاية الواحد + +833 +01:32:36,440 --> 01:32:45,360 +نقص ربع 1 على X تربيع من عند النص لغاية الواحد + +834 +01:32:45,360 --> 01:32:53,750 +يبقى يساوي ناقص ربع فيواحد على واحد تربية اللي هو + +835 +01:32:53,750 --> 01:33:01,470 +بواحد ناقص اللي هو مين واحد على نص تربية اللي هو + +836 +01:33:01,470 --> 01:33:12,760 +بربع يبقى ناقص ربع في واحد ناقص أربعبضل قداش ناقص + +837 +01:33:12,760 --> 01:33:20,120 +تلاتة يبقى هذا ناقص ربع فناقص تلاتة يبقى الجواب + +838 +01:33:20,120 --> 01:33:23,200 +قداش تلاتة أربعة + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3gx5rcf4Qwo.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3gx5rcf4Qwo.srt new file mode 100644 index 0000000000000000000000000000000000000000..e5cc27a4a5af9f1049e4f4c9c57aaa1a816c78fb --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3gx5rcf4Qwo.srt @@ -0,0 +1,2799 @@ +1 +00:00:22,140 --> 00:00:25,360 +بسم الله الرحمن الرحيم نعود للـ section اللي + +2 +00:00:25,360 --> 00:00:29,220 +ابتدأناه المرة الماضية وكان موضوعنا هو الـ extreme + +3 +00:00:29,220 --> 00:00:33,580 +values of a function القيم القصوى أو القيم + +4 +00:00:33,580 --> 00:00:37,880 +المتطرفة لدالة ما طبعا المرة اللي فاتت أخذنا الـ + +5 +00:00:37,880 --> 00:00:41,860 +absolute maximum و الـ absolute minimum و عرفنا + +6 +00:00:41,860 --> 00:00:45,380 +الـ absolute maximum أقصى قيمة بتاخدها الدالة على + +7 +00:00:45,380 --> 00:00:49,700 +كل الـ domain تبعها والـ Absolute minimum أقل قيمة + +8 +00:00:49,700 --> 00:00:52,940 +بتاخدها الدالة على كل الـ domain تبعها هذا اللي + +9 +00:00:52,940 --> 00:00:56,000 +أتعرضنا عليه المرة الماضية ولاقي أن الـ absolute + +10 +00:00:56,000 --> 00:00:59,800 +maximum أو الـ absolute minimum قد يحدث at interior + +11 +00:00:59,800 --> 00:01:04,100 +point عند نقطة داخلية في الـ domain وقد يكون عند الـ + +12 +00:01:04,100 --> 00:01:08,260 +end point باهمني سواء كانت هذه ولا هذه المهمة أن + +13 +00:01:08,260 --> 00:01:12,720 +عندي absolute maximum و absolute minimum لدالة ما + +14 +00:01:12,720 --> 00:01:17,280 +لم تكن constant function إذا كانت الـ function ليس + +15 +00:01:17,280 --> 00:01:21,340 +لديه أبسلوت ماكسما أو أبسلوت مينيموم، لكن ما خلى + +16 +00:01:21,340 --> 00:01:24,640 +ذلك إذا دلّا دلّا متصلة لازم يكون فيها لديها + +17 +00:01:24,640 --> 00:01:27,860 +أبسلوت ماكسما أو أبسلوت مينيموم على الـ domain + +18 +00:01:27,860 --> 00:01:34,330 +تبعها طيب نجي لتعريف جديد بدنا الـ local maximum و + +19 +00:01:34,330 --> 00:01:38,990 +الـ local minimum بدنا نقرّع كويس و نقارن بين هذا الـ + +20 +00:01:38,990 --> 00:01:43,130 +definition و الـ definition تبع المرة الماضية نقرأ + +21 +00:01:43,130 --> 00:01:46,390 +هذا الـ definition ثم نعود لـ definition المرة + +22 +00:01:46,390 --> 00:01:51,430 +الماضية بيقول الـ F has a local maximum أو local + +23 +00:01:51,430 --> 00:01:56,510 +minimum value at an interior point يبقى احنا الآن + +24 +00:01:56,510 --> 00:02:01,980 +مالناش علاقة بمين؟ بنتكلم عند الـ interior points + +25 +00:02:01,980 --> 00:02:06,740 +النقاط الداخلية للـ domain at interior point C + +26 +00:02:06,740 --> 00:02:11,200 +اللي موجودة في الـ domain الدالة F إذا F of X أقل + +27 +00:02:11,200 --> 00:02:16,440 +من أو يساوي F of C فـ F of C مالها أكبر ما يمكن ايش + +28 +00:02:16,440 --> 00:02:21,580 +بسميها local maximum أقل ما يمكن F of C أقل من + +29 +00:02:21,580 --> 00:02:33,260 +بسوين for all x in some open interval containing c + +30 +00:02:33,260 --> 00:02:39,080 +على فترة containing c طيب فلّع لي في تعريف المرة + +31 +00:02:39,080 --> 00:02:44,400 +الماضية أول definition في section 4-1 من المحاضرة + +32 +00:02:44,400 --> 00:02:51,380 +الماضية أول definition فاللي هقراه كويس و بنشوف هل + +33 +00:02:51,380 --> 00:02:54,920 +التعريف ده هو نفس تعريف المرة الماضية والله + +34 +00:02:54,920 --> 00:02:59,640 +بيختلف عنه وإذا بيختلف عنه ما وجه الاختلاف بين + +35 +00:02:59,640 --> 00:03:04,980 +التعريفين بس اقراه كويس وبعدين بنسأل اقراه كويس + +36 +00:03:05,710 --> 00:03:09,910 +definition المرة الماضية أول تعريف في بداية + +37 +00:03:09,910 --> 00:03:16,690 +المحاضرة في أول definition في section 4-1 آه في + +38 +00:03:16,690 --> 00:03:20,670 +فروقات ما بين التعريفين في اثنين وافعلوا يديهم + +39 +00:03:20,670 --> 00:03:26,630 +ثلاثة أربعة أيوة بدنا كمان نفكر كويس ونطلع في + +40 +00:03:26,630 --> 00:03:30,750 +فروقات ولا فيش فروقات إذا فيش فروقات بلاش خدوا نمشي + +41 +00:03:30,750 --> 00:03:36,040 +ولا في فروقات بدنا نعرفها آه يا ابن التعريف اللي + +42 +00:03:36,040 --> 00:03:40,280 +اجمالي اتقالت فيني تعريف من خلاله كله يعطوني الـ + +43 +00:03:40,280 --> 00:03:44,580 +absolute maximum و الـ absolute minimum والشرطة أن + +44 +00:03:44,580 --> 00:03:48,960 +كل الـ F اللي اجت للـ absolute maximum أكبر F + +45 +00:03:48,960 --> 00:03:49,340 +السيارة + +46 +00:03:55,290 --> 00:04:00,930 +هذه الجزء محلول منها ممتاز جدا يبقى أولا هذه تتكلم + +47 +00:04:00,930 --> 00:04:05,870 +عن النقاط الداخلية فقط هذه الفرق الأول أنك ما قلتش + +48 +00:04:05,870 --> 00:04:09,690 +intro point أنك قلنا على كل domain تبعه سواء كانوا + +49 +00:04:09,690 --> 00:04:13,490 +intro points أو end points سواء كان طرفي الـ + +50 +00:04:13,490 --> 00:04:17,690 +interval أو أي نقطة داخلية تمام؟ هنا قال لي لأ أنت + +51 +00:04:17,690 --> 00:04:20,270 +بتتكلم على نقطة داخلية في الـ domain + +52 +00:04:42,270 --> 00:04:47,740 +تعالى نشوف الفرق هذا على الرسم فلّع لي الرسم اللي + +53 +00:04:47,740 --> 00:04:53,120 +عنده، لو جيت عند النقطة C1 هذه، بدأ أخذ open + +54 +00:04:53,120 --> 00:04:57,120 +interval حواليها ضمن الـ domain، الـ domain من أين؟ + +55 +00:04:57,120 --> 00:05:03,000 +من هنا، بيبقى أنا أخذ جزء من الـ domain حوالي + +56 +00:05:03,000 --> 00:05:05,400 +النقطة C، الجزء الأحمر الـ interval + +57 +00:05:11,270 --> 00:05:16,830 +طيب بدأ أجي طالع لغاية ما قابل المنحنى تبعد + +58 +00:05:16,830 --> 00:05:22,130 +لجابلته هنا وهنا جاي الطالع جابلته هنا يبقى جابلته + +59 +00:05:22,130 --> 00:05:26,360 +هنا خلال الفترة اللي عندنا هذه، الفترة الحمراء اللي + +60 +00:05:26,360 --> 00:05:30,740 +أنتوا شايفينها، باجي أطالع فوق، بلاقي إن قيمة + +61 +00:05:30,740 --> 00:05:37,740 +الدالة F of C1 أكبر من أي قيمة حواليها، تمام؟ يبقى + +62 +00:05:37,740 --> 00:05:42,020 +هذه لوكلية local maximum من هنا قلنا هذه local + +63 +00:05:42,020 --> 00:05:47,940 +maximum and when عندي الـ C1 طيب تمام بدي أجي عند + +64 +00:05:47,940 --> 00:05:54,760 +الـ C2 هاي الـ C2 بدي أخذ open interval حارف وأجي + +65 +00:05:54,760 --> 00:06:00,660 +طالع بالسلامة هيك وأجي طالع من هناك + +66 +00:06:04,090 --> 00:06:09,490 +الدالة هنا بتاخد أقل قيمة خلال الفترة هذه لو + +67 +00:06:09,490 --> 00:06:14,270 +الـ Sum Opinent الجزء من الـ domain أخذت أقل ما + +68 +00:06:14,270 --> 00:06:22,150 +يمكن يبقى عند C2 الدالة بتاخد local minimum كويس طب + +69 +00:06:22,150 --> 00:06:26,630 +و الآن بدي أجي عند الـ C3 بدي أخذ open interval + +70 +00:06:26,630 --> 00:06:32,910 +حوالين الـ C3 وأجي طالع لغاية ما قابل المنحنى اللي + +71 +00:06:32,910 --> 00:06:37,870 +عندنا ومن هنا جيت طالع لغاية ما قابل المنحنى اللي + +72 +00:06:37,870 --> 00:06:44,330 +عندنا قابلته هنا وهنا إذا هنا الدالة بتاخد أكبر قيمة + +73 +00:06:44,330 --> 00:06:49,230 +من القيم اللي حواليها، يبقى هذه الـ local maximum، + +74 +00:06:49,230 --> 00:06:53,810 +طيب، بدا جهنم دي الـ C4، لسه ما تكلمتش، أنا ما تكلمت في + +75 +00:06:53,810 --> 00:06:58,050 +الـ local فقط، لما يخلص، بعدين بنرجع، نربط الكلام + +76 +00:06:58,050 --> 00:07:02,590 +هذا بالكلام العتيق بدي أجي الـ C4 بدي أخذ open + +77 +00:07:02,590 --> 00:07:06,750 +interval حواليها جد ما تكون الـ open interval تكون + +78 +00:07:06,750 --> 00:07:11,850 +قابلة المنحنى وهنا جهة طالع برضه قابلة المنحنى + +79 +00:07:11,850 --> 00:07:16,710 +هنا عندهم نقطتين لكن هنا ها ها الدنيا بتاخد أقل + +80 +00:07:16,710 --> 00:07:21,430 +قيمة لها خلال الفترة اللي عندنا هذه يبقى هذه local + +81 +00:07:21,430 --> 00:07:26,390 +minimum يبقى local minimum شو صار عندي؟ صار عندي + +82 +00:07:26,390 --> 00:07:28,050 +المنحنى على الشكل التالي + +83 +00:07:36,700 --> 00:07:42,380 +الأربع نقاط كلهم نقاط داخلية ما اتكلمتش لا عند أول + +84 +00:07:42,380 --> 00:07:48,260 +نقطة ولا عند آخر نقطة حتى الآن يبقى أن كل النقاط + +85 +00:07:48,260 --> 00:07:49,180 +الداخلية + +86 +00:07:52,530 --> 00:07:56,390 +أقل من F of C يعني F of C أكبر من الكل Local + +87 +00:07:56,390 --> 00:08:01,770 +Minimum إذا F of C أقل من الكل and some open + +88 +00:08:01,770 --> 00:08:06,430 +interval حوالي النقطة C اللي عندنا هذه تمام إذا + +89 +00:08:06,430 --> 00:08:09,850 +اللي جت عندي Local Minimum بدل الواحدة اثنين و + +90 +00:08:09,850 --> 00:08:13,930 +Local Maximum بدل الواحدة اثنين هدف الـ interior + +91 +00:08:13,930 --> 00:08:19,700 +points لكن ضال من عندنا طرفين بقول كويس ندي بدنا + +92 +00:08:19,700 --> 00:08:23,700 +نعرف عند الطرفين فيه أن دي local maximum ولا local + +93 +00:08:23,700 --> 00:08:28,180 +minimum حط أن هذا في صيغة الـ remark التالية قلت لو + +94 +00:08:28,180 --> 00:08:32,600 +كانت الدالة دالة متصلة على الـ closed interval a و b + +95 +00:08:32,600 --> 00:08:37,760 +النقطة الأولى الـ F has a local minimum local + +96 +00:08:37,760 --> 00:08:44,240 +minimum إذا F of X أكبر من أو تساوي من F of A وين F + +97 +00:08:44,240 --> 00:08:49,270 +of A هيهذه المسافة F of a بدي أجي ألاقي interval + +98 +00:08:49,270 --> 00:08:53,530 +حواليها من جهة اليسار ما عنديش يبقى بروح من وين من + +99 +00:08:53,530 --> 00:08:59,210 +جهة اليمين من عند الـ a بقول لو المسافة من هنا لهنا + +100 +00:08:59,210 --> 00:09:04,130 +سميتها delta يبقى إحداثي النقطة عادي بيصير جداش يا + +101 +00:09:04,130 --> 00:09:11,790 +شباب a زائد delta يبقى بدي أجي أطلع رأسي ات لغاية + +102 +00:09:11,790 --> 00:09:19,890 +هنا صارت هنا أقل قيمة للدالة خلال الفترة من a لغاية + +103 +00:09:19,890 --> 00:09:23,810 +a زائد دلتا يبقى هذه اللي بتكون الـ local minimum + +104 +00:09:23,810 --> 00:09:29,130 +يبقى بعدي بقوله إن النقطة هذه if has local minimum + +105 +00:09:29,130 --> 00:09:34,780 +عند x يساوي a إذا كان الـ F of A أقل من أو يساوي الـ F + +106 +00:09:34,780 --> 00:09:40,300 +of X أو الـ F of X أكبر من أو يساوي F of A لكل الـ X + +107 +00:09:40,300 --> 00:09:43,920 +اللي موجودة في الـ Interval من عند الـ A لغاية A + +108 +00:09:43,920 --> 00:09:48,280 +زائد Delta من عند الـ A مغلقة لأنه جاب اللي ما عنديش + +109 +00:09:48,280 --> 00:09:51,740 +ومن عند الـ A زائد Delta خلتها فترة مفتوحة Delta + +110 +00:09:51,740 --> 00:09:54,680 +جاب داشت جات ما بدأت أخذها واحد من عشرة اثنين من + +111 +00:09:54,680 --> 00:09:58,880 +عشرة واحد صحيها اثنين زي ما بده أخذ الفترة اللي بدك + +112 +00:09:58,880 --> 00:10:03,600 +بس بحيث ما تصطدمش بواحدة ثانية، تبقى القبلة جد ما + +113 +00:10:03,600 --> 00:10:08,810 +بده أخذ هذه، تمام؟ طيب، هذا لو كان ايش؟ Local من، + +114 +00:10:08,810 --> 00:10:13,410 +لو كان Local maximum، بدي يكون الـ F of X أقل من أو + +115 +00:10:13,410 --> 00:10:18,490 +يساوي الـ F of A، يعني الـ F of A أكبر ممتازة، أنا + +116 +00:10:18,490 --> 00:10:21,790 +ما عندي شيء، أنا عندي أقل، يبقى اللي بين جثين غير + +117 +00:10:21,790 --> 00:10:25,770 +متحقق عند النقطة مين يساوي A، بس أنا حاطيته لأنه + +118 +00:10:25,770 --> 00:10:28,550 +احتمال مش تبقى جاية من تحت المال، تبقى جاية من + +119 +00:10:28,550 --> 00:10:33,610 +فوق، صحيح ولا لا؟ تمام طب نيجي للنقطة الثانية عند + +120 +00:10:33,610 --> 00:10:39,330 +النقطة B الـ F has a local maximum عند الـ X يساوي + +121 +00:10:39,330 --> 00:10:45,410 +بيه الـ F of X أقل من أو يساوي F of B طلع لي هاي الـ + +122 +00:10:45,410 --> 00:10:51,070 +B أنا بيداجي جاب لي الـ B يبقى من هنا يبقى هذه النقطة + +123 +00:10:51,070 --> 00:10:57,610 +الإحداثي تبعها بـ - Delta صحيح ولا لأ؟ يبقى من عند + +124 +00:10:57,610 --> 00:11:02,130 +الـ B مغلقة ومن عند الـ B نقص Delta مفتوحة وجاء + +125 +00:11:02,130 --> 00:11:08,560 +الطلب السلامة هيك قابلت المنحنى هنا يبقى صارت + +126 +00:11:08,560 --> 00:11:14,000 +القيمة هي الحمراء اللي فوق عندها دي مالها أكبر ما + +127 +00:11:14,000 --> 00:11:20,620 +يمكن يبقى بيصير local maximum إذا أنا حددت الـ + +128 +00:11:20,620 --> 00:11:24,220 +local maximum و الـ local minimum على الـ closed + +129 +00:11:24,220 --> 00:11:28,850 +interval ايه بيبتدأ بالـ interior points وانتهيت + +130 +00:11:28,850 --> 00:11:33,930 +بمين؟ بالـ end points يبقى هذا كل اللي اتكلمته لسه + +131 +00:11:33,930 --> 00:11:37,190 +في الـ local maximum و الـ local minimum عرفنا شو + +132 +00:11:37,190 --> 00:11:42,190 +وضعه على الـ interior point وعرفنا شو وضعه على الـ end + +133 +00:11:42,190 --> 00:11:47,270 +point تمام؟ وكل زي ما أنت شايف فيه عند كل نقطة + +134 +00:11:47,270 --> 00:11:47,590 +بأخذ + +135 +00:11:52,500 --> 00:11:56,580 +بنرجع بالذاكرة لتعريف المرة الماضية + +136 +00:12:01,620 --> 00:12:07,960 +الـ domain تبعها ممتاز الـ domain من A إلى B أكبر + +137 +00:12:07,960 --> 00:12:12,200 +قيمة اللي عندي هذه فوق يبقى هذه قلت absolute + +138 +00:12:12,200 --> 00:12:17,020 +maximum يبقى الـ local maximum و absolute maximum + +139 +00:12:17,020 --> 00:12:21,180 +في نفس الوقت طبعا فبتدور أشوف في absolute minimum + +140 +00:12:21,180 --> 00:12:26,690 +ولا لأ بجعل منحنى بلاقي النقطة هذه أقل ما يمكن، لو + +141 +00:12:26,690 --> 00:12:31,090 +يوجد قيمة للدالة أقل منها، يبقى هذه كمان absolute + +142 +00:12:31,090 --> 00:12:36,990 +ما لها minimum لهذه الدالة، إذا ربطنا كلام المرة + +143 +00:12:36,990 --> 00:12:41,210 +الماضية بالمرة هذه، هذه المرة هي بيجي تأخذ مناطق + +144 +00:12:41,210 --> 00:12:46,710 +أو نقطة موضعية open interval، شغلة موضعية حوالي + +145 +00:12:46,710 --> 00:12:52,380 +النقطة حدات منها الـ local maximum، يعني قيمة عظمى أو + +146 +00:12:52,380 --> 00:12:56,480 +صغيرة محلية، لما أقول محلية يعني في منطقة دون + +147 +00:12:56,480 --> 00:13:00,340 +الأخرى من الـ domain تبع الدالة، لكن لما أقول + +148 +00:13:00,340 --> 00:13:03,480 +absolute maximum و absolute minimum، بدي أدور أكبر + +149 +00:13:03,480 --> 00:13:08,120 +قيمة على الفترة كل المعرف عليها الدالة، وأقل قيمة + +150 +00:13:08,120 --> 00:13:11,520 +على كل الفترة المعرف عليها الدالة، شايف شو الفرق + +151 +00:13:11,520 --> 00:13:17,690 +ما بين الاثنين؟ فرق شاسع، إذا كل absolute maximum + +152 +00:13:17,690 --> 00:13:22,950 +أو absolute minimum هي local maximum أو local + +153 +00:13:22,950 --> 00:13:30,270 +minimum، لكن العكس ليس بالضرورة صحيحا، تمام؟ طيب، + +154 +00:13:30,270 --> 00:13:34,090 +هذا لغاية، هذا لغاية النقطة هذه، تعالى شوف النظرية + +155 +00:13:34,090 --> 00:13:39,510 +هذه، ايش بتقول؟ النظرية بيقول لو كان الـ F لديه + +156 +00:13:39,510 --> 00:13:44,090 +local maximum أو local minimum value عند interior + +157 +00:13:44,090 --> 00:13:50,730 +point موجودة في دومين الدالة وكانت المشتقة معرفة + +158 +00:13:50,730 --> 00:13:55,350 +عندها، لازم تكون المشتقة عند هذه النقطة تساوي كده + +159 +00:13:55,350 --> 00:14:01,610 +تساوي zero أنا قرأت النظرية بالعربي وشوفوا قراءتي + +160 +00:14:01,610 --> 00:14:06,810 +هذه صح والله خطأ أنا لما قرأتها فهمت ما هي.. بدي + +161 +00:14:06,810 --> 00:14:11,990 +أروح أجيب الدالة وأشتقها أشتقها ولو أشتقها بدي + +162 +00:14:11,990 --> 00:14:15,250 +أشوف ما هي القيمة اللي عند المشتقة تساوي zero + +163 +00:14:15,250 --> 00:14:19,370 +القيمة اللي عندك تشتقها تبقى تساوي zero بتبقى هي + +164 +00:14:19,370 --> 00:14:23,750 +local maximum أو local minimum قراءتك صح ولا غلط؟ + +165 +00:14:23,750 --> 00:14:30,710 +عين الخطأ أنت قلبت الموضوع مئة وثمانين درجة الدالة + +166 +00:14:30,710 --> 00:14:33,790 +ما قالتش هيك، الدالة بتاعت نظرية ما قالتش هيك هذا + +167 +00:14:33,790 --> 00:14:39,870 +مفهوم خاطر طب بدنا نقرأ صح بقوله آه الدالة لو كان + +168 +00:14:39,870 --> 00:14:45,430 +لها local maximum أو local minimum إن وجد الـ local + +169 +00:14:45,430 --> 00:14:50,090 +maximum و الـ local minimum لهذه الدالة كان موجود + +170 +00:14:50,090 --> 00:14:57,690 +تمام ممتاز جدا، من المشتقة عند هذه المواقع المعرفة + +171 +00:14:58,020 --> 00:15:03,240 +الحدث ذلك يجب أن تكون المشتقة تساوي كده؟ zero شو + +172 +00:15:03,240 --> 00:15:08,340 +يعني المشتقة تساوي zero؟ يعني المماس للمنحنى + +173 +00:15:08,340 --> 00:15:14,640 +يكونوا أفقيا موازن لمحورك تعالى نشوف كلامنا هذا + +174 +00:15:14,640 --> 00:15:19,400 +على الطبيعة صحيح ولا لأ أنا عند هنا ايش قلت؟ Local + +175 +00:15:19,400 --> 00:15:26,610 +maximum لو جيت رسمت مماس يبقى هذا م + +201 +00:18:04,450 --> 00:18:07,550 +value له ال function مش هي كتبنا اللي لعلوان المرة + +202 +00:18:07,550 --> 00:18:11,110 +اللي فاتت فهيبقى بدنا نيجي لل extreme values هذه + +203 +00:18:11,110 --> 00:18:15,450 +بيقول لي دلّا if has extreme values only in the + +204 +00:18:15,450 --> 00:18:19,720 +following places وانا روح ادور على ال extreme + +205 +00:18:19,720 --> 00:18:24,780 +values لمين لهذه الدالة، القيم القصوى لمين لهذه + +206 +00:18:24,780 --> 00:18:29,340 +الدالة، فبقوللي في ثلاثة مواقع، الموقع الأول عند + +207 +00:18:29,340 --> 00:18:34,770 +النقاط الداخلية للمشتقة عندها يسوى وين؟زيرو فعلا + +208 +00:18:34,770 --> 00:18:41,330 +هاي C1 وC2 وC4 يبقى هاي المواقع اللي المشتقة عندها + +209 +00:18:41,330 --> 00:18:46,410 +تسوى Zero إذا هادي Extreme value عند C1 و Extreme + +210 +00:18:46,410 --> 00:18:52,010 +value عند C2 و Extreme value عند C4 النقطة الأولى + +211 +00:18:52,010 --> 00:18:55,990 +النقطة الثانية بدك interior point بهاي المشتقة + +212 +00:18:55,990 --> 00:19:00,910 +عندها مالها غير معرفة يبقى باجبيه عندها C3 هل + +213 +00:19:00,910 --> 00:19:07,090 +المشتقة لأ يبقى هاي أربعة extreme values تلاتة + +214 +00:19:07,090 --> 00:19:11,830 +المشتقة عندهم معرفة وتساوي zero الرابعة المشتقة + +215 +00:19:11,830 --> 00:19:19,190 +عندهم ما لا غير معرفة خلصنا؟ ما خلصناش لسه نقطة + +216 +00:19:19,190 --> 00:19:23,030 +تالتة بيقول ال end points of the domain of + +217 +00:19:23,030 --> 00:19:28,100 +function إذا عندك closed interval أو closed من شجة + +218 +00:19:28,100 --> 00:19:32,260 +و open من شجة تانية بدك تروح عندك closed تحسب قيم + +219 +00:19:32,260 --> 00:19:38,360 +الدالة لأن ده اعتبر قيم متطرفة إذا القيم المتطرفة + +220 +00:19:38,360 --> 00:19:43,340 +للدالة هي القيم اللي بتكون عندها طرفي ال interval + +221 +00:19:43,340 --> 00:19:48,420 +وكذلك إذا المشتقة عندها تساوي zero أو المشتقة + +222 +00:19:48,420 --> 00:19:52,340 +بتكون مالها غير معرفة يبقى من دور على ال extreme + +223 +00:19:52,340 --> 00:19:58,080 +values في ثلاثة مواعِظ، ادر بالك اه، ركزي كويس، + +224 +00:19:58,080 --> 00:20:01,860 +بعد شوية بدنا ناخد أمثلة على ذلك، بدروح أدور وين + +225 +00:20:01,860 --> 00:20:07,570 +ال extreme values، بدأ اشتقو ساوي ب Zero واطلع قيم + +226 +00:20:07,570 --> 00:20:13,090 +X اللى بتخلى المشتقة تساوي Zero اتنين بدى أدور على + +227 +00:20:13,090 --> 00:20:19,870 +القيم اللى بتخلى المشتقة غير معرفة تلاتة بروح أدور + +228 +00:20:19,870 --> 00:20:24,250 +ورا على الانفوس بكون جبتله Extreme values طبعا + +229 +00:20:24,250 --> 00:20:29,110 +يبقى هاية كل الكلام النظري حاطنا على الرسمة تبعتنا + +230 +00:20:29,110 --> 00:20:31,090 +أجاني التعريف تاني + +231 +00:20:48,600 --> 00:20:55,540 +ماذا يعني نقاط حرجة لدالة؟ + +232 +00:20:57,490 --> 00:21:03,110 +اللي المشتقة عندها تساوي Zero أو المشتقة عندها بس + +233 +00:21:03,110 --> 00:21:09,150 +in third point مش الأقراف يعني لو جينا سألنا حالنا + +234 +00:21:09,150 --> 00:21:14,850 +من خلال الرسم اللي عندنا ما هي ال critical points + +235 +00:21:14,850 --> 00:21:22,930 +بقولوا قداشر؟ أربعوC2 وC4 المشتقة عندها تساوي Zero + +236 +00:21:22,930 --> 00:21:29,510 +C3 المشتقة عندها Undefined يبقى هدول الأربعة هم ال + +237 +00:21:29,510 --> 00:21:35,050 +critical point نواصل ما كنا نتحدث به ونحاول أن + +238 +00:21:35,050 --> 00:21:40,110 +نجمل ال remark و ال definition بإتنين بمعلومة نجمل + +239 +00:21:40,110 --> 00:21:43,440 +اتنين بالمعلومة التالية المعروف بالتالية يقول from + +240 +00:21:43,440 --> 00:21:47,500 +the above remark and definition هاي ال remark و + +241 +00:21:47,500 --> 00:21:51,380 +هاي ال definition ايش بيقول هذا؟ we say that أن + +242 +00:21:51,380 --> 00:21:55,700 +the extreme values of هالحطلك بكلام في الملاحظة + +243 +00:21:55,700 --> 00:22:03,680 +التالية remark the + +244 +00:22:03,680 --> 00:22:15,280 +function the function f may have may have a + +245 +00:22:15,280 --> 00:22:25,820 +critical point may have a critical point at x + +246 +00:22:25,820 --> 00:22:38,280 +يساوي c and this point وهذه النقطة need not be + +247 +00:22:44,030 --> 00:22:56,470 +بـ Local Extreme Value مثال + +248 +00:22:56,470 --> 00:23:04,530 +شوف + +249 +00:23:04,530 --> 00:23:11,360 +يا سيدي بتقول ليه؟الدالة F ممكن يكونها critical + +250 +00:23:11,360 --> 00:23:17,240 +point عند X يساوي C لكن هذه النقطة ليست بالضرورة + +251 +00:23:17,240 --> 00:23:21,360 +أن تكون extreme value احنا نقول extreme value + +252 +00:23:21,360 --> 00:23:27,310 +المشتقة عندها بال zero أو غير معرفة أو end point + +253 +00:23:27,310 --> 00:23:31,170 +طبعا هنا بيقولوا لو عندك critical point ليس + +254 +00:23:31,170 --> 00:23:36,950 +بالضرورة أن تبقى extreme يعني مش كل critical point + +255 +00:23:36,950 --> 00:23:43,070 +هي extreme value لكن العكس طبعا كل value أكتر يجب + +256 +00:23:43,070 --> 00:23:49,170 +أن تكون كراتيكال points بس بشرط ما تكونش in points + +257 +00:23:49,170 --> 00:23:54,650 +طبعا طيب ندى النقطة هذه لو قلت لك خد لل F of X + +258 +00:23:54,650 --> 00:24:00,910 +يساوي X تكعيب اشتغل + +259 +00:24:00,910 --> 00:24:06,650 +يبقى F prime of X يساوي كده؟ تلاتة X تربيع هذه + +260 +00:24:06,650 --> 00:24:08,770 +بتساوي Zero وكتير + +261 +00:24:23,520 --> 00:24:30,290 +السؤال هو هل هي extreme؟ يعني هل عندها local + +262 +00:24:30,290 --> 00:24:36,590 +maximum أو local minimum تعالى نشوف هذا ال F of X + +263 +00:24:36,590 --> 00:24:43,590 +يساوي X تكعيب هذا محور X هذا Y هذه نقطة الأصل اللي + +264 +00:24:43,590 --> 00:24:49,410 +هي Zero لو جيت رسمت المنحنة اللي عندنا ديجيك + +265 +00:24:49,410 --> 00:24:54,770 +المنحنة بالشكل هذا يبقى هذا Y يساوي X تكعيب وين ال + +266 +00:24:54,770 --> 00:25:02,380 +Zero و أيه ال Zero بتاخد open interval حوالين الـ + +267 +00:25:02,380 --> 00:25:08,900 +zero حوالين هذه، مشان يبقى local maximum، بديها + +268 +00:25:08,900 --> 00:25:13,440 +تبقى هذه أكبر قيمة حوالها ومش هتكون local من + +269 +00:25:13,440 --> 00:25:17,000 +الوطني بهذه أقل قيمة في الفترة اللي حوالها، بنقول + +270 +00:25:17,000 --> 00:25:20,820 +والله كويس جينا حوالين ال zero، اللي جت قبل ال + +271 +00:25:20,820 --> 00:25:25,940 +zero قيمة دالة سالمة، بعد ال zero قيمة دالة يعني + +272 +00:25:25,940 --> 00:25:28,920 +هذا ما طلعتش أكتر من اللي حواليها و الله أقل من + +273 +00:25:28,920 --> 00:25:31,920 +اللي حواليها، مظبوط ولا لأ؟ إذا بنفع هذه تبقى + +274 +00:25:31,920 --> 00:25:37,560 +local maximum أو extreme value يبعتلك الله يبقى + +275 +00:25:37,560 --> 00:25:42,320 +من هنا قولنا x الساوية زيرو is a critical point + +276 +00:25:42,320 --> 00:25:51,620 +but ولكن ال x الساوية زيرو is not an extreme + +277 +00:25:53,880 --> 00:26:03,960 +أو Extreme Value لاحظ + +278 +00:26:03,960 --> 00:26:10,560 +أن ال F' موجود وتساوي 0 لكن هذه النقطة Critical + +279 +00:26:10,560 --> 00:26:17,120 +Point لكنها ليست Extreme Point خد هنا مراجعة لو + +280 +00:26:17,120 --> 00:26:27,070 +أخدت F of X يساوي X أس تلت إذا الدالة هي دي ال F is + +281 +00:26:27,070 --> 00:26:35,350 +defined at X يساوي Zero ده لا معرفة صحيح ولا لأ طب + +282 +00:26:35,350 --> 00:26:44,030 +خد F prime of X يبقى تلت X أس سالب تلتين يعني واحد + +283 +00:26:44,030 --> 00:26:51,670 +على تلاتة X أس تلتين هل هذه المشتقة معرفة عند Zero + +284 +00:26:52,460 --> 00:27:00,620 +لأ يبقى هذا بدي اعطيه لإن ال F prime is undefined + +285 +00:27:00,620 --> 00:27:07,820 +at X يساوي Zero المشتقة ماهياش معرفة عند Zero + +286 +00:27:07,820 --> 00:27:14,060 +معناته هذي critical points يبقى سا ال X يساوي Zero + +287 +00:27:14,060 --> 00:27:20,560 +is a critical point but + +288 +00:27:24,220 --> 00:27:30,300 +not an extreme point + +289 +00:27:31,980 --> 00:27:36,380 +تعالى تشوف هذا على الطبيعة يبقى لو جينا احنا رسمنا + +290 +00:27:36,380 --> 00:27:42,040 +هذه الدالة هذا محور X وهذا Y مرت علينا الدالة كتير + +291 +00:27:42,040 --> 00:27:47,040 +قبل ذلك مش اول مرة يبقى الدالة لو روحنا رسمناها + +292 +00:27:47,040 --> 00:27:54,700 +تجيني مش شكل هذا هيك يبقى هذا Y يساوي X أس طول أو + +293 +00:27:54,700 --> 00:27:58,300 +الجذر التالت ل X تمام؟ + +294 +00:28:00,500 --> 00:28:05,020 +يبقى هذا الجذر التالت ناقص اتطلع عند ال zero هو + +295 +00:28:05,020 --> 00:28:10,240 +the open interval حوالين ال zero قبل ال zero + +296 +00:28:10,240 --> 00:28:13,920 +السالب أو بعد ال zero موجبة يعني لا local maximum + +297 +00:28:13,920 --> 00:28:18,500 +ولا local minimum يبقى no extreme value يبقى هذه + +298 +00:28:18,500 --> 00:28:24,580 +ليست extreme value يبقى not extreme point يقول + +299 +00:28:24,580 --> 00:28:31,750 +extreme value وبلاش point يبقى extreme value تمام؟ + +300 +00:28:31,750 --> 00:28:39,830 +يبقى ممكن نقطة تبقى critical point، لكنها ليست + +301 +00:28:39,830 --> 00:28:44,830 +extreme value، هذه الملاحظة اللي بنقولها طيب، بدنا + +302 +00:28:44,830 --> 00:28:51,210 +نطرح السؤال التالي و نحاول أن نضغط الإجابة عليه، + +303 +00:28:51,210 --> 00:28:56,630 +ثم نبدأ إلى أمثلة على كل ما سبق، أمثلة عملية + +304 +00:29:09,010 --> 00:29:22,950 +السؤال بيقول ما يأتي how to find كيف + +305 +00:29:22,950 --> 00:29:34,430 +بدك توجد the absolute extreme + +306 +00:29:34,430 --> 00:29:36,230 +values + +307 +00:29:38,170 --> 00:29:44,510 +of continuous function + +308 +00:29:44,510 --> 00:29:54,350 +on the closed interval a وb الإجابة كالتالية + +309 +00:29:54,350 --> 00:30:02,490 +answer الإجابة + +310 +00:30:02,490 --> 00:30:06,970 +كالتالية النقطة الأولى أحسب + +311 +00:30:10,280 --> 00:30:16,460 +الـ F at all + +312 +00:30:16,460 --> 00:30:26,420 +critical points + +313 +00:30:26,420 --> 00:30:33,820 +نقطة + +314 +00:30:33,820 --> 00:30:35,360 +ثانية والاخيرة + +315 +00:30:39,630 --> 00:30:46,690 +أخذ الأكبر والأكبر + +316 +00:30:46,690 --> 00:30:49,990 +والأكبر + +317 +00:30:49,990 --> 00:30:58,410 +والأكبر + +318 +00:30:58,410 --> 00:31:08,490 +من هذه القيم مثال + +319 +00:31:13,980 --> 00:31:26,380 +أول مثال Find the absolute extreme + +320 +00:31:26,380 --> 00:31:29,640 +values + +321 +00:31:29,640 --> 00:31:38,700 +of the following functions + +322 +00:31:38,700 --> 00:31:41,260 +on + +323 +00:31:45,250 --> 00:31:51,690 +the given interval + +324 +00:31:51,690 --> 00:32:00,550 +given interval and اجرح + +325 +00:32:00,550 --> 00:32:12,940 +the function number a f of x يساوي أربع ناقص X + +326 +00:32:12,940 --> 00:32:20,360 +تربيع و ناقص ثلاثة أقل من أو يساوي X أقل من أو + +327 +00:32:20,360 --> 00:32:22,140 +يساوي الواحد + +328 +00:32:59,100 --> 00:33:03,120 +هاللي موجود .. هاللي موجود بدنا هي + +329 +00:33:07,650 --> 00:33:12,730 +طيب السؤال مرة تانية بقولك كيف بدك توجد ال + +330 +00:33:12,730 --> 00:33:17,030 +absolute extreme values هي جمعك بسيط اللي ما + +331 +00:33:17,030 --> 00:33:22,330 +extreme كنت قولك absolute extrema و سكت انا قولتك + +332 +00:33:22,330 --> 00:33:26,450 +absolute extreme values of continuous function على + +333 +00:33:26,450 --> 00:33:30,710 +الفترة a و b يبقى على الفترة a و b كيف بده اوجد ال + +334 +00:33:30,710 --> 00:33:34,810 +absolute maximum و ال absolute minimum لذلك احنا + +335 +00:33:34,810 --> 00:33:38,570 +المرة اللي فاتت بقينا بنجده من خلال الرسم نرسم + +336 +00:33:38,570 --> 00:33:41,890 +وندور ونأكي على قيمة على رسم أقل قيمة نقول هذه + +337 +00:33:41,890 --> 00:33:44,810 +absolute maximum وهذه absolute minimum الآن بدنا + +338 +00:33:44,810 --> 00:33:49,270 +نستخدم المشتقة في التعرف على وين ال critical + +339 +00:33:49,270 --> 00:33:53,610 +points وين ال extreme values ومن خلالها نجد اللي + +340 +00:33:53,610 --> 00:33:56,450 +هو مين ال absolute maximum و ال absolute minimum + +341 +00:33:56,450 --> 00:34:00,210 +دي بقى بنعمل خطوة تانية أول خطوة بدنا نحسب ال + +342 +00:34:00,210 --> 00:34:02,290 +critical points و ال inputs + +343 +00:34:07,450 --> 00:34:14,010 +أكبر قيمة عند هذه النقاط أكبر قيمة عند هذه النقاط + +344 +00:34:14,010 --> 00:34:21,430 +أكبر قيمة عند هذه النقاط نبدأ نطبق هذا الكلام على + +345 +00:34:21,430 --> 00:34:26,310 +أمثلة متعددة طبعا هذا المثال اللي بين أدينا جليهات + +346 +00:34:26,310 --> 00:34:29,390 +ال absolute extreme values لكل من الدول التالية + +347 +00:34:29,390 --> 00:34:34,070 +على الفترة التي قرسمها هذا السؤال أخدناه المرة + +348 +00:34:34,070 --> 00:34:41,340 +الماضية بنحل الان عمليا مش زي الرسم المرة الماضية + +349 +00:34:41,340 --> 00:34:45,660 +احنا فعلا رسمنا المرة الماضية وكان رسمها على الشكل + +350 +00:34:45,660 --> 00:34:51,920 +التالي هذا محور X هذا محور Y هذا نقطة الاصل Zero + +351 +00:34:51,920 --> 00:34:58,300 +وعند الأربعة بالشكل هذا وهنا واجف وين؟ عند اللي هو + +352 +00:34:58,300 --> 00:35:04,080 +الواحد وهنا هذا اللي هو سالب واحد وهذه سالب اتنين + +353 +00:35:04,080 --> 00:35:10,320 +وهذه سالب تلاتة ونزل اننا لمين؟ لغاية هنا جداش + +354 +00:35:10,320 --> 00:35:18,680 +اللي هو سالب خمسة تمام؟ وهذه اللي هي الأربعة هنا + +355 +00:35:19,350 --> 00:35:22,930 +المرة اللي فاتت قولنا حسبنا قداش F of سالب ثلاثة + +356 +00:35:22,930 --> 00:35:26,730 +طلعت سالب خمسة و قولنا F of Zero يساوي أربع يبقى + +357 +00:35:26,730 --> 00:35:28,590 +here ال absolute maximum و ال absolute minimum + +358 +00:35:28,590 --> 00:35:32,110 +الآن مديش اشتغل بالكلام اللي فات مدي اشتغل الشغل + +359 +00:35:32,110 --> 00:35:35,650 +الرياضي من اللي اتعلمنا اليوم بقوله ماشي الحال + +360 +00:35:35,650 --> 00:35:40,410 +يبقى أول شغلة بتروح اجيب له main F prime of X اللي + +361 +00:35:40,410 --> 00:35:50,450 +هو ناقص اتنين X تمام بنسويها ب Zero في غيرها يبقى + +362 +00:35:50,450 --> 00:36:00,170 +بقوله is the only بدل a is the only critical point + +363 +00:36:00,170 --> 00:36:08,060 +of the function f يبقى هذه هي critical point + +364 +00:36:08,060 --> 00:36:13,780 +الوحيدة يبقى بضروح ادور عندها وين كمان عند ال end + +365 +00:36:13,780 --> 00:36:20,640 +point تمام يبقى بضروح اجيبله ال F of zero يساوي + +366 +00:36:20,640 --> 00:36:26,280 +أربعة ناقص زيرو لكل تربيع يساوي قداش أربعة بروزها + +367 +00:36:26,280 --> 00:36:34,320 +وروح وخلهم بعد ذلك نجيب ال F of A و ال F of B يبقى + +368 +00:36:34,320 --> 00:36:42,040 +بده أجيب له ال F of سالب تلاتة يبقى أي أربع ناقص + +369 +00:36:42,040 --> 00:36:49,090 +ناقص تلاتة لكل تربيع يساوي سالب خمسة بعد ذلك بدي + +370 +00:36:49,090 --> 00:36:55,330 +أجيب له ال F of واحد أربعة ناقص واحد تربيع يساوي + +371 +00:36:55,330 --> 00:37:03,410 +كده؟ يساوي تلاتة هدول التنتين هم عند ال end points + +372 +00:37:03,410 --> 00:37:08,330 +اللي هو سالب واحد و تلاتة وهدي مين؟ هدي ال + +373 +00:37:08,330 --> 00:37:15,870 +critical point وهدي end at ال critical point + +374 +00:37:18,330 --> 00:37:26,190 +طب هاي حسبت كل القيم، من هدالة التلاتة، بتشوف أكبر + +375 +00:37:26,190 --> 00:37:30,110 +قيمة تبقى هي ال absolute maximum و أقل قيمة هي ال + +376 +00:37:30,110 --> 00:37:34,130 +absolute minimum، بادي يعني، مين الكبيرة فيهم؟ + +377 +00:37:34,130 --> 00:37:34,630 +أربع + +378 +00:37:38,810 --> 00:37:49,630 +absolute maximum قداش 4 at x يساوي 0 ال F has + +379 +00:37:49,630 --> 00:37:58,070 +absolute minimum سالب خمسة at x يساوي قداش سالب + +380 +00:37:58,070 --> 00:38:01,970 +تلاتة المرة اللي فات بجيه نجيبنا الرسم الآن بدينا + +381 +00:38:01,970 --> 00:38:09,800 +نحسب حسابات دقيقة نجي ناخد المثال اللي بعده يبقى يا + +382 +00:38:09,8 + +401 +00:40:30,300 --> 00:40:36,620 +وَهذا نقطة الأصل اللي هي Zero هذه shift جهتي + +402 +00:40:36,620 --> 00:40:42,250 +اليمين للـ absolute value بمقدار خمسة وبالشكل اللي + +403 +00:40:42,250 --> 00:40:47,190 +عندنا هذا تمام؟ بس قداش هذا اللي بدنا نعرفه الآن + +404 +00:40:47,190 --> 00:40:52,050 +ونحدده على الرسمة يبقى عند الخمسة دالة قابلة + +405 +00:40:52,050 --> 00:40:57,430 +للإشتقاق؟ لأ لإن عندي الخمسة المشتقة من اليمين + +406 +00:40:57,430 --> 00:41:04,160 +تختلف عن المشتقة من الشمال يبقى هنا بقول لـ at الـ X + +407 +00:41:04,160 --> 00:41:12,140 +يساوي خمسة الـ F prime is undefined لكن هل الدالة + +408 +00:41:12,140 --> 00:41:16,340 +معرفة عند X يساوي خمسة أو لا؟ معرفة، الدالة معرفة، + +409 +00:41:16,340 --> 00:41:21,660 +بس المشتقة اللي مش معرفة يبقى at X الـ F prime is + +410 +00:41:21,660 --> 00:41:28,300 +undefined يبقى هذا يعطيك أن X يساوي خمسة is a + +411 +00:41:28,300 --> 00:41:35,770 +critical أو إذا بدك Extreme كمان Critical and + +412 +00:41:35,770 --> 00:41:38,990 +Extreme + +413 +00:41:38,990 --> 00:41:47,970 +Value طيب تمام معناته بدنا نحسب F of خمسة فيه بره + +414 +00:41:47,970 --> 00:41:52,420 +Extreme Value؟ في شغالة يبقى دي the only extreme + +415 +00:41:52,420 --> 00:41:56,680 +value أو the only critical point يبقى F of خمسة + +416 +00:41:56,680 --> 00:42:01,560 +absolute value لـ خمسة ناقص خمسة و يساوي كده؟ Zero + +417 +00:42:01,560 --> 00:42:07,380 +بدنا نروح عند الطرفين يبقى بدنا نيجي ناخد F of + +418 +00:42:07,380 --> 00:42:12,040 +أربعة absolute value لـ الأربعة ناقص خمسة absolute + +419 +00:42:12,040 --> 00:42:18,480 +value للسالب واحد يبقى بواحد يبقى هنا عند الأربعة، + +420 +00:42:18,480 --> 00:42:23,880 +هي الأربعة بتيجي قبلها ممنوعة تطلع أكتر من واحد، + +421 +00:42:23,880 --> 00:42:29,590 +يبقى النقطة هذه إحداثياتها أربعة وواحد بعد ذلك + +422 +00:42:29,590 --> 00:42:36,730 +نجيب F of سبعة يبقى absolute value لـ سبعة ناقص + +423 +00:42:36,730 --> 00:42:43,670 +خمسة و يساوي قداش؟ اتنين يبقى هي بتيجي لك هي الستة هنا + +424 +00:42:43,670 --> 00:42:51,930 +و هي السبعة هنا اطلع النقطة هذه لسبعة و اتنين يبقى + +425 +00:42:51,930 --> 00:42:57,620 +هذا شكل الدالة فقط بغير باقي القيم اللي عندنا هنا + +426 +00:42:57,620 --> 00:43:04,340 +الـ F of خمسة بزيرو والـ F of أربعة بواحد والـ F of + +427 +00:43:04,340 --> 00:43:12,520 +سبعة باتنين مين الـ absolute maximum؟ سبعة ومين الـ + +428 +00:43:12,520 --> 00:43:18,980 +absolute minimum؟ الخمسة اللي هو Zero عند X يساوي + +429 +00:43:18,980 --> 00:43:26,400 +خمسة يبقى من هذا الكلام بقدر أقوله ما يأتي الـ F + +430 +00:43:26,400 --> 00:43:33,140 +has absolute minimum + +431 +00:43:33,140 --> 00:43:36,520 +zero + +432 +00:43:36,520 --> 00:43:45,280 +at x يساوي خمسة الـ F has absolute maximum اتنين + +433 +00:43:45,280 --> 00:43:50,580 +at x يساوي كده؟ at x يساوي سبعة + +434 +00:44:23,360 --> 00:44:35,340 +المثال الثاني example two determine + +435 +00:44:35,340 --> 00:44:41,560 +determine + +436 +00:44:41,560 --> 00:44:51,980 +the critical points of + +437 +00:44:51,980 --> 00:45:03,060 +the الـ function لدالة f of x يساوي x تربيع على x + +438 +00:45:03,060 --> 00:45:04,020 +ناقص اثنين + +439 +00:45:08,570 --> 00:45:13,830 +قال لي هات لي النقاط الحرجة للدالة اللي عندنا هذه بس + +440 +00:45:13,830 --> 00:45:16,730 +اللي بدهوا absolute maximum بس هات لي النقاط الحرجة + +441 +00:45:16,730 --> 00:45:20,930 +الله يعطيك العفو يقول لي ماشي إذا بدي أشتق وأشوف + +442 +00:45:20,930 --> 00:45:25,390 +وقت إيش بتساوي zero ووقت إيش بتكون غير معرفة يبقى + +443 +00:45:25,390 --> 00:45:31,090 +هذا solution السؤال هو هل هذه الدالة معرفة عند X + +444 +00:45:31,090 --> 00:45:36,890 +يساوي 2؟ لأ لأ يعني مثلا عندك X يساوي 2 لا يمكن أن + +445 +00:45:36,890 --> 00:45:40,970 +تكون critical point هذا فيه ملو طلاق ما طلقتش خلاص + +446 +00:45:40,970 --> 00:45:45,370 +بقول كفى الله المؤمن القتال تمام يبقى باجي بقول أول + +447 +00:45:45,370 --> 00:45:49,410 +خطوة الـ F is undefined + +448 +00:45:50,520 --> 00:45:55,680 +at x يساوي اثنين وكأنه الـ domain تبع الدالة من و + +449 +00:45:55,680 --> 00:46:00,300 +لا و اين من سالب infinity لغاية اثنين و اثنين + +450 +00:46:00,300 --> 00:46:06,240 +لـ infinity يعني هذا بده يعطينا كأنه domain الدالة F + +451 +00:46:06,240 --> 00:46:12,000 +بده يساوي من سالب infinity لغاية اثنين اتحاد اثنين + +452 +00:46:12,000 --> 00:46:16,100 +و infinity يعني استبعدنا من الـ real line بس فقط من + +453 +00:46:16,100 --> 00:46:22,760 +اثنين فبنجي نشتق الدالة يبقى الـ F prime of X يساوي + +454 +00:46:22,760 --> 00:46:33,080 +المقام في مشتقة البسط باثنين X ناقص البسط في مشتقة + +455 +00:46:33,080 --> 00:46:41,500 +المقام على مربع المقام الأصلي يبقى هذه بدها تساوي + +456 +00:46:41,500 --> 00:46:49,580 +أن الـ F prime of X بده يساوي اثنين X تربيع ناقص + +457 +00:46:49,580 --> 00:46:57,500 +أربعة X ناقص X تربيع على X ناقص اثنين لكل تربيع + +458 +00:46:57,650 --> 00:47:04,350 +يعني X تربيع ناقص أربعة X على X ناقص اثنين لكل + +459 +00:47:04,350 --> 00:47:09,790 +تربيع لو أخذت الـ X عامل مشترك بيظل الـ X ناقص أربعة + +460 +00:47:09,790 --> 00:47:16,880 +على X ناقص اثنين لكل تربيع إذا مشان أجيب الـ + +461 +00:47:16,880 --> 00:47:21,100 +critical points بدي أشوف وقت إيش بتساوي zero وقت + +462 +00:47:21,100 --> 00:47:27,780 +إيش ما هيش معرفة مظبوط يبقى لو حطيت الـ F prime of + +463 +00:47:27,780 --> 00:47:34,620 +X يساوي zero هذا معناه إن X في X ناقص أربعة على X + +464 +00:47:34,620 --> 00:47:39,140 +ناقص اثنين الكل تربيع يساوي مين؟ الـ zero مين اللي + +465 +00:47:39,140 --> 00:47:43,530 +بدي يساوي الـ zero؟ البسط ولا المقام؟ لو كان المقام + +466 +00:47:43,530 --> 00:47:48,950 +يساوي Zero كان الدالة صارت غير معرفة يبقى هذا + +467 +00:47:48,950 --> 00:47:59,030 +يساوي Zero only at X يساوي Zero و X يساوي أربعة الـ + +468 +00:47:59,030 --> 00:48:01,230 +F' + +469 +00:48:02,110 --> 00:48:06,830 +كمان is Undefined + +470 +00:48:08,150 --> 00:48:14,510 +at X يساوي اثنين إذا أقول الـ X يساوي اثنين هي + +471 +00:48:14,510 --> 00:48:20,310 +critical point لأ لأن دي غير معرفة عندها من الأساس + +472 +00:48:20,310 --> 00:48:24,530 +مش في domainها برا domainها يبقى ما أقدرش أقول إن هذه + +473 +00:48:24,530 --> 00:48:28,410 +critical point يبقى هنا الـ F present defined at X + +474 +00:48:28,410 --> 00:48:36,690 +يساوي اثنين ولكن الـ X يساوي اثنين is not a + +475 +00:48:36,690 --> 00:48:49,790 +critical point السبب because إن اثنين does not + +476 +00:48:49,790 --> 00:48:55,360 +belong لـ domain الدالة F مش موجودة في الـ domain أو + +477 +00:48:55,360 --> 00:48:59,400 +بالتالي ما هيش critical طب السؤال قال هات لي me + +478 +00:48:59,400 --> 00:49:09,820 +critical points بقول له the only critical points + +479 +00:49:09,820 --> 00:49:20,940 +are الـ X يساوي 0 و X يساوي 4 إيش رأيك هذول extreme + +480 +00:49:20,940 --> 00:49:28,420 +values ولابس ليك سوى اثنين لأ ما يجل إن الدالة غير + +481 +00:49:28,420 --> 00:49:48,400 +معرفة عندها نعطي + +482 +00:49:48,400 --> 00:49:49,420 +كمان مثال + +483 +00:50:17,900 --> 00:50:30,510 +القيم القصوى absolute and local هذه أو هذه سِيان of + +484 +00:50:30,510 --> 00:50:36,530 +the function لدالة + +485 +00:50:36,530 --> 00:50:46,330 +f of x يساوي الجذر التربيعي لثلاثة زائد اثنين x + +486 +00:50:46,330 --> 00:50:48,950 +ناقص x تربيع + +487 +00:51:04,410 --> 00:51:10,670 +سؤال مرة ثانية بيقول هات لي الـ extreme values سواء + +488 +00:51:10,670 --> 00:51:15,450 +كان absolute maximum أو absolute minimum أو local + +489 +00:51:15,450 --> 00:51:21,110 +maximum أو local minimum لـ الدالة f of x يساوي + +490 +00:51:21,110 --> 00:51:26,430 +الجذر التربيعي لثلاثة زائد اثنين x ناقص x تربيع هل + +491 +00:51:26,430 --> 00:51:32,460 +أعطاني interval يعني على كل الـ real line؟ لا مش + +492 +00:51:32,460 --> 00:51:38,180 +صحيح مش صحيح أنت بدك تروح وتشوف الدالة وين معرفة + +493 +00:51:38,180 --> 00:51:43,440 +هذه صحيح وبناء عليه بدك تشتغل إذا أول خطوة بده يحدد + +494 +00:51:43,440 --> 00:51:47,560 +بده يحدد domain هذه الدالة وبناء عليه بده يبدأ + +495 +00:51:47,560 --> 00:51:51,560 +يشتغل إذا لو بدنا نيجي ناخد domain الدالة + +496 +00:51:53,890 --> 00:52:01,410 +بنجي نقوله كل العناصر X بحيث إن كل المقدار اللي تحت + +497 +00:52:01,410 --> 00:52:09,740 +الجذر بديه أكبر من أو يساوي Zero يبقى هذا كل + +498 +00:52:09,740 --> 00:52:16,300 +العناصر X بحيث إنه أظن بقدر أحلل هذا إلى حاصل ضرب + +499 +00:52:16,300 --> 00:52:24,320 +قوسين وأكبر من أو يساوي الـ zero هنا ثلاثة وهنا + +500 +00:52:24,320 --> 00:52:34,500 +واحد وهنا X وهنا X وظلت الإشارة لو قلنا هذه بالناقص + +501 +00:52:34,500 --> 00:52:42,240 +بالناقص يبقى هذه بيكون بالزائد ناقص X وزائد 3X + +502 +00:52:42,240 --> 00:52:48,770 +وزائد 2X يبقى تحليلنا سليم 100% هذه يبقى كل العناصر + +503 +00:52:48,770 --> 00:52:54,230 +X بحيث إن ثلاثة ناقص X في واحد زائد X greater than + +504 +00:52:54,230 --> 00:53:01,280 +or equal to min to zero إذا أنا بروح أحدد الـ + +505 +00:53:01,280 --> 00:53:05,720 +domain من خلال هذه المعلومة إذا بروح أبحث إشارة + +506 +00:53:05,720 --> 00:53:11,880 +كل قوس من هذين القوسين يبقى بدي أروح أقول له بدي + +507 +00:53:11,880 --> 00:53:18,460 +إشارة الثلاث ناقص X بقول له هذا الـ real line + +508 +00:53:18,460 --> 00:53:25,120 +بتاخد الـ zero تبعها وين؟ عند الثلاث هي الثلاث إذا + +509 +00:53:25,120 --> 00:53:32,120 +لو جيت بعد الثلاث زي أربعة، بيصير هذه مالها؟ سالبة، + +510 +00:53:32,120 --> 00:53:38,340 +مظبوط، يبقى هذه سالبة، لو جيت قبل الثلاث زي + +511 +00:53:38,340 --> 00:53:45,860 +اثنين، يبقى موجبة، يبقى قبله موجبة، موجبة، موجبة، + +512 +00:53:45,860 --> 00:53:52,760 +شكلها بعد ذلك بدي أجيب إشارة القوس الثاني واحد + +513 +00:53:52,760 --> 00:53:59,600 +زائد X بياخد الـ zero تبعه وين؟ عند السالب واحد بعد + +514 +00:53:59,600 --> 00:54:06,240 +السالب واحد زي الـ zero بيصير بالموجب يبقى هاي موجب + +515 +00:54:06,240 --> 00:54:12,660 +موجب موجب موجب موجب الأخرى قبل السالب واحد زي سالب + +516 +00:54:12,660 --> 00:54:19,570 +اثنين بيصير سالبة طيب أنا بدي إشارة حاصل الضرب + +517 +00:54:19,570 --> 00:54:25,610 +ثلاثة ناقص X في واحد زائد X يبقى بنجي نقول هي الـ + +518 +00:54:25,610 --> 00:54:31,170 +real line وبروح بحدد الحدود الإقليمية اللي عندي + +519 +00:54:31,170 --> 00:54:39,070 +هاي هنا ثلاثة وهي هنا مين؟ له سالب واحد هنا سالب + +520 +00:54:39,070 --> 00:54:47,280 +هنا موجب هنا سالب طيب أنا بدي هذا الكلام يعني إما + +521 +00:54:47,280 --> 00:54:52,420 +zero أو أكبر من الـ zero موجب إذا ما عنديش إلا الفترة + +522 +00:54:52,420 --> 00:55:00,620 +المغلقة سالب واحد وثلاثة مش مصدق خد أربعة وعوض + +523 +00:55:00,620 --> 00:55:05,430 +في الجذر شوفوا بيطلع معرف ولا غير معرف بتلاقي ما هو + +524 +00:55:05,430 --> 00:55:11,550 +معرف يبقى أصبح domain الدالة هذه بده يساوي الفترة + +525 +00:55:11,550 --> 00:55:17,570 +من عند السالب واحد لغاية الثلاث يعني كل المنطقة + +526 +00:55:17,570 --> 00:55:23,670 +هذه يا شباب برا الحساب وهذه كمان برا الحساب بس + +527 +00:55:23,670 --> 00:55:28,330 +ما عنديش إلا من ولا وين؟ من سالب واحد إلى تغير هيك + +528 +00:55:28,330 --> 00:55:34,570 +ما ليش علاقة فيه طيب تعالى شوية إذا أنا حددت الـ + +529 +00:55:34,570 --> 00:55:39,390 +domain تبع هذه الدولار فبقى كويس إذا بدنا نرجع + +530 +00:55:39,390 --> 00:55:43,210 +نشتغل اللي دائماً اشتغلنا هنا بدنا نروح ندور على مين؟ + +531 +00:55:43,210 --> 00:55:46,910 +على الـ critical points اللي يمكن تكون extreme + +532 +00:55:46,910 --> 00:55:52,820 +ويمكن ما تكونش الله أعلم يبقى بدنا نيجي نشتق يبقى + +533 +00:55:52,820 --> 00:55:59,280 +بدنا نروح ناخد له الـ F prime of X فاضل الجذر واحد + +534 +00:55:59,280 --> 00:56:08,380 +على اثنين الجذر ثلاثة زائد اثنين X ناقص X تربيع في + +535 +00:56:08,380 --> 00:56:15,640 +مشتقة مداخل الجذر له اثنين ناقص اثنين X يبقى هذه + +536 +00:56:15,640 --> 00:56:22,020 +بدها تساوي واحد ناقص X على الجذر التربيعي لـ + +537 +00:56:22,020 --> 00:56:32,420 +ثلاثة زائد اثنين X ناقص X تربيع السؤال هو هل + +538 +00:56:32,420 --> 00:56:37,680 +المشتقة هذه معرفة عند السالب واحد والثلاثة؟ + +539 +00:56:39,640 --> 00:56:45,840 +معرفة؟ لأ يبقى هذول السالب واحد بدهم يطلعوا من الـ + +540 +00:56:45,840 --> 00:56:50,240 +domain تبع مين؟ تبع الدالة الأصلية يطلعوا يطلعوا + +541 +00:56:50,240 --> 00:56:50,480 +يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا + +542 +00:56:50,480 --> 00:56:53,020 +يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا + +543 +00:56:53,020 --> 00:56:55,520 +يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا + +544 +00:56:55,520 --> 00:56:56,580 +يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا + +545 +00:56:56,580 --> 00:57:03,680 +يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطلعوا يطل + +546 +00:57:03,700 --> 00:57:09,080 +الواحد ناقص x يساوي zero هذا معناه إن x يساوي + +547 +00:57:09,080 --> 00:57:17,030 +قداش؟ يساوي واحد طيب المشتقة هذه غير معرفة عند السالب + +548 +00:57:17,030 --> 00:57:22,690 +واحد والثلاثة عند السالب واحد والثلاثة بيصير المقام + +549 +00:57:22,690 --> 00:57:29,690 +zero تمام يبقى هذول يعتبروا critical points + +550 +00:57:29,690 --> 00:57:36,150 +كذلك المشتقة عندهم مالها؟ is undefined فبنجي نقول له + +551 +00:57:36,150 --> 00:57:43,680 +also الـ F prime is undefined + +552 +00:57:43,680 --> 00:57:53,220 +غير معرفة at X يساوي سالب واحد and X يساوي ثلاثة + +553 +00:57:55,100 --> 00:58:01,240 +حُط سالب واحد بصير هذه سالب اثنين وسالب واحد + +554 +00:58:01,240 --> 00:58:05,640 +بصير سالب ثلاثة وثلاثة zero عدد على صفر مالها؟ + +555 +00:58:05,640 --> 00:58:10,400 +نهاية والثلاثة زيها بالضبط تمامًا يبقى solid + +556 +00:58:10,400 --> 00:58:16,300 +critical point كم نقطة؟ أستبعد السالب واحد والثلاثة + +557 +00:58:16,300 --> 00:58:21,540 +بستبعدهمش لأن الدالة معرفة عندهم مش زي السؤال اللي + +558 +00:58:21,540 --> 00:58:25,800 +جاب لي اثنين ما كانش الدالة معرفة يبقى بنجي نقول له + +559 +00:58:25,800 --> 00:58:36,240 +الآن the critical points are اللي هم من؟ الـ X + +560 +00:58:36,240 --> 00:58:43,120 +يساوي سالب واحد والـ X يساوي واحد والـ X يساوي + +561 +00:58:43,120 --> 00:58:44,180 +ثلاثة + +562 +00:58:58,660 --> 00:59:06,900 +طالب الـ absolute وطلب الـ local طيب تعال نشوف الـ + +563 +00:59:06,900 --> 00:59:12,980 +absolute والـ local مين منهم absolute ومين منهم + +564 +00:59:12,980 --> 00:59:13,800 +local + +565 +00:59:35,880 --> 00:59:39,800 +أنت مش عارف ليش وقتاش ابني عرفت إن النقطة هي + +566 +00:59:39,800 --> 00:59:44,020 +extreme value اسمع يا أولى خلنا نتناقش عن ده + +567 +00:59:44,020 --> 00:59:47,120 +وأنتوا نستفيدوا هو هيجاوب اللي حاله أنا متأكد هي + +568 +00:59:47,120 --> 00:59:51,160 +يجاوب وقتاش + +569 +00:59:51,160 --> 00:59:53,340 +في المحاضرات اللي فاتت + +570 +00:59:55,920 --> 01:00:01,500 +لا ما كنتش أجيب مرة ساعة كنت أروح أشتق وكتبنا + +571 +01:00:01,500 --> 01:00:05,600 +هي فوق وقعد في الحالات التالية بيبقى لك سنة فعلاً + +572 +01:00:05,600 --> 01:0 + +601 +01:02:53,590 --> 01:03:02,660 +هذا كله عندنا إشارة الأمين واحد ناقص X بقول هي ال + +602 +01:03:02,660 --> 01:03:07,980 +real line وهي الواحد اللي عندي الآن بعد الواحد زي + +603 +01:03:07,980 --> 01:03:14,540 +اتنين والتلاتة بتكون سالب أو قبله موجب تمام؟ الآن + +604 +01:03:14,540 --> 01:03:21,960 +بدي أخد إشارة تلاتة ناقص X يبقى بروح وين؟ عندي + +605 +01:03:21,960 --> 01:03:26,930 +التلاتة التلاتة بتيجي بعد اتنين لو أخدت أربعة تبقى + +606 +01:03:26,930 --> 01:03:33,330 +سالب، مصبوح؟ جابلي التلاتة، ها جابلي تزاية اتنين، + +607 +01:03:33,330 --> 01:03:39,430 +بتكون موجب، موجب، موجب، بس ممنوعة ترجع عن سالب + +608 +01:03:39,430 --> 01:03:45,430 +واحد، وهنا ممنوعة تزيد عن مين؟ عن التلاتة، وعيزة + +609 +01:03:45,430 --> 01:03:49,270 +وهنا ممنوعة لحد هنا بس، لإن الـ domain تبع الدالة + +610 +01:03:49,270 --> 01:03:54,710 +كان من سالب واحد لوين؟ لغاية تلاتة بعد هيك بدك تروح + +611 +01:03:54,710 --> 01:04:01,310 +تجيب إشارة اللي هو الواحد زائد الـ X و برضه من عند + +612 +01:04:01,310 --> 01:04:07,490 +هنا لغاية تمينية تلاتة عندي السالب واحد بعد السالب + +613 +01:04:07,490 --> 01:04:11,790 +واحد هاي سالب واحد زي Zero بيصير موجب + +614 +01:04:14,650 --> 01:04:19,930 +مظبوط؟ وبقدرش اجابل السالب واحد بصير سالب بس + +615 +01:04:19,930 --> 01:04:27,430 +ماعنديش يبقى أنا مقيد بالحدود الإقليمية اللي عندي + +616 +01:04:27,430 --> 01:04:34,600 +هذه واي مين؟ واي الواحد يبقى بداجي أخد إشارة واحد + +617 +01:04:34,600 --> 01:04:40,240 +زائد اكس ولا واحد ناقص اكس اللي أنا في البصرة واحد + +618 +01:04:40,240 --> 01:04:46,480 +ناقص اكس على الجذر التربيعي لتلاتة زائد اتنين اكس + +619 +01:04:46,480 --> 01:04:52,440 +ناقص اكس تربيع وهذا الـ real line اللي عندنا يبقى + +620 +01:04:52,440 --> 01:04:59,210 +الفترة هذه سالبة وهذه موجبة يعني الدالة كانت + +621 +01:04:59,210 --> 01:05:08,690 +تزايدية وراحت صارت تناقصية، طبعا؟ يعني الدالة + +622 +01:05:08,690 --> 01:05:15,230 +كانت طالعة من تحت لفوق و من فوق نزلت شوية لتحت، يبقى + +623 +01:05:15,230 --> 01:05:23,000 +الـ absolute maximum جداش، absolute maximum absolute + +624 +01:05:23,000 --> 01:05:29,400 +maximum نين عند X يساوي واحد هذا الواحد و هذا + +625 +01:05:29,400 --> 01:05:36,440 +التلاتة و هذا السالب واحد الـ F has absolute + +626 +01:05:36,440 --> 01:05:45,960 +maximum و في نفس الوقت local maximum لنغيرك من زاد + +627 +01:05:45,960 --> 01:05:50,980 +إلى ناقص and local + +628 +01:05:51,970 --> 01:06:00,400 +ماكسيمم اتنين عند X يساوي واحد يبقى عند X يساوي + +629 +01:06:00,400 --> 01:06:04,660 +واحد فيه عندي absolute maximum و local maximum، + +630 +01:06:04,660 --> 01:06:09,480 +ضال مين؟ ضال عند السالب واحد وعندي التلاتة، إيش + +631 +01:06:09,480 --> 01:06:15,500 +رأيك عندي السالب واحد؟ كانت وين؟ تحت وقادر طالع + +632 +01:06:15,500 --> 01:06:20,460 +وعندي التلاتة كانت فوق ونزلة، يبقى عندي التلاتة + +633 +01:06:20,460 --> 01:06:26,900 +والواحد عشان فيه عندي local minimum وفي نفس الوقت + +634 +01:06:26,900 --> 01:06:32,700 +absolute minimum لأنه أقل ما يمكن وهو الصفر عندهم + +635 +01:06:32,700 --> 01:06:43,760 +يبقى هنا الـ F has absolute minimum and local + +636 +01:06:43,760 --> 01:06:56,230 +minimum at طبعا صفر at X يساوي سالب واحد and X + +637 +01:06:56,230 --> 01:07:02,530 +يساوي تلاتة إيش عرفك انه التنتين minimum لان اتنين + +638 +01:07:02,530 --> 01:07:08,130 +يعطوني مين نفس القيمة و الدالة من تحت اجت طالعة على + +639 +01:07:08,130 --> 01:07:12,170 +فوق و هنا نزلت شوية لتحت و هكذا + +640 +01:07:34,660 --> 01:07:36,960 +ناخد كمان مثال + +641 +01:07:50,570 --> 01:07:55,930 +طب حد فيكم بيقدر يقولي هذه معادلة إيش هي اللي تو + +642 +01:07:55,930 --> 01:08:04,090 +هذه هي Y يساوي الجذر التربيعي تلاتة زيادة اتنين X + +643 +01:08:04,090 --> 01:08:09,370 +ناقص X تربيع حد بيقدر يقولي معادلة إيش هذه؟ + +644 +01:08:12,760 --> 01:08:17,420 +طبعا دائرة بس مش دائرة كاملة نصف دائرة أقولي بس + +645 +01:08:17,420 --> 01:08:24,580 +مركزها ماهواش نقطة الاصل يعني هذه ها لو حبيت اعرف + +646 +01:08:24,580 --> 01:08:30,060 +مين هي هذه الدائرة باجي بقوله هذه Y تساوي الجذر + +647 +01:08:30,060 --> 01:08:34,780 +التربيعي هذه مشان تصير مربع كامل بضع فيها واحد و + +648 +01:08:34,780 --> 01:08:43,740 +بطرح واحد يعني هذه أربعة ناقص واحد زائد اتنين X ناقص + +649 +01:08:43,740 --> 01:08:48,200 +X تربيع أربعة ناقص واحد اللي هي بتلاتة ما سويتش شيء + +650 +01:08:48,200 --> 01:08:54,640 +تمام هذه بقدر أقول اللي هو الجذر التربيعي لأربعة + +651 +01:08:54,640 --> 01:09:01,300 +ناقص عامل مشترك بظل X تربيع ناقص اتنين X زائد واحد + +652 +01:09:01,300 --> 01:09:05,640 +أخدت من التلاتة ترامت عامل مشترك اللي هو الإشارة + +653 +01:09:05,830 --> 01:09:12,770 +سالب يبقى هذا الجذر التربيعي لأربعة ناقص X ناقص + +654 +01:09:12,770 --> 01:09:20,390 +واحد الكل تربيع يعني هذه لو ربعت بصير Y تربيع يساوي + +655 +01:09:20,390 --> 01:09:26,830 +أربعة ناقص X ناقص واحد الكل تربيع يعني هذه X ناقص + +656 +01:09:26,830 --> 01:09:32,110 +واحد الكل تربيع زائد Y تربيع تساوي أربعة هذه بس + +657 +01:09:32,110 --> 01:09:37,150 +مجرد معلومات زيادة مش هنأكدك الوضع اللي عندنا يبقى + +658 +01:09:37,150 --> 01:09:42,730 +لو جيت ارسمها باجي بقوله كويس هذا محور X هذا محور + +659 +01:09:42,730 --> 01:09:48,850 +Y هذا نقطة الأصل اللي هي Zero هذه دائرة مركزها + +660 +01:09:48,850 --> 01:09:53,930 +النقطة واحد و Zero يعني Shift جهة اليمين بمقدار + +661 +01:09:53,930 --> 01:09:58,950 +واحد واحد و Zero اللي هي النقطة هذه و نصف القطر + +662 +01:09:58,950 --> 01:10:05,390 +يساوي كده اتنين يبقى هذا اتنين يعني بيصير هذا كله + +663 +01:10:05,390 --> 01:10:10,750 +اتنين يعني هنا جداش بتبقى تلاتة و Zero وهنا بدي + +664 +01:10:10,750 --> 01:10:17,130 +ارجع اتنين له سالب واحد و Zero ونصف القطر اتنين + +665 +01:10:17,130 --> 01:10:22,150 +يبقى بدي اطلع هنا لغاية جد اقل قلي شوية يبقى + +666 +01:10:22,150 --> 01:10:27,270 +الدائرة بتجيلك هيك الشكل اللي عندها هنا هذا بدي + +667 +01:10:27,270 --> 01:10:35,590 +يكون اللي هو واحد واتنين لاحظ هذه absolute maximum + +668 +01:10:35,590 --> 01:10:41,750 +وفي نفس الوقت local maximum وهذه absolute minimum + +669 +01:10:41,750 --> 01:10:49,070 +وفي نفس الوقت local minimum يبقى هذه absolute and + +670 +01:10:49,070 --> 01:10:55,590 +local maximum + +671 +01:11:20,400 --> 01:11:27,680 +المثال الأخير في هذا الـ section هو مثال أربعة مثال + +672 +01:11:27,680 --> 01:11:40,400 +أربعة بيقول find the domain الـ domain و الـ + +673 +01:11:40,400 --> 01:11:46,420 +critical points و الـ + +674 +01:11:46,420 --> 01:11:52,840 +critical points and the extreme values and the + +675 +01:11:52,840 --> 01:11:54,900 +extreme + +676 +01:11:58,080 --> 01:12:09,660 +Values سواء كان absolute and local and local for + +677 +01:12:09,660 --> 01:12:21,060 +the function f of x يساوي x تربيع الجذر التربيعي + +678 +01:12:21,060 --> 01:12:22,760 +لتلاتة ناقص x + +679 +01:12:34,290 --> 01:12:54,590 +عظام الخلع دي كانت هنا منها زمان هذا + +680 +01:12:54,590 --> 01:12:55,790 +الرسمة حد بدهيها + +681 +01:13:00,630 --> 01:13:04,890 +طيب نرجع لسؤالنا مرة تانية قال هاتي الـ domain + +682 +01:13:04,890 --> 01:13:09,350 +أفضلها يبقى خليني نجيب الـ domain قبل ان نبدأ نشتغل + +683 +01:13:09,350 --> 01:13:14,570 +هذه يا شباب تعتبر function وهي تعتبر هي function + +684 +01:13:14,570 --> 01:13:18,890 +تانية وحاصل ضرب two functions حاصل ضرب الـ domain + +685 +01:13:18,890 --> 01:13:22,270 +تبعهم الـ intersection بين two domains هذي الـ + +686 +01:13:22,270 --> 01:13:30,650 +domain تبعها من ولا و يامهذا الـ domain هو الـ + +687 +01:13:30,650 --> 01:13:38,190 +F وكل + +688 +01:13:38,190 --> 01:13:44,070 +العناصر X بحيث أن التلاتة ناقص X بديها greater + +689 +01:13:44,070 --> 01:13:48,860 +than or equal to zero بديت كل الكمية اللي تحت الجذر + +690 +01:13:48,860 --> 01:13:53,780 +أكبر أو يساوي Zero يعني كل العناصر X بيحيطوا ان + +691 +01:13:53,780 --> 01:13:58,400 +تلاتة greater than or equal to X يعني X أقل من أو يساوي + +692 +01:13:58,400 --> 01:14:05,660 +قداش تلاتة يعني من سالب infinity لغاية تلاتة + +693 +01:14:05,660 --> 01:14:11,320 +close من عند التلاتة فهي جيبنا له المطلوب الأول من + +694 +01:14:11,320 --> 01:14:15,440 +المسألة أجرنا الرسم هذا انتهينا منها + +695 +01:14:22,420 --> 01:14:26,320 +طيب انتهينا من المطلوب الأول المطلوب التاني قال + +696 +01:14:26,320 --> 01:14:30,920 +هاتلي the critical points الـ critical points بده + +697 +01:14:30,920 --> 01:14:35,860 +اشتق وأسوي بالـ Zero أو تبقى غير معرفة باجي بقوله + +698 +01:14:35,860 --> 01:14:41,040 +كويس يبقى بده أجي أخد الـ F prime of X هذي مشتقة + +699 +01:14:41,040 --> 01:14:47,170 +حاصل ضرب دالتين الدالة في مشتقة الدالة الثانية واحد + +700 +01:14:47,170 --> 01:14:52,370 +على اتنين الجذر التربيعي اللي ثلاثة ناقص X في مشتقة + +701 +01:14:52,370 --> 01:14:57,390 +ما تحت الجذر اللي هو الجذر بسالب واحد يبقى هذه + +702 +01:14:57,390 --> 01:15:03,170 +الأولى في مشتقة الدالة الثانية زائد مشتقة الدالة + +703 +01:15:03,170 --> 01:15:10,480 +الأربعة X تربيع كله على اتنين الجذر التربيعي لتلاتة + +704 +01:15:10,480 --> 01:15:17,100 +ناقص X يبقى أصبحت النتيجة على الشكل التالي اتناشر + +705 +01:15:17,100 --> 01:15:24,940 +X ناقص خمسة X تربيع على اتنين الجذر التربيعي + +706 +01:15:24,940 --> 01:15:32,000 +لتلاتة ناقص X يعني هذا لو أخدت الـ X عامل مشترك بظل + +707 +01:15:32,000 --> 01:15:40,360 +12-5x كله على الاتنين الجذر التربيعي اللي تلاتة + +708 +01:15:40,360 --> 01:15:48,830 +ناقص x لو حطيت هذا الكلام يساوي Zero هذا بدي أعطيك + +709 +01:15:48,830 --> 01:15:54,790 +مين؟ الـ bus هو الذي يساوي Zero يبقى هذا يعطينا + +710 +01:15:54,790 --> 01:16:01,930 +مين؟ يعطينا ان X في 12 ناقص خمسة X بدي يساوي Zero + +711 +01:16:01,930 --> 01:16:09,590 +هذا بدي يعطيك ان X يساوي Zero و X يساوي 12 على + +712 +01:16:09,590 --> 01:16:17,350 +خمسة طيب سؤال هل المشتقة معرفة عند التلاتة؟ لأ طيب + +713 +01:16:17,350 --> 01:16:22,910 +التلاتة في الـ domain تبع الدالة؟ موجودة يبقى باجي + +714 +01:16:22,910 --> 01:16:29,470 +بقوله هنا الـ F prime is undefined + +715 +01:16:35,520 --> 01:16:43,580 +عند X يساوي تلاتة من هذا الكلام بس تنتج الـ points + +716 +01:16:43,580 --> 01:16:52,220 +اللي هم مين؟ X يساوي Zero والـ X يساوي اتناشر على + +717 +01:16:52,220 --> 01:17:00,680 +خمسة and الـ X بدي يساوي تلاتة are the critical + +718 +01:17:00,680 --> 01:17:03,460 +points + +719 +01:17:20,900 --> 01:17:32,410 +أو absolute minimum لمين؟ لهذه الدالة طيب لاحظ ان + +720 +01:17:32,410 --> 01:17:38,410 +التلاتة هادي هي end point لمين؟ للـ function اللي + +721 +01:17:38,410 --> 01:17:43,190 +عندنا يبقى هي كل القيم اللي بدي احسبهم بس وين في + +722 +01:17:43,190 --> 01:17:49,350 +تلاتة مواضع يبقى بداجي أقوله بدي احسبله الـ F of + +723 +01:17:49,350 --> 01:18:01,050 +Zero قداش تساوي؟ Zero مظبوط بدي أحسبله الـ F of 12 على + +724 +01:18:01,050 --> 01:18:07,910 +5 هو يساوي 12 على 5 الكل تربيع في الجذر التربيعي + +725 +01:18:07,910 --> 01:18:16,420 +اللي تلاتة ناقص 12 على خمسة مية وأربعة واربعين على + +726 +01:18:16,420 --> 01:18:23,700 +خمسة وعشرين الجذر التربيعي خمستاشر على تلت أخماس + +727 +01:18:23,700 --> 01:18:29,860 +خمستاشر لخمستاشر على تلت أخماس يبقى هاي القيمة بدنا + +728 +01:18:29,860 --> 01:18:38,280 +نحسبله كمان F of تلاتة F of تلاتة طبعا يبقى صفر + +729 +01:18:38,280 --> 01:18:46,570 +بصفر طبعا يبقى حسبته قداش قيمة الدالة عند النقاط + +730 +01:18:46,570 --> 01:18:52,890 +التلات اللي عندنا لكن انا بدي اعرف هي المشتقة، + +731 +01:18:52,890 --> 01:18:57,100 +إمشي هي المشتقة اللي عندي بدي اشوف وين الـ local + +732 +01:18:57,100 --> 01:19:01,540 +maximum و الـ local minimum و التزايد وما إلى ذلك + +733 +01:19:01,540 --> 01:19:05,940 +يبقى بدي احسب الإشارات اللي عندنا هنا بقوله بسيطة + +734 +01:19:05,940 --> 01:19:13,410 +جدا إذا بروح أخد إشارة من الـ X بقول له هاي الـ line + +735 +01:19:13,410 --> 01:19:19,490 +كله هاي الـ Zero بعد الـ Zero positive وقبل الـ Zero + +736 +01:19:19,490 --> 01:19:26,610 +إيه نجد بس ممنوع تفوت التلاتة صح؟ مش على الاطلاق + +737 +01:19:26,610 --> 01:19:33,390 +إذا لو قلت هنا تلاتة stop ممنوع تتعدىها بعدك بدات + +738 +01:19:33,390 --> 01:19:43,160 +ياخد إشارة اللي هو اتناشر ناقص خمسة X هذا الـ real + +739 +01:19:43,160 --> 01:19:48,600 +line قولنا الـ X عندها بتساوى Zero عند اتناشر على خمسة + +740 +01:19:48,600 --> 01:19:53,840 +اتناشر على خمسة يعني اتنين و خمسين يعني أقل من + +741 +01:19:53,840 --> 01:19:58,900 +تلاتة يعني اتناشر على خمسة بتجيني هنا يبقى هذا + +742 +01:19:58,900 --> 01:20:05,780 +اتناشر على خمسة إذا لو جيت بعد اتناشر على خمسة ها + +743 +01:20:05,780 --> 01:20:12,340 +بعد زي التلاتة مثلا بتكون سالبة مظبوط يبقى هذه هنا + +744 +01:20:12,340 --> 01:20:19,840 +إيه اتناشر على خمسة بتصير سالبة واي تلاتة تتعدى + +745 +01:20:19,840 --> 01:20:25,540 +ولو جيت قبلها تبقى موجبة وخليك ماشي زي ما بدك من + +746 +01:20:25,540 --> 01:20:32,330 +هنا لسالب infinity بتداجر للي بعدها لإتنين الجذر + +747 +01:20:32,330 --> 01:20:39,050 +التربيعي لتلاتة ناقص X هذا الـ real line وهذه بتاخد + +748 +01:20:39,050 --> 01:20:44,170 +الـ Zero تبعها وين؟ عند التلاتة بعد التلاتة ماعنديش + +749 +01:20:44,170 --> 01:20:51,460 +قبل التلاتة زي اتنين دايما وأبدابالموجب يبقى هذا + +750 +01:20:51,460 --> 01:20:56,780 +الموجب بالشكل اللي عندنا هذا كله طيب كويس نحط + +751 +01:20:56,780 --> 01:21:04,060 +الحدود الإقليمية يبقى هذا الحدود هذه الـ Zero وهذه + +752 +01:21:04,060 --> 01:21:13,260 +الاتناشر على خمسة وهذه مين؟ اللي هي التلاتة وهذه + +753 +01:21:13,260 --> 01:21:16,280 +هنا اللي هي الاتناشر على خمسة + +754 +01:21:18,590 --> 01:21:29,010 +وهذه هنا الـ Zero وهذه هنا من التلاتة طبعا زائد في + +755 +01:21:29,010 --> 01:21:35,350 +ناقص بناقص على زائد بناقص زائد في زائد بزائد على + +756 +01:21:35,350 --> 01:21:42,730 +زائد بزائد ناقص في زائد بناقص على زائد بناقص + +757 +01:21:42,730 --> 01:21:47,530 +بالشكل اللي عندنا هنا يعني الدالة كانت decreasing + +758 +01:21:48,510 --> 01:21:58,450 +صارت increasing رجعت decreasing تمام؟ السؤال هو، + +759 +01:21:58,450 --> 01:22:06,010 +في عندي absolute maximum؟ absolute maximum بقولش + +760 +01:22:06,010 --> 01:22:11,680 +local absolute maximum أنا جاي من عندي سالب + +761 +01:22:11,680 --> 01:22:15,280 +infinitive من مجال الله الله صحيح ما بقوله وجاي + +762 +01:22:15,280 --> 01:22:15,900 +نازل + +763 +01:22:40,050 --> 01:22:45,530 +لوكال ماكسيمم وين؟ عند اتناشر على خمسة هذه عند + +764 +01:22:45,530 --> 01:22:52,410 +اتناشر على خمسة عند اتناشر على خمسة F of اتناشر + +765 +01:22:52,410 --> 01:22:56,290 +على خمسة وين جيبناها؟ F of اتناشر على خمسة وين + +766 +01:22:56,290 --> 01:22:59,410 +رقمها؟ يبقى باجي بقوله الـ F + +767 +01:23:07,340 --> 01:23:14,720 +لوكال ماكسيمم هو مية وأربعة وأربعين على خمسة و + +768 +01:23:14,720 --> 01:23:21,500 +عشرين جذر تلت أخماس at X يساوي اتناشر على خمسة + +769 +01:23:26,610 --> 01:23:32,710 +كدوش قيمة الدالة عند الـ Zero لفه Zero وكذلك عند + +770 +01:23:32,710 --> 01:23:43,470 +من عند التلاتة يبقى الـ F has local بنفع كمان + +771 +01:23:43,470 --> 01:23:44,550 +absolute؟ + +772 \ No newline at end of file diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3gx5rcf4Qwo_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3gx5rcf4Qwo_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..34dbe81f180f2ed98e634689066fe1bdb7d60bfd --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/3gx5rcf4Qwo_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 4704, "start": 22.14, "end": 47.04, "text": "بسم الله الرحمن الرحيم نعود لل section اللي ابتدأناه المرة الماضية وكان موضوعنا هو ال extreme values of a function القيم القصوى أو القيم المتطرفة لدالت ما طبعا المرة اللي فاتة أخدنا ال absolute maximum و ال absolute minimum و عرفنا اللي absolute maximum أقصى قيمة بتاخدها الدالة على كل ال domain تبعها", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 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الدالة F إذا F of X أقل من أو يسوى F of C فF of C ما لها", "tokens": [3555, 1863, 2655, 4117, 19528, 43242, 2423, 39184, 10636, 2793, 28239, 4587, 41193, 32748, 47283, 1211, 10632, 24976, 39184, 9274, 412, 10636, 935, 383, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 9274, 32748, 6027, 3660, 479, 11933, 15730, 479, 295, 1783, 5551, 4587, 1211, 9154, 34051, 7251, 3794, 2407, 7578, 479, 295, 383, 6156, 37, 295, 383, 19446, 5296, 11296], "avg_logprob": -0.38886088901950466, "compression_ratio": 1.4709677419354839, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 119.24, "end": 120.0, "word": "بنتكلم", "probability": 0.5977783203125}, {"start": 120.0, "end": 120.44, "word": " عند", "probability": 0.6806640625}, {"start": 120.44, "end": 120.72, "word": " الـ", "probability": 0.438232421875}, {"start": 120.72, "end": 121.28, "word": " interior", "probability": 0.6376953125}, {"start": 121.28, "end": 121.98, "word": " points", "probability": 0.58740234375}, {"start": 121.98, 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712.5, "end": 716.58, "text": "بنرجع بالذاكرة لتعريف المرة الماضية", "tokens": [3555, 1863, 47341, 3615, 20666, 15730, 4117, 25720, 5296, 2655, 3615, 16572, 5172, 9673, 25720, 9673, 46958, 10632], "avg_logprob": -0.42105263471603394, "compression_ratio": 1.0476190476190477, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 712.5, "end": 713.9, "word": "بنرجع", "probability": 0.4811859130859375}, {"start": 713.9, "end": 714.6, "word": " بالذاكرة", "probability": 0.8101806640625}, {"start": 714.6, "end": 715.24, "word": " لتعريف", "probability": 0.87529296875}, {"start": 715.24, "end": 715.78, "word": " المرة", "probability": 0.976318359375}, {"start": 715.78, "end": 716.58, "word": " الماضية", "probability": 0.9944661458333334}], "temperature": 1.0}, {"id": 33, "seek": 74170, "start": 721.62, "end": 741.7, "text": "الـ domain تبعها ممتاز ال domain من A إلى B أكبر قيمة اللي عندي هذه فوق يبقى هذه قولت absolute maximum يبقى ال local maximum و absolute maximum في نفس الوقت طبعا فبتدور أشوف في absolute minimum ولا لا", "tokens": [6027, 39184, 9274, 6055, 3555, 3615, 11296, 3714, 2304, 2655, 31377, 2423, 9274, 9154, 316, 30731, 363, 5551, 4117, 26890, 12174, 32640, 3660, 13672, 1829, 18871, 16254, 29538, 6156, 30543, 7251, 3555, 4587, 7578, 29538, 12174, 12610, 2655, 8236, 6674, 7251, 3555, 4587, 7578, 2423, 2654, 6674, 4032, 8236, 6674, 8978, 8717, 36178, 2423, 30543, 2655, 23032, 3555, 3615, 995, 6156, 3555, 2655, 3215, 13063, 5551, 8592, 38688, 8978, 8236, 7285, 49429, 20193], "avg_logprob": -0.3105996533020123, "compression_ratio": 1.5815217391304348, "no_speech_prob": 0.0, "words": [{"start": 721.62, "end": 721.98, "word": "الـ", "probability": 0.428955078125}, {"start": 721.98, "end": 722.32, "word": " domain", "probability": 0.181396484375}, {"start": 722.32, "end": 723.12, "word": " تبعها", "probability": 0.81976318359375}, {"start": 723.12, "end": 723.78, "word": " ممتاز", "probability": 0.796173095703125}, {"start": 723.78, "end": 723.92, "word": " 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الدالة، إذا ربطنا كلام المرة الماضية بالمرة هذه، هذه المرة هي بيجي تاخد مناطق أو نقطة موضعية open interval، شغلة موضعية حوالي النقطة حدات منها ال local maximum، يعني قيم", "tokens": [3555, 7435, 30241, 9154, 5016, 1863, 7578, 4724, 1211, 4587, 7578, 28239, 47432, 3660, 29538, 5551, 4587, 1211, 19446, 7251, 43020, 12399, 45164, 7251, 29245, 3215, 12174, 32640, 3660, 24976, 3215, 6027, 3660, 5551, 4587, 1211, 9154, 11296, 12399, 7251, 3555, 4587, 7578, 29538, 9122, 2304, 7649, 8236, 19446, 46740, 7285, 46740, 24192, 32748, 6027, 3660, 12399, 11933, 15730, 12602, 3555, 9566, 8315, 28242, 10943, 9673, 25720, 9673, 46958, 10632, 20666, 2304, 25720, 29538, 12399, 29538, 9673, 25720, 39896, 4724, 1829, 7435, 1829, 6055, 47283, 3215, 9154, 41193, 4587, 34051, 8717, 47432, 3660, 3714, 2407, 11242, 3615, 10632, 1269, 15035, 12399, 13412, 17082, 37977, 3714, 2407, 11242, 3615, 10632, 11331, 2407, 6027, 1829, 28239, 47432, 3660, 11331, 3215, 9307, 9154, 11296, 2423, 2654, 6674, 12399, 37495, 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"word": " عند", "probability": 0.9228515625}, {"start": 1044.41, "end": 1045.01, "word": " هذه", "probability": 0.966796875}, {"start": 1045.01, "end": 1046.83, "word": " النقارة", "probability": 0.8382568359375}, {"start": 1046.83, "end": 1047.33, "word": " يبقى", "probability": 0.9053955078125}, {"start": 1047.33, "end": 1047.57, "word": " إذا", "probability": 0.96337890625}, {"start": 1047.57, "end": 1048.01, "word": " قرأت", "probability": 0.896240234375}, {"start": 1048.01, "end": 1048.53, "word": " نظرية", "probability": 0.969482421875}, {"start": 1048.53, "end": 1048.87, "word": " أو", "probability": 0.89404296875}, {"start": 1048.87, "end": 1049.45, "word": " عبارة", "probability": 0.9940185546875}, {"start": 1049.45, "end": 1050.29, "word": " بنقرأها", "probability": 0.91474609375}, {"start": 1050.29, "end": 1051.15, "word": " قراءة", "probability": 0.870849609375}, {"start": 1051.15, "end": 1051.61, "word": " صحيحة", "probability": 0.9419921875}, {"start": 1051.61, "end": 1051.77, "word": " مش", "probability": 0.72998046875}, {"start": 1051.77, "end": 1052.09, "word": " روح", "probability": 0.7965494791666666}, {"start": 1052.09, "end": 1052.45, "word": " نفسي", "probability": 0.5472819010416666}, {"start": 1052.45, "end": 1052.63, "word": " على", "probability": 0.82666015625}, {"start": 1052.63, "end": 1053.21, "word": " كيفنا", "probability": 0.68212890625}], "temperature": 1.0}, {"id": 46, "seek": 106440, "start": 1053.64, "end": 1064.4, "text": "قال، لو في Local maximum أو Local minimum موجودة والمشتقة معرفة، إذا يجب أن تكون المشتقة مالها تساوي Zero", "tokens": [4587, 6027, 12399, 45164, 8978, 22755, 6674, 34051, 22755, 7285, 3714, 29245, 23328, 3660, 16070, 2304, 8592, 2655, 28671, 20449, 28480, 3660, 12399, 11933, 15730, 7251, 7435, 3555, 14739, 6055, 30544, 9673, 8592, 2655, 28671, 3714, 6027, 11296, 6055, 3794, 995, 45865, 17182], "avg_logprob": -0.27237216518683866, "compression_ratio": 1.251908396946565, "no_speech_prob": 0.0, "words": [{"start": 1053.64, "end": 1054.14, "word": "قال،", "probability": 0.46588134765625}, {"start": 1054.14, "end": 1054.28, "word": " لو", "probability": 0.3818359375}, {"start": 1054.28, "end": 1054.52, "word": " في", "probability": 0.67236328125}, {"start": 1054.52, "end": 1054.88, "word": " Local", "probability": 0.32275390625}, {"start": 1054.88, "end": 1055.54, "word": " maximum", "probability": 0.4912109375}, {"start": 1055.54, "end": 1055.94, "word": " أو", "probability": 0.7509765625}, {"start": 1055.94, "end": 1056.34, "word": " Local", "probability": 0.91748046875}, {"start": 1056.34, "end": 1057.02, "word": " minimum", "probability": 0.97998046875}, {"start": 1057.02, "end": 1058.54, "word": " موجودة", "probability": 0.98486328125}, {"start": 1058.54, "end": 1059.96, "word": " والمشتقة", "probability": 0.822509765625}, {"start": 1059.96, "end": 1060.74, "word": " معرفة،", "probability": 0.89453125}, {"start": 1060.74, "end": 1060.96, "word": " إذا", "probability": 0.78515625}, {"start": 1060.96, "end": 1061.48, "word": " يجب", "probability": 0.9763997395833334}, {"start": 1061.48, "end": 1061.66, "word": " أن", "probability": 0.81640625}, {"start": 1061.66, "end": 1062.0, "word": " تكون", "probability": 0.96044921875}, {"start": 1062.0, "end": 1062.62, "word": " المشتقة", "probability": 0.9783935546875}, {"start": 1062.62, "end": 1063.16, "word": " مالها", "probability": 0.809326171875}, {"start": 1063.16, "end": 1064.12, "word": " تساوي", "probability": 0.958740234375}, {"start": 1064.12, "end": 1064.4, "word": " Zero", "probability": 0.65576171875}], "temperature": 1.0}, {"id": 47, "seek": 109641, "start": 1068.03, "end": 1096.41, "text": "خلّي الـ remark التاني اللي عندنا يعني بيقول لي إيش احنا حتى الآن من أول مدينة ماقلناش فيه extreme value ماقلناش فيه extreme كله بنتكلم عن المشتقة و ال local maximum لكن موضوع ال section ال extreme value له ال function مش هي كتبنا اللي لعلوان المرة اللي فاتت فهيبقى بدنا نيجي لل extreme values هذه بيقول لي دلّا if has extreme values only in the following places", "tokens": [9778, 1211, 11703, 1829, 2423, 39184, 7942, 16712, 7649, 1829, 13672, 1829, 43242, 8315, 37495, 22653, 4724, 1829, 39648, 32239, 11933, 1829, 8592, 1975, 5016, 8315, 11331, 49975, 6024, 48506, 9154, 5551, 12610, 3714, 3215, 9957, 3660, 19446, 4587, 1211, 1863, 33599, 8978, 3224, 8084, 2158, 19446, 4587, 1211, 1863, 33599, 8978, 3224, 8084, 28242, 3224, 4724, 29399, 4117, 19528, 18871, 9673, 8592, 2655, 28671, 4032, 2423, 2654, 6674, 44381, 3714, 2407, 11242, 45367, 2423, 3541, 2423, 8084, 2158, 46740, 2423, 2445, 37893, 39896, 9122, 2655, 3555, 8315, 13672, 1829, 5296, 30241, 2407, 7649, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 6156, 3224, 1829, 3555, 4587, 7578, 47525, 8315, 8717, 1829, 7435, 1829, 24976, 8084, 4190, 29538, 4724, 1829, 39648, 32239, 11778, 1211, 11703, 995, 498, 575, 8084, 4190, 787, 294, 264, 3480, 3190], "avg_logprob": -0.2875000004415159, "compression_ratio": 1.8745644599303135, "no_speech_prob": 0.0, 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"probability": 0.9443359375}, {"start": 1073.13, "end": 1073.43, "word": " الآن", "probability": 0.712890625}, {"start": 1073.43, "end": 1074.35, "word": " من", "probability": 0.96826171875}, {"start": 1074.35, "end": 1074.75, "word": " أول", "probability": 0.9150390625}, {"start": 1074.75, "end": 1075.07, "word": " مدينة", "probability": 0.789794921875}, {"start": 1075.07, "end": 1075.71, "word": " ماقلناش", "probability": 0.70654296875}, {"start": 1075.71, "end": 1075.97, "word": " فيه", "probability": 0.7071533203125}, {"start": 1075.97, "end": 1076.41, "word": " extreme", "probability": 0.8212890625}, {"start": 1076.41, "end": 1076.97, "word": " value", "probability": 0.98193359375}, {"start": 1076.97, "end": 1077.91, "word": " ماقلناش", "probability": 0.86875}, {"start": 1077.91, "end": 1078.07, "word": " فيه", "probability": 0.872314453125}, {"start": 1078.07, "end": 1078.23, "word": " extreme", "probability": 0.441650390625}, {"start": 1078.23, "end": 1078.59, "word": " كله", 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"probability": 0.734375}, {"start": 1083.87, "end": 1084.45, "word": " extreme", "probability": 0.95654296875}, {"start": 1084.45, "end": 1084.91, "word": " value", "probability": 0.98779296875}, {"start": 1084.91, "end": 1085.07, "word": " له", "probability": 0.3310546875}, {"start": 1085.07, "end": 1085.17, "word": " ال", "probability": 0.95703125}, {"start": 1085.17, "end": 1085.63, "word": " function", "probability": 0.958984375}, {"start": 1085.63, "end": 1086.11, "word": " مش", "probability": 0.9755859375}, {"start": 1086.11, "end": 1086.27, "word": " هي", "probability": 0.69091796875}, {"start": 1086.27, "end": 1086.59, "word": " كتبنا", "probability": 0.8853759765625}, {"start": 1086.59, "end": 1086.79, "word": " اللي", "probability": 0.646484375}, {"start": 1086.79, "end": 1087.23, "word": " لعلوان", "probability": 0.68756103515625}, {"start": 1087.23, "end": 1087.55, "word": " المرة", "probability": 0.882080078125}, {"start": 1087.55, "end": 1087.69, "word": " اللي", "probability": 0.9619140625}, {"start": 1087.69, "end": 1088.19, "word": " فاتت", "probability": 0.978515625}, {"start": 1088.19, "end": 1088.93, "word": " فهيبقى", "probability": 0.59521484375}, {"start": 1088.93, "end": 1089.09, "word": " بدنا", "probability": 0.767822265625}, {"start": 1089.09, "end": 1089.37, "word": " نيجي", "probability": 0.989501953125}, {"start": 1089.37, "end": 1089.55, "word": " لل", "probability": 0.787109375}, {"start": 1089.55, "end": 1090.23, "word": " extreme", "probability": 0.97265625}, {"start": 1090.23, "end": 1090.79, "word": " values", "probability": 0.72802734375}, {"start": 1090.79, "end": 1091.11, "word": " هذه", "probability": 0.448486328125}, {"start": 1091.11, "end": 1092.01, "word": " بيقول", "probability": 0.96923828125}, {"start": 1092.01, "end": 1092.13, "word": " لي", "probability": 0.4765625}, {"start": 1092.13, "end": 1092.69, "word": " دلّا", "probability": 0.6212158203125}, {"start": 1092.69, "end": 1092.95, "word": " if", "probability": 0.71875}, {"start": 1092.95, "end": 1093.29, "word": " has", "probability": 0.88427734375}, {"start": 1093.29, "end": 1093.91, "word": " extreme", "probability": 0.90185546875}, {"start": 1093.91, "end": 1094.35, "word": " values", "probability": 0.96337890625}, {"start": 1094.35, "end": 1094.89, "word": " only", "probability": 0.8759765625}, {"start": 1094.89, "end": 1095.27, "word": " in", "probability": 0.9736328125}, {"start": 1095.27, "end": 1095.45, "word": " the", "probability": 0.93017578125}, {"start": 1095.45, "end": 1095.79, "word": " following", "probability": 0.869140625}, {"start": 1095.79, "end": 1096.41, "word": " places", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 48, "seek": 111318, "start": 1096.64, "end": 1113.18, "text": "وانا روح ادور على ال extreme values لمين لهذه الدالة، القيم القصوى لمين لهذه الدالة، فبقوللي في ثلاثة مواقع، الموقع الأول عند النقاط الداخلية للمشتقة عندها يسوى وين؟", "tokens": [2407, 7649, 995, 12602, 2407, 5016, 1975, 3215, 13063, 15844, 2423, 8084, 4190, 32767, 9957, 46740, 24192, 32748, 6027, 3660, 12399, 25062, 32640, 25062, 9381, 2407, 7578, 32767, 9957, 46740, 24192, 32748, 6027, 3660, 12399, 6156, 3555, 39648, 20292, 8978, 38637, 1211, 5718, 104, 3660, 3714, 14407, 4587, 3615, 12399, 9673, 30543, 3615, 16247, 12610, 43242, 28239, 4587, 41193, 32748, 47283, 1211, 10632, 5296, 19528, 8592, 2655, 28671, 43242, 11296, 7251, 3794, 2407, 7578, 4032, 9957, 22807], "avg_logprob": -0.2592147443539057, "compression_ratio": 1.7159763313609468, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1096.64, "end": 1097.38, "word": "وانا", "probability": 0.5454915364583334}, {"start": 1097.38, "end": 1097.68, "word": " روح", "probability": 0.7043050130208334}, {"start": 1097.68, "end": 1098.5, "word": " ادور", "probability": 0.8260091145833334}, {"start": 1098.5, "end": 1099.14, "word": " على", "probability": 0.73779296875}, {"start": 1099.14, "end": 1099.28, "word": " ال", "probability": 0.80419921875}, {"start": 1099.28, "end": 1099.72, "word": " extreme", "probability": 0.80322265625}, {"start": 1099.72, "end": 1100.2, "word": " values", "probability": 0.90625}, {"start": 1100.2, "end": 1100.74, "word": " لمين", "probability": 0.67724609375}, {"start": 1100.74, "end": 1101.14, "word": " لهذه", "probability": 0.4993896484375}, {"start": 1101.14, "end": 1101.8, "word": " الدالة،", "probability": 0.8360595703125}, {"start": 1101.8, "end": 1102.42, "word": " القيم", "probability": 0.681640625}, {"start": 1102.42, "end": 1103.76, "word": " القصوى", "probability": 0.9776611328125}, {"start": 1103.76, "end": 1104.4, "word": " لمين", "probability": 0.871826171875}, {"start": 1104.4, "end": 1104.78, "word": " لهذه", "probability": 0.875732421875}, {"start": 1104.78, "end": 1105.14, "word": " الدالة،", "probability": 0.947998046875}, {"start": 1105.14, "end": 1105.56, "word": " فبقوللي", "probability": 0.53253173828125}, {"start": 1105.56, "end": 1105.72, "word": " في", "probability": 0.91845703125}, {"start": 1105.72, "end": 1106.66, "word": " ثلاثة", "probability": 0.95771484375}, {"start": 1106.66, "end": 1107.94, "word": " مواقع،", "probability": 0.94130859375}, {"start": 1107.94, "end": 1108.58, "word": " الموقع", "probability": 0.9103190104166666}, {"start": 1108.58, "end": 1109.0, "word": " الأول", "probability": 0.962158203125}, {"start": 1109.0, "end": 1109.34, "word": " عند", "probability": 0.93359375}, {"start": 1109.34, "end": 1110.06, "word": " النقاط", "probability": 0.9246419270833334}, {"start": 1110.06, "end": 1110.94, "word": " الداخلية", "probability": 0.9881591796875}, {"start": 1110.94, "end": 1111.74, "word": " للمشتقة", "probability": 0.86591796875}, {"start": 1111.74, "end": 1112.08, "word": " عندها", "probability": 0.9521484375}, {"start": 1112.08, "end": 1112.54, "word": " يسوى", "probability": 0.64453125}, {"start": 1112.54, "end": 1113.18, "word": " وين؟", "probability": 0.69580078125}], "temperature": 1.0}, {"id": 49, "seek": 114136, "start": 1113.43, "end": 1141.37, "text": "زيرو فعلا هاي C1 وC2 وC4 يبقى هاي المواقع اللي المشتقة عندها تسوى Zero إذا هادي Extreme value عند C1 و Extreme value عند C2 و Extreme value عند C4 النقطة الأولى النقطة الثانية بدك interior point بهاي المشتقة عندها مالها غير معرفة يبقى باجبيه عندها C3 هل المشتقة", "tokens": [11622, 13546, 2407, 6156, 3615, 15040, 8032, 47302, 383, 16, 4032, 34, 17, 4032, 34, 19, 7251, 3555, 4587, 7578, 8032, 47302, 9673, 14407, 4587, 3615, 13672, 1829, 9673, 8592, 2655, 28671, 43242, 11296, 6055, 3794, 2407, 7578, 17182, 11933, 15730, 8032, 995, 16254, 39525, 2158, 43242, 383, 16, 4032, 39525, 2158, 43242, 383, 17, 4032, 39525, 2158, 43242, 383, 19, 28239, 47432, 3660, 16247, 12610, 7578, 28239, 47432, 3660, 6024, 104, 7649, 10632, 47525, 4117, 10636, 935, 4724, 11296, 1829, 9673, 8592, 2655, 28671, 43242, 11296, 3714, 6027, 11296, 32771, 13546, 20449, 28480, 3660, 7251, 3555, 4587, 7578, 4724, 26108, 21292, 3224, 43242, 11296, 383, 18, 8032, 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Extreme values طبعا يبقى هاية كل الكلام النظري حاطنا على الرسمة تبعتنا أجاني التعريف تاني", "tokens": [2407, 8608, 995, 45865, 4724, 17182, 4032, 41193, 1211, 3615, 12174, 32640, 1783, 13672, 7578, 39894, 9778, 23942, 9673, 8592, 2655, 28671, 6055, 3794, 995, 45865, 17182, 1975, 2655, 1863, 9957, 47525, 7578, 5551, 3215, 13063, 15844, 25062, 32640, 13672, 7578, 39894, 9778, 23942, 9673, 8592, 2655, 28671, 32771, 13546, 20449, 28480, 3660, 6055, 1211, 9307, 3660, 4724, 32887, 5016, 5551, 3215, 13063, 4032, 23557, 15844, 2423, 7649, 5172, 41779, 4724, 30544, 10874, 3555, 2655, 43761, 39525, 4190, 23032, 3555, 3615, 995, 7251, 3555, 4587, 7578, 8032, 995, 10632, 28242, 2423, 28820, 10943, 28239, 19913, 16572, 11331, 41193, 8315, 15844, 34892, 38251, 3660, 6055, 3555, 34268, 8315, 5551, 7435, 7649, 1829, 16712, 3615, 16572, 5172, 6055, 7649, 1829], "avg_logprob": -0.28571428070549204, "compression_ratio": 1.8095238095238095, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 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"word": " كل", "probability": 0.97900390625}, {"start": 1225.67, "end": 1226.19, "word": " الكلام", "probability": 0.919921875}, {"start": 1226.19, "end": 1226.71, "word": " النظري", "probability": 0.9412434895833334}, {"start": 1226.71, "end": 1227.59, "word": " حاطنا", "probability": 0.7428385416666666}, {"start": 1227.59, "end": 1227.89, "word": " على", "probability": 0.88720703125}, {"start": 1227.89, "end": 1228.45, "word": " الرسمة", "probability": 0.9357096354166666}, {"start": 1228.45, "end": 1229.11, "word": " تبعتنا", "probability": 0.95751953125}, {"start": 1229.11, "end": 1230.03, "word": " أجاني", "probability": 0.81866455078125}, {"start": 1230.03, "end": 1230.67, "word": " التعريف", "probability": 0.848876953125}, {"start": 1230.67, "end": 1231.09, "word": " تاني", "probability": 0.8802083333333334}], "temperature": 1.0}, {"id": 54, "seek": 125554, "start": 1248.6, "end": 1255.54, "text": "ماذا يعني نقاط حرجة لدالة؟", "tokens": [2304, 45636, 995, 37495, 22653, 8717, 4587, 41193, 11331, 47341, 3660, 5296, 3215, 6027, 3660, 22807], "avg_logprob": -0.6746323529411765, "compression_ratio": 0.8727272727272727, "no_speech_prob": 0.0, "words": [{"start": 1248.6, "end": 1250.0, "word": "ماذا", "probability": 0.4974365234375}, {"start": 1250.0, "end": 1250.0, "word": " يعني", "probability": 0.6640625}, {"start": 1250.0, "end": 1250.6, "word": " نقاط", "probability": 0.70556640625}, {"start": 1250.6, "end": 1251.76, "word": " حرجة", "probability": 0.6644694010416666}, {"start": 1251.76, "end": 1255.54, "word": " لدالة؟", "probability": 0.51845703125}], "temperature": 1.0}, {"id": 55, "seek": 127697, "start": 1257.49, "end": 1276.97, "text": "اللي المشتقة عندها تساوي Zero أو المشتقة عندها بس in third point مش الأقراف يعني لو جينا سألنا حالنا من خلال الرسم اللي عندنا ما هي ال critical points بقولوا قداشر؟ أربع", "tokens": [6027, 20292, 9673, 8592, 2655, 28671, 43242, 11296, 6055, 3794, 995, 45865, 17182, 34051, 9673, 8592, 2655, 28671, 43242, 11296, 4724, 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قداشر؟", "probability": 0.7498046875}, {"start": 1276.03, "end": 1276.97, "word": " أربع", "probability": 0.7029622395833334}], "temperature": 1.0}, {"id": 56, "seek": 130155, "start": 1278.53, "end": 1301.55, "text": "وC2 وC4 المشتقة عندها تساوي Zero C3 المشتقة عندها Undefined يبقى هدول الأربعة هم ال critical point نواصل ما كنا نتحدث به ونحاول أن نجمل ال remark و ال definition بإتنين بمعلومة نجمل اتنين بالمعلومة التالية", "tokens": [2407, 34, 17, 4032, 34, 19, 9673, 8592, 2655, 28671, 43242, 11296, 6055, 3794, 995, 45865, 17182, 383, 18, 9673, 8592, 2655, 28671, 43242, 11296, 2719, 5666, 2001, 7251, 3555, 4587, 7578, 8032, 3215, 12610, 16247, 25513, 27884, 8032, 2304, 2423, 4924, 935, 8717, 2407, 33546, 1211, 19446, 9122, 8315, 8717, 2655, 24401, 12984, 39627, 4032, 1863, 5016, 995, 12610, 14739, 8717, 7435, 42213, 2423, 7942, 4032, 2423, 7123, 4724, 28814, 2655, 1863, 9957, 4724, 2304, 30241, 20498, 3660, 8717, 7435, 42213, 1975, 2655, 1863, 9957, 20666, 2304, 30241, 20498, 3660, 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0.8525390625}, {"start": 2437.3, "end": 2437.62, "word": " لل", "probability": 0.88525390625}, {"start": 2437.62, "end": 2438.2, "word": " absolute", "probability": 0.9111328125}, {"start": 2438.2, "end": 2438.92, "word": " value", "probability": 0.986328125}], "temperature": 1.0}, {"id": 100, "seek": 246317, "start": 2439.09, "end": 2463.17, "text": "بمقدار خمسة وبالشكل اللي عندنا هذا تمام؟ بس قداش هذا اللي بدنا نعرفه الآن ونحدده على الرسمة يبقى عند الخمسة دالة قابلة للاشتقاء؟ لأ لإن عندي الخمسة المشتقة من اليمين تختلف عن المشتقة من الشمال يبقى هنا بقول لؤات", "tokens": [3555, 2304, 28543, 9640, 16490, 2304, 3794, 3660, 46599, 6027, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 46811, 10943, 22807, 4724, 3794, 12174, 3215, 33599, 23758, 13672, 1829, 47525, 8315, 8717, 3615, 28480, 3224, 6024, 48506, 4032, 1863, 24401, 3215, 3224, 15844, 34892, 38251, 3660, 7251, 3555, 4587, 7578, 43242, 33962, 2304, 3794, 3660, 11778, 6027, 3660, 12174, 16758, 37977, 24976, 33599, 2655, 4587, 16606, 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{"start": 2450.37, "end": 2450.99, "word": " الخمسة", "probability": 0.96484375}, {"start": 2450.99, "end": 2451.43, "word": " دالة", "probability": 0.7981770833333334}, {"start": 2451.43, "end": 2452.05, "word": " قابلة", "probability": 0.9894205729166666}, {"start": 2452.05, "end": 2453.67, "word": " للاشتقاء؟", "probability": 0.8092447916666666}, {"start": 2453.67, "end": 2454.07, "word": " لأ", "probability": 0.977783203125}, {"start": 2454.07, "end": 2454.53, "word": " لإن", "probability": 0.8102213541666666}, {"start": 2454.53, "end": 2455.13, "word": " عندي", "probability": 0.7196044921875}, {"start": 2455.13, "end": 2455.79, "word": " الخمسة", "probability": 0.99365234375}, {"start": 2455.79, "end": 2456.57, "word": " المشتقة", "probability": 0.9000244140625}, {"start": 2456.57, "end": 2456.83, "word": " من", "probability": 0.99462890625}, {"start": 2456.83, "end": 2457.43, "word": " اليمين", "probability": 0.8583984375}, {"start": 2457.43, "end": 2458.49, "word": " تختلف", "probability": 0.9866536458333334}, {"start": 2458.49, "end": 2458.81, "word": " عن", "probability": 0.95654296875}, {"start": 2458.81, "end": 2459.61, "word": " المشتقة", "probability": 0.9725341796875}, {"start": 2459.61, "end": 2459.89, "word": " من", "probability": 0.99072265625}, {"start": 2459.89, "end": 2460.55, "word": " الشمال", "probability": 0.9837239583333334}, {"start": 2460.55, "end": 2461.43, "word": " يبقى", "probability": 0.93798828125}, {"start": 2461.43, "end": 2461.69, "word": " هنا", "probability": 0.986328125}, {"start": 2461.69, "end": 2462.33, "word": " بقول", "probability": 0.966796875}, {"start": 2462.33, "end": 2463.17, "word": " لؤات", "probability": 0.62353515625}], "temperature": 1.0}, {"id": 101, "seek": 248928, "start": 2463.66, "end": 2489.28, "text": "الـ X يساوي خمسة الـ F prime is undefined لكن هل الدالة معرفة أن X يساوي خمسة أو لا؟ معرفة، الدالة معرفة، بس المشتق اللي مش معرفة يبقى at X الـ F prime is undefined يبقى هذا يعطيك أن X يساوي خمسة is a critical", "tokens": [6027, 39184, 1783, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 2423, 39184, 479, 5835, 307, 674, 5666, 2001, 44381, 8032, 1211, 32748, 6027, 3660, 20449, 28480, 3660, 14739, 1783, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 34051, 20193, 22807, 20449, 28480, 3660, 12399, 32748, 6027, 3660, 20449, 28480, 3660, 12399, 4724, 3794, 9673, 8592, 2655, 4587, 13672, 1829, 37893, 20449, 28480, 3660, 7251, 3555, 4587, 7578, 412, 1783, 2423, 39184, 479, 5835, 307, 674, 5666, 2001, 7251, 3555, 4587, 7578, 23758, 7251, 3615, 9566, 1829, 4117, 14739, 1783, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 307, 257, 4924], "avg_logprob": -0.32015931606292725, "compression_ratio": 1.9226190476190477, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2463.66, "end": 2463.96, "word": "الـ", "probability": 0.3271484375}, {"start": 2463.96, "end": 2464.16, "word": " X", "probability": 0.392822265625}, {"start": 2464.16, "end": 2465.14, "word": " يساوي", 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معرفة", "probability": 0.962890625}, {"start": 2478.36, "end": 2480.36, "word": " يبقى", "probability": 0.81048583984375}, {"start": 2480.36, "end": 2480.76, "word": " at", "probability": 0.398193359375}, {"start": 2480.76, "end": 2480.98, "word": " X", "probability": 0.7119140625}, {"start": 2480.98, "end": 2481.2, "word": " الـ", "probability": 0.417266845703125}, {"start": 2481.2, "end": 2481.26, "word": " F", "probability": 0.6787109375}, {"start": 2481.26, "end": 2481.46, "word": " prime", "probability": 0.84375}, {"start": 2481.46, "end": 2481.66, "word": " is", "probability": 0.7421875}, {"start": 2481.66, "end": 2481.92, "word": " undefined", "probability": 0.7947591145833334}, {"start": 2481.92, "end": 2482.32, "word": " يبقى", "probability": 0.79400634765625}, {"start": 2482.32, "end": 2482.64, "word": " هذا", "probability": 0.81201171875}, {"start": 2482.64, "end": 2483.9, "word": " يعطيك", "probability": 0.653564453125}, {"start": 2483.9, "end": 2484.44, "word": " أن", "probability": 0.66552734375}, {"start": 2484.44, "end": 2484.98, "word": " X", "probability": 0.921875}, {"start": 2484.98, "end": 2485.62, "word": " يساوي", "probability": 0.9693603515625}, {"start": 2485.62, "end": 2486.86, "word": " خمسة", "probability": 0.9925537109375}, {"start": 2486.86, "end": 2487.56, "word": " is", "probability": 0.798828125}, {"start": 2487.56, "end": 2488.3, "word": " a", "probability": 0.7744140625}, {"start": 2488.3, "end": 2489.28, "word": " critical", "probability": 0.84521484375}], "temperature": 1.0}, {"id": 102, "seek": 250909, "start": 2490.71, "end": 2509.09, "text": "أو إذا بدك Extreme كمان Critical and Extreme Value طيب تمام معناته بدنا نحسب F of خمسة فيه بره Extreme Value؟", "tokens": [10721, 2407, 11933, 15730, 47525, 4117, 39525, 9122, 2304, 7649, 39482, 293, 39525, 39352, 23032, 1829, 3555, 46811, 10943, 20449, 8315, 47395, 47525, 8315, 8717, 5016, 35457, 479, 295, 16490, 2304, 3794, 3660, 8978, 3224, 4724, 2288, 3224, 39525, 39352, 22807], "avg_logprob": -0.27697173115752993, "compression_ratio": 1.204724409448819, "no_speech_prob": 0.0, "words": [{"start": 2490.71, "end": 2491.11, "word": "أو", "probability": 0.7099609375}, {"start": 2491.11, "end": 2491.27, "word": " إذا", "probability": 0.7249755859375}, {"start": 2491.27, "end": 2491.75, "word": " بدك", "probability": 0.751708984375}, {"start": 2491.75, "end": 2492.49, "word": " Extreme", "probability": 0.281005859375}, {"start": 2492.49, "end": 2493.09, "word": " كمان", "probability": 0.9700520833333334}, {"start": 2493.09, "end": 2494.11, "word": " Critical", "probability": 0.63232421875}, {"start": 2494.11, "end": 2495.77, "word": " and", "probability": 0.9111328125}, {"start": 2495.77, "end": 2498.99, "word": " Extreme", "probability": 0.78857421875}, {"start": 2498.99, "end": 2499.87, "word": " Value", "probability": 0.8232421875}, {"start": 2499.87, "end": 2502.57, "word": " طيب", "probability": 0.8328450520833334}, {"start": 2502.57, "end": 2503.11, "word": " 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extreme value او the only critical point يبقى F of خمسة absolute value ليه خمسة ناقص خمسة و يسوى كده؟ Zero بدنا نروح عند الطرفين يبقى بدنا نيجي ناخد F of أربعة absolute value للأربعة ناقص خمسة absolute value للسالد واحد يبقى بواحد", "tokens": [41185, 13412, 17082, 6027, 3660, 7251, 3555, 4587, 7578, 11778, 1829, 264, 787, 8084, 2158, 1975, 2407, 264, 787, 4924, 935, 7251, 3555, 4587, 7578, 479, 295, 16490, 2304, 3794, 3660, 8236, 2158, 32239, 3224, 16490, 2304, 3794, 3660, 8717, 995, 4587, 9381, 16490, 2304, 3794, 3660, 4032, 7251, 3794, 2407, 7578, 9122, 3215, 3224, 22807, 17182, 47525, 8315, 8717, 32887, 5016, 43242, 41950, 28480, 9957, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 1829, 7435, 1829, 8717, 47283, 3215, 479, 295, 5551, 25513, 27884, 8236, 2158, 24976, 10721, 25513, 27884, 8717, 995, 4587, 9381, 16490, 2304, 3794, 3660, 8236, 2158, 24976, 3794, 6027, 3215, 36764, 24401, 7251, 3555, 4587, 7578, 4724, 14407, 24401], "avg_logprob": -0.2186129439556808, "compression_ratio": 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"end": 2604.68, "text": "باقي القيام اللي عندنا هنا ال F of خمسة بزيرو وال F of أربعة بواحد وال F of سبعة باتنين مين ال absolute maximum؟ سبعة ومين ال absolute minimum؟ ال خمسة اللي هو Zero عند X يسوي خمسة يبقى من هذا الكلام بقدر أقوله ما يأتي", "tokens": [3555, 995, 38436, 25062, 1829, 10943, 13672, 1829, 43242, 8315, 34105, 2423, 479, 295, 16490, 2304, 3794, 3660, 4724, 11622, 13546, 2407, 16070, 479, 295, 5551, 25513, 27884, 4724, 14407, 24401, 16070, 479, 295, 8608, 3555, 27884, 4724, 9307, 1863, 9957, 3714, 9957, 2423, 8236, 6674, 22807, 8608, 3555, 27884, 4032, 2304, 9957, 2423, 8236, 7285, 22807, 2423, 16490, 2304, 3794, 3660, 13672, 1829, 31439, 17182, 43242, 1783, 7251, 3794, 45865, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 9154, 23758, 2423, 28820, 10943, 4724, 28543, 2288, 5551, 39648, 3224, 19446, 7251, 10721, 31371], "avg_logprob": -0.25641446615520275, "compression_ratio": 1.7614213197969544, "no_speech_prob": 0.0, "words": [{"start": 2575.76, "end": 2576.26, 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"probability": 0.82373046875}, {"start": 4837.61, "end": 4838.43, "word": " وهذه", "probability": 0.792724609375}, {"start": 4838.43, "end": 4839.05, "word": " بتاخد", "probability": 0.8766276041666666}, {"start": 4839.05, "end": 4839.19, "word": " ال", "probability": 0.86865234375}, {"start": 4839.19, "end": 4839.45, "word": " zero", "probability": 0.69140625}, {"start": 4839.45, "end": 4840.07, "word": " تبعها", "probability": 0.8958740234375}, {"start": 4840.07, "end": 4841.11, "word": " وين؟", "probability": 0.7220052083333334}, {"start": 4841.11, "end": 4841.61, "word": " عند", "probability": 0.755859375}, {"start": 4841.61, "end": 4842.25, "word": " التلاتة", "probability": 0.9534912109375}, {"start": 4842.25, "end": 4842.53, "word": " بعد", "probability": 0.402587890625}, {"start": 4842.53, "end": 4843.25, "word": " التلاتة", "probability": 0.971435546875}, {"start": 4843.25, "end": 4844.17, "word": " ماعنديش", "probability": 0.92490234375}, {"start": 4844.17, "end": 4845.07, "word": " قبل", "probability": 0.74951171875}, {"start": 4845.07, "end": 4845.83, "word": " التلاتة", "probability": 0.975830078125}, {"start": 4845.83, "end": 4846.13, "word": " زي", "probability": 0.968994140625}, {"start": 4846.13, "end": 4846.59, "word": " اتنين", "probability": 0.9146728515625}, {"start": 4846.59, "end": 4847.01, "word": " دايما", "probability": 0.7843424479166666}, {"start": 4847.01, "end": 4847.13, "word": " و", "probability": 0.72509765625}, {"start": 4847.13, "end": 4847.61, "word": " أبدا", "probability": 0.775390625}], "temperature": 1.0}, {"id": 201, "seek": 487628, "start": 4848.34, "end": 4876.28, "text": "بالموجة يبقى هذا الموجة بالشكل اللي عندنا هذا كله طيب كويس نحط الحدود الإقليمية يبقى هذا الحدود هذه ال zero وهذه الأتناشر على خمسة وهذه مين اللي هي التلاتة وهذه هنا اللي هي الأتناشر على خمسة", "tokens": [3555, 45340, 29245, 3660, 7251, 3555, 4587, 7578, 23758, 9673, 29245, 3660, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 28242, 3224, 23032, 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+ +25 +00:02:46,450 --> 00:02:51,870 +الـ Y تساوي F of X about the line X يساوي L X + +26 +00:02:51,870 --> 00:02:57,910 +يساوي L قد يكون محور Y وقد يكون خط موازي لمحور Y + +27 +00:02:57,910 --> 00:03:02,390 +لأن X يساوي رقم تمام سواء كان هذا الرقم موجب أو + +28 +00:03:02,390 --> 00:03:07,170 +سالب بهم ليش بهم انه في عند دوران حوالين هذا + +29 +00:03:07,170 --> 00:03:15,000 +المحور ال volume V يساوي تكمل من A لB لاتنيننق في + +30 +00:03:15,000 --> 00:03:20,700 +الارتفاع تبع الأسطوانة اتنين تهشيل ريض يصيب نصف + +31 +00:03:20,700 --> 00:03:27,380 +قطر القشرة الأسطواني القاعدة تبعتها فشيلها عيد في + +32 +00:03:27,380 --> 00:03:32,400 +الارتفاع تبع مين؟ تبع الأسطوانة تمام؟ او اختصر ما + +33 +00:03:32,400 --> 00:03:36,720 +قلت اكمل ايه لبلا اتنين باي اكس في ال F of X DX + +34 +00:03:36,720 --> 00:03:41,620 +تعالى نشوف هذا الكلام على الطبيعةأنا عندي ملحنة زي + +35 +00:03:41,620 --> 00:03:46,640 +ما انت شايفين Y تساوي F of X وخليته أعلى محور X + +36 +00:03:46,640 --> 00:03:50,680 +ممكن يتقاطع مع الله ينقله وممكن مايتقاطعش يبقى أنا + +37 +00:03:50,680 --> 00:03:54,360 +جبتك ال general form الشكل عام سواء تقاطع مع ال أو + +38 +00:03:54,360 --> 00:04:00,200 +لم يتقاطع هذا الملحنة حصرلي مساحة المساحة اللي + +39 +00:04:00,200 --> 00:04:03,580 +بينه و بين محور X اللي هي المساحة المظللة اللي + +40 +00:04:03,580 --> 00:04:09,000 +قدامنا هذه ما لها هذه هذه جامد دارت حوالين الخط + +41 +00:04:11,520 --> 00:04:16,080 +الخط اللي عندنا هذا يبقى هيجيني شكل في الناحية + +42 +00:04:16,080 --> 00:04:21,660 +التانية تماما زيك وجيني بالشكل هذا تمام يبقى هذا + +43 +00:04:21,660 --> 00:04:25,680 +المنحنة اللي هيجيني فوق بالشكل اللي عندنا هذازي + +44 +00:04:25,680 --> 00:04:30,400 +اللي هناك بالضبط و ال b اللي هناك هتيجيني ب زيها + +45 +00:04:30,400 --> 00:04:35,400 +هنا بس بإشارة مين سالم و ال a اللي هناك هيجيني a + +46 +00:04:35,400 --> 00:04:41,660 +زيها بس بإشارة سيبجي هذه سالم a و سالم bيبقى هذه + +47 +00:04:41,660 --> 00:04:47,520 +عند دورانها بدها ترسم لي محيط دائرة تمام؟ وهذه عند + +48 +00:04:47,520 --> 00:04:53,140 +دورانها كذلك بدها ترسملي محيط دائرة زي ما انتوا + +49 +00:04:53,140 --> 00:04:58,280 +شايفين بالشكل هذا يبقى هذا الشكل المجسم الناتج من + +50 +00:04:58,280 --> 00:05:03,040 +الدوران لسه ما اتكلمتش في الشلة انا اعطيتك شكل + +51 +00:05:03,040 --> 00:05:09,380 +المجسمهذه الشجرة التانية كمان بتكون برضه مظللة زي + +52 +00:05:09,380 --> 00:05:14,980 +اللي هناك بالضبط تماما يبقى هذا شكل المجسم الناتج + +53 +00:05:14,980 --> 00:05:21,440 +من الدوران هذه اللي جوا هيك هذه الصغيرة هذه بتكون + +54 +00:05:21,440 --> 00:05:26,660 +بالشكل هذه يعني كأنه في تجويف، كويس؟ الآن المجسم + +55 +00:05:26,660 --> 00:05:30,580 +اللي يعني يسيبك من التجويف، المنطقة هذه داير ميدور + +56 +00:05:30,580 --> 00:05:36,450 +حواليها وكله مصمدالان بناروح نعمل cylindrical + +57 +00:05:36,450 --> 00:05:40,490 +shell بدنا ناخد مقطع أو المقطع عادى على شكل + +58 +00:05:40,490 --> 00:05:46,550 +أسطوانة يبقى بالدادى في الحالة هذه بعكس من ما كنا + +59 +00:05:46,550 --> 00:05:51,210 +نعمل المرة اللى فاتت في ال disk و كذلك في ال + +60 +00:05:51,210 --> 00:05:55,900 +washerبجرب نفسي خط يقطع منطقة التكامل و عمودي على + +61 +00:05:55,900 --> 00:06:00,960 +محور الدوران، مظبوط؟ اليوم بدنا نعمل خط يقطع منطقة + +62 +00:06:00,960 --> 00:06:04,920 +التكامل وموازي لمحور الدوران، على عكس المرة اللي + +63 +00:06:04,920 --> 00:06:09,840 +فاتت، يبقى بدي اقول لو كان عندي هذا الخط بالشكل + +64 +00:06:09,840 --> 00:06:16,280 +اللي انه هذاوالحظون شايفينه؟ تمام يبقى هذه النقطة + +65 +00:06:16,280 --> 00:06:22,520 +عند ورا عنها بدها ترسم لمحيط دائرة بدها تجين هيك + +66 +00:06:22,520 --> 00:06:26,600 +بالشكل اللي عندنا هذا، هذا هيك، و هذا بده يجين + +67 +00:06:26,600 --> 00:06:31,540 +هيك، و هذا الخط الراسي هيه، و من هنا بدها تعمل + +68 +00:06:31,540 --> 00:06:39,800 +لمحيط دائرة بالشكل اللي عندنا هنا تمام؟طيب لو جيت + +69 +00:06:39,800 --> 00:06:44,800 +هذه نقطة الأصل على سبيل المثال يبقى هذا البعد لحد + +70 +00:06:44,800 --> 00:06:50,340 +هنا جداش بده يكون X يعني X البعد من نقطة الأصل هذه + +71 +00:06:50,340 --> 00:06:54,940 +لغاية النقطة هذه يبقى هذا هو X شايفين الأسطوانة + +72 +00:06:54,940 --> 00:06:59,220 +الخضر هذي الأسطوانة الخضر هذي اللي هي الشل زي ما + +73 +00:06:59,220 --> 00:07:02,700 +وريتكوا توي ساحية إحدى الورقات من الدفتر اللي + +74 +00:07:02,700 --> 00:07:07,470 +عملناه على شكل أسطوانةيبقى الخضرة هذه هو الـ + +75 +00:07:07,470 --> 00:07:12,210 +cylindrical shell القشرة الأسطونية، بدّى تجيب قداش + +76 +00:07:12,210 --> 00:07:17,670 +المساحة الجانبية لها، هذا نصف القطرة مقداش X، + +77 +00:07:17,670 --> 00:07:25,180 +المساحة الجانبية اتنين طهنق، يبقى اتنين by Xفي من؟ + +78 +00:07:25,180 --> 00:07:29,880 +في الارتفاع، الارتفاع هو F of X هذا، صحيح ولا لأ؟ + +79 +00:07:29,880 --> 00:07:35,940 +يبقى هذا هو الارتفاع اللي عندنا اللي هو F of X، + +80 +00:07:35,940 --> 00:07:39,600 +يبقى هذا بيعطينا المساحة الجانبية للوسط، وانا من + +81 +00:07:39,600 --> 00:07:44,340 +هنا قلنا ال volume يبدو يساوي تكامل 2 باي X في F + +82 +00:07:44,340 --> 00:07:51,190 +of XDX ان كامل عليها بطلعلي قداش حجم المجسم المصمد + +83 +00:07:51,190 --> 00:07:54,650 +داير مايدور اللي عندنا هذا يبقى واضح شكل الـ + +84 +00:07:54,650 --> 00:07:58,610 +cylindrical shell هذا لو كان التكامل بالنسبة لـ X + +85 +00:07:58,610 --> 00:08:03,530 +يبقى هنا بفرج عن المرتين الماضيتين ان المقطع اللي + +86 +00:08:03,530 --> 00:08:07,390 +هو الخط المستقيم اللي بنرسمه بدل ما كنا نرسمه + +87 +00:08:07,390 --> 00:08:11,390 +عمودي على محور الدوران اليوم نرسمه موازن لمحور + +88 +00:08:11,390 --> 00:08:15,670 +الدورانهذا الخط الموجود هو f of x + +89 +00:08:26,270 --> 00:08:30,750 +هذا الدوران حوالي الخط يكون محور Y أو موازي لمحور + +90 +00:08:30,750 --> 00:08:37,690 +Y ممكن يكون الدوران حوالي الخط موازي لمحور X تمام؟ + +91 +00:08:37,690 --> 00:08:42,930 +يبقى الحدث ذلك يصير التكمل بالنسبة إلى Y يبقى يصير + +92 +00:08:42,930 --> 00:08:48,310 +التكمل اتنين by Y F of Y Dy طبعا هذي كامتلة على + +93 +00:08:48,310 --> 00:08:53,450 +الشجتين كيف هذه وكيف هذه يبقى الفكرة في الأساس بس + +94 +00:08:53,870 --> 00:08:59,830 +تعرف اللي هو شكل النص في القطر تبع الـ cylindrical + +95 +00:08:59,830 --> 00:09:04,230 +shell وتعرف الارتفاع، ضروري كل مرة ارسم و مرة ارسم + +96 +00:09:04,230 --> 00:09:09,330 +هذا؟ لا مش ضروري، بس ارسملي منطقة التكامل، ارسملي + +97 +00:09:09,330 --> 00:09:15,130 +خط يوازي محور الدورانو حدد لقداش بقى الطرف الخط عن + +98 +00:09:15,130 --> 00:09:19,130 +المركز اللى عندك بيكون هذا هو نصف الخطر والخط اللى + +99 +00:09:19,130 --> 00:09:24,410 +رسمت بيكون هو الشيل هايت هو الارتفاع او الارتفاع + +100 +00:09:24,410 --> 00:09:28,410 +الجانبي للقصانة بعد هيك حدود التكامل ممكن تكون + +101 +00:09:28,410 --> 00:09:33,490 +محددة عندك ممكن انت بدك تحددها من حال مستقيمات مع + +102 +00:09:33,490 --> 00:09:38,150 +منحنيات او منحنيات مع بعضها الى اخرى كما سنراه بعد + +103 +00:09:38,150 --> 00:09:43,640 +قليلهذا كل جزء النظر اللي موجود في هذا الsection + +104 +00:09:43,640 --> 00:09:46,920 +بس الكلمتين اللي قدامك على اللوحة دول حدا اللي هو + +105 +00:09:46,920 --> 00:09:54,260 +اي تساؤل طيب نبدأ في الأمثلة نجي لأول مثال على هذا + +106 +00:09:54,260 --> 00:09:55,900 +الموضوع يبقى examples + +107 +00:10:03,850 --> 00:10:08,530 +أول مثال من هذه اللي ألمتله بوليفي ال volume of + +108 +00:10:08,530 --> 00:10:19,330 +the solid find the volume of the solid generated + +109 +00:10:19,330 --> 00:10:23,350 +by + +110 +00:10:23,350 --> 00:10:27,010 +revolving + +111 +00:10:28,290 --> 00:10:34,990 +Generated by the region revolving + +112 +00:10:34,990 --> 00:10:42,570 +the + +113 +00:10:42,570 --> 00:10:46,750 +region + +114 +00:10:46,750 --> 00:10:51,470 +between the + +115 +00:10:51,470 --> 00:10:51,990 +region + +116 +00:10:59,710 --> 00:11:07,430 +بين اتنين بيوندد والمغلقة + +117 +00:11:07,430 --> 00:11:19,770 +بيه by the curves المنحنات Y تساوي X تربيعو Y + +118 +00:11:19,770 --> 00:11:33,110 +يساوي اتنين ناقص X and X تساوي زيرو for X greater + +119 +00:11:33,110 --> 00:11:44,450 +than or equal to zero about the Y axis + +120 +00:11:57,220 --> 00:12:02,900 +خلّينا نرسم المنطقة + +121 +00:12:02,900 --> 00:12:06,360 +المحدودة بالمنحنات اللي عندنا نقول المنحنة + +122 +00:12:06,360 --> 00:12:11,420 +الأولاني Y تساوي X تربيع إذا لو جيت رسمت هذا + +123 +00:12:11,420 --> 00:12:18,880 +المنحنة هذا محور X هذا محور Y هذه نقطة الأصل يبقى + +124 +00:12:18,880 --> 00:12:27,700 +هذا Y تساوي X تربيعبعدها قال الخط المستقيم y تساوي + +125 +00:12:27,700 --> 00:12:33,020 +اتنين ناقص x إذا لو كانت ال x ب zero y يبقى دي اش + +126 +00:12:33,020 --> 00:12:40,420 +ب اتنين يبقى هذه اتنينوإذا كان الـ Y بـ Zero و X + +127 +00:12:40,420 --> 00:12:46,260 +باتنين يبقى باتنين هذه الاتنين اللي عندنا هذه يبقى + +128 +00:12:46,260 --> 00:12:52,140 +هذه كمان اتنين يبقى هتان النقطتان تقعان على الخط + +129 +00:12:52,140 --> 00:12:57,220 +المستقيم اللي عندنا يبقى أروح نرسمنا هذا الخط + +130 +00:12:57,220 --> 00:13:02,900 +المستقيم بالشكل هذا دوام يبقى هذا هو الخط المستقيم + +131 +00:13:10,240 --> 00:13:15,340 +يبقى هاي المنطقة اللى موجودة وين اللى موجودة أنا + +132 +00:13:15,340 --> 00:13:20,420 +يبقى باقي المنحنى هذا كله مش لازم ليه المهم هاي + +133 +00:13:20,420 --> 00:13:27,040 +المنحنى رسمناها وهذا الخط اللى همين Y يساوي اتنين + +134 +00:13:27,040 --> 00:13:31,820 +ناقص X هاي المنطقة المضلنة المنطقة المضلنة اللى + +135 +00:13:31,820 --> 00:13:36,510 +بدها تدور حوالين مين؟أو للمحور Y. إذا أنا بادر + +136 +00:13:36,510 --> 00:13:44,370 +أرسم خط يقطع منطقة التكامل وموازن لمحور Y. يبقى + +137 +00:13:44,370 --> 00:13:49,650 +بالدقج أقول له هذا خط يقطع منطقة التكامل وموازن + +138 +00:13:49,650 --> 00:14:03,820 +لمحور Y.النقطة هذه نصف + +139 +00:14:03,820 --> 00:14:09,840 +القطر يعني لو جيت من هنا رسمت نصف دائرة بيكون هذا + +140 +00:14:09,840 --> 00:14:15,120 +هو نصف قطر الدائرةطب والارتفاع تبع الدائرة الجزء + +141 +00:14:15,120 --> 00:14:19,360 +اللي في المنطقة المظلة للي تحت مالوش دعوة تمام؟ + +142 +00:14:19,360 --> 00:14:25,300 +اذا انا بدي اعرف جداش هذا طول الخط الأخضر جداش؟ + +143 +00:14:25,300 --> 00:14:30,740 +اتنين ناقص اكس اتنين ناقص اكس اللي هو بُعد الخط + +144 +00:14:30,740 --> 00:14:34,880 +اللي عندنا هذا عن محور X بدي اشيل هذا البُعد هذا + +145 +00:14:34,880 --> 00:14:42,190 +البُعد جداش؟هذا الخط أو هذا الجزء هو عبارة عن + +146 +00:14:42,190 --> 00:14:48,470 +اتنين ناقص X ناقص X تربيع يبقى هذا هو الذي يمثل + +147 +00:14:48,470 --> 00:14:54,060 +عندي هنا main ال F of X اللي هو الارتفاعتبع من؟ + +148 +00:14:54,060 --> 00:14:58,700 +تبع الاستوان او تبع الـ cylindrical shell يبقى + +149 +00:14:58,700 --> 00:15:03,620 +كويس يبقى بدي اكمل بالنسبة ل X اذا بدي اعرف X + +150 +00:15:03,620 --> 00:15:09,560 +ستتغير من و لا وين طبعا X ستتغير من Zero لغاية اخر + +151 +00:15:09,560 --> 00:15:14,670 +نقطة هنا اخر نقطة هنا جدوش انا مش عارفبنحل معادلة + +152 +00:15:14,670 --> 00:15:20,010 +الخط المستقيم مع مين مع منحنى ال parabola Y تساوي + +153 +00:15:20,010 --> 00:15:20,810 +X تربية + +154 +00:15:28,980 --> 00:15:35,040 +الشباب لو كملت هذا هيك بدي يحصل تقابل عن مين سالب + +155 +00:15:35,040 --> 00:15:39,460 +اتنين ماليش دعوة فيها هذه برا المنطقة يبقى انا + +156 +00:15:39,460 --> 00:15:44,960 +عندي بس اكس يسوي كدهش واحد اذا بدي اجي اقوله ال + +157 +00:15:44,960 --> 00:15:52,680 +volume V بدي يسوي تكامل من Zero لواحدللإتنين by X + +158 +00:15:52,680 --> 00:15:57,200 +في ال F of X F of X التفاجنا اللي هو البعد هذا + +159 +00:15:57,200 --> 00:16:05,160 +اللي هو مام اللي هو ال X اتنين ناقص X اتنين ناقص X + +160 +00:16:05,160 --> 00:16:11,610 +ناقص X تربية كله بالنسبة لمين؟ لل X أوهذا اتنين + +161 +00:16:11,610 --> 00:16:17,330 +باي برا تكامل من Zero لواحد ده لاتنين X ناقص X + +162 +00:16:17,330 --> 00:16:23,930 +تربية ناقص X تكييب كله بالنسبة الى DX النتيجة + +163 +00:16:23,930 --> 00:16:29,590 +تساوي اتنين باي هيها برا وتكامل هذا اللي هو X + +164 +00:16:29,590 --> 00:16:34,190 +تربية على اتنين مع الاتنين الله يسهل عليها ناقص X + +165 +00:16:34,190 --> 00:16:40,950 +تكييب على تلاتة ناقص X أس أربعة على أربعةكله من + +166 +00:16:40,950 --> 00:16:48,070 +أندي الـ0 لغاية الـ8 لغاية الـ1 يبقى يساوي 2πي + +167 +00:16:48,070 --> 00:16:56,670 +ناقص تلت ناقص ربع ناقص كل الباقي بقداش بـ0 هذا + +168 +00:16:56,670 --> 00:17:03,630 +الكلام بده يساوي 2πيالمضاعف المشترك كلهم كم؟ + +169 +00:17:03,630 --> 00:17:09,870 +أتناش، يبقى هنا أتناش، أتناش على تلاتة فيها أربعة، + +170 +00:17:09,870 --> 00:17:15,050 +و أتناش على أربعة فيها التلاتة، هذا الكلام بده + +171 +00:17:15,050 --> 00:17:15,750 +ساوي + +172 +00:17:19,080 --> 00:17:25,520 +تلاتة واربعة السبعة من اتناشر بطول جداش خمسة على + +173 +00:17:25,520 --> 00:17:33,460 +اتناشر يعني خمسة باي على ستة هذا قيمة الحجم تبع + +174 +00:17:33,460 --> 00:17:42,950 +المنطقة اللي هنا نعطي كمان مثال example twoأيضًا + +175 +00:17:42,950 --> 00:17:47,310 +يقول إنه يجد كمية الصليب على أي حال المثال الأول + +176 +00:17:47,310 --> 00:17:53,490 +يا شباب هو سؤال تسعة من الكتاب ومثال اتنين هو سؤال + +177 +00:17:53,490 --> 00:18:02,690 +واحد وعشرين من الكتاب يقول إنه يجد كمية + +178 +00:18:02,690 --> 00:18:05,570 +الصليب + +179 +00:18:17,530 --> 00:18:25,790 +Generated by revolving the region bounded + +180 +00:18:25,790 --> 00:18:28,850 +the + +181 +00:18:28,850 --> 00:18:43,390 +region bounded by the curves Y تساوي جذر ال X والY + +182 +00:18:43,390 --> 00:18:46,890 +تساوي Zero and + +183 +00:18:48,240 --> 00:18:56,360 +الـ y تساوي x ناقص اتنين about the + +184 +00:18:56,360 --> 00:19:03,940 +x axis حوالي المحور من؟ حوالي المحور اللي هو x + +185 +00:19:24,760 --> 00:19:34,200 +بنرجع الكلام اللي احنا كاتبينه مرة تانية تقدر + +186 +00:19:34,200 --> 00:19:37,560 +تحل بطريقتين يعني هذه انا بقدر أحلها بال + +187 +00:19:37,560 --> 00:19:42,280 +cylindrical shape بقدر أحلها بالوشة، بالشمتين بقدر + +188 +00:19:42,280 --> 00:19:46,340 +أحلها تمام؟ الحين اعطيك مثال، الحين اعطيك مثال + +189 +00:19:46,340 --> 00:19:49,120 +ونحله بالطريقة ونقول انه بيعطينا نفس النتيجة + +190 +00:19:49,120 --> 00:19:54,070 +وبالتالي اذا انا قيّدتك بطريقة انك تلتزم فيهاما + +191 +00:19:54,070 --> 00:19:59,170 +قيبتك خلاص لك الحرية. طبعا؟ سؤاله جيه السؤال يعني. + +192 +00:19:59,230 --> 00:20:02,070 +يعني انا اذا السؤال بالحل .. هذا السؤال بالحل بال + +193 +00:20:02,070 --> 00:20:06,770 +washer بسهولة كمان، غير أكيد لذا. طيب، على أي حال، + +194 +00:20:06,770 --> 00:20:13,240 +نرجع لمين؟ نرجع لسؤالنا ده.قال هاتلي حجم المجسم + +195 +00:20:13,240 --> 00:20:18,680 +المتولد بدوران المنطقة المحدودة بالمنحنى Y تساوي + +196 +00:20:18,680 --> 00:20:25,460 +جذر ال X معروف بالنسبالنا Y تساوي Zero محور X Y + +197 +00:20:25,460 --> 00:20:29,960 +تساوي X ناقص اتنين فبنرسمه والدوران بدي يكون + +198 +00:20:29,960 --> 00:20:34,520 +حوالين مين حوالين محور X إذا ليس بضرورة نرسم + +199 +00:20:34,520 --> 00:20:38,440 +الرسمة كاملة بدي نرسم بس المنطقة اللي بدها الدور + +200 +00:20:38,770 --> 00:20:43,190 +أذا انا لو روحت و قلت هذه المحور اللي عندنا هذا + +201 +00:20:43,190 --> 00:20:49,330 +محور X هذا محور Y هذه نقطة الاصل اللي هي Zero Y + +202 +00:20:49,330 --> 00:20:53,670 +تساوي جذر ال X يا ما رسمناه خلال الفصل هذا كله + +203 +00:20:53,670 --> 00:21:00,970 +بيعرف رسمه يبقى هذا Y تساوي جذر ال Xبعد ذلك يقول + +204 +00:21:00,970 --> 00:21:06,650 +لي Y تساوي زيرو Y تساوي زيرو هو ميان محور X Y + +205 +00:21:06,650 --> 00:21:12,690 +تساوي زيرو هو محور X بعد ذلك قال لي الخط Y تساوي X + +206 +00:21:12,690 --> 00:21:17,590 +ناقص اتنين بحدد النقطتين عليه و بوصل فيه ما بينهما + +207 +00:21:17,590 --> 00:21:24,010 +لو كانت ال X بزيرو ف Y بسالب اتنين يبقى I سالب + +208 +00:21:24,010 --> 00:21:31,440 +اتنينلو كانت Y بزيرو X باتنين يبقى انا من اتنين + +209 +00:21:31,440 --> 00:21:39,100 +بيأتي بوصل فيما بينهما و بمد الخط على استقامته + +210 +00:21:39,100 --> 00:21:45,800 +يبقى الآن المنطقة اللي احنا بدناها هي هذه المنطقة + +211 +00:21:45,800 --> 00:21:54,420 +والباقي كله مش لزملي تمام؟طيب، هذه المنطقة بدها + +212 +00:21:54,420 --> 00:21:59,800 +دور حوالين مين؟ حوالين محور X، بدى أروح أهلى + +213 +00:21:59,800 --> 00:22:03,860 +بالـCylindrical Shell، مش بالوشرة، يبقى موضوعنا + +214 +00:22:03,860 --> 00:22:08,400 +الـCylindrical Shell، يبقى بدأ أروح أرسم خط يقطع + +215 +00:22:08,400 --> 00:22:15,580 +هذه المنطقة وموازن لمحور الدورانيبقى باجي بقول لو + +216 +00:22:15,580 --> 00:22:22,300 +جيت أخد هذا الخط الأوفقي، الشكل أن هذا، قطع منطقة + +217 +00:22:22,300 --> 00:22:27,780 +التكامل وموازي لمحور الدوران، يبقى هذا يعتبر + +218 +00:22:27,780 --> 00:22:33,700 +ارتفاع الـCylindrical Shell، مظبوط؟ بدي نص القطر، + +219 +00:22:33,700 --> 00:22:39,840 +يبقى باجي بنزل عمود من هنا، بيكون هذا نصف القطر + +220 +00:22:40,850 --> 00:22:45,030 +طيب، هنا التكمل بيكون على عكس اللي جابله، اللي + +221 +00:22:45,030 --> 00:22:49,470 +جابله كاملة بالنسبة لمن؟ هنا بيكمل بالنسبة إلى Y، + +222 +00:22:49,470 --> 00:22:55,210 +إذا هذا البعد لو جيت goal taken أفقي، هذا Y، + +223 +00:22:55,210 --> 00:23:01,960 +الارتفاع Y يبقى بيكون نصف القطر، هذا هو Yيبقى طول + +224 +00:23:01,960 --> 00:23:05,980 +اللي عندي اعرف قداش الطول اللي عندنا هذا بدلالة + +225 +00:23:05,980 --> 00:23:14,380 +مين؟ بدلالة Y هذا Y تساوي جذر ال X يعني X يساوي Y + +226 +00:23:14,380 --> 00:23:21,460 +تربية يبقى X يساوي Y تربية اللي همين الجزء المنقطة + +227 +00:23:21,460 --> 00:23:29,020 +اللي عندنا هذا مصبوب يبقى هذا الجزء فقط هوX يساوي + +228 +00:23:29,020 --> 00:23:34,140 +Y تربية ربعنا الطرفين اللي هنا هذا الخط اللي هو + +229 +00:23:34,140 --> 00:23:42,280 +معادلة كانت ايش كانت Y تساوي X ناقص اتنين او X + +230 +00:23:42,280 --> 00:23:48,000 +يساوي Y زائد اتنين طبعا اذا ان باجي بقول البعد + +231 +00:23:48,000 --> 00:23:53,620 +الكبير ناقص البعد الصغير يبقى هذا الطول يمثل البعد + +232 +00:23:53,620 --> 00:24:00,730 +هذا كله ل Y زائد اتنيننقص البعد هذا اليومين Y + +233 +00:24:00,730 --> 00:24:06,770 +تربيه، ضالت عند ال Y ستتغير من عند Zero لعند بصر + +234 +00:24:06,770 --> 00:24:12,770 +جداش، لحد هنا تمام؟ يبقى بدي اعرف جداش الاحداث تبع + +235 +00:24:12,770 --> 00:24:18,510 +Y هذا، مشان هيك بروح احل المعادلة هذه بالنسبة لمين + +236 +00:24:18,510 --> 00:24:25,240 +الى Y هذه النقطة تقع وين؟ على المنحنيينيبقى بدي + +237 +00:24:25,240 --> 00:24:32,380 +أروح أسوي المعادلتين ببعض اللي هو Y تربية يسوي Y + +238 +00:24:32,380 --> 00:24:38,220 +زائد اتنين او بمعنى اخر لو عملت معادلة صفرية بيصير + +239 +00:24:38,220 --> 00:24:44,540 +Y تربية ناقص Y ناقص اتنين بدي يسوي قداش Zero او لو + +240 +00:24:44,540 --> 00:24:49,520 +حللتها اقواس بالشكل هذا بدي يسوي Zero يبقى هاي Y + +241 +00:24:49,740 --> 00:24:54,660 +هذا واي واي واحد وهذا اتنين وهذا ناقص وهذا زائد + +242 +00:24:54,660 --> 00:24:58,480 +زائد واي وناقص اتنين واي بناقص واي يبقى تحليلنا + +243 +00:24:58,480 --> 00:25:02,960 +سليم مائة بالمائة يبقى بناء على هدف يعطينا ان واي + +244 +00:25:02,960 --> 00:25:08,800 +تساوي سالب واحد والواي تساوي قداش اتنين ايش رأيك + +245 +00:25:08,800 --> 00:25:16,290 +في واي تساوي سالب واحد؟ مرفوض او لا؟هذا لو كملت + +246 +00:25:16,290 --> 00:25:20,570 +هكذا كملت المنحنة و بدى تقاطعني و تسلب واحد ماليش + +247 +00:25:20,570 --> 00:25:24,450 +علاقة فيها يبقى Y تساوي اتنين اللى هو البعد اللى + +248 +00:25:24,450 --> 00:25:30,570 +عندنا هذا يبقى بدى يصير التكمل عندي من Zero لغاية + +249 +00:25:30,570 --> 00:25:37,090 +قداش اتنين طيب هذه لو كانت Y تساوي اتنين يبقى ال X + +250 +00:25:37,090 --> 00:25:38,150 +تساوي قداش + +251 +00:25:42,010 --> 00:25:47,230 +أربعة يبقى النقطة هذه اللي احداثي تبعها اللي هو + +252 +00:25:47,230 --> 00:25:53,370 +أربعة و اتنين طبعا كيف أربعة و اتنين؟ شو المنحنة + +253 +00:25:53,370 --> 00:26:02,590 +هذا؟ يبقى اكس بقداش. أربعة بتتربع الطرفين. وين + +254 +00:26:02,590 --> 00:26:08,070 +اتنين؟ هذا اتنين البعد الأفق يا راجل. هذا البعد + +255 +00:26:08,070 --> 00:26:14,110 +رأسي.مش احنا طلعنا Y بإتنين، حط فيه أي معادلة + +256 +00:26:14,110 --> 00:26:19,170 +بدكيها، حط Y بإتنين، بصير X باربعة، حط Y بإتنين، + +257 +00:26:19,170 --> 00:26:22,510 +بصير X باربعة، لأن النقطة تقع على المنحنين، بتحقق + +258 +00:26:22,510 --> 00:26:28,790 +كل منهما، إذا إنت ال volume V، بده يسوى تكامل من + +259 +00:26:28,790 --> 00:26:36,370 +Zero لغاية كداشر لغاية إتنين، للإتنين by oneفي نصف + +260 +00:26:36,370 --> 00:26:40,950 +القطر اللي عندنا هذا نصف القطر اللي عندنا وهو Y زي + +261 +00:26:40,950 --> 00:26:47,890 +دي اتنين ناقص اللي هو مين هذا هذا Y زي دي اتنين + +262 +00:26:47,890 --> 00:26:57,770 +ناقص Y تربية يبقى في Y زي دي اتنين ناقص Y تربية كل + +263 +00:26:57,770 --> 00:27:03,770 +هذا الكلام بالنسبة لمين له دي Yيبقى ال volume V + +264 +00:27:03,770 --> 00:27:11,630 +يبقى يساوي 2Y برا تكامل من 0 لغاية 2 يدخل ال Y جوا + +265 +00:27:11,630 --> 00:27:19,310 +يبقى Y تربيه زائد 2Y ناقص Y تكييب كله بالنسبة + +266 +00:27:19,310 --> 00:27:27,580 +لمين؟ لـDY يبقى هذا الكلام يساوي 2Y VY تكيب على + +267 +00:27:27,580 --> 00:27:33,060 +ثلاثة زائد Y تربيع اتنين مع اتنين مع السلامة Y + +268 +00:27:33,060 --> 00:27:40,090 +أربع على أربع من Zero لغاية اتنينيساوى اتنين باى + +269 +00:27:40,090 --> 00:27:44,970 +برا يبقى تمانية + +270 +00:27:44,970 --> 00:27:55,250 +على تلاتة زائد اربعة ناقص ستاشر على اربعة اربعة + +271 +00:27:55,250 --> 00:28:01,750 +مع اربعة نصير يبقى هذا ستاشر باى على تلاتة هذا + +272 +00:28:01,750 --> 00:28:05,110 +حجمين حجم هذه المنطقة + +273 +00:28:10,000 --> 00:28:14,320 +ما رأيك تجي هنا على اللوحة نشوفك شوية ايه اللي حد + +274 +00:28:14,320 --> 00:28:19,400 +تعالي شو؟ عالي بالكوا يمكن نجاوب على بعض أسئلتكوا + +275 +00:28:19,400 --> 00:28:24,140 +اه تفضل انا + +276 +00:28:24,140 --> 00:28:29,680 +بكمل بالنسبة ل .. انا بكمل بالنسبة ل Y لو بالنسبة + +277 +00:28:29,680 --> 00:28:36,700 +ل X طيب انت من الصفر اللي هو اربعة ليه X؟مالك؟ طيب + +278 +00:28:36,700 --> 00:28:41,480 +اضحكوا زيه لأ لو كان لو ال .. لو ال قصد من Y تسوّر + +279 +00:28:41,480 --> 00:28:46,000 +من X لو كانتش فلال Y جدر ال X أبسوليوت ال X + +280 +00:28:46,000 --> 00:28:51,420 +أبسوليوت فلال X طيب هتكون على الجهتين؟ كيف حالك + +281 +00:28:51,420 --> 00:28:54,700 +انت بصيا بصيك الدورة .. استنى شوية بصيك الدورة + +282 +00:28:54,700 --> 00:28:57,780 +حواليها نفسها مش ايه؟ اه اه لإن على يمين محورك + +283 +00:28:57,780 --> 00:29:02,240 +زيهم ماجيبتش جديد طيب + +284 +00:29:02,240 --> 00:29:04,460 +نعطي كمان مثال + +285 +00:29:07,670 --> 00:29:13,590 +مثال تلاتة تلاتة + +286 +00:29:13,590 --> 00:29:17,210 +هي سؤال تسعة و عشرين من الكتاب يقول احصل على كمية + +287 +00:29:17,210 --> 00:29:26,150 +المجسم احصل على كمية المجسم + +288 +00:29:26,150 --> 00:29:28,310 +نحتاج حجم المجسم + +289 +00:29:37,130 --> 00:29:44,690 +تحول إلى المنطقة المنطقة + +290 +00:29:44,690 --> 00:29:51,910 +مجموعة من مجموعة + +291 +00:29:51,910 --> 00:30:01,070 +من Y تساوي X و Y تساوي X تربيع + +292 +00:30:06,520 --> 00:30:18,520 +the y axis حوالي المحور y by using باستخدام + +293 +00:30:18,520 --> 00:30:32,580 +نمرا a the shell method نمرا b the washer method + +294 +00:30:45,870 --> 00:30:46,910 +قولناها برسمها + +295 +00:30:53,920 --> 00:30:58,380 +سؤال مرة ثانية بيقول هات الحجم المجسم المتولد من + +296 +00:30:58,380 --> 00:31:04,820 +دوران المنطقة المحدودة بالخط Y تساوي X بالمنحنى Y + +297 +00:31:04,820 --> 00:31:10,080 +تساوي X تربيع والدوران حوالين محور Y بطريقتين + +298 +00:31:10,080 --> 00:31:13,700 +الطريقة اللي هو طريقة shell method اللي طريقتنا + +299 +00:31:13,700 --> 00:31:19,080 +قبل قليل والتانية ال washer method طريقتنا اللي هو + +300 +00:31:19,080 --> 00:31:20,920 +يوم أمس الأول + +301 +00:31:23,160 --> 00:31:29,460 +بنرسم و بعد ذلك بيصير خير يبقى هذا محور X هذا محور + +302 +00:31:29,460 --> 00:31:35,040 +Y هذا نقطة الاصل اللي هي Zero في ان المنحنة Y + +303 +00:31:35,040 --> 00:31:41,540 +تساوي X تربيع يبقى Y تساوي X تربيع المنحنة هجيلك + +304 +00:31:41,540 --> 00:31:41,940 +هيك + +305 +00:31:44,760 --> 00:31:52,380 +الخط التاني Y تساوي X يبقى Y تساوي X اللي هو الخط + +306 +00:31:52,380 --> 00:31:59,420 +اللي عندنا هذا يبقى هذا Y تساوي X هذا Y تساوي X + +307 +00:31:59,420 --> 00:32:04,180 +تربية حصروا المنطقة فيما بينهم اللي المنطقة + +308 +00:32:04,180 --> 00:32:09,570 +المضللة ديهذه المنطقة المظلة لابدها تدور حوالين + +309 +00:32:09,570 --> 00:32:15,150 +محور Y تمام؟ مدان بدها تدور حوالين محور Y يبقى + +310 +00:32:15,150 --> 00:32:22,390 +احنا بدنا نروح نرسم خط يقطع منطقة التكامل وموازن + +311 +00:32:22,390 --> 00:32:29,110 +لمحور Yيبقى لو جيت من هنا رسمت خط موازي لمحور Y + +312 +00:32:29,110 --> 00:32:34,970 +ويقطع منطقة التكامل يبقى هذا يعتبر الارتفاع + +313 +00:32:34,970 --> 00:32:40,690 +الجانبي للـ cylindrical shell بدي أعرف قداش طول + +314 +00:32:40,690 --> 00:32:48,490 +الخط الأخضر هذا بقوله تمام من هنا لهنا هذا Y تسوى + +315 +00:32:48,490 --> 00:32:57,620 +Xومن هنا لهنا هذا Y تسوى X تربيع، إذا هذا الخط + +316 +00:32:57,620 --> 00:33:04,120 +يكون الفرق بينهم اللي هو مين؟ X ناقص X تربيع، هذا + +317 +00:33:04,120 --> 00:33:12,240 +البعد، هذا البعد بيكون X نصف قطر من اللي هو + +318 +00:33:12,240 --> 00:33:18,810 +cylindrical shellبدلة ال X ستتغير من Zero لغاية + +319 +00:33:18,810 --> 00:33:25,760 +ابصر قداشيبقى بدي اعرف هنا اخر حاجة لذلك بدي احلي + +320 +00:33:25,760 --> 00:33:31,540 +المعادلتين هدول مع بعضهم يبقى انا عندي Y تساوي X + +321 +00:33:31,540 --> 00:33:39,060 +تربية وعندي Y تساوي X يبقى هذه ها بقدر اقول X + +322 +00:33:39,060 --> 00:33:44,820 +تربية ناقص X يساوي Zero او لو اخدت X عامل مشترك + +323 +00:33:44,820 --> 00:33:49,940 +بصير X ناقص واحد يساوي Zero يبقى X يساوي Zero و X + +324 +00:33:49,940 --> 00:33:55,790 +يساوي واحديبقى نقطة التقاطع الأولى عند الـ0 ونقطة + +325 +00:33:55,790 --> 00:34:02,850 +التقاطع التانية عند الـ1 يبقى بصير الـVolume V بدى + +326 +00:34:02,850 --> 00:34:11,050 +يسوى تكامل من 0 لغاية 1 للإتنين باي X في ال F of X + +327 +00:34:11,050 --> 00:34:15,390 +اللى همان X ناقص X تربية + +328 +00:34:20,080 --> 00:34:25,560 +يبقى X ناقص X تربية كل هذا الكلام بالنسبة إلى مين؟ + +329 +00:34:25,560 --> 00:34:32,620 +إلى DX يبقى هذا الكلام بيساوي 2π تكمل من 0 ل1 لل X + +330 +00:34:32,620 --> 00:34:40,820 +تربية ناقص X تكييب كله بالنسبة إلى DX يبقى 2π وهذه + +331 +00:34:40,820 --> 00:34:44,640 +عبارة عن X تكييب على 3 + +332 +00:34:47,470 --> 00:34:51,390 +نرجع لسؤالنا هذا مرة تانية وهو آخر مثال في هذا ال + +333 +00:34:51,390 --> 00:34:55,670 +section قال هاتلي حجم المجسم المتولد من دوران + +334 +00:34:55,670 --> 00:34:59,990 +المنطقة المحصورة بالمنحنى Y يساوي 2X ناقص X تربية + +335 +00:34:59,990 --> 00:35:04,810 +والخط المستقيم Y تساوي X والدوران بدي يكون مرة + +336 +00:35:04,810 --> 00:35:09,950 +حوالين محور Y ومرة حوالين خط موازي لمحور Y الهمين + +337 +00:35:09,950 --> 00:35:16,710 +X يساوي Yنعود للخط المستقيم Y2SWX نعود لهذا + +338 +00:35:16,710 --> 00:35:22,810 +المنحنى هذا المنحنى طبعا parabola انه Y دل في X و + +339 +00:35:22,810 --> 00:35:26,450 +X من الدرجة الثانية يبقى parabola بس معمولة لها + +340 +00:35:26,450 --> 00:35:30,310 +shift اذا بدى اعرف وين ال vertex بالضبط تبع هذه ال + +341 +00:35:30,310 --> 00:35:36,500 +parabola اذا بتروح اعمل اكمال للمربعيبقى هذه لو + +342 +00:35:36,500 --> 00:35:42,500 +جيت قلت Y تساوي بدنا نكمله مربع يعني قداش مضيف و + +343 +00:35:42,500 --> 00:35:50,400 +نطرح اربعة ولا واحد يعني انت بتحذر تحذير طيب مشان + +344 +00:35:50,400 --> 00:35:57,710 +تعرف قداش و ماحدش يولد تاني برنامج مضيف مربعمعامل + +345 +00:35:57,710 --> 00:36:05,710 +x على أربع أمثال معامل x تربية + +346 +00:36:09,680 --> 00:36:16,180 +بقول مربع معامل X كداش؟ أربعة أربعة أمثال معامل X + +347 +00:36:16,180 --> 00:36:20,700 +تربية أربعة في واحد تمام؟ اما هو واحد جد و ارمى + +348 +00:36:20,700 --> 00:36:24,520 +أربعة يبقى أربعة على أربعة في كداش؟ يبقى بضيف واحد + +349 +00:36:24,520 --> 00:36:31,640 +و بطرح واحد يبقى هذا Y بدي ساوي واحد ناقص واحد + +350 +00:36:31,640 --> 00:36:38,560 +زيدي اتنين X ناقص X تربيةهذا بدي اكتبه بالشكل اللي + +351 +00:36:38,560 --> 00:36:44,080 +انه هذا هذا ال Y ناقص واحد هذا كله بدي اخد منه + +352 +00:36:44,080 --> 00:36:49,820 +ناقص عامل مشترك مضال X تربيه يعني ناقص اتنين X + +353 +00:36:49,820 --> 00:36:58,320 +زائد واحد هذا معناه ان Y ناقص واحديساوي الناقص X + +354 +00:36:58,320 --> 00:37:04,320 +ناقص واحد لكل تربية يبقى هذه Parabola و ال vertex + +355 +00:37:04,320 --> 00:37:14,780 +واحد و واحد يبقى هذه Parabola open Down ولا Up؟ + +356 +00:37:14,780 --> 00:37:23,160 +Down بسبب الإشارة السالبة يبقى open down with + +357 +00:37:23,160 --> 00:37:25,760 +vertex + +358 +00:37:27,210 --> 00:37:35,510 +يبقى H و K يبقى واحد و واحد يبقى لو جيت قلت هذه + +359 +00:37:35,510 --> 00:37:40,690 +القيمة اللي عندنا واحد و جيت طالع هنا هذه واحد + +360 +00:37:40,690 --> 00:37:46,470 +يبقى أسارة النقطة هذه واحد و واحد يبقى واحد و واحد + +361 +00:37:46,470 --> 00:37:50,730 +تقع على الخط المستقيم و في نفس الوقت + +362 +00:37:59,220 --> 00:38:06,910 +السؤال هو هل ال Parabola تمر بنقطة الأصل؟نعم ليش؟ + +363 +00:38:06,910 --> 00:38:12,490 +ان لو حطيت ال X ب Zero و Y ب Zero يبقى ال parabola + +364 +00:38:12,490 --> 00:38:18,170 +هذه لو جيت رسمتها هتاخد الشكل التالي الشكل اللي + +365 +00:38:18,170 --> 00:38:22,990 +عندنا هذا هيك يبقى هذا ال parabola يبقى المنطقة + +366 +00:38:22,990 --> 00:38:30,250 +اللي محصورة فيما بينهما للمنطقة هذه تمام؟ يبقى من + +367 +00:38:30,250 --> 00:38:36,080 +هنا بدأنا الحل نمر أيه؟الدوران يكون حوالين محور Y + +368 +00:38:36,080 --> 00:38:43,880 +جل المطلوب الأول يبقى بدرح أرسم خط يقطع منطقة + +369 +00:38:43,880 --> 00:38:50,800 +التكامل وموازن لمحور الدوران يبقى هذا خط يقطع + +370 +00:38:50,800 --> 00:39:00,270 +منطقة التكامل وموازن لمحور الدورانيبقى هذه لو جيت + +371 +00:39:00,270 --> 00:39:06,530 +هنا إلى أسفل هذا البعد بدي يكون X اللي هو من نصف + +372 +00:39:06,530 --> 00:39:13,470 +القطر تبع دائرة cylindrical shell يبقى بدي أجي + +373 +00:39:13,470 --> 00:39:20,130 +أشوف ال X ستتغير من وين لوين أول قيمة Zero و أخر + +374 +00:39:20,130 --> 00:39:27,160 +قيمة كدهش واحد يبقى باجي بقوله ال volume Vبدي + +375 +00:39:27,160 --> 00:39:34,360 +أساوي تكامل للإتنين by X وهذا الكلام من Zero لغاية + +376 +00:39:34,360 --> 00:39:39,720 +واحد لل F of X F of X اللي هي المسافة اللي عندنا + +377 +00:39:39,720 --> 00:39:55,830 +هذه، هذه من هنا لهنا، اللي هي mainنقص X تربيه نقص + +378 +00:39:55,830 --> 00:39:57,190 +X تربيه + +379 +00:40:00,190 --> 00:40:08,950 +يبقى هذا في اتنين اكس ناقص اكس ترابية ناقص اكس كله + +380 +00:40:08,950 --> 00:40:13,870 +بالنسبة لمين الى دي اكس يبقى هذا الكلام يساوي + +381 +00:40:13,870 --> 00:40:19,750 +اتنين باي تكامل من زيرو لواحدهذا الـ X خلّيها برا + +382 +00:40:19,750 --> 00:40:25,630 +زي ما هي و عندك اتنين X و ناقص X بيبقى X واحدة + +383 +00:40:25,630 --> 00:40:32,750 +يبقى هذا X ناقص X تربية كله بالنسبة إلى DX أو ال + +384 +00:40:32,750 --> 00:40:40,610 +volume V بده يساويهي اتنين باي برا وهي تكامل من + +385 +00:40:40,610 --> 00:40:46,530 +Zero لغاية واحد لل X تربيه ناقص X تربيه X تكييب X + +386 +00:40:46,530 --> 00:40:52,810 +تربيه ناقص X تكييب كله بالنسبالي ديكت يبقى هذا + +387 +00:40:52,810 --> 00:41:00,250 +اتنين باي في X تكييب على تلاتة ناقص X أربع على + +388 +00:41:00,250 --> 00:41:07,640 +أربعة كله من Zero لغاية واحد يبقى اتنين بايفي تلت + +389 +00:41:07,640 --> 00:41:12,800 +ناقص ربع عملناها قبل شوية واحد على اتناش يبقى + +390 +00:41:12,800 --> 00:41:18,960 +النتيجة باي على ستة الآن بدنا نيجي للمطلوب التاني + +391 +00:41:18,960 --> 00:41:25,700 +نمرا V نمرا V بدا عيد الرسم تاني يبقى لو جينا + +392 +00:41:25,700 --> 00:41:32,380 +قعدنا الرسم تاني وقولنا هذا محور X هذا محور Y + +393 +00:41:32,380 --> 00:41:41,100 +تمام؟الخط Y تساوي X هذا الخط Y تساوي X جينا عنده + +394 +00:41:41,100 --> 00:41:46,780 +النقطة اللي هي واحد و واحد هذه واحد و رسمنا + +395 +00:41:46,780 --> 00:41:56,040 +المنحنة فمر بنقطة الأصل بهذا الشكل تمام؟ يبقى هاي + +396 +00:41:56,040 --> 00:42:03,100 +المنطقة اللي عندناالدوران بدي يكون حوالين الخط + +397 +00:42:03,100 --> 00:42:10,220 +اللي عندنا هذا main اللي هو x يساوي واحد، كويس، + +398 +00:42:10,220 --> 00:42:18,060 +يبقى بدي ارسم خط يقطع منطقة التكامل وموازن لمحور + +399 +00:42:18,060 --> 00:42:24,620 +الدورانيبقى هذا يعتبر مين؟ الـ cylindrical height، + +400 +00:42:24,620 --> 00:42:30,680 +بدي نص القطر، يبقى هذا لو جيت نزلت من هنا و قلت + +401 +00:42:30,680 --> 00:42:36,310 +هذا البعد كله X لأن هذا نقطة الأصل هي Zeroالدوران + +402 +00:42:36,310 --> 00:42:42,190 +حوالين محور Y حوالين للخط X يساوي واحد يبقى أين + +403 +00:42:42,190 --> 00:42:50,090 +نصف القطر؟ واحد ناقص X ممتاز هذه المسافة كلها وهذا + +404 +00:42:50,090 --> 00:42:59,210 +هو نصف القطر تمام؟ يبقى هذا واحد ناقص Xكويس يبقى + +405 +00:42:59,210 --> 00:43:06,550 +بدي يصير ال volume دي بدي يساوي تكمل لاتنين by + +406 +00:43:06,550 --> 00:43:14,070 +واحد ناقص six هذا اللي همين نصف القطر فاهمين؟ فيه؟ + +407 +00:43:14,410 --> 00:43:17,990 +الـ Height هذا الارتفاع هل اختلف عن الارتفاع اللي + +408 +00:43:17,990 --> 00:43:25,310 +هناك؟ هو هو يبقى 2X ناقص X تربية يبقى 2X ناقص X + +409 +00:43:25,310 --> 00:43:31,690 +تربية ناقص X كله بالنسبة ل X والـ X ستتغير من Zero + +410 +00:43:31,690 --> 00:43:40,210 +لغاية واحد كما هييبقى النتيجة تساوي أي اتنين باي و + +411 +00:43:40,210 --> 00:43:46,410 +أي تكامل من zero لفاية واحد وهنا واحد ناقص x + +412 +00:43:46,410 --> 00:43:54,080 +فاهمين؟في الـ x ناقص x تربيع كله بالنسبة الى dx + +413 +00:43:54,080 --> 00:44:02,100 +هذا الكلام يساوي 2πي تكمل من zero ل1 يبقى + +414 +00:44:02,100 --> 00:44:10,290 +x ناقص x تربيع ناقص x تربيع وزائد x تكييبكله + +415 +00:44:10,290 --> 00:44:16,270 +بالنسبة الى DX يبقى هذا الكلام بده يساوي اتنين باي + +416 +00:44:16,270 --> 00:44:23,410 +تكمل من Zero لاحق عن DX مافيش غيرها ونقص اتنين X + +417 +00:44:23,410 --> 00:44:30,130 +تربيع وزائد X تكييب كله بالنسبة الى من؟ الى DX + +418 +00:44:30,130 --> 00:44:36,780 +يبقى هذا الكلام بده يساوي اتنين باياكس تربيه عالى + +419 +00:44:36,780 --> 00:44:47,100 +اتنين ناقص تلتين اكس تكيب او هنا زائد اكس أس اربع + +420 +00:44:47,100 --> 00:44:52,660 +عالى اربع من زيرو لغاية واحد يبقى هذا الكلام بده + +421 +00:44:52,660 --> 00:45:04,890 +يساوي اتنين by فيه نص ناقص تلت زائد رابعكيف؟ اه + +422 +00:45:04,890 --> 00:45:10,430 +تلتين هذا ولا يما يبقى نص ناقص تلتين زي ربع في + +423 +00:45:10,430 --> 00:45:16,790 +اتنين باي يبقى هذا الكلام بده يساوي اتنين باي + +424 +00:45:16,790 --> 00:45:24,020 +المضاعف المشترك كله لهم له قداش اتناش12 على 2 هي 6 + +425 +00:45:24,020 --> 00:45:33,600 +في 1 ب 6 نقص 12 3 في 4 في 2 8 12 على 4 هي قداش 3 + +426 +00:45:34,740 --> 00:45:40,960 +يبقى تلاتة أو ستة تسعة يبقى اتنين باي في واحد على + +427 +00:45:40,960 --> 00:45:48,140 +اتناش يبقى باي على ستة كذلك يبقى هذا الحجم اللي + +428 +00:45:48,140 --> 00:45:53,360 +موجود هنا لحد هنا stop انتهى هذا ال section اللي + +429 +00:45:53,360 --> 00:45:57,080 +هو ستة اتنين وعليكم أرقام المسائل + +430 +00:46:00,430 --> 00:46:09,110 +يبقى exercises ستة اتنين المسائل التالية من واحد + +431 +00:46:09,110 --> 00:46:21,990 +للاحداشر القد ومن خمستاشر لتسعة وتلاتين القد كذلك + +432 +00:46:25,300 --> 00:46:29,740 +مين اللي قال ليس بالضرورة لأ لإن هاجر نضل على + +433 +00:46:29,740 --> 00:46:31,420 +الشجر نضل على الشجر تاني + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/778E9B2F8Qc_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/778E9B2F8Qc_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..0aa0932e002f8d0a762ab44bcfcce3d62e54bea7 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/778E9B2F8Qc_raw.srt @@ -0,0 +1,1732 @@ +1 +00:00:20,940 --> 00:00:25,320 +بسم الله الرحمن الرحيم المرة الماضية بدأنا فيها + +2 +00:00:25,320 --> 00:00:31,060 +تطبيقات على استخدام التكامل في حساب الحجوم واخدنا + +3 +00:00:31,060 --> 00:00:35,140 +على ذلك طريقتين الطريقة الأولى كانت طريقة ال disk + +4 +00:00:35,140 --> 00:00:40,820 +وهذا للمجسم المصمد ثم أخدنا طريقة ال washer وهذا + +5 +00:00:40,820 --> 00:00:46,180 +للمجسم اللي فيه تجويف من الداخلاليوم ناخد الطريقة + +6 +00:00:46,180 --> 00:00:51,460 +الثالثة وهي طريقة القشرة الأسطوانية يبقى + +7 +00:00:51,460 --> 00:00:56,900 +cylindrical shell قشرة أسطوانية أعطيك مثال هات + +8 +00:00:56,900 --> 00:00:59,480 +واحد يعطيني دفتر ويعطيني دفترك أشوف + +9 +00:01:02,410 --> 00:01:07,330 +الدفتر هذا لو عملناه على شكل أسطوانة بهذا الشكل + +10 +00:01:07,330 --> 00:01:11,570 +طبعا يبقى أيه أسطوانة بهذا الشكل زي ما انتوا + +11 +00:01:11,570 --> 00:01:15,790 +شايفين الفكرة ما الموضوع بدي أجيب حجم المجسم اللي + +12 +00:01:15,790 --> 00:01:22,020 +قدامي هذه فلو أخدت ورقة من الورق تبع الدفتريبقى + +13 +00:01:22,020 --> 00:01:28,240 +هذه الورقة تعتبر قشرة أسطوانية القشرة الأسطوانية + +14 +00:01:28,240 --> 00:01:34,280 +لو جبت المساحة الجانبية لها و كملت عليها بيعطيني + +15 +00:01:34,280 --> 00:01:38,680 +مقدار الحجم تبقى الأسطوانة داير ميدور + +16 +00:01:41,980 --> 00:01:50,540 +المساحة الجانبية للأسطوانة هو اتنين طهنق محيط + +17 +00:01:50,540 --> 00:01:54,380 +القاعدة اللي هو الكوندارة في الارتفاع تبع + +18 +00:01:54,380 --> 00:01:58,400 +الأسطوانة الدائرية القائمةيبقى اتنين طعنق هو + +19 +00:01:58,400 --> 00:02:02,360 +المساحة الجانبية للاستوانة بدي اكامل عليها بيعطيني + +20 +00:02:02,360 --> 00:02:07,640 +ايه بيعطيني جداش حجم المجسم او الاستوانة اللى + +21 +00:02:07,640 --> 00:02:11,520 +عندنا هذه واضح اضح لان هذه على الطبيعة بدنا نشوفها + +22 +00:02:11,520 --> 00:02:17,180 +من خلال الكلام اللى قدامنا هنا فضليبقى بنانيه + +23 +00:02:17,180 --> 00:02:20,540 +الكلام اللي احنا كاتبينه volumes by cylindrical + +24 +00:02:20,540 --> 00:02:25,620 +shells الحجوم باستخدام القشر الأسطوانية + +25 +00:02:46,450 --> 00:02:51,870 +الـ Y تساوي F of X about the line X يساوي L X + +26 +00:02:51,870 --> 00:02:57,910 +يساوي L قد يكون محور Y وقد يكون خط موازي لمحور Y + +27 +00:02:57,910 --> 00:03:02,390 +لأن X يساوي رقم تمام سواء كان هذا الرقم موجب أو + +28 +00:03:02,390 --> 00:03:07,170 +سالب بهم ليش بهم انه في عند دوران حوالين هذا + +29 +00:03:07,170 --> 00:03:15,000 +المحور ال volume V يساوي تكمل من A لB لاتنيننق في + +30 +00:03:15,000 --> 00:03:20,700 +الارتفاع تبع الأسطوانة اتنين تهشيل ريض يصيب نصف + +31 +00:03:20,700 --> 00:03:27,380 +قطر القشرة الأسطواني القاعدة تبعتها فشيلها عيد في + +32 +00:03:27,380 --> 00:03:32,400 +الارتفاع تبع مين؟ تبع الأسطوانة تمام؟ او اختصر ما + +33 +00:03:32,400 --> 00:03:36,720 +قلت اكمل ايه لبلا اتنين باي اكس في ال F of X DX + +34 +00:03:36,720 --> 00:03:41,620 +تعالى نشوف هذا الكلام على الطبيعةأنا عندي ملحنة زي + +35 +00:03:41,620 --> 00:03:46,640 +ما انت شايفين Y تساوي F of X وخليته أعلى محور X + +36 +00:03:46,640 --> 00:03:50,680 +ممكن يتقاطع مع الله ينقله وممكن مايتقاطعش يبقى أنا + +37 +00:03:50,680 --> 00:03:54,360 +جبتك ال general form الشكل عام سواء تقاطع مع ال أو + +38 +00:03:54,360 --> 00:04:00,200 +لم يتقاطع هذا الملحنة حصرلي مساحة المساحة اللي + +39 +00:04:00,200 --> 00:04:03,580 +بينه و بين محور X اللي هي المساحة المظللة اللي + +40 +00:04:03,580 --> 00:04:09,000 +قدامنا هذه ما لها هذه هذه جامد دارت حوالين الخط + +41 +00:04:11,520 --> 00:04:16,080 +الخط اللي عندنا هذا يبقى هيجيني شكل في الناحية + +42 +00:04:16,080 --> 00:04:21,660 +التانية تماما زيك وجيني بالشكل هذا تمام يبقى هذا + +43 +00:04:21,660 --> 00:04:25,680 +المنحنة اللي هيجيني فوق بالشكل اللي عندنا هذازي + +44 +00:04:25,680 --> 00:04:30,400 +اللي هناك بالضبط و ال b اللي هناك هتيجيني ب زيها + +45 +00:04:30,400 --> 00:04:35,400 +هنا بس بإشارة مين سالم و ال a اللي هناك هيجيني a + +46 +00:04:35,400 --> 00:04:41,660 +زيها بس بإشارة سيبجي هذه سالم a و سالم bيبقى هذه + +47 +00:04:41,660 --> 00:04:47,520 +عند دورانها بدها ترسم لي محيط دائرة تمام؟ وهذه عند + +48 +00:04:47,520 --> 00:04:53,140 +دورانها كذلك بدها ترسملي محيط دائرة زي ما انتوا + +49 +00:04:53,140 --> 00:04:58,280 +شايفين بالشكل هذا يبقى هذا الشكل المجسم الناتج من + +50 +00:04:58,280 --> 00:05:03,040 +الدوران لسه ما اتكلمتش في الشلة انا اعطيتك شكل + +51 +00:05:03,040 --> 00:05:09,380 +المجسمهذه الشجرة التانية كمان بتكون برضه مظللة زي + +52 +00:05:09,380 --> 00:05:14,980 +اللي هناك بالضبط تماما يبقى هذا شكل المجسم الناتج + +53 +00:05:14,980 --> 00:05:21,440 +من الدوران هذه اللي جوا هيك هذه الصغيرة هذه بتكون + +54 +00:05:21,440 --> 00:05:26,660 +بالشكل هذه يعني كأنه في تجويف، كويس؟ الآن المجسم + +55 +00:05:26,660 --> 00:05:30,580 +اللي يعني يسيبك من التجويف، المنطقة هذه داير ميدور + +56 +00:05:30,580 --> 00:05:36,450 +حواليها وكله مصمدالان بناروح نعمل cylindrical + +57 +00:05:36,450 --> 00:05:40,490 +shell بدنا ناخد مقطع أو المقطع عادى على شكل + +58 +00:05:40,490 --> 00:05:46,550 +أسطوانة يبقى بالدادى في الحالة هذه بعكس من ما كنا + +59 +00:05:46,550 --> 00:05:51,210 +نعمل المرة اللى فاتت في ال disk و كذلك في ال + +60 +00:05:51,210 --> 00:05:55,900 +washerبجرب نفسي خط يقطع منطقة التكامل و عمودي على + +61 +00:05:55,900 --> 00:06:00,960 +محور الدوران، مظبوط؟ اليوم بدنا نعمل خط يقطع منطقة + +62 +00:06:00,960 --> 00:06:04,920 +التكامل وموازي لمحور الدوران، على عكس المرة اللي + +63 +00:06:04,920 --> 00:06:09,840 +فاتت، يبقى بدي اقول لو كان عندي هذا الخط بالشكل + +64 +00:06:09,840 --> 00:06:16,280 +اللي انه هذاوالحظون شايفينه؟ تمام يبقى هذه النقطة + +65 +00:06:16,280 --> 00:06:22,520 +عند ورا عنها بدها ترسم لمحيط دائرة بدها تجين هيك + +66 +00:06:22,520 --> 00:06:26,600 +بالشكل اللي عندنا هذا، هذا هيك، و هذا بده يجين + +67 +00:06:26,600 --> 00:06:31,540 +هيك، و هذا الخط الراسي هيه، و من هنا بدها تعمل + +68 +00:06:31,540 --> 00:06:39,800 +لمحيط دائرة بالشكل اللي عندنا هنا تمام؟طيب لو جيت + +69 +00:06:39,800 --> 00:06:44,800 +هذه نقطة الأصل على سبيل المثال يبقى هذا البعد لحد + +70 +00:06:44,800 --> 00:06:50,340 +هنا جداش بده يكون X يعني X البعد من نقطة الأصل هذه + +71 +00:06:50,340 --> 00:06:54,940 +لغاية النقطة هذه يبقى هذا هو X شايفين الأسطوانة + +72 +00:06:54,940 --> 00:06:59,220 +الخضر هذي الأسطوانة الخضر هذي اللي هي الشل زي ما + +73 +00:06:59,220 --> 00:07:02,700 +وريتكوا توي ساحية إحدى الورقات من الدفتر اللي + +74 +00:07:02,700 --> 00:07:07,470 +عملناه على شكل أسطوانةيبقى الخضرة هذه هو الـ + +75 +00:07:07,470 --> 00:07:12,210 +cylindrical shell القشرة الأسطونية، بدّى تجيب قداش + +76 +00:07:12,210 --> 00:07:17,670 +المساحة الجانبية لها، هذا نصف القطرة مقداش X، + +77 +00:07:17,670 --> 00:07:25,180 +المساحة الجانبية اتنين طهنق، يبقى اتنين by Xفي من؟ + +78 +00:07:25,180 --> 00:07:29,880 +في الارتفاع، الارتفاع هو F of X هذا، صحيح ولا لأ؟ + +79 +00:07:29,880 --> 00:07:35,940 +يبقى هذا هو الارتفاع اللي عندنا اللي هو F of X، + +80 +00:07:35,940 --> 00:07:39,600 +يبقى هذا بيعطينا المساحة الجانبية للوسط، وانا من + +81 +00:07:39,600 --> 00:07:44,340 +هنا قلنا ال volume يبدو يساوي تكامل 2 باي X في F + +82 +00:07:44,340 --> 00:07:51,190 +of XDX ان كامل عليها بطلعلي قداش حجم المجسم المصمد + +83 +00:07:51,190 --> 00:07:54,650 +داير مايدور اللي عندنا هذا يبقى واضح شكل الـ + +84 +00:07:54,650 --> 00:07:58,610 +cylindrical shell هذا لو كان التكامل بالنسبة لـ X + +85 +00:07:58,610 --> 00:08:03,530 +يبقى هنا بفرج عن المرتين الماضيتين ان المقطع اللي + +86 +00:08:03,530 --> 00:08:07,390 +هو الخط المستقيم اللي بنرسمه بدل ما كنا نرسمه + +87 +00:08:07,390 --> 00:08:11,390 +عمودي على محور الدوران اليوم نرسمه موازن لمحور + +88 +00:08:11,390 --> 00:08:15,670 +الدورانهذا الخط الموجود هو f of x + +89 +00:08:26,270 --> 00:08:30,750 +هذا الدوران حوالي الخط يكون محور Y أو موازي لمحور + +90 +00:08:30,750 --> 00:08:37,690 +Y ممكن يكون الدوران حوالي الخط موازي لمحور X تمام؟ + +91 +00:08:37,690 --> 00:08:42,930 +يبقى الحدث ذلك يصير التكمل بالنسبة إلى Y يبقى يصير + +92 +00:08:42,930 --> 00:08:48,310 +التكمل اتنين by Y F of Y Dy طبعا هذي كامتلة على + +93 +00:08:48,310 --> 00:08:53,450 +الشجتين كيف هذه وكيف هذه يبقى الفكرة في الأساس بس + +94 +00:08:53,870 --> 00:08:59,830 +تعرف اللي هو شكل النص في القطر تبع الـ cylindrical + +95 +00:08:59,830 --> 00:09:04,230 +shell وتعرف الارتفاع، ضروري كل مرة ارسم و مرة ارسم + +96 +00:09:04,230 --> 00:09:09,330 +هذا؟ لا مش ضروري، بس ارسملي منطقة التكامل، ارسملي + +97 +00:09:09,330 --> 00:09:15,130 +خط يوازي محور الدورانو حدد لقداش بقى الطرف الخط عن + +98 +00:09:15,130 --> 00:09:19,130 +المركز اللى عندك بيكون هذا هو نصف الخطر والخط اللى + +99 +00:09:19,130 --> 00:09:24,410 +رسمت بيكون هو الشيل هايت هو الارتفاع او الارتفاع + +100 +00:09:24,410 --> 00:09:28,410 +الجانبي للقصانة بعد هيك حدود التكامل ممكن تكون + +101 +00:09:28,410 --> 00:09:33,490 +محددة عندك ممكن انت بدك تحددها من حال مستقيمات مع + +102 +00:09:33,490 --> 00:09:38,150 +منحنيات او منحنيات مع بعضها الى اخرى كما سنراه بعد + +103 +00:09:38,150 --> 00:09:43,640 +قليلهذا كل جزء النظر اللي موجود في هذا الsection + +104 +00:09:43,640 --> 00:09:46,920 +بس الكلمتين اللي قدامك على اللوحة دول حدا اللي هو + +105 +00:09:46,920 --> 00:09:54,260 +اي تساؤل طيب نبدأ في الأمثلة نجي لأول مثال على هذا + +106 +00:09:54,260 --> 00:09:55,900 +الموضوع يبقى examples + +107 +00:10:03,850 --> 00:10:08,530 +أول مثال من هذه اللي ألمتله بوليفي ال volume of + +108 +00:10:08,530 --> 00:10:19,330 +the solid find the volume of the solid generated + +109 +00:10:19,330 --> 00:10:23,350 +by + +110 +00:10:23,350 --> 00:10:27,010 +revolving + +111 +00:10:28,290 --> 00:10:34,990 +Generated by the region revolving + +112 +00:10:34,990 --> 00:10:42,570 +the + +113 +00:10:42,570 --> 00:10:46,750 +region + +114 +00:10:46,750 --> 00:10:51,470 +between the + +115 +00:10:51,470 --> 00:10:51,990 +region + +116 +00:10:59,710 --> 00:11:07,430 +بين اتنين بيوندد والمغلقة + +117 +00:11:07,430 --> 00:11:19,770 +بيه by the curves المنحنات Y تساوي X تربيعو Y + +118 +00:11:19,770 --> 00:11:33,110 +يساوي اتنين ناقص X and X تساوي زيرو for X greater + +119 +00:11:33,110 --> 00:11:44,450 +than or equal to zero about the Y axis + +120 +00:11:57,220 --> 00:12:02,900 +خلّينا نرسم المنطقة + +121 +00:12:02,900 --> 00:12:06,360 +المحدودة بالمنحنات اللي عندنا نقول المنحنة + +122 +00:12:06,360 --> 00:12:11,420 +الأولاني Y تساوي X تربيع إذا لو جيت رسمت هذا + +123 +00:12:11,420 --> 00:12:18,880 +المنحنة هذا محور X هذا محور Y هذه نقطة الأصل يبقى + +124 +00:12:18,880 --> 00:12:27,700 +هذا Y تساوي X تربيعبعدها قال الخط المستقيم y تساوي + +125 +00:12:27,700 --> 00:12:33,020 +اتنين ناقص x إذا لو كانت ال x ب zero y يبقى دي اش + +126 +00:12:33,020 --> 00:12:40,420 +ب اتنين يبقى هذه اتنينوإذا كان الـ Y بـ Zero و X + +127 +00:12:40,420 --> 00:12:46,260 +باتنين يبقى باتنين هذه الاتنين اللي عندنا هذه يبقى + +128 +00:12:46,260 --> 00:12:52,140 +هذه كمان اتنين يبقى هتان النقطتان تقعان على الخط + +129 +00:12:52,140 --> 00:12:57,220 +المستقيم اللي عندنا يبقى أروح نرسمنا هذا الخط + +130 +00:12:57,220 --> 00:13:02,900 +المستقيم بالشكل هذا دوام يبقى هذا هو الخط المستقيم + +131 +00:13:10,240 --> 00:13:15,340 +يبقى هاي المنطقة اللى موجودة وين اللى موجودة أنا + +132 +00:13:15,340 --> 00:13:20,420 +يبقى باقي المنحنى هذا كله مش لازم ليه المهم هاي + +133 +00:13:20,420 --> 00:13:27,040 +المنحنى رسمناها وهذا الخط اللى همين Y يساوي اتنين + +134 +00:13:27,040 --> 00:13:31,820 +ناقص X هاي المنطقة المضلنة المنطقة المضلنة اللى + +135 +00:13:31,820 --> 00:13:36,510 +بدها تدور حوالين مين؟أو للمحور Y. إذا أنا بادر + +136 +00:13:36,510 --> 00:13:44,370 +أرسم خط يقطع منطقة التكامل وموازن لمحور Y. يبقى + +137 +00:13:44,370 --> 00:13:49,650 +بالدقج أقول له هذا خط يقطع منطقة التكامل وموازن + +138 +00:13:49,650 --> 00:14:03,820 +لمحور Y.النقطة هذه نصف + +139 +00:14:03,820 --> 00:14:09,840 +القطر يعني لو جيت من هنا رسمت نصف دائرة بيكون هذا + +140 +00:14:09,840 --> 00:14:15,120 +هو نصف قطر الدائرةطب والارتفاع تبع الدائرة الجزء + +141 +00:14:15,120 --> 00:14:19,360 +اللي في المنطقة المظلة للي تحت مالوش دعوة تمام؟ + +142 +00:14:19,360 --> 00:14:25,300 +اذا انا بدي اعرف جداش هذا طول الخط الأخضر جداش؟ + +143 +00:14:25,300 --> 00:14:30,740 +اتنين ناقص اكس اتنين ناقص اكس اللي هو بُعد الخط + +144 +00:14:30,740 --> 00:14:34,880 +اللي عندنا هذا عن محور X بدي اشيل هذا البُعد هذا + +145 +00:14:34,880 --> 00:14:42,190 +البُعد جداش؟هذا الخط أو هذا الجزء هو عبارة عن + +146 +00:14:42,190 --> 00:14:48,470 +اتنين ناقص X ناقص X تربيع يبقى هذا هو الذي يمثل + +147 +00:14:48,470 --> 00:14:54,060 +عندي هنا main ال F of X اللي هو الارتفاعتبع من؟ + +148 +00:14:54,060 --> 00:14:58,700 +تبع الاستوان او تبع الـ cylindrical shell يبقى + +149 +00:14:58,700 --> 00:15:03,620 +كويس يبقى بدي اكمل بالنسبة ل X اذا بدي اعرف X + +150 +00:15:03,620 --> 00:15:09,560 +ستتغير من و لا وين طبعا X ستتغير من Zero لغاية اخر + +151 +00:15:09,560 --> 00:15:14,670 +نقطة هنا اخر نقطة هنا جدوش انا مش عارفبنحل معادلة + +152 +00:15:14,670 --> 00:15:20,010 +الخط المستقيم مع مين مع منحنى ال parabola Y تساوي + +153 +00:15:20,010 --> 00:15:20,810 +X تربية + +154 +00:15:28,980 --> 00:15:35,040 +الشباب لو كملت هذا هيك بدي يحصل تقابل عن مين سالب + +155 +00:15:35,040 --> 00:15:39,460 +اتنين ماليش دعوة فيها هذه برا المنطقة يبقى انا + +156 +00:15:39,460 --> 00:15:44,960 +عندي بس اكس يسوي كدهش واحد اذا بدي اجي اقوله ال + +157 +00:15:44,960 --> 00:15:52,680 +volume V بدي يسوي تكامل من Zero لواحدللإتنين by X + +158 +00:15:52,680 --> 00:15:57,200 +في ال F of X F of X التفاجنا اللي هو البعد هذا + +159 +00:15:57,200 --> 00:16:05,160 +اللي هو مام اللي هو ال X اتنين ناقص X اتنين ناقص X + +160 +00:16:05,160 --> 00:16:11,610 +ناقص X تربية كله بالنسبة لمين؟ لل X أوهذا اتنين + +161 +00:16:11,610 --> 00:16:17,330 +باي برا تكامل من Zero لواحد ده لاتنين X ناقص X + +162 +00:16:17,330 --> 00:16:23,930 +تربية ناقص X تكييب كله بالنسبة الى DX النتيجة + +163 +00:16:23,930 --> 00:16:29,590 +تساوي اتنين باي هيها برا وتكامل هذا اللي هو X + +164 +00:16:29,590 --> 00:16:34,190 +تربية على اتنين مع الاتنين الله يسهل عليها ناقص X + +165 +00:16:34,190 --> 00:16:40,950 +تكييب على تلاتة ناقص X أس أربعة على أربعةكله من + +166 +00:16:40,950 --> 00:16:48,070 +أندي الـ0 لغاية الـ8 لغاية الـ1 يبقى يساوي 2πي + +167 +00:16:48,070 --> 00:16:56,670 +ناقص تلت ناقص ربع ناقص كل الباقي بقداش بـ0 هذا + +168 +00:16:56,670 --> 00:17:03,630 +الكلام بده يساوي 2πيالمضاعف المشترك كلهم كم؟ + +169 +00:17:03,630 --> 00:17:09,870 +أتناش، يبقى هنا أتناش، أتناش على تلاتة فيها أربعة، + +170 +00:17:09,870 --> 00:17:15,050 +و أتناش على أربعة فيها التلاتة، هذا الكلام بده + +171 +00:17:15,050 --> 00:17:15,750 +ساوي + +172 +00:17:19,080 --> 00:17:25,520 +تلاتة واربعة السبعة من اتناشر بطول جداش خمسة على + +173 +00:17:25,520 --> 00:17:33,460 +اتناشر يعني خمسة باي على ستة هذا قيمة الحجم تبع + +174 +00:17:33,460 --> 00:17:42,950 +المنطقة اللي هنا نعطي كمان مثال example twoأيضًا + +175 +00:17:42,950 --> 00:17:47,310 +يقول إنه يجد كمية الصليب على أي حال المثال الأول + +176 +00:17:47,310 --> 00:17:53,490 +يا شباب هو سؤال تسعة من الكتاب ومثال اتنين هو سؤال + +177 +00:17:53,490 --> 00:18:02,690 +واحد وعشرين من الكتاب يقول إنه يجد كمية + +178 +00:18:02,690 --> 00:18:05,570 +الصليب + +179 +00:18:17,530 --> 00:18:25,790 +Generated by revolving the region bounded + +180 +00:18:25,790 --> 00:18:28,850 +the + +181 +00:18:28,850 --> 00:18:43,390 +region bounded by the curves Y تساوي جذر ال X والY + +182 +00:18:43,390 --> 00:18:46,890 +تساوي Zero and + +183 +00:18:48,240 --> 00:18:56,360 +الـ y تساوي x ناقص اتنين about the + +184 +00:18:56,360 --> 00:19:03,940 +x axis حوالي المحور من؟ حوالي المحور اللي هو x + +185 +00:19:24,760 --> 00:19:34,200 +بنرجع الكلام اللي احنا كاتبينه مرة تانية تقدر + +186 +00:19:34,200 --> 00:19:37,560 +تحل بطريقتين يعني هذه انا بقدر أحلها بال + +187 +00:19:37,560 --> 00:19:42,280 +cylindrical shape بقدر أحلها بالوشة، بالشمتين بقدر + +188 +00:19:42,280 --> 00:19:46,340 +أحلها تمام؟ الحين اعطيك مثال، الحين اعطيك مثال + +189 +00:19:46,340 --> 00:19:49,120 +ونحله بالطريقة ونقول انه بيعطينا نفس النتيجة + +190 +00:19:49,120 --> 00:19:54,070 +وبالتالي اذا انا قيّدتك بطريقة انك تلتزم فيهاما + +191 +00:19:54,070 --> 00:19:59,170 +قيبتك خلاص لك الحرية. طبعا؟ سؤاله جيه السؤال يعني. + +192 +00:19:59,230 --> 00:20:02,070 +يعني انا اذا السؤال بالحل .. هذا السؤال بالحل بال + +193 +00:20:02,070 --> 00:20:06,770 +washer بسهولة كمان، غير أكيد لذا. طيب، على أي حال، + +194 +00:20:06,770 --> 00:20:13,240 +نرجع لمين؟ نرجع لسؤالنا ده.قال هاتلي حجم المجسم + +195 +00:20:13,240 --> 00:20:18,680 +المتولد بدوران المنطقة المحدودة بالمنحنى Y تساوي + +196 +00:20:18,680 --> 00:20:25,460 +جذر ال X معروف بالنسبالنا Y تساوي Zero محور X Y + +197 +00:20:25,460 --> 00:20:29,960 +تساوي X ناقص اتنين فبنرسمه والدوران بدي يكون + +198 +00:20:29,960 --> 00:20:34,520 +حوالين مين حوالين محور X إذا ليس بضرورة نرسم + +199 +00:20:34,520 --> 00:20:38,440 +الرسمة كاملة بدي نرسم بس المنطقة اللي بدها الدور + +200 +00:20:38,770 --> 00:20:43,190 +أذا انا لو روحت و قلت هذه المحور اللي عندنا هذا + +201 +00:20:43,190 --> 00:20:49,330 +محور X هذا محور Y هذه نقطة الاصل اللي هي Zero Y + +202 +00:20:49,330 --> 00:20:53,670 +تساوي جذر ال X يا ما رسمناه خلال الفصل هذا كله + +203 +00:20:53,670 --> 00:21:00,970 +بيعرف رسمه يبقى هذا Y تساوي جذر ال Xبعد ذلك يقول + +204 +00:21:00,970 --> 00:21:06,650 +لي Y تساوي زيرو Y تساوي زيرو هو ميان محور X Y + +205 +00:21:06,650 --> 00:21:12,690 +تساوي زيرو هو محور X بعد ذلك قال لي الخط Y تساوي X + +206 +00:21:12,690 --> 00:21:17,590 +ناقص اتنين بحدد النقطتين عليه و بوصل فيه ما بينهما + +207 +00:21:17,590 --> 00:21:24,010 +لو كانت ال X بزيرو ف Y بسالب اتنين يبقى I سالب + +208 +00:21:24,010 --> 00:21:31,440 +اتنينلو كانت Y بزيرو X باتنين يبقى انا من اتنين + +209 +00:21:31,440 --> 00:21:39,100 +بيأتي بوصل فيما بينهما و بمد الخط على استقامته + +210 +00:21:39,100 --> 00:21:45,800 +يبقى الآن المنطقة اللي احنا بدناها هي هذه المنطقة + +211 +00:21:45,800 --> 00:21:54,420 +والباقي كله مش لزملي تمام؟طيب، هذه المنطقة بدها + +212 +00:21:54,420 --> 00:21:59,800 +دور حوالين مين؟ حوالين محور X، بدى أروح أهلى + +213 +00:21:59,800 --> 00:22:03,860 +بالـCylindrical Shell، مش بالوشرة، يبقى موضوعنا + +214 +00:22:03,860 --> 00:22:08,400 +الـCylindrical Shell، يبقى بدأ أروح أرسم خط يقطع + +215 +00:22:08,400 --> 00:22:15,580 +هذه المنطقة وموازن لمحور الدورانيبقى باجي بقول لو + +216 +00:22:15,580 --> 00:22:22,300 +جيت أخد هذا الخط الأوفقي، الشكل أن هذا، قطع منطقة + +217 +00:22:22,300 --> 00:22:27,780 +التكامل وموازي لمحور الدوران، يبقى هذا يعتبر + +218 +00:22:27,780 --> 00:22:33,700 +ارتفاع الـCylindrical Shell، مظبوط؟ بدي نص القطر، + +219 +00:22:33,700 --> 00:22:39,840 +يبقى باجي بنزل عمود من هنا، بيكون هذا نصف القطر + +220 +00:22:40,850 --> 00:22:45,030 +طيب، هنا التكمل بيكون على عكس اللي جابله، اللي + +221 +00:22:45,030 --> 00:22:49,470 +جابله كاملة بالنسبة لمن؟ هنا بيكمل بالنسبة إلى Y، + +222 +00:22:49,470 --> 00:22:55,210 +إذا هذا البعد لو جيت goal taken أفقي، هذا Y، + +223 +00:22:55,210 --> 00:23:01,960 +الارتفاع Y يبقى بيكون نصف القطر، هذا هو Yيبقى طول + +224 +00:23:01,960 --> 00:23:05,980 +اللي عندي اعرف قداش الطول اللي عندنا هذا بدلالة + +225 +00:23:05,980 --> 00:23:14,380 +مين؟ بدلالة Y هذا Y تساوي جذر ال X يعني X يساوي Y + +226 +00:23:14,380 --> 00:23:21,460 +تربية يبقى X يساوي Y تربية اللي همين الجزء المنقطة + +227 +00:23:21,460 --> 00:23:29,020 +اللي عندنا هذا مصبوب يبقى هذا الجزء فقط هوX يساوي + +228 +00:23:29,020 --> 00:23:34,140 +Y تربية ربعنا الطرفين اللي هنا هذا الخط اللي هو + +229 +00:23:34,140 --> 00:23:42,280 +معادلة كانت ايش كانت Y تساوي X ناقص اتنين او X + +230 +00:23:42,280 --> 00:23:48,000 +يساوي Y زائد اتنين طبعا اذا ان باجي بقول البعد + +231 +00:23:48,000 --> 00:23:53,620 +الكبير ناقص البعد الصغير يبقى هذا الطول يمثل البعد + +232 +00:23:53,620 --> 00:24:00,730 +هذا كله ل Y زائد اتنيننقص البعد هذا اليومين Y + +233 +00:24:00,730 --> 00:24:06,770 +تربيه، ضالت عند ال Y ستتغير من عند Zero لعند بصر + +234 +00:24:06,770 --> 00:24:12,770 +جداش، لحد هنا تمام؟ يبقى بدي اعرف جداش الاحداث تبع + +235 +00:24:12,770 --> 00:24:18,510 +Y هذا، مشان هيك بروح احل المعادلة هذه بالنسبة لمين + +236 +00:24:18,510 --> 00:24:25,240 +الى Y هذه النقطة تقع وين؟ على المنحنيينيبقى بدي + +237 +00:24:25,240 --> 00:24:32,380 +أروح أسوي المعادلتين ببعض اللي هو Y تربية يسوي Y + +238 +00:24:32,380 --> 00:24:38,220 +زائد اتنين او بمعنى اخر لو عملت معادلة صفرية بيصير + +239 +00:24:38,220 --> 00:24:44,540 +Y تربية ناقص Y ناقص اتنين بدي يسوي قداش Zero او لو + +240 +00:24:44,540 --> 00:24:49,520 +حللتها اقواس بالشكل هذا بدي يسوي Zero يبقى هاي Y + +241 +00:24:49,740 --> 00:24:54,660 +هذا واي واي واحد وهذا اتنين وهذا ناقص وهذا زائد + +242 +00:24:54,660 --> 00:24:58,480 +زائد واي وناقص اتنين واي بناقص واي يبقى تحليلنا + +243 +00:24:58,480 --> 00:25:02,960 +سليم مائة بالمائة يبقى بناء على هدف يعطينا ان واي + +244 +00:25:02,960 --> 00:25:08,800 +تساوي سالب واحد والواي تساوي قداش اتنين ايش رأيك + +245 +00:25:08,800 --> 00:25:16,290 +في واي تساوي سالب واحد؟ مرفوض او لا؟هذا لو كملت + +246 +00:25:16,290 --> 00:25:20,570 +هكذا كملت المنحنة و بدى تقاطعني و تسلب واحد ماليش + +247 +00:25:20,570 --> 00:25:24,450 +علاقة فيها يبقى Y تساوي اتنين اللى هو البعد اللى + +248 +00:25:24,450 --> 00:25:30,570 +عندنا هذا يبقى بدى يصير التكمل عندي من Zero لغاية + +249 +00:25:30,570 --> 00:25:37,090 +قداش اتنين طيب هذه لو كانت Y تساوي اتنين يبقى ال X + +250 +00:25:37,090 --> 00:25:38,150 +تساوي قداش + +251 +00:25:42,010 --> 00:25:47,230 +أربعة يبقى النقطة هذه اللي احداثي تبعها اللي هو + +252 +00:25:47,230 --> 00:25:53,370 +أربعة و اتنين طبعا كيف أربعة و اتنين؟ شو المنحنة + +253 +00:25:53,370 --> 00:26:02,590 +هذا؟ يبقى اكس بقداش. أربعة بتتربع الطرفين. وين + +254 +00:26:02,590 --> 00:26:08,070 +اتنين؟ هذا اتنين البعد الأفق يا راجل. هذا البعد + +255 +00:26:08,070 --> 00:26:14,110 +رأسي.مش احنا طلعنا Y بإتنين، حط فيه أي معادلة + +256 +00:26:14,110 --> 00:26:19,170 +بدكيها، حط Y بإتنين، بصير X باربعة، حط Y بإتنين، + +257 +00:26:19,170 --> 00:26:22,510 +بصير X باربعة، لأن النقطة تقع على المنحنين، بتحقق + +258 +00:26:22,510 --> 00:26:28,790 +كل منهما، إذا إنت ال volume V، بده يسوى تكامل من + +259 +00:26:28,790 --> 00:26:36,370 +Zero لغاية كداشر لغاية إتنين، للإتنين by oneفي نصف + +260 +00:26:36,370 --> 00:26:40,950 +القطر اللي عندنا هذا نصف القطر اللي عندنا وهو Y زي + +261 +00:26:40,950 --> 00:26:47,890 +دي اتنين ناقص اللي هو مين هذا هذا Y زي دي اتنين + +262 +00:26:47,890 --> 00:26:57,770 +ناقص Y تربية يبقى في Y زي دي اتنين ناقص Y تربية كل + +263 +00:26:57,770 --> 00:27:03,770 +هذا الكلام بالنسبة لمين له دي Yيبقى ال volume V + +264 +00:27:03,770 --> 00:27:11,630 +يبقى يساوي 2Y برا تكامل من 0 لغاية 2 يدخل ال Y جوا + +265 +00:27:11,630 --> 00:27:19,310 +يبقى Y تربيه زائد 2Y ناقص Y تكييب كله بالنسبة + +266 +00:27:19,310 --> 00:27:27,580 +لمين؟ لـDY يبقى هذا الكلام يساوي 2Y VY تكيب على + +267 +00:27:27,580 --> 00:27:33,060 +ثلاثة زائد Y تربيع اتنين مع اتنين مع السلامة Y + +268 +00:27:33,060 --> 00:27:40,090 +أربع على أربع من Zero لغاية اتنينيساوى اتنين باى + +269 +00:27:40,090 --> 00:27:44,970 +برا يبقى تمانية + +270 +00:27:44,970 --> 00:27:55,250 +على تلاتة زائد اربعة ناقص ستاشر على اربعة اربعة + +271 +00:27:55,250 --> 00:28:01,750 +مع اربعة نصير يبقى هذا ستاشر باى على تلاتة هذا + +272 +00:28:01,750 --> 00:28:05,110 +حجمين حجم هذه المنطقة + +273 +00:28:10,000 --> 00:28:14,320 +ما رأيك تجي هنا على اللوحة نشوفك شوية ايه اللي حد + +274 +00:28:14,320 --> 00:28:19,400 +تعالي شو؟ عالي بالكوا يمكن نجاوب على بعض أسئلتكوا + +275 +00:28:19,400 --> 00:28:24,140 +اه تفضل انا + +276 +00:28:24,140 --> 00:28:29,680 +بكمل بالنسبة ل .. انا بكمل بالنسبة ل Y لو بالنسبة + +277 +00:28:29,680 --> 00:28:36,700 +ل X طيب انت من الصفر اللي هو اربعة ليه X؟مالك؟ طيب + +278 +00:28:36,700 --> 00:28:41,480 +اضحكوا زيه لأ لو كان لو ال .. لو ال قصد من Y تسوّر + +279 +00:28:41,480 --> 00:28:46,000 +من X لو كانتش فلال Y جدر ال X أبسوليوت ال X + +280 +00:28:46,000 --> 00:28:51,420 +أبسوليوت فلال X طيب هتكون على الجهتين؟ كيف حالك + +281 +00:28:51,420 --> 00:28:54,700 +انت بصيا بصيك الدورة .. استنى شوية بصيك الدورة + +282 +00:28:54,700 --> 00:28:57,780 +حواليها نفسها مش ايه؟ اه اه لإن على يمين محورك + +283 +00:28:57,780 --> 00:29:02,240 +زيهم ماجيبتش جديد طيب + +284 +00:29:02,240 --> 00:29:04,460 +نعطي كمان مثال + +285 +00:29:07,670 --> 00:29:13,590 +مثال تلاتة تلاتة + +286 +00:29:13,590 --> 00:29:17,210 +هي سؤال تسعة و عشرين من الكتاب يقول احصل على كمية + +287 +00:29:17,210 --> 00:29:26,150 +المجسم احصل على كمية المجسم + +288 +00:29:26,150 --> 00:29:28,310 +نحتاج حجم المجسم + +289 +00:29:37,130 --> 00:29:44,690 +تحول إلى المنطقة المنطقة + +290 +00:29:44,690 --> 00:29:51,910 +مجموعة من مجموعة + +291 +00:29:51,910 --> 00:30:01,070 +من Y تساوي X و Y تساوي X تربيع + +292 +00:30:06,520 --> 00:30:18,520 +the y axis حوالي المحور y by using باستخدام + +293 +00:30:18,520 --> 00:30:32,580 +نمرا a the shell method نمرا b the washer method + +294 +00:30:45,870 --> 00:30:46,910 +قولناها برسمها + +295 +00:30:53,920 --> 00:30:58,380 +سؤال مرة ثانية بيقول هات الحجم المجسم المتولد من + +296 +00:30:58,380 --> 00:31:04,820 +دوران المنطقة المحدودة بالخط Y تساوي X بالمنحنى Y + +297 +00:31:04,820 --> 00:31:10,080 +تساوي X تربيع والدوران حوالين محور Y بطريقتين + +298 +00:31:10,080 --> 00:31:13,700 +الطريقة اللي هو طريقة shell method اللي طريقتنا + +299 +00:31:13,700 --> 00:31:19,080 +قبل قليل والتانية ال washer method طريقتنا اللي هو + +300 +00:31:19,080 --> 00:31:20,920 +يوم أمس الأول + +301 +00:31:23,160 --> 00:31:29,460 +بنرسم و بعد ذلك بيصير خير يبقى هذا محور X هذا محور + +302 +00:31:29,460 --> 00:31:35,040 +Y هذا نقطة الاصل اللي هي Zero في ان المنحنة Y + +303 +00:31:35,040 --> 00:31:41,540 +تساوي X تربيع يبقى Y تساوي X تربيع المنحنة هجيلك + +304 +00:31:41,540 --> 00:31:41,940 +هيك + +305 +00:31:44,760 --> 00:31:52,380 +الخط التاني Y تساوي X يبقى Y تساوي X اللي هو الخط + +306 +00:31:52,380 --> 00:31:59,420 +اللي عندنا هذا يبقى هذا Y تساوي X هذا Y تساوي X + +307 +00:31:59,420 --> 00:32:04,180 +تربية حصروا المنطقة فيما بينهم اللي المنطقة + +308 +00:32:04,180 --> 00:32:09,570 +المضللة ديهذه المنطقة المظلة لابدها تدور حوالين + +309 +00:32:09,570 --> 00:32:15,150 +محور Y تمام؟ مدان بدها تدور حوالين محور Y يبقى + +310 +00:32:15,150 --> 00:32:22,390 +احنا بدنا نروح نرسم خط يقطع منطقة التكامل وموازن + +311 +00:32:22,390 --> 00:32:29,110 +لمحور Yيبقى لو جيت من هنا رسمت خط موازي لمحور Y + +312 +00:32:29,110 --> 00:32:34,970 +ويقطع منطقة التكامل يبقى هذا يعتبر الارتفاع + +313 +00:32:34,970 --> 00:32:40,690 +الجانبي للـ cylindrical shell بدي أعرف قداش طول + +314 +00:32:40,690 --> 00:32:48,490 +الخط الأخضر هذا بقوله تمام من هنا لهنا هذا Y تسوى + +315 +00:32:48,490 --> 00:32:57,620 +Xومن هنا لهنا هذا Y تسوى X تربيع، إذا هذا الخط + +316 +00:32:57,620 --> 00:33:04,120 +يكون الفرق بينهم اللي هو مين؟ X ناقص X تربيع، هذا + +317 +00:33:04,120 --> 00:33:12,240 +البعد، هذا البعد بيكون X نصف قطر من اللي هو + +318 +00:33:12,240 --> 00:33:18,810 +cylindrical shellبدلة ال X ستتغير من Zero لغاية + +319 +00:33:18,810 --> 00:33:25,760 +ابصر قداشيبقى بدي اعرف هنا اخر حاجة لذلك بدي احلي + +320 +00:33:25,760 --> 00:33:31,540 +المعادلتين هدول مع بعضهم يبقى انا عندي Y تساوي X + +321 +00:33:31,540 --> 00:33:39,060 +تربية وعندي Y تساوي X يبقى هذه ها بقدر اقول X + +322 +00:33:39,060 --> 00:33:44,820 +تربية ناقص X يساوي Zero او لو اخدت X عامل مشترك + +323 +00:33:44,820 --> 00:33:49,940 +بصير X ناقص واحد يساوي Zero يبقى X يساوي Zero و X + +324 +00:33:49,940 --> 00:33:55,790 +يساوي واحديبقى نقطة التقاطع الأولى عند الـ0 ونقطة + +325 +00:33:55,790 --> 00:34:02,850 +التقاطع التانية عند الـ1 يبقى بصير الـVolume V بدى + +326 +00:34:02,850 --> 00:34:11,050 +يسوى تكامل من 0 لغاية 1 للإتنين باي X في ال F of X + +327 +00:34:11,050 --> 00:34:15,390 +اللى همان X ناقص X تربية + +328 +00:34:20,080 --> 00:34:25,560 +يبقى X ناقص X تربية كل هذا الكلام بالنسبة إلى مين؟ + +329 +00:34:25,560 --> 00:34:32,620 +إلى DX يبقى هذا الكلام بيساوي 2π تكمل من 0 ل1 لل X + +330 +00:34:32,620 --> 00:34:40,820 +تربية ناقص X تكييب كله بالنسبة إلى DX يبقى 2π وهذه + +331 +00:34:40,820 --> 00:34:44,640 +عبارة عن X تكييب على 3 + +332 +00:34:47,470 --> 00:34:51,390 +نرجع لسؤالنا هذا مرة تانية وهو آخر مثال في هذا ال + +333 +00:34:51,390 --> 00:34:55,670 +section قال هاتلي حجم المجسم المتولد من دوران + +334 +00:34:55,670 --> 00:34:59,990 +المنطقة المحصورة بالمنحنى Y يساوي 2X ناقص X تربية + +335 +00:34:59,990 --> 00:35:04,810 +والخط المستقيم Y تساوي X والدوران بدي يكون مرة + +336 +00:35:04,810 --> 00:35:09,950 +حوالين محور Y ومرة حوالين خط موازي لمحور Y الهمين + +337 +00:35:09,950 --> 00:35:16,710 +X يساوي Yنعود للخط المستقيم Y2SWX نعود لهذا + +338 +00:35:16,710 --> 00:35:22,810 +المنحنى هذا المنحنى طبعا parabola انه Y دل في X و + +339 +00:35:22,810 --> 00:35:26,450 +X من الدرجة الثانية يبقى parabola بس معمولة لها + +340 +00:35:26,450 --> 00:35:30,310 +shift اذا بدى اعرف وين ال vertex بالضبط تبع هذه ال + +341 +00:35:30,310 --> 00:35:36,500 +parabola اذا بتروح اعمل اكمال للمربعيبقى هذه لو + +342 +00:35:36,500 --> 00:35:42,500 +جيت قلت Y تساوي بدنا نكمله مربع يعني قداش مضيف و + +343 +00:35:42,500 --> 00:35:50,400 +نطرح اربعة ولا واحد يعني انت بتحذر تحذير طيب مشان + +344 +00:35:50,400 --> 00:35:57,710 +تعرف قداش و ماحدش يولد تاني برنامج مضيف مربعمعامل + +345 +00:35:57,710 --> 00:36:05,710 +x على أربع أمثال معامل x تربية + +346 +00:36:09,680 --> 00:36:16,180 +بقول مربع معامل X كداش؟ أربعة أربعة أمثال معامل X + +347 +00:36:16,180 --> 00:36:20,700 +تربية أربعة في واحد تمام؟ اما هو واحد جد و ارمى + +348 +00:36:20,700 --> 00:36:24,520 +أربعة يبقى أربعة على أربعة في كداش؟ يبقى بضيف واحد + +349 +00:36:24,520 --> 00:36:31,640 +و بطرح واحد يبقى هذا Y بدي ساوي واحد ناقص واحد + +350 +00:36:31,640 --> 00:36:38,560 +زيدي اتنين X ناقص X تربيةهذا بدي اكتبه بالشكل اللي + +351 +00:36:38,560 --> 00:36:44,080 +انه هذا هذا ال Y ناقص واحد هذا كله بدي اخد منه + +352 +00:36:44,080 --> 00:36:49,820 +ناقص عامل مشترك مضال X تربيه يعني ناقص اتنين X + +353 +00:36:49,820 --> 00:36:58,320 +زائد واحد هذا معناه ان Y ناقص واحديساوي الناقص X + +354 +00:36:58,320 --> 00:37:04,320 +ناقص واحد لكل تربية يبقى هذه Parabola و ال vertex + +355 +00:37:04,320 --> 00:37:14,780 +واحد و واحد يبقى هذه Parabola open Down ولا Up؟ + +356 +00:37:14,780 --> 00:37:23,160 +Down بسبب الإشارة السالبة يبقى open down with + +357 +00:37:23,160 --> 00:37:25,760 +vertex + +358 +00:37:27,210 --> 00:37:35,510 +يبقى H و K يبقى واحد و واحد يبقى لو جيت قلت هذه + +359 +00:37:35,510 --> 00:37:40,690 +القيمة اللي عندنا واحد و جيت طالع هنا هذه واحد + +360 +00:37:40,690 --> 00:37:46,470 +يبقى أسارة النقطة هذه واحد و واحد يبقى واحد و واحد + +361 +00:37:46,470 --> 00:37:50,730 +تقع على الخط المستقيم و في نفس الوقت + +362 +00:37:59,220 --> 00:38:06,910 +السؤال هو هل ال Parabola تمر بنقطة الأصل؟نعم ليش؟ + +363 +00:38:06,910 --> 00:38:12,490 +ان لو حطيت ال X ب Zero و Y ب Zero يبقى ال parabola + +364 +00:38:12,490 --> 00:38:18,170 +هذه لو جيت رسمتها هتاخد الشكل التالي الشكل اللي + +365 +00:38:18,170 --> 00:38:22,990 +عندنا هذا هيك يبقى هذا ال parabola يبقى المنطقة + +366 +00:38:22,990 --> 00:38:30,250 +اللي محصورة فيما بينهما للمنطقة هذه تمام؟ يبقى من + +367 +00:38:30,250 --> 00:38:36,080 +هنا بدأنا الحل نمر أيه؟الدوران يكون حوالين محور Y + +368 +00:38:36,080 --> 00:38:43,880 +جل المطلوب الأول يبقى بدرح أرسم خط يقطع منطقة + +369 +00:38:43,880 --> 00:38:50,800 +التكامل وموازن لمحور الدوران يبقى هذا خط يقطع + +370 +00:38:50,800 --> 00:39:00,270 +منطقة التكامل وموازن لمحور الدورانيبقى هذه لو جيت + +371 +00:39:00,270 --> 00:39:06,530 +هنا إلى أسفل هذا البعد بدي يكون X اللي هو من نصف + +372 +00:39:06,530 --> 00:39:13,470 +القطر تبع دائرة cylindrical shell يبقى بدي أجي + +373 +00:39:13,470 --> 00:39:20,130 +أشوف ال X ستتغير من وين لوين أول قيمة Zero و أخر + +374 +00:39:20,130 --> 00:39:27,160 +قيمة كدهش واحد يبقى باجي بقوله ال volume Vبدي + +375 +00:39:27,160 --> 00:39:34,360 +أساوي تكامل للإتنين by X وهذا الكلام من Zero لغاية + +376 +00:39:34,360 --> 00:39:39,720 +واحد لل F of X F of X اللي هي المسافة اللي عندنا + +377 +00:39:39,720 --> 00:39:55,830 +هذه، هذه من هنا لهنا، اللي هي mainنقص X تربيه نقص + +378 +00:39:55,830 --> 00:39:57,190 +X تربيه + +379 +00:40:00,190 --> 00:40:08,950 +يبقى هذا في اتنين اكس ناقص اكس ترابية ناقص اكس كله + +380 +00:40:08,950 --> 00:40:13,870 +بالنسبة لمين الى دي اكس يبقى هذا الكلام يساوي + +381 +00:40:13,870 --> 00:40:19,750 +اتنين باي تكامل من زيرو لواحدهذا الـ X خلّيها برا + +382 +00:40:19,750 --> 00:40:25,630 +زي ما هي و عندك اتنين X و ناقص X بيبقى X واحدة + +383 +00:40:25,630 --> 00:40:32,750 +يبقى هذا X ناقص X تربية كله بالنسبة إلى DX أو ال + +384 +00:40:32,750 --> 00:40:40,610 +volume V بده يساويهي اتنين باي برا وهي تكامل من + +385 +00:40:40,610 --> 00:40:46,530 +Zero لغاية واحد لل X تربيه ناقص X تربيه X تكييب X + +386 +00:40:46,530 --> 00:40:52,810 +تربيه ناقص X تكييب كله بالنسبالي ديكت يبقى هذا + +387 +00:40:52,810 --> 00:41:00,250 +اتنين باي في X تكييب على تلاتة ناقص X أربع على + +388 +00:41:00,250 --> 00:41:07,640 +أربعة كله من Zero لغاية واحد يبقى اتنين بايفي تلت + +389 +00:41:07,640 --> 00:41:12,800 +ناقص ربع عملناها قبل شوية واحد على اتناش يبقى + +390 +00:41:12,800 --> 00:41:18,960 +النتيجة باي على ستة الآن بدنا نيجي للمطلوب التاني + +391 +00:41:18,960 --> 00:41:25,700 +نمرا V نمرا V بدا عيد الرسم تاني يبقى لو جينا + +392 +00:41:25,700 --> 00:41:32,380 +قعدنا الرسم تاني وقولنا هذا محور X هذا محور Y + +393 +00:41:32,380 --> 00:41:41,100 +تمام؟الخط Y تساوي X هذا الخط Y تساوي X جينا 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163.27, "text": "أو ممكن يكون قرص مصمت بس فيه تجويف ممكن يكون شريحة تمام يبقى هناخد طريقة اللي هو الشريحة هذه و ناخد طريقة ال disk فنبدأ بطريقة ال disk في الأول فقال لي volume of revolution يعني حجم المجسم", "tokens": [10721, 2407, 3714, 43020, 7251, 30544, 12174, 2288, 9381, 3714, 9381, 2304, 2655, 4724, 3794, 8978, 3224, 6055, 7435, 45865, 5172, 3714, 43020, 7251, 30544, 13412, 16572, 5016, 3660, 46811, 10943, 7251, 3555, 4587, 7578, 8032, 1863, 47283, 3215, 23032, 16572, 28671, 13672, 1829, 31439, 25124, 16572, 5016, 3660, 29538, 4032, 8717, 47283, 3215, 23032, 16572, 28671, 2423, 12355, 6156, 1863, 44510, 10721, 4724, 9566, 16572, 28671, 2423, 12355, 8978, 16247, 12610, 6156, 4587, 6027, 32239, 5523, 295, 8894, 37495, 22653, 11331, 7435, 2304, 9673, 7435, 38251], "avg_logprob": -0.16521661694754253, "compression_ratio": 1.7486033519553073, "no_speech_prob": 0.0, "words": [{"start": 138.61, "end": 139.13, "word": "أو", "probability": 0.6033935546875}, {"start": 139.13, "end": 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b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/CSmgX_n9P2U_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..2ca4cae11a2007615959e4ef23b673dcc60ff560 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/CSmgX_n9P2U_raw.srt @@ -0,0 +1,3436 @@ +1 +00:00:20,670 --> 00:00:25,410 +بسم الله الرحمن الرحيم مثل ما خدنا تطبيقات على + +2 +00:00:25,410 --> 00:00:30,790 +التفاضل برضه بدنا نتاخد تطبيقات على التكامل بعد ما + +3 +00:00:30,790 --> 00:00:36,810 +خدنا في chapter 5 كيفية تكامل الدوال المختلفة يبقى + +4 +00:00:36,810 --> 00:00:42,100 +chapter 6 هو تطبيقات على استخدام التكاملفي هذه + +5 +00:00:42,100 --> 00:00:49,820 +التطبيقات سنحاول إيجاد الحجوم والمساحات واطوال + +6 +00:00:49,820 --> 00:00:54,920 +المنحنيات طبعا هنجد الحجوم وهذا جديد علينا لم + +7 +00:00:54,920 --> 00:01:00,900 +نتعرض لهم من قبل سنجد المساحات السطحية للمجسمات + +8 +00:01:00,900 --> 00:01:05,760 +لأن المساحة بين المنحنيات درسناها في chapter خمسة + +9 +00:01:05,760 --> 00:01:11,060 +في آخر section كانسيكشن خمسة ستة ولذلك المساحات + +10 +00:01:11,060 --> 00:01:15,940 +هنا ليست المساحات في المستوى وانما المساحات في + +11 +00:01:15,940 --> 00:01:21,900 +الفرار يعني مساحة اللي هو مجسم موجود في الفرار + +12 +00:01:21,900 --> 00:01:27,060 +هنبدأ بأول نقطة وهي إيجاد الحجوبيبقى applications + +13 +00:01:27,060 --> 00:01:32,780 +of definite integrals تطبيقات التكاملات المحدودة + +14 +00:01:32,780 --> 00:01:37,800 +section 61 volumes using cross sections يبقى بدنا + +15 +00:01:37,800 --> 00:01:44,440 +نحاول نوجد الحجوم باستخدام المقاطع للمين للمجسمات + +16 +00:01:44,440 --> 00:01:51,300 +المجسم هذا بده ينشأ عندنا من دوران بدنا ناخد مقطع + +17 +00:01:51,300 --> 00:01:55,420 +لهذا المجسم الناتجومن خلال المقطع اللى عندنا هذا + +18 +00:01:55,420 --> 00:02:01,560 +بدنا نحاول نوجد قداش حجم المجسم طبعا في هذا ال + +19 +00:02:01,560 --> 00:02:08,400 +section في عندى يا اما طريقة ال disk لو كان المقطع + +20 +00:02:08,400 --> 00:02:15,820 +هو عبارة عن اللى هو دائرة مصمة وبالتالي بسميها + +21 +00:02:15,820 --> 00:02:23,010 +disk يعني قرص مصمتأو ممكن يكون قرص مصمت بس فيه + +22 +00:02:23,010 --> 00:02:29,490 +تجويف ممكن يكون شريحة تمام يبقى هناخد طريقة اللي + +23 +00:02:29,490 --> 00:02:34,670 +هو الشريحة هذه و ناخد طريقة ال disk فنبدأ بطريقة + +24 +00:02:34,670 --> 00:02:40,630 +ال disk في الأول فقال لي volume of revolution يعني + +25 +00:02:40,630 --> 00:02:47,880 +حجم المجسمالناتج من الدوران revolution دوران solid + +26 +00:02:47,880 --> 00:02:53,520 +مجسم يبقى حجم المجسم الناتج من الدوران وبدا نتعرف + +27 +00:02:53,520 --> 00:02:59,560 +لأول طريقة The disk method طريقة القرص نعطيله + +28 +00:02:59,560 --> 00:03:05,140 +التعريف التالي يبقى volume of the solid حجم المجسم + +29 +00:03:05,140 --> 00:03:11,780 +generated المتولد او المتكونby revolving the + +30 +00:03:11,780 --> 00:03:17,660 +region between بدوران المنطقة المحصورة مابين الرسم + +31 +00:03:17,660 --> 00:03:23,280 +البياني لمنحنة دالة y to سوى r of x and the x axis + +32 +00:03:23,280 --> 00:03:28,760 +about the x axis يعني الدوران هيكون حوالين محور x + +33 +00:03:28,760 --> 00:03:35,130 +isيبقى لو جيت افترضت ان عندي منحنى زي ما انت شايف + +34 +00:03:35,130 --> 00:03:40,650 +Y تساوي R of X بدي اخلي هذا المنحنى يدور حوالين + +35 +00:03:40,650 --> 00:03:46,090 +محور X وبعد شوية هاخد مثلا خليه يدور حوالين خط + +36 +00:03:46,090 --> 00:03:50,630 +موازية محور Xبعد ذلك يمكن أن يكون المنحنة يدور + +37 +00:03:50,630 --> 00:03:56,650 +حوالين محور Y حسب طبيعة المنحنة أو حوالين خط موازي + +38 +00:03:56,650 --> 00:04:01,050 +لمحور Y كل هذا سناخد عليه أمثلة الحلات الأربع + +39 +00:04:01,050 --> 00:04:06,210 +دوران حول محور X حولين خط موازي لمحور X حولين محور + +40 +00:04:06,210 --> 00:04:11,750 +Y حولين خط موازي لمحورو ايه بنشوف كيف بنجيب الحجوم + +41 +00:04:11,750 --> 00:04:15,510 +في الحالات الأربع خلّينا في البداية لو كان الدوران + +42 +00:04:15,510 --> 00:04:20,930 +حول محور X نشوف كيف بنجد حجم المجسم الناتج من + +43 +00:04:20,930 --> 00:04:26,070 +الدوران يبقى هذه عندي R of X زي ما انت شايف بدي + +44 +00:04:26,070 --> 00:04:30,990 +أخليها الدور في الفرح بدي أريك ما هو شكل المجسم + +45 +00:04:30,990 --> 00:04:35,640 +الناتج من الدورانالان لما اقول محور الدوران هو + +46 +00:04:35,640 --> 00:04:41,560 +محور X يبقى اي نقطة خارج محور الدوران عن دورانها + +47 +00:04:41,560 --> 00:04:47,720 +سترسم محيط دائرة تمام تمام اذا النقطة هذه هنا + +48 +00:04:47,720 --> 00:04:54,330 +هترسم لي محيط دائرةيبقى لو جيت للدائرة و روحت قولت + +49 +00:04:54,330 --> 00:04:59,170 +هذه الدائرة اللي عندنا تمام هذه كمان النقطة + +50 +00:04:59,170 --> 00:05:04,450 +هترسملي محيط دائرة هذا هو نص قطرها يبقى لما اديت + +51 +00:05:04,450 --> 00:05:08,990 +هذا على استقامته بقدر طوله يبقى هتصبح الدائرة اللي + +52 +00:05:08,990 --> 00:05:16,650 +عندنا بهذا الشكل تمام يبقى الخط الخاري هذا هيصبح + +53 +00:05:16,650 --> 00:05:22,420 +على الشكل التالييبقى هذا المجسم اللى نتج منه دورة + +54 +00:05:22,420 --> 00:05:28,660 +كل نقطة على هذا المنحنى بترسم محيط دارة فحصل عندنا + +55 +00:05:28,660 --> 00:05:34,820 +من المجسم اللى أمامنا هذا بدنا نوجد حجم هذا المجسم + +56 +00:05:34,820 --> 00:05:39,220 +إذا بدي أروح أخد cross section من أعلى إلى أسفل + +57 +00:05:39,220 --> 00:05:44,520 +بدي أقطعه بمقطع و أشوف شكل المقطع السؤال هو ما هو + +58 +00:05:44,520 --> 00:05:50,350 +شكل المقطع؟دائرة كذلك يبقى الدائرة هذه لو روحت + +59 +00:05:50,350 --> 00:05:55,510 +رسمتها بدى يكون عندى خط بالشكل هذا يكتر ومن + +60 +00:05:55,510 --> 00:05:59,690 +الناحية التانية بيظهر ليش فهارسمه منقط خط بالشكل + +61 +00:05:59,690 --> 00:06:03,730 +اللى عندنا هنا يبقى هذه دائرة هذه دائرة هذه دائرة + +62 +00:06:03,730 --> 00:06:09,570 +يبقى هذا هو المقطع اللى عندنا هنا طيب مدام دائرة + +63 +00:06:09,570 --> 00:06:15,590 +حد بقدر يقولى قداش مساحة الدائرةنقتر بيه ممتاز جدا + +64 +00:06:15,590 --> 00:06:21,710 +يبقى انا لو هذه المساحة اعطيتها الرمز a يبقى a هذه + +65 +00:06:21,710 --> 00:06:26,550 +هي المساحة من هنا راح نقولنا ال volume v يسوى + +66 +00:06:26,550 --> 00:06:34,090 +تكامل من عند ال a هنا لغاية ال b هنا تكامل من a + +67 +00:06:34,090 --> 00:06:39,740 +إلى bلهذه المساحة اللي هي A of X بيعطيني حجم + +68 +00:06:39,740 --> 00:06:44,400 +المجسم كله يبقى تكامل هذه المساحة من عند ال A إلى + +69 +00:06:44,400 --> 00:06:48,940 +B يساوي تكامل من A إلى B مساحة درجة تحت النقطة + +70 +00:06:48,940 --> 00:06:54,820 +الربيعية وين نقلوا المسافة؟ من هنا لغاية هنا هذا + +71 +00:06:54,820 --> 00:06:59,960 +الخط اللي عندنا الغامق هذا هو مين؟ هذا هو نصف + +72 +00:06:59,960 --> 00:07:06,680 +القطريبقى نصف القطر البعد ما بين المنحنى ومحور X + +73 +00:07:09,870 --> 00:07:14,370 +R of X هو البعد اللي عندنا يبقى لما يقول طه نقطة + +74 +00:07:14,370 --> 00:07:20,650 +بيه يصير بي R of X لكل تربية يعد X يبقى هذا حجم + +75 +00:07:20,650 --> 00:07:26,290 +المجسم الناتج من الدوران يبقى نصف القطر هذا اللي + +76 +00:07:26,290 --> 00:07:32,150 +عندنا هو عبارة عن مين عبارة عن R of X ان كامل هذا + +77 +00:07:32,150 --> 00:07:38,050 +من A لB بنحصل على حجم المجسم الناتج من الدورانقد + +78 +00:07:38,050 --> 00:07:43,670 +يكون الدوران حسب طبيعة المنحنى حول محور Y إذا كان + +79 +00:07:43,670 --> 00:07:48,270 +الدوران حول محور Y يبقى بدنا نروح نكامل بالنسبة + +80 +00:07:48,270 --> 00:07:52,750 +لمين إلى Y وبالتالي بيصير ال volume في هذه الحالة + +81 +00:07:52,750 --> 00:07:57,430 +V سوى تكامل من C إلى D لل A of Y دي Y أو تكامل بI + +82 +00:07:57,430 --> 00:07:59,810 +R of Y لكل تربية مين + +83 +00:08:02,620 --> 00:08:07,700 +الان بعد هذا الكلاب نروح ناخد امثلة تطبيقية على + +84 +00:08:07,700 --> 00:08:12,580 +الكلام اللي احنا بنقوله ونشوف كيف هنحسب هذه الحجوم + +85 +00:08:12,580 --> 00:08:18,120 +بدنا نيجي لأول مثال على هذا الموضوع يبقى example + +86 +00:08:18,120 --> 00:08:18,620 +one + +87 +00:08:24,530 --> 00:08:29,530 +يبقى مشان احسب الحجم بدي شغلتين بدي اعرف بس حدود + +88 +00:08:29,530 --> 00:08:34,310 +التكامل من و لا و اين اتنين بدي اعرف قداش نص القطر + +89 +00:08:34,310 --> 00:08:38,150 +تبع المقطع اذا عرفت هذا بصير الشغل تكامل عادي + +90 +00:08:38,150 --> 00:08:43,920 +روتيني عادي لا شيء فيهيبقى هدول اهم حاجة عندي حدود + +91 +00:08:43,920 --> 00:08:49,960 +تكمن اتحددها الصح اتنين اللي هو مان نصف القطر تبع + +92 +00:08:49,960 --> 00:08:54,340 +اللي هو دائرة المقلة او تبع ال disk يبقى هذا اللي + +93 +00:08:54,340 --> 00:09:00,220 +رسمناه مظلة للي عندنا هذا هذا هو ال disk يبقى هذا + +94 +00:09:00,220 --> 00:09:04,300 +هو ال disk لان احنا قلنا بناخد اول طريقة اللي هي + +95 +00:09:04,300 --> 00:09:10,000 +ال disk مثال نعطي مثاليبقى example one بيقول ما + +96 +00:09:10,000 --> 00:09:16,540 +يأتي find the volume of the solid find the volume + +97 +00:09:16,540 --> 00:09:27,480 +of the solid generated by + +98 +00:09:27,480 --> 00:09:31,000 +revolving + +99 +00:09:31,000 --> 00:09:44,910 +the region bounded bythe region bounded by + +100 +00:09:44,910 --> 00:09:59,470 +والمحدود بي Y تساوي X تكيب وY تساوي Zero and X + +101 +00:09:59,470 --> 00:10:04,550 +يساوي اتنين about the X axis about + +102 +00:10:06,500 --> 00:10:09,520 +الـ X Axis + +103 +00:10:27,460 --> 00:10:31,460 +لما نحل مثال على هذا الموضوع يبقى أول شغلة بدنا + +104 +00:10:31,460 --> 00:10:36,180 +نعملها بدنا نرسم الرسمة مشان نقدر نحدد حدود + +105 +00:10:36,180 --> 00:10:41,680 +التكامل يبقى بيقول هاتلي حجم المجسم الناتج من + +106 +00:10:41,680 --> 00:10:47,700 +دوران المنطقة المحدودة بالمنحنى Y تساوي X تكايم + +107 +00:10:47,700 --> 00:10:53,340 +يبقى لو رحنا رسمنا المنحنى بالشكل هذا هذا محور X + +108 +00:10:53,570 --> 00:11:01,510 +هذا محور Y وهذا نقطة الأصل Z يبقى المنحنى Y تساوي + +109 +00:11:01,510 --> 00:11:07,370 +X تكييب منحنى رسمناه عدة مرات قبل ذلك يبقى ما هوش + +110 +00:11:07,370 --> 00:11:13,370 +جديد بالنسبة لنا يبقى هذا المنحنى الهمين يبقى Y + +111 +00:11:13,370 --> 00:11:15,470 +تساوي X تكييب + +112 +00:11:19,640 --> 00:11:24,700 +بعد هيك قال كمان محدود بمين؟ Y تساوي زيرو، مين Y + +113 +00:11:24,700 --> 00:11:29,860 +تساوي زيرو هذا؟ محور X، يبقى هذا الخط اللي هو Y + +114 +00:11:29,860 --> 00:11:35,320 +تساوي زيرو، بعد هيك قال الخط X يساوي اتنين، يبقى + +115 +00:11:35,320 --> 00:11:41,600 +خط رأسي بهذا الشكل X يساوي اتنين، يبقى هذا اتنين + +116 +00:11:41,810 --> 00:11:48,310 +يبقى بين محور X والمنحنى Y تساوي X تكييب والخط X + +117 +00:11:48,310 --> 00:11:53,750 +يساوي 2 يبقى عبارة عن المنطقة المظللة اللي عندنا + +118 +00:11:53,750 --> 00:12:01,020 +هذهما للمنطقة هذه؟ هذه بدها الدور حوالين محور X + +119 +00:12:01,020 --> 00:12:07,480 +تمام يبقى هل بدرورة ارسم المجسم الناتج من الدوران؟ + +120 +00:12:07,480 --> 00:12:13,520 +ليس بدورة لكن حدد نصف قطر ال disk تبعك بصير خلصه + +121 +00:12:13,520 --> 00:12:17,840 +يبقى مشان هك كأن المجسم موجود و بده يروح اعمل فيه + +122 +00:12:17,840 --> 00:12:23,510 +مهم مقطع المقطع هذابدي يكون ال disk تبعه بالشكل + +123 +00:12:23,510 --> 00:12:29,050 +اللي عندنا هذا يبقى هذا نصف القطر تبع ال disk + +124 +00:12:29,050 --> 00:12:35,330 +السؤال هو قداش مقدار نصف القطر هذا اكس تكعيب لان + +125 +00:12:35,330 --> 00:12:39,290 +اكس تكعيب هي المسافة بين محور X و المنحنة اللي فات + +126 +00:12:39,290 --> 00:12:43,890 +لان هذا المنحنة لو جيت كملته بدي يجيني بالشكل اللي + +127 +00:12:43,890 --> 00:12:50,970 +عندنا هذابالشكل هذا و بدي أجيني هذا هيك مش هذا + +128 +00:12:50,970 --> 00:12:57,860 +الشكلهذه حترسم لي محيط دائرة وهذه نقطة الأصل زي ما + +129 +00:12:57,860 --> 00:13:02,480 +هي ثابتة إذا هذا لو أخدت ال disk بدي يكون ال disk + +130 +00:13:02,480 --> 00:13:08,040 +بالشكل اللي عندنا هنا يبقى هذا نص القطر بدي أحدد + +131 +00:13:08,040 --> 00:13:12,740 +نص القطر والباقي بيصير كله شغل روتيني يبقى نص + +132 +00:13:12,740 --> 00:13:16,880 +القطر اللي عندنا هو عبارة عن المسافة هذه هي Y + +133 +00:13:16,880 --> 00:13:24,380 +تساوييبقى بروح بقوله ال volume V بدي يسوي تكامل ال + +134 +00:13:24,380 --> 00:13:30,820 +X هتتغير من وين ل وين من صفر لغاية اتنين لل باي R + +135 +00:13:30,820 --> 00:13:36,760 +of X اللي هي X تكيب الكل تربيع بالنسبة الى main + +136 +00:13:36,760 --> 00:13:42,160 +بالنسبة الى DX باي مقدار ثابت مالوش دعوة وهي تكامل + +137 +00:13:42,160 --> 00:13:50,510 +من صفر لاتنين وهذا X أُس 6 DXيبقى هذه تساوي باي + +138 +00:13:50,510 --> 00:13:58,670 +وهذه x السابعة على سبعة من zero لغاية اتنين يبقى + +139 +00:13:58,670 --> 00:14:06,910 +هذه باي على سبعة في اتنين والسبعة ناقص zero اتنين + +140 +00:14:06,910 --> 00:14:13,820 +والسبعة اللي هي جداش مية وتمانية وعشرينيبقى 128 + +141 +00:14:13,820 --> 00:14:22,160 +على 7 باي هذا حجم المجسم الناتج من الدوران وهذا من + +142 +00:14:22,160 --> 00:14:26,140 +أبسط أنواع المسائل اللي مافيش فيه تفكير ولا حاجة + +143 +00:14:26,140 --> 00:14:33,640 +مباشرة طيب نعطيك سؤال أتقل شوية example 2 + +144 +00:14:40,150 --> 00:14:44,750 +بقول find the + +145 +00:14:44,750 --> 00:14:58,630 +volume of the solid بنقدرش حجم المجسم generated by + +146 +00:14:58,630 --> 00:15:02,750 +revolving + +147 +00:15:02,750 --> 00:15:11,120 +the regionالناتج من دوران المنطقة in the first + +148 +00:15:11,120 --> 00:15:18,820 +quadrant in the first quadrant + +149 +00:15:18,820 --> 00:15:31,740 +في الربع الأول bounded above by bounded above + +150 +00:15:31,740 --> 00:15:34,420 +by + +151 +00:15:37,240 --> 00:15:42,440 +by the line y + +152 +00:15:42,440 --> 00:15:58,380 +تساوي 2 below ومن أسفل by the curve y يساوي 2 sin + +153 +00:15:58,380 --> 00:16:06,980 +x 2 sin x و ال x هذه محصورة بين ال zeroو مابين ال + +154 +00:16:06,980 --> 00:16:18,600 +by على اتنين and on the left و من الجهة اليسرى by + +155 +00:16:18,600 --> 00:16:32,560 +the y axis by the y axis بمحور y about the line y + +156 +00:16:32,560 --> 00:16:33,680 +تساو اتنين + +157 +00:17:04,310 --> 00:17:10,090 +سؤال مرة تانية بيقول هاتلي حجم المجسم المتولد من + +158 +00:17:10,090 --> 00:17:15,470 +دوران المنطقة في الربع الأول والمحدودة من أعلى + +159 +00:17:15,470 --> 00:17:20,530 +بالخط Y تساوي اتنين ومن أسفل بالمنحنى Y يساوي + +160 +00:17:20,530 --> 00:17:26,330 +اتنين sin X و X فقط من Zero لغاية Pi على اتنين and + +161 +00:17:26,330 --> 00:17:31,000 +on the left ومن الجهة اليسرى بمحور Yوالدوران + +162 +00:17:31,000 --> 00:17:37,460 +حوالين الخط Y تساوي 2 وليس حوالين محور X يبقى + +163 +00:17:37,460 --> 00:17:41,880 +المثال السابق ان الدوران حوالين هنا حوالين خط + +164 +00:17:41,880 --> 00:17:47,540 +موازي لمحور X إذا خلينا نرسم المنطقة اللي عندنا + +165 +00:17:47,540 --> 00:17:51,880 +هذه ونشوف كيف بدنا نحسب اللي هو main اللي هو + +166 +00:17:51,880 --> 00:17:58,060 +التكامل هذا يبقى هذا محور Xهذا محور why هذا الخط + +167 +00:17:58,060 --> 00:18:04,030 +اللي عندنا main اللي هو why تساوي كدهيساوى 2 يبقى + +168 +00:18:04,030 --> 00:18:11,170 +هذا من أعلى من أسهل جلّي بالمنحنى y تساوى 2 sin x + +169 +00:18:11,170 --> 00:18:16,090 +sin x أكبر قيمة باخد جداش واحد لما أضربه في اتنين + +170 +00:18:16,090 --> 00:18:21,690 +شير اتنين يعني أقصى حاجة بوصلها انه يمس الخط اللى + +171 +00:18:21,690 --> 00:18:25,610 +عندنا هذا مظبوط طب هو بياخد ال sin القيمة واحد + +172 +00:18:25,610 --> 00:18:31,500 +عندكش يساوي جداش by على اتنينأذا لو جيت قولت هذه + +173 +00:18:31,500 --> 00:18:37,220 +النقطة zero و جيت رسمت هذا المنحنى يقول المنحنى + +174 +00:18:37,220 --> 00:18:40,740 +بده يجيني بالشكل اللي عندنا هذا هذه النقطة اللي هي + +175 +00:18:40,740 --> 00:18:45,260 +πاي على اتنين يبقى انا بس بده اخد من zero لغاية + +176 +00:18:45,260 --> 00:18:49,620 +باي على اتنين باقي منحنى ال sign اللي من ناحية + +177 +00:18:49,620 --> 00:18:53,300 +التانية او من ناحية التانية ماليش علاقة فيهيبقى + +178 +00:18:53,300 --> 00:18:57,760 +أنا مقيد فقط في الجزء من zero لغاية باي على اتنين + +179 +00:18:57,760 --> 00:19:03,600 +يبقى هذا المنحنى اللى تحته هو Y يساوي اتنين sign + +180 +00:19:03,600 --> 00:19:08,680 +ال X واللي فوق Y تساوي اتنين وعلى الشمال محور Y + +181 +00:19:08,680 --> 00:19:14,700 +يبقى منطقة التكامل هي المنطقة اللى عندنا هذه فقط + +182 +00:19:14,700 --> 00:19:21,610 +لا غيرفبالمنطقة المظللة بالأحمر بدهاش تدور حوالين + +183 +00:19:21,610 --> 00:19:25,790 +محورك سواء إنما بده تدور حوالين مهم الخط كتير يعني + +184 +00:19:25,790 --> 00:19:32,050 +بده تدور لفوق مش لتحت تمام؟ إذا بداجي أشوف قداش + +185 +00:19:32,050 --> 00:19:36,730 +نصف قطر دائرة المقطع يعني قداش نصف قطر ال disk + +186 +00:19:36,730 --> 00:19:42,810 +يفجأة بروح بنزل عمود من منطقة التكامل على وين؟ على + +187 +00:19:42,810 --> 00:19:48,750 +محور الدورانيبقى بيكون هذا اللي عندنا هذا هو نصف + +188 +00:19:48,750 --> 00:19:56,690 +القطر لفوق، مين يرف يقول جديش نصف القطر اللي عندنا + +189 +00:19:56,690 --> 00:20:04,810 +هذا؟ فكر كويس، مالها؟ + +190 +00:20:04,810 --> 00:20:12,110 +يبقى نصف القطر عندنا اللي هو جديشممتع جدا يبقى + +191 +00:20:12,110 --> 00:20:17,590 +المسافة هذه كلها من هنا لهنا ايه المسافة عندنا من + +192 +00:20:17,590 --> 00:20:22,430 +هنا لهنا كلها اتنين تمام بدي اشيل منها المسافة + +193 +00:20:22,430 --> 00:20:26,730 +السفلية هذه المسافة السفلية اللي عندنا هذه بيبقى + +194 +00:20:26,730 --> 00:20:31,610 +بقعد المنحنى عن محور X جداش البقعد اتنين sign ال X + +195 +00:20:31,610 --> 00:20:36,570 +اذا هذا البقعد بيكون اتنين ناقص اتنين sign ال X + +196 +00:20:36,570 --> 00:20:43,760 +اذا هذا البقعداللي هو اتنين ناقص اتنين sign ال X + +197 +00:20:43,760 --> 00:20:49,480 +هذا يمثل نصف قطر ال disk يعني نصف قطر دائرة المقطع + +198 +00:20:49,480 --> 00:20:53,960 +ايوة ولا + +199 +00:20:53,960 --> 00:21:00,740 +محور Y ولا محور X انت شافش اللي مكتوب حوالين + +200 +00:21:00,740 --> 00:21:06,340 +الخطمينY تسوى اتنين موازي الى محور X اول مرة + +201 +00:21:06,340 --> 00:21:11,580 +سمناها هي الدوران لفوق تمام حد بدي يوصل تاني قبل + +202 +00:21:11,580 --> 00:21:15,800 +ما نفقد اذا مين اللي بحكي ايوة + +203 +00:21:18,700 --> 00:21:23,980 +مش بنزل عمود انت لو رسم دائرة انا بجيب نص قطر لانه + +204 +00:21:23,980 --> 00:21:28,420 +قبل شوية قلنا ليس بالضرورة اني ارسم الرسمة كلها + +205 +00:21:28,420 --> 00:21:33,360 +صحيح ولا لأ يفجأة انا باخد بس نص قطر دائرة المقطع + +206 +00:21:33,360 --> 00:21:38,720 +يعني نص قطر ال disk اللي عندكهذا لو دار لفوق يبقى + +207 +00:21:38,720 --> 00:21:43,140 +هذي بده تيجي هنا و هذي مكانها زي ما هي بده يصير + +208 +00:21:43,140 --> 00:21:47,580 +هذا نصف قطر دائرة المقطع واستفاد من عليك انها بس + +209 +00:21:47,580 --> 00:21:51,320 +يكفيني ارسم نصف القطر و الله يعطيك العافية ليس + +210 +00:21:51,320 --> 00:21:57,840 +بالضرورة ان ارسم رسمة كاملة لهمين؟ وين ما بدك من + +211 +00:21:57,840 --> 00:21:59,820 +هنا لغاية هنا + +212 +00:22:18,400 --> 00:22:23,840 +بتنزل عمود من المنطقة اللى عندك على محور الدوران + +213 +00:22:25,880 --> 00:22:31,480 +Y تسوى اتنين يبقى هذا نصف القطر يبقى ماضلش اللي هي + +214 +00:22:31,480 --> 00:22:36,440 +كامل وكامل عندنا هي من Zero لغاية كده ايش؟ لباية + +215 +00:22:36,440 --> 00:22:42,240 +على اتنين يبقى باجي بقوله Volume V يبقى تكامل من + +216 +00:22:42,240 --> 00:22:47,760 +Zero لباية على اتنين لباية فيه نصف القطر اللي هو + +217 +00:22:47,760 --> 00:22:55,610 +اتنين نقص اتنين Sin X لكل تربيه يقعدى Xيبقى هذا + +218 +00:22:55,610 --> 00:23:01,510 +بده يتساوي ال by هيها برا و هي تكامل من zero لغاية + +219 +00:23:01,510 --> 00:23:06,770 +by على ال X فتفكر التربيع اللي عندنا هذا يبقى هذا + +220 +00:23:06,770 --> 00:23:15,130 +ناطف تمانية sign ال X زائد أربعة sign تربيع ال X + +221 +00:23:15,130 --> 00:23:23,070 +كله بالنسبة إلى مين؟ إلى DX تمام؟طيب الآن ال term + +222 +00:23:23,070 --> 00:23:29,710 +الأول وال term التاني سهل تكامل، المشكلة في ال + +223 +00:23:29,710 --> 00:23:34,720 +term التالتيبقى ال term التالت بدنا نروح يكتبوا + +224 +00:23:34,720 --> 00:23:40,360 +بدلالة ضعف الزاوية يبقى هذا الكلام بده يساوي hi by + +225 +00:23:40,360 --> 00:23:46,120 +برة تكامل من zero لغاية pi على اتنين وهي ال ghost + +226 +00:23:46,120 --> 00:23:54,280 +هي الأربعة ناقص تمانية في sign ال x زائد 4سيني + +227 +00:23:54,280 --> 00:24:00,300 +التربية هي عبارة عن نص في واحد زاد يبقى هي أربع في + +228 +00:24:00,300 --> 00:24:08,060 +مص يفتح قوس واحد ناقص كوسيني اتنين X كل هذا الكلام + +229 +00:24:08,060 --> 00:24:16,320 +بالنسبة لمن ثلاث اكس هذا بده يساوي هي ال by برا + +230 +00:24:16,320 --> 00:24:22,460 +وهي تكامل من zero لغاية by على اتنينطبعا طلعلي الى + +231 +00:24:22,460 --> 00:24:27,840 +هنا اربعة فى نص باتنين اتنين فى واحد باتنين اتنين + +232 +00:24:27,840 --> 00:24:35,200 +واربعة ستة يبقى هذه بدها صير ستة ناقص تمانية sign + +233 +00:24:35,200 --> 00:24:42,880 +ال X زي ماهي مافيش فيها مشكلةنجي هنا و نضلي 2cos2x + +234 +00:24:42,880 --> 00:24:48,340 +يبقى ناقص 2cos2x + +235 +00:24:48,340 --> 00:24:56,590 +كل هذا الكلام بالنسبة إلى Dxيبقى نيجي نكامل يبقى + +236 +00:24:56,590 --> 00:25:02,250 +هذا أصبح ال volume V بده يسوي high by اللي برا و + +237 +00:25:02,250 --> 00:25:08,250 +بدنا نكامل تكمل ال 6 اللي هي في 6X و سلب 8 مالهاش + +238 +00:25:08,250 --> 00:25:15,170 +علاقة و تكمل ال signبسلب cosine مع سلب بصير موجة ب + +239 +00:25:15,170 --> 00:25:23,010 +تمانية cosine ال X واللي بعدها ناقص sine اتنين X + +240 +00:25:23,010 --> 00:25:28,230 +على اتنين بتروح مع الاتنين والكلام من zero لغاية + +241 +00:25:28,230 --> 00:25:29,230 +pi على اتنين + +242 +00:25:33,960 --> 00:25:41,860 +بنعود بالقيمة اللي فوق يبقى 6 في πاي على 2 يبقى 3 + +243 +00:25:41,860 --> 00:25:48,080 +باي يبقى هاي 3 باي اللي بعدها cosine باي على 2 هو + +244 +00:25:48,080 --> 00:25:52,280 +0 يبقى هاي زائد 0 ناقص + +245 +00:25:57,310 --> 00:26:02,810 +هذه القيمة اللي فوق ناقص اللي تحت ستة في زيرو + +246 +00:26:02,810 --> 00:26:10,110 +بقداش بزيرو و cosine صفر بواحد يبقى ناقص تمانية + +247 +00:26:10,110 --> 00:26:15,510 +ناقص مع ناقص بصير زائد صين الزيرو اللي هو بقداش + +248 +00:26:15,510 --> 00:26:23,720 +بزيرو يبقى النتيجة صارت بايتلاتة باقي ناقص تمانية + +249 +00:26:23,720 --> 00:26:29,480 +مين اللى بيحكي اللى فوق ناقص اللى تحت كوصيلة ستة + +250 +00:26:29,480 --> 00:26:34,440 +باقي طبعا يبقى دخلت سلب على كل واحدة منهم يبقى هذه + +251 +00:26:34,440 --> 00:26:38,000 +النتيجة النهائية لمين لحجم يبقى زى ما انت شايف كله + +252 +00:26:38,000 --> 00:26:43,280 +شغل روتيني بس حد الحدود التكمل صح اتنين احد النص + +253 +00:26:43,280 --> 00:26:51,430 +القطر صح بصير باقي الشغل روتيني عاديمثال رقم تلاتة + +254 +00:26:51,430 --> 00:27:01,070 +example three find the + +255 +00:27:01,070 --> 00:27:13,150 +volume of the solid generated by + +256 +00:27:13,150 --> 00:27:15,770 +revolving + +257 +00:27:17,990 --> 00:27:25,130 +by revolving the region bounded + +258 +00:27:25,130 --> 00:27:38,270 +by the line the region bounded by ال X بده يساوي + +259 +00:27:38,270 --> 00:27:47,300 +اتنين على Y زائد واحد وال X يساوي Zeroو ال y تساوي + +260 +00:27:47,300 --> 00:28:00,900 +zero and ال y يساوي تلاتة about the y axis اوليا + +261 +00:28:00,900 --> 00:28:12,600 +محور y السؤال + +262 +00:28:12,600 --> 00:28:20,420 +مرة تانيةبقول هاتلي حجم المجسم المتكون من دوران + +263 +00:28:20,420 --> 00:28:27,220 +المنطقة المحدودة بالمنحنى x يساوي اتنين على y زائد + +264 +00:28:27,220 --> 00:28:33,340 +واحد شكله هيك مش عارفينهلكن لو حطيته y as a + +265 +00:28:33,340 --> 00:28:37,900 +function of x هلاقي شكله صار معروف ومقلوف بالنسبة + +266 +00:28:37,900 --> 00:28:43,400 +لنا لكن هيك مش طبيعي مش عارفينه طيب لما نوصله سهلا + +267 +00:28:43,400 --> 00:28:49,240 +x يساوي zero و y تساوي zero محور y ومحور x ماعنداش + +268 +00:28:49,240 --> 00:28:53,880 +مشكلة فيهم و y تساوي تلتة ماعنداش مشكلة و الدوران + +269 +00:28:53,880 --> 00:28:59,220 +حوالين محور y احنا خدنا مثالين الأول حوالين محور x + +270 +00:28:59,440 --> 00:29:04,900 +الثاني حوله خط موازي لمحور X هذا منين؟ محور Y طب + +271 +00:29:04,900 --> 00:29:09,800 +نحاول نرسم هذه المنطقة مشان نرسم هذه المنطقة احنا + +272 +00:29:09,800 --> 00:29:16,920 +عندنا X يساوي 2 على Y زائد 1أو ممكن اكتب y زائد + +273 +00:29:16,920 --> 00:29:23,980 +واحد بده يساوي اتنين على اكس او ممكن اقول ان y + +274 +00:29:23,980 --> 00:29:32,480 +يساوي اتنين على اكس ناقص واحد ناقص واحد هدف تبع + +275 +00:29:32,480 --> 00:29:37,400 +shift واتنين ملاشه دعوة بتجرب على المنحناه دي + +276 +00:29:37,400 --> 00:29:42,320 +بجانب رسمة y تساوي واحد على اكس اظن ياما رسمناهاهي + +277 +00:29:42,320 --> 00:29:46,640 +مش جديدة بالنسبالنا يبقى هذا صارت مسألة سهلة جدا + +278 +00:29:46,640 --> 00:29:52,560 +إذا لو روحت رسمت المنحنة هياخد الشكل التالي يبقى + +279 +00:29:52,560 --> 00:29:59,180 +هذا عندنا محور X هذا محور Y هذا نقطة الأصل اللي هي + +280 +00:29:59,180 --> 00:30:04,640 +Zero يبقى هذا Y يستوي 2 على X و نجرب على محور Y و + +281 +00:30:04,640 --> 00:30:06,880 +shift إلى أسفل بمقدار + +282 +00:30:12,200 --> 00:30:19,540 +Y تساوي سالب واحد يبقى هذا Y تساوي سالب واحد يبقى + +283 +00:30:19,540 --> 00:30:24,220 +المنحنق يريد أن ينزل لتحت المقدار سلبي Y تساوي + +284 +00:30:24,220 --> 00:30:28,980 +واحد X عارفينه جوس على اليمين وجوس على الشمال من + +285 +00:30:28,980 --> 00:30:34,020 +هنابس مش كل الرسم بديها يبقى انا بروح برسم اللي + +286 +00:30:34,020 --> 00:30:38,140 +بديها يبقى اللي جوس اللي على اليمين بدي اعمله + +287 +00:30:38,140 --> 00:30:43,340 +shift لأسفل بمقدار واحد بس هوسع الرسم مشان الكل + +288 +00:30:43,340 --> 00:30:48,300 +يشوف يبقى بداجي اقول هذا المنحنى اللي عندنا تمام + +289 +00:30:48,300 --> 00:30:56,140 +يبقى هذا هو ال X يساوي اتنين على Y زائد واحد او Y + +290 +00:30:56,140 --> 00:31:00,780 +يساوي اتنين على X نقص واحد هذا والله هذا سيئابعد + +291 +00:31:00,780 --> 00:31:06,920 +هيك قال لي هذا محور X و هذا محور Y يبقى خلصنا من + +292 +00:31:06,920 --> 00:31:12,700 +هدول يبقى Y تساوي تلاتة يبقى بادروح أرسم له الخط + +293 +00:31:12,700 --> 00:31:17,980 +اللي عندنا هذا Y تساوي تلاتة إذا أصبحت المنطقة + +294 +00:31:17,980 --> 00:31:23,580 +اللي محصرة بين المنحنة ومحور X ومحور Y وخط Y تساوي + +295 +00:31:23,580 --> 00:31:28,660 +تلاتة اللي هي المنطقة المظللة اللي عندنا هذهيبقى + +296 +00:31:28,660 --> 00:31:34,820 +هذه المنطقة بدها دور وين؟ حوالين محور Y إذا بدي + +297 +00:31:34,820 --> 00:31:41,720 +أرسم خط يقطع هذه المنطقة و عمودي على محور الدوران + +298 +00:31:41,720 --> 00:31:48,660 +يبقى لو جيت هنا قلت ارسم هذا الخط العمودي تمام؟ + +299 +00:31:48,660 --> 00:31:57,210 +بدي أعرف قداش الطول تبعه يبقى من هنا لغاية هناهذا + +300 +00:31:57,210 --> 00:32:03,830 +X تساوي كم؟ نين على Y زائد واحد يبقى هذا هو نصف + +301 +00:32:03,830 --> 00:32:09,590 +القطر تمام؟ يبقى باجي بقوله يبقى بدي أكمل بالنسبة + +302 +00:32:09,590 --> 00:32:14,990 +إلى Y أقل قيمة بتاخدها Y هنا كم؟ و أكبر قيمة هنا + +303 +00:32:14,990 --> 00:32:19,050 +بتاخدها كم؟ تلاتة لأن هذا النقطة الإعدادية تبعها + +304 +00:32:19,050 --> 00:32:25,140 +تلاتة لأن الخط هذا Y تساوي تلاتةيبقى ال volume V + +305 +00:32:25,140 --> 00:32:33,680 +يبقى تكامل من Zero لغاية تلاتة لبي في R اله اتنين + +306 +00:32:33,680 --> 00:32:41,780 +على Y زائد واحد لكل تربيه D1 طيب هذا الكلام يبقى + +307 +00:32:41,780 --> 00:32:48,040 +يساوي لو ربعت هذا يصبح اربعة مع باي خليك برا يبقى + +308 +00:32:48,040 --> 00:32:54,510 +هاي اربعة باي خليها براY تكمل من Zero إلى تلاتة + +309 +00:32:54,510 --> 00:33:03,310 +للواحد على Y زائد واحد لكل تربيع D1 هذا يبدو يساوي + +310 +00:33:03,310 --> 00:33:09,730 +اربع باي في تكمل اللي بيعرف يكملها على طول كان بها + +311 +00:33:09,730 --> 00:33:17,690 +تعرفش حط لك تعويضة بنعرف نكملها على طول سالب واحد + +312 +00:33:17,690 --> 00:33:22,350 +على Y زائد واحد تعرفش ههبتروح تقول لي في ال همش + +313 +00:33:22,350 --> 00:33:29,310 +حطلي مثلا T تساوي Y زائد واحد يبقى DT بده يساوي + +314 +00:33:29,310 --> 00:33:38,010 +ميه؟ DY يبقى هذا بيصير تكامل لواحد على T تربيع و + +315 +00:33:38,010 --> 00:33:46,020 +DT بدل DY بقيت حدود التكامللما تبقى Y بثلاثة يبقى + +316 +00:33:46,020 --> 00:33:55,010 +T بقداش أربعة لما تبقى Y بزيرو يبقى T بقداش واحدأو + +317 +00:33:55,010 --> 00:33:58,470 +لو خلقتها زي ما هي و قولتلي سالب واحد على واي زائد + +318 +00:33:58,470 --> 00:34:02,770 +واحد بيطلع كلام مظبوط مية المية يبقى هذا الكلام + +319 +00:34:02,770 --> 00:34:09,670 +بده يساوي أربعة باي تكامل من واحد لغاية أربعة ل T + +320 +00:34:09,670 --> 00:34:17,130 +أس ناقص اتنين دي تي يبقى النتيجة تساوي أربعة باي و + +321 +00:34:17,130 --> 00:34:23,950 +T أس سالب واحد على سالب واحدوالحكي من عند الواحد + +322 +00:34:23,950 --> 00:34:31,230 +لغاية كده؟ أربعة يبقى سالب أربعة باي وهذه واحدة + +323 +00:34:31,230 --> 00:34:38,290 +عالتي من عند الواحد لغاية كده؟ لغاية الأربعة يبقى + +324 +00:34:38,290 --> 00:34:42,950 +هذا الكلام بده يساوي سالب أربعة باي مالوش دعوة + +325 +00:34:42,950 --> 00:34:51,690 +وهذا الرابع ناقص واحدو يساوي هي سالب اربعة باى برا + +326 +00:34:51,690 --> 00:34:59,110 +و ربع ناقص واحد بقداش بناقص تلت اربع يبقى الجواب + +327 +00:34:59,110 --> 00:35:06,750 +يساوي تلاتة باى فقط لغير هو حجم المجسم الناتج من + +328 +00:35:06,750 --> 00:35:08,030 +الدوران + +329 +00:35:38,230 --> 00:35:47,610 +تفضل تمام و التعويضة هذه ايش بتسوي اه كيف مش أخدنا + +330 +00:35:47,610 --> 00:35:52,250 +التكامل بالتعويض و لما الحد ما تحط تعويضة بتتغير + +331 +00:35:52,250 --> 00:35:57,150 +حدود طبقا للتعويضة الجديدة Zero تلاتة هذا للمتغير + +332 +00:35:57,150 --> 00:36:03,190 +Y ينعظرهم للمتغير T من واحد إلى أربعة طيب ناخد + +333 +00:36:03,190 --> 00:36:11,380 +كمان مثال رقم أربعةالرقم أربعة بقول find the + +334 +00:36:11,380 --> 00:36:21,640 +volume of the solid find the volume of the solid + +335 +00:36:21,640 --> 00:36:24,720 +generated + +336 +00:36:24,720 --> 00:36:27,800 +by + +337 +00:36:27,800 --> 00:36:32,300 +revolving + +338 +00:36:32,300 --> 00:36:34,820 +the + +339 +00:36:36,290 --> 00:36:43,270 +region اناتج من دوران المنطقة bounded by the lines + +340 +00:36:43,270 --> 00:36:51,330 +بالخطوط + +341 +00:36:51,330 --> 00:37:03,130 +المستقيمة y يسوى اتنين x y تسوى zero and ال x يسوى + +342 +00:37:03,130 --> 00:37:04,890 +واحد about + +343 +00:37:09,040 --> 00:37:20,500 +6 يساوي 1 احنا + +344 +00:37:20,500 --> 00:37:26,160 +حتى الآن خدنا ثلاثة امثلة مثال + +345 +00:37:26,160 --> 00:37:30,260 +الأول الدوران حوالين محوركس الثاني خط موازي + +346 +00:37:30,260 --> 00:37:33,600 +المحوركس الثالث الرابع + +347 +00:37:48,490 --> 00:37:53,840 +المنطقة المحصورة ما بين الخط Y تشوي 2Xيبقى y يساوي + +348 +00:37:53,840 --> 00:38:01,720 +2x ويبقى + +349 +00:38:01,720 --> 00:38:07,000 +y يساوي 2x ويبقى y يساوي 0 + +350 +00:38:19,500 --> 00:38:23,520 +يبقى المنطقة اللى محصورة بين التلاتة هذول هي + +351 +00:38:23,520 --> 00:38:30,620 +المنطقة المضللة اللى عندنا هذى تمام يبقى هذه + +352 +00:38:30,620 --> 00:38:37,200 +المنطقة الدوران حوالين مين؟ حوالين اللى هو X يساوي + +353 +00:38:37,200 --> 00:38:41,880 +واحد يعني خط موازي لمح ورا Y وبالتالي احنا بنكبل + +354 +00:38:41,880 --> 00:38:46,690 +بالنسبة ل Y ولا بالنسبة ل Xبالنسبة لويا لموازي + +355 +00:38:46,690 --> 00:38:54,130 +لمحور Y إذا بدأت أرسم خط يقطع منطقة التكامل بشكل + +356 +00:38:54,130 --> 00:39:01,790 +عن هذا يبقى هذا يمثل نصف قطر disk أو نصف قطر دائرة + +357 +00:39:01,790 --> 00:39:07,880 +في المقطعبدي اعرف قداش نقدار هذا نصف القطرة السؤال + +358 +00:39:07,880 --> 00:39:13,040 +هو قداش المسافة هذه + +359 +00:39:13,040 --> 00:39:22,720 +واحد نقص ثاني واحد نقص ثاني هذا الان solution + +360 +00:39:26,650 --> 00:39:36,030 +عندنا المنحنة Y تساوي 2X يعني لو أخدنا أي قيمة X + +361 +00:39:36,030 --> 00:39:41,830 +على أفكر تطلع Y على الرأسك هل بنقدر نكتب X بدلالة + +362 +00:39:41,830 --> 00:39:48,630 +Y نجابة نعم يعني هذه ال X بدها تساوي نص Y أو Y على + +363 +00:39:48,630 --> 00:39:53,920 +2يبقى لما اقول البعد X البعد X يمثل البعد اللى + +364 +00:39:53,920 --> 00:40:00,740 +عندنا هذا المنقط هكذا تمام؟ جداش البعد هذا من هنا + +365 +00:40:00,740 --> 00:40:07,280 +لهنا اللى هو مين؟ Y على 2 يبقى هذا البعد هو Y على + +366 +00:40:07,280 --> 00:40:12,510 +2 اللى هي معادلة الخط اللى عندنا هذا بدل ماقولY + +367 +00:40:12,510 --> 00:40:17,930 +تساوي اتنين X بدي اقول X يساوي كده Y بدل ما أخد + +368 +00:40:17,930 --> 00:40:24,090 +البعد الرأسي باخد البعد الأفقي وبالتالي هذا نصف + +369 +00:40:24,090 --> 00:40:30,870 +القطر اللي عندنا هذا بيصير واحد ناقص Y على مين على + +370 +00:40:30,870 --> 00:40:37,420 +اتنين مرة تانية بقولالبعد هذا كله واحد صحيح يعني + +371 +00:40:37,420 --> 00:40:42,060 +البعد هذا كله ايه واحد صحيح انا بدي طول الخط + +372 +00:40:42,060 --> 00:40:46,320 +الغامق اللي هو نصف قطر القرص او نصف قطر دائرة + +373 +00:40:46,320 --> 00:40:50,400 +المقطار يعني بدي اشيل منه الفراغ اللي جابله هذا + +374 +00:40:50,400 --> 00:40:54,340 +الفراغ اللي جابله هذا هو معاد الخط المستقيم اللي + +375 +00:40:54,340 --> 00:40:59,580 +عندها معاد الخط المستقيم y تساوي 2x وy تساوي 2x + +376 +00:40:59,580 --> 00:41:04,650 +هذي اللي هي 2xلأ انا بدي البعد هذا الأفقي و ليس + +377 +00:41:04,650 --> 00:41:09,990 +البعد الراسي يعني بدي x جديش تساوي اذا x يساوي y + +378 +00:41:09,990 --> 00:41:16,170 +على اتنين اذا هذا البعد اللي هو x يساوي y على + +379 +00:41:16,170 --> 00:41:21,810 +اتنين طبعا اذا بدي اقول ال y كله اللي الأفقي كله + +380 +00:41:21,810 --> 00:41:25,870 +اللي هو واحد بدي اشيل منه لهمين واعتين بيعطيني + +381 +00:41:25,870 --> 00:41:31,410 +جديش نصف القطر اللي عندنابقيت عندنا Y بده اشوف Y + +382 +00:41:31,410 --> 00:41:39,650 +تتغير من و لا وين هنا Y كده يا راجل و هنا Y بده + +383 +00:41:39,650 --> 00:41:43,530 +اشوفها كده تمام مش انا اشوفها كده بده احلي + +384 +00:41:43,530 --> 00:41:50,490 +المعادلاتين هذول مع بعض يبقى هنا ال X تساوي Y على + +385 +00:41:50,490 --> 00:41:56,930 +2 Y على 2 تساوي و ال X هذي تساوي كده + +386 +00:42:02,550 --> 00:42:10,250 +يبقى المسافة من هنا لغاية هنا البعد هذا كله اتنين + +387 +00:42:10,250 --> 00:42:16,310 +يعني Y تسوى اتنين و X تسوى كمانواحد يعني إحداث + +388 +00:42:16,310 --> 00:42:22,650 +النقطة هذا هو واحد واتنين إذا أصبح ال volume V + +389 +00:42:22,650 --> 00:42:29,230 +اللي أنا بديه هو تكمل من C إلى D C تتغير من Zero + +390 +00:42:29,230 --> 00:42:36,490 +لغاية اتنين لبي في نصف القطر نصف القطر واحد بدي + +391 +00:42:36,490 --> 00:42:43,470 +أشيل منه ال Y على اتنين الكل تربيه D واحداللي + +392 +00:42:43,470 --> 00:42:47,010 +بالنسبة لي لو كنت انا بصحى هذا الشخص اللي بكتب هذي + +393 +00:42:47,010 --> 00:42:50,950 +بياخد تلتين العلامة و بيظل التلت على حسابات التلت + +394 +00:42:50,950 --> 00:42:55,330 +ما هو الباقي فارق إذا حددت حدود التكمل صح و كتبت + +395 +00:42:55,330 --> 00:43:00,360 +المعادلة صح باقي شهر روتينييبقى هذا الكلام بده + +396 +00:43:00,360 --> 00:43:07,960 +يساوي hay by وهي تكمل من صفر لغاية اتنين واحد ناقص + +397 +00:43:07,960 --> 00:43:16,120 +y زائد رابع y تربيع كله بالنسبة الى مين الى dy + +398 +00:43:16,120 --> 00:43:21,700 +يعني فكت الجوش اللي عندنا هذا بده اكمل يبقى hay by + +399 +00:43:21,700 --> 00:43:29,440 +براوهذه تكاملها Y ناقص Y تربيع على اتنين وهذه زائد + +400 +00:43:29,440 --> 00:43:35,040 +Y تكعيب على قداش على اتناش من Zero لغاية قداش + +401 +00:43:35,040 --> 00:43:42,520 +اتنين النتيجة تسوى Hi Bye برة وبدنا نعود هذا اتنين + +402 +00:43:42,520 --> 00:43:49,820 +ناقص اتنين اربع على اتنين باتنين زائد تمانية على + +403 +00:43:49,820 --> 00:43:57,910 +اتناشر-000 كله راح معاه السلامة يبقى ألة المسألة + +404 +00:43:57,910 --> 00:44:03,910 +اتنين مع اتنين الله سهل عليها بيظل باي في جداش في + +405 +00:44:03,910 --> 00:44:10,430 +تمانية على اتناش على الأربعة فيها التلاتة على + +406 +00:44:10,430 --> 00:44:14,390 +الأربعة فيها اتنين وعلى الأربعة فيها التلاتة يبقى + +407 +00:44:14,390 --> 00:44:22,230 +اتنين باي على تلاتة قيمة هذا الحجبطيب اعطاناك الان + +408 +00:44:22,230 --> 00:44:26,850 +اربع امثلة على الاربع حالات محور X خط موازيله + +409 +00:44:26,850 --> 00:44:32,230 +ومحور Y خط موازيله طيب هذه الحالة الأولى اللى لو + +410 +00:44:32,230 --> 00:44:39,490 +كان المقطع disk مصمت قد يكون disk فيه تجويف كويس + +411 +00:44:39,490 --> 00:44:44,370 +من النتيجة شوه القصة هذا disk فيه تجويف هذا + +412 +00:44:44,370 --> 00:44:49,650 +بنسميها الطريقة التانية و هي طريقة ال washerواشر + +413 +00:44:49,650 --> 00:44:54,870 +يعني رندلة رندلة ايش رندلة اللي فاهم ده ال ring + +414 +00:44:54,870 --> 00:44:59,230 +ماشي ال ring ماشي لما تشوف صمولة بيحط تحتها حديدة + +415 +00:44:59,230 --> 00:45:02,910 +مثقوبة مظبوط حتي مشان تمسك الصمولة الحديدة + +416 +00:45:02,910 --> 00:45:07,010 +المثقوبة هذي بيسميها رندلة او واشر بلاش لما + +417 +00:45:07,010 --> 00:45:10,130 +تيجيكوا للتابع الغاز يجيبوكوا جرق الغاز بيعطيكوا + +418 +00:45:10,130 --> 00:45:14,830 +جلدة الصمرة هذي جلدة الصمرة اللي هو قرص بس مثقوب + +419 +00:45:14,830 --> 00:45:20,360 +من النص مظبوط يبقى هذه الواشر كذلكالعشرة الشكل هذا + +420 +00:45:20,360 --> 00:45:24,780 +لو ضيّعنا لأصفر اللي في المص بيصير washer بيظل في + +421 +00:45:24,780 --> 00:45:30,800 +الخارج و هكذا يبقى هذه موضوع main موضوع ال washer + +422 +00:45:30,800 --> 00:45:37,940 +بدنا نيجي نعرف متى نستخدم طريقة ال washer طبعا + +423 +00:45:37,940 --> 00:45:45,500 +طريقة ال disk إذا كان المقطع مصمتا مش فيه أي تجويف + +424 +00:45:53,020 --> 00:45:57,340 +إذا بدنا نجي للطريقة الثانية اللي هو the washer + +425 +00:45:57,340 --> 00:46:03,580 +method أخدنا أول طريقة اللي هي طريقة ال desk اتنين + +426 +00:46:03,580 --> 00:46:16,020 +the washer method we + +427 +00:46:16,020 --> 00:46:21,900 +use this method we use this + +428 +00:46:23,230 --> 00:46:33,270 +method نستخدم هذه الطريقة if the solid إذا كان + +429 +00:46:33,270 --> 00:46:38,270 +المجسم of revolution + +430 +00:46:38,270 --> 00:46:51,040 +of revolution has a holeموجود في ثقب او تجويف and + +431 +00:46:51,040 --> 00:46:59,840 +it بداخله وفي هذه الحالة بقوله the volume the + +432 +00:46:59,840 --> 00:47:10,570 +volume V بتساوي التكامل من A إلى B لل by لمينللـ R + +433 +00:47:10,570 --> 00:47:18,450 +of X لكل تربية ناقص R of X لكل تربية كله بالنسبة + +434 +00:47:18,450 --> 00:47:34,070 +الى DX where capital R of X نصف + +435 +00:47:34,070 --> 00:47:45,670 +القطر الخارجي andالـ r of x is the inner radius + +436 +00:47:45,670 --> 00:47:49,550 +نصف القطر الداخلي + +437 +00:48:21,870 --> 00:48:26,770 +نرجع لكلام اللي احنا كاتبينه هذا مرة تانية يبقى + +438 +00:48:26,770 --> 00:48:30,930 +طريقة الواشر method الواشر يا شباب على الشكل + +439 +00:48:30,930 --> 00:48:38,450 +التالي قرص بهذا الشكل يبقى هذا القرص الخارجي و قرص + +440 +00:48:38,450 --> 00:48:44,210 +داخلي او دائرة داخلية بهذا الشكل هذه المنطقة اللي + +441 +00:48:44,210 --> 00:48:50,530 +بينهم كلها منطقة مصمة و اللي في الداخل هذا تجويف + +442 +00:48:50,870 --> 00:48:57,150 +وهذا المركز تمام الخط + +443 +00:48:57,150 --> 00:49:04,370 +اللى عندنا هذا من هنا لهنا هذا اللى هو ال small r + +444 +00:49:04,370 --> 00:49:13,670 +of x نصف القطر الداخلي وهذا ال outer radius اللى + +445 +00:49:13,670 --> 00:49:16,710 +هو نصف القطر الخارجى + +446 +00:49:19,270 --> 00:49:24,070 +يعني المقطع لما نقطع لهذا التجويف هيكون في نص قطر + +447 +00:49:24,070 --> 00:49:29,790 +خارجي و في نص قطر داخلي كما سترا يبقى لو جينا + +448 +00:49:29,790 --> 00:49:37,670 +تخيلنا ان هذا محور X على سبيل المثال و هذا محور Y + +449 +00:49:37,670 --> 00:49:43,690 +و جيت للمنحنة اللي عندنا بهذا الشكل مثلا كان Y + +450 +00:49:43,690 --> 00:49:51,000 +تساوي R of Xو جينا لمنحنى ثانى المنحنى التانى كان + +451 +00:49:51,000 --> 00:50:00,720 +بالشكل هذا اللي هو Y تساوي R of X small تمام الان + +452 +00:50:00,720 --> 00:50:06,240 +على المنطقة A وB افترض انه بدأ هذا الكلام من عند + +453 +00:50:06,240 --> 00:50:15,570 +ال A و لغاية من و لغاية Bالاتنين هذول حصروا بينهم + +454 +00:50:15,570 --> 00:50:20,410 +مساحة اللي هي المساحة المظللة اللي عندنا هذه كلها + +455 +00:50:20,410 --> 00:50:27,150 +تمام هذا لو دار حوالين الخط اللي هو المحور y تساوي + +456 +00:50:27,150 --> 00:50:33,130 +x كان هو محور الدوران يبقى فيه ان حاجة اسمة outer + +457 +00:50:33,130 --> 00:50:38,030 +radius وفيه ان حاجة اسمة inner radius ال inner + +458 +00:50:38,030 --> 00:50:44,840 +radius عند اي لحظة هو الخط اللي عندنا هذايبقى هذا + +459 +00:50:44,840 --> 00:50:52,260 +هو r of x small ال outer radius هو الخط اللي عندنا + +460 +00:50:52,260 --> 00:50:52,860 +هذا + +461 +00:50:58,380 --> 00:51:01,640 +لأ احنا بياخدهم على نفس النقطة لإنك تجي على نفس + +462 +00:51:01,640 --> 00:51:06,420 +النقطة بالضبط تماما لكن ليس بالضرورة خد وين ما بدك + +463 +00:51:06,420 --> 00:51:11,300 +تمام بس انا رسمت بيدك مشان يوضح لك من وين لوين هذا + +464 +00:51:11,300 --> 00:51:16,480 +سميته مين اللي هو ال R of X بالشكل اللي عندنا هذا + +465 +00:51:17,150 --> 00:51:24,790 +يعني لو دار المجسم حوالين محور ال X بتلاقي هذا + +466 +00:51:24,790 --> 00:51:30,550 +النقطة صارت مدينة هذه على استقامتها لغاية هنا يبقى + +467 +00:51:30,550 --> 00:51:35,210 +هذه بدها تجيك الدائرة اللي عندك هذه او هذه بدها + +468 +00:51:35,210 --> 00:51:41,090 +تجيلك دائرة بالشكل اللي عندك هذا او هذا بده يجيلك + +469 +00:51:41,090 --> 00:51:46,880 +الخط اللي فوق او من هنا بده يجيلك mainبدي اجيلك + +470 +00:51:46,880 --> 00:51:53,340 +الخط اللى تحت بالشكل اللى عندك هذا هيك تمام يبقى + +471 +00:51:53,340 --> 00:51:58,420 +هذا اللى بدي يصير ايش بيصير عندك لو جيت اخدت disk + +472 +00:51:58,420 --> 00:52:00,760 +يبقى ال disk هاي معاه + +473 +00:52:09,040 --> 00:52:15,080 +لما ناخد ال disk مقطع واحد يبقى بده يجيلك الشكل + +474 +00:52:15,080 --> 00:52:20,420 +هذا هيك هذا مش هيظهر يبقى هيكون في الناحية التانية + +475 +00:52:20,420 --> 00:52:27,900 +بهذا الشكل هذا ههه بده يكون عندك بالشكل هذا وهذا + +476 +00:52:27,900 --> 00:52:34,100 +كمان بالشكل هذا كويسيبقى وين ال washer في هذه + +477 +00:52:34,100 --> 00:52:38,300 +الحالة ال washer المنطقة الحمرة هذه كلها + +478 +00:52:46,440 --> 00:52:50,480 +هذا المنطقة الحمرة اللي هو washer يبقى فيه تجويف + +479 +00:52:50,480 --> 00:52:55,300 +التجويف اللي هو المنطقة البيضة يبقى هذا هو ال + +480 +00:52:55,300 --> 00:53:01,580 +inner radius وهذا هو ال outer radius من هنا هيحصلك + +481 +00:53:01,580 --> 00:53:07,600 +بالأسود لغاية ما توصل لوين للنقطة هذه يبقى هذا كله + +482 +00:53:07,600 --> 00:53:13,960 +هذا هو ال R of X الشكل اللي عندنا وهذا من هنا لهنا + +483 +00:53:13,960 --> 00:53:20,490 +فقطهو ال inner radius R of X بالشكل اللي عندك + +484 +00:53:20,490 --> 00:53:26,770 +تعالى تشوف ايش اللي قال لي ال volume اللي قال لي + +485 +00:53:26,770 --> 00:53:31,730 +ال volume يجب ان تتكامل من A الى B لطه مضروبة في + +486 +00:53:31,730 --> 00:53:37,530 +مين في نقطة رمية هذا الكلام لو فكته لحد هى بيعطيني + +487 +00:53:37,530 --> 00:53:43,310 +المساحة تبع الدائرة الكبيرةهذا بيعطينا المساحة تبع + +488 +00:53:43,310 --> 00:53:48,330 +الدائرة الصغيرة لما تتنين من بعض بيصير المنطقة + +489 +00:53:48,330 --> 00:53:53,190 +المظللة بكمل عليها من A إلى B بجيبله حجم المجسم + +490 +00:53:53,190 --> 00:53:57,970 +الناتج من الدوران يبقى هذه ال washer هذي اللي انت + +491 +00:53:57,970 --> 00:54:03,460 +شايفهاوهذه اللى جوا هيها رسمتها لكنا للتوضيح يبقى + +492 +00:54:03,460 --> 00:54:07,000 +ال ultra radius من النقطة هذه لنقطة هذه ال inner + +493 +00:54:07,000 --> 00:54:10,620 +radius من النقطة هذه لوين لنقطة اللى عندنا لنقطة + +494 +00:54:10,620 --> 00:54:17,660 +طبعا هذه المركز المشترك للدائرتين او لل two disks + +495 +00:54:17,660 --> 00:54:22,100 +ال disk المجوافل على شكل دائرة و ال disk المصمت + +496 +00:54:22,100 --> 00:54:28,210 +الثاني واضح الكلام هذايبقى مشان نجيب ال volume في + +497 +00:54:28,210 --> 00:54:33,290 +هذه الحالة شو بالزامنين بالزامنين شغلتين الشغلة + +498 +00:54:33,290 --> 00:54:37,370 +الأولى بدك تحدد حدود التكامل زي ما كنا في حالة ال + +499 +00:54:37,370 --> 00:54:41,710 +disk الشغلة التانية بدك تحدد ال inner radius او + +500 +00:54:41,710 --> 00:54:46,710 +out of radius مثل + +501 +00:54:46,710 --> 00:54:50,690 +هذا الكلام لو كان بالنسبة ل Y لو كان الدوران + +502 +00:54:50,690 --> 00:54:56,190 +حوالين محور Y او حوالين خط موادي لمحور Yبنعمل نفس + +503 +00:54:56,190 --> 00:55:01,210 +السفينة بسيطة كامن من C إلى D ل I ل R of Y الكلتر + +504 +00:55:01,210 --> 00:55:05,050 +بيه ناقص R of Y الكلتر يعني نفس القصة بس بصير + +505 +00:55:05,050 --> 00:55:09,750 +بالنسبة ل Y كمان حدا فيكوا إليه أي تساؤل قبل أن + +506 +00:55:09,750 --> 00:55:14,350 +نذهب إلى الأمثلة طبعا هذا آخر جزء نظري موجود في + +507 +00:55:14,350 --> 00:55:18,250 +هذا ال section بس الكلمتين اللي قدامك علقوا علينا + +508 +00:55:18,250 --> 00:55:23,690 +حدا بديكوا إليه أي تساؤل ندخل للأمثلةتوكلنا على + +509 +00:55:23,690 --> 00:55:28,710 +الله يبقى بنجي لأول مثال على موضوع أو استخدام + +510 +00:55:28,710 --> 00:55:44,050 +الوشر method يبقى example one find + +511 +00:55:44,050 --> 00:55:49,970 +the volume of the sun يعني اكتب + +512 +00:55:49,970 --> 00:55:58,360 +انت وياه بدون صوت بقوليجب أن تجد قطعة المسلحة التي + +513 +00:55:58,360 --> 00:56:02,100 +تم + +514 +00:56:02,100 --> 00:56:04,400 +تجريها من حول المنطقة + +515 +00:56:24,070 --> 00:56:35,670 +bounded by the curve بالمنحنى y يساوي اربعة ناقص x + +516 +00:56:35,670 --> 00:56:47,530 +تربيع and the line والخط المستقيم y تساوي اتنين + +517 +00:56:47,530 --> 00:56:49,750 +ناقص x about + +518 +00:56:53,050 --> 00:57:13,030 +X Axis طبعا + +519 +00:57:13,030 --> 00:57:19,310 +ذكرناإن هذه الطريقة طريقة ال washroom نستخدمها إذا + +520 +00:57:19,310 --> 00:57:25,430 +كان في عندي تجويف أو ثقب في هذا المجسم واضح أن + +521 +00:57:25,430 --> 00:57:30,050 +الجزء الأبيض هذا كله يعتبر تجويف داخل المجسم + +522 +00:57:30,050 --> 00:57:33,770 +الكبير في هذا السؤال طبعا هو بيقول ليش في عندك + +523 +00:57:33,770 --> 00:57:37,990 +تجويف ولا ماعندكش انت لحالك من خلال الرسم بتستنتج + +524 +00:57:37,990 --> 00:57:43,210 +هل هناك تجويف ام لاإذا نرجع لمسألتنا نقرأ ونرسم + +525 +00:57:43,210 --> 00:57:44,310 +نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم + +526 +00:57:44,310 --> 00:57:46,610 +نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم + +527 +00:57:46,610 --> 00:57:51,710 +نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم + +528 +00:57:51,710 --> 00:57:55,310 +نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم + +529 +00:57:55,310 --> 00:57:55,610 +نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم + +530 +00:57:55,610 --> 00:57:55,610 +نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم نرسم + +531 +00:57:55,610 --> 00:58:06,130 +نرسم نرسم نرسم نرسم نرسم نرسم نرسم + +532 +00:58:06,130 --> 00:58:11,560 +نرسم نY تساوي ناقص X تربية يبقى الفرابولة مفتوحة + +533 +00:58:11,560 --> 00:58:17,140 +إلى أسفل زائد أربع يبقى shift إلى أعلى بمقدار أربع + +534 +00:58:17,140 --> 00:58:21,950 +يبقى الفرابولة بتجيني وينبالشكل اللي عندنا هذا + +535 +00:58:21,950 --> 00:58:28,690 +يبقى هذا ال Y تساوي اربع ناقص X تربيع طبعا لو حطيت + +536 +00:58:28,690 --> 00:58:33,550 +Y تساوي Zero بصير X باتنين و سالي باتنين يبقى + +537 +00:58:33,550 --> 00:58:38,610 +النقطة هذه سالي باتنين و النقطة هذه قداش اللي هو + +538 +00:58:38,610 --> 00:58:44,690 +الاتنين اللي هم نقطتي تقاطع المنحنة مع محور X تمام + +539 +00:58:47,770 --> 00:58:55,770 +خط y تساوي 2 ناقص x باجي بقول لو كانت x ب 0 يبقى y + +540 +00:58:55,770 --> 00:59:02,170 +ب 2 يبقى ب 2 نص اللي هي النقطة اللي عندنا هذه و لو + +541 +00:59:02,170 --> 00:59:08,290 +كانت y ب 0 يبقى x في قداش ب 2 يبقى لما y تساوي 0 x + +542 +00:59:08,290 --> 00:59:14,500 +ب 2 يبقى هتاني نقطة تانية تقعاني علىالخط المستقيم + +543 +00:59:14,500 --> 00:59:20,560 +يبقى لو وصلت ما بينهم و مديت الخط على استقامته + +544 +00:59:20,560 --> 00:59:26,660 +يكون هذا هو الخط اللى موجود عندنا اللى هو main y + +545 +00:59:26,660 --> 00:59:34,400 +تساوي 2 ناقص 6 الاتنين هدول حصروا لي مساحة في ما + +546 +00:59:34,400 --> 00:59:40,220 +بينهماقال لهات لي حجم المجسم المتولد من دوران + +547 +00:59:40,220 --> 00:59:44,940 +المنطقة المحدودة بالمنحنى والخط المستقيم يبقى هذا + +548 +00:59:44,940 --> 00:59:48,960 +الخط المستقيم وهذا المنحنى يبقى هذه المنطقة + +549 +00:59:48,960 --> 00:59:53,180 +المظللة المحصورة في ما بقيناهما هذه المنطقة بدها + +550 +00:59:53,180 --> 00:59:59,230 +دور وانحوالين محور X يبقى معنى هذا الكلام هذا + +551 +00:59:59,230 --> 01:00:05,050 +يعتبر تجويف فيما لو دارت هذه المنطقة تجويف موجود + +552 +01:00:05,050 --> 01:00:10,510 +داخل المجسم يبقى انا بدي وين ال outer radius وين + +553 +01:00:10,510 --> 01:00:15,330 +ال inner radius يبقى بالداخل ال outer radius بدي + +554 +01:00:15,330 --> 01:00:20,750 +ارسم خط يقطع المنطقة المظلة لو عمودي على محور + +555 +01:00:20,750 --> 01:00:28,500 +الدوران يبقى هذا يعتبر ميناوتر راديوس يبقى اوتر + +556 +01:00:28,500 --> 01:00:28,900 +راديوس + +557 +01:00:37,880 --> 01:00:44,700 +اللي هو capital R of X بدها تساوي أربع ناقص X + +558 +01:00:44,700 --> 01:00:49,400 +تربية بدنا ال inner radius ال inner radius هو + +559 +01:00:49,400 --> 01:00:56,600 +المسافة من هنا لهنا اللي هو منطقة الفراغ طب منطقة + +560 +01:00:56,600 --> 01:01:06,380 +الفراغ Y كده تساوي هنا؟يبقى هذه المنطقة فقط من هنا + +561 +01:01:06,380 --> 01:01:14,980 +لغاية هنا Y تساوي او R of X يبقى يساوي اتنين ناقص + +562 +01:01:14,980 --> 01:01:19,780 +X يبقى حددت ال outer radius و ال inner radius صار + +563 +01:01:19,780 --> 01:01:24,820 +شغل روتيني ده اللي عندى بدى حدد main حدود التكامل + +564 +01:01:25,160 --> 01:01:30,020 +أقل قيمة بتاخدها X اللي هو القيمة اللي عندنا هذه و + +565 +01:01:30,020 --> 01:01:33,680 +أكبر قيمة بتاخدها X اللي هو القيمة اللي عندنا هذه + +566 +01:01:33,680 --> 01:01:39,460 +هذه معروفة بقيت هذه مجهولة مشان أجيب هذه هي القيمة + +567 +01:01:39,460 --> 01:01:44,560 +بروح بحل المعادلتين مع بعض وبجيب قيمة X يبقى أنا + +568 +01:01:44,560 --> 01:01:51,790 +عندي أربع ناقص X تربيع يسوى اتنين ناقص Xبدي أنقل + +569 +01:01:51,790 --> 01:01:57,770 +هذه على الشجة التانية بصير X تربيع ناقص X ناقص 2 + +570 +01:01:57,770 --> 01:02:03,990 +بيبقى Zero يبقى جثين بالشكل اللي عندنا هذا بيبقى + +571 +01:02:03,990 --> 01:02:10,590 +Zero يبقى هذه X وهذه X وهذه واحد اتنين ناقص زائد + +572 +01:02:10,590 --> 01:02:16,690 +من هذه بقدر أقوله يبقى X بيبقى سالب واحد وهنا X + +573 +01:02:16,690 --> 01:02:23,290 +بيبقى نقطة اتنينالاتنين الحمد لله هي موجودة بقيت + +574 +01:02:23,290 --> 01:02:28,170 +هذه اللي هي قداش ناقص واحد إذا انحددت حدود التكامل + +575 +01:02:28,170 --> 01:02:33,430 +الباقى الشغل كله روتيني يبقى الرسمة ضرورية لإن + +576 +01:02:33,430 --> 01:02:39,550 +بتسهلي عملية من الشغل فباجي بقوله ال volume دي بده + +577 +01:02:39,550 --> 01:02:45,890 +يساوي تكامل من عنده سالب واحد لغاية اتنين لل by + +578 +01:02:45,890 --> 01:02:46,390 +three + +579 +01:02:55,310 --> 01:03:00,570 +أربعة ناقص X تربيع لكل تربيع + +580 +01:03:08,300 --> 01:03:14,820 +-x لكل تربية كله بالنسبة لمين الى dx يبقى هذا + +581 +01:03:14,820 --> 01:03:21,220 +الكلام بده يساوي تكامل من سلب واحد لغاية اتنين لبي + +582 +01:03:21,220 --> 01:03:28,500 +فيه يبقى 16-8x + +583 +01:03:28,500 --> 01:03:36,650 +تربية زائد x أس أربعالربع التاني هي ناقص أربعة + +584 +01:03:36,650 --> 01:03:43,690 +وهنا ناقص أربعة X بالصير زائد أربعة X وزايد X + +585 +01:03:43,690 --> 01:03:50,270 +تربية بالصير ناقص X تربية DX يعني فكته الجوس ودخلت + +586 +01:03:50,270 --> 01:03:56,090 +إشارة سالب على المقدار اللي جوايبقى هذا الكلام بده + +587 +01:03:56,090 --> 01:04:02,070 +يسوي high by برة تكمل من سلب واحد إلى اتنين اتطلع + +588 +01:04:02,070 --> 01:04:06,710 +لي هنا عندك سلب اربعة و عندك ستاشر بيظل كده؟ + +589 +01:04:06,710 --> 01:04:13,110 +اتناشر عندك هنا سلب تمانية اكس تربية و ناقص اكس + +590 +01:04:13,110 --> 01:04:19,870 +تربية بسلب تسعة اكس تربية عندك زائد اربعة اكس + +591 +01:04:19,870 --> 01:04:26,840 +مافيش غيرهاوعندك هنا زائد X أُص أربعة مافيش غيرها + +592 +01:04:26,840 --> 01:04:32,420 +كل هذا الكلام من نسبة إلى مين إلى DX يبقى هذا بدل + +593 +01:04:32,420 --> 01:04:41,140 +يساوي باي بدنا كامليبقى هذا 12x ناقص 3x تكيب على 3 + +594 +01:04:41,140 --> 01:04:50,700 +مع 9 بيظل 3 زائد 2x تربيع زائد x أس خمسة على خمسة + +595 +01:04:50,700 --> 01:04:56,680 +الكلام هذا من سالب واحد لغاية اتنين يبقى النتيجة + +596 +01:04:56,680 --> 01:05:02,480 +تساوي high by برة وبنعوض اتنين في اتناشر اربعة + +597 +01:05:02,480 --> 01:05:10,890 +وعشريننقص تلاتة في تمانية بارضه باربعة وعشرين وهنا + +598 +01:05:10,890 --> 01:05:17,630 +زائد اربعة في اتنين بتمانية وهنا زائد اتنين + +599 +01:05:17,630 --> 01:05:23,750 +وتلاتين على خمسة خلصنا القيمة اللي فوق ناقص القيمة + +600 +01:05:23,750 --> 01:05:28,510 +اللي تحت يبقى هاي ناقص بدي أشيل كل X و أحط مكانها + +601 +01:05:28,510 --> 01:05:36,270 +ناقص واحد يبقى ناقص اتناشرزائد تلاتة زائد اتنين + +602 +01:05:36,270 --> 01:05:42,750 +ناقص كمز هذا + +603 +01:05:42,750 --> 01:05:47,410 +الكلام ممكن يسوي هذه و هذه و هذه و هذه معاكم سلامة + +604 +01:05:47,410 --> 01:05:54,570 +بالتمانية زائد اتنين و تلاتين على خمسة زائد اتناشر + +605 +01:05:54,570 --> 01:06:04,380 +ناقص ثلاثة يبقى ناقص ثلاثةو عندك هنا ناقص اتنين و + +606 +01:06:04,380 --> 01:06:10,260 +هنا زائد خمس شكل اللي عندنا هذا يبقى هذا الكلام + +607 +01:06:10,260 --> 01:06:16,940 +بده يساوي by فيه تمانية و اتناشر عشرين عشرين شيل + +608 +01:06:16,940 --> 01:06:22,460 +منهم خمسة بيضل كده خمسة استاشر و عندك هنا اتنين و + +609 +01:06:22,460 --> 01:06:29,470 +تلاتين و واحد بتلاتة و تلاتين على خمسةيبقى هذا + +610 +01:06:29,470 --> 01:06:36,470 +الكلام بده يساوي باي في خمسة في خمستاشر بخمسة + +611 +01:06:36,470 --> 01:06:42,290 +وسبعين خمسة وسبعين بيضيف عليهم تلاتين بيصير مية و + +612 +01:06:42,290 --> 01:06:50,330 +تمانية مية و تمانية على خمسة باي هذا هو حجم المجسم + +613 +01:06:50,330 --> 01:06:52,350 +اللي موجود عندنا + +614 +01:07:15,390 --> 01:07:22,250 +بناخد كمان مثال تبقى + +615 +01:07:22,250 --> 01:07:30,230 +example two will + +616 +01:07:30,230 --> 01:07:36,690 +find the volume of + +617 +01:07:38,220 --> 01:07:44,720 +هذا صليت ان حجم المجسم generated by revolving + +618 +01:07:44,720 --> 01:07:52,960 +generated by revolving + +619 +01:07:52,960 --> 01:07:59,420 +generated by revolving ماتخليش اطرد اطردكوا برا + +620 +01:07:59,420 --> 01:08:04,360 +ماتخليش اضطرر لهذا الاسلوب احترم نفسك و بديش كلام + +621 +01:08:06,060 --> 01:08:13,700 +يبقى generated by revolving the + +622 +01:08:13,700 --> 01:08:23,640 +region bounded by + +623 +01:08:23,640 --> 01:08:30,220 +the parabola y + +624 +01:08:30,220 --> 01:08:34,660 +تساوي x تربيع below + +625 +01:08:37,620 --> 01:08:51,000 +by the x axis ومن أسفل بمحور x and on the right on + +626 +01:08:51,000 --> 01:09:02,540 +the right من جهة اليمين by the line بالخط + +627 +01:09:02,540 --> 01:09:07,240 +المستقيم x يساوي واحد + +628 +01:09:24,340 --> 01:09:27,060 +X يساوي اتنين + +629 +01:09:51,230 --> 01:09:56,150 +نرجع لسؤالنا مرة ثانية السؤال بيقول فات لحجم + +630 +01:09:56,150 --> 01:10:01,930 +المجسم المتولد من دوران المنطقة المحدودة بالبرابله + +631 +01:10:01,930 --> 01:10:08,230 +Y تساوي X تربيع و من أسفل بمحور X و من جهة اليمين + +632 +01:10:08,230 --> 01:10:14,660 +بالخط Y أو ال X تساوي واحد حوالين محور Yوالتانية + +633 +01:10:14,660 --> 01:10:19,680 +حوالينا الخط X يساوي 2 يبقى ده مش سؤال واحد وانما + +634 +01:10:19,680 --> 01:10:25,580 +سؤالين في آلة واحد يبقى بدنا نيجي نشوف كيف ننهل + +635 +01:10:25,580 --> 01:10:32,460 +هدين السؤالين ونبدأ بالنقطة A مشان نيجي للنقطة A + +636 +01:10:32,460 --> 01:10:40,240 +بدنا نروح نرسم المنطقة مشان نحدد حدود التكامليبقى + +637 +01:10:40,240 --> 01:10:46,780 +انا لو جيت قلت هاي المحاور هذا محور X هذا محور Y + +638 +01:10:46,780 --> 01:10:54,220 +هذا نقطة الأصل اللي هي Zero Y تساوي X تربيع بجيلي + +639 +01:10:54,220 --> 01:11:01,830 +بالشكل اللي عنها يبقى هذا Y تساوي X تربيعتمام؟ + +640 +01:11:01,830 --> 01:11:07,590 +جالي ومن أسفل بمحور X تحت بمحور X ومن الشجرة اللي + +641 +01:11:07,590 --> 01:11:13,110 +قمت بالخط X تساوي واحد يبقى لو جيت قلت هذا ال line + +642 +01:11:13,110 --> 01:11:18,510 +له X يساوي واحد يبقى المنطقة اللي عندنا هذه هي + +643 +01:11:18,510 --> 01:11:24,030 +المنطقة اللي محصورة عندنا هذه المنطقة بدها دور في + +644 +01:11:24,030 --> 01:11:28,500 +الحالة الأولى حوالي المين؟ حوالي المحور Yيبقى + +645 +01:11:28,500 --> 01:11:32,160 +معناه هذا الكلام بدي أكمل بالنسبة ل Y ولا بالنسبة + +646 +01:11:32,160 --> 01:11:38,660 +ل X؟ ل Y مادة بالنسبة ل Y إذا بدي أرسم خط يقطع + +647 +01:11:38,660 --> 01:11:44,920 +منطقة التكامل و عمودي على محور الدوران يبقى لو جيت + +648 +01:11:44,920 --> 01:11:50,320 +قلت هذا الخط اللي هو يقطع منطقة التكامل و عمودي + +649 +01:11:50,320 --> 01:11:57,360 +على محور الدوران بدي أعرف كده طول من هنا لغاية هنا + +650 +01:11:57,990 --> 01:12:04,910 +يبقى هذا يعتبر ال outer radius وهذا يعتبر inner + +651 +01:12:04,910 --> 01:12:10,850 +radius تمام تمام تمام + +652 +01:12:10,850 --> 01:12:18,670 +تمام تمام تمام تمام تمام تمام + +653 +01:12:18,670 --> 01:12:20,510 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +654 +01:12:20,510 --> 01:12:20,650 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +655 +01:12:20,650 --> 01:12:20,650 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +656 +01:12:20,650 --> 01:12:20,730 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +657 +01:12:20,730 --> 01:12:27,030 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +658 +01:12:27,030 --> 01:12:27,210 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +659 +01:12:27,210 --> 01:12:27,310 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +660 +01:12:27,310 --> 01:12:27,330 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +661 +01:12:27,330 --> 01:12:27,330 +تمام تمام تمام تمام تمام تمام تمام تمام تمام تمام + +662 +01:12:27,330 --> 01:12:30,650 +تمام تمام تمام تماميبقى المسافة هذه كلها شباب قداش + +663 +01:12:30,650 --> 01:12:38,390 +يبقى هذا X يساوي جذر ال Y و المسافة من هنا لهنا + +664 +01:12:38,390 --> 01:12:43,510 +جداش واحد صحيح اللي المسافة من هنا يبقى ال outer + +665 +01:12:43,510 --> 01:12:48,530 +radius يساوي واحد و ال inner radius اللي هو جداش + +666 +01:12:48,530 --> 01:12:58,210 +جذر ال Y يبقى أصبح عند هنا ال outer radiusالـ X + +667 +01:12:58,210 --> 01:13:06,270 +يساوي قداش واحد وال inner radius نصف القطر الداخلي + +668 +01:13:06,270 --> 01:13:13,450 +الـ X يساوي جانر ال Y يبقى الفرق في ما بينهما + +669 +01:13:13,450 --> 01:13:19,530 +يعطيني الحجم المجسم الناتج من الدوران دلوقتي بدي + +670 +01:13:19,530 --> 01:13:25,270 +أعرف Y تتغير من أين إلى أينيبقى Y هتتغير من هنا + +671 +01:13:25,270 --> 01:13:30,430 +لغاية هنا هذه أقل قيمة بتاخدها Y وهذه أكبر قيمة + +672 +01:13:30,430 --> 01:13:35,690 +بتاخدها Y مشان أطل أعرف قداش القيمة هذه بدروح أحل + +673 +01:13:35,690 --> 01:13:41,690 +المعادلتين هدول مالهم مع بعض يبقى احنا عندنا جذر + +674 +01:13:41,690 --> 01:13:47,130 +ال Y بده يسوى واحد هذا معناته ان Y تسوى قداش واحد + +675 +01:13:47,360 --> 01:13:52,400 +يبقى هذا النقطة لو كانت ال Y بواحد يبقى X بقداش + +676 +01:13:52,400 --> 01:13:57,420 +بواحد كذلك إذا نحدث النقطة هذه واحد وواحد يبقى ال + +677 +01:13:57,420 --> 01:14:03,540 +Y تتغير من Zero لغاية واحد يبقى بالداجي لل volume + +678 +01:14:03,540 --> 01:14:10,680 +V يساوي تكامل من Zero إلى واحد ال outer radius I + +679 +01:14:10,680 --> 01:14:15,360 +by I ال outer radius اتفجنا من هنا لهنا اللي هو + +680 +01:14:15,360 --> 01:14:22,070 +قداشواحد تربيع ناقص ال inner radius اللى هو من هنا + +681 +01:14:22,070 --> 01:14:27,630 +لغاية هنا اللى هو ال gathering ال y لكل تربيع و + +682 +01:14:27,630 --> 01:14:33,310 +التكامل كله بالنسبة لمين الى dy يبقى اشتغلت شغل + +683 +01:14:33,310 --> 01:14:36,410 +سليم مائة بالمائة يبقى النتيجة جد ما تطلع تطلع + +684 +01:14:36,410 --> 01:14:41,900 +ماتفرجش عننايبقى هذه بدها تساوي Hy برا و Hy تكمل + +685 +01:14:41,900 --> 01:14:48,540 +من zero لواحد لواحد ناقص Y كله Dy طبعا النتيجة + +686 +01:14:48,540 --> 01:14:55,040 +تساوي Hy برا و Hy ناقص Y تربيه على اتنين كله من + +687 +01:14:55,040 --> 01:15:01,240 +عند ال zero لغاية واحديبقى هذا بدي يعطيك باي وهنا + +688 +01:15:01,240 --> 01:15:08,980 +واحد ناقص نص والباقي كله بناقص زيرو ويسوي باي في + +689 +01:15:08,980 --> 01:15:16,600 +نص يعني باي على اتنين هذا هي الحجم المطلوب باي على + +690 +01:15:16,600 --> 01:15:23,560 +اتنين تمام فضل لو دار + +691 +01:15:23,560 --> 01:15:30,370 +حوالين محور Xبطل يصير في عندي washer يبقى برجع لل + +692 +01:15:30,370 --> 01:15:35,450 +desk تمام و هذا الفرق ما بين الاتنين هنا نظرا لإنه + +693 +01:15:35,450 --> 01:15:40,170 +ضرح حوالين محور wine يعني بالعربي لو حبيت أبينها + +694 +01:15:40,170 --> 01:15:46,530 +لك بده أقولك هنا هذه بدها توصل وهذه بدها تصير هيك + +695 +01:15:46,530 --> 01:15:55,100 +وهذه هيك وهذه من هنا هيك وهذه هيكطبعا؟ يبقى هذا + +696 +01:15:55,100 --> 01:16:00,180 +ايش؟ هاي الصارع عندك تجيب في هذا بدي أجيلك هيك + +697 +01:16:00,180 --> 01:16:05,620 +بالشكل اللي عندي او هذا بدي أجيلك هيك و هيك هذا + +698 +01:16:05,620 --> 01:16:11,780 +الشكل طبعا؟ يبقى هذه ال washer اللي عندي هذه ال + +699 +01:16:11,780 --> 01:16:18,620 +washer اللي عندي طبعا؟ + +700 +01:16:18,620 --> 01:16:21,600 +واضحيت؟ + +701 +01:16:21,970 --> 01:16:28,090 +يبقى كأنه ايش؟ قص طوانة وجوفناها بالتجويف الداخلي، + +702 +01:16:28,090 --> 01:16:37,730 +اه يبقى good سمعتش + +703 +01:16:37,730 --> 01:16:41,570 +قولنا له مش ممكن تكون نفس الحاجة ده؟ ليش؟ هو + +704 +01:16:41,570 --> 01:16:48,530 +المجسم بيطلع نفسه يعني؟المجسم بصير نفسه جرب احنا + +705 +01:16:48,530 --> 01:16:53,410 +حسبناها حوالي المحور Y وانت جربها حوالي المحور X + +706 +01:16:53,410 --> 01:16:58,990 +وهي اللي بقولك ال X ستتغير من عند ال zero لغاية + +707 +01:16:58,990 --> 01:17:05,610 +واحد و ال Y تساوي X تربيع هي موجودة عندك احسب + +708 +01:17:05,610 --> 01:17:13,560 +المساحة بالله و قل لجدكنرجع الان لنمر بيه من + +709 +01:17:13,560 --> 01:17:18,040 +المثلة يبقى لو جيت لنمر بيه من المثلة يبقى هذه + +710 +01:17:18,040 --> 01:17:25,680 +المحاولة وهذا محور X وهذا محور Y وهذا نقطة الأصل + +711 +01:17:25,680 --> 01:17:30,920 +اللي هي Zeroوالملحنة اللى عندنا رسمناها فكان بهذا + +712 +01:17:30,920 --> 01:17:38,200 +الشكل هذا y تساوي x تربيع و هذا الخط له x يساوي + +713 +01:17:38,200 --> 01:17:42,060 +واحد و هاي المساحة اللى موجودة عندنا اللى هي + +714 +01:17:42,060 --> 01:17:46,460 +المساحة اللى عندنا هذه واحداثيات النقطة هذه واحد + +715 +01:17:46,460 --> 01:17:51,610 +واحدجل الحالة التانية لو المساحة اللى ضارة حوالنا + +716 +01:17:51,610 --> 01:17:58,210 +الخط Y او X يسوى مين؟ اتنين يبقى X يسوى اتنين بدي + +717 +01:17:58,210 --> 01:18:08,710 +يجيلك هذا ال X يسوى قداش اتنين هذا الشكل تمام؟ + +718 +01:18:08,710 --> 01:18:17,860 +يبقى هذا الخط اللى هو X يسوى اتنينطيب مدام هيكي + +719 +01:18:17,860 --> 01:18:22,920 +بيكي عندي outer radius و inner radius إذا بدي أرسم + +720 +01:18:22,920 --> 01:18:28,460 +خط يقطع منطقة التكمل و عمودي على محور الدوران + +721 +01:18:28,460 --> 01:18:34,140 +بالشكل اللي عندنا هذا مثلا هذا الخط الأحمر هذا + +722 +01:18:34,140 --> 01:18:42,180 +يعتبر main outer radiusهذا من هنا لهنا يعتبر من ال + +723 +01:18:42,180 --> 01:18:47,300 +inner radius يبقى مشان اميزك فيما بيننا هذا ال + +724 +01:18:47,300 --> 01:18:51,560 +inner radius هو القط الأسود والقط الأحمر هو ال + +725 +01:18:51,560 --> 01:18:56,920 +outer radius السؤال هو المسافة من هنا لهنا كده؟ + +726 +01:18:56,920 --> 01:19:02,000 +اتنين بدي اشيل منها المسافة هذه يبقى لو جيت + +727 +01:19:02,000 --> 01:19:03,480 +المسافة هذه + +728 +01:19:11,580 --> 01:19:20,360 +يبقى المسافة هذه x يساوي جذر ال yطيب إذا ال volume + +729 +01:19:20,360 --> 01:19:26,900 +V بدي تساوي تشامل ل PY بدي اجيل ال outer radius ال + +730 +01:19:26,900 --> 01:19:31,700 +outer radius يصلهم من هنا لهنا يعني ال اتنين بدي + +731 +01:19:31,700 --> 01:19:38,540 +اشيل منها جذر ال Y يبقى ال اتنين ناقص جذر ال Y لكل + +732 +01:19:38,540 --> 01:19:43,080 +تربيع ناقص ال inner radius ال inner radius + +733 +01:19:43,080 --> 01:19:49,300 +المستفادة دي كلها باتنين بدي اشيل منها واحديبجى 2 + +734 +01:19:49,300 --> 01:19:54,900 +ناقص واحد لكل تربية كله بالنسبة الى مين الى dy + +735 +01:19:54,900 --> 01:20:01,180 +بقية حدود التكمل هل تغيرت؟لأ يبقى زي ما هي من صفر + +736 +01:20:01,180 --> 01:20:06,380 +لغاية واحد يبقى من صفر لغاية واحد كما هي يبقى + +737 +01:20:06,380 --> 01:20:11,760 +النتيجة تساوي high by برة و تكمل من صفر لغاية واحد + +738 +01:20:11,760 --> 01:20:19,780 +بده افكر قوس هذا اربع ناقص اتنين جدر ال Y والله + +739 +01:20:19,780 --> 01:20:25,560 +ناقص اربع جدر ال Y يبقى ناقص اربع جدر ال Y + +740 +01:20:39,070 --> 01:20:44,890 +يبقى النتيجة تساوي باى شكامه من صفر لغاية واحد + +741 +01:20:44,890 --> 01:20:51,760 +عندك ناقص واحد وزاد اربعة بيضل قداش تلاتةوهنا زائد + +742 +01:20:51,760 --> 01:21:00,460 +Y وهنا ناقص اربع Y اص نص كل هذا الكلام نسبة الى + +743 +01:21:00,460 --> 01:21:06,900 +مين الى BY يبقى اصبح ال volume V اللى عندنا بده + +744 +01:21:06,900 --> 01:21:14,720 +يسوي Hi Bye برا وبدنا نكامل يبقى تلاتة Y زائد Y + +745 +01:21:14,720 --> 01:21:23,540 +تربيه على اتنين ناقص اربعوالثالثة على اتنين على + +746 +01:21:23,540 --> 01:21:29,100 +ثلاثة على اتنين كله من صفر لغاية واحديبقى هذا + +747 +01:21:29,100 --> 01:21:35,860 +الكلام بده يساوي Pi في تلاتة Y زائد Y تربيع على + +748 +01:21:35,860 --> 01:21:43,320 +اتنين ناقص تمانية على تلاتة Y اقصى تلاتة على اتنين + +749 +01:21:43,320 --> 01:21:51,740 +كله من صفر لغاية واحد يبقى بده يساوي Pi في تلاتة + +750 +01:21:54,930 --> 01:22:02,050 +نقص تمانية على تلاتة والباقي كله نقص نقص نقص نقص + +751 +01:22:02,050 --> 01:22:05,610 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +752 +01:22:05,610 --> 01:22:06,130 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +753 +01:22:06,130 --> 01:22:06,890 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +754 +01:22:06,890 --> 01:22:09,390 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +755 +01:22:09,390 --> 01:22:11,210 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +756 +01:22:11,210 --> 01:22:17,850 +نقص نقص نقص نقص نقص + +757 +01:22:39,100 --> 01:22:45,840 +المثال الأخير في هذا ال section يبقى example تلاتة + +758 +01:22:45,840 --> 01:22:52,420 +بيقول ما يأتي find volume + +759 +01:22:55,020 --> 01:23:02,180 +of the solid generated + +760 +01:23:02,180 --> 01:23:05,400 +generated + +761 +01:23:05,400 --> 01:23:13,380 +by revolving the + +762 +01:23:13,380 --> 01:23:17,380 +region by + +763 +01:23:17,380 --> 01:23:21,240 +revolving the region bounded + +764 +01:23:25,050 --> 01:23:38,070 +by y تساوي x تربيع and y تساوي أربعة above the + +765 +01:23:38,070 --> 01:23:44,670 +line y + +766 +01:23:44,670 --> 01:23:50,430 +تساوي خمسة حولنا الخط y تساوي خمسة + +767 +01:24:17,270 --> 01:24:22,530 +نرجع لأسوالنا مرة تانية قولي هاتلي حجم المجسم + +768 +01:24:22,530 --> 01:24:28,710 +المتولد تعالى يا ابنيا تعالى كيف حالك انت من وقتاش + +769 +01:24:28,710 --> 01:24:32,370 +احنا بنرد على الجولات في المحاضراتتعالى عوضى وقعد + +770 +01:24:32,370 --> 01:24:37,310 +وإلا بخليك تاخد دفاعك ومتعودش على القعب المرة يا + +771 +01:24:37,310 --> 01:24:38,370 +جوال يا محاضرة + +772 +01:24:45,180 --> 01:24:49,340 +مرة تانية يبقى find the volume of the solid هاتلي + +773 +01:24:49,340 --> 01:24:53,860 +حجم المجسم المتولد بدوران المنطقة المحدودة + +774 +01:24:53,860 --> 01:24:59,180 +بالمنحنى Y تساوي X تربية وY تساوي أربع حوالين الخط + +775 +01:24:59,180 --> 01:25:05,670 +Y تساوي خمسة يبقى لو روحت رسمت المنطقة هذهيبقى هاي + +776 +01:25:05,670 --> 01:25:12,790 +المحاور هذا محور X وهذا محور Y وهذا نقطة الاصل + +777 +01:25:12,790 --> 01:25:17,270 +اللي هي Zero Y تساوي X تربيع الكل بيعرفه برابولة + +778 +01:25:17,270 --> 01:25:24,310 +بالشكل اللي عندنا هذا هيك يبقى هذا Y تساوي X تربيع + +779 +01:25:24,310 --> 01:25:32,210 +التاني الخط Y تساوي 4 يبقى هذا الخط Y تساوي 4 + +780 +01:25:33,310 --> 01:25:37,950 +المساحة اللي بينهم اللي هي المساحة المظلة لهذه + +781 +01:25:37,950 --> 01:25:46,370 +دهرت حوالين الخط Y تساوي خمسة يبقى محور الدوران + +782 +01:25:46,370 --> 01:25:52,210 +وان فوق يبقى لو جيت قلت هذا الخط الأحمر اللي عندما + +783 +01:25:52,210 --> 01:25:56,970 +اديته على استقامته بالشكل اللي عندنا هنا قلنا هذا + +784 +01:25:56,970 --> 01:25:59,790 +Y تساوي خمسة + +785 +01:26:04,490 --> 01:26:09,130 +يبقى هذا النقطة اللي هي أربعة و هذا النقطة اللي هي + +786 +01:26:09,130 --> 01:26:16,050 +قداشر خمسة لحدات صادلة المنطقة المظللة دارت حولنا + +787 +01:26:16,050 --> 01:26:23,170 +الخط Y تساوي خمسةيبقى انا بدى ال outer radius و + +788 +01:26:23,170 --> 01:26:28,290 +بدى ال inner radius طبعا ال outer radius بنجى على + +789 +01:26:28,290 --> 01:26:34,910 +منطقة التكامل و بنرسم خط عمودي على محور الدوران + +790 +01:26:34,910 --> 01:26:40,230 +يبقى هذا هو ال outer radius حد فيكوا بقدر يقولي + +791 +01:26:40,230 --> 01:26:46,870 +قداش الطول تبع هذا الخط هاي واحد اتنين تلات اه يا + +792 +01:26:46,870 --> 01:26:55,530 +ابنيخمسة ناقص جاذر ال Y جاذر ال Y جابها من وين؟ من + +793 +01:26:55,530 --> 01:27:02,790 +هذه تمام صح كلامه خمسة ناقص جاذر ال Y وفكرته صح بس + +794 +01:27:02,790 --> 01:27:10,610 +غلط غلط صغيرة بسيطة بتعرفي تصحيحها ايه؟ اربع ناقص + +795 +01:27:10,610 --> 01:27:13,990 +جاذر ال Y يا راجل مسافة لحد هنا + +796 +01:27:16,560 --> 01:27:20,160 +خمسة ناقص X تربية هذا هو الصحيحة تعالى نشوف + +797 +01:27:20,160 --> 01:27:26,460 +المسافة من هنا لهنا لو كمل هذه كلها المسافة ليه + +798 +01:27:26,460 --> 01:27:32,000 +ملحانة هذا يبقى المسافة هذه لو كانت هذه المسافة من + +799 +01:27:32,000 --> 01:27:38,120 +هنا لهنا X يبقى هذا بصير X تربيةيبقى الخط الأسود + +800 +01:27:38,120 --> 01:27:43,600 +هذا اللي عندك هذا كله بيصير main اللي هو خمسة + +801 +01:27:43,600 --> 01:27:48,780 +المسافة من هنا لهنا ناقص هذه اللي هو ناقص X تربيع + +802 +01:27:48,780 --> 01:27:55,350 +وهذا هو ال outer radius اللي هو main ال R of Xعن + +803 +01:27:55,350 --> 01:27:59,810 +طريق التجويف + +804 +01:27:59,810 --> 01:28:03,910 +من الاربعة لغاية كده خمسة + +805 +01:28:15,360 --> 01:28:24,660 +واحد ضالت عند ال X بدها تتغير من أقل قيمة لها الى + +806 +01:28:24,660 --> 01:28:30,960 +أكبر قيمة لها هيها لذلك سنحل المعادلات مع بعض + +807 +01:28:34,490 --> 01:28:42,050 +يبقى احنا عندنا y تساوي x تربيع يبقى هذه هي من ال + +808 +01:28:42,050 --> 01:28:47,830 +x تربيع وهنا عندنا y تساوي كده؟ اربعة معناه هذا + +809 +01:28:47,830 --> 01:28:52,570 +الكلام ان ال x بدأ تساوي زائد او ناقص يبقى هنا + +810 +01:28:52,570 --> 01:28:59,020 +بيصير ال x بسالب اتنين وهنا ال x بقدر؟ اتنينإذا + +811 +01:28:59,020 --> 01:29:04,940 +أصبح ال volume V متساوي تكامل من سالب اتنين إلى + +812 +01:29:04,940 --> 01:29:10,640 +اتنين إلى باي لل outer radius الكل تربيع الخمسة + +813 +01:29:10,640 --> 01:29:17,300 +ناقص X تربيع الخمسة ناقص X تربيع الكل تربيع ناقص + +814 +01:29:17,300 --> 01:29:23,540 +ال small radius اللي هو واحد لكل تربيع كله بالنسبة + +815 +01:29:23,540 --> 01:29:30,840 +إلى ماميعني صار هذا تكامل من سالب اتنين الى اتنين + +816 +01:29:30,840 --> 01:29:37,620 +لبي بده فك الجزء يبقى هاي خمسة وعشرين ناقص عشرة X + +817 +01:29:37,620 --> 01:29:45,900 +تربيع زائد X أس أربع ناقص واحد في DX اظن ناقص واحد + +818 +01:29:45,900 --> 01:29:48,320 +وزائد خمسة وعشرين بيظل جداش + +819 +01:29:57,170 --> 01:30:05,390 +عشرة اكس تربيع زائد اكس اص اربعة ناقص واحد في DX + +820 +01:30:05,870 --> 01:30:10,730 +أظن ناقص واحد وزائد خمسة وعشرين بيظل جداش اربع + +821 +01:30:10,730 --> 01:30:16,110 +وعشرين يبقى تكمل من سالب اتنين الى اتنين لبي في + +822 +01:30:16,110 --> 01:30:23,830 +الاربع وعشرين ناقص عشرة x تربية زائد x أس اربع كله + +823 +01:30:23,830 --> 01:30:28,510 +بالنسبة لمام الى dx الدالة دي even function + +824 +01:30:28,510 --> 01:30:36,550 +هيكفينيهذا اتنين وتكامل من صفر للاتنين وهي البي + +825 +01:30:36,550 --> 01:30:45,030 +برا يبقى اتنين باي وضل عندك هنا للاربع وعشرين ناقص + +826 +01:30:45,030 --> 01:30:52,830 +عشرة X تربيع زائد X أُس أربعة كله بالنسبة إلى من؟ + +827 +01:30:52,830 --> 01:31:00,140 +إلى DX عملنا ليش؟ لأن هذه الدالةEvent Function + +828 +01:31:00,140 --> 01:31:05,880 +يبقى نظرة لإنها دالة زوجية والـ Symmetric Interval + +829 +01:31:05,880 --> 01:31:10,880 +من سالب اتنين إلى اتنين X تربية و X أُس أربعة يبقى + +830 +01:31:10,880 --> 01:31:15,280 +ماعنديش أسس فردية يبقى هذه Evil Function على طول + +831 +01:31:15,390 --> 01:31:21,430 +الخط يبقى النتيجة يساوي هي اتنين باي برا يبقى اربع + +832 +01:31:21,430 --> 01:31:28,570 +وعشرين اكس عشرة على تلاتة اكس تكيب زي اكس وخمسة + +833 +01:31:28,570 --> 01:31:36,070 +على خمسة من صفر لغاية اتنين يبقى هذا اتنين باي في + +834 +01:31:36,070 --> 01:31:42,570 +اتنين في اربع وعشرين بتمانية واربعين ناقص تمانية + +835 +01:31:42,570 --> 01:31:50,850 +في عشرة بتمانينعلى تلاتة زائد اتنين اقصد خمسة التي + +836 +01:31:50,850 --> 01:31:55,690 +هي اتنين و تلاتين على خمسة والباقي كله ب zero + +837 +01:31:55,690 --> 01:32:01,510 +ماعنا مشكلة في هذه الحالة يبقى نتيجته ساوي اتنين + +838 +01:32:01,510 --> 01:32:07,530 +by هذا بقدر اقول كله على خمستاشر يبقى بيننا نيجي + +839 +01:32:07,530 --> 01:32:14,020 +نضرب تمانية و اربعين في خمستاشرخمسة في تمانية اب + +840 +01:32:14,020 --> 01:32:20,120 +اربعين خمسة في اربع وعشرين اربع وعشرين تمانية + +841 +01:32:20,120 --> 01:32:26,680 +واربعين اتناشر سبعمية وعشرين يبقى هذه السبعمية + +842 +01:32:26,680 --> 01:32:33,380 +وعشرين ناقص خمستاشر ع تلاتة فيها الخمسة اربعمية + +843 +01:32:33,380 --> 01:32:41,750 +زائد تلاتة اللي هو ستة وتسعينيبقى هنا ستة وتسعين + +844 +01:32:41,750 --> 01:32:49,610 +بصير عندي ستة وتسعة واثنين احداشر يبقى تمانمية + +845 +01:32:49,610 --> 01:32:56,170 +وستاش بده اشيل منها اربعمية بيظل اربعمية وستاش + +846 +01:32:56,170 --> 01:33:04,880 +تمام؟يبقى هذه يساوي اتنين باى اربعمية وست عشر كله + +847 +01:33:04,880 --> 01:33:15,470 +على كدهش على خمستاشر يبقى تمانميةو 32 باي على 15 + +848 +01:33:15,470 --> 01:33:24,090 +هذا مقدار الحجم الجسم المتكون من الدوران وصلنا الى + +849 +01:33:24,090 --> 01:33:30,250 +نهاية ال section بدنا أرقام المسائل ل exercises + +850 +01:33:30,250 --> 01:33:37,230 +ستة واحدة يبقى هنا بنجي بنقول exercisesستة واحد + +851 +01:33:37,230 --> 01:33:47,690 +المثال من خمستاشر لغاية تسعة واربعين الاد من اللي + +852 +01:33:47,690 --> 01:33:55,350 +بده يسأل ايه اتفضل ماعرفتش كيف يبقى تعالي ارسم + +853 +01:33:55,350 --> 01:34:01,940 +الرسم هذي لفوق وشوف هذا بصير صدوف ولا لايبقى لو + +854 +01:34:01,940 --> 01:34:10,700 +جينا رسمنا هذه بده يصير هيك مظبوط يا سيدي؟ و هذا + +855 +01:34:10,700 --> 01:34:17,680 +الخط .. الخط هي جانبك و هذا الخط التاني بده يصير + +856 +01:34:17,680 --> 01:34:23,440 +هيك يبقى هذا مصمد بالشكل اللي عندك كده لأن هذه + +857 +01:34:23,440 --> 01:34:30,860 +عملتلك دائرةالشكل هذا و هذه عملتلك دارة بالشكل + +858 +01:34:30,860 --> 01:34:36,480 +اللي عندك كان، مظبوط هيك؟ عرفته ولا ماعرفتش؟ حد + +859 +01:34:36,480 --> 01:34:40,360 +بدي يسأل تاني؟ انا بيعطيك العافية + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/IyP7ckHqPQY_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/IyP7ckHqPQY_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..f7d8ba7cad1fd56226f0c499cf688c8cc4024519 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/IyP7ckHqPQY_raw.srt @@ -0,0 +1,3452 @@ +1 +00:00:20,820 --> 00:00:25,800 +بسم الله الرحمن الرحيم عودنا على بدء سابقا قبل + +2 +00:00:25,800 --> 00:00:30,380 +حوالي عشرة أيام او ما يزيد كنا بنتكلم عن رسم البني + +3 +00:00:30,380 --> 00:00:35,220 +للمنحنيات بنذكر تذكير كيف كنا بنرسم هذه المنحنيات + +4 +00:00:35,220 --> 00:00:40,840 +بنعمل قدر خطواتالخطوة الأولى بنشوف تقاطة المنحنة + +5 +00:00:40,840 --> 00:00:45,800 +المحورية الإحداثية عن طريق مرة نحط X ب Zero نشوف + +6 +00:00:45,800 --> 00:00:49,840 +قداش قيمة Y نحط Y ب Zero نشوف قداش قيمة X وبالتالي + +7 +00:00:49,840 --> 00:00:55,220 +بنجيب نقاط تقاطة المنحنة مع محاور الإحداثيةقطة + +8 +00:00:55,220 --> 00:01:01,180 +ثانية نجيب الاسمتوتز خطوط التقارب لمهم للمنحنة + +9 +00:01:01,180 --> 00:01:06,900 +وخطوط التقارب لا تكون الا لفنكشن فيها بصف ومقام + +10 +00:01:06,900 --> 00:01:10,620 +يعني rational function زي مهمزي ال function + +11 +00:01:10,620 --> 00:01:14,800 +بتبعتنا هذه يبقى هذه فيها فيها ال symptoms يبقى + +12 +00:01:14,800 --> 00:01:18,400 +قبلنا نجيبها ال symptoms بعد هيك بنجيب المشتقة + +13 +00:01:18,400 --> 00:01:21,680 +الأولى منها بنحسب حاجتين ال local maximum و ال + +14 +00:01:21,680 --> 00:01:24,900 +local minimum و ال increasing و ال decreasing يعني + +15 +00:01:24,900 --> 00:01:29,340 +فترة التزايد و فترة التنقص و كذلك موقع نهاية + +16 +00:01:29,340 --> 00:01:34,060 +العموظة المحلية بعد هيك بنروح نجيب المشتقة الثانية + +17 +00:01:34,060 --> 00:01:37,300 +و منها بنجيب ال concave up و ال concave down + +18 +00:01:37,600 --> 00:01:42,200 +الانحناء الى أسفل والانحناء الى أعلى او التقوس الى + +19 +00:01:42,200 --> 00:01:46,660 +أعلى والتقوس الى أسفل وكذلك بنجيب ال inflection + +20 +00:01:46,660 --> 00:01:52,240 +points ان موجودة بعد هيك بنروح نرسم الرسم اللي لنا + +21 +00:01:52,240 --> 00:01:57,140 +من خلال المعلومات اللتي حصلنا عليها هيك كنا بنعمل + +22 +00:01:57,140 --> 00:02:01,980 +يبقى لازلنا بنعمل نفس التكتيك وهي مثال بين يدينا + +23 +00:02:02,370 --> 00:02:06,710 +بقولي ارسم اللي هو المنحنة اللي عندنا هذه باجي + +24 +00:02:06,710 --> 00:02:09,910 +بقوله X لا يساوي اتنين يبقى ساوي اقل و الله ماجليش + +25 +00:02:09,910 --> 00:02:14,170 +انا بقوله الدالة غير معرفة ان X ساوي اتنين يبقى + +26 +00:02:14,170 --> 00:02:18,590 +الخطوة الاولى بان نشوف نقاط التقاط مع محوري + +27 +00:02:18,590 --> 00:02:25,330 +الاحداثيات يبقى بده احط X بزيرو يبقى باجي بقوله لو + +28 +00:02:25,330 --> 00:02:32,170 +كانت ال X تساوي زيروY يساوي ناقص ثلاثة على ناقص + +29 +00:02:32,170 --> 00:02:42,310 +اتنين و يساوي ثلاثة على اتنين و يساوي ناقص + +30 +00:02:42,310 --> 00:02:43,190 +ثلاثة على ناقص اتنين و يساوي ناقص ثلاثة على ناقص + +31 +00:02:43,190 --> 00:02:46,450 +اتنين و يساوي ناقص ثلاثة على ناقص اتنين و يساوي + +32 +00:02:46,450 --> 00:02:47,990 +ناقص ثلاثة على ناقص اتنين و يساوي ناقص ثلاثة على + +33 +00:02:47,990 --> 00:02:51,970 +ناقص اتنين و يساوي ناقص ثلاثة على ناقص اتنين و + +34 +00:02:51,970 --> 00:02:56,610 +يساوي ناقص ثلاثة على ناقص اتنين و يساوي ناقص ثلاثة + +35 +00:02:56,610 --> 00:03:05,670 +على ناقص اتنين و يof intersections with the + +36 +00:03:05,670 --> 00:03:11,970 +coordinate axes + +37 +00:03:11,970 --> 00:03:14,610 +R + +38 +00:03:16,980 --> 00:03:34,400 +النقطة الأولى وانتهينا + +39 +00:03:34,400 --> 00:03:39,020 +من الخطوة الأولى بدنا نروح للخطوة الثانية بفضل من + +40 +00:03:39,020 --> 00:03:44,490 +حد ما نشوف المعادلة لإن بصف مقامدرجة البصر أكبر من + +41 +00:03:44,490 --> 00:03:50,110 +أو تساوي درجة المقام أنه نقسم جسمها مطولة يبقى + +42 +00:03:50,110 --> 00:03:55,730 +بتروح أقسم ال X تربية ناقص ثلاثة تقسيم ال X ناقص + +43 +00:03:55,730 --> 00:04:01,740 +اتنين فيها ال X ب X تربية ناقص اتنين Xزاد بيصير + +44 +00:04:01,740 --> 00:04:07,860 +ناقص بيصير زاد بتروح هادي بظل 2x ناقص ثلاثة الباقي + +45 +00:04:07,860 --> 00:04:11,140 +من الدرجة الأولى والمقسوم عليه من الدرجة الأولى + +46 +00:04:11,140 --> 00:04:17,080 +بواصل عملية القسمة يبقى 2x على x فيها جداش فيها + +47 +00:04:17,080 --> 00:04:23,180 +ليه اتنين ب2x ناقص اربعة زاد بيصير ناقص وهادي زاد + +48 +00:04:23,180 --> 00:04:29,470 +بظل هنا جداش واحدإذاً الدالة اللي عندنا y تساوي x + +49 +00:04:29,470 --> 00:04:34,830 +تربيع ناقص ثلاثة على x ناقص اتنين يساوي خارج القسم + +50 +00:04:34,830 --> 00:04:40,330 +هو x زائد اتنين الباقي هو واحد لسه بدي اجسمه على x + +51 +00:04:40,330 --> 00:04:46,250 +ناقص اتنينطبعا خارج قسم هذا هو دالة خطية يبقى هذا + +52 +00:04:46,250 --> 00:04:50,930 +بدي يكون main هو ال oblique asymptote يبقى بعدي + +53 +00:04:50,930 --> 00:04:58,310 +بقوله y تساوي x زائد اتنين هذا is the oblique + +54 +00:04:58,310 --> 00:05:00,450 +asymptote + +55 +00:05:05,380 --> 00:05:11,260 +هل هالدالة معرفة عن X يساوي 2؟ لأ يبقى في احتمال + +56 +00:05:11,260 --> 00:05:17,100 +قوي جدا ان يكون هذا vertical asymptote مشان هيك + +57 +00:05:17,100 --> 00:05:21,180 +بتروح اخد ال limit لما ال X بدي روح لل 2 من جهة + +58 +00:05:21,180 --> 00:05:27,290 +اليمين او من جهة اليساريبقى بدى أخد limit لما ال X + +59 +00:05:27,290 --> 00:05:33,150 +بدى يروح لل إتنين مثلا من جهتي اليسار لمن؟ لل X + +60 +00:05:33,150 --> 00:05:38,650 +زائد اتنين زائد واحد على X ناقص اتنين بدى أشوف كده + +61 +00:05:38,650 --> 00:05:43,910 +الشهادة بدها تعطينا الجواب كالتالي تعويض مباشر + +62 +00:05:43,910 --> 00:05:49,460 +اتنين زائد اتنين زائد واحد علىأنا رايح للإتنين من + +63 +00:05:49,460 --> 00:05:54,620 +جهة الشمال يعني أقل من إتنين بحاجة بسيطة جدا يبقى + +64 +00:05:54,620 --> 00:05:59,940 +المقام هذا بيكون very small negative quantity يبقى + +65 +00:05:59,940 --> 00:06:06,580 +very small negative quantity يبقى الجواب أربعة + +66 +00:06:06,580 --> 00:06:13,940 +ناقص infinity يبقى الجواب ناقص infinity بالمثل أنت + +67 +00:06:13,940 --> 00:06:17,560 +بدك تروح تشوف في ال symptom التاني و الله بس أنا + +68 +00:06:17,830 --> 00:06:23,250 +إحنا هيك يكفينا لكن إنت لو روحت شييت لي هيك مش غلط + +69 +00:06:23,250 --> 00:06:28,190 +أخدت ال limit لمن؟ لما ال X بدي يروح للإتنين من + +70 +00:06:28,190 --> 00:06:33,090 +جهة الشمال لل X زائد اتنين زائد واحد على X نقص + +71 +00:06:33,090 --> 00:06:37,710 +اتنين حتى تلاقيه يبقى يساوي كده؟ infinity يبقى + +72 +00:06:37,710 --> 00:06:44,730 +بناء عليه ال X يساوي اتنين هذا main is a vertical + +73 +00:06:44,730 --> 00:06:47,570 +asymptote + +74 +00:06:53,850 --> 00:06:58,990 +تمام يبقى هيك خلصنا لل symptoms بدنا نيجي لمين + +75 +00:06:58,990 --> 00:07:02,870 +للاشتقاق ونشوف ال increasing و ال decreasing و ال + +76 +00:07:02,870 --> 00:07:06,610 +local maximum و ال local minimum اذا بدنا نيجي + +77 +00:07:06,610 --> 00:07:13,750 +نقوله ال F of X عندنا اللي هي مين X زائد 2 زائد 1 + +78 +00:07:13,750 --> 00:07:20,230 +على X ناقص 2 بدنا نشتقها يبقى ال F prime of X + +79 +00:07:20,230 --> 00:07:31,190 +تساوي1 مُشتقة 2 بـ 0 سالب 1 x ناقص 2 لكل تربيعممكن + +80 +00:07:31,190 --> 00:07:37,170 +اخلها بالشكل هذا وممكن احطها بشكل اخر مشان انحدد + +81 +00:07:37,170 --> 00:07:41,530 +اللي هو اللي وين بتاخد قيم موجبة وين بتاخد قيم + +82 +00:07:41,530 --> 00:07:47,190 +سالمة فلو جيت وحطيها كل المقامات بصير X ناقص اتنين + +83 +00:07:47,190 --> 00:07:53,480 +لكل تربية ب X ناقص اتنين لكل تربية ناقص واحدX ناقص + +84 +00:07:53,480 --> 00:07:58,800 +اتنين لكل تربية بدا فك تبعت البصر لان هذه يبجي هذه + +85 +00:07:58,800 --> 00:08:04,700 +لو فكتها بتبجي على الشكل التالي X تربية ناقص اربعة + +86 +00:08:04,700 --> 00:08:12,340 +X زائد اربعة ناقص واحد بناء عليها أصبحت ال F prime + +87 +00:08:12,340 --> 00:08:18,850 +of Xاما بالشكل اللى عندنا هذا اما بالشكل الجديد + +88 +00:08:18,850 --> 00:08:25,190 +الشكل الجديد هو X تربية ناقص اربعة X زائد تلاتة X + +89 +00:08:25,190 --> 00:08:30,830 +ناقص اتنين لكل تربية هذه لو جيتها حللت هيبقى X + +90 +00:08:30,830 --> 00:08:37,470 +ناقص واحد X ناقص تلاتة X ناقص اتنين لكل تربية + +91 +00:08:37,470 --> 00:08:43,040 +بالشكل اللى عندنا هذاهذا جيد يبقى أسعار ال F prime + +92 +00:08:43,040 --> 00:08:47,760 +لها شكل الشكل الأول هي اللي فوق والشكل التاني اللي + +93 +00:08:47,760 --> 00:08:52,640 +منه تحت طبعا اللي تحت سهل جدا منه أحدد إشارة + +94 +00:08:52,640 --> 00:09:00,120 +المشتقة الأولى يبقى لو جيت أخد اشارة X ناقص واحد + +95 +00:09:00,120 --> 00:09:05,220 +أقول هذا ال real line وهذا النقطة بياخد ال zero + +96 +00:09:05,220 --> 00:09:11,460 +تبقى عند X يساوي واحد بعد الواحد كلها positiveزي + +97 +00:09:11,460 --> 00:09:17,960 +ما انت شايف و قبله ايه؟ negative لو جيت أخدت إشارة + +98 +00:09:17,960 --> 00:09:23,380 +ال X ناقص تلاتة هذا ال real line و بياخد ال zero + +99 +00:09:23,380 --> 00:09:28,980 +تبع وين؟ عندي التلاتة بعد التلاتة positive و قبل + +100 +00:09:28,980 --> 00:09:35,380 +التلاتة كله negativeطبعا بدي اروح اجي اخد اشارة ال + +101 +00:09:35,380 --> 00:09:41,300 +X ناقص اتنين لكل تربيع بتاخد ال zero تبعها عند + +102 +00:09:41,300 --> 00:09:46,680 +اتنين بعد اتنين positive و قبل اتنين positive + +103 +00:09:46,680 --> 00:09:53,910 +لانها كمية مربعةفيبدأ إشارة المقدار ككل X ناقص + +104 +00:09:53,910 --> 00:09:59,850 +واحد في X ناقص تلاتة على X ناقص اتنين لكل تاربيع + +105 +00:09:59,850 --> 00:10:05,330 +وهذا ال real line وهي التلاتة وهي اتنين وهي الواحد + +106 +00:10:05,330 --> 00:10:11,250 +اتنين تلاتة موجة سالب سالب موجةيبقى ده اللي هنا + +107 +00:10:11,250 --> 00:10:15,910 +كانت increasing صارت decreasing بقيت decreasing + +108 +00:10:15,910 --> 00:10:21,630 +صارت increasing بالشكل اللي عندنا هذا فبعدين بقول + +109 +00:10:21,630 --> 00:10:30,310 +ال if is increasing ده التزايدية على الفترة من ان + +110 +00:10:30,310 --> 00:10:34,610 +سالب infinity لغاية مين الواحد + +111 +00:10:37,670 --> 00:10:43,660 +على الفترة التانية من عين تلاتة لغاية Infinityالان + +112 +00:10:43,660 --> 00:10:52,780 +ال f is decreasing ده لتناقصية on الفترة من عند + +113 +00:10:52,780 --> 00:10:58,040 +الواحد لغاية اتنين كفترة مفتوحة مفتوحة ليش؟ لإن ده + +114 +00:10:58,040 --> 00:11:05,500 +لغير معرفة عند اتنين and on اتنين و لغاية تلاتة و + +115 +00:11:05,500 --> 00:11:09,760 +closed من عندين، من عند التلاتةطبعا واضح ان عندي + +116 +00:11:09,760 --> 00:11:15,440 +الواحد فيه local وعندي التلاتة فيه local واتنين + +117 +00:11:15,440 --> 00:11:20,860 +مافيش لإنه ضلت نازلة وضلت نازلة طيب بدنا نروح نجيب + +118 +00:11:20,860 --> 00:11:27,100 +له F of واحد اللي هو واحد تربيه ناقص تلاتة على + +119 +00:11:27,100 --> 00:11:31,940 +واحد ناقص اتنين ويسوي ناقص اتنين على ناقص واحد + +120 +00:11:31,940 --> 00:11:38,470 +يسوي قداش اتنينبنجيب له f of تلاتة اللي هو بده + +121 +00:11:38,470 --> 00:11:43,610 +يسوي تلاتة تربيه ناقص تلاتة على تلاتة ناقص اتنين + +122 +00:11:43,610 --> 00:11:50,680 +ويسوي كدهش؟ ستةإذا من هذا الكلام بنقول ال F has + +123 +00:11:50,680 --> 00:12:01,980 +local maximum اتنين at x تساوي واحد and local + +124 +00:12:01,980 --> 00:12:10,870 +minimum and local minimum ستة at x يساوي تلاتةمش + +125 +00:12:10,870 --> 00:12:14,390 +هتروح تستغرب تقول ال local maximum اتنين و ال + +126 +00:12:14,390 --> 00:12:19,070 +local minimum ستة لا غرابة في ذلك و زي ما هنشوف + +127 +00:12:19,070 --> 00:12:24,870 +الآن من خلال ال main من خلال الرسم خلصنا قصة + +128 +00:12:24,870 --> 00:12:29,350 +المشتقة الأولى بدنا نروح لمين؟ للمشتقة الثانية + +129 +00:12:29,350 --> 00:12:35,190 +بدنا نروح لل F double prime of X مين أسهل؟ نشتقل + +130 +00:12:35,190 --> 00:12:38,770 +اللي في المربع هذه ولا اللي تاعة؟ اللي في المربع + +131 +00:12:38,770 --> 00:12:44,920 +السالي كتيريبقى مشتقة الواحد ب zero ومشتقة هذا ب + +132 +00:12:44,920 --> 00:12:52,440 +سالب سالب اتنين على المقدار تكيب يعني اتنين على + +133 +00:12:52,440 --> 00:12:55,620 +اكس ناقص اتنين لكل تكيب + +134 +00:12:58,610 --> 00:13:04,470 +يبقى هذا المشتقة الثانية مباشرة طيب لو قلت هذه + +135 +00:13:04,470 --> 00:13:09,310 +تساوي زيرو فهي لها حل يعني اتنين تساوي زيرو ممكن + +136 +00:13:09,310 --> 00:13:14,590 +يبقى فيش إمكانية طيب المشتقة الثانية غير معرفة وين + +137 +00:13:14,590 --> 00:13:20,470 +عند اتنين في عند اتنين inflection point بنشوف اذا + +138 +00:13:20,470 --> 00:13:24,310 +الدلة متصلة ولا لا وفي concavity ولا لا واضح انه + +139 +00:13:24,310 --> 00:13:28,640 +عند اتنين الدلة غيرإذا ليه يمكن تبقى الإتنين + +140 +00:13:28,640 --> 00:13:34,360 +inflection point على الإطلاق إذا بدرح أخد إشارة + +141 +00:13:34,360 --> 00:13:38,420 +الإتنين طبعا موجبة على طول الخط ماعندي مشكلة يبقى + +142 +00:13:38,420 --> 00:13:43,900 +المشكلة في إشارة مين؟ X ناقص إتنين يبقى بدهجة + +143 +00:13:43,900 --> 00:13:50,120 +يقوله إشارة الإتنين على X ناقص إتنين لكل تكيب + +144 +00:13:50,120 --> 00:13:56,700 +ويقول له هذا الرقم اللي هو الإتنيناذا لو جيت بعد + +145 +00:13:56,700 --> 00:14:01,060 +اتنين زي تلاتة مثلا بس يقول البنجو سين هذا ماله + +146 +00:14:01,060 --> 00:14:07,480 +موجب واللي فوق موجب على موجب بموجب لو جيت قبل + +147 +00:14:07,480 --> 00:14:12,900 +اتنين زي واحد يبقى البنجو سين سالب واحد تكيب بسالب + +148 +00:14:12,900 --> 00:14:16,660 +اتنين على كمية سالبة بكمية سالبة يبقى اللي قبله + +149 +00:14:16,660 --> 00:14:22,500 +سالبة يبقى concave down هذي concave up يبقى باجي + +150 +00:14:22,500 --> 00:14:35,850 +بقوله the graphup if is concave down على الفترة من + +151 +00:14:35,850 --> 00:14:46,130 +سالب infinity لغاية اتنين and concave up on الفترة + +152 +00:14:46,130 --> 00:14:50,870 +من اتنين لغاية infinityعند اتنين ماعنديش + +153 +00:14:50,870 --> 00:14:56,730 +inflection point لإن الدالة غير معرفة no + +154 +00:14:56,730 --> 00:15:02,410 +inflection point + +155 +00:15:02,410 --> 00:15:16,530 +at x يساوى اتنين because ال F is discontinuous + +156 +00:15:16,530 --> 00:15:18,710 +at + +157 +00:15:27,090 --> 00:15:31,750 +تبقى الدالة مقتصرة عند هذه النقطة اتنين اتدالة + +158 +00:15:31,750 --> 00:15:35,790 +تغير اتجاه الconcavity فعلا غيرت اتجاه الconcavity + +159 +00:15:37,590 --> 00:15:43,210 +الأن من خلال المعلومات اللي عندنا بناروح نرسم رسمة + +160 +00:15:43,210 --> 00:15:49,270 +هذه ال function هذه الشجة كلها عندنا بس تلت نقاط + +161 +00:15:49,270 --> 00:15:52,710 +لإتنين هدول اللي هو zero و تلاتة ع اتنين و سلب جدر + +162 +00:15:52,710 --> 00:15:56,770 +تلاتة و zero و جدر تلاتة و zero عن اكس يسوى اتنين + +163 +00:15:56,770 --> 00:16:00,230 +اللي هو oblique asymptote و اكس يسوى اتنين اللي هو + +164 +00:16:00,230 --> 00:16:06,290 +vertical asymptoteيبقى من خلال هذه المعلومات التي + +165 +00:16:06,290 --> 00:16:12,530 +حصل عليها أن نروح نعرف ما هو شكل الرسم البياني + +166 +00:16:12,530 --> 00:16:15,210 +لهذه الدالة + +167 +00:16:28,400 --> 00:16:34,080 +لو ان هذا محور X هذا محور Y هذا نقطة الاصل اللي هي + +168 +00:16:34,080 --> 00:16:38,380 +Zero قولت لك لما تيجي ترسم أول شغلة تروح ترسمها + +169 +00:16:38,380 --> 00:16:42,560 +ليه ال asymptote يبقى انا كان عندي أبلغة asymptote + +170 +00:16:42,560 --> 00:16:49,140 +لو Y تساوي X زائد 2 لو كانت X ب Zero فالY بقداش ب + +171 +00:16:49,140 --> 00:16:56,320 +2لو كانت ال Y ب Zero X ب سالب اتنين يبقى بروح بوصل + +172 +00:16:56,320 --> 00:17:02,160 +بينهم و بمد هذا على استقامته الى ما شاء الله يبقى + +173 +00:17:02,160 --> 00:17:06,920 +هذا ال oblige asymptote Y X يساوي زائد اتنين في + +174 +00:17:06,920 --> 00:17:11,600 +عندي vertical asymptote اللي هو X يساوي اتنينX + +175 +00:17:11,600 --> 00:17:18,140 +يساوي اتنين يبقى هذا X يساوي اتنين وهو ال Vertical + +176 +00:17:18,140 --> 00:17:23,920 +Asymptote او هذه Zero و اتنين وهذه ناقص اتنين و + +177 +00:17:23,920 --> 00:17:28,750 +Zero يبقى رحسمة ال Asymptotesبروح نرسم ال local + +178 +00:17:28,750 --> 00:17:32,710 +maximum و ال local minimum قال لي في عندي local + +179 +00:17:32,710 --> 00:17:37,430 +maximum اتنين عند x يساوي واحد واحد بدأ تيجي هنا + +180 +00:17:37,430 --> 00:17:42,430 +هي واحد لإن هذه اتنين القيمة اتنين يبقى اي اتنين + +181 +00:17:42,430 --> 00:17:48,140 +اقبلها بالضبط تماما يبقى في عندي local maximumبعد + +182 +00:17:48,140 --> 00:17:52,240 +ذلك ال local minimum عن تلاتة و ستة يبقى لو رحت و + +183 +00:17:52,240 --> 00:17:56,500 +قلت هي تلاتة و قد اطلع ستة يبقى هذا النقطة اللي هي + +184 +00:17:56,500 --> 00:18:03,420 +تلاتة و ستة local maximum تمام بعد ذلك هذا ال + +185 +00:18:03,420 --> 00:18:08,080 +asymptote يبقى ال function بدها تظل نازلة معاه هذا + +186 +00:18:08,080 --> 00:18:12,360 +ال asymptote ال function بدها تظل نازلة معاه + +187 +00:18:12,360 --> 00:18:18,900 +بالشكل اللي عندنا هذا تماميبقى هذا هي ال function + +188 +00:18:18,900 --> 00:18:23,560 +هذا الان asymptote يبقى ال function بدها تبقى + +189 +00:18:23,560 --> 00:18:27,580 +ماشية معاه وهذا بدها تبقى ماشية معاه بالشكل اللي + +190 +00:18:27,580 --> 00:18:32,000 +عندنا هذا اللي أنا مش عارف، هل رسمي هذا صحيح؟ + +191 +00:18:32,000 --> 00:18:36,200 +والله مش صحيح، إذا بدي أروح أشوف ال concave up و + +192 +00:18:36,200 --> 00:18:40,850 +ال concave downتأكد من صحة الكلام + +193 +00:18:55,060 --> 00:19:01,460 +مظبوط و من اتنين لغاية infinity concave up تمام + +194 +00:19:01,460 --> 00:19:05,220 +يبقى ال concave مظبوط تعالى ال increasing ال + +195 +00:19:05,220 --> 00:19:10,140 +increasing من سلب infinity لغاية الواحد لأن النقطة + +196 +00:19:10,140 --> 00:19:17,920 +هذه واحد و اتنين تمام و كذلك increasing من تلاتة + +197 +00:19:17,920 --> 00:19:23,110 +لغاية infinity مظبوطبنجي للـ Decreasing، الـ + +198 +00:19:23,110 --> 00:19:27,870 +Decreasing من عند الواحد لغاية اتنين ومن اتنين + +199 +00:19:27,870 --> 00:19:32,830 +لغاية التلاتة وهي Decreasing، مظبوط؟ تمام تمام + +200 +00:19:32,830 --> 00:19:37,770 +يبقى راسمنا دقيق مية المية لغبار على ذلك، حد اللي + +201 +00:19:37,770 --> 00:19:43,580 +هو اي تساول هنا؟طيب، الحين هذا أو الأسئلة اللي + +202 +00:19:43,580 --> 00:19:48,500 +فاتت هذا هذا السؤال والأسئلة السابقة كلها بلون + +203 +00:19:48,500 --> 00:19:55,480 +واحد بدنا نحاول نعطيك سؤال بلون آخر يختلف عن شكل + +204 +00:19:55,480 --> 00:20:02,460 +المسائل السابقة كليا السؤال بيقول ايه؟ بيقول يرسم + +205 +00:20:02,460 --> 00:20:14,400 +لل function سؤال خمسة اجراففى الـ function f of x + +206 +00:20:14,400 --> 00:20:21,720 +بده يساوي الـ cosine الـ x زائد جذر تلاتة sine الـ + +207 +00:20:21,720 --> 00:20:27,580 +x والـ x هذه أكبر من أو تساوي zero هو أقل من أو + +208 +00:20:27,580 --> 00:20:34,580 +يساوي اتنين باىطبعا لو نظرت لهذا السؤال يختلف كليا + +209 +00:20:34,580 --> 00:20:39,040 +عن المثال السابق في شكله جاب ال beginner يقول + +210 +00:20:39,040 --> 00:20:42,900 +polynomial يا اما rational function، polynomial في + +211 +00:20:42,900 --> 00:20:49,280 +البسطة و polynomial في المقع إذا هذا يختلف نشوف + +212 +00:20:49,280 --> 00:20:53,600 +كيف نحل السؤال من هذا القبيل + +213 +00:21:09,690 --> 00:21:16,580 +شوف يا زيالان انا بدي اقتصر رسمة فقط على ال + +214 +00:21:16,580 --> 00:21:21,800 +interval من صفر لغاية اتنين by يعني ال period تبع + +215 +00:21:21,800 --> 00:21:25,580 +ال sign و نفس ال period تبع man ال cosine بدي اعرف + +216 +00:21:25,580 --> 00:21:30,840 +ما هو شكل هذه الدلة بنقوله بسيطة جدا اذا انا بدي + +217 +00:21:30,840 --> 00:21:36,920 +اشوف من وين بدها تبدأ بدل مااخد تقاطع منحنى مع + +218 +00:21:36,920 --> 00:21:42,130 +محور الاحدثية بدي اشوف من وين بدها تبدأأذا لو جيت + +219 +00:21:42,130 --> 00:21:48,090 +أخدت F of Zero يبقى F of Zero بده تساوي Cos Zero + +220 +00:21:48,090 --> 00:21:53,110 +جدر تلاتة Sine Zero Sine Zero ب Zero و Cos الصفر + +221 +00:21:53,110 --> 00:21:59,010 +يبقى داشر ب واحد لو رحت قلت لك بدي أخد كمان F of + +222 +00:21:59,010 --> 00:22:06,490 +اتنين By يبقى Cos اتنين By زائد جدر تلاتة Sine + +223 +00:22:06,490 --> 00:22:11,570 +اتنين By هذه Zero وهذه واحدةيبقى واحد معناته هذا + +224 +00:22:11,570 --> 00:22:20,210 +الكلام the points النقاط اللي هي ال zero واحد and + +225 +00:22:20,210 --> 00:22:30,530 +اتنين by واحد lie on the graph هذا بدل اقول تقاطة + +226 +00:22:30,530 --> 00:22:34,590 +مع محور الاحداثيات طبعا الشراكة هذه الأولى جابت + +227 +00:22:34,590 --> 00:22:40,390 +للتقاطة مع محور Yهذه التانية بدأت تجيب لي وين + +228 +00:22:40,390 --> 00:22:44,790 +بينتهي المنحنة لكن هذه وين بيبدأ المنحنة وهذه وين + +229 +00:22:44,790 --> 00:22:49,150 +بينتهي المنحنة خلّي التقاطة مع محور X نجيبه الآن + +230 +00:22:49,150 --> 00:22:55,130 +بطريقة ثانية طب مشان هيك إذا بدي أبدأ شغلي في عندي + +231 +00:22:55,130 --> 00:22:59,670 +حاجة اسمها قسمت تهينة لأ يبقى قصة لو قسمت الصفة + +232 +00:22:59,670 --> 00:23:04,600 +على شجة يبقى تروح لمين؟للمشتقة وشوف كيف بدي احسبها + +233 +00:23:04,600 --> 00:23:11,060 +اذا انا بدي اجيل ال F prime of X مشتقة ال cos بسلب + +234 +00:23:11,060 --> 00:23:19,610 +sin X زائد جذر تلاتة في cos Xهذه ههه مش زي + +235 +00:23:19,610 --> 00:23:22,990 +المشتقات اللي فعلها تحط اجواز و تشوف الشرط الجوز + +236 +00:23:22,990 --> 00:23:27,370 +الأول و الثاني و اضرب او اقسم و تطلع الإشارات هذه + +237 +00:23:27,370 --> 00:23:30,850 +صار فيها مشكلة مافيش عنده اجواز و مافيش عامل مشركة + +238 +00:23:30,850 --> 00:23:36,070 +و كذا بسيطة بنسألك السؤال التالي هل هناك نقطة هذه + +239 +00:23:36,070 --> 00:23:40,390 +المشتقة غير معرفة عندها على الفترة من Zero لإتنين + +240 +00:23:40,390 --> 00:23:44,550 +Byلا من zero لأتنين باي ولا حتى لكل ال real life + +241 +00:23:44,550 --> 00:23:47,930 +كلها معرفة على الكل يبقى معاها ان ده مشكلة فيها ده + +242 +00:23:47,930 --> 00:23:53,570 +اذا المشكلة واجتشها دي بدأت ساوي zeroأبدا بحط هذه + +243 +00:23:53,570 --> 00:23:59,050 +تساوي zero وبجي بحل المعادلة هذه إذا هذه لو نجلنا + +244 +00:23:59,050 --> 00:24:03,650 +ال sign على الشجرة التانية بصير ان ال sign ال x + +245 +00:24:03,650 --> 00:24:10,730 +بيساوي جذر تلاتة في cosine ال x اكسم على cosine + +246 +00:24:10,730 --> 00:24:18,030 +بيصير sign على cosine لبتان ال x بيساوي جذر تلاتة + +247 +00:24:18,390 --> 00:24:23,950 +معنى هذا الكلام ان ال X بتتساوي أبصر قدريش تعالى + +248 +00:24:23,950 --> 00:24:28,290 +نسألك السؤال التالف الظل طلع قيمة موجب و الله سالب + +249 +00:24:28,290 --> 00:24:33,350 +اه موجب اه الظل يكون موجب في أي الأرباع الأول + +250 +00:24:33,350 --> 00:24:37,890 +والتالف اذا انا عندى بدل الزاوية زاويتين يعني عندى + +251 +00:24:37,890 --> 00:24:43,380 +نقطتينالتانى عندهم بدى يساوي جداش جذر تلاتة يعني + +252 +00:24:43,380 --> 00:24:47,640 +المشتقة بدها تساوي جداش وإن المشتقة هي المشتقة هي + +253 +00:24:47,640 --> 00:24:48,040 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +254 +00:24:48,040 --> 00:24:48,240 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +255 +00:24:48,240 --> 00:24:50,040 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +256 +00:24:50,040 --> 00:24:53,680 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +257 +00:24:53,680 --> 00:24:55,000 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +258 +00:24:55,000 --> 00:24:55,320 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +259 +00:24:55,320 --> 00:24:55,960 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +260 +00:24:55,960 --> 00:24:56,100 +المشتقة هي المشتقة هي المشتقة هي المشتقة هي + +261 +00:24:56,100 --> 00:25:00,820 +المشتقة هي المشتقة هي المشتقةتلاتة يعني ستين درجة + +262 +00:25:00,820 --> 00:25:06,960 +يبقى X بدها تساوي باي على تلاتة وال X التانية بدها + +263 +00:25:06,960 --> 00:25:10,920 +تساوي في الربع التالت يبقى بسيطة جدا مية و تمانين + +264 +00:25:10,920 --> 00:25:16,120 +و بس اضيف عليها باية على تلاتة مية و تمانين زائد + +265 +00:25:16,120 --> 00:25:20,660 +باية على تلاتة اللي هو كدهاش اربعة باية على تلاتة + +266 +00:25:20,660 --> 00:25:26,820 +يبقى اربعة باية على تلاتة يبقى هذول ايش يعتبرون + +267 +00:25:26,820 --> 00:25:34,380 +شباب؟لكن انا بدأ اقسم من ال real line عالميا حسب + +268 +00:25:34,380 --> 00:25:38,900 +النقاط اللى عندي يبقى انا بناء عليه لو جيت قولت + +269 +00:25:38,900 --> 00:25:43,760 +هذا ال real line و بدي ابدا من عند ال zero وانتهي + +270 +00:25:43,760 --> 00:25:49,970 +بمينبال إتنين باي إذا في النص يكون هنا قد ياش باي + +271 +00:25:49,970 --> 00:25:54,710 +في النص كمان هنا بيكون باي على اتنين وفي النص + +272 +00:25:54,710 --> 00:26:00,490 +التاني بيكون تلاتة باي على اتنين بهاي جسم تمين ال + +273 +00:26:00,490 --> 00:26:06,130 +real life الان بدأت أشوف موقع النقاط الحارجة عندي + +274 +00:26:06,130 --> 00:26:11,530 +عالميا على الرسم الأول باي على تلاتة يعني ستين + +275 +00:26:11,530 --> 00:26:16,850 +درجةستين دولار يعني تلتين الخط تقريبا يبقى هنا هاي + +276 +00:26:16,850 --> 00:26:22,070 +باي على تلاتة التانية ميتين واربعين يبقى هاي + +277 +00:26:22,070 --> 00:26:26,930 +الميتين المية و تمانين بدي اضيف عليها ستين يبقى + +278 +00:26:26,930 --> 00:26:33,090 +كمان هذه اربع باي على تلاتة اذا احنا انقسمت الفترة + +279 +00:26:33,090 --> 00:26:37,490 +اللي عندنا هذه من صفر الاتنين باي الى ثلاث فترات + +280 +00:26:37,790 --> 00:26:41,390 +الفترة الأولى من Zero لغاية بايع تلاتة، التانية من + +281 +00:26:41,390 --> 00:26:45,090 +بايع تلاتة لأربع بايع تلاتة، التالتة من أربع بايع + +282 +00:26:45,090 --> 00:26:51,990 +تلاتة لغاية نان بايم، بدأ أشوف إشارة الـF'، وين + +283 +00:26:51,990 --> 00:26:56,890 +الـF'؟ هذه الـF' اللي عندنا، يبقى هذه بدأ أخد + +284 +00:26:56,890 --> 00:27:02,990 +عليها إشارةالـ F prime of X اللي هو الخطة اللي + +285 +00:27:02,990 --> 00:27:07,250 +عندنا هنا بدي اجي على الفترة من Zero لغاية باية + +286 +00:27:07,250 --> 00:27:11,830 +تلاتة الفترة الأولى لقبل النقطة الحارجة خد أي + +287 +00:27:11,830 --> 00:27:16,730 +زاوية قبل باية على تلاتة باية على ستة تلاتين درجة + +288 +00:27:16,730 --> 00:27:24,440 +فبجي بقوله جي تلاتين بنصهي نهجة تلاتين بجذر تلاتة + +289 +00:27:24,440 --> 00:27:29,020 +على اتنين عامة بسيط تلاتة على اتنين واحد ونص ونقص + +290 +00:27:29,020 --> 00:27:33,560 +نص بظل واحد موجب ولا سالم اذا اي زاوية تاخدها في + +291 +00:27:33,560 --> 00:27:41,190 +هذه الفترة هتعطينا قيمة موجبةعلى الفترة من باى على + +292 +00:27:41,190 --> 00:27:46,110 +تلاتة لغاية اربعة باية تلاتة خد باية اتنين خد باية + +293 +00:27:46,110 --> 00:27:49,470 +اتنين خد اللي بدكيها لوقت ما توصل لغاية اربعة باية + +294 +00:27:49,470 --> 00:27:53,970 +تلاتة فلو أخدنا باى مثلا يبقى باجي بقوله sign باى + +295 +00:27:53,970 --> 00:27:58,590 +بزيرو كسامية وتمانين بسالب واحد في جدر تلاتة + +296 +00:27:58,590 --> 00:28:02,450 +بسالبينيعني كمية سالبة لو أخدت باي على اتنين مش + +297 +00:28:02,450 --> 00:28:07,610 +باي يبقى بصير هادي بزيره صار بايتين بواحد بالسالب + +298 +00:28:07,610 --> 00:28:14,310 +يبقى بصير هادي كلها من سالبة هادي كلها من عند ال + +299 +00:28:14,310 --> 00:28:18,390 +باية تلاتة لغاية أربعة باية تلاتة طيب بدي أخد من + +300 +00:28:18,390 --> 00:28:21,930 +أربعة باية تلاتة لاتنين باي لو أخدت تلاتة باية على + +301 +00:28:21,930 --> 00:28:25,580 +اتنينتلاتة بعدين للمتين والسبعين ضرر يعني كوصين + +302 +00:28:25,580 --> 00:28:29,840 +للمتين والسبعين بزيرو صين للمتين والسبعين بسلب + +303 +00:28:29,840 --> 00:28:35,660 +واحد مع السلب بيصير موجب اذا الفترة هذه كلها بدها + +304 +00:28:35,660 --> 00:28:42,500 +تكون فترة موجبة يبقى الدالة كانت increasing صارت + +305 +00:28:42,500 --> 00:28:47,820 +عند هنا decreasing رجعت هنا صارت ايه؟ صارت + +306 +00:28:47,820 --> 00:28:53,620 +increasing اذا بروح بقوله ما ياتيالـ F is + +307 +00:28:53,620 --> 00:29:01,780 +increasing دالة زيودية على الفترة من Zero لغاية + +308 +00:29:01,780 --> 00:29:09,880 +باية تلاتة and on كمان أربعة باية على تلاتة لغاية + +309 +00:29:09,880 --> 00:29:19,670 +اتنين بايةالـ F is decreasing ذالت نقصية على + +310 +00:29:19,670 --> 00:29:26,710 +الفترة من عند ال باي على تلاتة لغاية أربع باي على + +311 +00:29:26,710 --> 00:29:29,870 +تلاتة بدنا نجيب ال local maximum و ال local + +312 +00:29:29,870 --> 00:29:35,910 +minimum إذا بدنا نروح نحسب قيمة الدالة اللي عندنا + +313 +00:29:42,370 --> 00:29:48,670 +يبقى بناروح نحسب F of Pi على تلاتة بنرجع على رأس + +314 +00:29:48,670 --> 00:29:54,930 +المسألة بدنا نشيل كل X ونحط مكانها اللي همين Pi + +315 +00:29:54,930 --> 00:30:04,710 +على تلاتة يبقى بصير Cos Pi على تلاتةزائد جذر تلاتة + +316 +00:30:04,710 --> 00:30:12,950 +صاعد باية على تلاتة ويساوي جت ستين اللي هي بنص وجه + +317 +00:30:12,950 --> 00:30:21,240 +ستين جذر تلاتة على اتنين يبقى الجواب كله اتنينبدي + +318 +00:30:21,240 --> 00:30:28,760 +اخد f of التانية اللي هو أربع باقي على تلاتة ويسوى + +319 +00:30:28,760 --> 00:30:34,560 +ال cosine أربع باقي على تلاتة جذر تلاتة ال sign + +320 +00:30:34,560 --> 00:30:40,140 +أربع باقي على تلاتة ويسوى أربع باقي على تلاتة في + +321 +00:30:40,140 --> 00:30:43,840 +الرابع التالت في الرابع التالت يجيب التمامسالب + +322 +00:30:43,840 --> 00:30:49,820 +يعني المية وتمانين زائد بايع تلاتة لجتا بايع على + +323 +00:30:49,820 --> 00:30:56,620 +تلاتة بس بالسالب يبقى اللي هو سالب نص زائد جذر + +324 +00:30:56,620 --> 00:31:02,880 +تلاتة برضه ال sign سالب يبقى سالب جذر تلاتة على + +325 +00:31:02,880 --> 00:31:08,180 +الإتنين يبقى الجواب قداش سالب اتنين يبقى بروح + +326 +00:31:08,180 --> 00:31:19,610 +بقوله ال F has localالـ F has local maximum local + +327 +00:31:19,610 --> 00:31:27,130 +maximum مجدش اتنين ات اكس يسوى باي على تلاتة and + +328 +00:31:27,130 --> 00:31:36,690 +local minimum سالب اتنين ات اكس يسوى اربع باي على + +329 +00:31:36,690 --> 00:31:41,360 +تلاتةخلصنا ال local maximum و ال local minimum و + +330 +00:31:41,360 --> 00:31:43,760 +ال increasing و ال decreasing يبقى ضايق ال + +331 +00:31:43,760 --> 00:31:47,060 +inflection point او ال concave up و ال concave + +332 +00:31:47,060 --> 00:31:53,440 +down اذا بدنا نروح نجيب له ال f w prime of x ال f + +333 +00:31:53,440 --> 00:32:01,560 +prime of x هي بنشتقها كمان مرةيبقى سالب cosine X + +334 +00:32:01,560 --> 00:32:08,520 +وبعد اتفاض cosine بسالب sin يبقى سالب جدر تلاتة في + +335 +00:32:08,520 --> 00:32:13,940 +sin X طبعا هذه معرفة على طول إذا بدي أحط ال F + +336 +00:32:13,940 --> 00:32:18,710 +double prime ب zero ونشوف إيش بدها تعطينايبقى لو + +337 +00:32:18,710 --> 00:32:25,470 +حطينا هذه تساوي zero هذا بده يعطينا انه جذر تلاتة + +338 +00:32:25,470 --> 00:32:30,730 +في صين ال X جذر تلاتة في صين X بده يساوي سالب + +339 +00:32:30,730 --> 00:32:36,510 +cosine ال X يبقى معناه هذا الكلام انه تان ال X + +340 +00:32:36,510 --> 00:32:45,410 +بساوي سالب واحد على جذر تلاتةالظلق لقيمة سالبة + +341 +00:32:45,410 --> 00:32:49,570 +يبقى الزاوية موجة في الرابع الثاني و رابع الرابع + +342 +00:32:49,570 --> 00:32:53,330 +لأنه ظل موجة في الرابع الأول و التالت إذا سالب في + +343 +00:32:53,330 --> 00:32:59,890 +التاني و الرابع يعني معنى هذا الكلام إن ال X يساوي + +344 +00:33:00,670 --> 00:33:04,090 +بقى اللي بقول مين الزاوية اللي جيبت من واحد على + +345 +00:33:04,090 --> 00:33:07,630 +جدر تلاتة ليه باي على ستة طوحة من المائة و تمانين + +346 +00:33:07,630 --> 00:33:15,570 +بصير خمسة باي على ستة خمسة باي على ستة و X التانية + +347 +00:33:15,570 --> 00:33:22,990 +أحد عشر باي على ستة اترحهم كذلك من مين؟ من اتنين + +348 +00:33:22,990 --> 00:33:28,530 +باي لدورة كاملة يبقى جيبنا ال X خمسة باي أو على ال + +349 +00:33:28,530 --> 00:33:32,310 +calculator عندك انت بتجيبها دورييبقى خمسة ضاي على + +350 +00:33:32,310 --> 00:33:36,270 +ستة او احداشر لو تلاتمية و تلاتين درجة ومية و + +351 +00:33:36,270 --> 00:33:41,990 +خمسين درجة يبقى هاي طلعنا اللي هو النقاط اللي قد + +352 +00:33:41,990 --> 00:33:47,110 +تكون conflicting points الله أعلم أنا مش متأكد لكن + +353 +00:33:47,110 --> 00:33:50,950 +أنا بقول الدالة الأصلية دالة متصلة على كل ال real + +354 +00:33:50,950 --> 00:33:56,090 +lineالسؤال هو والله عند هذه النقاط، إذا الدالة + +355 +00:33:56,090 --> 00:34:01,510 +غيرت اتجاه الـconcavity تبعها، بيكون فعلا عندنا، + +356 +00:34:01,510 --> 00:34:06,550 +عندنا اللي هو inflection point. إذا أنا لو جيت، + +357 +00:34:06,550 --> 00:34:10,980 +قلت هذا الـreal line كله.وبدأنا من عند ال zero + +358 +00:34:10,980 --> 00:34:16,640 +وانت هنا عند من؟ عند اتنين باي يبقى في النص هنا + +359 +00:34:16,640 --> 00:34:23,280 +باي وفي النص هنا قداش باي على اتنين وفي النص هنا + +360 +00:34:23,280 --> 00:34:29,540 +قداش تلاتة باي على الأتنين احنا النقاط اللي هالنا + +361 +00:34:29,540 --> 00:34:34,420 +خمسة باي ع ست يعني مية وخمسين درجة مية وخمسين درجة + +362 +00:34:34,420 --> 00:34:41,240 +يعني بتجيني هنايبقى هذا خمسة باى على ستة التانية + +363 +00:34:41,240 --> 00:34:46,660 +هيها احداشر باى على ستة تلاتمية و تلاتين درجة يبقى + +364 +00:34:46,660 --> 00:34:51,900 +هذا احداشر باى على مين على ستة الان بدنا نجي في + +365 +00:34:51,900 --> 00:34:57,320 +الفترة الأولى بدنا نجي على المشتقة f double prime + +366 +00:34:57,320 --> 00:35:01,540 +اشوف فموجة بو الله سلبة اذا بدي اعوض باي زاوية + +367 +00:35:01,540 --> 00:35:05,840 +خلال الفترة دى مثلالو أخد مبايع اثنين بيصير Zero + +368 +00:35:05,840 --> 00:35:12,420 +هنا واحد بيصير سالب يعني قيمة سالبة، إذا خلال هذه + +369 +00:35:12,420 --> 00:35:17,640 +الفترة كلها قيمة سالبة، بالدادية على الفترة من هنا + +370 +00:35:17,640 --> 00:35:22,990 +لغاية هناخد أي زاوية من هنا و التكن باي تلاتة باي + +371 +00:35:22,990 --> 00:35:27,390 +اتنين اللي بدك إياها يبقى لو أخدت باي cosine باي + +372 +00:35:27,390 --> 00:35:31,710 +بيزيرو كوصين مية و تمانين بسلب واحد مع سلب بيصير + +373 +00:35:31,710 --> 00:35:36,990 +موجم إذا خلال هذه الفترة بتكون هذه كلها مالها + +374 +00:35:36,990 --> 00:35:42,190 +بالموجم بتبدي الفترة الصغيرة الأخيرة خد اللي بدك + +375 +00:35:42,190 --> 00:35:46,770 +إياها و التكن اتنين باي بيصير هذه zero و هنا اتنين + +376 +00:35:46,770 --> 00:35:53,890 +بايبواحد و عندك سالب يبقى بصير سالب يبقى المنحنة + +377 +00:35:53,890 --> 00:36:01,370 +هنا concave down هنا concave up هنا ماله concave + +378 +00:36:01,370 --> 00:36:07,790 +down بالشكل اللي عنها اذا بروح بقوله ما يأتي the + +379 +00:36:07,790 --> 00:36:12,850 +graph is + +380 +00:36:12,850 --> 00:36:17,570 +concave down + +381 +00:36:19,520 --> 00:36:26,540 +على الفترة الأولى من عند الـ zero لغاية جداش لخمسة + +382 +00:36:26,540 --> 00:36:35,100 +by على ستة خمسة by على ستة and on وكذلك من + +383 +00:36:35,100 --> 00:36:43,620 +الاحداشر by على ستة و لغاية جداش و لغاية اتنين by + +384 +00:36:43,620 --> 00:36:53,540 +andConcave up مفتوح إلى أعلى على الفترة من خمسة + +385 +00:36:53,540 --> 00:37:00,160 +باي على ستة إلى أحد عشر باي على ستة بالشكل اللي + +386 +00:37:00,160 --> 00:37:04,930 +عندنا هناالدالة متصلة وتغير الـconcavity يبقى + +387 +00:37:04,930 --> 00:37:08,470 +النقطتين هذول ما لهم inflection points + +388 +00:37:31,970 --> 00:37:35,150 +هذه الزاوية 150 فى الرابع التانى يبقى ال cosine + +389 +00:37:35,150 --> 00:37:41,630 +بالسالم او جهة ابايا على ستة اللي هو جدر تلاتة على + +390 +00:37:41,630 --> 00:37:47,030 +اتنين خمسة ابايا على ستة اللي جهة بتابعها بنص فى + +391 +00:37:47,030 --> 00:37:51,230 +جدر تلاتة يبقى بزايد جدر تلاتة على اتنين ويسوى قد + +392 +00:37:51,230 --> 00:38:01,490 +ياش Zeroالان F of 11 Pi على 6 Cos 11 Pi على 6 زي + +393 +00:38:01,490 --> 00:38:09,870 +جدر 3 Sin 11 Pi على 6 ويساويهذه ال 11 باية على 6 + +394 +00:38:09,870 --> 00:38:13,870 +موجودة في الرابع الرابع في الرابع الرابع ال cosine + +395 +00:38:13,870 --> 00:38:21,830 +موجب يبقى زائد جذر 3 على 2 وهذا ناقص جذر 3 على 2 + +396 +00:38:21,830 --> 00:38:30,690 +وهو Zero يبقى باجي بقوله the inflection points are + +397 +00:38:31,470 --> 00:38:38,870 +اللي هم النقطة الأولى اللي هي خمسة by على ستة و + +398 +00:38:38,870 --> 00:38:43,890 +zero and احداشر + +399 +00:38:50,480 --> 00:38:55,300 +خلصنا ال concavity وخلصنا النقاط لم يبقى لنا اللي + +400 +00:38:55,300 --> 00:39:01,360 +هي عملية الرسم يبقى لو جيت رسمت وقلت هذا المنحنى + +401 +00:39:01,360 --> 00:39:07,790 +لأن هذا محور X وهذا محور Yأقصى قيمة بتاخدها الدالة + +402 +00:39:07,790 --> 00:39:11,210 +اللي هو الاتنين و أقل قيمة اللي هو الـminimum اللي + +403 +00:39:11,210 --> 00:39:16,050 +هو السالب اتنين يبقى لو جيت قولت هذا الخط اللي هو + +404 +00:39:16,050 --> 00:39:21,690 +الاتنين و هذا الخط المناظر اللي هو جداش سالب اتنين + +405 +00:39:21,690 --> 00:39:27,250 +وهذه النقطة الأصل اللي هي zero بدي أكبر الخط من + +406 +00:39:27,250 --> 00:39:34,710 +ناحية هذه بس علشان هي الرسمة كلها على اليمينيبقى + +407 +00:39:34,710 --> 00:39:40,570 +لو جيت قولت هاي الخط هنا وهذا اللي هو سالب اتنين + +408 +00:39:40,570 --> 00:39:47,650 +وهذا ال zero وهذا اللي هو اتنين وهذا محور Y من + +409 +00:39:47,650 --> 00:39:53,470 +Zero لغاية اتنين با يبقى هاد اتنين باالمنحنة هيبدأ + +410 +00:39:53,470 --> 00:40:01,970 +عند النقطة 01 وينتهي + +411 +00:40:01,970 --> 00:40:08,810 +عند النقطة 2x1 لنقطة 2x1 + +412 +00:40:15,980 --> 00:40:19,260 +بعد كده السيمتوت مافيهش عندي بده اروح لل local + +413 +00:40:19,260 --> 00:40:23,240 +maximum و ال local minimum خليني ارتب الخطة لان + +414 +00:40:23,240 --> 00:40:31,560 +هذه يبقى باي على اتنينيبقى هذه تلاتة باي على + +415 +00:40:31,560 --> 00:40:36,240 +الإتنين الـ inflection points عند النقطة خمسة باي + +416 +00:40:36,240 --> 00:40:43,540 +على ستة و Zero يبقى هذه النقطة الخمسة باي على ستة + +417 +00:40:43,540 --> 00:40:47,780 +و النقطة اللي بقى أحد عشر باي على ستة يبقى هذه + +418 +00:40:47,780 --> 00:40:55,350 +النقطة الخمسة باي على ستةبعد هيك، بتجي لل local + +419 +00:40:55,350 --> 00:41:00,570 +maximum، وين ال local؟ اه، هي عندك local maximum + +420 +00:41:00,570 --> 00:41:05,310 +اتنين، عند ال by على تلاتة عند ستين درجة يبقى هي + +421 +00:41:05,310 --> 00:41:10,470 +ال by على تلاتة، by على تلاتة عند local maximum + +422 +00:41:10,470 --> 00:41:14,790 +هنا، اتنين بالشكل اللي عندنا هناهو عندى local + +423 +00:41:14,790 --> 00:41:19,970 +minimum local مصالف اتنين عند اربعة باية على تلاتة + +424 +00:41:19,970 --> 00:41:24,790 +يعني متين واربعين درجة متين واربعين يعني عنده + +425 +00:41:24,790 --> 00:41:30,450 +النقطة هذه تقريبا و بدك تنزل تحت يبقى هذه local + +426 +00:41:30,450 --> 00:41:35,980 +minimum بالشكل اللى عندنا بعد هيكجالي ادالة + +427 +00:41:35,980 --> 00:41:41,380 +increasing من Zero لغاية باية تلاتة، مظبوط؟ من + +428 +00:41:41,380 --> 00:41:46,720 +Zero لغاية باية تلاتة increasing، يبجي هذه المنحنة + +429 +00:41:46,720 --> 00:41:52,410 +اللي عندنا هنابعديها decreasing من عند ال باية + +430 +00:41:52,410 --> 00:41:59,070 +تلاتة لغاية هذه اربعة باية على تلاتة يبقى هذه + +431 +00:41:59,070 --> 00:42:05,150 +decreasing ويمر بال inflection point وهك بصير + +432 +00:42:05,150 --> 00:42:10,250 +مفتوح الاعلى بعديها يجلي increasing ويمر بال + +433 +00:42:10,250 --> 00:42:15,530 +inflection point وهك وبعدها بصير + +434 +00:42:19,340 --> 00:42:23,820 +تأكد ان معلوماتنا صح و لا لأ هذي increasing و + +435 +00:42:23,820 --> 00:42:28,340 +decreasing و increasing مظبوط مائة لمائة نجي هل من + +436 +00:42:28,340 --> 00:42:32,040 +عندي ال zero لخمسة باية على ستة concave down ولا + +437 +00:42:32,040 --> 00:42:36,760 +لأ طلع لان concave مظبوط هل من خمسة باية على ستة + +438 +00:42:36,760 --> 00:42:40,670 +لان احداشر باية على ستة concave up مظبوطالان من + +439 +00:42:40,670 --> 00:42:44,910 +احداشر بايع الستة لغاية اتنين بايكون كيف؟ down + +440 +00:42:44,910 --> 00:42:50,550 +يبقى الاسفل يبقى رسم لدقيق مية لمية هذا الان + +441 +00:42:50,550 --> 00:42:55,910 +النقطة والنقطة الثانية اللي عندنا هاده هدوله ال + +442 +00:42:55,910 --> 00:43:05,170 +inflection pointsالنقطتين اللي عندنا هدول طبعا هذه + +443 +00:43:05,170 --> 00:43:13,050 +النقطة اللي هي اربع باي ع تلاتة وسالي باتنين وهذه + +444 +00:43:13,050 --> 00:43:18,150 +اللي هي باي ع تلاتة واتنين هذه local maximum وهذه + +445 +00:43:18,150 --> 00:43:19,690 +local minimum + +446 +00:43:29,920 --> 00:43:36,100 +النقطة الأعلى هي ال local minimum والنقطة الأعلى + +447 +00:43:36,100 --> 00:43:37,700 +هي local maximum + +448 +00:43:42,000 --> 00:43:46,380 +يبقى انا بدي ارسم فعلا هذه لو بدك تقولي هذا بقولك + +449 +00:43:46,380 --> 00:43:54,940 +هذه صحيح هذه local minimum هذه هنا كمان local + +450 +00:43:54,940 --> 00:44:01,030 +maximum اقولك زيادة على ذلكهذه absolute maximum + +451 +00:44:01,030 --> 00:44:05,390 +وهذه absolute minimum لأن أقصى قيمة بياخدها هي + +452 +00:44:05,390 --> 00:44:08,890 +اتنين خلال فترة من zero لاتنين باي وأقل قيمة + +453 +00:44:08,890 --> 00:44:11,930 +بياخدها سالب اتنين من zero لاتنين باي يبقى هذه + +454 +00:44:11,930 --> 00:44:15,130 +absolute minimum وهذه absolute maximum فيه ما لو + +455 +00:44:15,130 --> 00:44:18,030 +طلبها، لأنه ما طلبش هو جالي ارسم وخلاص ونقوله + +456 +00:44:18,030 --> 00:44:23,110 +رسمنا يعطيك العافيةتمام؟ إذا لحد هنا انتهى هذا ال + +457 +00:44:23,110 --> 00:44:29,470 +section وإليكم أرقام المسائل على هذا ال section + +458 +00:44:29,470 --> 00:44:36,010 +اللي هو exercises أربعة أربعة يبقى باجي بقوله + +459 +00:44:36,010 --> 00:44:44,690 +exercises أربعة أربعة المسائل التالية من واحد + +460 +00:44:44,690 --> 00:44:53,130 +لواحد و تسعين ال wholeبنضيف عليها من تلاتة وتسعين + +461 +00:44:53,130 --> 00:45:02,370 +لستة وتسعين ومن مية واحد لمية واطماش مية واحد لمية + +462 +00:45:02,370 --> 00:45:03,490 +واطماش + +463 +00:45:21,800 --> 00:45:24,900 +السلام عليكم ورحمة الله وبركاته + +464 +00:45:54,540 --> 00:46:06,120 +هذا بده الرسمة طيب + +465 +00:46:06,120 --> 00:46:15,040 +هذا انتهى عليك سكشن اربعة اربعة الرسم ايه السمس + +466 +00:46:15,040 --> 00:46:18,140 +فيها + +467 +00:46:18,140 --> 00:46:23,040 +سمتت؟ لأ روحنا حطينا ال local maximum و ال local + +468 +00:46:23,040 --> 00:46:28,380 +minimumوالـ inflection points بعد ذلك دورنا ال + +469 +00:46:28,380 --> 00:46:33,580 +increasing دورنا ال decreasing و بعدين شوفنا هل + +470 +00:46:33,580 --> 00:46:37,120 +الرسمة كان كيف أبوك و كيف دان و لا جناها تمام يقول + +471 +00:46:37,120 --> 00:46:43,000 +بصمنا خلاص طيب الان بدنا نيجي لامام الحلقات اللي + +472 +00:46:43,000 --> 00:46:45,800 +بده الرسمة او خلاص؟ الرسم خلاص؟ + +473 +00:46:59,710 --> 00:47:04,790 +الان بروح ل section أربعة خمسة و أربعة ستة و + +474 +00:47:04,790 --> 00:47:09,990 +بقولهم الله سهل عليكم بروح ل أربعة سبعة اللي هو ال + +475 +00:47:09,990 --> 00:47:16,130 +antiderivative آخر + +476 +00:47:16,130 --> 00:47:23,690 +section في الشبطة وهو مقدمة لموضوع التكامل تمام؟ + +477 +00:47:23,690 --> 00:47:28,050 +ال antiderivative بدنا نعطي تعريف قلها definition + +478 +00:47:30,840 --> 00:47:39,660 +A function capital F is an + +479 +00:47:39,660 --> 00:47:45,820 +antiderivative of + +480 +00:47:45,820 --> 00:47:57,640 +F on an interval I + +481 +00:48:20,360 --> 00:48:27,860 +نقطة مهمة جدا the most general + +482 +00:48:29,770 --> 00:48:36,210 +the most general antiderivative + +483 +00:48:36,210 --> 00:48:39,230 +antiderivative + +484 +00:48:39,230 --> 00:48:53,190 +of f on ال interval I on interval I is capital F + +485 +00:48:53,190 --> 00:49:07,360 +of X زائد constant C whereI of C is constant نجي + +486 +00:49:07,360 --> 00:49:14,240 +لـ some antiderivatives + +487 +00:49:14,240 --> 00:49:21,440 +some antiderivatives أو antiderivative formulas + +488 +00:55:31,970 --> 00:55:35,890 +طبعا اللي احبه مشتقة الدول المثلثية الستة بلا جهد + +489 +00:55:35,890 --> 00:55:44,470 +كله كلام بسيط ولا حاجة مولاشي + +490 +00:55:44,470 --> 00:55:49,730 +يبقى + +491 +00:55:49,730 --> 00:55:52,550 +في الاندونيزيا الموضوع ال antiderivative + +492 +00:55:52,550 --> 00:55:57,610 +antiderivative تفاضل لما اقول antiderivative يعني + +493 +00:55:57,610 --> 00:56:02,390 +انا بدي اشتغل شغل ضب التفاضلضد التفاضل اتعلمناه في + +494 +00:56:02,390 --> 00:56:05,330 +السنوية يعني عبارة عن ايش؟ بس مابديش اقول تكامل + +495 +00:56:05,330 --> 00:56:08,710 +حتى اللحظة لما نوصل لتكامل بدي اقول تكامل زي ما + +496 +00:56:08,710 --> 00:56:13,290 +هعرفه بعد قليل طبعا يبقى انا بدي اقول ضد التفاضل + +497 +00:56:13,290 --> 00:56:18,230 +antiderivative يبقى ضد التفاضل شو يعني ضد التفاضل + +498 +00:56:18,230 --> 00:56:23,810 +التعريف بيقولي ما يأتي بيقولي اتبع لك capital F + +499 +00:56:23,810 --> 00:56:27,720 +خلي بالك كافي عند الكتابةكابتل F هي الـ + +500 +00:56:27,720 --> 00:56:32,940 +Antiderivative للـ small f على فترة محددة والتي + +501 +00:56:32,940 --> 00:56:39,800 +تكون الفترة I إذا كان مشتق الكابتل F هي الـ small + +502 +00:56:39,800 --> 00:56:45,880 +f لكل X الموجود أويا في الـ interval I يبقى كابتل + +503 +00:56:45,880 --> 00:56:49,980 +F هي الـ Antiderivative للدالة small f إذا كان + +504 +00:56:49,980 --> 00:56:57,120 +مشتق كابتل F أعطتنا مهمةأعطتني اللي هو اعطتني ليه + +505 +00:56:57,120 --> 00:57:01,840 +ال small f لكن لو جيت قولتك مثلا ال X تكيب هذه + +506 +00:57:01,840 --> 00:57:06,560 +مشتقتها جداش تقول لي تلاتة X تربية لو قولتك X تكيب + +507 +00:57:06,560 --> 00:57:12,180 +زائد مية جداش مشتقتها تلاتة X تربية اذا نفس المشتق + +508 +00:57:12,180 --> 00:57:18,140 +لك الفرق بين الدلاتين جداش مقدار ثابت اذا انا بدي + +509 +00:57:18,140 --> 00:57:23,120 +روح اتلاشى القطأ ان وجد هذا القطأفبروح بقول هنا + +510 +00:57:23,120 --> 00:57:27,560 +the most general antiderivative of f على ال + +511 +00:57:27,560 --> 00:57:32,820 +interval I هو يبارعا capital F of X زي ال main زي + +512 +00:57:32,820 --> 00:57:38,860 +ال constant C يبقى هنا أضفتلها مقدار ثابت لا يؤثر + +513 +00:57:38,860 --> 00:57:45,190 +على شكل ال main على شكل ال derivativeالدالة هادى + +514 +00:57:45,190 --> 00:57:50,810 +هو ارض سيم الانتي دريفاتيف بروح بحط لهزاية كونستان + +515 +00:57:50,810 --> 00:57:56,410 +سي حتى اتخلص من المشكلة سواء كانت سي بزيرو او غير + +516 +00:57:56,410 --> 00:58:00,090 +زيرو قولنا where c is كونستان يبقى كل الشغل عندي + +517 +00:58:00,090 --> 00:58:04,630 +حطيت سي بمقدار 7 الكلام اللى بقوله بده اروح اطبقه + +518 +00:58:04,630 --> 00:58:10,100 +على ارض الواقع فروحنا عملنا جدوللبعض الدوال + +519 +00:58:10,100 --> 00:58:14,340 +الشهيرة بدنا نجيبلها الـ Antiderivative تبعهانجي + +520 +00:58:14,340 --> 00:58:19,900 +للدالة الأولى ال X to the power N ال X هو المتغير + +521 +00:58:19,900 --> 00:58:25,620 +ان هذا is a real number بس بشرط ال N ممنوع يتساوي + +522 +00:58:25,620 --> 00:58:30,280 +سالب واحد لكن ان شاء الله في كل كلاصة ب .. هناخد + +523 +00:58:30,280 --> 00:58:34,040 +لو كانت ال X بدي تساوي سالب واحد شو بدي يكون شكل + +524 +00:58:34,040 --> 00:58:38,600 +ال antiderivative في هذه الحالة او التكامل للدالة + +525 +00:58:38,600 --> 00:58:42,320 +برضه هنعرفه لو كانت ال X يساوي كده سالب واحد طبعا + +526 +00:58:42,320 --> 00:58:47,360 +ماعطيناش كيكلأن في موضوع لغة مات بيدخل في الموضوع + +527 +00:58:47,360 --> 00:58:51,620 +لكن احنا حتى الآن ماعناش لغة مات يبقى ال X to the + +528 +00:58:51,620 --> 00:58:54,740 +power and the antiderivative اللي هو بضيف للأس + +529 +00:58:54,740 --> 00:59:00,160 +واحد و بقسم على الأس الجديد و بقوله زائد كونستانسي + +530 +00:59:00,160 --> 00:59:03,400 +وهذا اللي كنا زمان من كامله في الثانوية تمالوم + +531 +00:59:03,400 --> 00:59:11,110 +سميته كامل غير المحدودSin KX بدي بسأل نفسي قداش + +532 +00:59:11,110 --> 00:59:17,890 +الدالة او قداش تفاضل الـSin هو Cos أنا بديش تفاضل + +533 +00:59:17,890 --> 00:59:23,550 +الـSin أنا بدي الـAntiderivative للـSin يعني ما هي + +534 +00:59:23,550 --> 00:59:28,010 +الدالة اللي مشتقدة بتعطينا الـSin بقول لو جيت + +535 +00:59:28,010 --> 00:59:32,250 +اشتقدت تفاضل الـCos سالب الـSin بروح السالب مع + +536 +00:59:32,250 --> 00:59:37,860 +السالبدرب مشتقة تزوجه K بتروح مع K بضال قداش SIN + +537 +00:59:37,860 --> 00:59:43,580 +الككس والـ C مشتقة تبزيره SIN الككس إذا بناء عليه + +538 +00:59:43,580 --> 00:59:47,720 +الـ Antiderivative لـ SIN الككس هو سالب واحد على K + +539 +00:59:47,720 --> 00:59:53,300 +Cos K X زائد Const C لو بدجاجي للككس كدوش متقعة + +540 +00:59:53,300 --> 00:59:58,260 +الـ SIN هو Cos يبقى لو جيت أشتق هذه هو Cos ضرب K + +541 +00:59:58,260 --> 01:00:02,460 +بتروح مع K بتعطيني Cosإذا الـ Antiderivative لـ + +542 +01:00:02,460 --> 01:00:08,520 +Cos X هو 1 على K لـ Sin K X زي الكنستانسي تفاضل ال + +543 +01:00:08,520 --> 01:00:13,040 +10 بسكتربيع هذا ال Antiderivative لسكتربيع هي 10 + +544 +01:00:13,040 --> 01:00:18,760 +مقسومة على 1 على K بالمثل تفاضل كتان بسالب + +545 +01:00:18,760 --> 01:00:22,680 +كوسيكنتربيع هذا ال Antiderivative لكوسيكنتربيع K X + +546 +01:00:22,860 --> 01:00:27,780 +الوثالب واحد على كلكو تان كك زائد كونستان سي تفاضل + +547 +01:00:27,780 --> 01:00:32,540 +تسيك بسيك تان إذا الـ Antiderivative لسيك ككس تان + +548 +01:00:32,540 --> 01:00:38,780 +ككس هو واحد على ك في مين في سيك الككس يعني كأنه + +549 +01:00:38,780 --> 01:00:43,040 +انا برجع ترجيه ابدأ اللي انفضله بترجعه لمين اللي + +550 +01:00:43,040 --> 01:00:47,130 +اصل قبل التفاضل بدل المضربفي تفاضل الزاوية بقسم + +551 +01:00:47,130 --> 01:00:51,790 +على تفاضل الزاوية لان عندي ال antiderivative لكو + +552 +01:00:51,790 --> 01:00:55,810 +سي كانت كوتان هي سالي كو سي كانت كك مقصومة على مين + +553 +01:00:55,810 --> 01:01:00,630 +على ك زائد كونستران سي لو اشتقت هذه بتعطيني مين + +554 +01:01:00,630 --> 01:01:05,810 +هذه هي ال antiderivative لمين لدلها بعد هيك لو + +555 +01:01:05,810 --> 01:01:09,650 +كانت دالة اي f of x سواء اللي في الجدول او غيرهم + +556 +01:01:09,650 --> 01:01:14,230 +فبدي ال antiderivative لك في ال f smallيبقى كيب + +557 +01:01:14,230 --> 01:01:17,510 +اقول ان انت مالكش دعوة و الف اصمه لانت دريفتيف هي + +558 +01:01:17,510 --> 01:01:22,410 +ال capital F of X زائد constant C الان لو كانت + +559 +01:01:22,410 --> 01:01:26,690 +الكيب سالب واحد يبقى بيصير الانت دريفتيف لسالب F + +560 +01:01:26,690 --> 01:01:31,070 +of X هي سالب capital F of X زائد constant C يبقى + +561 +01:01:31,070 --> 01:01:33,950 +الكيب حاطينا سالب واحد لو كان المجموع الجبري + +562 +01:01:33,950 --> 01:01:38,370 +لدالتين الانت دريفتيف يبقى المجموع الجبري لتو انت + +563 +01:01:38,370 --> 01:01:38,970 +دريفتيف + +564 +01:01:50,480 --> 01:01:54,340 +من خلال جدور بدنا نروح نحسب ال ant derivatives + +565 +01:01:54,340 --> 01:02:00,490 +للدوال المختلفة الاتية يبقى انا عند x والسلب 4زائد + +566 +01:02:00,490 --> 01:02:04,570 +اتنين X زائد تلاتة يبقى هذا مجموع جبري لثلاث دوال + +567 +01:02:04,570 --> 01:02:09,310 +وليس لدالتين يبقى ال ant derivative للأولى زائد ال + +568 +01:02:09,310 --> 01:02:11,830 +ant derivative للتانية زائد ال ant derivative + +569 +01:02:11,830 --> 01:02:16,470 +للتالتة وكلهم بتحطلهم منهم كالكلاصين يبقى باجي + +570 +01:02:16,470 --> 01:02:24,460 +بقوله هنا ال antiالخطوة التالية هي يبقى هنا x أس + +571 +01:02:24,460 --> 01:02:29,880 +بدي أضيف للأس واحد و أقسم على الأس الجديد لو أضفت + +572 +01:02:29,880 --> 01:02:35,040 +للأس واحد جديش بصير عندى هذا سالب تلاتة على سالب + +573 +01:02:35,040 --> 01:02:41,720 +تلاتةاللي هو لإتنين هاي X بتضيف للأس واحد بيصير + +574 +01:02:41,720 --> 01:02:49,700 +جداش تنين على اتنين زائد تلاتة هادي أصلا X أس Zero + +575 +01:02:49,700 --> 01:02:56,900 +بدي أضف لها واحد اللي هو Zeroزائد واحد على مين على + +576 +01:02:56,900 --> 01:03:03,720 +واحد زائد constant C يبقى النتيجة تساوي X السلب + +577 +01:03:03,720 --> 01:03:08,560 +تلاتة على سلب تلاتة لاتنين مع اتنين الله سهل عليها + +578 +01:03:08,560 --> 01:03:18,180 +يبقى X تربيع زائد تلاتة X زائد constant Cنأخد سؤال + +579 +01:03:18,180 --> 01:03:23,900 +آخر نمر اتنين بدنا ال antiderivative لل X أص ناقص + +580 +01:03:23,900 --> 01:03:28,940 +تلاتة على اتنين زائد ال X تربيع بد ال + +581 +01:03:28,940 --> 01:03:35,280 +antiderivative لها ال antiderivative is يبقى X أص + +582 +01:03:35,960 --> 01:03:41,380 +هذا باعتباره نص اللي برا مالوش دعوة كويس يبقى x + +583 +01:03:41,380 --> 01:03:46,140 +بالضبط اللي هو احنا بصير جداش سالي باتنين على جداش + +584 +01:03:46,140 --> 01:03:52,560 +على سالي باتنين زائد x تكييب على تلاتة زائد + +585 +01:03:52,560 --> 01:03:59,780 +constant C يبقى ناقص ربع x اص ناقص اتنين زائد x + +586 +01:03:59,780 --> 01:04:04,560 +تكييب على تلاتة زائد constant C + +587 +01:04:09,120 --> 01:04:18,900 +نقطة تالتة بدنا اللي هو جذر ال X زائد واحد على جذر + +588 +01:04:18,900 --> 01:04:25,740 +Xبنفضل نعيد صياغة المثلة يبقى لو قعدنا صياغة + +589 +01:04:25,740 --> 01:04:31,500 +المثلة مانصير هذي X أص نص زاد X أص نص طلعها فوق + +590 +01:04:31,500 --> 01:04:36,860 +بصير جداش X أص سالف نص بد ال antiderivative ال + +591 +01:04:36,860 --> 01:04:44,400 +antiderivative isX أُس جدّاش تلاتة على اتنين مقسوم + +592 +01:04:44,400 --> 01:04:51,500 +على تلاتة على اتنين X أُس على جداش زائد constant C + +593 +01:04:51,500 --> 01:04:58,760 +يعني هذي بيصير طولتين X أس تلاتة على اتنين زائد + +594 +01:04:58,760 --> 01:05:06,530 +اتنين جذر ال X زائد constant Cالنقطة الرابعة ال + +595 +01:05:06,530 --> 01:05:14,250 +نقطة الرابعة بدنا سالب نص X و سالب تلاتة على اتنين + +596 +01:05:14,250 --> 01:05:21,790 +بد ال antiderivative لها يبقى ال antiderivative as + +597 +01:05:21,790 --> 01:05:30,430 +شوف يا زيد يبقى سالب نص مالوش دعوةأي كي بيظل زي ما + +598 +01:05:30,430 --> 01:05:33,990 +هو مقدار فارق بدي ال antiderivative الاكس او + +599 +01:05:33,990 --> 01:05:38,150 +الثلاثة على اتنين يبقى X بيضيف لل أس واحد بيظل + +600 +01:05:38,150 --> 01:05:42,690 +جديد سالب نص سالب تلاتة على اتنين زائد واحد بيظل + +601 +01:05:42,690 --> 01:05:49,990 +سالب نص مقسوما على سالب نص زائد constant C سالب نص + +602 +01:05:49,990 --> 01:05:57,850 +مع سالب نص بيظل X أس سالب نص زائد constant C خمسة + +603 +01:05:59,750 --> 01:06:10,610 +خمسة بدنا cosine لمين ل by x على اتنين زائد by في + +604 +01:06:10,610 --> 01:06:16,210 +cosine ال x بدنا ال antiderivative لها يبقى ال + +605 +01:06:16,210 --> 01:06:22,530 +antiderivative is تعالى تطلعلي لل cosine هذا ال + +606 +01:06:22,530 --> 01:06:27,380 +cosine عندنايبقى ال cosine اللي هو رقم تلاتة يبقى + +607 +01:06:27,380 --> 01:06:33,880 +واحد على كي في ال sign وين ال kn هنا باي على اتنين + +608 +01:06:33,880 --> 01:06:42,520 +يبقى واحد على باي على اتنين وهذه ال sign باي اكس + +609 +01:06:42,520 --> 01:06:50,680 +على اتنينهذه ال constant مالوش دعوة و cosine X هي + +610 +01:06:50,680 --> 01:06:56,920 +مين؟ sine X بقول زائد constant C لو قعدنا ترتيب + +611 +01:06:56,920 --> 01:07:04,760 +هيبقى وصير اتنين على باي sine باي X على اتنين زائد + +612 +01:07:04,760 --> 01:07:13,440 +باي في sine X زائد constant C طيب بدنا نيجي لستة + +613 +01:07:17,350 --> 01:07:26,090 +ستة اللي هو ناقص تلاتة على اتنين كو سي كان تربيع + +614 +01:07:26,090 --> 01:07:34,550 +لتلاتة اكس على اتنين بدنا ال ant derivative لها + +615 +01:07:34,550 --> 01:07:42,010 +يبقى ال ant derivative is سالب تلاتة على اتنين + +616 +01:07:42,010 --> 01:07:48,240 +مانوش دعوة ونرجع لمينالكثير كان تربية الكثير كان + +617 +01:07:48,240 --> 01:07:54,640 +تربية هي فوق يبقى سالب واحد على كيف الكتان يبقى + +618 +01:07:54,640 --> 01:08:04,630 +هذا نصف وهي سالب واحد على تلاتة على اتنينوهنا كتان + +619 +01:08:04,630 --> 01:08:11,410 +تلاتة X على اتنين زائد constant C سالب تلاتة على + +620 +01:08:11,410 --> 01:08:14,210 +اتنين في البسطة و سالب تلاتة على اتنين في المقام + +621 +01:08:14,210 --> 01:08:20,270 +مع السلامة يبقى بضالة ان بس جداش كتان تلاتة X على + +622 +01:08:20,270 --> 01:08:23,570 +اتنين زائد constant C + +623 +01:08:35,320 --> 01:08:47,800 +طيب نجي لها سبعة سبعة بدنا نسالي باي cos by x على + +624 +01:08:47,800 --> 01:08:57,000 +اتنين cot by x على اتنين برضه بدنا نجيب ال + +625 +01:08:57,000 --> 01:09:05,510 +antiderivative لهايبقى ال antiderivative is سالب + +626 +01:09:05,510 --> 01:09:11,510 +باي مالاش دعوة طلعليه هدى ال cosecant كتان هى ال + +627 +01:09:11,510 --> 01:09:15,570 +cosecant كتان يبقى سالب واحد على ك في مين في ال + +628 +01:09:15,570 --> 01:09:23,450 +cosecant يبقى سالب واحد باي على اتنين في مين + +629 +01:09:31,010 --> 01:09:36,270 +نختصر نقص مع نقص بتروح والبي مع تروح والاتنين + +630 +01:09:36,270 --> 01:09:42,350 +بتصير في ال bus يبجي اتنين كوسيكان باي اكس على + +631 +01:09:42,350 --> 01:09:52,010 +اتنين زائد constant c نمره تمانيةتمانية بدنا اربع + +632 +01:09:52,010 --> 01:10:00,950 +six تلاتة اكس تان تلاتة اكس يبقى ال antiderivative + +633 +01:10:00,950 --> 01:10:10,390 +الها is خد بالك هنا اربع مالاش دعوةتمام؟ وهذه الآن + +634 +01:10:10,390 --> 01:10:16,330 +سك فيه تان يعني عندي سك فيه تان يبقى واحد على ك في + +635 +01:10:16,330 --> 01:10:24,770 +سك يبقى واحد على تلاتة في سك تلاتة X زائد كل أسطن + +636 +01:10:24,770 --> 01:10:35,700 +C يعني أربع أتلات سك تلاتة X زائد كل أسطن Cزي ما + +637 +01:10:35,700 --> 01:10:39,780 +انت شايف هذا اليدر كله اعتمد على مشتقة الدوال + +638 +01:10:39,780 --> 01:10:45,300 +المثلثية الستة يبقى اللي عارف المشتقات بيلاقي هذا + +639 +01:10:45,300 --> 01:10:52,270 +كله كلام بسيط وحتى أبسط من البسيطولذلك إذا ما + +640 +01:10:52,270 --> 01:10:56,550 +أعطيتك الدواء المثلثية الستة جوجل تدير بالك، متكرر + +641 +01:10:56,550 --> 01:11:01,350 +معاك كتير في Calculus A و Calculus B و Calculus C + +642 +01:11:01,350 --> 01:11:06,250 +و في الفيزيا و ربما في الكيميا و ما إلى ذلك، إذا + +643 +01:11:06,250 --> 01:11:09,570 +لا يستغنى عنهم بتاتا + +644 +01:11:25,960 --> 01:11:31,220 +طيب نطور معلوماتنا حاجة وسيطة هيك ناخد هذا التعريف + +645 +01:11:31,220 --> 01:11:38,700 +و بعدين عليه شوية أمثلة يبقى definition the set of + +646 +01:11:38,700 --> 01:11:47,680 +all antiderivatives the set of all antiderivatives + +647 +01:11:47,680 --> 01:11:51,940 +of + +648 +01:11:53,100 --> 01:11:59,620 +دالة F is the + +649 +01:11:59,620 --> 01:12:02,140 +indefinite integral + +650 +01:12:24,830 --> 01:12:39,970 +بالنسبة ل X بالنسبة ل X and denoted by تكامل + +651 +01:12:39,970 --> 01:12:42,670 +لل F of X DX + +652 +01:12:47,590 --> 01:12:57,950 +ال F of X is called the integrand + +653 +01:12:57,950 --> 01:13:02,770 +and + +654 +01:13:02,770 --> 01:13:14,350 +X is the variable of integration + +655 +01:13:21,770 --> 01:13:27,730 +مثال واحد انتج + +656 +01:13:27,730 --> 01:13:35,070 +اتجارات + +657 +01:13:35,070 --> 01:13:37,470 +محدودة + +658 +01:13:51,900 --> 01:13:59,520 +أول واحدة من هذه التكاملات تكامل واحد ناقص X تربيع + +659 +01:13:59,520 --> 01:14:07,220 +ناقص تلاتة X أس خمسة كل بالنسبة إلى DX + +660 +01:14:39,260 --> 01:14:42,580 +يبقى اخر نقطة موجودة عندنا في هذا ال section اللي + +661 +01:14:42,580 --> 01:14:47,480 +هو موضوع التكامل غير المحدود طبعا عندنا انواعين من + +662 +01:14:47,480 --> 01:14:51,860 +انواع التكامل التكامل المحدود والتكامل غير المحدود + +663 +01:14:51,860 --> 01:14:56,570 +التكامل المحدود خليه لل chapter القادمالتكامل غير + +664 +01:14:56,570 --> 01:15:00,970 +المحدود مرتبط تماما بالانتي دريفتيف او كما قلنا + +665 +01:15:00,970 --> 01:15:06,150 +قبل قليل هو عبارة عن الانتي دريفتيف اذا انا باجي + +666 +01:15:06,150 --> 01:15:10,650 +بقول the set of all antiderivatives of الدلة F is + +667 +01:15:10,650 --> 01:15:14,950 +the indefinite integral of الدلة F with respect to + +668 +01:15:14,950 --> 01:15:21,080 +X and denoted by تكامل F of X DXطبعا ال + +669 +01:15:21,080 --> 01:15:25,120 +antiderivative لدالة F يكون capital F of X زائد + +670 +01:15:25,120 --> 01:15:29,620 +constant C يبقى هذا اللي هو ال general + +671 +01:15:29,620 --> 01:15:33,340 +antiderivative يبقى هذا هو التكامل تبع مين الدالة + +672 +01:15:33,340 --> 01:15:38,220 +يبقى كل ال antiderivatives لدالة في C هذا قد يكون + +673 +01:15:38,220 --> 01:15:43,490 +أرقام مختلفة إذا هذا بيكون كله عبارة عن مينالـ + +674 +01:15:43,490 --> 01:15:47,610 +Indefinite Integral أو التكامل غير المحدود للدلة F + +675 +01:15:47,610 --> 01:15:55,170 +بالنسبة للمتغير X وبديله الرمز تكامل F of X DX الـ + +676 +01:15:55,170 --> 01:16:00,810 +F of X is called the Integrand Integrand بالعربي + +677 +01:16:00,810 --> 01:16:07,950 +يعني الدلة المراد تكاملهايبقى f of x أدالة المرأة + +678 +01:16:07,950 --> 01:16:13,190 +التكامل الانتجرال و ال x هذا بنقول التكامل بنسبة + +679 +01:16:13,190 --> 01:16:16,650 +لمين ده المتغير x the variable of integration + +680 +01:16:16,650 --> 01:16:21,260 +قلوله المتغير تبع من تبع التكاملالان بدنا نبدأ + +681 +01:16:21,260 --> 01:16:24,240 +نشتغل زي الـ Antiderivative اللي توبس بدي اسميه من + +682 +01:16:24,240 --> 01:16:28,760 +هنا ورايا هي تكامل وانتقل الكل شوية يبقى قاللي + +683 +01:16:28,760 --> 01:16:33,360 +هاتليهاش التكاملات غير المحدودة التالية و بدلي + +684 +01:16:33,360 --> 01:16:38,060 +بأول تكامل تكامل لواحد ناقص X تربيع ناقص تلاتة X + +685 +01:16:38,060 --> 01:16:46,600 +أس خمسة DX يبقى باجي بقوله solutionهذا التكامل + +686 +01:16:46,600 --> 01:16:52,180 +عبارة عن تكامل واحد ناقص X تربيع ناقص تلاتة X أُس + +687 +01:16:52,180 --> 01:16:59,440 +خمسة DX يبقى بده يستوي هذا مقدار ثابت له واحد يبقى + +688 +01:16:59,440 --> 01:17:04,140 +هذا أصلا X أُس Zero لما مقدر فيه الا واحد بيصير X + +689 +01:17:04,140 --> 01:17:12,810 +أُس على يبقى X فقط لغايةنقص X تربي يعني X تكييب + +690 +01:17:12,810 --> 01:17:18,310 +على تلاتة ناقص تلاتة مالاش دعوة X أُس خمسة بيصير X + +691 +01:17:18,310 --> 01:17:24,990 +أُس ستة على ستة زائد كونستان C يبقى الجواب صار X + +692 +01:17:24,990 --> 01:17:32,470 +ناقص X تكييب على تلاتة تلاتة على ستة بيبقى نصف X + +693 +01:17:32,470 --> 01:17:40,150 +أُس ستة زائد كونستان C السؤال اللي بعدنمر اتنين + +694 +01:17:40,150 --> 01:17:50,570 +بدنا تكامل لخمس ناقص اتنين على اكس تكييب زائدي + +695 +01:17:50,570 --> 01:17:57,580 +اتنين اكس كل وين في دي اكسبقول له بسيطة يبقى انا + +696 +01:17:57,580 --> 01:18:02,500 +بتعيد ترتيب المثل أجيب المشتغل يبقى بالداجي أقول + +697 +01:18:02,500 --> 01:18:10,480 +له هذا integration لخمس نقصي اتنين X أس سالب تلاتة + +698 +01:18:10,480 --> 01:18:18,240 +زيدي اتنين X كله بالنسبة إلى DX بقول اه خمس مالوش + +699 +01:18:18,240 --> 01:18:24,920 +دعوة و بصير X أس واحد على واحد يبقى ب Xنقص اتنين + +700 +01:18:24,920 --> 01:18:29,680 +اكس بدي اضيف للأس واحد و اقسم للأس الجديد بصير + +701 +01:18:29,680 --> 01:18:34,780 +جداش سالي باتنين على الأس الجديد اللي هو السالي + +702 +01:18:34,780 --> 01:18:40,220 +باتنين زائدي اتنين اكس تربيه على اتنين زائد + +703 +01:18:40,220 --> 01:18:46,580 +constant C يبقى النتيجة اكس على خمسةنقص اتنين مع + +704 +01:18:46,580 --> 01:18:51,700 +نقص اتنين الله يسهل عليها يبقى X أساليب اتنين و + +705 +01:18:51,700 --> 01:18:56,200 +اتنين مع اتنين مع السلامة يبقى X تربية زائد + +706 +01:18:56,200 --> 01:19:05,240 +constant C سؤال التالت بدنا تكامل لمن؟ + +707 +01:19:05,240 --> 01:19:17,670 +ل X أساليب تلاتة في X زائد واحد في DXفيش حاجة اسمه + +708 +01:19:17,670 --> 01:19:21,950 +تكامل المقدار الأول ضرب تكامل المقدار الثاني يبقى + +709 +01:19:21,950 --> 01:19:29,610 +بدي أفكها و أشوف كيف بيصير هذه تكامل X أسالب اتنين + +710 +01:19:29,610 --> 01:19:35,930 +زائد X أسالب تلاتة كله في DXالآن بضيف الأس واحد + +711 +01:19:35,930 --> 01:19:42,850 +وبقسم على الأس الجديد يبقى هذا X أس سالب واحد على + +712 +01:19:42,850 --> 01:19:49,130 +سالب واحد زاد X أس سالب اتنين على سالب اتنين زاد + +713 +01:19:49,130 --> 01:19:56,850 +constant C أو سالب X أس سالب واحد سالب نص X أس + +714 +01:19:56,850 --> 01:20:03,650 +سالب اتنين زاد constant C أربع بدنا تكامل + +715 +01:20:06,200 --> 01:20:15,160 +للـ X في جذر الـ X زائد جذر الـ X كله على X تربيع + +716 +01:20:15,160 --> 01:20:20,040 +بالنسبالة دي X مافيش حاجة اسمها تكمل البسط على + +717 +01:20:20,040 --> 01:20:25,420 +تكمل المقام مافيش عنها ولا تكمل الطرف الأول في + +718 +01:20:25,420 --> 01:20:31,070 +تكمل الطرف الاياك و ثم اياكيبدأ يعيد الترتيب تبع + +719 +01:20:31,070 --> 01:20:36,710 +المثلة يبدأ يتكامن هذه x في x أُص نص يعني x أُص + +720 +01:20:36,710 --> 01:20:41,670 +جداش تلاتة على اتنين يبدأ هذا x أُص تلاتة على + +721 +01:20:41,670 --> 01:20:47,410 +اتنين زاد x أُص نص هذه لو طلعتها فهو تبصير x أُص + +722 +01:20:47,410 --> 01:20:53,490 +جداشأو لو أزعت ماعنديش مشكلة أسيان هذه و الله هذه + +723 +01:20:53,490 --> 01:21:00,610 +بدي أدخل هذه جوا الجوس يبقى بصير تكامل X أس سالب + +724 +01:21:00,610 --> 01:21:09,050 +نص زائد اللي هو X أس سالب تلاتة على اتنين كله في + +725 +01:21:09,050 --> 01:21:14,770 +DXتمام؟ إذا بدأ الكاميرا بضيف للأس واحد و أقسم على + +726 +01:21:14,770 --> 01:21:22,350 +الأس الجديد يبقى بيصير X أس نص على نص زاد X أس + +727 +01:21:22,350 --> 01:21:31,130 +ناقص نص على ناقص نص زاد constant C او اتنين جذر ال + +728 +01:21:31,130 --> 01:21:42,030 +X ناقص اتنين X أس سالب نص زاد constant Cسؤال + +729 +01:21:42,030 --> 01:21:48,770 +الخامس بدا تكامل لنص + +730 +01:21:48,770 --> 01:22:01,150 +في كثيكان تربيع ال X ناقص كثيكان ال X في كتان ال X + +731 +01:22:01,150 --> 01:22:07,730 +كل هذا الكلام بالنسبة إلى مين؟ إلى DXالمقدار + +732 +01:22:07,730 --> 01:22:11,770 +الثابت له دعرة؟ قال له ايش دعرة؟ يبقى يا ناص خلّيك + +733 +01:22:11,770 --> 01:22:19,710 +برا، بظهر لعنا، تكامل كوسيكا تربيعسالب كتان لإن + +734 +01:22:19,710 --> 01:22:23,550 +انتفاض كتان بسالب كوسيكانت تربيع إذا انتكمل + +735 +01:22:23,550 --> 01:22:30,310 +كوسيكانت تربيع بسالب كتان ال X نجي كوسيكانت كتان + +736 +01:22:30,310 --> 01:22:38,510 +بسالب كوسيكانت مع سالب بصير موجب اللي هو كوسيكانت + +737 +01:22:38,510 --> 01:22:46,430 +ال X كله زائد constant C ستة بدنا تكامل + +738 +01:22:49,740 --> 01:22:58,880 +للي اتنين زي التان تربيع ثيتا كله في دي ثيتا اه + +739 +01:22:58,880 --> 01:23:04,020 +هاد اللي ماخدناش اشوف ناشطة كامل تان تربيع ايه + +740 +01:23:04,020 --> 01:23:09,540 +اتفضل اتنين اصلا واحد زي دورها كويس كويس يبقى + +741 +01:23:09,540 --> 01:23:14,710 +اختراحواحد بيقول بدي أشيل اتنين و بدي أكتبها واحد + +742 +01:23:14,710 --> 01:23:18,330 +زائد واحد زائد تان تربيع و أشيل واحد زائد تان + +743 +01:23:18,330 --> 01:23:21,370 +تربيع و أحط بدل سك تربيع و بيقولوا والله كلها + +744 +01:23:21,370 --> 01:23:24,230 +مظبوط ميان ميان و واحد قال لي لأ لأ لأ انا بدي + +745 +01:23:24,230 --> 01:23:29,030 +أشيل تان تربيع و أحط بدل سك تربيع ناقص واحد مش هي + +746 +01:23:29,030 --> 01:23:32,170 +نفسها برضه يبقى سواء كان هادي والله هادي سيانة + +747 +01:23:32,170 --> 01:23:35,730 +ماتفرجش ان انا ليش سك تربية لإن السك تربية بعرف ال + +748 +01:23:35,730 --> 01:23:40,130 +antiderivative بس التان تربية بعرفوش تمامأذا هذه + +749 +01:23:40,130 --> 01:23:47,290 +لو روحت كتبتها على الشكل التالي تكامل اتنين زائد + +750 +01:23:47,290 --> 01:23:54,810 +تربية ثيتا ناقص واحد دي ثيتا يعني شيلت التان تربية + +751 +01:23:55,060 --> 01:24:00,760 +حطيت بدلها من المتطابقات المثلثية تعت شبتر one اها + +752 +01:24:00,760 --> 01:24:05,680 +section اللي هو واحد تلاتة حاطبها sector بيها ناقص + +753 +01:24:05,680 --> 01:24:13,580 +واحد بدل ان تكامل واحد زائد sector بيها ثيتا كله + +754 +01:24:13,580 --> 01:24:18,440 +في دي ثيتا تكامل واحد بثيتا وتكامل ال sector بيها + +755 +01:24:18,440 --> 01:24:28,490 +بتان ثيتا زائد constant Cطيب سبعة بدنا تكامل اللي + +756 +01:24:28,490 --> 01:24:36,130 +هو واحد ناقص كتان تربيع ثيتا كله في دي ثيتا + +757 +01:24:40,270 --> 01:24:45,270 +بختلف عن السؤال اللى قبله نفس الفكرة إذا باجي بقول + +758 +01:24:45,270 --> 01:24:51,550 +هذا الواحد مانوش ده وهي النقل كتان تربية لكسكن + +759 +01:24:51,550 --> 01:24:58,980 +تربية ثيتا ناقص واحد شكل ان كله في دي ثيتاهذا لو + +760 +01:24:58,980 --> 01:25:05,300 +فكت القوس بصير ناقص ناقص واحد بواحد واحد اتنين + +761 +01:25:05,300 --> 01:25:13,420 +يبقى بيصير تكامل لاتنين ناقص كوسيكا تربيع ثيتا في + +762 +01:25:13,420 --> 01:25:19,460 +دي ثيتا يبقى الجواب باتنين ثيتا وكوسيكا تربيع + +763 +01:25:19,460 --> 01:25:25,600 +بيصير زائد كتان ثيتا زائد constant C + +764 +01:25:27,860 --> 01:25:36,520 +سبعة هنا بنجي ليه تمانية تمانية تكامل ل cosecant + +765 +01:25:36,520 --> 01:25:43,200 +theta على مين؟ cosecant theta على cosecant theta + +766 +01:25:43,200 --> 01:25:51,480 +ناقص sin theta كله في دي theta cosecant + +767 +01:25:51,480 --> 01:25:55,740 +و sin بينفعش تخلي لونين في المثلة كلهم بتخليهم لون + +768 +01:25:55,740 --> 01:26:01,210 +واحدالـ cosecant هي مقلوب مين؟ مقلوب الـ sine يبقى + +769 +01:26:01,210 --> 01:26:10,410 +هذا تكامل واحد على sin θ واحد على sin θ نقص sin θ + +770 +01:26:10,410 --> 01:26:21,120 +كله في dθيبقى تكامل واحد على صين الثيتا يبقى + +771 +01:26:21,120 --> 01:26:29,180 +صين ثيتا يبقى واحد ناقص صين تربيه من الثيتا اظن ان + +772 +01:26:29,180 --> 01:26:35,020 +هذه دي ثيتا بيصير تكامل واحد على واحد ناقص صين + +773 +01:26:35,020 --> 01:26:38,820 +تربيه ثيتا دي ثيتا لو جلبنا الصين فوق بتطير مع + +774 +01:26:38,820 --> 01:26:43,870 +الصين اللي فوق بتظهر مثلا واحد ناقص صين تربيهكوصين + +775 +01:26:43,870 --> 01:26:51,310 +تربية يبقى تكامل 1 على كوصين تربية θ دي ثيتا + +776 +01:27:25,690 --> 01:27:32,390 +طيب نجي نكمل هذا الكلام يسمى تكامل كيف تكامل هذه + +777 +01:27:32,390 --> 01:27:42,730 +تكامل + +778 +01:27:42,730 --> 01:27:52,730 +تكامل تكامل تكامل تكامل تكامل + +779 +01:27:52,730 --> 01:27:54,330 +تكامل + +780 +01:27:57,670 --> 01:28:07,910 +تكامل X على الجذري التربيعي لتلاتة زائد X تربيع DX + +781 +01:28:25,200 --> 01:28:30,780 +بسيطة الشغل فيك جدا ميزم صعب المسألة الجدران بدي + +782 +01:28:30,780 --> 01:28:34,100 +اشيل اللي تحت الجدران و احطه باي variable جديد اذا + +783 +01:28:34,100 --> 01:28:41,360 +لو حطيتي T تساوي تلاتة زائد X ترمية يبقى D T تفضل + +784 +01:28:41,360 --> 01:28:48,070 +تلاتة بالزيرو واحد اتنين X DXبصير النص دي تي بدى + +785 +01:28:48,070 --> 01:28:52,190 +يساوي ال X DX إذا ال X DX بقدر أخيلها أو أكتملها + +786 +01:28:52,190 --> 01:29:00,910 +كده نص دي تي تاوية تمامة يبقى تكمل هذا نص وهذا دي + +787 +01:29:00,910 --> 01:29:06,640 +تي وهذا جذري تييبقى بدل المهم كالكة هيك كتبناها + +788 +01:29:06,640 --> 01:29:12,800 +بشكل قلطة يانص خليك برا مالكش دعوة ويتكامل تيوس نص + +789 +01:29:12,800 --> 01:29:17,820 +لو طلعتها بوجهي بصير تيوس جداش سالم نص في دي يبقى + +790 +01:29:17,820 --> 01:29:22,410 +صارت فرقة ولا لامش مستاهلة صارت يبقى هذا الكلام + +791 +01:29:22,410 --> 01:29:27,970 +يسوى نص مالكش دعوة و هذه T أص نص على نص زائد + +792 +01:29:27,970 --> 01:29:34,330 +constant C هذه مع هذه يبقى الجواب جذر ال T زائد + +793 +01:29:34,330 --> 01:29:40,630 +constant C بدي أشيل ال T و أحط متها ليه تلاتة زائد + +794 +01:29:40,630 --> 01:29:46,890 +X تربيع زائد constant C طيب + +795 +01:29:48,000 --> 01:29:58,460 +خدلي سؤال عشر تكامل لمن لكوصين تربيع لمن X على + +796 +01:29:58,460 --> 01:30:07,140 +أربعة X على أربعة DX في مرة علينا في الجدول توكو + +797 +01:30:07,140 --> 01:30:13,060 +ساين تربيع أو ساين تربيع في الشمكانية ولا سؤال + +798 +01:30:13,060 --> 01:30:22,250 +بسيط بحولها بدل لضعف الزاويةأحنا بنعرف أن تربيع X + +799 +01:30:22,250 --> 01:30:28,190 +يساوي نص في واحد زائد كوصين اتنين X، مظبوط؟ إذاً + +800 +01:30:28,190 --> 01:30:36,910 +هذه بدها تساوي تكامل ونص في واحد زائد كوصين اتنين + +801 +01:30:36,910 --> 01:30:43,060 +المقدار هذا يصير كم؟ X على اتنين DXيعني بدى اضرب + +802 +01:30:43,060 --> 01:30:46,700 +هدى فى اتنين هدى X هدى جده مرة تانى اضرب هدى فى + +803 +01:30:46,700 --> 01:30:51,660 +اتنين بصير X على مين على الاتنين بقوله يا نص خلّيك + +804 +01:30:51,660 --> 01:30:57,580 +برا مالكش دعوة وتكمل الواحد بقداش ب X وتكمل ال + +805 +01:30:57,580 --> 01:31:04,340 +cosine ب sine X على اتنين بدك تجسم على مين على + +806 +01:31:04,340 --> 01:31:10,090 +الزاوية اللى هى النصزائد constant C يبقى بناء عليه + +807 +01:31:10,090 --> 01:31:17,650 +الجواب مص ال X زائد نين تنجلة بتروح زائد sign X + +808 +01:31:17,650 --> 01:31:28,530 +على اتنين زائد constant C مثال رقم اتنين مثال + +809 +01:31:28,530 --> 01:31:33,350 +اتنين بسيط مش مثل النقطة واحدة مش كتير يبقى بيقول + +810 +01:31:33,350 --> 01:31:43,630 +برضه من الكتابةVerify اتأكد ان ذات تكامل تلاتة X + +811 +01:31:43,630 --> 01:31:52,590 +زائد خمسة قص ناقص اتنين DX بدل ساوي ناقص تلاتة X + +812 +01:31:52,590 --> 01:31:59,010 +زائد خمسة قص ناقص واحد على تلاتة زائد + +813 +01:32:03,070 --> 01:32:13,970 +تأكد انه تكامل هذا بده يساوي هذا ايش + +814 +01:32:13,970 --> 01:32:23,250 +رايكم؟ كيف بنا نثبت هذا الكلام؟ بدون ما أكاملممتاز + +815 +01:32:23,250 --> 01:32:28,090 +جدا يعني لو اشتقت هذه اللي على اليمين بده تطلع + +816 +01:32:28,090 --> 01:32:32,510 +اللي جوا هذه، مظبوط؟ اذا تعالوا نشتق هذه ونشوف + +817 +01:32:32,510 --> 01:32:40,750 +يفجأة انا بدي اقول له solution اها بدي اخد D على + +818 +01:32:40,750 --> 01:32:48,090 +DX لسالم 3X زائد 5 والسالم 1 على 3 زائد constant + +819 +01:32:48,090 --> 01:32:55,950 +CY سواءسالب تلث مالكش دعوة بعد هيك بجي بقول الأس + +820 +01:32:55,950 --> 01:33:02,390 +في القوس مرفوعة + +821 +01:33:02,390 --> 01:33:08,170 +لنفس الأس مطروح من واحد في مشتقة مداخل القوس مشتقة + +822 +01:33:08,170 --> 01:33:13,330 +مداخل القوس اللي هي كده؟ تلاتة تمام تمام ومشتقة + +823 +01:33:13,330 --> 01:33:20,310 +الـCزيرو لإنه constant بقول اه ناقص مع ناقص بزاد و + +824 +01:33:20,310 --> 01:33:25,510 +تلاتة مع تلاتة مع السلامة يبقى ضال الجواب تلاتة X + +825 +01:33:25,510 --> 01:33:34,790 +زاد خمسة أس ناقص اتنين هى هذه صح ولا لا يبقى هذه + +826 +01:33:34,790 --> 01:33:42,510 +لو سميتها المثلة star يبقى باجي بقوله star hold + +827 +01:33:42,510 --> 01:33:49,570 +صحيحةأخر مثال في هذا ال section بيقول لي ما يعطي + +828 +01:33:49,570 --> 01:33:54,630 +مثال تلاتة بيقول + +829 +01:33:54,630 --> 01:34:03,790 +لي find a curve find a curve بدنا منحنا y تساوي f + +830 +01:34:03,790 --> 01:34:16,290 +of x with true partiesله الخواص التالي ان دي + +831 +01:34:16,290 --> 01:34:26,170 +square y by دي x square بده يسوى ستة اكس و اتس + +832 +01:34:26,170 --> 01:34:40,330 +اجراف passes اتس اجراف passes اترا زيرو واحد + +833 +01:35:09,600 --> 01:35:17,060 +سؤال مرة تانيةبقول هاتلي شكل المنحنى Y كدالة في X + +834 +01:35:17,060 --> 01:35:21,460 +الذي له الخواص التالية خاصية الأولى مشتقة الثانية + +835 +01:35:21,460 --> 01:35:27,900 +اله تساوي 6X الرسم البياني اله يمر بهذه النقطة إذا + +836 +01:35:27,900 --> 01:35:33,010 +هذه النقطة تحقق المنحنىالخاصية التالتة انه + +837 +01:35:33,010 --> 01:35:37,310 +الهيروزينتال تانجنتال بنفس النقطة يعني المماس تبقى + +838 +01:35:37,310 --> 01:35:42,590 +يكون ماله أفوقيا بقوله بسيطة جدا نبدأ بالمعلومة + +839 +01:35:42,590 --> 01:35:48,170 +الأولى قال دي سكوير واي على دي اكس سكوير يساوي ستة + +840 +01:35:48,170 --> 01:35:53,830 +اكس اظن لو كملناها مرة بتروح المشتقة الثانية ويظل + +841 +01:35:53,830 --> 01:35:58,950 +بينا انها المشتقة الأولى يبقى باجي بقوله by + +842 +01:35:58,950 --> 01:36:00,290 +integration + +843 +01:36:02,630 --> 01:36:07,990 +بتكمل بيبقى عند مين دي y على دي x هذه بدها تساوي + +844 +01:36:07,990 --> 01:36:14,230 +ستة x تربيع على اتنين زائد constant وليكن c one + +845 +01:36:14,230 --> 01:36:23,390 +طيب يعني هذه بدها تساوي تلاتة x تربيع زائد c one + +846 +01:36:23,390 --> 01:36:31,140 +هذا مين مشتقل ايش راح جلي هناالمماس أفقي عند + +847 +01:36:31,140 --> 01:36:36,500 +النقطة 01 إذا من خلالها بقدر يجيب ال constant C1 + +848 +01:36:36,500 --> 01:36:45,870 +فبجي بقول له at النقطة 01 we haveيبقى الهيروزونتال + +849 +01:36:45,870 --> 01:36:51,570 +تانجلت يعني الاسلوب تبعه كده؟ بزيرو يبقى هذا + +850 +01:36:51,570 --> 01:36:57,230 +الاسلوب تبعه بزيرو هو dy على dx تمام؟ بده يساوي + +851 +01:36:57,230 --> 01:37:04,190 +مين؟ بده يساوي تلاتة في زيرو لكل تربيع زي كنصة C1 + +852 +01:37:04,190 --> 01:37:11,980 +يبقى بناء على C1 كده بده يساوي؟يبقى بناء على dy + +853 +01:37:11,980 --> 01:37:21,760 +على dx يبقى باس ثلاثة اكس مصدور طيب نروح كامل + +854 +01:37:21,760 --> 01:37:30,060 +لنطلب شكل ال y as a function of x بقوله الآن برضه + +855 +01:37:30,060 --> 01:37:32,060 +by integration + +856 +01:37:34,980 --> 01:37:40,360 +بالتكامل هذه تكاملها بقدرش يبقى Y هذه تكاملها + +857 +01:37:40,360 --> 01:37:46,080 +بقدرش يبقى تلاتة X تكييب ع تلاتة زائد كنص فانتاني + +858 +01:37:46,080 --> 01:37:54,740 +وليكن C2 يبقى هذه بدأت تساوي X تكييب زائد C2 ايش + +859 +01:37:54,740 --> 01:38:00,280 +راح جليه؟ جلي هذا الملحنة يمر بالنقطة هذه إذا باجي + +860 +01:38:00,280 --> 01:38:01,560 +بقوله at + +861 +01:38:05,960 --> 01:38:13,400 +يبقى ال Y بقداش واحد وC بقداش Zero زائد C اتنين + +862 +01:38:13,400 --> 01:38:19,080 +يبقى C اتنين بده يساوي قداش واحد يبقى المنحنة اللي + +863 +01:38:19,080 --> 01:38:26,080 +بده يا Y تساوي X كيب زائد واحد + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/KpIUQyUiT5o.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/KpIUQyUiT5o.srt new file mode 100644 index 0000000000000000000000000000000000000000..e352514bcc1bc385439a53a418859cb7ef5d0ce3 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/KpIUQyUiT5o.srt @@ -0,0 +1,3230 @@ +1 +00:00:21,180 --> 00:00:25,970 +بسم الله الرحمن الرحيم، ننتقل الآن لآخر كلمتين + +2 +00:00:25,970 --> 00:00:30,070 +قولناهم في المحاضرة الماضية، كنا بنتحدث على ال + +3 +00:00:30,070 --> 00:00:36,590 +piecewise function، يبقى الدالة المكونة من عدة قطع + +4 +00:00:36,590 --> 00:00:41,910 +أو من عدة أجزاء، واخدنا على ذلك ثلاثة أمثلة، وهذا هو + +5 +00:00:41,910 --> 00:00:46,550 +المثال الرابع والأخير إن شاء الله على ال piecewise + +6 +00:00:46,550 --> 00:00:50,530 +function، ثم بعدها ننتقل إلى نقطة أخرى + +7 +00:00:52,850 --> 00:00:58,450 +المثال الرقم أربعة بيقول find a formula، هات لصيغة + +8 +00:00:58,450 --> 00:01:02,590 +for the function with the corresponding graph، اللي + +9 +00:01:02,590 --> 00:01:07,750 +إلها الرسم المقابل، يكبر cross bonding مقابل graph + +10 +00:01:07,750 --> 00:01:12,270 +رسم، يكبر الرسم تبعها بالشكل المقابل، عندنا أيوة + +11 +00:01:12,270 --> 00:01:17,810 +بالشكل هذا، الشكل الغامق اللي عندنا هذا هيك، أيوة + +12 +00:01:17,810 --> 00:01:20,470 +وهنا بجيك الشكل اللي عندنا هذا + +13 +00:01:27,280 --> 00:01:37,160 +وهذا كذلك بشكل كويس + +14 +00:01:37,160 --> 00:01:43,220 +يبقى هذا اللي قدامنا مكونًا من كام جزء يا شباب؟ من + +15 +00:01:43,220 --> 00:01:47,540 +ثلاثة أجزاء، يبقى الحل يكون على الشكل التالي + +16 +00:01:47,540 --> 00:01:54,460 +solution، يبقى إحنا عندنا piecewise function مكونًا + +17 +00:01:54,460 --> 00:02:00,150 +من ثلاثة أجزاء، بنجي للجزء الأول، واضح إن إحداثية + +18 +00:02:00,150 --> 00:02:05,130 +النقطة هذه قداش؟ سالب واحد، واحد، يعني هذه لو جيت + +19 +00:02:05,130 --> 00:02:10,290 +نازل رأسي، بيكون إن هذا يعني سالب واحد، طيب هذا + +20 +00:02:10,290 --> 00:02:12,070 +الخط اللي بيبدأ من صفر + +21 +00:02:17,960 --> 00:02:25,320 +يبقى F of X يساوي كم؟ سالب X، يبقى هذا F of X يساوي + +22 +00:02:25,320 --> 00:02:32,600 +سالب X، وبشرط X أكبر من أو تساوي سالب واحد وأقل من + +23 +00:02:32,600 --> 00:02:38,780 +كم؟ من الـ Zero، على الفترة من سالب واحد لغاية Zero + +24 +00:02:38,780 --> 00:02:43,980 +هذا هو الجزء الأول، بدنا نيجي للجزء الثاني، إحداثيات + +25 +00:02:43,980 --> 00:02:49,920 +النقطة هذه قداش؟ واحد، واحد، يعني لو جيت نازل رأسي + +26 +00:02:49,920 --> 00:02:54,660 +هيك بيكون النقطة هذه قداش؟ واحد، يبقى الجزء الثاني + +27 +00:02:54,660 --> 00:02:58,620 +محصور من وين أو معرف على الفترة من وين لوين؟ من صفر + +28 +00:02:58,620 --> 00:03:03,990 +لواحد، طب قداش اللي هو معادلة هذا الخط؟ هذا أفقي + +29 +00:03:03,990 --> 00:03:10,530 +واحد، يعني Y تساوي واحد، يبقى هنا واحد، وبالشرط إن ال + +30 +00:03:10,530 --> 00:03:17,170 +X أكبر من ال zero ولا تساوي، لإن عند ال zero الدالة + +31 +00:03:17,170 --> 00:03:24,550 +غير معرفة وأقل من أو يساوي من ال واحد، يبقى بالشكل + +32 +00:03:24,550 --> 00:03:29,730 +اللي عندنا هذا، خلصنا الجزء الثاني هذا، يبقى كأنه ما + +33 +00:03:29,730 --> 00:03:34,730 +لم يبقى عندنا إلا من الجزء الثالث، يبقى الجزء + +34 +00:03:34,730 --> 00:03:40,230 +الثالث كذلك عبارة عن خط مستقيم، مشان أعرف معادلة + +35 +00:03:40,230 --> 00:03:46,730 +الخط المستقيم بلزمني ميله ونقطة واقعة عليه، تمام، + +36 +00:03:46,730 --> 00:03:52,350 +بدي أجيب ميله، يبقى عندي بدل نقطة نقطة نقطة، هذه + +37 +00:03:52,350 --> 00:03:59,060 +الإحداثيات تبعها كم؟ ثلاثة، صفر، وبالتالي بقدر أجيب ال + +38 +00:03:59,060 --> 00:04:04,820 +slope تبع الخط اللي عندنا هنا، فبجيب أقول في الها + +39 +00:04:04,820 --> 00:04:10,920 +مش هيك، ال slope اللي هو بديله الرمز M اللي هو + +40 +00:04:10,920 --> 00:04:17,340 +الميل يساوي فرق الصادات على فرق السينات، يبقى واحد + +41 +00:04:17,340 --> 00:04:24,350 +ناقص Zero على واحد ناقص ثلاثة، ويساوي جداته يساوي + +42 +00:04:24,350 --> 00:04:28,450 +السالب نص، يبقى الميل اللي عندنا وجدناه يساوي + +43 +00:04:28,450 --> 00:04:33,330 +السالب نص، الآن بدنا نقطة واقعة عليه، فبناخد نقطة مين؟ + +44 +00:04:33,330 --> 00:04:39,510 +واحد، واحد، سمعتوا بالخط المستقيم اللي هو معادلته Y + +45 +00:04:39,510 --> 00:04:48,880 +يساوي M في X ناقص X not زائد Y not، سكتوا الشباب، + +46 +00:04:48,880 --> 00:04:53,860 +ما سمعتوا مش فيه هذه؟ بلاش، هنجيب نفس المعادلة بس + +47 +00:04:53,860 --> 00:05:02,400 +بصيغة أخرى، أخذتوها إن ال Y ناقص Y not على X ناقص X + +48 +00:05:02,400 --> 00:05:08,180 +not يساوي الميل، هذه أخذتوها يعني، هذه هي هذه + +49 +00:05:09,280 --> 00:05:13,460 +بالضبط بالحرف الواحد، طب اضرب ضرب تبادل، يفجأة لو + +50 +00:05:13,460 --> 00:05:19,280 +ضربنا ضرب تبادل يصير Y ناقص Y not يساوي M في X + +51 +00:05:19,280 --> 00:05:23,860 +ناقص X not، ناقص Y not، هد على الشجة، هدف، تطلع + +52 +00:05:23,860 --> 00:05:27,980 +المعادلة، هدى، يفجأة المعادلة هدى، + +53 +00:05:27,980 --> 00:05:33,520 +الاثنين are the same، الاثنين نفس الشيء بتضبط تمامًا + +54 +00:05:34,650 --> 00:05:40,730 +يبقى بناء عليه المعادلة بصير Y يساوي الميل ناقص نص + +55 +00:05:40,730 --> 00:05:48,110 +في X ناقص واحد زائد واحد، أو إن شئتم فقولوا ناقص نص + +56 +00:05:48,110 --> 00:05:58,360 +X زائد نص زائد واحد، يعني إيه؟ يعني ناقص نص X ناقص + +57 +00:05:58,360 --> 00:06:06,020 +نص X زائد ثلاثة على اثنين، يبقى أصبح كأنه خط + +58 +00:06:06,020 --> 00:06:10,300 +المستقيم اللي كنا بنقوله في الإعدادي والثانوي، صارت + +59 +00:06:10,300 --> 00:06:16,510 +تساوي ألف سين زائد باء، مظبوط؟ الألف بيكون هو الميل + +60 +00:06:16,510 --> 00:06:20,510 +تبع الخط المستقيم وبقى طول الجزء المقطوع من محور + +61 +00:06:20,510 --> 00:06:27,950 +الصادات، إلا إننا هنقول المعادلة هذه أو هذه، أو ال Y + +62 +00:06:27,950 --> 00:06:35,410 +تساوي MX زائد B، يبقى هذه معادلة خط المستقيم في + +63 +00:06:35,410 --> 00:06:40,030 +ال general form، وهذه هعطيكم إياها في محاضرة اليوم + +64 +00:06:40,260 --> 00:06:45,800 +بعد قليل، إن هذه ليه معادلة خط المستقيم في صيغتها + +65 +00:06:45,800 --> 00:06:52,940 +أو في صورتها العامة، على أي حال هذه هذه هذه كلها + +66 +00:06:52,940 --> 00:06:58,400 +are the same، ال M هي الميل، باء أو ال B هو طول الجزء + +67 +00:06:58,400 --> 00:07:04,760 +المقطوع من محور Y أو من محور الصادات، ما رأيك إذا أخذت + +68 +00:07:04,760 --> 00:07:10,920 +النص عامل مشترك برة + +69 +00:07:10,920 --> 00:07:18,540 +يبقى عندك ثلاثة ناقص X، إذا الجزء الثالث يصبح نصه + +70 +00:07:18,540 --> 00:07:26,620 +بره وهنا ثلاثة ناقص X، و X محصورة ما بين الواحد و + +71 +00:07:26,620 --> 00:07:33,830 +بين من وبين الثلاثة، طبعًا اللحظة إن الواحد هنا + +72 +00:07:33,830 --> 00:07:40,710 +مكرر، كررتها والله، مسحتها بتفرقش عندنا، اثنين are + +73 +00:07:40,710 --> 00:07:45,370 +the same، يعني لو خلتها برضه مافيش مشكلة، لكن ماقدرش + +74 +00:07:45,370 --> 00:07:51,830 +أحط يساوي عند الثلاثة لإن هذا التجويف موجود على + +75 +00:07:51,830 --> 00:07:58,220 +الخط المستقيم، يبقى هي كتبنا شكل المعادلة من خلال + +76 +00:07:58,220 --> 00:08:02,960 +المعلومات اللي موجودة عندنا، أنا بدأ أسأل سؤال + +77 +00:08:02,960 --> 00:08:08,140 +زيادة، مشان نربط القديم بالجديد، لو سألتك قلت لك + +78 +00:08:08,140 --> 00:08:14,900 +قداش بالله domain الـF، علمًا إن ال domain هي مكتوب + +79 +00:08:14,900 --> 00:08:20,620 +قدامك على اللوح ومرسوم، بدي تقولي من كده إلى كده + +80 +00:08:20,620 --> 00:08:26,650 +أيضًا من سالب ثلاثة لغاية الواحد، مفتوح من عند + +81 +00:08:26,650 --> 00:08:32,050 +الثلاثة، وماعندي سالب واحد فقط، يعني كل الفترة هذه + +82 +00:08:32,050 --> 00:08:39,050 +بدون استثناء، آه، يعني برضه نشيل ال zero، ماشي، يبقى + +83 +00:08:39,050 --> 00:08:43,970 +ال domain بقوله الفترة من عند الناقص واحد لغاية + +84 +00:08:43,970 --> 00:08:51,210 +الثلاثة، مفتوحة ومغلقة، بدي أشيل منها ال zero as a + +85 +00:08:51,210 --> 00:08:57,190 +set، تمام؟ أو بذات صيغة صيغة أخرى، تقول لي من عندنا + +86 +00:08:57,190 --> 00:09:04,370 +ناقص واحد لغاية ال zero، اتحاد zero و ثلاثة as an + +87 +00:09:04,370 --> 00:09:09,390 +open interval، مافيش مشكلة، طيب بدنا نروح نجيب ال + +88 +00:09:09,390 --> 00:09:16,110 +range بتاعة الدالة F، يعني هتاخد قيم من وين لوين؟ + +89 +00:09:16,110 --> 00:09:17,370 +أيوة + +90 +00:09:20,050 --> 00:09:27,010 +من عند ال zero لغاية ما تفوتش أبدًا، يبقى من عند ال + +91 +00:09:27,010 --> 00:09:33,970 +zero مفتوحة، لأن هنا، هنا بتاخدش قيم، لغاية قداش؟ + +92 +00:09:33,970 --> 00:09:39,090 +لغاية الواحد، ومن عند الواحد مقفلة، لإن كل القيم + +93 +00:09:39,090 --> 00:09:44,620 +هذه وهذه كلها بواحد صحيح، يبقى هي جزء من ال domain + +94 +00:09:44,620 --> 00:09:49,580 +و ال range لهذه، زيادة معلومات زيادة على ما هو + +95 +00:09:49,580 --> 00:09:56,120 +مطلوب في المسألة، طيب لما نيجي لحاجة اسمها + +96 +00:09:56,120 --> 00:10:00,720 +increasing and decreasing function، دالة التزايد ودالة + +97 +00:10:00,720 --> 00:10:08,360 +التناقص، يبقى increasing and + +98 +00:10:08,360 --> 00:10:10,720 +decreasing + +99 +00:10:16,290 --> 00:10:21,230 +الدوال التزايدية والدوال التناقصية + +100 +00:10:27,650 --> 00:10:32,990 +الـ F بـ A function، نفترض إن الـ F عبارة عن دالة + +101 +00:10:32,990 --> 00:10:44,450 +defined، معرفة on an interval I، معرفة على فترة I + +102 +00:10:44,450 --> 00:10:52,810 +and let، وافترض إن ال X واحد وال X اثنين موجودة + +103 +00:10:52,810 --> 00:11:06,150 +في الفترة I، نمرة واحد، ال F of X2 is greater than F + +104 +00:11:06,150 --> 00:11:14,370 +of X1 whenever X1 + +105 +00:11:14,370 --> 00:11:16,910 +less than X2 + +106 +00:11:22,590 --> 00:11:32,070 +is said to be increasing، is said to be increasing + +107 +00:11:32,070 --> 00:11:35,490 +on + +108 +00:11:35,490 --> 00:11:48,750 +الفترة I، نمرة اثنين، F ال F of X اثنين أقل من f of x1 + +109 +00:11:48,750 --> 00:11:56,450 +whenever x1 أقل من x2، then f is said to be + +110 +00:11:56,450 --> 00:12:02,710 +decreasing on the interval I + +111 +00:12:09,770 --> 00:12:15,750 +لما نعود نقرأ التعريف من أول وجديد، نحاول نفهم هذا + +112 +00:12:15,750 --> 00:12:21,170 +التعريف، نرسم رسم توضيحي لمعنى هذا التعريف، حتى هذه + +113 +00:12:21,170 --> 00:12:25,450 +المعلومات تثبت في دماغنا، يبقى النقطة اللي دي لما + +114 +00:12:25,450 --> 00:12:29,390 +نتعرض لل increasing function and decreasing + +115 +00:12:29,390 --> 00:12:36,050 +function، الدالة التزايدية والدالة التناقصية، بيقول + +116 +00:12:36,050 --> 00:12:42,550 +افترض إن ال F هي دالة معرفة على فترة I، ولم أحدد هذه + +117 +00:12:42,550 --> 00:12:48,050 +الفترة closed ولا open ولا half closed ولا half + +118 +00:12:48,050 --> 00:12:52,430 +open، سيا أي فترة من الفترات، إيش ما تكون إيه تكون + +119 +00:12:52,430 --> 00:12:59,540 +ماعليهاش، قول، أخذت two elements X1 وX2 موجودين في + +120 +00:12:59,540 --> 00:13:06,920 +هذه الفترة، بقول والله إذا كان f of x2 أكبر من f of + +121 +00:13:06,920 --> 00:13:17,060 +x1، علمًا إن x1 أقل من x2، إن حدث ذلك، يبقى الدالة دالة + +122 +00:13:17,060 --> 00:13:21,560 +تزايدية على + +123 +00:13:21,560 --> 00:13:22,840 +الفترة I + +124 +00:13:27,550 --> 00:13:35,230 +نمرة اثنين، إذا ال F of X2 أقل من F of X1 لما ال X1 + +125 +00:13:35,230 --> 00:13:41,410 +أقل من X2، يبقى دالة بتقول عليها نمالة، دالة تناقصية + +126 +00:13:41,410 --> 00:13:46,450 +دالة decreasing على الفترة اللي عندنا هذه، طب تعالَ + +127 +00:13:46,450 --> 00:13:51,070 +نشوف هذا الكلام على الطبيعة، حتى هذا المفهوم يرسخ + +128 +00:13:51,070 --> 00:13:58,290 +في دماغنا، فمثال، لو جتخدت محاور، كنت هذا محور X وهذا + +129 +00:13:58,290 --> 00:14:05,510 +محور Y، وهذه نقطة الأصل اللي عندنا، وروحت رسمت منحنى + +130 +00:14:05,510 --> 00:14:11,490 +دالة بأي طريقة كانت، فطلعت الدالة بالشكل اللي عندنا + +131 +00:14:11,490 --> 00:14:20,270 +هذا، يبقى هذه اللي هي منحنى الدالة Y تساوي F of X + +132 +00:14:21,110 --> 00:14:26,670 +الدالة هذه معرفة على الفترة من عند النقطة هذه مثلًا + +133 +00:14:26,670 --> 00:14:32,170 +لغاية من لغاية النقطة هذه، يبقى هذه الفترة اللي + +134 +00:14:32,170 --> 00:14:37,930 +عندنا I، بغض النظر هل هي مفتوحة مغلقة نصف مفتوحة + +135 +00:14:37,930 --> 00:14:44,920 +نصف مغلقة، ما بتفرق عندنا، روحنا أخدنا أي نقطتين موجودتين + +136 +00:14:44,920 --> 00:14:50,080 +على ال interval اللي عندنا هذه، نفترض إنه كان هذه + +137 +00:14:50,080 --> 00:14:57,080 +هي النقطة الأولى X1، وهذه النقطة الثانية هي X2، يبقى + +138 +00:14:57,080 --> 00:15:05,480 +من اللي أصغر X1 ولا X2؟ X1 أصغر، يبقى هذه X1 أقل من + +139 +00:15:05,480 --> 00:15:13,440 +X2، تعالى نشوف قيم الدالة عند هتين النقطتين، جيت هنا + +140 +00:15:13,440 --> 00:15:19,460 +على المسافة اللي عندنا هذه هيك، فكانت هذه F of X + +141 +00:15:19,460 --> 00:15:25,340 +واحد، جيت على قيمة الدالة هنا، وجيت طالع لجيت هذه + +142 +00:15:25,340 --> 00:15:33,500 +مين f of x2؟ من اللي أكبر؟ من خلال الرسم واضح إن f of + +143 +00:15:33,500 --> 00:15:41,480 +x2 مسافة من هنا لهنا أكبر من f of x1، يبقى إذا f of + +144 +00:15:41,480 --> 00:15:47,950 +x2 أكبر من f of x1 لما اكس واحد أقل من اكس اثنين + +145 +00:15:47,950 --> 00:15:52,190 +يبقى الدالة زي ما أنت شايف طالعة تزايدية، أو سهل + +146 +00:15:52,190 --> 00:15:56,930 +عليها من هنا أقول إن الدالة هذه مالها؟ increasing + +147 +00:15:56,930 --> 00:16:02,610 +function، يبقى هذه الدالة بسميها increasing + +148 +00:16:02,610 --> 00:16:10,710 +function، يبقى هذه الدالة تزايدية، لكن لو جيت قلت + +149 +00:16:10,710 --> 00:16:18,060 +هاه المحاور، هذا محور X وهذا محور Y وهذه نقطة الأصل + +150 +00:16:18,060 --> 00:16:23,600 +و روحت رسمت منحنى الدالة بقدر الله، طلع منحنى + +151 +00:16:23,600 --> 00:16:30,460 +الدالة عندك على الفترة اللي عندنا هذه اللي هي اللي + +152 +00:16:30,460 --> 00:16:36,120 +سميها الفترة I، من عند النقطة هذه لغاية أهم النقطة + +153 +00:16:36,120 --> 00:16:41,730 +هذه، لاحظوا في اللي قبلها أخدت X سالبة لإنها قبل ال 0 + +154 +00:16:41,730 --> 00:16:46,950 +وهنا X2 موجبة، يجب أن يكون X1 نيجاتيف و X2 + +155 +00:16:46,950 --> 00:16:51,250 +بوزيتيف، يجب أن يكون بمانت، هذه أقل من هذه، هنا بدأ + +156 +00:16:51,250 --> 00:16:55,810 +أخدتهم اثنتين بالسالب، اثنتين بالموجبة، ليس بالضرورة + +157 +00:16:55,810 --> 00:17:02,320 +مرة سالبة ومرة موجبة، افترضنا أخدت النقطة هذه x1 + +158 +00:17:02,320 --> 00:17:09,660 +وأخدت النقطة الثانية هذه x2، يبقى x1 هي المسافة + +159 +00:17:09,660 --> 00:17:15,060 +الصغيرة هذه، وx2 هي المسافة الكبرى اللي عندنا هذه + +160 +00:17:15,400 --> 00:17:21,640 +يبقى مضمون إن X1 ماله؟ أقل من X2، اللي هو ال term + +161 +00:17:21,640 --> 00:17:27,780 +اللي عندنا هذا، يبقى أي X1 أقل من X2 بدي أروح أشوف + +162 +00:17:27,780 --> 00:17:36,900 +F of X1 و F of X2، طلعنا رأسي هيك فكان هذه F of X1 + +163 +00:17:37,690 --> 00:17:44,670 +هنا طلعنا رأسي كمان بالشكل هذا، فصار هذه F of X2 + +164 +00:17:44,670 --> 00:17:53,230 +يبقى مين اللي أصغر فيهم؟ F of X2 أصغر من F of X1 و + +165 +00:17:53,230 --> 00:18:00,970 +X1 كذلك أصغر من X2، يبقى لما تبقى ال X1 أقل من X2 + +166 +00:18:00,970 --> 00:18:07,220 +فإن ال F of X2 أقل، إن حدث ذلك، يبقى الدالة + +167 +00:18:07,220 --> 00:18:10,380 +التناقصية + +168 +00:18:10,380 --> 00:18:18,420 +يبقى هادي decreasing function، دالة تناقصية، اللاحظ + +169 +00:18:18,420 --> 00:18:24,620 +إن ال condition هذا لم يتغير في الحالتين، يعني ال + +170 +00:18:24,620 --> 00:18:31,040 +domain لم يتغير، يبقى لا تغير من قيمتين اللي موجودة + +171 +00:18:31,040 --> 00: + +201 +00:22:23,000 --> 00:22:33,050 +بالشكل هذا يبقى إذن Y يساوي نصف X تكعيب ارسم رسمتنا + +202 +00:22:33,050 --> 00:22:39,350 +المطلوب الثاني فترات التزايد وفترات التناقص السؤال + +203 +00:22:39,350 --> 00:22:46,390 +الآن للحدود بدنا نعرف وين فترات التزايد للدالة وين + +204 +00:22:46,390 --> 00:22:52,200 +فترات التناقص لهذه الدالة هل الدالة تزايدية على + +205 +00:22:52,200 --> 00:22:56,600 +طول؟ أو هل الدالة تناقصية على طول؟ أيوه يا أخي + +206 +00:22:56,600 --> 00:23:03,960 +العرب زي دائماً تسكر لما نهاني أيوة أنت آه آه أيوه + +207 +00:23:03,960 --> 00:23:10,920 +تناقصة من سالب ما لا نهاية يعني الدالة تناقصية من + +208 +00:23:10,920 --> 00:23:17,500 +سالب infinity إلى ما لا نهاية و لا تزايدية مش سالة كويس من + +209 +00:23:17,500 --> 00:23:18,860 +سالب infinity إلى infinity ايش؟ + +210 +00:23:31,990 --> 00:23:37,130 +تعال نشوف الكلام اللي بيحكي هذا أو يدعيه صح ولا + +211 +00:23:37,130 --> 00:23:42,750 +خطأ بيقول زميلكم شو اسمك أنت؟ عبدالهادي؟ + +212 +00:23:45,490 --> 00:23:50,850 +عبدالهادي زميلي بيقول ما يأتي بيقول من سالب + +213 +00:23:50,850 --> 00:23:56,430 +infinity لغاية ال zero decreasing و من عند ال zero + +214 +00:23:56,430 --> 00:24:02,680 +لغاية infinity increasing هكذا يزعم تمام؟ بدنا نشوف + +215 +00:24:02,680 --> 00:24:07,880 +هل الزعم هذا جاي من الضمانة يعني متأكدة الكلام مئة + +216 +00:24:07,880 --> 00:24:12,760 +المئة والله الزعم احتمال يكون صدق واحتمال يكون + +217 +00:24:12,760 --> 00:24:17,400 +ما هو صدق تعال نشوف بدنا نطبق التعريف اللي عندنا + +218 +00:24:17,400 --> 00:24:20,580 +هنا يبقى خلينا نيجي على الفترة الأولى اللي قال + +219 +00:24:20,580 --> 00:24:28,020 +فيها هذه تناقصية إذا بدي أخذ قيمتين X واحد وقيمة + +220 +00:24:28,020 --> 00:24:34,320 +ثانية X اثنين يبقى عشان دي X واحد أقل من X اثنين + +221 +00:24:34,320 --> 00:24:40,060 +صحيح ولا لأ؟ لأنه ناقص ثلاثة أقل من ناقص اثنين + +222 +00:24:40,060 --> 00:24:45,340 +صحيح ولا لأ؟ يبقى بدي أنزل رأسي لغاية مقابل + +223 +00:24:45,340 --> 00:24:51,580 +المنحنى ومن هنا بدي أنزل رأسي لغاية مقابل المنحنى + +224 +00:24:51,580 --> 00:25:00,880 +من اللي أصغر هذه والله هذه آه هذه أصغر يعني f of x2 + +225 +00:25:00,880 --> 00:25:09,920 +أكبر من f of x1 لأن ناقص واحد وناقص عشرة ناقص واحد + +226 +00:25:09,920 --> 00:25:18,110 +أكبر من ناقص عشرة تمام يبقى f of x2 أكبر من f of x + +227 +00:25:18,110 --> 00:25:23,090 +واحد ده ما x واحد أقل من x اثنين أكبر يعني مشي + +228 +00:25:23,090 --> 00:25:29,710 +الثاني هو إنما من يبقى زعمه اللي زعمه خطأ تمام؟ + +229 +00:25:29,710 --> 00:25:34,190 +طبعاً هو جالك ايش؟ جالك ناقص عشرة أكبر من ناقص واحد + +230 +00:25:34,190 --> 00:25:39,930 +وبناء عليه زعم هذا الزعم مظبوط؟ يبقى يا عبدالهادي + +231 +00:25:40,210 --> 00:25:45,850 +ناقصة عشرة أصغر من ناقص واحد وأصغر من ناقص اثنين + +232 +00:25:45,850 --> 00:25:51,330 +وأصغر من ناقص ثمانية تمام إذا بصير الفترة من سالب + +233 +00:25:51,330 --> 00:25:54,810 +infinity إلى zero increasing ولا decreasing + +234 +00:25:56,780 --> 00:26:01,420 +increasing والجزء اللي على اليمين باصمين لك عليه + +235 +00:26:01,420 --> 00:26:07,740 +الدالة تزايدية كل ما تكبر x بالزيادة قيمة y أو + +236 +00:26:07,740 --> 00:26:12,520 +بالزيادة قيمة f من هنا الدالة هذه increasing على + +237 +00:26:12,520 --> 00:26:19,680 +كل الـ real line بلا ستة يبقى هنا بقوله if is + +238 +00:26:19,680 --> 00:26:21,960 +increasing + +239 +00:26:23,080 --> 00:26:28,580 +هو إن الفترة من سالب infinity لإنفينيتي كلها + +240 +00:26:28,580 --> 00:26:34,980 +باستثناء ما عنديش decreasing بالمرة طيب نيجي لنمرة + +241 +00:26:34,980 --> 00:26:43,320 +B وما أدرك ما هي نمرة B ايه نمرة B طلع عليه كويس f of + +242 +00:26:43,320 --> 00:26:52,460 +x بده يساوي سالب واحد على absolute value لـ x هذه + +243 +00:26:52,460 --> 00:27:01,160 +تساوي أحد أمرين يا إما السالب واحد على x لما الـ x + +244 +00:27:01,160 --> 00:27:05,560 +أكبر من Zero أو تساوي + +245 +00:27:12,580 --> 00:27:19,920 +لسالب يعني صارت واحد على x لما الـ x مالها أقل من + +246 +00:27:19,920 --> 00:27:26,180 +Zero مظبوط ولا لا؟ صحيح؟ يعني أنا بس شيلت الـ + +247 +00:27:26,180 --> 00:27:30,780 +absolute value و حطيته تاريخ بصير سالب سالب بصير + +248 +00:27:30,780 --> 00:27:36,400 +موجبة بقى تمام؟ طيب بدنا نيجي نرسم رسمتنا هذه هي + +249 +00:27:36,400 --> 00:27:43,020 +المحاور وهذا محور x وهذا محور y هذه نقطة الأصل + +250 +00:27:43,020 --> 00:27:49,280 +الهيمان Zero رسمة واحد على x يجب أن أرسمها قبل + +251 +00:27:49,280 --> 00:27:57,360 +إشارة السالب قبل إشارة السالب يبقى هيها هيك هيها + +252 +00:27:57,360 --> 00:28:05,280 +هيك يبقى المنقطة هذه رسمة من؟ واحد على x فقط لا + +253 +00:28:05,280 --> 00:28:11,640 +غير مش هذا سؤالنا، احنا سؤالنا واحد على absolute + +254 +00:28:11,640 --> 00:28:16,160 +value of x لما أقول absolute value of x يبقى بطل + +255 +00:28:16,160 --> 00:28:21,140 +يصير عندي سالب، ايش بيصير؟ موجب، يعني هذا الجثة + +256 +00:28:21,140 --> 00:28:27,500 +ايش بده يحصل له؟ بده ينقلب ويصير فوق يبقى لو جيت هيك + +257 +00:28:27,500 --> 00:28:33,500 +بالشكل اللي عندنا هنا بده يصير هذا مع هذا هو رسمة + +258 +00:28:33,500 --> 00:28:39,560 +واحد على absolute value of x يبقى المنحنى فوق هذا + +259 +00:28:39,560 --> 00:28:45,080 +رسمة واحد على absolute value of x مش هذا سؤالنا + +260 +00:28:45,080 --> 00:28:50,340 +سؤالنا السالب واحد على absolute value of x يعني + +261 +00:28:50,340 --> 00:28:54,960 +أنا بأضرب الدالة كلها في إشارة يعني اللي كان في + +262 +00:28:54,960 --> 00:28:59,120 +قيمة موجبة ما بدها تصير سالبة، و اللي كانت سالبة، + +263 +00:28:59,120 --> 00:29:04,300 +يبقى احنا هذه جلبناها و صارت فوق، يبقى ما بقالش + +264 +00:29:04,300 --> 00:29:09,260 +عندي تحت ولا حاجة، كل الدالة صارت فوق، سبقت بإشارة + +265 +00:29:09,260 --> 00:29:15,880 +من، تنقلب كلها وصير وين؟ وصير تحت، يبقى بدها تصير + +266 +00:29:15,880 --> 00:29:18,840 +الخط المتواصل هذا + +267 +00:29:22,190 --> 00:29:29,690 +ومن هنا بنفس الطريقة هيك هذا y تساوي سالب واحد على + +268 +00:29:29,690 --> 00:29:35,470 +absolute value of x تمام؟ يبقى هيئة سمن الدالة + +269 +00:29:35,470 --> 00:29:40,310 +اللي عندنا هذه قبل ما أجاوب على باقي السؤال اللي خاطر + +270 +00:29:40,310 --> 00:29:46,570 +أسأله السؤال التالي قداش domain هذه الدالة؟ من + +271 +00:29:46,570 --> 00:29:54,510 +وين؟ أيوة رمى عدى زيرو موافقين يبقى الـ domain + +272 +00:29:54,510 --> 00:29:59,470 +من سالب infinity لـ infinity عدى الـ zero طب بدنا + +273 +00:29:59,470 --> 00:30:07,190 +نيجي للـ range الـ range هاي هاج قدامك اصطلع فيه بدي + +274 +00:30:07,190 --> 00:30:14,590 +واحد من الشجرة هذه أيوة أيوة من سالب مفتوح يعني من + +275 +00:30:14,590 --> 00:30:22,080 +السالب ما لا نهاية يعني من سالب infinity إلى zero as an + +276 +00:30:22,080 --> 00:30:26,220 +open interval يبقى الـ domain كل الـ real numbers عدى الـ zero + +277 +00:30:26,220 --> 00:30:32,080 +لأن عند Zero تنزل لسالب Infinity تمام هذا الـ + +278 +00:30:32,080 --> 00:30:37,160 +domain الـ range بتاخدش قيم موجبة إنما بس القيم + +279 +00:30:37,160 --> 00:30:41,300 +السالبة اللي أسفل عندنا يبقى من عند السالب + +280 +00:30:41,300 --> 00:30:46,360 +Infinity لغاية من Zero يبقى هذا السؤال زيادة على + +281 +00:30:46,360 --> 00:30:51,340 +ما هو مطلوب أجبنا عليه ربطناه بأول نقطة أخذناها في + +282 +00:30:51,340 --> 00:30:55,550 +هذا section وهي الـ domain والـ Range فبدأ نكمل + +283 +00:30:55,550 --> 00:31:00,350 +سؤالنا Orson رسمنا قال لي هاتلي فترات التزايد + +284 +00:31:00,350 --> 00:31:06,970 +وفترات التناقص لهذه الدالة امسكولي الفترة من سالب + +285 +00:31:06,970 --> 00:31:13,350 +infinity لغاية ال zero بدي أعرف الدالة increasing و + +286 +00:31:13,350 --> 00:31:18,710 +والله decreasing يلا بدي واحد من الشجرة هذه يلا + +287 +00:31:18,710 --> 00:31:27,780 +شوف يلا أنتو القوم الكبير أيوة هذه واحد، اثنين و + +288 +00:31:27,780 --> 00:31:32,800 +نصف، ثلاثة، آه هذه أو هذه أو هذه أو هذه أو هذه أو + +289 +00:31:32,800 --> 00:31:33,800 +هذه أو هذه أو هذه أو هذه أو هذه أو + +290 +00:31:33,800 --> 00:31:36,220 +هذه أو هذه أو هذه أو هذه أو هذه أو + +291 +00:31:36,220 --> 00:31:36,400 +هذه أو هذه أو هذه أو هذه أو + +292 +00:31:36,400 --> 00:31:36,500 +هذه أو هذه أو هذه أو + +293 +00:31:36,500 --> 00:31:38,340 +هذه أو هذه أو هذه أو + +294 +00:31:38,340 --> 00:31:38,560 +هذه أو هذه أو هذه أو + +295 +00:31:39,470 --> 00:31:43,670 +Increasing ولا Decreasing؟ Decreasing كان عكسيا، + +296 +00:31:43,670 --> 00:31:49,730 +الكلام مصحح، ليش؟ لأن الوقت أخذ أي x هنا واحد و + +297 +00:31:49,730 --> 00:31:59,810 +أي x2 هنا تمام؟ x1 أجل من x2 لكن f of x2 أجل من f + +298 +00:31:59,810 --> 00:32:07,230 +of x1 يبقى على الفترة هذه Decreasing on + +299 +00:32:08,410 --> 00:32:14,490 +من سالب infinity لغاية zero as an open interval + +300 +00:32:14,490 --> 00:32:20,950 +طيب بدنا نيجي من zero لغاية infinity من هنا للاخر + +301 +00:32:20,950 --> 00:32:26,970 +بدنا واحد مش شجرة دي أيوة decrease برضه تناقصية + +302 +00:32:26,970 --> 00:32:34,410 +يعني + +303 +00:32:34,410 --> 00:32:42,450 +اسمع يا شباب شو اسمك أنت يا ابني محمد .. محمد ايش؟ + +304 +00:32:42,450 --> 00:32:48,910 +محمد رمزي، بنا نرمز لنصف اليمين تبع الدالة، هل هو + +305 +00:32:48,910 --> 00:32:52,830 +increasing ولا decreasing؟ اعتبر حاجتك، ما قلتش + +306 +00:32:52,830 --> 00:32:56,810 +قبل ذلك، تقول من جديد، + +307 +00:32:56,810 --> 00:32:58,210 +بس هيمشي شويه الشباب + +308 +00:33:01,140 --> 00:33:09,200 +يعني لو أخذت x واحد و أنا x اثنين بصير f of x + +309 +00:33:09,200 --> 00:33:16,740 +اثنين أكبر من f of x واحد لأن كله هذا تابع يبقى + +310 +00:33:16,740 --> 00:33:21,760 +الجزء هذا ماله increasing function يبقى على المص + +311 +00:33:21,760 --> 00:33:29,500 +هذا بقول increasing ده تزايدية على الفترة من zero + +312 +00:33:29,500 --> 00:33:31,380 +لغاية infinity + +313 +00:33:54,740 --> 00:34:00,980 +طيب هذا نمرة B من المثلة بدنا نيجي لنمرة C يبقى + +314 +00:34:00,980 --> 00:34:08,660 +نمرة C نمرة الـ C تبدأ لمكونة من جزئين يبقى عندنا f + +315 +00:34:08,660 --> 00:34:15,120 +of x أحد أمرين يا إما ناقص x لما الـ x أقل من الـ + +316 +00:34:15,120 --> 00:34:19,480 +Zero يا إما ثلاثة لما الـ x greater than or equal + +317 +00:34:19,480 --> 00:34:24,920 +to Zero بدنا نروح نرسم الرسم البياني لهذه الـ + +318 +00:34:24,920 --> 00:34:30,340 +function يعني هذا محور x وهذا محور y وهذا نقطة + +319 +00:34:30,340 --> 00:34:32,280 +الأصل اللي هي Zero + +320 +00:34:38,090 --> 00:34:43,170 +خط مستقيم x أقل من Zero + +321 +00:34:48,520 --> 00:34:54,880 +تساوي سالب x ومن هنا مالها مفتوحة لأن ما عنديش + +322 +00:34:54,880 --> 00:35:02,400 +يساوي تمام يبقى هذه y تساوي سالب x نيجي لغاية بعد + +323 +00:35:02,400 --> 00:35:08,250 +الـ zero الدالة دائماً وأبداً مش ساوية قداش وكذلك عند + +324 +00:35:08,250 --> 00:35:13,090 +الـ Zero بدأ يساوي ثلاثة يبقى ثلاثة بدنا نطلع فوق + +325 +00:35:13,090 --> 00:35:19,230 +هي النقطة هذه ثلاثة يبقى الخط المستقيم اللي عندنا + +326 +00:35:19,230 --> 00:35:26,690 +هذا يبقى هذا y يساوي ثلاثة قبل ما نجاوب على الجزء + +327 +00:35:26,690 --> 00:35:31,830 +الثاني برضه لخاطر أسأل على domain هذه الدالة من و + +328 +00:35:31,830 --> 00:35:39,560 +لا وين بده domain الدالة هذه قداش؟ كل الـ real numbers كلامه + +329 +00:35:39,560 --> 00:35:45,980 +صحيح بلا استثناء of all real numbers بدنا الـ range + +330 +00:35:45,980 --> 00:35:52,660 +الـ range من وين + +331 +00:35:52,660 --> 00:35:58,920 +لوين تاني الـ range مش الـ domain الـ range + +332 +00:36:06,230 --> 00:36:13,750 +أيوه بس من صفر لثلاثة بزيدش هذا + +333 +00:36:13,750 --> 00:36:19,210 +الخط أنا راجع لسالب x لسالب Infinity وهو طالع + +334 +00:36:19,210 --> 00:36:22,690 +والله سهل عليه بوقف عندي الثلاث و والله بضل طالع + +335 +00:36:22,690 --> 00:36:26,490 +يعني + +336 +00:36:26,490 --> 00:36:27,370 +قداش بصير + +337 +00:36:33,800 --> 00:36:42,280 +من صفر لسالب Infinity تحت؟ أيوه، + +338 +00:36:42,280 --> 00:36:46,420 +من وين؟ من zero لـ infinity، كيف نزلت لسالب + +339 +00:36:46,420 --> 00:36:50,360 +Infinity؟ طبعاً احنا طالعين فوق الـ Domain سالب ماشي + +340 +00:36:50,360 --> 00:36:54,520 +الحال، بس الـ Ring طالع فوق، هي رسم الخط المستقيم + +341 +00:36:54,520 --> 00:36:59,000 +والله يسهل عليه، ماشي، ماشي، ماشي، إلى أن يرث الله + +342 +00:36:59,000 --> 00:37:03,520 +الأرض ومن عليها، وماشي، موقفش، تمام؟ يبقى لحد وين + +343 +00:37:03,520 --> 00:37:09,000 +رايح؟ لسالب Infinity ولا لـInfinity؟ احكي يا ابني + +344 +00:37:09,000 --> 00:37:13,400 +ايه؟ طلع الـ y هذه اللي يبقى لـ Infinity يبقى + +345 +00:37:13,400 --> 00:37:19,040 +من zero لـ Infinity من عند الـ zero open و من عند الـ + +346 +00:37:19,040 --> 00:37:22,440 +Infinity open و هذا الطبيعي يبقى الـ range من zero لـ + +347 +00:37:22,440 --> 00:37:28,260 +Infinity as an open interval عمره ما ياخذ قيمة سالبة + +348 +00:37:28,560 --> 00:37:32,880 +طيب ماشي الحل مادام هيك بدنا نعيد لك السؤال ثاني + +349 +00:37:32,880 --> 00:37:37,840 +أنت أيوه من سالب Infinity لغاية الـ zero الجزء + +350 +00:37:37,840 --> 00:37:45,280 +الأول اتدال عليه increasing ولا decreasing خط + +351 +00:37:45,280 --> 00:37:50,720 +اللي نازل هذا من فوق و رايح على النقطة الأصل كيف؟ + +352 +00:37:50,720 --> 00:37:59,430 +مش سامع كويس يبقى هنا هذا decreasing function يبقى + +353 +00:37:59,430 --> 00:38:08,470 +الـ f is decreasing on الـ interval من سالب Infinity + +354 +00:38:08,470 --> 00:38:11,790 +لغاية الـ zero طب بعد الـ zero + +355 +00:38:15,720 --> 00:38:20,640 +يعني ايش؟ يعني ثابت، يعني increasing و decreasing + +356 +00:38:20,640 --> 00:38:27,560 +في نفس الوقت؟ يعني يا جيربي، تبقى increasing و + +357 +00:38:27,560 --> 00:38:31,840 +decreasing في نفس الوقت؟ يا راجل، كيف increasing و + +358 +00:38:31,840 --> 00:38:37,800 +decreasing؟ بدي أفهم هذه كيف تمام؟ يبقى فش حاجة + +359 +00:38:37,800 --> 00:38:42,000 +اسمها increasing و decreasing في نفس الوقت على + +360 +00:38:42,000 --> 00:38:46,520 +فترة تماماً على الفترة يا إما increasing يا decreasing + +361 +00:38:46,520 --> 00:38:50,140 +يا يمكن شوية على فترة increasing و شوية decreasing + +362 +00:38:50,140 --> 00:38:54,380 +لكن على الفترة اللي بدنا إياها تبعت السؤال النهائي + +363 +00:38:54,380 --> 00:38:59,780 +بُسميها constant function neither increasing nor + +364 +00:38:59,780 --> 00:39:04,940 +decreasing لا تزايد ولا تنقص يبقى ثابت ده اللي + +365 +00:39:04,940 --> 00:39:10,140 +ثابت هالـ constant function يبقى باجي بقول الـ f is + +366 +00:39:10,140 --> 00:39:19,890 +neither increasing nor decreasing + +367 +00:39:22,280 --> 00:39:29,540 +on الفترة من عند الـ zero لغاية infinity بالشكل + +368 +00:39:29,540 --> 00:39:35,180 +اللي عندنا هذا يبقى هذه class interval أو بين جثتين + +369 +00:39:35,180 --> 00:39:43,440 +بنسّميها constant function يبقى دالة ثابتة كويس هذا + +370 +00:39:43,440 --> 00:39:51,150 +بالنسبة إلى C بدنا نيجي بالنسبة إلى D يبقى دي بيقول + +371 +00:39:51,150 --> 00:39:58,090 +الـ f of x يساوي الـ square root لتسعة ناقص x تربيع + +372 +00:39:58,090 --> 00:40:05,090 +السؤال لكم ما عدلتش هذه f of x يساوي الجذر التربيعي + +373 +00:40:05,090 --> 00:40:10,990 +لتسعة ناقص x تربيع يعني y تساوي الجذر التربيعي + +374 +00:40:10,990 --> 00:40:16,950 +لتسعة ناقص x تربيع ما عدلتش دائرة ممتازة ده مركزها + +375 +00:40:18,230 + +401 +00:43:10,930 --> 00:43:17,430 +معرفة هنا ومعرفة هنا تمام بعد هيك الـ F is + +402 +00:43:17,430 --> 00:43:27,840 +decreasing on الفترة من Zero لغاية تلاتة يبقى هنا + +403 +00:43:27,840 --> 00:43:37,280 +هذه increasing وهنا decreasing ده التناقصية على + +404 +00:43:37,280 --> 00:43:49,190 +هذه الفترة أيوة وأنا بدأ أسأل مش سامع كويس زلل + +405 +00:43:49,190 --> 00:43:54,990 +ليش؟ وزلل ليش عشان مقفل الفترة؟ صح ولا لأ تلامنا؟ + +406 +00:43:54,990 --> 00:44:04,230 +في نقطة مشتركة ما بين الفترتين، مظبوط ولا لأ؟ كيف؟ + +407 +00:44:04,230 --> 00:44:11,830 +ما نقلة ذلك، بطل تحسب لهنا و بتتوقف لهنا، بتتوقف + +408 +00:44:11,830 --> 00:44:13,830 +لعندها، increasing ولا لأ؟ + +409 +00:44:27,600 --> 00:44:38,800 +ننتقل الآن إلى نقطة أخرى بعد الـ increasing و + +410 +00:44:38,800 --> 00:44:44,630 +الـ decreasing والـ even والـ odd functions الدوال + +411 +00:44:44,630 --> 00:45:04,750 +الزوجية والدوال الفردية اه + +412 +00:45:04,750 --> 00:45:10,690 +لو نزل يبقى متجسمة لفترات على فترة increasing وعلى + +413 +00:45:10,690 --> 00:45:15,210 +فترة دانية decreasing وهكذا لبعض increasing لبعض + +414 +00:45:15,210 --> 00:45:24,130 +decreasing تمام تمام طيب نجي لنقطة جديدة الـ even + +415 +00:45:24,130 --> 00:45:27,150 +and + +416 +00:45:27,150 --> 00:45:40,730 +odd functions وكذلك الـ symmetry التماثل من الرسالة + +417 +00:45:40,730 --> 00:45:45,110 +ايوة هدى + +418 +00:45:45,110 --> 00:45:54,650 +ولا هدى دي فوق كيف هدى + +419 +00:45:54,650 --> 00:46:03,510 +X واحد وهدى X اثنين مين اللي صغيرة فيها أقل من X2، + +420 +00:46:03,510 --> 00:46:12,790 +من الكبيرة فيهم؟ من الكبيرة ومن الصغيرة؟ مش هذه F + +421 +00:46:12,790 --> 00:46:20,760 +of X2 وهذه F of X1؟ يبقى f of x2 مالها يبقى + +422 +00:46:20,760 --> 00:46:26,800 +decreasing ولا حسب التعريف f of x2 أقل من f of x1 + +423 +00:46:26,800 --> 00:46:31,020 +ده ما x1 أقل من x2 يبقى decreasing مظبوط ولا لأ + +424 +00:46:31,020 --> 00:46:39,960 +يبقى صح ولا لأ لا هي عمرنا ما قلنا x1 أقل من x2 + +425 +00:46:39,960 --> 00:46:49,010 +يعني x2 أكبر من x1 صح ولا لأ لما ندى نقول أن X1 أقل + +426 +00:46:49,010 --> 00:46:54,690 +من X2 بدك تجرها من ناحية تانية ما عنى مشكلة X2 أكبر + +427 +00:46:54,690 --> 00:47:00,450 +من X1 F of + +428 +00:47:00,450 --> 00:47:08,390 +X2 أيوة تجي الله يا راجل هدى أكبر من هدى + +429 +00:47:14,950 --> 00:47:19,910 +خلاص؟ مسحوبة؟ حط + +430 +00:47:19,910 --> 00:47:26,110 +وين ما بدك واكتب مين اللي فيهم الصغراء هذا عامل + +431 +00:47:26,110 --> 00:47:29,570 +مش لشان واحد أقل من اثنين يعني اكس واحد أقل من + +432 +00:47:29,570 --> 00:47:33,030 +اثنين لأ بدأ أكتب ايه يا ربي؟ + +433 +00:47:44,770 --> 00:47:52,820 +يبقى f of b أقل من f of a يبقى decreasing مظبوط؟ F + +434 +00:47:52,820 --> 00:47:57,880 +of B أكبر من F of A يبقى increasing يبقى X واحد و + +435 +00:47:57,880 --> 00:48:03,060 +X اثنان هذا رمز أطول ما قلنا إجباري وليس القرآن + +436 +00:48:03,060 --> 00:48:08,200 +نزل من السماء أيوة يا راجل كل الكلام فارق كله + +437 +00:48:08,200 --> 00:48:11,180 +أخذته في الثانوية نفسي بسبق أن عربة بقيت بالإنجليزية + +438 +00:48:11,180 --> 00:48:13,400 +بس مش أكثر أما كله أخذته هذا + +439 +00:48:25,180 --> 00:48:32,140 +ما سمعتش قناة هناك اي رنز ما أنت أن القيمة تبعها تبقى + +440 +00:48:32,140 --> 00:48:36,920 +تحسب F of X يعني F of A وF of B يبقى أنا بتقيت + +441 +00:48:36,920 --> 00:48:42,360 +بالقيم و ليش ده بالرموز ارمز زي ما بدك وبعدين أنت + +442 +00:48:42,360 --> 00:48:47,720 +ويا تعالي هنا على الهجوم يلا بسرعة نشوف اكتشافاتك + +443 +00:48:47,720 --> 00:48:52,060 +للسافر كولومبوس يلا يا ابني أرهج بسرعة + +444 +00:48:56,210 --> 00:49:03,090 +فضل هنا هيا الجلام واحكي خلّي + +445 +00:49:03,090 --> 00:49:06,550 +مالك هنا يا شباب نسمع يمكن نلاقي حاجة جديدة ما + +446 +00:49:06,550 --> 00:49:10,130 +نعرفش تفضل مثلا + +447 +00:49:10,930 --> 00:49:14,810 +هذه سالب خمسة وهذه سالب واحد مثلا + +448 +00:49:44,690 --> 00:49:51,410 +خلاص أنت ويا نجي لثلاث نقاط مهمة الآن في الشغل + +449 +00:49:51,410 --> 00:49:57,430 +اللي هي الدالة الزوجية والدالة الفردية وتماثل + +450 +00:49:57,430 --> 00:50:03,790 +المنحنى symmetry تماثل هناخد تماثل بالنسبة لمحور X + +451 +00:50:03,790 --> 00:50:10,330 +تماثل بالنسبة لمحور Y تماثل بالنسبة لنقطة الأصل + +452 +00:50:10,330 --> 00:50:16,570 +تمام طيب بدنا نعطي تعريف للـ even والـ odd function + +453 +00:50:16,570 --> 00:50:22,110 +ثم تعريف للـ symmetry بالنسبة للـ x والـ y ونقطة + +454 +00:50:22,110 --> 00:50:30,170 +الأصل يبقى بالضبط للـ definition تعريف الأول the + +455 +00:50:30,170 --> 00:50:32,350 +function + +456 +00:50:34,290 --> 00:50:45,750 +F is called an even function + +457 +00:50:45,750 --> 00:50:56,750 +if F of ناقص X بدها تساوي F of X لكل X الموجودة في + +458 +00:50:56,750 --> 00:50:58,410 +دمية دالة F + +459 +00:51:01,090 --> 00:51:08,930 +الـ function F is called an odd function F الـ F + +460 +00:51:08,930 --> 00:51:15,630 +of سالب X يساوي سالب F of X لكل الـ X اللي موجودة + +461 +00:51:15,630 --> 00:51:26,250 +في دمين الدالة F نمرة تلاتة The graph of + +462 +00:51:26,250 --> 00:51:43,910 +the function is symmetric يكون متماثلا about the x + +463 +00:51:43,910 --> 00:51:55,610 +axis حوالين محور x means that يعني أنه ايش means + +464 +00:51:55,610 --> 00:52:07,280 +that أن الـ x والـ y lie on the graph if and only + +465 +00:52:07,280 --> 00:52:17,420 +if إذا و فقط إذا كان الـ x وناقص y lie on the + +466 +00:52:17,420 --> 00:52:18,080 +graph + +467 +00:52:56,730 --> 00:52:59,950 +أخذتوا الدالة الزوجية والدالة الفردية في المرحلة + +468 +00:52:59,950 --> 00:53:07,350 +الثانوية بالمرة نهائية خلاص مصدقين يا عم حتى لو + +469 +00:53:07,350 --> 00:53:13,110 +أخذت مدي أعتبرك مش ماخد وبدنا نبدأ من الصفر بس + +470 +00:53:13,110 --> 00:53:20,290 +مديك تطلع فاهم ايه اللي مديه طيب بين إيدينا ثلاث + +471 +00:53:20,290 --> 00:53:27,630 +نقاط رئيسة الـ even function الدالة الزوجية الـ Odd + +472 +00:53:27,630 --> 00:53:33,550 +function الدالة الفردية تلاتة السيمتري والسيمتري + +473 +00:53:33,550 --> 00:53:38,950 +هنقسمه إلى ثلاث نقاط سيمتري بالنسبة لمحور X سيمتري + +474 +00:53:38,950 --> 00:53:45,090 +بالنسبة لمحور Y سيمتري بالنسبة لنقطة الأصل بدنا + +475 +00:53:45,090 --> 00:53:51,190 +نيجي للتعريف اللي بين إيدينا تعريف الأول بيقول + +476 +00:53:51,190 --> 00:53:58,050 +الدالة F بقول عنها دالة زوجية even function F الـ F + +477 +00:53:58,050 --> 00:54:03,950 +of سالب X بدها تساوي F of X لكل الـ X اللي موجودة في + +478 +00:54:03,950 --> 00:54:09,670 +دمية الـ F بلا استثناء يعني ايش قصدك تقول اه لما + +479 +00:54:09,670 --> 00:54:15,710 +أقول f of ناقص x بدها تساوي الـ f of x يعني ايش يعني + +480 +00:54:15,710 --> 00:54:21,030 +لو جيت على الدالة اللي عندنا شيلت x وحطيت مكانها + +481 +00:54:21,030 --> 00:54:27,630 +سالب x تبقى الدالة كما هي بدون تغيير أبسط الأمثلة + +482 +00:54:27,630 --> 00:54:33,830 +لو قلت لك f of x يساوي x تربيع شيل الـ x وحط مكانها + +483 +00:54:33,830 --> 00:54:40,530 +ناقص x بصير ناقص x الكل اللي هي مين؟ X تربيع يبقى + +484 +00:54:40,530 --> 00:54:47,170 +هذه بسميها ايه؟ دالة زوجية طيب تمام نيجي للدالة + +485 +00:54:47,170 --> 00:54:53,970 +الفردية الدالة F بقول عنها دالة فردية إذا كان F of + +486 +00:54:53,970 --> 00:54:59,410 +ناقص X يساوي ناقص F of X لكل الـ X اللي موجودة في + +487 +00:54:59,410 --> 00:55:04,590 +domain الدالة F بمعنى لو شيلت الـ X وحطيت مكانها + +488 +00:55:04,590 --> 00:55:08,410 +ناقص X اللي هو الـ variable تبع الـ function بدأ + +489 +00:55:08,410 --> 00:55:14,250 +تطلع نفس الدالة الأصلية بس مسبوقة بإشارة إن حدث + +490 +00:55:14,250 --> 00:55:19,850 +ذلك بقول هذه odd function يبقى هذه هي دالة فردية + +491 +00:55:19,850 --> 00:55:25,030 +طيب يبقى في فروقات الآن ما بين الدالة الفردية + +492 +00:55:25,030 --> 00:55:30,640 +والدالة الزوجية الدالة الزوجية لا تتأثر بتغيير + +493 +00:55:30,640 --> 00:55:35,640 +الإشارة الدالة الفردية إذا غيرت الإشارة بدأ تجي + +494 +00:55:35,640 --> 00:55:41,200 +إشارة سالب لكل الـ function بلا ستة نعم مظبوط هيك + +495 +00:55:41,200 --> 00:55:46,500 +طيب نجي لحكاية التماثل خلي بالك معايا هنا نجي نمرة + +496 +00:55:46,500 --> 00:55:51,020 +ثلاثة الـ graph of the function is symmetric about + +497 +00:55:51,020 --> 00:55:57,140 +the x axis المنحنة تبع الدالة يكون متماثلا بالنسبة + +498 +00:55:57,140 --> 00:56:02,480 +لمحور X المقصود بالبلدي يعني الرسم اللي أعلى محور X + +499 +00:56:02,480 --> 00:56:09,000 +بيظهر الرسم زيها بالضبط وعلى نفس البعد من محور X + +500 +00:56:09,000 --> 00:56:13,900 +يبقى لو كانت اللي فوق محور X الـ Y عندها بالموجبة + +501 +00:56:13,900 --> 00:56:19,610 +تظهر رسم زيها تحت محور X بيصير مين؟ بالسالب، يعني + +502 +00:56:19,610 --> 00:56:24,610 +لو كانت النقطة X وY موجودة على المنحنى، بدها تظهر + +503 +00:56:24,610 --> 00:56:30,830 +جبلها تحت نقطة X وY، الإحداث السيني زي ما هو، + +504 +00:56:30,830 --> 00:56:35,320 +الخلاف صار في من؟ في الإحداث الصادي فراح قال لي هذه + +505 +00:56:35,320 --> 00:56:40,680 +معناها ايش means that تعني أنه لو النقطة x و y + +506 +00:56:40,680 --> 00:56:48,340 +وقعت على المنحنى يبقى يجب أن النقطة x وسالب y تقع + +507 +00:56:48,340 --> 00:56:55,840 +كذلك عالميا على المنحنى تمام تمام أيضا بالـ if هذا + +508 +00:56:55,840 --> 00:57:05,300 +اختصار لكلمة if and only if اللي كنتوا في الثانوية + +509 +00:57:05,300 --> 00:57:12,660 +بتقولولها إذا و فقط إذا كان مش هيك؟ طيب إذا وفقت + +510 +00:57:12,660 --> 00:57:18,260 +إذا كان ترجمته بالإنجليزية if and only if وتختصر + +511 +00:57:18,260 --> 00:57:24,500 +إلى IFF هذا من ناحية اللغة لكن من ناحية الرياضيات + +512 +00:57:24,500 --> 00:57:30,940 +ايش معناها؟ if and only if يعني هذه العبارة ممكن + +513 +00:57:30,940 --> 00:57:36,740 +تقراها من الشمال لليمين وممكن من اليمين للشمال هذا + +514 +00:57:36,740 --> 00:57:42,420 +بالكلام البلدي لكن بالكلام الرياضي لو أعطيت النقطة + +515 +00:57:42,420 --> 00:57:47,320 +هذه والمنحنى كانت متمثل بالنسبة لمحور X لازم + +516 +00:57:47,320 --> 00:57:52,720 +تلاقي النقطة هذه موجودة على المنحنى والعكس لو كان + +517 +00:57:52,720 --> 00:57:57,600 +المنحنى متمثل بالنسبة لمحور X لاجيت النقطة هذه على + +518 +00:57:57,600 --> 00:58:04,280 +المنحنى لازم تلاقي النقطة هذه موجودة على المنحنى + +519 +00:58:04,280 --> 00:58:10,420 +يعني الاتجاه بيصير في اتجاهين متعاكسين وكل الاتجاهين + +520 +00:58:10,420 --> 00:58:19,220 +يكونوا صحيحا طيب ايش رأيك أنا بدي أربط الـ symmetry + +521 +00:58:19,220 --> 00:58:26,020 +بالـ even والـ odd function وبعد هيك هرسملك اللي هو + +522 +00:58:26,020 --> 00:58:31,880 +التلات رسومات كيف تربطهم بيقول لك اه الـ even + +523 +00:58:31,880 --> 00:58:37,800 +function الدالة الزوجية ولو روحت رسمت المنحنى + +524 +00:58:37,800 --> 00:58:44,600 +تبعها بيكون متمثل بالنسبة لمحور Y يعني الرسم اللي + +525 +00:58:44,600 --> 00:58:49,600 +على يمين محور Y زي الرسم اللي على شمال محور Y + +526 +00:58:49,600 --> 00:58:57,110 +تمام؟ يعني ايش؟ يعني لو قلنا هذا مجسم أو هذا بني + +527 +00:58:57,110 --> 00:59:03,370 +آدم واجب فينا وهذا المحور هو محور وي المرأة + +528 +00:59:03,370 --> 00:59:09,330 +المستوية يبقى صورة هذا المجسم بتظهر وين؟ على الشجة + +529 +00:59:09,330 --> 00:59:13,450 +التانية وعلى نفس البعد يبقى المنحنى اللي على + +530 +00:59:13,450 --> 00:59:19,220 +اليمين بدها يظهر منحنى تاني على شمال محور زى وعلى + +531 +00:59:19,220 --> 00:59:25,940 +نفس main وعلى نفس البعد بمعنى آخر لو كانت النقطة x + +532 +00:59:25,940 --> 00:59:33,480 +و y على يمين محور y على منحنى تظهر نقطة مقابلة على + +533 +00:59:33,480 --> 00:59:40,240 +الشمال اللي من سالب x و y اجباله تمام هي x و y + +534 +00:59:40,240 --> 00:59:44,990 +يبقى هنا سالب x و y يبقى إذا وقعت النقطة X وY على + +535 +00:59:44,990 --> 00:59:50,730 +المنحنى فتظهر النقطة سالب X وY على المنحنى هذا + +536 +00:59:50,730 --> 00:59:57,270 +التماثل بالنسبة لمحور Y وهي الدالة الزوجية ضايل + +537 +00:59:57,270 --> 01:00:01,710 +عندي كمان نقطة بدنا نخلصه ضايل مين الدالة الفردية + +538 +01:00:01,710 --> 01:00:08,190 +الدالة الفردية معناها أن الرسم البياني للدالة + +539 +01:00:08,190 --> 01:00:15,070 +متماثل بالنسبة لنقطة الأصل معناه أن أي نقطة ليحدث + +540 +01:00:15,070 --> 01:00:23,070 +إلى x و y بدها تظهر نقطة سالب x وسالب y يعني + +541 +01:00:23,070 --> 01:00:27,190 +البعد على محور x من الناحية دي بدها يظهر بعد من + +542 +01:00:27,190 --> 01:00:31,010 +الناحية التانية بعد هنا بدها يظهر على نفس البعد + +543 +01:00:31,010 --> 01:00:34,970 +نقطة مناضرة لها من الناحية التانية يبقى هذا + +544 +01:00:34,970 --> 01:00:40,250 +التماثل بالنسبة يعني لو وقعت نقطة في الربع الأول + +545 +01:00:40,580 --> 01:00:44,820 +نظرتها بتيجي في الثالث لو وقعت في الثاني نظرتها + +546 +01:00:44,820 --> 01:00:47,540 +بتيجي في الرابع الرابع + +547 +01:00:50,180 --> 01:00:55,640 +نرسم الرسمات وبعد ذلك بنكون جوابنا على الأسئلة + +548 +01:00:55,640 --> 01:00:59,960 +اللي بتدور في دماغك وأنت ما أنت داري أو داري سيام + +549 +01:00:59,960 --> 01:01:05,420 +يبقى بدي أكتب هذا على شكل الـ remark التالية remark + +550 +01:01:05,420 --> 01:01:11,760 +زي علامة أو زي شغلة مشهورة أو ما إلى ذلك يبقى هنا + +551 +01:01:11,760 --> 01:01:12,620 +remark + +552 +01:01:15,190 --> 01:01:20,190 +الـ remark بتقول ما يتعجسمها إلى نقطتين النقطة + +553 +01:01:20,190 --> 01:01:25,530 +الأولى the graph of + +554 +01:01:25,530 --> 01:01:35,670 +an even function الدالة الزوجية is symmetric + +555 +01:01:35,670 --> 01:01:39,290 +متماثلا + +556 +01:01:39,290 --> 01:01:43,450 +about the + +557 +01:01:44,350 --> 01:01:56,190 +Y Axis حوالين محور Y ليش؟ since لأن الـ F سالب X + +558 +01:01:56,190 --> 01:02:06,130 +بدها تساوي من الـ F of X أي أنه that is أي أنه a + +559 +01:02:06,130 --> 01:02:10,710 +point XY + +560 +01:02:10,710 --> 01:02:11,230 +Lie + +561 +01:02:14,820 --> 01:02:28,740 +on the graph if and only if سالب x و y lie on the + +562 +01:02:28,740 --> 01:02:32,880 +graph نمرة + +563 +01:02:32,880 --> 01:02:47,820 +اثنين the graph of an odd function is symmetric + +564 +01:02:47,820 --> 01:02:51,940 +about + +565 +01:02:51,940 --> 01:03:05,500 +the origin تمثل بالنسبة لنقطة الأصل since نظرا لإنه + +566 +01:03:05,990 --> 01:03:20,630 +الـ F of سالب X دي تساوي سالب F of X that is IN a + +567 +01:03:20,630 --> 01:03:32,520 +point النقطة والـ y lie on the graph على الرسم + +568 +01:03:32,520 --> 01:03:43,760 +البياني if and only if سالب x وسالب y lie on the + +569 +01:03:43,760 --> 01:03:44,940 +graph + +570 +01:03:47,920 --> 01:03:52,900 +إلا إن هذا الكلام بدي أرسمه على الطبيعة مشان شوفه + +571 +01:03:52,900 --> 01:03:57,800 +على الطبيعة كيف بيحصل تماثل بالنسبة لـ X تماثل + +572 +01:03:57,800 --> 01:04:02,940 +بالنسبة لـ Y تماثل بالنسبة للـ origin وكيف علاقته هذا + +573 +01:04:02,940 --> 01:04:08,220 +مع الـ even والـ odd function مع الدالة الزوجية و + +574 +01:04:08,220 --> 01:04:15,570 +الدالة الفردية لذلك بالداخل الحالي هنا رقم ثلاثة + +575 +01:04:15,570 --> 01:04:21,710 +قال للرسم البياني للدالة يكون متمثلا حول محور X + +576 +01:04:21,710 --> 01: + +601 +01:06:58,580 --> 01:07:03,600 +يبقى الإحداث الأول مش هيحصل عليه أي تغيير وإنما + +602 +01:07:03,600 --> 01:07:08,800 +الإحداث الثاني هو اللي بيحصل عليه تغيير من هنا + +603 +01:07:08,800 --> 01:07:14,350 +بقول المنحنة اللي قدامنا هذا متمثل بالنسبة لمحور الـ X + +604 +01:07:14,350 --> 01:07:20,270 +طيب انتهينا من النقطة الأولى اللي بتاعت الرسم الآن + +605 +01:07:20,270 --> 01:07:25,230 +بدي أربط الـ even والـ odd مع مين؟ مع باقي الـ + +606 +01:07:25,230 --> 01:07:31,170 +symmetry يبقى بدّأجي أخد التماثل بالنسبة لمحور الـ Y + +607 +01:07:31,170 --> 01:07:34,310 +يبقى + +608 +01:07:34,310 --> 01:07:41,250 +هذا منحنى محور الـ X وهذا محور الـ Y وهذه نقطة الأصل اللي + +609 +01:07:41,250 --> 01:07:50,730 +هي Zero لو رسمت منحنى وطلع المنحنى بالشكل اللي + +610 +01:07:50,730 --> 01:07:58,750 +عندنا فكان + +611 +01:07:58,750 --> 01:08:01,050 +المنحنى بالشكل اللي عندنا + +612 +01:08:06,160 --> 01:08:10,780 +المنحنى هذا هي محور الـ Y جاي في النص يبقى الرسم + +613 +01:08:10,780 --> 01:08:14,980 +اللي على اليمين زي مين؟ زي الرسم اللي على الشمال + +614 +01:08:14,980 --> 01:08:21,560 +بالضبط تمامًا يبقى ما في مشكلة الرسم ازاي؟ ماهي ماشية + +615 +01:08:21,560 --> 01:08:28,450 +بالشكل هذا بدي أخد أي نقطة موجودة هنا يبقى النقطة + +616 +01:08:28,450 --> 01:08:33,550 +هذه لو نزلتها بيكون البعد هذا ماله؟ X والبعد هذا + +617 +01:08:33,550 --> 01:08:40,240 +يبقى النقطة هذه اللي إحداث تبعها XY لو جيت من هذه + +618 +01:08:40,240 --> 01:08:47,320 +النقطة نزلت عمود على محور الـ Y ومديته على استقامته + +619 +01:08:47,320 --> 01:08:55,720 +هنا يبقى هذه النقطة بتكون جد هذه بالضبط تمامًا اللي + +620 +01:08:55,720 --> 01:09:01,040 +هي هذه جد هذه بالضبط تمامًا وبالتالي بيصير إحداث + +621 +01:09:01,040 --> 01:09:10,060 +النقطة هذه ناقص X وY بالضبط تمامًا طيب هذه Y يعني + +622 +01:09:10,060 --> 01:09:17,200 +هذه X وهذه مين؟ F of X صحيح ولا لا؟ هذه اللي هو + +623 +01:09:17,200 --> 01:09:26,060 +سالب X و F of سالب X لإحداث تبعها البعد الرأسي هذا + +624 +01:09:26,060 --> 01:09:31,430 +هو نفس البعد الرأسي هذا ولا لا؟ يبقى النقطة هذه + +625 +01:09:31,430 --> 01:09:37,170 +البعد هذا جد البعد هذا البعد من هو؟ f of x وهذا + +626 +01:09:37,170 --> 01:09:42,370 +البعد من؟ يبقى اثنين هذول بيساووا بعض f of سالب x + +627 +01:09:42,370 --> 01:09:46,690 +بيساووا مع بعض f of x مش هذا تعريف الـ even function + +628 +01:09:46,690 --> 01:09:52,670 +ولا لا؟ إذا الـ even function هي الرسم البياني لها + +629 +01:09:52,670 --> 01:09:58,230 +دالة هذه الدالة رسمتها متمثل بالنسبة لمحور الـ Y يعني + +630 +01:09:58,230 --> 01:10:02,350 +الجزء اللي على يمين محور الـ Y زي الجزء اللي على + +631 +01:10:02,350 --> 01:10:08,810 +الشمال محور كأنه هو هو بس مقلوب عبر مرآة مستوية + +632 +01:10:08,810 --> 01:10:13,970 +يعني لو حطيت المرآة المستوية على محور الـ Y تظهر الرسم + +633 +01:10:13,970 --> 01:10:19,050 +هذه مقلوبة وين؟ في النهاية تنزعي أنت الصبح لما بدك + +634 +01:10:19,050 --> 01:10:23,890 +تيجي على الجامعة توقف قدام المرآة لو قلنا المرآة + +635 +01:10:23,890 --> 01:10:27,690 +هذه المحور ويبقى تظهر صورتك وين؟ على الناحية + +636 +01:10:27,690 --> 01:10:32,570 +التانية بس مقلوبة أنا متجه غربًا الصورة بتبين وين؟ + +637 +01:10:32,570 --> 01:10:40,020 +شرقًا يبقى الصورة مقلوبة عبر مين؟ محور هذه الآن بشكل + +638 +01:10:40,020 --> 01:10:44,220 +لو أنا موجهة على محور الـ Y من الناحية هذه بيصير موجهة + +639 +01:10:44,220 --> 01:10:49,740 +على محور الـ Y من الناحية الثانية يبقى المنحنى متماثل + +640 +01:10:49,740 --> 01:10:54,980 +بالنسبة لمحور الـ Y وبالتالي هذه بقول عنها even + +641 +01:10:54,980 --> 01:11:00,850 +function يبقى الرسم البياني للدالة الزوجية يكون + +642 +01:11:00,850 --> 01:11:08,490 +متماثلًا بالنسبة لمحور الـ Y طيب نجي للنقطة الثالثة + +643 +01:11:08,490 --> 01:11:16,770 +والأخيرة يبقى لو جيت قلت هذا محور الـ X هذا محور الـ Y هذا + +644 +01:11:16,770 --> 01:11:24,670 +نقطة الأصل تمام بأجي بقول لو أخذت المنحنى مثلًا Y + +645 +01:11:24,670 --> 01:11:32,910 +تساوي X تكعيب الشكل اللي عندها يبقى هذا Y تساوي X + +646 +01:11:32,910 --> 01:11:40,210 +تكعيب جينا قلنا لك خدك أي نقطة على المنحنى والتكن + +647 +01:11:40,210 --> 01:11:45,730 +مثلًا النقطة اللي عندك هذه جدّاش الإحداث تبعها تقول لي + +648 +01:11:45,730 --> 01:11:52,350 +هذه x و y يبقى هذه النقطة x و y قلت لك بالله وصل لي + +649 +01:11:52,350 --> 01:11:59,900 +لنقطة الأصل ومد المستقيم على استقامته بتقول لي هي + +650 +01:11:59,900 --> 01:12:05,700 +هيك على نقطة الأصل وصلته من الناحية الثانية تمام + +651 +01:12:05,700 --> 01:12:10,640 +يبقى المنحنى صار بالشكل اللي عندنا هذا + +652 +01:12:14,370 --> 01:12:20,310 +يبقى وصلنا هذا على استقامته بالشكل اللي عندنا هذا + +653 +01:12:20,310 --> 01:12:25,630 +صار الخط اللي عندي هذا قدام مين؟ الخط اللي عندنا هذا + +654 +01:12:25,630 --> 01:12:32,590 +هذه النقطة x و y لكن هذه لو جيت رأسك هذه سالب x + +655 +01:12:39,590 --> 01:12:46,990 +يبقى هذا المنحنى متماثل بالنسبة لنقطة الأصل لأن أي + +656 +01:12:46,990 --> 01:12:51,630 +نقطة على بعضها عن نقطة الأصل من هذه الناحية يساوي + +657 +01:12:51,630 --> 01:12:57,350 +نفس البعد اللي على المنحنى من وين؟ من الناحية الأخرى + +658 +01:12:57,350 --> 01:13:03,290 +رياضيًا يعني لو وقعت النقطة x و y على المنحنى فإن + +659 +01:13:03,290 --> 01:13:09,450 +النقطة ناقص x و ناقص y تقع على المنحنى مثل ما عشان + +660 +01:13:09,450 --> 01:13:14,110 +الـ graph of an odd function is symmetric about the + +661 +01:13:14,110 --> 01:13:21,630 +origin ليش؟ لأن الـ F of ناقص x الـ F of ناقص X بدو + +662 +01:13:21,630 --> 01:13:27,650 +يساوي ناقص F of X اللي هي F of X اللي هي Y تمام؟ + +663 +01:13:27,650 --> 01:13:32,510 +من هنا قلنا هذا معنى أيش؟ معنى التماثل بالنسبة للـ + +664 +01:13:32,510 --> 01:13:37,010 +origin يبقى الـ odd function رسمتها دائمًا وأبدًا + +665 +01:13:37,010 --> 01:13:41,410 +متماثلة بالنسبة لنقطة الأصل الـ even function + +666 +01:13:41,410 --> 01:13:45,730 +رسمتها متماثلة دائمًا وأبدًا بالنسبة لمين؟ لمحور + +667 +01:13:45,730 --> 01:13:47,270 +اسأل السؤال اللي بغلبة + +668 +01:13:55,740 --> 01:14:04,560 +مش وهمي حقيقي حقيقي اه ومن هنا رسمتك اللي هو + +669 +01:14:04,560 --> 01:14:13,380 +القطع الناقص هذا رسمة حقيقية اه ممتاز + +670 +01:14:13,380 --> 01:14:18,770 +جدًا السؤال هو بقيت لفترات التزايد والتنقص اللي + +671 +01:14:18,770 --> 01:14:22,930 +ما لهاش داعي بالـ even والـ odd هنا صح؟ طب أقول لك ماشي + +672 +01:14:22,930 --> 01:14:28,890 +الحال أنا بالداجي كيف؟ فاستنى شوية ما احنا هنجاوب + +673 +01:14:28,890 --> 01:14:35,070 +عليه الآن هل الرسم هذه هي رسمة اقتران؟ بطلنا + +674 +01:14:35,070 --> 01:14:39,030 +increasing و decreasing مظبوط؟ يجب ويحطها على + +675 +01:14:39,030 --> 01:14:41,910 +الشجرة احنا الـ increasing والـ decreasing كلها + +676 +01:14:41,910 --> 01:14:45,190 +بالنسبة لي function وقتاش الـ function increasing + +677 +01:14:45,190 --> 01:14:48,390 +وقتاش الـ function decreasing أيوة اللي رفع أيديه + +678 +01:14:48,390 --> 01:14:56,710 +هنا بطل؟ أيوة الدائرة أنت فيها ثلاثة دائرة مالها؟ + +679 +01:14:56,710 --> 01:15:00,790 +بتحطها ده ثلاثة ليه؟ بالملون والسحر طب أنا بسألك + +680 +01:15:00,790 --> 01:15:09,200 +هي الدائرة دالة؟ ممكن يكون ده ممكن لا حسب + +681 +01:15:09,200 --> 01:15:13,380 +الـ Interval اللي بتاخدها عليها صحيح ولا لا؟ + +682 +01:15:13,380 --> 01:15:18,580 +وبالتالي ما أقدرش أحكم لأن أنا بقول ايه even + +683 +01:15:18,580 --> 01:15:24,360 +function أو odd function يبقى دائرة أنا مش عارف + +684 +01:15:24,360 --> 01:15:28,520 +غير لما أشوفها هي نص دائرة نص يمين ولا شمال + +685 +01:15:28,520 --> 01:15:31,740 +ولا فوق ولا تحت وبالتالي بيصير اختلف الكلام + +686 +01:15:31,740 --> 01:15:32,160 +أيوة + +687 +01:15:39,010 --> 01:15:44,770 +تمام ايش مكتوب قدامك على اللوح هنا؟ مكتوب الـ Odd + +688 +01:15:44,770 --> 01:15:49,770 +ها الـ Symmetric حوالين مين؟ والله حوالين محور الـ x + +689 +01:15:49,770 --> 01:15:55,790 +Right Believe + +690 +01:15:55,790 --> 01:16:00,830 +it بدل ما كانت موجهة بصرة سالبة Believe it هي + +691 +01:16:04,490 --> 01:16:12,190 +X شرطها مختلفة لكن صورتهم نفسها F of X يساوي F of + +692 +01:16:12,190 --> 01:16:16,670 +ناقص X يا + +693 +01:16:16,670 --> 01:16:21,040 +راجل أنا قلت لك هيكتفهمونيش غلط اسمه يا ابني أنت + +694 +01:16:21,040 --> 01:16:26,600 +وياه احنا بنتكلم على مين؟ على الـ even function بس + +695 +01:16:26,600 --> 01:16:29,960 +اسمع برضه عودنا للدائرة تاني يا راجل وين هي + +696 +01:16:29,960 --> 01:16:35,690 +الدائرة؟ ما عنديش دائرة قطعة النقص ما روش function و + +697 +01:16:35,690 --> 01:16:42,530 +بعد ايه؟ احنا هذا اللي رسمناها الـ ellipse بس لمعنى + +698 +01:16:42,530 --> 01:16:48,810 +الـ symmetry المنحنى قلنا تمام؟ أو الـ S طيب يبقى + +699 +01:16:48,810 --> 01:16:53,210 +المنحنى يكونوا متماثلين ولم أقر رسمة الـ function + +700 +01:16:53,210 --> 01:16:56,790 +المنحنى قد يكون function وقد لا يكون function + +701 +01:16:56,790 --> 01:17:02,490 +خربطش بين التنتين أيوة أستاذ أقبل نقص لتحت الـ cell + +702 +01:17:02,490 --> 01:17:06,510 +لو قرناها كل واحد حاجة ماشي الحاجة بنفع ولا بنفعش؟ + +703 +01:17:06,510 --> 01:17:13,290 +بنفع ماشي يبقى شيلنا اللي فوق وخلّينا y less than + +704 +01:17:13,290 --> 01:17:21,980 +zero كتبنا القطع الناقص معادلته X تربيع على A تربيع + +705 +01:17:21,980 --> 01:17:27,960 +زي Y تربيع على B تربيع يساوي واحد ورحت وحطيت + +706 +01:17:27,960 --> 01:17:34,400 +condition Y أقل من أو تساوي Zero يبقى بيصير اللي + +707 +01:17:34,400 --> 01:17:38,980 +فوق بسلامته هذا كله مش موجوده في شغل النص في + +708 +01:17:38,980 --> 01:17:43,110 +السفلي أي vertical line اللي يقطعه إلا في نقطة + +709 +01:17:43,110 --> 01:17:49,930 +واحدة صار function ما هو سؤالك even غصب عني وعنك + +710 +01:17:49,930 --> 01:17:55,450 +عارف ليش؟ لأن النصف اللي على اليمين بيصير زي النصف + +711 +01:17:55,450 --> 01:18:02,490 +اللي على الشمال ما بدأش سؤالها دي خلاص + +712 +01:18:02,490 --> 01:18:05,930 +ده اللي عارف يسأل ثاني؟ بدنا نفوت للنقطة اللي + +713 +01:18:05,930 --> 01:18:12,120 +بعدها أو النقطة اللي بعدها بدنا نعطي مثل على الـ + +714 +01:18:12,120 --> 01:18:17,740 +odd والـ even قبل نحكم على الـ function هل هي odd و + +715 +01:18:17,740 --> 01:18:23,840 +لا even بمعنى بدنا نطبق التعريف اللي احنا حطناه + +716 +01:18:23,840 --> 01:18:30,020 +قدامنا وبواسطة هذا التعريف نحكم على الـ function هل + +717 +01:18:30,020 --> 01:18:39,880 +هي even ولا odd ولا even ولا odd يبقى example + +718 +01:18:50,850 --> 01:18:57,950 +determine whether حدد + +719 +01:18:57,950 --> 01:19:06,750 +لهال the following functions الدوال + +720 +01:19:06,750 --> 01:19:15,990 +التالية are even odd or + +721 +01:19:17,650 --> 01:19:26,710 +neither يعني لا even ولا odd نمر ايه الـ F of X + +722 +01:19:26,710 --> 01:19:34,310 +يساوي X أُس أربعة absolute value للـ X تكعيب زائد + +723 +01:19:34,310 --> 01:19:42,150 +خمسة solution قال + +724 +01:19:42,150 --> 01:19:48,980 +شوف لهذه الدالة هل هي even ولا odd والله لا even + +725 +01:19:48,980 --> 01:19:55,420 +ولا odd والله ايش رايح نضيف عليها even و odd في + +726 +01:19:55,420 --> 01:20:05,220 +نفس الوقت بنفع بنفع في حالة واحدة فقط لا غير لو + +727 +01:20:05,220 --> 01:20:11,000 +كانت f of x تساوي zero بيصير الـ function even و odd + +728 +01:20:11,000 --> 01:20:15,740 +في نفس الوقت لكن غير هيك يبعت لك الله مش صحيح طيب + +729 +01:20:15,740 --> 01:20:19,940 +على أي حال يبقى يا even يا odd + +730 +01:20:38,720 --> 01:20:46,160 +زائد خمسة تمام هذه ايش رأيك فيها X أُس أربعة زي + +731 +01:20:46,160 --> 01:20:55,060 +ما هي X أُس أربعة زائد absolute value هذه سالب X في + +732 +01:20:55,060 --> 01:21:02,900 +سالب X في سالب X يعني سالب X لكل تكعيب زائد خمسة + +733 +01:21:12,310 --> 01:21:17,170 +أول خاصية من خواص القيمة المطلقة اللي خدتوها في + +734 +01:21:17,170 --> 01:21:23,510 +الثانوية إن absolute value لـ -x هي absolute value لـ + +735 +01:21:23,510 --> 01:21:29,250 +-x absolute value للسالب تلاتة هي absolute value + +736 +01:21:29,250 --> 01:21:34,150 +للتلاتة اللي هي بتلاتة مظبوط أو لا؟ وقص عليها كل + +737 +01:21:34,150 --> 01:21:38,430 +الـ real numbers إذا absolute value للسالب X هي + +738 +01:21:38,430 --> 01:21:44,920 +absolute value لـ X إذا هذه عبارة عن ايش؟ absolute + +739 +01:21:44,920 --> 01:21:53,060 +value لـ X تكعيب يبقى هذه بدها تساوي X أُس 4 زائد + +740 +01:21:53,060 --> 01:21:59,420 +absolute value لـ X تكعيب زائد خمسة طبقًا لهذه + +741 +01:21:59,420 --> 01:22:05,380 +الخاصية طب هذه مين هي؟ مش هي الدالة الأصلية؟ يبقى + +742 +01:22:05,380 --> 01:22:11,210 +هذه بدها تساوي F of X الأصلية يبقى بناء على يسار F + +743 +01:22:11,210 --> 01:22:16,890 +of سلب X يساوي مين؟ يبقى دالة هذه مالها؟ even + +744 +01:22:16,890 --> 01:22:24,930 +function يبقى sol F is an even function يبقى دالة + +745 +01:22:24,930 --> 01:22:33,170 +زوجية نمر بها F of X يساوي X على X تربيع ناقص + +746 +01:22:33,170 --> 01:22:37,710 +تلاتة بتعرف هذه دالة زوجية والله ده ده ده ده ده ده + +747 +01:22:37,710 --> 01:22:38,130 +ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده + +748 +01:22:38,130 --> 01:22:38,170 +ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده + +749 +01:22:38,170 --> 01:22:38,190 +ده ده ده ده ده ده ده + +750 +01:22:44,170 --> 01:22:45,830 +أنا مش عارف ايه السؤال + +751 +01:22:49,110 --> 01:22:53,950 +بتشيل كل X وبتحط مكانها سالب X وبعدين بطلع أشوف + +752 +01:22:53,950 --> 01:22:58,510 +شو النتيجة إن طلعت الدالة الأصلية يبقى even مع + +753 +01:22:58,510 --> 01:23:04,510 +طلعت الدالة الأصلية يمكن odd ويمكن لا even ولا odd + +754 +01:23:04,510 --> 01:23:08,410 +هذه اللي احنا قاعدين بندور عليه مظبوط هذه طلعت من؟ + +755 +01:23:08,410 --> 01:23:13,570 +الدالة الأصلية إذن الدالة هذه even يعني سعر F of + +756 +01:23:13,570 --> 01:23:18,010 +سالب X هو F of X مظبوط يا ابني؟ مش هيك كان + +757 +01:23:18,010 --> 01:23:23,220 +التعريف؟ طيب نيجي للتانية F of X يساوي X على X + +758 +01:23:23,220 --> 01:23:31,980 +تربيع سالب ثلاثة الآن أنا بدي أخد من F of سالب X + +759 +01:23:31,980 --> 01:23:40,300 +يبقى سالب X سالب X لكل تربيع سالب تلاتة شلت كل X و + +760 +01:23:40,300 --> 01:23:47,730 +حطيت مكانها سالب X يبقى هذه بدها تساوي سالب X على + +761 +01:23:47,730 --> 01:23:56,230 +هذه X تربيع ناقص ثلاثة هذه بقدر أقول خد لي السالب + +762 +01:23:56,230 --> 01:24:03,750 +برا بيظل X على X تربيع ناقص ثلاثة اللي بين جسينها + +763 +01:24:03,750 --> 01:24:10,470 +دي مين؟ هذه F of X الأصلية يبقى هي السالب برا وهي + +764 +01:24:10,470 --> 01:24:18,390 +الـ F of X ايش صار عندي F of سالب X يساوي قداش؟ سالب + +765 +01:24:18,390 --> 01:24:25,330 +F of X هذه الأصلية وهذه اللي توصلنا لها بناء عليه + +766 +01:24:25,330 --> 01:24:34,550 +الـ F دي مالها؟ odd function يبقى فال F is an odd + +767 +01:24:34,550 --> 01:24:38,950 +function نجي + +768 +01:24:38,950 --> 01:24:46,290 +لنمرى الـ C نمرى C الـ F of X absolute value للـ X + +769 +01:24:46,290 --> 01:24:54,690 +زائد واحد بدي أشوفها even ولا odd يبقى solution + +770 +01:24:54,690 --> 01:25:03,570 +بدي أخد الـ F of سالب X absolute value لسالب X زائد + +771 +01:25:03,570 --> 01:25:07,290 +واحد هل هي الدالة الأصلية اللي فوق؟ + +772 +01:25:10,830 --> 01:25:18,530 +هي اللي فوق يبقى هذه لا تساوي F of X يعني هذه ما + +773 +0 + +801 +01:29:05,920 --> 01:29:10,860 +مستقيم، خط مستقيم، يبقى هذه المقصود فيها، أظن هذه + +802 +01:29:10,860 --> 01:29:16,610 +التي وعدت فيها قبل شوية في بداية المحاضرة، طيب يبقى + +803 +01:29:16,610 --> 01:29:23,170 +هذه معادلة خط مستقيم، أو كنت بتقوله في الثانوية Y + +804 +01:29:23,170 --> 01:29:32,670 +يساوي MX زائد B، الـ M هذا طول الجزء الميل، والـ B هو + +805 +01:29:32,670 --> 01:29:37,410 +طول الجزء المقطوع من محور الصادات Y intercept + +806 +01:29:37,410 --> 01:29:44,710 +وهذا هو الـ slope، طيب كويس، يبقى الـ M هذا يرمز + +807 +01:29:44,710 --> 01:29:56,130 +للسلوب تبع الـ line، وهذا الـ Y intercept يعني طول + +808 +01:29:56,130 --> 01:30:01,770 +الجزء المقطوع من محور الصادات، الآن بدأ ناخد المستقيم + +809 +01:30:01,770 --> 01:30:08,560 +هذا في حالاته المختلفة، تمام، فبجي بقول لو كان عندي + +810 +01:30:08,560 --> 01:30:16,280 +محاور بالشكل هذا، هذا محور X وهذا محور Y، وحبيت أرسم + +811 +01:30:16,280 --> 01:30:22,760 +الخط المستقيم الذي عندنا، افترض هذا الخط المستقيم + +812 +01:30:22,760 --> 01:30:31,260 +تمام، يبقى هذا الخط الذي معادلته Y تساوي MX زائد B + +813 +01:30:31,260 --> 01:30:38,260 +وين الـ B؟ وين الـ M هذه؟ أحنا بنقول إن الـ B هي الـ Y + +814 +01:30:38,260 --> 01:30:45,300 +intercept، يبقى B هي المسافة التي عندنا هذه، تمام؟ + +815 +01:30:45,300 --> 01:30:53,000 +يعني إحداثي النقطة هذه هو صفر و M، طيب وين الـ M؟ الـ + +816 +01:30:53,000 --> 01:30:58,500 +M الـ slope يعني الظل الزاوية التي بيعملها لي مع + +817 +01:30:58,500 --> 01:31:05,180 +الاتجاه الموجب لـ X axis، يبقى هذا الخط المستقيم + +818 +01:31:05,180 --> 01:31:11,140 +الذي عندنا واضح إن الـ slope تبعه عامل موجب ولا سالب؟ + +819 +01:31:11,140 --> 01:31:16,620 +موجب، لأن الزاوية زاوية حادة، لكن لو الخط المستقيم + +820 +01:31:16,620 --> 01:31:22,680 +أجى من الناحية الثانية، بصير Y تساوي سالب MX زائد B + +821 +01:31:22,680 --> 01:31:29,060 +الخط المستقيم هذا بدنا نيجي ناخد له عدة حالات + +822 +01:31:29,060 --> 01:31:36,160 +الحالة الأولى لو كانت الـ M تساوي صفر، يعني الميل + +823 +01:31:36,160 --> 01:31:41,500 +تبع الخط المستقيم تساوي صفر، يعني إيش؟ موازي لمحور + +824 +01:31:41,500 --> 01:31:48,320 +الصادات، أو منطبق عليه، وموازي يعني جاي فوق أو جاي + +825 +01:31:48,320 --> 01:31:56,570 +تحت، يبقى بدي أجي آخذ نمرة واحد: الـ M تساوي صفر + +826 +01:31:56,570 --> 01:32:03,610 +والـ B لا تساوي صفر، يبقى بدي أرسم هذه المحاور + +827 +01:32:03,610 --> 01:32:11,820 +التي عندنا، هذا محور X هذا Y، هذا صفر، M تساوي صفر + +828 +01:32:11,820 --> 01:32:17,960 +part of term هذه بيصير f of x تساوي كذا، ش بيعني؟ يعني + +829 +01:32:17,960 --> 01:32:24,720 +بيصير عندنا Y تساوي B، والله إذا B أكبر من الـ + +830 +01:32:24,720 --> 01:32:32,560 +صفر، بده يجينا الخط المستقيم فوق، يبقى هذا Y تساوي + +831 +01:32:32,560 --> 01:32:40,260 +B، و B greater than zero، طيب الخط المستقيم ممكن + +832 +01:32:40,260 --> 01:32:46,440 +يكون بالسالب، إذا Y يساوي كمية سالبة، يبقى بده يجينا + +833 +01:32:46,440 --> 01:32:54,060 +الخط هذا Y تساوي سالب B، و B أكبر من الـ صفر، طيب + +834 +01:32:54,060 --> 01:32:59,880 +ليش كتبت الـ B أكبر من الـ صفر؟ مشان أضمن أنها تبقى + +835 +01:32:59,880 --> 01:33:06,360 +هذه سالبة، مظبوط؟ يبقى Y تساوي سالب 3، الـ 3 + +836 +01:33:06,360 --> 01:33:11,480 +أكبر من الـ صفر، يبقى مضمون هذا يظل يأخذ قيمة سالبة + +837 +01:33:11,480 --> 01:33:18,500 +مش مشكلة، يبقى Y تساوي B، و B أقل من الـ صفر، عادي + +838 +01:33:18,500 --> 01:33:23,180 +جداً، نفس الكتابة، يبقى Y تساوي سالب B، و B موجبة + +839 +01:33:23,180 --> 01:33:29,320 +دائماً وأبداً مشان أضمن أن هذا يظل من السالب، طيب + +840 +01:33:29,320 --> 01:33:37,160 +ممكن ما يكونش Y تساوي B، ممكن يكون الـ X يساوي A، رقم + +841 +01:33:37,160 --> 01:33:42,720 +والـ A هذا ممكن يكون موجب، وممكن يكون سالب، يبقى + +842 +01:33:42,720 --> 01:33:49,920 +بيصير عندي هذه المحاور، وهذا محور X وهذا محور Y، Y + +843 +01:33:49,920 --> 01:34:00,280 +تساوي A هي، يبقى هذا Y تساوي A، المسافة من هنا لهنا + +844 +01:34:02,040 --> 01:34:11,300 +X يساوي A؟ X بده يساوي A، والـ A positive، والـ A + +845 +01:34:11,300 --> 01:34:16,600 +greater than zero، لكن لو اجت الخط الذي عندنا هذا + +846 +01:34:17,650 --> 01:34:24,430 +يبقى هذا X يساوي سالب A، والـ A كذلك أكبر من الـ + +847 +01:34:24,430 --> 01:34:30,250 +صفر، عشان أضمن إن هذا سالب، يبقى X يساوي A موازية + +848 +01:34:30,250 --> 01:34:35,410 +لمحور Y من جهة اليمين، X يساوي سالب A موازية لمحور + +849 +01:34:35,410 --> 01:34:41,350 +Y من جهة اليسار، يبقى هذه الحالة الأولى، الخطوط + +850 +01:34:41,350 --> 01:34:47,120 +المستقيمة الموازية لمحور X أو الموازية لمحور Y، ممكن + +851 +01:34:47,120 --> 01:34:53,860 +الـ M ما تكونش بصفر تكون رقم، ولكن الـ B هي التي + +852 +01:34:53,860 --> 01:34:59,060 +بتبقى بصفر، طب لو الـ B هذه صارت بصفر، الخط + +853 +01:34:59,060 --> 01:35:05,460 +المستقيم ماله؟ بده يمر بنقطة الأصل، يبقى بدنا نيجي + +854 +01:35:05,460 --> 01:35:14,660 +للحالة الثانية: الـ M لا تساوي صفر، والـ B تساوي + +855 +01:35:14,660 --> 01:35:21,730 +صفر، الحالة، الخطوط المستقيمة ستكون بهذا الشكل، يبقى + +856 +01:35:21,730 --> 01:35:28,330 +هذا محور X، هذا محور Y، هذه نقطة الأصل التي هي الـ + +857 +01:35:28,330 --> 01:35:34,390 +صفر، فتاخذ أول شغلة، لو كان الـ M بواحد يبقى بيصير + +858 +01:35:34,390 --> 01:35:43,520 +معادلة f of x تساوي X، يعني Y تساوي X، يبقى بدرجيك + +859 +01:35:43,520 --> 01:35:48,960 +الخط الذي عندك هذا بالشكل هذا، هيك، و مده على + +860 +01:35:48,960 --> 01:35:56,020 +استقامة، يبقى هذا الـ f of x بده يساوي الـ X أو الـ Y + +861 +01:35:56,020 --> 01:36:00,020 +يساوي الـ X، الزاوية هذه بـ 45، والزاوية هذه + +862 +01:36:00,020 --> 01:36:04,720 +بـ 45، هذه في علم الرياضيات بيسموها الـ + +863 +01:36:04,720 --> 01:36:13,680 +identity function، دالة الوحدة، يبقى هذه بنسميها الـ + +864 +01:36:13,680 --> 01:36:25,940 +identity function، يبقى هذه دالة الوحدة، إيش لو كان + +865 +01:36:25,940 --> 01:36:34,070 +f of x يساوي نص X، يبقى إيش بده يصير؟ بده يصير الخط + +866 +01:36:34,070 --> 01:36:38,950 +هنا في الشق هذه، من هذا وفوق ولا منه وتحت؟ منه + +867 +01:36:38,950 --> 01:36:43,630 +وتحت، لأن عند X يساوي 1 بيصير قيمته نص، بس هذا + +868 +01:36:43,630 --> 01:36:49,070 +عند الواحد بيصير قيمته 1، يبقى هذا الخط الأزرق + +869 +01:36:49,070 --> 01:36:59,830 +هذا هيك، بدي أجيك اللي هو Y تساوي نص X، يعني M تساوي + +870 +01:36:59,830 --> 01:37:06,830 +نص، طب لو كم Y تساوي 2X؟ فوق، بدي أجي منه فوق + +871 +01:37:06,830 --> 01:37:17,210 +يبقى هذا الخط، بدي أجيك هناك، خط هنا Y تساوي 2 + +872 +01:37:17,210 --> 01:37:21,130 +X، عارفين ليش يا شباب؟ لأن لو قلت هي النقطة التي + +873 +01:37:21,130 --> 01:37:25,770 +هي 1، بس هي عند الواحد قيمته نص، هذا عند الواحد + +874 +01:37:25,770 --> 01:37:30,730 +قيمته أيضاً 1، هذا عند الواحد قيمته أيضاً 2 + +875 +01:37:30,730 --> 01:37:38,870 +وهكذا، طب واحد يقول لي طيب Y تساوي ناقص X مش موجب + +876 +01:37:38,870 --> 01:37:44,670 +بتجي من الشق الثانية، يبقى من الشق الثانية + +877 +01:37:44,670 --> 01:37:51,690 +بتجينا الخط Y تساوي سالب X، وهكذا ما ينطبق على + +878 +01:37:51,690 --> 01:37:57,370 +الموجب ينطبق على السالب عندنا، يبقى هذا الوضع + +879 +01:37:57,370 --> 01:38:00,250 +للخطوط المستقيمة في حالتها + +880 +01:38:07,690 --> 01:38:19,270 +التناسب الطردي والتناسب العكسي، يبقى definition two +881 +01:38:19,270 --> 01:38:20,270 +variables + +882 +01:38:38,590 --> 01:38:48,150 +يوجد تناسب وتناسب عكسي، إذا واحد دائماً + +883 +01:38:52,100 --> 01:39:07,200 +دائماً وأبداً a constant multiple of + +884 +01:39:07,200 --> 01:39:15,320 +the other that + +885 +01:39:15,320 --> 01:39:36,950 +is، أي أنه Y تساوي K في X، for non zero constant K + +886 +01:39:36,950 --> 01:39:45,010 +Also + +887 +01:39:45,010 --> 01:40:00,950 +وكذلك Y تساوي K في واحد على X، يعني + +888 +01:40:00,950 --> 01:40:09,050 +إن Y is inversely + +889 +01:40:09,050 --> 01:40:11,450 +proportional + +890 +01:40:17,290 --> 01:40:18,890 +عن طريق الـ X + +891 +01:40:27,240 --> 01:40:33,400 +أنا عندي متغيرين، واحد X واحد Y، المتغيرين هذول are + +892 +01:40:33,400 --> 01:40:40,740 +proportional، يعني يتناسبوا تناسباً طردياً if one is + +893 +01:40:40,740 --> 01:40:44,600 +always a constant multiple of the other، إذا كان + +894 +01:40:44,600 --> 01:40:50,700 +أحدهم مضاعفات الآخر، جدّه مرة ونص، جدّه مرتين، جدّه خمس + +895 +01:40:50,700 --> 01:40:56,440 +مرات، جدّه سبع مرات وثلت، اربع زي ما بدك مضاعفاته + +896 +01:40:56,720 --> 01:41:03,260 +That is، بدي أصيغ السطرين هذول بصيغة رياضية، فباجي + +897 +01:41:03,260 --> 01:41:13,060 +بقول له Y تساوي K، حيث K عدد حقيقي غير صفري، 2، 3 + +898 +01:41:13,060 --> 01:41:18,260 +1.5، 20، 500 زي ما بدك، تمام، for none + +899 +01:41:18,260 --> 01:41:24,370 +zero constant K، لمقدار ثابت غير الصفر، يبقى هذا + +900 +01:41:24,370 --> 01:41:29,510 +التناسب الطبيعي، لما أقول متغيرين متناسبين بقدر + +901 +01:41:29,510 --> 01:41:35,030 +أحول التناسب إلى تساوي وبضرب في مين؟ في مقدار ثابت + +902 +01:41:35,030 --> 01:41:39,250 +يبقى هذا الذي تعلمناه في الفيزياء كل حياتنا، نحول + +903 +01:41:39,250 --> 01:41:42,930 +التناسب إلى تساوي بضرب في مقدار ثابت، المقدار + +904 +01:41:42,930 --> 01:41:48,330 +الثابت الذي هو K، مقدار ثابت غير الصفر، المعادلة + +905 +01:41:48,330 --> 01:41:55,490 +الثانية Y تساوي K على X، تناسب عكسي، يبقى means يعني + +906 +01:41:55,490 --> 01:42:02,170 +إن Y is inversely proportional، تتناسب تناسباً عكسياً + +907 +01:42:02,170 --> 01:42:08,240 +مع من؟ مع المتغير الثاني الذي هو X، واضح كلامي + +908 +01:42:08,240 --> 01:42:13,940 +هنا؟ طيب، لحد هنا stop، لسه لما ننتهي بعد، لكن بدي + +909 +01:42:13,940 --> 01:42:19,940 +أعطيكم أرقام المسائل مشان تبدوا تشتغلوا وتحضروا + +910 +01:42:19,940 --> 01:42:20,640 +الـ discussion + +911 +01:42:23,160 --> 01:42:29,420 +المناقشة، أيوه، بدرس روح تمرن حالك في الأسئلة + +912 +01:42:29,420 --> 01:42:37,520 +التالية، exercises، واحد واحد، المسائل من واحد لغاية + +913 +01:42:37,520 --> 01:42:45,120 +57، الـ odd numbers، اه، الأرقام الفردية من + +914 +01:42:45,120 --> 01:42:47,840 +واحد لـ 57 diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/KpIUQyUiT5o_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/KpIUQyUiT5o_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..cb2c40334a414099b9cdd5525d51430a1e0b74b2 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/KpIUQyUiT5o_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 2264, "start": 21.18, "end": 22.64, "text": "بسم الله الرحمن الرحيم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640], "avg_logprob": -0.03613281212747097, "compression_ratio": 1.0789473684210527, "no_speech_prob": 0.0, "words": [{"start": 21.18, "end": 21.5, "word": "بسم", "probability": 0.923828125}, {"start": 21.5, "end": 21.7, "word": " الله", "probability": 0.97509765625}, {"start": 21.7, "end": 22.12, "word": " الرحمن", "probability": 0.9700520833333334}, {"start": 22.12, "end": 22.64, "word": " الرحيم", "probability": 0.9957682291666666}], "temperature": 1.0}, {"id": 2, "seek": 5053, 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قدامنا مكونا من كام جزء يا شباب؟ من ثلاثة أجزاء يبقى الحل يكون على الشكل التالي solution يبقى احنا عندنا piecewise function مكونا من ثلاثة أجزاء", "tokens": [2407, 3224, 15730, 9122, 8848, 23275, 4724, 8592, 28820, 9122, 45865, 3794, 7251, 3555, 4587, 7578, 23758, 13672, 1829, 12174, 3215, 10943, 8315, 3714, 4117, 2407, 8315, 9154, 9122, 10943, 10874, 11622, 38207, 35186, 13412, 3555, 16758, 22807, 9154, 38637, 1211, 5718, 104, 3660, 5551, 7435, 11622, 16606, 7251, 3555, 4587, 7578, 21542, 1211, 7251, 30544, 15844, 25124, 28820, 16712, 6027, 1829, 3827, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 43242, 8315, 2522, 3711, 2445, 3714, 4117, 2407, 8315, 9154, 38637, 1211, 5718, 104, 3660, 5551, 7435, 11622, 16606], "avg_logprob": -0.23975694990820354, "compression_ratio": 1.7183908045977012, "no_speech_prob": 0.0, "words": [{"start": 87.28, "end": 87.94, "word": "وهذا", "probability": 0.5270589192708334}, {"start": 87.94, "end": 88.76, "word": " كذلك", "probability": 0.88134765625}, 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{"start": 1074.05, "end": 1074.65, "word": " كذلك", "probability": 0.9803059895833334}, {"start": 1074.65, "end": 1075.27, "word": " أصغر", "probability": 0.988525390625}, {"start": 1075.27, "end": 1075.59, "word": " من", "probability": 0.9970703125}, {"start": 1075.59, "end": 1076.87, "word": " X2", "probability": 0.9951171875}, {"start": 1076.87, "end": 1077.67, "word": " يبجى", "probability": 0.957275390625}, {"start": 1077.67, "end": 1077.95, "word": " لما", "probability": 0.921875}, {"start": 1077.95, "end": 1078.51, "word": " تبجى", "probability": 0.931396484375}, {"start": 1078.51, "end": 1078.63, "word": " ال", "probability": 0.75927734375}, {"start": 1078.63, "end": 1079.33, "word": " X1", "probability": 0.8525390625}, {"start": 1079.33, "end": 1079.77, "word": " أقل", "probability": 0.8341471354166666}, {"start": 1079.77, "end": 1080.01, "word": " من", "probability": 0.9921875}, {"start": 1080.01, "end": 1080.97, "word": " X2", "probability": 0.99658203125}, {"start": 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"probability": 0.325439453125}, {"start": 1092.2, "end": 1093.5, "word": " decreasing", "probability": 0.75341796875}, {"start": 1093.5, "end": 1096.26, "word": " function", "probability": 0.94482421875}, {"start": 1096.26, "end": 1097.08, "word": " دلة", "probability": 0.357666015625}, {"start": 1097.08, "end": 1097.76, "word": " تناقصية", "probability": 0.97392578125}, {"start": 1097.76, "end": 1098.42, "word": " اللاحظ", "probability": 0.6644694010416666}, {"start": 1098.42, "end": 1099.0, "word": " إن", "probability": 0.4287109375}, {"start": 1099.0, "end": 1099.18, "word": " ال", "probability": 0.962890625}, {"start": 1099.18, "end": 1099.78, "word": " condition", "probability": 0.94873046875}, {"start": 1099.78, "end": 1100.44, "word": " هذا", "probability": 0.7021484375}, {"start": 1100.44, "end": 1100.92, "word": " لم", "probability": 0.94580078125}, {"start": 1100.92, "end": 1102.0, "word": " يتغير", "probability": 0.9967041015625}, {"start": 1102.0, "end": 1102.2, "word": " في", "probability": 0.93798828125}, {"start": 1102.2, "end": 1103.08, "word": " الحالتين", "probability": 0.9810791015625}, {"start": 1103.08, "end": 1104.2, "word": " يعني", "probability": 0.802001953125}, {"start": 1104.2, "end": 1104.62, "word": " ال", "probability": 0.90380859375}, {"start": 1104.62, "end": 1105.06, "word": " domain", "probability": 0.9716796875}, {"start": 1105.06, "end": 1105.6, "word": " لم", "probability": 0.94921875}, {"start": 1105.6, "end": 1106.56, "word": " يتغير", "probability": 0.9952392578125}, {"start": 1106.56, "end": 1106.86, "word": " يبقى", "probability": 0.83013916015625}, {"start": 1106.86, "end": 1107.4, "word": " لاتغير", "probability": 0.74346923828125}, {"start": 1107.4, "end": 1107.64, "word": " من", "probability": 0.9375}], "temperature": 1.0}, {"id": 47, "seek": 112218, "start": 1109.36, "end": 1122.18, "text": "قيمتين اللي موجودة في ال range f of x2 أكبر من f of x1 يعني f of x2 أقل من f of x1 يبقى هذه decreasing وهذه increasing", "tokens": [4587, 32640, 2655, 9957, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 3613, 283, 295, 2031, 17, 5551, 4117, 26890, 9154, 283, 295, 2031, 16, 37495, 22653, 283, 295, 2031, 17, 5551, 4587, 1211, 9154, 283, 295, 2031, 16, 7251, 3555, 4587, 7578, 29538, 23223, 37037, 24192, 5662], "avg_logprob": -0.234375, "compression_ratio": 1.3553719008264462, "no_speech_prob": 0.0, "words": [{"start": 1109.3600000000001, "end": 1110.16, "word": "قيمتين", "probability": 0.69732666015625}, {"start": 1110.16, "end": 1110.38, "word": " اللي", "probability": 0.643310546875}, {"start": 1110.38, "end": 1111.04, "word": " موجودة", "probability": 0.8770751953125}, {"start": 1111.04, "end": 1111.22, "word": " في", "probability": 0.76708984375}, {"start": 1111.22, "end": 1111.46, "word": " ال", "probability": 0.8857421875}, {"start": 1111.46, "end": 1112.16, "word": " range", "probability": 0.69482421875}, {"start": 1112.16, "end": 1112.88, "word": " f", "probability": 0.387451171875}, {"start": 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2295.72, "end": 2323.04, "text": "يعني ايش؟ يعني ثابت، يعني increasing و decreasing في نفس الوقت؟ يعني يا جيربي، تبقى increasing و decreasing في نفس الوقت؟ يا رايل، كيف increasing و decreasing؟ بدي أفهم هذه كيف تمام؟ يبقى فش حاجة اسمها increasing و decreasing في نفس الوقت على فترة تمامة", "tokens": [40228, 22653, 1975, 1829, 8592, 22807, 37495, 22653, 38637, 16758, 2655, 12399, 37495, 22653, 5662, 4032, 23223, 8978, 8717, 36178, 2423, 30543, 2655, 22807, 37495, 22653, 35186, 10874, 13546, 21292, 12399, 6055, 3555, 4587, 7578, 5662, 4032, 23223, 8978, 8717, 36178, 2423, 30543, 2655, 22807, 35186, 12602, 995, 26895, 12399, 9122, 33911, 5662, 4032, 23223, 22807, 4724, 16254, 5551, 5172, 16095, 29538, 9122, 33911, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 6156, 8592, 11331, 26108, 3660, 24525, 2304, 11296, 5662, 4032, 23223, 8978, 8717, 36178, 2423, 30543, 2655, 15844, 6156, 2655, 25720, 46811, 10943, 3660], "avg_logprob": -0.15014648670330644, "compression_ratio": 2.182857142857143, 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الفترة اللى بدنا يها تبعت السؤال النهائي بسميها constant function neither increasing nor decreasing لا تزايد ولا تنقص يبقى ثابوت ده اللى ثابت هال constant function يبقى باجي بقول ال F is neither", "tokens": [3615, 27188, 2655, 25720, 35186, 1975, 15042, 5662, 35186, 23223, 35186, 7251, 43020, 13412, 2407, 10632, 15844, 6156, 2655, 25720, 5662, 4032, 13412, 2407, 10632, 23223, 44381, 15844, 27188, 2655, 25720, 13672, 7578, 47525, 8315, 7251, 11296, 6055, 3555, 34268, 21136, 33604, 6027, 28239, 3224, 16373, 1829, 4724, 38251, 1829, 11296, 5754, 2445, 9662, 5662, 6051, 23223, 20193, 6055, 11622, 995, 25708, 49429, 6055, 1863, 4587, 9381, 7251, 3555, 4587, 7578, 38637, 16758, 35473, 11778, 3224, 13672, 7578, 38637, 16758, 2655, 8032, 6027, 5754, 2445, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 2423, 479, 307, 9662], "avg_logprob": -0.29261363696570347, "compression_ratio": 1.9813953488372094, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 2323.28, "end": 2323.5, 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0.7109375}, {"start": 3488.94, "end": 3490.42, "word": " الاتجاهين", "probability": 0.878076171875}, {"start": 3490.42, "end": 3491.72, "word": " يكونوا", "probability": 0.9680989583333334}, {"start": 3491.72, "end": 3493.12, "word": " صحيحا", "probability": 0.9197265625}, {"start": 3493.12, "end": 3495.28, "word": " طيب", "probability": 0.6983235677083334}, {"start": 3495.28, "end": 3496.06, "word": " ايش", "probability": 0.8424479166666666}, {"start": 3496.06, "end": 3496.52, "word": " رأيك", "probability": 0.86346435546875}, {"start": 3496.52, "end": 3496.86, "word": " انا", "probability": 0.7320556640625}, {"start": 3496.86, "end": 3497.24, "word": " بدي", "probability": 0.767822265625}, {"start": 3497.24, "end": 3498.12, "word": " اربع", "probability": 0.81494140625}, {"start": 3498.12, "end": 3498.58, "word": " ال", "probability": 0.7216796875}, {"start": 3498.58, "end": 3499.22, "word": " symmetry", "probability": 0.73779296875}, {"start": 3499.22, "end": 3499.96, "word": " بال", "probability": 0.9072265625}, {"start": 3499.96, "end": 3500.94, "word": " even", "probability": 0.900390625}, {"start": 3500.94, "end": 3501.64, "word": " وال", "probability": 0.498779296875}, {"start": 3501.64, "end": 3502.16, "word": " odd", "probability": 0.7490234375}, {"start": 3502.16, "end": 3503.12, "word": " function", "probability": 0.90869140625}], "temperature": 1.0}, {"id": 147, "seek": 353112, "start": 3503.82, "end": 3531.12, "text": "و بعد هيك هرسملك اللي هو التلات رسومات كيف تربطهم بيقولك اه ال even function الدالة الزوجية و لو روحت رسمت المنحنة تبعها بيكون متمثل بالنسبة لمحور Y يعني الرسم اللي على يمين محور Y زي الرسم اللي على شمال محور Y تمام؟", "tokens": [2407, 39182, 39896, 4117, 8032, 2288, 38251, 23275, 13672, 1829, 31439, 16712, 1211, 9307, 12602, 3794, 20498, 9307, 9122, 33911, 6055, 25513, 9566, 16095, 4724, 1829, 39648, 4117, 1975, 3224, 2423, 754, 2445, 32748, 6027, 3660, 6024, 110, 29245, 10632, 4032, 45164, 12602, 2407, 33753, 12602, 38251, 2655, 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نقطة الأصل تمام باجي بقول لو أخدت المنحنة مثلا Y تساوي X تكيب الشكل اللي عندها يبقى هذا Y تساوي X تكيب", "tokens": [1829, 3555, 4587, 7578, 45164, 10874, 36081, 12174, 12610, 2655, 23758, 3714, 5016, 13063, 1783, 23758, 3714, 5016, 13063, 398, 23758, 8717, 47432, 3660, 16247, 36520, 46811, 10943, 4724, 26108, 1829, 4724, 39648, 45164, 5551, 9778, 3215, 2655, 9673, 1863, 5016, 1863, 3660, 50113, 15040, 398, 6055, 3794, 995, 45865, 1783, 6055, 4117, 1829, 3555, 25124, 28820, 13672, 1829, 43242, 11296, 7251, 3555, 4587, 7578, 23758, 398, 6055, 3794, 995, 45865, 1783, 6055, 4117, 1829, 3555], "avg_logprob": -0.13463879250860833, "compression_ratio": 1.75, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 4271.43, "end": 4271.87, "word": "يبقى", "probability": 0.7989501953125}, {"start": 4271.87, "end": 4272.09, "word": " لو", "probability": 0.861328125}, {"start": 4272.09, "end": 4272.45, "word": " جيت", "probability": 0.901123046875}, {"start": 4272.45, "end": 4272.89, "word": 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{"start": 4343.07, "end": 4343.55, "word": " ميم", "probability": 0.600830078125}, {"start": 4343.55, "end": 4344.67, "word": " الخط", "probability": 0.96533203125}, {"start": 4344.67, "end": 4344.93, "word": " اللي", "probability": 0.986572265625}, {"start": 4344.93, "end": 4345.35, "word": " عندنا", "probability": 0.9736328125}, {"start": 4345.35, "end": 4345.63, "word": " هذا", "probability": 0.9638671875}, {"start": 4345.63, "end": 4346.39, "word": " هذه", "probability": 0.333984375}, {"start": 4346.39, "end": 4346.97, "word": " النقطة", "probability": 0.9425455729166666}, {"start": 4346.97, "end": 4347.21, "word": " x", "probability": 0.450439453125}, {"start": 4347.21, "end": 4347.49, "word": " و", "probability": 0.8173828125}, {"start": 4347.49, "end": 4347.67, "word": " y", "probability": 0.76416015625}, {"start": 4347.67, "end": 4348.13, "word": " لكن", "probability": 0.79052734375}, {"start": 4348.13, "end": 4348.69, "word": " هذه", "probability": 0.82080078125}, {"start": 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تاني؟", "probability": 0.9080810546875}, {"start": 4684.49, "end": 4684.73, "word": " بدنا", "probability": 0.882080078125}, {"start": 4684.73, "end": 4685.13, "word": " نفوت", "probability": 0.8772786458333334}, {"start": 4685.13, "end": 4685.75, "word": " للنقطة", "probability": 0.9268798828125}, {"start": 4685.75, "end": 4685.93, "word": " اللي", "probability": 0.97509765625}, {"start": 4685.93, "end": 4686.49, "word": " بعدها", "probability": 0.936279296875}, {"start": 4686.49, "end": 4687.39, "word": " أو", "probability": 0.71484375}, {"start": 4687.39, "end": 4688.29, "word": " النقطة", "probability": 0.9401041666666666}, {"start": 4688.29, "end": 4688.47, "word": " اللي", "probability": 0.99267578125}, {"start": 4688.47, "end": 4688.85, "word": " بعدها", "probability": 0.972900390625}, {"start": 4688.85, "end": 4689.15, "word": " بدنا", "probability": 0.81591796875}, {"start": 4689.15, "end": 4689.61, "word": " نعطي", "probability": 0.989990234375}, {"start": 4689.61, "end": 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or", "tokens": [49136, 533, 1968, 11331, 3215, 3215, 46740, 6027, 264, 3480, 6828, 32748, 2407, 6027, 1829, 16712, 6027, 10632, 366, 754, 7401, 420], "avg_logprob": -0.3445991821911024, "compression_ratio": 1.1195652173913044, "no_speech_prob": 0.0, "words": [{"start": 4730.85, "end": 4732.25, "word": "determine", "probability": 0.536865234375}, {"start": 4732.25, "end": 4733.65, "word": " whether", "probability": 0.2481689453125}, {"start": 4733.65, "end": 4737.95, "word": " حدد", "probability": 0.9318033854166666}, {"start": 4737.95, "end": 4738.59, "word": " لهال", "probability": 0.438720703125}, {"start": 4738.59, "end": 4739.35, "word": " the", "probability": 0.5126953125}, {"start": 4739.35, "end": 4739.99, "word": " following", "probability": 0.88525390625}, {"start": 4739.99, "end": 4741.49, "word": " functions", "probability": 0.89404296875}, {"start": 4741.49, "end": 4746.75, "word": " الدوالي", "probability": 0.757568359375}, {"start": 4746.75, "end": 4747.41, "word": " التالية", "probability": 0.9363606770833334}, {"start": 4747.41, "end": 4748.77, "word": " are", "probability": 0.88330078125}, {"start": 4748.77, "end": 4751.11, "word": " even", "probability": 0.7900390625}, {"start": 4751.11, "end": 4754.09, "word": " odd", "probability": 0.62890625}, {"start": 4754.09, "end": 4755.99, "word": " or", "probability": 0.79296875}], "temperature": 1.0}, {"id": 199, "seek": 478375, "start": 4757.65, "end": 4783.75, "text": "neither يعني لا even ولا odd نمر ايه ال F of X يسوى X قصة أربعة absolute value لل X تكيب زائد خمسة solution قال شوف لهذه الدالة", "tokens": [716, 1839, 37495, 22653, 20193, 754, 49429, 7401, 8717, 29973, 1975, 1829, 3224, 2423, 479, 295, 1783, 7251, 3794, 2407, 7578, 1783, 12174, 9381, 3660, 5551, 25513, 27884, 8236, 2158, 24976, 1783, 6055, 4117, 1829, 3555, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 3827, 50239, 13412, 38688, 46740, 24192, 32748, 6027, 3660], "avg_logprob": -0.3419811208293123, "compression_ratio": 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+ +2 +00:00:25,970 --> 00:00:30,070 +قولناهم المحاضرة الماضية كنا بنتحدث على ال + +3 +00:00:30,070 --> 00:00:36,590 +piecewise function يبقى الدالة المكونة من عدة قطع + +4 +00:00:36,590 --> 00:00:41,910 +أو من عدة أجزاء واخدنا على ذلك ثلاثة أمثلة وهذا هو + +5 +00:00:41,910 --> 00:00:46,550 +المثال الرابع والأخر ان شاء الله على ال piecewise + +6 +00:00:46,550 --> 00:00:50,530 +function ثم بعدها ننتقل إلى نقطة أخرى + +7 +00:00:52,850 --> 00:00:58,450 +المثال الرقم أربعة بيقول find a formula هات لصيغة + +8 +00:00:58,450 --> 00:01:02,590 +for the function with the corresponding graph اللي + +9 +00:01:02,590 --> 00:01:07,750 +إلها الرسم المقابل يكبر cross bonding مقابل graph + +10 +00:01:07,750 --> 00:01:12,270 +رسم يكبر الرسم تبعها بالشكل المقابل عندنا أيوة + +11 +00:01:12,270 --> 00:01:17,810 +بالشكل هذا الشكل الغامق اللي عندنا هذا هيك أيوة + +12 +00:01:17,810 --> 00:01:20,470 +وهنا بجيك الشكل اللي عندنا هذا + +13 +00:01:27,280 --> 00:01:37,160 +وهذا كذلك بشكل كويس + +14 +00:01:37,160 --> 00:01:43,220 +يبقى هذا اللي قدامنا مكونا من كام جزء يا شباب؟ من + +15 +00:01:43,220 --> 00:01:47,540 +ثلاثة أجزاء يبقى الحل يكون على الشكل التالي + +16 +00:01:47,540 --> 00:01:54,460 +solution يبقى احنا عندنا piecewise function مكونا + +17 +00:01:54,460 --> 00:02:00,150 +من ثلاثة أجزاءبنجي للجزء الأول واضح ان احداثية + +18 +00:02:00,150 --> 00:02:05,130 +النقطة هذه قداش سالب واحد واحد يعني هذه لو جيت + +19 +00:02:05,130 --> 00:02:10,290 +نازا الرأسي بيكون ان هذا يعنى سالب واحد طيب هذا + +20 +00:02:10,290 --> 00:02:12,070 +الخط اللي بيبدأ 00 + +21 +00:02:17,960 --> 00:02:25,320 +يبقى F of X يساوي كم؟ سالب X يبقى هذا F of X يساوي + +22 +00:02:25,320 --> 00:02:32,600 +سالب X وبشرط X أكبر من أو تساوي سالب واحد وأقل من + +23 +00:02:32,600 --> 00:02:38,780 +كم؟من الـ Zero على الفترة من سالب واحد لغاية Zero + +24 +00:02:38,780 --> 00:02:43,980 +هذا هو الجزء الأول بدنا نيجي للجزء التاني احداثيات + +25 +00:02:43,980 --> 00:02:49,920 +النقطة هذه قداشر واحد و واحد يعني لو جيت نازل رأسي + +26 +00:02:49,920 --> 00:02:54,660 +هيك بيكون النقطة هذه قداشر واحد يبقى الجزء الثاني + +27 +00:02:54,660 --> 00:02:58,620 +محصور من وين أو معرف على الفترة من وين لوين من صفر + +28 +00:02:58,620 --> 00:03:03,990 +لواحد طب قداشر اللي هو معادلة هذا الخطهذا أفقي + +29 +00:03:03,990 --> 00:03:10,530 +واحد يعني Y تساوي واحد يبقى هنا واحد وبالشرط ان ال + +30 +00:03:10,530 --> 00:03:17,170 +X أكبر من ال zero ولا تساوي لإن عند ال zero الدالة + +31 +00:03:17,170 --> 00:03:24,550 +غير معرفة وأقل من أو يساوي من ال واحد يبقى بالشكل + +32 +00:03:24,550 --> 00:03:29,730 +اللي عندنا هذا خلصنا الجزء الثاني هذايبقى كأنه ما + +33 +00:03:29,730 --> 00:03:34,730 +لم يبقى عندنا إلا من الجزء الثالث يبقى الجزء + +34 +00:03:34,730 --> 00:03:40,230 +الثالث كذلك عبارة عن خط مستقيم مشان أعرف معادلة + +35 +00:03:40,230 --> 00:03:46,730 +الخط المستقيم بلزمني ميلو ونقطة واقعة عليه تمام، + +36 +00:03:46,730 --> 00:03:52,350 +بدي أجيب ميلو، يبقى عندي بدل نقطة نقطة نقطة، هذه + +37 +00:03:52,350 --> 00:03:59,060 +الأحداث تبعها كم؟ تلاتة وزيرووبالتالي بقدر أجيب ال + +38 +00:03:59,060 --> 00:04:04,820 +slope تبع الخطة اللي عندنا هنا فبجيب أقول في الها + +39 +00:04:04,820 --> 00:04:10,920 +مش هيك ال slope اللي هو بديله الرمز M اللي هو + +40 +00:04:10,920 --> 00:04:17,340 +الميل يسوى فرق الصدات على فرق الصينة يبقى واحد + +41 +00:04:17,340 --> 00:04:24,350 +ناقص Zero على واحد ناقص ثلاثة ويسوى جداتو يساوي + +42 +00:04:24,350 --> 00:04:28,450 +الناقص نص يبقى الميال اللي عندنا وجدناه يساوي + +43 +00:04:28,450 --> 00:04:33,330 +السلب نص الآن بدنا نقطة واقع عليه فجعلنا نقطة مين + +44 +00:04:33,330 --> 00:04:39,510 +واحد و واحد سمعتوا بالخط المستقيم اللي هو معدته Y + +45 +00:04:39,510 --> 00:04:48,880 +يساوي M في X ناقص X node زائد Y nodeسكت الشبابه، + +46 +00:04:48,880 --> 00:04:53,860 +ماسمعتوا مش فيه هذه؟ بلاش، هنجيب نفس المعادلة بس + +47 +00:04:53,860 --> 00:05:02,400 +بصيرة أخرى، أخدته إن ال Y ناقص Y not على X ناقص X + +48 +00:05:02,400 --> 00:05:08,180 +not يساوي المال، هذه أخدتوها يعني، هذه هي هذه + +49 +00:05:09,280 --> 00:05:13,460 +بالظبط بالحرف الواحد طب اضرب ضرب تبادل يفجأة لو + +50 +00:05:13,460 --> 00:05:19,280 +ضربنا ضرب تبادل يصير y ناقص y node يسوى m في x + +51 +00:05:19,280 --> 00:05:23,860 +ناقص x node ناقص y node هد على الشجة هدف تطلع + +52 +00:05:23,860 --> 00:05:27,980 +المعادلة هدى يفجأة المعادلة هدى او المعادلة هدى + +53 +00:05:27,980 --> 00:05:33,520 +الاتنين are the same اتنين نفس الشيء بتضبط تماما + +54 +00:05:34,650 --> 00:05:40,730 +يبقى بناء عليه المعادلة بصير Y يسوى الميل ناقص نص + +55 +00:05:40,730 --> 00:05:48,110 +في X ناقص واحد زائد واحد او ان شئتم فقولوا ناقص نص + +56 +00:05:48,110 --> 00:05:58,360 +X زائد نص زائد واحديعني ايه؟ يعني ناقص نص X ناقص + +57 +00:05:58,360 --> 00:06:06,020 +نص X زائد تلاتة على اتنين يبقى أصبح كأنه خط + +58 +00:06:06,020 --> 00:06:10,300 +المستقيم اللي كنا بنقوله في الإعدادي والثانويوسات + +59 +00:06:10,300 --> 00:06:16,510 +تساوي ألف سين زائد با، مظبوط؟الف بيكون هو الميل + +60 +00:06:16,510 --> 00:06:20,510 +تبع الخط المستقيم وبقى طول الجزر المقطوع من محور + +61 +00:06:20,510 --> 00:06:27,950 +الصداد الا اننا هنقول المعادلة هذه او هذه او ال Y + +62 +00:06:27,950 --> 00:06:35,410 +تساوي MX زائد B يبقى هذه معادلتها خط المستقيم في + +63 +00:06:35,410 --> 00:06:40,030 +ال general form وهذه هعطيكوا إياها في محاضرة اليوم + +64 +00:06:40,260 --> 00:06:45,800 +بعد قليل أن هذه ليه معادلة خط المستقيم في صيغتها + +65 +00:06:45,800 --> 00:06:52,940 +أو في صورتها العامة على أي حال هذه هذه هذه كلها + +66 +00:06:52,940 --> 00:06:58,400 +are the same ال M هي المل با أو ال بي هو طول الجزء + +67 +00:06:58,400 --> 00:07:04,760 +المقطوع من محور Y أو من محور الصدرما رأيك إذا أخذت + +68 +00:07:04,760 --> 00:07:10,920 +النص عام المشترك برا + +69 +00:07:10,920 --> 00:07:18,540 +يبقى عندك تلاتة ناقص X إذا الجزء التالت يصبح نصه + +70 +00:07:18,540 --> 00:07:26,620 +برا وهنا تلاتة ناقص X و X محصورة ما بين الواحد و + +71 +00:07:26,620 --> 00:07:33,830 +بين من و بين التلاتةطبعا اللحظة ان الواحد هنا + +72 +00:07:33,830 --> 00:07:40,710 +مكرر، كررتها والله مسحتها بتفرقش عندنا، اتنين are + +73 +00:07:40,710 --> 00:07:45,370 +the same يعني لو خلتها برضه مافي مشكلة، لكن ماقدرش + +74 +00:07:45,370 --> 00:07:51,830 +احط يساوي عند التلاتة لإن هذا التجويف موجود على + +75 +00:07:51,830 --> 00:07:58,220 +الخاط المستقيميبقى هي كتبنا شكل المعادلة من خلال + +76 +00:07:58,220 --> 00:08:02,960 +المعلومات اللي موجودة عندنا أنا بدأ أسأل سؤال + +77 +00:08:02,960 --> 00:08:08,140 +زيادة مشان نربط القديم بالجديد لو سألتلك قلتلك + +78 +00:08:08,140 --> 00:08:14,900 +قداش بالله domain الـF علمًا أن ال domain هي مكتوب + +79 +00:08:14,900 --> 00:08:20,620 +قدامك على اللوح ومرسوم بدي تقولي من كده إلى كده + +80 +00:08:20,620 --> 00:08:26,650 +أيضًامن سالب تلاتة لغاية الواحد مفتوح من عند + +81 +00:08:26,650 --> 00:08:32,050 +التلاتة وماعندي سالب واحد فقط يعني كل الفترة هذه + +82 +00:08:32,050 --> 00:08:39,050 +بدون استثناء اه يعني برضه نشيل ال zero ماشي يبقى + +83 +00:08:39,050 --> 00:08:43,970 +ال domain بقوله الفترة من عند الناقص واحد لغاية + +84 +00:08:43,970 --> 00:08:51,210 +التلاتة مفتوحة ومغلقة بدي أشيل منها ال zero as a + +85 +00:08:51,210 --> 00:08:57,190 +setتمام؟ او بذاك صيغة صيغة اخرى تقول لي من عندنا + +86 +00:08:57,190 --> 00:09:04,370 +ناقص واحد لغاية ال zero اتحاد zero و تلاتة as an + +87 +00:09:04,370 --> 00:09:09,390 +open interval مافي مشكلة طيب بدنا نروح نجيب ال + +88 +00:09:09,390 --> 00:09:16,110 +range بتابع الدالة F يعني هتاخد قيم من وين لوين + +89 +00:09:16,110 --> 00:09:17,370 +ايوة + +90 +00:09:20,050 --> 00:09:27,010 +من عند الـ zero لغاية بتفوتش أبدا، يبقى من عند ال + +91 +00:09:27,010 --> 00:09:33,970 +zero مفتوحة، لأن هنا، هنا بتاخدش قيم، لغاية قداش، + +92 +00:09:33,970 --> 00:09:39,090 +لغاية الواحد، ومن عند الواحد مقفلة، لإن كل القيم + +93 +00:09:39,090 --> 00:09:44,620 +هذه و هذه كلها بواحد صحيحيبقى هي جزء من ال domain + +94 +00:09:44,620 --> 00:09:49,580 +و ال range لهذه زيادة معلومات زيادة على ما هو + +95 +00:09:49,580 --> 00:09:56,120 +مطلوب في المسألة طيب لما نيجي لحاجة اسمة + +96 +00:09:56,120 --> 00:10:00,720 +increasing and decreasing function دلت التزايد و + +97 +00:10:00,720 --> 00:10:08,360 +دلت التناقص يبقى increasing and + +98 +00:10:08,360 --> 00:10:10,720 +decreasing + +99 +00:10:16,290 --> 00:10:21,230 +الدوال التزايدية والدوال التناقصية + +100 +00:10:27,650 --> 00:10:32,990 +الـ F بـ A function نفترض ان الـ F عبارة عن دالة + +101 +00:10:32,990 --> 00:10:44,450 +defined معرفة on an interval I معرفة على فترة I + +102 +00:10:44,450 --> 00:10:52,810 +and let و افترض ان ال X واحد و ال X اتنين موجودة + +103 +00:10:52,810 --> 00:11:06,150 +في الفترة I نمرا واحدالـ F of X2 is greater than F + +104 +00:11:06,150 --> 00:11:14,370 +of X1 whenever X1 + +105 +00:11:14,370 --> 00:11:16,910 +less than X2 + +106 +00:11:22,590 --> 00:11:32,070 +is said to be increasing is said to be increasing + +107 +00:11:32,070 --> 00:11:35,490 +on + +108 +00:11:35,490 --> 00:11:48,750 +الفترة I نمر اتنين F ال F of X اتنينأقل من f of x1 + +109 +00:11:48,750 --> 00:11:56,450 +whenever x1 أقل من x2 then f is said to be + +110 +00:11:56,450 --> 00:12:02,710 +decreasing on the interval I + +111 +00:12:09,770 --> 00:12:15,750 +لما نعود نقرأ التعريف من أول و جديد نحاول نفهم هذا + +112 +00:12:15,750 --> 00:12:21,170 +التعريف نرسم رسم توضيحي لمعنى هذا التعريف حتى هذه + +113 +00:12:21,170 --> 00:12:25,450 +المعلومات تثبت في دماغنا يبقى النقطة اللي دي لما + +114 +00:12:25,450 --> 00:12:29,390 +نتعرض لل increasing function and decreasing + +115 +00:12:29,390 --> 00:12:36,050 +function الدالة التزايدية والدالة التناقصيةبيقول + +116 +00:12:36,050 --> 00:12:42,550 +افترض ال F هي دالة معرفة على فترة I ولم احدد هذه + +117 +00:12:42,550 --> 00:12:48,050 +الفترة closed ولا open ولا half closed ولا half + +118 +00:12:48,050 --> 00:12:52,430 +open سيا اي فترة من الفترات ايش ما تكون ايه تكون + +119 +00:12:52,430 --> 00:12:59,540 +ماعليهاش قولأخذت two elements x1 وx2 موجودين في + +120 +00:12:59,540 --> 00:13:06,920 +هذه الفترة بقول والله إذا كان f of x2 أكبر من f of + +121 +00:13:06,920 --> 00:13:17,060 +x1 علما إن x1 أقل من x2 إن حدث ذلكيبقى الدالة دالة + +122 +00:13:17,060 --> 00:13:21,560 +تزايدية على + +123 +00:13:21,560 --> 00:13:22,840 +الفترة I + +124 +00:13:27,550 --> 00:13:35,230 +نمر اتنين اذا ال F of X2 اقل من F of X1 لما ال X1 + +125 +00:13:35,230 --> 00:13:41,410 +اقل من X2 يبقى دالة بتقول عليها نمالة دالة تناقصية + +126 +00:13:41,410 --> 00:13:46,450 +دالة decreasing على الفترة اللي عندنا هذه طب تعالى + +127 +00:13:46,450 --> 00:13:51,070 +نشوف هذا الكلام على الطبيعة حتى هذا المفهوم يرسخ + +128 +00:13:51,070 --> 00:13:58,290 +في دماغنا فمثلالو جتخدت محاور كنت هذا محور X وهذا + +129 +00:13:58,290 --> 00:14:05,510 +محور Y وهذه نقطة الأصل اللي عندنا وروحت رسمت منحنى + +130 +00:14:05,510 --> 00:14:11,490 +دالة بأي طريقة كانت فطلعت الدالة بالشكل اللي عندنا + +131 +00:14:11,490 --> 00:14:20,270 +هذا يبقى هذه اللي هي منحنى الدالة Y تساوي F of X + +132 +00:14:21,110 --> 00:14:26,670 +الدالة هذه معرفة على الفترة من عند النقطة هذه مثلا + +133 +00:14:26,670 --> 00:14:32,170 +لغاية من لغاية النقطة هذه يبقى هذه الفترة اللي + +134 +00:14:32,170 --> 00:14:37,930 +عندنا I بغض النظر هل هي مفتوحة مغلقة نصف مفتوحة + +135 +00:14:37,930 --> 00:14:44,920 +نصف مغلقة ما بتفرق عننارحت اخد اي نقطتين موجودتين + +136 +00:14:44,920 --> 00:14:50,080 +على ال interval اللي عندنا هذه نفترض انه كان هذه + +137 +00:14:50,080 --> 00:14:57,080 +هي النقطة الاولى X1 وهذه النقطة الثانية هي X2 يبقى + +138 +00:14:57,080 --> 00:15:05,480 +من اللي اصغر X1 ولا X2؟ X1 اصغر يبقى هذه X1أقل من + +139 +00:15:05,480 --> 00:15:13,440 +X2 تعالى نشوف قيم الدالة عند هتين النقطتين جيت هنا + +140 +00:15:13,440 --> 00:15:19,460 +على المسافة اللى عندنا هذه هيك فكانت هذه F of X + +141 +00:15:19,460 --> 00:15:25,340 +واحد جيت على قيمة الدالة هنا وجيت طالع لجيت هذه + +142 +00:15:25,340 --> 00:15:33,500 +مينf of x2 من اللي أكبر من خلال الرسم واضح أن f of + +143 +00:15:33,500 --> 00:15:41,480 +x2 مسافة من هنا لهنا أكبر من f of x1 يبقى إذا f of + +144 +00:15:41,480 --> 00:15:47,950 +x2 أكبر من f of x1لما اكس واحد اقل من اكس اتنين + +145 +00:15:47,950 --> 00:15:52,190 +يبقى الدالة زي ما انت شايف طالعة تزايدية او سهل + +146 +00:15:52,190 --> 00:15:56,930 +عليها من هنا اقول ان الدالة هذه مالها increasing + +147 +00:15:56,930 --> 00:16:02,610 +function يبقى هذه الدالة بسميها increasing + +148 +00:16:02,610 --> 00:16:10,710 +function يبقى هذه الدالة تزايدية لكن لو جيت قلت + +149 +00:16:10,710 --> 00:16:18,060 +هاي المحاولةهذا محور X وهذا محور Y وهذه نقطة الاصل + +150 +00:16:18,060 --> 00:16:23,600 +و روحت رسمت منحنى الدالة بقدر الله طلع منحنى + +151 +00:16:23,600 --> 00:16:30,460 +الدالة عندك على الفترة اللى عندنا هذه اللى هى اللى + +152 +00:16:30,460 --> 00:16:36,120 +سميها الفترة I من عنده النقطة هذه لغاية مهم النقطة + +153 +00:16:36,120 --> 00:16:41,730 +هذهلاحظوا في اللي قبلها خدت X سالبة لانها قبل الـ0 + +154 +00:16:41,730 --> 00:16:46,950 +و هنا X2 موجبة يجب ان يكون X1 نيجاتيب و X2 + +155 +00:16:46,950 --> 00:16:51,250 +positive يجب ان يكون بمانت هذه أقل من هذه هنا بدأ + +156 +00:16:51,250 --> 00:16:55,810 +اخدهم يتنتين بالسالب يتنتين بالموجبة ليس بالضرورة + +157 +00:16:55,810 --> 00:17:02,320 +مرة سالبة و مرة موجبة افترضانه اخدت النقطة هذه x1 + +158 +00:17:02,320 --> 00:17:09,660 +واخدت النقطة التانية هذه x2 يبقى x1 هي المسافة + +159 +00:17:09,660 --> 00:17:15,060 +الصغيرة هذه وx2 هي المسافة الكبرى اللى عندنا هذه + +160 +00:17:15,400 --> 00:17:21,640 +يبقى مضمون إن X1 ماله أقل من X2 اللي هو ال term + +161 +00:17:21,640 --> 00:17:27,780 +اللي عندنا هذا يبقى أي X1 أقل من X2 بدى أروح أشوف + +162 +00:17:27,780 --> 00:17:36,900 +F of X1 و F of X2 طلعنا رأسي هيك فكان هذه F of X1 + +163 +00:17:37,690 --> 00:17:44,670 +هنا طلعنا رأسي كمان بالشكل هذا فصار هذه F of X2 + +164 +00:17:44,670 --> 00:17:53,230 +يبجى مين اللي أصغر فيهم؟ F of X2 أصغر من F of X1 و + +165 +00:17:53,230 --> 00:18:00,970 +X1 كذلك أصغر من X2 يبجى لما تبجى ال X1 أقل من X2 + +166 +00:18:00,970 --> 00:18:07,220 +فإن ال F of X2 أقلإن حدث ذلك، يبقى الدالة + +167 +00:18:07,220 --> 00:18:10,380 +التناقصية + +168 +00:18:10,380 --> 00:18:18,420 +يبقى هادى decreasing function دلة تناقصية اللاحظ + +169 +00:18:18,420 --> 00:18:24,620 +إن ال condition هذا لم يتغير في الحالتين يعني ال + +170 +00:18:24,620 --> 00:18:31,040 +domain لم يتغير يبقى لاتغير منقيمتين اللي موجودة + +171 +00:18:31,040 --> 00:18:35,900 +في ال range f of x2 أكبر من f of x1 يعني f of x2 + +172 +00:18:35,900 --> 00:18:42,180 +أقل من f of x1 يبقى هذه decreasing وهذه increasing + +173 +00:18:42,830 --> 00:18:49,130 +طيب بنحاول نعطي أمثلة توضيحية على ال increasing + +174 +00:18:49,130 --> 00:18:54,430 +functions و ال decreasing functions الرسمتين مع + +175 +00:18:54,430 --> 00:19:01,610 +التعريف لتوضيح معنى التعريف من الناحية الهندسية + +176 +00:19:01,610 --> 00:19:07,610 +طيب نعطي مثال المثال بيقول ما يأتي example + +177 +00:19:20,900 --> 00:19:36,040 +Sketch the graph of the following functions + +178 +00:19:36,040 --> 00:19:40,260 +ارسم لي كل من الدول التالية and determine + +179 +00:19:45,820 --> 00:19:57,000 +وحدد ليه determine the intervals of + +180 +00:19:57,000 --> 00:20:02,980 +increasing and + +181 +00:20:02,980 --> 00:20:05,600 +decreasing + +182 +00:20:07,050 --> 00:20:12,750 +حدد لي فترات التزايد والتناقص لكل من الدوالة + +183 +00:20:12,750 --> 00:20:25,950 +التالية نمرا A Y تساوي نص X تكيب نمرا B Y تساوي + +184 +00:20:25,950 --> 00:20:34,400 +سالب واحد على absolute value ل Xنمر الـ C ال F of + +185 +00:20:34,400 --> 00:20:45,140 +X يساوي سالب X لما ال X أقل من Zero و اتنين او + +186 +00:20:45,140 --> 00:20:51,520 +تلاتة لما ال X greater than or equal to Zero ونمر + +187 +00:20:51,520 --> 00:21:00,290 +ال Dالـ F of X يساوي الجدرى التربية لتسعة ناقص X + +188 +00:21:00,290 --> 00:21:10,430 +تربية خلّي + +189 +00:21:10,430 --> 00:21:17,910 +براك هنا السؤال دو شقينالشق الأول جالي أرسم رسمة + +190 +00:21:17,910 --> 00:21:23,690 +كل دالة من الدوالي التالية وبعد ما تخلص رسم بدأك + +191 +00:21:23,690 --> 00:21:29,420 +تحددلي فترات التزايدوالتناقص لكل دالة من هذه + +192 +00:21:29,420 --> 00:21:34,780 +الدوال الثلاث يجب أن نأتي إلى النقطة الأولى وهي + +193 +00:21:34,780 --> 00:21:41,860 +نمرة A يقول ي يساوي نص X تكييب نص X تكييب ولا تلت + +194 +00:21:41,860 --> 00:21:48,640 +X تكييب ولا ميت X تكييب بيظل الشكل العام متشابه + +195 +00:21:48,640 --> 00:21:53,960 +بتقرب على محور Y أو بتبعدعلى محور Y يبقى أصل + +196 +00:21:53,960 --> 00:21:59,120 +الدالة Y تساوي ضربناها في رقم أقل من واحد الصحيح + +197 +00:21:59,120 --> 00:22:04,640 +يعني بتفتح مبتعدة عن محور Yأكبر من واحدة صحيح تقرب + +198 +00:22:04,640 --> 00:22:09,000 +على محور Y يعني ما علينا مش مشكلة يبقى لو جينا + +199 +00:22:09,000 --> 00:22:15,440 +قولنا هاي المحاور هذا محور X هذا محور Y هذه نقطة + +200 +00:22:15,440 --> 00:22:23,000 +الأصل اللي هي Zero يبقى Y يساوي نص X تكيب بدأ تجين + +201 +00:22:23,000 --> 00:22:33,050 +بالشكل هذايبقى ادي Y يساوي نص X تكيب ارسم رسمنا + +202 +00:22:33,050 --> 00:22:39,350 +المطلوب التاني فترات التزايد وفترات التناقص السؤال + +203 +00:22:39,350 --> 00:22:46,390 +الآن للحدود بدنا نعرف وين فترات التزايد للدالة وين + +204 +00:22:46,390 --> 00:22:52,200 +فترات التناقص لهذه الدالةهل الدالة تزايدية على + +205 +00:22:52,200 --> 00:22:56,600 +طول؟ او هل الدالة تناقصية على طول؟ ايوه يا أخي + +206 +00:22:56,600 --> 00:23:03,960 +العرب زي دايما تسكر لما نهاني ايوة انت اه اه ايوه + +207 +00:23:03,960 --> 00:23:10,920 +تناقصة من سلب ما لا يهاني يعني الدالة تناقصية من + +208 +00:23:10,920 --> 00:23:17,500 +سلب infinity لانفي و لا تزايدية مش سالة كويس من + +209 +00:23:17,500 --> 00:23:18,860 +سفر ل infinity ايش؟ + +210 +00:23:31,990 --> 00:23:37,130 +تعالى نشوف الكلام اللى بيحكي هذا او يدعيه صح ولا + +211 +00:23:37,130 --> 00:23:42,750 +خطأ بيقول زميلكوا شو اسمك انت؟ عبدالهادي؟ + +212 +00:23:45,490 --> 00:23:50,850 +عبدالهد ازمالي بيقول ما يأتي بيقول من سالب + +213 +00:23:50,850 --> 00:23:56,430 +infinity لغاية ال zero decreasing و من عند ال zero + +214 +00:23:56,430 --> 00:24:02,680 +لغاية infinity increasing هكذا يزعمتمام؟ بدنا نشوف + +215 +00:24:02,680 --> 00:24:07,880 +هل الزعم هذا جاي من الضمانة يعني متأكدة الكلام مية + +216 +00:24:07,880 --> 00:24:12,760 +المية و الله الزعم احتمال يكون صدق و احتمال يكون + +217 +00:24:12,760 --> 00:24:17,400 +ماهواش صدق تعالى نشوف بدنا نطبق التعريف اللى عندنا + +218 +00:24:17,400 --> 00:24:20,580 +هنا يبقى خلّينا نيجي على الفترة الأولى اللى قال + +219 +00:24:20,580 --> 00:24:28,020 +فيها هذه تناقصية اذا بدي اخد قيمتين I X واحد وقيمة + +220 +00:24:28,020 --> 00:24:34,320 +تانية I X اتنينيبقى عشان دي X واحد أقل من X اتنين + +221 +00:24:34,320 --> 00:24:40,060 +صحيح ولا لأ؟ لأنه ناقص تلاتة أقل من ناقص اتنين + +222 +00:24:40,060 --> 00:24:45,340 +صحيح ولا لأ؟ يبقى بداجي أنزل رأسي لغاية مقابل + +223 +00:24:45,340 --> 00:24:51,580 +المنحنة ومن هنا بدي أنزل رأسي لغاية مقابل المنحنة + +224 +00:24:51,580 --> 00:25:00,880 +من اللي أصغر هذه والله هذهأه هذه أصغر يعني f of x2 + +225 +00:25:00,880 --> 00:25:09,920 +أكبر من f of x1 لإن ناقص واحد وناقص عشرة ناقص واحد + +226 +00:25:09,920 --> 00:25:18,110 +أكبر من ناقص عشرة تمام يبقى f of x2 أكبر منF of X + +227 +00:25:18,110 --> 00:25:23,090 +واحد ده ما X واحد اقل من X اتنين اكبر يعني مشي + +228 +00:25:23,090 --> 00:25:29,710 +التاني هو انما من يبقى زعمه اللي زعمه خطأ تمام؟ + +229 +00:25:29,710 --> 00:25:34,190 +طبعا هو جالك ايش؟ جالك ناقص عشرة اكبر من ناقص واحد + +230 +00:25:34,190 --> 00:25:39,930 +وبناء عليه زعم هذا الزعم مظبوط؟ يبقى يا عبدالهادي + +231 +00:25:40,210 --> 00:25:45,850 +ماقص عشرة أصغر من ناقص واحد وأصغر من ناقص اتنين + +232 +00:25:45,850 --> 00:25:51,330 +وأصغر من ناقص تمانية تمام إذا بصير الفترة من سالب + +233 +00:25:51,330 --> 00:25:54,810 +infinity إلى zero increasing ولا decreasing + +234 +00:25:56,780 --> 00:26:01,420 +increasing والجزء اللي على الأمين باصمين لك عليه + +235 +00:26:01,420 --> 00:26:07,740 +الدالة تزايدية كل ما تكبر X بالزيادة قيمة Y أو + +236 +00:26:07,740 --> 00:26:12,520 +بالزيادة قيمة F من هنا الدالة هذه increasing على + +237 +00:26:12,520 --> 00:26:19,680 +كل ال real line بلا ستة يبقى هنا بقوله if is + +238 +00:26:19,680 --> 00:26:21,960 +increasing + +239 +00:26:23,080 --> 00:26:28,580 +هو ان الفترة من سالب infinity لإنفينيتي كلها + +240 +00:26:28,580 --> 00:26:34,980 +بلاستثناء ماعنديش decreasing بالمرة طيب نيجي لنمرة + +241 +00:26:34,980 --> 00:26:43,320 +B وما أدرك هما نمرة B ايه نمرة B طلعليه كويس F of + +242 +00:26:43,320 --> 00:26:52,460 +X بده يساوي سالب واحد على absolute value ل Xهذه + +243 +00:26:52,460 --> 00:27:01,160 +تساوي أحد أمرين يا إما السالب واحد على X لما ال X + +244 +00:27:01,160 --> 00:27:05,560 +أكبر من Zero ولا تساوي + +245 +00:27:12,580 --> 00:27:19,920 +لسالب يعني صارت واحد على X لما ال X مالها أقل من + +246 +00:27:19,920 --> 00:27:26,180 +Zero مظبوط ولا لا؟ صحيح؟ يعني أنا بس شيلت ال + +247 +00:27:26,180 --> 00:27:30,780 +absolute value و حطيته تاريخ بصير سالب سالب بصير + +248 +00:27:30,780 --> 00:27:36,400 +موجة بقى تمام؟ طيب بدنا نيجي نرسم رسمتنا هذه هي + +249 +00:27:36,400 --> 00:27:43,020 +المحاور وهذا محور X وهذا محور Yهذه نقطة الأصل + +250 +00:27:43,020 --> 00:27:49,280 +الهيمان Zero رسمة واحد على إكس يجب أن أرسمها قبل + +251 +00:27:49,280 --> 00:27:57,360 +إشارة السالب قبل إشارة السالب يبقى هيها هيك هيها + +252 +00:27:57,360 --> 00:28:05,280 +هيك يبقى المنقطة هذه رسمة من؟ واحد على إكس فقط لا + +253 +00:28:05,280 --> 00:28:11,640 +غيرمش هذا سؤالنا، احنا سؤالنا واحد على absolute + +254 +00:28:11,640 --> 00:28:16,160 +value of X لما أقول absolute value of X يبقى بطل + +255 +00:28:16,160 --> 00:28:21,140 +يصير عندي سالم، إيش بيصير؟ موجب، يعني هذا الجثة + +256 +00:28:21,140 --> 00:28:27,500 +إيش بده يحصل له؟ بده ينقلب ويصير فاضيبقى لو جيت هك + +257 +00:28:27,500 --> 00:28:33,500 +بالشكل اللي عندنا هنا بده يصير هذا مع هذا هو رسمة + +258 +00:28:33,500 --> 00:28:39,560 +واحد على absolute value of X يبقى المنجق فوق هذا + +259 +00:28:39,560 --> 00:28:45,080 +رسمة واحد على absolute value of X مش هذا سؤالنا + +260 +00:28:45,080 --> 00:28:50,340 +سؤالنا السالب واحد على absolute value of X يعني + +261 +00:28:50,340 --> 00:28:54,960 +أنا برابط الدالة كلها في إشاراتيعني اللي كان في + +262 +00:28:54,960 --> 00:28:59,120 +قيمة موجة مابدها تصير سالبة، و اللي كانت سالبة، + +263 +00:28:59,120 --> 00:29:04,300 +يبقى احنا هذه جلبناها و صارت فوق، يبقى مابقالش + +264 +00:29:04,300 --> 00:29:09,260 +عندي تحت ولا حاجة، كل الدالة صارت فوق، سبقت بإشارة + +265 +00:29:09,260 --> 00:29:15,880 +مين، تنجلب كلها وصير وين؟ وصير تحت، يبقى بده يصير + +266 +00:29:15,880 --> 00:29:18,840 +الخط المتواصل هذا + +267 +00:29:22,190 --> 00:29:29,690 +ومن هنا بنفس الطريقة هيك هذا Y تساوي سالب واحد على + +268 +00:29:29,690 --> 00:29:35,470 +absolute value of X تمام؟ يبقى هيرة سمن الدالة + +269 +00:29:35,470 --> 00:29:40,310 +اللي عندنا هذه قبل مجاوب على باقي السؤال اللي خاطر + +270 +00:29:40,310 --> 00:29:46,570 +اسأله السؤال التالي قداش domain هذه الدالة؟ من + +271 +00:29:46,570 --> 00:29:54,510 +ويلة وين؟ ايوةارمى عدى زيرو موافقين يبقى ال domain + +272 +00:29:54,510 --> 00:29:59,470 +من سالب infinity ل infinity عدى ال zero طب بدنا + +273 +00:29:59,470 --> 00:30:07,190 +نيجي لل range ال range هاي هاج قدامك اصطلع فيه بدي + +274 +00:30:07,190 --> 00:30:14,590 +واحد من الشجر هذه ايوة ايوة من سفر مفتوح يعني من + +275 +00:30:14,590 --> 00:30:22,080 +السفر الفوق يعنيمن سلب infinity إلى zero as an + +276 +00:30:22,080 --> 00:30:26,220 +open intervalيبقى ال domain كل الريا الله المعدد + +277 +00:30:26,220 --> 00:30:32,080 +Zero لأن عند Zero تنزل لسالب Infinity تمام هذا ال + +278 +00:30:32,080 --> 00:30:37,160 +domain ال range بتاخدش قيم موجبة انما بس القيم + +279 +00:30:37,160 --> 00:30:41,300 +السالبة اللي أسفل عندنا يبقى من عند السالب + +280 +00:30:41,300 --> 00:30:46,360 +Infinity لغاية من Zero يبقى هذا السؤال زيادة على + +281 +00:30:46,360 --> 00:30:51,340 +ما هو مطلوب أجبنا عليه ربطناه بأول نقطة أخدناها في + +282 +00:30:51,340 --> 00:30:55,550 +هذا section وهي ال domainوالـ Range فبدأ نكمل + +283 +00:30:55,550 --> 00:31:00,350 +سؤالنا Orson رسمنا قال لي هاتلي فترات التزايد + +284 +00:31:00,350 --> 00:31:06,970 +وفترات التناقص لهذه الدلة امسكولي الفترة من سالب + +285 +00:31:06,970 --> 00:31:13,350 +infinity لغاية ال zero بدي اعرف الدلة increasing و + +286 +00:31:13,350 --> 00:31:18,710 +الله decreasing يالا بدي واحد من الشجة هذه يالا + +287 +00:31:18,710 --> 00:31:27,780 +شوف يالا انتوا القوم الكبير ايوةهذه واحد، اتنين و + +288 +00:31:27,780 --> 00:31:32,800 +نص، ثلاثة، اه هذه او هذه او هذه او هذه او هذه او + +289 +00:31:32,800 --> 00:31:33,800 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +290 +00:31:33,800 --> 00:31:36,220 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +291 +00:31:36,220 --> 00:31:36,400 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +292 +00:31:36,400 --> 00:31:36,500 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +293 +00:31:36,500 --> 00:31:36,500 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +294 +00:31:36,500 --> 00:31:36,500 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +295 +00:31:36,500 --> 00:31:38,340 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +296 +00:31:38,340 --> 00:31:38,340 +هذه او هذه او هذه او هذه او هذه او هذه او هذه او + +297 +00:31:38,340 --> 00:31:38,560 +هذه او هذه او هذه او هذه او هذه او هذه او هذه ا + +298 +00:31:39,470 --> 00:31:43,670 +Increasing ولا Decreasing؟ Decreasing كان عقوسيا، + +299 +00:31:43,670 --> 00:31:49,730 +الكلام مصحيح، ليش؟ لأن الوقت أخد أي X هنا واحد و + +300 +00:31:49,730 --> 00:31:59,810 +أي X2 هنا تمام؟ X1 أجل من X2 لكن F of X2 أجل من F + +301 +00:31:59,810 --> 00:32:07,230 +of X1 يبقى على الفترة هذه Decreasing on + +302 +00:32:08,410 --> 00:32:14,490 +من سالب infinity لغاية zero as an open interval + +303 +00:32:14,490 --> 00:32:20,950 +طيب بدنا نيجي من zero لغاية infinity من هنا للاخر + +304 +00:32:20,950 --> 00:32:26,970 +بدنا واحد مش شجيه دي أيوة decrease برضه تناقصية + +305 +00:32:26,970 --> 00:32:34,410 +يعني + +306 +00:32:34,410 --> 00:32:42,450 +اسمع يا شباب شو اسمك انت يا ابنيمحمد .. محمد ايش؟ + +307 +00:32:42,450 --> 00:32:48,910 +محمد رمزي، بنا ترمزنا لنص اليمين تبع الدلة، هل هو + +308 +00:32:48,910 --> 00:32:52,830 +increasing ولا decreasing؟ اعتبر حاجتك، ماقولتش + +309 +00:32:52,830 --> 00:32:56,810 +قبل ذلك، تقولي من جديد، + +310 +00:32:56,810 --> 00:32:58,210 +بس هيمشي شوكوا الشباب + +311 +00:33:01,140 --> 00:33:09,200 +يعني لو أخدت x واحد و أنا x اتنين بصير f of x + +312 +00:33:09,200 --> 00:33:16,740 +اتنينأكبر من F of X واحد لإن كله هذا تاع يبقى + +313 +00:33:16,740 --> 00:33:21,760 +الجزء هذا ماله increasing function يبقى على المص + +314 +00:33:21,760 --> 00:33:29,500 +هذا بقول increasing ده لتزايدية على الفترة من zero + +315 +00:33:29,500 --> 00:33:31,380 +لغاية infinity + +316 +00:33:54,740 --> 00:34:00,980 +طيب هذا نمرة B من المثلة بدنا نيجي لنمرة C يبقى + +317 +00:34:00,980 --> 00:34:08,660 +نمرة Cنمر الـ C تبدأ لمكوّنة من جزئين يبقى عندنا F + +318 +00:34:08,660 --> 00:34:15,120 +of X أحد أمرين يا إما ناقص X لما الـ X أقل من الـ + +319 +00:34:15,120 --> 00:34:19,480 +Zero يا إما تلاتة لما الـ X greater than or equal + +320 +00:34:19,480 --> 00:34:24,920 +to Zero بدنا نروح نرسم الرسم البياني لهذه ال + +321 +00:34:24,920 --> 00:34:30,340 +function يعني هذا محور X وهذا محور Y وهذا نقطة + +322 +00:34:30,340 --> 00:34:32,280 +الأصل اللي هي Zero + +323 +00:34:38,090 --> 00:34:43,170 +خاط مستقيم X أقل من Zero + +324 +00:34:48,520 --> 00:34:54,880 +تساوي سالب X ومن هنا مالها مفتوحة لإن ماعنديش + +325 +00:34:54,880 --> 00:35:02,400 +يساوي تمام يبقى هذه Y يساوي سالب X نجي لغاية بعد + +326 +00:35:02,400 --> 00:35:08,250 +ال zero الدالة دائما و أبدا مش ساوية قداشوكذلك عند + +327 +00:35:08,250 --> 00:35:13,090 +الـ Zero بدأ يساوي تلاتة يبقى تلاتة بدنا نطلع فوق + +328 +00:35:13,090 --> 00:35:19,230 +هي النقطة هذه تلاتة يبقى الخط المستقيم اللي عندنا + +329 +00:35:19,230 --> 00:35:26,690 +هذا يبقى هذا Y يساوي تلاتة قبل ما نجاوب على الجزء + +330 +00:35:26,690 --> 00:35:31,830 +الثاني برضه لخاطر أسأل على domain هذه الدالة من و + +331 +00:35:31,830 --> 00:35:39,560 +لا وين بده domain الدالة هذهكداش؟ كل الار كلامه + +332 +00:35:39,560 --> 00:35:45,980 +صحيح بلا استثناء of all real numbers بدنا ال range + +333 +00:35:45,980 --> 00:35:52,660 +ال range من وين + +334 +00:35:52,660 --> 00:35:58,920 +لوين تاني ال range مش ال domain ال range + +335 +00:36:06,230 --> 00:36:13,750 +أيوة بس من صفر لتلاتة بزيدش هذا + +336 +00:36:13,750 --> 00:36:19,210 +الخط أنا راجع لسالب X لسالب Infinite و هو طالع + +337 +00:36:19,210 --> 00:36:22,690 +الله سهل عليه بوقف عندي التلاتة و الله بضل طالع + +338 +00:36:22,690 --> 00:36:26,490 +يعني + +339 +00:36:26,490 --> 00:36:27,370 +قدش بصير + +340 +00:36:33,800 --> 00:36:42,280 +من صفر لسالب infinity تحت؟ ايوة، + +341 +00:36:42,280 --> 00:36:46,420 +من وين؟ من zero ل infinity، كيف نزلت لسالب + +342 +00:36:46,420 --> 00:36:50,360 +infinity؟ طبعا احنا طالعين فوقالـ Domain سلب ماشي + +343 +00:36:50,360 --> 00:36:54,520 +الحال، بس الـRing طالع فوق، هي رسم الخط المستقيم + +344 +00:36:54,520 --> 00:36:59,000 +الله يسهل عليه، ماشي، ماشي، ماشي، إلى أن يرث الله + +345 +00:36:59,000 --> 00:37:03,520 +الأرض ومن عليها، وماشي، موقفش، تمام؟ يبقى لحد وين + +346 +00:37:03,520 --> 00:37:09,000 +رايح؟ لسلب Infinity ولا لـInfinity؟أحكي يا ابني + +347 +00:37:09,000 --> 00:37:13,400 +ايه؟ طلع اليهرة هذه اللي يبقى الهاتف infinity يبقى + +348 +00:37:13,400 --> 00:37:19,040 +من zero ل infinity من عند ال zero open و من عند ال + +349 +00:37:19,040 --> 00:37:22,440 +infinity open و هذا الطبيعي يبقى ال ring من zero ل + +350 +00:37:22,440 --> 00:37:28,260 +infinity as an open until عمره ما ياخد قيمة سالبة + +351 +00:37:28,560 --> 00:37:32,880 +طيب ماشي الحل مادام هيك بدنا نعيد لك السؤال تاني + +352 +00:37:32,880 --> 00:37:37,840 +انت أيوة من سالب infinity لغاية ال zero الجزء + +353 +00:37:37,840 --> 00:37:45,280 +الأول اتدال عليه increasing و لا decreasing خط + +354 +00:37:45,280 --> 00:37:50,720 +اللي نازل هذا من فوق و رايح على النقطة الأصلي كيف؟ + +355 +00:37:50,720 --> 00:37:59,430 +مش سامع كويسيبقى هنا هذا decreasing function يبقى + +356 +00:37:59,430 --> 00:38:08,470 +ال F is decreasing on ال interval من سلب infinity + +357 +00:38:08,470 --> 00:38:11,790 +لغاية ال zero طب بعد ال zero + +358 +00:38:15,720 --> 00:38:20,640 +يعني ايش؟ يعني ثابت، يعني increasing و decreasing + +359 +00:38:20,640 --> 00:38:27,560 +في نفس الوقت؟ يعني يا جيربي، تبقى increasing و + +360 +00:38:27,560 --> 00:38:31,840 +decreasing في نفس الوقت؟ يا رايل، كيف increasing و + +361 +00:38:31,840 --> 00:38:37,800 +decreasing؟ بدي أفهم هذه كيف تمام؟ يبقى فش حاجة + +362 +00:38:37,800 --> 00:38:42,000 +اسمها increasing و decreasing في نفس الوقت على + +363 +00:38:42,000 --> 00:38:46,520 +فترة تمامةع الفترة يا اما increasing يا decreasing + +364 +00:38:46,520 --> 00:38:50,140 +يا يمكن شوية على فترة increasing و شوية decreasing + +365 +00:38:50,140 --> 00:38:54,380 +لكن على الفترة اللى بدنا يها تبعت السؤال النهائي + +366 +00:38:54,380 --> 00:38:59,780 +بسميها constant function neither increasing nor + +367 +00:38:59,780 --> 00:39:04,940 +decreasing لا تزايد ولا تنقص يبقى ثابوت ده اللى + +368 +00:39:04,940 --> 00:39:10,140 +ثابت هال constant function يبقى باجي بقول ال F is + +369 +00:39:10,140 --> 00:39:19,890 +neitherincreasing nor decreasing + +370 +00:39:22,280 --> 00:39:29,540 +on الفترة من عند الـ zero لغاية infinity بالشكل + +371 +00:39:29,540 --> 00:39:35,180 +اللي عندنا هذا يبقى هذه class interval او بين جثين + +372 +00:39:35,180 --> 00:39:43,440 +بنسميها constant function يبقى دالة ثابتة كويس هذا + +373 +00:39:43,440 --> 00:39:51,150 +بالنسبة الى C بدنا نيجي بالنسبة الى Dيبقى دي بيقول + +374 +00:39:51,150 --> 00:39:58,090 +ال F of X يساوي ال square root لتسعة ناقص X تربية + +375 +00:39:58,090 --> 00:40:05,090 +السؤال لكم ما عدلتش هذه F of X يساوي الجدر التربية + +376 +00:40:05,090 --> 00:40:10,990 +لتسعة ناقص X تربية يعني Y تساوي الجدر التربية + +377 +00:40:10,990 --> 00:40:16,950 +لتسعة ناقص X تربية ما عدلتش دائرة ممتازة ده مركزها + +378 +00:40:18,230 --> 00:40:30,890 +النقطة الأصل و نص قطرها يبقى + +379 +00:40:30,890 --> 00:40:39,210 +دائرة مركزها النقطة الأصل و نص قطرها يبقى دائرة + +380 +00:40:39,210 --> 00:40:41,750 +مركزها النقطة الأصل و نص قطرها يبقى دائرة مركزها + +381 +00:40:41,750 --> 00:40:41,750 +النقطة الأصل و نص قطرها يبقى دائرة مركزها النقطة + +382 +00:40:41,750 --> 00:40:41,950 +الأصل و نص قطرها يبقى دائرة مركزها النقطة الأصل و + +383 +00:40:41,950 --> 00:40:44,290 +نص قطرها يبقى دائرة مركزها النقطة الأصل و نص قطرها + +384 +00:40:44,290 --> 00:40:54,120 +يبقىهل هي هذه أو تلك يبقى هذا محور X هذا محور Y + +385 +00:40:54,120 --> 00:41:01,860 +بجي بطلع قبل الجذر في عندي سالب وموجب ولا بس موجب؟ + +386 +00:41:01,860 --> 00:41:06,700 +وين هو السالب والموجب؟ يبقى أنا مش كاتب إلا موجب + +387 +00:41:06,700 --> 00:41:12,200 +عارفين لو كنت كاتب سالب وموجب بطلت الصير function + +388 +00:41:13,080 --> 00:41:21,050 +يا سالب فقط يا إما موجب فقط حتى تصبحيبقى هنا + +389 +00:41:21,050 --> 00:41:28,090 +الإشارة Y تساوي قيمة موجبة فقط إذا أنا عندي نص + +390 +00:41:28,090 --> 00:41:31,910 +الدائرة اللي على اليمين و الله اللي على الشمال و + +391 +00:41:31,910 --> 00:41:33,990 +الله اللي فوق و الله اللي تحت + +392 +00:41:48,620 --> 00:41:53,760 +أذا هذه لو جيت رسمتها تعطيني النص في الدائرة + +393 +00:41:53,760 --> 00:42:02,380 +العلوي بهذا الشكل هذه سالب تلاتة و Zero هذه تلاتة + +394 +00:42:02,380 --> 00:42:09,600 +و Zero هذه Zero و تلاتة وهذه نقطة الأصل اللي هي + +395 +00:42:09,600 --> 00:42:17,430 +Zero ارسم رسمنا ال domain من و لا و اين؟سالب تلاتة + +396 +00:42:17,430 --> 00:42:23,510 +لا تلاتة و ال range من zero لغاية تلاتة تمام تمام + +397 +00:42:23,510 --> 00:42:28,390 +طيب مش هذا اللي بدنا .. بدنا وين increasing وين + +398 +00:42:28,390 --> 00:42:32,750 +decreasing او هل هي increasing على طول او + +399 +00:42:32,750 --> 00:42:37,110 +decreasing على طول يالا بدنا من هنا من الشجة دي و + +400 +00:42:37,110 --> 00:42:43,250 +النصف الأخيرة ايوة اللي في مقرافع يده الشماليعني + +401 +00:42:43,250 --> 00:42:50,370 +بيقول الامير عفر إيده الشمال من ثالث ثلاثة إلى + +402 +00:42:50,370 --> 00:42:54,330 +زيرو إلى increasing + +403 +00:42:56,170 --> 00:43:05,650 +ممتاز جدا يبقى هنا ال F is increasing دالة تزايدية + +404 +00:43:05,650 --> 00:43:10,930 +على الفترة من سالف تلاتة لغاية Zero لأن الدالة + +405 +00:43:10,930 --> 00:43:17,430 +معرفة هنا ومعرفة هنا تمام بعد هيك ال F is + +406 +00:43:17,430 --> 00:43:27,840 +decreasing onالفترة من Zero لغاية تلاتة يبقى هنا + +407 +00:43:27,840 --> 00:43:37,280 +هذه increasing وهنا decreasing ده التناقصية على + +408 +00:43:37,280 --> 00:43:49,190 +هذه الفترة ايوة وانا بدأ أسأل مش سامع كويسوزلل + +409 +00:43:49,190 --> 00:43:54,990 +ليش؟ وزلل ليش عشان مقفل الفترة؟ صح ولا لأ تلامنا؟ + +410 +00:43:54,990 --> 00:44:04,230 +في نقطة مشتركة ما بين الفترتين، مظبوط ولا لأ؟ كيف؟ + +411 +00:44:04,230 --> 00:44:11,830 +مانقلة ذلك، بطل تحسب لهنا و بتداوقف لهنا، بتداوقف + +412 +00:44:11,830 --> 00:44:13,830 +لعندها، increasing ولا لأ؟ + +413 +00:44:27,600 --> 00:44:38,800 +ننتقل الآن إلى نقطة أخرى بعد ال increasing و + +414 +00:44:38,800 --> 00:44:44,630 +ال decreasingالو ال even و ال odd functions الدوال + +415 +00:44:44,630 --> 00:45:04,750 +الزوجية و الدوال الفردية اه + +416 +00:45:04,750 --> 00:45:10,690 +لو نزليبقى متجسمة لفترات على فترة increasing وعلى + +417 +00:45:10,690 --> 00:45:15,210 +فترة دانية decreasing و هكذا لبعض increasing لبعض + +418 +00:45:15,210 --> 00:45:24,130 +decreasing تمام تمام طيب نجي لنقطة جديدة ال even + +419 +00:45:24,130 --> 00:45:27,150 +and + +420 +00:45:27,150 --> 00:45:40,730 +odd functions و كذلك ال symmetryالتماثل من الرسالة + +421 +00:45:40,730 --> 00:45:45,110 +ايوة هدى + +422 +00:45:45,110 --> 00:45:54,650 +ولا هدى دى فوق كيف هدى + +423 +00:45:54,650 --> 00:46:03,510 +X واحد و هدى X اتنين مين اللى صغيرة فيهاأقل من X2، + +424 +00:46:03,510 --> 00:46:12,790 +من الكبيرة فيهم؟ من الكبيرة ومن الصغيرة؟ مش هذه F + +425 +00:46:12,790 --> 00:46:20,760 +of X2 و هذه F of X1؟يبقى f of x2 مالها يبقى + +426 +00:46:20,760 --> 00:46:26,800 +decreasing ولا حسب التعريف f of x2 أقل من f of x1 + +427 +00:46:26,800 --> 00:46:31,020 +ده ما x1 أقل من x2 يبقى decreasing مظبوط ولا لأ + +428 +00:46:31,020 --> 00:46:39,960 +يبقى صح ولا لأ لا هي عمرنا ما جولنا x1 أقل من x2 + +429 +00:46:39,960 --> 00:46:49,010 +يعني x2 أكبر من x1 صح ولا لألما ندى نقول ان X1 أقل + +430 +00:46:49,010 --> 00:46:54,690 +من X2 بدك تجرها من ناحية تانية ماعنى مشكلة X2 أكبر + +431 +00:46:54,690 --> 00:47:00,450 +من X1 F of + +432 +00:47:00,450 --> 00:47:08,390 +X2 ايوة تجي الله يا راجل هدى أكبر من هدى + +433 +00:47:14,950 --> 00:47:19,910 +خلاص؟ مسحوبة؟ حط + +434 +00:47:19,910 --> 00:47:26,110 +وين ما بدك و اكتب مين اللي فيهم الصغراء هذا عامل + +435 +00:47:26,110 --> 00:47:29,570 +مش لشان واحد اقل من اتنين يعني اكس واحد اقل من + +436 +00:47:29,570 --> 00:47:33,030 +اتنين لأ بدا اكتب ايه يا ربي؟ + +437 +00:47:44,770 --> 00:47:52,820 +يبقى f of b أقل من f of a يبقى decreasingمظبوط؟ F + +438 +00:47:52,820 --> 00:47:57,880 +of B أكبر من F of A يبقى increasing يبقى X واحد و + +439 +00:47:57,880 --> 00:48:03,060 +X اثنان هذا رمز اطول مانقال اجباري و ليس القرآن + +440 +00:48:03,060 --> 00:48:08,200 +نزل من السماء ايوة يا راجل كل الكلام فارق كله + +441 +00:48:08,200 --> 00:48:11,180 +أخدته في الثانوية نفسي بسبق ان عربة بقيت بانجليزي + +442 +00:48:11,180 --> 00:48:13,400 +بس مش أكتر اما كله أخدته هذا + +443 +00:48:25,180 --> 00:48:32,140 +سمعتش قناة هناك اي رنز ما انت ان القيمة تبعها تبقى + +444 +00:48:32,140 --> 00:48:36,920 +تحسب F of X يعني F of A و F of B يبقى انا بتقيت + +445 +00:48:36,920 --> 00:48:42,360 +بالقيم وليش ده بالرموز ارمز زي ما بدك و بعدين انت + +446 +00:48:42,360 --> 00:48:47,720 +ويا تعالي هنا على الهجوم يالا بسرعة نشوف اكتشافاتك + +447 +00:48:47,720 --> 00:48:52,060 +للسوفر كولومبوس يالا يا ابني ارهج بسرعة + +448 +00:48:56,210 --> 00:49:03,090 +فضل هنا هايا الجلام و احكي خلّي + +449 +00:49:03,090 --> 00:49:06,550 +مالك هنا يا شباب نسمع يمكن نلاقي حاجة جديدة ما + +450 +00:49:06,550 --> 00:49:10,130 +نعرفاش تفضل مثلا + +451 +00:49:10,930 --> 00:49:14,810 +هذه سالب خمسة وهذه سالب واحد مثلا + +452 +00:49:44,690 --> 00:49:51,410 +خلاص انت ويا نجي لثلاث نقاط مهمة الآن في الشغل + +453 +00:49:51,410 --> 00:49:57,430 +اللي هي الدالة الزوجية والدالة الفردية وتماثل + +454 +00:49:57,430 --> 00:50:03,790 +المنحنى symmetry تماثل هناخد تماثل بالنسبة لمحور X + +455 +00:50:03,790 --> 00:50:10,330 +تماثل بالنسبة لمحور Yتماثل بالنسبة لنقطة الأصل + +456 +00:50:10,330 --> 00:50:16,570 +تمام طيب بدنا نعطي تعريف لل even و ال odd function + +457 +00:50:16,570 --> 00:50:22,110 +ثم تعريف لل symmetry بالنسبة لل x و ال y و نقطة + +458 +00:50:22,110 --> 00:50:30,170 +الأصل يبقى بالضاجي لل definition تعريف الأول the + +459 +00:50:30,170 --> 00:50:32,350 +function + +460 +00:50:34,290 --> 00:50:45,750 +F is called an even function + +461 +00:50:45,750 --> 00:50:56,750 +if F of ناقص X بدي سوى F of X لكل X الموجودة في + +462 +00:50:56,750 --> 00:50:58,410 +دمية دالة F + +463 +00:51:01,090 --> 00:51:08,930 +الـ function F is called an odd function F الـ F + +464 +00:51:08,930 --> 00:51:15,630 +of سالب X يساوي سالب F of X لكل الـ X اللي موجودة + +465 +00:51:15,630 --> 00:51:26,250 +في دمين الدالة F نمرة تلاتة The graph of + +466 +00:51:26,250 --> 00:51:43,910 +the functionis symmetric يكون متماثلا about the x + +467 +00:51:43,910 --> 00:51:55,610 +axis حوالين محور x means that يعني انه ايش means + +468 +00:51:55,610 --> 00:52:07,280 +thatإن الـ x و ال y lie on the graph if and only + +469 +00:52:07,280 --> 00:52:17,420 +if إذا و فقط إذا كان ال x و ناقص y lie on the + +470 +00:52:17,420 --> 00:52:18,080 +graph + +471 +00:52:56,730 --> 00:52:59,950 +خدتوا الدالة الزوجية والدالة الفردية في المرحلة + +472 +00:52:59,950 --> 00:53:07,350 +الثانوية بالمرة نهائية خلاص مصدقين يا عم حتى لو + +473 +00:53:07,350 --> 00:53:13,110 +أخدت مدي أعتبرك مش ماخد وبدنا نبدأ من الصفر بس + +474 +00:53:13,110 --> 00:53:20,290 +مديك تطلع فاهم أيه اللي مديه طيب بين إيدينا ثلاث + +475 +00:53:20,290 --> 00:53:27,630 +نقاط رئيسة ال even function الدالة الزوجيةالـ Odd + +476 +00:53:27,630 --> 00:53:33,550 +function الدالة الفردية تلاتة السيمتري والسيمتري + +477 +00:53:33,550 --> 00:53:38,950 +هنقسمه إلى تلات نقاط سيمتري بالنسبة لمحور X سيمتري + +478 +00:53:38,950 --> 00:53:45,090 +بالنسبة لمحور Y سيمتري بالنسبة لنقطة الأصل بدنا + +479 +00:53:45,090 --> 00:53:51,190 +نيجي للتعريف اللي بين أديناتعريف الأول بيقول + +480 +00:53:51,190 --> 00:53:58,050 +الدالة F بقول عنها دالة زوجية even function F ال F + +481 +00:53:58,050 --> 00:54:03,950 +of سلب X بديه ساوي F of X لكل ال X اللي موجودة في + +482 +00:54:03,950 --> 00:54:09,670 +دمية ال F بلا استثناءيعني ايش قصدك تقول اه لما + +483 +00:54:09,670 --> 00:54:15,710 +اقول f of ناقص x بده يساوي ال f of x يعني ايش يعني + +484 +00:54:15,710 --> 00:54:21,030 +لو جيت على الدالة اللي عندنا شيلت x وحطيت مكانها + +485 +00:54:21,030 --> 00:54:27,630 +سالب x تبقى الدالة كما هي بدون تغيير أبسط الأمثلة + +486 +00:54:27,630 --> 00:54:33,830 +لو قلتك f of x يساوي x تربية شيل ال x وحق مكانها + +487 +00:54:33,830 --> 00:54:40,530 +ناقص x بصير ناقص x الكلاللي هي مين؟ X تربيع يبقى + +488 +00:54:40,530 --> 00:54:47,170 +هذه بسميها ايه؟ دالة زوجية طيب تمام نيجي للدالة + +489 +00:54:47,170 --> 00:54:53,970 +الفردية الدالة F بقول عنها دالة فردية إذا كان F of + +490 +00:54:53,970 --> 00:54:59,410 +ناقص X يساوي ناقص F of X لكل ال X اللي موجودة في + +491 +00:54:59,410 --> 00:55:04,590 +domain الدالة F بمعنىلو شيلت ال X وحطيت مكانها + +492 +00:55:04,590 --> 00:55:08,410 +ناقص X اللي هو ال variable تبع ال function بدا + +493 +00:55:08,410 --> 00:55:14,250 +تطلع نفس الدالة الأصلية بس مسبوقة بإشارة إن حدث + +494 +00:55:14,250 --> 00:55:19,850 +ذلك بقول هذه odd function يبقى هذه هي دالة فردية + +495 +00:55:19,850 --> 00:55:25,030 +طيب يبقى في فروقات الآن ما بين الدالة الفردية + +496 +00:55:25,030 --> 00:55:30,640 +والدالة الزوجيةالدالة الزوجية لا تتأثر بتغيير + +497 +00:55:30,640 --> 00:55:35,640 +الإشارةالدالة الفردية إذا غيرت الإشارة بدأ تجي + +498 +00:55:35,640 --> 00:55:41,200 +إشارة سالب لكل ال function بلا ستة نعم مظبوط هيك + +499 +00:55:41,200 --> 00:55:46,500 +طيب نجي لحكاية التماثل خلي بالك معايا هنا نجي نمرة + +500 +00:55:46,500 --> 00:55:51,020 +تلاتة ال graph of the function is symmetric about + +501 +00:55:51,020 --> 00:55:57,140 +the x axis المنحنة تبع الدالة يكون متماثلا بالنسبة + +502 +00:55:57,140 --> 00:56:02,480 +لمحور X المقصود بالبلديعني الرسم اللي أعلى محور X + +503 +00:56:02,480 --> 00:56:09,000 +بيظهر الرسم زيها بالضبط وعلى نفس البعد من محور X + +504 +00:56:09,000 --> 00:56:13,900 +يبقى لو كانت اللي فوق محور X ال Y عندها بالموجة + +505 +00:56:13,900 --> 00:56:19,610 +تظهر رسم زيها تحت محور X بيصير مين؟بالسالب، يعني + +506 +00:56:19,610 --> 00:56:24,610 +لو كانت النقطة X وY موجودة على المنحنة، بدا تظهر + +507 +00:56:24,610 --> 00:56:30,830 +جبلها تحت نقطة X وY، الإحداث السيني زي ما هو، + +508 +00:56:30,830 --> 00:56:35,320 +الخلاف صار في من؟ في الإحداث الصادرفراح قال لي هذه + +509 +00:56:35,320 --> 00:56:40,680 +معناها ايش means that تعني انه لو النقطة x و y + +510 +00:56:40,680 --> 00:56:48,340 +وقعت على المنحنة يبقى يجب ان النقطة x و سالب y تقع + +511 +00:56:48,340 --> 00:56:55,840 +كذلك عالميا على المنحنة تمام تمام ايضا بال if هذا + +512 +00:56:55,840 --> 00:57:05,300 +اختصار لكلمة if and only ifاللي كنتوا في الثانوية + +513 +00:57:05,300 --> 00:57:12,660 +بتقولولها إذا و فقط إذا كان مش هيك؟طيب إذا وفقت + +514 +00:57:12,660 --> 00:57:18,260 +إذا كان ترجمته بالإنقليزي if and only if وتختصر + +515 +00:57:18,260 --> 00:57:24,500 +إلى IFF هذا من ناحية اللغة لكن من ناحية المرياضية + +516 +00:57:24,500 --> 00:57:30,940 +إيش معناها؟ if and only if يعني هذه العبارة ممكن + +517 +00:57:30,940 --> 00:57:36,740 +تقراها من الشمال لليمين وممكن من اليمين للشمال هذا + +518 +00:57:36,740 --> 00:57:42,420 +بالكلام البلديلكن بالكلام الرياضي لو أعطيت النقطة + +519 +00:57:42,420 --> 00:57:47,320 +هذه و المنحنة كانت متمثل بالنسبة لمحور X لازم + +520 +00:57:47,320 --> 00:57:52,720 +تلاقي النقطة هذه موجودة على المنحنة و العكس لو كان + +521 +00:57:52,720 --> 00:57:57,600 +المنحنة متمثل بالنسبة لمحور X لاجيت النقطة هذه على + +522 +00:57:57,600 --> 00:58:04,280 +المنحنة لازم تلاقي النقطة هذه موجودة على المنحنة + +523 +00:58:04,280 --> 00:58:10,420 +يعني الاتجاه بصيرفي اتجاهين متعاكسين وكل الاتجاهين + +524 +00:58:10,420 --> 00:58:19,220 +يكونوا صحيحا طيب ايش رأيك انا بدي اربع ال symmetry + +525 +00:58:19,220 --> 00:58:26,020 +بال even وال odd functionو بعد هيك هرسملك اللي هو + +526 +00:58:26,020 --> 00:58:31,880 +التلات رسومات كيف تربطهم بيقولك اه ال even + +527 +00:58:31,880 --> 00:58:37,800 +function الدالة الزوجية و لو روحت رسمت المنحنة + +528 +00:58:37,800 --> 00:58:44,600 +تبعها بيكون متمثل بالنسبة لمحور Y يعني الرسم اللي + +529 +00:58:44,600 --> 00:58:49,600 +على يمين محور Y زي الرسم اللي على شمال محور Y + +530 +00:58:49,600 --> 00:58:57,110 +تمام؟يعني إيش؟ يعني لو قلنا هذا مجسم أو هذا بني + +531 +00:58:57,110 --> 00:59:03,370 +آدم واجب فينا وهذا المحور هو محور وي المرأة + +532 +00:59:03,370 --> 00:59:09,330 +المستوية يبقى صورة هذا المجسم بتظهر وين؟ على الشجة + +533 +00:59:09,330 --> 00:59:13,450 +التانية وعلى نفس البعد يبقى المنحنة اللي على + +534 +00:59:13,450 --> 00:59:19,220 +اليمينبدى يظهر منحنى تانى على شمال محور زى وعلى + +535 +00:59:19,220 --> 00:59:25,940 +نفس main وعلى نفس البعد بمعنى اخر لو كانت النقطة x + +536 +00:59:25,940 --> 00:59:33,480 +و y على يمين محور y على منحنى تظهر نقطة مقابلة على + +537 +00:59:33,480 --> 00:59:40,240 +الشمال اللى من سالب x و y اجباله تمام هى x و y + +538 +00:59:40,240 --> 00:59:44,990 +يبقى هنا سالب x و yيبقى إذا وقت النقطة X وY على + +539 +00:59:44,990 --> 00:59:50,730 +المنحنة فتظهر النقطة سالب X وY على المنحنة هذا + +540 +00:59:50,730 --> 00:59:57,270 +التماثل بالنسبة لمحور Y وهي الدالة الزوجية ضايل + +541 +00:59:57,270 --> 01:00:01,710 +عندي كمان نقطة بدنا نخلصه ضايل مين الدالة الفردية + +542 +01:00:01,710 --> 01:00:08,190 +الدالة الفردية معناها أن الرسم البياني للدالة + +543 +01:00:08,190 --> 01:00:15,070 +متماثل بالنسبة لنقطة الأصلمعناه ان اي نقطة ليحدث + +544 +01:00:15,070 --> 01:00:23,070 +الى x و y بدها تظهر نقطة سالب x و سالب y يعني + +545 +01:00:23,070 --> 01:00:27,190 +البعد على محور x من الناحية دي بده يظهر بعد من + +546 +01:00:27,190 --> 01:00:31,010 +الناحية التانية بعد هنا بده يظهر على نفس البعد + +547 +01:00:31,010 --> 01:00:34,970 +نقطة مناضرة لها من الناحية التانية يبقى هذا + +548 +01:00:34,970 --> 01:00:40,250 +التماثل بالنسبة يعني لو وقعت نقطة في الرابع الأول + +549 +01:00:40,580 --> 01:00:44,820 +نظرتها بتيجي في التالت لو وقعت في التاني نظرتها + +550 +01:00:44,820 --> 01:00:47,540 +بتيجي في الرابع الرابع + +551 +01:00:50,180 --> 01:00:55,640 +نرسم الرسمات وبعد ذلك بنكون جوابنا على الأسئلة + +552 +01:00:55,640 --> 01:00:59,960 +اللى بتدور فى دماغك وانت ماانتش دارى او دارى سيام + +553 +01:00:59,960 --> 01:01:05,420 +يبقى بدي اكتب هذا على شكل ال remark التالية remark + +554 +01:01:05,420 --> 01:01:11,760 +زى علامة او زى شغلة مشهورة او ما إلى ذلك يبقى هنا + +555 +01:01:11,760 --> 01:01:12,620 +remark + +556 +01:01:15,190 --> 01:01:20,190 +الـ remark بتقول ما يتعجسمها إلى نقطتين النقطة + +557 +01:01:20,190 --> 01:01:25,530 +الأولى the graph of + +558 +01:01:25,530 --> 01:01:35,670 +an even function الدالة الزوجية is symmetric + +559 +01:01:35,670 --> 01:01:39,290 +متماثلا + +560 +01:01:39,290 --> 01:01:43,450 +about the + +561 +01:01:44,350 --> 01:01:56,190 +Y Axis حوالين محور X لإيش؟ since لإن ال F سلب X + +562 +01:01:56,190 --> 01:02:06,130 +بده يسوى من ال F of X أي أنة that is أي أنة a + +563 +01:02:06,130 --> 01:02:10,710 +point XY + +564 +01:02:10,710 --> 01:02:11,230 +Lie + +565 +01:02:14,820 --> 01:02:28,740 +on the graph if and only if سلب x و y lie on the + +566 +01:02:28,740 --> 01:02:32,880 +graph نمره + +567 +01:02:32,880 --> 01:02:47,820 +اتنين the graph of an odd functionis symmetric + +568 +01:02:47,820 --> 01:02:51,940 +about + +569 +01:02:51,940 --> 01:03:05,500 +the origin تمثل بالنصب لنقطة الأصل since نظرا لإنه + +570 +01:03:05,990 --> 01:03:20,630 +الـ F of سالب X دي ساوي سالب F of X that is I N, a + +571 +01:03:20,630 --> 01:03:32,520 +point النقطةوالـ y lie on the graph على الرسم + +572 +01:03:32,520 --> 01:03:43,760 +البياني if and only if سلب x وسلب y lie on the + +573 +01:03:43,760 --> 01:03:44,940 +graph + +574 +01:03:47,920 --> 01:03:52,900 +إلا إن هذا الكلام بدي أرسمه على الطبيعة مشان شوفه + +575 +01:03:52,900 --> 01:03:57,800 +على الطبيعة كيف بيحصل تمثل بالنسبة ل X تمثل + +576 +01:03:57,800 --> 01:04:02,940 +بالنسبة ل Y تمثل بالنسبة لل origin وكيف علاقته هذا + +577 +01:04:02,940 --> 01:04:08,220 +مع ال even و ال odd function مع الدالة الزوجية و + +578 +01:04:08,220 --> 01:04:15,570 +الدالة الفرديةلذلك بالداجل الحالي هنا رقم تلاتة + +579 +01:04:15,570 --> 01:04:21,710 +قال للرسم البياني للدالة يكون متمثلا حول محور X + +580 +01:04:21,710 --> 01:04:28,110 +معناه هذا إن لو وقعت النقطة X وY على المنحنة فإن + +581 +01:04:28,110 --> 01:04:34,730 +النقطة X و سالف Y تقع على المنحنة والعكس بالعكس + +582 +01:04:34,730 --> 01:04:43,340 +افترض عند محاور شكل هذا هذا محور Xوهذا محور Y رحنا + +583 +01:04:43,340 --> 01:04:49,780 +رسمنا أي منحنى فمثلا كان المنحنى اللي عندنا بالشكل + +584 +01:04:49,780 --> 01:04:53,220 +هذا جينا + +585 +01:04:53,220 --> 01:05:00,860 +أخدنا أي نقطة على المنحنى ولي تكون النقطة XY يبقى + +586 +01:05:00,860 --> 01:05:07,260 +وين ال X؟ يبقى هذا البعد هو X وهذا البعد ماله؟ هو + +587 +01:05:07,260 --> 01:05:13,680 +Yالنقطة المناظرة في تماثل بالنسبة لمحور X يعني + +588 +01:05:13,680 --> 01:05:19,120 +الرسم اللي أعلى محور X في رسم زيها بالضبط تماما + +589 +01:05:19,120 --> 01:05:24,960 +باسم مقلوبة أسفل محور X يعني لو مديت هذا على + +590 +01:05:24,960 --> 01:05:32,020 +استقامته بديكون الطول هذا جد الطول هذاهذا Y موجب + +591 +01:05:32,020 --> 01:05:41,000 +هذا Y سالب يبقى هذه سالب Y يبقى هذه سالب Y لكن ال + +592 +01:05:41,000 --> 01:05:47,660 +X هذه هل تغيرت؟ لأ يبقى إحداث النقطة هذه بظل X زي + +593 +01:05:47,660 --> 01:05:55,360 +ما هو سالب Yيبقى إن حدث ذلك أي نقطة على المنحنة X + +594 +01:05:55,360 --> 01:06:00,820 +وY اللى جيتك بالها أسفل منها تماما وعلى نفس البعد + +595 +01:06:00,820 --> 01:06:06,760 +من محور X نقطة تانية إحداثيها X و سالب Y يبقى هذا + +596 +01:06:06,760 --> 01:06:11,300 +النقطة معاها أو المنحنة بيكون متماثل بالنسبة لمحور + +597 +01:06:11,300 --> 01:06:17,780 +X يعني لو قلتلك هذه النقطة كانت واحد وواحديكون + +598 +01:06:17,780 --> 01:06:21,900 +النقطة هذه واحد و سالب واحد فواحد تاني يقول لي طب + +599 +01:06:21,900 --> 01:06:25,940 +لو كانت النقطة في الشجة التانية بقول له في الشجة + +600 +01:06:25,940 --> 01:06:32,940 +التانية يعني وين؟ يعني هنا تمام؟ يبقى هذه بصير + +601 +01:06:32,940 --> 01:06:41,300 +عنده هنا سالب X يبقى سالب X و Y تمام؟ بدها تظهر + +602 +01:06:41,300 --> 01:06:46,480 +نقطة جبالها على الشكل هذاالـ X مش هيحصل فيها ولا + +603 +01:06:46,480 --> 01:06:53,060 +حاجة يبقى السالب X ستبقى كما هي بس ال Y هذا ايش + +604 +01:06:53,060 --> 01:06:58,580 +بده يصير لها ده يصير سالب Y يبقى سالب X وسالب Y + +605 +01:06:58,580 --> 01:07:03,600 +يبقى الإحداث الأول مش هيحصل عليه أي تغيير وانما + +606 +01:07:03,600 --> 01:07:08,800 +الإحداث الثاني هو اللي بيحصل عليه تغيير من هنا + +607 +01:07:08,800 --> 01:07:14,350 +بقول المنحنة اللي قدامنا هذا متمثل بالنسبةلمحور X + +608 +01:07:14,350 --> 01:07:20,270 +طيب انتهينا من النقطة الأولى اللى تعتى الرسم الان + +609 +01:07:20,270 --> 01:07:25,230 +بدى اربط ال even و ال odd مع مين مع باقي ال + +610 +01:07:25,230 --> 01:07:31,170 +symmetry يبقى بداجى اخد التماثل بالنسبة لمحور Y + +611 +01:07:31,170 --> 01:07:34,310 +يبقى + +612 +01:07:34,310 --> 01:07:41,250 +هذا منحنا محور X وهذا محور Y وهذا نقطة الأصل اللى + +613 +01:07:41,250 --> 01:07:50,730 +هي Zeroلو رسمت منحنى وطلع المنحنى بالشكل اللى + +614 +01:07:50,730 --> 01:07:58,750 +عندنا فكان + +615 +01:07:58,750 --> 01:08:01,050 +المنحنى بالشكل اللى عندنا + +616 +01:08:06,160 --> 01:08:10,780 +المنحنى هذا هي محور و Y جاي في النص يبقى الرسم + +617 +01:08:10,780 --> 01:08:14,980 +اللي على اليمين زي مين زي الرسم اللي على الشمال + +618 +01:08:14,980 --> 01:08:21,560 +بالضبط تماما يبقى مافي مشكلة الرسم ازاي ماهي ماشية + +619 +01:08:21,560 --> 01:08:28,450 +بالشكل هذابدي اخد اي نقطة موجودة هنا يبقى النقطة + +620 +01:08:28,450 --> 01:08:33,550 +هذه لو نزلتك بيكون البعد هذا ماله X والبعد هذا + +621 +01:08:33,550 --> 01:08:40,240 +يبقى النقطة هذه اللي احدثت تبعها XYلو جيت من هذه + +622 +01:08:40,240 --> 01:08:47,320 +النقطة نزلت عمود على محور Y ومديته على استقامته + +623 +01:08:47,320 --> 01:08:55,720 +هنا يبقى هذه النقطة بتكون جد هذه بالضبط تماما اللي + +624 +01:08:55,720 --> 01:09:01,040 +هي هذه جد هذه بالضبط تماما وبالتالي بيصير إحداث + +625 +01:09:01,040 --> 01:09:10,060 +النقطة هذه ناقص X وY بالضبط تماماطيب هذه Y يعني + +626 +01:09:10,060 --> 01:09:17,200 +هذه X وهذه مين؟ F of X صحيح ولا لا؟ هذه اللي هو + +627 +01:09:17,200 --> 01:09:26,060 +سلب X و F of سالب X لحداتي تبعها البعد الرأسي هذا + +628 +01:09:26,060 --> 01:09:31,430 +هو نفس البعد الرأسي هذا ولا لا؟يبقى النقطة هذه + +629 +01:09:31,430 --> 01:09:37,170 +البعد هذا جد البعد هذا البعد من هو f of x وهذا + +630 +01:09:37,170 --> 01:09:42,370 +البعد من يبقى اتنين هذول بيسووا بعض f of سالب x + +631 +01:09:42,370 --> 01:09:46,690 +بيسووا معين f of x مش هذا تعريف ال even function + +632 +01:09:46,690 --> 01:09:52,670 +ولا لاإذا ال even function هي الرسم البياني لها + +633 +01:09:52,670 --> 01:09:58,230 +دالة هذه الدالة رسمتها متمثلة بالنسبة لمحور Y يعني + +634 +01:09:58,230 --> 01:10:02,350 +الجزء اللي على يمين محور Y زي الجزء اللي على + +635 +01:10:02,350 --> 01:10:08,810 +الشمال محورك كأنه هو هو بس مقلوب عبر مرآة مستوية + +636 +01:10:08,810 --> 01:10:13,970 +يعني لو حطيت المرآة المستوية على محور Y تظهر الرسم + +637 +01:10:13,970 --> 01:10:19,050 +هذه مقلوبة وين؟في النهاية تنزعى انت الصبح لما بدك + +638 +01:10:19,050 --> 01:10:23,890 +تيجى على الجامعة توقف قدام المرآة لو قولنا المرآة + +639 +01:10:23,890 --> 01:10:27,690 +هذه المحور ويبقى تظهر صورتك وين؟ على الناحية + +640 +01:10:27,690 --> 01:10:32,570 +التانية بس مقلوبة انا متجه غربنا الصورة بتبين وين؟ + +641 +01:10:32,570 --> 01:10:40,020 +شرقا يبقى الصورة مقلوبة عبر مين؟ محورهذه الان بشكل + +642 +01:10:40,020 --> 01:10:44,220 +لو انا موجهه على محور Y من الناحية هذه بيصير موجهه + +643 +01:10:44,220 --> 01:10:49,740 +على محور Y من الناحية الثانية يبقى المنحنة متماثل + +644 +01:10:49,740 --> 01:10:54,980 +بالنسبة لمحور Y وبالتالي هذه بقول عنها even + +645 +01:10:54,980 --> 01:11:00,850 +functionيبقى الرسم البياني للدالة الزوجية يكون + +646 +01:11:00,850 --> 01:11:08,490 +متماثلا بالنسبة لمحور Y طيب نجل النقطة الثالثة + +647 +01:11:08,490 --> 01:11:16,770 +والاخيرةيبقى لو جيت قولت هذا محور X هذا محور Y هذا + +648 +01:11:16,770 --> 01:11:24,670 +نقطة الأصل تمام باجي بقول لو أخدت المنحنة مثلا Y + +649 +01:11:24,670 --> 01:11:32,910 +تساوي X تكيب الشكل اللي عندها يبقى هذا Y تساوي X + +650 +01:11:32,910 --> 01:11:40,210 +تكيبجينا قولنا لك خدك اي نقطة على المنحنة و التكن + +651 +01:11:40,210 --> 01:11:45,730 +مثلا النقطة اللي عندك هذه جداش الإحداث تبعها تقولي + +652 +01:11:45,730 --> 01:11:52,350 +هذه x و y يبقى هذه النقطة x و y قولتلك بالله وصللي + +653 +01:11:52,350 --> 01:11:59,900 +لنقطة الأصل و مد المستقيم على استقامتهبتقول لي هي + +654 +01:11:59,900 --> 01:12:05,700 +هيك على نقطة الاصل وصلته من الناحية التانية تمام + +655 +01:12:05,700 --> 01:12:10,640 +يبقى المنحنة صار بالشكل اللي عندنا هذا + +656 +01:12:14,370 --> 01:12:20,310 +يبقى وصلنا هذا على استقامته بالشكل اللي عندنا هذا + +657 +01:12:20,310 --> 01:12:25,630 +صار الخط اللي عندي هذا قد ميم الخط اللي عندنا هذا + +658 +01:12:25,630 --> 01:12:32,590 +هذه النقطة x و y لكن هذه لو جيت رأسك هذه سالب x + +659 +01:12:39,590 --> 01:12:46,990 +يبقى هذا المنحنى متماثل بالنسبة لنقطة الأصل لأن أي + +660 +01:12:46,990 --> 01:12:51,630 +نقطة علي بعضها عن نقطة الأصل من هذه الناحية يسوى + +661 +01:12:51,630 --> 01:12:57,350 +نفس البعد اللي على المنحنى من وينمن الناحية الأخرى + +662 +01:12:57,350 --> 01:13:03,290 +رياضيا يعني لو وقعت النقطة x و y على المنحنة فإن + +663 +01:13:03,290 --> 01:13:09,450 +النقطة ناقص x و ناقص y تقع على المنحنة مثل ما عشان + +664 +01:13:09,450 --> 01:13:14,110 +ال graph of an odd function is symmetric about the + +665 +01:13:14,110 --> 01:13:21,630 +origin ليش؟ لأن ال F of ناقص xالـ F of ناقص X بدو + +666 +01:13:21,630 --> 01:13:27,650 +يساوي ناقص F of X اللي هي F of X اللي هي Y تمام؟ + +667 +01:13:27,650 --> 01:13:32,510 +من هنا قولنا هذا معنى أيش؟ معنى التماثل بالنسبة لل + +668 +01:13:32,510 --> 01:13:37,010 +origin يبقى ال odd function رسمتها دائما و أبدا + +669 +01:13:37,010 --> 01:13:41,410 +متماثلة بالنسبة لنقطة الاصل ال even function + +670 +01:13:41,410 --> 01:13:45,730 +رسمتها متماثلة دائما و أبدا بالنسبة لميه؟ لمحولة + +671 +01:13:45,730 --> 01:13:47,270 +اسأل السؤال اللي بغلبة + +672 +01:13:55,740 --> 01:14:04,560 +مش وهمي، حقيقي، حقيقي، اه و من هنا رسمتك اللي هو + +673 +01:14:04,560 --> 01:14:13,380 +القطع الناقص هذا رسمة حقيقية، اه ممتاز + +674 +01:14:13,380 --> 01:14:18,770 +جدا، السؤال هوبقيت لفترات التزايد والتنقص اللي + +675 +01:14:18,770 --> 01:14:22,930 +ملايش داعو بال even و ال odd هنا صح؟ طب أقولك ماشي + +676 +01:14:22,930 --> 01:14:28,890 +الحال أنا بالداجي كيف؟ فاستنى شوية ما احنا هنجاوب + +677 +01:14:28,890 --> 01:14:35,070 +عليه، الآن هل الرسم هذه هي رسمة اقتران؟ بطلنا + +678 +01:14:35,070 --> 01:14:39,030 +increasing و decreasing؟مظبوط؟ يجب ويحطها على + +679 +01:14:39,030 --> 01:14:41,910 +الشجرة احنا ال increasing و ال decreasing كلها + +680 +01:14:41,910 --> 01:14:45,190 +بالنسبالي function وقتاش ال function increasing + +681 +01:14:45,190 --> 01:14:48,390 +وقتاش ال function decreasing ايوة اللي رفع أيديه + +682 +01:14:48,390 --> 01:14:56,710 +هنا بطل؟ ايوة الدائرة انت فيها ثلاثة دائرة مالها؟ + +683 +01:14:56,710 --> 01:15:00,790 +بتحطها ده ثلاثة ليه؟ بالملون و السحر طب انا بسألك + +684 +01:15:00,790 --> 01:15:09,200 +هي الدائرة دالةممكن يكون ده، لممكن لا، حسب + +685 +01:15:09,200 --> 01:15:13,380 +الـInterval اللي بتاخدها عليها، صحيح ولا لا؟ + +686 +01:15:13,380 --> 01:15:18,580 +وبالتالي ماقدرش أحكم، لإن أنا بقول أيه، even + +687 +01:15:18,580 --> 01:15:24,360 +function أو odd function، يبقى دائرة أنا مش عارف، + +688 +01:15:24,360 --> 01:15:28,520 +غير لما أشوفها، هي نص دائرة، نص يمين، ولا شمال، + +689 +01:15:28,520 --> 01:15:31,740 +ولا فوق، ولا تحت، وبالتالي بيصيح اختلف الكلام، + +690 +01:15:31,740 --> 01:15:32,160 +أيوة + +691 +01:15:39,010 --> 01:15:44,770 +تمام ايش مكتوب قدامك على اللوح هنا؟ مكتوب الـOdd + +692 +01:15:44,770 --> 01:15:49,770 +ها الـSymmetric حوالين مين؟ و الله حوالين محوركس + +693 +01:15:49,770 --> 01:15:55,790 +Right Believe + +694 +01:15:55,790 --> 01:16:00,830 +it بدل ما كانت موجه بصرة سالبة Believe it هي + +695 +01:16:04,490 --> 01:16:12,190 +X شرطها مختلفة لكن صورتهم نفسها F of X يسوى F of + +696 +01:16:12,190 --> 01:16:16,670 +ناقص X يا + +697 +01:16:16,670 --> 01:16:21,040 +راجل أنا قلتلك هيكتفهمنيش غلط اسمه يا ابني أنت + +698 +01:16:21,040 --> 01:16:26,600 +وياه احنا بنتكلم على مين على ال even function بس + +699 +01:16:26,600 --> 01:16:29,960 +اسمع برضه عودنا للدائرة تاني يا راجل وين هي + +700 +01:16:29,960 --> 01:16:35,690 +الدائرة ماعنديش دائرة قطعة النقص مارواش functionو + +701 +01:16:35,690 --> 01:16:42,530 +بعد ايه؟ احنا هذا اللي رسمناها ال ellipse بس لمعنى + +702 +01:16:42,530 --> 01:16:48,810 +ال symmetry المنحنى جولنا تمام؟ او ال S طيب يبقى + +703 +01:16:48,810 --> 01:16:53,210 +المنحنى يكونوا متماثلين و لم اقر رسمة ال function + +704 +01:16:53,210 --> 01:16:56,790 +المنحنى قد يكون function و قد لا يكون function + +705 +01:16:56,790 --> 01:17:02,490 +خربطش بين التنتين ايوة استاذ اقبل نقص لتحت ال cell + +706 +01:17:02,490 --> 01:17:06,510 +لو قرناها كل واحد حاجةماشي الحاجة، بنفع ولا بنفعش؟ + +707 +01:17:06,510 --> 01:17:13,290 +بنفع، ماشي يبقى شيلنا اللي فوق وخلّينا y less than + +708 +01:17:13,290 --> 01:17:21,980 +zeroكتبنا القطع الناقص معادلته X تربيع على A تربيع + +709 +01:17:21,980 --> 01:17:27,960 +زي Y تربيع على B تربيع يساوي واحد و روحت و حطيت + +710 +01:17:27,960 --> 01:17:34,400 +condition Y أقل من أو تساوي Zero يبقى بصير اللي + +711 +01:17:34,400 --> 01:17:38,980 +فوق بسلامته هذا كله مش موجوده في شغل النص في + +712 +01:17:38,980 --> 01:17:43,110 +السفليأي vertical line اللي يقطعه إلا في نقطة + +713 +01:17:43,110 --> 01:17:49,930 +واحدة صار function ما هو سؤالك even غصب عني وعنك، + +714 +01:17:49,930 --> 01:17:55,450 +عارف ليش؟ لإن النصف اللي على اليمين بيصير زي النصف + +715 +01:17:55,450 --> 01:18:02,490 +اللي على الإشمع، مابدأش سؤالها دي خلاص، + +716 +01:18:02,490 --> 01:18:05,930 +ده اللي عارف يسأل تاني؟ بدنا نفوت للنقطة اللي + +717 +01:18:05,930 --> 01:18:12,120 +بعدها أو النقطة اللي بعدها بدنا نعطي مثالعلى الـ + +718 +01:18:12,120 --> 01:18:17,740 +odd و ال even قبل نحكم على ال function هل هي odd و + +719 +01:18:17,740 --> 01:18:23,840 +لا even بمعنى بدنا نطبق التعريف اللي احنا حطناه + +720 +01:18:23,840 --> 01:18:30,020 +قدامنا وبواسطة هذا التعريف نحكم على ال function هل + +721 +01:18:30,020 --> 01:18:39,880 +هي even و لا odd و لا even و لا odd يبقى example + +722 +01:18:50,850 --> 01:18:57,950 +determine whether حدد + +723 +01:18:57,950 --> 01:19:06,750 +لهال the following functions الدوالي + +724 +01:19:06,750 --> 01:19:15,990 +التالية are even odd or + +725 +01:19:17,650 --> 01:19:26,710 +neither يعني لا even ولا odd نمر ايه ال F of X + +726 +01:19:26,710 --> 01:19:34,310 +يسوى X قصة أربعة absolute value لل X تكيب زائد + +727 +01:19:34,310 --> 01:19:42,150 +خمسة solution قال + +728 +01:19:42,150 --> 01:19:48,980 +شوف لهذه الدالةهل هي even ولا odd و الله لا even + +729 +01:19:48,980 --> 01:19:55,420 +ولا odd و الله ايش رايح نضيف عليها even و odd في + +730 +01:19:55,420 --> 01:20:05,220 +نفس الوقت بنفع بنفع في حالة واحدة فقط لا غير لو + +731 +01:20:05,220 --> 01:20:11,000 +كانت f of x تساوي zeroبصير الـ function even و odd + +732 +01:20:11,000 --> 01:20:15,740 +في نفس الوقت لكن غير هيك يبعتلك الله مش صحيح طيب + +733 +01:20:15,740 --> 01:20:19,940 +على أي حال يبقى يا even يا odd + +734 +01:20:38,720 --> 01:20:46,160 +زائد خمسة تمام هذه ايش رأيك فيها X أص أربعة زي + +735 +01:20:46,160 --> 01:20:55,060 +ماني X أص أربعة زائد absolute value هذه سالب X في + +736 +01:20:55,060 --> 01:21:02,900 +سالب X في سالب X يعني سالب X لكل تكييب زائد خمسة + +737 +01:21:12,310 --> 01:21:17,170 +أول خاصية من قواص القيمة المطلقة اللي خدتوها في + +738 +01:21:17,170 --> 01:21:23,510 +الثانوية ان absolute value ل-x هي absolute value ل + +739 +01:21:23,510 --> 01:21:29,250 +-xabsolute value للسالب تلاتة هي absolute value + +740 +01:21:29,250 --> 01:21:34,150 +للتلاتة اللي هي بتلاتة، مظبوط او لا؟ و قص عليها كل + +741 +01:21:34,150 --> 01:21:38,430 +ال real numbers، اذا absolute value للسالب X هي + +742 +01:21:38,430 --> 01:21:44,920 +absolute value لX، اذا هذه عبارة عن ايش؟absolute + +743 +01:21:44,920 --> 01:21:53,060 +value ل X تكييب يبقى هذه بدها تساوي X أُس 4 زائد + +744 +01:21:53,060 --> 01:21:59,420 +absolute value ل X تكييب زائد خمسة طبقا لهذه + +745 +01:21:59,420 --> 01:22:05,380 +الخاصية طب هذه مين هي؟ مش هي الدالة الأصلية؟ يبقى + +746 +01:22:05,380 --> 01:22:11,210 +هذه بدها تساوي F of X الأصليةيبقى بناء على يسار F + +747 +01:22:11,210 --> 01:22:16,890 +of سلب X يساوي مين؟ يبقى دالة هذه مالها؟ even + +748 +01:22:16,890 --> 01:22:24,930 +function يبقى sol F is an even function يبقى دالة + +749 +01:22:24,930 --> 01:22:33,170 +زوجية نمر بيها F of X يساوي X على X تربية ناقص + +750 +01:22:33,170 --> 01:22:37,710 +تلتة بتعرف هذه دالة زوجية والله ده ده ده ده ده ده + +751 +01:22:37,710 --> 01:22:38,130 +ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده + +752 +01:22:38,130 --> 01:22:38,170 +ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده + +753 +01:22:38,170 --> 01:22:38,170 +ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده ده + +754 +01:22:38,170 --> 01:22:38,190 +ده ده ده ده ده ده ده ده + +755 +01:22:44,170 --> 01:22:45,830 +أنا مش عارف أيه السؤال + +756 +01:22:49,110 --> 01:22:53,950 +بتشيل كل X و بتحط مكانها سالم X وبعدين بطلع أشوف + +757 +01:22:53,950 --> 01:22:58,510 +شو النتيجة ان طلعت الدالة الأصلية يبقى even مع + +758 +01:22:58,510 --> 01:23:04,510 +طلعة الدالة الأصلية يمكن odd ويمكن لا even ولا odd + +759 +01:23:04,510 --> 01:23:08,410 +هذه اللي احنا قاعدين بندور عليه مظبوط هذه طلعت من؟ + +760 +01:23:08,410 --> 01:23:13,570 +الدالة الأصلية إذن الدالة هذه even يعني سعر F of + +761 +01:23:13,570 --> 01:23:18,010 +سالم X هو F of X مظبوط يا ابني؟ مش هيك كان + +762 +01:23:18,010 --> 01:23:23,220 +التعريف؟طيب نيجي للتانية F of X يساوي X على X + +763 +01:23:23,220 --> 01:23:31,980 +تربية سالب ثلاثة الان انا بدي اخد من F of سالب X + +764 +01:23:31,980 --> 01:23:40,300 +يبقى سالب X سالب X لكل تربية سالب تلاتة شلت كل X و + +765 +01:23:40,300 --> 01:23:47,730 +حطيت مكانهاسالب X يبقى هذه بدها تساوي سالب X على + +766 +01:23:47,730 --> 01:23:56,230 +هذه X تربيع ناقص ثلاثة هذه بقدر اقول خدلي السالب + +767 +01:23:56,230 --> 01:24:03,750 +برا بيظل X على X تربيع ناقص ثلاثة اللي بين جسينها + +768 +01:24:03,750 --> 01:24:10,470 +دي مين؟ هذه F of X الأصلية يبقى هي السالب برا وهي + +769 +01:24:10,470 --> 01:24:18,390 +ال F of Xأيش صار عندى F of سالب X يساوي قداش سالب + +770 +01:24:18,390 --> 01:24:25,330 +F of X هذه الأصلية وهذه اللى توصلنا لها بناء عليه + +771 +01:24:25,330 --> 01:24:34,550 +ال F دى مالها odd function يبقى فال F is an odd + +772 +01:24:34,550 --> 01:24:38,950 +function نجى + +773 +01:24:38,950 --> 01:24:46,290 +لنمرى ال Cنمرى C ال F of X absolute value لل X + +774 +01:24:46,290 --> 01:24:54,690 +زائد واحد بدي أشوفها even و لا odd يبقى solution + +775 +01:24:54,690 --> 01:25:03,570 +بدي أخد ال F of سالب X absolute value لسالب X زائد + +776 +01:25:03,570 --> 01:25:07,290 +واحد هل هي الدالة الأصلية اللي فوق؟ + +777 +01:25:10,830 --> 01:25:18,530 +هي اللي فوق يبقى هذه لا تساوي F of X يعني هذه ما + +778 +01:25:18,530 --> 01:25:28,510 +لها not even طيب بلاش هل هذه تساوي سالم X زائد + +779 +01:25:28,510 --> 01:25:35,880 +واحد؟مش ممكنية، يبقى هذه مش هذه، مختلفة كلياً، + +780 +01:25:35,880 --> 01:25:42,480 +يبقى هذه لا تساوي هذه، يبقى ما لها كمعنى not، odd، + +781 +01:25:42,480 --> 01:25:48,100 +يبقى بناء علي هذه لا even ولا would يبقى neither، + +782 +01:25:48,100 --> 01:25:56,740 +يبقى هذا بكل معناته إيش؟ إن ال F is neither even + +783 +01:25:56,740 --> 01:26:06,360 +nor oddطيب شو رايك؟ نمر دي اللي أخدت ال F of X + +784 +01:26:06,360 --> 01:26:15,000 +يساوي ال X تكييب ناقص ثلاثة X يبقى + +785 +01:26:15,000 --> 01:26:22,640 +هذا ال F of ناقص X ناقص X لكل تكييب ناقص ثلاثة في + +786 +01:26:22,640 --> 01:26:33,420 +ناقص Xهذه بناقص x تكيب زائد ثلاثة x هل هذه هي + +787 +01:26:33,420 --> 01:26:43,560 +الدالة الأصلية يبقى لا تساوي f of x يبقى not even + +788 +01:26:45,080 --> 01:26:50,320 +طيب شو رأيك؟ بدأ أخد سالب عامل مشترك منها يبقى هاي + +789 +01:26:50,320 --> 01:26:57,560 +السالب برا، إيش ضال عندي؟ X تكيب سالب تلاتة X، + +790 +01:26:57,560 --> 01:27:02,040 +مظبوط؟ طيب اللي بين جثين، هي الأصلية اللي فوق؟ + +791 +01:27:02,040 --> 01:27:10,380 +يبقى هذه يساوي ناقص ال F over X، يبقى odd function + +792 +01:27:12,070 --> 01:27:19,290 +طيب بدنا نيجي لنقطة جديدة غير ال even و ال odd و + +793 +01:27:19,290 --> 01:27:20,510 +ال symmetry + +794 +01:27:34,550 --> 01:27:38,610 +يبقى بنا نجي لآخر نقطة في هذا ال section اللي هي + +795 +01:27:38,610 --> 01:27:43,610 +حاجة اسمها ال common functions يبقى ال common + +796 +01:27:44,910 --> 01:27:49,370 +Linear functions يعني الدوال العادية يعني الدول + +797 +01:27:49,370 --> 01:27:54,650 +اللي هتدرج معاك طيلة هذا الفصل و احنا بنشتغل فيه + +798 +01:27:54,650 --> 01:28:00,250 +calculus ايه اول نوع من هذه الأنواع اللي هي ال + +799 +01:28:00,250 --> 01:28:07,570 +linear functions الدوال الخطية بدنا نعطيلها تعريف + +800 +01:28:07,570 --> 01:28:13,210 +التعريف بيقول ما يأتي a function f + +801 +01:28:19,150 --> 01:28:32,470 +الشكل التالي f of x يساوي mx زائد b where ال m and + +802 +01:28:32,470 --> 01:28:46,860 +ال b are constantsهدول ثوابت constants is called a + +803 +01:28:46,860 --> 01:28:49,620 +linear function + +804 +01:28:52,840 --> 01:29:00,080 +يبقى الدلل بشكل هذا بسميها دلّة خطية، يعني بالبلد + +805 +01:29:00,080 --> 01:29:05,920 +دي دلّة خطية لو رسمتها، شو بتكون رسمتها؟ خط + +806 +01:29:05,920 --> 01:29:10,860 +مستقيم، خط مستقيم، يبقى هاي المقصود فيها، أظن هذه + +807 +01:29:10,860 --> 01:29:16,610 +اللي وعدت فيها قبل شوية في بداية المحاضرةطيب يبقى + +808 +01:29:16,610 --> 01:29:23,170 +هذه معادلة خط مستقيم او كنت بتقوله في الثانوية Y + +809 +01:29:23,170 --> 01:29:32,670 +يساوي MX زائد B ال M هذا طول الجزء الميل وال B هو + +810 +01:29:32,670 --> 01:29:37,410 +طول الجزء المخطوعة من محور الصعدات Y intercept + +811 +01:29:37,410 --> 01:29:44,710 +وهذا هو ال slowالمين طيب كويس يبقى ال M هذا بيرمز + +812 +01:29:44,710 --> 01:29:56,130 +للسلوب تبع ال line وهذا ال Y intercept يعني طول + +813 +01:29:56,130 --> 01:30:01,770 +الجزء المخطوة من محور الصدر الآن بدأ ناخد المستقيم + +814 +01:30:01,770 --> 01:30:08,560 +هذا في حالاته المختلفة تمامفبجي بقول لو كان عندى + +815 +01:30:08,560 --> 01:30:16,280 +محاور بالشكل هذا هذا محور X وهذا محور Y وحبيت ارسم + +816 +01:30:16,280 --> 01:30:22,760 +الخط المستقيم اللى عندنا افترض هذا الخط المستقيم + +817 +01:30:22,760 --> 01:30:31,260 +تمام يبقى هذا الخط اللى معادلته Y تساوي MX زائد B + +818 +01:30:31,260 --> 01:30:38,260 +وين ال B وين ال M هذهأحنا بنقول ان ال B هي ال Y + +819 +01:30:38,260 --> 01:30:45,300 +intercept يبقى B هي المسافة اللي عندنا هذه تمام؟ + +820 +01:30:45,300 --> 01:30:53,000 +يعني إحداث النقطة هذه هو Zero و M طيب وين ال M؟ ال + +821 +01:30:53,000 --> 01:30:58,500 +M ال slope يعني الظلمة الزاوية اللي بيعملها لي مع + +822 +01:30:58,500 --> 01:31:05,180 +الاتجاه الموجدلل X axis يبقى هذا الخط المستقيم + +823 +01:31:05,180 --> 01:31:11,140 +اللي عندنا واضح ان ال mail تبع عماله موجب ولا سالب + +824 +01:31:11,140 --> 01:31:16,620 +موجب لإن الزاوية زاوية حدة لكن لو الخط المستقيم + +825 +01:31:16,620 --> 01:31:22,680 +أجى من الناحية التانية بصير Y تساوي سلب MX زائد B + +826 +01:31:22,680 --> 01:31:29,060 +الخط المستقيم هذا بدنا نيجي ناخدله عدة حالات + +827 +01:31:29,060 --> 01:31:36,160 +الحالة الأولىلو كانت ال M تساوي Zero يعني الميل + +828 +01:31:36,160 --> 01:31:41,500 +تبع الخط المستخدم تساوي Zero يعني ايش؟ موازي لمحور + +829 +01:31:41,500 --> 01:31:48,320 +الصينة او منطبق عليه وموازي يعني جاي فوق او جاي + +830 +01:31:48,320 --> 01:31:56,570 +تحتيبقى بدي اجي اخد نمرة واحد F ال M تساوي Zero + +831 +01:31:56,570 --> 01:32:03,610 +وال B لا تساوي Zero يبقى بدي اقصير هذه المحاور + +832 +01:32:03,610 --> 01:32:11,820 +اللي عندنا هذا محور X هذا Y هذا Zeroم تساوي زيرو + +833 +01:32:11,820 --> 01:32:17,960 +part of term هذي بيصير f of x تساوي كدهش بيه يعني + +834 +01:32:17,960 --> 01:32:24,720 +بيصير عندنا y تساوي بيه والله إذا بيه أكبر من ال + +835 +01:32:24,720 --> 01:32:32,560 +zero بده يجينا الخط المستقيم فوق يبقى هذا y تساوي + +836 +01:32:32,560 --> 01:32:40,260 +بيه و ال b greater than zeroطيب الخط المستقيم ممكن + +837 +01:32:40,260 --> 01:32:46,440 +يكون بالسالب إذا y يسوي كمية سالبة يبقى بده يجينا + +838 +01:32:46,440 --> 01:32:54,060 +الخط هذا y تسوي سالب b و ال b أكبر من ال zero طيب + +839 +01:32:54,060 --> 01:32:59,880 +ليش كتبت ال b أكبر من ال zero؟ مشان أضمن أنها تبقى + +840 +01:32:59,880 --> 01:33:06,360 +هذه سالبة، مظبوط؟ يبقى y تسوي سالب تلاتةالتلاتة + +841 +01:33:06,360 --> 01:33:11,480 +أكبر من ال zero يبقى مضمون هذا يظل ياش قيمة سالبة + +842 +01:33:11,480 --> 01:33:18,500 +مش مشكلة يبقى y تساوي بي و بي أقل من ال zero عادى + +843 +01:33:18,500 --> 01:33:23,180 +جدا نفس الكتابة يبقى y تساوي سالب بي و بي موجبة + +844 +01:33:23,180 --> 01:33:29,320 +دائما و أبدا مشان أضمن أن هذا يظل من السالب طيب + +845 +01:33:29,320 --> 01:33:37,160 +ممكن مايكونش y تساوي بي ممكن يكون ال Xيساوي A رقم + +846 +01:33:37,160 --> 01:33:42,720 +و ال A هذا ممكن يكون موجب و ممكن يكون سالب يبقى + +847 +01:33:42,720 --> 01:33:49,920 +بصير عندي هذه المحاور و هذا محور X و هذا محور Y Y + +848 +01:33:49,920 --> 01:34:00,280 +تساوي A هي يبقى هذا Y تساوي A ال مسافة من هنا لهنا + +849 +01:34:02,040 --> 01:34:11,300 +اكس يساوي ايه؟ اكس بده يساوي a والa positive والa + +850 +01:34:11,300 --> 01:34:16,600 +greater than zero لكن لو جت الخط اللي عندنا هذا + +851 +01:34:17,650 --> 01:34:24,430 +يبقى هذا X يساوي سالب A والـ A كذلك أكبر من الـ + +852 +01:34:24,430 --> 01:34:30,250 +Zero عشان أطبع أن هذا سالب يبقى X يساوي A موازية + +853 +01:34:30,250 --> 01:34:35,410 +لمحور Y من جهة اليمين X يساوي سالب A موازية لمحور + +854 +01:34:35,410 --> 01:34:41,350 +Y من جهة الشمال يبقى هذه الحالة الأولى الخطوط + +855 +01:34:41,350 --> 01:34:47,120 +المستقيمة الموازية لمحور X أو الموازية لمحور Yممكن + +856 +01:34:47,120 --> 01:34:53,860 +ال M ما تكونش ب Zero تكون رقم ولكن ال B هي اللي + +857 +01:34:53,860 --> 01:34:59,060 +بتبقى ب Zero طب لو ال B هذه صارت ب Zero الخط + +858 +01:34:59,060 --> 01:35:05,460 +المستقيم ماله؟ بده يمر بنقطة الأصل يبقى بدنا نيجي + +859 +01:35:05,460 --> 01:35:14,660 +للنقطة الثانية F ال M لا تساوي Zero وال B تساوي + +860 +01:35:14,660 --> 01:35:21,730 +Zeroالحالة القطوط المستقيمة ستكون بهذا الشكل يبقى + +861 +01:35:21,730 --> 01:35:28,330 +هذا محور X هذا محور Y هذه نقطة الأصل اللي هي الـ + +862 +01:35:28,330 --> 01:35:34,390 +Zero فتاخد أول شغلة لو كان ال M بواحد يبقاش مصير + +863 +01:35:34,390 --> 01:35:43,520 +معادلةF of X يساوي X يعني Y تساوي X يبقى بدرجيك + +864 +01:35:43,520 --> 01:35:48,960 +الخط اللي عندك هذا بالشكل هذا هيك و مده على + +865 +01:35:48,960 --> 01:35:56,020 +استقالة يبقى هذا ال F of X بده يساوي ال X أو ال Y + +866 +01:35:56,020 --> 01:36:00,020 +يساوي ال X الزاوية هذه بخمسة و أربعين والزاوية هذه + +867 +01:36:00,020 --> 01:36:04,720 +بخمسة و أربعينهذه في علم الرياضيات بيسموها ال + +868 +01:36:04,720 --> 01:36:13,680 +identity function دالة الوحدة يبقى هذه بنسميها ال + +869 +01:36:13,680 --> 01:36:25,940 +identity function يبقى هذه دالة الوحدة ايه لو كان + +870 +01:36:25,940 --> 01:36:34,070 +F of X يسوى مص Xيبقى ايش بده يصير؟ بده يصير الخط + +871 +01:36:34,070 --> 01:36:38,950 +هنا في الشجة هذه، من هذا و فوق ولا منه و تحت؟ منه + +872 +01:36:38,950 --> 01:36:43,630 +و تحت، لإن عند X يساوي واحد بيصير قيمته نص، بس هذا + +873 +01:36:43,630 --> 01:36:49,070 +عند الواحد بيصير قيمته واحد، يبقى هذا الخط الأزرق + +874 +01:36:49,070 --> 01:36:59,830 +هذا هيكبدي أجيلك اللي هو Y تساوي نص X يعني M تساوي + +875 +01:36:59,830 --> 01:37:06,830 +نص طب لو كم Y تساوي اتنين X فوق بدي أجي منه فوق + +876 +01:37:06,830 --> 01:37:17,210 +يبقى هذا الخط بدي أجيك هناكخط هنا y تساوي اتنين + +877 +01:37:17,210 --> 01:37:21,130 +اكس عارفين ليش يا شباب لإن لو قلت هي النقطة اللي + +878 +01:37:21,130 --> 01:37:25,770 +هي واحد بس هي عند الواحد قيمته نص هذا عند الواحد + +879 +01:37:25,770 --> 01:37:30,730 +قيمته جداش واحد هذا عند الواحد قيمته جداش اتنين + +880 +01:37:30,730 --> 01:37:38,870 +وهكذاطب واحد يقول لي طيب y تساوي ناقص x مش موجب + +881 +01:37:38,870 --> 01:37:44,670 +ضغوط تيجي من الشجة التانية يبقى من الشجة التانية + +882 +01:37:44,670 --> 01:37:51,690 +تجينا الخط y تساوي سالب x و هكذا ما ينطبق على + +883 +01:37:51,690 --> 01:37:57,370 +الموجب ينطبق على السالب عندنا يبقى هذا الوضع + +884 +01:37:57,370 --> 01:38:00,250 +للخطوط المستقيمة في حالتها + +885 +01:38:07,690 --> 01:38:19,270 +التناسب الطردي والتناسب العكسي يبقى definition two + +886 +01:38:19,270 --> 01:38:20,270 +variables + +887 +01:38:38,590 --> 01:38:48,150 +يوجد اتناسب وتناسب انترضيا اذا واحد دائما + +888 +01:38:52,100 --> 01:39:07,200 +دائما و أبدا a constant multiple of + +889 +01:39:07,200 --> 01:39:15,320 +the other that + +890 +01:39:15,320 --> 01:39:36,950 +is أي أنهY تساوي K في X for non zero constant K + +891 +01:39:36,950 --> 01:39:45,010 +Also + +892 +01:39:45,010 --> 01:40:00,950 +و كذلكY يساوي K في واحد على X يعني + +893 +01:40:00,950 --> 01:40:09,050 +ان Y is inversely + +894 +01:40:09,050 --> 01:40:11,450 +proportional + +895 +01:40:17,290 --> 01:40:18,890 +عن طريق الـ X + +896 +01:40:27,240 --> 01:40:33,400 +أنا عندى متغيرين واحد X واحد Y المتغيرين هذول are + +897 +01:40:33,400 --> 01:40:40,740 +proportional يعنى يتناسبوا تناسبا طرديا if one is + +898 +01:40:40,740 --> 01:40:44,600 +always a constant multiple of the other إذا كان + +899 +01:40:44,600 --> 01:40:50,700 +أحدهم مضاعفات الآخر جده مرة و نص جده مرتين جده خمس + +900 +01:40:50,700 --> 01:40:56,440 +مرات جده سبعة مرات و تلت تربع زى ما بدك مضاعفاته + +901 +01:40:56,720 --> 01:41:03,260 +That is بدي أصيغ السطرين هدول بصيغة رياضية فباجي + +902 +01:41:03,260 --> 01:41:13,060 +بقوله Y يساوي K حيث K عدد حقيقي غير صفري نين تلاتة + +903 +01:41:13,060 --> 01:41:18,260 +واحد و نص عشرين خمسمية زي ما بدك تمام for none + +904 +01:41:18,260 --> 01:41:24,370 +zero constant K لمقدار ثابت غير الصفريبقى هذا + +905 +01:41:24,370 --> 01:41:29,510 +التناسب الطبيعي لما اقول متغيرين متناسبين بقدر + +906 +01:41:29,510 --> 01:41:35,030 +اقلب التناسب الى تساوي و بضغط فى مين فى مقدار ثابت + +907 +01:41:35,030 --> 01:41:39,250 +يبقى هذا اللى اتعلمناه في الفيزيا كل حياتنابجلب + +908 +01:41:39,250 --> 01:41:42,930 +التناسب إلى تساوي بضرب في مقدار ثابت المقدار + +909 +01:41:42,930 --> 01:41:48,330 +الثابت اللي هو K مقدار ثابت غير الصفر المعادلة + +910 +01:41:48,330 --> 01:41:55,490 +التانية Y يساوي K على X تناسب عكسي يبقى means يعني + +911 +01:41:55,490 --> 01:42:02,170 +ان Y is inversely proportional تتناسب تناسبا عكسيا + +912 +01:42:02,170 --> 01:42:08,240 +مع من مع ال variable التاني اللي هو Xواضح كلامي + +913 +01:42:08,240 --> 01:42:13,940 +هنا؟ طيب لحد هنا stop لسه لما ننتهي بعد لكن بدي + +914 +01:42:13,940 --> 01:42:19,940 +أعطيكوا أرقام المسائل مشان تبدوا تشتغلوا و تحضروا + +915 +01:42:19,940 --> 01:42:20,640 +ال discussion + +916 +01:42:23,160 --> 01:42:29,420 +المناقشة ايو بدرس روح اتمرن ديلك في الأسئلة + +917 +01:42:29,420 --> 01:42:37,520 +التالية exercises واحد واحد المسائل من واحد لغاية + +918 +01:42:37,520 --> 01:42:45,120 +سبعة و خمسين ال odd numbers اه الأرقام الفردية من + +919 +01:42:45,120 --> 01:42:47,840 +واحد لسبعة و خمسين + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Ly_WmKy_z00_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Ly_WmKy_z00_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..0e284131902330957870c40ef30209f21be9c2de --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Ly_WmKy_z00_postprocess.srt @@ -0,0 +1,3728 @@ +1 +00:00:21,240 --> 00:00:25,220 +بسم الله الرحمن الرحيم انتهينا من المرة الماضية + +2 +00:00:25,220 --> 00:00:32,360 +اللي كان بتحدث عن ال extreme values سواء كانت + +3 +00:00:32,360 --> 00:00:36,300 +local maximum و local minimum أو absolute maximum + +4 +00:00:36,300 --> 00:00:41,100 +و absolute minimumبننتقل الى ال section اللي يليه + +5 +00:00:41,100 --> 00:00:46,400 +هو section 4-2 بتحدث عن the main value theorem + +6 +00:00:46,400 --> 00:00:52,540 +نظرية القيمة المتوسطة قبل ما نبدأ بنظرية القيمة + +7 +00:00:52,540 --> 00:00:58,030 +المتوسطة بدأ ناخد نظرية أخرى وهي نظرية roleيبقى + +8 +00:00:58,030 --> 00:01:04,450 +بين أيدنا الان rules theorem تنص على ما يقتين + +9 +00:01:04,450 --> 00:01:09,230 +بيقول افترض ان y تساوي f of x ده المتصلة على + +10 +00:01:09,230 --> 00:01:14,370 +الفترة المغلقة a وb وفي نفس الوقت هذه ال function + +11 +00:01:14,370 --> 00:01:20,370 +قابلة للاشتقاء على الفترة المفتوحة a وb يبقى هاي + +12 +00:01:20,370 --> 00:01:27,700 +شرطينشرب التالت لو كان f of a يساوي f of b فهناك + +13 +00:01:27,700 --> 00:01:32,640 +أقل نمبر c في الأفترى a وb بحيث أن f prime of c + +14 +00:01:32,640 --> 00:01:38,160 +يساوي 0 يبقى هذه النظرية بتقولي أنا في عندي + +15 +00:01:38,160 --> 00:01:42,420 +function تساوي y تساوي f of x إذا هذه ال function + +16 +00:01:42,420 --> 00:01:49,290 +حققتلي ثلاثة شروط وهمالشرط الأول، الدلق متصل على + +17 +00:01:49,290 --> 00:01:54,250 +الفترة المغلقة A وB. إثنان، قابل الاشتقاق على + +18 +00:01:54,250 --> 00:02:01,290 +الفترة المفتوحة A وB. تلاتة، قيمة F of A بدأت ساوي + +19 +00:02:01,290 --> 00:02:10,120 +F of B. إن حدث ذلكيبقى لازم أكدر ألاقي نقطة C أو + +20 +00:02:10,120 --> 00:02:15,680 +عدد C في الفترة A وB على الأقل نقطة اللي لم يكن + +21 +00:02:15,680 --> 00:02:19,860 +أكتر يعني ممكن عدد ممكن اتنين ممكن تلاتة ممكن + +22 +00:02:19,860 --> 00:02:24,580 +أربعة الاخرين يعني على الأقل لازم ألاقي نقطة واحدة + +23 +00:02:24,580 --> 00:02:29,880 +في الفترة A وB at which بحيث أن ال F prime of C + +24 +00:02:29,880 --> 00:02:35,510 +بده يساوي قداش بده يساوي Zero تمام تماميبقى هذه + +25 +00:02:35,510 --> 00:02:40,670 +الشروط التلاتة عندنا اللي همين نظرية رول وهي تمهيد + +26 +00:02:40,670 --> 00:02:46,370 +لنظرية القيمة المتاسبة تعالى نفهم هذا النص على + +27 +00:02:46,370 --> 00:02:51,150 +الطبيعة، الآن نجد طالع على الرسمة الأولى اللي + +28 +00:02:51,150 --> 00:02:56,000 +عندناهذا المنحنى اللي انت شايفينه هو منحنى Della Y + +29 +00:02:56,000 --> 00:03:01,280 +تساوي F of X أو المنحنى اللي عنده هو منحنى Della Y + +30 +00:03:01,280 --> 00:03:06,240 +تساوي F of X تعالى نشوف هل الشروط الثلاثة متحقق + +31 +00:03:06,240 --> 00:03:11,020 +على كل من الرسم الأولى والثانيةأم لا؟ زي ما انت + +32 +00:03:11,020 --> 00:03:17,000 +شايف الخط متواصل بلا استثناء على الفترة المغلقة A + +33 +00:03:17,000 --> 00:03:21,560 +وB الدالة معرفة، تمام؟ إذن الدالة continuous على + +34 +00:03:21,560 --> 00:03:26,460 +الفترة A وB باجي على الفترة المفتوحة A وB هل + +35 +00:03:26,460 --> 00:03:30,440 +الدالة قابلة لاشتقاق أم لا؟ طبعا قابلة لاشتقاق + +36 +00:03:30,440 --> 00:03:34,080 +لأنه لا يوجد لا كسب ولا corner ولا vertical + +37 +00:03:34,080 --> 00:03:39,450 +tangent ولا discontinuityالاربعة تبعة عدم الاتصال، + +38 +00:03:39,450 --> 00:03:44,770 +عدم ال differentiation لتبالى، واضح؟ إذا أهدي زيها + +39 +00:03:44,770 --> 00:03:50,150 +طالع على المنحنى، مافيش عندي ولا عند أي نقطة في + +40 +00:03:50,150 --> 00:03:55,470 +vertical tangent ولا كسب ولا corner ولا vertical + +41 +00:03:55,470 --> 00:03:58,810 +tangent أو discontinuity مافيش عندي ولا حالة من + +42 +00:03:58,810 --> 00:04:02,150 +الحالات الأربعة، إذا اتدى لقاء بالاشتقاء في الرسم + +43 +00:04:02,150 --> 00:04:07,610 +الأولى وفي الرسم الثانيبالـ F of A يسوى F of B، هي + +44 +00:04:07,610 --> 00:04:12,570 +قيمة الدالة عند A، و هي قيمة الدالة عند B جايت وين + +45 +00:04:12,570 --> 00:04:17,830 +على نفس الخط. قيمة الدالة عند A تسوى قيمة الدالة + +46 +00:04:17,830 --> 00:04:23,390 +عند B نفس الخط الأفقي الموازي لمحور X. يبقى الآن + +47 +00:04:23,390 --> 00:04:28,750 +تحققت الشروط التلاتة. بيقول، there exists أو there + +48 +00:04:28,750 --> 00:04:33,470 +is at least على الأقل فيها نقطة واحدة.لكن ممكن + +49 +00:04:33,470 --> 00:04:37,310 +ألاقياش أكتر من نقطة، النقطة هذه ما لها؟ قيمة + +50 +00:04:37,310 --> 00:04:42,550 +المشتقة عندها يساوي مين؟ يساوي زيري، يعني المماس + +51 +00:04:42,550 --> 00:04:44,970 +عند هذه النقطة بيكون ما له؟ + +52 +00:04:49,200 --> 00:04:54,900 +الخط اللي يواصل بين F of A وF of B يواظه خط أفقي + +53 +00:05:07,880 --> 00:05:13,680 +الان يجب ان يكون F prime of C1 يسوى 0 يعني المماس + +54 +00:05:13,680 --> 00:05:19,280 +أفقي F prime of C2 يسوى 0 معناته المماس أفقي F + +55 +00:05:19,280 --> 00:05:24,170 +prime of C3 يسوى 0 معناته المماس أفقيوالخط اللى + +56 +00:05:24,170 --> 00:05:28,710 +وصل بين F of A و F of B برضه زى ما انت شايف موازن + +57 +00:05:28,710 --> 00:05:33,590 +للممثات التلاتة اللى عندنا يبقى بناء علي من الآن + +58 +00:05:33,590 --> 00:05:39,610 +فصاعدا إذا تحققت الشروط التلاتة إجبارى على الأقل + +59 +00:05:39,610 --> 00:05:44,850 +لازم ألاقي ولو نقطة واحدة عندها قيمة المشتقة يساوي + +60 +00:05:44,850 --> 00:05:48,720 +Zero يمكن ألاقي تنتينيمكن تلاتة، يمكن أربعة، ماعنا + +61 +00:05:48,720 --> 00:05:52,740 +مشكلة. المهم على الأقل إذا وجدت الشروط الداء + +62 +00:05:52,740 --> 00:05:58,360 +الدالة أو تحققت الشروط الداء الثلاثة لدالة ما لازم + +63 +00:05:58,360 --> 00:06:02,960 +ألاجي ولو نقطة واحدة في الفترة المفتوحة A وB بحيث + +64 +00:06:02,960 --> 00:06:07,240 +أن المشتق عنها تساوي مين؟ تساوي Zero. تعالى نشوف + +65 +00:06:07,240 --> 00:06:12,000 +هذا بأمثلة عملية. بيقول لي بييني أن هذه الدالة + +66 +00:06:12,000 --> 00:06:20,310 +تحقق hypothesis فرضياتمفردها فرضية بس بدل الـI هذي + +67 +00:06:20,310 --> 00:06:26,990 +بحط بدالها I يبقى لو كانت I بكون hypothesis فرض + +68 +00:06:26,990 --> 00:06:33,310 +واحد بالـA يبقى الجمع hypothesis فرضيات يعني إيش + +69 +00:06:33,310 --> 00:06:37,610 +الفرضيات عن الفرضيات التلاتة اللي هنا يبقى بيقول + +70 +00:06:37,610 --> 00:06:42,750 +إن هذه ال function تحقق فرضيات نظرية رول على + +71 +00:06:42,750 --> 00:06:49,090 +الفترة المغلقة من Zero لغايةبعد ذلك هاتلي قيمة C + +72 +00:06:49,090 --> 00:06:55,750 +أو قيم C اللى موجودة فى الفترة المفتوحة 04 بحيث ان + +73 +00:06:55,750 --> 00:07:00,910 +قيمة المشتقة عندها تساوي كداش تساوي Zero يبقى احنا + +74 +00:07:00,910 --> 00:07:04,410 +فى الأول اللى بدنا نشوف فالتلات فرضيات متحققة ولا + +75 +00:07:04,410 --> 00:07:09,770 +ان كانت متحققة يبقى غصب عن اللى مايرضى لازم ألاقي + +76 +00:07:09,770 --> 00:07:16,270 +نقطة C قيمة المشتقة عندها تساوي صفربالدالي لمن؟ + +77 +00:07:16,270 --> 00:07:21,690 +لدلة اللي عندنا هذه، الدلة هذه الدمية انتبعها من + +78 +00:07:21,690 --> 00:07:28,150 +ويل لويلبنعندي Zero لغاية Infinity، عند Zero + +79 +00:07:28,150 --> 00:07:32,630 +الدالة معرفة، بظبط ولا لا؟ لأنه أنا عند الجدرد، + +80 +00:07:32,630 --> 00:07:36,950 +معناته continuous على الفترة من Zero إلى Infinity، + +81 +00:07:36,950 --> 00:07:40,070 +يعني continuous على الفترة من أين اللي وين؟ من + +82 +00:07:40,070 --> 00:07:45,050 +Zero لأربعة.يفجأة باجي بقوله ال domain تبع الدالة + +83 +00:07:45,050 --> 00:07:50,650 +F، بده يساوي من Zero لغاية Infinity.هذا بده يعطينا + +84 +00:07:50,650 --> 00:07:59,870 +ان ال F is continuous on الفترة من Zero لغاية + +85 +00:07:59,870 --> 00:08:05,790 +كدهش؟ لغاية أربعة يبقى اتحقق الشرف الأول عندي طبعا + +86 +00:08:05,790 --> 00:08:09,950 +يمكن واحد يقولي احنا ماخدنا ذلك بقوله كيف؟وقال لـ + +87 +00:08:09,950 --> 00:08:14,730 +continuous function بدي أشوف ال limit تبعته عند أي + +88 +00:08:14,730 --> 00:08:21,270 +نقطة و بدي أشوف مين و بدي أشوف قيمتها بقول هذا + +89 +00:08:21,270 --> 00:08:24,730 +كلام صحيح عند نقطة على interval يقول بدي أشوف + +90 +00:08:24,730 --> 00:08:28,250 +طرفية ال interval و بدي أشوف مين الفنص هذه قصة + +91 +00:08:28,250 --> 00:08:31,970 +طويلة جدا لكن احنا بجيب و أقول هذه الدالة معرفة من + +92 +00:08:31,970 --> 00:08:36,890 +و إلى وينمن Zero لإنفينتي، مدى أن معرفتي جاذبوا + +93 +00:08:36,890 --> 00:08:40,010 +منها، إذن هي ده اللي متواصلة عليها، لو في نقطة + +94 +00:08:40,010 --> 00:08:45,410 +ماشية متواصلة، سحبناها منها، إذن هذه أغنطني عن مين + +95 +00:08:45,410 --> 00:08:49,010 +ماين أكواد الشغل الطويل تبعنا اللي بدي أثبت ال + +96 +00:08:49,010 --> 00:08:53,370 +continuity على interval لهذه ال function طيب كويس، + +97 +00:08:53,370 --> 00:08:58,510 +ضال ال differentiability، إذن أنا عند ال F of X + +98 +00:08:58,510 --> 00:09:06,070 +بدي أتساوياللي هو x على 2 ناقص جذر ال X روح نشتق + +99 +00:09:06,070 --> 00:09:13,930 +يبقى ال F prime of X يساوي نص ناقص واحد على اتنين + +100 +00:09:13,930 --> 00:09:19,250 +جذر ال X في مشتقة ما تحت الجذر اللي هو قداشر واحد + +101 +00:09:20,640 --> 00:09:26,300 +وين هذا ال domain تبع ال f prime؟ هو domain ال f + +102 +00:09:26,300 --> 00:09:31,340 +ماعدى النقاط المشتقة عندها غير معرفة هل الدالة + +103 +00:09:31,340 --> 00:09:37,020 +معرفة عند ال zero؟ إذا بدنا نشيل ال zero فقط لغر و + +104 +00:09:37,020 --> 00:09:43,660 +الباقي بيبقى كما هو يبقى هذا معناه ان ال f is + +105 +00:09:43,660 --> 00:09:51,590 +differentiable on الفترة من zero لاربععند اي نقطة + +106 +00:09:51,590 --> 00:09:56,270 +خلال الفترة من Zero لاربع المعطاعة المشتقة هذه + +107 +00:09:56,270 --> 00:10:01,190 +معرفة، إذا هذه الـ function مالها ده المتصل عالميا + +108 +00:10:01,190 --> 00:10:06,670 +على هذه الفترة وفي نفس الوقت قابلة للاشتقاء يبقى + +109 +00:10:06,670 --> 00:10:10,650 +هيجب بقاش two conditions فهي لعند ال condition + +110 +00:10:10,650 --> 00:10:15,970 +التالت بده أروح أجيب له ال F of Zero أظن تساوي + +111 +00:10:15,970 --> 00:10:22,930 +Zeroزيرو جدر زيرو بزيرو بزيرو بد أجيب له ال F of + +112 +00:10:22,930 --> 00:10:29,170 +أربع يبقى هذا بتسوي أربع على اتنين ناقص جدر الأربع + +113 +00:10:29,170 --> 00:10:34,090 +يعني اتنين ناقص اتنين يسوي جدر زيرو معناه هذا + +114 +00:10:34,090 --> 00:10:40,420 +الكلام ان ال F of zero بد يسوي مين؟الـ F of أربعة + +115 +00:10:40,420 --> 00:10:47,860 +وبالتالي تحققت شروط من نظرية rule يبقى هنا sir the + +116 +00:10:47,860 --> 00:10:54,800 +function F of X يبدأ تسوى X على اتنين ناقص جذر ال + +117 +00:10:54,800 --> 00:11:06,360 +X satisfy the hypothesis the + +118 +00:11:06,360 --> 00:11:16,370 +hypothesis ofthe rules theorem يبقى معناه ان هذه + +119 +00:11:16,370 --> 00:11:21,550 +ال function تحقق نظرية rule معناته ايش؟ هذا بدي + +120 +00:11:21,550 --> 00:11:29,130 +اعطيك there exist رقم c موجود في الفترة 04 such + +121 +00:11:29,130 --> 00:11:37,920 +that بحيث هو ان ال f prime of c بدي سوى قداشزيرو + +122 +00:11:37,920 --> 00:11:43,220 +قال هاتلي ال C هذه، بديها، قال find the value of C + +123 +00:11:43,220 --> 00:11:46,780 +اللي موجودة في الفترة zero أربعة و اللي المشتقة + +124 +00:11:46,780 --> 00:11:51,240 +عندها بدأت ساوي زيرو، بنقوله بسيطة جدا ال F prime + +125 +00:11:51,240 --> 00:11:56,720 +of C يعني بدي أجي على ال F prime و لل F prime هيها + +126 +00:11:57,290 --> 00:12:02,950 +بدي أشيل كل X و أحط مكانها C يبقى معناته هذا + +127 +00:12:02,950 --> 00:12:08,590 +الكلام ناقص ناقص واحد على اتنين جدري ال C بده يسوي + +128 +00:12:08,590 --> 00:12:14,630 +قداش Zero او انشيتهم فاقولوا واحد على اتنين جدري + +129 +00:12:14,630 --> 00:12:22,650 +ال C يسوي قداشنص او بمعنى اخر اتنين جذر ال C يساوي + +130 +00:12:22,650 --> 00:12:28,470 +اتنين يبقى جذر ال C يساوي كدهش لو ربعنا الطرفين + +131 +00:12:28,470 --> 00:12:35,190 +بيصير عندنا C تساوي واحد اذا عندك C تساوي واحد + +132 +00:12:35,190 --> 00:12:41,140 +بيكون F prime of واحد بيساوي كدهشالنص صحيح كلامنا + +133 +00:12:41,140 --> 00:12:46,480 +و الله كله كلام تعالى شوف f prime of واحد حط هنا + +134 +00:12:46,480 --> 00:12:52,750 +واحد بصير مص ناقص نص يساوي زيروك بكلامنا صحيحهذا + +135 +00:12:52,750 --> 00:12:57,870 +هو نظرية رول ومثال عليها نذهب إلى العمود الفقري + +136 +00:12:57,870 --> 00:13:01,910 +تبع هذا المجلد وهو العنوان اللي نراه فيه هو ال + +137 +00:13:01,910 --> 00:13:08,490 +main value theorem يبقى بعد هذا بالداجي the main + +138 +00:13:08,490 --> 00:13:15,050 +value theorem ال + +139 +00:13:15,050 --> 00:13:17,850 +main value theorem تنص على ما يأتي + +140 +00:13:20,260 --> 00:13:29,000 +فترب انه Suppose that the function + +141 +00:13:29,000 --> 00:13:40,880 +اللي هي Y تساوي F of X is continuous is + +142 +00:13:40,880 --> 00:13:49,300 +continuous on a closed interval + +143 +00:14:00,950 --> 00:14:10,830 +على الفترة المفتوحة A وB ثم هناك + +144 +00:14:19,430 --> 00:14:28,670 +يوجد على الأقل في + +145 +00:14:28,670 --> 00:14:32,130 +الفترة + +146 +00:14:32,130 --> 00:14:34,350 +المفتوحة A وB + +147 +00:14:39,840 --> 00:14:49,240 +بحيث ان ال F of B ناقص ال F of A على B ناقص ال A + +148 +00:14:49,240 --> 00:14:52,940 +فهو F prime of C + +149 +00:15:24,550 --> 00:15:25,690 +خلّاله كويس هنا. + +150 +00:15:34,170 --> 00:15:39,430 +هذي there exist يوجد، there exist يوجد + +151 +00:15:41,990 --> 00:15:44,230 +اللي هي بالإنجليزي بسمة مجنوبة على الشجرة التانية + +152 +00:15:44,230 --> 00:15:50,990 +معناته there exists يوجد طيب بدنا نيجي لنظرية + +153 +00:15:50,990 --> 00:15:56,050 +القيمة المتواصفة the main value term لو دققت في + +154 +00:15:56,050 --> 00:16:01,850 +نظرية القيمة المتواصفة بلاقي فيها فرقين فقط ما + +155 +00:16:01,850 --> 00:16:08,370 +بينها وبين نظرية role الفرق الأول هو حد بيقدر + +156 +00:16:08,370 --> 00:16:16,140 +يكتشفهأيوة ان الشرب التالت مش موجود F of A بديه + +157 +00:16:16,140 --> 00:16:19,200 +يسوي F of B مش موجود الشرب الثاني او النقطة + +158 +00:16:19,200 --> 00:16:23,400 +الثانية ايوة + +159 +00:16:23,400 --> 00:16:27,740 +نجلي تسوى Zero هنا ليس بالضرورة تسوى Zero ممكن + +160 +00:16:27,740 --> 00:16:33,380 +تسوى Zero او لا تسوى Zero نظرية و نظرية rule الفرق + +161 +00:16:33,380 --> 00:16:38,850 +ما بين الاتنين هدولهو فقط الشرط هذا ونتيجة ان هذا + +162 +00:16:38,850 --> 00:16:42,850 +الشرط تصبح نتيجة ومخالفة الشرط هذا ان هناك f of a + +163 +00:16:42,850 --> 00:16:47,850 +يسوى f of b بالخط الواصل بينهم أوفقي تمام انهم خط + +164 +00:16:47,850 --> 00:16:50,870 +واصلي يبقى المماس بيكون أوفق يبقى f prime يسوى + +165 +00:16:50,870 --> 00:16:55,810 +zero هنا شال الشرط هذا مجرد شال الشرط هذا يبقى f + +166 +00:16:55,810 --> 00:17:01,690 +prime of c يسوى f of b نقص f of a على b نقص ال a + +167 +00:17:03,320 --> 00:17:07,760 +أفترض أن الدالة دالة متصلة على الفترة المولقة وهو + +168 +00:17:07,760 --> 00:17:12,140 +الشرط الأول من نظرية رول، قابل الاشتقاق على الفترة + +169 +00:17:12,140 --> 00:17:15,120 +المفتوحة الشرط التالي من نظرية رول، الشرط التالت + +170 +00:17:15,120 --> 00:17:20,380 +اختفى، then there is at least يوجد على الأقل نقطة + +171 +00:17:20,380 --> 00:17:26,060 +إن لم يكن أكثرفي الفترة A وB at which ال F of B + +172 +00:17:26,060 --> 00:17:32,360 +نقص ال F of A على B نقص ال A بدل سوء ال F prime of + +173 +00:17:32,360 --> 00:17:37,140 +C هناك بيجيني أقول المماس أفقي، هل يا ترى هنا + +174 +00:17:37,140 --> 00:17:38,400 +المماس أفقي؟ + +175 +00:17:59,100 --> 00:18:07,600 +الان ليس بالضرورة ان F of A تساوي F of Bليس + +176 +00:18:07,600 --> 00:18:14,320 +بالضرورة، كويس؟ يبقى هذه اللي هي ال F of A وهذه ال + +177 +00:18:14,320 --> 00:18:23,220 +F of B، هذا الخط الواصل بينهما، تمام؟ طيب، الأن لو + +178 +00:18:23,220 --> 00:18:30,320 +بدى أجيب ميل هذا الخطيبقى بدى أروح أرسم من هنا خط + +179 +00:18:30,320 --> 00:18:35,740 +عفوقي بالشكل لأن هذا بيعمل ليه زاوية قائمة صحيح + +180 +00:18:35,740 --> 00:18:41,900 +ولا لأ؟ إذا الخط اللى عنها ده من A إلى B المسافة + +181 +00:18:41,900 --> 00:18:49,940 +من هنا لغاية هنا هي B ناقص ال A صحيح ولا لأ؟ والخط + +182 +00:18:49,940 --> 00:18:58,450 +الراسي هذا هو ال F of Aوالخط هذا كله هو F of B إذا + +183 +00:18:58,450 --> 00:19:05,650 +بصير المسافة هذه لحالها فقط F of B ناقص F of A + +184 +00:19:05,650 --> 00:19:14,630 +يبقى المسافة هذه F of B ناقص F of A تعالي الآن لو + +185 +00:19:14,630 --> 00:19:21,620 +جيت عند النقطة اللي عندنايبقى حلاجة النقطة C بحيث + +186 +00:19:21,620 --> 00:19:27,560 +لو رسمت المماس عند هذه النقطة أيه المماس اللي + +187 +00:19:27,560 --> 00:19:35,240 +عندنا يمس المنحنة عند هذه النقطة يبقى هذا المماس + +188 +00:19:35,240 --> 00:19:46,040 +منه F prime of C يبقى اتنين هذول متوازين + +189 +00:19:46,240 --> 00:19:53,840 +فبيقول ف prime of C اللي هو ميل المماس للمنحنة عند + +190 +00:19:53,840 --> 00:19:59,820 +النقطة C بدي say F of B نقص F of A على B نقص ال A + +191 +00:19:59,820 --> 00:20:04,550 +اللي هو ميل الوطر اللي عندنا هذايبقى الاتنين هدول + +192 +00:20:04,550 --> 00:20:08,350 +بيساوي بعضهم، يبقى هذا معنى النظرية من الناحية + +193 +00:20:08,350 --> 00:20:14,150 +الهندسية المماث عند النقطة C المل تبعه يساوي المل + +194 +00:20:14,150 --> 00:20:17,890 +الخط الواصل ما بين ال F of A والF of B اللي هما + +195 +00:20:17,890 --> 00:20:21,650 +بيساووش بعض، في رول كانوا بيساوي واحد، يعني هذا + +196 +00:20:21,650 --> 00:20:28,190 +المل يساوي Zero، من هنا أتى الفرق في ما بينهماهذه + +197 +00:20:28,190 --> 00:20:32,550 +نظرية القيمة المتوسطة الآن بدنا ناخد بعض الأمثلة + +198 +00:20:32,550 --> 00:20:40,090 +على هذه النظرية أول مثال بيقول ما يأتي by example + +199 +00:20:40,090 --> 00:20:45,150 +one is + +200 +00:20:45,150 --> 00:20:54,950 +the functionهل الدالة f of x تساوي احد امرين اتنين + +201 +00:20:54,950 --> 00:21:01,410 +x ناقص تلاتة لما ال x محصورة ما بين ال zero و ما + +202 +00:21:01,410 --> 00:21:08,310 +بين اتنين او ستة x اللي هو ال term التاني ناقص x + +203 +00:21:08,310 --> 00:21:16,440 +تربية ناقص سبعةو ال X هذه محصورة ما بين اتنين وبين + +204 +00:21:16,440 --> 00:21:23,820 +التلاتة satisfy the + +205 +00:21:23,820 --> 00:21:34,640 +hypothesis of + +206 +00:21:34,640 --> 00:21:36,400 +the mean value theorem + +207 +00:21:54,860 --> 00:22:00,600 +خلّيني أبدأ كدا نعطيني مثلة f of x بعض عن p's y's + +208 +00:22:00,600 --> 00:22:06,100 +function ومعرفة على الفترة من zero إلى تلاتة يعني + +209 +00:22:06,100 --> 00:22:10,480 +ال domain تبع الدالة فقط بدي أخد من أين إلى أين من + +210 +00:22:10,480 --> 00:22:15,240 +zero إلى تلاتة بقول هل الدالة هذه تحقق شروط ال + +211 +00:22:15,240 --> 00:22:19,260 +main value theorem ولا لأ بقوله كويس يقول الخطوة + +212 +00:22:19,260 --> 00:22:24,330 +الأولى بدي أشوف هلهي continuous على الفترة المغلقة + +213 +00:22:24,330 --> 00:22:30,250 +من Zero لثلاثة ولا لأ اول شي بقوله domain الدالة F + +214 +00:22:30,250 --> 00:22:35,470 +يساوي الفترة المغلقة من Zero إلى ثلاثة من Zero إلى + +215 +00:22:35,470 --> 00:22:39,190 +اتنين ومن اتنين لثلاثة يبقى احنا مقيدين بهذه + +216 +00:22:39,190 --> 00:22:45,360 +الفترة الان هذه دالة خطيةده اللي خاطية، ده اللي + +217 +00:22:45,360 --> 00:22:50,360 +متاصلة، هذه ده اللي من الدرجة الثانية، منحنة، برضه + +218 +00:22:50,360 --> 00:22:54,600 +متاصلة، يبقى المشكلة وين؟ عند نقطة الالتقاء، ممكن + +219 +00:22:54,600 --> 00:22:58,920 +يكون منحنة بالشكل هذا أو الخط المستقيم جاي من فوق، + +220 +00:22:58,920 --> 00:23:04,190 +لا يلتقي معاه، مظبوط؟إذا أثبتنا إن اتنين بيلتقوا + +221 +00:23:04,190 --> 00:23:09,090 +مع بعض، فالدالة مالها؟ دالة متصلة، إذا المشكلتنا + +222 +00:23:09,090 --> 00:23:14,550 +حصلة وين؟ حصلة عند اتنين طب، مش هنشوف الدالة متصلة + +223 +00:23:14,550 --> 00:23:18,890 +عند اتنين ولا لأ، بدي أشوف هل قيمة الدالة عند + +224 +00:23:18,890 --> 00:23:24,450 +اتنين تساوي نهاية الدالة عند اتنين ولا لأ، إذا بجي + +225 +00:23:24,450 --> 00:23:29,950 +بقوله بدي أخد ال F of اتنينإتنين حصلة في ال term + +226 +00:23:29,950 --> 00:23:34,870 +الأول يجي اتنين في اتنين ناقص تلاتة و يسوى كده؟ + +227 +00:23:34,870 --> 00:23:43,370 +واحد طيب أليس تهادي هي limit لل F of X لما ال X + +228 +00:23:43,370 --> 00:23:49,800 +بده يروح لليتنين من جهة الشمال؟صحيح ولا لأ؟ يبقى + +229 +00:23:49,800 --> 00:23:53,520 +هدول بيساوي بعض، يبقى لو قدرت أثبت أن ال limit ال + +230 +00:23:53,520 --> 00:23:57,200 +F of X لما ال X بتروح لإتنين من جهة اليمين بيساوي + +231 +00:23:57,200 --> 00:24:01,960 +النتيجة هذه، بيبقى الدالة دالة مبتصرة، بصير نهاية + +232 +00:24:01,960 --> 00:24:06,160 +الدالة تساوي قيمة الدالة عند تلك النقطة. إذا + +233 +00:24:06,160 --> 00:24:12,060 +بيدروح أخد limit ال F of X لما ال X بيروح لإتنين + +234 +00:24:12,060 --> 00:24:17,780 +من جهة اليمين.يبقى هذا ال limit لما ال X بده تروح + +235 +00:24:17,780 --> 00:24:22,080 +للإتنين من جهة اليمين إذا احنا رايحين للإتنين من + +236 +00:24:22,080 --> 00:24:27,920 +جهة اليمين يبقى وين؟ الجزء الثاني من ال function + +237 +00:24:27,920 --> 00:24:34,820 +يبقى بيصير 6X ناقص X تربية ناقص 7 هذه polynomial + +238 +00:24:34,820 --> 00:24:40,850 +من الدرجة الثانيةيبقى تعويض مباشر يبقى ستة في + +239 +00:24:40,850 --> 00:24:48,310 +اتنين ناقص اتنين تربية ناقص سبعة ما يساوي اتناشر + +240 +00:24:48,310 --> 00:24:55,990 +وهذه اربعة وناقص اربعة وناقص سبعة اللي هو ناقص + +241 +00:24:55,990 --> 00:25:01,430 +أحداشر يبقى اتناشر ناقص أحداشر اللي هو قداشر نفس + +242 +00:25:01,430 --> 00:25:08,720 +القيمة اللي عندنا هذه يبقى بناء عليه الساملما ال X + +243 +00:25:08,720 --> 00:25:13,580 +يذهب إلى الاتنين سواء كان يمين او شمال تساوي ال F + +244 +00:25:13,580 --> 00:25:18,740 +of اتنين تساوي واحد هذا سيعطينا ان ال F is + +245 +00:25:18,740 --> 00:25:27,200 +continuous على كل الفترة من 0 لغاية 8 لغاية 3 + +246 +00:25:29,870 --> 00:25:36,090 +هل الدالة قابلة للاشتراك على الفترة المفتوحة من + +247 +00:25:36,090 --> 00:25:42,370 +Zero لغاية تلاتة ولا لأ؟ تبقى مشكلتنا وين؟ عند + +248 +00:25:42,370 --> 00:25:46,750 +اتنين، نفس الطريقة، هل ال continuous بيعطيني + +249 +00:25:46,750 --> 00:25:51,650 +differentiability؟ليس بالضرورة، هذا كلام ليس + +250 +00:25:51,650 --> 00:25:56,250 +دقيقًا. إذا ما أقدرش، بس لو كانت قابلة للاشتقاء، + +251 +00:25:56,250 --> 00:25:59,830 +بقول automatic continuous غصبًا على ميربع، إذا ما + +252 +00:25:59,830 --> 00:26:04,010 +أقدرش أقول إن ده قابل للاشتقاك، شفه و هيك، اللي + +253 +00:26:04,010 --> 00:26:10,210 +أروح أثبتها. طيب، لو روحت أنا جيبت المشتقة من جهة + +254 +00:26:10,210 --> 00:26:16,560 +الشمال عند اتنين.تمام؟ يبقى المشتقة من جهة الشمال + +255 +00:26:16,560 --> 00:26:21,400 +يعني X أقل من الإتنين يبقى بده اشتق تساوي كده + +256 +00:26:21,400 --> 00:26:27,760 +تساوي اتنين طب لو بده اجيب المشتقة من جهة اليمين + +257 +00:26:27,760 --> 00:26:36,160 +عند اتنينيبقى بده يصير الستة ناقص اتنين X والحكي + +258 +00:26:36,160 --> 00:26:43,140 +هذا كله عند X يسوي قداش اتنين يبقى بيصير الستة + +259 +00:26:43,140 --> 00:26:48,200 +ناقص اتنين في اتنين يسوي قداش كمان اتنين نفس + +260 +00:26:48,200 --> 00:26:55,890 +القيمةيبقى هنا بقول له sir ال F prime او ال F is + +261 +00:26:55,890 --> 00:27:04,070 +differentiable at X يساوي اتنين هذا معناه ان ال F + +262 +00:27:04,070 --> 00:27:11,580 +isDifferentiable على الفترة المفتوحة من Zero لتلتة + +263 +00:27:11,580 --> 00:27:15,500 +لإن الاشتقاق الأولى مافيش فيه مشكلة واشتقاق الثاني + +264 +00:27:15,500 --> 00:27:20,680 +مافيه مشكلة المشكلة تكمن عند نقطة الالتقاء هل هي + +265 +00:27:20,680 --> 00:27:25,140 +Corner هل هي Castle هل هي Vertical Tangent هل هي + +266 +00:27:25,140 --> 00:27:26,000 +Discontinuity + +267 +00:27:29,900 --> 00:27:35,820 +السؤال يقول هل يتدل هذي تحقق شروط الـ Mean Value + +268 +00:27:35,820 --> 00:27:40,660 +Theorem ولا لأ؟ هم الشرطين اتحققوا، خلاص انتهينا، + +269 +00:27:40,660 --> 00:27:48,360 +يبقى ناسا الـF satisfy the + +270 +00:27:48,360 --> 00:27:50,520 +hypothesis + +271 +00:27:53,220 --> 00:27:59,540 +of the main value theorem + +272 +00:28:25,820 --> 00:28:31,160 +نمتقل إلى مثال آخر example + +273 +00:28:31,160 --> 00:28:37,820 +two show + +274 +00:28:37,820 --> 00:28:43,520 +that the + +275 +00:28:43,520 --> 00:28:53,080 +function f of x يسوى x زائد واحد علي x satisfy + +276 +00:28:56,550 --> 00:29:06,830 +هي حياثيات أساسية + +277 +00:29:06,830 --> 00:29:11,690 +قيمة ثيرم على الانترال + +278 +00:29:16,500 --> 00:29:28,600 +interval على الفترة المغلقة نص و اتنين and find + +279 +00:29:28,600 --> 00:29:32,480 +all + +280 +00:29:32,480 --> 00:29:40,680 +values of + +281 +00:29:40,680 --> 00:29:42,480 +C + +282 +00:29:44,060 --> 00:29:51,460 +that satisfy + +283 +00:29:51,460 --> 00:29:57,620 +the main value theorem + +284 +00:30:30,510 --> 00:30:38,030 +ولا نعود لمثال مرة أخرىالـ F of X تساوي X زائد + +285 +00:30:38,030 --> 00:30:43,330 +واحد بيين لي أن هذه الدلة تحقق نظرية القيم + +286 +00:30:43,330 --> 00:30:49,030 +المتوسطة على الفترة من نص لغاية اتنين وبعد ذلك + +287 +00:30:49,030 --> 00:30:55,790 +هتلي كل قيم C التي تحقق الهو ال main value theorem + +288 +00:30:55,790 --> 00:31:00,450 +على الفترة اللي هو نص و اتنين بقوله بسيطة، اذا + +289 +00:31:00,450 --> 00:31:05,770 +بدأو حدرس ال continuity لهذه الدلةأحنا عندنا ال F + +290 +00:31:05,770 --> 00:31:12,910 +of X يساوي X زائد واحد على X ال discontinuity حاصل + +291 +00:31:12,910 --> 00:31:18,070 +وين؟ في ال zero فقط ليه غير؟ ال discontinuity + +292 +00:31:18,070 --> 00:31:22,600 +الموجودة أو النقطة zero موجودة في الفترة ديلأ يبقى + +293 +00:31:22,600 --> 00:31:29,320 +هذه f of x is undefined + +294 +00:31:29,320 --> 00:31:36,580 +غير معرفة at x تساوي zero ليه ماهياش موجودة في + +295 +00:31:36,580 --> 00:31:43,200 +الفترة النص و اتنين معنى هذا الكلام ان دلدله متصلة + +296 +00:31:43,200 --> 00:31:48,820 +على الفترة هذه يبقى this means + +297 +00:31:50,230 --> 00:31:56,550 +that هذا يعني ان ال if is continuous + +298 +00:31:57,770 --> 00:32:04,150 +على الفترة المغنقة نص و اتنين لان ال discontinuity + +299 +00:32:04,150 --> 00:32:10,170 +فقط عند ال zero و zero خارج هذه الفترة نجي لمين ال + +300 +00:32:10,170 --> 00:32:14,530 +differentiability مش هنشوفه قبل اشتقاق ولا لا يبقى + +301 +00:32:14,530 --> 00:32:22,350 +لو جيت اشتقطة f prime of x يستوي واحد نقص واحد على + +302 +00:32:22,350 --> 00:32:31,460 +x تربيه المشتقة هذه غير معرفةخارج الفترة هذه يبقى + +303 +00:32:31,460 --> 00:32:39,320 +هذا ال f prime بده تساوي كده هذه is undefined كمان + +304 +00:32:39,320 --> 00:32:46,360 +غير محرفة at x يساوي zero اللي مش موجودة في الفترة + +305 +00:32:46,360 --> 00:32:53,010 +اللي هي النص و اتنين هذا معناه ان ال fis + +306 +00:32:53,010 --> 00:33:00,570 +differentiable on الفترة نص و اتنين إذا انتحققوا + +307 +00:33:00,570 --> 00:33:09,830 +الشرطين تبعين ال main value theorem يبقى F of X + +308 +00:33:09,830 --> 00:33:19,810 +تساوي X زائد واحد على X satisfy the hypothesis + +309 +00:33:25,100 --> 00:33:35,140 +of the mean value theorem يبقى المطموب الأول من + +310 +00:33:35,140 --> 00:33:42,560 +المسألة حققنا هذا على ال interval on ال interval + +311 +00:33:42,560 --> 00:33:49,520 +نص و اتنى بيقول هاتلي قيم C التي تحقق ال mean + +312 +00:33:49,520 --> 00:33:58,720 +value theoremبقوله by the mean value theorem there + +313 +00:33:58,720 --> 00:34:06,940 +exists c موجود في الفترة المفتوحة مص و اتنين such + +314 +00:34:06,940 --> 00:34:07,680 +that + +315 +00:34:10,060 --> 00:34:18,600 +الـ F of اتنين ناقص الـ F of نص على اتنين ناقص نص + +316 +00:34:18,600 --> 00:34:25,640 +يقدر يساوي الـ F prime of Cمش هنحقق هذا، بدي أعرف + +317 +00:34:25,640 --> 00:34:32,120 +قداش F of اتنين و قداش ال F of نص، يبقى بدي أشيل + +318 +00:34:32,120 --> 00:34:42,660 +هنا و أقول هذا اتنين زائد نص ناقص ال F of نص نص + +319 +00:34:42,660 --> 00:34:50,550 +زائد واحد على نصكله على قداش اتنين ناقص نصف بيبقى + +320 +00:34:50,550 --> 00:34:56,190 +واحد و نصف اللي هو تلاتة على اتنين بده يساوي F + +321 +00:34:56,190 --> 00:35:01,750 +prime of C هي F prime بس بده اشيل كل X و أحط + +322 +00:35:01,750 --> 00:35:08,230 +مكانها C يبقى واحد ناقص واحد على C تربية + +323 +00:35:15,240 --> 00:35:20,940 +طبعا ناقص المقدار هذا كله حطوه لبنجوسين برضه جداش + +324 +00:35:20,940 --> 00:35:27,070 +اتنين و نص يعني جداش مقلع زيرو يبقى هذا معناهإن + +325 +00:35:27,070 --> 00:35:32,890 +واحد ناقص واحد على C تربية تساوي Zero هذا معناه إن + +326 +00:35:32,890 --> 00:35:37,730 +واحد على C تربية تساوي واحد هذا معناه إن C تربية + +327 +00:35:37,730 --> 00:35:44,710 +تساوي واحد هذا معناه إن C تربية تساوي زائد أو ناقص + +328 +00:35:44,710 --> 00:35:49,870 +واحدتعال، طيب، الآن هل السالب واحد موجودة في + +329 +00:35:49,870 --> 00:35:55,870 +الفترة هذه؟ لأ، يبقى الـC تساوي السالب واحد، does + +330 +00:35:55,870 --> 00:36:02,350 +not belong للفترة اللي هي المصوتنا، يبقى هذه ايه؟ + +331 +00:36:02,350 --> 00:36:08,400 +مرفوضةيبقى هذا مرفوضة، هذا بدّه يعطيك ان الـC + +332 +00:36:08,400 --> 00:36:13,600 +تساوي واحد هي المطموعة اللي موجودة في الفترة ما + +333 +00:36:13,600 --> 00:36:19,180 +بين نص و اتنين يبقى الـC اللي بدّه يهي الـC تساوي + +334 +00:36:19,180 --> 00:36:26,280 +واحد صحيح كويس، + +335 +00:36:26,280 --> 00:36:32,200 +يقول أعطيك العافية خلاص، مكملش، انتهينا، ماتحققش، + +336 +00:36:32,200 --> 00:36:39,250 +يبقى انتهينا منهنأخد مثال + +337 +00:36:39,250 --> 00:36:48,010 +يبقى example three show + +338 +00:36:48,010 --> 00:36:55,950 +that show that sign ال B + +339 +00:37:01,030 --> 00:37:09,530 +اقل من أو يساوي absolute value ل B ناقص ال A for + +340 +00:37:09,530 --> 00:37:16,670 +any numbers + +341 +00:37:16,670 --> 00:37:20,970 +A and B + +342 +00:37:31,510 --> 00:37:35,830 +طبعا السؤالين اللي فاتوا كانوا واضحات قال بييلي ان + +343 +00:37:35,830 --> 00:37:40,090 +هذه الدالة بتحقق شروط ال main value theorem و + +344 +00:37:40,090 --> 00:37:43,750 +بعدين هات لقيمة C هنا أباني سؤال لا جالي main + +345 +00:37:43,750 --> 00:37:46,910 +value theorem ولا جابلي سيرة ال main value theorem + +346 +00:37:46,910 --> 00:37:51,730 +يبقى كله بترجع لشطاطة كال انت صاحي ولا لأ فاهم + +347 +00:37:51,730 --> 00:37:57,100 +الموضوع لأهذا طبعا أحد أسئلة الكتاب زي ما هو نصا + +348 +00:37:57,100 --> 00:38:00,600 +زي هيك قال يبين لي أن ال absolute value ل sign ال + +349 +00:38:00,600 --> 00:38:05,640 +B ناقص sign ال A أقل من أو يسوى B ناقص عليه ك + +350 +00:38:05,640 --> 00:38:11,580 +absolute value لأي قيمة A أو B بقوله والله كويس + +351 +00:38:11,580 --> 00:38:15,650 +السؤال هوأنا بدي أجرب الـ Mean Value Theorem، لكي + +352 +00:38:15,650 --> 00:38:19,250 +أجرب الـ Mean Value Theorem، بدي فانكشن عندنا، + +353 +00:38:19,250 --> 00:38:22,550 +السؤال هو مين الـ function في هذه المثلة؟ الـ sine + +354 +00:38:22,550 --> 00:38:28,130 +ال X، يبقى أنا بس انتيجة استنتاجي من خلال مين؟ من + +355 +00:38:28,130 --> 00:38:31,910 +خلال الكلام اللي موجود عندى، ال sine ال B ناقص ال + +356 +00:38:31,910 --> 00:38:35,910 +sine ال A، يعني هذا قيمة للـ function عند بي وقيمة + +357 +00:38:35,910 --> 00:38:39,910 +أخرى للـ function وين، عند بي يبقى أول خطوة بقول + +358 +00:38:39,910 --> 00:38:49,980 +لهالـ f of x يساوي صين الـ x مدام صين الـ x يبقى + +359 +00:38:49,980 --> 00:38:56,400 +الصين الـ x فيها discontinuity يبقى هذه f of x هذه + +360 +00:38:56,400 --> 00:39:03,660 +الصين الـ x continuous for all x بالاستثناء كل الـ + +361 +00:39:03,660 --> 00:39:10,430 +real lineطيب، معنى هذا الكلام إن ال F is + +362 +00:39:10,430 --> 00:39:18,330 +continuous على الفترة A وB اللي هي جزء من مين؟ جزء + +363 +00:39:18,330 --> 00:39:23,570 +من ال real life خد أي close خد اللي بدكيها، zero + +364 +00:39:23,570 --> 00:39:28,150 +واحد، zero اتنين، واحد وخمسة، عشرة وخمسمية، أي + +365 +00:39:28,150 --> 00:39:33,370 +فترة بدكيهاإن شاء الله تقول لي ناقص ثلاثة وواحد، + +366 +00:39:33,370 --> 00:39:37,730 +سيئات، أي فترة بدي أخدها لأن ماعطليش قيود على A + +367 +00:39:37,730 --> 00:39:42,410 +وB، مين ما يكون الـA وB، وكون أخدت لبس الـU value + +368 +00:39:42,410 --> 00:39:46,990 +مين أصغر ومين أكبر، لا قيمة لها هذا السيئات، طيب + +369 +00:39:46,990 --> 00:39:52,060 +تمام، يبقى بالك كنتني واصل على هذه الفترةهل هي + +370 +00:39:52,060 --> 00:39:57,500 +differentiable ولا لا؟ إذا بجي بقوله F prime of X + +371 +00:39:57,500 --> 00:40:05,260 +تفضل الـSin بCos X المشتقة دي في نقطة ماهياش معرفة + +372 +00:40:06,040 --> 00:40:14,480 +يبقى هذا الـ if a parameter is defined برضه for + +373 +00:40:14,480 --> 00:40:20,920 +all x belastate لأ معناه هذا الكلب ان ال if is + +374 +00:40:20,920 --> 00:40:29,110 +differentiable على الفترة المفتوحة a و bإذا انتحقق + +375 +00:40:29,110 --> 00:40:35,370 +الشرطين، تبعين من؟ تبعين الـMain Value Theorem، + +376 +00:40:35,370 --> 00:40:40,950 +معناه اللازم ألاقي على الأقل ولو نقطة C، بحيث + +377 +00:40:40,950 --> 00:40:48,130 +نظرية القيمة المتوسطة تبقى صحيحة يبقى الـF of X + +378 +00:40:48,130 --> 00:40:55,950 +يساوي الصين الـX satisfy the hypothesis + +379 +00:40:58,260 --> 00:41:06,640 +of the mean value theory هذا معناه إيش؟ إنه يوجد + +380 +00:41:06,640 --> 00:41:14,820 +there exists C موجودة في الفترة المفتوحة A وB such + +381 +00:41:14,820 --> 00:41:25,430 +that بحيث أن ال F of Bنقص ال F of A على B نقص ال A + +382 +00:41:25,430 --> 00:41:28,870 +بدي يسوي F prime of C + +383 +00:41:32,500 --> 00:41:39,600 +الان بده اجي لل F of B اللي هي مين؟ صين ال B نقل + +384 +00:41:39,600 --> 00:41:47,740 +صين ال A على B اه بدت تتخلق المثل عندى، مش هيك؟ + +385 +00:41:47,740 --> 00:41:53,080 +يبقى هذا الكلام بده يساوي F prime اللي هو جباش، + +386 +00:41:53,080 --> 00:42:00,990 +cosine يبقى هذا cosine ال Cطب ايش رأيك؟ بتاخد ال + +387 +00:42:00,990 --> 00:42:08,270 +absolute value للترفين تمام؟ هذا الكلام بده يساوي + +388 +00:42:08,270 --> 00:42:15,570 +هذا بده يعطيلك absolute value ل sign ال B ناقص + +389 +00:42:15,570 --> 00:42:23,870 +sign ال A على absolute value لل B ناقص ال E يساوي + +390 +00:42:23,870 --> 00:42:27,850 +absolute value لكو sign ال C + +391 +00:42:34,810 --> 00:42:42,420 +كده؟ يعني دايما هو أكتر من الواحديبقى اذا كوصين + +392 +00:42:42,420 --> 00:42:45,800 +الـC لما ربك يحط فيه البركة بيصير واحد + +393 +00:43:09,470 --> 00:43:13,870 +يبقى لو ضربت الطرفين فيها لا تتغير ال inequality + +394 +00:43:13,870 --> 00:43:19,250 +يبقى لو ضربت الطرفين بيصير عند مين absolute value + +395 +00:43:19,250 --> 00:43:26,290 +لل sign ال B ناقص A اللي هو sign ال A كله ك + +396 +00:43:26,290 --> 00:43:32,230 +absolute value أقل من أو يساوي ال B ناقص ال A أظن + +397 +00:43:32,230 --> 00:43:33,250 +وهو المطلوب + +398 +00:43:41,840 --> 00:43:47,800 +كيف ايش؟ احنا موضوعنا موضوع ال mean value theorem، + +399 +00:43:47,800 --> 00:43:53,560 +مظبوط؟ ماعنديش معلومات غيرها حتى اللحظة، يا هي + +400 +00:43:53,560 --> 00:43:59,180 +نظرية رول، مظبوط ولا لا؟طيب، يبقى أنا مين أسهل + +401 +00:43:59,180 --> 00:44:04,360 +ليه؟ هذه النظرية ولا نظرية رول؟ هذه لإن أنا بدأ + +402 +00:44:04,360 --> 00:44:08,760 +شرطين، بدليش الشرط التالت ومن الصعب إني أجيب الشرط + +403 +00:44:08,760 --> 00:44:12,660 +التالت، مظبوط؟ يبقى automatically أنا سنتاج لحالة + +404 +00:44:12,660 --> 00:44:16,280 +إنها نظرية رول طيب، بعدين أنا بدي أعطيك كمان مثال + +405 +00:44:16,280 --> 00:44:20,440 +بفكرة جديدة مختلفة وشوف كيف بدك تعرفها، هل هي + +406 +00:44:20,440 --> 00:44:25,380 +نظرية رول ولا غير نظرية رول؟ خد؟ أيوة + +407 +00:44:29,820 --> 00:44:34,240 +إذا لا تحقق نظر L في الشرطين بقدرش أقول there + +408 +00:44:34,240 --> 00:44:43,760 +exist C بقدرش مش إمكانية أبدا + +409 +00:44:43,760 --> 00:44:48,080 +مش ال cosine قداش cosine ال C أكبر قيمة بياخدوه + +410 +00:44:48,080 --> 00:44:54,640 +وأقل قيمة Zeroأقل من أو يساوي واحد يعني أقل من أو + +411 +00:44:54,640 --> 00:44:58,020 +يساوي واحد، مظبوط ولا لأ؟ يبقى هنا أقل من أو يساوي + +412 +00:44:58,020 --> 00:45:02,340 +واحد، اضرب ضرب تبادلي، بصي ال sign بيناقص sign ليه + +413 +00:45:02,340 --> 00:45:06,920 +ك absolute value أقل من أو يساوي واحد ضرب absolute + +414 +00:45:06,920 --> 00:45:09,880 +value ليه بيناقص عليه، وهو المطلوب + +415 +00:45:30,790 --> 00:45:39,790 +حد بدأ يسأل تاني؟ و بالمثال الرابع؟ مثال أربعة؟ + +416 +00:45:48,950 --> 00:45:56,470 +وقول الـ suppose that + +417 +00:45:56,470 --> 00:46:06,190 +ال F is continuous on + +418 +00:46:06,190 --> 00:46:12,110 +الفترة المغلقة Zero وأربع + +419 +00:46:18,670 --> 00:46:29,750 +وال F of 0 يبدو يساوي واحد and الاتنين + +420 +00:46:29,750 --> 00:46:37,130 +اقل من او يساوي ال F prime of X اقل من او يساوي + +421 +00:46:37,130 --> 00:46:46,610 +خمسة for all X الموجودة في الفترة المفتوحة Zero + +422 +00:46:46,610 --> 00:46:57,850 +وأربعالسؤال هو show that بيّلي إنه التسعة أقل من + +423 +00:46:57,850 --> 00:47:05,590 +أو يساوي ال F of أربعة أقل من أو يساوي الواحد + +424 +00:47:05,590 --> 00:47:06,330 +وعشرين + +425 +00:47:18,040 --> 00:47:23,840 +نقرر من السؤالين، السؤال هذا لا اعطاني قيمة لدالة + +426 +00:47:23,840 --> 00:47:28,760 +ولا اعطاني شكل دالة ولا اعطاني continuous ولا + +427 +00:47:28,760 --> 00:47:32,850 +differentialعلى ده حالة من خلال المعطية تبعت المثل + +428 +00:47:32,850 --> 00:47:38,050 +استنتجت شكل الدالة و روحت اشتقيت الدالة و أثبتت + +429 +00:47:38,050 --> 00:47:41,510 +انها دالة متصلة على كل ال real line وبالتالي أخدت + +430 +00:47:41,510 --> 00:47:45,270 +فترة من هذا ال real line و بعدين أثبتت انها + +431 +00:47:45,270 --> 00:47:48,690 +differentiable وبالتالي استخدمت ال main value + +432 +00:47:48,690 --> 00:47:53,310 +theoremهذا السؤال قال لي ال F ده اللي متصل على + +433 +00:47:53,310 --> 00:47:57,690 +فترة 0 و 4 يبقى أعطاني main condition الأول تبع ال + +434 +00:47:57,690 --> 00:47:59,890 +main .. وماقلليش هستخدم ال main value theorem + +435 +00:47:59,890 --> 00:48:04,570 +قاللي أنت حر سوي اللي بدك إياه، و أعطاني معلومات و + +436 +00:48:04,570 --> 00:48:08,470 +أنا لحالي بدي أستنتج الشغلة اللي ممكن أحلبها main + +437 +00:48:08,470 --> 00:48:14,050 +السؤالقال ياف دالة مقتصرة على فترة المغلقة 0 4 + +438 +00:48:14,050 --> 00:48:21,230 +وقيمة الدالة عند 0 تساوي 1 صحيح وقيمة المشتقة + +439 +00:48:21,230 --> 00:48:28,670 +محصورة بين 2 و5 لكل ال X اللي موجودة وينأربعة + +440 +00:48:28,670 --> 00:48:33,050 +محصورة + +441 +00:48:33,050 --> 00:48:36,390 +بين التسعة وما بين الواحد وعشرين + +442 +00:48:42,160 --> 00:48:45,540 +بقول طيب ايش؟ من وين بيزيجي بقولها؟ بعدين بقول اه + +443 +00:48:45,540 --> 00:48:49,480 +ماهي F of 4 موجودة في نظرية ال mean value theorem + +444 +00:48:49,480 --> 00:48:55,240 +نجان نقلوها Z بجانها F of 4 و F of 0 على 4 ناقصة 0 + +445 +00:48:55,240 --> 00:48:58,760 +بتساوي F prime of Z مش هيك نظرية ال mean value اذا + +446 +00:48:58,760 --> 00:49:04,700 +انا بدي ابحث هل ال F اللي عندي هني هل تحقق شروط ال + +447 +00:49:04,700 --> 00:49:08,360 +mean value theorem ام لا والله إذا حققتها بقدر + +448 +00:49:08,360 --> 00:49:12,380 +استخدم ال mean value و أحل السؤال ما حققتهابروح + +449 +00:49:12,380 --> 00:49:17,100 +أكبس في شغلة تانية يمكن ولا ربما الله أعلم يبقى + +450 +00:49:17,100 --> 00:49:22,760 +احنا بنقول الدلة دلة متصلة على الفترة المغلقة يبقى + +451 +00:49:22,760 --> 00:49:31,120 +الخطوة الأولى بقوله ال F is continuous على الفترة + +452 +00:49:31,120 --> 00:49:32,740 +المغلقة 04 + +453 +00:49:35,230 --> 00:49:40,790 +بدي أشوف هل الدالة قابلة للاشتقاق على الفترة + +454 +00:49:40,790 --> 00:49:46,790 +المفتوحة 04 ولا لأ باجي بكمل قراية الأسئلة F of 0 + +455 +00:49:46,790 --> 00:49:51,110 +تسوى 1 هذا مالعيش علاقة بالاشتقاق هذه قيمة الدالة + +456 +00:49:51,110 --> 00:49:56,330 +عند نقطة بيعطيني كمان condition إن قيمة المشتقة + +457 +00:49:56,330 --> 00:50:01,490 +محصورة بين 2 و 5 لكل ال X + +458 +00:50:05,320 --> 00:50:10,640 +ماذا تستنتج من هذه العبارة؟ اه مدام انها قيم + +459 +00:50:10,640 --> 00:50:15,360 +محصولة، اذا الدالة قابلة لاشتقاق خلال هذه الفترة، + +460 +00:50:15,360 --> 00:50:18,900 +يبقى جبت ال condition التاني التابع مين؟ ال main + +461 +00:50:18,900 --> 00:50:25,370 +value theorem، باجي بقولهلإتنين أقل من أو يساوي f + +462 +00:50:25,370 --> 00:50:31,250 +prime of x أقل من أو يساوي لكل ال x اللي موجودة في + +463 +00:50:31,250 --> 00:50:39,770 +الفترة 0 4 هذا شو تعني means that هذا تعني أن ال f + +464 +00:50:39,770 --> 00:50:50,790 +is differentiable on الفترة 0 4المشتقة محصورة بين + +465 +00:50:50,790 --> 00:50:55,790 +2 و 5 لكل ال X اللي في 0 و 4 يبقى الدالة قابلة + +466 +00:50:55,790 --> 00:51:00,330 +الاشتقاء خلال هذه الفترة وقيمة المشتقة محصورة + +467 +00:51:00,330 --> 00:51:05,990 +دائما و أبدا بين 2 و 5 يبقى الدالة قابلة الاشتقاء + +468 +00:51:05,990 --> 00:51:11,130 +خلال هذه الفترة من ال two conditions لإتنين هدول + +469 +00:51:11,130 --> 00:51:22,500 +بقدر أقوله إذاالـ if satisfy the hypothesis + +470 +00:51:26,590 --> 00:51:35,730 +of the main value theorem اذا هذه النظرية تحقق او + +471 +00:51:35,730 --> 00:51:41,790 +هذه الدالة F تحقق شروط نظرية القيمة المتواصلة مدام + +472 +00:51:41,790 --> 00:51:45,870 +هيك هذا شو معناه يبقى هناك + +473 +00:51:53,470 --> 00:52:03,830 +بحيث ان such that f prime of c بده ساوي اللي هو ال + +474 +00:52:03,830 --> 00:52:10,070 +F of أربعة ناقص ال F of Zero على أربعة ناقص ال + +475 +00:52:10,070 --> 00:52:18,790 +Zero طبعا؟ طيب، باجي بقوله هذا شو معناه؟ F of + +476 +00:52:18,790 --> 00:52:23,290 +أربعة لازمالي في الإجابةيبقى ماقدرش ألعب فيها ولا + +477 +00:52:23,290 --> 00:52:29,270 +حاجة ال F of zero مقاطع في المثل بواحد يبقى باشي + +478 +00:52:29,270 --> 00:52:34,230 +لو بكتب بدالها واحد اربعة ناقص zero اللي هو بقدراش + +479 +00:52:34,230 --> 00:52:41,590 +باربعة بده يسوى F prime of C يبقى هذا بده يسوى F + +480 +00:52:41,590 --> 00:52:49,900 +prime of Cالان f prime of x محصورة بين اتنين وخمسة + +481 +00:52:49,900 --> 00:52:54,400 +لكل ال x اللي محصورة في ال بينزير واربع، إذا معنى + +482 +00:52:54,400 --> 00:52:58,320 +هذا الكلام إن القيمة هذه محصورة بين مين ومين؟ بين + +483 +00:52:58,320 --> 00:53:06,700 +اتنين وخمسة، يبقى باجي بقوله بما أنلإتنين أقل من f + +484 +00:53:06,700 --> 00:53:12,840 +prime of x أقل من أو يسوى خمسة لكل ال x اللي + +485 +00:53:12,840 --> 00:53:17,180 +موجودة في zero أربعة إذا أنت تنطبق على الكلام اللي + +486 +00:53:17,180 --> 00:53:24,620 +إحنا جايب له هذا since هذا يبقى we have أن ال f of + +487 +00:53:24,620 --> 00:53:32,730 +أربعة ناقص الواحدأربعة محصورة ما بين اتنين وبين + +488 +00:53:32,730 --> 00:53:41,870 +مان وبين الخمسة، بصبر؟ لأن هذه F'C واحنا عنا F'X + +489 +00:53:41,870 --> 00:53:46,890 +لكل X اللي موجودة في الفترة هذه محصورة هنا، إذن C + +490 +00:53:46,890 --> 00:53:50,710 +موجودة في هذه الفترة، إذن F'C بدي يكون محصور بين + +491 +00:53:50,710 --> 00:53:51,270 +اتنين + +492 +00:54:01,640 --> 00:54:08,040 +أقل من او يساوي F of أربعة ناقص واحد اقل من او + +493 +00:54:08,040 --> 00:54:13,720 +يساوي أربعة في خمسة وعشرينواضيف لي واحد للثلاثة + +494 +00:54:13,720 --> 00:54:21,060 +أطراف بيصير تسعة أقل من أو يساوي ال F of أربعة أقل + +495 +00:54:21,060 --> 00:54:28,340 +من أو يساوي الواحد وعشرين وهو المطلوب ايوة ادي + +496 +00:54:28,340 --> 00:54:33,920 +بالك سؤال زي هذا مرة جيبناه في إحدى الامتحانات + +497 +00:54:33,920 --> 00:54:41,310 +عميلي بدي أسأل ال condition التاني هذاوالله هذا + +498 +00:54:41,310 --> 00:54:45,890 +اللي هنا، ممتاز جدا، طلعلي في أصله في المثلة، + +499 +00:54:45,890 --> 00:54:52,270 +بيقوللي أصله في المثلة إن F prime of X محصورة + +500 +00:54:52,270 --> 00:54:58,650 +دائما بين 2 و 5 لكل ال X اللي موجودة في الفترة من + +501 +00:54:58,650 --> 00:55:03,740 +0 ل4يبقى انا لو جيت على الفترة من zero لاربعة وجبت + +502 +00:55:03,740 --> 00:55:07,180 +المشتقة، المشتقة محصورة بين اتنين وخمسة، يعني + +503 +00:55:07,180 --> 00:55:11,980 +المشتقة exist، راح ولا لا؟ يبقى المشتقة موجودة + +504 +00:55:11,980 --> 00:55:15,580 +خلال الفترة من zero لاربعة، وهو ال condition + +505 +00:55:15,580 --> 00:55:19,390 +التاني من شروط ال main value termأعطانيها + +506 +00:55:19,390 --> 00:55:23,150 +continuous و هي differentiable بسبب تطبيق ال main + +507 +00:55:23,150 --> 00:55:28,450 +value theorem روحنا و طبقنا ال main value theorem + +508 +00:55:28,450 --> 00:55:32,770 +there exists c موجودة في الفترة من 0 ل 4 فهو f + +509 +00:55:32,770 --> 00:55:38,090 +prime of c بيسوي f of b نقص f of a على b مقص ال a + +510 +00:55:38,090 --> 00:55:42,890 +f of 0 معطب 1 شيلته و حطيته 1 4 نقص 0 بيسوي f + +511 +00:55:42,890 --> 00:55:48,330 +prime of cبرجع لل condition المشتقة لكل ال X + +512 +00:55:48,330 --> 00:55:53,470 +الموجودة من صفر لاربع محصورة بين اتنين و خمسة ال C + +513 +00:55:53,470 --> 00:55:58,830 +موجودة في الفترة 0 و 4 اذا F prime of C بيكون + +514 +00:55:58,830 --> 00:56:03,230 +محصورة ما بين اتنين و خمسة لكن ال F prime of C هي + +515 +00:56:03,230 --> 00:56:07,580 +F اربع نقص واحد على اربعبشيلة بحط f of أربعة ناقص + +516 +00:56:07,580 --> 00:56:11,200 +واحد على أربعة محصورة بين اتنين أو خمسة بحل + +517 +00:56:11,200 --> 00:56:15,120 +الانقلاد يصير ال F of أربعة محصورة بين التسعة وما + +518 +00:56:15,120 --> 00:56:21,620 +بين الواحد وعشرين في عندنا بعض النتائج على هذه + +519 +00:56:21,620 --> 00:56:27,140 +النظرية نعطيكم بدل النتيجة تنتين يبقى بالداجة + +520 +00:56:27,140 --> 00:56:30,580 +للنتيجة الأولى لهذه النظرية Crawler one + +521 +00:56:40,560 --> 00:56:51,040 +النتيجة الأولى بقول F F prime of X يساوي Zero at + +522 +00:56:51,040 --> 00:57:06,000 +each point X عند كل نقطة X of an open interval + +523 +00:57:13,040 --> 00:57:25,020 +ثم ال F of X يكون كونستانت C لكل + +524 +00:57:25,020 --> 00:57:33,520 +X الموجودة في الفترة المفتوحة A وB حيث + +525 +00:57:33,520 --> 00:57:37,240 +C هو كونستانت + +526 +00:58:13,710 --> 00:58:19,380 +خلّيني أقولك واحدالسؤال مرة تانية بقول لو كان f + +527 +00:58:19,380 --> 00:58:25,280 +prime of x يساوي 0 عند كل نقطة x في الفترة + +528 +00:58:25,280 --> 00:58:34,080 +المفتوحة a و b then f of x بدي ساوي constant c و + +529 +00:58:34,080 --> 00:58:40,020 +ال c هذه عبارة عن element موجود في الفترة a و b + +530 +00:58:40,020 --> 00:58:46,350 +بنقوله بسيطة جدا تعالى نشوف ال proofيعني الـ + +531 +00:58:46,350 --> 00:58:51,290 +crawler هذه بتقول لو كانت المشتقة لدالة تساوي zero + +532 +00:58:51,290 --> 00:58:56,250 +إذا هذه الدالة تعتبر دالة ثابتة طبعا أنا أخدنا في + +533 +00:58:56,250 --> 00:58:59,290 +ال chapter اللي فات في ال derivatives إن مشتقة + +534 +00:58:59,290 --> 00:59:03,530 +المقنعر ثابت يساوي، هذه بتقول للعكس، لو كانت + +535 +00:59:03,530 --> 00:59:10,330 +المشتقة تساوي zero إذا هذه الدالة دالةطيب تعالى + +536 +00:59:10,330 --> 00:59:16,110 +نشوف يبقى انا عند المشتقة تساوي zero بده احاول ان + +537 +00:59:16,110 --> 00:59:21,350 +هذه المشتقة تساوي مقدارا ثابتا بنقوله بسيطة جدا + +538 +00:59:21,350 --> 00:59:27,690 +يبقى انا بدى استفيدCrollary يعني نتيجة، نتيجة على + +539 +00:59:27,690 --> 00:59:31,970 +مين؟ نتيجة على نظرية ال main value theorem يعني + +540 +00:59:31,970 --> 00:59:36,850 +معناته أنا في البرهان بدي أطبق نظرية ال main value + +541 +00:59:36,850 --> 00:59:41,180 +theoremطبعا من وين لوين انا مش شايف انه closed + +542 +00:59:41,180 --> 00:59:46,220 +interval مش شايف انا هيك تمام فباجي بقوله بدي اطبق + +543 +00:59:46,220 --> 00:59:50,480 +اه بدي اجيب الشروط بحدافيرها الموجودة على الكلام + +544 +00:59:50,480 --> 00:59:55,060 +اللي موجود عندنا هذا بيقول ان المشتقة تساوي zero + +545 +00:59:55,060 --> 01:00:00,840 +عند كل نقطة موجودة في ال open interval ايش يعني + +546 +01:00:00,840 --> 01:00:05,500 +يعني الدلق قابل الاشتقاق على الفترة المفتوحة هذه + +547 +01:00:06,020 --> 01:00:11,580 +يبقى انا اول ما ابدأ بدي اقول اللي افترض عندي x1 و + +548 +01:00:11,580 --> 01:00:20,460 +x2 موجودة في الفترة المفتوحة a و b such that بحيث + +549 +01:00:20,460 --> 01:00:30,340 +ان ال x1 اقل من ال x2 على سبيل المثال اخدت نقطتين + +550 +01:00:30,590 --> 01:00:38,930 +في الفترة المفتوحة بحيث ان ال X1 أقل من X2 يعني ال + +551 +01:00:38,930 --> 01:00:44,530 +X1 و X2 لا بتساوي ال A ولا بتساوي ال B يعني لو جيت + +552 +01:00:44,530 --> 01:00:51,350 +قلت هذا ال real line واخدت هذه A واخدت هذه Bيبقى + +553 +01:00:51,350 --> 01:00:58,210 +اخد هنا x1 واخد هنا x2 واضح ان x1 اقل من ماين من + +554 +01:00:58,210 --> 01:01:05,450 +x2 طب يعني هدول قيمتين لا يمكن ان يتساوي صحيح ولا + +555 +01:01:05,450 --> 01:01:06,010 +لا؟ + +556 +01:01:12,060 --> 01:01:18,300 +إذا أثبت أن قيمة الدالة عند X1 هي نفس قيمة الدالة + +557 +01:01:18,300 --> 01:01:23,690 +عند X2 يبقى هذه دالة ياشيتابع الانكس واحد وانكس + +558 +01:01:23,690 --> 01:01:28,110 +اتنين ليس قيم محددة، أي قيم موجودة في الانكس، + +559 +01:01:28,110 --> 01:01:31,670 +عشوائي أنا أخدتهم، ليس اتنين اتنين بعينهم وفلان + +560 +01:01:31,670 --> 01:01:35,170 +وفلان، لأ زي ما انا اقول انا بدي اخد اي طلاب اتنين + +561 +01:01:35,170 --> 01:01:39,270 +من الصرف، بس لو قلت تعيا محمد انت ابن فلان وانت + +562 +01:01:39,270 --> 01:01:43,670 +تعيا اسلمان، يعني ان انا اخترت اتنين بعينهم يعني، + +563 +01:01:43,670 --> 01:01:46,370 +يبقى هذا لا ينطق على الأخر، بس لو قلت اخدت اي + +564 +01:01:46,370 --> 01:01:49,520 +اتنينفتحنا الباب واخدنا اي اتنين يبقى خلاص اي + +565 +01:01:49,520 --> 01:01:54,060 +اتنين ينطبق عليها كل ما هو في القاعة تمام؟ يبقى + +566 +01:01:54,060 --> 01:01:58,440 +احنا بدنا نيجي هنا بدأ اخد two element X واحد و X + +567 +01:01:58,440 --> 01:02:05,760 +اتنين عشوائيا موجددات واحدفى الفترة اللى عندنا + +568 +01:02:05,760 --> 01:02:09,160 +المفتوحة A وB يعني ماعرفك لما نقول X1 و X2 لا + +569 +01:02:09,160 --> 01:02:15,440 +بتساوي و لا بتساوي B تمام الآن احنا عندنا ال F + +570 +01:02:15,440 --> 01:02:21,720 +prime of X يساوي Zero على الفترة المفتوحة A وB + +571 +01:02:21,720 --> 01:02:29,720 +معناته ايش؟ معناته ان ال F is differentiable on + +572 +01:02:29,720 --> 01:02:38,320 +الفترة المفتوحة A وBصحيح ولا لا؟ طيب سنة شوية بس + +573 +01:02:38,320 --> 01:02:46,520 +هذا معناه ان ال F is differentiable on الفترة + +574 +01:02:46,520 --> 01:02:53,670 +المغلقة X واحد و X اتنينلأن X1 و X2 جزء من الفترة + +575 +01:02:53,670 --> 01:02:58,430 +هذه كلها صحيح ولا لأ يبقى الدالة قابلة اشتقاق على + +576 +01:02:58,430 --> 01:03:03,410 +الفترة مدام قابلة اشتقاق إذا continuous يبقى هذا + +577 +01:03:03,410 --> 01:03:11,610 +يعطينا ان ال F is continuous on the closed + +578 +01:03:11,610 --> 01:03:22,160 +interval X1 و X2and differentiable on الفترة + +579 +01:03:22,160 --> 01:03:30,670 +المفتوحة x1 و x2يعني if a differentiable على اللي + +580 +01:03:30,670 --> 01:03:34,350 +closed مش بتضلها differentiable على اللي أقل منها + +581 +01:03:34,350 --> 01:03:38,010 +مش على الأقل منها وزيادة شوية برا لإنه على كل + +582 +01:03:38,010 --> 01:03:43,090 +الفترة من a إلى b معادة a وb يبقى اتحقق الشرطين + +583 +01:03:43,090 --> 01:03:50,550 +تبعات ال mean value theorem صحيح؟ يبقى هنا ال if + +584 +01:03:50,550 --> 01:03:56,330 +satisfy the hypothesis + +585 +01:03:58,340 --> 01:04:07,740 +of the mean value theorem هذا معناه ايش؟ there + +586 +01:04:07,740 --> 01:04:15,440 +exist c موجودة في الفترة x واحد و x اتنين such + +587 +01:04:15,440 --> 01:04:28,550 +that بحيث ان ifنقص f of x2 نقص f of x1 على x2 نقص + +588 +01:04:28,550 --> 01:04:32,490 +x1 بيسوي f prime of c + +589 +01:04:41,730 --> 01:04:55,800 +فقط فقط فقط فقط فقط فقط فقطزيرو يبقى هذا الكلام + +590 +01:04:55,800 --> 01:05:04,260 +بده يعطينا ان ال F of X2 ناقص F of X1 على X2 ناقص + +591 +01:05:04,260 --> 01:05:12,320 +X1 بده يساوي زيرو ايه السبب؟ because ان ال F prime + +592 +01:05:12,320 --> 01:05:19,280 +of X بده يساوي زيرو على الفترة كلها A وB يعني على + +593 +01:05:19,280 --> 01:05:24,470 +الفترة X1 وX2 بيه جزء منهاطيب مادام زيرو يبقى مين + +594 +01:05:24,470 --> 01:05:29,010 +اللي بيساوي زيرو البصد ولا المقعد؟ يبقى هنا بقوله + +595 +01:05:29,010 --> 01:05:34,770 +سوء ال F of X اتنين من عقص ال F of X واحد بيساوي + +596 +01:05:34,770 --> 01:05:41,680 +زيرو هذا معناته ان ال F of X اتنين بيساوي مين؟الـ + +597 +01:05:41,680 --> 01:05:49,920 +F of X1 لكل الـ X1 والـ X2 اللي موجودة في الفترة + +598 +01:05:49,920 --> 01:05:56,860 +المفتوحة A وB يعني X1 وX2 اي نقطتين ما تفسيرك لهذا + +599 +01:05:56,860 --> 01:06:07,060 +الكلام ان ده ثابت هذا معناه ان الـ F is a constant + +600 +01:06:07,060 --> 01:06:09,480 +function + +601 +01:06:11,380 --> 01:06:20,140 +on الفترة A وB هذا معناه ان ال F of X بدي ساوي + +602 +01:06:20,140 --> 01:06:29,160 +constant C على كل الفترة A وB وهو المطلوب شايف إذا + +603 +01:06:29,160 --> 01:06:34,020 +إلها جران يبقى closed جوهز يبقى مفتوحة في المثلة + +604 +01:06:34,020 --> 01:06:38,000 +فوق جالك open interval مظبوط + +605 +01:06:40,100 --> 01:06:45,580 +تعال هنا شوف تعال خلّي بالكم و أنا يا شباب نشوف مع + +606 +01:06:45,580 --> 01:06:49,220 +رأيه يبقى + +607 +01:06:49,220 --> 01:06:53,260 +F of X اتنين بسوء F of X واحد على كل ال X واحد و X + +608 +01:06:53,260 --> 01:06:56,460 +اتنين الموجودة في ال A و B احنا عاملنا الفترة كده؟ + +609 +01:06:56,460 --> 01:06:59,720 +A و B و X اتنين واحد خد X واحد و X اتنين الموجودة + +610 +01:06:59,720 --> 01:07:05,980 +داخل هذه الفترة يعني ماعنديش لا A ولا B مظبوط هك؟ + +611 +01:07:14,190 --> 01:07:22,390 +أحنا أخدنا X وحدة من X عشوائيا من A وB ممنوع + +612 +01:07:22,390 --> 01:07:27,570 +على الكلام لأنه مش موجود ال A وB من أساسها اه مش + +613 +01:07:27,570 --> 01:07:37,030 +موجودة خلاص طيب في كمان اكرولريه تاني أبسط + +614 +01:07:37,030 --> 01:07:38,470 +منها شوية يعني + +615 +01:07:58,890 --> 01:08:13,430 +عند كل نقطة x in an open interval + +616 +01:08:14,720 --> 01:08:22,240 +بقية مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +617 +01:08:22,240 --> 01:08:27,940 +مفتاح مفتاح مفتاح + +618 +01:08:27,940 --> 01:08:37,700 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +619 +01:08:37,700 --> 01:08:38,080 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +620 +01:08:38,080 --> 01:08:38,220 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +621 +01:08:38,220 --> 01:08:38,720 +مفتاح مفتاح مفتاح مفتاح مفتاح م + +622 +01:08:43,120 --> 01:08:53,120 +بحيث ان ال F of X يساوي ال G of X زائد constant C + +623 +01:08:53,120 --> 01:09:00,360 +لكل ال X اللي موجودة في الفترة المفتوحة A وB + +624 +01:09:03,790 --> 01:09:20,790 +أي أن الـ F ناقص الـ G is a constant function + +625 +01:09:20,790 --> 01:09:26,070 +on الفترة A وB + +626 +01:09:48,490 --> 01:09:54,750 +معطيني ان مشتقتين لدى اللى بيكونوا متساويتين نعطيك + +627 +01:09:54,750 --> 01:09:59,030 +مثال قبل ما نجي لـ Crawler هذا لو قولتك F of X + +628 +01:09:59,030 --> 01:10:06,390 +يساوي X تكيب كده مشتقتها؟ X تربية لو قولتك F of X + +629 +01:10:06,390 --> 01:10:12,970 +يساوي X تكيب زائد ميةمشتقتة كمان تلاتة إذا + +630 +01:10:12,970 --> 01:10:18,530 +المدلتين هدول مشتقاتهم متساوية، انت قداش الفرق فيه + +631 +01:10:18,530 --> 01:10:23,430 +ما بينهما؟ المية هو مقدار تابع، تمام؟ فالفرق ما + +632 +01:10:23,430 --> 01:10:28,310 +بين الاتنين هذا مقدار تابع، هذا على سبيل المثال + +633 +01:10:28,310 --> 01:10:30,690 +طيب، يبقى برجع تاني + +634 +01:10:34,820 --> 01:10:40,400 +الفرق ما بين الدلتين كان مقدارا ثابتا + +635 +01:10:44,690 --> 01:10:49,290 +each point x in an open interval a وb يبقى + +636 +01:10:49,290 --> 01:10:52,690 +المشتقتان متساويتين على كل نقطة على الفترة + +637 +01:10:52,690 --> 01:10:57,970 +المفتوحة a وb then there exists a constant c لازم + +638 +01:10:57,970 --> 01:11:02,910 +يجي اللاجئ مقدار c بحيث ان ال f of x سوى g of x + +639 +01:11:02,910 --> 01:11:07,680 +زائد c يعني الفرق فيما بينهماهو مقدار ثابت اللي هو + +640 +01:11:07,680 --> 01:11:13,200 +C لكل ال X اللي موجودة في A وB ذاتة ان ال F ناقص G + +641 +01:11:13,200 --> 01:11:17,540 +is a constant function يعني لو جبت هذا على الشجة + +642 +01:11:17,540 --> 01:11:21,600 +تانية بصير الفرق بينهم يسوي C يبقى الفرق بينهم + +643 +01:11:21,600 --> 01:11:27,240 +يسوي مقدارا ثابتا بدنا نروح نثبت صحة هذا الكلام + +644 +01:11:27,240 --> 01:11:36,280 +يبقى أنا عندي هذه المعطياتأول خطوة لت ال f' of x + +645 +01:11:36,280 --> 01:11:42,400 +تساوي g' of x لكل ال x الموجودة في ال open + +646 +01:11:42,400 --> 01:11:50,610 +interval a و bبقدر اخلها معادلة صفرية يبقى ال F + +647 +01:11:50,610 --> 01:11:56,950 +prime of X ناقص G prime of X يساوي كده؟ يساوي Zero + +648 +01:11:56,950 --> 01:12:04,710 +خلّي هذه المعلومة عندك وبدأجي اقول افترض ان ال H + +649 +01:12:04,710 --> 01:12:12,420 +of X بده يساوي ال F of X ناقص ال G of Xبدي افترض + +650 +01:12:12,420 --> 01:12:18,420 +ان عندي دالة هذه الدالة هي الفرق ما بين هتين + +651 +01:12:18,420 --> 01:12:24,660 +الدالتين طب لو جيت و قولت لك اشتق هذه الدالة يبقى + +652 +01:12:24,660 --> 01:12:31,060 +باجي بقوله يبقى ال H prime of X يساوي ال F prime + +653 +01:12:31,060 --> 01:12:39,170 +of X ناقص G prime of Xطب من المعادل اللي فوق يبقى + +654 +01:12:39,170 --> 01:12:45,050 +هذا الكلام إيش بقدر أستنتج منه بقدر أستنتج إن ال H + +655 +01:12:45,050 --> 01:12:52,230 +prime of X يساوي ماين؟ يساوي Zero طلعلي هنا في ال + +656 +01:12:52,230 --> 01:12:57,290 +crawler الأولى لو دلة يساوي Zero إذا هذه الدلة + +657 +01:12:57,290 --> 01:13:05,210 +تساوي مقدارا ثابتا ثم باجي بقوله By crawlerي + +658 +01:13:06,910 --> 01:13:18,230 +when we have ان ال H of X بده يساوي ال C و ال C is + +659 +01:13:18,230 --> 01:13:26,110 +constant يبقى هذا مقدارا ثابتا يبقى سعر عندي ال H + +660 +01:13:26,110 --> 01:13:33,970 +of X بده يساوي اللي انا فرضه كده F of Xماقص الـ g + +661 +01:13:33,970 --> 01:13:39,550 +of x بدي يسوي المقدار الثابت لأن هذا يبقى بناء + +662 +01:13:39,550 --> 01:13:45,890 +عليه هذا بدي يعطيك ان ال f of x بدي يسوي ال g of x + +663 +01:13:45,890 --> 01:13:55,550 +زائد constant c وهو المطلوب هذا معناه ان ال f ماقص + +664 +01:13:55,550 --> 01:14:06,150 +ال g is a constant functionوهو اللي مفروض بقى بيه + +665 +01:14:06,150 --> 01:14:14,270 +كويس نيجوا الآن ايوه نقولك + +666 +01:14:14,270 --> 01:14:19,570 +اثبت ال quarry one و بعدين اثبت التاني يعني مش هيك + +667 +01:14:19,570 --> 01:14:24,350 +والله بضهك يعني نعيد ال quarry one نكتبهن اول و + +668 +01:14:24,350 --> 01:14:31,550 +جديدشوف، إذا طلب دائما و أبدا إثبات جزء يعتمد على + +669 +01:14:31,550 --> 01:14:35,670 +جزء آخر، بيعطيلك نمره إيه يثبتلي الجزء الأول و + +670 +01:14:35,670 --> 01:14:41,690 +بعدين بطلب إثبات الجزء الثاني، ليش صعبي ليه؟ ولا + +671 +01:14:41,690 --> 01:14:48,690 +صعب ولا هادر، بدك تعتبره صعب انت، هذا شأنك + +672 +01:15:04,810 --> 01:15:10,870 +نأخد بعض الأمثلة على الـ two crawlers هذول اللي + +673 +01:15:10,870 --> 01:15:15,890 +عندنا بس قبل ما ناخد الأمثلة خدنا الملاحظة البسيطة + +674 +01:15:15,890 --> 01:15:17,070 +هذه النقطة + +675 +01:15:37,350 --> 01:15:46,010 +الأعلى اتروا صحيحة على الفترة المفتوحة من A إلى + +676 +01:15:46,010 --> 01:15:53,610 +Infinityومن سالب infinity لغاية ال V ان سالب + +677 +01:15:53,610 --> 01:15:56,390 +infinity و infinity + +678 +01:16:44,500 --> 01:16:47,640 +السؤال هو مصطلح + +679 +01:16:50,300 --> 01:17:06,900 +الـ F of X تساوي تلاتة for all X give reasons + +680 +01:17:06,900 --> 01:17:14,860 +for your + +681 +01:17:14,860 --> 01:17:17,160 +answer + +682 +01:17:51,440 --> 01:17:58,420 +نرجع مرة تانية. ايوة. اكيد انه لازم يكون المماث + +683 +01:17:58,420 --> 01:18:01,420 +يكون نقطة من خلالها، يكون مماث واحد، يعني مايكونش + +684 +01:18:01,420 --> 01:18:03,500 +يكون مماث عشان يبقى يجي من خلالها من خلالها، + +685 +01:18:03,500 --> 01:18:08,440 +بالاختران التابع، يعني إذا بنعمل مماث النقطة، + +686 +01:18:08,440 --> 01:18:13,240 +هيقاطع كل النقاط؟ لأ، بصير نفس المماث عند جميع + +687 +01:18:13,240 --> 01:18:21,020 +النقاطوهيحول لنفس الميل مثلا خط أفقي أو خط مائل + +688 +01:18:21,020 --> 01:18:27,730 +سياد، و أين ما يكون الخط بدي سياد نفس الميلكله من + +689 +01:18:27,730 --> 01:18:32,910 +أوله إلى آخره، هذا خط مستقيل نرجع لأسئلتنا مرة + +690 +01:18:32,910 --> 01:18:37,250 +أخرى، يفترض أن قيمة الدالة عند السلب واحد هي + +691 +01:18:37,250 --> 01:18:43,610 +تلاتة، والـF prime of X بدأ يساوي Zero لكل X بلا + +692 +01:18:43,610 --> 01:18:48,380 +استثناءفي الدموعين طبعا تبع الدالة بسهل بقولك must + +693 +01:18:48,380 --> 01:18:54,620 +f of x يسوى تلاتة هل يجب ان ال f of x يسوى تلاتة + +694 +01:18:54,620 --> 01:18:59,520 +for all x يعني يعني هل يتدالى دالة ثابتة وتسوى + +695 +01:18:59,520 --> 01:19:04,680 +تلاتة لجميع قيم x بلا ستناء اعطيني سبب ان كان نعم + +696 +01:19:04,680 --> 01:19:09,820 +لماذا وان كان لأ لماذا نقوله بسيطة جدا احنا عندنا + +697 +01:19:09,820 --> 01:19:16,590 +الان ال f prime of x يسوى zeroصحيح ولا لا؟ + +698 +01:19:16,590 --> 01:19:22,410 +بالكرولري الأولى يبقى F of X ساوي مقدار ثابت يبقى + +699 +01:19:22,410 --> 01:19:34,330 +باجي بقوله هذا بده يعطيلك by the above krolary + +700 +01:19:34,330 --> 01:19:39,530 +when + +701 +01:19:39,530 --> 01:19:51,670 +we haveإن ال F of X بده يساوي مقدارا ثابتا for all + +702 +01:19:51,670 --> 01:20:01,910 +X بلا استثناء where C is constant مين + +703 +01:20:01,910 --> 01:20:04,930 +اللي بيقولي في الامتحان؟ أنت؟ قول تاني + +704 +01:20:09,690 --> 01:20:13,950 +يعني انا لو جالك سؤال زي هيك، مش لازم اقولك اثبت + +705 +01:20:13,950 --> 01:20:17,430 +ال crawler في الأول و بعدين السؤال عليها، هيك اللي + +706 +01:20:17,430 --> 01:20:24,550 +بصير، ولا مانعك بالعرفش نحط امتحانات؟ بسيط، + +707 +01:20:24,550 --> 01:20:29,550 +شوف يا سيدي في وضع الامتحانات، لما يجيبك سؤال و + +708 +01:20:29,550 --> 01:20:33,390 +بدي انحل على شغلة معينة، بقولك اثبتها و بعدين + +709 +01:20:33,390 --> 01:20:38,710 +بعطيك السؤالعليها ومن الخطأ جدا ان نجيب سؤال + +710 +01:20:38,710 --> 01:20:43,110 +بمطلوب ان المطلوب الثاني يعتمد على المطلوب الأول + +711 +01:20:43,110 --> 01:20:46,050 +طب انا ماقدرسش أحل المطلوب الأول بقدر أحل المطلوب + +712 +01:20:46,050 --> 01:20:50,450 +التاني؟ لأ وبالتالي هذا من الخطأ في او في + +713 +01:20:50,450 --> 01:20:54,630 +استراتيجية الخطأ تبع مين تبع الامتحانات اللي ممكن + +714 +01:20:54,630 --> 01:21:00,830 +يقع فيها بعض الناس على أي حال ولا يهمك بنحط + +715 +01:21:00,830 --> 01:21:06,390 +امتحانات قبل أن تليدك أمكوبالتالي مش جديد علينا + +716 +01:21:06,390 --> 01:21:13,950 +هذا طيب نرجع مرة تانية احنا عندنا f prime of x بده + +717 +01:21:13,950 --> 01:21:18,850 +يساوي قداش بده يساوي zero بالكرولري اول وحدة يبقى + +718 +01:21:18,850 --> 01:21:23,250 +ده ال f of x يساوي مقدارا ثابتا لجميع قيم x + +719 +01:21:23,250 --> 01:21:27,340 +بالاستثناءفبرا اندي معلومة، شو المعلومة بتقول؟ + +720 +01:21:27,340 --> 01:21:33,120 +بتقول لي F of سالب واحد بده يساوي تلاتة يبقى الأن + +721 +01:21:33,120 --> 01:21:40,260 +since بما أن F of سالب واحد يساوي تلاتة وأنا جايل + +722 +01:21:40,260 --> 01:21:46,780 +هنا ياشيالـ F of X يسوي مقدار ثابت لكل ال X's بلا + +723 +01:21:46,780 --> 01:21:52,580 +استئناف تمام يبقى من الاتنين هدول مع بعض بقدر + +724 +01:21:52,580 --> 01:22:00,080 +استنتج ان ال F of X بده تسوي تلاتة for all X بلا + +725 +01:22:00,080 --> 01:22:05,680 +استئناف خلصنا؟ يبقى must ولا ما must ايش؟ must + +726 +01:22:09,570 --> 01:22:16,970 +خُد لك كمان مثال يبقى + +727 +01:22:16,970 --> 01:22:27,090 +example two find + +728 +01:22:27,090 --> 01:22:31,370 +the + +729 +01:22:31,370 --> 01:22:36,270 +function f of x + +730 +01:22:40,440 --> 01:22:55,240 +الـ F' of X يسوى تمانية ناقص كوسيكا تربيع X and + +731 +01:22:55,240 --> 01:23:01,740 +the graph and + +732 +01:23:01,740 --> 01:23:09,020 +the graph of دلة F passing + +733 +01:23:15,560 --> 01:23:23,260 +passing through the point يمر + +734 +01:23:23,260 --> 01:23:30,080 +خلال النقطة الى اربعة + +735 +01:23:30,080 --> 01:23:31,720 +وزرع + +736 +01:23:42,980 --> 01:23:47,560 +سؤال مرة تانية بيقولي هاتلي الدالة f of x + +737 +01:23:47,560 --> 01:23:52,240 +المشتقتها بتساوي القيمة اللي عندها دي، يبقى دي + +738 +01:23:52,240 --> 01:23:54,740 +ليست على الكورولة الأولى، الكورولة الأولى بتقول + +739 +01:23:54,740 --> 01:23:59,160 +المشتقة بتساوي جديش، zero هذي قالها لأ بتساوي دالة + +740 +01:23:59,160 --> 01:24:05,410 +تانية، طيب نشوفوالرسم الباني لهذه الدالة اللى احنا + +741 +01:24:05,410 --> 01:24:11,190 +بدنا يمر بالنقطة باية على اربعة وزيره بقولكوا ياسي + +742 +01:24:11,190 --> 01:24:16,150 +يبقى الكرولري الاولى لايمكن ان تحل هذه المثلة يبقى + +743 +01:24:16,150 --> 01:24:20,910 +اللى ممكن يحل المثلة هدميا الكرولري التانية يبقى + +744 +01:24:20,910 --> 01:24:30,510 +انا بدي افترضإن عندي دالة g of x مشتقتها تساوي من؟ + +745 +01:24:30,510 --> 01:24:36,990 +تساوي ال F prime حتى أقدر أطبق من؟ اللي هو التاني + +746 +01:24:36,990 --> 01:24:43,110 +هذي يبقى التماني هذي مشتقت من؟ تمانية X إذا I + +747 +01:24:43,110 --> 01:24:51,680 +تمانية Xوالدالة التانية هذه مشتقت من؟ كتان يبقى + +748 +01:24:51,680 --> 01:24:59,580 +زائد كتان ال X بدي افترض ان عندي دالة مشتقتها + +749 +01:24:59,580 --> 01:25:05,780 +تساوي المشتقة اللي عندها هذا بدي اعطيلهان ال g + +750 +01:25:05,780 --> 01:25:15,060 +prime of x يساوي تمانية ناقص كوسيكا تربيع ال x هذا + +751 +01:25:15,060 --> 01:25:22,980 +بد يعطيك ان ال f prime of x تساوي ال g prime of x + +752 +01:25:22,980 --> 01:25:29,980 +وتساوي تمانية ناقص + +753 +01:25:29,980 --> 01:25:32,480 +كوسيكا تربيع ال x + +754 +01:25:39,670 --> 01:25:46,270 +بتقول لو كان ال F' بده يساوي G' يبقى الفرق في ما + +755 +01:25:46,270 --> 01:25:54,000 +بينهما يساويمقدارا ثابتا، مظبوط؟ يبقى هذا معناه، + +756 +01:25:54,000 --> 01:26:00,960 +معناه ايش؟ لما يكون F' يسوى G' حسب نص انه يبقى + +757 +01:26:00,960 --> 01:26:05,820 +الفرق ما بين الدالتين بديه يسوى مقدارا ثابتا، + +758 +01:26:05,820 --> 01:26:11,440 +ممتاز جدا، يبقى معنى هذا الكلام ان ال F of X ناقص + +759 +01:26:11,440 --> 01:26:17,590 +ال G of Xبدي يساوي كده؟ بدي يساوي مقدارا ثابتا + +760 +01:26:17,590 --> 01:26:25,310 +اللي هو C معناه هذا الكلام ان ال F of X بدي يساوي + +761 +01:26:25,310 --> 01:26:31,230 +ال G of X زائد constant C معناه هذا الكلام ان ال F + +762 +01:26:31,230 --> 01:26:36,710 +of X بدي يساوي ال G of X اللي هي تمانية X زائد + +763 +01:26:36,710 --> 01:26:45,040 +كتانالـ X صحيح ولا لأ؟ زائد كونستانت C يبقى أنا + +764 +01:26:45,040 --> 01:26:50,980 +جبتله شكل ال F of X لكن بدلالة من؟ المتغير C قال + +765 +01:26:50,980 --> 01:26:56,680 +لي إن الدلة المنحنة تبعها يمر بالنقطة بي على أربعة + +766 +01:26:56,680 --> 01:27:02,260 +و زيرو إذا بداجي أعوض في الدلة هذه يبقى هنا باجي + +767 +01:27:02,260 --> 01:27:12,730 +بقوله at اللي هو by أربعة و زيرو we haveالـ F باي + +768 +01:27:12,730 --> 01:27:17,810 +عالى أربعة بده تسوى Zero يبقى Zero بده تسوى تمانية + +769 +01:27:17,810 --> 01:27:24,850 +في باي عالى أربعة زائد كتان باي عالى أربعة زائد + +770 +01:27:24,850 --> 01:27:26,030 +كنص تان C + +771 +01:27:28,800 --> 01:27:35,900 +هذا يصبح اتنين باى وهذا كتان باى على اربع اللي هو + +772 +01:27:35,900 --> 01:27:42,600 +واحد صحيح زائد كونستان سي يساوي كده؟ Zero يبقى + +773 +01:27:42,600 --> 01:27:48,560 +بناء عليه أصبح الكونستان سي يساوي سالب اتنين باى + +774 +01:27:48,560 --> 01:27:49,700 +سالب كده؟ + +775 +01:28:07,620 --> 01:28:13,240 +باقية نقطة أخيرة شباب النقطة الأخيرة حاططها في ال + +776 +01:28:13,240 --> 01:28:17,860 +exercises وليس في الجزء النظري + +777 +01:28:21,430 --> 01:28:28,690 +النقطة هذه حساب الأصفر لدلة ما counting zeros + +778 +01:28:28,690 --> 01:28:35,390 +تمام؟ يبقى هاطلق في صيغة ال remark التالية remark + +779 +01:28:35,390 --> 01:28:40,110 +التي + +780 +01:28:40,110 --> 01:28:45,610 +counting zeros + +781 +01:28:45,610 --> 01:28:56,300 +حساب أصفر دلة بيقول افترضإن ال F ب إيه + +782 +01:28:56,300 --> 01:29:09,100 +continuous ب إيه continuous a function on the + +783 +01:29:09,100 --> 01:29:16,820 +closed interval a و b and differentiable على + +784 +01:29:16,820 --> 01:29:26,760 +الفترة المفتوحة a و bالنقطة الأولى if ال F of A + +785 +01:29:26,760 --> 01:29:40,280 +and ال F of B have opposite signs + +786 +01:29:40,280 --> 01:29:48,360 +إشاراتهم مختلفة and نمر + +787 +01:29:48,360 --> 01:29:59,340 +اتنينالـ F' أكبر من الـ 0 على الفترة المفتوحة A و + +788 +01:29:59,340 --> 01:30:09,300 +B أو الـ F' أقل من الـ 0 على الفترة المفتوحة A و B + +789 +01:30:09,300 --> 01:30:13,760 +فالـ F + +790 +01:30:13,760 --> 01:30:17,900 +لديه بالضبط + +791 +01:30:19,690 --> 01:30:41,630 +بالضبط one zero between a and b example show + +792 +01:30:41,630 --> 01:30:42,630 +that the function + +793 +01:30:50,490 --> 01:30:58,650 +F of X واحد على واحد ناقص X زيدي الجدري التربيعي + +794 +01:30:58,650 --> 01:31:08,490 +لواحد زائد X ناقص تلاتة واحد من عشرة have + +795 +01:31:08,490 --> 01:31:19,190 +one zero على الفترة المفتوحة سالب واحد وواحد + +796 +01:31:48,070 --> 01:31:53,030 +counting zeros يعني حساب أصفار الدالة يعني السؤال + +797 +01:31:53,030 --> 01:31:58,970 +هو اجتاش بوبمان أن الدالة تساوي zero عند نقطة ما + +798 +01:32:00,000 --> 01:32:03,400 +بقول ايش؟ لو كانت الدلة دالة متصلة على الفترة + +799 +01:32:03,400 --> 01:32:09,860 +المغلقة A وB يبقى احنا افترض عندنا function وقولنا + +800 +01:32:09,860 --> 01:32:15,540 +هذا محور X وهذا Y وهذا ال function اللي عندنا وروح + +801 +01:32:15,540 --> 01:32:22,540 +نقولنا على الفترة اللي عندنا Fوهنا من ال B افترض + +802 +01:32:22,540 --> 01:32:29,380 +الدالة دالة كانت متصلة على الفترة A وB وقبل اشتقاق + +803 +01:32:29,380 --> 01:32:35,240 +على الفترة المفتوحة A وB لو كان ال F of A و F of B + +804 +01:32:35,240 --> 01:32:40,920 +of opposite signs يعني إشارتهم مختلفتين يعني واحدة + +805 +01:32:40,920 --> 01:32:47,330 +موجبة والتانيةيبقى رسمي هذا صحيح هيك؟ لأ مش صحيح F + +806 +01:32:47,330 --> 01:32:52,870 +of A هي موجبة و F of B موجبة وقال لأ التنتين of + +807 +01:32:52,870 --> 01:32:58,290 +opposite signs يبقى معنى هذا الكلام بده تكون واحدة + +808 +01:32:58,290 --> 01:33:06,710 +تحت محور X والتانيةأعلى محور X يبقى لو قلنا هذا X + +809 +01:33:06,710 --> 01:33:11,330 +وهذا Y بديجيك المنحنة مثلا بالشكل اللي عندك هنا + +810 +01:33:11,330 --> 01:33:18,770 +خلّي هذه مثلا اللي هو النقطة A وهذه اللي عندك + +811 +01:33:18,770 --> 01:33:26,110 +التانية اللي هي النقطة Bيبقى هذه F of A مالها أقل + +812 +01:33:26,110 --> 01:33:32,890 +من الـ Zero وهنا هذه F of B أكبر من الـ Zero أو + +813 +01:33:32,890 --> 01:33:39,630 +العكس ممكن F of A فوق و F of B تحت سيال ايوة ايش + +814 +01:33:39,630 --> 01:33:44,130 +بيقولي الدالة دالة متاصلة ماشي هي دالة متاصلة + +815 +01:33:44,130 --> 01:33:48,150 +اتنين قابل اشتراك قابل اشتراك ماعنديش لا تصب ولا + +816 +01:33:48,150 --> 01:33:51,910 +كورن ولا vertical tangent ولا discontinuityطيب، + +817 +01:33:51,910 --> 01:33:56,650 +اتنين، الـF of A والـF of B have opposite signs، + +818 +01:33:56,650 --> 01:34:00,190 +إشارتهم مختلفة، يعني واحدة موجبة والتانية، لحظة + +819 +01:34:00,190 --> 01:34:04,730 +الـF of B هي موجبة والـF of A سالبة، اتنين، كان + +820 +01:34:04,730 --> 01:34:10,650 +مشتقت الدالة على الفترة A وB يا إما موجبة دائما + +821 +01:34:10,650 --> 01:34:15,330 +وأبدا، يا إما سالبة دائما، الدالة هذه دالة + +822 +01:34:15,330 --> 01:34:20,650 +تزايدية، صحيح ولا لأ؟ إذا مشتقتها دائما وأبدا، + +823 +01:34:20,650 --> 01:34:25,870 +موجبةلو كانت ذالة تناقصية، بقى مستقلتها سالمة، مش + +824 +01:34:25,870 --> 01:34:31,550 +التان تان في انا الواحد or تعني ان هذه اولت، ان + +825 +01:34:31,550 --> 01:34:39,020 +حدث ذلكيبقى إذا القيمتين هدول متساوية، مختلفتين في + +826 +01:34:39,020 --> 01:34:44,900 +الإشارة، و الدالة دالة زيودية أو دالة نقصية، إذا + +827 +01:34:44,900 --> 01:34:50,920 +غصب عن اللي مايرضى بده تقطع مين؟ محور X، يبقى لما + +828 +01:34:50,920 --> 01:34:54,580 +تقطع محور X عند هذا النقطة، تبقى قيمة الدالة عند + +829 +01:34:54,580 --> 01:35:00,040 +هذا النقطة تساوي كده؟ تساوي Zero، تمام؟يبقى هي + +830 +01:35:00,040 --> 01:35:04,420 +معناها هيك فبيقول ليش ان حدث ذلك يبقى ال F is + +831 +01:35:04,420 --> 01:35:09,300 +exactly one zero between ال A و ال B ال zero هذا + +832 +01:35:09,300 --> 01:35:13,520 +بدرجيني مابين مين؟ مابين ال A و ال B + +833 +01:35:21,960 --> 01:35:31,620 +أخدت ايه؟ Intermediate Value Theorem اه ماقلناش + +834 +01:35:31,620 --> 01:35:36,020 +والله عكس الإشارة ولا جيبنا سيرة تهالي والله يا + +835 +01:35:36,020 --> 01:35:38,480 +حبيبي ال Intermediate Value Theorem قلت لو خدنا + +836 +01:35:38,480 --> 01:35:44,280 +رقم موجود بين ال A وال Bبين ال F of A و ال F of B + +837 +01:35:44,280 --> 01:35:46,960 +بلا جيل و أصل ما بين ال A و ال B هذا ال + +838 +01:35:46,960 --> 01:35:51,240 +intermediate value theorem و ليست هذه مظبوط هذه + +839 +01:35:51,240 --> 01:35:54,620 +بتختلف كليا عن ال intermediate value theorem هذه + +840 +01:35:54,620 --> 01:35:58,820 +بتقول دلدلة متصلة و قابلة الاشتقاء متصلة على + +841 +01:35:58,820 --> 01:36:01,880 +closed interval و قابل اشتقاق على الفترة + +842 +01:36:05,600 --> 01:36:09,080 +يوجد كمان زيادة على ذلك two conditions ال + +843 +01:36:09,080 --> 01:36:12,880 +condition الأولى أن ال F وB وF وB إشارتهم مختلفة + +844 +01:36:12,880 --> 01:36:16,020 +واحدة موجبة واحدة سلبية يعني واحدة فوق محور X + +845 +01:36:16,020 --> 01:36:19,560 +وواحدة تحت محور X كلها متاصلة إذن automatically + +846 +01:36:19,560 --> 01:36:24,320 +هتقطع محور X مصبوط؟ مدام هتقطع هتقطع في نخ موجودة + +847 +01:36:24,320 --> 01:36:28,100 +بين ال A و ال B بمجرد تقطع محور X تقبل قيمة الدالة + +848 +01:36:28,100 --> 01:36:33,200 +عندها تساوي Zero فجالي فإن ال F is exactly one + +849 +01:36:33,200 --> 01:36:37,910 +zero ما بين ال A و ال Bنثبت هذا الكلام عمليا نقول + +850 +01:36:37,910 --> 01:36:41,970 +لو كان موجة نقطة البداية هي نفسها نقطة الموجة + +851 +01:36:41,970 --> 01:36:43,050 +نفسها نقطة الموجة نفسها نقطة الموجة نفسها نقطة + +852 +01:36:43,050 --> 01:36:45,790 +الموجة نفسها نقطة الموجة نفسها نقطة الموجة نفسها + +853 +01:36:45,790 --> 01:36:48,990 +نقطة الموجة نفسها نقطة الموجة نفسها نقطة الموجة + +854 +01:36:48,990 --> 01:36:52,690 +نفسها نقطة الموجة نفسها نقطة الموجة نفسها نقطة + +855 +01:36:58,710 --> 01:37:03,130 +بهمنيش، بهمني إنها بدأت تحت و بدأت فوق، بس إنت لما + +856 +01:37:03,130 --> 01:37:07,610 +بده رد عليك عليها شكل موجة، يبقى انت فهذا الشرط + +857 +01:37:07,610 --> 01:37:12,170 +تمام؟ بطلة تزيديها على قول أو تنقصيها على قول، + +858 +01:37:12,170 --> 01:37:16,110 +يبقى أنت صارتش تشتغل ضد الطيار، ماشي؟ احنا بيقول + +859 +01:37:16,110 --> 01:37:20,330 +بتحقق ال conditions في ان و احدلو كان هذا الكلام + +860 +01:37:20,330 --> 01:37:23,630 +صحيح وشيلنا الشرط هذا، بصير مش نقطة، بصير ما شاء + +861 +01:37:23,630 --> 01:37:27,530 +الله عليها نقطة، يعني zeros كتير، مش واحدة، تمام؟ + +862 +01:37:27,530 --> 01:37:31,750 +احنا بيقول، there exists exactly one، بالضبط واحدة + +863 +01:37:31,750 --> 01:37:36,770 +مافيش غيرها، قيمة الدالة عندها تساوي صفر، تمام؟ + +864 +01:37:36,770 --> 01:37:40,010 +طيب، بيقول الشهداء، the function هذي have one zero + +865 +01:37:40,010 --> 01:37:45,560 +في الفترة من سالب واحد إلى واحد،فبجي بقول ال F of + +866 +01:37:45,560 --> 01:37:52,700 +X هذه اللي تساوي واحد على واحد ناقص X زائد الجدرى + +867 +01:37:52,700 --> 01:37:57,280 +التربية على واحد زائد X ثلاثة وواحد من عشرة هذه + +868 +01:37:57,280 --> 01:37:58,920 +الدمين تبعها من وين لوين + +869 +01:38:05,280 --> 01:38:13,660 +يبقى هذه الدالة معرفة + +870 +01:38:13,660 --> 01:38:28,340 +من سالب واحد لواحد كفترة + +871 +01:38:28,340 --> 01:38:34,570 +مفتوحة وليست مغلقةلأن عند الواحد هذه undefined طب + +872 +01:38:34,570 --> 01:38:38,150 +احنا ال main value theorem اول نص اللي بيقولك + +873 +01:38:38,150 --> 01:38:43,010 +closed interval مدام continuous على الفترة دي اذا + +874 +01:38:43,010 --> 01:38:46,770 +انا بدي اخد جزء من هذه الفترة اضمن ال continuity + +875 +01:38:46,770 --> 01:38:53,850 +عليها يبقى بجي بقول الساعة ال F is continuous + +876 +01:38:55,450 --> 01:39:02,530 +أن الفترة المغلقة سالب زيرو تسعة من عشرة لغاية + +877 +01:39:02,530 --> 01:39:07,350 +زيرو تسعة من عشرة مضمون هيك ولا لا؟ اندس سالب واحد + +878 +01:39:07,350 --> 01:39:15,190 +كده؟ اندس سالب واحد؟ احنا بنقولك ها دي ماشي، اندس + +879 +01:39:15,190 --> 01:39:19,490 +سالب واحد مغلق، هاه؟ ولا همك، continuous من اندس + +880 +01:39:19,490 --> 01:39:24,100 +سالب واحد، كلامك مظبوطتمام؟ لكن هاي السبعة تلاقي + +881 +01:39:24,100 --> 01:39:27,580 +السالب واحد والواحد كمان، مش هان تبقى مبسوط خالص، + +882 +01:39:27,580 --> 01:39:32,720 +يبقى من ناقص 9 على 9 اللي هو كفترة مغلقة دالة + +883 +01:39:32,720 --> 01:39:35,600 +continuous عليها، بدي أشوف هال difference أقول + +884 +01:39:35,600 --> 01:39:39,940 +عليها ولا لأ، معناته بدي أروح أشتق، إذا بدي أخد ال + +885 +01:39:39,940 --> 01:39:47,680 +F prime of X يساوي السالب واحد على واحد ناقص X لكل + +886 +01:39:47,680 --> 01:39:52,830 +تقريبيا في مشتقةاللي هو المقدار اللي هو سالب واحد + +887 +01:39:52,830 --> 01:39:56,890 +يبقى بيصير موجب يبقى واحد على واحد نقص اكسل كل + +888 +01:39:56,890 --> 01:40:02,030 +تربية زائد واحد على اتنين الجذر التربية على واحد + +889 +01:40:02,030 --> 01:40:06,590 +زائد اكسل وده كونه مقدار تمت طيب برضه إيش رأيك على + +890 +01:40:06,590 --> 01:40:10,710 +الفترة هذه قابلة للاشتقاق على الفترة المفتوحة ولا + +891 +01:40:10,710 --> 01:40:13,150 +لا؟ يبقى هادى + +892 +01:40:20,140 --> 01:40:25,440 +الفترة المفتوحة سالب واحد و واحد يبقى ال F is + +893 +01:40:25,440 --> 01:40:34,400 +differentiable on سالب زير و تسعة من عشرة و زير و + +894 +01:40:34,400 --> 01:40:39,540 +تسعة من عشرة مش هدول الشرطين تبعات ال mean value + +895 +01:40:39,540 --> 01:40:45,960 +theoremيبقى هما الشرطين اللي انا جايلهم هنا بدي + +896 +01:40:45,960 --> 01:40:51,820 +اجيب له ال F of A و ال F of B يبقى بدي اجيب له ال + +897 +01:40:51,820 --> 01:41:01,700 +F of سالب Zero تسعة من عشرة يعني ال F of سالب تسعة + +898 +01:41:01,700 --> 01:41:06,590 +على عشرةيبقى هذا الكلام دي ثابت داجي على الدالة + +899 +01:41:06,590 --> 01:41:15,190 +الأصلية و اقول واحد على واحد ناقص ناقص تسعة على + +900 +01:41:15,190 --> 01:41:24,590 +عشرة زائد الجذري التربيهي لواحد ناقص تسعة على عشرة + +901 +01:41:25,090 --> 01:41:29,030 +طبعا هي زيد بس احنا مااخدينها بالناقص يبقى ناقص + +902 +01:41:29,030 --> 01:41:35,810 +بعدها ناقص تلاتة واحد من عشرة يبقى هذا الكلام + +903 +01:41:35,810 --> 01:41:44,680 +يساوي هذا بيصير واحد على واحد زائد تسعة على عشرةزي + +904 +01:41:44,680 --> 01:41:50,240 +دي الجذري التربيعي كله على عشرة بيظل عشرة ناقص + +905 +01:41:50,240 --> 01:41:56,320 +تسعة اللي هو بقداش بواحد ناقص تلاتة واحد من عشرة + +906 +01:41:56,320 --> 01:42:03,940 +هذه يا شباب بيصير عشرة على تسعة عشر يبقى هذه عشرة + +907 +01:42:03,940 --> 01:42:12,360 +عشرة عشرةهذه عشرة وعشرة تسعة تطلع على عشرة فوق + +908 +01:42:12,360 --> 01:42:20,980 +وهنا على عشرة تسعة عشر عشرة تسعة عشر زائد اللي هو + +909 +01:42:20,980 --> 01:42:26,980 +عشر تحت الجدر الترميعي ناقص ثلاثة وواحد من عشرة شو + +910 +01:42:26,980 --> 01:42:31,500 +رأيك؟ هذا و هذا ميجيوش واحد صحيح وهذا سالب يبقى + +911 +01:42:31,500 --> 01:42:36,140 +هذه قيمة أقل من ال zero صحيح ولا لا؟ + +912 +01:42:38,820 --> 01:42:46,080 +ماشي يبقى بدنا نيجي ناخد F of 0 9 من 10 بنفس + +913 +01:42:46,080 --> 01:42:56,160 +الطريقةيبقى هذا بدأ يصير F of 9 على 10 ويسوى 1 على + +914 +01:42:56,160 --> 01:43:06,180 +1 ناقص 9 على 10 زائد الجدر التربية ل 1 زائد 9 على + +915 +01:43:06,180 --> 01:43:14,880 +10 ناقص 3 1 من 10 النتيجة تساوي هذا يبقى هنا عشرة + +916 +01:43:14,880 --> 01:43:22,210 +بنقلب فوق بصير عشرةزاد الجذري التربيعي لمين؟ لتسعة + +917 +01:43:22,210 --> 01:43:26,950 +عشرة على عشرة ناقص ثلاثة واحد من عشرة، موجي ابو + +918 +01:43:26,950 --> 01:43:31,520 +الله سالي بقىيبقى أكبر من الـ zero تحقق ال + +919 +01:43:31,520 --> 01:43:36,100 +condition الأول بدنا نيجي ال condition التاني بدى + +920 +01:43:36,100 --> 01:43:42,080 +أشتقها هيشتقناها ال F prime of X يبقى ال F prime + +921 +01:43:42,080 --> 01:43:50,320 +of X بده يسوى واحد على واحد ناقص X الكل تربية زائد + +922 +01:43:50,320 --> 01:43:57,930 +واحد على اتنين الجذر التربية لواحد زائد Xأيش رأيك؟ + +923 +01:43:57,930 --> 01:44:03,270 +هذه عمرها بتاخد قيمة سالبة؟ يبقى هذه أكبر من الـ0 + +924 +01:44:03,270 --> 01:44:11,030 +لكل الـX اللي موجودة سالب 09 و 09 بالشكل اللي + +925 +01:44:11,030 --> 01:44:16,430 +عندنا هنا يبقى اتحقق من ال condition الثاني بدي + +926 +01:44:16,430 --> 01:44:23,710 +بقوله by the above remark + +927 +01:44:25,800 --> 01:44:33,580 +There exists C موجودة في الفترة من سالب واحد إلى + +928 +01:44:33,580 --> 01:44:41,940 +واحد أو انشطة فاقل في الفترة تبعتنا او سالب واحد + +929 +01:44:41,940 --> 01:44:42,640 +وواحد + +930 +01:44:47,560 --> 01:44:57,860 +بحيث أن ال F of C بده ساوي Zero يبقى فى ال F has + +931 +01:44:57,860 --> 01:45:06,360 +one zero on الفترة من سالب واحد إلى واحد وهو + +932 +01:45:06,360 --> 01:45:07,520 +المطلوب + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Ly_WmKy_z00_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Ly_WmKy_z00_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..1d3f2018838ac56ddda16d1ddbbce0e87706afc8 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Ly_WmKy_z00_raw.srt @@ -0,0 +1,3740 @@ +1 +00:00:21,240 --> 00:00:25,220 +بسم الله الرحمن الرحيم انتهينا من المرة الماضية + +2 +00:00:25,220 --> 00:00:32,360 +اللي كان بتحدث عن ال extreme values سواء كانت + +3 +00:00:32,360 --> 00:00:36,300 +local maximum و local minimum أو absolute maximum + +4 +00:00:36,300 --> 00:00:41,100 +و absolute minimumبننتقل الى ال section اللي يليه + +5 +00:00:41,100 --> 00:00:46,400 +هو section 4-2 بتحدث عن the main value theorem + +6 +00:00:46,400 --> 00:00:52,540 +نظرية القيمة المتوسطة قبل ما نبدأ بنظرية القيمة + +7 +00:00:52,540 --> 00:00:58,030 +المتوسطة بدأ ناخد نظرية أخرى وهي نظرية roleيبقى + +8 +00:00:58,030 --> 00:01:04,450 +بين أيدنا الان rules theorem تنص على ما يقتين + +9 +00:01:04,450 --> 00:01:09,230 +بيقول افترض ان y تساوي f of x ده المتصلة على + +10 +00:01:09,230 --> 00:01:14,370 +الفترة المغلقة a وb وفي نفس الوقت هذه ال function + +11 +00:01:14,370 --> 00:01:20,370 +قابلة للاشتقاء على الفترة المفتوحة a وb يبقى هاي + +12 +00:01:20,370 --> 00:01:27,700 +شرطينشرب التالت لو كان f of a يساوي f of b فهناك + +13 +00:01:27,700 --> 00:01:32,640 +أقل نمبر c في الأفترى a وb بحيث أن f prime of c + +14 +00:01:32,640 --> 00:01:38,160 +يساوي 0 يبقى هذه النظرية بتقولي أنا في عندي + +15 +00:01:38,160 --> 00:01:42,420 +function تساوي y تساوي f of x إذا هذه ال function + +16 +00:01:42,420 --> 00:01:49,290 +حققتلي ثلاثة شروط وهمالشرط الأول، الدلق متصل على + +17 +00:01:49,290 --> 00:01:54,250 +الفترة المغلقة A وB. إثنان، قابل الاشتقاق على + +18 +00:01:54,250 --> 00:02:01,290 +الفترة المفتوحة A وB. تلاتة، قيمة F of A بدأت ساوي + +19 +00:02:01,290 --> 00:02:10,120 +F of B. إن حدث ذلكيبقى لازم أكدر ألاقي نقطة C أو + +20 +00:02:10,120 --> 00:02:15,680 +عدد C في الفترة A وB على الأقل نقطة اللي لم يكن + +21 +00:02:15,680 --> 00:02:19,860 +أكتر يعني ممكن عدد ممكن اتنين ممكن تلاتة ممكن + +22 +00:02:19,860 --> 00:02:24,580 +أربعة الاخرين يعني على الأقل لازم ألاقي نقطة واحدة + +23 +00:02:24,580 --> 00:02:29,880 +في الفترة A وB at which بحيث أن ال F prime of C + +24 +00:02:29,880 --> 00:02:35,510 +بده يساوي قداش بده يساوي Zero تمام تماميبقى هذه + +25 +00:02:35,510 --> 00:02:40,670 +الشروط التلاتة عندنا اللي همين نظرية رول وهي تمهيد + +26 +00:02:40,670 --> 00:02:46,370 +لنظرية القيمة المتاسبة تعالى نفهم هذا النص على + +27 +00:02:46,370 --> 00:02:51,150 +الطبيعة، الآن نجد طالع على الرسمة الأولى اللي + +28 +00:02:51,150 --> 00:02:56,000 +عندناهذا المنحنى اللي انت شايفينه هو منحنى Della Y + +29 +00:02:56,000 --> 00:03:01,280 +تساوي F of X أو المنحنى اللي عنده هو منحنى Della Y + +30 +00:03:01,280 --> 00:03:06,240 +تساوي F of X تعالى نشوف هل الشروط الثلاثة متحقق + +31 +00:03:06,240 --> 00:03:11,020 +على كل من الرسم الأولى والثانيةأم لا؟ زي ما انت + +32 +00:03:11,020 --> 00:03:17,000 +شايف الخط متواصل بلا استثناء على الفترة المغلقة A + +33 +00:03:17,000 --> 00:03:21,560 +وB الدالة معرفة، تمام؟ إذن الدالة continuous على + +34 +00:03:21,560 --> 00:03:26,460 +الفترة A وB باجي على الفترة المفتوحة A وB هل + +35 +00:03:26,460 --> 00:03:30,440 +الدالة قابلة لاشتقاق أم لا؟ طبعا قابلة لاشتقاق + +36 +00:03:30,440 --> 00:03:34,080 +لأنه لا يوجد لا كسب ولا corner ولا vertical + +37 +00:03:34,080 --> 00:03:39,450 +tangent ولا discontinuityالاربعة تبعة عدم الاتصال، + +38 +00:03:39,450 --> 00:03:44,770 +عدم ال differentiation لتبالى، واضح؟ إذا أهدي زيها + +39 +00:03:44,770 --> 00:03:50,150 +طالع على المنحنى، مافيش عندي ولا عند أي نقطة في + +40 +00:03:50,150 --> 00:03:55,470 +vertical tangent ولا كسب ولا corner ولا vertical + +41 +00:03:55,470 --> 00:03:58,810 +tangent أو discontinuity مافيش عندي ولا حالة من + +42 +00:03:58,810 --> 00:04:02,150 +الحالات الأربعة، إذا اتدى لقاء بالاشتقاء في الرسم + +43 +00:04:02,150 --> 00:04:07,610 +الأولى وفي الرسم الثانيبالـ F of A يسوى F of B، هي + +44 +00:04:07,610 --> 00:04:12,570 +قيمة الدالة عند A، و هي قيمة الدالة عند B جايت وين + +45 +00:04:12,570 --> 00:04:17,830 +على نفس الخط. قيمة الدالة عند A تسوى قيمة الدالة + +46 +00:04:17,830 --> 00:04:23,390 +عند B نفس الخط الأفقي الموازي لمحور X. يبقى الآن + +47 +00:04:23,390 --> 00:04:28,750 +تحققت الشروط التلاتة. بيقول، there exists أو there + +48 +00:04:28,750 --> 00:04:33,470 +is at least على الأقل فيها نقطة واحدة.لكن ممكن + +49 +00:04:33,470 --> 00:04:37,310 +ألاقياش أكتر من نقطة، النقطة هذه ما لها؟ قيمة + +50 +00:04:37,310 --> 00:04:42,550 +المشتقة عندها يساوي مين؟ يساوي زيري، يعني المماس + +51 +00:04:42,550 --> 00:04:44,970 +عند هذه النقطة بيكون ما له؟ + +52 +00:04:49,200 --> 00:04:54,900 +الخط اللي يواصل بين F of A وF of B يواظه خط أفقي + +53 +00:05:07,880 --> 00:05:13,680 +الان يجب ان يكون F prime of C1 يسوى 0 يعني المماس + +54 +00:05:13,680 --> 00:05:19,280 +أفقي F prime of C2 يسوى 0 معناته المماس أفقي F + +55 +00:05:19,280 --> 00:05:24,170 +prime of C3 يسوى 0 معناته المماس أفقيوالخط اللى + +56 +00:05:24,170 --> 00:05:28,710 +وصل بين F of A و F of B برضه زى ما انت شايف موازن + +57 +00:05:28,710 --> 00:05:33,590 +للممثات التلاتة اللى عندنا يبقى بناء علي من الآن + +58 +00:05:33,590 --> 00:05:39,610 +فصاعدا إذا تحققت الشروط التلاتة إجبارى على الأقل + +59 +00:05:39,610 --> 00:05:44,850 +لازم ألاقي ولو نقطة واحدة عندها قيمة المشتقة يساوي + +60 +00:05:44,850 --> 00:05:48,720 +Zero يمكن ألاقي تنتينيمكن تلاتة، يمكن أربعة، ماعنا + +61 +00:05:48,720 --> 00:05:52,740 +مشكلة. المهم على الأقل إذا وجدت الشروط الداء + +62 +00:05:52,740 --> 00:05:58,360 +الدالة أو تحققت الشروط الداء الثلاثة لدالة ما لازم + +63 +00:05:58,360 --> 00:06:02,960 +ألاجي ولو نقطة واحدة في الفترة المفتوحة A وB بحيث + +64 +00:06:02,960 --> 00:06:07,240 +أن المشتق عنها تساوي مين؟ تساوي Zero. تعالى نشوف + +65 +00:06:07,240 --> 00:06:12,000 +هذا بأمثلة عملية. بيقول لي بييني أن هذه الدالة + +66 +00:06:12,000 --> 00:06:20,310 +تحقق hypothesis فرضياتمفردها فرضية بس بدل الـI هذي + +67 +00:06:20,310 --> 00:06:26,990 +بحط بدالها I يبقى لو كانت I بكون hypothesis فرض + +68 +00:06:26,990 --> 00:06:33,310 +واحد بالـA يبقى الجمع hypothesis فرضيات يعني إيش + +69 +00:06:33,310 --> 00:06:37,610 +الفرضيات عن الفرضيات التلاتة اللي هنا يبقى بيقول + +70 +00:06:37,610 --> 00:06:42,750 +إن هذه ال function تحقق فرضيات نظرية رول على + +71 +00:06:42,750 --> 00:06:49,090 +الفترة المغلقة من Zero لغايةبعد ذلك هاتلي قيمة C + +72 +00:06:49,090 --> 00:06:55,750 +أو قيم C اللى موجودة فى الفترة المفتوحة 04 بحيث ان + +73 +00:06:55,750 --> 00:07:00,910 +قيمة المشتقة عندها تساوي كداش تساوي Zero يبقى احنا + +74 +00:07:00,910 --> 00:07:04,410 +فى الأول اللى بدنا نشوف فالتلات فرضيات متحققة ولا + +75 +00:07:04,410 --> 00:07:09,770 +ان كانت متحققة يبقى غصب عن اللى مايرضى لازم ألاقي + +76 +00:07:09,770 --> 00:07:16,270 +نقطة C قيمة المشتقة عندها تساوي صفربالدالي لمن؟ + +77 +00:07:16,270 --> 00:07:21,690 +لدلة اللي عندنا هذه، الدلة هذه الدمية انتبعها من + +78 +00:07:21,690 --> 00:07:28,150 +ويل لويلبنعندي Zero لغاية Infinity، عند Zero + +79 +00:07:28,150 --> 00:07:32,630 +الدالة معرفة، بظبط ولا لا؟ لأنه أنا عند الجدرد، + +80 +00:07:32,630 --> 00:07:36,950 +معناته continuous على الفترة من Zero إلى Infinity، + +81 +00:07:36,950 --> 00:07:40,070 +يعني continuous على الفترة من أين اللي وين؟ من + +82 +00:07:40,070 --> 00:07:45,050 +Zero لأربعة.يفجأة باجي بقوله ال domain تبع الدالة + +83 +00:07:45,050 --> 00:07:50,650 +F، بده يساوي من Zero لغاية Infinity.هذا بده يعطينا + +84 +00:07:50,650 --> 00:07:59,870 +ان ال F is continuous on الفترة من Zero لغاية + +85 +00:07:59,870 --> 00:08:05,790 +كدهش؟ لغاية أربعة يبقى اتحقق الشرف الأول عندي طبعا + +86 +00:08:05,790 --> 00:08:09,950 +يمكن واحد يقولي احنا ماخدنا ذلك بقوله كيف؟وقال لـ + +87 +00:08:09,950 --> 00:08:14,730 +continuous function بدي أشوف ال limit تبعته عند أي + +88 +00:08:14,730 --> 00:08:21,270 +نقطة و بدي أشوف مين و بدي أشوف قيمتها بقول هذا + +89 +00:08:21,270 --> 00:08:24,730 +كلام صحيح عند نقطة على interval يقول بدي أشوف + +90 +00:08:24,730 --> 00:08:28,250 +طرفية ال interval و بدي أشوف مين الفنص هذه قصة + +91 +00:08:28,250 --> 00:08:31,970 +طويلة جدا لكن احنا بجيب و أقول هذه الدالة معرفة من + +92 +00:08:31,970 --> 00:08:36,890 +و إلى وينمن Zero لإنفينتي، مدى أن معرفتي جاذبوا + +93 +00:08:36,890 --> 00:08:40,010 +منها، إذن هي ده اللي متواصلة عليها، لو في نقطة + +94 +00:08:40,010 --> 00:08:45,410 +ماشية متواصلة، سحبناها منها، إذن هذه أغنطني عن مين + +95 +00:08:45,410 --> 00:08:49,010 +ماين أكواد الشغل الطويل تبعنا اللي بدي أثبت ال + +96 +00:08:49,010 --> 00:08:53,370 +continuity على interval لهذه ال function طيب كويس، + +97 +00:08:53,370 --> 00:08:58,510 +ضال ال differentiability، إذن أنا عند ال F of X + +98 +00:08:58,510 --> 00:09:06,070 +بدي أتساوياللي هو x على 2 ناقص جذر ال X روح نشتق + +99 +00:09:06,070 --> 00:09:13,930 +يبقى ال F prime of X يساوي نص ناقص واحد على اتنين + +100 +00:09:13,930 --> 00:09:19,250 +جذر ال X في مشتقة ما تحت الجذر اللي هو قداشر واحد + +101 +00:09:20,640 --> 00:09:26,300 +وين هذا ال domain تبع ال f prime؟ هو domain ال f + +102 +00:09:26,300 --> 00:09:31,340 +ماعدى النقاط المشتقة عندها غير معرفة هل الدالة + +103 +00:09:31,340 --> 00:09:37,020 +معرفة عند ال zero؟ إذا بدنا نشيل ال zero فقط لغر و + +104 +00:09:37,020 --> 00:09:43,660 +الباقي بيبقى كما هو يبقى هذا معناه ان ال f is + +105 +00:09:43,660 --> 00:09:51,590 +differentiable on الفترة من zero لاربععند اي نقطة + +106 +00:09:51,590 --> 00:09:56,270 +خلال الفترة من Zero لاربع المعطاعة المشتقة هذه + +107 +00:09:56,270 --> 00:10:01,190 +معرفة، إذا هذه الـ function مالها ده المتصل عالميا + +108 +00:10:01,190 --> 00:10:06,670 +على هذه الفترة وفي نفس الوقت قابلة للاشتقاء يبقى + +109 +00:10:06,670 --> 00:10:10,650 +هيجب بقاش two conditions فهي لعند ال condition + +110 +00:10:10,650 --> 00:10:15,970 +التالت بده أروح أجيب له ال F of Zero أظن تساوي + +111 +00:10:15,970 --> 00:10:22,930 +Zeroزيرو جدر زيرو بزيرو بزيرو بد أجيب له ال F of + +112 +00:10:22,930 --> 00:10:29,170 +أربع يبقى هذا بتسوي أربع على اتنين ناقص جدر الأربع + +113 +00:10:29,170 --> 00:10:34,090 +يعني اتنين ناقص اتنين يسوي جدر زيرو معناه هذا + +114 +00:10:34,090 --> 00:10:40,420 +الكلام ان ال F of zero بد يسوي مين؟الـ F of أربعة + +115 +00:10:40,420 --> 00:10:47,860 +وبالتالي تحققت شروط من نظرية rule يبقى هنا sir the + +116 +00:10:47,860 --> 00:10:54,800 +function F of X يبدأ تسوى X على اتنين ناقص جذر ال + +117 +00:10:54,800 --> 00:11:06,360 +X satisfy the hypothesis the + +118 +00:11:06,360 --> 00:11:16,370 +hypothesis ofthe rules theorem يبقى معناه ان هذه + +119 +00:11:16,370 --> 00:11:21,550 +ال function تحقق نظرية rule معناته ايش؟ هذا بدي + +120 +00:11:21,550 --> 00:11:29,130 +اعطيك there exist رقم c موجود في الفترة 04 such + +121 +00:11:29,130 --> 00:11:37,920 +that بحيث هو ان ال f prime of c بدي سوى قداشزيرو + +122 +00:11:37,920 --> 00:11:43,220 +قال هاتلي ال C هذه، بديها، قال find the value of C + +123 +00:11:43,220 --> 00:11:46,780 +اللي موجودة في الفترة zero أربعة و اللي المشتقة + +124 +00:11:46,780 --> 00:11:51,240 +عندها بدأت ساوي زيرو، بنقوله بسيطة جدا ال F prime + +125 +00:11:51,240 --> 00:11:56,720 +of C يعني بدي أجي على ال F prime و لل F prime هيها + +126 +00:11:57,290 --> 00:12:02,950 +بدي أشيل كل X و أحط مكانها C يبقى معناته هذا + +127 +00:12:02,950 --> 00:12:08,590 +الكلام ناقص ناقص واحد على اتنين جدري ال C بده يسوي + +128 +00:12:08,590 --> 00:12:14,630 +قداش Zero او انشيتهم فاقولوا واحد على اتنين جدري + +129 +00:12:14,630 --> 00:12:22,650 +ال C يسوي قداشنص او بمعنى اخر اتنين جذر ال C يساوي + +130 +00:12:22,650 --> 00:12:28,470 +اتنين يبقى جذر ال C يساوي كدهش لو ربعنا الطرفين + +131 +00:12:28,470 --> 00:12:35,190 +بيصير عندنا C تساوي واحد اذا عندك C تساوي واحد + +132 +00:12:35,190 --> 00:12:41,140 +بيكون F prime of واحد بيساوي كدهشالنص صحيح كلامنا + +133 +00:12:41,140 --> 00:12:46,480 +و الله كله كلام تعالى شوف f prime of واحد حط هنا + +134 +00:12:46,480 --> 00:12:52,750 +واحد بصير مص ناقص نص يساوي زيروك بكلامنا صحيحهذا + +135 +00:12:52,750 --> 00:12:57,870 +هو نظرية رول ومثال عليها نذهب إلى العمود الفقري + +136 +00:12:57,870 --> 00:13:01,910 +تبع هذا المجلد وهو العنوان اللي نراه فيه هو ال + +137 +00:13:01,910 --> 00:13:08,490 +main value theorem يبقى بعد هذا بالداجي the main + +138 +00:13:08,490 --> 00:13:15,050 +value theorem ال + +139 +00:13:15,050 --> 00:13:17,850 +main value theorem تنص على ما يأتي + +140 +00:13:20,260 --> 00:13:29,000 +فترب انه Suppose that the function + +141 +00:13:29,000 --> 00:13:40,880 +اللي هي Y تساوي F of X is continuous is + +142 +00:13:40,880 --> 00:13:49,300 +continuous on a closed interval + +143 +00:14:00,950 --> 00:14:10,830 +على الفترة المفتوحة A وB ثم هناك + +144 +00:14:19,430 --> 00:14:28,670 +يوجد على الأقل في + +145 +00:14:28,670 --> 00:14:32,130 +الفترة + +146 +00:14:32,130 --> 00:14:34,350 +المفتوحة A وB + +147 +00:14:39,840 --> 00:14:49,240 +بحيث ان ال F of B ناقص ال F of A على B ناقص ال A + +148 +00:14:49,240 --> 00:14:52,940 +فهو F prime of C + +149 +00:15:24,550 --> 00:15:25,690 +خلّاله كويس هنا. + +150 +00:15:34,170 --> 00:15:39,430 +هذي there exist يوجد، there exist يوجد + +151 +00:15:41,990 --> 00:15:44,230 +اللي هي بالإنجليزي بسمة مجنوبة على الشجرة التانية + +152 +00:15:44,230 --> 00:15:50,990 +معناته there exists يوجد طيب بدنا نيجي لنظرية + +153 +00:15:50,990 --> 00:15:56,050 +القيمة المتواصفة the main value term لو دققت في + +154 +00:15:56,050 --> 00:16:01,850 +نظرية القيمة المتواصفة بلاقي فيها فرقين فقط ما + +155 +00:16:01,850 --> 00:16:08,370 +بينها وبين نظرية role الفرق الأول هو حد بيقدر + +156 +00:16:08,370 --> 00:16:16,140 +يكتشفهأيوة ان الشرب التالت مش موجود F of A بديه + +157 +00:16:16,140 --> 00:16:19,200 +يسوي F of B مش موجود الشرب الثاني او النقطة + +158 +00:16:19,200 --> 00:16:23,400 +الثانية ايوة + +159 +00:16:23,400 --> 00:16:27,740 +نجلي تسوى Zero هنا ليس بالضرورة تسوى Zero ممكن + +160 +00:16:27,740 --> 00:16:33,380 +تسوى Zero او لا تسوى Zero نظرية و نظرية rule الفرق + +161 +00:16:33,380 --> 00:16:38,850 +ما بين الاتنين هدولهو فقط الشرط هذا ونتيجة ان هذا + +162 +00:16:38,850 --> 00:16:42,850 +الشرط تصبح نتيجة ومخالفة الشرط هذا ان هناك f of a + +163 +00:16:42,850 --> 00:16:47,850 +يسوى f of b بالخط الواصل بينهم أوفقي تمام انهم خط + +164 +00:16:47,850 --> 00:16:50,870 +واصلي يبقى المماس بيكون أوفق يبقى f prime يسوى + +165 +00:16:50,870 --> 00:16:55,810 +zero هنا شال الشرط هذا مجرد شال الشرط هذا يبقى f + +166 +00:16:55,810 --> 00:17:01,690 +prime of c يسوى f of b نقص f of a على b نقص ال a + +167 +00:17:03,320 --> 00:17:07,760 +أفترض أن الدالة دالة متصلة على الفترة المولقة وهو + +168 +00:17:07,760 --> 00:17:12,140 +الشرط الأول من نظرية رول، قابل الاشتقاق على الفترة + +169 +00:17:12,140 --> 00:17:15,120 +المفتوحة الشرط التالي من نظرية رول، الشرط التالت + +170 +00:17:15,120 --> 00:17:20,380 +اختفى، then there is at least يوجد على الأقل نقطة + +171 +00:17:20,380 --> 00:17:26,060 +إن لم يكن أكثرفي الفترة A وB at which ال F of B + +172 +00:17:26,060 --> 00:17:32,360 +نقص ال F of A على B نقص ال A بدل سوء ال F prime of + +173 +00:17:32,360 --> 00:17:37,140 +C هناك بيجيني أقول المماس أفقي، هل يا ترى هنا + +174 +00:17:37,140 --> 00:17:38,400 +المماس أفقي؟ + +175 +00:17:59,100 --> 00:18:07,600 +الان ليس بالضرورة ان F of A تساوي F of Bليس + +176 +00:18:07,600 --> 00:18:14,320 +بالضرورة، كويس؟ يبقى هذه اللي هي ال F of A وهذه ال + +177 +00:18:14,320 --> 00:18:23,220 +F of B، هذا الخط الواصل بينهما، تمام؟ طيب، الأن لو + +178 +00:18:23,220 --> 00:18:30,320 +بدى أجيب ميل هذا الخطيبقى بدى أروح أرسم من هنا خط + +179 +00:18:30,320 --> 00:18:35,740 +عفوقي بالشكل لأن هذا بيعمل ليه زاوية قائمة صحيح + +180 +00:18:35,740 --> 00:18:41,900 +ولا لأ؟ إذا الخط اللى عنها ده من A إلى B المسافة + +181 +00:18:41,900 --> 00:18:49,940 +من هنا لغاية هنا هي B ناقص ال A صحيح ولا لأ؟ والخط + +182 +00:18:49,940 --> 00:18:58,450 +الراسي هذا هو ال F of Aوالخط هذا كله هو F of B إذا + +183 +00:18:58,450 --> 00:19:05,650 +بصير المسافة هذه لحالها فقط F of B ناقص F of A + +184 +00:19:05,650 --> 00:19:14,630 +يبقى المسافة هذه F of B ناقص F of A تعالي الآن لو + +185 +00:19:14,630 --> 00:19:21,620 +جيت عند النقطة اللي عندنايبقى حلاجة النقطة C بحيث + +186 +00:19:21,620 --> 00:19:27,560 +لو رسمت المماس عند هذه النقطة أيه المماس اللي + +187 +00:19:27,560 --> 00:19:35,240 +عندنا يمس المنحنة عند هذه النقطة يبقى هذا المماس + +188 +00:19:35,240 --> 00:19:46,040 +منه F prime of C يبقى اتنين هذول متوازين + +189 +00:19:46,240 --> 00:19:53,840 +فبيقول ف prime of C اللي هو ميل المماس للمنحنة عند + +190 +00:19:53,840 --> 00:19:59,820 +النقطة C بدي say F of B نقص F of A على B نقص ال A + +191 +00:19:59,820 --> 00:20:04,550 +اللي هو ميل الوطر اللي عندنا هذايبقى الاتنين هدول + +192 +00:20:04,550 --> 00:20:08,350 +بيساوي بعضهم، يبقى هذا معنى النظرية من الناحية + +193 +00:20:08,350 --> 00:20:14,150 +الهندسية المماث عند النقطة C المل تبعه يساوي المل + +194 +00:20:14,150 --> 00:20:17,890 +الخط الواصل ما بين ال F of A والF of B اللي هما + +195 +00:20:17,890 --> 00:20:21,650 +بيساووش بعض، في رول كانوا بيساوي واحد، يعني هذا + +196 +00:20:21,650 --> 00:20:28,190 +المل يساوي Zero، من هنا أتى الفرق في ما بينهماهذه + +197 +00:20:28,190 --> 00:20:32,550 +نظرية القيمة المتوسطة الآن بدنا ناخد بعض الأمثلة + +198 +00:20:32,550 --> 00:20:40,090 +على هذه النظرية أول مثال بيقول ما يأتي by example + +199 +00:20:40,090 --> 00:20:45,150 +one is + +200 +00:20:45,150 --> 00:20:54,950 +the functionهل الدالة f of x تساوي احد امرين اتنين + +201 +00:20:54,950 --> 00:21:01,410 +x ناقص تلاتة لما ال x محصورة ما بين ال zero و ما + +202 +00:21:01,410 --> 00:21:08,310 +بين اتنين او ستة x اللي هو ال term التاني ناقص x + +203 +00:21:08,310 --> 00:21:16,440 +تربية ناقص سبعةو ال X هذه محصورة ما بين اتنين وبين + +204 +00:21:16,440 --> 00:21:23,820 +التلاتة satisfy the + +205 +00:21:23,820 --> 00:21:34,640 +hypothesis of + +206 +00:21:34,640 --> 00:21:36,400 +the mean value theorem + +207 +00:21:54,860 --> 00:22:00,600 +خلّيني أبدأ كدا نعطيني مثلة f of x بعض عن p's y's + +208 +00:22:00,600 --> 00:22:06,100 +function ومعرفة على الفترة من zero إلى تلاتة يعني + +209 +00:22:06,100 --> 00:22:10,480 +ال domain تبع الدالة فقط بدي أخد من أين إلى أين من + +210 +00:22:10,480 --> 00:22:15,240 +zero إلى تلاتة بقول هل الدالة هذه تحقق شروط ال + +211 +00:22:15,240 --> 00:22:19,260 +main value theorem ولا لأ بقوله كويس يقول الخطوة + +212 +00:22:19,260 --> 00:22:24,330 +الأولى بدي أشوف هلهي continuous على الفترة المغلقة + +213 +00:22:24,330 --> 00:22:30,250 +من Zero لثلاثة ولا لأ اول شي بقوله domain الدالة F + +214 +00:22:30,250 --> 00:22:35,470 +يساوي الفترة المغلقة من Zero إلى ثلاثة من Zero إلى + +215 +00:22:35,470 --> 00:22:39,190 +اتنين ومن اتنين لثلاثة يبقى احنا مقيدين بهذه + +216 +00:22:39,190 --> 00:22:45,360 +الفترة الان هذه دالة خطيةده اللي خاطية، ده اللي + +217 +00:22:45,360 --> 00:22:50,360 +متاصلة، هذه ده اللي من الدرجة الثانية، منحنة، برضه + +218 +00:22:50,360 --> 00:22:54,600 +متاصلة، يبقى المشكلة وين؟ عند نقطة الالتقاء، ممكن + +219 +00:22:54,600 --> 00:22:58,920 +يكون منحنة بالشكل هذا أو الخط المستقيم جاي من فوق، + +220 +00:22:58,920 --> 00:23:04,190 +لا يلتقي معاه، مظبوط؟إذا أثبتنا إن اتنين بيلتقوا + +221 +00:23:04,190 --> 00:23:09,090 +مع بعض، فالدالة مالها؟ دالة متصلة، إذا المشكلتنا + +222 +00:23:09,090 --> 00:23:14,550 +حصلة وين؟ حصلة عند اتنين طب، مش هنشوف الدالة متصلة + +223 +00:23:14,550 --> 00:23:18,890 +عند اتنين ولا لأ، بدي أشوف هل قيمة الدالة عند + +224 +00:23:18,890 --> 00:23:24,450 +اتنين تساوي نهاية الدالة عند اتنين ولا لأ، إذا بجي + +225 +00:23:24,450 --> 00:23:29,950 +بقوله بدي أخد ال F of اتنينإتنين حصلة في ال term + +226 +00:23:29,950 --> 00:23:34,870 +الأول يجي اتنين في اتنين ناقص تلاتة و يسوى كده؟ + +227 +00:23:34,870 --> 00:23:43,370 +واحد طيب أليس تهادي هي limit لل F of X لما ال X + +228 +00:23:43,370 --> 00:23:49,800 +بده يروح لليتنين من جهة الشمال؟صحيح ولا لأ؟ يبقى + +229 +00:23:49,800 --> 00:23:53,520 +هدول بيساوي بعض، يبقى لو قدرت أثبت أن ال limit ال + +230 +00:23:53,520 --> 00:23:57,200 +F of X لما ال X بتروح لإتنين من جهة اليمين بيساوي + +231 +00:23:57,200 --> 00:24:01,960 +النتيجة هذه، بيبقى الدالة دالة مبتصرة، بصير نهاية + +232 +00:24:01,960 --> 00:24:06,160 +الدالة تساوي قيمة الدالة عند تلك النقطة. إذا + +233 +00:24:06,160 --> 00:24:12,060 +بيدروح أخد limit ال F of X لما ال X بيروح لإتنين + +234 +00:24:12,060 --> 00:24:17,780 +من جهة اليمين.يبقى هذا ال limit لما ال X بده تروح + +235 +00:24:17,780 --> 00:24:22,080 +للإتنين من جهة اليمين إذا احنا رايحين للإتنين من + +236 +00:24:22,080 --> 00:24:27,920 +جهة اليمين يبقى وين؟ الجزء الثاني من ال function + +237 +00:24:27,920 --> 00:24:34,820 +يبقى بيصير 6X ناقص X تربية ناقص 7 هذه polynomial + +238 +00:24:34,820 --> 00:24:40,850 +من الدرجة الثانيةيبقى تعويض مباشر يبقى ستة في + +239 +00:24:40,850 --> 00:24:48,310 +اتنين ناقص اتنين تربية ناقص سبعة ما يساوي اتناشر + +240 +00:24:48,310 --> 00:24:55,990 +وهذه اربعة وناقص اربعة وناقص سبعة اللي هو ناقص + +241 +00:24:55,990 --> 00:25:01,430 +أحداشر يبقى اتناشر ناقص أحداشر اللي هو قداشر نفس + +242 +00:25:01,430 --> 00:25:08,720 +القيمة اللي عندنا هذه يبقى بناء عليه الساملما ال X + +243 +00:25:08,720 --> 00:25:13,580 +يذهب إلى الاتنين سواء كان يمين او شمال تساوي ال F + +244 +00:25:13,580 --> 00:25:18,740 +of اتنين تساوي واحد هذا سيعطينا ان ال F is + +245 +00:25:18,740 --> 00:25:27,200 +continuous على كل الفترة من 0 لغاية 8 لغاية 3 + +246 +00:25:29,870 --> 00:25:36,090 +هل الدالة قابلة للاشتراك على الفترة المفتوحة من + +247 +00:25:36,090 --> 00:25:42,370 +Zero لغاية تلاتة ولا لأ؟ تبقى مشكلتنا وين؟ عند + +248 +00:25:42,370 --> 00:25:46,750 +اتنين، نفس الطريقة، هل ال continuous بيعطيني + +249 +00:25:46,750 --> 00:25:51,650 +differentiability؟ليس بالضرورة، هذا كلام ليس + +250 +00:25:51,650 --> 00:25:56,250 +دقيقًا. إذا ما أقدرش، بس لو كانت قابلة للاشتقاء، + +251 +00:25:56,250 --> 00:25:59,830 +بقول automatic continuous غصبًا على ميربع، إذا ما + +252 +00:25:59,830 --> 00:26:04,010 +أقدرش أقول إن ده قابل للاشتقاك، شفه و هيك، اللي + +253 +00:26:04,010 --> 00:26:10,210 +أروح أثبتها. طيب، لو روحت أنا جيبت المشتقة من جهة + +254 +00:26:10,210 --> 00:26:16,560 +الشمال عند اتنين.تمام؟ يبقى المشتقة من جهة الشمال + +255 +00:26:16,560 --> 00:26:21,400 +يعني X أقل من الإتنين يبقى بده اشتق تساوي كده + +256 +00:26:21,400 --> 00:26:27,760 +تساوي اتنين طب لو بده اجيب المشتقة من جهة اليمين + +257 +00:26:27,760 --> 00:26:36,160 +عند اتنينيبقى بده يصير الستة ناقص اتنين X والحكي + +258 +00:26:36,160 --> 00:26:43,140 +هذا كله عند X يسوي قداش اتنين يبقى بيصير الستة + +259 +00:26:43,140 --> 00:26:48,200 +ناقص اتنين في اتنين يسوي قداش كمان اتنين نفس + +260 +00:26:48,200 --> 00:26:55,890 +القيمةيبقى هنا بقول له sir ال F prime او ال F is + +261 +00:26:55,890 --> 00:27:04,070 +differentiable at X يساوي اتنين هذا معناه ان ال F + +262 +00:27:04,070 --> 00:27:11,580 +isDifferentiable على الفترة المفتوحة من Zero لتلتة + +263 +00:27:11,580 --> 00:27:15,500 +لإن الاشتقاق الأولى مافيش فيه مشكلة واشتقاق الثاني + +264 +00:27:15,500 --> 00:27:20,680 +مافيه مشكلة المشكلة تكمن عند نقطة الالتقاء هل هي + +265 +00:27:20,680 --> 00:27:25,140 +Corner هل هي Castle هل هي Vertical Tangent هل هي + +266 +00:27:25,140 --> 00:27:26,000 +Discontinuity + +267 +00:27:29,900 --> 00:27:35,820 +السؤال يقول هل يتدل هذي تحقق شروط الـ Mean Value + +268 +00:27:35,820 --> 00:27:40,660 +Theorem ولا لأ؟ هم الشرطين اتحققوا، خلاص انتهينا، + +269 +00:27:40,660 --> 00:27:48,360 +يبقى ناسا الـF satisfy the + +270 +00:27:48,360 --> 00:27:50,520 +hypothesis + +271 +00:27:53,220 --> 00:27:59,540 +of the main value theorem + +272 +00:28:25,820 --> 00:28:31,160 +نمتقل إلى مثال آخر example + +273 +00:28:31,160 --> 00:28:37,820 +two show + +274 +00:28:37,820 --> 00:28:43,520 +that the + +275 +00:28:43,520 --> 00:28:53,080 +function f of x يسوى x زائد واحد علي x satisfy + +276 +00:28:56,550 --> 00:29:06,830 +هي حياثيات أساسية + +277 +00:29:06,830 --> 00:29:11,690 +قيمة ثيرم على الانترال + +278 +00:29:16,500 --> 00:29:28,600 +interval على الفترة المغلقة نص و اتنين and find + +279 +00:29:28,600 --> 00:29:32,480 +all + +280 +00:29:32,480 --> 00:29:40,680 +values of + +281 +00:29:40,680 --> 00:29:42,480 +C + +282 +00:29:44,060 --> 00:29:51,460 +that satisfy + +283 +00:29:51,460 --> 00:29:57,620 +the main value theorem + +284 +00:30:30,510 --> 00:30:38,030 +ولا نعود لمثال مرة أخرىالـ F of X تساوي X زائد + +285 +00:30:38,030 --> 00:30:43,330 +واحد بيين لي أن هذه الدلة تحقق نظرية القيم + +286 +00:30:43,330 --> 00:30:49,030 +المتوسطة على الفترة من نص لغاية اتنين وبعد ذلك + +287 +00:30:49,030 --> 00:30:55,790 +هتلي كل قيم C التي تحقق الهو ال main value theorem + +288 +00:30:55,790 --> 00:31:00,450 +على الفترة اللي هو نص و اتنين بقوله بسيطة، اذا + +289 +00:31:00,450 --> 00:31:05,770 +بدأو حدرس ال continuity لهذه الدلةأحنا عندنا ال F + +290 +00:31:05,770 --> 00:31:12,910 +of X يساوي X زائد واحد على X ال discontinuity حاصل + +291 +00:31:12,910 --> 00:31:18,070 +وين؟ في ال zero فقط ليه غير؟ ال discontinuity + +292 +00:31:18,070 --> 00:31:22,600 +الموجودة أو النقطة zero موجودة في الفترة ديلأ يبقى + +293 +00:31:22,600 --> 00:31:29,320 +هذه f of x is undefined + +294 +00:31:29,320 --> 00:31:36,580 +غير معرفة at x تساوي zero ليه ماهياش موجودة في + +295 +00:31:36,580 --> 00:31:43,200 +الفترة النص و اتنين معنى هذا الكلام ان دلدله متصلة + +296 +00:31:43,200 --> 00:31:48,820 +على الفترة هذه يبقى this means + +297 +00:31:50,230 --> 00:31:56,550 +that هذا يعني ان ال if is continuous + +298 +00:31:57,770 --> 00:32:04,150 +على الفترة المغنقة نص و اتنين لان ال discontinuity + +299 +00:32:04,150 --> 00:32:10,170 +فقط عند ال zero و zero خارج هذه الفترة نجي لمين ال + +300 +00:32:10,170 --> 00:32:14,530 +differentiability مش هنشوفه قبل اشتقاق ولا لا يبقى + +301 +00:32:14,530 --> 00:32:22,350 +لو جيت اشتقطة f prime of x يستوي واحد نقص واحد على + +302 +00:32:22,350 --> 00:32:31,460 +x تربيه المشتقة هذه غير معرفةخارج الفترة هذه يبقى + +303 +00:32:31,460 --> 00:32:39,320 +هذا ال f prime بده تساوي كده هذه is undefined كمان + +304 +00:32:39,320 --> 00:32:46,360 +غير محرفة at x يساوي zero اللي مش موجودة في الفترة + +305 +00:32:46,360 --> 00:32:53,010 +اللي هي النص و اتنين هذا معناه ان ال fis + +306 +00:32:53,010 --> 00:33:00,570 +differentiable on الفترة نص و اتنين إذا انتحققوا + +307 +00:33:00,570 --> 00:33:09,830 +الشرطين تبعين ال main value theorem يبقى F of X + +308 +00:33:09,830 --> 00:33:19,810 +تساوي X زائد واحد على X satisfy the hypothesis + +309 +00:33:25,100 --> 00:33:35,140 +of the mean value theorem يبقى المطموب الأول من + +310 +00:33:35,140 --> 00:33:42,560 +المسألة حققنا هذا على ال interval on ال interval + +311 +00:33:42,560 --> 00:33:49,520 +نص و اتنى بيقول هاتلي قيم C التي تحقق ال mean + +312 +00:33:49,520 --> 00:33:58,720 +value theoremبقوله by the mean value theorem there + +313 +00:33:58,720 --> 00:34:06,940 +exists c موجود في الفترة المفتوحة مص و اتنين such + +314 +00:34:06,940 --> 00:34:07,680 +that + +315 +00:34:10,060 --> 00:34:18,600 +الـ F of اتنين ناقص الـ F of نص على اتنين ناقص نص + +316 +00:34:18,600 --> 00:34:25,640 +يقدر يساوي الـ F prime of Cمش هنحقق هذا، بدي أعرف + +317 +00:34:25,640 --> 00:34:32,120 +قداش F of اتنين و قداش ال F of نص، يبقى بدي أشيل + +318 +00:34:32,120 --> 00:34:42,660 +هنا و أقول هذا اتنين زائد نص ناقص ال F of نص نص + +319 +00:34:42,660 --> 00:34:50,550 +زائد واحد على نصكله على قداش اتنين ناقص نصف بيبقى + +320 +00:34:50,550 --> 00:34:56,190 +واحد و نصف اللي هو تلاتة على اتنين بده يساوي F + +321 +00:34:56,190 --> 00:35:01,750 +prime of C هي F prime بس بده اشيل كل X و أحط + +322 +00:35:01,750 --> 00:35:08,230 +مكانها C يبقى واحد ناقص واحد على C تربية + +323 +00:35:15,240 --> 00:35:20,940 +طبعا ناقص المقدار هذا كله حطوه لبنجوسين برضه جداش + +324 +00:35:20,940 --> 00:35:27,070 +اتنين و نص يعني جداش مقلع زيرو يبقى هذا معناهإن + +325 +00:35:27,070 --> 00:35:32,890 +واحد ناقص واحد على C تربية تساوي Zero هذا معناه إن + +326 +00:35:32,890 --> 00:35:37,730 +واحد على C تربية تساوي واحد هذا معناه إن C تربية + +327 +00:35:37,730 --> 00:35:44,710 +تساوي واحد هذا معناه إن C تربية تساوي زائد أو ناقص + +328 +00:35:44,710 --> 00:35:49,870 +واحدتعال، طيب، الآن هل السالب واحد موجودة في + +329 +00:35:49,870 --> 00:35:55,870 +الفترة هذه؟ لأ، يبقى الـC تساوي السالب واحد، does + +330 +00:35:55,870 --> 00:36:02,350 +not belong للفترة اللي هي المصوتنا، يبقى هذه ايه؟ + +331 +00:36:02,350 --> 00:36:08,400 +مرفوضةيبقى هذا مرفوضة، هذا بدّه يعطيك ان الـC + +332 +00:36:08,400 --> 00:36:13,600 +تساوي واحد هي المطموعة اللي موجودة في الفترة ما + +333 +00:36:13,600 --> 00:36:19,180 +بين نص و اتنين يبقى الـC اللي بدّه يهي الـC تساوي + +334 +00:36:19,180 --> 00:36:26,280 +واحد صحيح كويس، + +335 +00:36:26,280 --> 00:36:32,200 +يقول أعطيك العافية خلاص، مكملش، انتهينا، ماتحققش، + +336 +00:36:32,200 --> 00:36:39,250 +يبقى انتهينا منهنأخد مثال + +337 +00:36:39,250 --> 00:36:48,010 +يبقى example three show + +338 +00:36:48,010 --> 00:36:55,950 +that show that sign ال B + +339 +00:37:01,030 --> 00:37:09,530 +اقل من أو يساوي absolute value ل B ناقص ال A for + +340 +00:37:09,530 --> 00:37:16,670 +any numbers + +341 +00:37:16,670 --> 00:37:20,970 +A and B + +342 +00:37:31,510 --> 00:37:35,830 +طبعا السؤالين اللي فاتوا كانوا واضحات قال بييلي ان + +343 +00:37:35,830 --> 00:37:40,090 +هذه الدالة بتحقق شروط ال main value theorem و + +344 +00:37:40,090 --> 00:37:43,750 +بعدين هات لقيمة C هنا أباني سؤال لا جالي main + +345 +00:37:43,750 --> 00:37:46,910 +value theorem ولا جابلي سيرة ال main value theorem + +346 +00:37:46,910 --> 00:37:51,730 +يبقى كله بترجع لشطاطة كال انت صاحي ولا لأ فاهم + +347 +00:37:51,730 --> 00:37:57,100 +الموضوع لأهذا طبعا أحد أسئلة الكتاب زي ما هو نصا + +348 +00:37:57,100 --> 00:38:00,600 +زي هيك قال يبين لي أن ال absolute value ل sign ال + +349 +00:38:00,600 --> 00:38:05,640 +B ناقص sign ال A أقل من أو يسوى B ناقص عليه ك + +350 +00:38:05,640 --> 00:38:11,580 +absolute value لأي قيمة A أو B بقوله والله كويس + +351 +00:38:11,580 --> 00:38:15,650 +السؤال هوأنا بدي أجرب الـ Mean Value Theorem، لكي + +352 +00:38:15,650 --> 00:38:19,250 +أجرب الـ Mean Value Theorem، بدي فانكشن عندنا، + +353 +00:38:19,250 --> 00:38:22,550 +السؤال هو مين الـ function في هذه المثلة؟ الـ sine + +354 +00:38:22,550 --> 00:38:28,130 +ال X، يبقى أنا بس انتيجة استنتاجي من خلال مين؟ من + +355 +00:38:28,130 --> 00:38:31,910 +خلال الكلام اللي موجود عندى، ال sine ال B ناقص ال + +356 +00:38:31,910 --> 00:38:35,910 +sine ال A، يعني هذا قيمة للـ function عند بي وقيمة + +357 +00:38:35,910 --> 00:38:39,910 +أخرى للـ function وين، عند بي يبقى أول خطوة بقول + +358 +00:38:39,910 --> 00:38:49,980 +لهالـ f of x يساوي صين الـ x مدام صين الـ x يبقى + +359 +00:38:49,980 --> 00:38:56,400 +الصين الـ x فيها discontinuity يبقى هذه f of x هذه + +360 +00:38:56,400 --> 00:39:03,660 +الصين الـ x continuous for all x بالاستثناء كل الـ + +361 +00:39:03,660 --> 00:39:10,430 +real lineطيب، معنى هذا الكلام إن ال F is + +362 +00:39:10,430 --> 00:39:18,330 +continuous على الفترة A وB اللي هي جزء من مين؟ جزء + +363 +00:39:18,330 --> 00:39:23,570 +من ال real life خد أي close خد اللي بدكيها، zero + +364 +00:39:23,570 --> 00:39:28,150 +واحد، zero اتنين، واحد وخمسة، عشرة وخمسمية، أي + +365 +00:39:28,150 --> 00:39:33,370 +فترة بدكيهاإن شاء الله تقول لي ناقص ثلاثة وواحد، + +366 +00:39:33,370 --> 00:39:37,730 +سيئات، أي فترة بدي أخدها لأن ماعطليش قيود على A + +367 +00:39:37,730 --> 00:39:42,410 +وB، مين ما يكون الـA وB، وكون أخدت لبس الـU value + +368 +00:39:42,410 --> 00:39:46,990 +مين أصغر ومين أكبر، لا قيمة لها هذا السيئات، طيب + +369 +00:39:46,990 --> 00:39:52,060 +تمام، يبقى بالك كنتني واصل على هذه الفترةهل هي + +370 +00:39:52,060 --> 00:39:57,500 +differentiable ولا لا؟ إذا بجي بقوله F prime of X + +371 +00:39:57,500 --> 00:40:05,260 +تفضل الـSin بCos X المشتقة دي في نقطة ماهياش معرفة + +372 +00:40:06,040 --> 00:40:14,480 +يبقى هذا الـ if a parameter is defined برضه for + +373 +00:40:14,480 --> 00:40:20,920 +all x belastate لأ معناه هذا الكلب ان ال if is + +374 +00:40:20,920 --> 00:40:29,110 +differentiable على الفترة المفتوحة a و bإذا انتحقق + +375 +00:40:29,110 --> 00:40:35,370 +الشرطين، تبعين من؟ تبعين الـMain Value Theorem، + +376 +00:40:35,370 --> 00:40:40,950 +معناه اللازم ألاقي على الأقل ولو نقطة C، بحيث + +377 +00:40:40,950 --> 00:40:48,130 +نظرية القيمة المتوسطة تبقى صحيحة يبقى الـF of X + +378 +00:40:48,130 --> 00:40:55,950 +يساوي الصين الـX satisfy the hypothesis + +379 +00:40:58,260 --> 00:41:06,640 +of the mean value theory هذا معناه إيش؟ إنه يوجد + +380 +00:41:06,640 --> 00:41:14,820 +there exists C موجودة في الفترة المفتوحة A وB such + +381 +00:41:14,820 --> 00:41:25,430 +that بحيث أن ال F of Bنقص ال F of A على B نقص ال A + +382 +00:41:25,430 --> 00:41:28,870 +بدي يسوي F prime of C + +383 +00:41:32,500 --> 00:41:39,600 +الان بده اجي لل F of B اللي هي مين؟ صين ال B نقل + +384 +00:41:39,600 --> 00:41:47,740 +صين ال A على B اه بدت تتخلق المثل عندى، مش هيك؟ + +385 +00:41:47,740 --> 00:41:53,080 +يبقى هذا الكلام بده يساوي F prime اللي هو جباش، + +386 +00:41:53,080 --> 00:42:00,990 +cosine يبقى هذا cosine ال Cطب ايش رأيك؟ بتاخد ال + +387 +00:42:00,990 --> 00:42:08,270 +absolute value للترفين تمام؟ هذا الكلام بده يساوي + +388 +00:42:08,270 --> 00:42:15,570 +هذا بده يعطيلك absolute value ل sign ال B ناقص + +389 +00:42:15,570 --> 00:42:23,870 +sign ال A على absolute value لل B ناقص ال E يساوي + +390 +00:42:23,870 --> 00:42:27,850 +absolute value لكو sign ال C + +391 +00:42:34,810 --> 00:42:42,420 +كده؟ يعني دايما هو أكتر من الواحديبقى اذا كوصين + +392 +00:42:42,420 --> 00:42:45,800 +الـC لما ربك يحط فيه البركة بيصير واحد + +393 +00:43:09,470 --> 00:43:13,870 +يبقى لو ضربت الطرفين فيها لا تتغير ال inequality + +394 +00:43:13,870 --> 00:43:19,250 +يبقى لو ضربت الطرفين بيصير عند مين absolute value + +395 +00:43:19,250 --> 00:43:26,290 +لل sign ال B ناقص A اللي هو sign ال A كله ك + +396 +00:43:26,290 --> 00:43:32,230 +absolute value أقل من أو يساوي ال B ناقص ال A أظن + +397 +00:43:32,230 --> 00:43:33,250 +وهو المطلوب + +398 +00:43:41,840 --> 00:43:47,800 +كيف ايش؟ احنا موضوعنا موضوع ال mean value theorem، + +399 +00:43:47,800 --> 00:43:53,560 +مظبوط؟ ماعنديش معلومات غيرها حتى اللحظة، يا هي + +400 +00:43:53,560 --> 00:43:59,180 +نظرية رول، مظبوط ولا لا؟طيب، يبقى أنا مين أسهل + +401 +00:43:59,180 --> 00:44:04,360 +ليه؟ هذه النظرية ولا نظرية رول؟ هذه لإن أنا بدأ + +402 +00:44:04,360 --> 00:44:08,760 +شرطين، بدليش الشرط التالت ومن الصعب إني أجيب الشرط + +403 +00:44:08,760 --> 00:44:12,660 +التالت، مظبوط؟ يبقى automatically أنا سنتاج لحالة + +404 +00:44:12,660 --> 00:44:16,280 +إنها نظرية رول طيب، بعدين أنا بدي أعطيك كمان مثال + +405 +00:44:16,280 --> 00:44:20,440 +بفكرة جديدة مختلفة وشوف كيف بدك تعرفها، هل هي + +406 +00:44:20,440 --> 00:44:25,380 +نظرية رول ولا غير نظرية رول؟ خد؟ أيوة + +407 +00:44:29,820 --> 00:44:34,240 +إذا لا تحقق نظر L في الشرطين بقدرش أقول there + +408 +00:44:34,240 --> 00:44:43,760 +exist C بقدرش مش إمكانية أبدا + +409 +00:44:43,760 --> 00:44:48,080 +مش ال cosine قداش cosine ال C أكبر قيمة بياخدوه + +410 +00:44:48,080 --> 00:44:54,640 +وأقل قيمة Zeroأقل من أو يساوي واحد يعني أقل من أو + +411 +00:44:54,640 --> 00:44:58,020 +يساوي واحد، مظبوط ولا لأ؟ يبقى هنا أقل من أو يساوي + +412 +00:44:58,020 --> 00:45:02,340 +واحد، اضرب ضرب تبادلي، بصي ال sign بيناقص sign ليه + +413 +00:45:02,340 --> 00:45:06,920 +ك absolute value أقل من أو يساوي واحد ضرب absolute + +414 +00:45:06,920 --> 00:45:09,880 +value ليه بيناقص عليه، وهو المطلوب + +415 +00:45:30,790 --> 00:45:39,790 +حد بدأ يسأل تاني؟ و بالمثال الرابع؟ مثال أربعة؟ + +416 +00:45:48,950 --> 00:45:56,470 +وقول الـ suppose that + +417 +00:45:56,470 --> 00:46:06,190 +ال F is continuous on + +418 +00:46:06,190 --> 00:46:12,110 +الفترة المغلقة Zero وأربع + +419 +00:46:18,670 --> 00:46:29,750 +وال F of 0 يبدو يساوي واحد and الاتنين + +420 +00:46:29,750 --> 00:46:37,130 +اقل من او يساوي ال F prime of X اقل من او يساوي + +421 +00:46:37,130 --> 00:46:46,610 +خمسة for all X الموجودة في الفترة المفتوحة Zero + +422 +00:46:46,610 --> 00:46:57,850 +وأربعالسؤال هو show that بيّلي إنه التسعة أقل من + +423 +00:46:57,850 --> 00:47:05,590 +أو يساوي ال F of أربعة أقل من أو يساوي الواحد + +424 +00:47:05,590 --> 00:47:06,330 +وعشرين + +425 +00:47:18,040 --> 00:47:23,840 +نقرر من السؤالين، السؤال هذا لا اعطاني قيمة لدالة + +426 +00:47:23,840 --> 00:47:28,760 +ولا اعطاني شكل دالة ولا اعطاني continuous ولا + +427 +00:47:28,760 --> 00:47:32,850 +differentialعلى ده حالة من خلال المعطية تبعت المثل + +428 +00:47:32,850 --> 00:47:38,050 +استنتجت شكل الدالة و روحت اشتقيت الدالة و أثبتت + +429 +00:47:38,050 --> 00:47:41,510 +انها دالة متصلة على كل ال real line وبالتالي أخدت + +430 +00:47:41,510 --> 00:47:45,270 +فترة من هذا ال real line و بعدين أثبتت انها + +431 +00:47:45,270 --> 00:47:48,690 +differentiable وبالتالي استخدمت ال main value + +432 +00:47:48,690 --> 00:47:53,310 +theoremهذا السؤال قال لي ال F ده اللي متصل على + +433 +00:47:53,310 --> 00:47:57,690 +فترة 0 و 4 يبقى أعطاني main condition الأول تبع ال + +434 +00:47:57,690 --> 00:47:59,890 +main .. وماقلليش هستخدم ال main value theorem + +435 +00:47:59,890 --> 00:48:04,570 +قاللي أنت حر سوي اللي بدك إياه، و أعطاني معلومات و + +436 +00:48:04,570 --> 00:48:08,470 +أنا لحالي بدي أستنتج الشغلة اللي ممكن أحلبها main + +437 +00:48:08,470 --> 00:48:14,050 +السؤالقال ياف دالة مقتصرة على فترة المغلقة 0 4 + +438 +00:48:14,050 --> 00:48:21,230 +وقيمة الدالة عند 0 تساوي 1 صحيح وقيمة المشتقة + +439 +00:48:21,230 --> 00:48:28,670 +محصورة بين 2 و5 لكل ال X اللي موجودة وينأربعة + +440 +00:48:28,670 --> 00:48:33,050 +محصورة + +441 +00:48:33,050 --> 00:48:36,390 +بين التسعة وما بين الواحد وعشرين + +442 +00:48:42,160 --> 00:48:45,540 +بقول طيب ايش؟ من وين بيزيجي بقولها؟ بعدين بقول اه + +443 +00:48:45,540 --> 00:48:49,480 +ماهي F of 4 موجودة في نظرية ال mean value theorem + +444 +00:48:49,480 --> 00:48:55,240 +نجان نقلوها Z بجانها F of 4 و F of 0 على 4 ناقصة 0 + +445 +00:48:55,240 --> 00:48:58,760 +بتساوي F prime of Z مش هيك نظرية ال mean value اذا + +446 +00:48:58,760 --> 00:49:04,700 +انا بدي ابحث هل ال F اللي عندي هني هل تحقق شروط ال + +447 +00:49:04,700 --> 00:49:08,360 +mean value theorem ام لا والله إذا حققتها بقدر + +448 +00:49:08,360 --> 00:49:12,380 +استخدم ال mean value و أحل السؤال ما حققتهابروح + +449 +00:49:12,380 --> 00:49:17,100 +أكبس في شغلة تانية يمكن ولا ربما الله أعلم يبقى + +450 +00:49:17,100 --> 00:49:22,760 +احنا بنقول الدلة دلة متصلة على الفترة المغلقة يبقى + +451 +00:49:22,760 --> 00:49:31,120 +الخطوة الأولى بقوله ال F is continuous على الفترة + +452 +00:49:31,120 --> 00:49:32,740 +المغلقة 04 + +453 +00:49:35,230 --> 00:49:40,790 +بدي أشوف هل الدالة قابلة للاشتقاق على الفترة + +454 +00:49:40,790 --> 00:49:46,790 +المفتوحة 04 ولا لأ باجي بكمل قراية الأسئلة F of 0 + +455 +00:49:46,790 --> 00:49:51,110 +تسوى 1 هذا مالعيش علاقة بالاشتقاق هذه قيمة الدالة + +456 +00:49:51,110 --> 00:49:56,330 +عند نقطة بيعطيني كمان condition إن قيمة المشتقة + +457 +00:49:56,330 --> 00:50:01,490 +محصورة بين 2 و 5 لكل ال X + +458 +00:50:05,320 --> 00:50:10,640 +ماذا تستنتج من هذه العبارة؟ اه مدام انها قيم + +459 +00:50:10,640 --> 00:50:15,360 +محصولة، اذا الدالة قابلة لاشتقاق خلال هذه الفترة، + +460 +00:50:15,360 --> 00:50:18,900 +يبقى جبت ال condition التاني التابع مين؟ ال main + +461 +00:50:18,900 --> 00:50:25,370 +value theorem، باجي بقولهلإتنين أقل من أو يساوي f + +462 +00:50:25,370 --> 00:50:31,250 +prime of x أقل من أو يساوي لكل ال x اللي موجودة في + +463 +00:50:31,250 --> 00:50:39,770 +الفترة 0 4 هذا شو تعني means that هذا تعني أن ال f + +464 +00:50:39,770 --> 00:50:50,790 +is differentiable on الفترة 0 4المشتقة محصورة بين + +465 +00:50:50,790 --> 00:50:55,790 +2 و 5 لكل ال X اللي في 0 و 4 يبقى الدالة قابلة + +466 +00:50:55,790 --> 00:51:00,330 +الاشتقاء خلال هذه الفترة وقيمة المشتقة محصورة + +467 +00:51:00,330 --> 00:51:05,990 +دائما و أبدا بين 2 و 5 يبقى الدالة قابلة الاشتقاء + +468 +00:51:05,990 --> 00:51:11,130 +خلال هذه الفترة من ال two conditions لإتنين هدول + +469 +00:51:11,130 --> 00:51:22,500 +بقدر أقوله إذاالـ if satisfy the hypothesis + +470 +00:51:26,590 --> 00:51:35,730 +of the main value theorem اذا هذه النظرية تحقق او + +471 +00:51:35,730 --> 00:51:41,790 +هذه الدالة F تحقق شروط نظرية القيمة المتواصلة مدام + +472 +00:51:41,790 --> 00:51:45,870 +هيك هذا شو معناه يبقى هناك + +473 +00:51:53,470 --> 00:52:03,830 +بحيث ان such that f prime of c بده ساوي اللي هو ال + +474 +00:52:03,830 --> 00:52:10,070 +F of أربعة ناقص ال F of Zero على أربعة ناقص ال + +475 +00:52:10,070 --> 00:52:18,790 +Zero طبعا؟ طيب، باجي بقوله هذا شو معناه؟ F of + +476 +00:52:18,790 --> 00:52:23,290 +أربعة لازمالي في الإجابةيبقى ماقدرش ألعب فيها ولا + +477 +00:52:23,290 --> 00:52:29,270 +حاجة ال F of zero مقاطع في المثل بواحد يبقى باشي + +478 +00:52:29,270 --> 00:52:34,230 +لو بكتب بدالها واحد اربعة ناقص zero اللي هو بقدراش + +479 +00:52:34,230 --> 00:52:41,590 +باربعة بده يسوى F prime of C يبقى هذا بده يسوى F + +480 +00:52:41,590 --> 00:52:49,900 +prime of Cالان f prime of x محصورة بين اتنين وخمسة + +481 +00:52:49,900 --> 00:52:54,400 +لكل ال x اللي محصورة في ال بينزير واربع، إذا معنى + +482 +00:52:54,400 --> 00:52:58,320 +هذا الكلام إن القيمة هذه محصورة بين مين ومين؟ بين + +483 +00:52:58,320 --> 00:53:06,700 +اتنين وخمسة، يبقى باجي بقوله بما أنلإتنين أقل من f + +484 +00:53:06,700 --> 00:53:12,840 +prime of x أقل من أو يسوى خمسة لكل ال x اللي + +485 +00:53:12,840 --> 00:53:17,180 +موجودة في zero أربعة إذا أنت تنطبق على الكلام اللي + +486 +00:53:17,180 --> 00:53:24,620 +إحنا جايب له هذا since هذا يبقى we have أن ال f of + +487 +00:53:24,620 --> 00:53:32,730 +أربعة ناقص الواحدأربعة محصورة ما بين اتنين وبين + +488 +00:53:32,730 --> 00:53:41,870 +مان وبين الخمسة، بصبر؟ لأن هذه F'C واحنا عنا F'X + +489 +00:53:41,870 --> 00:53:46,890 +لكل X اللي موجودة في الفترة هذه محصورة هنا، إذن C + +490 +00:53:46,890 --> 00:53:50,710 +موجودة في هذه الفترة، إذن F'C بدي يكون محصور بين + +491 +00:53:50,710 --> 00:53:51,270 +اتنين + +492 +00:54:01,640 --> 00:54:08,040 +أقل من او يساوي F of أربعة ناقص واحد اقل من او + +493 +00:54:08,040 --> 00:54:13,720 +يساوي أربعة في خمسة وعشرينواضيف لي واحد للثلاثة + +494 +00:54:13,720 --> 00:54:21,060 +أطراف بيصير تسعة أقل من أو يساوي ال F of أربعة أقل + +495 +00:54:21,060 --> 00:54:28,340 +من أو يساوي الواحد وعشرين وهو المطلوب ايوة ادي + +496 +00:54:28,340 --> 00:54:33,920 +بالك سؤال زي هذا مرة جيبناه في إحدى الامتحانات + +497 +00:54:33,920 --> 00:54:41,310 +عميلي بدي أسأل ال condition التاني هذاوالله هذا + +498 +00:54:41,310 --> 00:54:45,890 +اللي هنا، ممتاز جدا، طلعلي في أصله في المثلة، + +499 +00:54:45,890 --> 00:54:52,270 +بيقوللي أصله في المثلة إن F prime of X محصورة + +500 +00:54:52,270 --> 00:54:58,650 +دائما بين 2 و 5 لكل ال X اللي موجودة في الفترة من + +501 +00:54:58,650 --> 00:55:03,740 +0 ل4يبقى انا لو جيت على الفترة من zero لاربعة وجبت + +502 +00:55:03,740 --> 00:55:07,180 +المشتقة، المشتقة محصورة بين اتنين وخمسة، يعني + +503 +00:55:07,180 --> 00:55:11,980 +المشتقة exist، راح ولا لا؟ يبقى المشتقة موجودة + +504 +00:55:11,980 --> 00:55:15,580 +خلال الفترة من zero لاربعة، وهو ال condition + +505 +00:55:15,580 --> 00:55:19,390 +التاني من شروط ال main value termأعطانيها + +506 +00:55:19,390 --> 00:55:23,150 +continuous و هي differentiable بسبب تطبيق ال main + +507 +00:55:23,150 --> 00:55:28,450 +value theorem روحنا و طبقنا ال main value theorem + +508 +00:55:28,450 --> 00:55:32,770 +there exists c موجودة في الفترة من 0 ل 4 فهو f + +509 +00:55:32,770 --> 00:55:38,090 +prime of c بيسوي f of b نقص f of a على b مقص ال a + +510 +00:55:38,090 --> 00:55:42,890 +f of 0 معطب 1 شيلته و حطيته 1 4 نقص 0 بيسوي f + +511 +00:55:42,890 --> 00:55:48,330 +prime of cبرجع لل condition المشتقة لكل ال X + +512 +00:55:48,330 --> 00:55:53,470 +الموجودة من صفر لاربع محصورة بين اتنين و خمسة ال C + +513 +00:55:53,470 --> 00:55:58,830 +موجودة في الفترة 0 و 4 اذا F prime of C بيكون + +514 +00:55:58,830 --> 00:56:03,230 +محصورة ما بين اتنين و خمسة لكن ال F prime of C هي + +515 +00:56:03,230 --> 00:56:07,580 +F اربع نقص واحد على اربعبشيلة بحط f of أربعة ناقص + +516 +00:56:07,580 --> 00:56:11,200 +واحد على أربعة محصورة بين اتنين أو خمسة بحل + +517 +00:56:11,200 --> 00:56:15,120 +الانقلاد يصير ال F of أربعة محصورة بين التسعة وما + +518 +00:56:15,120 --> 00:56:21,620 +بين الواحد وعشرين في عندنا بعض النتائج على هذه + +519 +00:56:21,620 --> 00:56:27,140 +النظرية نعطيكم بدل النتيجة تنتين يبقى بالداجة + +520 +00:56:27,140 --> 00:56:30,580 +للنتيجة الأولى لهذه النظرية Crawler one + +521 +00:56:40,560 --> 00:56:51,040 +النتيجة الأولى بقول F F prime of X يساوي Zero at + +522 +00:56:51,040 --> 00:57:06,000 +each point X عند كل نقطة X of an open interval + +523 +00:57:13,040 --> 00:57:25,020 +ثم ال F of X يكون كونستانت C لكل + +524 +00:57:25,020 --> 00:57:33,520 +X الموجودة في الفترة المفتوحة A وB حيث + +525 +00:57:33,520 --> 00:57:37,240 +C هو كونستانت + +526 +00:58:13,710 --> 00:58:19,380 +خلّيني أقولك واحدالسؤال مرة تانية بقول لو كان f + +527 +00:58:19,380 --> 00:58:25,280 +prime of x يساوي 0 عند كل نقطة x في الفترة + +528 +00:58:25,280 --> 00:58:34,080 +المفتوحة a و b then f of x بدي ساوي constant c و + +529 +00:58:34,080 --> 00:58:40,020 +ال c هذه عبارة عن element موجود في الفترة a و b + +530 +00:58:40,020 --> 00:58:46,350 +بنقوله بسيطة جدا تعالى نشوف ال proofيعني الـ + +531 +00:58:46,350 --> 00:58:51,290 +crawler هذه بتقول لو كانت المشتقة لدالة تساوي zero + +532 +00:58:51,290 --> 00:58:56,250 +إذا هذه الدالة تعتبر دالة ثابتة طبعا أنا أخدنا في + +533 +00:58:56,250 --> 00:58:59,290 +ال chapter اللي فات في ال derivatives إن مشتقة + +534 +00:58:59,290 --> 00:59:03,530 +المقنعر ثابت يساوي، هذه بتقول للعكس، لو كانت + +535 +00:59:03,530 --> 00:59:10,330 +المشتقة تساوي zero إذا هذه الدالة دالةطيب تعالى + +536 +00:59:10,330 --> 00:59:16,110 +نشوف يبقى انا عند المشتقة تساوي zero بده احاول ان + +537 +00:59:16,110 --> 00:59:21,350 +هذه المشتقة تساوي مقدارا ثابتا بنقوله بسيطة جدا + +538 +00:59:21,350 --> 00:59:27,690 +يبقى انا بدى استفيدCrollary يعني نتيجة، نتيجة على + +539 +00:59:27,690 --> 00:59:31,970 +مين؟ نتيجة على نظرية ال main value theorem يعني + +540 +00:59:31,970 --> 00:59:36,850 +معناته أنا في البرهان بدي أطبق نظرية ال main value + +541 +00:59:36,850 --> 00:59:41,180 +theoremطبعا من وين لوين انا مش شايف انه closed + +542 +00:59:41,180 --> 00:59:46,220 +interval مش شايف انا هيك تمام فباجي بقوله بدي اطبق + +543 +00:59:46,220 --> 00:59:50,480 +اه بدي اجيب الشروط بحدافيرها الموجودة على الكلام + +544 +00:59:50,480 --> 00:59:55,060 +اللي موجود عندنا هذا بيقول ان المشتقة تساوي zero + +545 +00:59:55,060 --> 01:00:00,840 +عند كل نقطة موجودة في ال open interval ايش يعني + +546 +01:00:00,840 --> 01:00:05,500 +يعني الدلق قابل الاشتقاق على الفترة المفتوحة هذه + +547 +01:00:06,020 --> 01:00:11,580 +يبقى انا اول ما ابدأ بدي اقول اللي افترض عندي x1 و + +548 +01:00:11,580 --> 01:00:20,460 +x2 موجودة في الفترة المفتوحة a و b such that بحيث + +549 +01:00:20,460 --> 01:00:30,340 +ان ال x1 اقل من ال x2 على سبيل المثال اخدت نقطتين + +550 +01:00:30,590 --> 01:00:38,930 +في الفترة المفتوحة بحيث ان ال X1 أقل من X2 يعني ال + +551 +01:00:38,930 --> 01:00:44,530 +X1 و X2 لا بتساوي ال A ولا بتساوي ال B يعني لو جيت + +552 +01:00:44,530 --> 01:00:51,350 +قلت هذا ال real line واخدت هذه A واخدت هذه Bيبقى + +553 +01:00:51,350 --> 01:00:58,210 +اخد هنا x1 واخد هنا x2 واضح ان x1 اقل من ماين من + +554 +01:00:58,210 --> 01:01:05,450 +x2 طب يعني هدول قيمتين لا يمكن ان يتساوي صحيح ولا + +555 +01:01:05,450 --> 01:01:06,010 +لا؟ + +556 +01:01:12,060 --> 01:01:18,300 +إذا أثبت أن قيمة الدالة عند X1 هي نفس قيمة الدالة + +557 +01:01:18,300 --> 01:01:23,690 +عند X2 يبقى هذه دالة ياشيتابع الانكس واحد وانكس + +558 +01:01:23,690 --> 01:01:28,110 +اتنين ليس قيم محددة، أي قيم موجودة في الانكس، + +559 +01:01:28,110 --> 01:01:31,670 +عشوائي أنا أخدتهم، ليس اتنين اتنين بعينهم وفلان + +560 +01:01:31,670 --> 01:01:35,170 +وفلان، لأ زي ما انا اقول انا بدي اخد اي طلاب اتنين + +561 +01:01:35,170 --> 01:01:39,270 +من الصرف، بس لو قلت تعيا محمد انت ابن فلان وانت + +562 +01:01:39,270 --> 01:01:43,670 +تعيا اسلمان، يعني ان انا اخترت اتنين بعينهم يعني، + +563 +01:01:43,670 --> 01:01:46,370 +يبقى هذا لا ينطق على الأخر، بس لو قلت اخدت اي + +564 +01:01:46,370 --> 01:01:49,520 +اتنينفتحنا الباب واخدنا اي اتنين يبقى خلاص اي + +565 +01:01:49,520 --> 01:01:54,060 +اتنين ينطبق عليها كل ما هو في القاعة تمام؟ يبقى + +566 +01:01:54,060 --> 01:01:58,440 +احنا بدنا نيجي هنا بدأ اخد two element X واحد و X + +567 +01:01:58,440 --> 01:02:05,760 +اتنين عشوائيا موجددات واحدفى الفترة اللى عندنا + +568 +01:02:05,760 --> 01:02:09,160 +المفتوحة A وB يعني ماعرفك لما نقول X1 و X2 لا + +569 +01:02:09,160 --> 01:02:15,440 +بتساوي و لا بتساوي B تمام الآن احنا عندنا ال F + +570 +01:02:15,440 --> 01:02:21,720 +prime of X يساوي Zero على الفترة المفتوحة A وB + +571 +01:02:21,720 --> 01:02:29,720 +معناته ايش؟ معناته ان ال F is differentiable on + +572 +01:02:29,720 --> 01:02:38,320 +الفترة المفتوحة A وBصحيح ولا لا؟ طيب سنة شوية بس + +573 +01:02:38,320 --> 01:02:46,520 +هذا معناه ان ال F is differentiable on الفترة + +574 +01:02:46,520 --> 01:02:53,670 +المغلقة X واحد و X اتنينلأن X1 و X2 جزء من الفترة + +575 +01:02:53,670 --> 01:02:58,430 +هذه كلها صحيح ولا لأ يبقى الدالة قابلة اشتقاق على + +576 +01:02:58,430 --> 01:03:03,410 +الفترة مدام قابلة اشتقاق إذا continuous يبقى هذا + +577 +01:03:03,410 --> 01:03:11,610 +يعطينا ان ال F is continuous on the closed + +578 +01:03:11,610 --> 01:03:22,160 +interval X1 و X2and differentiable on الفترة + +579 +01:03:22,160 --> 01:03:30,670 +المفتوحة x1 و x2يعني if a differentiable على اللي + +580 +01:03:30,670 --> 01:03:34,350 +closed مش بتضلها differentiable على اللي أقل منها + +581 +01:03:34,350 --> 01:03:38,010 +مش على الأقل منها وزيادة شوية برا لإنه على كل + +582 +01:03:38,010 --> 01:03:43,090 +الفترة من a إلى b معادة a وb يبقى اتحقق الشرطين + +583 +01:03:43,090 --> 01:03:50,550 +تبعات ال mean value theorem صحيح؟ يبقى هنا ال if + +584 +01:03:50,550 --> 01:03:56,330 +satisfy the hypothesis + +585 +01:03:58,340 --> 01:04:07,740 +of the mean value theorem هذا معناه ايش؟ there + +586 +01:04:07,740 --> 01:04:15,440 +exist c موجودة في الفترة x واحد و x اتنين such + +587 +01:04:15,440 --> 01:04:28,550 +that بحيث ان ifنقص f of x2 نقص f of x1 على x2 نقص + +588 +01:04:28,550 --> 01:04:32,490 +x1 بيسوي f prime of c + +589 +01:04:41,730 --> 01:04:55,800 +فقط فقط فقط فقط فقط فقط فقطزيرو يبقى هذا الكلام + +590 +01:04:55,800 --> 01:05:04,260 +بده يعطينا ان ال F of X2 ناقص F of X1 على X2 ناقص + +591 +01:05:04,260 --> 01:05:12,320 +X1 بده يساوي زيرو ايه السبب؟ because ان ال F prime + +592 +01:05:12,320 --> 01:05:19,280 +of X بده يساوي زيرو على الفترة كلها A وB يعني على + +593 +01:05:19,280 --> 01:05:24,470 +الفترة X1 وX2 بيه جزء منهاطيب مادام زيرو يبقى مين + +594 +01:05:24,470 --> 01:05:29,010 +اللي بيساوي زيرو البصد ولا المقعد؟ يبقى هنا بقوله + +595 +01:05:29,010 --> 01:05:34,770 +سوء ال F of X اتنين من عقص ال F of X واحد بيساوي + +596 +01:05:34,770 --> 01:05:41,680 +زيرو هذا معناته ان ال F of X اتنين بيساوي مين؟الـ + +597 +01:05:41,680 --> 01:05:49,920 +F of X1 لكل الـ X1 والـ X2 اللي موجودة في الفترة + +598 +01:05:49,920 --> 01:05:56,860 +المفتوحة A وB يعني X1 وX2 اي نقطتين ما تفسيرك لهذا + +599 +01:05:56,860 --> 01:06:07,060 +الكلام ان ده ثابت هذا معناه ان الـ F is a constant + +600 +01:06:07,060 --> 01:06:09,480 +function + +601 +01:06:11,380 --> 01:06:20,140 +on الفترة A وB هذا معناه ان ال F of X بدي ساوي + +602 +01:06:20,140 --> 01:06:29,160 +constant C على كل الفترة A وB وهو المطلوب شايف إذا + +603 +01:06:29,160 --> 01:06:34,020 +إلها جران يبقى closed جوهز يبقى مفتوحة في المثلة + +604 +01:06:34,020 --> 01:06:38,000 +فوق جالك open interval مظبوط + +605 +01:06:40,100 --> 01:06:45,580 +تعال هنا شوف تعال خلّي بالكم و أنا يا شباب نشوف مع + +606 +01:06:45,580 --> 01:06:49,220 +رأيه يبقى + +607 +01:06:49,220 --> 01:06:53,260 +F of X اتنين بسوء F of X واحد على كل ال X واحد و X + +608 +01:06:53,260 --> 01:06:56,460 +اتنين الموجودة في ال A و B احنا عاملنا الفترة كده؟ + +609 +01:06:56,460 --> 01:06:59,720 +A و B و X اتنين واحد خد X واحد و X اتنين الموجودة + +610 +01:06:59,720 --> 01:07:05,980 +داخل هذه الفترة يعني ماعنديش لا A ولا B مظبوط هك؟ + +611 +01:07:14,190 --> 01:07:22,390 +أحنا أخدنا X وحدة من X عشوائيا من A وB ممنوع + +612 +01:07:22,390 --> 01:07:27,570 +على الكلام لأنه مش موجود ال A وB من أساسها اه مش + +613 +01:07:27,570 --> 01:07:37,030 +موجودة خلاص طيب في كمان اكرولريه تاني أبسط + +614 +01:07:37,030 --> 01:07:38,470 +منها شوية يعني + +615 +01:07:58,890 --> 01:08:13,430 +عند كل نقطة x in an open interval + +616 +01:08:14,720 --> 01:08:22,240 +بقية مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +617 +01:08:22,240 --> 01:08:27,940 +مفتاح مفتاح مفتاح + +618 +01:08:27,940 --> 01:08:37,700 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +619 +01:08:37,700 --> 01:08:38,080 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +620 +01:08:38,080 --> 01:08:38,220 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +621 +01:08:38,220 --> 01:08:38,220 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +622 +01:08:38,220 --> 01:08:38,220 +مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح + +623 +01:08:38,220 --> 01:08:38,720 +مفتاح مفتاح مفتاح مفتاح مفتاح م + +624 +01:08:43,120 --> 01:08:53,120 +بحيث ان ال F of X يساوي ال G of X زائد constant C + +625 +01:08:53,120 --> 01:09:00,360 +لكل ال X اللي موجودة في الفترة المفتوحة A وB + +626 +01:09:03,790 --> 01:09:20,790 +أي أن الـ F ناقص الـ G is a constant function + +627 +01:09:20,790 --> 01:09:26,070 +on الفترة A وB + +628 +01:09:48,490 --> 01:09:54,750 +معطيني ان مشتقتين لدى اللى بيكونوا متساويتين نعطيك + +629 +01:09:54,750 --> 01:09:59,030 +مثال قبل ما نجي لـ Crawler هذا لو قولتك F of X + +630 +01:09:59,030 --> 01:10:06,390 +يساوي X تكيب كده مشتقتها؟ X تربية لو قولتك F of X + +631 +01:10:06,390 --> 01:10:12,970 +يساوي X تكيب زائد ميةمشتقتة كمان تلاتة إذا + +632 +01:10:12,970 --> 01:10:18,530 +المدلتين هدول مشتقاتهم متساوية، انت قداش الفرق فيه + +633 +01:10:18,530 --> 01:10:23,430 +ما بينهما؟ المية هو مقدار تابع، تمام؟ فالفرق ما + +634 +01:10:23,430 --> 01:10:28,310 +بين الاتنين هذا مقدار تابع، هذا على سبيل المثال + +635 +01:10:28,310 --> 01:10:30,690 +طيب، يبقى برجع تاني + +636 +01:10:34,820 --> 01:10:40,400 +الفرق ما بين الدلتين كان مقدارا ثابتا + +637 +01:10:44,690 --> 01:10:49,290 +each point x in an open interval a وb يبقى + +638 +01:10:49,290 --> 01:10:52,690 +المشتقتان متساويتين على كل نقطة على الفترة + +639 +01:10:52,690 --> 01:10:57,970 +المفتوحة a وb then there exists a constant c لازم + +640 +01:10:57,970 --> 01:11:02,910 +يجي اللاجئ مقدار c بحيث ان ال f of x سوى g of x + +641 +01:11:02,910 --> 01:11:07,680 +زائد c يعني الفرق فيما بينهماهو مقدار ثابت اللي هو + +642 +01:11:07,680 --> 01:11:13,200 +C لكل ال X اللي موجودة في A وB ذاتة ان ال F ناقص G + +643 +01:11:13,200 --> 01:11:17,540 +is a constant function يعني لو جبت هذا على الشجة + +644 +01:11:17,540 --> 01:11:21,600 +تانية بصير الفرق بينهم يسوي C يبقى الفرق بينهم + +645 +01:11:21,600 --> 01:11:27,240 +يسوي مقدارا ثابتا بدنا نروح نثبت صحة هذا الكلام + +646 +01:11:27,240 --> 01:11:36,280 +يبقى أنا عندي هذه المعطياتأول خطوة لت ال f' of x + +647 +01:11:36,280 --> 01:11:42,400 +تساوي g' of x لكل ال x الموجودة في ال open + +648 +01:11:42,400 --> 01:11:50,610 +interval a و bبقدر اخلها معادلة صفرية يبقى ال F + +649 +01:11:50,610 --> 01:11:56,950 +prime of X ناقص G prime of X يساوي كده؟ يساوي Zero + +650 +01:11:56,950 --> 01:12:04,710 +خلّي هذه المعلومة عندك وبدأجي اقول افترض ان ال H + +651 +01:12:04,710 --> 01:12:12,420 +of X بده يساوي ال F of X ناقص ال G of Xبدي افترض + +652 +01:12:12,420 --> 01:12:18,420 +ان عندي دالة هذه الدالة هي الفرق ما بين هتين + +653 +01:12:18,420 --> 01:12:24,660 +الدالتين طب لو جيت و قولت لك اشتق هذه الدالة يبقى + +654 +01:12:24,660 --> 01:12:31,060 +باجي بقوله يبقى ال H prime of X يساوي ال F prime + +655 +01:12:31,060 --> 01:12:39,170 +of X ناقص G prime of Xطب من المعادل اللي فوق يبقى + +656 +01:12:39,170 --> 01:12:45,050 +هذا الكلام إيش بقدر أستنتج منه بقدر أستنتج إن ال H + +657 +01:12:45,050 --> 01:12:52,230 +prime of X يساوي ماين؟ يساوي Zero طلعلي هنا في ال + +658 +01:12:52,230 --> 01:12:57,290 +crawler الأولى لو دلة يساوي Zero إذا هذه الدلة + +659 +01:12:57,290 --> 01:13:05,210 +تساوي مقدارا ثابتا ثم باجي بقوله By crawlerي + +660 +01:13:06,910 --> 01:13:18,230 +when we have ان ال H of X بده يساوي ال C و ال C is + +661 +01:13:18,230 --> 01:13:26,110 +constant يبقى هذا مقدارا ثابتا يبقى سعر عندي ال H + +662 +01:13:26,110 --> 01:13:33,970 +of X بده يساوي اللي انا فرضه كده F of Xماقص الـ g + +663 +01:13:33,970 --> 01:13:39,550 +of x بدي يسوي المقدار الثابت لأن هذا يبقى بناء + +664 +01:13:39,550 --> 01:13:45,890 +عليه هذا بدي يعطيك ان ال f of x بدي يسوي ال g of x + +665 +01:13:45,890 --> 01:13:55,550 +زائد constant c وهو المطلوب هذا معناه ان ال f ماقص + +666 +01:13:55,550 --> 01:14:06,150 +ال g is a constant functionوهو اللي مفروض بقى بيه + +667 +01:14:06,150 --> 01:14:14,270 +كويس نيجوا الآن ايوه نقولك + +668 +01:14:14,270 --> 01:14:19,570 +اثبت ال quarry one و بعدين اثبت التاني يعني مش هيك + +669 +01:14:19,570 --> 01:14:24,350 +والله بضهك يعني نعيد ال quarry one نكتبهن اول و + +670 +01:14:24,350 --> 01:14:31,550 +جديدشوف، إذا طلب دائما و أبدا إثبات جزء يعتمد على + +671 +01:14:31,550 --> 01:14:35,670 +جزء آخر، بيعطيلك نمره إيه يثبتلي الجزء الأول و + +672 +01:14:35,670 --> 01:14:41,690 +بعدين بطلب إثبات الجزء الثاني، ليش صعبي ليه؟ ولا + +673 +01:14:41,690 --> 01:14:48,690 +صعب ولا هادر، بدك تعتبره صعب انت، هذا شأنك + +674 +01:15:04,810 --> 01:15:10,870 +نأخد بعض الأمثلة على الـ two crawlers هذول اللي + +675 +01:15:10,870 --> 01:15:15,890 +عندنا بس قبل ما ناخد الأمثلة خدنا الملاحظة البسيطة + +676 +01:15:15,890 --> 01:15:17,070 +هذه النقطة + +677 +01:15:37,350 --> 01:15:46,010 +الأعلى اتروا صحيحة على الفترة المفتوحة من A إلى + +678 +01:15:46,010 --> 01:15:53,610 +Infinityومن سالب infinity لغاية ال V ان سالب + +679 +01:15:53,610 --> 01:15:56,390 +infinity و infinity + +680 +01:16:44,500 --> 01:16:47,640 +السؤال هو مصطلح + +681 +01:16:50,300 --> 01:17:06,900 +الـ F of X تساوي تلاتة for all X give reasons + +682 +01:17:06,900 --> 01:17:14,860 +for your + +683 +01:17:14,860 --> 01:17:17,160 +answer + +684 +01:17:51,440 --> 01:17:58,420 +نرجع مرة تانية. ايوة. اكيد انه لازم يكون المماث + +685 +01:17:58,420 --> 01:18:01,420 +يكون نقطة من خلالها، يكون مماث واحد، يعني مايكونش + +686 +01:18:01,420 --> 01:18:03,500 +يكون مماث عشان يبقى يجي من خلالها من خلالها، + +687 +01:18:03,500 --> 01:18:08,440 +بالاختران التابع، يعني إذا بنعمل مماث النقطة، + +688 +01:18:08,440 --> 01:18:13,240 +هيقاطع كل النقاط؟ لأ، بصير نفس المماث عند جميع + +689 +01:18:13,240 --> 01:18:21,020 +النقاطوهيحول لنفس الميل مثلا خط أفقي أو خط مائل + +690 +01:18:21,020 --> 01:18:27,730 +سياد، و أين ما يكون الخط بدي سياد نفس الميلكله من + +691 +01:18:27,730 --> 01:18:32,910 +أوله إلى آخره، هذا خط مستقيل نرجع لأسئلتنا مرة + +692 +01:18:32,910 --> 01:18:37,250 +أخرى، يفترض أن قيمة الدالة عند السلب واحد هي + +693 +01:18:37,250 --> 01:18:43,610 +تلاتة، والـF prime of X بدأ يساوي Zero لكل X بلا + +694 +01:18:43,610 --> 01:18:48,380 +استثناءفي الدموعين طبعا تبع الدالة بسهل بقولك must + +695 +01:18:48,380 --> 01:18:54,620 +f of x يسوى تلاتة هل يجب ان ال f of x يسوى تلاتة + +696 +01:18:54,620 --> 01:18:59,520 +for all x يعني يعني هل يتدالى دالة ثابتة وتسوى + +697 +01:18:59,520 --> 01:19:04,680 +تلاتة لجميع قيم x بلا ستناء اعطيني سبب ان كان نعم + +698 +01:19:04,680 --> 01:19:09,820 +لماذا وان كان لأ لماذا نقوله بسيطة جدا احنا عندنا + +699 +01:19:09,820 --> 01:19:16,590 +الان ال f prime of x يسوى zeroصحيح ولا لا؟ + +700 +01:19:16,590 --> 01:19:22,410 +بالكرولري الأولى يبقى F of X ساوي مقدار ثابت يبقى + +701 +01:19:22,410 --> 01:19:34,330 +باجي بقوله هذا بده يعطيلك by the above krolary + +702 +01:19:34,330 --> 01:19:39,530 +when + +703 +01:19:39,530 --> 01:19:51,670 +we haveإن ال F of X بده يساوي مقدارا ثابتا for all + +704 +01:19:51,670 --> 01:20:01,910 +X بلا استثناء where C is constant مين + +705 +01:20:01,910 --> 01:20:04,930 +اللي بيقولي في الامتحان؟ أنت؟ قول تاني + +706 +01:20:09,690 --> 01:20:13,950 +يعني انا لو جالك سؤال زي هيك، مش لازم اقولك اثبت + +707 +01:20:13,950 --> 01:20:17,430 +ال crawler في الأول و بعدين السؤال عليها، هيك اللي + +708 +01:20:17,430 --> 01:20:24,550 +بصير، ولا مانعك بالعرفش نحط امتحانات؟ بسيط، + +709 +01:20:24,550 --> 01:20:29,550 +شوف يا سيدي في وضع الامتحانات، لما يجيبك سؤال و + +710 +01:20:29,550 --> 01:20:33,390 +بدي انحل على شغلة معينة، بقولك اثبتها و بعدين + +711 +01:20:33,390 --> 01:20:38,710 +بعطيك السؤالعليها ومن الخطأ جدا ان نجيب سؤال + +712 +01:20:38,710 --> 01:20:43,110 +بمطلوب ان المطلوب الثاني يعتمد على المطلوب الأول + +713 +01:20:43,110 --> 01:20:46,050 +طب انا ماقدرسش أحل المطلوب الأول بقدر أحل المطلوب + +714 +01:20:46,050 --> 01:20:50,450 +التاني؟ لأ وبالتالي هذا من الخطأ في او في + +715 +01:20:50,450 --> 01:20:54,630 +استراتيجية الخطأ تبع مين تبع الامتحانات اللي ممكن + +716 +01:20:54,630 --> 01:21:00,830 +يقع فيها بعض الناس على أي حال ولا يهمك بنحط + +717 +01:21:00,830 --> 01:21:06,390 +امتحانات قبل أن تليدك أمكوبالتالي مش جديد علينا + +718 +01:21:06,390 --> 01:21:13,950 +هذا طيب نرجع مرة تانية احنا عندنا f prime of x بده + +719 +01:21:13,950 --> 01:21:18,850 +يساوي قداش بده يساوي zero بالكرولري اول وحدة يبقى + +720 +01:21:18,850 --> 01:21:23,250 +ده ال f of x يساوي مقدارا ثابتا لجميع قيم x + +721 +01:21:23,250 --> 01:21:27,340 +بالاستثناءفبرا اندي معلومة، شو المعلومة بتقول؟ + +722 +01:21:27,340 --> 01:21:33,120 +بتقول لي F of سالب واحد بده يساوي تلاتة يبقى الأن + +723 +01:21:33,120 --> 01:21:40,260 +since بما أن F of سالب واحد يساوي تلاتة وأنا جايل + +724 +01:21:40,260 --> 01:21:46,780 +هنا ياشيالـ F of X يسوي مقدار ثابت لكل ال X's بلا + +725 +01:21:46,780 --> 01:21:52,580 +استئناف تمام يبقى من الاتنين هدول مع بعض بقدر + +726 +01:21:52,580 --> 01:22:00,080 +استنتج ان ال F of X بده تسوي تلاتة for all X بلا + +727 +01:22:00,080 --> 01:22:05,680 +استئناف خلصنا؟ يبقى must ولا ما must ايش؟ must + +728 +01:22:09,570 --> 01:22:16,970 +خُد لك كمان مثال يبقى + +729 +01:22:16,970 --> 01:22:27,090 +example two find + +730 +01:22:27,090 --> 01:22:31,370 +the + +731 +01:22:31,370 --> 01:22:36,270 +function f of x + +732 +01:22:40,440 --> 01:22:55,240 +الـ F' of X يسوى تمانية ناقص كوسيكا تربيع X and + +733 +01:22:55,240 --> 01:23:01,740 +the graph and + +734 +01:23:01,740 --> 01:23:09,020 +the graph of دلة F passing + +735 +01:23:15,560 --> 01:23:23,260 +passing through the point يمر + +736 +01:23:23,260 --> 01:23:30,080 +خلال النقطة الى اربعة + +737 +01:23:30,080 --> 01:23:31,720 +وزرع + +738 +01:23:42,980 --> 01:23:47,560 +سؤال مرة تانية بيقولي هاتلي الدالة f of x + +739 +01:23:47,560 --> 01:23:52,240 +المشتقتها بتساوي القيمة اللي عندها دي، يبقى دي + +740 +01:23:52,240 --> 01:23:54,740 +ليست على الكورولة الأولى، الكورولة الأولى بتقول + +741 +01:23:54,740 --> 01:23:59,160 +المشتقة بتساوي جديش، zero هذي قالها لأ بتساوي دالة + +742 +01:23:59,160 --> 01:24:05,410 +تانية، طيب نشوفوالرسم الباني لهذه الدالة اللى احنا + +743 +01:24:05,410 --> 01:24:11,190 +بدنا يمر بالنقطة باية على اربعة وزيره بقولكوا ياسي + +744 +01:24:11,190 --> 01:24:16,150 +يبقى الكرولري الاولى لايمكن ان تحل هذه المثلة يبقى + +745 +01:24:16,150 --> 01:24:20,910 +اللى ممكن يحل المثلة هدميا الكرولري التانية يبقى + +746 +01:24:20,910 --> 01:24:30,510 +انا بدي افترضإن عندي دالة g of x مشتقتها تساوي من؟ + +747 +01:24:30,510 --> 01:24:36,990 +تساوي ال F prime حتى أقدر أطبق من؟ اللي هو التاني + +748 +01:24:36,990 --> 01:24:43,110 +هذي يبقى التماني هذي مشتقت من؟ تمانية X إذا I + +749 +01:24:43,110 --> 01:24:51,680 +تمانية Xوالدالة التانية هذه مشتقت من؟ كتان يبقى + +750 +01:24:51,680 --> 01:24:59,580 +زائد كتان ال X بدي افترض ان عندي دالة مشتقتها + +751 +01:24:59,580 --> 01:25:05,780 +تساوي المشتقة اللي عندها هذا بدي اعطيلهان ال g + +752 +01:25:05,780 --> 01:25:15,060 +prime of x يساوي تمانية ناقص كوسيكا تربيع ال x هذا + +753 +01:25:15,060 --> 01:25:22,980 +بد يعطيك ان ال f prime of x تساوي ال g prime of x + +754 +01:25:22,980 --> 01:25:29,980 +وتساوي تمانية ناقص + +755 +01:25:29,980 --> 01:25:32,480 +كوسيكا تربيع ال x + +756 +01:25:39,670 --> 01:25:46,270 +بتقول لو كان ال F' بده يساوي G' يبقى الفرق في ما + +757 +01:25:46,270 --> 01:25:54,000 +بينهما يساويمقدارا ثابتا، مظبوط؟ يبقى هذا معناه، + +758 +01:25:54,000 --> 01:26:00,960 +معناه ايش؟ لما يكون F' يسوى G' حسب نص انه يبقى + +759 +01:26:00,960 --> 01:26:05,820 +الفرق ما بين الدالتين بديه يسوى مقدارا ثابتا، + +760 +01:26:05,820 --> 01:26:11,440 +ممتاز جدا، يبقى معنى هذا الكلام ان ال F of X ناقص + +761 +01:26:11,440 --> 01:26:17,590 +ال G of Xبدي يساوي كده؟ بدي يساوي مقدارا ثابتا + +762 +01:26:17,590 --> 01:26:25,310 +اللي هو C معناه هذا الكلام ان ال F of X بدي يساوي + +763 +01:26:25,310 --> 01:26:31,230 +ال G of X زائد constant C معناه هذا الكلام ان ال F + +764 +01:26:31,230 --> 01:26:36,710 +of X بدي يساوي ال G of X اللي هي تمانية X زائد + +765 +01:26:36,710 --> 01:26:45,040 +كتانالـ X صحيح ولا لأ؟ زائد كونستانت C يبقى أنا + +766 +01:26:45,040 --> 01:26:50,980 +جبتله شكل ال F of X لكن بدلالة من؟ المتغير C قال + +767 +01:26:50,980 --> 01:26:56,680 +لي إن الدلة المنحنة تبعها يمر بالنقطة بي على أربعة + +768 +01:26:56,680 --> 01:27:02,260 +و زيرو إذا بداجي أعوض في الدلة هذه يبقى هنا باجي + +769 +01:27:02,260 --> 01:27:12,730 +بقوله at اللي هو by أربعة و زيرو we haveالـ F باي + +770 +01:27:12,730 --> 01:27:17,810 +عالى أربعة بده تسوى Zero يبقى Zero بده تسوى تمانية + +771 +01:27:17,810 --> 01:27:24,850 +في باي عالى أربعة زائد كتان باي عالى أربعة زائد + +772 +01:27:24,850 --> 01:27:26,030 +كنص تان C + +773 +01:27:28,800 --> 01:27:35,900 +هذا يصبح اتنين باى وهذا كتان باى على اربع اللي هو + +774 +01:27:35,900 --> 01:27:42,600 +واحد صحيح زائد كونستان سي يساوي كده؟ Zero يبقى + +775 +01:27:42,600 --> 01:27:48,560 +بناء عليه أصبح الكونستان سي يساوي سالب اتنين باى + +776 +01:27:48,560 --> 01:27:49,700 +سالب كده؟ + +777 +01:28:07,620 --> 01:28:13,240 +باقية نقطة أخيرة شباب النقطة الأخيرة حاططها في ال + +778 +01:28:13,240 --> 01:28:17,860 +exercises وليس في الجزء النظري + +779 +01:28:21,430 --> 01:28:28,690 +النقطة هذه حساب الأصفر لدلة ما counting zeros + +780 +01:28:28,690 --> 01:28:35,390 +تمام؟ يبقى هاطلق في صيغة ال remark التالية remark + +781 +01:28:35,390 --> 01:28:40,110 +التي + +782 +01:28:40,110 --> 01:28:45,610 +counting zeros + +783 +01:28:45,610 --> 01:28:56,300 +حساب أصفر دلة بيقول افترضإن ال F ب إيه + +784 +01:28:56,300 --> 01:29:09,100 +continuous ب إيه continuous a function on the + +785 +01:29:09,100 --> 01:29:16,820 +closed interval a و b and differentiable على + +786 +01:29:16,820 --> 01:29:26,760 +الفترة المفتوحة a و bالنقطة الأولى if ال F of A + +787 +01:29:26,760 --> 01:29:40,280 +and ال F of B have opposite signs + +788 +01:29:40,280 --> 01:29:48,360 +إشاراتهم مختلفة and نمر + +789 +01:29:48,360 --> 01:29:59,340 +اتنينالـ F' أكبر من الـ 0 على الفترة المفتوحة A و + +790 +01:29:59,340 --> 01:30:09,300 +B أو الـ F' أقل من الـ 0 على الفترة المفتوحة A و B + +791 +01:30:09,300 --> 01:30:13,760 +فالـ F + +792 +01:30:13,760 --> 01:30:17,900 +لديه بالضبط + +793 +01:30:19,690 --> 01:30:41,630 +بالضبط one zero between a and b example show + +794 +01:30:41,630 --> 01:30:42,630 +that the function + +795 +01:30:50,490 --> 01:30:58,650 +F of X واحد على واحد ناقص X زيدي الجدري التربيعي + +796 +01:30:58,650 --> 01:31:08,490 +لواحد زائد X ناقص تلاتة واحد من عشرة have + +797 +01:31:08,490 --> 01:31:19,190 +one zero على الفترة المفتوحة سالب واحد وواحد + +798 +01:31:48,070 --> 01:31:53,030 +counting zeros يعني حساب أصفار الدالة يعني السؤال + +799 +01:31:53,030 --> 01:31:58,970 +هو اجتاش بوبمان أن الدالة تساوي zero عند نقطة ما + +800 +01:32:00,000 --> 01:32:03,400 +بقول ايش؟ لو كانت الدلة دالة متصلة على الفترة + +801 +01:32:03,400 --> 01:32:09,860 +المغلقة A وB يبقى احنا افترض عندنا function وقولنا + +802 +01:32:09,860 --> 01:32:15,540 +هذا محور X وهذا Y وهذا ال function اللي عندنا وروح + +803 +01:32:15,540 --> 01:32:22,540 +نقولنا على الفترة اللي عندنا Fوهنا من ال B افترض + +804 +01:32:22,540 --> 01:32:29,380 +الدالة دالة كانت متصلة على الفترة A وB وقبل اشتقاق + +805 +01:32:29,380 --> 01:32:35,240 +على الفترة المفتوحة A وB لو كان ال F of A و F of B + +806 +01:32:35,240 --> 01:32:40,920 +of opposite signs يعني إشارتهم مختلفتين يعني واحدة + +807 +01:32:40,920 --> 01:32:47,330 +موجبة والتانيةيبقى رسمي هذا صحيح هيك؟ لأ مش صحيح F + +808 +01:32:47,330 --> 01:32:52,870 +of A هي موجبة و F of B موجبة وقال لأ التنتين of + +809 +01:32:52,870 --> 01:32:58,290 +opposite signs يبقى معنى هذا الكلام بده تكون واحدة + +810 +01:32:58,290 --> 01:33:06,710 +تحت محور X والتانيةأعلى محور X يبقى لو قلنا هذا X + +811 +01:33:06,710 --> 01:33:11,330 +وهذا Y بديجيك المنحنة مثلا بالشكل اللي عندك هنا + +812 +01:33:11,330 --> 01:33:18,770 +خلّي هذه مثلا اللي هو النقطة A وهذه اللي عندك + +813 +01:33:18,770 --> 01:33:26,110 +التانية اللي هي النقطة Bيبقى هذه F of A مالها أقل + +814 +01:33:26,110 --> 01:33:32,890 +من الـ Zero وهنا هذه F of B أكبر من الـ Zero أو + +815 +01:33:32,890 --> 01:33:39,630 +العكس ممكن F of A فوق و F of B تحت سيال ايوة ايش + +816 +01:33:39,630 --> 01:33:44,130 +بيقولي الدالة دالة متاصلة ماشي هي دالة متاصلة + +817 +01:33:44,130 --> 01:33:48,150 +اتنين قابل اشتراك قابل اشتراك ماعنديش لا تصب ولا + +818 +01:33:48,150 --> 01:33:51,910 +كورن ولا vertical tangent ولا discontinuityطيب، + +819 +01:33:51,910 --> 01:33:56,650 +اتنين، الـF of A والـF of B have opposite signs، + +820 +01:33:56,650 --> 01:34:00,190 +إشارتهم مختلفة، يعني واحدة موجبة والتانية، لحظة + +821 +01:34:00,190 --> 01:34:04,730 +الـF of B هي موجبة والـF of A سالبة، اتنين، كان + +822 +01:34:04,730 --> 01:34:10,650 +مشتقت الدالة على الفترة A وB يا إما موجبة دائما + +823 +01:34:10,650 --> 01:34:15,330 +وأبدا، يا إما سالبة دائما، الدالة هذه دالة + +824 +01:34:15,330 --> 01:34:20,650 +تزايدية، صحيح ولا لأ؟ إذا مشتقتها دائما وأبدا، + +825 +01:34:20,650 --> 01:34:25,870 +موجبةلو كانت ذالة تناقصية، بقى مستقلتها سالمة، مش + +826 +01:34:25,870 --> 01:34:31,550 +التان تان في انا الواحد or تعني ان هذه اولت، ان + +827 +01:34:31,550 --> 01:34:39,020 +حدث ذلكيبقى إذا القيمتين هدول متساوية، مختلفتين في + +828 +01:34:39,020 --> 01:34:44,900 +الإشارة، و الدالة دالة زيودية أو دالة نقصية، إذا + +829 +01:34:44,900 --> 01:34:50,920 +غصب عن اللي مايرضى بده تقطع مين؟ محور X، يبقى لما + +830 +01:34:50,920 --> 01:34:54,580 +تقطع محور X عند هذا النقطة، تبقى قيمة الدالة عند + +831 +01:34:54,580 --> 01:35:00,040 +هذا النقطة تساوي كده؟ تساوي Zero، تمام؟يبقى هي + +832 +01:35:00,040 --> 01:35:04,420 +معناها هيك فبيقول ليش ان حدث ذلك يبقى ال F is + +833 +01:35:04,420 --> 01:35:09,300 +exactly one zero between ال A و ال B ال zero هذا + +834 +01:35:09,300 --> 01:35:13,520 +بدرجيني مابين مين؟ مابين ال A و ال B + +835 +01:35:21,960 --> 01:35:31,620 +أخدت ايه؟ Intermediate Value Theorem اه ماقلناش + +836 +01:35:31,620 --> 01:35:36,020 +والله عكس الإشارة ولا جيبنا سيرة تهالي والله يا + +837 +01:35:36,020 --> 01:35:38,480 +حبيبي ال Intermediate Value Theorem قلت لو خدنا + +838 +01:35:38,480 --> 01:35:44,280 +رقم موجود بين ال A وال Bبين ال F of A و ال F of B + +839 +01:35:44,280 --> 01:35:46,960 +بلا جيل و أصل ما بين ال A و ال B هذا ال + +840 +01:35:46,960 --> 01:35:51,240 +intermediate value theorem و ليست هذه مظبوط هذه + +841 +01:35:51,240 --> 01:35:54,620 +بتختلف كليا عن ال intermediate value theorem هذه + +842 +01:35:54,620 --> 01:35:58,820 +بتقول دلدلة متصلة و قابلة الاشتقاء متصلة على + +843 +01:35:58,820 --> 01:36:01,880 +closed interval و قابل اشتقاق على الفترة + +844 +01:36:05,600 --> 01:36:09,080 +يوجد كمان زيادة على ذلك two conditions ال + +845 +01:36:09,080 --> 01:36:12,880 +condition الأولى أن ال F وB وF وB إشارتهم مختلفة + +846 +01:36:12,880 --> 01:36:16,020 +واحدة موجبة واحدة سلبية يعني واحدة فوق محور X + +847 +01:36:16,020 --> 01:36:19,560 +وواحدة تحت محور X كلها متاصلة إذن automatically + +848 +01:36:19,560 --> 01:36:24,320 +هتقطع محور X مصبوط؟ مدام هتقطع هتقطع في نخ موجودة + +849 +01:36:24,320 --> 01:36:28,100 +بين ال A و ال B بمجرد تقطع محور X تقبل قيمة الدالة + +850 +01:36:28,100 --> 01:36:33,200 +عندها تساوي Zero فجالي فإن ال F is exactly one + +851 +01:36:33,200 --> 01:36:37,910 +zero ما بين ال A و ال Bنثبت هذا الكلام عمليا نقول + +852 +01:36:37,910 --> 01:36:41,970 +لو كان موجة نقطة البداية هي نفسها نقطة الموجة + +853 +01:36:41,970 --> 01:36:43,050 +نفسها نقطة الموجة نفسها نقطة الموجة نفسها نقطة + +854 +01:36:43,050 --> 01:36:45,790 +الموجة نفسها نقطة الموجة نفسها نقطة الموجة نفسها + +855 +01:36:45,790 --> 01:36:48,990 +نقطة الموجة نفسها نقطة الموجة نفسها نقطة الموجة + +856 +01:36:48,990 --> 01:36:52,690 +نفسها نقطة الموجة نفسها نقطة الموجة نفسها نقطة + +857 +01:36:52,690 --> 01:36:52,690 +الموجة + +858 +01:36:58,710 --> 01:37:03,130 +بهمنيش، بهمني إنها بدأت تحت و بدأت فوق، بس إنت لما + +859 +01:37:03,130 --> 01:37:07,610 +بده رد عليك عليها شكل موجة، يبقى انت فهذا الشرط + +860 +01:37:07,610 --> 01:37:12,170 +تمام؟ بطلة تزيديها على قول أو تنقصيها على قول، + +861 +01:37:12,170 --> 01:37:16,110 +يبقى أنت صارتش تشتغل ضد الطيار، ماشي؟ احنا بيقول + +862 +01:37:16,110 --> 01:37:20,330 +بتحقق ال conditions في ان و احدلو كان هذا الكلام + +863 +01:37:20,330 --> 01:37:23,630 +صحيح وشيلنا الشرط هذا، بصير مش نقطة، بصير ما شاء + +864 +01:37:23,630 --> 01:37:27,530 +الله عليها نقطة، يعني zeros كتير، مش واحدة، تمام؟ + +865 +01:37:27,530 --> 01:37:31,750 +احنا بيقول، there exists exactly one، بالضبط واحدة + +866 +01:37:31,750 --> 01:37:36,770 +مافيش غيرها، قيمة الدالة عندها تساوي صفر، تمام؟ + +867 +01:37:36,770 --> 01:37:40,010 +طيب، بيقول الشهداء، the function هذي have one zero + +868 +01:37:40,010 --> 01:37:45,560 +في الفترة من سالب واحد إلى واحد،فبجي بقول ال F of + +869 +01:37:45,560 --> 01:37:52,700 +X هذه اللي تساوي واحد على واحد ناقص X زائد الجدرى + +870 +01:37:52,700 --> 01:37:57,280 +التربية على واحد زائد X ثلاثة وواحد من عشرة هذه + +871 +01:37:57,280 --> 01:37:58,920 +الدمين تبعها من وين لوين + +872 +01:38:05,280 --> 01:38:13,660 +يبقى هذه الدالة معرفة + +873 +01:38:13,660 --> 01:38:28,340 +من سالب واحد لواحد كفترة + +874 +01:38:28,340 --> 01:38:34,570 +مفتوحة وليست مغلقةلأن عند الواحد هذه undefined طب + +875 +01:38:34,570 --> 01:38:38,150 +احنا ال main value theorem اول نص اللي بيقولك + +876 +01:38:38,150 --> 01:38:43,010 +closed interval مدام continuous على الفترة دي اذا + +877 +01:38:43,010 --> 01:38:46,770 +انا بدي اخد جزء من هذه الفترة اضمن ال continuity + +878 +01:38:46,770 --> 01:38:53,850 +عليها يبقى بجي بقول الساعة ال F is continuous + +879 +01:38:55,450 --> 01:39:02,530 +أن الفترة المغلقة سالب زيرو تسعة من عشرة لغاية + +880 +01:39:02,530 --> 01:39:07,350 +زيرو تسعة من عشرة مضمون هيك ولا لا؟ اندس سالب واحد + +881 +01:39:07,350 --> 01:39:15,190 +كده؟ اندس سالب واحد؟ احنا بنقولك ها دي ماشي، اندس + +882 +01:39:15,190 --> 01:39:19,490 +سالب واحد مغلق، هاه؟ ولا همك، continuous من اندس + +883 +01:39:19,490 --> 01:39:24,100 +سالب واحد، كلامك مظبوطتمام؟ لكن هاي السبعة تلاقي + +884 +01:39:24,100 --> 01:39:27,580 +السالب واحد والواحد كمان، مش هان تبقى مبسوط خالص، + +885 +01:39:27,580 --> 01:39:32,720 +يبقى من ناقص 9 على 9 اللي هو كفترة مغلقة دالة + +886 +01:39:32,720 --> 01:39:35,600 +continuous عليها، بدي أشوف هال difference أقول + +887 +01:39:35,600 --> 01:39:39,940 +عليها ولا لأ، معناته بدي أروح أشتق، إذا بدي أخد ال + +888 +01:39:39,940 --> 01:39:47,680 +F prime of X يساوي السالب واحد على واحد ناقص X لكل + +889 +01:39:47,680 --> 01:39:52,830 +تقريبيا في مشتقةاللي هو المقدار اللي هو سالب واحد + +890 +01:39:52,830 --> 01:39:56,890 +يبقى بيصير موجب يبقى واحد على واحد نقص اكسل كل + +891 +01:39:56,890 --> 01:40:02,030 +تربية زائد واحد على اتنين الجذر التربية على واحد + +892 +01:40:02,030 --> 01:40:06,590 +زائد اكسل وده كونه مقدار تمت طيب برضه إيش رأيك على + +893 +01:40:06,590 --> 01:40:10,710 +الفترة هذه قابلة للاشتقاق على الفترة المفتوحة ولا + +894 +01:40:10,710 --> 01:40:13,150 +لا؟ يبقى هادى + +895 +01:40:20,140 --> 01:40:25,440 +الفترة المفتوحة سالب واحد و واحد يبقى ال F is + +896 +01:40:25,440 --> 01:40:34,400 +differentiable on سالب زير و تسعة من عشرة و زير و + +897 +01:40:34,400 --> 01:40:39,540 +تسعة من عشرة مش هدول الشرطين تبعات ال mean value + +898 +01:40:39,540 --> 01:40:45,960 +theoremيبقى هما الشرطين اللي انا جايلهم هنا بدي + +899 +01:40:45,960 --> 01:40:51,820 +اجيب له ال F of A و ال F of B يبقى بدي اجيب له ال + +900 +01:40:51,820 --> 01:41:01,700 +F of سالب Zero تسعة من عشرة يعني ال F of سالب تسعة + +901 +01:41:01,700 --> 01:41:06,590 +على عشرةيبقى هذا الكلام دي ثابت داجي على الدالة + +902 +01:41:06,590 --> 01:41:15,190 +الأصلية و اقول واحد على واحد ناقص ناقص تسعة على + +903 +01:41:15,190 --> 01:41:24,590 +عشرة زائد الجذري التربيهي لواحد ناقص تسعة على عشرة + +904 +01:41:25,090 --> 01:41:29,030 +طبعا هي زيد بس احنا مااخدينها بالناقص يبقى ناقص + +905 +01:41:29,030 --> 01:41:35,810 +بعدها ناقص تلاتة واحد من عشرة يبقى هذا الكلام + +906 +01:41:35,810 --> 01:41:44,680 +يساوي هذا بيصير واحد على واحد زائد تسعة على عشرةزي + +907 +01:41:44,680 --> 01:41:50,240 +دي الجذري التربيعي كله على عشرة بيظل عشرة ناقص + +908 +01:41:50,240 --> 01:41:56,320 +تسعة اللي هو بقداش بواحد ناقص تلاتة واحد من عشرة + +909 +01:41:56,320 --> 01:42:03,940 +هذه يا شباب بيصير عشرة على تسعة عشر يبقى هذه عشرة + +910 +01:42:03,940 --> 01:42:12,360 +عشرة عشرةهذه عشرة وعشرة تسعة تطلع على عشرة فوق + +911 +01:42:12,360 --> 01:42:20,980 +وهنا على عشرة تسعة عشر عشرة تسعة عشر زائد اللي هو + +912 +01:42:20,980 --> 01:42:26,980 +عشر تحت الجدر الترميعي ناقص ثلاثة وواحد من عشرة شو + +913 +01:42:26,980 --> 01:42:31,500 +رأيك؟ هذا و هذا ميجيوش واحد صحيح وهذا سالب يبقى + +914 +01:42:31,500 --> 01:42:36,140 +هذه قيمة أقل من ال zero صحيح ولا لا؟ + +915 +01:42:38,820 --> 01:42:46,080 +ماشي يبقى بدنا نيجي ناخد F of 0 9 من 10 بنفس + +916 +01:42:46,080 --> 01:42:56,160 +الطريقةيبقى هذا بدأ يصير F of 9 على 10 ويسوى 1 على + +917 +01:42:56,160 --> 01:43:06,180 +1 ناقص 9 على 10 زائد الجدر التربية ل 1 زائد 9 على + +918 +01:43:06,180 --> 01:43:14,880 +10 ناقص 3 1 من 10 النتيجة تساوي هذا يبقى هنا عشرة + +919 +01:43:14,880 --> 01:43:22,210 +بنقلب فوق بصير عشرةزاد الجذري التربيعي لمين؟ لتسعة + +920 +01:43:22,210 --> 01:43:26,950 +عشرة على عشرة ناقص ثلاثة واحد من عشرة، موجي ابو + +921 +01:43:26,950 --> 01:43:31,520 +الله سالي بقىيبقى أكبر من الـ zero تحقق ال + +922 +01:43:31,520 --> 01:43:36,100 +condition الأول بدنا نيجي ال condition التاني بدى + +923 +01:43:36,100 --> 01:43:42,080 +أشتقها هيشتقناها ال F prime of X يبقى ال F prime + +924 +01:43:42,080 --> 01:43:50,320 +of X بده يسوى واحد على واحد ناقص X الكل تربية زائد + +925 +01:43:50,320 --> 01:43:57,930 +واحد على اتنين الجذر التربية لواحد زائد Xأيش رأيك؟ + +926 +01:43:57,930 --> 01:44:03,270 +هذه عمرها بتاخد قيمة سالبة؟ يبقى هذه أكبر من الـ0 + +927 +01:44:03,270 --> 01:44:11,030 +لكل الـX اللي موجودة سالب 09 و 09 بالشكل اللي + +928 +01:44:11,030 --> 01:44:16,430 +عندنا هنا يبقى اتحقق من ال condition الثاني بدي + +929 +01:44:16,430 --> 01:44:23,710 +بقوله by the above remark + +930 +01:44:25,800 --> 01:44:33,580 +There exists C موجودة في الفترة من سالب واحد إلى + +931 +01:44:33,580 --> 01:44:41,940 +واحد أو انشطة فاقل في الفترة تبعتنا او سالب واحد + +932 +01:44:41,940 --> 01:44:42,640 +وواحد + +933 +01:44:47,560 --> 01:44:57,860 +بحيث أن ال F of C بده ساوي Zero يبقى فى ال F has + +934 +01:44:57,860 --> 01:45:06,360 +one zero on الفترة من سالب واحد إلى واحد وهو + +935 +01:45:06,360 --> 01:45:07,520 +المطلوب + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/M3v3LVuH5Us_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/M3v3LVuH5Us_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..9e8f0a7575924d796b245cad3aa9c08808eaaa77 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/M3v3LVuH5Us_raw.srt @@ -0,0 +1,2796 @@ +1 +00:00:21,290 --> 00:00:25,450 +بسم الله الرحمن الرحيم ننتقل الان الى section + +2 +00:00:25,450 --> 00:00:29,410 +تلاتة اتنين في ال derivative المرة اللى فاتت كنا + +3 +00:00:29,410 --> 00:00:36,150 +بناخد المشتقة عند نقطة واحدة فقط الان بدنا نعممها + +4 +00:00:36,150 --> 00:00:41,590 +عن جميع النقاط اللى الدالة معرفة عليها فباجي بقول + +5 +00:00:41,590 --> 00:00:46,450 +ال derivative as a function المشتقة كدالة يعني + +6 +00:00:46,450 --> 00:00:50,170 +المشتق ال function هذه بتطلع عندنا دالة جديدة + +7 +00:00:50,850 --> 00:00:53,410 +التعريف يقول معناه الـ derivative of the function + +8 +00:00:53,410 --> 00:00:57,950 +f of x with respect to x is the function f prime + +9 +00:00:57,950 --> 00:01:02,950 +of x يبقى المشتقة in general ليس عند نقطة وإنما + +10 +00:01:02,950 --> 00:01:07,310 +على كل ديمان تبع الدالة f بدي أسميه f prime of x + +11 +00:01:07,310 --> 00:01:11,270 +حيث ال f prime of x هي ال limit لما ال h بتروح ل + +12 +00:01:11,270 --> 00:01:14,610 +zero فال f of x زائد ال h تنقص ال f of x على h + +13 +00:01:14,610 --> 00:01:17,910 +المرة الماضية لما كنا بقول المشتقة عند نقطة بجينا + +14 +00:01:17,910 --> 00:01:19,790 +نقول f prime of + +15 +00:01:37,040 --> 00:01:44,450 +بشرط ان ال limit تبقى موجودةالـ domain للـ f' كون + +16 +00:01:44,450 --> 00:01:52,430 +صارت عندي function جديدة f' حصلنا عليها من هذه ال + +17 +00:01:52,430 --> 00:01:57,110 +limit إذا هذه الدالة جديدة لها domain، بدي أعرف شو + +18 +00:01:57,110 --> 00:02:01,390 +ال domain تبعها، فال domain تبع ال f' هو نفس ال + +19 +00:02:01,390 --> 00:02:05,900 +domain تبع الدالة f بس بدي أشيل منه النقاطاللي + +20 +00:02:05,900 --> 00:02:09,820 +بتخلّي ال limit هذه مالها does not exist يعني إذا + +21 +00:02:09,820 --> 00:02:13,320 +في إن عندي نقطة أو نقطتين أو تلاتة بيخلّي المشتقة + +22 +00:02:13,320 --> 00:02:17,420 +غير معرفة بدي أشيلهم من domain ده ال F وإذا مافيش + +23 +00:02:17,420 --> 00:02:21,060 +عندي ولا نقطة بيشيل domain ال F prime هو من؟ + +24 +00:02:24,230 --> 00:02:29,490 +النقطة التالية لو كانت الدالة مشتقتها موجودة عند + +25 +00:02:29,490 --> 00:02:34,090 +النقطة X تساوي ايه يبقى بروح بقول ان ال F is + +26 +00:02:34,090 --> 00:02:38,830 +differentiable عند النقطة X يساوي ايه دي ايضا بال + +27 +00:02:38,830 --> 00:02:42,230 +F اختصار لكلمة differentiable + +28 +00:02:50,320 --> 00:02:55,320 +Differentiable قابل الاشتقاق بختصرها الى DIW يبقى + +29 +00:02:55,320 --> 00:03:00,360 +بقول ان الدالة قابل الاشتقاق عند النقطة X يساوي A + +30 +00:03:00,360 --> 00:03:05,260 +النقطة البعدة لو المشتقة تبع الدالة F exist عند كل + +31 +00:03:05,260 --> 00:03:10,340 +نقطة في دمينها يبقى بقول ان الدالة differentiable + +32 +00:03:10,340 --> 00:03:15,830 +على الدمين تبعها كلهبش بدنا نرمز المشتقة بأحد + +33 +00:03:15,830 --> 00:03:20,650 +الرموز التالية، يا إما f prime of x، يا إما dy على + +34 +00:03:20,650 --> 00:03:27,830 +dx، يا إما df على dx، يا إما dx لدالف، dx هذا يعني + +35 +00:03:27,830 --> 00:03:33,830 +d على dx، بعض الكتب تعطيها الرمز لأن هذا يا إما ال + +36 +00:03:33,830 --> 00:03:36,350 +y prime، لكن الرموز لدرجة + +37 +00:03:41,640 --> 00:03:46,440 +الرمز الأخر الرمز الأول الرمز التاني هذه هي الرموز + +38 +00:03:46,440 --> 00:03:50,360 +الدارجة في الغالب لكن لو فتحت أي كتاب كالقلص و + +39 +00:03:50,360 --> 00:03:54,380 +لاقيت الرمز هذا من حد ما تشوفه هذا رمز يدل المشتقة + +40 +00:03:54,380 --> 00:04:00,160 +الأولى لدالة Fطيب لو دي F على دي X بدي أحسبها عند + +41 +00:04:00,160 --> 00:04:06,420 +نقطة X يساوي A يبقى بيعطيها الرمز التالي F prime + +42 +00:04:06,420 --> 00:04:12,680 +of A يا إما دي F على دي X عند X يساوي A يا إما دي + +43 +00:04:12,680 --> 00:04:17,960 +Y على دي X عند X يساوي من؟ يساوي Aلأن النقطة + +44 +00:04:17,960 --> 00:04:21,600 +الأخيرة التعريف اللي فوق هذا بدي أعيد صياغته + +45 +00:04:21,600 --> 00:04:28,860 +بطريقة أخرى فبجي بقول هنا لو حطنا z تساوي x زائد h + +46 +00:04:28,860 --> 00:04:32,980 +في التعريف اللي فوق يبقى بدي أعرف التعريف اللي فوق + +47 +00:04:32,980 --> 00:04:37,760 +شو بدي يكون شكله نظرا لوجود ال H عندي من هنا بدي + +48 +00:04:37,760 --> 00:04:43,240 +أجيب ال H يبقى ال H هتساوي zنقص ال X يبقى ال H + +49 +00:04:43,240 --> 00:04:48,000 +تساوي Z نقص ال X وبالتالي التعريف اللي فوق هيأخد + +50 +00:04:48,000 --> 00:04:54,540 +الشكل التالي ال F prime of X يساوي limit ال H اللي + +51 +00:04:54,540 --> 00:04:58,700 +عندها ده بده يشيله ويحط متى ليه ال Z نقص X بده + +52 +00:04:58,700 --> 00:05:04,220 +يروح لوين ل Zero X زاد H اللي هي ب Z F of X زي ما + +53 +00:05:04,220 --> 00:05:09,550 +هي H اللي هي Z نقص ال Xيبقى التعريف اللى فوق هنا + +54 +00:05:09,550 --> 00:05:14,770 +هو نفس التعريف اللى تحته بس غير شكل مين الرموز او + +55 +00:05:14,770 --> 00:05:19,690 +بمعنى اخر هنا لو اضفت X للطرفين بصير ال Z بدأ تروح + +56 +00:05:19,690 --> 00:05:25,050 +لمين؟ لل X يبقى بصير التعريف ال F prime of X هو ال + +57 +00:05:25,050 --> 00:05:30,110 +limitلما Z بدأ تروح لل X لل F of Z ناقص ال F of X + +58 +00:05:30,110 --> 00:05:38,630 +على Z ناقص ال X يعني أصبح عندي شكلاني للتعريف هذا + +59 +00:05:38,630 --> 00:05:44,110 +هو الشكل الأول المشتقة عند أي نقطة وهذا كمان تعريف + +60 +00:05:44,110 --> 00:05:49,550 +المشتقة عند أي نقطة والاتنين هدول are equivalent + +61 +00:05:49,800 --> 00:05:54,720 +استخدم المناسب بالنسبة لك و كله هيعطيني نفس + +62 +00:05:54,720 --> 00:05:58,940 +النتيجة سواء استخدمت الصيغة اللى فوق او الصيغة + +63 +00:05:58,940 --> 00:06:04,000 +اللى تحت الاتنين are the same نبدأ ناخد اول مثال + +64 +00:06:04,000 --> 00:06:08,000 +من هذه الأمثلة كتطبيق على الكلام اللى احنا قلناه + +65 +00:06:08,000 --> 00:06:13,020 +هنابقول لو كانت ده ال F of X يساوي واحد ناقص X على + +66 +00:06:13,020 --> 00:06:17,240 +اتنين X بدنا نوجد شغل تاني بدنا نوجد المشتقة عند + +67 +00:06:17,240 --> 00:06:22,820 +اي لحظة او عند اي نقطة بعدين بدي اجيب المشتقة عند + +68 +00:06:22,820 --> 00:06:29,190 +X يساوي سالم واحدطيب يبقى انا بتروح هطبق التعريف + +69 +00:06:29,190 --> 00:06:32,610 +الأول على سبيل المثال طبعا هطبق مرة التعريف الأول + +70 +00:06:32,610 --> 00:06:36,890 +و مرة التعريف الثاني عشان نعرف كيف نستخدم هذا + +71 +00:06:36,890 --> 00:06:42,130 +التعريف يبقى لو بده اجي لل F prime of X هذا ال + +72 +00:06:42,130 --> 00:06:47,590 +limit لما ال H بده تروح لل zero لل F of X زائد ال + +73 +00:06:47,590 --> 00:06:53,690 +H نقص ال F of X على H يبقى ال limit لما ال H بده + +74 +00:06:53,690 --> 00:06:59,380 +تروح لل zero تمام؟يبقى بيقول F of X زائد H يبقى + +75 +00:06:59,380 --> 00:07:05,940 +بدي أشيل كل X هنا و أحط مكانها X زائد الـH يبقى + +76 +00:07:05,940 --> 00:07:14,420 +بيصير واحد ناقص X زائد الـH على الإتنين في X زائد + +77 +00:07:14,420 --> 00:07:21,970 +الـH ناقص F of X كما هيعلى اتنين X وكل هذا مقصوما + +78 +00:07:21,970 --> 00:07:27,430 +على مين؟ مقصوما على H يبقى هذا الكلام بده يساوي ال + +79 +00:07:27,430 --> 00:07:33,780 +limit لما ال H بدها تروح لل zeroبتوحد المقامات + +80 +00:07:33,780 --> 00:07:39,400 +لدالة اللي فوق، الاتنين مشترك في ما بينهما، ال X + +81 +00:07:39,400 --> 00:07:44,820 +مافيش غيرها، ال X زائد ال H مافيش غيرها، يبقى وحدة + +82 +00:07:44,820 --> 00:07:49,900 +المقامات بالنسبة للبسط، لو جسمت المقدار هذا على + +83 +00:07:49,900 --> 00:07:55,600 +المقدار هذا بيظل كدهش؟بيبقى X فقط لا غير يبقى هذا + +84 +00:07:55,600 --> 00:08:02,880 +عبارة عن X في واحد ناقص X ناقص H وصلنا للناقص اللي + +85 +00:08:02,880 --> 00:08:07,180 +عندنا هذه بدنا نجسم هذا المقدار على هذا بيبقى + +86 +00:08:07,180 --> 00:08:17,720 +لاندي قداش X زائد H مضربة في من؟ في الواحد ناقص X + +87 +00:08:18,450 --> 00:08:22,570 +يبقى قالة ال limit اللي عندي إلى الشكل التالي هي + +88 +00:08:22,570 --> 00:08:29,450 +limit لما ال H بدها تروح لل zero وهذا ال H وهذا 2X + +89 +00:08:29,450 --> 00:08:35,850 +هتنزل في المقام وهذا ال X زائد ال Hوالبسط بيصير x + +90 +00:08:35,850 --> 00:08:43,430 +ناقص x تربية ناقص hx فكيت الجوث الأول بدي افك + +91 +00:08:43,430 --> 00:08:50,630 +الجوث التاني يبقى هنا ناقص x ناقص فناقص بزايد x + +92 +00:08:50,630 --> 00:09:00,490 +تربية بعدها ناقص h ناقص فناقص بزايد hxهذا الكلام + +93 +00:09:00,490 --> 00:09:06,790 +بده يساوي limit لما ال H بدها تروح ل zero تعالى + +94 +00:09:06,790 --> 00:09:11,690 +هنا عندى اللي هو سالب X تربيه وموجب X تربيه مع + +95 +00:09:11,690 --> 00:09:18,890 +السلامة سالب H X وموجب H X موجب ال X وسالب X مع + +96 +00:09:18,890 --> 00:09:25,330 +السلامة لم يبقى عندى إلا من سالب H في البصد يبقى + +97 +00:09:25,330 --> 00:09:33,900 +هاي سالب Hالمقام H في 2X X زائد الـH نختصر الـH مع + +98 +00:09:33,900 --> 00:09:39,480 +الـH كذلك يبقى النتيجة limit لما الـH بدأ تروح + +99 +00:09:39,480 --> 00:09:50,300 +للـ0 ل-1 على 2X X زائد الـHبص مقدار ثابت يبقى + +100 +00:09:50,300 --> 00:09:55,820 +نهاية المقدار الثابت بالمقدار الثابت itself الان + +101 +00:09:55,820 --> 00:10:01,380 +هذا ليهاش X ليهاش دلع يبقى 2X اللي بين قوسين + +102 +00:10:01,380 --> 00:10:05,560 +polynomial من الدرجة الأولى يبقى تعويض مباشر عن H + +103 +00:10:05,560 --> 00:10:14,140 +ب0 يبقى لدي كده X يبقى النتيجة سالب 1 على 2X تربيع + +104 +00:10:14,140 --> 00:10:20,120 +هذا مقدار مشتقة الدلعيبقى ال F prime of X يبقى + +105 +00:10:20,120 --> 00:10:27,400 +يسوى واحد على اتنين X تربية طيب هذا اللي هو + +106 +00:10:27,400 --> 00:10:31,720 +المطلوب الأول كل اللي اشتغلنا من البداية هذا كان + +107 +00:10:31,720 --> 00:10:37,260 +نمرة A بداجي الألة نمرة B نمرة B قال يحسب لمقدار + +108 +00:10:37,260 --> 00:10:42,740 +هذه المشتقع ال main and سالب واحد إذا باجي بقوله F + +109 +00:10:42,740 --> 00:10:48,920 +prime of سالب واحد يسوىالمشتقة موجودة هي في prime + +110 +00:10:48,920 --> 00:10:52,780 +of X يساوي النتيجة هذه يبقى ما علي اللي أشيل ال X + +111 +00:10:52,780 --> 00:10:57,640 +و أحط مكانها سالب واحد يبقى ايه سالب واحد على + +112 +00:10:57,640 --> 00:11:03,940 +اتنين في سالب واحد تربيع يبقى الجواب قداش سالب نص + +113 +00:11:03,940 --> 00:11:09,920 +يبقى قيمة المشتقة عند السالب واحد تساوي قداش تساوي + +114 +00:11:09,920 --> 00:11:21,470 +سالب نصروح ناخد كمان مثال اخر مثال + +115 +00:11:21,470 --> 00:11:30,410 +رقم اتنين بيقول ف ال F of X يسوي جذر ال X + +116 +00:11:33,320 --> 00:11:42,560 +أول جدلنا اللي هو ال F prime of X and ال F prime + +117 +00:11:42,560 --> 00:11:44,560 +of 81 + +118 +00:11:48,580 --> 00:11:55,780 +يبقى بدنا من؟ بدنا الـ F' of X والـ F' of 1.80 + +119 +00:11:55,780 --> 00:12:01,120 +بقوله كويس يبقى بدنا نيجي نطبق التعريف تبع الـ F' + +120 +00:12:01,520 --> 00:12:05,160 +of X بعدين بقوله solution + +121 +00:12:14,670 --> 00:12:21,330 +حسب التعريف بدأ أزال كل X و أكتب مكانها X زائد H + +122 +00:12:21,330 --> 00:12:27,790 +في الدالة المعرفة يبقى الجذر التربيعي لل X زائد H + +123 +00:12:27,790 --> 00:12:35,310 +ناقص ال F of X اللي هو جذر ال X على H لما ال H بدأ + +124 +00:12:35,310 --> 00:12:40,820 +تروح لل Zeroتعويض المباشر هجيبلي Zero على Zero كون + +125 +00:12:40,820 --> 00:12:46,680 +عندي جذور اذا هروح عشان اضرب في المرافق يبقى هذا + +126 +00:12:46,680 --> 00:12:52,260 +الكلام لو ضربته بدي اضربه في جذر التربية ل X زائد + +127 +00:12:52,260 --> 00:12:59,800 +ال H زائد جذر ال X و اقسم على جذر ال X زائد ال H + +128 +00:12:59,800 --> 00:13:04,880 +زائد جذر ال X بالشكل اللي عندنا هذا + +129 +00:13:26,510 --> 00:13:32,630 +يبقى آلة المثل للشكل التالي f prime of x يسوى ال + +130 +00:13:32,630 --> 00:13:38,550 +limit لما ال h بدها تروح لمين لزرع ال bus هو الفرق + +131 +00:13:38,550 --> 00:13:42,910 +بين المربعين يبقى مربع الأولى ناقص مربع الثانية + +132 +00:13:42,910 --> 00:13:49,130 +مربع الأولى هو ال x زائد ال h ناقص ال x هذا اللي + +133 +00:13:49,130 --> 00:13:54,990 +هو ال bus على المقام h في الجدر التربية ل x زائد + +134 +00:13:54,990 --> 00:14:01,720 +ال hزائد جذر الـ X سالب H وموجة بـ H مع السلامة + +135 +00:14:01,720 --> 00:14:06,700 +يبقى ألت المسألة limit لما الـ H بدأ تروح للـ Zero + +136 +00:14:06,700 --> 00:14:13,840 +للـ H على H في الجذر التربية لـ X زائد الـ H زائد + +137 +00:14:13,840 --> 00:14:18,760 +جذر الـ X برضه الـ H مع الـ H اللي ساعد عليها يبقى + +138 +00:14:18,760 --> 00:14:24,260 +ألت إلى limitلما الـH بدها تروح لمين؟ للـ0 + +139 +00:14:24,260 --> 00:14:29,640 +للـfunction اللي عندنا واحد على الجذر التربية لـX + +140 +00:14:29,640 --> 00:14:35,540 +زائد H زائد جذر الـX لما الـH بدها تروح لـ0 يبقى + +141 +00:14:35,540 --> 00:14:42,280 +الterm هذا بروح لوين؟ للـ0 يبقى واحد على جذر الـX + +142 +00:14:42,280 --> 00:14:48,040 +زائد جذر الـX يبقى واحد على مين؟ على الاتنين جذر + +143 +00:14:48,040 --> 00:14:54,770 +الـXطب ليش احنا جيبنا هذا السؤال؟ جيبناه متعمدين؟ + +144 +00:14:54,770 --> 00:15:01,770 +ليش؟ بديك تعرف من الآن فصاعدا ان مشتقة جذر ال X هي + +145 +00:15:01,770 --> 00:15:07,630 +عبارة عن واحد على اتنين جذر ال X، من الآن فصاعدا، + +146 +00:15:07,630 --> 00:15:13,260 +اتنينلو كان الجذر هذا polynomial من الدرجة الأولى + +147 +00:15:13,260 --> 00:15:19,200 +ومعامل X هو الواحد الصحيح زي جذر X زي عشرة جذر X + +148 +00:15:19,200 --> 00:15:23,900 +ناقص خمسين شو مشتقته؟ برضه واحد على اتنين نفس + +149 +00:15:23,900 --> 00:15:29,910 +الجذر لكن لو كان المعامل تبع X فيه رقمطبق اللي + +150 +00:15:29,910 --> 00:15:34,250 +قعدت السلسلة لسه بدي اضرب في هذا الرقم يبقى انسى + +151 +00:15:34,250 --> 00:15:39,110 +لسه ماخدناش قاعدة السلسلة تمام او chain rule يبقى + +152 +00:15:39,110 --> 00:15:44,310 +احنا بس بنقولك لو كان عندك جدر والمعامل تبعك هو + +153 +00:15:44,310 --> 00:15:50,020 +الواحد الصحيح يبقى مشتقته واحد على اتنين الجدرإذا + +154 +00:15:50,020 --> 00:15:54,540 +بلزمش إنه نعمل خطوات هذه إنه نعمل خطوات حتى نصل + +155 +00:15:54,540 --> 00:15:57,640 +للقانون هذا لكن لو جابلك هذا السؤال في الامتحان + +156 +00:15:57,640 --> 00:16:02,240 +ماكنتش تشتغل الشغلات هذه مظبوط لكن هذا إذا كان + +157 +00:16:02,240 --> 00:16:06,520 +قالك بالتعريف لكن ماقالش لك التعريف تكتبوا أتنين + +158 +00:16:06,520 --> 00:16:12,010 +جدر ال X ليش؟ لأن جدر ال X هذي أصلا X أص نصمش تقتل + +159 +00:16:12,010 --> 00:16:16,190 +انا اخدها المرة الجاية نص اكس نص ناقص نص يعني واحد + +160 +00:16:16,190 --> 00:16:20,110 +ع اتنين جدر ال X مصبوح وبالتالي بصير القصة + +161 +00:16:20,110 --> 00:16:23,750 +retrieval بس لشان التعريف يبقى روحنا اشتغلنا ببين + +162 +00:16:23,750 --> 00:16:29,030 +بالتعريف المطلوب الثاني بدنا ال F prime of واحد و + +163 +00:16:29,030 --> 00:16:34,540 +تمانينيبقى هذا الكلام واحد على اتنين الجذر التربيه + +164 +00:16:34,540 --> 00:16:39,020 +الواحد والتمانين واحد على اتنين في تسعة يبقى جداش + +165 +00:16:39,020 --> 00:16:46,800 +واحد على تمانتاشر مقدار المشتقة الأولى نعطي كمان + +166 +00:16:46,800 --> 00:16:51,600 +مثال على التعريف الثاني او على استخدام التعريف + +167 +00:16:51,600 --> 00:16:54,320 +الثاني يبقى example تلاتة + +168 +00:16:59,430 --> 00:17:02,450 +أمثلة تلاتة بيقول use the formula + +169 +00:17:07,230 --> 00:17:13,810 +استخدم الصيغة اللي هي ال F prime of X يسوي ال + +170 +00:17:13,810 --> 00:17:22,570 +limit لما Z بدها تروح لل X لل F of Z ناقص ال F of + +171 +00:17:22,570 --> 00:17:31,390 +X على Z ناقص ال X to find لإيجاد + +172 +00:17:33,470 --> 00:17:43,610 +f prime of x for the function little for the + +173 +00:17:43,610 --> 00:17:52,870 +function f of x يساوي x تربية ناقص ثلاثة x زائد + +174 +00:17:52,870 --> 00:17:59,330 +أربعة زائد أربعة and find + +175 +00:18:10,320 --> 00:18:12,240 +يساوي اتنين + +176 +00:18:41,940 --> 00:18:50,080 +بقول استخدم الصيرة الثانية للتعريف to find المشتقة + +177 +00:18:50,080 --> 00:18:55,320 +الأولى للدالة f للدالة f of x ساوي x تربية ناقص 3x + +178 +00:18:55,320 --> 00:19:01,540 +زات 4 ومن ثم هات لمعادلة المماثل المنحنةعند النقطة + +179 +00:19:01,540 --> 00:19:06,880 +x سواء من اتنين يبقى هنا قيدني بمن بالتعريف الثاني + +180 +00:19:06,880 --> 00:19:10,500 +لو ما قيدنيش يبقى ايه للخيار يا بيستخدم الصيغة + +181 +00:19:10,500 --> 00:19:15,300 +الأولى يا بيستخدم من الصيغة الثانية سيان يبقى باجي + +182 +00:19:15,300 --> 00:19:23,100 +بقولهالـ f prime of x اللي هي عبارة عن main اللي + +183 +00:19:23,100 --> 00:19:27,920 +هو ال limit اللي جال عليها دي يبقى limit لما z بدأ + +184 +00:19:27,920 --> 00:19:37,300 +تروح لل x لل f of z ناقص ال f of x كله على z ناقص + +185 +00:19:37,300 --> 00:19:44,030 +ال xهذا الكلام بده يساوي ال limit لما Z بدها تروح + +186 +00:19:44,030 --> 00:19:49,070 +لل X F of Z معناته بده يجي على الدالة دي و استبدل + +187 +00:19:49,070 --> 00:19:57,420 +المتغير X بالمتغير Z يبقى بصير Z تربيعنقص تلاتة Z + +188 +00:19:57,420 --> 00:20:04,060 +زائد أربعة ناقص ال F of X الدالة كما هي X تربية + +189 +00:20:04,060 --> 00:20:12,740 +ناقص تلاتة X زائد أربعة كله على مين على Z ناقص ال + +190 +00:20:12,740 --> 00:20:20,510 +Xهذا الكلام بده يساوي ال f prime of x بده يساوي ال + +191 +00:20:20,510 --> 00:20:29,010 +limit لما z بدها تروح لل x ل z تربيع ناقص تلاتة z + +192 +00:20:29,010 --> 00:20:35,110 +زائد أربعةبدا افك الجوس اللى فوق يبقى ناقص X تربية + +193 +00:20:35,110 --> 00:20:43,570 +زائد تلاتة X ناقص أربعة على Z ناقص ال X زائد أربعة + +194 +00:20:43,570 --> 00:20:47,950 +وناقص أربعة مافيش غيرهم اكثر من هيك اختصارات + +195 +00:20:47,950 --> 00:20:54,410 +مباشرة ماعنديش لكن ممكن احنا نروح نخلق اختصارات + +196 +00:20:54,410 --> 00:21:01,670 +اخرى كيف؟طلعلي لـ Z تربية وناقص X تربية هذي بدأ + +197 +00:21:01,670 --> 00:21:07,910 +أخدهم مع بعض يبقى هذي بصير Z تربية ناقص X تربية + +198 +00:21:07,910 --> 00:21:14,430 +بضل عندى ناقص تلاتة Z وزائد تلاتة X يعني ممكن أخد + +199 +00:21:14,430 --> 00:21:20,670 +ناقص تلاتة عامل مشترك يبقى هذي ناقص تلاتة عامل + +200 +00:21:20,670 --> 00:21:28,740 +مشترك بضل عندى مين؟زد ناقص ال X يبقى زد ناقص ال X + +201 +00:21:28,740 --> 00:21:35,760 +كله على زد ناقص ال X هذا الكلام بده يساوي يبقى ال + +202 +00:21:35,760 --> 00:21:41,540 +F prime of X يساوي هذا بده يروح أحلله الفرق بين + +203 +00:21:41,540 --> 00:21:51,980 +المربعين يبقى هاي Zناقص x في z زائد x ناقص ثلاثة + +204 +00:21:51,980 --> 00:21:58,260 +في z ناقص x على z ناقص ال x + +205 +00:22:01,430 --> 00:22:07,690 +يساوي واضح ان Z ناقص X ممكن اخدها عامل مشترك من + +206 +00:22:07,690 --> 00:22:13,070 +الطرفين يبقى هذا Z ناقص X + +207 +00:22:16,180 --> 00:22:26,020 +زائد X ناقص ثلاثة كله على مين؟ على Z ناقص X وهذا + +208 +00:22:26,020 --> 00:22:32,820 +بدي أخدله ال limit لما Z بديها تروح لمين؟ لل Xيبقى + +209 +00:22:32,820 --> 00:22:38,440 +النتيجة هذا الجوز هيروح مع مين؟ مع المقام وتصفى ال + +210 +00:22:38,440 --> 00:22:45,000 +limit على الشكل التالي limit لما z بدها تروح لل x + +211 +00:22:45,000 --> 00:22:54,280 +ل z ناقص x ناقص تلاتة يبقى أصبحت ال f prime of x + +212 +00:22:54,280 --> 00:23:02,140 +يساويزد زائد ال X ناقص ثلاثة لما زد بدأ تروح لل X + +213 +00:23:02,140 --> 00:23:07,220 +يعني معناته بده يشيل كل زد ويعود معناه ب X ليش؟ + +214 +00:23:07,220 --> 00:23:15,000 +لأن هذه دالة خطية يبقى بصير عندي X زائد ال X ناقص + +215 +00:23:15,000 --> 00:23:21,940 +ثلاثة يعني اتنين X ناقص ثلاثة هذه مشتقة تمين + +216 +00:23:21,940 --> 00:23:26,500 +الدالة اللي عنها طب المشتقة هذه عبارة عن إيش؟ + +217 +00:23:27,310 --> 00:23:33,790 +السلوب ممتاز، السلوب تبع من؟ التانجنت عند أي لحظة + +218 +00:23:33,790 --> 00:23:42,270 +يبقى هذه في نفس الوقت بدها تساوي السلوب of the + +219 +00:23:42,270 --> 00:23:50,980 +tangent عند أي x في دمين الدالة اللي عندهاهو راح + +220 +00:23:50,980 --> 00:23:56,200 +ايش قال لي قال لي هاتلي ال tangent عند x يساوي + +221 +00:23:56,200 --> 00:24:01,140 +تمام عشان اجيب له المماس بدي x node و y node يعني + +222 +00:24:01,140 --> 00:24:06,260 +بدي احداثي نقطة يكمل هو ماعطاني x وماعطانيش mainY + +223 +00:24:06,260 --> 00:24:13,000 +أو ماعطانيش F أو V2 لذلك بروح أخدله من ال F أو V2 + +224 +00:24:13,000 --> 00:24:20,100 +F أو V2 بترجح اتعود في الدلة الأصلية يبقى 2 تربية + +225 +00:24:20,100 --> 00:24:28,240 +ناقص 3 في 2 زائد 4 Y يساوي 8 ناقص 6 يساوي 2 يبقى + +226 +00:24:28,240 --> 00:24:38,890 +بناء عليه أصبحت the point ofTangency as X node وY + +227 +00:24:38,890 --> 00:24:46,170 +node بدها تساوي 2 و2 ال X بتنين طلعت Y بتنين كذلك + +228 +00:24:46,170 --> 00:24:58,970 +اذا باجي بقوله the equation of the tangent as ال Y + +229 +00:24:58,970 --> 00:25:05,230 +يساوي ال middleفي الـ X ناقص الـ X node زائد الـ Y + +230 +00:25:05,230 --> 00:25:10,550 +node إذا مشان أجيب معادلة المماس للمنحنة بدي + +231 +00:25:10,550 --> 00:25:16,770 +شغلتين بدي ميل الماس المماس للمنحنة اتنين بدي + +232 +00:25:16,770 --> 00:25:24,010 +إحداث نقطة واقع عليه إحداث النقطة موجودالمين المين + +233 +00:25:24,010 --> 00:25:31,570 +ممكن اجيبه من وين من هنا and ال f prime of اتنين + +234 +00:25:31,570 --> 00:25:37,950 +يساوي اتنين في اتنين ناقص تلاتة اللي هو قداش واحد + +235 +00:25:37,950 --> 00:25:44,150 +يبقى هذا ال slope of the tangent صار قداش صار واحد + +236 +00:25:44,150 --> 00:25:50,070 +يبقى بناء ان عليه بدي يصير y يساوي واحد في ال x + +237 +00:25:50,070 --> 00:25:52,110 +ناقص اتنين زائد + +238 +00:26:11,300 --> 00:26:19,200 +تعريف جديد يقول ما يأتي Definition + +239 +00:26:29,160 --> 00:26:40,100 +فترة مفتوحة على فترة + +240 +00:26:40,100 --> 00:26:47,680 +مفتوحة if it has a derivative + +241 +00:26:58,110 --> 00:27:08,550 +عند كل نقطة موجودة + +242 +00:27:08,550 --> 00:27:10,530 +في هذه الفترة + +243 +00:27:12,990 --> 00:27:16,710 +زي ما أخدنا الاشتراك على فترة مفتوحة، فبناخد + +244 +00:27:16,710 --> 00:27:22,030 +الاشتراك على فترة مغلقة يبقى definition the + +245 +00:27:22,030 --> 00:27:31,470 +function if is differentiable على الفترة المغلقة + +246 +00:27:31,470 --> 00:27:36,290 +if it + +247 +00:27:36,290 --> 00:27:50,770 +is differentiable onالفترة المفتوحة إذا كان + +248 +00:27:51,500 --> 00:28:00,480 +the limits إذا النهايات لإتنين limit لما ال H بدها + +249 +00:28:00,480 --> 00:28:07,800 +تروح ل Zero من جهة اليمين لل F of Zero زائد ال H + +250 +00:28:07,800 --> 00:28:20,330 +ناقص ال F of A زائد ال Hنقص الـ F of A كل هذا على + +251 +00:28:20,330 --> 00:28:29,030 +H and limit لما الـ H بدأ تروح للـ Zero من جهتي + +252 +00:28:29,030 --> 00:28:40,800 +الشماللماين؟ لل F of B زائد ال H ناقص ال F of B + +253 +00:28:40,800 --> 00:28:47,460 +كله على H ال two limits هذه بقول عنها معلها exists + +254 +00:29:23,820 --> 00:29:27,300 +خلّي بالك الـ two definitions الدفينيشن الأول + +255 +00:29:27,300 --> 00:29:31,780 +بتكلم على المشتقة على open interval الدفينيشن + +256 +00:29:31,780 --> 00:29:37,500 +التاني بتكلم على مشتقة على closed interval نجيب + +257 +00:29:37,500 --> 00:29:42,420 +الدفينيشن الأول الـ y تسوي f of x is + +258 +00:29:42,420 --> 00:29:48,060 +differentiable on an open interval if it has a + +259 +00:29:48,060 --> 00:29:52,420 +derivative إذا إلها مشتقة at each point of the + +260 +00:29:52,420 --> 00:30:00,240 +intervalعند كل نقطة من هذه الفترة.يعني بالداجة على + +261 +00:30:00,240 --> 00:30:03,920 +الفترة المفتوحة، لو كانت الدالة قابلة الاشتراك عند + +262 +00:30:03,920 --> 00:30:08,780 +كل نقطة من نقاط الفترة المفتوحة، بقول الدالة قابلة + +263 +00:30:08,780 --> 00:30:13,040 +الاشتراك على كل هذه الفترة.طب لو كانت الفترة + +264 +00:30:13,040 --> 00:30:20,390 +مغلقة،بدي أخد الفترة المفتوحة وبعدين أخد من طرفي + +265 +00:30:20,390 --> 00:30:24,910 +الانترول فبقى بقول الدالة if قابل اشتراك على + +266 +00:30:24,910 --> 00:30:29,750 +الفترة المغلقة اللي عندنا if it is differentiable + +267 +00:30:29,750 --> 00:30:34,740 +على الفترة a وbإذا كانت قابلة شقاق على الفترة + +268 +00:30:34,740 --> 00:30:38,480 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +269 +00:30:38,480 --> 00:30:39,480 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +270 +00:30:39,480 --> 00:30:40,880 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +271 +00:30:40,880 --> 00:30:41,640 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +272 +00:30:41,640 --> 00:30:43,220 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +273 +00:30:43,220 --> 00:30:45,360 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +274 +00:30:45,360 --> 00:30:46,680 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +275 +00:30:46,680 --> 00:30:49,400 +المفتوحة A وB وإذا كانت قابلة شقاق على الفترة + +276 +00:30:49,400 --> 00:30:54,580 +المفتوحة A وBيبقى انا بدي اذهب الى a من جهة اليمين + +277 +00:30:54,580 --> 00:30:59,120 +و بدي اذهب الى b من جهة اليسار + +278 +00:31:21,340 --> 00:31:32,920 +هذا بنسميه right hand derivative at + +279 +00:31:32,920 --> 00:31:46,820 +x يسوى a هذا بنسميه left hand derivative at + +280 +00:31:46,820 --> 00:31:55,220 +x يسوى bتمام؟يبقى إذا الـ right-handed derivative + +281 +00:31:55,220 --> 00:31:58,540 +و الـ left-handed derivative under peripheral + +282 +00:31:58,540 --> 00:32:02,660 +interval exist زائد الـ function قابل اشتراك على + +283 +00:32:02,660 --> 00:32:07,420 +كل الفترة المفتوحة يبقى في هذه الحالة بقول الدالة + +284 +00:32:07,420 --> 00:32:13,480 +قابلة للاشتراك على كل الفترة المغلقة اللي عندنا + +285 +00:32:13,480 --> 00:32:19,380 +طبعا الان بنأخد بعض الأمثلة على ذلك هذا التعريف + +286 +00:32:19,380 --> 00:32:41,980 +كيف نستخدمه؟مثال واحد مثال + +287 +00:32:41,980 --> 00:32:45,660 +واحد + +288 +00:32:45,660 --> 00:32:49,980 +مثال واحد + +289 +00:32:49,980 --> 00:32:50,000 +مثال واحد مثال واحد مثال واحد مثال واحد مثال واحد + +290 +00:32:50,170 --> 00:33:00,710 +قول X أم لا هذا السؤال هل + +291 +00:33:00,710 --> 00:33:07,670 +الدالة قابلة للاشتقاق لجميع قيم X لل absolute + +292 +00:33:07,670 --> 00:33:08,730 +value ولا لا؟ + +293 +00:33:12,210 --> 00:33:16,430 +من سالب infinity إلى infinity فهو بيسأل هل الدالة + +294 +00:33:16,430 --> 00:33:21,070 +قابلة إشتقاق على كل ال domain تبعه يعني كل ال real + +295 +00:33:21,070 --> 00:33:24,350 +line ولا لأ؟ فنقول الله والله ما احنا عارفين، هو + +296 +00:33:24,350 --> 00:33:28,290 +بيسأل سواء احنا نقول له يا إما قابلة إشتقاق، يا + +297 +00:33:28,290 --> 00:33:31,650 +إما على الأقل بدي أجيبله نقطة دالة غير قابلة + +298 +00:33:31,650 --> 00:33:35,870 +لإشتقاق عندها وبالتالي الجواب أنها ليس قابلة + +299 +00:33:35,870 --> 00:33:41,370 +لإشتقاق for all x، يعني لو جبحالة واحدة الدالة غير + +300 +00:33:41,370 --> 00:33:47,590 +قابل الاشتقاق عندها بيكون اللي هو الدالة غير قابل + +301 +00:33:47,590 --> 00:33:51,710 +الاشتقاق على الفترة اللي عندنا يعني بكافة نجيب + +302 +00:33:51,710 --> 00:33:56,550 +counterexample واحد يعني مثال واحد يثبت أنها ليست + +303 +00:33:56,550 --> 00:34:01,010 +قابل الاشتقاق على كل الفترة اللي عندنا بيقولوا + +304 +00:34:01,010 --> 00:34:09,010 +ماشي هذا ال absolute valueممكن ارجع لتعريفة و اقول + +305 +00:34:09,010 --> 00:34:15,290 +هي x ناقص تلاتة بالشكل ان هذا العبارة عن جزء اين + +306 +00:34:15,290 --> 00:34:21,930 +الجزء الاول هو عبارة عن x ناقص تلاتة لما ال x اكبر + +307 +00:34:21,930 --> 00:34:29,010 +من او تسوى كدهتلاتة ولا Zero؟ تلاتة طيب يالله + +308 +00:34:29,010 --> 00:34:36,690 +تلاتة وهنا ناقص X ناقص تلاتة يعني تلاتة ناقص X لما + +309 +00:34:36,690 --> 00:34:43,740 +ال X مالها أقل من تلاتة تمام؟بدي بقوله والله كويس + +310 +00:34:43,740 --> 00:34:52,540 +اذا انا بدي اجي اخد f prime of x وين عندى التلاتة + +311 +00:34:52,540 --> 00:34:58,300 +تمام بس لما تبقى اكبر منى التلاتة يعنى كأنه انا + +312 +00:34:58,300 --> 00:35:02,400 +رايح لها التلاتة من وين من جهة اللى بدي اقوله f + +313 +00:35:02,400 --> 00:35:08,460 +primeمن جهة + +314 +00:35:08,460 --> 00:35:14,080 +اليمين يبقى هذا الكلام بيساوي ال limit لما ال H + +315 +00:35:14,080 --> 00:35:19,540 +بدها تروح ل zero من جهة اليمين بيجي للدالة اللي + +316 +00:35:19,540 --> 00:35:26,080 +عندنا هنا اللي هي عبارة عن مين ال Xزائد الـ H ناقص + +317 +00:35:26,080 --> 00:35:31,060 +التلاتة ناقص ال F والله اكتبها لك نظري وبعدين + +318 +00:35:31,060 --> 00:35:36,380 +بنعوض تعملاش تقولي كيف هاد يجي يبقى هادي بدنا + +319 +00:35:36,380 --> 00:35:42,200 +نقوله F of X naught زائد ال H ناقص ال F of X + +320 +00:35:42,200 --> 00:35:47,440 +naught على H بتاخد ال limit لما ال H بدها تروح ل + +321 +00:35:47,440 --> 00:35:53,060 +Zero من جهة اليمينيبقى هذه الـ limit لما الـ H + +322 +00:35:53,060 --> 00:35:59,860 +بدها تروح لـ 0 من جهة اليمين، مش لتلاتةاذا X راحت + +323 +00:35:59,860 --> 00:36:04,260 +لي تلاتة معناه ان H راحت لين لزيرو هاي المقصود + +324 +00:36:04,260 --> 00:36:10,440 +فيها يبقى الـH بتروح لي زيرو من جهة اليمين يبقى + +325 +00:36:10,440 --> 00:36:14,940 +بداجي لل X node X node عندي بقى درجة تلاتة يبقى + +326 +00:36:14,940 --> 00:36:23,020 +تلاتة زائد H ناقص تلاتة هاي الدالة الأولى ناقص F + +327 +00:36:23,020 --> 00:36:29,170 +of X nodeاللي هو تلاتة ناقص تلاتة كله هذا على مين؟ + +328 +00:36:29,170 --> 00:36:34,750 +على H يبقى هذا الكلام بده يسوي ال limit لما ال H + +329 +00:36:34,750 --> 00:36:40,230 +بدها تروح لوين؟ ل Zero من جهة اليمين بيصير عندنا + +330 +00:36:40,230 --> 00:36:44,970 +مين؟ تلاتة و سالب تلاتة مع السلامة يبقى بضال قداش + +331 +00:36:44,970 --> 00:36:50,370 +عندنا H و هنا H و هذه كلها ب Zero اللي هو الجواب + +332 +00:36:50,370 --> 00:36:58,120 +قداش بده يعطينا واحد صحيحبتروح أخد المشتقة للدالة + +333 +00:36:58,120 --> 00:37:04,080 +من جهة مين؟ من جهة الشمال يعني هذا ال limit لما ال + +334 +00:37:04,080 --> 00:37:11,780 +H بدها تروح ل zero من جهة الشمال لل F of تلاتة + +335 +00:37:11,780 --> 00:37:18,940 +زائد ال H ناقص F of تلاتة على H يعني ال limit لما + +336 +00:37:18,940 --> 00:37:24,830 +ال H بدها تروح ل zero من جهة الشمال0 من جهة الشمال + +337 +00:37:24,830 --> 00:37:29,870 +يعني كأنه احنا رايحين ليه تلاتة من جهة من الشمال + +338 +00:37:29,870 --> 00:37:36,470 +يبقى تدالة تلاتة ناقص X يبقى بروح بقوله تلاتة ناقص + +339 +00:37:36,470 --> 00:37:43,050 +X زائد ال H ناقص تلاتة ناقص تلاتة كله على مين؟ على + +340 +00:37:43,050 --> 00:37:48,390 +H يبقى هذا الكلام بده يساوي ال limit لما ال H بده + +341 +00:37:48,390 --> 00:37:57,070 +تروح ل 0 من جهة الشماللمن؟ لتلاتة ناقص X ناقص H + +342 +00:38:08,690 --> 00:38:13,070 +لأن الـ X حطينها مدالها تلاتة عن الـ X non تمام؟ + +343 +00:38:13,070 --> 00:38:19,730 +يبقى تلاتة ناقص ثلاثة ناقص ال H و هذه كما هي ناقص + +344 +00:38:19,730 --> 00:38:25,870 +ب Zero على مين؟ على H هذه هتروح مع هذه يبقى ال + +345 +00:38:25,870 --> 00:38:31,490 +limit لما ال H بتروح ل Zero من جهة الشمال لسلب H + +346 +00:38:31,490 --> 00:38:37,190 +على H اللي هو كده؟ سلب واحد يبقى إيش رأيك؟ المشتقة + +347 +00:38:37,190 --> 00:38:44,680 +موجودة؟يبقى بالصير عندنا if prime of تلاتة does + +348 +00:38:44,680 --> 00:38:53,980 +not existمش موجودة هذا يعني ان ال F is not + +349 +00:38:53,980 --> 00:39:01,920 +differentiable at X يساوي تلتة يعني الدالة غير + +350 +00:39:01,920 --> 00:39:08,740 +قابلة لاشتقاق عند X يساوي تلتة طيب سؤال لو روحنا و + +351 +00:39:08,740 --> 00:39:15,160 +قولنا هذا المحور هذا محور X وهذا Y وهذه أصلا + +352 +00:39:15,160 --> 00:39:21,360 +الدالة الهيمينabsolute value ل X عملنا لها shift + +353 +00:39:21,360 --> 00:39:27,120 +جهة اليمين بمقدار تلاتة يبقى صارت ال function + +354 +00:39:27,120 --> 00:39:33,240 +بالشكل اللي عندنا هذا يبقى هذا absolute value ل X + +355 +00:39:33,240 --> 00:39:40,630 +ناقص تلاتة المشكلة وين؟المشكلة عندى التلاتة صارت، + +356 +00:39:40,630 --> 00:39:46,810 +عندى التلاتة الدالة غير قابلة للاشتقاء، طب هنا + +357 +00:39:46,810 --> 00:39:51,390 +الرسم هذه، إيش بنقول عن النقطة هذه بالنسبة للرسم؟ + +358 +00:39:52,860 --> 00:39:57,180 +حرجة critical point ماشي موافقة حرجة لكن هل احنا + +359 +00:39:57,180 --> 00:40:03,080 +ايش بنقول طيب لما تلاقي شغلتين او لما تلاقي حيطة + +360 +00:40:03,080 --> 00:40:04,100 +من هنا او حيطة من هنا او حيطة من هنا او حيطة من + +361 +00:40:04,100 --> 00:40:04,120 +هنا او حيطة من هنا او حيطة من هنا او حيطة من هنا + +362 +00:40:04,120 --> 00:40:04,420 +او حيطة من هنا او حيطة من هنا او حيطة من هنا او + +363 +00:40:04,420 --> 00:40:04,620 +حيطة من هنا او حيطة من هنا او حيطة من هنا او حيطة + +364 +00:40:04,620 --> 00:40:05,340 +من هنا او حيطة من هنا او حيطة من هنا او حيطة من + +365 +00:40:05,340 --> 00:40:09,360 +هنا او حيطة من هنا او حيطة من هنا او حيطة من هنا + +366 +00:40:09,360 --> 00:40:22,560 +او حيطة من هنا او حيطة من هنا او حي + +367 +00:40:22,590 --> 00:40:28,030 +يبقى هذا اللي عندنا corner يبقى أول حالة من + +368 +00:40:28,030 --> 00:40:33,330 +الحالات اللي ده اللي عندها غير قابل الاشتقاق لو + +369 +00:40:33,330 --> 00:40:37,460 +كان عندي cornerالـ Limit من اليمين لا تساوي الـ + +370 +00:40:37,460 --> 00:40:42,100 +Limit من الشمال، لماذا؟ لأن المماس هنا للمنحنة هو + +371 +00:40:42,100 --> 00:40:46,820 +نفس المنحنة، بيعملني الزاوية حادة يبقى الظل موجب، + +372 +00:40:46,820 --> 00:40:51,580 +لكن الخط هذا بيعملني زاوية مالها منفرجة يبقى الظل، + +373 +00:40:51,580 --> 00:40:55,060 +بيعطيني قيمة سلم، يعني عندي التلاتة صار المياه + +374 +00:40:55,060 --> 00:40:59,920 +موجب وسلم في نفس اللحظة، بنفع هذا الكلام؟ بنفعك، + +375 +00:40:59,920 --> 00:41:05,120 +طب يوصلك كمان سؤالعند ال corner هنا كم مماسة بتقدر + +376 +00:41:05,120 --> 00:41:11,300 +ترسمها؟ كتير، مظبوط، ومن معنى هذا الكلام أن الدالة + +377 +00:41:11,300 --> 00:41:16,800 +غير قابلة للاشتقاء طيب، على أي حال سنرجع إلى هذه + +378 +00:41:16,800 --> 00:41:22,180 +الحالات بعد قليل، ولكن كل اللي بدياك تعرفه أن + +379 +00:41:22,180 --> 00:41:28,430 +الدالة هه، لو كان الرسم البياني في cornerيبقى + +380 +00:41:28,430 --> 00:41:35,430 +الدالة غير قابلة للاشتقاء عند هذا ال corner طيب فى + +381 +00:41:35,430 --> 00:41:41,150 +كمان سؤال مغلبني شوية هل ال absolute value لل X + +382 +00:41:41,150 --> 00:41:49,510 +ناقص ثلاثة دالة متصلة عندك تسوى تلاتة متصلة لكنها + +383 +00:41:49,510 --> 00:41:56,550 +يعني الاتصال بيعطينيش اشتقاقلو كانت الدالة متصلة + +384 +00:41:56,550 --> 00:42:03,010 +قد تكون قابلة للاشتراك وقد لا تكون مش مضمون السؤال + +385 +00:42:03,010 --> 00:42:07,790 +هو هل العكس صحيح و لا غير صحيح؟ يعني لو كانت + +386 +00:42:07,790 --> 00:42:14,270 +الدالة قابلة للاشتراك إذا هي بقى متصلة يبقى خليني + +387 +00:42:14,270 --> 00:42:22,750 +أحطها لك في صيغة ال remark التالية remark F + +388 +00:42:23,600 --> 00:42:34,000 +the function is differentiable then it is + +389 +00:42:34,000 --> 00:42:40,680 +continuous but + +390 +00:42:40,680 --> 00:42:45,360 +.. ولكن the converse + +391 +00:42:47,340 --> 00:43:00,640 +is not true always أو not true خلاصالعكس ليس + +392 +00:43:00,640 --> 00:43:04,220 +بالضرورة + +393 +00:43:04,220 --> 00:43:09,440 +صحيحا يبقى الدالة F لو كانت دالة قابلة لإشتقاق إذا + +394 +00:43:09,440 --> 00:43:15,460 +هي إجباري دالة متصلة لكن العكس the converse العكس + +395 +00:43:15,460 --> 00:43:21,880 +ليس صحيحا يعني لو كانت الدالة متصلة ليس بالضرورة + +396 +00:43:21,880 --> 00:43:26,460 +أن تكون قابلة لمين؟ قابلة للإشتقاق + +397 +00:43:34,240 --> 00:43:39,040 +ناخد كمان مثال example + +398 +00:43:39,040 --> 00:43:42,440 +let + +399 +00:43:42,440 --> 00:43:50,920 +ال F of X دي ساوي الجذر التربيه ل X ناقص سبعة + +400 +00:43:54,730 --> 00:44:05,650 +او ايش دولنا؟ نمرة A بدي domain ال F نمرة B بدي ال + +401 +00:44:05,650 --> 00:44:18,590 +F prime of X نمرة C بدي domain ال F prime solution + +402 +00:44:23,510 --> 00:44:28,650 +بدي احسبله domain الدالة F فبجي بقوله domain + +403 +00:44:28,650 --> 00:44:36,230 +الدالة F كل العناصر X بحيث N و اجتشد دالة هذه + +404 +00:44:36,230 --> 00:44:48,150 +معرفة إذا كل القيمة اللي تحت الجدر كانت سالبة يعني + +405 +00:44:48,150 --> 00:44:52,150 +مش صحيح كلامييبقى إذا كل القيمة اللي تحت الجدرد + +406 +00:44:52,150 --> 00:44:59,110 +كانت موجبة أو صفر يبقى إذا كان ال X نقل سبعة + +407 +00:44:59,110 --> 00:45:04,530 +greater than or equal to zero يعني هذه كل العناصر + +408 +00:45:04,530 --> 00:45:12,290 +X بحيث أن ال X greater than or equal to seven يعني + +409 +00:45:12,290 --> 00:45:18,210 +هذا الكلام closed interval من سبعة لغاية infinity + +410 +00:45:18,210 --> 00:45:24,100 +تمام؟طيب هذا كله نمرة A جيبنا domain الدالة، بدأ + +411 +00:45:24,100 --> 00:45:29,320 +أجي لنمرة B، نمرة B قاللي هاتلي المشتقة، أروح أبدأ + +412 +00:45:29,320 --> 00:45:33,000 +من جديد، والله جاهز هيعملها في المثال اللي جابلي + +413 +00:45:33,000 --> 00:45:38,540 +شوية، يبقى باجي بقوله from the + +414 +00:45:40,790 --> 00:45:49,630 +اللي قبل هذا from a previous + +415 +00:45:49,630 --> 00:45:59,890 +example من مثال سابق اللي + +416 +00:45:59,890 --> 00:46:05,890 +هو ال F prime of X يسوى واحد على اتنين الجذر + +417 +00:46:05,890 --> 00:46:12,580 +التربيهي ل X ناقص سبعةليش؟ لأن معامل X هو الواحد + +418 +00:46:12,580 --> 00:46:17,740 +الصحيح يبقى تفاضل الجدر واحد على اتنين الجدر بدنا + +419 +00:46:17,740 --> 00:46:22,900 +عشان نقعد نكرر ما كنا في المثال قبل السنة يبقى هذا + +420 +00:46:22,900 --> 00:46:28,540 +نمرا B نمرا C نمرا C قال هتلي domain ال F prime + +421 +00:46:28,540 --> 00:46:34,740 +يبقى domain ال F prime هو domain ال Fما هذا النقاط + +422 +00:46:34,740 --> 00:46:40,420 +اللي بتخليلي المشتقة غير معرفة، المشتقة غير معرفة + +423 +00:46:40,420 --> 00:46:47,730 +عند من؟ عند السبعة، لكن غير هيكغير السبعة معرفة، + +424 +00:46:47,730 --> 00:46:55,150 +يبقى باجي بقوله ال domain بتبع ال F prime هو عبارة + +425 +00:46:55,150 --> 00:47:02,690 +عن domain الدلة F، بدي أطرح منه فقط الرقم سبعة + +426 +00:47:03,130 --> 00:47:08,030 +الرقم سبعة ليش؟ لأن عند الرقم سبعة المشتقة + +427 +00:47:08,030 --> 00:47:14,530 +undefined غير معرفة يبقى هذا الكلام بده يساوي ال + +428 +00:47:14,530 --> 00:47:21,450 +interval من سبعة لغاية infinity بده أشيل منه الرقم + +429 +00:47:21,450 --> 00:47:27,190 +سبعة يبقى بده يعطيني ال open interval سبعة و + +430 +00:47:27,190 --> 00:47:28,130 +infinity + +431 +00:47:35,700 --> 00:47:44,220 +طيب بدنا نجي نشوف الأماكن اللي الدالة عندها تكون + +432 +00:47:44,220 --> 00:47:51,000 +غير قابلة للاشتقاء عندنا + +433 +00:47:51,000 --> 00:47:58,300 +أربعة أماكن على الرسم البياني للدالة الدالة عندها + +434 +00:47:58,300 --> 00:48:05,430 +تكون غير قابلة للاشتقاءماشي الحالات الأربعة بنقول + +435 +00:48:05,430 --> 00:48:11,990 +ما يأتي لو كان الرسم البياني فيه corner زي ما قلنا + +436 +00:48:11,990 --> 00:48:17,470 +توف المثال السابق تمام؟ الحال التاني لو كان في + +437 +00:48:17,470 --> 00:48:25,310 +عندي sharp turn رجوح حد بنسميه كسب يعني المنحلة + +438 +00:48:25,310 --> 00:48:33,830 +بيكون فيه زي رأس مدبّب الحالة التالتة واجتيشلو + +439 +00:48:33,830 --> 00:48:39,150 +عندي vertical tangent يبقى + +440 +00:48:39,150 --> 00:48:44,810 +الظل تبقى بقداش ب infinity يبقى الأصبع تتدلة غير + +441 +00:48:44,810 --> 00:48:49,290 +المشتقة غير معرفة الحالة الرابعة لو عندي + +442 +00:48:49,290 --> 00:48:50,670 +discontinuity + +443 +00:48:58,390 --> 00:49:04,810 +الاربعية هحطلك في صيغة ال remark التالية يبقى + +444 +00:49:04,810 --> 00:49:12,150 +remark the + +445 +00:49:12,150 --> 00:49:23,210 +function f of xis not + +446 +00:49:23,210 --> 00:49:37,430 +differentiable at a point x يساوي c in the + +447 +00:49:37,430 --> 00:49:44,230 +following cases + +448 +00:49:45,370 --> 00:49:56,410 +في الحالات التالية نمرة واحد if the graph اذا + +449 +00:49:56,410 --> 00:50:08,890 +الرسم البياني has a corner because + +450 +00:50:11,900 --> 00:50:17,880 +زي ما شوفنا في المثال السابق قبل قليل they one + +451 +00:50:17,880 --> 00:50:23,140 +sided derivative + +452 +00:50:23,140 --> 00:50:27,440 +differ + +453 +00:50:27,440 --> 00:50:34,100 +يعني بيختلف المشتقة من اليمين على المشتقة من + +454 +00:50:34,100 --> 00:50:34,720 +الشمال + +455 +00:50:38,800 --> 00:50:50,480 +The graph is الرسم البياني has a cusp كسب يعني + +456 +00:50:50,480 --> 00:50:57,320 +sharp turn رجوع + +457 +00:50:57,320 --> 00:51:01,940 +حاد للمنحنة الحالة التالتة + +458 +00:51:04,700 --> 00:51:14,300 +إذا كانت الكرافة لديها تجنب + +459 +00:51:14,300 --> 00:51:17,940 +رقمي مماسا رأسيا + +460 +00:51:31,090 --> 00:51:39,710 +إذا كانت الصورة مستمرة + +461 +00:52:14,600 --> 00:52:20,280 +يبقى فيها عندي أربع حالات الأربع حالات هدول بيكون + +462 +00:52:20,280 --> 00:52:27,480 +عندي المنحنة أو الدالة غير قابلة للاشتقاء معادلة + +463 +00:52:27,480 --> 00:52:31,780 +المنحنة بتبقى عندها غير قابلة للاشتقاء مين هي + +464 +00:52:31,780 --> 00:52:36,700 +الأماكن أو النقط اللي الدالة عندها بتكون غير قابلة + +465 +00:52:36,700 --> 00:52:42,480 +للاشتقاء حالة الأولىلو ال graph has a corner يبقى + +466 +00:52:42,480 --> 00:52:46,700 +فيه corner زي اللي توقف absolute value لمن؟ لل X + +467 +00:52:46,700 --> 00:52:51,620 +ناقص ثلاثة because the one sided derivative differ + +468 +00:52:51,620 --> 00:52:56,980 +لأن المشتقة من اليمين غير المشتقة من الشمال وهذه + +469 +00:52:56,980 --> 00:53:04,520 +الحالة أشرنا إليها قبل قليل يبقى هذا X، هذه Y، هذه + +470 +00:53:04,520 --> 00:53:09,120 +Zero، يبقى هنا هذا ما نسميه corner + +471 +00:53:14,410 --> 00:53:19,190 +بالتالي المشتقة من اليمين لأو المشتقة من اليمين + +472 +00:53:19,460 --> 00:53:25,180 +لاتساوى المشتقة من الشمال الحالة الأولى لو كان + +473 +00:53:25,180 --> 00:53:30,040 +عندي corner يبقى الدالة غير قابل اشتقاق الحالة + +474 +00:53:30,040 --> 00:53:36,000 +الثانية بيقول if the graph has a cusp رجوع حاد + +475 +00:53:36,000 --> 00:53:41,760 +للمنحنة طبعا احنا خدنا function قبل ذلك اللي هي ال + +476 +00:53:41,760 --> 00:53:47,490 +function التالي هذا Xوهذا Y فكانت رسمة الدالة + +477 +00:53:47,490 --> 00:53:52,930 +بتنزلك و بتطلع هيك عندي ال zero حد ماذا ذكرها يا + +478 +00:53:52,930 --> 00:54:00,630 +شهود؟ Y تسوى X أُص تلاتة على اتنين والله اتنين على + +479 +00:54:00,630 --> 00:54:08,270 +تلاتة2 ع 3 طولتين كويس يبقى هذي Y يساوي X أس + +480 +00:54:08,270 --> 00:54:15,090 +طولتين هذا A اللي هو كسب كسب يعني إيه؟ يعني لو جيت + +481 +00:54:15,090 --> 00:54:18,850 +مماس من اليمين و مماس من الشمال اتنين are + +482 +00:54:18,850 --> 00:54:23,790 +different اتنين لو بدي ارسم مماس عند هذه النقطة + +483 +00:54:23,790 --> 00:54:28,770 +برسم لنهاية من من المماسات ليس بالضرورة أن يكون + +484 +00:54:28,770 --> 00:54:32,750 +الرأس المدبب إلى أسفلممكن يكون الرأس مدبب إلى + +485 +00:54:32,750 --> 00:54:37,050 +أعلى، يعني لو جينا و قولنا هذه المحاور و قولنا هذا + +486 +00:54:37,050 --> 00:54:43,070 +محور X و هذا ممكن المنحنة يجي لكيك و يجي نازلك، + +487 +00:54:43,070 --> 00:54:51,230 +يبقى كمان هذا كاسبيبقى عند النقطة هذه ل X يساوي C + +488 +00:54:51,230 --> 00:54:56,050 +بيكون في عندي كاصمة يبقى هذا الشكل كذا سواء كان + +489 +00:54:56,050 --> 00:55:01,390 +الرأس المدبب إلى أسفل أو الرأس المدبب إلى أعلى طيب + +490 +00:55:01,390 --> 00:55:04,230 +الحالة التانية بقول تالتة بقول لو كان عندي + +491 +00:55:04,230 --> 00:55:08,510 +vertical tangentأظن المحاضرة الماضية أخدنا ال + +492 +00:55:08,510 --> 00:55:12,590 +vertical tangent و قلنا القوة ده مش موجود في الجزء + +493 +00:55:12,590 --> 00:55:19,790 +النظري لكن موجود في التمرين و كان عندنا دالة زي + +494 +00:55:19,790 --> 00:55:25,830 +من؟ زي الدالة هذي X و Y و المنحنة جينا رسمناها و + +495 +00:55:25,830 --> 00:55:34,530 +أجا نازل هيك بالشكل هذول هو من؟ Y تساوي X أسطلهذا + +496 +00:55:34,530 --> 00:55:37,950 +محور Y هذا vertical tangent + +497 +00:55:45,350 --> 00:55:49,970 +عند الـ Zero طبعا السؤال اللي أتناه كل مرة فتخلنا + +498 +00:55:49,970 --> 00:55:55,890 +فيه إزاحة جهة اليمين بمقدار واحد ممكن أجربلك ياه + +499 +00:55:55,890 --> 00:56:00,910 +شوية و أقولك هاي المحاول هذا محور X هذا محور Y + +500 +00:56:00,910 --> 00:56:06,870 +أجانبه انحنى هكذا وجهت عند النقطة دي بدي أرسم مماس + +501 +00:56:06,870 --> 00:56:11,930 +فكان المماس على الشكل التالي + +502 +00:56:15,890 --> 00:56:22,190 +يبقى هذا مين vertical tangent كمان هذا vertical + +503 +00:56:22,190 --> 00:56:28,070 +tangent تمام + +504 +00:56:28,070 --> 00:56:36,170 +يبقى عند x يساوي c الدالة كذلك غير قابلة للاشتقاء + +505 +00:56:36,170 --> 00:56:40,290 +الحالة الرابعة لو عندك discontinuity الدالة غير + +506 +00:56:40,290 --> 00:56:45,580 +متصلة عند هذا النقطة تقدر تلص مماس عندهافي المنحنة + +507 +00:56:45,580 --> 00:56:52,600 +توجد ثقوب في المنحنة يبقى لو جينا قولنا افترض عندك + +508 +00:56:52,600 --> 00:56:58,280 +اي منحنة بالشكل اللي عندنا هذا محور X و هذا محور Y + +509 +00:56:58,450 --> 00:57:03,890 +و اخترسمت المنحنة فكان المنحنة جاي بالشكل هذا و + +510 +00:57:03,890 --> 00:57:11,210 +عند X يساوي C في عند هنا اياش ثقب تقدر عند هذا + +511 +00:57:11,210 --> 00:57:17,710 +الثقب ترسم مماس يبعتلك الله لأن المماس بده احداث + +512 +00:57:17,710 --> 00:57:22,480 +نقطة عند هذه النقطة لا تقع على المنحنةإذا لن تصير + +513 +00:57:22,480 --> 00:57:27,600 +أنت رسم ماسك وبالتالي لا يمكن أن يكون في عندك هنا + +514 +00:57:27,600 --> 00:57:32,260 +الدالة قابلة لا continuity ولا differentiability + +515 +00:57:32,640 --> 00:57:38,020 +لكن اتطلع في الحالات اللي عندنا هذه كلها، الدالة + +516 +00:57:38,020 --> 00:57:42,980 +متصلة، لكنها غير قابلة للاشتقاء، لكن في الحالة + +517 +00:57:42,980 --> 00:57:49,440 +الأخيرة، لا دالة متصلة ولا حتى قابلة للاشتقاء، ما + +518 +00:57:49,440 --> 00:57:55,500 +علينا، يبقى هدول الأربع حالات بتكون ملم فيهم تماما + +519 +00:57:55,980 --> 00:58:00,640 +عند الـ Cusp أو الـ Corner تقدر ترسم مالا نهاية من + +520 +00:58:00,640 --> 00:58:04,640 +المماسات عند الـ Discontinuity ماقدرش ارسم ولا + +521 +00:58:04,640 --> 00:58:11,880 +مماس على الإطلاق طيب نبدأ نأيجي ناخد بعض الأمثلة + +522 +00:58:11,880 --> 00:58:17,500 +أول مثال example بيقول + +523 +00:58:17,500 --> 00:58:28,030 +ما يأتي example oneبيقولي show that + +524 +00:58:28,030 --> 00:58:38,900 +the function بييلي ان الدالة f of xيساوي أحد أمرين + +525 +00:58:38,900 --> 00:58:47,600 +يا إما ال X تربيع في sign واحد على X لما ال X لا + +526 +00:58:47,600 --> 00:58:55,540 +تساوي Zero يا إما Zero لما ال X تساوي Zero is + +527 +00:58:55,540 --> 00:58:58,660 +differentiable + +528 +00:58:58,660 --> 00:59:09,770 +at X يساوي Zero andفاين f prime of zero + +529 +00:59:47,420 --> 00:59:52,240 +السؤال اللى قدامنا بيقول يبين لإن هذه الدالة قابلة + +530 +00:59:52,240 --> 00:59:58,160 +للاشتقاء قويا عند X يساوي Zero وبيجيب قداش قيمة + +531 +00:59:58,160 --> 01:00:05,140 +هذه المشتقة بيقول له بسيطة احنا عندنا ال F prime + +532 +01:00:05,140 --> 01:00:12,190 +of Zeroبتجيب المشتقة عند الصفر يبقى هذه بدها تساوي + +533 +01:00:12,190 --> 01:00:19,670 +limit لما ال H بدها تروح لل zero لل F of zero زائد + +534 +01:00:19,670 --> 01:00:27,830 +ال H ناقص F of zero على H يبقى هذه المشتقة عند + +535 +01:00:27,830 --> 01:00:37,530 +الصفر يبقى بدها تجيب ال F prime of zeroأشوف هل هي + +536 +01:00:37,530 --> 01:00:42,670 +exist و الله ماهياش exist إذا طلعت does not exist + +537 +01:00:42,670 --> 01:00:47,170 +يبقى خلاص ال F prime زيرون لا يمكن نجدها و إذا + +538 +01:00:47,170 --> 01:00:51,390 +طلعت مانا مانت الدالة قابلة الاشتقاق عند زيرون و + +539 +01:00:51,390 --> 01:00:56,530 +قيمتها القيمة لمن اللي بتطلع بقوله كويس يبقى هذه + +540 +01:00:56,530 --> 01:01:03,540 +ال limit لما ال H بدها تروح لزيرونبتداجي للدالة + +541 +01:01:03,540 --> 01:01:09,880 +بدي أشيل كل X و أكتب بدلها من Zero زائد H يبقى هاي + +542 +01:01:09,880 --> 01:01:16,880 +Zero زائد H لكل تربيع Sine واحد على Zero زائد ال H + +543 +01:01:16,880 --> 01:01:23,760 +ناقص F of Zero قيمة الدالة عند Zero بجداش ب Zero + +544 +01:01:23,760 --> 01:01:29,990 +كل هذا الكلام مقسوم على جداش على Hيبقى هذا بده + +545 +01:01:29,990 --> 01:01:35,770 +يساوي ال limit لما ال H بدها تروح لل zero لل H + +546 +01:01:35,770 --> 01:01:43,330 +تربيع في ال sign واحد على H كله مقسوم العالمين على + +547 +01:01:43,330 --> 01:01:49,650 +H والباقي كله طار طبعا في اختصارات عندنا وبتالي ال + +548 +01:01:49,650 --> 01:01:56,400 +limitلما الـ H بدها تروح لـ 0 للـ H في الـ sign 1 + +549 +01:01:56,400 --> 01:02:03,360 +على H أظن هذه حسبناها قبل ذلك بدل المرة مرتين يبقى + +550 +01:02:03,360 --> 01:02:09,500 +النتيجة تساوي 0 وهذا previous example + +551 +01:02:11,160 --> 01:02:18,900 +مثال سابق معناته اللي limit هذه exist وتساوي zero + +552 +01:02:18,900 --> 01:02:20,160 +يبقى + +553 +01:02:22,760 --> 01:02:32,120 +الـ F is differentiable at X يساوي Zero and ال F + +554 +01:02:32,120 --> 01:02:36,840 +prime of Zero بده يساوي قداش بده يساوي Zero طيب + +555 +01:02:36,840 --> 01:02:43,040 +هذا مثال بسيط و مباشر نعطيكم مثال و نشوف شو رأيكم + +556 +01:02:43,040 --> 01:02:46,720 +فيه يبقى example to + +557 +01:02:51,110 --> 01:03:01,190 +بقول ما يأتي for what values + +558 +01:03:01,190 --> 01:03:14,150 +of a and b will the function + +559 +01:03:14,150 --> 01:03:29,260 +f of xيساوي أحد أمرين يا إما اللي هو AX لما ال X + +560 +01:03:29,260 --> 01:03:40,730 +أقل من اتنين يا إما AX تربيةنقص بـ x زائد تلاتة + +561 +01:03:40,730 --> 01:03:48,950 +لما الـ x greater than or equal to two ماله هذا ب + +562 +01:03:48,950 --> 01:03:56,310 +differentiable at x يساوي اتنين + +563 +01:04:09,070 --> 01:04:16,170 +سؤال مرة تانية بقول لي ما هي القيم التي تأخذها كل + +564 +01:04:16,170 --> 01:04:22,630 +من أو كل من a و b بحيث ال function هذا تبقى قابل + +565 +01:04:22,630 --> 01:04:28,830 +للاشتقاق عند x يساوي اتنين هذا النوع من المسائل مر + +566 +01:04:28,830 --> 01:04:34,110 +علينا قبل ذلك مرتين مرة في ال limit و مرة في ال + +567 +01:04:34,110 --> 01:04:39,810 +continuityفي ال derivative و كله في كل الأمور + +568 +01:04:39,810 --> 01:04:45,590 +بيقول هاتلي قيمة الثابت ايه تمام؟ يبقى ادير بالك + +569 +01:04:45,590 --> 01:04:50,410 +من الحكاية هذا بدك تكون دقيق لانه لا يكاد يخلو + +570 +01:04:50,410 --> 01:04:54,050 +ممكن يجيك على ال limit ممكن يجيك على ال continuity + +571 +01:04:54,050 --> 01:04:58,210 +ممكن يجيك على ال differentiability وقد قتينا بهذه + +572 +01:04:58,210 --> 01:05:03,510 +النوعية من الأسئلة قبل ذلك عدة مراتيبقى السؤال + +573 +01:05:03,510 --> 01:05:08,470 +بيقول بدي قيم ايه و بيه بحيث الدالة تبقى ايه قعب + +574 +01:05:08,470 --> 01:05:13,430 +الاشتقاء قعب الاشتقاء معناته المشتقة من اليمين بدت + +575 +01:05:13,430 --> 01:05:18,430 +سوى المشتقة من اللي يشمل عند x يسوى من الاتنين + +576 +01:05:18,430 --> 01:05:25,750 +تمام يبقى بدي اخد اول حاجة if ال x اقل من الاتنين + +577 +01:05:26,740 --> 01:05:35,220 +يبقى بدنا نروح نحسب المشتقة عندي اتنين بس من وين؟ + +578 +01:05:35,220 --> 01:05:40,240 +اقل من اتنين اقل من اتنين يبقى من وين؟ من جهة + +579 +01:05:40,240 --> 01:05:47,160 +اليسار يبقى ال limit لما ال H بدها تروح ل zero من + +580 +01:05:47,160 --> 01:05:51,260 +وين؟ من جهة اليسار اقل من اتنين يبقى هاي ال + +581 +01:05:51,260 --> 01:05:58,850 +functionيبقى بدنا نيجي ناخد F of 2 زائد H يبقى A + +582 +01:05:58,850 --> 01:06:11,130 +في 2 زائد ال H ناقص ال A في 2 كله على H يبقى هذه + +583 +01:06:11,130 --> 01:06:19,570 +تساوي ال F prime من جهة الشمال عند 2 تساويLimit + +584 +01:06:19,570 --> 01:06:27,310 +لما الـ H بدها تروح لـ 0 من جهة الشمال لـ 2A زائد + +585 +01:06:27,310 --> 01:06:35,570 +الـ A H ناقص 2A كله على مين على الـ H؟ هذه وهذه مع + +586 +01:06:35,570 --> 01:06:41,610 +بعضها الـ H مع الـ H يبقى نتيجة كده بدها تساوي فقط + +587 +01:06:41,610 --> 01:06:47,200 +لغية يبقى هذا المشتقة من جهة الشمالزي ما جيبنا + +588 +01:06:47,200 --> 01:06:52,980 +المشتقة من جهة الشمال بدنا نجيب المشتقة من وين؟ من + +589 +01:06:52,980 --> 01:06:59,580 +جهة اليمين يبقى ال limit لما ال H بدها تروح لل + +590 +01:06:59,580 --> 01:07:06,080 +zero من جهة اليمين تمام؟ ال zero من جهة اليمين + +591 +01:07:06,080 --> 01:07:10,060 +معناته X أكبر من الأتنين يبقى هاي الدالة اللي + +592 +01:07:10,060 --> 01:07:15,540 +عندنا يبقى بده أشيل كل X و أكتب مكانها 2 زائد H + +593 +01:07:15,840 --> 01:07:24,020 +يبقى a في اتنين زائد h لكل تربيع ناقص بيه في + +594 +01:07:24,020 --> 01:07:33,420 +الاتنين زائد h زائد تلاتة ناقصهذه كلها F of A زائد + +595 +01:07:33,420 --> 01:07:43,740 +H ناقص F of اتنين يبقى ناقص A في اتنين ترابية ناقص + +596 +01:07:43,740 --> 01:07:51,260 +B في اتنين زائد تلاتة وهيقفلنا ال course وكل هذا + +597 +01:07:51,260 --> 01:07:58,690 +مقسوم العالمين على H يبقى النتيجة limitلما ال H + +598 +01:07:58,690 --> 01:08:03,890 +بدها تروح ل zero من جهة اليمين يبقى هذا الترم شباب + +599 +01:08:03,890 --> 01:08:11,650 +يبقى هذا اتنين في اتنين باربعة A زائد اربعة H في A + +600 +01:08:11,650 --> 01:08:21,150 +يبقى زائد اربعة H زائد H تربية في A يبقى زائد A H + +601 +01:08:21,150 --> 01:08:21,690 +تربية + +602 +01:08:26,200 --> 01:08:37,850 +ناقص اتنين B ناقص H في B زائد تلاتةنجي للقصة + +603 +01:08:37,850 --> 01:08:47,450 +التانية ناقص أربعة A زائد اتنين B ناقص ثلاثة كل + +604 +01:08:47,450 --> 01:08:53,390 +هذا الكلام مقسوما على H مين اللي بيسأله؟ ايه؟ هذا + +605 +01:08:53,390 --> 01:08:58,290 +الطواريب الباشر. ليه؟ يقول A اتنين زائد H ناقص A + +606 +01:08:58,290 --> 01:09:00,270 +تبين T. هذا الأولى؟ + +607 +01:09:05,540 --> 01:09:14,080 +الـF prime عند الـA limit لما الـH بتروح لـ0 للـF + +608 +01:09:14,080 --> 01:09:24,440 +of A زائد الـH ناقص الـF of A على H كيف؟ + +609 +01:09:24,440 --> 01:09:27,780 +هو اللي فوق هي + +610 +01:09:31,310 --> 01:09:35,970 +ماختلفناش مش احنا جزئين الان رايحين لاتنين من جهة + +611 +01:09:35,970 --> 01:09:39,690 +الشمال يعني هذه مش موجودة عني مش موجودة هنا اللي + +612 +01:09:39,690 --> 01:09:43,530 +فوق، مظبوط ولا لا؟ يبقى انا بشتغل على اللي فوق + +613 +01:09:43,530 --> 01:09:46,850 +دونها، هي اجي الدور على اللي مين، على اللي تحت، + +614 +01:09:46,850 --> 01:09:51,770 +اصحت خربط من الشجتات، انا قلتك رايح لاتنين من جهة + +615 +01:09:51,770 --> 01:09:57,880 +الشمال، اخدت ال F Prime من جهة الشمال، تمام؟طيب + +616 +01:09:57,880 --> 01:10:03,300 +نجي نكمل هنا كل علاج نجي نختصر أظن الأربعة ا + +617 +01:10:03,300 --> 01:10:12,540 +والسالب أربعة ا مع السلامة عندك هنا سالبي + +618 +01:10:12,540 --> 01:10:18,640 +اتنين بيه وزيدي اتنين بيهموجة بتلاتة و سالب تلاتة + +619 +01:10:18,640 --> 01:10:24,380 +يبقى هذا كله راح كل مافيش غير كده تمام؟ يبقى هذا + +620 +01:10:24,380 --> 01:10:29,480 +الكلام بده يساوي ال limit لما ال H بده يروح ل zero + +621 +01:10:29,480 --> 01:10:35,600 +من جهة اليمين بده ياخد H عام المشترك بيبقى عندي 4A + +622 +01:10:35,600 --> 01:10:44,280 +زيد A H ناقص Bكل هذا الكلام على مين؟ على H يبقى + +623 +01:10:44,280 --> 01:10:50,020 +بتروح الـH هذه مع الـH هذه يبقى ال limit لما الـH + +624 +01:10:50,020 --> 01:10:58,780 +بدها تروح للـ0 من جهتي اليمين للـ4A زائد A H ناقص + +625 +01:10:58,780 --> 01:11:03,240 +B لما الـH بدها تروح للـ0 هذا ال term كله بيروح + +626 +01:11:03,240 --> 01:11:13,050 +بجداش بـ0 بظل الناتج 4A ناقص Bجلد دالة قابلة + +627 +01:11:13,050 --> 01:11:18,710 +للاشتقاق عندي اتنين إذا ما دام دالة قابلة للاشتقاق + +628 +01:11:18,710 --> 01:11:25,270 +عندي اتنين بدأ يكون المشتقة من اليمين تساوي + +629 +01:11:25,270 --> 01:11:32,690 +المشتقة من أين؟ من الشمال يبقى + +630 +01:11:32,690 --> 01:11:41,780 +باجي بقوله since بما أن يعني ال F isdifferentiable + +631 +01:11:41,780 --> 01:11:51,160 +at x يساوي اتنين we have ان المشتقة من الشمال + +632 +01:11:51,160 --> 01:12:00,350 +للاتنينبدي يساوي المشتقة من اليمين للإتنين هذا + +633 +01:12:00,350 --> 01:12:06,910 +معناه إيش؟ معناه إن الـA اللي طلعناها في الأول بدي + +634 +01:12:06,910 --> 01:12:15,610 +يساوي أربعة A ناقص الـB هذا معناه إن B يساوي تلاتة + +635 +01:12:15,610 --> 01:12:16,950 +A من اللي بيسأل؟ + +636 +01:12:24,760 --> 01:12:32,160 +خدنا ال term الأول و التاني ال term التاني يا + +637 +01:12:32,160 --> 01:12:36,500 +راجل أخدنا اللي فوق لحالها و أخدنا اللي تحت لحالها + +638 +01:12:36,500 --> 01:12:40,500 +جزئين مظبوط و هنا اشتغل نفس الشغل + +639 +01:12:47,010 --> 01:12:51,770 +يعني لما جيت اشتغلت في اللي فوق مثلا جيبت الدال + +640 +01:12:51,770 --> 01:12:56,750 +اللي تحته و حاطيتها مع اللي فوق طلع + +641 +01:12:56,750 --> 01:12:57,710 +فيها كويس + +642 +01:13:06,820 --> 01:13:11,000 +طيب ليش استغلت التنتين في أن عندنا نفس النقطة؟ + +643 +01:13:11,000 --> 01:13:14,420 +لأنه الاتنين ملتجيات على نفس النقطة، النقطة موجودة + +644 +01:13:14,420 --> 01:13:19,600 +على المنحنات والله + +645 +01:13:19,600 --> 01:13:24,540 +هو صح يا راجل، عشان امتحان فيزيا، عشان امتحان + +646 +01:13:24,540 --> 01:13:31,390 +فيزيا، خلّي بالك، خلّي بالك و صح صح، كويسطيب، على + +647 +01:13:31,390 --> 01:13:36,630 +أي حال، أنا عندي هذه معادلة في كام مجهول؟ فيه + +648 +01:13:36,630 --> 01:13:41,550 +مجهولين، بدي كمان معادلة تانية مش هنقدر أحلها، + +649 +01:13:41,550 --> 01:13:49,510 +أيوة، قول اذا + +650 +01:13:49,510 --> 01:13:55,510 +قابل الاشتقاق، يجب أن تكون متصلة، مظبوط + +651 +01:14:00,890 --> 01:14:09,090 +طب جالا ليه؟ يعني + +652 +01:14:09,090 --> 01:14:14,790 +لو أخدنا اتصاله فقط، بيكون حالينا المشكلة؟ طب أنا + +653 +01:14:14,790 --> 01:14:18,030 +الحين ما هو اللي ضايل علينا، إيش بيستخدم قرار + +654 +01:14:18,030 --> 01:14:22,130 +سياسي الاتصال؟ بس إنت إستعجلت، لو صبرتك دقيقتين، + +655 +01:14:22,130 --> 01:14:26,820 +فانتهت الشغل هذه، شوف ال CDالان انا من الاشتقاق + +656 +01:14:26,820 --> 01:14:33,260 +جبت معادلة بمجهولين تمام؟ اذا بدي كمان معادلة مش + +657 +01:14:33,260 --> 01:14:37,160 +هنجب احل المثل او المعادلة بتربط المجهولين ايضا + +658 +01:14:37,160 --> 01:14:42,380 +فماعنديش الا مين الا ال continuity لهذه الدالة + +659 +01:14:42,380 --> 01:14:52,080 +فباجي بقوله since بما انالـ F is differentiable at + +660 +01:14:52,080 --> 01:15:03,160 +X يساوى اتنين نحن لدينا ان ال F is continuous at X + +661 +01:15:03,160 --> 01:15:09,620 +يساوى اتنين مش امكانية كويس يبقى بده أروح أجيب له + +662 +01:15:09,620 --> 01:15:16,930 +F of اتنينخاصية الاتصال قيمة الدالة عند نقطة يساوي + +663 +01:15:16,930 --> 01:15:18,810 +نهاية الدالة عند نفس النقطة + +664 +01:15:43,270 --> 01:15:50,170 +زائد تلاتة تمام طب هدى قداش تساوي بيب تلاتة ايه + +665 +01:15:50,170 --> 01:15:58,710 +اذا بقدر اقول هدى تساوي اربعة ايه ناقص اتنين في + +666 +01:15:58,710 --> 01:16:08,110 +تلاتة ايه زائد تلاتة مظبوط هيك يبقى شلت البي وحطيت + +667 +01:16:08,110 --> 01:16:14,280 +بدالها اللى هو تلاتة ايه من فوقيبقى هذا بده يسمى + +668 +01:16:14,280 --> 01:16:22,680 +قداش اللي هو أربعة إيه ناقص ستة إيه زي التلاتة + +669 +01:16:22,680 --> 01:16:30,210 +يعني بيبقى القداش ناقص اتنين إيه زي التلاتةهذا + +670 +01:16:30,210 --> 01:16:34,390 +قيمة الدالة عند اتنين بدي اروح اجيب limit لل + +671 +01:16:34,390 --> 01:16:41,770 +function يبقى انا بدي limit لل F of X لما ال X بدي + +672 +01:16:41,770 --> 01:16:47,690 +اروح لل اتنين على سبيل المثال من جهة الشمال لأن من + +673 +01:16:47,690 --> 01:16:52,910 +جهة اليمين هتعطيني النتيجة هذهمظبوط ولا لأ؟ و + +674 +01:16:52,910 --> 01:16:56,290 +كونها continuous يبقى ال limit من اليمين بدها تسوي + +675 +01:16:56,290 --> 01:16:59,990 +ال limit من الشمال يبقى بتكفيني بس ال limit من + +676 +01:16:59,990 --> 01:17:04,590 +الشمال من جهة الشمال للدالة يبقى هاي ال limit لما + +677 +01:17:04,590 --> 01:17:09,050 +ال X بده يروح للاتنين من جهة الشمال اتنين من جهة + +678 +01:17:09,050 --> 01:17:16,290 +الشمال يبقى Xبالعكس من الدرجة الأولى يجب التعويض + +679 +01:17:16,290 --> 01:17:24,470 +مباشر يبقى هذا بتعطيك اتنين ايه الان since بما ان + +680 +01:17:24,470 --> 01:17:36,650 +ال F is continuous at X يساوي اتنين we have إذا + +681 +01:17:36,650 --> 01:17:42,020 +القيمتين هدول لازم مالهم يساووا بعضيبقى بدى يصير + +682 +01:17:42,020 --> 01:17:50,820 +نقص اتنين ا زائد تلاتة بدها تساوي لاتنين ايه تمام + +683 +01:17:50,820 --> 01:17:58,480 +يبقى بناء عليه الأربعة ايه بدها تساوي تلاتة يبقى + +684 +01:17:58,480 --> 01:18:04,320 +ال ايه بدى يساوي قداش تلات تربع and + +685 +01:18:06,570 --> 01:18:15,910 +الـ B يساوي تلاتة في تلت اربع يعني ان الـ B يساوي + +686 +01:18:15,910 --> 01:18:21,330 +تسعة اربع يبقى لو كانت الـ A بتلت اربع و الـ B + +687 +01:18:21,330 --> 01:18:26,670 +بتلت تسعة اربع بصير الدالة قابلة للاشتقاق عن + +688 +01:18:26,670 --> 01:18:31,250 +الاتنينوبالتالي بيصير continuous عند وين؟ عند + +689 +01:18:31,250 --> 01:18:36,710 +الاتنين أيضا لحد هنا انتهى هذا ال section ويلايكم + +690 +01:18:36,710 --> 01:18:40,850 +أرقام + +691 +01:18:40,850 --> 01:18:48,850 +المسائل exercises تلاتة اتنين يبقى exercises تلاتة + +692 +01:18:48,850 --> 01:18:52,850 +اتنين المسائل التالية + +693 +01:18:54,650 --> 01:19:05,710 +من واحد لغاية واحد و تلاتين القد وبنضيف عليهم سبعة + +694 +01:19:05,710 --> 01:19:15,490 +و تلاتين و تسعة و تلاتين واتنين واربعين وتلاتة + +695 +01:19:15,490 --> 01:19:25,000 +واربعينوخمسة واربعين وسبعة واربعين وتسعة واربعين + +696 +01:19:25,000 --> 01:19:37,880 +وتلاتة وخمسين واربعة وخمسين وخمسة وخمسين وتمانية + +697 +01:19:37,880 --> 01:19:39,220 +وخمسين + +698 +01:19:43,640 --> 01:19:49,260 +المرة القادمة ان شاء الله بنبدأ في قواعد الاشتقاق + +699 +01:19:49,260 --> 01:19:51,900 +اللي انتم استعجلين عليها + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OAHmrcZi8vg_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OAHmrcZi8vg_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..f8a3b74b4918ca83e5f5fd6a020dd2cc8d616346 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OAHmrcZi8vg_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 3343, "start": 20.67, "end": 33.43, "text": "أنا راح نكمل مابتدأناه في 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لكن لما كانت X تربية صار الاحتمال واحد فقط", "tokens": [1211, 19452, 5296, 15042, 6055, 3555, 4587, 7578, 1783, 1975, 33753, 2304, 6027, 1783, 6055, 30544, 3714, 29245, 3555, 1975, 33753, 2304, 6027, 6055, 30544, 8608, 6027, 3555, 32239, 8592, 5296, 28814, 1863, 1783, 47525, 11296, 6055, 32887, 5016, 24976, 4018, 7251, 3555, 4587, 7578, 11933, 15730, 12602, 39319, 2655, 5296, 4018, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 6055, 3555, 4587, 7578, 2423, 1783, 20666, 2304, 29245, 3555, 4032, 28814, 15730, 12602, 39319, 2655, 5296, 4018, 9154, 10874, 3224, 3660, 25124, 2304, 6027, 6055, 3555, 4587, 7578, 2423, 1783, 6024, 110, 16373, 3555, 21136, 6027, 3555, 7251, 3555, 4587, 7578, 42963, 33753, 2304, 6027, 16472, 3224, 4032, 2288, 3215, 9307, 44381, 5296, 15042, 25961, 2655, 1783, 6055, 25513, 10632, 20328, 9640, 42963, 33753, 2304, 6027, 36764, 24401, 6156, 47432], "avg_logprob": -0.18082060545455408, "compression_ratio": 2.2256410256410257, "no_speech_prob": 5.960464477539063e-08, 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"probability": 0.610595703125}, {"start": 385.33, "end": 385.51, "word": " لو", "probability": 0.94189453125}, {"start": 385.51, "end": 385.77, "word": " كنت", "probability": 0.83056640625}, {"start": 385.77, "end": 386.31, "word": " أضرب", "probability": 0.8098958333333334}, {"start": 386.31, "end": 386.55, "word": " في", "probability": 0.8857421875}, {"start": 386.55, "end": 386.97, "word": " X", "probability": 0.59130859375}, {"start": 386.97, "end": 387.37, "word": " هذه", "probability": 0.640625}], "temperature": 1.0}, {"id": 17, "seek": 40654, "start": 388.02, "end": 406.54, "text": "بصير لو كانت موجبة ال inequality بتبقى كما هي لو كانت سالبة تنقلب ال inequality وبالتالي وردنا مظبوط مشان نتخلص من هذه المشكلة دي براح بدرم في مين في absolute value اكس absolute value اكس دائما و أبدا تزيد تفوى بالتالي ماعندي مشكلة", "tokens": [3555, 9381, 13546, 45164, 25961, 2655, 3714, 29245, 49401, 2423, 16970, 39894, 3555, 4587, 7578, 9122, 15042, 39896, 45164, 25961, 2655, 8608, 6027, 49401, 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"probability": 0.7171630859375}, {"start": 395.36, "end": 396.38, "word": " مظبوط", "probability": 0.829345703125}, {"start": 396.38, "end": 397.0, "word": " مشان", "probability": 0.5687255859375}, {"start": 397.0, "end": 397.62, "word": " نتخلص", "probability": 0.889599609375}, {"start": 397.62, "end": 397.76, "word": " من", "probability": 0.97705078125}, {"start": 397.76, "end": 397.88, "word": " هذه", "probability": 0.41650390625}, {"start": 397.88, "end": 398.52, "word": " المشكلة", "probability": 0.980712890625}, {"start": 398.52, "end": 398.62, "word": " دي", "probability": 0.800537109375}, {"start": 398.62, "end": 398.9, "word": " براح", "probability": 0.7522786458333334}, {"start": 398.9, "end": 399.28, "word": " بدرم", "probability": 0.6586100260416666}, {"start": 399.28, "end": 399.44, "word": " في", "probability": 0.6005859375}, {"start": 399.44, "end": 399.8, "word": " مين", "probability": 0.78564453125}, {"start": 399.8, "end": 400.36, "word": " في", "probability": 0.60791015625}, {"start": 400.36, "end": 400.88, "word": " absolute", "probability": 0.8955078125}, {"start": 400.88, "end": 401.34, "word": " value", "probability": 0.96923828125}, {"start": 401.34, "end": 401.66, "word": " اكس", "probability": 0.6796468098958334}, {"start": 401.66, "end": 401.94, "word": " absolute", "probability": 0.5380859375}, {"start": 401.94, "end": 402.38, "word": " value", "probability": 0.98583984375}, {"start": 402.38, "end": 402.74, "word": " اكس", "probability": 0.8977864583333334}, {"start": 402.74, "end": 403.06, "word": " دائما", "probability": 0.837890625}, {"start": 403.06, "end": 403.18, "word": " و", "probability": 0.802734375}, {"start": 403.18, "end": 403.64, "word": " أبدا", "probability": 0.7176106770833334}, {"start": 403.64, "end": 404.5, "word": " تزيد", "probability": 0.6829427083333334}, {"start": 404.5, "end": 404.88, "word": " تفوى", "probability": 0.7237548828125}, {"start": 404.88, "end": 405.34, "word": " بالتالي", "probability": 0.813720703125}, {"start": 405.34, "end": 406.04, "word": " ماعندي", "probability": 0.9580078125}, {"start": 406.04, "end": 406.54, "word": " مشكلة", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 18, "seek": 42743, "start": 406.63, "end": 427.43, "text": "تبقى الـ Inquality كما هي، طبعا، يبقى لو روحت ضربت في absolute value ل X بس يبقى ال mean is zero أقل من أو يسوى absolute value ل X في ال sign واحد على X ك absolute value أقل من أو يسوى absolute value ل X", "tokens": [2655, 3555, 4587, 7578, 2423, 39184, 682, 11286, 9122, 15042, 39896, 12399, 23032, 3555, 3615, 995, 12399, 7251, 3555, 4587, 7578, 45164, 12602, 2407, 33753, 48812, 25513, 2655, 8978, 8236, 2158, 5296, 1783, 4724, 3794, 7251, 3555, 4587, 7578, 2423, 914, 307, 4018, 5551, 4587, 1211, 9154, 34051, 7251, 3794, 2407, 7578, 8236, 2158, 5296, 1783, 8978, 2423, 1465, 36764, 24401, 15844, 1783, 9122, 8236, 2158, 5551, 4587, 1211, 9154, 34051, 7251, 3794, 2407, 7578, 8236, 2158, 5296, 1783], "avg_logprob": 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"end": 1087.98, "word": " اللي", "probability": 0.93994140625}, {"start": 1087.98, "end": 1088.22, "word": " بدي", "probability": 0.763916015625}, {"start": 1088.22, "end": 1088.52, "word": " اعطاه", "probability": 0.724853515625}, {"start": 1088.52, "end": 1088.74, "word": " هنا", "probability": 0.80029296875}], "temperature": 1.0}, {"id": 44, "seek": 110541, "start": 1089.09, "end": 1105.41, "text": "جالي الـ definition لتلف بـ function defined على an open interval containing x node except possibly مادة ممكن عند x node itself", "tokens": [7435, 6027, 1829, 2423, 39184, 7123, 5296, 2655, 46538, 4724, 39184, 2445, 7642, 15844, 364, 1269, 15035, 19273, 2031, 9984, 3993, 6264, 3714, 18513, 3660, 3714, 43020, 43242, 2031, 9984, 2564], "avg_logprob": -0.5136718470603228, "compression_ratio": 1.203125, "no_speech_prob": 0.0, "words": [{"start": 1089.09, "end": 1089.59, "word": "جالي", "probability": 0.4252115885416667}, {"start": 1089.59, "end": 1089.65, "word": " الـ", "probability": 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there exists يوجد الـ E بالإنجليزي بس مغلوبة يعني أن هناك موجب فرياضيتنا هناك موجب دلتة أكبر من الـ zero بلاقي قيمة لدلتة مالها تبقى موجبة دائم هنا بحيث أن", "tokens": [28814, 15730, 5551, 9778, 3215, 8315, 6225, 3215, 3215, 5551, 3714, 29245, 3555, 5551, 4117, 26890, 9154, 2423, 39184, 4018, 456, 8198, 7251, 29245, 3215, 2423, 39184, 462, 20666, 28814, 1863, 7435, 20292, 11622, 1829, 4724, 3794, 3714, 17082, 1211, 37746, 3660, 37495, 22653, 14739, 34105, 4117, 3714, 29245, 3555, 6156, 16572, 46958, 36081, 8315, 34105, 4117, 3714, 29245, 3555, 11778, 1211, 2655, 3660, 5551, 4117, 26890, 9154, 2423, 39184, 4018, 4724, 15040, 38436, 12174, 32640, 3660, 5296, 3215, 1211, 2655, 3660, 3714, 6027, 11296, 6055, 3555, 4587, 7578, 3714, 29245, 49401, 11778, 16373, 2304, 34105, 4724, 5016, 1829, 12984, 14739], "avg_logprob": -0.42463236287528394, "compression_ratio": 1.7083333333333333, "no_speech_prob": 0.0, "words": [{"start": 1236.31, "end": 1236.69, "word": "إذا", "probability": 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"word": " ما", "probability": 0.97509765625}, {"start": 2182.97, "end": 2183.73, "word": " تستوعب", "probability": 0.91650390625}, {"start": 2183.73, "end": 2184.77, "word": " الموضوع", "probability": 0.996826171875}, {"start": 2184.77, "end": 2185.47, "word": " بدنا", "probability": 0.850341796875}, {"start": 2185.47, "end": 2185.75, "word": " نيجي", "probability": 0.9805908203125}, {"start": 2185.75, "end": 2186.25, "word": " لأول", "probability": 0.9405924479166666}, {"start": 2186.25, "end": 2186.87, "word": " مثال", "probability": 0.968017578125}, {"start": 2186.87, "end": 2187.43, "word": " بيقول", "probability": 0.8981119791666666}, {"start": 2187.43, "end": 2187.73, "word": " ما", "probability": 0.97802734375}, {"start": 2187.73, "end": 2188.33, "word": " يأتي", "probability": 0.8984375}, {"start": 2188.33, "end": 2189.39, "word": " يبقى", "probability": 0.944091796875}, {"start": 2189.39, "end": 2190.01, "word": " example", "probability": 0.89794921875}, {"start": 2190.01, "end": 2190.97, "word": " one", "probability": 0.68505859375}, {"start": 2190.97, "end": 2195.89, "word": " show", "probability": 0.85693359375}, {"start": 2195.89, "end": 2196.45, "word": " that", "probability": 0.94482421875}, {"start": 2196.45, "end": 2198.09, "word": " show", "probability": 0.75537109375}], "temperature": 1.0}, {"id": 93, "seek": 221607, "start": 2199.17, "end": 2216.07, "text": "ذات limit لما ال X بدها تروح للإتنين لدلة خمسة X ناقص أربع يساوي مين؟ يساوي ستة", "tokens": [8848, 9307, 4948, 5296, 15042, 2423, 1783, 47525, 11296, 6055, 32887, 5016, 24976, 28814, 2655, 1863, 9957, 5296, 3215, 37977, 16490, 2304, 3794, 3660, 1783, 8717, 995, 4587, 9381, 5551, 25513, 3615, 7251, 3794, 995, 45865, 3714, 9957, 22807, 7251, 3794, 995, 45865, 8608, 2655, 3660], "avg_logprob": -0.23603723974938087, "compression_ratio": 1.238532110091743, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2199.17, "end": 2200.13, "word": "ذات", "probability": 0.541259765625}, {"start": 2200.13, "end": 2203.01, "word": " limit", "probability": 0.8505859375}, {"start": 2203.01, "end": 2205.05, "word": " لما", "probability": 0.832275390625}, {"start": 2205.05, "end": 2205.25, "word": " ال", "probability": 0.86083984375}, {"start": 2205.25, "end": 2205.69, "word": " X", "probability": 0.57763671875}, {"start": 2205.69, "end": 2206.89, "word": " بدها", "probability": 0.7314453125}, {"start": 2206.89, "end": 2207.47, "word": " تروح", "probability": 0.9796549479166666}, {"start": 2207.47, "end": 2208.57, "word": " للإتنين", "probability": 0.8046875}, {"start": 2208.57, "end": 2209.97, "word": " لدلة", "probability": 0.6105143229166666}, {"start": 2209.97, "end": 2210.97, "word": " خمسة", "probability": 0.908447265625}, {"start": 2210.97, "end": 2211.33, "word": " X", "probability": 0.8330078125}, {"start": 2211.33, "end": 2212.47, "word": " ناقص", "probability": 0.9552001953125}, {"start": 2212.47, "end": 2213.05, "word": " أربع", "probability": 0.7560221354166666}, {"start": 2213.05, "end": 2213.61, "word": " يساوي", "probability": 0.954833984375}, {"start": 2213.61, "end": 2214.57, "word": " مين؟", "probability": 0.6669108072916666}, {"start": 2214.57, "end": 2215.45, "word": " يساوي", "probability": 0.9710693359375}, {"start": 2215.45, "end": 2216.07, "word": " ستة", "probability": 0.9578450520833334}], "temperature": 1.0}, {"id": 94, "seek": 223932, "start": 2218.88, "end": 2239.32, "text": "بقى احنا مقترحين انه limit لهذه الدالة بده يساوي ستة بدنا نتأكد هذا اقتراحنا صح ولا لأ لإنه قلنا هنا إيش but we verify that the suspected limit is correct يعني احنا بنتأكد انه limit المقترح هذه صحيحة ولا لأ", "tokens": [3555, 4587, 7578, 1975, 5016, 8315, 3714, 38149, 2288, 5016, 9957, 16472, 3224, 4948, 46740, 24192, 32748, 6027, 3660, 47525, 3224, 7251, 3794, 995, 45865, 8608, 2655, 3660, 47525, 8315, 8717, 2655, 10721, 4117, 3215, 23758, 1975, 38149, 23557, 5016, 8315, 20328, 5016, 49429, 5296, 10721, 5296, 28814, 1863, 3224, 12174, 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"word": " احنا", "probability": 0.9571940104166666}, {"start": 2235.48, "end": 2236.2, "word": " بنتأكد", "probability": 0.932421875}, {"start": 2236.2, "end": 2236.62, "word": " انه", "probability": 0.759521484375}, {"start": 2236.62, "end": 2236.86, "word": " limit", "probability": 0.67041015625}, {"start": 2236.86, "end": 2237.48, "word": " المقترح", "probability": 0.9400634765625}, {"start": 2237.48, "end": 2237.78, "word": " هذه", "probability": 0.44921875}, {"start": 2237.78, "end": 2238.64, "word": " صحيحة", "probability": 0.98818359375}, {"start": 2238.64, "end": 2239.06, "word": " ولا", "probability": 0.966796875}, {"start": 2239.06, "end": 2239.32, "word": " لأ", "probability": 0.878173828125}], "temperature": 1.0}, {"id": 95, "seek": 226303, "start": 2239.63, "end": 2263.03, "text": "طبعا لو جاءك كده السؤال في الامتحان بتقول والله بسيط ديدا بنعوض لإنها linear 2x5 هو 10-7 يساوي 6 في خاطرك مع السلامة لا انا بروح بصيلك السؤال صياغة أخرى بروح بقولك use epsilon delta definition to show that بيبقى مش فيها كلام بتعمل زي ذاك بتاخد zero", "tokens": [9566, 3555, 3615, 995, 45164, 10874, 16606, 4117, 9122, 3215, 3224, 21136, 33604, 6027, 8978, 2423, 10943, 2655, 5016, 7649, 39894, 39648, 16070, 43761, 4724, 3794, 1829, 9566, 11778, 1829, 28259, 44945, 3615, 2407, 11242, 5296, 28814, 1863, 11296, 8213, 568, 87, 20, 31439, 1266, 12, 22, 7251, 3794, 995, 45865, 1386, 8978, 16490, 41193, 31747, 20449, 21136, 37440, 3660, 20193, 1975, 8315, 4724, 32887, 5016, 4724, 9381, 1829, 23275, 21136, 33604, 6027, 20328, 1829, 5718, 118, 3660, 5551, 34740, 7578, 4724, 32887, 5016, 4724, 39648, 4117, 764, 17889, 8289, 7123, 281, 855, 300, 4724, 1829, 3555, 4587, 7578, 37893, 8978, 11296, 28242, 10943, 39894, 25957, 1211, 30767, 1829, 29910, 995, 4117, 39894, 47283, 3215, 4018], "avg_logprob": -0.31917735959729576, "compression_ratio": 1.528957528957529, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2239.63, "end": 2240.19, "word": "طبعا", "probability": 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{"start": 2255.57, "end": 2256.49, "word": " definition", "probability": 0.9130859375}, {"start": 2256.49, "end": 2257.13, "word": " to", "probability": 0.97119140625}, {"start": 2257.13, "end": 2257.51, "word": " show", "probability": 0.9619140625}, {"start": 2257.51, "end": 2258.29, "word": " that", "probability": 0.955078125}, {"start": 2258.29, "end": 2260.01, "word": " بيبقى", "probability": 0.7108154296875}, {"start": 2260.01, "end": 2260.37, "word": " مش", "probability": 0.468505859375}, {"start": 2260.37, "end": 2260.65, "word": " فيها", "probability": 0.7137451171875}, {"start": 2260.65, "end": 2261.05, "word": " كلام", "probability": 0.950927734375}, {"start": 2261.05, "end": 2261.75, "word": " بتعمل", "probability": 0.7948404947916666}, {"start": 2261.75, "end": 2261.95, "word": " زي", "probability": 0.980224609375}, {"start": 2261.95, "end": 2262.19, "word": " ذاك", "probability": 0.78173828125}, {"start": 2262.19, "end": 2262.67, "word": " بتاخد", "probability": 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"probability": 0.873046875}, {"start": 2628.11, "end": 2628.59, "word": " هو", "probability": 0.034393310546875}, {"start": 2628.59, "end": 2632.23, "word": " 5X", "probability": 0.55029296875}, {"start": 2632.23, "end": 2633.37, "word": " ناقص", "probability": 0.6849365234375}, {"start": 2633.37, "end": 2633.97, "word": " 4", "probability": 0.8173828125}, {"start": 2633.97, "end": 2635.43, "word": " ناقص", "probability": 0.82666015625}, {"start": 2635.43, "end": 2635.85, "word": " 6", "probability": 0.95361328125}, {"start": 2635.85, "end": 2641.59, "word": " فهذا", "probability": 0.3676350911458333}, {"start": 2641.59, "end": 2642.49, "word": " المقدر", "probability": 0.674713134765625}, {"start": 2642.49, "end": 2643.09, "word": " يجب", "probability": 0.6533610026041666}, {"start": 2643.09, "end": 2643.25, "word": " أن", "probability": 0.51171875}, {"start": 2643.25, "end": 2643.55, "word": " يكون", "probability": 0.5999755859375}, {"start": 2643.55, "end": 2645.71, "word": " أقل", "probability": 0.89599609375}, {"start": 2645.71, "end": 2646.05, "word": " من", "probability": 0.96630859375}, {"start": 2646.05, "end": 2646.69, "word": " Epsilon", "probability": 0.530029296875}], "temperature": 1.0}, {"id": 112, "seek": 266478, "start": 2646.96, "end": 2664.78, "text": "بقول كويس هذا بده يساوي خمسة X ناقص عشرة هذا بده يساوي خمسة X ناقص اتنين هذا بده يساوي خمسة absolute value ل X ناقص اتنين", "tokens": [3555, 39648, 9122, 45865, 3794, 23758, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 1783, 8717, 995, 4587, 9381, 6225, 8592, 25720, 23758, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 1783, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 23758, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 8236, 2158, 5296, 1783, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957], "avg_logprob": -0.12936580181121826, "compression_ratio": 1.8611111111111112, "no_speech_prob": 0.0, "words": [{"start": 2646.96, "end": 2647.52, "word": "بقول", "probability": 0.779052734375}, {"start": 2647.52, "end": 2648.22, "word": " كويس", "probability": 0.9049479166666666}, {"start": 2648.22, "end": 2648.96, "word": " هذا", "probability": 0.73681640625}, {"start": 2648.96, "end": 2649.46, "word": " بده", "probability": 0.3521728515625}, {"start": 2649.46, "end": 2650.0, "word": " يساوي", "probability": 0.9378662109375}, {"start": 2650.0, "end": 2651.1, "word": " خمسة", "probability": 0.899169921875}, {"start": 2651.1, "end": 2651.48, "word": " X", "probability": 0.302978515625}, {"start": 2651.48, "end": 2652.22, "word": " ناقص", "probability": 0.9599609375}, {"start": 2652.22, "end": 2652.8, "word": " عشرة", "probability": 0.9342447916666666}, {"start": 2652.8, "end": 2653.58, "word": " هذا", "probability": 0.71484375}, {"start": 2653.58, "end": 2654.06, "word": " بده", "probability": 0.95068359375}, {"start": 2654.06, "end": 2654.62, "word": " يساوي", "probability": 0.987548828125}, {"start": 2654.62, "end": 2655.8, "word": " خمسة", "probability": 0.9864501953125}, {"start": 2655.8, "end": 2656.36, "word": " X", "probability": 0.51171875}, {"start": 2656.36, "end": 2657.46, "word": " ناقص", "probability": 0.9927978515625}, {"start": 2657.46, "end": 2658.08, "word": " اتنين", "probability": 0.9659423828125}, {"start": 2658.08, "end": 2659.02, "word": " هذا", "probability": 0.8876953125}, {"start": 2659.02, "end": 2659.58, "word": " بده", "probability": 0.966552734375}, {"start": 2659.58, "end": 2660.12, "word": " يساوي", "probability": 0.9913330078125}, {"start": 2660.12, "end": 2661.4, "word": " خمسة", "probability": 0.98291015625}, {"start": 2661.4, "end": 2662.22, "word": " absolute", "probability": 0.7490234375}, {"start": 2662.22, "end": 2662.9, "word": " value", "probability": 0.990234375}, {"start": 2662.9, "end": 2663.06, "word": " ل", "probability": 0.521484375}, {"start": 2663.06, "end": 2663.56, "word": " X", "probability": 0.61572265625}, {"start": 2663.56, "end": 2664.22, "word": " ناقص", "probability": 0.992919921875}, {"start": 2664.22, "end": 2664.78, "word": " اتنين", "probability": 0.984619140625}], "temperature": 1.0}, {"id": 113, "seek": 268293, "start": 2665.27, "end": 2682.93, "text": "هذه أقل من إبسلون على خمسة إذا هذا أقل من هذه الخمسة اللي برا وهذه إبسلون على خمسة هذه اللي هي قدش تساوي إبسلون", "tokens": [3224, 24192, 5551, 4587, 1211, 9154, 11933, 3555, 3794, 1211, 11536, 15844, 16490, 2304, 3794, 3660, 11933, 15730, 23758, 5551, 4587, 1211, 9154, 29538, 33962, 2304, 3794, 3660, 13672, 1829, 4724, 23557, 37037, 24192, 11933, 3555, 3794, 1211, 11536, 15844, 16490, 2304, 3794, 3660, 29538, 13672, 1829, 39896, 12174, 3215, 8592, 6055, 3794, 995, 45865, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.22912398224971334, "compression_ratio": 1.8773584905660377, "no_speech_prob": 0.0, "words": [{"start": 2665.27, "end": 2666.17, "word": "هذه", "probability": 0.57373046875}, {"start": 2666.17, "end": 2667.31, "word": " أقل", "probability": 0.9200846354166666}, {"start": 2667.31, "end": 2667.63, "word": " من", "probability": 0.96240234375}, {"start": 2667.63, "end": 2669.73, "word": " إبسلون", "probability": 0.78111572265625}, {"start": 2669.73, "end": 2670.01, "word": " على", "probability": 0.74462890625}, {"start": 2670.01, "end": 2670.77, "word": " خمسة", "probability": 0.9754638671875}, {"start": 2670.77, "end": 2671.39, "word": " إذا", "probability": 0.6246337890625}, {"start": 2671.39, "end": 2672.07, "word": " هذا", "probability": 0.27392578125}, {"start": 2672.07, "end": 2673.17, "word": " أقل", "probability": 0.97607421875}, {"start": 2673.17, "end": 2673.51, "word": " من", "probability": 0.97900390625}, {"start": 2673.51, "end": 2673.91, "word": " هذه", "probability": 0.490966796875}, {"start": 2673.91, "end": 2674.57, "word": " الخمسة", "probability": 0.9813232421875}, {"start": 2674.57, "end": 2674.73, "word": " اللي", "probability": 0.610107421875}, {"start": 2674.73, "end": 2675.19, "word": " برا", "probability": 0.904541015625}, {"start": 2675.19, "end": 2676.41, "word": " وهذه", "probability": 0.87158203125}, {"start": 2676.41, "end": 2677.65, "word": " إبسلون", "probability": 0.9509765625}, {"start": 2677.65, "end": 2678.51, "word": " على", "probability": 0.86767578125}, {"start": 2678.51, "end": 2679.39, "word": " خمسة", "probability": 0.994140625}, {"start": 2679.39, "end": 2680.01, "word": " هذه", "probability": 0.4609375}, {"start": 2680.01, "end": 2680.15, "word": " اللي", "probability": 0.81640625}, {"start": 2680.15, "end": 2680.31, "word": " هي", "probability": 0.85693359375}, {"start": 2680.31, "end": 2680.65, "word": " قدش", "probability": 0.556396484375}, {"start": 2680.65, "end": 2681.53, "word": " تساوي", "probability": 0.966796875}, {"start": 2681.53, "end": 2682.93, "word": " إبسلون", "probability": 0.95400390625}], "temperature": 1.0}, {"id": 114, "seek": 270470, "start": 2683.14, "end": 2704.7, "text": "يبقى فعلا الفرق ما بين الاتنين هدول سواء الخمسة x ناقص الأربعة ناقص الستة أقل من مين من إبسلن يعني لما ناخد delta بإبسلن على خمسة النتيجة فعلا بصير الفرق بين الفوفكس وإيه الماله أقل من إبسلن", "tokens": [1829, 3555, 4587, 7578, 6156, 3615, 15040, 27188, 2288, 4587, 19446, 49374, 2423, 9307, 1863, 9957, 8032, 3215, 12610, 8608, 2407, 16606, 33962, 2304, 3794, 3660, 2031, 8717, 995, 4587, 9381, 16247, 25513, 27884, 8717, 995, 4587, 9381, 21136, 2655, 3660, 5551, 4587, 1211, 9154, 3714, 9957, 9154, 11933, 3555, 3794, 1211, 1863, 37495, 22653, 5296, 15042, 8717, 47283, 3215, 8289, 4724, 28814, 3555, 3794, 1211, 1863, 15844, 16490, 2304, 3794, 3660, 28239, 31371, 7435, 3660, 6156, 3615, 15040, 4724, 9381, 13546, 27188, 2288, 4587, 49374, 27188, 38688, 4117, 3794, 4032, 28814, 1829, 3224, 9673, 6027, 3224, 5551, 4587, 1211, 9154, 11933, 3555, 3794, 1211, 1863], "avg_logprob": -0.17391939753683927, "compression_ratio": 1.8369565217391304, "no_speech_prob": 0.0, "words": [{"start": 2683.14, "end": 2683.76, "word": "يبقى", "probability": 0.8499755859375}, 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"probability": 0.9010009765625}, {"start": 2692.24, "end": 2693.04, "word": " الستة", "probability": 0.8704427083333334}, {"start": 2693.04, "end": 2693.66, "word": " أقل", "probability": 0.88671875}, {"start": 2693.66, "end": 2693.92, "word": " من", "probability": 0.9814453125}, {"start": 2693.92, "end": 2694.32, "word": " مين", "probability": 0.79150390625}, {"start": 2694.32, "end": 2694.84, "word": " من", "probability": 0.734375}, {"start": 2694.84, "end": 2695.44, "word": " إبسلن", "probability": 0.74892578125}, {"start": 2695.44, "end": 2695.78, "word": " يعني", "probability": 0.798828125}, {"start": 2695.78, "end": 2696.04, "word": " لما", "probability": 0.96923828125}, {"start": 2696.04, "end": 2696.68, "word": " ناخد", "probability": 0.9866536458333334}, {"start": 2696.68, "end": 2697.04, "word": " delta", "probability": 0.32470703125}, {"start": 2697.04, "end": 2697.72, "word": " بإبسلن", "probability": 0.9630533854166666}, {"start": 2697.72, "end": 2698.0, "word": " على", "probability": 0.7578125}, {"start": 2698.0, "end": 2698.68, "word": " خمسة", "probability": 0.983154296875}, {"start": 2698.68, "end": 2699.58, "word": " النتيجة", "probability": 0.913818359375}, {"start": 2699.58, "end": 2700.0, "word": " فعلا", "probability": 0.98583984375}, {"start": 2700.0, "end": 2700.36, "word": " بصير", "probability": 0.9169921875}, {"start": 2700.36, "end": 2700.78, "word": " الفرق", "probability": 0.9892578125}, {"start": 2700.78, "end": 2700.96, "word": " بين", "probability": 0.7216796875}, {"start": 2700.96, "end": 2701.56, "word": " الفوفكس", "probability": 0.61883544921875}, {"start": 2701.56, "end": 2701.9, "word": " وإيه", "probability": 0.614501953125}, {"start": 2701.9, "end": 2702.46, "word": " الماله", "probability": 0.7674153645833334}, {"start": 2702.46, "end": 2703.68, "word": " أقل", "probability": 0.9679361979166666}, {"start": 2703.68, "end": 2704.0, "word": " من", "probability": 0.99169921875}, {"start": 2704.0, "end": 2704.7, "word": " إبسلن", "probability": 0.9876953125}], "temperature": 1.0}, {"id": 115, "seek": 272367, "start": 2704.89, "end": 2723.67, "text": "يبقى هى تحققنا من ان الكلام اللى عملناه صحيح يبقى بقوله تأكدنا thus limit لخمسة X ناقص أربعة لما ال X بدى يروح لاتنين بدى يساوي ستة بدى اسألكوا السؤال التالى", "tokens": [1829, 3555, 4587, 7578, 8032, 7578, 6055, 5016, 4587, 4587, 8315, 9154, 16472, 2423, 28820, 10943, 13672, 7578, 6225, 42213, 8315, 3224, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 4724, 39648, 3224, 6055, 10721, 4117, 3215, 8315, 8807, 4948, 5296, 9778, 2304, 3794, 3660, 1783, 8717, 995, 4587, 9381, 5551, 25513, 27884, 5296, 15042, 2423, 1783, 47525, 7578, 7251, 32887, 5016, 5296, 9307, 1863, 9957, 47525, 7578, 7251, 3794, 995, 45865, 8608, 2655, 3660, 47525, 7578, 24525, 10721, 23275, 14407, 21136, 33604, 6027, 16712, 6027, 7578], "avg_logprob": -0.20969460396604103, "compression_ratio": 1.5872093023255813, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2704.89, "end": 2705.23, "word": "يبقى", "probability": 0.79296875}, {"start": 2705.23, "end": 2705.39, "word": " هى", "probability": 0.447998046875}, {"start": 2705.39, "end": 2706.27, "word": " تحققنا", "probability": 0.95869140625}, {"start": 2706.27, "end": 2706.49, "word": " من", "probability": 0.88330078125}, {"start": 2706.49, "end": 2706.81, "word": " ان", "probability": 0.77197265625}, {"start": 2706.81, "end": 2707.33, "word": " الكلام", "probability": 0.8702799479166666}, {"start": 2707.33, "end": 2707.53, "word": " اللى", "probability": 0.991943359375}, {"start": 2707.53, "end": 2708.07, "word": " عملناه", "probability": 0.9801025390625}, {"start": 2708.07, "end": 2708.69, "word": " صحيح", "probability": 0.9530029296875}, {"start": 2708.69, "end": 2709.53, "word": " يبقى", "probability": 0.9393310546875}, {"start": 2709.53, "end": 2710.01, "word": " بقوله", "probability": 0.8665364583333334}, {"start": 2710.01, "end": 2711.77, "word": " تأكدنا", "probability": 0.90244140625}, {"start": 2711.77, "end": 2712.65, "word": " thus", "probability": 0.205810546875}, {"start": 2712.65, "end": 2713.71, "word": " limit", "probability": 0.7900390625}, {"start": 2713.71, "end": 2715.45, "word": " لخمسة", "probability": 0.798681640625}, {"start": 2715.45, "end": 2715.77, "word": " X", "probability": 0.368896484375}, {"start": 2715.77, "end": 2716.41, "word": " ناقص", "probability": 0.844970703125}, {"start": 2716.41, "end": 2717.03, "word": " أربعة", "probability": 0.8045247395833334}, {"start": 2717.03, "end": 2717.67, "word": " لما", "probability": 0.93798828125}, {"start": 2717.67, "end": 2717.81, "word": " ال", "probability": 0.88916015625}, {"start": 2717.81, "end": 2718.07, "word": " X", "probability": 0.9306640625}, {"start": 2718.07, "end": 2718.41, "word": " بدى", "probability": 0.533203125}, {"start": 2718.41, "end": 2718.65, "word": " يروح", "probability": 0.9423828125}, {"start": 2718.65, "end": 2719.31, "word": " لاتنين", "probability": 0.7762451171875}, {"start": 2719.31, "end": 2720.11, "word": " بدى", "probability": 0.754150390625}, {"start": 2720.11, "end": 2720.79, "word": " يساوي", "probability": 0.86572265625}, {"start": 2720.79, "end": 2721.47, "word": " ستة", "probability": 0.9534505208333334}, {"start": 2721.47, "end": 2722.03, "word": " بدى", "probability": 0.7171630859375}, {"start": 2722.03, "end": 2722.57, "word": " اسألكوا", "probability": 0.8392333984375}, {"start": 2722.57, "end": 2723.05, "word": " السؤال", "probability": 0.9762369791666666}, {"start": 2723.05, "end": 2723.67, "word": " التالى", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 116, "seek": 274625, "start": 2724.75, "end": 2746.25, "text": "هل احنا بشغل هذا حسبنا limit لدى الله؟ لأ احنا بس تأكدنا ان ال limit صحيح اللي ليس الا، اذا في هذا ال section كتبتلك اول سطرين احنا هنا بنحسبش limit في هذا ال section بل بنتأكد هل ال limit اللي عملناها او المعطاها هل هي صحيحة او لا، ايش بدك تسأل؟", "tokens": [3224, 1211, 1975, 5016, 8315, 4724, 8592, 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absolute value بقى يقول absolute value ل A زائد ال B أقل من أو يسوي absolute value ل A زائد absolute value ل B صحيح ولا لا؟ سكت الشعب", "tokens": [2304, 19913, 3555, 2407, 9566, 49429, 20193, 22807, 16490, 1211, 11703, 1829, 29538, 9673, 30241, 20498, 3660, 4032, 37279, 6027, 7578, 5551, 8848, 37983, 4117, 16490, 2407, 33546, 2423, 8236, 2158, 9154, 16490, 2407, 33546, 2423, 8236, 2158, 4724, 4587, 7578, 7251, 39648, 8236, 2158, 5296, 316, 30767, 16373, 3215, 2423, 363, 5551, 4587, 1211, 9154, 34051, 7251, 3794, 45865, 8236, 2158, 5296, 316, 30767, 16373, 3215, 8236, 2158, 5296, 363, 20328, 5016, 1829, 5016, 49429, 20193, 22807, 8608, 4117, 2655, 25124, 3615, 3555], "avg_logprob": -0.23253676119972677, "compression_ratio": 1.8411764705882352, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 4605.89, "end": 4606.51, "word": "مظبوط", "probability": 0.766796875}, {"start": 4606.51, "end": 4606.67, "word": " ولا", "probability": 0.82666015625}, {"start": 4606.67, "end": 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{"start": 4624.35, "end": 4624.59, "word": " ل", "probability": 0.98828125}, {"start": 4624.59, "end": 4624.89, "word": " B", "probability": 0.75048828125}, {"start": 4624.89, "end": 4625.37, "word": " صحيح", "probability": 0.935546875}, {"start": 4625.37, "end": 4625.53, "word": " ولا", "probability": 0.955078125}, {"start": 4625.53, "end": 4626.81, "word": " لا؟", "probability": 0.9091796875}, {"start": 4626.81, "end": 4627.33, "word": " سكت", "probability": 0.9508463541666666}, {"start": 4627.33, "end": 4627.85, "word": " الشعب", "probability": 0.9860026041666666}], "temperature": 1.0}, {"id": 195, "seek": 464463, "start": 4628.37, "end": 4644.63, "text": "مرت عليكم هذه؟ لأ؟ اخسرها طيب، بدي اعتبره لأ؟ خليني معاهم اللي بيقول لأ لأ لأ لأ طيب السؤال ليش مرة يساوي مرة أقل من تعالي نقولك", "tokens": [2304, 43500, 25894, 24793, 29538, 22807, 5296, 10721, 22807, 1975, 9778, 3794, 2288, 11296, 23032, 1829, 3555, 12399, 4724, 16254, 1975, 34268, 26890, 3224, 5296, 10721, 22807, 16490, 1211, 9957, 1829, 20449, 995, 16095, 13672, 1829, 4724, 1829, 39648, 5296, 10721, 5296, 10721, 5296, 10721, 5296, 10721, 23032, 1829, 3555, 21136, 33604, 6027, 32239, 8592, 3714, 25720, 7251, 3794, 995, 45865, 3714, 25720, 5551, 4587, 1211, 9154, 37279, 6027, 1829, 8717, 39648, 4117], "avg_logprob": -0.280405394128851, "compression_ratio": 1.6666666666666667, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 4628.37, "end": 4629.25, "word": "مرت", "probability": 0.5390625}, {"start": 4629.25, "end": 4629.67, "word": " عليكم", "probability": 0.869873046875}, {"start": 4629.67, "end": 4630.29, "word": " هذه؟", "probability": 0.851318359375}, {"start": 4630.29, "end": 4632.01, "word": " لأ؟", "probability": 0.5004475911458334}, {"start": 4632.01, "end": 4633.71, "word": " اخسرها", "probability": 0.71435546875}, {"start": 4633.71, "end": 4634.53, "word": " طيب،", "probability": 0.71612548828125}, {"start": 4634.53, "end": 4634.99, "word": " بدي", "probability": 0.627685546875}, {"start": 4634.99, "end": 4635.53, "word": " اعتبره", "probability": 0.92919921875}, {"start": 4635.53, "end": 4636.35, "word": " لأ؟", "probability": 0.81298828125}, {"start": 4636.35, "end": 4636.93, "word": " خليني", "probability": 0.8223876953125}, {"start": 4636.93, "end": 4637.31, "word": " معاهم", "probability": 0.6962890625}, {"start": 4637.31, "end": 4637.45, "word": " اللي", "probability": 0.92529296875}, {"start": 4637.45, "end": 4637.73, "word": " بيقول", "probability": 0.94482421875}, {"start": 4637.73, "end": 4637.95, "word": " لأ", "probability": 0.72802734375}, {"start": 4637.95, "end": 4638.29, "word": " لأ", "probability": 0.9052734375}, {"start": 4638.29, "end": 4638.93, "word": " لأ", "probability": 0.6820068359375}, {"start": 4638.93, "end": 4639.33, "word": " لأ", "probability": 0.8642578125}, {"start": 4639.33, "end": 4640.29, "word": " طيب", "probability": 0.8190104166666666}, {"start": 4640.29, "end": 4641.21, "word": " السؤال", "probability": 0.97021484375}, {"start": 4641.21, "end": 4641.59, "word": " ليش", "probability": 0.91796875}, {"start": 4641.59, "end": 4641.99, "word": " مرة", "probability": 0.93017578125}, {"start": 4641.99, "end": 4642.55, "word": " يساوي", "probability": 0.80029296875}, {"start": 4642.55, "end": 4642.91, "word": " مرة", "probability": 0.9599609375}, {"start": 4642.91, "end": 4643.37, "word": " أقل", "probability": 0.8642578125}, {"start": 4643.37, "end": 4643.59, "word": " من", "probability": 0.869140625}, {"start": 4643.59, "end": 4644.05, "word": " تعالي", "probability": 0.71337890625}, {"start": 4644.05, "end": 4644.63, "word": " نقولك", "probability": 0.9021809895833334}], "temperature": 1.0}, {"id": 196, "seek": 466557, "start": 4644.99, "end": 4665.57, "text": "إذا اتحدت a و b في الإشارة يعني كان ال a و ال b بالموجب أو ال a و ال b بالسالم مثلا 2 و 5 يبقى 2 زائد 5 يبقى 7 يبقى 7 أبسول يتولى ل 7 ب7 أبسول يتولى ل 2 ب2 أبسول يتولى ل 5 ب5 و 2 ب7 بأي تساوي", "tokens": [28814, 15730, 1975, 2655, 24401, 2655, 257, 4032, 272, 8978, 33688, 8592, 9640, 3660, 37495, 22653, 25961, 2423, 257, 4032, 2423, 272, 20666, 2304, 29245, 3555, 34051, 2423, 257, 4032, 2423, 272, 20666, 3794, 45340, 50113, 15040, 568, 4032, 1025, 7251, 3555, 4587, 7578, 568, 30767, 16373, 3215, 1025, 7251, 3555, 4587, 7578, 1614, 7251, 3555, 4587, 7578, 1614, 5551, 3555, 3794, 12610, 7251, 2655, 12610, 7578, 5296, 1614, 4724, 22, 5551, 3555, 3794, 12610, 7251, 2655, 12610, 7578, 5296, 568, 4724, 17, 5551, 3555, 3794, 12610, 7251, 2655, 12610, 7578, 5296, 1025, 4724, 20, 4032, 568, 4724, 22, 4724, 10721, 1829, 6055, 3794, 995, 45865], "avg_logprob": -0.2302862141176919, "compression_ratio": 1.9556962025316456, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 4644.99, "end": 4645.39, "word": "إذا", "probability": 0.6654052734375}, {"start": 4645.39, "end": 4646.39, "word": " اتحدت", "probability": 0.93017578125}, {"start": 4646.39, "end": 4646.69, "word": " a", "probability": 0.35546875}, {"start": 4646.69, "end": 4646.95, "word": " و", "probability": 0.86474609375}, {"start": 4646.95, "end": 4647.21, "word": " b", "probability": 0.5224609375}, {"start": 4647.21, "end": 4647.41, "word": " في", "probability": 0.8515625}, {"start": 4647.41, "end": 4648.29, "word": " الإشارة", "probability": 0.97607421875}, {"start": 4648.29, "end": 4649.01, "word": " يعني", "probability": 0.6810302734375}, {"start": 4649.01, "end": 4649.43, "word": " كان", "probability": 0.8203125}, {"start": 4649.43, "end": 4649.65, "word": " ال", "probability": 0.53271484375}, {"start": 4649.65, "end": 4649.93, "word": " a", "probability": 0.78369140625}, {"start": 4649.93, "end": 4650.07, "word": " و", "probability": 0.798828125}, {"start": 4650.07, "end": 4650.15, "word": " ال", "probability": 0.70068359375}, {"start": 4650.15, "end": 4650.33, "word": " b", "probability": 0.96728515625}, {"start": 4650.33, "end": 4651.07, "word": " بالموجب", "probability": 0.9390869140625}, {"start": 4651.07, "end": 4651.29, "word": " أو", "probability": 0.7265625}, {"start": 4651.29, "end": 4651.49, "word": " ال", "probability": 0.9013671875}, {"start": 4651.49, "end": 4651.71, "word": " a", "probability": 0.904296875}, {"start": 4651.71, "end": 4651.83, "word": " و", "probability": 0.98779296875}, {"start": 4651.83, "end": 4651.95, "word": " ال", "probability": 0.91162109375}, {"start": 4651.95, "end": 4652.19, "word": " b", "probability": 0.990234375}, {"start": 4652.19, "end": 4653.01, "word": " بالسالم", "probability": 0.7810872395833334}, {"start": 4653.01, "end": 4653.75, "word": " مثلا", "probability": 0.891845703125}, {"start": 4653.75, "end": 4654.17, "word": " 2", "probability": 0.465576171875}, {"start": 4654.17, "end": 4654.35, "word": " و", "probability": 0.79833984375}, {"start": 4654.35, "end": 4654.75, "word": " 5", "probability": 0.86279296875}, {"start": 4654.75, "end": 4656.11, "word": " يبقى", "probability": 0.9544677734375}, {"start": 4656.11, "end": 4656.63, "word": " 2", "probability": 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4670.45, "end": 4670.81, "word": " السالب", "probability": 0.7230631510416666}, {"start": 4670.81, "end": 4671.21, "word": " سبعة", "probability": 0.9503580729166666}, {"start": 4671.21, "end": 4671.47, "word": " absolute", "probability": 0.476318359375}, {"start": 4671.47, "end": 4671.83, "word": " value", "probability": 0.9599609375}, {"start": 4671.83, "end": 4672.99, "word": " بالسبعة", "probability": 0.7443033854166666}, {"start": 4672.99, "end": 4673.63, "word": " absolute", "probability": 0.68505859375}, {"start": 4673.63, "end": 4673.99, "word": " value", "probability": 0.982421875}, {"start": 4673.99, "end": 4674.39, "word": " السالب", "probability": 0.9558919270833334}, {"start": 4674.39, "end": 4674.79, "word": " اتنين", "probability": 0.9888916015625}, {"start": 4674.79, "end": 4675.15, "word": " باتنين", "probability": 0.7869873046875}, {"start": 4675.15, "end": 4675.41, "word": " absolute", "probability": 0.8583984375}, {"start": 4675.41, "end": 4675.79, "word": " value", 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{"start": 4692.53, "end": 4693.07, "word": " سالف", "probability": 0.9762369791666666}, {"start": 4693.07, "end": 4693.77, "word": " خمسة", "probability": 0.9881591796875}, {"start": 4693.77, "end": 4694.11, "word": " تعني", "probability": 0.895263671875}, {"start": 4694.11, "end": 4694.71, "word": " سالف", "probability": 0.9275716145833334}, {"start": 4694.71, "end": 4695.11, "word": " تلاتة", "probability": 0.9007568359375}, {"start": 4695.11, "end": 4695.61, "word": " absolute", "probability": 0.67431640625}, {"start": 4695.61, "end": 4696.69, "word": " تلاتة", "probability": 0.9642333984375}, {"start": 4696.69, "end": 4697.25, "word": " طيب", "probability": 0.84130859375}, {"start": 4697.25, "end": 4697.67, "word": " absolute", "probability": 0.845703125}, {"start": 4697.67, "end": 4698.07, "word": " value", "probability": 0.98974609375}, {"start": 4698.07, "end": 4698.31, "word": " ليه", "probability": 0.57720947265625}, {"start": 4698.31, "end": 4698.71, "word": " اتنين", 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و", "probability": 0.9931640625}, {"start": 4902.71, "end": 4903.65, "word": " تلاتين", "probability": 0.9957275390625}, {"start": 4903.65, "end": 4904.07, "word": " من", "probability": 0.98095703125}, {"start": 4904.07, "end": 4904.37, "word": " واحد", "probability": 0.97412109375}, {"start": 4904.37, "end": 4904.59, "word": " ل", "probability": 0.98681640625}, {"start": 4904.59, "end": 4905.53, "word": " إبس", "probability": 0.953125}, {"start": 4905.53, "end": 4905.99, "word": " من", "probability": 0.98974609375}, {"start": 4905.99, "end": 4906.21, "word": " على", "probability": 0.80126953125}, {"start": 4906.21, "end": 4906.99, "word": " سبعة", "probability": 0.99267578125}, {"start": 4906.99, "end": 4907.15, "word": " و", "probability": 0.9921875}, {"start": 4907.15, "end": 4908.03, "word": " تلاتين", "probability": 0.995361328125}, {"start": 4908.03, "end": 4908.29, "word": " من", "probability": 0.984375}, {"start": 4908.29, "end": 4909.83, "word": " واحد", "probability": 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"text": "هذا minimum الصغرة فيهما هذا minimum الواحد والإبسلون الصغرة في الإتنين يبقى لصغيرة هي بتكون main قيمة يعني الصغرة القيمتين ليش ان ال epsilon أنا مش عارفها بس لو عارفها رقما جدًا يعني افترض قاللي في البداية given epsilon تسوى خمسين", "tokens": [3224, 15730, 7285, 31767, 17082, 25720, 8978, 3224, 15042, 23758, 7285, 2423, 14407, 24401, 16070, 28814, 3555, 3794, 1211, 11536, 31767, 17082, 25720, 8978, 33688, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 5296, 9381, 17082, 48923, 39896, 39894, 30544, 2135, 12174, 32640, 3660, 37495, 22653, 31767, 17082, 25720, 25062, 32640, 2655, 9957, 32239, 8592, 16472, 2423, 17889, 41850, 37893, 6225, 9640, 5172, 11296, 4724, 3794, 45164, 6225, 9640, 5172, 11296, 12602, 4587, 15042, 10874, 3215, 14111, 995, 37495, 22653, 1975, 5172, 2655, 43042, 50239, 20292, 8978, 29739, 28259, 10632, 2212, 17889, 6055, 3794, 2407, 7578, 16490, 2304, 3794, 9957], "avg_logprob": -0.2759375122189522, "compression_ratio": 1.8421052631578947, "no_speech_prob": 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"word": " ثم", "probability": 0.803466796875}, {"start": 5703.54, "end": 5707.46, "word": " نأخذ", "probability": 0.718536376953125}, {"start": 5707.46, "end": 5709.28, "word": " دلتا", "probability": 0.77838134765625}, {"start": 5709.28, "end": 5710.94, "word": " لكي", "probability": 0.3990885416666667}, {"start": 5710.94, "end": 5712.9, "word": " تكون", "probability": 0.7783203125}, {"start": 5712.9, "end": 5713.56, "word": " نصف", "probability": 0.4024149576822917}, {"start": 5713.56, "end": 5714.12, "word": " طول", "probability": 0.3480224609375}, {"start": 5714.12, "end": 5719.82, "word": " نصف", "probability": 0.89453125}, {"start": 5719.82, "end": 5721.34, "word": " طول", "probability": 0.98828125}, {"start": 5721.34, "end": 5725.5, "word": " الانترال", "probability": 0.603515625}], "temperature": 1.0}, {"id": 243, "seek": 575940, "start": 5732.54, "end": 5759.4, "text": "but if it is not symmetric اذا لم تكن متماثلة about x0 about x0 we take دلتة we take", "tokens": [5955, 498, 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{"id": 245, "seek": 579589, "start": 5791.75, "end": 5795.89, "text": "of the interval", "tokens": [2670, 264, 15035], "avg_logprob": -0.2374267503619194, "compression_ratio": 0.6521739130434783, "no_speech_prob": 0.0, "words": [{"start": 5791.75, "end": 5792.51, "word": "of", "probability": 0.46728515625}, {"start": 5792.51, "end": 5793.99, "word": " the", "probability": 0.9228515625}, {"start": 5793.99, "end": 5795.89, "word": " interval", "probability": 0.9921875}], "temperature": 1.0}, {"id": 246, "seek": 582198, "start": 5820.98, "end": 5821.98, "text": "ماذا يفعل؟", "tokens": [2304, 45636, 995, 7251, 5172, 30241, 22807], "avg_logprob": -1.2636719048023224, "compression_ratio": 0.6785714285714286, "no_speech_prob": 0.050567626953125, "words": [{"start": 5820.98, "end": 5821.08, "word": "ماذا", "probability": 0.435516357421875}, {"start": 5821.08, "end": 5821.98, "word": " يفعل؟", "probability": 0.355010986328125}], "temperature": 1.0}, {"id": 247, "seek": 590293, "start": 5902.13, 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"end": 5980.94, "word": " المحاضرة", "probability": 0.9822998046875}, {"start": 5980.94, "end": 5981.7, "word": " example", "probability": 0.76220703125}], "temperature": 1.0}, {"id": 251, "seek": 601740, "start": 5988.6, "end": 6017.4, "text": "بقول الـ F of X يساوي الجذر التربيعي للـ X ناقص سبعة والـ L تساوي أربعة والـ X نود يساوي تلاتة وعشرين والإبسلون تساوي واحد Find Delta that satisfies", "tokens": [3555, 39648, 2423, 39184, 479, 295, 1783, 7251, 3794, 995, 45865, 25724, 8848, 2288, 16712, 2288, 21292, 3615, 1829, 24976, 39184, 1783, 8717, 995, 4587, 9381, 8608, 3555, 27884, 16070, 39184, 441, 6055, 3794, 995, 45865, 5551, 25513, 27884, 16070, 39184, 1783, 8717, 23328, 7251, 3794, 995, 45865, 6055, 1211, 9307, 3660, 4032, 3615, 46309, 9957, 16070, 28814, 3555, 3794, 1211, 11536, 6055, 3794, 995, 45865, 36764, 24401, 11809, 18183, 300, 44271], "avg_logprob": -0.24336473092640917, "compression_ratio": 1.5126582278481013, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 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6008.68, "end": 6009.52, "word": " واحد", "probability": 0.98486328125}, {"start": 6009.52, "end": 6010.98, "word": " Find", "probability": 0.45703125}, {"start": 6010.98, "end": 6013.1, "word": " Delta", "probability": 0.52734375}, {"start": 6013.1, "end": 6015.14, "word": " that", "probability": 0.81298828125}, {"start": 6015.14, "end": 6017.4, "word": " satisfies", "probability": 0.884765625}], "temperature": 1.0}, {"id": 252, "seek": 603579, "start": 6021.81, "end": 6035.79, "text": "that satisfies the definition of the formal limit", "tokens": [6780, 44271, 264, 7123, 295, 264, 9860, 4948], "avg_logprob": -0.3172743055555556, "compression_ratio": 0.9607843137254902, "no_speech_prob": 0.0, "words": [{"start": 6021.81, "end": 6022.33, "word": "that", "probability": 0.1097412109375}, {"start": 6022.33, "end": 6023.07, "word": " satisfies", "probability": 0.8564453125}, {"start": 6023.07, "end": 6024.71, "word": " the", "probability": 0.93017578125}, {"start": 6024.71, "end": 6027.09, "word": " definition", "probability": 0.939453125}, {"start": 6027.09, "end": 6029.03, "word": " of", "probability": 0.9853515625}, {"start": 6029.03, "end": 6030.39, "word": " the", "probability": 0.88232421875}, {"start": 6030.39, "end": 6032.29, "word": " formal", "probability": 0.90576171875}, {"start": 6032.29, "end": 6035.79, "word": " limit", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 253, "seek": 606179, "start": 6047.73, "end": 6061.79, "text": "معطيني f of x ومعطيني ال L ومعطيني ال X0 ومعطيني ال Y وطالب باسمين Delta تبعت التعريف من جله بسيطة جدا يبقى هاي التعريف", "tokens": [2304, 3615, 9566, 9957, 1829, 283, 295, 2031, 4032, 2304, 3615, 9566, 9957, 1829, 2423, 441, 4032, 2304, 3615, 9566, 9957, 1829, 2423, 1783, 15, 4032, 2304, 3615, 9566, 9957, 1829, 2423, 398, 4032, 9566, 6027, 3555, 4724, 32277, 2304, 9957, 18183, 6055, 3555, 34268, 16712, 3615, 16572, 5172, 9154, 10874, 43761, 4724, 3794, 1829, 9566, 3660, 10874, 28259, 7251, 3555, 4587, 7578, 8032, 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"word": " ستين", "probability": 0.97705078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 6244.6355, "duration_after_vad": 5891.896250000042} \ No newline at end of file diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OAHmrcZi8vg_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OAHmrcZi8vg_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..03de9fb64dcd4e7dab295ce285a07620141a09e2 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OAHmrcZi8vg_raw.srt @@ -0,0 +1,4096 @@ +1 +00:00:20,670 --> 00:00:24,570 +أنا راح نكمل مابتدأناه في المرة الماضية و المرة + +2 +00:00:24,570 --> 00:00:28,590 +الماضية أخر حاجة كنا نتحدث فيها وهي sandwich + +3 +00:00:28,590 --> 00:00:33,430 +theorem أعطانا هذه النظرية و أعطانا عليها مثالين + +4 +00:00:33,830 --> 00:00:38,210 +والان هذه الـ remark متعلقة تماما بما يسمى بـ + +5 +00:00:38,210 --> 00:00:42,670 +Sandoz theorem ال remark بتقول ما يأتي for any + +6 +00:00:42,670 --> 00:00:47,410 +function f of x إذا كان limit لل absolute value لل + +7 +00:00:47,410 --> 00:00:51,270 +f of x لما ال x ده تروح إلى c بده يساوي 0 then + +8 +00:00:51,270 --> 00:00:55,330 +limit لل function بدون absolute value كمان بدها + +9 +00:00:55,330 --> 00:01:02,360 +تساويها ده ساوي 0 طيب نروح نثبت صحة هذه النظريةبعد + +10 +00:01:02,360 --> 00:01:07,620 +ذلك اقول لك ميتي لو أخدت الدالة f of x ودالة + +11 +00:01:07,620 --> 00:01:13,620 +absolute value لل f of x بدي اقارن ما بين التنتين + +12 +00:01:13,620 --> 00:01:19,980 +انا بقول هذه اقل من او تساوي هذه انا ادعى يا ناس + +13 +00:01:19,980 --> 00:01:23,720 +هل الادعاء هذا صحيح ولا غير صحيح تعني اتفهم على + +14 +00:01:23,720 --> 00:01:29,180 +الموضوعالأهم ممكن تكون ال F of X تاخد قيم موجبة + +15 +00:01:29,180 --> 00:01:33,580 +دائما و أبدا يبقى إذا كانت F of X بالموجبة ال + +16 +00:01:33,580 --> 00:01:39,340 +absolute value لها يبقى شو بيحصل تساوي تمام لكن لو + +17 +00:01:39,340 --> 00:01:43,040 +كانت F of X بالسالي بال absolute value لها بيصير + +18 +00:01:43,040 --> 00:01:47,820 +موجب يبقى بيصير هذه أقل من هذه ولا لا إذا هذه + +19 +00:01:47,820 --> 00:01:52,200 +دائما و أبدا أقل من 100 من ال absolute value ل X + +20 +00:01:52,200 --> 00:01:59,470 +دائما و أبداالسؤال هو او تساويها هل هي اكبر من او + +21 +00:01:59,470 --> 00:02:05,490 +تساوي سالم absolute value لل F of X ام لا تعالى + +22 +00:02:05,490 --> 00:02:10,790 +نشوف بدنا ناخدها لو كانت موجبة لو كانت سالمة لو + +23 +00:02:10,790 --> 00:02:15,510 +كانت F of X بالموجب يبقى absolute value لها + +24 +00:02:15,510 --> 00:02:21,270 +بالموجب يبقى السالم لها اقل يبقى هذه اقل بالفعل + +25 +00:02:21,270 --> 00:02:26,730 +هذه لو كانت موجبةلو كانت f of x بالسالب absolute + +26 +00:02:26,730 --> 00:02:30,930 +value اللي هي بيصير موجة مسبوقة بإشارة سالب بيصير + +27 +00:02:30,930 --> 00:02:35,430 +سالب و هذه السالب يبقى اتنين are equal يبقى ال + +28 +00:02:35,430 --> 00:02:38,830 +inequality هذه صحيحة دائما و أبدا + +29 +00:02:43,360 --> 00:02:50,140 +أقل من أو يساوي absolute value لل F of X for all X + +30 +00:02:50,140 --> 00:02:55,220 +بناستي اتناء موضوعنا موضوع من إيجاد ال limit + +31 +00:02:59,180 --> 00:03:04,560 +يبقى بناء عليه limit لما ال X بدها تروح ل C ل- + +32 +00:03:04,560 --> 00:03:09,760 +absolute value ل F of X أقل من أو يسوى limit لما + +33 +00:03:09,760 --> 00:03:15,380 +ال X بدها تروح ل C ل F of X أقل من أو يسوى limit + +34 +00:03:15,380 --> 00:03:20,380 +لما ال X tends to C لل absolute value ل F of X + +35 +00:03:22,130 --> 00:03:27,930 +تمام؟ طيب، الان في عندي معطيات حتى الان لم استخدم + +36 +00:03:27,930 --> 00:03:32,370 +هذه المعطيات، طلعلي في المعطيات تاني، ايش بتقول + +37 +00:03:32,370 --> 00:03:36,450 +ليه؟ بتقول لي ال limit لل absolute value للدالة + +38 +00:03:36,450 --> 00:03:40,010 +بده يساوي Zero إذا ال limit لهذه الدالة بده يساوي + +39 +00:03:40,010 --> 00:03:44,730 +Zero مضروب فقداش؟ سالب Zero والله موجه ب Zero مهو + +40 +00:03:44,730 --> 00:03:50,030 +بقاش؟ ب Zeroأقل من أو يساوي ال limit لما ال X بدي + +41 +00:03:50,030 --> 00:03:57,210 +روح ل C لل F of X أقل من أو يساوي هذه معطاب من B0 + +42 +00:03:57,210 --> 00:04:02,050 +صار limit الطرف الشمال يساوي limit الطرف اليمنى + +43 +00:04:02,050 --> 00:04:05,090 +يبقى ال limit للدلة اللى فى النصف بدي يساوي نفس + +44 +00:04:05,090 --> 00:04:11,010 +القيمة by sandwich theorem بروح بقوله by sandwich + +45 +00:04:11,010 --> 00:04:15,670 +theorem we have + +46 +00:04:18,360 --> 00:04:24,220 +Limit للـ F of X لما الـ X بده يروح إلى C يساوي + +47 +00:04:24,220 --> 00:04:31,780 +Zero وهو المطلوب بدنا نعطي مثال على ذلك Example + +48 +00:04:31,780 --> 00:04:40,980 +Find Limit لما الـ X بدها تروح لـ Zero للـ X في + +49 +00:04:40,980 --> 00:04:49,590 +الـSin 1 على Xطبعا احنا سابقا اخدنا limit لل X + +50 +00:04:49,590 --> 00:04:55,030 +تربية ال sign واحد على X مظبوط مرة اللي فاتت على + +51 +00:04:55,030 --> 00:04:59,130 +sandwich theorem اخدنا limit X تربية ثمين في sign + +52 +00:04:59,130 --> 00:05:03,830 +واحد على X هذه X وليست X تربية طبعا و هناك فرق + +53 +00:05:03,830 --> 00:05:08,350 +شاسمة بين الاتنين لما كانت X تربية فال X ان كانت + +54 +00:05:08,350 --> 00:05:11,410 +سالبة و الله موجب و رضّعها بصير موجب وبالتالي تبقى + +55 +00:05:11,410 --> 00:05:15,900 +ال inequality كما هيلكن لما تبقى X احتمال X تكون + +56 +00:05:15,900 --> 00:05:21,220 +موجب احتمال تكون سالب ليش لإن X بدها تروح لل zero + +57 +00:05:21,220 --> 00:05:24,820 +يبقى إذا راحت ل zero من جهة اليمين تبقى ال X + +58 +00:05:24,820 --> 00:05:28,560 +بالموجب وإذا راحت ل zero من جهة الشمال تبقى ال X + +59 +00:05:28,560 --> 00:05:32,460 +الزائب السالب يبقى الاحتمال انه وردات لكن لما كانت + +60 +00:05:32,460 --> 00:05:42,010 +X تربية صار الاحتمال واحد فقطسنحل هذه المسألة + +61 +00:05:44,990 --> 00:05:49,030 +أنا المثال هذا بدي ايه على مين؟ على ال remark يعني + +62 +00:05:49,030 --> 00:05:54,170 +بدي يكون فيه عند مين absolute value لمين لف دولار + +63 +00:05:54,170 --> 00:05:58,770 +باجي بس للسؤال التالي انا لو بدي ابدا زي المرة + +64 +00:05:58,770 --> 00:06:03,370 +اللي فاتتي بقى بدي اقول sign واحد على X أكبر من أو + +65 +00:06:03,370 --> 00:06:08,130 +يسوى سالب واحد وموجب واحد لكن لو قلت absolute + +66 +00:06:08,130 --> 00:06:13,090 +value ل sign واحد على X بصير من هو اللي وين؟من + +67 +00:06:13,090 --> 00:06:19,690 +zero لغاية واحد لأن هذا absolute value لا يمكن أن + +68 +00:06:19,690 --> 00:06:24,590 +يطلع لي قيمة سالبة يبقى من zero لغاية واحد ممتازة + +69 +00:06:24,590 --> 00:06:29,860 +الحين لو كنت أضرب في X هذهبصير لو كانت موجبة ال + +70 +00:06:29,860 --> 00:06:33,800 +inequality بتبقى كما هي لو كانت سالبة تنقلب ال + +71 +00:06:33,800 --> 00:06:37,880 +inequality وبالتالي وردنا مظبوط مشان نتخلص من هذه + +72 +00:06:37,880 --> 00:06:41,660 +المشكلة دي براح بدرم في مين في absolute value اكس + +73 +00:06:41,660 --> 00:06:45,340 +absolute value اكس دائما و أبدا تزيد تفوى بالتالي + +74 +00:06:45,340 --> 00:06:50,490 +ماعندي مشكلةتبقى الـ Inquality كما هي، طبعا، يبقى + +75 +00:06:50,490 --> 00:06:54,830 +لو روحت ضربت في absolute value ل X بس يبقى ال mean + +76 +00:06:54,830 --> 00:07:00,490 +is zero أقل من أو يسوى absolute value ل X في ال + +77 +00:07:00,490 --> 00:07:05,690 +sign واحد على X ك absolute value أقل من أو يسوى + +78 +00:07:05,690 --> 00:07:11,630 +absolute value ل Xأو بمعنى آخر هذه بقدر أقول + +79 +00:07:11,630 --> 00:07:16,990 +كالتالي هذه عندك zero أقل من أو يسوى absolute + +80 +00:07:16,990 --> 00:07:22,990 +value ل X في sin 1 على X أقل من أو يسوى absolute + +81 +00:07:22,990 --> 00:07:29,270 +value ل Xأبسلوت في أبسلوت في أبسلوت واحدة لماذا؟ + +82 +00:07:29,270 --> 00:07:32,270 +لأنه من خواص ال absolute value أخدنا absolute + +83 +00:07:32,270 --> 00:07:36,170 +value ل a بي ثم absolute value ل a في absolute + +84 +00:07:36,170 --> 00:07:42,810 +value ل b هذه إحدى خواص ال absolute value تمام؟ + +85 +00:07:42,810 --> 00:07:47,430 +طيب، استنى شوية، بنروح ناخد limit لهذه ال + +86 +00:07:47,430 --> 00:07:52,190 +inequality يبقى بناء عليه، بيصير عندنا ال limit + +87 +00:07:53,190 --> 00:07:59,970 +لزيرو لما ال X بدها تروح لوين لزيرو أقل من أو يسوي + +88 +00:07:59,970 --> 00:08:04,790 +ال limit لما ال X بدها تروح لزيرو لمين لل absolute + +89 +00:08:04,790 --> 00:08:10,370 +value ل X في sine واحد على X أقل من أو يسوي ال + +90 +00:08:10,370 --> 00:08:14,750 +limit لما ال X بدها تروح لزيرو ل absolute value ل + +91 +00:08:14,750 --> 00:08:20,330 +Xالان نهاية المقدار الثابت بالمقدار الثابت itself + +92 +00:08:20,330 --> 00:08:26,570 +أقل من أو يساوي ال limit لما ال X بده يروح ل 0 لل + +93 +00:08:26,570 --> 00:08:32,890 +absolute value لل X في sin 1 على X أقل من أو يساوي + +94 +00:08:32,890 --> 00:08:38,290 +جداش ال limit لهذه الدالة؟ Zero اللي مايعرفش يتذكر + +95 +00:08:38,290 --> 00:08:42,610 +لرسمة ال absolute valueتحركت لها من جهة اليمين + +96 +00:08:42,610 --> 00:08:45,810 +بلاجيها نزل لزيرو تحركت لها من جهة الشمال بلاجيها + +97 +00:08:45,810 --> 00:08:50,910 +نزل لوين لزيرو اذا هذه ال limit بتساوي مين بالزيرو + +98 +00:08:50,910 --> 00:08:55,010 +اذا بالساندوش ثيرم تبع المرة الماضية limit لهذه + +99 +00:08:55,010 --> 00:09:01,750 +الدالة بقداش بزيرو يبقى بروح بقوله buy sandwich + +100 +00:09:01,750 --> 00:09:03,490 +theorem + +101 +00:09:05,990 --> 00:09:10,790 +الـ Limit لما الـ X بدها تروح للـ Zero لـ Absolute + +102 +00:09:10,790 --> 00:09:16,670 +Value لـ X في الصين واحد على X يساوي Zero حتى الآن + +103 +00:09:16,670 --> 00:09:21,810 +حتى الآن ماوصلناش للمطلوب المطلوب بديه بدون + +104 +00:09:21,810 --> 00:09:25,790 +Absolute Value باجي برجع لل remark ال remark بتقول + +105 +00:09:25,790 --> 00:09:28,970 +إذا ال Limit لل Absolute Value بده يساوي Zero إذا + +106 +00:09:28,970 --> 00:09:32,730 +ال Limit لل function itself بده يعطينا Zero بروح + +107 +00:09:32,730 --> 00:09:35,210 +بقوله By The + +108 +00:09:37,530 --> 00:09:42,010 +above remark ال + +109 +00:09:42,010 --> 00:09:46,570 +limit لما ال x بده تروح لل zero اللي ال x في ال + +110 +00:09:46,570 --> 00:09:51,210 +sign واحد على x بده يساوي ماين بده يساوي zero + +111 +00:09:51,210 --> 00:09:58,360 +حلقله يتساول هناطيب، دير بالك، هذا السؤال ههلهلك + +112 +00:09:58,360 --> 00:10:03,080 +بطريقة أخرى برضه اليوم، تمام؟ بس في ال section + +113 +00:10:03,080 --> 00:10:09,940 +القادم بعد قليل يبقى هذا section اتنين اتنين اليك + +114 +00:10:09,940 --> 00:10:17,120 +exercises اتنين اتنين المسائل التالية، من واحد + +115 +00:10:17,120 --> 00:10:23,930 +لخمسة وستينالـ Odd numbers وكذلك من خمسة و سبعين + +116 +00:10:23,930 --> 00:10:33,990 +لتمانين ومن خمسة و سبعين لغاية تمانين حالي + +117 +00:10:33,990 --> 00:10:34,730 +بدي أسأل؟ + +118 +00:10:42,540 --> 00:10:47,400 +قلنا بأن عدوك لك كمان مرة ال X هذا اللي بتضرب فيها + +119 +00:10:47,400 --> 00:10:51,360 +عارفها موجب ولا سالبة؟ لو موجبة ماعنديش مشكلة، بس + +120 +00:10:51,360 --> 00:10:54,660 +لما تكون سالبة لأن X بتروح لزيرو، ما هي بتروح + +121 +00:10:54,660 --> 00:10:58,660 +لزيرو، احتمالا تكون موجبة، احتمالا تكون سالبة، لو + +122 +00:10:58,660 --> 00:11:05,080 +انضربت الفي X السالي بيبقى تنقلب ال inequality هذه + +123 +00:11:05,080 --> 00:11:09,320 +و بدل ما كان تقل منه ايش بيصير اكبر منه وبالتالي + +124 +00:11:09,320 --> 00:11:11,720 +انقلبت ال inequality لنا ال inequality الجديدة + +125 +00:11:11,720 --> 00:11:15,020 +مشان ماجلبش ال inequality بروح بضرب امام في + +126 +00:11:15,020 --> 00:11:19,220 +absolute اتنين انا عندي absolute لو ضربت ال X + +127 +00:11:19,220 --> 00:11:21,680 +التانية مقدرش ادخلها داخل absolute + +128 +00:11:25,700 --> 00:11:30,900 +مافعلش اشي مافعلش كل حاجة بيكون بنقولك لو كانت + +129 +00:11:30,900 --> 00:11:34,340 +سالب اي فرض ماكتبتش لأ بسلوة value او قلت sin واحد + +130 +00:11:34,340 --> 00:11:38,040 +ال X بقدر اقول بين zero و واحد سالب واحد ال واحد + +131 +00:11:38,040 --> 00:11:42,200 +على طول الخط بدك تدرب في X بعرفش بده يصير عندك two + +132 +00:11:42,200 --> 00:11:48,460 +inequalities مش واحدة وبالتاليتورطنا مظبوط لكن بال + +133 +00:11:48,460 --> 00:11:52,540 +absolute ان حلت المشكلة اتنين انا بدي اجيب مباشر + +134 +00:11:52,540 --> 00:11:57,240 +مثال عالميا على ال remark على كيفية استخدام ال + +135 +00:11:57,240 --> 00:12:04,100 +remark تمام طيب ننتقل الان الى section اتنين تلاتة + +136 +00:12:04,100 --> 00:12:08,140 +اللى هو ال section اللى يليه مباشرة + +137 +00:12:26,890 --> 00:12:39,790 +Area section اتنين تلاتة Precise + +138 +00:12:39,790 --> 00:12:42,270 +Definition + +139 +00:12:44,000 --> 00:12:51,700 +definition of a limit in + +140 +00:12:51,700 --> 00:13:03,800 +this section هذا + +141 +00:13:03,800 --> 00:13:12,420 +الsection we does not tell her we does not + +142 +00:13:17,020 --> 00:13:31,080 +how to find a limit of a function but + +143 +00:13:31,080 --> 00:13:38,720 +we verify بدا + +144 +00:13:38,720 --> 00:13:49,730 +نتحقق نتأكد thatthe suspected that the suspected + +145 +00:13:49,730 --> 00:14:06,250 +limit is correct كون صحيحة definition + +146 +00:14:06,250 --> 00:14:10,350 +let + +147 +00:14:10,350 --> 00:14:20,990 +ال Fbe a function defined on + +148 +00:14:20,990 --> 00:14:31,630 +an open interval containing + +149 +00:14:31,630 --> 00:14:35,510 +x0 + +150 +00:14:35,510 --> 00:14:38,490 +except possibility + +151 +00:14:45,230 --> 00:14:53,370 +except possibility at x node itself at x node + +152 +00:14:53,370 --> 00:14:59,550 +itself يبقى + +153 +00:14:59,550 --> 00:15:07,730 +limit لل f of x لما ال x بدى تروح لل x node بدى + +154 +00:15:07,730 --> 00:15:13,890 +يساوي ال ال means that تعني ان + +155 +00:15:59,360 --> 00:16:03,660 +يبقى العنوان اللي احنا رافعينه ترجمة العربية له + +156 +00:16:03,660 --> 00:16:10,080 +الصياغة الرياضية الدقيقة للنهاية طبعا احنا المرة + +157 +00:16:10,080 --> 00:16:13,940 +اللي فاتت بجينا نقول limit لل function يعني كل ما + +158 +00:16:13,940 --> 00:16:18,700 +اقتربت X من X node كل ما اقتربت F of X من L وعبرنا + +159 +00:16:18,700 --> 00:16:22,740 +عن هذا رياضيا نقول limit F of X لما ال X بتروح ل X + +160 +00:16:22,740 --> 00:16:27,550 +node بدي ساوي مين؟ بدي ساوي Lهنا بدنا نعطي تعريف + +161 +00:16:27,550 --> 00:16:32,710 +جديد أو صياغة جديدة لهذه ال limit يبقى precise + +162 +00:16:32,710 --> 00:16:39,250 +معناته الدقيق التعريف الدقيق لمين للنهاية بأول + +163 +00:16:39,250 --> 00:16:43,580 +سطرين بقول ليشبقول احنا في هذا ال section بدناش + +164 +00:16:43,580 --> 00:16:47,240 +نحسب نهايات زى ما كنا بنحسب نهايات في ال section + +165 +00:16:47,240 --> 00:16:52,940 +الماضى، ها إيش بدنا نعمل؟ بدنا نتأكد أو نتحقق من + +166 +00:16:52,940 --> 00:16:57,600 +إن النهاية المقترحة هي نهاية صحيحةيعني معناته + +167 +00:16:57,600 --> 00:17:02,520 +هيعطيني دالة ويعطيني limit لهذه الدالة واحنا بدنا + +168 +00:17:02,520 --> 00:17:06,760 +نتأكد ان القيمة اللي اعطاها لهذه مالها قيمة صحية + +169 +00:17:06,760 --> 00:17:10,800 +يبقى اللي بتطلع ورايا يبطلع هنا ويصحصح معاه كويس + +170 +00:17:10,800 --> 00:17:17,940 +لإن هذا ال section السهل الممتنعيعني في حد ذاته + +171 +00:17:17,940 --> 00:17:22,200 +سهل لكن كلكوا هتداجوا منه من أولكوا الى آخركوا + +172 +00:17:22,200 --> 00:17:27,060 +تمام رغم أنه سهل لكن ممكن يبقى فاتح معايا انا همشي + +173 +00:17:27,060 --> 00:17:32,000 +معاك step by step تمام فبيقول ليش in this section + +174 +00:17:32,000 --> 00:17:34,980 +في هذا ال section we does not tell how to find a + +175 +00:17:34,980 --> 00:17:38,240 +limit of a function احنا مش هنقولك كيف توجد + +176 +00:17:38,240 --> 00:17:43,040 +النهاية ل function هشوفنا نعملBut we verify بإن + +177 +00:17:43,040 --> 00:17:48,540 +نتأكد أو نتحقق من إن Suspected limit النهاية + +178 +00:17:48,540 --> 00:17:53,740 +المقترحة Suspected يعني مقترح is correct تكون + +179 +00:17:53,740 --> 00:17:58,300 +نهاية صحية يبقى هذا كل شغلنا في هذا section + +180 +00:17:58,300 --> 00:18:02,960 +بيعطينا limit واني بتتحقق او اتأكد ان هذه ال limit + +181 +00:18:02,960 --> 00:18:07,340 +هي صحيحة للدالة المطار طب ان نشوف ايش ال + +182 +00:18:07,340 --> 00:18:10,030 +definition اللي بدي اعطاه هناجالي الـ definition + +183 +00:18:10,030 --> 00:18:13,950 +لتلف بـ function defined على an open interval + +184 +00:18:13,950 --> 00:18:23,770 +containing x node except possibly مادة ممكن + +185 +00:18:23,770 --> 00:18:28,630 +عند x node itselfأحنا لما ناخدنا ال section الماضي + +186 +00:18:28,630 --> 00:18:32,690 +اتنين اتنين beginning والممكن ان تكون نهاية الدالة + +187 +00:18:32,690 --> 00:18:37,650 +موجودة و الدالة غير معرفة عند هذه النقطة مظبوط + +188 +00:18:37,650 --> 00:18:41,490 +يعني الدالة معرفة ولا غير معرفة ماتفرجش عندي + +189 +00:18:41,490 --> 00:18:48,050 +بالنسبة لإيجادفقال هنا الهيفوفيكش معرفة على كل ال + +190 +00:18:48,050 --> 00:18:53,950 +open interval المجتملة على النقطة x0 معادة عند x0 + +191 +00:18:53,950 --> 00:19:00,390 +itself بدا تبقى معرفة وممكن تكون غير معرفة except + +192 +00:19:00,390 --> 00:19:05,370 +معادة possibly ممكن يعني ممكن عند ال x0 تكون + +193 +00:19:05,370 --> 00:19:09,510 +الدالة معرفة وممكن ما تكونش معرفة مش هتفرج معايا + +194 +00:19:09,510 --> 00:19:15,240 +بالنسبة لمين لإيجاد ال limitبيقول لي limit f of x + +195 +00:19:15,240 --> 00:19:18,220 +لما الـ x بتروح الـ x و انت تساوي الـ means that + +196 +00:19:18,220 --> 00:19:23,900 +ماذا تعني يبقى هذا التعريف الجديد بتقول لي for + +197 +00:19:23,900 --> 00:19:34,160 +every for every epsilon greater than zero there + +198 +00:19:34,160 --> 00:19:41,900 +exists delta greater than zero such that بحيث ان + +199 +00:19:49,660 --> 00:19:58,360 +أقل من X ناقص X node أقل من Delta then absolute + +200 +00:19:58,360 --> 00:20:07,980 +value لل F of X ناقص ال L أقل من ال Epsilon مرة + +201 +00:20:07,980 --> 00:20:12,950 +تانيةLimit f of x لما الـ x تروح إلى الـ x نهضي + +202 +00:20:12,950 --> 00:20:18,530 +الساوية الـ L means that تعني ما يأتي for every + +203 +00:20:18,530 --> 00:20:22,610 +epsilon greater than zero يعني إذا أعطينا epsilon + +204 +00:20:22,610 --> 00:20:27,250 +greater than يعني real عدد real كثري موجب ماعندي + +205 +00:20:27,250 --> 00:20:32,270 +مشكلة تمام يبقى أنا كل اللي بديه يكون عدد موجب + +206 +00:20:32,270 --> 00:20:37,890 +تمام معله أكبر من ال zero هاي الموجبإذا أخدنا عدد + +207 +00:20:37,890 --> 00:20:42,530 +أ موجب أكبر من الـ zero there exists يوجد الـ E + +208 +00:20:42,530 --> 00:20:46,630 +بالإنجليزي بس مغلوبة يعني أن هناك موجب فرياضيتنا + +209 +00:20:46,630 --> 00:20:52,490 +هناك موجب دلتة أكبر من الـ zero بلاقي قيمة لدلتة + +210 +00:20:52,490 --> 00:20:58,530 +مالها تبقى موجبة دائم هنا بحيث أنالـ zero أقل من + +211 +00:20:58,530 --> 00:21:03,870 +ال X نقص ال X node أقل من دلتا يبقى خاتة ال + +212 +00:21:03,870 --> 00:21:07,090 +absolute value لل X نقص X node بدلجيها دائما و + +213 +00:21:07,090 --> 00:21:11,030 +أبدا موجبة لإن absolute و في نفس الوقت أقل من + +214 +00:21:11,030 --> 00:21:16,280 +delta إن حدث ذلكيبقى يجب أن يكون الفرق ما من ال F + +215 +00:21:16,280 --> 00:21:22,480 +of X وL ال absolute value أقل من إبسلون يبقى هذا + +216 +00:21:22,480 --> 00:21:27,680 +التعريف هو التعريف عندنا لجديد هنا فاهمين؟ طبعا لأ + +217 +00:21:27,680 --> 00:21:34,960 +كله طلاسم تمام؟ الآن بدنا نفك هذه الطلاسم و نبيّلك + +218 +00:21:34,960 --> 00:21:40,800 +أن هذه الطلاسم هي التعريف اللي انت أخدته هذا قبل + +219 +00:21:40,800 --> 00:21:46,020 +ذلك بال doubleتمام بس قبل ما فهمك هذا الكلام ايه + +220 +00:21:46,020 --> 00:21:50,200 +خاطر افك الinquality هذي وفك الinquality هذي اشوف + +221 +00:21:50,200 --> 00:21:55,360 +بده توصلني لوين فلو جيت فكت الinquality هذي هذي + +222 +00:21:55,360 --> 00:22:00,880 +معناها انه x ناقص ال x node اقل من delta و اكبر من + +223 +00:22:00,880 --> 00:22:04,920 +سالب delta مش هي خاصة ال absolute value خاصة ان ال + +224 +00:22:04,920 --> 00:22:10,100 +delta معجبةضيف لـ X node للطرفين أو للثلاثة أطراف + +225 +00:22:10,100 --> 00:22:16,600 +بيصير X node ناقص Delta أقل من X أقل من X node + +226 +00:22:16,600 --> 00:22:22,840 +زائد Delta يعني الـ X هذي ك variable بدي يتحرك + +227 +00:22:22,840 --> 00:22:30,360 +خلال هذه الفترة إن حدث ذلك يبقى هذا بده يعطيك ان + +228 +00:22:30,360 --> 00:22:37,380 +ال F of X ناقص ال Lأقل من إبسلون وأكبر من مين؟ من + +229 +00:22:37,380 --> 00:22:43,760 +سالب إبسلون طب إيه نهاية دالة يعني رقم real؟ بضيف + +230 +00:22:43,760 --> 00:22:49,880 +للثلاثة L إذا لو ضفت للثلاثة أطراف L بصير ال L + +231 +00:22:49,880 --> 00:22:57,810 +ناقص إبسلون أقل من F of Xأقل من ال L زائد Epsilon + +232 +00:22:57,810 --> 00:23:03,710 +طيب مشان نفهم هذا التعريف فهما دقيقا تعالى نرسم + +233 +00:23:03,710 --> 00:23:11,290 +رسمة و نشوف كيف بنحاول نفهم منها هذا التعريف افترض + +234 +00:23:11,290 --> 00:23:19,750 +هذا محور X وهذا محور Y وهذه نقطة الأصلروحنا رسمنا + +235 +00:23:19,750 --> 00:23:24,750 +منحنى دالة فكان منحنى الدالة على سبيل المثال بهذا + +236 +00:23:24,750 --> 00:23:32,700 +الشكل افترض هذا المنحنى هو Y تساوي F of Xأخذت + +237 +00:23:32,700 --> 00:23:38,120 +النقطة الى الـ main نقطة والتكن هذه النقطة هي مثلا + +238 +00:23:38,120 --> 00:23:44,960 +عندنا هنا ال X node تمام عند ال X node ممكن الدالة + +239 +00:23:44,960 --> 00:23:51,940 +تبقى معرفة وممكن الدالة ما تكونش معرفة لكن نهاية + +240 +00:23:51,940 --> 00:23:58,120 +الدالة هنا مالها exist والتكن ال تمام + +241 +00:24:00,300 --> 00:24:05,220 +نجي للتعريف ايش بيقولي بيقول التعريف given epsilon + +242 +00:24:05,220 --> 00:24:08,400 +greater than zero او اذا اعطيت epsilon greater + +243 +00:24:08,400 --> 00:24:13,580 +than zero يبقى انا بدي اروح اخد مسافة على محور Y + +244 +00:24:13,580 --> 00:24:19,660 +موجبة واسميها ايش epsilon يبقى انا لو جيت هنا هنا + +245 +00:24:19,660 --> 00:24:28,470 +هنا وقلتهذه المسافة كلها من هنا لهنا ابسلون تمام؟ + +246 +00:24:28,470 --> 00:24:33,330 +هو ايه من حنا الدالة ماشي هيك كويس؟ يبقى بتبقى + +247 +00:24:33,330 --> 00:24:40,190 +النقطة اللي فوق هذه جداش الإحداث تبعها L زائد + +248 +00:24:40,190 --> 00:24:45,990 +ابسلون يبقى هذا L زائد ابسلون طيب لو أخدت النقطة + +249 +00:24:45,990 --> 00:24:53,350 +هذه تحت هنايبقى هذه كمان قداش إبسلون يبقى هذا بصير + +250 +00:24:53,350 --> 00:24:59,070 +ال L ناقص إبسلون اللي احنا جالين عليها يعني F of X + +251 +00:24:59,070 --> 00:25:04,070 +لاخد لازم تاخد قيمة محصورة ما بين ما بين القيمتين + +252 +00:25:04,070 --> 00:25:09,930 +طيب بداجي أمشي أفق هنا هيك لغاية ما جابنا النقطة + +253 +00:25:09,930 --> 00:25:15,430 +هذه تمام؟ و أجي نازل رأسيالشكل اللي عندنا هذا و من + +254 +00:25:15,430 --> 00:25:20,150 +هنا بداجي ماشي أفق هيك لعيط ما جابل النقطة هذه و + +255 +00:25:20,150 --> 00:25:25,330 +أنزل هيك رأسي بالشكل اللي عندنا هذا تمام طيب + +256 +00:25:25,330 --> 00:25:31,530 +المسافة هذه لو كانت جد المسافة هذه بالضرر يبقى هذه + +257 +00:25:31,530 --> 00:25:37,010 +delta وهذه main delta إذا إحداث النقطة هذا جداش + +258 +00:25:37,010 --> 00:25:44,930 +بدي يكونهذه كلها x node وهذه دلتا يبقى x node ناقص + +259 +00:25:44,930 --> 00:25:51,630 +دلتا هذه قداش بتكون x node زائد دلتا اللي بنقول x + +260 +00:25:51,630 --> 00:25:56,390 +بتتحرك داخل من؟ داخل الفترة اللي عندنا هذهإذاً X + +261 +00:25:56,390 --> 00:26:02,250 +ستتحرك داخل الفترة من عند النقطة هذه لعند وين لعند + +262 +00:26:02,250 --> 00:26:06,890 +النقطة اللي عندنا هذه إذاً خلّينا ناخد X وينما + +263 +00:26:06,890 --> 00:26:12,230 +تيجي تيجي و التقن على سبيل المثال X عند النقطة هذه + +264 +00:26:12,230 --> 00:26:19,710 +بأختيمن X node نقص دلتا إلى X node زائد دلتا و + +265 +00:26:19,710 --> 00:26:26,550 +جاءت طالع بالسلامة لغاية ما قبلت المنحنة يبقى هذه + +266 +00:26:26,550 --> 00:26:32,330 +النقطة ايش بصير احداثية X و F of X وين ال F of X + +267 +00:26:32,330 --> 00:26:44,270 +يبقى لو جيت ماشي أفق هنا فهي F of Xهذه هي نظرية + +268 +00:26:44,270 --> 00:26:49,850 +القيمة المتوسطة وهي + +269 +00:26:49,850 --> 00:26:51,010 +نظرية القيمة البينية + +270 +00:26:59,040 --> 00:27:05,400 +أحنا الآن قلنا هذه L عند النقطة هذه لي جبال ال X + +271 +00:27:05,400 --> 00:27:11,160 +node قد تكون معرفة و قد تكون غير معرفة قلنا هذه + +272 +00:27:11,160 --> 00:27:16,130 +الأسوأ إنها ماهياش معرفةفروحت قليل ثقوب موجود على + +273 +00:27:16,130 --> 00:27:20,810 +منحنى Della Y تساوي F of X وهي ال L اللي جباله أجد + +274 +00:27:20,810 --> 00:27:25,950 +تعرفيش بقولي إذا أخدت إبسلون greater than zero + +275 +00:27:25,950 --> 00:27:30,490 +لازم تلاقي Delta greater than zero روحت أخدت + +276 +00:27:30,490 --> 00:27:35,890 +إبسلون اللي فوق أمشي طلعت عندمين Delta اللي هي + +277 +00:27:35,890 --> 00:27:42,130 +تحتهالو أخدت إبسلون تحتك تقلع دلتا ليه اللي تحتك؟ + +278 +00:27:42,130 --> 00:27:47,450 +يبقى أي قيمة بتاخدها لإبسلون بتجابلها مين قيمة + +279 +00:27:47,450 --> 00:27:52,830 +لدلتا يبقى إبسلون موقع لإنهم يعطيك رقم انت بدك + +280 +00:27:52,830 --> 00:27:57,550 +تروح تجيب مين؟ دلتا يبقى دلتا بتعتمد على مين؟ على + +281 +00:27:57,550 --> 00:28:02,660 +إبسلونأنا عندي في القاع مثلا سبعين طالب كل واحد + +282 +00:28:02,660 --> 00:28:07,520 +أخد إبسلون شكل يبقى كل واحد بتطلع معاه دلتا شكل + +283 +00:28:07,520 --> 00:28:12,140 +مختلفة عن التانية وكله صح كل دلتا بتطلع معاك + +284 +00:28:12,140 --> 00:28:15,880 +بتعتمد على إبسلون اللي أخدته هذا + +285 +00:28:19,680 --> 00:28:24,520 +هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا + +286 +00:28:24,520 --> 00:28:24,880 +هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا هنا + +287 +00:28:24,880 --> 00:28:24,880 +هنا هنا هنا هنا + +288 +00:28:39,190 --> 00:28:44,270 +الحمرة صحيح ولا لأ المسافة بين X و X node مش أقل + +289 +00:28:44,270 --> 00:28:48,650 +من Delta ولا لأ طب ليش ال absolute value لأن X + +290 +00:28:48,650 --> 00:28:52,810 +ممكن تكون على الشجة التانية فإن كانت X node على + +291 +00:28:52,810 --> 00:28:56,890 +الشجة التانية بصير X node أكبر من مين من X و بكالة + +292 +00:28:56,890 --> 00:29:00,910 +بتطلع قيمة سالبة لما ناخد ال absolute value بطلت + +293 +00:29:00,910 --> 00:29:04,210 +أصير سالبة بصير مين بصير موجة إذا لما أخدت ال + +294 +00:29:04,210 --> 00:29:08,020 +absolute value لو وقعت بعد ال X nodeوالله قبل ال X + +295 +00:29:08,020 --> 00:29:11,900 +node فقضيتها محلولة ماعنديش مشاكل يبقى فهمنا ليش + +296 +00:29:11,900 --> 00:29:17,020 +ال absolute value طيب ممتاز جدا يبقى صار ال X + +297 +00:29:17,020 --> 00:29:20,880 +ستتحرك في الفترة اللي عندنا هذه قد تكون ال X نقص X + +298 +00:29:20,880 --> 00:29:25,820 +node موجبة وقد تكون ال X نقص ال X node مالها سالفة + +299 +00:29:25,820 --> 00:29:31,000 +طيب نيجي الآن جبال ال X اطلع اطلع لجيهة ال F of X + +300 +00:29:31,000 --> 00:29:35,870 +النقطة اللي عندنا هذهوالـ L هي يبقى هذا الفرق ما + +301 +00:29:35,870 --> 00:29:43,610 +بين F of X و L F of X ناقص الـ L تمام؟ أخدتله من + +302 +00:29:43,610 --> 00:29:47,410 +ال absolute value لإن احتمال كمان يكون موجب + +303 +00:29:47,410 --> 00:29:52,410 +واحتمال سالب أنا عندي على الرسم L أكبر من مين؟ من + +304 +00:29:52,410 --> 00:29:55,310 +ال F of X لذا اللي بقول F of X ناقص اللي اللي + +305 +00:29:55,310 --> 00:29:58,410 +بتطلع سالب هو الله موجبيبقى انا باخد absolute + +306 +00:29:58,410 --> 00:30:03,870 +value ضمنت انها موجبة تمام ولا بقى اتنين المسافة + +307 +00:30:03,870 --> 00:30:07,770 +هي في x نقص ال L وهي ال epsilon هذه من الاكبر + +308 +00:30:07,770 --> 00:30:12,470 +epsilon ولا المسافة هذه المسافة هذه اقل من ال + +309 +00:30:12,470 --> 00:30:18,590 +epsilon صحيح ولا ال epsilon من هنا لهنا هيأو من + +310 +00:30:18,590 --> 00:30:22,870 +هنا لهنا لكن المسافة بين F of X و L للمسافة هذه + +311 +00:30:22,870 --> 00:30:28,050 +واضح أنها أقل من مين؟ أقل من الـ Epsilon يبقى .. + +312 +00:30:28,050 --> 00:30:34,680 +بس ورا شوية يبقى الطلاسم هذه ان فكت ولا لافكرت بس + +313 +00:30:34,680 --> 00:30:41,600 +لسه لأ فكرناها لأ بس لسه ما جيبناش علاقة هذه بمين + +314 +00:30:41,600 --> 00:30:46,520 +بموضوع ال limit صحيح ولا لأ؟ ايوة تعالى نحط هذه + +315 +00:30:46,520 --> 00:30:50,460 +الطلاسم بمفهوم ال limit اللي عندنا المرة اللي + +316 +00:30:50,460 --> 00:30:54,600 +فاتوا احنا بنشرح في ال limit بقولنا ايش؟ بقولنا if + +317 +00:30:54,600 --> 00:31:00,500 +ال X approaches X node اذا اقتربت X من X node then + +318 +00:31:00,500 --> 00:31:07,640 +if of X approachesكل ما اقتربت X من X node كل ما + +319 +00:31:07,640 --> 00:31:12,340 +اقتربت F of X من L و بنروح انعبر عن هذا رياضيا ب + +320 +00:31:12,340 --> 00:31:15,840 +limit F of X لما ال X بتروح ال X node بده يساوي L + +321 +00:31:15,840 --> 00:31:20,040 +مش شئ قلنا طيب تعالى نشوف الكلام اللي قلته لك هو + +322 +00:31:20,040 --> 00:31:26,650 +اللي على اللوح والله غيره تعالى نشوفطبعا ان كل ما + +323 +00:31:26,650 --> 00:31:32,430 +اقتربت X من X node يجب ان نشوف ال F of X بتجرب من + +324 +00:31:32,430 --> 00:31:38,610 +L ولا لا يبقى لو جبت X node حط X هنا يبقى جربت + +325 +00:31:38,610 --> 00:31:45,160 +امشي جربت على L صحيح ولا لا؟إذا كلما اقتربت X من X + +326 +00:31:45,160 --> 00:31:50,140 +node كلما اقتربت F of X من من من ال L يبقى limit + +327 +00:31:50,140 --> 00:31:53,960 +ال F of X لما ال X بتروح ال X node بدأت ساوي ال L + +328 +00:31:53,960 --> 00:31:57,960 +صحيح ولا لا يبقى هذا المعنى اللي احنا بنقوله يبقى + +329 +00:31:57,960 --> 00:32:01,440 +الكلام العتيجي تبع ال section اللي فات هو الكلام + +330 +00:32:01,440 --> 00:32:05,540 +الجديد اللي اليوم بس المرة دي حاطينها على شكل رموز + +331 +00:32:05,540 --> 00:32:11,200 +Epsilon وDeltaماشي يا سيدي طب بدي أقول هذا الكلام + +332 +00:32:11,200 --> 00:32:18,700 +للمرة الأخيرة تمام؟ الان احنا كاتبين فرق عنوان + +333 +00:32:18,700 --> 00:32:23,720 +دقيق لمفهوم النهاية المرة اللي فاتت قولنا عنوان + +334 +00:32:23,720 --> 00:32:28,660 +عام و بقينا نصيغوا كلام if x approaches to x0 then + +335 +00:32:28,660 --> 00:32:32,140 +f of x approaches to L وبالتالي limit of f of x + +336 +00:32:32,140 --> 00:32:35,430 +لما ال X بتروح لل X0 بده يساوي Lهذا ما كنا نقوله + +337 +00:32:35,430 --> 00:32:40,630 +في السيقشن الماضي الان نقوله نفسه بس بطريقة جديدة + +338 +00:32:40,630 --> 00:32:44,830 +فبقول التعريف ما يتيلت ال f of x بيبقى function + +339 +00:32:44,830 --> 00:32:48,890 +معرفة على open interval و ال open interval تحتوي + +340 +00:32:48,890 --> 00:32:52,010 +على ال x node و عند ال x node الدلة ممكن تكون + +341 +00:32:52,010 --> 00:32:56,470 +معرفة و ممكن ماتكونش معرفة بيهمنيش لأن انا بدي + +342 +00:32:56,470 --> 00:33:02,880 +limit بديش قيمة دلةبقول الان عند ال limit ال f of + +343 +00:33:02,880 --> 00:33:07,900 +x لما ال x تروح لل x non بدي يسوى ال تعني انه يعني + +344 +00:33:07,900 --> 00:33:14,200 +انا بدي اجيب تعريف الها بطريقة جديدة given epsilon + +345 +00:33:14,200 --> 00:33:19,140 +greater than zero اذا اعطيت ابسلون greater than + +346 +00:33:19,140 --> 00:33:24,600 +zero there exists delta greater than zero او delta + +347 +00:33:24,600 --> 00:33:25,840 +greater than + +348 +00:33:28,460 --> 00:33:33,760 +بالنسبة للـ x ناقص x0 هو أكبر من 0 لأنه absolute + +349 +00:33:33,760 --> 00:33:40,860 +وفي نفس الوقت أقل من مين دلتا إن حدث ذلك يجب أن + +350 +00:33:40,860 --> 00:33:43,680 +يكون الفرق ما بين f of x وL + +351 +00:33:50,540 --> 00:33:55,480 +هذا الكلام يجب أن نفهمه من خلال الرسم فبقول كل ما + +352 +00:33:55,480 --> 00:34:01,640 +اقتربت ال X من X node كل ما اقتربت ال F of X من + +353 +00:34:01,640 --> 00:34:08,010 +Delta إذا لما نكون قريبين جدا على X nodeبصير ال f + +354 +00:34:08,010 --> 00:34:12,330 +of x قريبة جدا علميا ال يبقى limit ال f of x لما + +355 +00:34:12,330 --> 00:34:19,270 +ال x بتروح ال x node بدي ساول ال واضح تمام طيب + +356 +00:34:19,270 --> 00:34:22,930 +يبقى اذا انت فهمت خمسين في المية معناته انت very + +357 +00:34:22,930 --> 00:34:27,150 +good مش very good excellentطب و الخمسين التانية + +358 +00:34:27,150 --> 00:34:30,910 +بدنا نجيبهم من وين؟ بدنا نجيبهم من الأمثلة و أحل + +359 +00:34:30,910 --> 00:34:35,270 +المسائل يبقى انتهى الجزء النظري تبع ال section هذي + +360 +00:34:35,270 --> 00:34:41,630 +ضايل جزئية بسيطة سنتعرض لها خلال محاضرة اليوم ان + +361 +00:34:41,630 --> 00:34:50,510 +شاء الله وين هو الإثبات؟ تبع ال remark هو إثبات + +362 +00:34:50,510 --> 00:34:57,060 +خطوة واحدة و التانية ياخد limit خلصناأه قد يكون + +363 +00:34:57,060 --> 00:35:00,820 +ليش لأ مش .. كل حاجة بأثبتها لك بيصير مطلوب، ما + +364 +00:35:00,820 --> 00:35:04,720 +أثبتتها ايش لك؟ خلص المسامة عينك فيهاماشي يا سيدي، + +365 +00:35:04,720 --> 00:35:08,080 +لكن لا يعني مطلوب أنها بتتيجي في الامتحان، أنا + +366 +00:35:08,080 --> 00:35:12,180 +بديك تفهم شغلات أو تعرف شغلات ماكنتش بتعرفها + +367 +00:35:12,180 --> 00:35:16,600 +سابقا، هي اللي بهمنا، يعني هالمختبع كده بدنا ننفضه + +368 +00:35:16,600 --> 00:35:21,920 +و نواصلك شوية، انك كل يوم بتاخد معلومات جديدة ربما + +369 +00:35:21,920 --> 00:35:26,660 +لم تتعرف عليها في الثانوية العامة أو سليقت سلقا في + +370 +00:35:26,660 --> 00:35:31,450 +الثانوية العامة، احنا اليومنطبخ مخكك على نار هادية + +371 +00:35:31,450 --> 00:35:37,490 +وليس سلقان، تمام؟ ليش؟ لأن انت بعد أربع سنين ربما + +372 +00:35:37,490 --> 00:35:42,870 +تقف مكاني في هذا المكان و تشرح نفس الكلام للطلاب + +373 +00:35:42,870 --> 00:35:47,270 +وارد جدا انك تصير معيد، طبعا جيبت الأول عدو فقط + +374 +00:35:47,270 --> 00:35:51,610 +اتت، بصير معيد في الكليةوبالتالي بصورة تشرح هذا + +375 +00:35:51,610 --> 00:35:55,190 +الكلام للطلاب في ال discussion مش بتروح ال + +376 +00:35:55,190 --> 00:35:58,770 +discussion ولا لا وبالتالي إذا أنت مش فاهم اليوم + +377 +00:35:58,770 --> 00:36:04,070 +هل بتقدر تفهم بكرا؟ ليس ممكن لأن القاعدة معروفة + +378 +00:36:04,070 --> 00:36:09,070 +فاقد الشيء لا يعطيه اللي ماعدش أبضعة من ون يجيب + +379 +00:36:09,070 --> 00:36:14,330 +أبضعة يصرمعندوش أصلا طيب نبدأ ناخد بعض أمثلة على + +380 +00:36:14,330 --> 00:36:20,090 +هذا وسنبدأ بالتسلسل بأبسط أنواع الأمثلة ثم لا تقل + +381 +00:36:20,090 --> 00:36:25,470 +شوية ثم لا تقل شوية لغاية ما تستوعب الموضوع بدنا + +382 +00:36:25,470 --> 00:36:35,890 +نيجي لأول مثال بيقول ما يأتي يبقى example one show + +383 +00:36:35,890 --> 00:36:49,970 +that showذات limit لما ال X بدها تروح للإتنين لدلة + +384 +00:36:49,970 --> 00:36:56,070 +خمسة X ناقص أربع يساوي مين؟ يساوي ستة + +385 +00:36:58,880 --> 00:37:03,920 +بقى احنا مقترحين انه limit لهذه الدالة بده يساوي + +386 +00:37:03,920 --> 00:37:09,520 +ستة بدنا نتأكد هذا اقتراحنا صح ولا لأ لإنه قلنا + +387 +00:37:09,520 --> 00:37:13,840 +هنا إيش but we verify that the suspected limit is + +388 +00:37:13,840 --> 00:37:17,780 +correct يعني احنا بنتأكد انه limit المقترح هذه + +389 +00:37:17,780 --> 00:37:22,290 +صحيحة ولا لأطبعا لو جاءك كده السؤال في الامتحان + +390 +00:37:22,290 --> 00:37:26,270 +بتقول والله بسيط ديدا بنعوض لإنها linear 2x5 هو 10 + +391 +00:37:26,270 --> 00:37:31,170 +-7 يساوي 6 في خاطرك مع السلامة لا انا بروح بصيلك + +392 +00:37:31,170 --> 00:37:35,570 +السؤال صياغة أخرى بروح بقولك use epsilon delta + +393 +00:37:35,570 --> 00:37:41,750 +definition to show that بيبقى مش فيها كلام بتعمل + +394 +00:37:41,750 --> 00:37:47,120 +زي ذاك بتاخد zeroيبقى ضروري تتقيد بما هو مطلوب، + +395 +00:37:47,120 --> 00:37:51,820 +ماشي يا سيدي؟ طيب، الآن بدنا مشان تحل السؤال أو + +396 +00:37:51,820 --> 00:37:55,740 +مشان تحفظ ال definition اللي هذا حاول تكتبه فيه + +397 +00:37:55,740 --> 00:38:01,500 +مقدمة كل سؤال وبالتالي بترسخ اللي هو معناه التعريف + +398 +00:38:01,500 --> 00:38:07,440 +في دماغها، فبقى اللي نقوله solution تعريف + +399 +00:38:09,780 --> 00:38:14,040 +إبسلون greater than zero يبقى إذا وضعت إبسلون + +400 +00:38:14,040 --> 00:38:18,440 +greater than zero there exists Delta greater than + +401 +00:38:18,440 --> 00:38:26,780 +zero such that الـ zero أقل من ال X ناقص ال X node + +402 +00:38:26,780 --> 00:38:33,200 +أقل من Delta implies هذا يطلب أن ال absolute value + +403 +00:38:33,200 --> 00:38:39,940 +لل F of X ناقص ال L أقل من إبسلونالان بدنا نبدأ + +404 +00:38:39,940 --> 00:38:46,140 +نطبق تعريف عمليا بقول له zero اقل من ال X ناقص + +405 +00:38:46,140 --> 00:38:49,540 +يبقى + +406 +00:38:49,540 --> 00:38:56,450 +بشيلها و بحط مكانها اتنين اقل من دلتة مجهولةيبقى + +407 +00:38:56,450 --> 00:39:03,770 +إبسل المواطع دلتا مجهولة هذا يتطلب f of x اللي هي + +408 +00:39:03,770 --> 00:39:11,910 +خمسة x ناقص الأربعة ناقص ال L اللي هي قداش ستة أقل + +409 +00:39:11,910 --> 00:39:21,990 +من مين؟ أقل من الإبسل بعد ذلك سيبلي هذه كما هيو + +410 +00:39:21,990 --> 00:39:26,610 +بروح نشتغل في مين؟ في الانقلة اللي عندنا هنا فباجي + +411 +00:39:26,610 --> 00:39:32,750 +بقول له هذه بدها تعطيك absolute value لخمسة X ناقص + +412 +00:39:32,750 --> 00:39:39,290 +أربعة و ناقص ستة و ناقص عشرة تمام؟ اللي هي بدها + +413 +00:39:39,290 --> 00:39:46,120 +تساوي absolute value لخمسة في X ناقص اتنيناللي هي + +414 +00:39:46,120 --> 00:39:52,140 +بدأ تساوي خمسة في absolute value لل X ناقص اتنين + +415 +00:39:52,140 --> 00:39:58,360 +وكل هذا الكلام اقل من main اقل من epsilon لحد هنا + +416 +00:39:58,360 --> 00:40:03,580 +في مشكلة ماعنديش مشكلة كله مباشرة طيب بنحب نحيط + +417 +00:40:03,580 --> 00:40:08,700 +اكالم ان هذا المثال هو ابسط انواع الأمثلة على + +418 +00:40:08,700 --> 00:40:12,060 +الموضوع ماشي طيب الان + +419 +00:40:14,780 --> 00:40:19,740 +ممكن نقسم الطرفين على خمسة إذا لو جسمنا الطرفين + +420 +00:40:19,740 --> 00:40:24,100 +على خمسة إيش بيصير عندنا absolute value لل X ناقص + +421 +00:40:24,100 --> 00:40:30,160 +اتنين أقل من epsilon على خمسة اتطلعلي في النتيجة + +422 +00:40:30,160 --> 00:40:35,060 +التي توصلنا إليها هذه و اتطلعلي في النتيجة الطرف + +423 +00:40:35,060 --> 00:40:40,520 +الشمال مش هو الطرف الشمال اللي هناطرف الشمال هنا + +424 +00:40:40,520 --> 00:40:45,400 +مشهور طرف الشمال هنا يعني شغلتنا بدنا نروح نمسك + +425 +00:40:45,400 --> 00:40:49,600 +الطرف هذا اللي في اليمين و نقعد نفكفك فيه لغاية ما + +426 +00:40:49,600 --> 00:40:55,100 +وصل لشكل مين شكل الطرف الشمالأول ما بدأت معاك + +427 +00:40:55,100 --> 00:40:59,100 +الكلام اليوم قلت لك given epsilon greater than + +428 +00:40:59,100 --> 00:41:03,320 +zero there exists delta greater than zero يبقى حسب + +429 +00:41:03,320 --> 00:41:07,200 +epsilon اللي بتاخدها بيطلع مين دلتا يعني دلتا + +430 +00:41:07,200 --> 00:41:12,900 +تعتمد على مين تعتمد على epsilon من هذه بقدر أقوله + +431 +00:41:12,900 --> 00:41:23,020 +إذا سا دلتا يساوي epsilon على خمسةالطرف اليمين هو + +432 +00:41:23,020 --> 00:41:27,800 +الطرف اليمين لأن هذا بالضبط تماما يبقى دلتا ممكن + +433 +00:41:27,800 --> 00:41:32,480 +اخدها ابسلون على خمسة يبقى طالع الدلتا تعتمد علي + +434 +00:41:32,480 --> 00:41:37,120 +مينتعتمد على قيمته بس هو لذلك السبعين طالب اللي + +435 +00:41:37,120 --> 00:41:42,700 +جاعدين قدامي لو كل واحد فيهم أخد epsilon تختلف عن + +436 +00:41:42,700 --> 00:41:47,100 +التانية هيطلع عندي سبعين delta بتختلف عن التانية + +437 +00:41:47,100 --> 00:41:51,380 +يعني ايش؟ يعني لما ال X بده تروح لل X node واحد + +438 +00:41:51,380 --> 00:41:55,040 +يدخل المسافة بينه وبينها أربعة صنطين واحد يدخل + +439 +00:41:55,040 --> 00:41:59,020 +المسافة بينه وبينها تلاتة ونص واحد يدخل المسافة + +440 +00:41:59,020 --> 00:42:02,780 +بينه وبينها اتنين صنطينواحد يخلي مسافة منه بينها + +441 +00:42:02,780 --> 00:42:06,720 +واحد و تلت اربعة صنطي واحد يخليها صنطي واحد واحد + +442 +00:42:06,720 --> 00:42:10,820 +يخليها نص صنطي واحد يخليها واحد من عشرة صنطي يعني + +443 +00:42:10,820 --> 00:42:15,720 +ميلي واحد وهكذا يعني جداش بتاخد ابسنن جداش بتطلع + +444 +00:42:15,720 --> 00:42:20,080 +اللي هو جداش بتاخد ابسنن جداش بتطلع عندك مين دلتا + +445 +00:42:20,080 --> 00:42:26,160 +وهكذا تمام وابعت الصورة طيبوانتوا في الصف السابع + +446 +00:42:26,160 --> 00:42:30,480 +والثامن بجيتوا لما تحلوا معادلة و تتأكد حالك صح + +447 +00:42:30,480 --> 00:42:35,460 +ولا غلط ممكن تروحوا تقولوا التحقيق مش هيك وممكن + +448 +00:42:35,460 --> 00:42:39,180 +تروحوا تتحقق هل الإجابة تبقى تأكد صح ولا لا احنا + +449 +00:42:39,180 --> 00:42:43,740 +بدنا نجري تحقيق الان واسع النطاق مع مين مع النتيجة + +450 +00:42:43,740 --> 00:42:48,540 +اللى توصلنا لها احنا لحد هنا انتهينا لكن احنا الان + +451 +00:42:48,540 --> 00:42:55,050 +بدنا نعمل تحقيق نتأكد منه هل النتيجةالتي توصلنا + +452 +00:42:55,050 --> 00:43:00,510 +إليها صحيحة أم النتيجة التي توصلنا إليها غير + +453 +00:43:00,510 --> 00:43:08,210 +صحيحة؟ هذه مجرد تأكيد ليس إذا يبقى بحط له عنوان + +454 +00:43:08,210 --> 00:43:17,340 +صغير و بقوله showing that delta worksيعني بدي + +455 +00:43:17,340 --> 00:43:22,520 +ابيله ان دلتا اللى حصلنا عليها ايبسلون على خمسة + +456 +00:43:22,520 --> 00:43:29,700 +تؤدي لغرض قل مطلوب بقوله تمام اذا انا باجي zero + +457 +00:43:29,700 --> 00:43:38,700 +اقل absolute value لل X ناقص كم كان ناقص اقل من + +458 +00:43:38,700 --> 00:43:52,230 +دلتا كم دلتا اخدتها ايبسلون على خمسةF of X هو 5X + +459 +00:43:52,230 --> 00:44:01,590 +ناقص 4 ناقص 6 فهذا + +460 +00:44:01,590 --> 00:44:09,460 +المقدر يجب أن يكون أقل من Epsilonبقول كويس هذا بده + +461 +00:44:09,460 --> 00:44:17,460 +يساوي خمسة X ناقص عشرة هذا بده يساوي خمسة X ناقص + +462 +00:44:17,460 --> 00:44:24,220 +اتنين هذا بده يساوي خمسة absolute value ل X ناقص + +463 +00:44:24,220 --> 00:44:33,910 +اتنينهذه أقل من إبسلون على خمسة إذا هذا أقل من هذه + +464 +00:44:33,910 --> 00:44:40,310 +الخمسة اللي برا وهذه إبسلون على خمسة هذه اللي هي + +465 +00:44:40,310 --> 00:44:45,940 +قدش تساوي إبسلونيبقى فعلا الفرق ما بين الاتنين + +466 +00:44:45,940 --> 00:44:53,920 +هدول سواء الخمسة x ناقص الأربعة ناقص الستة أقل من + +467 +00:44:53,920 --> 00:44:58,680 +مين من إبسلن يعني لما ناخد delta بإبسلن على خمسة + +468 +00:44:58,680 --> 00:45:02,460 +النتيجة فعلا بصير الفرق بين الفوفكس وإيه الماله + +469 +00:45:02,460 --> 00:45:07,530 +أقل من إبسلنيبقى هى تحققنا من ان الكلام اللى + +470 +00:45:07,530 --> 00:45:15,770 +عملناه صحيح يبقى بقوله تأكدنا thus limit لخمسة X + +471 +00:45:15,770 --> 00:45:21,470 +ناقص أربعة لما ال X بدى يروح لاتنين بدى يساوي ستة + +472 +00:45:21,470 --> 00:45:27,490 +بدى اسألكوا السؤال التالىهل احنا بشغل هذا حسبنا + +473 +00:45:27,490 --> 00:45:32,310 +limit لدى الله؟ لأ احنا بس تأكدنا ان ال limit صحيح + +474 +00:45:32,310 --> 00:45:35,810 +اللي ليس الا، اذا في هذا ال section كتبتلك اول + +475 +00:45:35,810 --> 00:45:39,770 +سطرين احنا هنا بنحسبش limit في هذا ال section بل + +476 +00:45:39,770 --> 00:45:44,290 +بنتأكد هل ال limit اللي عملناها او المعطاها هل هي + +477 +00:45:44,290 --> 00:45:46,250 +صحيحة او لا، ايش بدك تسأل؟ + +478 +00:45:50,070 --> 00:45:55,390 +انت لسه في اول الطريق يا راجل اصبر اصبر شوية كل ما + +479 +00:45:55,390 --> 00:46:00,470 +انت اجلك شوية صبرك بالله شوية احنا بنقولك ياه بدي + +480 +00:46:00,470 --> 00:46:04,690 +يعطيك سفره بدي يعطيك نهاية سوى قيمة محددة هي الصفر + +481 +00:46:04,690 --> 00:46:06,210 +على صفر قيمة محددة + +482 +00:46:08,980 --> 00:46:13,120 +هذا إذا استخدمت طرق مختلفة، صحيح الحساب، بعدين + +483 +00:46:13,120 --> 00:46:16,820 +انطلق Zero ع Zero، لكن من البداية بيقولك limit + +484 +00:46:16,820 --> 00:46:22,480 +كذا، بيقولك سوى كذا، مايقولش مش صحيح، لأ، تجب صحيح + +485 +00:46:22,480 --> 00:46:26,620 +كذا، مش صحيح، + +486 +00:46:26,620 --> 00:46:29,900 +يراد اللي بيعطيك ده، اللي بيقولك بيل، ان limit + +487 +00:46:29,900 --> 00:46:34,560 +لهذه، ده لا يسوى كذا، تمام؟ كانت صفر على صفر كانت، + +488 +00:46:34,560 --> 00:46:39,400 +مش عارف إيه، بدك تثبت هال انت، تمام؟طيب نعطيك مثال + +489 +00:46:39,400 --> 00:46:44,200 +آخر أتقل شوية، بدي أعتبر أنه حتى لأن من هذه + +490 +00:46:44,200 --> 00:46:48,180 +المثالة مافهمتش ولا كلمة، كويس؟ و بدي أتقلك شوية و + +491 +00:46:48,180 --> 00:46:52,900 +شوية، تفهم ولا لا؟ قول من + +492 +00:46:52,900 --> 00:46:58,900 +وين جبتها؟ ليه و إيه؟ شايف هذه ولا لا؟ و أعطيك + +493 +00:46:58,900 --> 00:47:04,460 +سبعة الله تضرب في خمس ولا لا؟ تضرب في خمس يلا، وهو + +494 +00:47:04,460 --> 00:47:15,060 +المطلوب، هذا هو سؤالكلأ ما قلت أقل منها، هذه أقل، + +495 +00:47:15,060 --> 00:47:20,640 +يبقى هذه أقل، تمام؟ صار الطرف الشمال هو الطرف + +496 +00:47:20,640 --> 00:47:25,200 +الشمال، إذا الطرف الليمين هو الطرف اليمين، مظبوط؟ + +497 +00:47:29,110 --> 00:47:34,530 +خطوات تعملها لتتأكد + +498 +00:47:34,530 --> 00:47:36,750 +أن كلامك صحيح + +499 +00:47:54,920 --> 00:48:09,760 +Use Epsilon Delta Definition To Show That Limit + +500 +00:48:09,760 --> 00:48:13,120 +لما + +501 +00:48:13,120 --> 00:48:20,880 +ال X بدأ تروح لل سبعة للجذري الترابيعي لل X ناقص + +502 +00:48:20,880 --> 00:48:22,540 +تلاتة يساوي اتنين + +503 +00:48:53,150 --> 00:48:56,910 +خلّي بالا كدا السؤال اللي واجهتك اللي مضحك عنه + +504 +00:48:56,910 --> 00:49:00,990 +ممكن يكون بهذه الصيغة use epsilon delta definition + +505 +00:49:00,990 --> 00:49:04,490 +to show data ويعطيك مثل ايش ما يكون شكلها يكون + +506 +00:49:04,490 --> 00:49:10,150 +بهمنشطيب بدنا نبدأ بنفس مباديرنا في المثال السابق + +507 +00:49:10,150 --> 00:49:16,550 +يبقى بالدرجة اقوله given epsilon greater than zero + +508 +00:49:16,550 --> 00:49:22,430 +there exists delta greater than zero such that + +509 +00:49:22,430 --> 00:49:31,870 +بحيث ان f0 اقل من ال X نقص ال X node اقل من دلتا + +510 +00:49:31,870 --> 00:49:39,340 +implies ان ال F of Xنقص ال L أقل من مين من إبسلون + +511 +00:49:39,340 --> 00:49:46,600 +طب نجي نعوض هنا يبقى Zero أقل من ال X نقص ال X + +512 +00:49:46,600 --> 00:49:53,590 +node ال X node عندي هنا كده؟ سبعة تمامأقل من دلتا + +513 +00:49:53,590 --> 00:49:57,930 +مش عارفها بدي اياها هذا بدي يتطلب absolute value + +514 +00:49:57,930 --> 00:50:02,570 +لل F of X اللي هو الجدرى التربية لل X ناقص ثلاثة + +515 +00:50:02,570 --> 00:50:10,230 +ناقص الولي اتنين أقل من مين أقل من إبسلونهذا + +516 +00:50:10,230 --> 00:50:12,910 +السؤال ليس مثل السؤال السابق خد عمل مشاركة روح + +517 +00:50:12,910 --> 00:50:18,890 +يطلع معاك دغري يبقى بده اروح افكر انا بده هنا اخلق + +518 +00:50:18,890 --> 00:50:24,630 +في هذا الطرف لماين ال X ناقص سبعة بده هنا يكون X + +519 +00:50:24,630 --> 00:50:29,270 +ناقص سبعة يبقى اول ما بيجي في لماين اضرب في + +520 +00:50:29,270 --> 00:50:34,170 +المرافق تمام يبقى باجي بقوله هذا بده يعطينا + +521 +00:50:34,170 --> 00:50:35,350 +absolute value + +522 +00:50:52,330 --> 00:51:00,030 +ما له هذا هذا اقل من ابسلان اذا ايش اللي صار عندنا + +523 +00:51:08,490 --> 00:51:15,330 +أقل من X نقص سبعة أقل من Delta implies + +524 +00:51:23,400 --> 00:51:28,220 +فرق بين المربعين إذا بالدرجة لأصله مربع الأولى + +525 +00:51:28,220 --> 00:51:33,980 +ناقص مربع الثانية إذا المربع الأولى هو عبارة عن X + +526 +00:51:33,980 --> 00:51:40,000 +ناقص تلاتة المربع الثاني اللي هو ناقص أربعة تمام + +527 +00:51:40,000 --> 00:51:46,460 +على المقام اللي هو absolute value للجذر التربيه ل + +528 +00:51:46,460 --> 00:51:53,240 +X ناقص تلاتة زائد اتنين أقل من مين أقل من إبسلون + +529 +00:51:53,380 --> 00:51:59,740 +إذا مشكلتي anyway مافيش اللي فوق سألة هادى اللى + +530 +00:51:59,740 --> 00:52:05,640 +عبارة عن مين absolute value لل X ناقص سبعة في مين + +531 +00:52:05,640 --> 00:52:13,200 +في واحد على ال absolute valueالـ X لاقص 3 زائد 2 + +532 +00:52:13,200 --> 00:52:19,780 +أقل من الـ Y يبقى أنا لو تخلصت من هذا المقدار + +533 +00:52:19,780 --> 00:52:26,650 +بتبقى قصتي محلولة أو لو استبدلت هذا المقدار برقمطب + +534 +00:52:26,650 --> 00:52:30,590 +خلصت، مظبوط؟ إذا هذا السؤال مش زي السؤال اللي + +535 +00:52:30,590 --> 00:52:34,810 +قبله، اضطريت للضرب في المرافق و الضرب من المرافق + +536 +00:52:34,810 --> 00:52:39,050 +طلع لي term جديد، بدي أحاول أتخلص من ال term + +537 +00:52:39,050 --> 00:52:43,910 +الجديد شوفوا كيف بدي أتخلص من ال term الجديد برقم، + +538 +00:52:43,910 --> 00:52:48,350 +بقى دي بقوله كويس، هي المسألة، بدي أتعرف على + +539 +00:52:48,350 --> 00:52:53,780 +domain ده اللي هدي من وين له وينبقى باجي بقوله ان + +540 +00:52:53,780 --> 00:52:59,840 +انا بدي اجيب له domain دالة F كل العناصر X بحيث ان + +541 +00:53:00,350 --> 00:53:05,570 +الـ X ناقص تلاتة بديها أكبر من أو تساوي زيرو حتى + +542 +00:53:05,570 --> 00:53:11,190 +يكون الجذر هذا معرف صحيح ولا لأ يعني هذا كل + +543 +00:53:11,190 --> 00:53:15,870 +العناصر X بحيث أن الـ X greater than or equal من + +544 +00:53:15,870 --> 00:53:21,850 +تلاتة يعني الفترة من عند التلاتة لغاية ال infinity + +545 +00:53:21,850 --> 00:53:28,330 +أمتاز جدا طب فاتحلي عينك كويس أنا عندها هذا ال + +546 +00:53:28,330 --> 00:53:32,420 +real lineو ال domain تبع الدلة بيبدأ من عند + +547 +00:53:32,420 --> 00:53:37,800 +التلاتة و يجي رايح على ما لا نهاية قبل التلاتة + +548 +00:53:37,800 --> 00:53:43,620 +ماعنديش function انا عند ال X بتروح لوين ل 7 اذا + +549 +00:53:43,620 --> 00:53:48,520 +لو جيت على الرسم هنا و قلت هذه النقطة اللي هي + +550 +00:53:48,520 --> 00:53:54,020 +السبعة السؤال هو قداش أقصى قيمة ل Delta + +551 +00:53:58,780 --> 00:54:03,720 +أربعة صحيح و لا لأ لأ بدي أقول قبل التلاتة هذي + +552 +00:54:03,720 --> 00:54:08,760 +ممنوع ممنوع أتحرك و أنا ال X بتروح على سبعة يعني + +553 +00:54:08,760 --> 00:54:13,780 +ممكن أروح من اليمين و ممكن أروح للشمال يبقى أقصى + +554 +00:54:13,780 --> 00:54:19,000 +قيمة ممكن تكون قداش X بدها تروح لسبعة ممكن Delta + +555 +00:54:19,000 --> 00:54:23,090 +تكون أربعة حوالين مين؟هو ممكن ناخد أربعة لليمين و + +556 +00:54:23,090 --> 00:54:26,930 +أربعة للشمال + +557 +00:54:26,930 --> 00:54:39,150 +يبقى هنا sense بما أن ال X بدأ تروح للسبعة + +558 +00:54:41,710 --> 00:54:47,350 +بدي يصير عندنا مين؟ ان دلتا تساوي سبعة ناقص ثلاثة + +559 +00:54:47,350 --> 00:54:51,850 +يساوي قداش أربع طيب شوف لك هذه المعلومة أيش + +560 +00:54:51,850 --> 00:54:56,570 +الفايدة منها أيش الفايدة من دلتا بدها تروح لأربع + +561 +00:54:56,570 --> 00:55:02,870 +يبقى انا عند مين؟ عند ال X ناقص سبعة أقل من دلتا + +562 +00:55:02,870 --> 00:55:09,390 +اذا بدي يصير عند ال X ناقص السبعة أقل من مين؟ أقل + +563 +00:55:09,390 --> 00:55:16,600 +من أربعأو بمعنى آخر هذا معناته ان ال X ناقص السبعة + +564 +00:55:16,600 --> 00:55:22,480 +أقل من أربعة و أكبر من مين؟ من سالب أربعة اضيفلي + +565 +00:55:22,480 --> 00:55:27,700 +السبعة للثلاثة أطراف يبقى لو أضفنا السبعة للثلاثة + +566 +00:55:27,700 --> 00:55:35,480 +أطراف بيصير هنا قداش تلاتة أقل من X أقل من سبعة و + +567 +00:55:35,480 --> 00:55:42,660 +أربعة قداش الواحداشطيب X إذا ستتحرك من و لا وين؟ + +568 +00:55:42,660 --> 00:55:47,880 +من تلاتة لأحداش لكن احنا بدنا مين؟ بدنا X ناقص + +569 +00:55:47,880 --> 00:55:53,720 +تلاتة إذا من هنا بده يخلق X ناقص تلاتة يبقى هذا + +570 +00:55:53,720 --> 00:56:01,720 +بده يعطيلك إن Zero أقل من X ناقص تلاتة أقل من + +571 +00:56:01,720 --> 00:56:02,740 +تمانية + +572 +00:56:05,630 --> 00:56:11,070 +أضفنا سالب تلاتة للتلاتة الأطراف يبقى هاي جبت من + +573 +00:56:11,070 --> 00:56:16,290 +ال X ناقصة ايش بلزمني كمان الجذر خد الجذر التربية + +574 +00:56:16,290 --> 00:56:22,110 +للطرفين يبقى بصير الجذر ال zero بال zero أقل من + +575 +00:56:22,110 --> 00:56:27,050 +الجذر التربية إلى X ناقص تلاتة أقل من الجذر + +576 +00:56:27,050 --> 00:56:32,360 +التربية إلى تمانيةطيب انا ال X ناقص ثلاثة بدى + +577 +00:56:32,360 --> 00:56:37,380 +اضافيلها كمان قداش اذا بدى اروح اضيف للثلاثة اطراف + +578 +00:56:37,380 --> 00:56:43,900 +اتنين بصير عند هنا اتنين اقل من الجدر التربيع لل X + +579 +00:56:43,900 --> 00:56:49,620 +ناقص ثلاثة زائد اتنين اقل من اتنين زائد جدر + +580 +00:56:49,620 --> 00:56:55,010 +التمانيةطيب ممتاز انا مابديش هدف ال bus مابدياه + +581 +00:56:55,010 --> 00:57:00,470 +وين؟ في المقام طيب لو أخدت absolute و absolute و + +582 +00:57:00,470 --> 00:57:05,870 +absolute بتتغير؟هذه موجبة وهذه موجبة يبقى ال + +583 +00:57:05,870 --> 00:57:12,190 +absolute لها لن يتغير وبدي أنزلها في المقام بيصير + +584 +00:57:12,190 --> 00:57:18,730 +عند النص الأقل من بيصير أكبر من وهذه واحد على + +585 +00:57:18,730 --> 00:57:24,750 +absolute value لل X ناقص ثلاثة زائد اتنين وهذه + +586 +00:57:24,750 --> 00:57:33,410 +أكبر من واحد على اتنين زائد جذر تمانيةطيب استنى + +587 +00:57:33,410 --> 00:57:39,250 +شوية هى واحد على المقام اه الصحيحية ايش بديه اقل + +588 +00:57:39,250 --> 00:57:44,820 +ولا اكبر؟بدي أقل يعني هنا إذا ما بديش إياها أكبر + +589 +00:57:44,820 --> 00:57:50,880 +بدي إياها من أقل يبقى بصير هذا الكلام كله أقل من + +590 +00:57:50,880 --> 00:57:56,880 +جداش من نص حلته المشكلة يبقى المشكلة العويصة اللي + +591 +00:57:56,880 --> 00:58:02,760 +عندك حلتها very easy بسهولة يبقى بنان عليه بدي + +592 +00:58:02,760 --> 00:58:08,900 +أجيب رقم بدل هذهبدي هذه تجيبلي أصغر من الرقم، أقل + +593 +00:58:08,900 --> 00:58:12,960 +من الرقم، كلها اللي انت شايفه هذه طب ايش سويتك؟ + +594 +00:58:12,960 --> 00:58:17,420 +تعرفش تجيب الدمان الدلس تاني؟ شو اسمك انت؟ شو اسمك + +595 +00:58:17,420 --> 00:58:23,700 +انت؟ محمل ايش؟ أبو دجا ولا أبو دان؟ أبو دجا من + +596 +00:58:23,700 --> 00:58:29,040 +بنسيلة عبسان، عبسان الكبيري مش عبسان الصغيري كمان + +597 +00:58:29,040 --> 00:58:35,120 +طيب خلي بركوا هناشيخ محمد أبو دجا بناخدها as an + +598 +00:58:35,120 --> 00:58:38,680 +example يا محمد يا أبو دجا والكلام للسماية ال + +599 +00:58:38,680 --> 00:58:43,160 +definition هذا فيه مشكلة ممتاز يبقى ال domain من + +600 +00:58:43,160 --> 00:58:49,160 +تلاتة لإنفينيتيطيب ال X بتروح لوين؟ لل سبعة وين + +601 +00:58:49,160 --> 00:58:54,380 +السبعة بتيجي بعد التلاتة يبقى Delta لا يمكن أن + +602 +00:58:54,380 --> 00:58:59,200 +تكون أكتر من المسافة هذه يبقى بدي أخد Delta بأربعة + +603 +00:58:59,200 --> 00:59:04,080 +لما أخد Delta بأربعة بصير هذه أقل من Delta أقل من + +604 +00:59:04,080 --> 00:59:08,380 +أربعة هذه فيديو تحلت طال ال X ما بين تلاتة و + +605 +00:59:08,380 --> 00:59:12,900 +أحداشرطب انا بدي من؟ بدي x ناقص تلاتة بطرح من + +606 +00:59:12,900 --> 00:59:18,140 +الطرفين تلاتة هيترح لمنها تلاتة تمام؟ بدي جدر باخد + +607 +00:59:18,140 --> 00:59:23,820 +الجدر للطرفين بدي للجدر يكون مضاف لاتنين روحنا + +608 +00:59:23,820 --> 00:59:28,220 +أضافنا اتنين للكل بدي شي أكل في ال bus بدي أكل في + +609 +00:59:28,220 --> 00:59:32,300 +المقام قلب ساعة + +610 +00:59:32,300 --> 00:59:40,330 +بهذه؟كلام بسيط، هذا trivial بسيط و غلط، أيوة كيف؟ + +611 +00:59:40,330 --> 00:59:44,710 +يا راجل ما أنت شايف هل الدالة معرفة قبل التلاتة؟ + +612 +00:59:44,710 --> 00:59:48,030 +يعني ال domain من تلاتة و طلعة و ال limit محسوب + +613 +00:59:48,030 --> 00:59:54,970 +اوين؟ يعني X0 هذه اللي هي عبارة عن main X0 يبقى + +614 +00:59:54,970 --> 01:00:00,230 +حوالين X0، إذا بتقدر أزيد عن التلاتة يبقى أقصى + +615 +01:00:00,230 --> 01:00:04,740 +قيمة لDelta بقدر أخدها اللي من تلاتة لسبعةمصبوط + +616 +01:00:04,740 --> 01:00:09,020 +ولا لا؟ انا قلت ثلاثة سبعة ثانية أربعة ثم حطيناها + +617 +01:00:09,020 --> 01:00:13,560 +أربعة وطلعت X من و لا و لا اضفت لها سالب ثلاثة + +618 +01:00:13,560 --> 01:00:17,240 +واخدت الجدرب بعدين اضفت لها اتنين ووصلنا للنتيجة + +619 +01:00:17,240 --> 01:00:20,300 +اللي لنا يبقى هذه لو انا اقراها واحد على المقدار + +620 +01:00:20,300 --> 01:00:25,040 +أقل من مين من نصف اذا بدي ارجع لمسألة الأساسية + +621 +01:00:25,040 --> 01:00:29,680 +يبقى لما ارجع لمسألة الأساسية اللي فوق high zero + +622 +01:00:30,030 --> 01:00:36,810 +أقل من ال X ناقص سبعة أقل من Delta implies اللي + +623 +01:00:36,810 --> 01:00:43,070 +توصلنا له احنا X ناقص سبعة في واحد على absolute + +624 +01:00:43,070 --> 01:00:48,810 +value للجدر التربية لل X ناقص ثلاثة زائد اتنين + +625 +01:00:48,810 --> 01:00:55,030 +تمام هذا ايش بدي يكون أقل من اللي هو absolute + +626 +01:00:55,030 --> 01:01:03,210 +value لل X ناقص سبعة في نصفهذا اتخلصت منه و حطيت + +627 +01:01:03,210 --> 01:01:09,330 +اقل من نص لان هى اقل من نص وهذا كله اقل من مين؟ من + +628 +01:01:09,330 --> 01:01:12,910 +ابسلون اللى هي الأساسية لعن نهاية + +629 +01:01:16,590 --> 01:01:20,190 +أضرب كله في اتنين لو ضربت كله في اتنين ايش بيصير + +630 +01:01:20,190 --> 01:01:25,650 +عندنا بيصير absolute value لل X نقص سبعة اقل من + +631 +01:01:25,650 --> 01:01:33,050 +مين اقل من اتنين ابسلون طلعلي في هادي وطلعلي في + +632 +01:01:33,050 --> 01:01:40,970 +هادي ووصلنا يبقى دلتة ويبقى داشر اتنين ابسلون يبقى + +633 +01:01:40,970 --> 01:01:47,370 +دلتة هنا يساوي اتنين ابسلونيبقى دلتا اللى بدنا ياه + +634 +01:01:47,370 --> 01:01:53,470 +اعتمد على مين بقى اللى التحقيق بكون خلصنا حقك من + +635 +01:01:53,470 --> 01:01:58,150 +اللى موصلناك ايوة مالذي قبل مالذي قبل مالذي قبل + +636 +01:01:58,150 --> 01:02:01,130 +مالذي قبل مالذي قبل مالذي قبل مالذي قبل مالذي قبل + +637 +01:02:01,130 --> 01:02:02,650 +مالذي قبل مالذي قبل مالذي قبل مالذي قبل مالذي قبل + +638 +01:02:02,650 --> 01:02:08,610 +مالذي قبل مالذي قبل مالذي قبل مالذي قبل مالذي قبل + +639 +01:02:08,610 --> 01:02:09,810 +مالذي قبل مالذي قبل مالذي قبل مالذي قبل مالذي قبل + +640 +01:02:09,810 --> 01:02:09,810 +مالذي قبل مالذي قبل مالذي قبل مالذي قبل مالذي قبل + +641 +01:02:09,810 --> 01:02:14,900 +مالذي قأنا جابت ال domain عشان أعرف قداش أكبر قيمة + +642 +01:02:14,900 --> 01:02:22,500 +لديلتا بدأ أخدها بنفع أي + +643 +01:02:22,500 --> 01:02:27,840 +رقم من تلاتة لسبعة أنا أخدت أكبر واحد من تلاتة + +644 +01:02:27,840 --> 01:02:32,580 +لأربعة من نقص من عند ال zero لغاية الأربعة من + +645 +01:02:32,580 --> 01:02:37,120 +تلاتة لسبعة لهو أربعة أي رقم بدك تاخده من ال zero + +646 +01:02:37,120 --> 01:02:44,620 +لأربعة ماعنديش مشكلةخلاص؟ طيب بدنا نتحقق من صحة + +647 +01:02:44,620 --> 01:03:01,400 +هذا الكلام قلي + +648 +01:03:01,400 --> 01:03:09,800 +منك معاكالان احنا عندنا zero اقل من x نقص سبعة اقل + +649 +01:03:09,800 --> 01:03:15,820 +من دلتا كده ايش دلتا قولنا اتنين ابسل تمام هذا + +650 +01:03:15,820 --> 01:03:21,170 +يتطلب absolute valueالدرجة الديش كانت اللي هو + +651 +01:03:21,170 --> 01:03:27,310 +الجدر التربيعي لل X ناقص ثلاثة زائد اتنين امشي + +652 +01:03:27,310 --> 01:03:33,830 +امشي لما نمشينا وقولنا وصلناها لل X ناقص السبعة في + +653 +01:03:33,830 --> 01:03:38,770 +واحد على الجدر التربيعي لل X ناقص ثلاثة زائد اتنين + +654 +01:03:38,770 --> 01:03:44,550 +absolute value مش هيك وصلناها هاي هاي عندك مديش + +655 +01:03:44,550 --> 01:03:49,380 +اعيد الدرب من جديد تمام؟ بعد الجدر التناقص؟بعد + +656 +01:03:49,380 --> 01:03:52,600 +ايش؟ + +657 +01:03:52,600 --> 01:03:58,300 +يا راجل هيها، زائب في المقام، ما له؟ هيها، جدها + +658 +01:03:58,300 --> 01:04:02,920 +مكفوك، هيها، شافها؟ انا كتبت هذه الحيلة، يعني + +659 +01:04:02,920 --> 01:04:05,760 +مابديش لسه انا اضرب من أول و جديد، اعيد نفس الكرة + +660 +01:04:06,150 --> 01:04:11,070 +لأ انا مسكت هي من البداية امشي وصلها لغاية هنا + +661 +01:04:11,070 --> 01:04:18,990 +تمام؟ الحين هذه اقل من مين؟ اقل من ال X نقص سبعة + +662 +01:04:18,990 --> 01:04:28,010 +في نص تمام؟ طيب هذه اقل من ال X دلتة عند مقداش + +663 +01:04:28,010 --> 01:04:38,360 +يعني هذه اقل من دلتة في نصدلتا عندى بقداش؟ اتنان + +664 +01:04:38,360 --> 01:04:44,380 +ابسلون يبقى هذه بده تساوي اتنين ابسلون في نص يعني + +665 +01:04:44,380 --> 01:04:49,780 +قداش ابسلون يبقى هى بتحقق تحقق تمام يبقى بقى دى + +666 +01:04:49,780 --> 01:04:56,320 +بقوله سا limit لما ال X بده تروح للسبعة للجدرى + +667 +01:04:56,320 --> 01:05:04,530 +التربية لل X ناقص تلاتة يساوي اتنين تمام؟طيب الله + +668 +01:05:04,530 --> 01:05:08,830 +يعطيك العافية حد بده يسأل تاني هنا؟ أيوة اللي هو + +669 +01:05:08,830 --> 01:05:15,650 +مين؟ تعال هنا على اللوح يالا إلحق يالا بدنا نشوف + +670 +01:05:15,650 --> 01:05:20,550 +إيش بده يسأل وماذا ستكون الإجابة بس تعال اطلع هنا + +671 +01:05:20,550 --> 01:05:28,030 +يا راجل خلي الشباب يستفيدوا من هناك من هناك أيوة + +672 +01:05:28,030 --> 01:05:37,260 +طيب لحد هنا تمام هذه؟نجينا لرأس المسألة و نزلناهذه + +673 +01:05:37,260 --> 01:05:42,680 +الطرف الشمال زي ما هو الطرف هذا هيو كان نزلته زي + +674 +01:05:42,680 --> 01:05:48,900 +ما هو غيرتش شيء هذا أقل من المقدار هذا في نص هيو + +675 +01:05:48,900 --> 01:05:53,920 +أقل من نص شيلت هذا و حطيت بدل نصه اللي هي الأقل + +676 +01:05:53,920 --> 01:06:01,020 +منه مظبوط؟ طيب هذا الأن أقل من إبسل نزلت الإبسل زي + +677 +01:06:01,020 --> 01:06:04,800 +ما هو أضرب الطرفين في اتنين صارت هذا + +678 +01:06:08,570 --> 01:06:14,790 +خلاص؟ حد بدى يسأل تانى؟ طب المثال اللى بعده + +679 +01:06:38,770 --> 01:06:52,770 +مثال 3 استخدم ابسلون دلتا ديفينيشن لتوضيح ذلك قيمة + +680 +01:06:52,770 --> 01:07:00,430 +لما الاكس بده تروح لتلاتة للاكس تكيب يسبق 27 + +681 +01:07:18,130 --> 01:07:24,670 +لأ لأ لأ لأ لأ لأ لأ لأ + +682 +01:07:24,670 --> 01:07:24,670 +لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ + +683 +01:07:24,670 --> 01:07:25,090 +لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ + +684 +01:07:25,090 --> 01:07:26,230 +لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ + +685 +01:07:26,230 --> 01:07:26,750 +لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ + +686 +01:07:26,750 --> 01:07:27,190 +لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ + +687 +01:07:27,190 --> 01:07:27,730 +لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ + +688 +01:07:27,730 --> 01:07:33,070 +لأ + +689 +01:07:33,070 --> 01:07:34,250 +لأ + +690 +01:07:43,100 --> 01:07:46,220 +والحين بدنا نعيد نفس التكتيك اللي قلناها في + +691 +01:07:46,220 --> 01:07:49,760 +المثالين بدنا نعيده في المثال التالت كمان نفس + +692 +01:07:49,760 --> 01:07:53,400 +المفهوم يعني لو حتى مافهمتش ولا كلمة من المثالين + +693 +01:07:53,400 --> 01:07:55,980 +السواد بدنا نعيده نفس الكلام في المثال التالت + +694 +01:07:55,980 --> 01:08:01,180 +وبالتالي بس كل واحد في فكرة بسيطة بتختلف عن مين عن + +695 +01:08:01,180 --> 01:08:07,910 +اي ثانية لكن نفس التكتيكطيب نجي الآن للسؤال بيقول + +696 +01:08:07,910 --> 01:08:12,210 +استخدم لبس من دلتا definition to show that limit + +697 +01:08:12,210 --> 01:08:15,650 +الاكس تكيب لما عليك تروح لتلاتة بدسة ومين سبعة + +698 +01:08:15,650 --> 01:08:19,730 +وعشرين بدنا نحط التعريف يبقى باجي بقوله given + +699 +01:08:22,730 --> 01:08:31,310 +أبسلون أكتر من زيرو هناك دلتا أكتر من زيرو بحيث أن + +700 +01:08:31,310 --> 01:08:37,910 +الزيرو أقل من ال X ناقص ال X node أقل من دلتا يعني + +701 +01:08:37,910 --> 01:08:44,610 +أن ال F of X ناقص ال L أقل من مين؟ أقل من الأبسلون + +702 +01:08:50,220 --> 01:08:56,400 +بنعيش نعوض تحويل مباشر يبقى zero أقل من ال X ال X + +703 +01:08:56,400 --> 01:09:03,300 +node بقدراش تلاتة أقل من Delta M plus F of X ال X + +704 +01:09:03,300 --> 01:09:11,520 +تكيب نقص ال L التي هي 27 أقل من Epsilon هل اختلفت + +705 +01:09:11,520 --> 01:09:16,640 +البداية عن البداية السابقة للمثال ولا حاجة طيب + +706 +01:09:18,740 --> 01:09:22,340 +هذه ماليش علاقة فيها بخليها و بره عشان و الفين في + +707 +01:09:22,340 --> 01:09:29,020 +التانية بطل على هذه شو شكل هذه خرق بين المجتعبين + +708 +01:09:29,020 --> 01:09:33,860 +طب هنا عندي x ناقص ثلاثة إذا بدي أخليك هنا جديد x + +709 +01:09:33,860 --> 01:09:40,320 +ناقص ثلاثة إذا هذه x ناقص ثلاثة هي ال absolute + +710 +01:09:40,320 --> 01:09:48,430 +value x تربيع زي التلاتة x زي التسعةمش 6x مش ضعف + +711 +01:09:48,430 --> 01:09:53,430 +حصل ضرب الكيمية مش مربعها ده جوس الكل تربيها ده + +712 +01:09:53,430 --> 01:09:57,830 +فرق بينها مكعبين بتاخد الجدر التكييب لل term الأول + +713 +01:09:57,830 --> 01:10:01,910 +بتاخد الجدر التكييب لل x تكييب اللي هو x بتاخد + +714 +01:10:01,910 --> 01:10:04,830 +الجدر التكييب لل term التاني اللي هو تلاتة و + +715 +01:10:04,830 --> 01:10:09,490 +الإشارة زي ما هي بعدك الجوس التاني مربع الأولى + +716 +01:10:09,490 --> 01:10:14,830 +الإشارة ناقص بصير زائد عكس تماما حصل ضرب ليه اتنين + +717 +01:10:15,000 --> 01:10:22,920 +مربع القيمة التانية تمام هذا المقدار ماله أقل من + +718 +01:10:22,920 --> 01:10:31,360 +مين أقل من إمسن هذا هو هذا ماتغيرش يبقى كل اللي + +719 +01:10:31,360 --> 01:10:36,100 +بقدر أقوله هذا معناه absolute value لل X ناقص + +720 +01:10:36,100 --> 01:10:41,400 +تلاتة في ال absolute value لل X تربية زي التلاتة X + +721 +01:10:41,400 --> 01:10:46,980 +زي التسعة أقل من مينمن ال epsilon اذا انا بدى + +722 +01:10:46,980 --> 01:10:53,180 +اتخلص من المقدار هذا برقم لان ال X ناقص ثلاثة + +723 +01:10:53,180 --> 01:10:58,120 +موجودة عندى هنا وين موجودة على الإشمال بدالى اسألك + +724 +01:10:58,120 --> 01:11:03,980 +بدالى اسألك اتمنى من من و لا وين كل ال real line + +725 +01:11:03,980 --> 01:11:07,040 +مظبوط اذا هذا لا بقدم ولا بخدمه مش زى السؤال اللى + +726 +01:11:07,040 --> 01:11:11,390 +قبلهيبقى مفتوحة الدنيا قدامك الله ميسرها خالص + +727 +01:11:11,390 --> 01:11:19,130 +ممتاز جدا يبقى هنا ال domain لدالة F بدى يساوي من + +728 +01:11:19,130 --> 01:11:23,710 +سالب infinity الى infinity اذا هذه ماتجيبتليش جديد + +729 +01:11:23,710 --> 01:11:29,650 +لكن انا عندى ال X بتروح لوين لتلاتة + +730 +01:11:29,650 --> 01:11:35,390 +طيب تعالى نشوف القصة عادي خلي بالك هنا هذا ال real + +731 +01:11:35,390 --> 01:11:41,400 +lineو هاد ال X بدها تروح لوين؟ ليه التلاتة؟ سؤال + +732 +01:11:41,400 --> 01:11:47,260 +الدلتا بتاخد قيم سالبة؟ لانها تكون قيم سالبة، + +733 +01:11:47,260 --> 01:11:51,700 +مظبوط، يبقى الدلتا دايما أكبر قيم واجبةيعني قداش + +734 +01:11:51,700 --> 01:11:57,160 +أكبر قيمة لـ Delta ممكن تكون تلاتة مش غيرهم صحيح + +735 +01:11:57,160 --> 01:12:01,980 +ولا ليش؟ لإن هي الـ Zero قبل الـ Zero بدأ الصيف + +736 +01:12:01,980 --> 01:12:07,320 +تاخد قيم سالبة يبقى أقصى قيمة لـ Delta بتبقى أياش؟ + +737 +01:12:07,320 --> 01:12:13,320 +تلاتة يعني X ستتحرك في الفترة من Zero لتلاتة وممكن + +738 +01:12:13,320 --> 01:12:18,170 +بعد مين؟بعد التلاتة اللي عندنا هذا مش هيك طيب + +739 +01:12:18,170 --> 01:12:22,410 +تعالى نشوف الكلام اللي عندنا هذا إيش بدنا نستفيد + +740 +01:12:22,410 --> 01:12:34,690 +منه يبقى باجي بقوله الان since بما أن ال X بدأ + +741 +01:12:34,690 --> 01:12:43,540 +تروح ليه تلاتة andالـ Delta دائما أكبر من 0 يبقى + +742 +01:12:43,540 --> 01:12:56,700 +وي can take Delta to be any number + +743 +01:12:56,700 --> 01:13:06,700 +in الفترة من 0 لغاية 3 قد ما بدك خده، أي رقم يعجبك + +744 +01:13:06,700 --> 01:13:13,500 +من 0 ل3واحد اتنين تلاتة واحد و نص واحد و تلاتة + +745 +01:13:13,500 --> 01:13:17,700 +اربعة اتنين زي ما كل واحد ياخد رقم شكل ايش بتاخد + +746 +01:13:17,700 --> 01:13:21,360 +بتلاقي ابسنط بتعتمد عليها خالي بالك هنا الان لو + +747 +01:13:21,360 --> 01:13:26,120 +أخدنا delta بواحد على سبيل المثال يبقى باجي بقوله + +748 +01:13:26,120 --> 01:13:31,060 +زي ما احد اقترح اول اقترح قالي واحد F delta تساوي + +749 +01:13:31,060 --> 01:13:35,260 +واحد شوف هذه ايش بيجي بالك طبعا واحد ممكن ياخدها + +750 +01:13:35,260 --> 01:13:40,380 +اتنينطبعا كله بيختلف عن الثاني وبالتالي مافيش + +751 +01:13:40,380 --> 01:13:48,900 +مشكلة اقل ايوة ال domain + +752 +01:13:48,900 --> 01:13:51,740 +سبعة ده لمن صفره واطلع ولا ال domain كله ال real + +753 +01:13:51,740 --> 01:13:56,700 +line هذا كنت مقيد انا بال domain لكن قبل شوية قول + +754 +01:13:56,700 --> 01:14:00,710 +ان هذا ال domain كله ال real lineطب ليش أنا تقيت + +755 +01:14:00,710 --> 01:14:04,650 +من صفر لثلاثة لأن ال delta دائما و أبدا موجب يبقى + +756 +01:14:04,650 --> 01:14:08,150 +بقدرش أرجع قبل الصفر و أخد قيم سالمة يبقى ال delta + +757 +01:14:08,150 --> 01:14:13,190 +بقدر أخد أي رقم من صفر لويان لثلاثة عرفت ليش؟ طيب + +758 +01:14:14,140 --> 01:14:17,720 +أخدناها اقترح واحد الشباب ان ياخد دلتا بهذا قلت له + +759 +01:14:17,720 --> 01:14:22,400 +ماشي شوف هذه اللي وين بدها توصلنا الان احنا عندنا + +760 +01:14:22,400 --> 01:14:27,160 +مين؟ عندنا هنا ال absolute value ل X ناقص ثلاثة + +761 +01:14:27,160 --> 01:14:32,080 +اقل من Delta يبقى X ناقص ثلاثة بيصير اقل من مين؟ + +762 +01:14:32,080 --> 01:14:38,720 +من واحد الان sense بمعنىSolute value للـ X ناقص + +763 +01:14:38,720 --> 01:14:44,280 +ثلاثة أقل من Delta و Delta أخدناها يساوي واحد هذا + +764 +01:14:44,280 --> 01:14:50,980 +معناه أن X ناقص ثلاثة أقل من 100 من الواحد هذا + +765 +01:14:50,980 --> 01:14:55,560 +معناهان الاكس ناقص ثلاثة اقل من واحد و اكبر من + +766 +01:14:55,560 --> 01:15:01,760 +مين؟ من سالب واحد ضيف تلاتة للثلاثة اطراف بصير + +767 +01:15:01,760 --> 01:15:08,760 +اتنين اقل من اكس اقل من مين؟ من اربعة يبقى ان حدث + +768 +01:15:08,760 --> 01:15:15,090 +ذلكفال X دائما و أبدا ممكن تكون مالها يساوي أربعة + +769 +01:15:15,090 --> 01:15:21,670 +أو أقل من مين أو أقل من أربعة يعني احنا بنقدر ناخد + +770 +01:15:21,670 --> 01:15:29,570 +انه any number in 0 لغاية 3 طب ليش ماخدتش تلاتة؟ + +771 +01:15:30,900 --> 01:15:35,840 +خلتها closed interval لأن ال function ممكن تكون + +772 +01:15:35,840 --> 01:15:39,560 +عندها مش معرفة، صحيح ولا لا؟ وبالتالي ماعندي + +773 +01:15:39,560 --> 01:15:44,060 +مشكلة، يبقى أنا خلتها فترة مفتوحة لإن ده قد تكون + +774 +01:15:44,060 --> 01:15:48,300 +غير معرفة، لكن مسألتنا هذه، عند التلاتة معرفة ولا + +775 +01:15:48,300 --> 01:15:53,080 +لا؟معرفة عند التلاتة وعند الأربعة وعند المية وعند + +776 +01:15:53,080 --> 01:15:58,620 +الألف يبقى بإمكاني أخدها هنا من zero لتلاتة ك + +777 +01:15:58,620 --> 01:16:03,180 +closed interval يعني هنا بقدر أقوله بدل ما هي + +778 +01:16:03,180 --> 01:16:07,280 +مفتوحة بقدر أقوله closed بالشكل اللي عنها هنا + +779 +01:16:07,280 --> 01:16:12,840 +ولمّا أقوله closed يبقى هذه بدها تصير أقل من أو + +780 +01:16:12,840 --> 01:16:18,240 +يساوي وهنا أقل من أو يساوي وهنا أقل من أو يساوي + +781 +01:16:18,240 --> 01:16:24,570 +أربعةمية المية يبقى الدمية له دور كبير في الموضوع + +782 +01:16:24,570 --> 01:16:29,550 +طيب إذا أنا لو أخدت ال X يساوي أربعة شوف إيش اللي + +783 +01:16:29,550 --> 01:16:35,590 +بده يصير يبقى باجي بقوله F ال X تساوي أربعة then + +784 +01:16:35,590 --> 01:16:41,770 +أنا مشكلتي مع مين مع هذا؟ يبقى أنا عندي X تربية + +785 +01:16:41,770 --> 01:16:48,910 +زائد تلاتة X زائد تسعةمظبوط ولا لا؟ خلّي هذه + +786 +01:16:48,910 --> 01:16:53,450 +المعلومة و تعالى أذكرك خواص ال absolute value من + +787 +01:16:53,450 --> 01:16:57,250 +خواص ال absolute value بقى يقول absolute value ل A + +788 +01:16:57,250 --> 01:17:03,110 +زائد ال B أقل من أو يسوي absolute value ل A زائد + +789 +01:17:03,110 --> 01:17:09,670 +absolute value ل B صحيح ولا لا؟ سكت الشعبمرت عليكم + +790 +01:17:09,670 --> 01:17:17,310 +هذه؟ لأ؟ اخسرها طيب، بدي اعتبره لأ؟ خليني معاهم + +791 +01:17:17,310 --> 01:17:22,550 +اللي بيقول لأ لأ لأ لأ طيب السؤال ليش مرة يساوي + +792 +01:17:22,550 --> 01:17:28,290 +مرة أقل من تعالي نقولكإذا اتحدت a و b في الإشارة + +793 +01:17:28,290 --> 01:17:32,190 +يعني كان ال a و ال b بالموجب أو ال a و ال b + +794 +01:17:32,190 --> 01:17:38,490 +بالسالم مثلا 2 و 5 يبقى 2 زائد 5 يبقى 7 يبقى 7 + +795 +01:17:38,490 --> 01:17:42,450 +أبسول يتولى ل 7 ب7 أبسول يتولى ل 2 ب2 أبسول يتولى + +796 +01:17:42,450 --> 01:17:47,970 +ل 5 ب5 و 2 ب7 بأي تساويلو كانوا التنتين بالسالب + +797 +01:17:47,970 --> 01:17:51,210 +يبقى السالب اتنين والسالب خمسة السالب سبعة + +798 +01:17:51,210 --> 01:17:54,790 +absolute value بالسبعة absolute value السالب اتنين + +799 +01:17:54,790 --> 01:17:57,310 +باتنين absolute value السالب خمسة بخمسة يبقى + +800 +01:17:57,310 --> 01:18:03,170 +السابعة يبقى اذا اتحدت الاشارتان فدائما بيحدث + +801 +01:18:03,170 --> 01:18:06,870 +التساوتطب بده يخلّي واحدة موجبة والتانية سلبة و + +802 +01:18:06,870 --> 01:18:10,770 +بده يخلّي الكبيرة بالسالف بده يقولي اتنين و سالف + +803 +01:18:10,770 --> 01:18:15,610 +خمسة اتنين و سالف خمسة تعني سالف تلاتة absolute + +804 +01:18:15,610 --> 01:18:19,450 +تلاتة طيب absolute value ليه اتنين و اتنين و + +805 +01:18:19,450 --> 01:18:22,430 +absolute value لسالف خمسة و خمسة سبعة تلاتة قل من + +806 +01:18:22,430 --> 01:18:26,850 +سبعةمظبوط ولا لا؟ يبقى ال equality هذه دائما و + +807 +01:18:26,850 --> 01:18:31,950 +أبدا صحيحة لكل real number إذا تساوت a و b في + +808 +01:18:31,950 --> 01:18:36,350 +الإشارة يبقى في هذه الحالة بيحدث التساوي بين + +809 +01:18:36,350 --> 01:18:41,500 +المقدارينإذا اختلفت A وB في الهشارة بيحصل الـ أقل + +810 +01:18:41,500 --> 01:18:45,620 +من، حط له المعلومة عندك و بدنا نطبقها، إذا هذه + +811 +01:18:45,620 --> 01:18:50,720 +دائما و أبدا أقل من أو تساوي absolute value ل X + +812 +01:18:50,720 --> 01:18:56,540 +تربية زيد absolute value ل 3X زيد absolute value ل + +813 +01:18:56,540 --> 01:19:04,180 +9تمام؟ طيب هذه أقل من أو تساوي هذه أربعة تربية + +814 +01:19:04,180 --> 01:19:10,600 +بقداش؟ ستة عشر تلاتة في أربعة باطناش زائد تسعة + +815 +01:19:10,600 --> 01:19:18,380 +تمانية و عشرين وتسعة قداش سبعة و تلاتينطيب إذا صار + +816 +01:19:18,380 --> 01:19:25,040 +هذا المقدار أقل من مين؟ من سبعة و تلاتين، ممتاز + +817 +01:19:25,040 --> 01:19:30,000 +جدا، يبقى أنا بدي أرجع لمسألة هنا، يبقى أنا عندي + +818 +01:19:30,000 --> 01:19:39,210 +zero أقل من ال Xنقص ثلاثة أقل من delta implies شوف + +819 +01:19:39,210 --> 01:19:46,310 +ايش اللي حصل عندنا المثلة كانت x ناقص ثلاثة في x + +820 +01:19:46,310 --> 01:19:55,200 +تربية زائد تلاتة x زائد تسعةهذا أقل من أو يساوي + +821 +01:19:55,200 --> 01:20:01,300 +اللي هو ال X ناقص ثلاثة في جداش في سبعة و تلاتين + +822 +01:20:01,300 --> 01:20:08,680 +وهذا كله أقل من مين أقل من ال epsilon طبعا طلّالي + +823 +01:20:08,680 --> 01:20:15,520 +في يديممكن اقسم كله عقداش على سبعة و تلاتين يبقى + +824 +01:20:15,520 --> 01:20:22,440 +بيصير ال X ناقص ثلاثة اقل من ال epsilon على سبعة و + +825 +01:20:22,440 --> 01:20:30,880 +تلاتين تمام؟ اذا كم قيمة ل delta صارت عندى؟ Delta + +826 +01:20:30,880 --> 01:20:38,640 +عندى هنا بواحدو delta هنا هذا بده يعطيلك انه delta + +827 +01:20:38,640 --> 01:20:46,480 +تساوي epsilon على سبعة و تلاتين ليش هاي هذه وهاي + +828 +01:20:46,480 --> 01:20:53,340 +هذه اللي عندنا طب ده اسألكوا سؤال القيمة اللي طلعت + +829 +01:20:53,340 --> 01:20:58,880 +ان هذه اعتمدت على الواحد اثناء الحسابات ولا لاأه + +830 +01:20:58,880 --> 01:21:03,700 +اعتمدت اعتمدت لأن هذه اعتمدت على الواحد هيه + +831 +01:21:03,700 --> 01:21:08,840 +والاربعة جن حسبناها بقى السبعة وتلاتين اذا اعتمدت + +832 +01:21:08,840 --> 01:21:12,880 +عليها الابسن على السبعة وتلاتين اعتمدت علي مام على + +833 +01:21:12,880 --> 01:21:17,000 +الواحد الان الابسن على السبعة وتلاتين يمكن تكون + +834 +01:21:17,000 --> 01:21:22,800 +اكبر من الواحد ويمكن تكون اقل من الواحد مين فيهم + +835 +01:21:22,800 --> 01:21:26,040 +دلتاب؟ الواحد والابسن على السبعة وتلاتين + +836 +01:21:29,010 --> 01:21:32,330 +من واحد ل سبعة و تلاتين من واحد ل إبس من على سبعة + +837 +01:21:32,330 --> 01:21:34,370 +و تلاتين من واحد ل إبس من على سبعة و تلاتين من + +838 +01:21:34,370 --> 01:21:34,390 +واحد ل إبس من على سبعة و تلاتين من واحد ل إبس من + +839 +01:21:34,390 --> 01:21:35,030 +على سبعة و تلاتين من واحد ل إبس من على سبعة و + +840 +01:21:35,030 --> 01:21:35,170 +تلاتين من واحد ل إبس من على سبعة و تلاتين من واحد + +841 +01:21:35,170 --> 01:21:36,490 +ل إبس من على سبعة و تلاتين من واحد ل إبس من على + +842 +01:21:36,490 --> 01:21:38,110 +سبعة و تلاتين من واحد ل إبس من على سبعة و تلاتين + +843 +01:21:38,110 --> 01:21:41,550 +من واحد ل إبس من على سبعة و تلاتين من واحد ل إبس + +844 +01:21:41,550 --> 01:21:47,150 +من على سبعة و تلاتين من واحد ل إبس من على سبعة و + +845 +01:21:47,150 --> 01:21:53,930 +تلاتين من واحد ل إبس + +846 +01:21:53,930 --> 01:21:57,020 +منفـDelta بدت ساوي واحد، وإذا كانت الأسر هي + +847 +01:21:57,020 --> 01:22:00,200 +epsilon على سبعة و تلاتين يبقى Delta بدت ساوي + +848 +01:22:00,200 --> 01:22:03,980 +epsilon على سبعة و تلاتين، اللي يبقى هنا بقوله إذا + +849 +01:22:03,980 --> 01:22:10,980 +Delta بدت ساوي minimum الواحد والepsilon على سبعة + +850 +01:22:10,980 --> 01:22:17,080 +و تلاتين، يعني قيمتين ولا قيمة واحدة؟هذا minimum + +851 +01:22:17,080 --> 01:22:24,020 +الصغرة فيهما هذا minimum الواحد والإبسلون الصغرة + +852 +01:22:24,020 --> 01:22:28,400 +في الإتنين يبقى لصغيرة هي بتكون main قيمة يعني + +853 +01:22:28,400 --> 01:22:32,180 +الصغرة القيمتين ليش ان ال epsilon أنا مش عارفها بس + +854 +01:22:32,180 --> 01:22:36,400 +لو عارفها رقما جدًا يعني افترض قاللي في البداية + +855 +01:22:36,400 --> 01:22:42,250 +given epsilon تسوى خمسينخمسين ع سبعة و تلاتين اكبر + +856 +01:22:42,250 --> 01:22:47,030 +من وحدة صحية اذا دلتر بدأت ساعة و واحد ما خلال لكن + +857 +01:22:47,030 --> 01:22:52,900 +لو كانت epsilon قليها عشرينأقل من واحد يبقى دلتا + +858 +01:22:52,900 --> 01:22:57,340 +بدل ساوي إبسن على سبعة و تلاتين و هكذا تمام طيب + +859 +01:22:57,340 --> 01:23:02,160 +لكن أصلا إبسن على سبعة و تلاتين لما استخدمت حساب + +860 +01:23:02,160 --> 01:23:06,680 +همين الواحد الصحيح خلي هذا المعلومة في دماغك و + +861 +01:23:06,680 --> 01:23:12,520 +الآن عند التحقيق بدنا نبين هذا الكلام يبقى باجي + +862 +01:23:12,520 --> 01:23:13,940 +بقوله showing + +863 +01:23:22,960 --> 01:23:33,300 +0 أقل من X ناقص 3 أقل من Deltaالدلتا بدأ أخدها + +864 +01:23:33,300 --> 01:23:37,700 +ابسلن على سبعة و تلاتين لأنها اعتمدت على مين عند + +865 +01:23:37,700 --> 01:23:43,960 +حسابها على مين على الواحد implies انه ال F of X + +866 +01:23:43,960 --> 01:23:49,560 +اللي هي ال X تكيب ناقص سبعة و عشرين بدي أثبت ان + +867 +01:23:49,560 --> 01:23:56,260 +هذه أقل من مين من الابسلن يبقى هذه تساويالـ X ناقص + +868 +01:23:56,260 --> 01:24:03,660 +تلاتة في الـ X تربيع زائد تلاتة X زائد تسعة هذه + +869 +01:24:03,660 --> 01:24:13,890 +أقل من Delta وهذه أقل من سبعة وتلاتينطيب دلتا + +870 +01:24:13,890 --> 01:24:17,570 +عندنا ليه إبسلون على سبعة و تلاتين اللي هي بدها + +871 +01:24:17,570 --> 01:24:24,010 +تساوي إبسلون على سبعة و تلاتين في سبعة و تلاتين + +872 +01:24:24,010 --> 01:24:28,330 +يبقى هذه اللي هي بدها تساوي مين إبسلون يبقى هذا + +873 +01:24:28,330 --> 01:24:33,950 +بده يعطيلك إن ال X تكيب نقص سبعة و عشرين أقل من + +874 +01:24:33,950 --> 01:24:40,170 +مين أقل من الإبسلون وبالتالي راس limit + +875 +01:24:54,130 --> 01:25:01,180 +قبل قليل وعدكوا بواعدلما حلت المثال في ال section + +876 +01:25:01,180 --> 01:25:05,400 +السابق كان limit X في side 1 على X ثم X تروح على + +877 +01:25:05,400 --> 01:25:10,000 +Zero ثم اتناه يساوي Zero الان بواسطة هذا ال + +878 +01:25:10,000 --> 01:25:14,520 +section ميدي اثبت فعلا ان ال limit هذا كمان يساوي + +879 +01:25:14,520 --> 01:25:23,960 +له Zero يرجع بنا نفيق بواعدنا الذي وعدناكم إياه هو + +880 +01:25:23,960 --> 01:25:26,280 +اعتبر هذا المثال رقم أربعة + +881 +01:25:34,220 --> 01:25:43,480 +يبقى مثال يبقى + +882 +01:25:43,480 --> 01:25:50,240 +مثال يبقى مثال يبقى مثال يبقى مثال يبقى مثل مثل + +883 +01:25:50,240 --> 01:25:50,480 +مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل + +884 +01:25:50,480 --> 01:25:50,480 +مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل + +885 +01:25:50,480 --> 01:25:50,480 +مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل + +886 +01:25:50,480 --> 01:25:50,480 +مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل + +887 +01:25:50,480 --> 01:25:50,480 +مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل + +888 +01:25:50,480 --> 01:25:50,520 +مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل + +889 +01:25:50,520 --> 01:25:50,900 +مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل مثل + +890 +01:25:50,900 --> 01:25:58,620 +مثللما الـ X بدأ تذهب للـ Zero للـ X في الـ Sine + +891 +01:25:58,620 --> 01:26:04,080 +واحد على X يساوي Zero solution + +892 +01:26:04,080 --> 01:26:12,900 +برضه + +893 +01:26:12,900 --> 01:26:17,280 +بدأ زي ما بدأنا في الأمثلة تلاتة السابقة + +894 +01:26:28,940 --> 01:26:36,680 +بحيث أن 0 أقل من X ناقص الـ Zero أقل من Delta + +895 +01:26:45,550 --> 01:26:50,770 +يبقى الطرف الشمال Zero أقل من absolute value ل X + +896 +01:26:50,770 --> 01:26:56,550 +أقل من delta implies هذا من تعريف ال absolute + +897 +01:26:56,550 --> 01:27:03,050 +value بصير absolute value ل X في absolute value لل + +898 +01:27:03,050 --> 01:27:10,050 +sign واحد على X أقل من مين؟ أقل من الepsilon أو + +899 +01:27:10,050 --> 01:27:18,790 +خلّيني أعملها على الشكل التاليأليست هذه أقل من + +900 +01:27:18,790 --> 01:27:24,050 +absolute value ل X في واحد لأن أعلى قيمة بياخدها + +901 +01:27:24,050 --> 01:27:26,770 +ال absolute value لصيني واحد ل X هي الواحدة الصحية + +902 +01:27:26,770 --> 01:27:31,970 +تمام يبقى هذا بيصير absolute value ل X ل واحد هذا + +903 +01:27:31,970 --> 01:27:35,830 +بده يساوي absolute value ل X اللي هي أقل من مين + +904 +01:27:35,830 --> 01:27:42,210 +أقل من ال epsilon اطلعلي للنتيجة هذه والنتيجة اللي + +905 +01:27:42,210 --> 01:27:47,930 +عندنا هذهيبقى الطرف الشمال هو الطرف الشمال يبقى + +906 +01:27:47,930 --> 01:27:55,510 +هنا ساة ال delta تساومين epsilon itself كويس مادام + +907 +01:27:55,510 --> 01:28:02,790 +طلبنا نتأكد شغلنا هذا صح ولا لأ يبقى showing that + +908 +01:28:02,790 --> 01:28:05,950 +ان delta works + +909 +01:28:11,880 --> 01:28:18,940 +أقل من ال absolute value ناقص ال zero أقل من دلتة + +910 +01:28:18,940 --> 01:28:20,480 +يبدأ تسوي epsilon + +911 +01:28:23,050 --> 01:28:28,370 +absolute value للـ x في الـ sine واحد على x ناقص + +912 +01:28:28,370 --> 01:28:33,490 +الـ zero بدي أثبت أن هذه أقل من الـ y طيب هذه + +913 +01:28:33,490 --> 01:28:38,650 +تساوي مين؟ absolute value للـ x absolute value للـ + +914 +01:28:38,650 --> 01:28:44,950 +sine واحد على x مالها هذه؟ أقل من وقت تساوي + +915 +01:28:44,950 --> 01:28:51,890 +absolute value للـ x في من؟ في الواحدطيب هذه + +916 +01:28:51,890 --> 01:28:57,890 +absolute value of x هي عبارة عن مين؟ دلتا يبقى هذه + +917 +01:28:57,890 --> 01:29:05,960 +أقل من delta في واحددلتا بقداش بالإبسنان في واحد + +918 +01:29:05,960 --> 01:29:13,200 +اللي هو بالإبسنان يبقى سا اللي هو ال X ساين واحد + +919 +01:29:13,200 --> 01:29:19,100 +على X ناقص ال zero أقل من مين أقل من إبسنان + +920 +01:29:19,100 --> 01:29:26,380 +وبالتالي Thus وكذا limit ال X في ال ساين واحد على + +921 +01:29:26,380 --> 01:29:31,530 +X لما ال X بدي روح لل Zeroبتساوي الـ zero كذلك + +922 +01:29:31,530 --> 01:29:37,750 +وهذا يتفق مع النتيجة اللى حسبناها قبل ساعة زمان + +923 +01:29:37,750 --> 01:29:44,850 +تقريبا اللى هو نهاية ال section الماضى طيب بنحاول + +924 +01:29:44,850 --> 01:29:52,670 +نعطيكوا مثال عددي نعطي قيمة لإبسلون نطلب قيمة دلتا + +925 +01:29:52,670 --> 01:29:58,710 +نعطيكوا ال نعطيكوا الشغل زي هيكيبقى اكتب لي مثال + +926 +01:29:58,710 --> 01:30:15,950 +خمسة بيقول + +927 +01:30:15,950 --> 01:30:26,910 +لي Fالـ F of X يساوي X تربيع زائد ستة X زائد خمسة + +928 +01:30:26,910 --> 01:30:35,770 +على X زائد خمسة والـ X naught يساوي سالب خمسة and + +929 +01:30:35,770 --> 01:30:43,710 +الـ Epsilon يساوي Zero Zero خمسة يعني خمسة من مية + +930 +01:30:43,710 --> 01:30:47,390 +fine وجدنا + +931 +01:30:48,400 --> 01:30:56,360 +نمر ايه بدي limit f of x لما ال x بدي روح لل x + +932 +01:30:56,360 --> 01:31:04,540 +naught نمر بي find delta + +933 +01:31:04,540 --> 01:31:13,240 +اللي greater than zero such thatبحيث هو أن الـ + +934 +01:31:13,240 --> 01:31:22,600 +zero أقل من الـ X0 أقل من Delta implies أن ال F of + +935 +01:31:22,600 --> 01:31:38,600 +X ناقص ال L أقل من إبسلون خلّي + +936 +01:31:38,600 --> 01:31:39,060 +بالك هنا + +937 +01:31:47,300 --> 01:31:53,900 +يبقى احنا بدنا limit لل F of X لما ال X بده يروح + +938 +01:31:53,900 --> 01:31:59,680 +ال X نضله جداش سالب خمسة يبقى limit لما ال X بده + +939 +01:31:59,680 --> 01:32:06,100 +يروح ليه سالب خمسة لمن ل X زائد واحد في X زائد + +940 +01:32:06,100 --> 01:32:12,380 +خمسة على X زائد خمسةالسؤال هو هل الدالة معرفة عند + +941 +01:32:12,380 --> 01:32:16,720 +X يسوى سالب خمسة؟ لأ، لكن ال limit ممكن تكون + +942 +01:32:16,720 --> 01:32:21,240 +موجودة، مالهاش علاقة، بدي بقوله كويس يبقى القوس + +943 +01:32:21,240 --> 01:32:26,100 +هذا بدي روح مع القوس هذا، النتيجة ال limit لما ال + +944 +01:32:26,100 --> 01:32:33,630 +X بدي روح لسالب خمسة لمين، لل X زائد واحدتمام؟ + +945 +01:32:33,630 --> 01:32:38,090 +يبقى هذا الكلام تعويض مباشر لإنها Line ناقص خمسة + +946 +01:32:38,090 --> 01:32:43,150 +زي واحد مايساوي قداش سالم أربعة هذه اللي هي بنقول + +947 +01:32:43,150 --> 01:32:49,370 +عليها اللي مش معطاعة فوق في رأس المثل يبقى أول جد + +948 +01:32:49,370 --> 01:32:55,180 +نقله ال limit هذا نجي لنمر يابيننمر بيبقى الهتلي + +949 +01:32:55,180 --> 01:33:00,160 +دلتا الأكبر من ال zero بحيث تكون هذه محققة بقول + +950 +01:33:00,160 --> 01:33:06,680 +بسيطة جدا يبقى احنا عندنا zero أقل من ال X ناقص مع + +951 +01:33:06,680 --> 01:33:14,690 +ناقص بالصغير زائد خمسة هذه أقل من دلتاimplies ان + +952 +01:33:14,690 --> 01:33:20,590 +ال F of X سرط اللي هي مين بعد اختصارات X زائد واحد + +953 +01:33:20,590 --> 01:33:27,910 +ناقص اللي هي L اللي هي بناقص أربعة تمام أقل من + +954 +01:33:27,910 --> 01:33:32,130 +إبسلون، إبسلون موطن هو 005 + +955 +01:33:33,350 --> 01:33:41,810 +بقول هذا يعني ان الاكس زائد خمسة اقل من zero zero + +956 +01:33:41,810 --> 01:33:49,450 +خمسة طلع لهنا وطلع لهنا يبقى هذا بدي اعطيك ان دلتا + +957 +01:33:49,450 --> 01:33:56,420 +تساوي ال epsilon تساوي zero zero خمسةبقى بده دلتا + +958 +01:33:56,420 --> 01:34:01,880 +جبناله دلتا اضع الاخر نقطة صغيرة في ال section + +959 +01:34:01,880 --> 01:34:16,860 +اللى وعدناكوا فيها قبل قليل اخر + +960 +01:34:16,860 --> 01:34:21,720 +نقطة بتقول ما يأتي هنكتب علي الشكل التالي remark + +961 +01:34:30,060 --> 01:34:44,520 +إذا أعطتنا ناقص الـ L أقل من إبسنل إذا أعطتنا ناقص + +962 +01:34:44,520 --> 01:34:48,220 +الـ L ناقص الـ L أقل من إبسنل + +963 +01:34:57,280 --> 01:35:07,460 +عن الـ X نود ثم نأخذ + +964 +01:35:07,460 --> 01:35:19,820 +دلتا لكي تكون نصف طول نصف + +965 +01:35:19,820 --> 01:35:25,500 +طول الانترال + +966 +01:35:32,540 --> 01:35:47,640 +but if it is not symmetric اذا لم تكن متماثلة + +967 +01:35:47,640 --> 01:35:53,380 +about x0 about + +968 +01:35:53,380 --> 01:35:59,400 +x0 we take دلتة we take + +969 +01:36:03,260 --> 01:36:15,020 +delta to be we take it to be the distance from + +970 +01:36:15,020 --> 01:36:30,240 +distance from x node to near endpoint near + +971 +01:36:30,240 --> 01:36:35,890 +endpointof the interval + +972 +01:37:00,980 --> 01:37:01,980 +ماذا يفعل؟ + +973 +01:38:22,130 --> 01:38:27,130 +مرة تانيةبنقول إذا الـ absolute influence نقص إلا + +974 +01:38:27,130 --> 01:38:31,310 +قلبي مثلا أعطتني interval symmetric about x node + +975 +01:38:31,310 --> 01:38:34,630 +زي الرسمة اللي قبل قليل كانت دلتة اللي على اليمين + +976 +01:38:34,630 --> 01:38:38,850 +زي دلتة اللي على الشمال يبقى في هذه الحالة بيقول + +977 +01:38:38,850 --> 01:38:44,230 +بناخد دلتة هو نص الفترة كلها من x node نقص دلتة + +978 +01:38:44,230 --> 01:38:49,510 +إلى x node زائد دلتة لكن إذا كانت الرسمة هنا not + +979 +01:38:49,510 --> 01:38:54,490 +symmetric about x node طلعلي هيطلعت قيمة لدلتة + +980 +01:38:54,730 --> 01:38:58,450 +وهيطلع في قيمة تانية، هل الاتنين دونها درجة بعض؟ + +981 +01:38:58,450 --> 01:39:02,990 +لأ، يبقى مافيش تساوي بين الاتنين فمين منهم delta؟ + +982 +01:39:02,990 --> 01:39:07,270 +الكبيرة هذه ولا الصغيرة؟ طبعا الصغيرة لإيش؟ لأن + +983 +01:39:07,270 --> 01:39:11,230 +أنا بدي أجرب على x0 بدرجة أقل لDelta كبيرة، يبقى + +984 +01:39:11,230 --> 01:39:15,440 +باخد Delta الصغر فيهم لإن أنا بدي أقترب من 100من + +985 +01:39:15,440 --> 01:39:19,060 +الـ X node فبقول إذا كانت ماهياش متمادة لحوالي X + +986 +01:39:19,060 --> 01:39:22,920 +node we take Delta to be the distance from X node + +987 +01:39:22,920 --> 01:39:28,600 +المسافة من X node إلى أقرب near end point هذي أقرب + +988 +01:39:28,600 --> 01:39:31,740 +لها إذا هذي Delta هذي أقرب لها إذا هذي Delta لكن + +989 +01:39:31,740 --> 01:39:36,260 +واضح إن هذي هي Delta اللي هي main أقرب بالنسبة لها + +990 +01:39:36,260 --> 01:39:41,700 +نوضح لك هذه مثال عددي وبيه ننهي المحاضرة example + +991 +01:39:48,600 --> 01:39:56,900 +بقول الـ F of X يساوي الجذر التربيعي للـ X ناقص + +992 +01:39:56,900 --> 01:40:04,340 +سبعة والـ L تساوي أربعة والـ X نود يساوي تلاتة + +993 +01:40:04,340 --> 01:40:15,140 +وعشرين والإبسلون تساوي واحد Find Delta that + +994 +01:40:15,140 --> 01:40:17,400 +satisfies + +995 +01:40:21,810 --> 01:40:35,790 +that satisfies the definition of the formal limit + +996 +01:40:47,730 --> 01:40:53,730 +معطيني f of x ومعطيني ال L ومعطيني ال X0 ومعطيني + +997 +01:40:53,730 --> 01:40:58,830 +ال Y وطالب باسمين Delta تبعت التعريف من جله بسيطة + +998 +01:40:58,830 --> 01:41:01,790 +جدا يبقى هاي التعريف + +999 +01:41:12,470 --> 01:41:18,730 +بحيث أن Zero أقل من X ناقص X نود اللي هي قداش + +1000 +01:41:18,730 --> 01:41:25,430 +تلاتة وعشرين أقل من Delta Delta مجهولة implies ال + +1001 +01:41:25,430 --> 01:41:31,170 +F of X اللي هو الجدرى التربية ل X ناقص سبعة ناقص L + +1002 +01:41:31,170 --> 01:41:37,510 +اللي هي قداش أربعةأقل من إبسلون، إبسل هو مقطع كده؟ + +1003 +01:41:37,510 --> 01:41:42,270 +واحد صحيح هذه جاهزة ماعندي مشكلة، يبقى بدي أحل + +1004 +01:41:42,270 --> 01:41:46,930 +مشكلة تادي فمشان أحلها باجي بقوله الجذر التربية ل + +1005 +01:41:46,930 --> 01:41:52,150 +X ناقص سبعة ناقص أربعة أقل من واحد وأكبر من مين؟ + +1006 +01:41:52,150 --> 01:41:57,590 +من سلب واحد، اضيفي أربعة لثلاثة أطراف بيصير تلاتة + +1007 +01:41:57,590 --> 01:42:03,770 +أقل من ال X ناقص سبعة أقل من مين؟ من خمسةرابع + +1008 +01:42:03,770 --> 01:42:09,690 +ثلاثة أطراف يبقى تسعة أقل من ال X ناقص سبعة أقل من + +1009 +01:42:09,690 --> 01:42:15,090 +مين من خمسة و عشرين ضيف سبعة على ثلاثة أطراف بيرث + +1010 +01:42:15,090 --> 01:42:21,830 +سبعة و تسعة ستاشر أقل من X أقل مني اتنين و تلاتين + +1011 +01:42:21,830 --> 01:42:28,130 +تمام يعني لما يكون عندي real line و هذه النقطة + +1012 +01:42:28,130 --> 01:42:33,630 +اللي هي تلاتة و عشرينهذه النقطة السادسة وهذه + +1013 +01:42:33,630 --> 01:42:35,990 +النقطة السادسة وهذه النقطة السادسة وهذه النقطة + +1014 +01:42:35,990 --> 01:42:38,130 +السادسة وهذه النقطة ستة + +1015 +01:42:41,080 --> 01:42:46,980 +بيقول هنا Delta هيها from X naught to near end + +1016 +01:42:46,980 --> 01:42:51,640 +point of the interval أيوة يبقى Delta هي المسافة + +1017 +01:42:51,640 --> 01:43:00,340 +من 16 لمين ل23 لمين هي الأقرب على ال 23 يبقى بناء + +1018 +01:43:00,340 --> 01:43:08,260 +عليه صرت ال X موجودة من 16 لغاية 32 يبقى هنا sense + +1019 +01:43:09,280 --> 01:43:20,560 +16 is the near point of X يساوي تلاتة و عشرين + +1020 +01:43:31,910 --> 01:43:38,370 +يبقى بدنا منك exercises اتنين تلاتة يبقى exercises + +1021 +01:43:38,370 --> 01:43:47,830 +اتنين تلاتة المسائل التالية اللي هو من واحد لتسعة + +1022 +01:43:47,830 --> 01:43:56,610 +واربعين القدروزيادة على ذلك من واحد وخمسين لغاية + +1023 +01:43:56,610 --> 01:44:02,970 +اربعة وخمسين وانضيف عليهم من سبعة وخمسين لغاية + +1024 +01:44:02,970 --> 01:44:03,550 +ستين + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OD0ap5i8Mj0_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OD0ap5i8Mj0_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..155cd24d990b547d7dd8419764970418b89371ab --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OD0ap5i8Mj0_postprocess.srt @@ -0,0 +1,3328 @@ +1 +00:00:21,080 --> 00:00:25,660 +بسم الله الرحمن الرحيم في ال two sections الماضية + +2 +00:00:25,660 --> 00:00:31,620 +كنا بنتحدث فقط عن اللي هو الاشتقاق من خلال التعريف + +3 +00:00:31,620 --> 00:00:35,160 +اليوم بدنا نذكر القواعد الاشتقاق اللي خدتها في + +4 +00:00:35,160 --> 00:00:39,540 +الثانوية العامة زي ما أنت شايف لا يوجد فيها حرف + +5 +00:00:39,540 --> 00:00:44,340 +جديد وإنما توذكر بمدرسة في الثانوية العامة بعد ذلك + +6 +00:00:44,340 --> 00:00:49,940 +سنذهب إلى أمثلة توضيحية على القواعد اللي موجودة + +7 +00:00:49,940 --> 00:00:55,590 +عندنايبقى differentiation rules قواعد الاشتقاق اول + +8 +00:00:55,590 --> 00:01:00,050 +قاعد بتقول لو كانت الدالة دالة ثابتة f of x يساوي + +9 +00:01:00,050 --> 00:01:05,110 +c حيث c constant اذا مشتقة هذه الدالة تساوي قداش؟ + +10 +00:01:05,110 --> 00:01:09,650 +Zero فالمشتقة في الثانوية العامة تعلمنا ان مشتقة + +11 +00:01:09,650 --> 00:01:14,350 +المقدار الثابت تساوي صفر يعني لو كانت f of x يساوي + +12 +00:01:14,350 --> 00:01:19,170 +خمسة اذا ال f prime of x يساوي لو كان f of x يساوي + +13 +00:01:19,170 --> 00:01:19,950 +باي + +14 +00:01:31,360 --> 00:01:35,680 +بالنسبة للنقطة الثانية if n is a non zero real + +15 +00:01:35,680 --> 00:01:42,340 +number then d على dx للx to the power n هو ال n في + +16 +00:01:42,340 --> 00:01:48,470 +x أُس n ناقص واحدطبعا الان اي real number لا يساوي + +17 +00:01:48,470 --> 00:01:52,250 +zero طبعا ليش اشتراطنا لا يساوي zero لأنه لو كان + +18 +00:01:52,250 --> 00:01:56,970 +يساوي zero لأصبح x أوز zero بقداش يعني مقدار ثابت + +19 +00:01:56,970 --> 00:02:01,790 +وقتالي مشتقته تساوي مين تساوي صفر طيب يبقى الان قد + +20 +00:02:01,790 --> 00:02:05,010 +يكون positive قد يكون negative قد يكون rational + +21 +00:02:05,010 --> 00:02:10,010 +غيره إلى آخره يبقى مشتقته على طول خط n x أوز n + +22 +00:02:10,010 --> 00:02:15,660 +ناقص واحدالنقطة الثالثة F في الـ C is constant + +23 +00:02:15,660 --> 00:02:20,120 +يبقى بدنا نجمع الحالتين الاتنين هدول مع بعض يبقى D + +24 +00:02:20,120 --> 00:02:25,600 +على DX ل C في F of X C المقدار الثابت بقوله خليك + +25 +00:02:25,600 --> 00:02:30,700 +على شجة و بروح بشتق مين بشتقت ده ل F of X زي ما + +26 +00:02:30,700 --> 00:02:35,940 +كنت بتقوله مشتقت تلاتة إكسوس خمسة في الثانوية بقول + +27 +00:02:35,940 --> 00:02:41,340 +تلاتة سبيكة و مشتقت إكسوس خمسةخمسة X أُص أربعة + +28 +00:02:41,340 --> 00:02:46,100 +وبالتالي بيصير خمستاشر X أُص أربعة يبقى الـC بيظل + +29 +00:02:46,100 --> 00:02:50,840 +كأنه مالوش دعوة تماما بالق بالـderivativeالان for + +30 +00:02:50,840 --> 00:02:54,920 +example ال D على DX ل C X to the power N بقول ال C + +31 +00:02:54,920 --> 00:02:58,600 +مقدرتها بتخليك زي ما انت و ال X أس N من النقطة + +32 +00:02:58,600 --> 00:03:04,060 +الثانية مشتقتها N X أس N ناقص واحد النقطة الرابعة + +33 +00:03:04,060 --> 00:03:07,760 +F ال U و ال V are differentiable functions of X + +34 +00:03:07,760 --> 00:03:12,700 +يبقى then D على DX ل U زاد أو ناقص V تساوي مشتقة + +35 +00:03:12,700 --> 00:03:16,560 +ال U زاد أو ناقص مشتقة ال V بجيتها بتقول في + +36 +00:03:16,560 --> 00:03:22,240 +الثانوية العامةمشتقة المجموع الجبري لدالتين يساوي + +37 +00:03:22,240 --> 00:03:25,600 +المجموع الجبري لمشتقتيهما + +38 +00:03:33,500 --> 00:03:38,280 +مجموعة الاتير ممكن تكون تلت دوال اربع دوال ان من + +39 +00:03:38,280 --> 00:03:42,640 +الدوال يبقى المشتقة هتدخل على كل دالة من هذه + +40 +00:03:42,640 --> 00:03:48,840 +الدوال يبقى D على DX U1 زي دو ناقص U2 زي دو ناقص + +41 +00:03:48,840 --> 00:03:56,680 +U3 زي دو ناقص UN يبقى DU1 على DX زي دو ناقص DU2زاد + +42 +00:03:56,680 --> 00:04:00,820 +او نقص دي و تلاتة على دي اكس زاد او نقص نظل ماشي + +43 +00:04:00,820 --> 00:04:06,680 +لغاية ما نوصل لمشتقة ال U ان بنسبة ال X الان + +44 +00:04:06,680 --> 00:04:11,920 +بننتقل لحاصل الضرب والقسمة فباجي بقول if U and V + +45 +00:04:11,920 --> 00:04:17,660 +are differentiable functions of X then ال D على DX + +46 +00:04:17,660 --> 00:04:21,800 +ل U في ال V يسوى الدالة الأولى في مشتقة الدالة + +47 +00:04:21,800 --> 00:04:27,290 +الثانية زي دي الدالة الثانية في مشتقةالدالة الأولى + +48 +00:04:27,290 --> 00:04:31,950 +مرة تانية الأولى في مشتقة الدالة الثانية زائد + +49 +00:04:31,950 --> 00:04:37,370 +الدالة الثانية في مشتقة من الأولى يبقى U في DV على + +50 +00:04:37,370 --> 00:04:44,370 +DX زائد ال V في DU على DX النقطة السادسة مشتقة + +51 +00:04:44,370 --> 00:04:51,390 +خارج قسم الدالتين يساوي المقام في مشتقة الباصنقص + +52 +00:04:51,390 --> 00:04:57,110 +البصد في مشتقة المقام على مربع المقام الأصلي مرة + +53 +00:04:57,110 --> 00:05:00,750 +تانية كتير من الشباب غلطتهم وين؟ من خلال السنوات + +54 +00:05:00,750 --> 00:05:05,970 +الماضية بقال نلمس بيقول البصد في مشتقة المقام نقص + +55 +00:05:05,970 --> 00:05:09,530 +المقام في مشتقة المقام يعني بيقلب الإشارة هذا طبعا + +56 +00:05:09,530 --> 00:05:15,870 +كلام خطأ فمرة تانية بركز و بقولالمقام في مشتقة الـ + +57 +00:05:15,870 --> 00:05:20,610 +bus ناقص الـ bus في مشتقة المقام على مربع المقام + +58 +00:05:20,610 --> 00:05:25,810 +الأصلي ناخد special case حالة خاصة منه قلنا in + +59 +00:05:25,810 --> 00:05:30,710 +particular كحالة خاصة مشتقة واحد على V يعني لو + +60 +00:05:30,710 --> 00:05:34,510 +كانت ال U ده اللي ثابت اللي هو بالواحد الصحيح + +61 +00:05:34,730 --> 00:05:39,970 +فمشتقتها سالب واحد على V تربية في الـDV على DX، من + +62 +00:05:39,970 --> 00:05:44,290 +أين أتي هذا؟ أتي من الخطوة اللي فوق، فلما أتي أقول + +63 +00:05:44,290 --> 00:05:49,570 +المقام في مشتقة الفاصلة، يصير Zeroبضلش عنده إلا + +64 +00:05:49,570 --> 00:05:55,910 +ناقص للبسط في مشتقة المقام على مربع المقام الأصلي + +65 +00:05:55,910 --> 00:06:00,130 +يبقى لما بدي جهد أطبقها هنا بدي أقول المقام في + +66 +00:06:00,130 --> 00:06:04,850 +مشتقة البسط ب zero طار ناقص البسط اللي هو واحد في + +67 +00:06:04,850 --> 00:06:09,150 +مشتقة المقام اللي هو dv على dx على مربع المقام + +68 +00:06:09,150 --> 00:06:10,490 +الأصلي اللي هو main + +69 +00:06:26,320 --> 00:06:31,770 +بالتالي ماعنديش أي تغيير في مثل هذه الحالةيبقى هذا + +70 +00:06:31,770 --> 00:06:35,310 +بالنسبة للمشتقات العادية الآن، يعني المشتقات من + +71 +00:06:35,310 --> 00:06:39,510 +الرطبة الأولى، لو ده مشتق من الرطبة الثانية أو + +72 +00:06:39,510 --> 00:06:43,710 +الثالثة أو الرابعة، فبقول المشتقة الثانية، المشتقة + +73 +00:06:43,710 --> 00:06:49,750 +التالتة، المشتقة الرابعة، المشتقة النونيةيبقى مرة + +74 +00:06:49,750 --> 00:06:54,550 +تانية بقول second derivative and higher derivative + +75 +00:06:54,550 --> 00:06:59,930 +المشتقة الثانية والمشتقات العليا فباجي بقول لو كان + +76 +00:06:59,930 --> 00:07:04,890 +مشتقة ال y هي y prime بديلها رمز dy على dx بتجيب + +77 +00:07:04,890 --> 00:07:09,410 +المشتقة الثانية بديلها رمز y double primeاللي دي + +78 +00:07:09,410 --> 00:07:14,030 +على دي اكس لدي ي على دي اكس اما باعطيها الرمز هذا + +79 +00:07:14,030 --> 00:07:18,810 +او الرمز هذا او دي square ي على دي اكس square و + +80 +00:07:18,810 --> 00:07:25,770 +هكذا لو اد المشتقة التالتة ي يساوي دي تكييب ي على + +81 +00:07:25,770 --> 00:07:30,570 +دي اكس تكييب and so on لغاية ما اوصل للمشتقة انها + +82 +00:07:30,570 --> 00:07:36,590 +دي مش y مرفوعة للأس n وانما y to the derivative n + +83 +00:07:37,020 --> 00:07:42,020 +لما تشوف الانو بين قصين هذه تعني مشتقة ولا تعني قص + +84 +00:07:42,020 --> 00:07:48,580 +يبقى y to the derivative ان هي dny على dxn يعني + +85 +00:07:48,580 --> 00:07:52,720 +المشتقة النونية لدالة y بالنسبة لمن او لأكس + +86 +00:07:52,720 --> 00:07:56,660 +example one بيقول find y prime for each of the + +87 +00:07:56,660 --> 00:08:00,520 +following يبقى بنجيب المشتقة الأولى لكل مما يأتي + +88 +00:08:00,920 --> 00:08:06,200 +النقطة الأولى Y تسوى أربعة جذر ال X ناقص خمسة على + +89 +00:08:06,200 --> 00:08:11,280 +X بما نشتق باستخدام قواعد الاشتقاق اللي موجودة + +90 +00:08:11,280 --> 00:08:13,920 +عندنا يبقى باجي بدون له solution + +91 +00:08:16,980 --> 00:08:22,780 +ممكن أشتق مباشرة و ممكن أروح أبسط الدالة ثم أقوم + +92 +00:08:22,780 --> 00:08:29,280 +بعملية الاشتقاق فبدأت أقول Y' يساوية الأربعة مالاش + +93 +00:08:29,280 --> 00:08:33,180 +دعوة اللي هي constant لقولنا مشتقة C في ال F of X + +94 +00:08:33,180 --> 00:08:37,420 +يساوي C في مشتقة الدالة يبقى الأربعة مالاش دعوة + +95 +00:08:37,420 --> 00:08:42,130 +الجذر ال X أخدناها قبل ذلك كمثالوأقول لك دول دير + +96 +00:08:42,130 --> 00:08:48,390 +بالك، دول بتكتبالي واحد على اتنين جذر ال X، ناقص، + +97 +00:08:48,390 --> 00:08:53,490 +هذه الآن مقدار ثابت على دلة، طلعليه مقدار ثابت + +98 +00:08:53,490 --> 00:08:58,450 +يساوي السالب واحد على الدلة تربية في مشتقة هذه + +99 +00:08:58,450 --> 00:09:05,090 +الدلة، إذا سالم خمسة ملاش دعوة على X تربية في + +100 +00:09:05,090 --> 00:09:09,130 +مشتقة من ال X اللي بيقدرش بواحد صحيح + +101 +00:09:26,970 --> 00:09:28,850 +المثال الثاني + +102 +00:09:31,520 --> 00:09:42,840 +Y تساوي تلاتة الجذر التالت ل X تربيع ناقص اتنين + +103 +00:09:42,840 --> 00:09:50,680 +على الجذر التربيعي ل X تكعيب لما نشوف مثل ذلك + +104 +00:09:50,680 --> 00:09:56,700 +بنفضل ارتب شكل المسألة قبل ان نقوم بعملية التفاضل + +105 +00:09:56,700 --> 00:10:03,210 +يبقى الحل على الشكل التالي solutionلو جيت قلت ال Y + +106 +00:10:03,210 --> 00:10:07,910 +يسوى التلاتة مالاش داعو اكون اصلا هذا تعني X تربية + +107 +00:10:07,910 --> 00:10:14,110 +اقص طلت يعني X اقص كده ايش؟ اتنين على تلاتة طلتين + +108 +00:10:14,110 --> 00:10:19,670 +ناقص اتنين هذه الجدر التربية ل X تكيب يعني X تكيب + +109 +00:10:19,670 --> 00:10:25,860 +اقص نص يعني X اقص تلاتةعلى اتنين ونطلعها فوق بيصير + +110 +00:10:25,860 --> 00:10:31,840 +X أس سالب تلاتة على اتنين تمام إذا حطيت المسألة + +111 +00:10:31,840 --> 00:10:37,820 +بشكل جديد الآن بقدر أقوله المشتقة الأولى Y prime + +112 +00:10:37,820 --> 00:10:44,320 +السابق تلاتة مالاش دعوة نيجي هذه الأس في X مرفوعة + +113 +00:10:44,320 --> 00:10:49,920 +للأس مطروح منه واحد يبقى طولتين ناقص واحد لان دي + +114 +00:10:49,920 --> 00:10:58,500 +قداش سالب طولأنت أين منها؟ ناقص اتنين في سالب + +115 +00:10:58,500 --> 00:11:04,540 +تلاتة على اتنين X أس سالب تلاتة على اتنين سالب + +116 +00:11:04,540 --> 00:11:10,040 +واحد يعني كده؟ سالب خمسة على اتنين سالب خمسة على + +117 +00:11:10,040 --> 00:11:16,160 +اتنين Y ساوي تلاتة مع تلاتة بيبقى ليه اتنين X أس + +118 +00:11:16,160 --> 00:11:22,250 +سالب طولتنين كمان مع اتنين وزائد في ناقص في ناقص + +119 +00:11:22,250 --> 00:11:28,870 +بزائد تنين مع اتنين بيظل تلاتة اكس والسالب خمسة + +120 +00:11:28,870 --> 00:11:41,550 +على اتنين النقطة نمرسىY تساوي خمسة + +121 +00:11:41,550 --> 00:11:49,270 +زائد اتنين X زائد X تربيع كله على الجذر التربيعي + +122 +00:11:49,270 --> 00:11:55,800 +لXطبعا زي ما رتبنا المسألة اللى فوق بنفضل ارتب + +123 +00:11:55,800 --> 00:12:01,800 +المسألة هذه اولا ثم نقوم بعملية الاشتقاق يبقى هنا + +124 +00:12:01,800 --> 00:12:09,700 +بدي اروح اكتب المسألة على الشكل التالي Y to 7كيف + +125 +00:12:09,700 --> 00:12:15,100 +بقدر ارتبها؟ بقدر اوزع ال bus على مين؟ على المقام، + +126 +00:12:15,100 --> 00:12:20,700 +يبقى ده بصير خمسة على جدر ال X، يعني خمسة X + +127 +00:12:20,700 --> 00:12:27,860 +والسالب نص، يبقى هاي خمسة X والسالب نص، زائد اتنين + +128 +00:12:28,660 --> 00:12:35,060 +هذا X على جذر X يعني X على X أص نص يبقى فوق جذر X + +129 +00:12:35,060 --> 00:12:47,440 +أص نص يبقى زائد 2X أص نص يعني 2 جذر Xطيب زائد x أس + +130 +00:12:47,440 --> 00:12:54,340 +نص و هنا اتنين بيبقى x أس تلاتة على اتنين هذا بده + +131 +00:12:54,340 --> 00:13:01,060 +يعطيلك ان y prime يساوي نشتق يبقى هاي خمسة و هاي + +132 +00:13:01,060 --> 00:13:09,420 +سالب نص x أس سالب تلاتة على اتنينيبقى ناقص نص X أس + +133 +00:13:09,420 --> 00:13:16,880 +سالب تلاتة على اتنين و هنا زائد اتنين في نص X أس + +134 +00:13:16,880 --> 00:13:24,820 +نص سالب واحد دول جديد سالب نص يبقى سالب نص اللي + +135 +00:13:24,820 --> 00:13:28,500 +بعده زائد تلاتة على اتنين + +136 +00:13:32,990 --> 00:13:38,890 +لو حبينا نقيت بس ترتيبها يبقى ناقص خمسة على اتنين + +137 +00:14:10,090 --> 00:14:16,930 +هذه نمرة C من المثلة نروح لنمرة D يبقى نمرة D + +138 +00:14:16,930 --> 00:14:26,790 +بتقول ما يأتي Y تساوي X تربية زيدي اتنين X X تربية + +139 +00:14:26,790 --> 00:14:34,310 +زيدي اتنين X على X تربية ناقص واحدبنجيب مشتقتها + +140 +00:14:34,310 --> 00:14:41,110 +يبقى مشتقتها هي عبارة عن مشتقت خارج قسمة دالتين + +141 +00:14:41,110 --> 00:14:48,800 +يبقى ال y prime يساوي المقامفي مشتقة البصد مشتقة + +142 +00:14:48,800 --> 00:14:54,340 +البصد اللي هو اتنين اكس زائد اتنين ناقص البصد اللي + +143 +00:14:54,340 --> 00:15:01,120 +هو اكس تربية زائد اتنين اكس في مشتقة المقام اللي + +144 +00:15:01,120 --> 00:15:09,100 +هو باتنين اكس كل هذا مقسوما على مربع المقام الأصلي + +145 +00:15:09,800 --> 00:15:16,180 +تمام يبقى هذا الكلام بدي اعطينا Y' يساوي بدي احاول + +146 +00:15:16,180 --> 00:15:20,760 +اختصر اللي هو الكلكة اللي قدامي هذه فباجي بقول + +147 +00:15:20,760 --> 00:15:32,140 +اتنين X تكعيب زائد اتنين X تربيعنقص اتنين اكس نقص + +148 +00:15:32,140 --> 00:15:37,660 +اتنين، هذه فكية الجوس الأول الجوس التاني ناقص + +149 +00:15:37,660 --> 00:15:47,640 +اتنين اكس تكعيب وكمان ناقص اربعة اكس تربيععلى + +150 +00:15:47,640 --> 00:15:55,720 +المقام x تربية ناقص واحد لكل تربية يبقى ال y prime + +151 +00:15:55,720 --> 00:16:03,040 +يبقى يساوي 2x تكييب و ناقص 2x تكييب مع السلامة عند + +152 +00:16:03,040 --> 00:16:10,480 +2x تربية و ناقص 4x تربية يبقى ناقص 2x تربيةنقص + +153 +00:16:10,480 --> 00:16:15,820 +اتنين X نقص اتنين في غيرهم على X تربيع نقص واحد + +154 +00:16:15,820 --> 00:16:21,620 +لكل تربيع اختصارات مافيهش يبقى بروح و بخليها زي ما + +155 +00:16:21,620 --> 00:16:39,440 +هي نمرأ ايه؟ بدنا Y تساوي X تربيع زائد تلاتةفى جدر + +156 +00:16:39,440 --> 00:16:50,300 +ال X ناقص تلاتة فى تلاتة X أسطلتين ناقص اتنين + +157 +00:16:50,300 --> 00:17:00,840 +فكرلى + +158 +00:17:00,840 --> 00:17:08,710 +كيف انه نشتق هذه الظلةهذه الدالة مش دالتين وانما + +159 +00:17:08,710 --> 00:17:15,790 +بدل الدالة تلات دوال، يعني حاصل ضرب ثلاث دوال، + +160 +00:17:15,790 --> 00:17:22,720 +بدنا نيجي نشوف كيف نشتقهمطبعاً في أكثر من اقتراح + +161 +00:17:22,720 --> 00:17:27,200 +الاقتراح الأول نضرب هذول اتنين في بعض و بعدين يصير + +162 +00:17:27,200 --> 00:17:32,020 +مشتق تتحصل ضرب دلتين او نضرب اتنين هذول في بعض و + +163 +00:17:32,020 --> 00:17:35,980 +بعدين يحصل ضرب دلتين او تضرب اي اتنين في بعض و + +164 +00:17:35,980 --> 00:17:39,940 +بعدين يحصل ضرب دلتين او نضرب التلاتة في بعض ثم + +165 +00:17:39,940 --> 00:17:46,860 +نشتق هذه وجهة نظر تمام؟ لكن هناك وجهة نظر أخرى وهي + +166 +00:17:46,860 --> 00:17:51,700 +المشتق الأولزائل التاني والتاني وزائل الأول + +167 +00:17:51,700 --> 00:18:00,240 +والتاني يعني كيف نشتغل الأول والتاني يعني يعني + +168 +00:18:00,240 --> 00:18:04,100 +الأول والتاني نشتغل على زائل الأول والتاني زائل + +169 +00:18:04,100 --> 00:18:07,220 +التاني والتاني طب والتالت لو نشتغل الأول والتاني + +170 +00:18:07,220 --> 00:18:12,620 +التالت أين بدي يروح؟يعني نشتق اتنين و نثبت واحد، + +171 +00:18:12,620 --> 00:18:23,920 +صحيح هذا الكلام، اه ايوة ايوة تمام تمام يبقى زميلك + +172 +00:18:23,920 --> 00:18:31,380 +و هذا شو اسمك انت؟ محمد؟أبو ايه؟ عمد أبو نصر. عمد + +173 +00:18:31,380 --> 00:18:35,040 +أبو نصر تمام؟ انتظر على السؤال فبيقول ما يأتيك + +174 +00:18:35,040 --> 00:18:39,860 +عندي تلت أقوات بيقول بطول القص و بثبت اتنين على + +175 +00:18:39,860 --> 00:18:43,200 +عكس ما اقول انت بتشتق اتنين و تثبت واحد، لأ هو + +176 +00:18:43,200 --> 00:18:47,840 +جالك بشتق واحد و بثبت اتنين، بعد هيك بدي بشتق اللي + +177 +00:18:47,840 --> 00:18:51,260 +فالنص و بثبت اللي قبله و اللي بعده، بعد هيك بدي + +178 +00:18:51,260 --> 00:18:55,110 +للاخير و بشتق الأخر و بثبت الأولوالثاني هو فعلا + +179 +00:18:55,110 --> 00:19:01,730 +هادي مستوحى من مشتقة حاصن ضرب دالتين بالضبط تماما، + +180 +00:19:01,730 --> 00:19:08,950 +يبقى على طول الخطوط، لا تغلبش عليك ولا تضرب ولا + +181 +00:19:08,950 --> 00:19:12,370 +وانت بتجمع بعد عملية الضرب غلط ولا عليك، لا لا لا + +182 +00:19:12,370 --> 00:19:16,310 +فيش أسال من هناك، بدي اشتق الأول، يبقى الأول قداش + +183 +00:19:16,310 --> 00:19:22,910 +2Xوثبت القوسين الآخرين اللي هو جدر ال X ناقص تلاتة + +184 +00:19:22,910 --> 00:19:29,510 +في تلاتة X أس تلتين ناقص اتنين زائد الأول بدي + +185 +00:19:29,510 --> 00:19:35,360 +أثبته زي ما هوفى مشتقة الثانية اللى هو واحد على + +186 +00:19:35,360 --> 00:19:42,160 +اتنين جذر ال X ثمين فى التالت زى ما هو له تلاتة X + +187 +00:19:42,160 --> 00:19:48,780 +أسطلتين ناقص اتنين زاد الجثين الأولانيات زى ما هم + +188 +00:19:48,780 --> 00:19:57,610 +X تربيع زائد تلاتة ثمينفي جذر ال X ناقص تلاتة في + +189 +00:19:57,610 --> 00:20:03,350 +مشتقة الأخر مشتقة سالب اتنين مع السلامة وهذا تلاتة + +190 +00:20:03,350 --> 00:20:12,250 +في طلتين X والسالب طول يبقى تلاتة في طلتين + +191 +00:20:15,520 --> 00:20:21,480 +طبعا تلاتة مع تلاتة بتروح و بيقول بس اتنين X أسالب + +192 +00:20:21,480 --> 00:20:26,540 +تلت يبقى هي المشتقة طبعا هذا بيسهل الشغل بعد هيك + +193 +00:20:26,540 --> 00:20:30,900 +لو كانوا بدل التلات أقواص أربع أقواص أو خمس أقواص + +194 +00:20:30,900 --> 00:20:35,530 +أو ستة أو جد ما بدكفاضل واحد واتثبت الباقي، فاضل + +195 +00:20:35,530 --> 00:20:38,230 +التاني واتثبت اللي جابله واللي بعده، فاضل التابت + +196 +00:20:38,230 --> 00:20:41,590 +واتثبت اللي جابله واللي بعده، بيكون فاضلت ولا تروح + +197 +00:20:41,590 --> 00:20:47,410 +تضرب ولا تجسم ولا تغلب حالك، طبعا؟ طيب، نيجي + +198 +00:20:47,410 --> 00:20:51,870 +للمثال الثاني example 2 + +199 +00:20:58,500 --> 00:21:06,940 +حاجة اسمه إلى نقطتين النقطة a find the second + +200 +00:21:06,940 --> 00:21:12,600 +derivative المشتق + +201 +00:21:12,600 --> 00:21:25,540 +الثاني of y تساوي x تربيع ناقص x أس تلتي + +202 +00:21:30,130 --> 00:21:36,030 +يبقى بدنا المشتقة الثانية لمن؟ ل X تربيع ناقص X أس + +203 +00:21:36,030 --> 00:21:41,270 +تلتين بقولها بسيطة يعني بدنا نشتق هذه الدالة كم + +204 +00:21:41,270 --> 00:21:48,610 +مرة مرتين يبقى بداشي أقوله Y prime اتنين X ناقص + +205 +00:21:48,610 --> 00:21:56,760 +تلتين X أس كده؟ كده؟تلتين سالب واحد كده ايش بيظل؟ + +206 +00:21:56,760 --> 00:22:02,820 +سالب تلت ثم بعد هيك بروح اجيب مين؟ مشتقة ثانية + +207 +00:22:02,820 --> 00:22:07,880 +يبقى المشتقة الثانية Y double prime تساوي مشتقة + +208 +00:22:07,880 --> 00:22:14,200 +الأولى باتنين وهذه ناقص تلتين مالاش دعوة وهذا سالب + +209 +00:22:14,200 --> 00:22:21,110 +تلت Xسالب تلت سالب واحد يعني سالب واحد و تلت يبقى + +210 +00:22:21,110 --> 00:22:27,810 +سالب اربع على تلتة يبقى قلة النتيجة الاتنين ناقص + +211 +00:22:27,810 --> 00:22:35,510 +فناقص بزايد اتنين على تسعة اكس او سالب اربع على + +212 +00:22:35,510 --> 00:22:41,330 +تلتة نمر + +213 +00:22:41,330 --> 00:22:43,730 +بي find + +214 +00:22:48,160 --> 00:22:56,540 +الـ y to the derivative m for the function لدى ال + +215 +00:22:56,540 --> 00:23:01,300 +y تساوي واحد على x زي التلاتة + +216 +00:23:07,500 --> 00:23:11,660 +مشان أجيب المشتقة النونية نروح أجيب المشتقة الأولى + +217 +00:23:11,660 --> 00:23:16,160 +و التانية و التالتة و الرابعة و الخمسة لغاية ما + +218 +00:23:16,160 --> 00:23:22,000 +اهتدي إلى شكل المشتقة النونية كيف كانت تالية + +219 +00:23:22,000 --> 00:23:24,060 +solution؟ + +220 +00:23:27,020 --> 00:23:36,020 +الان بده يجي الى Y' يساوي مشتقة هذه سالب واحد على + +221 +00:23:36,020 --> 00:23:42,180 +X زائد تلاتة لكل تربيع في مشتقة ما ده ما الا اللي + +222 +00:23:42,180 --> 00:23:47,080 +هو المقام اللي هو بقداشي بواحد يبقى النتيجة صارت + +223 +00:23:47,080 --> 00:23:53,480 +سالب واحد على X زائد تلاتة لكل تربيع + +224 +00:23:55,690 --> 00:24:00,970 +بنروح نجيب المشتقة الثانية يعني يا شباب هذه كأنها + +225 +00:24:00,970 --> 00:24:11,420 +ايش؟ كأنها سالب X زائد تلاتة كله سالب اتنينطيب هده + +226 +00:24:11,420 --> 00:24:18,240 +هي الـYW' هي السالب اللي برا وهي سالب اتنين وهي + +227 +00:24:18,240 --> 00:24:22,740 +الجس زي ما هو وبدنا نطرح منه واحد بيصير السالب + +228 +00:24:22,740 --> 00:24:26,780 +اتنين سالب واحد سالب تلاتة في تفاضل مداخل القس + +229 +00:24:26,780 --> 00:24:30,640 +اللي هو الجداش بواحد يعني في الـDV على DX اللي هو + +230 +00:24:30,640 --> 00:24:38,140 +بواحد يبقى النتيجة صارت اللي هو اتنين X زائد تلاتة + +231 +00:24:38,140 --> 00:24:43,560 +وسالب تلاتةالسلام عليكمطيب بدنا نروح نجيب المشتقة + +232 +00:24:43,560 --> 00:24:50,880 +التالتة يساوي هاي اتنين اللي برا وهاي سالب تلاتة و + +233 +00:24:50,880 --> 00:24:58,520 +هذا ال X زائد تلاتة أس سالب كدهش؟ سالب تلاتة سالب + +234 +00:24:58,520 --> 00:25:02,820 +واحد اللي هو سالب أربعة في مشتقة مداخل القوس اللي + +235 +00:25:02,820 --> 00:25:12,230 +هو بواحد طيب الآن لو جيت المشتقة الرابعةيساوي + +236 +00:25:12,230 --> 00:25:19,990 +اتنين في سالب تلاتة في سالب اربعة في ال X زائد + +237 +00:25:19,990 --> 00:25:29,530 +تلاتة قص سالب خمسةما .. وين اللي مضربنهاش؟ وين + +238 +00:25:29,530 --> 00:25:34,870 +اللي محطنهاش؟ التالتة هي التالتة هي اتنين سالب + +239 +00:25:34,870 --> 00:25:39,370 +تلاتة فيكس زي اربعة سالب تلاتة سالب واحد سالب + +240 +00:25:39,370 --> 00:25:44,320 +اربعة كيف مكتبنهاش عاد؟على كلام كان سليم مائة + +241 +00:25:44,320 --> 00:25:51,240 +بالمائة، لا غبار عليه، تمام؟ طيب، بس تنى شوية، + +242 +00:25:51,240 --> 00:25:57,200 +الآن هذا ويه الساوي، سلب في سلب الموجب يبقى اتنين + +243 +00:25:57,200 --> 00:26:04,420 +في تلاتة في اربعةfix زائد تلاتة كله أساليب خمسة + +244 +00:26:04,420 --> 00:26:10,480 +إيش رأيك بدي أصيغ هذه الصياغة أخرى لو رجعنا هيك في + +245 +00:26:10,480 --> 00:26:15,620 +الهمش للثانوية العامة بقينا نقول مضروب الأربعة + +246 +00:26:15,620 --> 00:26:21,160 +أربعة في تلاتة في اتنين في واحد مش هيك بيناجي أول؟ + +247 +00:26:22,540 --> 00:26:27,540 +صح؟ يعني كنت تكتبوها هيك و الله واحدة و نقطة مش + +248 +00:26:27,540 --> 00:26:33,380 +هيك يعني فهي ممتازة يعني يبقى مضروب الأربعة اللي + +249 +00:26:33,380 --> 00:26:40,360 +هو أربعة في مضروب التلاتة هيك كنت تكتبوها أو أربعة + +250 +00:26:40,360 --> 00:26:45,680 +في تلاتة في مضروب اتنين + +251 +00:26:55,950 --> 00:27:07,370 +4×3×2×1 4×3×2×1 4×3×2×1 4×3×2×1 4×3×2×1 + +252 +00:27:07,370 --> 00:27:12,430 +4×3×2×1 + +253 +00:27:15,030 --> 00:27:21,110 +هذه هي السلب برة اتنين في تلاتة مش هي مضغوبة تلاتة + +254 +00:27:21,110 --> 00:27:25,870 +ايضا لان تلاتة في اتنين في واحد اذا هذه تلاتة + +255 +00:27:25,870 --> 00:27:34,770 +factorial في ال X زائد تلاتة كله أس سالب أربع لو + +256 +00:27:34,770 --> 00:27:41,370 +جيت لهذه أليست هذه هي اتنين factorial في X زائد + +257 +00:27:41,370 --> 00:27:47,420 +تلاتة كله أس سالب تلاتة؟هذه أليست هي واحد + +258 +00:27:47,420 --> 00:27:53,360 +factorial فاهمين؟ fixed زي التلاتة او ناقص اتنين + +259 +00:27:53,360 --> 00:27:59,620 +طيب ممتاز اذا لو ضلت ماشي على الشكل هذه هوصل + +260 +00:27:59,620 --> 00:28:05,020 +للمشتقانونية what's the matter استنى شوية عدت عشان + +261 +00:28:05,020 --> 00:28:10,030 +اجيب شكل المشتقانونية بدي اقارنبين نتائج التي + +262 +00:28:10,030 --> 00:28:15,890 +توصلت اليها هذا المشتقة كده ايش؟ اربعة النتيجة + +263 +00:28:15,890 --> 00:28:22,070 +اربعة factorial X زي تلتة أس سالب خمسة يبقى اربعة + +264 +00:28:22,070 --> 00:28:27,720 +اربعة سالب خمسة تعال خد المشتقة التالتةتلاتة + +265 +00:28:27,720 --> 00:28:33,600 +factorial بس بشرط سالب، وهنا كده؟ سالب أربع، تعليل + +266 +00:28:33,600 --> 00:28:37,800 +المشتقة التانية، اتنين factorial والسالب تلاتة + +267 +00:28:37,800 --> 00:28:43,500 +الجوز، تعليل Y prime، يبقى واحد factorial X زي + +268 +00:28:43,500 --> 00:28:50,470 +التلاتة يسوى سلب اتنين، يبقى المباحظ ما يأتيحد + +269 +00:28:50,470 --> 00:28:55,870 +موجب، حد سالب، مش كله موجب ولا كله سالب، مرة موجب، + +270 +00:28:55,870 --> 00:28:59,850 +مرة سالب، مرة موجب، مرة سلب، اي واحدة، اتنين، + +271 +00:28:59,850 --> 00:29:07,070 +رتبتي المشتقة هي تبعت ال factorialمشتقة رابعة + +272 +00:29:07,070 --> 00:29:10,870 +اربعة factorial المشتقة التانية التانية factorial + +273 +00:29:10,870 --> 00:29:15,970 +المشتقة الأولى واحد factorial اتنين والله تلاتة ال + +274 +00:29:15,970 --> 00:29:19,110 +ghost في الحالات الأربعة زي ما هو بس اللي بتغير + +275 +00:29:19,110 --> 00:29:24,970 +main plus في حالة المشتقة الأولى كان سالب اتنينفى + +276 +00:29:24,970 --> 00:29:28,370 +عادة المشتقة التانية كان سالب تلاتة فى عادة + +277 +00:29:28,370 --> 00:29:32,330 +المشتقة الرابعة كأه فى المشتقة التالتة صار سالب + +278 +00:29:32,330 --> 00:29:36,670 +أربعة فى عادة المشتقة الرابعة صار سالب خمسة و هكذا + +279 +00:29:36,670 --> 00:29:42,470 +إذا بناء على هذه المقارنة بقدر أكتب شكل المشتقة + +280 +00:29:42,470 --> 00:29:48,210 +النونية يبقى يا باجي بقول سالب واحد to the power n + +281 +00:29:48,210 --> 00:29:54,000 +و بدي أرجعلها لسه أتأكد شغل صح و الله غلطأربعة + +282 +00:29:54,000 --> 00:29:58,580 +أربعة factorial تلاتة تلاتة factorial يبقى N N + +283 +00:29:58,580 --> 00:30:05,940 +factorial ال X زائد تلاتة زي ما هو المشتق الرابعة + +284 +00:30:05,940 --> 00:30:11,640 +بسالب خمسة يبقى بدأ يقول سالب N وكمان سالب واحد + +285 +00:30:11,640 --> 00:30:17,280 +يعني المشتق قد يبدأ يحطه بشرة سالب وأطرح منها واحد + +286 +00:30:17,590 --> 00:30:21,230 +الرابعة بصالب خمسة، التالتة بصالب أربعة، التانية + +287 +00:30:21,230 --> 00:30:26,970 +بصالب تلاتة، الأولى بصالب اتنين وهكذا، يعني أقل من + +288 +00:30:26,970 --> 00:30:31,570 +رتبة المشتقة ضمن بصالب واحد، الرتبة بصالب وكمان + +289 +00:30:31,570 --> 00:30:37,430 +تطرح منها صالب واحدنرجع لهذا تأكد شغلي صح و لا + +290 +00:30:37,430 --> 00:30:41,910 +غلط، إن كان صح كلبها، إن كان غلط بنعمله التصحيح + +291 +00:30:41,910 --> 00:30:45,870 +اللي لازم، بدالي أقول لو بدى المشتقة الأولى، يبقى + +292 +00:30:45,870 --> 00:30:49,970 +مكان الإناش بده أحط واحد، يبقى Y prime، يبقى بده + +293 +00:30:49,970 --> 00:30:55,130 +أحط هنا واحد وهنا واحد، يبقى واحد بصير هذه سالب، + +294 +00:30:55,130 --> 00:31:00,580 +الجواز والسالب اتنينسالب الجوس السالب اتنين اللي + +295 +00:31:00,580 --> 00:31:06,100 +المشغل اه والله هذه مظبوطة تمام نسيت السلب بس هنا + +296 +00:31:06,100 --> 00:31:13,300 +يعني تمام؟ بنجر مين؟ لو كانت ال N بإتنين يبقى هذه + +297 +00:31:13,300 --> 00:31:18,700 +السالب واحد تربية بالموجب بصير اتنين factorial X + +298 +00:31:18,700 --> 00:31:23,340 +زي التلاتة و السالب تلاتة لأن ال N بإتنين سالب + +299 +00:31:23,340 --> 00:31:27,280 +اتنين سالب واحد سالب تلاتة يبقى ال Y double prime + +300 +00:31:27,520 --> 00:31:31,160 +بصير اتنين factorial X زي التلاتة والسلب اتنين + +301 +00:31:31,160 --> 00:31:35,300 +وهكذا بلاحظ الكلام هذا صحيح دائما وابدا إذا + +302 +00:31:35,300 --> 00:31:41,020 +المشتقة النونية يسلب واحد أس ان ان factorial في X + +303 +00:31:41,020 --> 00:31:45,720 +زي التلاتة to the power سلب ان سالب واحد طيب لو + +304 +00:31:45,720 --> 00:31:50,010 +نجيت الإشارة حسب ما نكاتب مش صحيحةيعني لاجئة + +305 +00:31:50,010 --> 00:31:53,570 +المشتقلة و لا بدل ما هي سالب لاجئتها موجبة كيف + +306 +00:31:53,570 --> 00:31:59,330 +تصحيها بكل بساطة بس جبل انكتب زائد واحد تبقى خلصت + +307 +00:31:59,330 --> 00:32:04,830 +منها المشكلة دائما انا بحط اس ان لاجئتها مظبوطة + +308 +00:32:04,830 --> 00:32:08,810 +كان بها ما لاجئتها بس بضيف واحد بصير مظبوطة تمام + +309 +00:32:08,810 --> 00:32:11,450 +مائة بالمئة هذا السؤال اللي كنت تسأله و لا غيره + +310 +00:32:13,090 --> 00:32:20,470 +الاشتغال بقى عشان أقول X زي أتردد كله سلب M ومتصفر + +311 +00:32:20,470 --> 00:32:26,860 +الداخل دولةأحنا ما خدناش تقول X زي كتبة احنا ما + +312 +00:32:26,860 --> 00:32:27,200 +خدناش تقول X زي كتبة احنا ما خدناش تقول X زي كتبة + +313 +00:32:27,200 --> 00:32:28,140 +احنا ما خدناش تقول X زي كتبة احنا ما خدناش تقول X + +314 +00:32:28,140 --> 00:32:31,740 +زي كتبة احنا ما خدناش تقول X زي كتبة احنا ما خدناش + +315 +00:32:31,740 --> 00:32:34,140 +تقول X زي كتبة احنا ما خدناش تقول X زي كتبة احنا + +316 +00:32:34,140 --> 00:32:36,420 +ما خدناش تقول X زي كتبة احنا ما خدناش تقول X زي + +317 +00:32:36,420 --> 00:32:37,400 +كتبة احنا ما خدناش تقول X زي كتبة احنا ما خدناش + +318 +00:32:37,400 --> 00:32:44,460 +تقول X زي كتبة احنا ما خدناش تقول X زي كتبة احنا + +319 +00:32:44,460 --> 00:32:51,140 +ما خدناش تقول X زي كتبةإن شاء الله تشيروني حد بدي + +320 +00:32:51,140 --> 00:32:55,860 +أسأل تاني؟ المشتق اللي هو واحد على اثنين جاذر ال + +321 +00:32:55,860 --> 00:33:05,380 +X؟ المشتق + +322 +00:33:05,380 --> 00:33:07,700 +اللي هو واحد على اثنين جاذر ال X؟ المشتق اللي هو + +323 +00:33:07,700 --> 00:33:09,380 +واحد على اثنين جاذر ال X؟ المشتق اللي هو واحد على + +324 +00:33:09,380 --> 00:33:11,060 +X؟ المشتق اللي هو واحد على اثنين جاذر ال X؟ المشتق + +325 +00:33:11,060 --> 00:33:13,520 +اللي هو واحد على اثنين جاذر ال X؟ المشتق اللي هو + +326 +00:33:13,520 --> 00:33:16,800 +واحد على اثنين جاذر ال X؟ المشتق اللي هو واحد على + +327 +00:33:16,800 --> 00:33:18,360 +اثنين جاذر ال X؟ المش + +328 +00:33:22,760 --> 00:33:28,060 +أي سؤال بده مشتقة العاشرة الـ20% بنشوف النتيجة هنا + +329 +00:33:28,060 --> 00:33:31,440 +وبنعمل مقارنة وبنقل عليها بنستنتجها سواء كان + +330 +00:33:31,440 --> 00:33:35,260 +الـSin أو الـCos أو جدر الـX أو أي شغلة من الشغلات + +331 +00:33:35,260 --> 00:33:39,460 +هذه شوف مادام الشقاق بطلقلك نفس الدالة بس بتغير + +332 +00:33:39,460 --> 00:33:43,400 +الأس لازم يكون في شكل المشتقة أنونيا + +333 +00:33:46,830 --> 00:33:51,610 +الإشارة عندي ناقص واحد، حاطيتها وص إن، مظبوط؟ يبقى + +334 +00:33:51,610 --> 00:33:55,510 +هذه بحطها لأي إشارة بعد ذلك، مدام موجة بسالب موجة + +335 +00:33:55,510 --> 00:33:59,310 +بسالب، بحط هذه، إذا والله لاجيتها، لما أتيت عوض + +336 +00:33:59,310 --> 00:34:02,090 +مستقلة والتانية والتالتة، لاجيته الصحيح، يبقى + +337 +00:34:02,090 --> 00:34:07,150 +الوضع صحيح، لاجيتها غلط، بس للأس هذا بحط إن زائد + +338 +00:34:07,150 --> 00:34:10,890 +واحد، والباقي كما هو، يعني اللي كانت موجة بصير + +339 +00:34:10,890 --> 00:34:13,910 +سالب، واللي كانت سالب بصير موجة، بتطلع معناة دورية + +340 +00:34:14,140 --> 00:34:29,560 +ماشى يا سيدي طيب ننتقل الى المثال اللى يليه المثال + +341 +00:34:29,560 --> 00:34:40,150 +اللى بعده مثال رقم تلاتة يبقى تلاتةبقول الف ال F + +342 +00:34:40,150 --> 00:34:47,850 +of اتنين يساوي اتنين and ال F prime of اتنين يساوي + +343 +00:34:47,850 --> 00:34:56,470 +تلاتة and ال F prime of اتنين يساوي تلاتة find + +344 +00:34:56,470 --> 00:35:04,930 +وجدلي الي هو Dy by DX for + +345 +00:35:22,290 --> 00:35:26,070 +نجي الان للمشتق اللي عندنا هذا يبقى solution + +346 +00:35:29,390 --> 00:35:34,610 +الان في ان y يساوي f of x علي x تربية زايد f of x + +347 +00:35:34,610 --> 00:35:39,530 +عند x يساوي اتنين مطلوب قداش مقدار المشتق عند x + +348 +00:35:39,530 --> 00:35:43,390 +يساوي اتنين اذا بدنا نروح نشتق الدالة و نعوض + +349 +00:35:43,390 --> 00:35:48,970 +بالمعطيئات اللي موجودة عندنا يبقى ال y prime يساوي + +350 +00:35:48,970 --> 00:35:56,590 +هذه خارج قسم الدالتين يبقى المقام في مشتقة البسط + +351 +00:35:57,840 --> 00:36:07,460 +ناقص ال bus في مشتقة المقام 2x زائد f prime of x + +352 +00:36:07,460 --> 00:36:15,570 +كل هذا مقسوم على مربع المقام الأصلي لكل تربيةبعد + +353 +00:36:15,570 --> 00:36:21,810 +هيك بدنا نروح نجيب ال y prime عند x يسوي كده؟ 2 + +354 +00:36:21,810 --> 00:36:27,850 +يبقى بدنا نشيل كل x ونحط مكانها 2 يبقى هذا الكلام + +355 +00:36:27,850 --> 00:36:36,450 +بد يسوي 2 تربيه زائد ال F of 2 في ال F prime of 2 + +356 +00:36:36,450 --> 00:36:45,380 +ناقص ال F of 2 اتنين في اتنينزائد F prime of اتنين + +357 +00:36:45,380 --> 00:36:52,400 +كله مقسوما على اتنين تربيع زائد F of اتنين الكل + +358 +00:36:52,400 --> 00:37:00,380 +تربيع النتيجة تساوي اربعة زائد F of اتنين مقطع + +359 +00:37:00,380 --> 00:37:05,320 +اللي هو بقداش باتنين F prime of اتنين اللي هي + +360 +00:37:05,320 --> 00:37:12,450 +بقداش بتلاتةيبقى مضروب فيه تلاتة ناقص F of 2 ب2 + +361 +00:37:12,450 --> 00:37:19,050 +أربع زائد F prime of 2 اللي هو بتلاتة كل هذا + +362 +00:37:19,050 --> 00:37:25,770 +الكلام مقسوما على اللي هو أربع زائد F of 2 ب2 الكل + +363 +00:37:25,770 --> 00:37:32,180 +تربيةنجا اتنين زي اربعة ستة في تلاتة اب تمانتاشر + +364 +00:37:32,180 --> 00:37:37,940 +ناقص تلاتة و اربعة سبعة في اتنين اب اربعة طاشر كل + +365 +00:37:37,940 --> 00:37:44,500 +هذا الكلام على ستة و تلاتين يبقى على ستة و تلاتين + +366 +00:37:44,500 --> 00:37:50,080 +بيضل اربعة على ستة و تلاتين يقبل جواب قداش تسوى + +367 +00:37:50,080 --> 00:37:57,130 +يبقى النتيجة تساوي تسوىيعني انت بدك تحاول تستخدم + +368 +00:37:57,130 --> 00:38:01,630 +المعطيات اللي عندك بالطريقة المناسبة ال dash tag + +369 +00:38:01,630 --> 00:38:07,050 +بعد هيك اعوض باتنين بعد هيك اروح استخدم المعطيات + +370 +00:38:07,050 --> 00:38:14,630 +اللي عندي للحصول على الإجابة المطلوبة كان هذا هو + +371 +00:38:14,630 --> 00:38:21,710 +المثال رقم تلاتة بدنا نروح لمثال رقم أربعة مثال + +372 +00:38:21,710 --> 00:38:24,030 +رقم أربعة بيقول ما يأتي + +373 +00:38:28,070 --> 00:38:36,330 +مثال رقم اربعة بيقول find an + +374 +00:38:36,330 --> 00:38:47,510 +equation for the line perpendicular اللي + +375 +00:38:47,510 --> 00:38:52,110 +بيكون عمودي perpendicular to the tangent + +376 +00:38:58,720 --> 00:39:12,640 +to the tangent of the curve المنحنة y تساوي x تكيب + +377 +00:39:12,640 --> 00:39:23,700 +ناقص أربعة x زائد واحد at the point عند النقطة + +378 +00:39:23,700 --> 00:39:28,200 +اتنين واحد نمرى ب + +379 +00:39:31,040 --> 00:39:35,700 +بقول find equations + +380 +00:39:35,700 --> 00:39:38,740 +for + +381 +00:39:38,740 --> 00:39:45,040 +the tangents for + +382 +00:39:45,040 --> 00:39:52,180 +the tangents to the curve to + +383 +00:39:52,180 --> 00:40:03,670 +the curve at the pointsعند النقاط at the points + +384 +00:40:03,670 --> 00:40:11,430 +where the slope is تمانية + +385 +00:40:37,100 --> 00:40:42,280 +سؤال مرة تانية سؤال فيه مطلوبين المطلوب الأول + +386 +00:40:42,280 --> 00:40:48,640 +بيقول هات لمعاد الخط الذي يكون عموديا على مماثل + +387 +00:40:48,640 --> 00:40:55,060 +منحنى y يساوي x تكيب نقص 4x زاد 1 عند النقطة 2 و1 + +388 +00:40:55,060 --> 00:41:00,520 +يعني انا في عندي منحنى في مماس في نقطة تماث في + +389 +00:41:00,520 --> 00:41:06,300 +عمودي عند نقطة التماس اللي هو 2 و1مش هجيب معادلة + +390 +00:41:06,300 --> 00:41:14,680 +العمودي بدي ميله و نقطة واقع عليه نقطة واقع عليه + +391 +00:41:14,680 --> 00:41:20,140 +هي الموجودة بضل قداش ميله ميله بدي اجيبه من مين + +392 +00:41:20,140 --> 00:41:24,450 +لمينعن طريق ميلي المماثل المنحنة لأن عندي قاعدة في + +393 +00:41:24,450 --> 00:41:30,090 +الهندسة التحليلية بتقول حاصل ضرب ميلي المستقيمين + +394 +00:41:30,090 --> 00:41:34,730 +المتعمدين يساوي إذا بدأت أستخدم القاعدة في الحصول + +395 +00:41:34,730 --> 00:41:39,370 +على ميلي العمودي ومن ثم أروح أجيب معادلته + +396 +00:41:45,010 --> 00:41:49,930 +معادلات المماثات للمنحنة المعادلة المماثات للمنحنة + +397 +00:41:49,930 --> 00:41:51,330 +المعادلة المماثات للمنحنة المعادلة المماثات + +398 +00:41:51,330 --> 00:41:51,770 +للمنحنة المعادلة المماثات للمنحنة المعادلة + +399 +00:41:51,770 --> 00:41:52,950 +للمنحنة المماثات للمنحنة المماثات للمنحنة المماثات + +400 +00:41:52,950 --> 00:41:57,770 +للمنحنة المماثات للمنحنة + +401 +00:41:57,770 --> 00:42:03,690 +المماثات للمنحنة المماثات للمنحنة المماثات للمنحنة + +402 +00:42:03,690 --> 00:42:09,070 +المماثات للمنحنة + +403 +00:42:13,710 --> 00:42:21,770 +يبقى هذا الكلام بده يساوي اللي تلاتة X تربية تلاتة + +404 +00:42:21,770 --> 00:42:29,920 +X تربية ناقص أربعةالان هذا يسوي ميل المماس للمنحنة + +405 +00:42:29,920 --> 00:42:41,580 +يبقى هذا يسوي slope of the tangent عند اي لحظة طب + +406 +00:42:41,580 --> 00:42:47,520 +انا بدي slope of the tangent وين؟ عند النقطة اتنين + +407 +00:42:47,520 --> 00:42:57,830 +وواحد يبقى باجي بقوله the slope ofthe tangent at + +408 +00:42:57,830 --> 00:42:59,550 +the point + +409 +00:43:10,330 --> 00:43:16,310 +يبقى هذا الكلام يسوى تلاتة في اتنين تربية ناقص + +410 +00:43:16,310 --> 00:43:19,570 +اربعة اربعة في تلاتة في اتناشر ناقص اربعة يسوى + +411 +00:43:19,570 --> 00:43:23,470 +تلاتة في اتنين تربية ناقص اربعة يبقى هذا الاسلوب + +412 +00:43:23,470 --> 00:43:32,090 +تبع ال tangent هذا لو رحت اعطيته الرمز M1الان انا + +413 +00:43:32,090 --> 00:43:40,310 +عندي حاصل ضرب ميلي المستقيمين المتعمدين يساوي كده؟ + +414 +00:43:40,310 --> 00:43:44,830 +سالب واحد بما ان حاصل ضرب الاول في التاني يساوي + +415 +00:43:44,830 --> 00:43:50,170 +سالب واحد هذا بده يعطيناانه تمانية في M اتنين + +416 +00:43:50,170 --> 00:43:57,310 +يساوي سالب واحد يبقى M اتنين يساوي سالب تمان يبقى + +417 +00:43:57,310 --> 00:44:08,130 +هذا الاسلوب of the perpendicular line + +418 +00:44:08,130 --> 00:44:15,730 +to the tangentيبقى هذا ميل العمودي على مين؟ على + +419 +00:44:15,730 --> 00:44:20,270 +الممسك النقطة المعروفة والميل معروف إذا بقدر أجيب + +420 +00:44:20,270 --> 00:44:31,970 +معادلة العمودي يبقى هنا from the equation Y ساوي M + +421 +00:44:31,970 --> 00:44:41,070 +في X ناقص X node زائد Y node the equation + +422 +00:44:43,010 --> 00:44:51,390 +of the perpendicular line + +423 +00:44:51,390 --> 00:45:01,550 +is y تساوي الميل له قداش سالب تمان في ال X ناقص + +424 +00:45:01,550 --> 00:45:06,650 +اتنين زائد واحدهذه المعادلة انتهينا منها لكن بدي + +425 +00:45:06,650 --> 00:45:12,770 +اعيد ترتيبها فبقول لو ضربنا كله في تمانية بصير + +426 +00:45:12,770 --> 00:45:23,120 +تمانية Y يسوى ناقص X زائد اتنين زائد تمانيةدربنا + +427 +00:45:23,120 --> 00:45:29,220 +كله في من؟ في تمانية او صار معادلة العمودي هي + +428 +00:45:29,220 --> 00:45:36,520 +تمانية Y يسوى ناقص X زائد عشرة هذه هي المعادلة + +429 +00:45:36,520 --> 00:45:43,540 +المطلوبة ويتالى خلصنا الجزء الاول من المثلة بداخل + +430 +00:45:43,540 --> 00:45:48,950 +الجزء التانيالجزء التاني قال لي هاتلي معادلة + +431 +00:45:48,950 --> 00:45:54,470 +المماثات كل المماثات اللي مالها يساوي كده؟ يساوي + +432 +00:45:54,470 --> 00:45:58,410 +تمانية، مدام المال يساوي تمانية، إذا بدي أجيب + +433 +00:45:58,410 --> 00:46:03,390 +النقاط اللي المال عندها يساوي كده؟ يساوي تمانية، + +434 +00:46:03,390 --> 00:46:08,910 +لما نجيب للنقاط والمال معروف، بصير سهل يجيب معادلة + +435 +00:46:08,910 --> 00:46:15,250 +هذه المماثات، فبعدين بقوله ما يأتي، بدنا نحاولنجيب + +436 +00:46:15,250 --> 00:46:23,170 +احداث النقاط هذه الان الاسلوب اللى هو بده يساوي ال + +437 +00:46:23,170 --> 00:46:31,090 +dy على dx اللى هو مين اللى هو تلاتة x تربية ناقص + +438 +00:46:31,090 --> 00:46:37,250 +اربعة يساوي كده؟ يساوي تمانية طبعا x هذه عند اى + +439 +00:46:37,250 --> 00:46:45,120 +نقطةIn general هذه المعادلة هتعطيني تلاتة X تربيع + +440 +00:46:45,120 --> 00:46:53,580 +يساوي كده؟ 12 يبقى X تربيع يساوي 4 يبقى ال X بدها + +441 +00:46:53,580 --> 00:46:59,000 +ساوي زائد او ناقص 2 يبقى عندي كام نقطة بصير + +442 +00:46:59,000 --> 00:47:07,690 +للتماث؟ نقطة 2 يبقى النقطة الأولى F X يساوي 2ثم + +443 +00:47:07,690 --> 00:47:11,210 +لماذا تساوي واحدة اظن؟ + +444 +00:47:21,800 --> 00:47:29,920 +فالـ X يسوى سالب اتنين ثم الـ Y يسوى سالب اتنين + +445 +00:47:29,920 --> 00:47:37,240 +الكل تكيب سالب اربعة في سالب اتنين زائد واحد و + +446 +00:47:37,240 --> 00:47:43,620 +يسوى كمان جداش واحد يبقى أصبح عندي نقطتين للتماث + +447 +00:47:43,620 --> 00:47:49,500 +The points of tangency + +448 +00:47:51,320 --> 00:48:00,620 +النقاط التماس هي 2 و 1 and سلبي 2 و 1 يبقى كم مقسم + +449 +00:48:00,620 --> 00:48:12,320 +دي؟ 2 يبقى بقى دي بقوله the first tangent is y سوى + +450 +00:48:12,320 --> 00:48:19,320 +الميل قداش؟بنعطيها تمانية يبقى اي تمانية في X ناقص + +451 +00:48:19,320 --> 00:48:27,800 +اتنين زائد الواحد او ال Y تساوي تمانية X ناقص + +452 +00:48:27,800 --> 00:48:35,980 +ستاشر زائد واحد يبقى ال Y يساوي تمانية X ناقص + +453 +00:48:35,980 --> 00:48:42,190 +خمستاشرهذا المماس الأول نجيب المماس الثاني the + +454 +00:48:42,190 --> 00:48:52,330 +second tangent المماس الثاني و أيه سوى نفسي المية + +455 +00:48:52,330 --> 00:49:00,610 +اللي هو قدراش تمانية يبقى أيه تمانية فكس ناقص ناقص + +456 +00:49:00,610 --> 00:49:09,140 +اتنين زائد واحدأو ان شئتم فقولوا Y تساوي تمانية X + +457 +00:49:09,140 --> 00:49:14,360 +طبعا نقص نقص اتنين بزايد اتنين في تمانية بستاشر + +458 +00:49:14,360 --> 00:49:25,500 +زايد واحد او Y يساوي تمانية X زايد سبعتاشر تمام؟ + +459 +00:49:25,500 --> 00:49:31,180 +طب ده اسألكوا سؤال هل الممثلين هدول متوازين؟ + +460 +00:49:35,370 --> 00:49:40,530 +متوازين؟ مش عارفين الشباب؟ ما هي ما اعطيك نفس + +461 +00:49:40,530 --> 00:49:43,750 +الميلي اللي هو تمانية وما هي المعامل تبع ال X هو + +462 +00:49:43,750 --> 00:49:47,070 +الميلي ويساوي تمانية إذا مادام نفس الميلي يبقى + +463 +00:49:47,070 --> 00:49:51,370 +الممثلين متوازين وعطيتكوا مثال قبل ذلك وطلعوا + +464 +00:49:51,370 --> 00:49:57,730 +ورسمتوا زيادة وقلت لكوا وبينتوا كل ممثل متوازينهو + +465 +00:49:57,730 --> 00:50:03,710 +الـ X نفسه، 2,3,1 هنا والله فوق، فوق، فوق، فوق، + +466 +00:50:03,710 --> 00:50:07,750 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +467 +00:50:07,750 --> 00:50:08,350 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +468 +00:50:08,350 --> 00:50:08,370 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +469 +00:50:08,370 --> 00:50:08,430 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +470 +00:50:08,430 --> 00:50:14,750 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +471 +00:50:14,750 --> 00:50:15,470 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +472 +00:50:15,470 --> 00:50:19,770 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +473 +00:50:23,800 --> 00:50:30,780 +المثال الأخير في هذا ال section بيقول ما يأتي مثال + +474 +00:50:30,780 --> 00:50:38,660 +خمسة find + +475 +00:50:38,660 --> 00:50:45,760 +the values of + +476 +00:50:45,760 --> 00:50:52,020 +a and b if the tangent + +477 +00:50:54,840 --> 00:51:01,200 +the tangent to the curve + +478 +00:51:04,440 --> 00:51:17,200 +للمنحنة y تساوي ax تربية زائد bx has slope برضه + +479 +00:51:17,200 --> 00:51:26,220 +تمانية at the point واحد وخمسة + +480 +00:51:37,050 --> 00:51:43,230 +سؤال مرة ثانية بيقول هاتلي قيمة a و b إذا كان + +481 +00:51:43,230 --> 00:51:49,630 +المماس للمنحنة ميله تمانية عند هذه النقطة أنا عندي + +482 +00:51:49,630 --> 00:51:56,490 +مجهولين ومعطيني الميل وعند النقطة هذه يبقى بدي + +483 +00:51:56,490 --> 00:52:00,910 +أروح أشتق مش هنجيب ال slope يبقى أول خطوة بدي + +484 +00:52:00,910 --> 00:52:10,190 +أقوله y prime يساوي اتنين a x زائد bالان y' عند من + +485 +00:52:10,190 --> 00:52:18,090 +عند x يساوي كم؟ يساوي واحد يساوي كم؟ يساوي تمانية + +486 +00:52:18,090 --> 00:52:23,610 +الاسلوب يساوي تمانية عند النقطة هذه هذا ايش معناه؟ + +487 +00:52:23,610 --> 00:52:28,190 +هذا معناه انك تشيل كل x و تضعه في مكان كم؟ واحد + +488 +00:52:28,190 --> 00:52:35,540 +يبقى اتنين a في واحدزائد بيه يساوي كده؟ تمانية + +489 +00:52:35,540 --> 00:52:43,060 +يبقى صار اتنين ايه؟ زائد بيه يساوي تمانية طيب هذه + +490 +00:52:43,060 --> 00:52:48,060 +معلومة تربط بين المجهولين الاتنين بدنا كمان معلومة + +491 +00:52:48,060 --> 00:52:54,700 +النقطة هذه النقطة في التماس تقع على المماس وتقع + +492 +00:52:54,700 --> 00:53:03,330 +على المنحنة إذا تحقق معادلات المنحنة إذا andأت + +493 +00:53:03,330 --> 00:53:09,910 +اللي هي النقطة واحد وخمسة ويهاب يبقى بده يشيل ال Y + +494 +00:53:09,910 --> 00:53:14,070 +ويحط مكانها خمسة ويشيل X ويحط مكانها واحد يبقى + +495 +00:53:14,070 --> 00:53:22,070 +خمسة بدها تساوي A في واحد تربيه زائد B في واحد هذا + +496 +00:53:22,070 --> 00:53:28,670 +بده يعطيك A زائد B بده يساوي كده؟ بده يساوي خمسة + +497 +00:53:29,560 --> 00:53:35,940 +طيب الان انا عندي معادلتين اتنين a زائد b يساوي + +498 +00:53:35,940 --> 00:53:41,080 +تمانية شو رايك انا بضربها في سالب واحد بصير سالب a + +499 +00:53:41,080 --> 00:53:46,140 +سالب b يساوي سالب خمسة و اجمع يعني بدي احل + +500 +00:53:46,140 --> 00:53:52,460 +المعادلتين الاتنين هدول مع بعض بطلع عندي جداش ال a + +501 +00:53:52,460 --> 00:53:58,730 +يساوي تلاتةأجمع بضل عندي هنا a و بضل عندي هنا + +502 +00:53:58,730 --> 00:54:05,210 +تلاتة طيب لما a تسوى تلاتة بي تسوى خمسة نقص تلاتة + +503 +00:54:05,210 --> 00:54:12,730 +اللي هو الجداش اتنين and ال b يسوى اتنينلاحظ هنا + +504 +00:54:12,730 --> 00:54:16,810 +انتهى هذا ال section اللي هو التلاتة تلاتة وإليك + +505 +00:54:16,810 --> 00:54:20,010 +أرقام المسائل + +506 +00:54:49,570 --> 00:54:55,590 +هي في الزاوية عندك يبقى exercises تلاتة تلاتة + +507 +00:54:55,590 --> 00:55:05,310 +المسائل التالية من واحد لواحد وخمسين الأد و بنضيف + +508 +00:55:05,310 --> 00:55:13,650 +عليها كمان اللي هو من خمسة وخمسين لتمانية وخمسينو + +509 +00:55:13,650 --> 00:55:22,130 +كذلك من واحد و ستين لغاية اربعة و ستين واحد و ستين + +510 +00:55:22,130 --> 00:55:29,810 +لغاية اربعة و ستين والان بنروح ل section تلاتة + +511 +00:55:29,810 --> 00:55:36,250 +اربعة بنقول الله يسهل عليك و بنروح لتلاتة خمسة + +512 +00:55:36,250 --> 00:55:41,230 +اللي هو ال derivatives of + +513 +00:55:52,060 --> 00:56:00,980 +مشتقة الدوال المثلثية اول شي قبل ما نبدأ في مشتقة + +514 +00:56:00,980 --> 00:56:08,100 +الدوال المثلثية نذكر في شغل اخدناها قبل ذلك الشغل + +515 +00:56:08,100 --> 00:56:20,700 +هذهit should be noted that + +516 +00:56:20,700 --> 00:56:29,400 +limit لصين ال X ع ال X لما ال X تروح لزينه يساوي + +517 +00:56:29,400 --> 00:56:35,970 +كده؟ واحد هذه مرت علينا قبل هيكبدي اخد مثال عليها + +518 +00:56:35,970 --> 00:56:43,550 +وبعد هيك نروح لمين لمشتقة الدوال المثلثية بدي ال + +519 +00:56:43,550 --> 00:56:49,990 +limit لما ال X بدها تروح لل zero ل cosine ال X + +520 +00:56:49,990 --> 00:57:02,690 +ناقص واحد على مين على X شوفوا + +521 +00:57:02,690 --> 00:57:09,140 +يا زيديطبعا الطاولة المباشرة بيجيب 0 على 0 لكن انا + +522 +00:57:09,140 --> 00:57:16,780 +بدى اكتب هدى على الشكل التالي شو + +523 +00:57:16,780 --> 00:57:21,320 +رايك اخد سالب عامل مشترك بصير limit لما ال X بده + +524 +00:57:21,320 --> 00:57:27,780 +تروح ل 0 للواحد ناقص cosine X على X سويتش اشي ولا + +525 +00:57:27,780 --> 00:57:31,840 +حاجة حتى الان بده ضرب في مرافق ال bus طبعا كده ضرب + +526 +00:57:31,840 --> 00:57:39,270 +ليشمشان اخلق النظرية هذه مشان اقدر استخدمها يبقى + +527 +00:57:39,270 --> 00:57:44,610 +هذه لو روح ضربت في المرافق واحد زائد cosine ال X + +528 +00:57:44,610 --> 00:57:50,450 +على واحد زائد cosine ال X يبقى هذه بدها تسوي ال + +529 +00:57:50,450 --> 00:57:57,090 +limit لما ال X بدها تروح لوين؟ ل Zero لمن؟ للبسط + +530 +00:57:57,090 --> 00:58:03,860 +فرق بين المربعينواحد ناقص cosine تربية ال X على X + +531 +00:58:03,860 --> 00:58:10,900 +في واحد زائد cosine ال X أو هذا سالب limit لما ال + +532 +00:58:10,900 --> 00:58:15,520 +X بده تروح ل zero واحد ناقص cosine تربية من حساب + +533 +00:58:15,520 --> 00:58:21,800 +المثلثات لو sin تربية ال X على X في واحدزائد + +534 +00:58:21,800 --> 00:58:26,820 +cosine ال X أول متطابقة مثلثية أخدناها في section + +535 +00:58:26,820 --> 00:58:30,820 +واحد تلاتة كان cosine تربيه ال X زائد sine تربيه + +536 +00:58:30,820 --> 00:58:34,960 +ال X يساوي قداش واحد إذا واحد ماقص cosine تربيه ال + +537 +00:58:34,960 --> 00:58:39,920 +X هي sine تربيه ال X إذا هداني خلقت في المثلةصين + +538 +00:58:39,920 --> 00:58:44,520 +ال X على X يبقى هذه الصارت على الشكل التالي هي + +539 +00:58:44,520 --> 00:58:51,020 +السالب وهي limit لما ال X بدها تروح ل 0 لصين X على + +540 +00:58:51,020 --> 00:59:01,060 +X في صين X على 1 زائد Cos Xالان بدأ ادخل ال limit + +541 +00:59:01,060 --> 00:59:07,680 +علي كل منهما يبقى هذا الكلام يساوي سالب limit لما + +542 +00:59:07,680 --> 00:59:13,120 +ال x بدأ تروح لل zero ل sine ال x على x في limit + +543 +00:59:13,120 --> 00:59:18,220 +لما ال x بدأ تروح لل zero ل sine ال x على واحد + +544 +00:59:18,220 --> 00:59:25,750 +زائد cosine ال x ال limit هذا كده؟هي فوق عندي + +545 +00:59:25,750 --> 00:59:33,030 +بواحد صحيح يبقى هاي السالب وهي واحد هذه في قداش + +546 +00:59:33,030 --> 00:59:41,370 +Zero على واحد زائد واحد النتيجة كلها قداش Zero كده + +547 +00:59:41,370 --> 00:59:47,080 +من الأن فصاعدا limit هذه كلها بتساوي قداش Zeroطب + +548 +00:59:47,080 --> 00:59:51,940 +شو دخل هذا في ال trigonometric؟ اه هذه الأزمالي و + +549 +00:59:51,940 --> 00:59:58,200 +هذه الأزمالي الآن في البرهان في إثبات مشتقة الدوال + +550 +00:59:58,200 --> 01:00:05,020 +المثلثية إذا بدنا نيجي نستخدم التنتين هدول في + +551 +01:00:05,020 --> 01:00:11,560 +إيجاد مشتقة الدوال المثلثية المختلفة + +552 +01:00:13,140 --> 01:00:17,560 +بدنا نجي لأول مشتقة من هذه المشتقات + +553 +01:00:23,580 --> 01:00:30,280 +الـ F prime of X يسوي كده؟ Cos X يعني مشتقة الجيب + +554 +01:00:30,280 --> 01:00:37,880 +هو مين؟ جيب التمام بدنا نثبت صحة هذا الكلام بدنا + +555 +01:00:37,880 --> 01:00:44,080 +نرجع للإثبات للتعريف يبقى احنا كان عندنا F prime + +556 +01:00:44,080 --> 01:00:50,750 +of Xيسوي ال limit لما ال H بده تروح لل zero لل F + +557 +01:00:50,750 --> 01:00:56,190 +of X زي ال H ناقص ال F of X كله على H مش هذا كان + +558 +01:00:56,190 --> 01:01:01,320 +التعريف اللي لناالـ F of X هي من؟ صين الـ X إذا + +559 +01:01:01,320 --> 01:01:06,780 +بدي أجي على الصين أشيل كل X و أحط مكانها X زائد H + +560 +01:01:06,780 --> 01:01:12,360 +يبقى الـ F prime of X يساوي ال limit لما الـ H + +561 +01:01:12,360 --> 01:01:17,900 +بدها تروح لـ Zero بدي أجي على الصين أشيل الـ X و + +562 +01:01:17,900 --> 01:01:23,360 +أكتب مكانها X زائد الـ H الـ F of X زي ما هي الصين + +563 +01:01:23,360 --> 01:01:30,590 +X كله على من؟ على Hتعويض المباشر بيجيب لـ 0 على 0 + +564 +01:01:30,590 --> 01:01:36,550 +لإن الـ sine is 0 بـ 0 و ال H بـ 0 بيصير 0 ناقص 0 + +565 +01:01:36,550 --> 01:01:40,550 +على 0 و ما شاء الله عليها كمية غير معينة يبقى + +566 +01:01:40,550 --> 01:01:46,310 +استخدم صلاحياتك و اشتغل الشغل اللي بدكيه H بدأ + +567 +01:01:46,310 --> 01:01:51,290 +تروح لـ 0 لو رجعنا بالذكرة إلى الوراق هذا الـ sine + +568 +01:01:51,290 --> 01:01:55,960 +back graphic و الـ sine cosine زاد cosine sineيبقى + +569 +01:01:55,960 --> 01:02:01,460 +هذا بقدر اقول هو عبارة عن sine ال X في cosine ال H + +570 +01:02:01,460 --> 01:02:06,840 +ماله زائد إشارة زائد يبقى بطلها زائد كما هي cosine + +571 +01:02:06,840 --> 01:02:12,760 +ال X في sine ال H هذا مفكوك الأول ناقص sine ال X + +572 +01:02:12,760 --> 01:02:18,840 +كما هو كله مقسوما على مين على H يسوى ال limit لما + +573 +01:02:18,840 --> 01:02:25,040 +ال H tends to zero طلعلي للمقدار الأول والأخيريبقى + +574 +01:02:25,040 --> 01:02:31,600 +بينهم sin x عامل مشترك يبقى هذا sin x عامل مشترك + +575 +01:02:31,600 --> 01:02:42,600 +يبقى cos h ناقص واحد زائد cos x في sin h كله مقصوم + +576 +01:02:42,600 --> 01:02:50,860 +على مين؟ على h بدى اوزع ال limit لترمز + +577 +01:02:51,070 --> 01:02:58,010 +يبقى هذا ال limit لما ال H بده يروح ل 0 لمن؟ ل sin + +578 +01:02:58,010 --> 01:03:06,690 +X cos H ناقص واحد على H زاد limit لما ال H بدها + +579 +01:03:06,690 --> 01:03:16,310 +تروح ل 0 لcos X في sin H كله على H يساويالـ limit + +580 +01:03:16,310 --> 01:03:21,410 +هذه لمين؟ لكل حاجة فيها H أي حاجة فيها H تعتبر + +581 +01:03:21,410 --> 01:03:26,230 +مقدار ثابت بالنسبة لمين لل limit ونهاية المقدار + +582 +01:03:26,230 --> 01:03:30,850 +الثابت بالمقدار الثابت itself السؤال هو sign ال X + +583 +01:03:30,850 --> 01:03:35,710 +هذه إيها علاقة بال limit هنا مافيها Hيبقى هذا + +584 +01:03:35,710 --> 01:03:41,510 +يعتبر مقدار ثابت بقوله شرفنا مرة يبقى هذا sin X + +585 +01:03:41,510 --> 01:03:48,090 +باقية limit لما ال H بده تروح ل zero لcos H ناقص + +586 +01:03:48,090 --> 01:03:55,450 +واحد على H زاد هذه بنفس الطريقة cos X برة limit + +587 +01:03:55,450 --> 01:04:02,840 +لما ال H بده تروح ل zero لsin H على Hهذا الكلام + +588 +01:04:02,840 --> 01:04:12,580 +يساوي صين ال X في هذا ال limit هيكداش؟ Zero يبقى + +589 +01:04:12,580 --> 01:04:19,400 +هذه Zero الله يسهل عليها Z Cos X وهذه بقداش؟ يبقى + +590 +01:04:19,400 --> 01:04:27,460 +النتيجة تساوي Cos X إذا من الأن فصاعدا مشتقة Sin X + +591 +01:04:27,460 --> 01:04:36,040 +هي بقداش؟ بCos X كيف؟ مين اللي بيحكي سامعني؟ + +592 +01:04:36,040 --> 01:04:45,590 +سامعني إيش بتقول؟كل حاجة بأثبتها قدامك مطلوبة اللي + +593 +01:04:45,590 --> 01:04:50,010 +بأثبتهاش مسامحينك فيها وإذا بدك تسير من .. أنا مش + +594 +01:04:50,010 --> 01:04:53,770 +مسامحك وإذا بدك تسير من أهل العلم حتى اللي + +595 +01:04:53,770 --> 01:05:01,410 +بأثبتهاش بتروح تثبتها طيب نمره اتنين F ال F of X + +596 +01:05:01,410 --> 01:05:10,180 +يساوي cosine ال X thenالـ F prime of X بسالب صين + +597 +01:05:10,180 --> 01:05:16,280 +الـ X يالا يا محمد العشي والكلام للسامعين لبروف + +598 +01:05:16,280 --> 01:05:23,480 +بدنا ال F prime of X يبقى ال limit لما ال H بدها + +599 +01:05:23,480 --> 01:05:33,160 +تروح ل zero لمين؟ لcos X زائد H ناقص cos X كله على + +600 +01:05:33,160 --> 01:05:39,740 +Hمش هيك التعريف؟ اه يطبق ده مباشرة يبقى هذا الكلام + +601 +01:05:39,740 --> 01:05:45,960 +بده يسوي ال limit لما ال H بدها تروح ل zero تمام؟ + +602 +01:05:45,960 --> 01:05:50,680 +بده افك ال cosine، cosine، cosine سالب، sine، sine + +603 +01:05:50,680 --> 01:05:58,760 +يبقى cosine ال X cosine ال H ناقص sine ال X في + +604 +01:05:58,760 --> 01:06:08,270 +sineالـ H ناقص Cos X كل هذا على H يساوي Limit لما + +605 +01:06:08,270 --> 01:06:14,030 +الـ H بدها تروح لـ Zero برضه ال term الأول والأخير + +606 +01:06:14,030 --> 01:06:21,010 +بده ياخد Cos X عام المشترك يبقى Cos X عام المشترك + +607 +01:06:21,010 --> 01:06:29,260 +وضل Cos H ناقص واحدعلى H ناقص limit لما الـH بده + +608 +01:06:29,260 --> 01:06:38,600 +تروح لـ0 لمين؟ لـsin X في sin H على H مرة ثانية + +609 +01:06:38,600 --> 01:06:44,270 +هذا القصيد مالهوش دعوة بطله برايبقى هذا cosine ال + +610 +01:06:44,270 --> 01:06:50,010 +X في limit لما ال H بده تروح لل zero ل cosine ال H + +611 +01:06:50,010 --> 01:06:55,790 +ناقص واحد على H ناقص sine ال X برا في limit لما ال + +612 +01:06:55,790 --> 01:07:01,530 +H بده تروح لل zero ل sine ال H على Hيبقى هذا + +613 +01:07:01,530 --> 01:07:10,710 +cosine X وهذا كم؟ بزرع ناقص sine X وهذا كم؟ بواحد + +614 +01:07:10,710 --> 01:07:17,370 +يبقى النتيجة ناقص sine X يبقى من الأنفا صاعدا + +615 +01:07:17,370 --> 01:07:24,870 +مشتقة ال cosine بسالب sineلحد هنا الاشتقاق من خلال + +616 +01:07:24,870 --> 01:07:28,770 +التعريف الله يعطيك العافية مكفي بدنا نشتق بطريقة + +617 +01:07:28,770 --> 01:07:36,690 +أخرى يبقى بدنا نيجي لنمرة تلاتة بدنا D على DX لتان + +618 +01:07:36,690 --> 01:07:46,480 +ال X يبقى باجي بقوله D على DX ليه؟الان بقدر اكتبها + +619 +01:07:46,480 --> 01:07:51,980 +بدلالة الـSin والـCos وبالتالي بقدر استخدم نتيجتي + +620 +01:07:51,980 --> 01:07:58,500 +ال derivative اللي عندنا يبقى هذا الـSin X على Cos + +621 +01:07:58,500 --> 01:08:05,370 +X الان هذه مشتقة خارج قسم الدالتينيبقى هذا الكلام + +622 +01:08:05,370 --> 01:08:14,850 +يساوي المقام في مشتقة البصد ناقص البصد اللي هو sin + +623 +01:08:14,850 --> 01:08:23,010 +X في مشتقة المقام ال cosine بسالب sin X كله على + +624 +01:08:23,010 --> 01:08:31,780 +مربع المقام الأصليالنتيجة تساوي cosine تربيع ناقص + +625 +01:08:31,780 --> 01:08:38,800 +فناقص بزايد sin تربيع ال X كله على cosine تربيع ال + +626 +01:08:38,800 --> 01:08:43,720 +X cosine تربيع ال X زايد sin تربيع ال X من أول + +627 +01:08:43,720 --> 01:08:50,060 +متطابقة الجديد بواحد صحيح يبقى النتيجة واحد على + +628 +01:08:50,060 --> 01:08:56,410 +cosine تربيع ال X ال cosine مقلوب منسك يبقى هذا + +629 +01:08:56,410 --> 01:09:01,510 +الكلام بدي يساوي سك تربيه على ال X يبقى من الألف + +630 +01:09:01,510 --> 01:09:09,090 +صاعدا مشتقة التاني بقداشاذا good exercise لك اللي + +631 +01:09:09,090 --> 01:09:16,750 +هو نمرة أربعة exercise لك بدك تثبتلي ان دي على DX + +632 +01:09:16,750 --> 01:09:26,530 +لمين لكتان ال X اللي دي على DX لكسين ال X على سين + +633 +01:09:26,530 --> 01:09:34,200 +ال X يسوى سالب كسيكن تربيع ال Xبنفس الطريقة هيك + +634 +01:09:34,200 --> 01:09:37,660 +عملتلك المقام في وشطقة ال bus نقص ال bus في وشطقة + +635 +01:09:37,660 --> 01:09:43,060 +المقام على مربع المقام الأصلي وعطيتك النتيجة بنجي + +636 +01:09:43,060 --> 01:09:52,980 +لخمسة بدنا d على dx لمن لسك ال x يبقى d على dx + +637 +01:09:52,980 --> 01:10:01,520 +السكة مر عن مين واحد على cosineقبل شوية قلنا مشتقة + +638 +01:10:01,520 --> 01:10:09,060 +واحد على V سالب واحد على V تربية في DV على DX يبقى + +639 +01:10:09,060 --> 01:10:15,900 +سالب واحد على cosine تربية ال X في مشتقة ال cosine + +640 +01:10:15,900 --> 01:10:24,870 +سالب sin Xإذن النتيجة تساوي سالب في سالب بموجب sin + +641 +01:10:24,870 --> 01:10:30,810 +X على cos تربيع X اللي بقدر اكتبها على الشكل + +642 +01:10:30,810 --> 01:10:39,210 +التالي واحد على cosine X في sin X على cosine X + +643 +01:10:39,210 --> 01:10:46,410 +واحد على cosineبسك الاكس صين عكو صين تاني الاكس + +644 +01:10:52,310 --> 01:11:00,210 +بسك ال X في تان ال X، آخر حاجة، good exercise لك، + +645 +01:11:00,210 --> 01:11:09,970 +لكن ايه؟ D على DX لا cosecant X، يعني D على DX ال + +646 +01:11:09,970 --> 01:11:18,000 +cosecant الواحد على صين Xيبقى السالب كثيقة ال X + +647 +01:11:18,000 --> 01:11:25,300 +كتان ال X يبقى أصبح مباركة لك كل مشتقة الدوال + +648 +01:11:25,300 --> 01:11:32,920 +المثلثية الستة إذا نحن ناخد بعض الأمثلة على هذه + +649 +01:11:32,920 --> 01:11:37,700 +الدوال المثلثية الستة + +650 +01:11:52,770 --> 01:11:59,790 +أول مثال بيقول ما يأتي example + +651 +01:11:59,790 --> 01:12:06,730 +one find + +652 +01:12:06,730 --> 01:12:19,990 +y prime for eachof the following ان المشتق لكل مما + +653 +01:12:19,990 --> 01:12:33,730 +يأتي نمرة واحد Y تساوي X في cos X ناقص X تربيع في + +654 +01:12:33,730 --> 01:12:43,960 +sin X فتح معايا كويس يبقى solutionبالنواية prime + +655 +01:12:43,960 --> 01:12:51,580 +يساوي هذه تعتبر حاصل ضرب دالتين يبقى الدالة الأولى + +656 +01:12:51,580 --> 01:12:57,280 +في مشتقة الدالة الثانية ففضل cosine بسلب sin X + +657 +01:12:57,280 --> 01:13:04,660 +زائد الدالة الثانية في مشتقة الأولى لواحد صحيح + +658 +01:13:04,660 --> 01:13:11,180 +خلصنا منها ناقص دالة الأولى في مشتقة الدالة + +659 +01:13:11,180 --> 01:13:19,040 +الثانيةهيناقص للكل زائد الدالة الثانية في مشتقة + +660 +01:13:19,040 --> 01:13:26,780 +الدالة الأولى اللى هى اتنين X بهذا الشكلنعيد + +661 +01:13:26,780 --> 01:13:37,600 +ترتيبها y' يسوى ناقص x في sin x زائد cos x ناقص x + +662 +01:13:37,600 --> 01:13:45,120 +تربيع في cos x ناقص 2x في sin x + +663 +01:13:48,290 --> 01:13:55,850 +وهذا نفس الشيء يبقى سالب تلاتة x في sin x زائد + +664 +01:13:55,850 --> 01:14:02,590 +cosine x ناقص x تربيع في cosine x + +665 +01:14:05,570 --> 01:14:14,990 +النقطة الثانية y تساوي cosine تربيع x على 2 ناقص + +666 +01:14:14,990 --> 01:14:24,850 +sin تربيع x على 2 طلع + +667 +01:14:24,850 --> 01:14:30,550 +عليه كويس احنا طوأ خدنا مشتقة الدول المثلثية الستة + +668 +01:14:30,550 --> 01:14:36,100 +لكن مااخدناش مشتقات مربعاتهافحصيح ولا لا؟ لكن لو + +669 +01:14:36,100 --> 01:14:43,240 +رجعنا بالذاكرة إلى الوراء بقينا نقول cosine 2x + +670 +01:14:43,240 --> 01:14:49,380 +يساوي cosine تربيع ال X ناقص sine تربيع ال X زو + +671 +01:14:49,380 --> 01:14:54,320 +اللي جوا نص اللي برا يبقى بناء عليه cosine ال X + +672 +01:14:54,320 --> 01:15:00,160 +ايش تساوي؟ cosine تربيع X على 2 ناقص sine تربيع X + +673 +01:15:00,160 --> 01:15:09,480 +على 2 هي هذه؟يبقى أصل المسألة Y يساوي من Cos X + +674 +01:15:09,480 --> 01:15:16,920 +خلاص يبقى فرطة يبقى بناء على Y' يساوي سالب Sin X + +675 +01:15:16,920 --> 01:15:21,580 +هذه ممكن اشتقها ان شاء الله بعد ما ناخد Chain Rule + +676 +01:15:21,580 --> 01:15:26,340 +ال section الجاي ونروحها نشتقها بدون ما نعمل الشغل + +677 +01:15:26,340 --> 01:15:37,630 +هذه على أي حال تلاتة Y تساويY تساوي X في صين X في + +678 +01:15:37,630 --> 01:15:49,570 +تاني X يبقى هذا مشتقة ايش؟ حاصل ضرب ثلاث دول قبل + +679 +01:15:49,570 --> 01:15:54,890 +شوية أخدنا مشتقة حاصل ضرب ثلاثة أقوات، متذكر؟ طيب + +680 +01:15:54,890 --> 01:15:57,630 +يالا نشوف، يبقى solution + +681 +01:16:00,050 --> 01:16:06,510 +الـ y' يساوي مشتقة الأولى بواحد بضال قداش sin x في + +682 +01:16:06,510 --> 01:16:15,810 +تان ال x زاد ال x مشتقة ال sin ب cos x في تان ال x + +683 +01:16:19,860 --> 01:16:29,360 +زاد اكس في صين ال X مشتقت التان بمين؟ بسكت ربيع ال + +684 +01:16:29,360 --> 01:16:39,590 +X في اختصارات؟ بالمرة؟طيب هذه sin X في تان ال X + +685 +01:16:39,590 --> 01:16:49,050 +زاد X أليست هذه هي sin X على cosine X إذا ال + +686 +01:16:49,050 --> 01:16:55,390 +cosine مع ال cosine بتروح بيبقى X في sin X هذه مش + +687 +01:16:55,390 --> 01:17:02,770 +فيها اي اشكالية يبقى X في sin X في سكتة ربيع X + +688 +01:17:05,740 --> 01:17:11,920 +هذا النقطة من نقطة التالتة النقطة الرابعة النقطة + +689 +01:17:11,920 --> 01:17:18,800 +الرابعة بيقول لي Y تساوي واحد زائد تان ال X على + +690 +01:17:18,800 --> 01:17:26,200 +واحد ناقص تان ال X بدنا نشتقها طبعا واضح هذه + +691 +01:17:26,200 --> 01:17:35,540 +مشتقتاش خارج قسم الدالتينيبقى باجي بقوله Y' يساوي + +692 +01:17:35,540 --> 01:17:43,240 +المقام في مين؟فى مشتقة البصر الواحد بـ0 والتان + +693 +01:17:43,240 --> 01:17:50,620 +بـsec تربيه ال X ناقص البصر واحد زائد تان ال X فى + +694 +01:17:50,620 --> 01:17:58,280 +مشتقة المقام سالب sec تربيه ال X كله على مربع + +695 +01:17:58,280 --> 01:18:04,820 +المقام الأصلي واحد ناقص تان X لكل تربيه + +696 +01:18:09,050 --> 01:18:15,150 +هذا الكلام يساوي نفك الأقواع السادى يبقى sector P + +697 +01:18:15,150 --> 01:18:21,310 +على X ناقص تاني X في sector P على X + +698 +01:18:24,290 --> 01:18:34,310 +نقص فنقص بزائد يبقى زائد سك تربيع ال X زائد تان ال + +699 +01:18:34,310 --> 01:18:42,190 +X في سك تربيع ال X كله مقسوما واحد ناقص تان ال X + +700 +01:18:42,190 --> 01:18:49,050 +لكل تربيعأظن هذا موجب وهذا سلب مع السلامة يبقى + +701 +01:18:49,050 --> 01:18:59,290 +النتيجة صارت Y' يسوى 2×6 تربية X واحد ناقص تان X + +702 +01:18:59,290 --> 01:19:13,710 +لكل تربية نقطة الخامسة Y تساوي تان X ناقص Xبنجيب y + +703 +01:19:13,710 --> 01:19:20,550 +prime يبقى y prime يصيب تفاضل ال 10 ب 6 تربيه ال x + +704 +01:19:20,550 --> 01:19:27,750 +و بتفاضل ال x طيب 6 تربيه اناقص 1 بقداش 10 تربيه + +705 +01:19:27,750 --> 01:19:39,390 +ال x النقطة السادسة y تسوى sign + +706 +01:19:39,390 --> 01:19:51,340 +ال xعلى واحد زائد cosine ال X طبعا خارج قسم + +707 +01:19:51,340 --> 01:20:00,660 +الدالتين يبقى ال Y' يساوي المقام في مشتقة البسط + +708 +01:20:00,660 --> 01:20:08,520 +ناقص البسطفى مشتقة المقام مشتقة الواحد Zero مشتقة + +709 +01:20:08,520 --> 01:20:15,260 +ال cosine سالب sine يبقى سالب sine ال X كله على + +710 +01:20:15,260 --> 01:20:22,220 +مربع المقام الأصلي واحد زاد cosine X لكل تربيع بدا + +711 +01:20:22,220 --> 01:20:28,980 +فك القوة السادة يبقى cosine Xزائد cosine تربية ال + +712 +01:20:28,980 --> 01:20:36,320 +X ناقص في ناقص يبقى زائد sine تربية ال X كله على + +713 +01:20:36,320 --> 01:20:44,760 +واحد زائد cosine X الكل تربية ويساوي cosine X زائد + +714 +01:20:46,250 --> 01:20:50,130 +طلّالي cosine تربيه زي cosine تربيه هذه كلها كمدهش + +715 +01:20:50,130 --> 01:20:57,290 +يبقى زائد واحد زائد cosine X لكل تربيه عظيم البسط + +716 +01:20:57,290 --> 01:21:01,710 +هو المقدار بين القوسين يبقى هذا الكلام دي ساعة + +717 +01:21:01,710 --> 01:21:07,150 +واحد على واحد زائد cosine X + +718 +01:21:23,670 --> 01:21:37,130 +طب المثال الثاني then find yw prime for each of + +719 +01:21:37,130 --> 01:21:43,910 +the following نمر + +720 +01:21:43,910 --> 01:21:52,730 +أيه؟ y تساوي x تربيع في صين ال xالأمثلة السابقة + +721 +01:21:52,730 --> 01:21:55,770 +كان كله بدنا المشتقة الأولى هنا بدنا المشتقة + +722 +01:21:55,770 --> 01:22:02,590 +الثانية يبقى solution مشان يجيب المشتقة ثانية لازم + +723 +01:22:02,590 --> 01:22:08,490 +يجيب المشتقة يبقى y prime يساوي حاصل ضرب داليتين + +724 +01:22:08,490 --> 01:22:16,970 +يبقى x تربيه في cosine ال x زائداللي هو اتنين اكس + +725 +01:22:16,970 --> 01:22:23,390 +ثمين في صين ال X بدنا نجيب المشتقة الثانية حاصل + +726 +01:22:23,390 --> 01:22:29,130 +ضرب دالتين و كذلك حاصل ضرب دالتين يبقى الدالة + +727 +01:22:29,130 --> 01:22:36,870 +الأولى في مشتقة الدالة الثانية زائد الدالة الثانية + +728 +01:22:36,870 --> 01:22:46,190 +في مشتقة الدالة الأولى الterm التاني زائد2x في + +729 +01:22:46,190 --> 01:22:52,730 +cosine ال X الأولى في مشتقة التانية زائد التانية + +730 +01:22:52,730 --> 01:22:58,330 +في مشتقة الأولى هي التانية و مشتقة الأولى اللي هي + +731 +01:22:58,330 --> 01:23:05,130 +باتنين يبقى آلة المثلة السالب x تربيع في sine ال X + +732 +01:23:05,130 --> 01:23:13,950 +زائد 2x في cosine ال X و 2x بيصير كده؟ أربعةx cos + +733 +01:23:13,950 --> 01:23:22,790 +x زيدي اتنين sin x مافيش غيرها طيب نمر بإيه؟ y + +734 +01:23:22,790 --> 01:23:35,170 +تساوم كسيكنت ال x لنقش اكتر من هيك كافي طيب + +735 +01:23:35,170 --> 01:23:44,860 +يبقى y prime سالب كسيكنت ال x كتان ال xبنواي + +736 +01:23:44,860 --> 01:23:51,080 +double prime سالب مانوش دعوة، خلّيه برا هذا حاصل + +737 +01:23:51,080 --> 01:24:02,960 +ضرب دلتين، يبقى cosecant لكس تفاضل كتان سالب + +738 +01:24:02,960 --> 01:24:09,860 +cosecant تربيع قبل قليل، يبقى سالب cosecant تربيع + +739 +01:24:09,860 --> 01:24:15,500 +لكسالدول المثلثية دير بالك مشتقتهم مثل ملح الطعام + +740 +01:24:15,500 --> 01:24:21,240 +لا يستغنى عنهم بدك تعرف مشتقت الدول الستة مثل اسمك + +741 +01:24:21,240 --> 01:24:25,320 +ال sine بي cosine ال cosine بي سالب sine ال tan بي + +742 +01:24:25,320 --> 01:24:29,040 +سيك تربيع ال cotan بي سالب cosecant تربيع ال sec + +743 +01:24:29,040 --> 01:24:32,780 +بي sec tan و ال cosecant بي سالب cosecant cotan زي + +744 +01:24:32,780 --> 01:24:36,860 +اسمك تكون عارفهطيب يبقى الدالة الأولى في مشتقة + +745 +01:24:36,860 --> 01:24:43,560 +الدالة الثانية زائد الدالة الثانية في مشتقة ال + +746 +01:24:43,560 --> 01:24:50,720 +cosecant له سالب cosecant ال X كتان ال X وهيقفلنا + +747 +01:24:50,720 --> 01:24:56,350 +القوسالان بداخل الاشارة جوا يبقى ناقص فناقص بزايد + +748 +01:24:56,350 --> 01:25:02,510 +كثيكان تكيب ال X هذا الترم الأول الترم التاني ناقص + +749 +01:25:02,510 --> 01:25:10,530 +فناقص كذلك بزايد اللي هو كثيكان تل X كتان تربيع ال + +750 +01:25:10,530 --> 01:25:14,390 +X بقى + +751 +01:25:14,390 --> 01:25:21,180 +الاخر مثالأه طبعا ضيعت هو العشر دقائق ما بين + +752 +01:25:21,180 --> 01:25:26,920 +الأسلسل عطلان لما بجدرة جادرة وصلنا هنا يبقى + +753 +01:25:26,920 --> 01:25:32,280 +example تلاتة أخر + +754 +01:25:32,280 --> 01:25:33,040 +مثال + +755 +01:25:46,910 --> 01:25:54,930 +أول نقطة بدنا limit لما ال X بده تروح لل zero لمن؟ + +756 +01:25:54,930 --> 01:26:04,870 +لل sign if تحجز يبقى باي زائد تان ال X على من؟ على + +757 +01:26:04,870 --> 01:26:10,090 +تان ال X نقص اتنين في سك ال X + +758 +01:26:13,200 --> 01:26:17,460 +اللي بسيطة اللي متهادي سهلة، اللي متهادي معاها + +759 +01:26:17,460 --> 01:26:22,380 +صلاحيات، سيب النسبة المثلثية بتدخل وين؟ على + +760 +01:26:22,380 --> 01:26:27,850 +الزاوية، اللي بين قسين تعتبر زاوية لمين؟للـ sign + +761 +01:26:27,850 --> 01:26:33,510 +يبقى هذه بدها تساوي الـ sign افتح قرص يبقى ال + +762 +01:26:33,510 --> 01:26:38,030 +limit ندخل داخل ال sign على مين؟ على الزاوية يبقى + +763 +01:26:38,030 --> 01:26:43,110 +ال sign وهي limit دخلناها على مين؟ على الزاوية هذا + +764 +01:26:43,110 --> 01:26:49,760 +الكلام بده يساوي هاي ال signالان limit ال bus على + +765 +01:26:49,760 --> 01:26:54,380 +limit المقام limit المقدار الثابت بالمقدار الثابت + +766 +01:26:54,380 --> 01:27:01,860 +itself ten zero ب zero يبقى زائد zero على ten zero + +767 +01:27:01,860 --> 01:27:08,260 +ب zero ناقص اتنين six zero يبقى داشر بواحد يبقى + +768 +01:27:08,260 --> 01:27:14,280 +صارت المسألة sign لسالب pi على اتنين ال sign اد + +769 +01:27:14,280 --> 01:27:19,590 +والله evenيبقى سالب برا باي على اتنين ساي باي على + +770 +01:27:19,590 --> 01:27:26,850 +اتنين يبقى داشر بواحد يبقى سالب واحد هذا نمره نقطة + +771 +01:27:26,850 --> 01:27:33,350 +الأولى النقطة الثانية بدنا ال limit لما ال X بدها + +772 +01:27:33,350 --> 01:27:45,970 +تروح لل zero ل cosine باي X على صين ال Xبرضه بنفس + +773 +01:27:45,970 --> 01:27:52,010 +الطريقة cosine ال cosine و ال limit تدخل جوا على + +774 +01:27:52,010 --> 01:27:59,550 +الزاوية لما ال x بدي روح لل zero لل by x على sine + +775 +01:27:59,550 --> 01:28:05,570 +ال x و هي الساوية ال cosine ال by هذا مقدار ثابت + +776 +01:28:06,010 --> 01:28:11,390 +يبقى بقدر أطلعه برا ال limit وهذا ال limit لما ال + +777 +01:28:11,390 --> 01:28:17,510 +X بده تروح لل zero لل X على ال sign ال X هذا ال + +778 +01:28:17,510 --> 01:28:22,030 +limit كله بقداش يبقى هذا ال limit اللي في الداخل + +779 +01:28:22,030 --> 01:28:29,390 +كله بحصار cosine باي cosine 180 بقداش نفس الإجابة + +780 +01:28:29,390 --> 01:28:35,270 +اللي فوق للسؤال الأول النقطة الأخيرةالثالثة + +781 +01:28:35,270 --> 01:28:41,530 +والاخيرة بدنا limit لما theta بدها تروح لل πاية + +782 +01:28:41,530 --> 01:28:50,010 +على أربعة لتان theta ناقص واحد على ثيتا ناقص باية + +783 +01:28:50,010 --> 01:28:56,670 +على أربعة هذا يعني طيب بنلطف شكلها شوية هيك ونشوف + +784 +01:28:56,670 --> 01:29:02,170 +وين بدها توصل هالدنيا لو جيت قولتلك هذه عبارة عن + +785 +01:29:02,170 --> 01:29:09,200 +limitبقى أضيف سالب باى أربعة للطرفين يبقى بصير + +786 +01:29:09,200 --> 01:29:15,480 +ثيتا سالب باى على أربعة بدا تروح لوين لزيرو لمن + +787 +01:29:15,480 --> 01:29:23,060 +لتان ثيتا ناقص واحد على ثيتا ناقص باى على أربعة + +788 +01:29:23,060 --> 01:29:31,940 +ممكن أشيل الواحد و أحط بدله تان باى على أربعةصح؟ + +789 +01:29:31,940 --> 01:29:34,880 +ضل الخمسة و أربعين و واحد، بقى دي شوف الكلام عندك، + +790 +01:29:34,880 --> 01:29:40,620 +و بعد هيك أجيبها عن طريق اللي هو تان ناقص تان على + +791 +01:29:40,620 --> 01:29:44,960 +واحد مش عارف ايه، هي واحدة، طيب فكرة، فكرة تانية، + +792 +01:29:44,960 --> 01:29:48,380 +واحد قال لي بدي أشيل ت تناقص بيه أربع كلها و أحطها + +793 +01:29:48,380 --> 01:29:52,850 +ال variable الجديد، قول لله ماشيقال يعني في الـ H + +794 +01:29:52,850 --> 01:29:59,530 +مش هيك، حط لي X يساوي ثيتا ناقص Pi على أربعة، + +795 +01:29:59,530 --> 01:30:03,450 +قولنا له ماشي، قال لي يبقى X زائد Pi على أربعة + +796 +01:30:03,450 --> 01:30:07,310 +تساوي ثيتاأنا مش حافظ السبق اتبع التوجيه اللي يقول + +797 +01:30:07,310 --> 01:30:10,310 +هذا التوجيه هو الجواب يسوي مش ماليش علاقة بيها + +798 +01:30:10,310 --> 01:30:13,770 +احنا بنشتغل شغل رياضي مش حافظينه بدنا نطبق على + +799 +01:30:13,770 --> 01:30:17,570 +الحفظ العتيب احنا بنشتغل شغل رياضي سليم كأننا لا + +800 +01:30:17,570 --> 01:30:24,130 +نعرف شيئا عن السبق يبقى هذه بدها تصير ال limit لما + +801 +01:30:24,130 --> 01:30:31,700 +ال X بدها تروح لل zero لتان ثيتا ل Xزائد باي على + +802 +01:30:31,700 --> 01:30:39,600 +أربعة ناقص واحد كله على X يبقى المثال أخدت شكلًا + +803 +01:30:39,600 --> 01:30:44,760 +جديدًا يبقى هذا الكلام بيصير ال limit لما ال X + +804 +01:30:44,760 --> 01:30:50,700 +بدها تروح لل zero التان هذي بقدر أفكها يبقى باجي + +805 +01:30:50,700 --> 01:30:59,180 +بقوله تان ال Xزائد تان باي على أربعة على واحد ناقص + +806 +01:30:59,180 --> 01:31:06,300 +تان ال X تان باي على أربعة وعندي ناقص ولسه كله + +807 +01:31:06,300 --> 01:31:12,200 +مجسوم على X كل الخمسة واربعين بواحد هذا الكلام + +808 +01:31:12,200 --> 01:31:20,890 +يساويLimit لما الـ X بده يروح للـ Zero نجي لتان ال + +809 +01:31:20,890 --> 01:31:27,390 +X زائد واحد وضل الخمسة واربعين بواحد وضل الخمسة + +810 +01:31:27,390 --> 01:31:35,750 +واربعين بواحد على واحد ناقص تان ال X كله ناقص واحد + +811 +01:31:35,750 --> 01:31:42,520 +على Xطب ايش رايك نوحد المقامات للكل؟ فهذا الكلام + +812 +01:31:42,520 --> 01:31:50,220 +بده يساوي limit لما ال X بده يروح ل zero هذا شرط + +813 +01:31:50,220 --> 01:31:57,040 +الكسر و بده نوحد المقامات للكل واحد ناقص تاني ال X + +814 +01:31:57,040 --> 01:32:06,340 +بظل تاني ال X زائد واحد و بعد هيك ناقص واحدزائد + +815 +01:32:06,340 --> 01:32:12,620 +تان ال X وكله مقسوم على مين على X يبقى ال limit + +816 +01:32:12,620 --> 01:32:18,360 +لما ال X بده تروح لل zero ناقص واحد وزائد واحد مع + +817 +01:32:18,360 --> 01:32:25,920 +السلامة يبقى بصيري اتنين تان ال X على X في واحد + +818 +01:32:25,920 --> 01:32:33,810 +ناقص تان ال Xأو ان شئتم فقولوا يتنين خليك برا و + +819 +01:32:33,810 --> 01:32:41,070 +هاي limit لما ال X بده تروح ل zero لتان ال X على X + +820 +01:32:41,070 --> 01:32:49,890 +فمين في واحد على واحد ناقص تان ال X هذه حافظينها + +821 +01:32:49,890 --> 01:32:54,830 +ضمن الثانوية بواحد انا مش حافظها يبقى بده ساوي + +822 +01:32:54,830 --> 01:32:57,010 +تنين limit + +823 +01:33:07,440 --> 01:33:18,240 +Limit لما ال X تروح ل Zero واحد ناقص + +824 +01:33:18,240 --> 01:33:27,470 +تاني X يسوى اتنين وهذه كلها بواحدوهذه كلها بواحد + +825 +01:33:27,470 --> 01:33:34,150 +على cosine صفر بواحد وهذه zero وكمان بواحد يبقى + +826 +01:33:34,150 --> 01:33:40,670 +الجواب قداشر اتنين يبقى exercises تلاتة خمسة + +827 +01:33:40,670 --> 01:33:45,570 +المسائل التالية خلاص + +828 +01:33:45,570 --> 01:33:55,680 +exercises تلاتة خمسةالمسائل من واحد لسبعة و تلاتين + +829 +01:33:55,680 --> 01:34:00,440 +القد + +830 +01:34:00,440 --> 01:34:13,400 +و من تلاتة و اربعين لتلاتة و خمسين القد + +831 +01:34:13,400 --> 01:34:20,800 +طبعا و كذلك من سبعة و خمسين لغاية ستين + +832 +01:34:25,290 --> 01:34:25,970 +خدت واحدة + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OD0ap5i8Mj0_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OD0ap5i8Mj0_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..a8f0879d031f046030726e743457ffb241320f7e --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OD0ap5i8Mj0_raw.srt @@ -0,0 +1,3344 @@ +1 +00:00:21,080 --> 00:00:25,660 +بسم الله الرحمن الرحيم في ال two sections الماضية + +2 +00:00:25,660 --> 00:00:31,620 +كنا بنتحدث فقط عن اللي هو الاشتقاق من خلال التعريف + +3 +00:00:31,620 --> 00:00:35,160 +اليوم بدنا نذكر القواعد الاشتقاق اللي خدتها في + +4 +00:00:35,160 --> 00:00:39,540 +الثانوية العامة زي ما أنت شايف لا يوجد فيها حرف + +5 +00:00:39,540 --> 00:00:44,340 +جديد وإنما توذكر بمدرسة في الثانوية العامة بعد ذلك + +6 +00:00:44,340 --> 00:00:49,940 +سنذهب إلى أمثلة توضيحية على القواعد اللي موجودة + +7 +00:00:49,940 --> 00:00:55,590 +عندنايبقى differentiation rules قواعد الاشتقاق اول + +8 +00:00:55,590 --> 00:01:00,050 +قاعد بتقول لو كانت الدالة دالة ثابتة f of x يساوي + +9 +00:01:00,050 --> 00:01:05,110 +c حيث c constant اذا مشتقة هذه الدالة تساوي قداش؟ + +10 +00:01:05,110 --> 00:01:09,650 +Zero فالمشتقة في الثانوية العامة تعلمنا ان مشتقة + +11 +00:01:09,650 --> 00:01:14,350 +المقدار الثابت تساوي صفر يعني لو كانت f of x يساوي + +12 +00:01:14,350 --> 00:01:19,170 +خمسة اذا ال f prime of x يساوي لو كان f of x يساوي + +13 +00:01:19,170 --> 00:01:19,950 +باي + +14 +00:01:31,360 --> 00:01:35,680 +بالنسبة للنقطة الثانية if n is a non zero real + +15 +00:01:35,680 --> 00:01:42,340 +number then d على dx للx to the power n هو ال n في + +16 +00:01:42,340 --> 00:01:48,470 +x أُس n ناقص واحدطبعا الان اي real number لا يساوي + +17 +00:01:48,470 --> 00:01:52,250 +zero طبعا ليش اشتراطنا لا يساوي zero لأنه لو كان + +18 +00:01:52,250 --> 00:01:56,970 +يساوي zero لأصبح x أوز zero بقداش يعني مقدار ثابت + +19 +00:01:56,970 --> 00:02:01,790 +وقتالي مشتقته تساوي مين تساوي صفر طيب يبقى الان قد + +20 +00:02:01,790 --> 00:02:05,010 +يكون positive قد يكون negative قد يكون rational + +21 +00:02:05,010 --> 00:02:10,010 +غيره إلى آخره يبقى مشتقته على طول خط n x أوز n + +22 +00:02:10,010 --> 00:02:15,660 +ناقص واحدالنقطة الثالثة F في الـ C is constant + +23 +00:02:15,660 --> 00:02:20,120 +يبقى بدنا نجمع الحالتين الاتنين هدول مع بعض يبقى D + +24 +00:02:20,120 --> 00:02:25,600 +على DX ل C في F of X C المقدار الثابت بقوله خليك + +25 +00:02:25,600 --> 00:02:30,700 +على شجة و بروح بشتق مين بشتقت ده ل F of X زي ما + +26 +00:02:30,700 --> 00:02:35,940 +كنت بتقوله مشتقت تلاتة إكسوس خمسة في الثانوية بقول + +27 +00:02:35,940 --> 00:02:41,340 +تلاتة سبيكة و مشتقت إكسوس خمسةخمسة X أُص أربعة + +28 +00:02:41,340 --> 00:02:46,100 +وبالتالي بيصير خمستاشر X أُص أربعة يبقى الـC بيظل + +29 +00:02:46,100 --> 00:02:50,840 +كأنه مالوش دعوة تماما بالق بالـderivativeالان for + +30 +00:02:50,840 --> 00:02:54,920 +example ال D على DX ل C X to the power N بقول ال C + +31 +00:02:54,920 --> 00:02:58,600 +مقدرتها بتخليك زي ما انت و ال X أس N من النقطة + +32 +00:02:58,600 --> 00:03:04,060 +الثانية مشتقتها N X أس N ناقص واحد النقطة الرابعة + +33 +00:03:04,060 --> 00:03:07,760 +F ال U و ال V are differentiable functions of X + +34 +00:03:07,760 --> 00:03:12,700 +يبقى then D على DX ل U زاد أو ناقص V تساوي مشتقة + +35 +00:03:12,700 --> 00:03:16,560 +ال U زاد أو ناقص مشتقة ال V بجيتها بتقول في + +36 +00:03:16,560 --> 00:03:22,240 +الثانوية العامةمشتقة المجموع الجبري لدالتين يساوي + +37 +00:03:22,240 --> 00:03:25,600 +المجموع الجبري لمشتقتيهما + +38 +00:03:33,500 --> 00:03:38,280 +مجموعة الاتير ممكن تكون تلت دوال اربع دوال ان من + +39 +00:03:38,280 --> 00:03:42,640 +الدوال يبقى المشتقة هتدخل على كل دالة من هذه + +40 +00:03:42,640 --> 00:03:48,840 +الدوال يبقى D على DX U1 زي دو ناقص U2 زي دو ناقص + +41 +00:03:48,840 --> 00:03:56,680 +U3 زي دو ناقص UN يبقى DU1 على DX زي دو ناقص DU2زاد + +42 +00:03:56,680 --> 00:04:00,820 +او نقص دي و تلاتة على دي اكس زاد او نقص نظل ماشي + +43 +00:04:00,820 --> 00:04:06,680 +لغاية ما نوصل لمشتقة ال U ان بنسبة ال X الان + +44 +00:04:06,680 --> 00:04:11,920 +بننتقل لحاصل الضرب والقسمة فباجي بقول if U and V + +45 +00:04:11,920 --> 00:04:17,660 +are differentiable functions of X then ال D على DX + +46 +00:04:17,660 --> 00:04:21,800 +ل U في ال V يسوى الدالة الأولى في مشتقة الدالة + +47 +00:04:21,800 --> 00:04:27,290 +الثانية زي دي الدالة الثانية في مشتقةالدالة الأولى + +48 +00:04:27,290 --> 00:04:31,950 +مرة تانية الأولى في مشتقة الدالة الثانية زائد + +49 +00:04:31,950 --> 00:04:37,370 +الدالة الثانية في مشتقة من الأولى يبقى U في DV على + +50 +00:04:37,370 --> 00:04:44,370 +DX زائد ال V في DU على DX النقطة السادسة مشتقة + +51 +00:04:44,370 --> 00:04:51,390 +خارج قسم الدالتين يساوي المقام في مشتقة الباصنقص + +52 +00:04:51,390 --> 00:04:57,110 +البصد في مشتقة المقام على مربع المقام الأصلي مرة + +53 +00:04:57,110 --> 00:05:00,750 +تانية كتير من الشباب غلطتهم وين؟ من خلال السنوات + +54 +00:05:00,750 --> 00:05:05,970 +الماضية بقال نلمس بيقول البصد في مشتقة المقام نقص + +55 +00:05:05,970 --> 00:05:09,530 +المقام في مشتقة المقام يعني بيقلب الإشارة هذا طبعا + +56 +00:05:09,530 --> 00:05:15,870 +كلام خطأ فمرة تانية بركز و بقولالمقام في مشتقة الـ + +57 +00:05:15,870 --> 00:05:20,610 +bus ناقص الـ bus في مشتقة المقام على مربع المقام + +58 +00:05:20,610 --> 00:05:25,810 +الأصلي ناخد special case حالة خاصة منه قلنا in + +59 +00:05:25,810 --> 00:05:30,710 +particular كحالة خاصة مشتقة واحد على V يعني لو + +60 +00:05:30,710 --> 00:05:34,510 +كانت ال U ده اللي ثابت اللي هو بالواحد الصحيح + +61 +00:05:34,730 --> 00:05:39,970 +فمشتقتها سالب واحد على V تربية في الـDV على DX، من + +62 +00:05:39,970 --> 00:05:44,290 +أين أتي هذا؟ أتي من الخطوة اللي فوق، فلما أتي أقول + +63 +00:05:44,290 --> 00:05:49,570 +المقام في مشتقة الفاصلة، يصير Zeroبضلش عنده إلا + +64 +00:05:49,570 --> 00:05:55,910 +ناقص للبسط في مشتقة المقام على مربع المقام الأصلي + +65 +00:05:55,910 --> 00:06:00,130 +يبقى لما بدي جهد أطبقها هنا بدي أقول المقام في + +66 +00:06:00,130 --> 00:06:04,850 +مشتقة البسط ب zero طار ناقص البسط اللي هو واحد في + +67 +00:06:04,850 --> 00:06:09,150 +مشتقة المقام اللي هو dv على dx على مربع المقام + +68 +00:06:09,150 --> 00:06:10,490 +الأصلي اللي هو main + +69 +00:06:26,320 --> 00:06:31,770 +بالتالي ماعنديش أي تغيير في مثل هذه الحالةيبقى هذا + +70 +00:06:31,770 --> 00:06:35,310 +بالنسبة للمشتقات العادية الآن، يعني المشتقات من + +71 +00:06:35,310 --> 00:06:39,510 +الرطبة الأولى، لو ده مشتق من الرطبة الثانية أو + +72 +00:06:39,510 --> 00:06:43,710 +الثالثة أو الرابعة، فبقول المشتقة الثانية، المشتقة + +73 +00:06:43,710 --> 00:06:49,750 +التالتة، المشتقة الرابعة، المشتقة النونيةيبقى مرة + +74 +00:06:49,750 --> 00:06:54,550 +تانية بقول second derivative and higher derivative + +75 +00:06:54,550 --> 00:06:59,930 +المشتقة الثانية والمشتقات العليا فباجي بقول لو كان + +76 +00:06:59,930 --> 00:07:04,890 +مشتقة ال y هي y prime بديلها رمز dy على dx بتجيب + +77 +00:07:04,890 --> 00:07:09,410 +المشتقة الثانية بديلها رمز y double primeاللي دي + +78 +00:07:09,410 --> 00:07:14,030 +على دي اكس لدي ي على دي اكس اما باعطيها الرمز هذا + +79 +00:07:14,030 --> 00:07:18,810 +او الرمز هذا او دي square ي على دي اكس square و + +80 +00:07:18,810 --> 00:07:25,770 +هكذا لو اد المشتقة التالتة ي يساوي دي تكييب ي على + +81 +00:07:25,770 --> 00:07:30,570 +دي اكس تكييب and so on لغاية ما اوصل للمشتقة انها + +82 +00:07:30,570 --> 00:07:36,590 +دي مش y مرفوعة للأس n وانما y to the derivative n + +83 +00:07:37,020 --> 00:07:42,020 +لما تشوف الانو بين قصين هذه تعني مشتقة ولا تعني قص + +84 +00:07:42,020 --> 00:07:48,580 +يبقى y to the derivative ان هي dny على dxn يعني + +85 +00:07:48,580 --> 00:07:52,720 +المشتقة النونية لدالة y بالنسبة لمن او لأكس + +86 +00:07:52,720 --> 00:07:56,660 +example one بيقول find y prime for each of the + +87 +00:07:56,660 --> 00:08:00,520 +following يبقى بنجيب المشتقة الأولى لكل مما يأتي + +88 +00:08:00,920 --> 00:08:06,200 +النقطة الأولى Y تسوى أربعة جذر ال X ناقص خمسة على + +89 +00:08:06,200 --> 00:08:11,280 +X بما نشتق باستخدام قواعد الاشتقاق اللي موجودة + +90 +00:08:11,280 --> 00:08:13,920 +عندنا يبقى باجي بدون له solution + +91 +00:08:16,980 --> 00:08:22,780 +ممكن أشتق مباشرة و ممكن أروح أبسط الدالة ثم أقوم + +92 +00:08:22,780 --> 00:08:29,280 +بعملية الاشتقاق فبدأت أقول Y' يساوية الأربعة مالاش + +93 +00:08:29,280 --> 00:08:33,180 +دعوة اللي هي constant لقولنا مشتقة C في ال F of X + +94 +00:08:33,180 --> 00:08:37,420 +يساوي C في مشتقة الدالة يبقى الأربعة مالاش دعوة + +95 +00:08:37,420 --> 00:08:42,130 +الجذر ال X أخدناها قبل ذلك كمثالوأقول لك دول دير + +96 +00:08:42,130 --> 00:08:48,390 +بالك، دول بتكتبالي واحد على اتنين جذر ال X، ناقص، + +97 +00:08:48,390 --> 00:08:53,490 +هذه الآن مقدار ثابت على دلة، طلعليه مقدار ثابت + +98 +00:08:53,490 --> 00:08:58,450 +يساوي السالب واحد على الدلة تربية في مشتقة هذه + +99 +00:08:58,450 --> 00:09:05,090 +الدلة، إذا سالم خمسة ملاش دعوة على X تربية في + +100 +00:09:05,090 --> 00:09:09,130 +مشتقة من ال X اللي بيقدرش بواحد صحيح + +101 +00:09:26,970 --> 00:09:28,850 +المثال الثاني + +102 +00:09:31,520 --> 00:09:42,840 +Y تساوي تلاتة الجذر التالت ل X تربيع ناقص اتنين + +103 +00:09:42,840 --> 00:09:50,680 +على الجذر التربيعي ل X تكعيب لما نشوف مثل ذلك + +104 +00:09:50,680 --> 00:09:56,700 +بنفضل ارتب شكل المسألة قبل ان نقوم بعملية التفاضل + +105 +00:09:56,700 --> 00:10:03,210 +يبقى الحل على الشكل التالي solutionلو جيت قلت ال Y + +106 +00:10:03,210 --> 00:10:07,910 +يسوى التلاتة مالاش داعو اكون اصلا هذا تعني X تربية + +107 +00:10:07,910 --> 00:10:14,110 +اقص طلت يعني X اقص كده ايش؟ اتنين على تلاتة طلتين + +108 +00:10:14,110 --> 00:10:19,670 +ناقص اتنين هذه الجدر التربية ل X تكيب يعني X تكيب + +109 +00:10:19,670 --> 00:10:25,860 +اقص نص يعني X اقص تلاتةعلى اتنين ونطلعها فوق بيصير + +110 +00:10:25,860 --> 00:10:31,840 +X أس سالب تلاتة على اتنين تمام إذا حطيت المسألة + +111 +00:10:31,840 --> 00:10:37,820 +بشكل جديد الآن بقدر أقوله المشتقة الأولى Y prime + +112 +00:10:37,820 --> 00:10:44,320 +السابق تلاتة مالاش دعوة نيجي هذه الأس في X مرفوعة + +113 +00:10:44,320 --> 00:10:49,920 +للأس مطروح منه واحد يبقى طولتين ناقص واحد لان دي + +114 +00:10:49,920 --> 00:10:58,500 +قداش سالب طولأنت أين منها؟ ناقص اتنين في سالب + +115 +00:10:58,500 --> 00:11:04,540 +تلاتة على اتنين X أس سالب تلاتة على اتنين سالب + +116 +00:11:04,540 --> 00:11:10,040 +واحد يعني كده؟ سالب خمسة على اتنين سالب خمسة على + +117 +00:11:10,040 --> 00:11:16,160 +اتنين Y ساوي تلاتة مع تلاتة بيبقى ليه اتنين X أس + +118 +00:11:16,160 --> 00:11:22,250 +سالب طولتنين كمان مع اتنين وزائد في ناقص في ناقص + +119 +00:11:22,250 --> 00:11:28,870 +بزائد تنين مع اتنين بيظل تلاتة اكس والسالب خمسة + +120 +00:11:28,870 --> 00:11:41,550 +على اتنين النقطة نمرسىY تساوي خمسة + +121 +00:11:41,550 --> 00:11:49,270 +زائد اتنين X زائد X تربيع كله على الجذر التربيعي + +122 +00:11:49,270 --> 00:11:55,800 +لXطبعا زي ما رتبنا المسألة اللى فوق بنفضل ارتب + +123 +00:11:55,800 --> 00:12:01,800 +المسألة هذه اولا ثم نقوم بعملية الاشتقاق يبقى هنا + +124 +00:12:01,800 --> 00:12:09,700 +بدي اروح اكتب المسألة على الشكل التالي Y to 7كيف + +125 +00:12:09,700 --> 00:12:15,100 +بقدر ارتبها؟ بقدر اوزع ال bus على مين؟ على المقام، + +126 +00:12:15,100 --> 00:12:20,700 +يبقى ده بصير خمسة على جدر ال X، يعني خمسة X + +127 +00:12:20,700 --> 00:12:27,860 +والسالب نص، يبقى هاي خمسة X والسالب نص، زائد اتنين + +128 +00:12:28,660 --> 00:12:35,060 +هذا X على جذر X يعني X على X أص نص يبقى فوق جذر X + +129 +00:12:35,060 --> 00:12:47,440 +أص نص يبقى زائد 2X أص نص يعني 2 جذر Xطيب زائد x أس + +130 +00:12:47,440 --> 00:12:54,340 +نص و هنا اتنين بيبقى x أس تلاتة على اتنين هذا بده + +131 +00:12:54,340 --> 00:13:01,060 +يعطيلك ان y prime يساوي نشتق يبقى هاي خمسة و هاي + +132 +00:13:01,060 --> 00:13:09,420 +سالب نص x أس سالب تلاتة على اتنينيبقى ناقص نص X أس + +133 +00:13:09,420 --> 00:13:16,880 +سالب تلاتة على اتنين و هنا زائد اتنين في نص X أس + +134 +00:13:16,880 --> 00:13:24,820 +نص سالب واحد دول جديد سالب نص يبقى سالب نص اللي + +135 +00:13:24,820 --> 00:13:28,500 +بعده زائد تلاتة على اتنين + +136 +00:13:32,990 --> 00:13:38,890 +لو حبينا نقيت بس ترتيبها يبقى ناقص خمسة على اتنين + +137 +00:14:10,090 --> 00:14:16,930 +هذه نمرة C من المثلة نروح لنمرة D يبقى نمرة D + +138 +00:14:16,930 --> 00:14:26,790 +بتقول ما يأتي Y تساوي X تربية زيدي اتنين X X تربية + +139 +00:14:26,790 --> 00:14:34,310 +زيدي اتنين X على X تربية ناقص واحدبنجيب مشتقتها + +140 +00:14:34,310 --> 00:14:41,110 +يبقى مشتقتها هي عبارة عن مشتقت خارج قسمة دالتين + +141 +00:14:41,110 --> 00:14:48,800 +يبقى ال y prime يساوي المقامفي مشتقة البصد مشتقة + +142 +00:14:48,800 --> 00:14:54,340 +البصد اللي هو اتنين اكس زائد اتنين ناقص البصد اللي + +143 +00:14:54,340 --> 00:15:01,120 +هو اكس تربية زائد اتنين اكس في مشتقة المقام اللي + +144 +00:15:01,120 --> 00:15:09,100 +هو باتنين اكس كل هذا مقسوما على مربع المقام الأصلي + +145 +00:15:09,800 --> 00:15:16,180 +تمام يبقى هذا الكلام بدي اعطينا Y' يساوي بدي احاول + +146 +00:15:16,180 --> 00:15:20,760 +اختصر اللي هو الكلكة اللي قدامي هذه فباجي بقول + +147 +00:15:20,760 --> 00:15:32,140 +اتنين X تكعيب زائد اتنين X تربيعنقص اتنين اكس نقص + +148 +00:15:32,140 --> 00:15:37,660 +اتنين، هذه فكية الجوس الأول الجوس التاني ناقص + +149 +00:15:37,660 --> 00:15:47,640 +اتنين اكس تكعيب وكمان ناقص اربعة اكس تربيععلى + +150 +00:15:47,640 --> 00:15:55,720 +المقام x تربية ناقص واحد لكل تربية يبقى ال y prime + +151 +00:15:55,720 --> 00:16:03,040 +يبقى يساوي 2x تكييب و ناقص 2x تكييب مع السلامة عند + +152 +00:16:03,040 --> 00:16:10,480 +2x تربية و ناقص 4x تربية يبقى ناقص 2x تربيةنقص + +153 +00:16:10,480 --> 00:16:15,820 +اتنين X نقص اتنين في غيرهم على X تربيع نقص واحد + +154 +00:16:15,820 --> 00:16:21,620 +لكل تربيع اختصارات مافيهش يبقى بروح و بخليها زي ما + +155 +00:16:21,620 --> 00:16:39,440 +هي نمرأ ايه؟ بدنا Y تساوي X تربيع زائد تلاتةفى جدر + +156 +00:16:39,440 --> 00:16:50,300 +ال X ناقص تلاتة فى تلاتة X أسطلتين ناقص اتنين + +157 +00:16:50,300 --> 00:17:00,840 +فكرلى + +158 +00:17:00,840 --> 00:17:08,710 +كيف انه نشتق هذه الظلةهذه الدالة مش دالتين وانما + +159 +00:17:08,710 --> 00:17:15,790 +بدل الدالة تلات دوال، يعني حاصل ضرب ثلاث دوال، + +160 +00:17:15,790 --> 00:17:22,720 +بدنا نيجي نشوف كيف نشتقهمطبعاً في أكثر من اقتراح + +161 +00:17:22,720 --> 00:17:27,200 +الاقتراح الأول نضرب هذول اتنين في بعض و بعدين يصير + +162 +00:17:27,200 --> 00:17:32,020 +مشتق تتحصل ضرب دلتين او نضرب اتنين هذول في بعض و + +163 +00:17:32,020 --> 00:17:35,980 +بعدين يحصل ضرب دلتين او تضرب اي اتنين في بعض و + +164 +00:17:35,980 --> 00:17:39,940 +بعدين يحصل ضرب دلتين او نضرب التلاتة في بعض ثم + +165 +00:17:39,940 --> 00:17:46,860 +نشتق هذه وجهة نظر تمام؟ لكن هناك وجهة نظر أخرى وهي + +166 +00:17:46,860 --> 00:17:51,700 +المشتق الأولزائل التاني والتاني وزائل الأول + +167 +00:17:51,700 --> 00:18:00,240 +والتاني يعني كيف نشتغل الأول والتاني يعني يعني + +168 +00:18:00,240 --> 00:18:04,100 +الأول والتاني نشتغل على زائل الأول والتاني زائل + +169 +00:18:04,100 --> 00:18:07,220 +التاني والتاني طب والتالت لو نشتغل الأول والتاني + +170 +00:18:07,220 --> 00:18:12,620 +التالت أين بدي يروح؟يعني نشتق اتنين و نثبت واحد، + +171 +00:18:12,620 --> 00:18:23,920 +صحيح هذا الكلام، اه ايوة ايوة تمام تمام يبقى زميلك + +172 +00:18:23,920 --> 00:18:31,380 +و هذا شو اسمك انت؟ محمد؟أبو ايه؟ عمد أبو نصر. عمد + +173 +00:18:31,380 --> 00:18:35,040 +أبو نصر تمام؟ انتظر على السؤال فبيقول ما يأتيك + +174 +00:18:35,040 --> 00:18:39,860 +عندي تلت أقوات بيقول بطول القص و بثبت اتنين على + +175 +00:18:39,860 --> 00:18:43,200 +عكس ما اقول انت بتشتق اتنين و تثبت واحد، لأ هو + +176 +00:18:43,200 --> 00:18:47,840 +جالك بشتق واحد و بثبت اتنين، بعد هيك بدي بشتق اللي + +177 +00:18:47,840 --> 00:18:51,260 +فالنص و بثبت اللي قبله و اللي بعده، بعد هيك بدي + +178 +00:18:51,260 --> 00:18:55,110 +للاخير و بشتق الأخر و بثبت الأولوالثاني هو فعلا + +179 +00:18:55,110 --> 00:19:01,730 +هادي مستوحى من مشتقة حاصن ضرب دالتين بالضبط تماما، + +180 +00:19:01,730 --> 00:19:08,950 +يبقى على طول الخطوط، لا تغلبش عليك ولا تضرب ولا + +181 +00:19:08,950 --> 00:19:12,370 +وانت بتجمع بعد عملية الضرب غلط ولا عليك، لا لا لا + +182 +00:19:12,370 --> 00:19:16,310 +فيش أسال من هناك، بدي اشتق الأول، يبقى الأول قداش + +183 +00:19:16,310 --> 00:19:22,910 +2Xوثبت القوسين الآخرين اللي هو جدر ال X ناقص تلاتة + +184 +00:19:22,910 --> 00:19:29,510 +في تلاتة X أس تلتين ناقص اتنين زائد الأول بدي + +185 +00:19:29,510 --> 00:19:35,360 +أثبته زي ما هوفى مشتقة الثانية اللى هو واحد على + +186 +00:19:35,360 --> 00:19:42,160 +اتنين جذر ال X ثمين فى التالت زى ما هو له تلاتة X + +187 +00:19:42,160 --> 00:19:48,780 +أسطلتين ناقص اتنين زاد الجثين الأولانيات زى ما هم + +188 +00:19:48,780 --> 00:19:57,610 +X تربيع زائد تلاتة ثمينفي جذر ال X ناقص تلاتة في + +189 +00:19:57,610 --> 00:20:03,350 +مشتقة الأخر مشتقة سالب اتنين مع السلامة وهذا تلاتة + +190 +00:20:03,350 --> 00:20:12,250 +في طلتين X والسالب طول يبقى تلاتة في طلتين + +191 +00:20:15,520 --> 00:20:21,480 +طبعا تلاتة مع تلاتة بتروح و بيقول بس اتنين X أسالب + +192 +00:20:21,480 --> 00:20:26,540 +تلت يبقى هي المشتقة طبعا هذا بيسهل الشغل بعد هيك + +193 +00:20:26,540 --> 00:20:30,900 +لو كانوا بدل التلات أقواص أربع أقواص أو خمس أقواص + +194 +00:20:30,900 --> 00:20:35,530 +أو ستة أو جد ما بدكفاضل واحد واتثبت الباقي، فاضل + +195 +00:20:35,530 --> 00:20:38,230 +التاني واتثبت اللي جابله واللي بعده، فاضل التابت + +196 +00:20:38,230 --> 00:20:41,590 +واتثبت اللي جابله واللي بعده، بيكون فاضلت ولا تروح + +197 +00:20:41,590 --> 00:20:47,410 +تضرب ولا تجسم ولا تغلب حالك، طبعا؟ طيب، نيجي + +198 +00:20:47,410 --> 00:20:51,870 +للمثال الثاني example 2 + +199 +00:20:58,500 --> 00:21:06,940 +حاجة اسمه إلى نقطتين النقطة a find the second + +200 +00:21:06,940 --> 00:21:12,600 +derivative المشتق + +201 +00:21:12,600 --> 00:21:25,540 +الثاني of y تساوي x تربيع ناقص x أس تلتي + +202 +00:21:30,130 --> 00:21:36,030 +يبقى بدنا المشتقة الثانية لمن؟ ل X تربيع ناقص X أس + +203 +00:21:36,030 --> 00:21:41,270 +تلتين بقولها بسيطة يعني بدنا نشتق هذه الدالة كم + +204 +00:21:41,270 --> 00:21:48,610 +مرة مرتين يبقى بداشي أقوله Y prime اتنين X ناقص + +205 +00:21:48,610 --> 00:21:56,760 +تلتين X أس كده؟ كده؟تلتين سالب واحد كده ايش بيظل؟ + +206 +00:21:56,760 --> 00:22:02,820 +سالب تلت ثم بعد هيك بروح اجيب مين؟ مشتقة ثانية + +207 +00:22:02,820 --> 00:22:07,880 +يبقى المشتقة الثانية Y double prime تساوي مشتقة + +208 +00:22:07,880 --> 00:22:14,200 +الأولى باتنين وهذه ناقص تلتين مالاش دعوة وهذا سالب + +209 +00:22:14,200 --> 00:22:21,110 +تلت Xسالب تلت سالب واحد يعني سالب واحد و تلت يبقى + +210 +00:22:21,110 --> 00:22:27,810 +سالب اربع على تلتة يبقى قلة النتيجة الاتنين ناقص + +211 +00:22:27,810 --> 00:22:35,510 +فناقص بزايد اتنين على تسعة اكس او سالب اربع على + +212 +00:22:35,510 --> 00:22:41,330 +تلتة نمر + +213 +00:22:41,330 --> 00:22:43,730 +بي find + +214 +00:22:48,160 --> 00:22:56,540 +الـ y to the derivative m for the function لدى ال + +215 +00:22:56,540 --> 00:23:01,300 +y تساوي واحد على x زي التلاتة + +216 +00:23:07,500 --> 00:23:11,660 +مشان أجيب المشتقة النونية نروح أجيب المشتقة الأولى + +217 +00:23:11,660 --> 00:23:16,160 +و التانية و التالتة و الرابعة و الخمسة لغاية ما + +218 +00:23:16,160 --> 00:23:22,000 +اهتدي إلى شكل المشتقة النونية كيف كانت تالية + +219 +00:23:22,000 --> 00:23:24,060 +solution؟ + +220 +00:23:27,020 --> 00:23:36,020 +الان بده يجي الى Y' يساوي مشتقة هذه سالب واحد على + +221 +00:23:36,020 --> 00:23:42,180 +X زائد تلاتة لكل تربيع في مشتقة ما ده ما الا اللي + +222 +00:23:42,180 --> 00:23:47,080 +هو المقام اللي هو بقداشي بواحد يبقى النتيجة صارت + +223 +00:23:47,080 --> 00:23:53,480 +سالب واحد على X زائد تلاتة لكل تربيع + +224 +00:23:55,690 --> 00:24:00,970 +بنروح نجيب المشتقة الثانية يعني يا شباب هذه كأنها + +225 +00:24:00,970 --> 00:24:11,420 +ايش؟ كأنها سالب X زائد تلاتة كله سالب اتنينطيب هده + +226 +00:24:11,420 --> 00:24:18,240 +هي الـYW' هي السالب اللي برا وهي سالب اتنين وهي + +227 +00:24:18,240 --> 00:24:22,740 +الجس زي ما هو وبدنا نطرح منه واحد بيصير السالب + +228 +00:24:22,740 --> 00:24:26,780 +اتنين سالب واحد سالب تلاتة في تفاضل مداخل القس + +229 +00:24:26,780 --> 00:24:30,640 +اللي هو الجداش بواحد يعني في الـDV على DX اللي هو + +230 +00:24:30,640 --> 00:24:38,140 +بواحد يبقى النتيجة صارت اللي هو اتنين X زائد تلاتة + +231 +00:24:38,140 --> 00:24:43,560 +وسالب تلاتةالسلام عليكمطيب بدنا نروح نجيب المشتقة + +232 +00:24:43,560 --> 00:24:50,880 +التالتة يساوي هاي اتنين اللي برا وهاي سالب تلاتة و + +233 +00:24:50,880 --> 00:24:58,520 +هذا ال X زائد تلاتة أس سالب كدهش؟ سالب تلاتة سالب + +234 +00:24:58,520 --> 00:25:02,820 +واحد اللي هو سالب أربعة في مشتقة مداخل القوس اللي + +235 +00:25:02,820 --> 00:25:12,230 +هو بواحد طيب الآن لو جيت المشتقة الرابعةيساوي + +236 +00:25:12,230 --> 00:25:19,990 +اتنين في سالب تلاتة في سالب اربعة في ال X زائد + +237 +00:25:19,990 --> 00:25:29,530 +تلاتة قص سالب خمسةما .. وين اللي مضربنهاش؟ وين + +238 +00:25:29,530 --> 00:25:34,870 +اللي محطنهاش؟ التالتة هي التالتة هي اتنين سالب + +239 +00:25:34,870 --> 00:25:39,370 +تلاتة فيكس زي اربعة سالب تلاتة سالب واحد سالب + +240 +00:25:39,370 --> 00:25:44,320 +اربعة كيف مكتبنهاش عاد؟على كلام كان سليم مائة + +241 +00:25:44,320 --> 00:25:51,240 +بالمائة، لا غبار عليه، تمام؟ طيب، بس تنى شوية، + +242 +00:25:51,240 --> 00:25:57,200 +الآن هذا ويه الساوي، سلب في سلب الموجب يبقى اتنين + +243 +00:25:57,200 --> 00:26:04,420 +في تلاتة في اربعةfix زائد تلاتة كله أساليب خمسة + +244 +00:26:04,420 --> 00:26:10,480 +إيش رأيك بدي أصيغ هذه الصياغة أخرى لو رجعنا هيك في + +245 +00:26:10,480 --> 00:26:15,620 +الهمش للثانوية العامة بقينا نقول مضروب الأربعة + +246 +00:26:15,620 --> 00:26:21,160 +أربعة في تلاتة في اتنين في واحد مش هيك بيناجي أول؟ + +247 +00:26:22,540 --> 00:26:27,540 +صح؟ يعني كنت تكتبوها هيك و الله واحدة و نقطة مش + +248 +00:26:27,540 --> 00:26:33,380 +هيك يعني فهي ممتازة يعني يبقى مضروب الأربعة اللي + +249 +00:26:33,380 --> 00:26:40,360 +هو أربعة في مضروب التلاتة هيك كنت تكتبوها أو أربعة + +250 +00:26:40,360 --> 00:26:45,680 +في تلاتة في مضروب اتنين + +251 +00:26:55,950 --> 00:27:07,370 +4×3×2×1 4×3×2×1 4×3×2×1 4×3×2×1 4×3×2×1 + +252 +00:27:07,370 --> 00:27:12,430 +4×3×2×1 + +253 +00:27:15,030 --> 00:27:21,110 +هذه هي السلب برة اتنين في تلاتة مش هي مضغوبة تلاتة + +254 +00:27:21,110 --> 00:27:25,870 +ايضا لان تلاتة في اتنين في واحد اذا هذه تلاتة + +255 +00:27:25,870 --> 00:27:34,770 +factorial في ال X زائد تلاتة كله أس سالب أربع لو + +256 +00:27:34,770 --> 00:27:41,370 +جيت لهذه أليست هذه هي اتنين factorial في X زائد + +257 +00:27:41,370 --> 00:27:47,420 +تلاتة كله أس سالب تلاتة؟هذه أليست هي واحد + +258 +00:27:47,420 --> 00:27:53,360 +factorial فاهمين؟ fixed زي التلاتة او ناقص اتنين + +259 +00:27:53,360 --> 00:27:59,620 +طيب ممتاز اذا لو ضلت ماشي على الشكل هذه هوصل + +260 +00:27:59,620 --> 00:28:05,020 +للمشتقانونية what's the matter استنى شوية عدت عشان + +261 +00:28:05,020 --> 00:28:10,030 +اجيب شكل المشتقانونية بدي اقارنبين نتائج التي + +262 +00:28:10,030 --> 00:28:15,890 +توصلت اليها هذا المشتقة كده ايش؟ اربعة النتيجة + +263 +00:28:15,890 --> 00:28:22,070 +اربعة factorial X زي تلتة أس سالب خمسة يبقى اربعة + +264 +00:28:22,070 --> 00:28:27,720 +اربعة سالب خمسة تعال خد المشتقة التالتةتلاتة + +265 +00:28:27,720 --> 00:28:33,600 +factorial بس بشرط سالب، وهنا كده؟ سالب أربع، تعليل + +266 +00:28:33,600 --> 00:28:37,800 +المشتقة التانية، اتنين factorial والسالب تلاتة + +267 +00:28:37,800 --> 00:28:43,500 +الجوز، تعليل Y prime، يبقى واحد factorial X زي + +268 +00:28:43,500 --> 00:28:50,470 +التلاتة يسوى سلب اتنين، يبقى المباحظ ما يأتيحد + +269 +00:28:50,470 --> 00:28:55,870 +موجب، حد سالب، مش كله موجب ولا كله سالب، مرة موجب، + +270 +00:28:55,870 --> 00:28:59,850 +مرة سالب، مرة موجب، مرة سلب، اي واحدة، اتنين، + +271 +00:28:59,850 --> 00:29:07,070 +رتبتي المشتقة هي تبعت ال factorialمشتقة رابعة + +272 +00:29:07,070 --> 00:29:10,870 +اربعة factorial المشتقة التانية التانية factorial + +273 +00:29:10,870 --> 00:29:15,970 +المشتقة الأولى واحد factorial اتنين والله تلاتة ال + +274 +00:29:15,970 --> 00:29:19,110 +ghost في الحالات الأربعة زي ما هو بس اللي بتغير + +275 +00:29:19,110 --> 00:29:24,970 +main plus في حالة المشتقة الأولى كان سالب اتنينفى + +276 +00:29:24,970 --> 00:29:28,370 +عادة المشتقة التانية كان سالب تلاتة فى عادة + +277 +00:29:28,370 --> 00:29:32,330 +المشتقة الرابعة كأه فى المشتقة التالتة صار سالب + +278 +00:29:32,330 --> 00:29:36,670 +أربعة فى عادة المشتقة الرابعة صار سالب خمسة و هكذا + +279 +00:29:36,670 --> 00:29:42,470 +إذا بناء على هذه المقارنة بقدر أكتب شكل المشتقة + +280 +00:29:42,470 --> 00:29:48,210 +النونية يبقى يا باجي بقول سالب واحد to the power n + +281 +00:29:48,210 --> 00:29:54,000 +و بدي أرجعلها لسه أتأكد شغل صح و الله غلطأربعة + +282 +00:29:54,000 --> 00:29:58,580 +أربعة factorial تلاتة تلاتة factorial يبقى N N + +283 +00:29:58,580 --> 00:30:05,940 +factorial ال X زائد تلاتة زي ما هو المشتق الرابعة + +284 +00:30:05,940 --> 00:30:11,640 +بسالب خمسة يبقى بدأ يقول سالب N وكمان سالب واحد + +285 +00:30:11,640 --> 00:30:17,280 +يعني المشتق قد يبدأ يحطه بشرة سالب وأطرح منها واحد + +286 +00:30:17,590 --> 00:30:21,230 +الرابعة بصالب خمسة، التالتة بصالب أربعة، التانية + +287 +00:30:21,230 --> 00:30:26,970 +بصالب تلاتة، الأولى بصالب اتنين وهكذا، يعني أقل من + +288 +00:30:26,970 --> 00:30:31,570 +رتبة المشتقة ضمن بصالب واحد، الرتبة بصالب وكمان + +289 +00:30:31,570 --> 00:30:37,430 +تطرح منها صالب واحدنرجع لهذا تأكد شغلي صح و لا + +290 +00:30:37,430 --> 00:30:41,910 +غلط، إن كان صح كلبها، إن كان غلط بنعمله التصحيح + +291 +00:30:41,910 --> 00:30:45,870 +اللي لازم، بدالي أقول لو بدى المشتقة الأولى، يبقى + +292 +00:30:45,870 --> 00:30:49,970 +مكان الإناش بده أحط واحد، يبقى Y prime، يبقى بده + +293 +00:30:49,970 --> 00:30:55,130 +أحط هنا واحد وهنا واحد، يبقى واحد بصير هذه سالب، + +294 +00:30:55,130 --> 00:31:00,580 +الجواز والسالب اتنينسالب الجوس السالب اتنين اللي + +295 +00:31:00,580 --> 00:31:06,100 +المشغل اه والله هذه مظبوطة تمام نسيت السلب بس هنا + +296 +00:31:06,100 --> 00:31:13,300 +يعني تمام؟ بنجر مين؟ لو كانت ال N بإتنين يبقى هذه + +297 +00:31:13,300 --> 00:31:18,700 +السالب واحد تربية بالموجب بصير اتنين factorial X + +298 +00:31:18,700 --> 00:31:23,340 +زي التلاتة و السالب تلاتة لأن ال N بإتنين سالب + +299 +00:31:23,340 --> 00:31:27,280 +اتنين سالب واحد سالب تلاتة يبقى ال Y double prime + +300 +00:31:27,520 --> 00:31:31,160 +بصير اتنين factorial X زي التلاتة والسلب اتنين + +301 +00:31:31,160 --> 00:31:35,300 +وهكذا بلاحظ الكلام هذا صحيح دائما وابدا إذا + +302 +00:31:35,300 --> 00:31:41,020 +المشتقة النونية يسلب واحد أس ان ان factorial في X + +303 +00:31:41,020 --> 00:31:45,720 +زي التلاتة to the power سلب ان سالب واحد طيب لو + +304 +00:31:45,720 --> 00:31:50,010 +نجيت الإشارة حسب ما نكاتب مش صحيحةيعني لاجئة + +305 +00:31:50,010 --> 00:31:53,570 +المشتقلة و لا بدل ما هي سالب لاجئتها موجبة كيف + +306 +00:31:53,570 --> 00:31:59,330 +تصحيها بكل بساطة بس جبل انكتب زائد واحد تبقى خلصت + +307 +00:31:59,330 --> 00:32:04,830 +منها المشكلة دائما انا بحط اس ان لاجئتها مظبوطة + +308 +00:32:04,830 --> 00:32:08,810 +كان بها ما لاجئتها بس بضيف واحد بصير مظبوطة تمام + +309 +00:32:08,810 --> 00:32:11,450 +مائة بالمئة هذا السؤال اللي كنت تسأله و لا غيره + +310 +00:32:13,090 --> 00:32:20,470 +الاشتغال بقى عشان أقول X زي أتردد كله سلب M ومتصفر + +311 +00:32:20,470 --> 00:32:26,860 +الداخل دولةأحنا ما خدناش تقول X زي كتبة احنا ما + +312 +00:32:26,860 --> 00:32:27,200 +خدناش تقول X زي كتبة احنا ما خدناش تقول X زي كتبة + +313 +00:32:27,200 --> 00:32:28,140 +احنا ما خدناش تقول X زي كتبة احنا ما خدناش تقول X + +314 +00:32:28,140 --> 00:32:31,740 +زي كتبة احنا ما خدناش تقول X زي كتبة احنا ما خدناش + +315 +00:32:31,740 --> 00:32:34,140 +تقول X زي كتبة احنا ما خدناش تقول X زي كتبة احنا + +316 +00:32:34,140 --> 00:32:36,420 +ما خدناش تقول X زي كتبة احنا ما خدناش تقول X زي + +317 +00:32:36,420 --> 00:32:37,400 +كتبة احنا ما خدناش تقول X زي كتبة احنا ما خدناش + +318 +00:32:37,400 --> 00:32:44,460 +تقول X زي كتبة احنا ما خدناش تقول X زي كتبة احنا + +319 +00:32:44,460 --> 00:32:51,140 +ما خدناش تقول X زي كتبةإن شاء الله تشيروني حد بدي + +320 +00:32:51,140 --> 00:32:55,860 +أسأل تاني؟ المشتق اللي هو واحد على اثنين جاذر ال + +321 +00:32:55,860 --> 00:33:05,380 +X؟ المشتق + +322 +00:33:05,380 --> 00:33:07,700 +اللي هو واحد على اثنين جاذر ال X؟ المشتق اللي هو + +323 +00:33:07,700 --> 00:33:09,380 +واحد على اثنين جاذر ال X؟ المشتق اللي هو واحد على + +324 +00:33:09,380 --> 00:33:09,380 +اثنين جاذر ال X؟ المشتق اللي هو واحد على اثنين + +325 +00:33:09,380 --> 00:33:09,380 +جاذر ال X؟ المشتق اللي هو واحد على اثنين جاذر ال + +326 +00:33:09,380 --> 00:33:11,060 +X؟ المشتق اللي هو واحد على اثنين جاذر ال X؟ المشتق + +327 +00:33:11,060 --> 00:33:13,520 +اللي هو واحد على اثنين جاذر ال X؟ المشتق اللي هو + +328 +00:33:13,520 --> 00:33:16,800 +واحد على اثنين جاذر ال X؟ المشتق اللي هو واحد على + +329 +00:33:16,800 --> 00:33:18,360 +اثنين جاذر ال X؟ المش + +330 +00:33:22,760 --> 00:33:28,060 +أي سؤال بده مشتقة العاشرة الـ20% بنشوف النتيجة هنا + +331 +00:33:28,060 --> 00:33:31,440 +وبنعمل مقارنة وبنقل عليها بنستنتجها سواء كان + +332 +00:33:31,440 --> 00:33:35,260 +الـSin أو الـCos أو جدر الـX أو أي شغلة من الشغلات + +333 +00:33:35,260 --> 00:33:39,460 +هذه شوف مادام الشقاق بطلقلك نفس الدالة بس بتغير + +334 +00:33:39,460 --> 00:33:43,400 +الأس لازم يكون في شكل المشتقة أنونيا + +335 +00:33:46,830 --> 00:33:51,610 +الإشارة عندي ناقص واحد، حاطيتها وص إن، مظبوط؟ يبقى + +336 +00:33:51,610 --> 00:33:55,510 +هذه بحطها لأي إشارة بعد ذلك، مدام موجة بسالب موجة + +337 +00:33:55,510 --> 00:33:59,310 +بسالب، بحط هذه، إذا والله لاجيتها، لما أتيت عوض + +338 +00:33:59,310 --> 00:34:02,090 +مستقلة والتانية والتالتة، لاجيته الصحيح، يبقى + +339 +00:34:02,090 --> 00:34:07,150 +الوضع صحيح، لاجيتها غلط، بس للأس هذا بحط إن زائد + +340 +00:34:07,150 --> 00:34:10,890 +واحد، والباقي كما هو، يعني اللي كانت موجة بصير + +341 +00:34:10,890 --> 00:34:13,910 +سالب، واللي كانت سالب بصير موجة، بتطلع معناة دورية + +342 +00:34:14,140 --> 00:34:29,560 +ماشى يا سيدي طيب ننتقل الى المثال اللى يليه المثال + +343 +00:34:29,560 --> 00:34:40,150 +اللى بعده مثال رقم تلاتة يبقى تلاتةبقول الف ال F + +344 +00:34:40,150 --> 00:34:47,850 +of اتنين يساوي اتنين and ال F prime of اتنين يساوي + +345 +00:34:47,850 --> 00:34:56,470 +تلاتة and ال F prime of اتنين يساوي تلاتة find + +346 +00:34:56,470 --> 00:35:04,930 +وجدلي الي هو Dy by DX for + +347 +00:35:22,290 --> 00:35:26,070 +نجي الان للمشتق اللي عندنا هذا يبقى solution + +348 +00:35:29,390 --> 00:35:34,610 +الان في ان y يساوي f of x علي x تربية زايد f of x + +349 +00:35:34,610 --> 00:35:39,530 +عند x يساوي اتنين مطلوب قداش مقدار المشتق عند x + +350 +00:35:39,530 --> 00:35:43,390 +يساوي اتنين اذا بدنا نروح نشتق الدالة و نعوض + +351 +00:35:43,390 --> 00:35:48,970 +بالمعطيئات اللي موجودة عندنا يبقى ال y prime يساوي + +352 +00:35:48,970 --> 00:35:56,590 +هذه خارج قسم الدالتين يبقى المقام في مشتقة البسط + +353 +00:35:57,840 --> 00:36:07,460 +ناقص ال bus في مشتقة المقام 2x زائد f prime of x + +354 +00:36:07,460 --> 00:36:15,570 +كل هذا مقسوم على مربع المقام الأصلي لكل تربيةبعد + +355 +00:36:15,570 --> 00:36:21,810 +هيك بدنا نروح نجيب ال y prime عند x يسوي كده؟ 2 + +356 +00:36:21,810 --> 00:36:27,850 +يبقى بدنا نشيل كل x ونحط مكانها 2 يبقى هذا الكلام + +357 +00:36:27,850 --> 00:36:36,450 +بد يسوي 2 تربيه زائد ال F of 2 في ال F prime of 2 + +358 +00:36:36,450 --> 00:36:45,380 +ناقص ال F of 2 اتنين في اتنينزائد F prime of اتنين + +359 +00:36:45,380 --> 00:36:52,400 +كله مقسوما على اتنين تربيع زائد F of اتنين الكل + +360 +00:36:52,400 --> 00:37:00,380 +تربيع النتيجة تساوي اربعة زائد F of اتنين مقطع + +361 +00:37:00,380 --> 00:37:05,320 +اللي هو بقداش باتنين F prime of اتنين اللي هي + +362 +00:37:05,320 --> 00:37:12,450 +بقداش بتلاتةيبقى مضروب فيه تلاتة ناقص F of 2 ب2 + +363 +00:37:12,450 --> 00:37:19,050 +أربع زائد F prime of 2 اللي هو بتلاتة كل هذا + +364 +00:37:19,050 --> 00:37:25,770 +الكلام مقسوما على اللي هو أربع زائد F of 2 ب2 الكل + +365 +00:37:25,770 --> 00:37:32,180 +تربيةنجا اتنين زي اربعة ستة في تلاتة اب تمانتاشر + +366 +00:37:32,180 --> 00:37:37,940 +ناقص تلاتة و اربعة سبعة في اتنين اب اربعة طاشر كل + +367 +00:37:37,940 --> 00:37:44,500 +هذا الكلام على ستة و تلاتين يبقى على ستة و تلاتين + +368 +00:37:44,500 --> 00:37:50,080 +بيضل اربعة على ستة و تلاتين يقبل جواب قداش تسوى + +369 +00:37:50,080 --> 00:37:57,130 +يبقى النتيجة تساوي تسوىيعني انت بدك تحاول تستخدم + +370 +00:37:57,130 --> 00:38:01,630 +المعطيات اللي عندك بالطريقة المناسبة ال dash tag + +371 +00:38:01,630 --> 00:38:07,050 +بعد هيك اعوض باتنين بعد هيك اروح استخدم المعطيات + +372 +00:38:07,050 --> 00:38:14,630 +اللي عندي للحصول على الإجابة المطلوبة كان هذا هو + +373 +00:38:14,630 --> 00:38:21,710 +المثال رقم تلاتة بدنا نروح لمثال رقم أربعة مثال + +374 +00:38:21,710 --> 00:38:24,030 +رقم أربعة بيقول ما يأتي + +375 +00:38:28,070 --> 00:38:36,330 +مثال رقم اربعة بيقول find an + +376 +00:38:36,330 --> 00:38:47,510 +equation for the line perpendicular اللي + +377 +00:38:47,510 --> 00:38:52,110 +بيكون عمودي perpendicular to the tangent + +378 +00:38:58,720 --> 00:39:12,640 +to the tangent of the curve المنحنة y تساوي x تكيب + +379 +00:39:12,640 --> 00:39:23,700 +ناقص أربعة x زائد واحد at the point عند النقطة + +380 +00:39:23,700 --> 00:39:28,200 +اتنين واحد نمرى ب + +381 +00:39:31,040 --> 00:39:35,700 +بقول find equations + +382 +00:39:35,700 --> 00:39:38,740 +for + +383 +00:39:38,740 --> 00:39:45,040 +the tangents for + +384 +00:39:45,040 --> 00:39:52,180 +the tangents to the curve to + +385 +00:39:52,180 --> 00:40:03,670 +the curve at the pointsعند النقاط at the points + +386 +00:40:03,670 --> 00:40:11,430 +where the slope is تمانية + +387 +00:40:37,100 --> 00:40:42,280 +سؤال مرة تانية سؤال فيه مطلوبين المطلوب الأول + +388 +00:40:42,280 --> 00:40:48,640 +بيقول هات لمعاد الخط الذي يكون عموديا على مماثل + +389 +00:40:48,640 --> 00:40:55,060 +منحنى y يساوي x تكيب نقص 4x زاد 1 عند النقطة 2 و1 + +390 +00:40:55,060 --> 00:41:00,520 +يعني انا في عندي منحنى في مماس في نقطة تماث في + +391 +00:41:00,520 --> 00:41:06,300 +عمودي عند نقطة التماس اللي هو 2 و1مش هجيب معادلة + +392 +00:41:06,300 --> 00:41:14,680 +العمودي بدي ميله و نقطة واقع عليه نقطة واقع عليه + +393 +00:41:14,680 --> 00:41:20,140 +هي الموجودة بضل قداش ميله ميله بدي اجيبه من مين + +394 +00:41:20,140 --> 00:41:24,450 +لمينعن طريق ميلي المماثل المنحنة لأن عندي قاعدة في + +395 +00:41:24,450 --> 00:41:30,090 +الهندسة التحليلية بتقول حاصل ضرب ميلي المستقيمين + +396 +00:41:30,090 --> 00:41:34,730 +المتعمدين يساوي إذا بدأت أستخدم القاعدة في الحصول + +397 +00:41:34,730 --> 00:41:39,370 +على ميلي العمودي ومن ثم أروح أجيب معادلته + +398 +00:41:45,010 --> 00:41:49,930 +معادلات المماثات للمنحنة المعادلة المماثات للمنحنة + +399 +00:41:49,930 --> 00:41:51,330 +المعادلة المماثات للمنحنة المعادلة المماثات + +400 +00:41:51,330 --> 00:41:51,770 +للمنحنة المعادلة المماثات للمنحنة المعادلة + +401 +00:41:51,770 --> 00:41:51,770 +المماثات للمنحنة المعادلة المماثات للمنحنة + +402 +00:41:51,770 --> 00:41:51,770 +المعادلة المماثات للمنحنة المعادلة المماثات + +403 +00:41:51,770 --> 00:41:52,950 +للمنحنة المماثات للمنحنة المماثات للمنحنة المماثات + +404 +00:41:52,950 --> 00:41:57,770 +للمنحنة المماثات للمنحنة + +405 +00:41:57,770 --> 00:42:03,690 +المماثات للمنحنة المماثات للمنحنة المماثات للمنحنة + +406 +00:42:03,690 --> 00:42:09,070 +المماثات للمنحنة + +407 +00:42:13,710 --> 00:42:21,770 +يبقى هذا الكلام بده يساوي اللي تلاتة X تربية تلاتة + +408 +00:42:21,770 --> 00:42:29,920 +X تربية ناقص أربعةالان هذا يسوي ميل المماس للمنحنة + +409 +00:42:29,920 --> 00:42:41,580 +يبقى هذا يسوي slope of the tangent عند اي لحظة طب + +410 +00:42:41,580 --> 00:42:47,520 +انا بدي slope of the tangent وين؟ عند النقطة اتنين + +411 +00:42:47,520 --> 00:42:57,830 +وواحد يبقى باجي بقوله the slope ofthe tangent at + +412 +00:42:57,830 --> 00:42:59,550 +the point + +413 +00:43:10,330 --> 00:43:16,310 +يبقى هذا الكلام يسوى تلاتة في اتنين تربية ناقص + +414 +00:43:16,310 --> 00:43:19,570 +اربعة اربعة في تلاتة في اتناشر ناقص اربعة يسوى + +415 +00:43:19,570 --> 00:43:23,470 +تلاتة في اتنين تربية ناقص اربعة يبقى هذا الاسلوب + +416 +00:43:23,470 --> 00:43:32,090 +تبع ال tangent هذا لو رحت اعطيته الرمز M1الان انا + +417 +00:43:32,090 --> 00:43:40,310 +عندي حاصل ضرب ميلي المستقيمين المتعمدين يساوي كده؟ + +418 +00:43:40,310 --> 00:43:44,830 +سالب واحد بما ان حاصل ضرب الاول في التاني يساوي + +419 +00:43:44,830 --> 00:43:50,170 +سالب واحد هذا بده يعطيناانه تمانية في M اتنين + +420 +00:43:50,170 --> 00:43:57,310 +يساوي سالب واحد يبقى M اتنين يساوي سالب تمان يبقى + +421 +00:43:57,310 --> 00:44:08,130 +هذا الاسلوب of the perpendicular line + +422 +00:44:08,130 --> 00:44:15,730 +to the tangentيبقى هذا ميل العمودي على مين؟ على + +423 +00:44:15,730 --> 00:44:20,270 +الممسك النقطة المعروفة والميل معروف إذا بقدر أجيب + +424 +00:44:20,270 --> 00:44:31,970 +معادلة العمودي يبقى هنا from the equation Y ساوي M + +425 +00:44:31,970 --> 00:44:41,070 +في X ناقص X node زائد Y node the equation + +426 +00:44:43,010 --> 00:44:51,390 +of the perpendicular line + +427 +00:44:51,390 --> 00:45:01,550 +is y تساوي الميل له قداش سالب تمان في ال X ناقص + +428 +00:45:01,550 --> 00:45:06,650 +اتنين زائد واحدهذه المعادلة انتهينا منها لكن بدي + +429 +00:45:06,650 --> 00:45:12,770 +اعيد ترتيبها فبقول لو ضربنا كله في تمانية بصير + +430 +00:45:12,770 --> 00:45:23,120 +تمانية Y يسوى ناقص X زائد اتنين زائد تمانيةدربنا + +431 +00:45:23,120 --> 00:45:29,220 +كله في من؟ في تمانية او صار معادلة العمودي هي + +432 +00:45:29,220 --> 00:45:36,520 +تمانية Y يسوى ناقص X زائد عشرة هذه هي المعادلة + +433 +00:45:36,520 --> 00:45:43,540 +المطلوبة ويتالى خلصنا الجزء الاول من المثلة بداخل + +434 +00:45:43,540 --> 00:45:48,950 +الجزء التانيالجزء التاني قال لي هاتلي معادلة + +435 +00:45:48,950 --> 00:45:54,470 +المماثات كل المماثات اللي مالها يساوي كده؟ يساوي + +436 +00:45:54,470 --> 00:45:58,410 +تمانية، مدام المال يساوي تمانية، إذا بدي أجيب + +437 +00:45:58,410 --> 00:46:03,390 +النقاط اللي المال عندها يساوي كده؟ يساوي تمانية، + +438 +00:46:03,390 --> 00:46:08,910 +لما نجيب للنقاط والمال معروف، بصير سهل يجيب معادلة + +439 +00:46:08,910 --> 00:46:15,250 +هذه المماثات، فبعدين بقوله ما يأتي، بدنا نحاولنجيب + +440 +00:46:15,250 --> 00:46:23,170 +احداث النقاط هذه الان الاسلوب اللى هو بده يساوي ال + +441 +00:46:23,170 --> 00:46:31,090 +dy على dx اللى هو مين اللى هو تلاتة x تربية ناقص + +442 +00:46:31,090 --> 00:46:37,250 +اربعة يساوي كده؟ يساوي تمانية طبعا x هذه عند اى + +443 +00:46:37,250 --> 00:46:45,120 +نقطةIn general هذه المعادلة هتعطيني تلاتة X تربيع + +444 +00:46:45,120 --> 00:46:53,580 +يساوي كده؟ 12 يبقى X تربيع يساوي 4 يبقى ال X بدها + +445 +00:46:53,580 --> 00:46:59,000 +ساوي زائد او ناقص 2 يبقى عندي كام نقطة بصير + +446 +00:46:59,000 --> 00:47:07,690 +للتماث؟ نقطة 2 يبقى النقطة الأولى F X يساوي 2ثم + +447 +00:47:07,690 --> 00:47:11,210 +لماذا تساوي واحدة اظن؟ + +448 +00:47:21,800 --> 00:47:29,920 +فالـ X يسوى سالب اتنين ثم الـ Y يسوى سالب اتنين + +449 +00:47:29,920 --> 00:47:37,240 +الكل تكيب سالب اربعة في سالب اتنين زائد واحد و + +450 +00:47:37,240 --> 00:47:43,620 +يسوى كمان جداش واحد يبقى أصبح عندي نقطتين للتماث + +451 +00:47:43,620 --> 00:47:49,500 +The points of tangency + +452 +00:47:51,320 --> 00:48:00,620 +النقاط التماس هي 2 و 1 and سلبي 2 و 1 يبقى كم مقسم + +453 +00:48:00,620 --> 00:48:12,320 +دي؟ 2 يبقى بقى دي بقوله the first tangent is y سوى + +454 +00:48:12,320 --> 00:48:19,320 +الميل قداش؟بنعطيها تمانية يبقى اي تمانية في X ناقص + +455 +00:48:19,320 --> 00:48:27,800 +اتنين زائد الواحد او ال Y تساوي تمانية X ناقص + +456 +00:48:27,800 --> 00:48:35,980 +ستاشر زائد واحد يبقى ال Y يساوي تمانية X ناقص + +457 +00:48:35,980 --> 00:48:42,190 +خمستاشرهذا المماس الأول نجيب المماس الثاني the + +458 +00:48:42,190 --> 00:48:52,330 +second tangent المماس الثاني و أيه سوى نفسي المية + +459 +00:48:52,330 --> 00:49:00,610 +اللي هو قدراش تمانية يبقى أيه تمانية فكس ناقص ناقص + +460 +00:49:00,610 --> 00:49:09,140 +اتنين زائد واحدأو ان شئتم فقولوا Y تساوي تمانية X + +461 +00:49:09,140 --> 00:49:14,360 +طبعا نقص نقص اتنين بزايد اتنين في تمانية بستاشر + +462 +00:49:14,360 --> 00:49:25,500 +زايد واحد او Y يساوي تمانية X زايد سبعتاشر تمام؟ + +463 +00:49:25,500 --> 00:49:31,180 +طب ده اسألكوا سؤال هل الممثلين هدول متوازين؟ + +464 +00:49:35,370 --> 00:49:40,530 +متوازين؟ مش عارفين الشباب؟ ما هي ما اعطيك نفس + +465 +00:49:40,530 --> 00:49:43,750 +الميلي اللي هو تمانية وما هي المعامل تبع ال X هو + +466 +00:49:43,750 --> 00:49:47,070 +الميلي ويساوي تمانية إذا مادام نفس الميلي يبقى + +467 +00:49:47,070 --> 00:49:51,370 +الممثلين متوازين وعطيتكوا مثال قبل ذلك وطلعوا + +468 +00:49:51,370 --> 00:49:57,730 +ورسمتوا زيادة وقلت لكوا وبينتوا كل ممثل متوازينهو + +469 +00:49:57,730 --> 00:50:03,710 +الـ X نفسه، 2,3,1 هنا والله فوق، فوق، فوق، فوق، + +470 +00:50:03,710 --> 00:50:07,750 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +471 +00:50:07,750 --> 00:50:08,350 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +472 +00:50:08,350 --> 00:50:08,370 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +473 +00:50:08,370 --> 00:50:08,430 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +474 +00:50:08,430 --> 00:50:14,750 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +475 +00:50:14,750 --> 00:50:15,470 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +476 +00:50:15,470 --> 00:50:19,770 +فوق، فوق، فوق، فوق، فوق، فوق، فوق، فوق، + +477 +00:50:23,800 --> 00:50:30,780 +المثال الأخير في هذا ال section بيقول ما يأتي مثال + +478 +00:50:30,780 --> 00:50:38,660 +خمسة find + +479 +00:50:38,660 --> 00:50:45,760 +the values of + +480 +00:50:45,760 --> 00:50:52,020 +a and b if the tangent + +481 +00:50:54,840 --> 00:51:01,200 +the tangent to the curve + +482 +00:51:04,440 --> 00:51:17,200 +للمنحنة y تساوي ax تربية زائد bx has slope برضه + +483 +00:51:17,200 --> 00:51:26,220 +تمانية at the point واحد وخمسة + +484 +00:51:37,050 --> 00:51:43,230 +سؤال مرة ثانية بيقول هاتلي قيمة a و b إذا كان + +485 +00:51:43,230 --> 00:51:49,630 +المماس للمنحنة ميله تمانية عند هذه النقطة أنا عندي + +486 +00:51:49,630 --> 00:51:56,490 +مجهولين ومعطيني الميل وعند النقطة هذه يبقى بدي + +487 +00:51:56,490 --> 00:52:00,910 +أروح أشتق مش هنجيب ال slope يبقى أول خطوة بدي + +488 +00:52:00,910 --> 00:52:10,190 +أقوله y prime يساوي اتنين a x زائد bالان y' عند من + +489 +00:52:10,190 --> 00:52:18,090 +عند x يساوي كم؟ يساوي واحد يساوي كم؟ يساوي تمانية + +490 +00:52:18,090 --> 00:52:23,610 +الاسلوب يساوي تمانية عند النقطة هذه هذا ايش معناه؟ + +491 +00:52:23,610 --> 00:52:28,190 +هذا معناه انك تشيل كل x و تضعه في مكان كم؟ واحد + +492 +00:52:28,190 --> 00:52:35,540 +يبقى اتنين a في واحدزائد بيه يساوي كده؟ تمانية + +493 +00:52:35,540 --> 00:52:43,060 +يبقى صار اتنين ايه؟ زائد بيه يساوي تمانية طيب هذه + +494 +00:52:43,060 --> 00:52:48,060 +معلومة تربط بين المجهولين الاتنين بدنا كمان معلومة + +495 +00:52:48,060 --> 00:52:54,700 +النقطة هذه النقطة في التماس تقع على المماس وتقع + +496 +00:52:54,700 --> 00:53:03,330 +على المنحنة إذا تحقق معادلات المنحنة إذا andأت + +497 +00:53:03,330 --> 00:53:09,910 +اللي هي النقطة واحد وخمسة ويهاب يبقى بده يشيل ال Y + +498 +00:53:09,910 --> 00:53:14,070 +ويحط مكانها خمسة ويشيل X ويحط مكانها واحد يبقى + +499 +00:53:14,070 --> 00:53:22,070 +خمسة بدها تساوي A في واحد تربيه زائد B في واحد هذا + +500 +00:53:22,070 --> 00:53:28,670 +بده يعطيك A زائد B بده يساوي كده؟ بده يساوي خمسة + +501 +00:53:29,560 --> 00:53:35,940 +طيب الان انا عندي معادلتين اتنين a زائد b يساوي + +502 +00:53:35,940 --> 00:53:41,080 +تمانية شو رايك انا بضربها في سالب واحد بصير سالب a + +503 +00:53:41,080 --> 00:53:46,140 +سالب b يساوي سالب خمسة و اجمع يعني بدي احل + +504 +00:53:46,140 --> 00:53:52,460 +المعادلتين الاتنين هدول مع بعض بطلع عندي جداش ال a + +505 +00:53:52,460 --> 00:53:58,730 +يساوي تلاتةأجمع بضل عندي هنا a و بضل عندي هنا + +506 +00:53:58,730 --> 00:54:05,210 +تلاتة طيب لما a تسوى تلاتة بي تسوى خمسة نقص تلاتة + +507 +00:54:05,210 --> 00:54:12,730 +اللي هو الجداش اتنين and ال b يسوى اتنينلاحظ هنا + +508 +00:54:12,730 --> 00:54:16,810 +انتهى هذا ال section اللي هو التلاتة تلاتة وإليك + +509 +00:54:16,810 --> 00:54:20,010 +أرقام المسائل + +510 +00:54:49,570 --> 00:54:55,590 +هي في الزاوية عندك يبقى exercises تلاتة تلاتة + +511 +00:54:55,590 --> 00:55:05,310 +المسائل التالية من واحد لواحد وخمسين الأد و بنضيف + +512 +00:55:05,310 --> 00:55:13,650 +عليها كمان اللي هو من خمسة وخمسين لتمانية وخمسينو + +513 +00:55:13,650 --> 00:55:22,130 +كذلك من واحد و ستين لغاية اربعة و ستين واحد و ستين + +514 +00:55:22,130 --> 00:55:29,810 +لغاية اربعة و ستين والان بنروح ل section تلاتة + +515 +00:55:29,810 --> 00:55:36,250 +اربعة بنقول الله يسهل عليك و بنروح لتلاتة خمسة + +516 +00:55:36,250 --> 00:55:41,230 +اللي هو ال derivatives of + +517 +00:55:52,060 --> 00:56:00,980 +مشتقة الدوال المثلثية اول شي قبل ما نبدأ في مشتقة + +518 +00:56:00,980 --> 00:56:08,100 +الدوال المثلثية نذكر في شغل اخدناها قبل ذلك الشغل + +519 +00:56:08,100 --> 00:56:20,700 +هذهit should be noted that + +520 +00:56:20,700 --> 00:56:29,400 +limit لصين ال X ع ال X لما ال X تروح لزينه يساوي + +521 +00:56:29,400 --> 00:56:35,970 +كده؟ واحد هذه مرت علينا قبل هيكبدي اخد مثال عليها + +522 +00:56:35,970 --> 00:56:43,550 +وبعد هيك نروح لمين لمشتقة الدوال المثلثية بدي ال + +523 +00:56:43,550 --> 00:56:49,990 +limit لما ال X بدها تروح لل zero ل cosine ال X + +524 +00:56:49,990 --> 00:57:02,690 +ناقص واحد على مين على X شوفوا + +525 +00:57:02,690 --> 00:57:09,140 +يا زيديطبعا الطاولة المباشرة بيجيب 0 على 0 لكن انا + +526 +00:57:09,140 --> 00:57:16,780 +بدى اكتب هدى على الشكل التالي شو + +527 +00:57:16,780 --> 00:57:21,320 +رايك اخد سالب عامل مشترك بصير limit لما ال X بده + +528 +00:57:21,320 --> 00:57:27,780 +تروح ل 0 للواحد ناقص cosine X على X سويتش اشي ولا + +529 +00:57:27,780 --> 00:57:31,840 +حاجة حتى الان بده ضرب في مرافق ال bus طبعا كده ضرب + +530 +00:57:31,840 --> 00:57:39,270 +ليشمشان اخلق النظرية هذه مشان اقدر استخدمها يبقى + +531 +00:57:39,270 --> 00:57:44,610 +هذه لو روح ضربت في المرافق واحد زائد cosine ال X + +532 +00:57:44,610 --> 00:57:50,450 +على واحد زائد cosine ال X يبقى هذه بدها تسوي ال + +533 +00:57:50,450 --> 00:57:57,090 +limit لما ال X بدها تروح لوين؟ ل Zero لمن؟ للبسط + +534 +00:57:57,090 --> 00:58:03,860 +فرق بين المربعينواحد ناقص cosine تربية ال X على X + +535 +00:58:03,860 --> 00:58:10,900 +في واحد زائد cosine ال X أو هذا سالب limit لما ال + +536 +00:58:10,900 --> 00:58:15,520 +X بده تروح ل zero واحد ناقص cosine تربية من حساب + +537 +00:58:15,520 --> 00:58:21,800 +المثلثات لو sin تربية ال X على X في واحدزائد + +538 +00:58:21,800 --> 00:58:26,820 +cosine ال X أول متطابقة مثلثية أخدناها في section + +539 +00:58:26,820 --> 00:58:30,820 +واحد تلاتة كان cosine تربيه ال X زائد sine تربيه + +540 +00:58:30,820 --> 00:58:34,960 +ال X يساوي قداش واحد إذا واحد ماقص cosine تربيه ال + +541 +00:58:34,960 --> 00:58:39,920 +X هي sine تربيه ال X إذا هداني خلقت في المثلةصين + +542 +00:58:39,920 --> 00:58:44,520 +ال X على X يبقى هذه الصارت على الشكل التالي هي + +543 +00:58:44,520 --> 00:58:51,020 +السالب وهي limit لما ال X بدها تروح ل 0 لصين X على + +544 +00:58:51,020 --> 00:59:01,060 +X في صين X على 1 زائد Cos Xالان بدأ ادخل ال limit + +545 +00:59:01,060 --> 00:59:07,680 +علي كل منهما يبقى هذا الكلام يساوي سالب limit لما + +546 +00:59:07,680 --> 00:59:13,120 +ال x بدأ تروح لل zero ل sine ال x على x في limit + +547 +00:59:13,120 --> 00:59:18,220 +لما ال x بدأ تروح لل zero ل sine ال x على واحد + +548 +00:59:18,220 --> 00:59:25,750 +زائد cosine ال x ال limit هذا كده؟هي فوق عندي + +549 +00:59:25,750 --> 00:59:33,030 +بواحد صحيح يبقى هاي السالب وهي واحد هذه في قداش + +550 +00:59:33,030 --> 00:59:41,370 +Zero على واحد زائد واحد النتيجة كلها قداش Zero كده + +551 +00:59:41,370 --> 00:59:47,080 +من الأن فصاعدا limit هذه كلها بتساوي قداش Zeroطب + +552 +00:59:47,080 --> 00:59:51,940 +شو دخل هذا في ال trigonometric؟ اه هذه الأزمالي و + +553 +00:59:51,940 --> 00:59:58,200 +هذه الأزمالي الآن في البرهان في إثبات مشتقة الدوال + +554 +00:59:58,200 --> 01:00:05,020 +المثلثية إذا بدنا نيجي نستخدم التنتين هدول في + +555 +01:00:05,020 --> 01:00:11,560 +إيجاد مشتقة الدوال المثلثية المختلفة + +556 +01:00:13,140 --> 01:00:17,560 +بدنا نجي لأول مشتقة من هذه المشتقات + +557 +01:00:23,580 --> 01:00:30,280 +الـ F prime of X يسوي كده؟ Cos X يعني مشتقة الجيب + +558 +01:00:30,280 --> 01:00:37,880 +هو مين؟ جيب التمام بدنا نثبت صحة هذا الكلام بدنا + +559 +01:00:37,880 --> 01:00:44,080 +نرجع للإثبات للتعريف يبقى احنا كان عندنا F prime + +560 +01:00:44,080 --> 01:00:50,750 +of Xيسوي ال limit لما ال H بده تروح لل zero لل F + +561 +01:00:50,750 --> 01:00:56,190 +of X زي ال H ناقص ال F of X كله على H مش هذا كان + +562 +01:00:56,190 --> 01:01:01,320 +التعريف اللي لناالـ F of X هي من؟ صين الـ X إذا + +563 +01:01:01,320 --> 01:01:06,780 +بدي أجي على الصين أشيل كل X و أحط مكانها X زائد H + +564 +01:01:06,780 --> 01:01:12,360 +يبقى الـ F prime of X يساوي ال limit لما الـ H + +565 +01:01:12,360 --> 01:01:17,900 +بدها تروح لـ Zero بدي أجي على الصين أشيل الـ X و + +566 +01:01:17,900 --> 01:01:23,360 +أكتب مكانها X زائد الـ H الـ F of X زي ما هي الصين + +567 +01:01:23,360 --> 01:01:30,590 +X كله على من؟ على Hتعويض المباشر بيجيب لـ 0 على 0 + +568 +01:01:30,590 --> 01:01:36,550 +لإن الـ sine is 0 بـ 0 و ال H بـ 0 بيصير 0 ناقص 0 + +569 +01:01:36,550 --> 01:01:40,550 +على 0 و ما شاء الله عليها كمية غير معينة يبقى + +570 +01:01:40,550 --> 01:01:46,310 +استخدم صلاحياتك و اشتغل الشغل اللي بدكيه H بدأ + +571 +01:01:46,310 --> 01:01:51,290 +تروح لـ 0 لو رجعنا بالذكرة إلى الوراق هذا الـ sine + +572 +01:01:51,290 --> 01:01:55,960 +back graphic و الـ sine cosine زاد cosine sineيبقى + +573 +01:01:55,960 --> 01:02:01,460 +هذا بقدر اقول هو عبارة عن sine ال X في cosine ال H + +574 +01:02:01,460 --> 01:02:06,840 +ماله زائد إشارة زائد يبقى بطلها زائد كما هي cosine + +575 +01:02:06,840 --> 01:02:12,760 +ال X في sine ال H هذا مفكوك الأول ناقص sine ال X + +576 +01:02:12,760 --> 01:02:18,840 +كما هو كله مقسوما على مين على H يسوى ال limit لما + +577 +01:02:18,840 --> 01:02:25,040 +ال H tends to zero طلعلي للمقدار الأول والأخيريبقى + +578 +01:02:25,040 --> 01:02:31,600 +بينهم sin x عامل مشترك يبقى هذا sin x عامل مشترك + +579 +01:02:31,600 --> 01:02:42,600 +يبقى cos h ناقص واحد زائد cos x في sin h كله مقصوم + +580 +01:02:42,600 --> 01:02:50,860 +على مين؟ على h بدى اوزع ال limit لترمز + +581 +01:02:51,070 --> 01:02:58,010 +يبقى هذا ال limit لما ال H بده يروح ل 0 لمن؟ ل sin + +582 +01:02:58,010 --> 01:03:06,690 +X cos H ناقص واحد على H زاد limit لما ال H بدها + +583 +01:03:06,690 --> 01:03:16,310 +تروح ل 0 لcos X في sin H كله على H يساويالـ limit + +584 +01:03:16,310 --> 01:03:21,410 +هذه لمين؟ لكل حاجة فيها H أي حاجة فيها H تعتبر + +585 +01:03:21,410 --> 01:03:26,230 +مقدار ثابت بالنسبة لمين لل limit ونهاية المقدار + +586 +01:03:26,230 --> 01:03:30,850 +الثابت بالمقدار الثابت itself السؤال هو sign ال X + +587 +01:03:30,850 --> 01:03:35,710 +هذه إيها علاقة بال limit هنا مافيها Hيبقى هذا + +588 +01:03:35,710 --> 01:03:41,510 +يعتبر مقدار ثابت بقوله شرفنا مرة يبقى هذا sin X + +589 +01:03:41,510 --> 01:03:48,090 +باقية limit لما ال H بده تروح ل zero لcos H ناقص + +590 +01:03:48,090 --> 01:03:55,450 +واحد على H زاد هذه بنفس الطريقة cos X برة limit + +591 +01:03:55,450 --> 01:04:02,840 +لما ال H بده تروح ل zero لsin H على Hهذا الكلام + +592 +01:04:02,840 --> 01:04:12,580 +يساوي صين ال X في هذا ال limit هيكداش؟ Zero يبقى + +593 +01:04:12,580 --> 01:04:19,400 +هذه Zero الله يسهل عليها Z Cos X وهذه بقداش؟ يبقى + +594 +01:04:19,400 --> 01:04:27,460 +النتيجة تساوي Cos X إذا من الأن فصاعدا مشتقة Sin X + +595 +01:04:27,460 --> 01:04:36,040 +هي بقداش؟ بCos X كيف؟ مين اللي بيحكي سامعني؟ + +596 +01:04:36,040 --> 01:04:45,590 +سامعني إيش بتقول؟كل حاجة بأثبتها قدامك مطلوبة اللي + +597 +01:04:45,590 --> 01:04:50,010 +بأثبتهاش مسامحينك فيها وإذا بدك تسير من .. أنا مش + +598 +01:04:50,010 --> 01:04:53,770 +مسامحك وإذا بدك تسير من أهل العلم حتى اللي + +599 +01:04:53,770 --> 01:05:01,410 +بأثبتهاش بتروح تثبتها طيب نمره اتنين F ال F of X + +600 +01:05:01,410 --> 01:05:10,180 +يساوي cosine ال X thenالـ F prime of X بسالب صين + +601 +01:05:10,180 --> 01:05:16,280 +الـ X يالا يا محمد العشي والكلام للسامعين لبروف + +602 +01:05:16,280 --> 01:05:23,480 +بدنا ال F prime of X يبقى ال limit لما ال H بدها + +603 +01:05:23,480 --> 01:05:33,160 +تروح ل zero لمين؟ لcos X زائد H ناقص cos X كله على + +604 +01:05:33,160 --> 01:05:39,740 +Hمش هيك التعريف؟ اه يطبق ده مباشرة يبقى هذا الكلام + +605 +01:05:39,740 --> 01:05:45,960 +بده يسوي ال limit لما ال H بدها تروح ل zero تمام؟ + +606 +01:05:45,960 --> 01:05:50,680 +بده افك ال cosine، cosine، cosine سالب، sine، sine + +607 +01:05:50,680 --> 01:05:58,760 +يبقى cosine ال X cosine ال H ناقص sine ال X في + +608 +01:05:58,760 --> 01:06:08,270 +sineالـ H ناقص Cos X كل هذا على H يساوي Limit لما + +609 +01:06:08,270 --> 01:06:14,030 +الـ H بدها تروح لـ Zero برضه ال term الأول والأخير + +610 +01:06:14,030 --> 01:06:21,010 +بده ياخد Cos X عام المشترك يبقى Cos X عام المشترك + +611 +01:06:21,010 --> 01:06:29,260 +وضل Cos H ناقص واحدعلى H ناقص limit لما الـH بده + +612 +01:06:29,260 --> 01:06:38,600 +تروح لـ0 لمين؟ لـsin X في sin H على H مرة ثانية + +613 +01:06:38,600 --> 01:06:44,270 +هذا القصيد مالهوش دعوة بطله برايبقى هذا cosine ال + +614 +01:06:44,270 --> 01:06:50,010 +X في limit لما ال H بده تروح لل zero ل cosine ال H + +615 +01:06:50,010 --> 01:06:55,790 +ناقص واحد على H ناقص sine ال X برا في limit لما ال + +616 +01:06:55,790 --> 01:07:01,530 +H بده تروح لل zero ل sine ال H على Hيبقى هذا + +617 +01:07:01,530 --> 01:07:10,710 +cosine X وهذا كم؟ بزرع ناقص sine X وهذا كم؟ بواحد + +618 +01:07:10,710 --> 01:07:17,370 +يبقى النتيجة ناقص sine X يبقى من الأنفا صاعدا + +619 +01:07:17,370 --> 01:07:24,870 +مشتقة ال cosine بسالب sineلحد هنا الاشتقاق من خلال + +620 +01:07:24,870 --> 01:07:28,770 +التعريف الله يعطيك العافية مكفي بدنا نشتق بطريقة + +621 +01:07:28,770 --> 01:07:36,690 +أخرى يبقى بدنا نيجي لنمرة تلاتة بدنا D على DX لتان + +622 +01:07:36,690 --> 01:07:46,480 +ال X يبقى باجي بقوله D على DX ليه؟الان بقدر اكتبها + +623 +01:07:46,480 --> 01:07:51,980 +بدلالة الـSin والـCos وبالتالي بقدر استخدم نتيجتي + +624 +01:07:51,980 --> 01:07:58,500 +ال derivative اللي عندنا يبقى هذا الـSin X على Cos + +625 +01:07:58,500 --> 01:08:05,370 +X الان هذه مشتقة خارج قسم الدالتينيبقى هذا الكلام + +626 +01:08:05,370 --> 01:08:14,850 +يساوي المقام في مشتقة البصد ناقص البصد اللي هو sin + +627 +01:08:14,850 --> 01:08:23,010 +X في مشتقة المقام ال cosine بسالب sin X كله على + +628 +01:08:23,010 --> 01:08:31,780 +مربع المقام الأصليالنتيجة تساوي cosine تربيع ناقص + +629 +01:08:31,780 --> 01:08:38,800 +فناقص بزايد sin تربيع ال X كله على cosine تربيع ال + +630 +01:08:38,800 --> 01:08:43,720 +X cosine تربيع ال X زايد sin تربيع ال X من أول + +631 +01:08:43,720 --> 01:08:50,060 +متطابقة الجديد بواحد صحيح يبقى النتيجة واحد على + +632 +01:08:50,060 --> 01:08:56,410 +cosine تربيع ال X ال cosine مقلوب منسك يبقى هذا + +633 +01:08:56,410 --> 01:09:01,510 +الكلام بدي يساوي سك تربيه على ال X يبقى من الألف + +634 +01:09:01,510 --> 01:09:09,090 +صاعدا مشتقة التاني بقداشاذا good exercise لك اللي + +635 +01:09:09,090 --> 01:09:16,750 +هو نمرة أربعة exercise لك بدك تثبتلي ان دي على DX + +636 +01:09:16,750 --> 01:09:26,530 +لمين لكتان ال X اللي دي على DX لكسين ال X على سين + +637 +01:09:26,530 --> 01:09:34,200 +ال X يسوى سالب كسيكن تربيع ال Xبنفس الطريقة هيك + +638 +01:09:34,200 --> 01:09:37,660 +عملتلك المقام في وشطقة ال bus نقص ال bus في وشطقة + +639 +01:09:37,660 --> 01:09:43,060 +المقام على مربع المقام الأصلي وعطيتك النتيجة بنجي + +640 +01:09:43,060 --> 01:09:52,980 +لخمسة بدنا d على dx لمن لسك ال x يبقى d على dx + +641 +01:09:52,980 --> 01:10:01,520 +السكة مر عن مين واحد على cosineقبل شوية قلنا مشتقة + +642 +01:10:01,520 --> 01:10:09,060 +واحد على V سالب واحد على V تربية في DV على DX يبقى + +643 +01:10:09,060 --> 01:10:15,900 +سالب واحد على cosine تربية ال X في مشتقة ال cosine + +644 +01:10:15,900 --> 01:10:24,870 +سالب sin Xإذن النتيجة تساوي سالب في سالب بموجب sin + +645 +01:10:24,870 --> 01:10:30,810 +X على cos تربيع X اللي بقدر اكتبها على الشكل + +646 +01:10:30,810 --> 01:10:39,210 +التالي واحد على cosine X في sin X على cosine X + +647 +01:10:39,210 --> 01:10:46,410 +واحد على cosineبسك الاكس صين عكو صين تاني الاكس + +648 +01:10:52,310 --> 01:11:00,210 +بسك ال X في تان ال X، آخر حاجة، good exercise لك، + +649 +01:11:00,210 --> 01:11:09,970 +لكن ايه؟ D على DX لا cosecant X، يعني D على DX ال + +650 +01:11:09,970 --> 01:11:18,000 +cosecant الواحد على صين Xيبقى السالب كثيقة ال X + +651 +01:11:18,000 --> 01:11:25,300 +كتان ال X يبقى أصبح مباركة لك كل مشتقة الدوال + +652 +01:11:25,300 --> 01:11:32,920 +المثلثية الستة إذا نحن ناخد بعض الأمثلة على هذه + +653 +01:11:32,920 --> 01:11:37,700 +الدوال المثلثية الستة + +654 +01:11:52,770 --> 01:11:59,790 +أول مثال بيقول ما يأتي example + +655 +01:11:59,790 --> 01:12:06,730 +one find + +656 +01:12:06,730 --> 01:12:19,990 +y prime for eachof the following ان المشتق لكل مما + +657 +01:12:19,990 --> 01:12:33,730 +يأتي نمرة واحد Y تساوي X في cos X ناقص X تربيع في + +658 +01:12:33,730 --> 01:12:43,960 +sin X فتح معايا كويس يبقى solutionبالنواية prime + +659 +01:12:43,960 --> 01:12:51,580 +يساوي هذه تعتبر حاصل ضرب دالتين يبقى الدالة الأولى + +660 +01:12:51,580 --> 01:12:57,280 +في مشتقة الدالة الثانية ففضل cosine بسلب sin X + +661 +01:12:57,280 --> 01:13:04,660 +زائد الدالة الثانية في مشتقة الأولى لواحد صحيح + +662 +01:13:04,660 --> 01:13:11,180 +خلصنا منها ناقص دالة الأولى في مشتقة الدالة + +663 +01:13:11,180 --> 01:13:19,040 +الثانيةهيناقص للكل زائد الدالة الثانية في مشتقة + +664 +01:13:19,040 --> 01:13:26,780 +الدالة الأولى اللى هى اتنين X بهذا الشكلنعيد + +665 +01:13:26,780 --> 01:13:37,600 +ترتيبها y' يسوى ناقص x في sin x زائد cos x ناقص x + +666 +01:13:37,600 --> 01:13:45,120 +تربيع في cos x ناقص 2x في sin x + +667 +01:13:48,290 --> 01:13:55,850 +وهذا نفس الشيء يبقى سالب تلاتة x في sin x زائد + +668 +01:13:55,850 --> 01:14:02,590 +cosine x ناقص x تربيع في cosine x + +669 +01:14:05,570 --> 01:14:14,990 +النقطة الثانية y تساوي cosine تربيع x على 2 ناقص + +670 +01:14:14,990 --> 01:14:24,850 +sin تربيع x على 2 طلع + +671 +01:14:24,850 --> 01:14:30,550 +عليه كويس احنا طوأ خدنا مشتقة الدول المثلثية الستة + +672 +01:14:30,550 --> 01:14:36,100 +لكن مااخدناش مشتقات مربعاتهافحصيح ولا لا؟ لكن لو + +673 +01:14:36,100 --> 01:14:43,240 +رجعنا بالذاكرة إلى الوراء بقينا نقول cosine 2x + +674 +01:14:43,240 --> 01:14:49,380 +يساوي cosine تربيع ال X ناقص sine تربيع ال X زو + +675 +01:14:49,380 --> 01:14:54,320 +اللي جوا نص اللي برا يبقى بناء عليه cosine ال X + +676 +01:14:54,320 --> 01:15:00,160 +ايش تساوي؟ cosine تربيع X على 2 ناقص sine تربيع X + +677 +01:15:00,160 --> 01:15:09,480 +على 2 هي هذه؟يبقى أصل المسألة Y يساوي من Cos X + +678 +01:15:09,480 --> 01:15:16,920 +خلاص يبقى فرطة يبقى بناء على Y' يساوي سالب Sin X + +679 +01:15:16,920 --> 01:15:21,580 +هذه ممكن اشتقها ان شاء الله بعد ما ناخد Chain Rule + +680 +01:15:21,580 --> 01:15:26,340 +ال section الجاي ونروحها نشتقها بدون ما نعمل الشغل + +681 +01:15:26,340 --> 01:15:37,630 +هذه على أي حال تلاتة Y تساويY تساوي X في صين X في + +682 +01:15:37,630 --> 01:15:49,570 +تاني X يبقى هذا مشتقة ايش؟ حاصل ضرب ثلاث دول قبل + +683 +01:15:49,570 --> 01:15:54,890 +شوية أخدنا مشتقة حاصل ضرب ثلاثة أقوات، متذكر؟ طيب + +684 +01:15:54,890 --> 01:15:57,630 +يالا نشوف، يبقى solution + +685 +01:16:00,050 --> 01:16:06,510 +الـ y' يساوي مشتقة الأولى بواحد بضال قداش sin x في + +686 +01:16:06,510 --> 01:16:15,810 +تان ال x زاد ال x مشتقة ال sin ب cos x في تان ال x + +687 +01:16:19,860 --> 01:16:29,360 +زاد اكس في صين ال X مشتقت التان بمين؟ بسكت ربيع ال + +688 +01:16:29,360 --> 01:16:39,590 +X في اختصارات؟ بالمرة؟طيب هذه sin X في تان ال X + +689 +01:16:39,590 --> 01:16:49,050 +زاد X أليست هذه هي sin X على cosine X إذا ال + +690 +01:16:49,050 --> 01:16:55,390 +cosine مع ال cosine بتروح بيبقى X في sin X هذه مش + +691 +01:16:55,390 --> 01:17:02,770 +فيها اي اشكالية يبقى X في sin X في سكتة ربيع X + +692 +01:17:05,740 --> 01:17:11,920 +هذا النقطة من نقطة التالتة النقطة الرابعة النقطة + +693 +01:17:11,920 --> 01:17:18,800 +الرابعة بيقول لي Y تساوي واحد زائد تان ال X على + +694 +01:17:18,800 --> 01:17:26,200 +واحد ناقص تان ال X بدنا نشتقها طبعا واضح هذه + +695 +01:17:26,200 --> 01:17:35,540 +مشتقتاش خارج قسم الدالتينيبقى باجي بقوله Y' يساوي + +696 +01:17:35,540 --> 01:17:43,240 +المقام في مين؟فى مشتقة البصر الواحد بـ0 والتان + +697 +01:17:43,240 --> 01:17:50,620 +بـsec تربيه ال X ناقص البصر واحد زائد تان ال X فى + +698 +01:17:50,620 --> 01:17:58,280 +مشتقة المقام سالب sec تربيه ال X كله على مربع + +699 +01:17:58,280 --> 01:18:04,820 +المقام الأصلي واحد ناقص تان X لكل تربيه + +700 +01:18:09,050 --> 01:18:15,150 +هذا الكلام يساوي نفك الأقواع السادى يبقى sector P + +701 +01:18:15,150 --> 01:18:21,310 +على X ناقص تاني X في sector P على X + +702 +01:18:24,290 --> 01:18:34,310 +نقص فنقص بزائد يبقى زائد سك تربيع ال X زائد تان ال + +703 +01:18:34,310 --> 01:18:42,190 +X في سك تربيع ال X كله مقسوما واحد ناقص تان ال X + +704 +01:18:42,190 --> 01:18:49,050 +لكل تربيعأظن هذا موجب وهذا سلب مع السلامة يبقى + +705 +01:18:49,050 --> 01:18:59,290 +النتيجة صارت Y' يسوى 2×6 تربية X واحد ناقص تان X + +706 +01:18:59,290 --> 01:19:13,710 +لكل تربية نقطة الخامسة Y تساوي تان X ناقص Xبنجيب y + +707 +01:19:13,710 --> 01:19:20,550 +prime يبقى y prime يصيب تفاضل ال 10 ب 6 تربيه ال x + +708 +01:19:20,550 --> 01:19:27,750 +و بتفاضل ال x طيب 6 تربيه اناقص 1 بقداش 10 تربيه + +709 +01:19:27,750 --> 01:19:39,390 +ال x النقطة السادسة y تسوى sign + +710 +01:19:39,390 --> 01:19:51,340 +ال xعلى واحد زائد cosine ال X طبعا خارج قسم + +711 +01:19:51,340 --> 01:20:00,660 +الدالتين يبقى ال Y' يساوي المقام في مشتقة البسط + +712 +01:20:00,660 --> 01:20:08,520 +ناقص البسطفى مشتقة المقام مشتقة الواحد Zero مشتقة + +713 +01:20:08,520 --> 01:20:15,260 +ال cosine سالب sine يبقى سالب sine ال X كله على + +714 +01:20:15,260 --> 01:20:22,220 +مربع المقام الأصلي واحد زاد cosine X لكل تربيع بدا + +715 +01:20:22,220 --> 01:20:28,980 +فك القوة السادة يبقى cosine Xزائد cosine تربية ال + +716 +01:20:28,980 --> 01:20:36,320 +X ناقص في ناقص يبقى زائد sine تربية ال X كله على + +717 +01:20:36,320 --> 01:20:44,760 +واحد زائد cosine X الكل تربية ويساوي cosine X زائد + +718 +01:20:46,250 --> 01:20:50,130 +طلّالي cosine تربيه زي cosine تربيه هذه كلها كمدهش + +719 +01:20:50,130 --> 01:20:57,290 +يبقى زائد واحد زائد cosine X لكل تربيه عظيم البسط + +720 +01:20:57,290 --> 01:21:01,710 +هو المقدار بين القوسين يبقى هذا الكلام دي ساعة + +721 +01:21:01,710 --> 01:21:07,150 +واحد على واحد زائد cosine X + +722 +01:21:23,670 --> 01:21:37,130 +طب المثال الثاني then find yw prime for each of + +723 +01:21:37,130 --> 01:21:43,910 +the following نمر + +724 +01:21:43,910 --> 01:21:52,730 +أيه؟ y تساوي x تربيع في صين ال xالأمثلة السابقة + +725 +01:21:52,730 --> 01:21:55,770 +كان كله بدنا المشتقة الأولى هنا بدنا المشتقة + +726 +01:21:55,770 --> 01:22:02,590 +الثانية يبقى solution مشان يجيب المشتقة ثانية لازم + +727 +01:22:02,590 --> 01:22:08,490 +يجيب المشتقة يبقى y prime يساوي حاصل ضرب داليتين + +728 +01:22:08,490 --> 01:22:16,970 +يبقى x تربيه في cosine ال x زائداللي هو اتنين اكس + +729 +01:22:16,970 --> 01:22:23,390 +ثمين في صين ال X بدنا نجيب المشتقة الثانية حاصل + +730 +01:22:23,390 --> 01:22:29,130 +ضرب دالتين و كذلك حاصل ضرب دالتين يبقى الدالة + +731 +01:22:29,130 --> 01:22:36,870 +الأولى في مشتقة الدالة الثانية زائد الدالة الثانية + +732 +01:22:36,870 --> 01:22:46,190 +في مشتقة الدالة الأولى الterm التاني زائد2x في + +733 +01:22:46,190 --> 01:22:52,730 +cosine ال X الأولى في مشتقة التانية زائد التانية + +734 +01:22:52,730 --> 01:22:58,330 +في مشتقة الأولى هي التانية و مشتقة الأولى اللي هي + +735 +01:22:58,330 --> 01:23:05,130 +باتنين يبقى آلة المثلة السالب x تربيع في sine ال X + +736 +01:23:05,130 --> 01:23:13,950 +زائد 2x في cosine ال X و 2x بيصير كده؟ أربعةx cos + +737 +01:23:13,950 --> 01:23:22,790 +x زيدي اتنين sin x مافيش غيرها طيب نمر بإيه؟ y + +738 +01:23:22,790 --> 01:23:35,170 +تساوم كسيكنت ال x لنقش اكتر من هيك كافي طيب + +739 +01:23:35,170 --> 01:23:44,860 +يبقى y prime سالب كسيكنت ال x كتان ال xبنواي + +740 +01:23:44,860 --> 01:23:51,080 +double prime سالب مانوش دعوة، خلّيه برا هذا حاصل + +741 +01:23:51,080 --> 01:24:02,960 +ضرب دلتين، يبقى cosecant لكس تفاضل كتان سالب + +742 +01:24:02,960 --> 01:24:09,860 +cosecant تربيع قبل قليل، يبقى سالب cosecant تربيع + +743 +01:24:09,860 --> 01:24:15,500 +لكسالدول المثلثية دير بالك مشتقتهم مثل ملح الطعام + +744 +01:24:15,500 --> 01:24:21,240 +لا يستغنى عنهم بدك تعرف مشتقت الدول الستة مثل اسمك + +745 +01:24:21,240 --> 01:24:25,320 +ال sine بي cosine ال cosine بي سالب sine ال tan بي + +746 +01:24:25,320 --> 01:24:29,040 +سيك تربيع ال cotan بي سالب cosecant تربيع ال sec + +747 +01:24:29,040 --> 01:24:32,780 +بي sec tan و ال cosecant بي سالب cosecant cotan زي + +748 +01:24:32,780 --> 01:24:36,860 +اسمك تكون عارفهطيب يبقى الدالة الأولى في مشتقة + +749 +01:24:36,860 --> 01:24:43,560 +الدالة الثانية زائد الدالة الثانية في مشتقة ال + +750 +01:24:43,560 --> 01:24:50,720 +cosecant له سالب cosecant ال X كتان ال X وهيقفلنا + +751 +01:24:50,720 --> 01:24:56,350 +القوسالان بداخل الاشارة جوا يبقى ناقص فناقص بزايد + +752 +01:24:56,350 --> 01:25:02,510 +كثيكان تكيب ال X هذا الترم الأول الترم التاني ناقص + +753 +01:25:02,510 --> 01:25:10,530 +فناقص كذلك بزايد اللي هو كثيكان تل X كتان تربيع ال + +754 +01:25:10,530 --> 01:25:14,390 +X بقى + +755 +01:25:14,390 --> 01:25:21,180 +الاخر مثالأه طبعا ضيعت هو العشر دقائق ما بين + +756 +01:25:21,180 --> 01:25:26,920 +الأسلسل عطلان لما بجدرة جادرة وصلنا هنا يبقى + +757 +01:25:26,920 --> 01:25:32,280 +example تلاتة أخر + +758 +01:25:32,280 --> 01:25:33,040 +مثال + +759 +01:25:46,910 --> 01:25:54,930 +أول نقطة بدنا limit لما ال X بده تروح لل zero لمن؟ + +760 +01:25:54,930 --> 01:26:04,870 +لل sign if تحجز يبقى باي زائد تان ال X على من؟ على + +761 +01:26:04,870 --> 01:26:10,090 +تان ال X نقص اتنين في سك ال X + +762 +01:26:13,200 --> 01:26:17,460 +اللي بسيطة اللي متهادي سهلة، اللي متهادي معاها + +763 +01:26:17,460 --> 01:26:22,380 +صلاحيات، سيب النسبة المثلثية بتدخل وين؟ على + +764 +01:26:22,380 --> 01:26:27,850 +الزاوية، اللي بين قسين تعتبر زاوية لمين؟للـ sign + +765 +01:26:27,850 --> 01:26:33,510 +يبقى هذه بدها تساوي الـ sign افتح قرص يبقى ال + +766 +01:26:33,510 --> 01:26:38,030 +limit ندخل داخل ال sign على مين؟ على الزاوية يبقى + +767 +01:26:38,030 --> 01:26:43,110 +ال sign وهي limit دخلناها على مين؟ على الزاوية هذا + +768 +01:26:43,110 --> 01:26:49,760 +الكلام بده يساوي هاي ال signالان limit ال bus على + +769 +01:26:49,760 --> 01:26:54,380 +limit المقام limit المقدار الثابت بالمقدار الثابت + +770 +01:26:54,380 --> 01:27:01,860 +itself ten zero ب zero يبقى زائد zero على ten zero + +771 +01:27:01,860 --> 01:27:08,260 +ب zero ناقص اتنين six zero يبقى داشر بواحد يبقى + +772 +01:27:08,260 --> 01:27:14,280 +صارت المسألة sign لسالب pi على اتنين ال sign اد + +773 +01:27:14,280 --> 01:27:19,590 +والله evenيبقى سالب برا باي على اتنين ساي باي على + +774 +01:27:19,590 --> 01:27:26,850 +اتنين يبقى داشر بواحد يبقى سالب واحد هذا نمره نقطة + +775 +01:27:26,850 --> 01:27:33,350 +الأولى النقطة الثانية بدنا ال limit لما ال X بدها + +776 +01:27:33,350 --> 01:27:45,970 +تروح لل zero ل cosine باي X على صين ال Xبرضه بنفس + +777 +01:27:45,970 --> 01:27:52,010 +الطريقة cosine ال cosine و ال limit تدخل جوا على + +778 +01:27:52,010 --> 01:27:59,550 +الزاوية لما ال x بدي روح لل zero لل by x على sine + +779 +01:27:59,550 --> 01:28:05,570 +ال x و هي الساوية ال cosine ال by هذا مقدار ثابت + +780 +01:28:06,010 --> 01:28:11,390 +يبقى بقدر أطلعه برا ال limit وهذا ال limit لما ال + +781 +01:28:11,390 --> 01:28:17,510 +X بده تروح لل zero لل X على ال sign ال X هذا ال + +782 +01:28:17,510 --> 01:28:22,030 +limit كله بقداش يبقى هذا ال limit اللي في الداخل + +783 +01:28:22,030 --> 01:28:29,390 +كله بحصار cosine باي cosine 180 بقداش نفس الإجابة + +784 +01:28:29,390 --> 01:28:35,270 +اللي فوق للسؤال الأول النقطة الأخيرةالثالثة + +785 +01:28:35,270 --> 01:28:41,530 +والاخيرة بدنا limit لما theta بدها تروح لل πاية + +786 +01:28:41,530 --> 01:28:50,010 +على أربعة لتان theta ناقص واحد على ثيتا ناقص باية + +787 +01:28:50,010 --> 01:28:56,670 +على أربعة هذا يعني طيب بنلطف شكلها شوية هيك ونشوف + +788 +01:28:56,670 --> 01:29:02,170 +وين بدها توصل هالدنيا لو جيت قولتلك هذه عبارة عن + +789 +01:29:02,170 --> 01:29:09,200 +limitبقى أضيف سالب باى أربعة للطرفين يبقى بصير + +790 +01:29:09,200 --> 01:29:15,480 +ثيتا سالب باى على أربعة بدا تروح لوين لزيرو لمن + +791 +01:29:15,480 --> 01:29:23,060 +لتان ثيتا ناقص واحد على ثيتا ناقص باى على أربعة + +792 +01:29:23,060 --> 01:29:31,940 +ممكن أشيل الواحد و أحط بدله تان باى على أربعةصح؟ + +793 +01:29:31,940 --> 01:29:34,880 +ضل الخمسة و أربعين و واحد، بقى دي شوف الكلام عندك، + +794 +01:29:34,880 --> 01:29:40,620 +و بعد هيك أجيبها عن طريق اللي هو تان ناقص تان على + +795 +01:29:40,620 --> 01:29:44,960 +واحد مش عارف ايه، هي واحدة، طيب فكرة، فكرة تانية، + +796 +01:29:44,960 --> 01:29:48,380 +واحد قال لي بدي أشيل ت تناقص بيه أربع كلها و أحطها + +797 +01:29:48,380 --> 01:29:52,850 +ال variable الجديد، قول لله ماشيقال يعني في الـ H + +798 +01:29:52,850 --> 01:29:59,530 +مش هيك، حط لي X يساوي ثيتا ناقص Pi على أربعة، + +799 +01:29:59,530 --> 01:30:03,450 +قولنا له ماشي، قال لي يبقى X زائد Pi على أربعة + +800 +01:30:03,450 --> 01:30:07,310 +تساوي ثيتاأنا مش حافظ السبق اتبع التوجيه اللي يقول + +801 +01:30:07,310 --> 01:30:10,310 +هذا التوجيه هو الجواب يسوي مش ماليش علاقة بيها + +802 +01:30:10,310 --> 01:30:13,770 +احنا بنشتغل شغل رياضي مش حافظينه بدنا نطبق على + +803 +01:30:13,770 --> 01:30:17,570 +الحفظ العتيب احنا بنشتغل شغل رياضي سليم كأننا لا + +804 +01:30:17,570 --> 01:30:24,130 +نعرف شيئا عن السبق يبقى هذه بدها تصير ال limit لما + +805 +01:30:24,130 --> 01:30:31,700 +ال X بدها تروح لل zero لتان ثيتا ل Xزائد باي على + +806 +01:30:31,700 --> 01:30:39,600 +أربعة ناقص واحد كله على X يبقى المثال أخدت شكلًا + +807 +01:30:39,600 --> 01:30:44,760 +جديدًا يبقى هذا الكلام بيصير ال limit لما ال X + +808 +01:30:44,760 --> 01:30:50,700 +بدها تروح لل zero التان هذي بقدر أفكها يبقى باجي + +809 +01:30:50,700 --> 01:30:59,180 +بقوله تان ال Xزائد تان باي على أربعة على واحد ناقص + +810 +01:30:59,180 --> 01:31:06,300 +تان ال X تان باي على أربعة وعندي ناقص ولسه كله + +811 +01:31:06,300 --> 01:31:12,200 +مجسوم على X كل الخمسة واربعين بواحد هذا الكلام + +812 +01:31:12,200 --> 01:31:20,890 +يساويLimit لما الـ X بده يروح للـ Zero نجي لتان ال + +813 +01:31:20,890 --> 01:31:27,390 +X زائد واحد وضل الخمسة واربعين بواحد وضل الخمسة + +814 +01:31:27,390 --> 01:31:35,750 +واربعين بواحد على واحد ناقص تان ال X كله ناقص واحد + +815 +01:31:35,750 --> 01:31:42,520 +على Xطب ايش رايك نوحد المقامات للكل؟ فهذا الكلام + +816 +01:31:42,520 --> 01:31:50,220 +بده يساوي limit لما ال X بده يروح ل zero هذا شرط + +817 +01:31:50,220 --> 01:31:57,040 +الكسر و بده نوحد المقامات للكل واحد ناقص تاني ال X + +818 +01:31:57,040 --> 01:32:06,340 +بظل تاني ال X زائد واحد و بعد هيك ناقص واحدزائد + +819 +01:32:06,340 --> 01:32:12,620 +تان ال X وكله مقسوم على مين على X يبقى ال limit + +820 +01:32:12,620 --> 01:32:18,360 +لما ال X بده تروح لل zero ناقص واحد وزائد واحد مع + +821 +01:32:18,360 --> 01:32:25,920 +السلامة يبقى بصيري اتنين تان ال X على X في واحد + +822 +01:32:25,920 --> 01:32:33,810 +ناقص تان ال Xأو ان شئتم فقولوا يتنين خليك برا و + +823 +01:32:33,810 --> 01:32:41,070 +هاي limit لما ال X بده تروح ل zero لتان ال X على X + +824 +01:32:41,070 --> 01:32:49,890 +فمين في واحد على واحد ناقص تان ال X هذه حافظينها + +825 +01:32:49,890 --> 01:32:54,830 +ضمن الثانوية بواحد انا مش حافظها يبقى بده ساوي + +826 +01:32:54,830 --> 01:32:57,010 +تنين limit + +827 +01:33:07,440 --> 01:33:18,240 +Limit لما ال X تروح ل Zero واحد ناقص + +828 +01:33:18,240 --> 01:33:27,470 +تاني X يسوى اتنين وهذه كلها بواحدوهذه كلها بواحد + +829 +01:33:27,470 --> 01:33:34,150 +على cosine صفر بواحد وهذه zero وكمان بواحد يبقى + +830 +01:33:34,150 --> 01:33:40,670 +الجواب قداشر اتنين يبقى exercises تلاتة خمسة + +831 +01:33:40,670 --> 01:33:45,570 +المسائل التالية خلاص + +832 +01:33:45,570 --> 01:33:55,680 +exercises تلاتة خمسةالمسائل من واحد لسبعة و تلاتين + +833 +01:33:55,680 --> 01:34:00,440 +القد + +834 +01:34:00,440 --> 01:34:13,400 +و من تلاتة و اربعين لتلاتة و خمسين القد + +835 +01:34:13,400 --> 01:34:20,800 +طبعا و كذلك من سبعة و خمسين لغاية ستين + +836 +01:34:25,290 --> 01:34:25,970 +خدت واحدة + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OuNt_E3bc1Y.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OuNt_E3bc1Y.srt new file mode 100644 index 0000000000000000000000000000000000000000..eeb124bb01a1ac6a80e2114ce0e517793d45e526 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OuNt_E3bc1Y.srt @@ -0,0 +1,2716 @@ +1 +00:00:20,940 --> 00:00:24,620 +بسم الله الرحمن الرحيم الموضوع اللي قدر بين إيدينا + +2 +00:00:24,620 --> 00:00:28,480 +اليوم اللي هو one sided limit طبعًا ابتدأنا من + +3 +00:00:28,480 --> 00:00:32,540 +section 1 لغاية section 3 ما أخذنا في أي يوم من + +4 +00:00:32,540 --> 00:00:36,100 +الأيام ال limit من اليمين أو ال limit من الشمال + +5 +00:00:36,100 --> 00:00:39,540 +وإنما بجأنا نأخذ limit سعالية بدلًا من محكمة limit + +6 +00:00:39,540 --> 00:00:44,220 +ثم limit سعادية ثم ال section الماضي كان بواسط + +7 +00:00:44,220 --> 00:00:48,240 +epsilon و delta definition النظرية بتقول ليش؟ + +8 +00:00:48,240 --> 00:00:52,220 +بالبلدي قبل ما نقرأها روح نأخذ ال limit للدالة من + +9 +00:00:52,220 --> 00:00:56,380 +اليمين وال limit للدالة من الشمال إذا اثنين تساووا + +10 +00:00:56,380 --> 00:00:59,140 +يبقى ال limit exist وتساوي القيم اللي بتطلع هذا + +11 +00:00:59,140 --> 00:01:03,220 +باختصار، تمام؟ الكلام اللي سمعته هو مكتوب جبنانا، + +12 +00:01:03,220 --> 00:01:07,340 +بنقول a function f of x has a limit as x + +13 +00:01:07,340 --> 00:01:12,140 +approaches c لها limit لما ال x بتروح ل c and only + +14 +00:01:12,140 --> 00:01:16,970 +if و فقط إذا كان it has a left hand and right + +15 +00:01:16,970 --> 00:01:20,390 +hand limits إذا ال limit من اليمين موجودة وال + +16 +00:01:20,390 --> 00:01:24,570 +limit من الشمال موجودة عند تلك النقطة there يعني + +17 +00:01:24,570 --> 00:01:29,710 +هناك عند النقطة اللي عندنا هذه اللي هي c and these + +18 +00:01:29,710 --> 00:01:33,690 +limits are equal وال two limits هدول بيكونوا + +19 +00:01:33,690 --> 00:01:35,290 +متساويتين ذاتي + +20 +00:01:39,000 --> 00:01:42,480 +في السطر وبدأت صيغة رياضيًا بالسطرة اللي قدامنا + +21 +00:01:42,480 --> 00:01:46,020 +هذه فبجب أقول limit ال F of X لما ال X بدها تروح + +22 +00:01:46,020 --> 00:01:52,340 +إلى C يساوي ال L if and only if limit ال F of X + +23 +00:01:52,340 --> 00:01:56,440 +لما ال X بدها تروح إلى C من جهة اليسار بدها تساوي L + +24 +00:01:56,440 --> 00:01:59,620 +وفي نفس الوقت limit ال F of X لما ال X بدها تروح + +25 +00:01:59,620 --> 00:02:04,620 +إلى C من جهة اليمين بدها تساوي نفس النتيجة اللي هي + +26 +00:02:04,620 --> 00:02:08,690 +L يبقى إذا تساوت النتيجة للـ function من اليمين + +27 +00:02:08,690 --> 00:02:14,110 +والنتيجة من اليسار يبقى ال limit exists وتساوي هذه + +28 +00:02:14,110 --> 00:02:18,730 +القيمة اللي طلعت أنا بنبدأ نأخذ أمثلة مختلفة + +29 +00:02:18,730 --> 00:02:23,780 +على ميم على الكلام اللي قلنا هذا طبعًا أنا عارف أنه + +30 +00:02:23,780 --> 00:02:28,660 +بعض الأسئلة بتدور في دماغك، لكن هذه الأسئلة بدي + +31 +00:02:28,660 --> 00:02:34,500 +أجاوبها، بدي أسألها أنا وسنجاوب عليها بعد قليل، بس + +32 +00:02:34,500 --> 00:02:39,320 +نأخذ بعض الأمثلة على الـ graph of a function as + +33 +00:02:39,320 --> 00:02:42,280 +shown in the following figure رسمي اللي قدامنا هذه + +34 +00:02:42,280 --> 00:02:46,860 +بيقول احسب لل limit إذا كانت موجودة وإذا مش + +35 +00:02:46,860 --> 00:02:50,880 +موجودة مسامحينك فيها ال limit الأولى بيقول اللي + +36 +00:02:50,880 --> 00:02:54,240 +limit ال F of X لما ال X بدها تروح لسالب واحد من + +37 +00:02:54,240 --> 00:02:58,900 +جهة اليمين يبقى باجي لسالب واحد هي السالب واحد أنا + +38 +00:02:58,900 --> 00:03:03,180 +رايح له من جهة مين؟ من جهة اليمين يبقى الدالة كل ما + +39 +00:03:03,180 --> 00:03:06,200 +اقترب من سالب واحد من جهة اليمين الدالة طالعة + +40 +00:03:06,200 --> 00:03:12,300 +لمين؟ للواحد يبقى هذه ال limit تساوي واحد صحيح نجي + +41 +00:03:12,300 --> 00:03:16,140 +لبعدها limit ال f of x لما ال x بدها تروح ل zero + +42 +00:03:16,140 --> 00:03:21,160 +إذا روحت ل zero من جهة الشمال بلاقي هذه نزل أوين ل + +43 +00:03:21,160 --> 00:03:25,540 +zero وإذا روحت ل zero من جهة اليمين بلاقي هذه نزل + +44 +00:03:25,540 --> 00:03:29,380 +أوين ل zero يبقى ال limit من اليمين بدها تساوي ال + +45 +00:03:29,380 --> 00:03:33,500 +limit من الشمال يبقى بتساوي قداش zero الآن بنأخذ + +46 +00:03:33,500 --> 00:03:36,740 +limit لل F of X لما ال X بدها تروح لل واحد من جهة + +47 +00:03:36,740 --> 00:03:40,600 +اليسار يبقى احنا رايحين لل واحد من جهة اليسار + +48 +00:03:40,600 --> 00:03:44,600 +الدالة طالعة لوين؟ لل اثنين يبقى ال limit هنا + +49 +00:03:44,600 --> 00:03:50,660 +تساوي كده ايش؟ تساوي اثنين بنأخذ limit لل F of X لما + +50 +00:03:50,660 --> 00:03:54,620 +ال X بدها تروح لل واحد من جهة اليمين يبقى احنا + +51 +00:03:54,620 --> 00:03:59,020 +رايحين لل واحد من جهة اليمين بدي أقول الدالة رايحة + +52 +00:03:59,020 --> 00:04:09,800 +لوين؟ يبقى النتيجة تساوي واحد بناء عليه من جهة + +53 +00:04:09,800 --> 00:04:15,540 +اليمين بواحد من جهة الشمال باثنين اختلفت القيمتان + +54 +00:04:15,540 --> 00:04:20,760 +يبقى ال limit ما لها does not exist يبقى هذه بقوله + +55 +00:04:20,760 --> 00:04:30,300 +does not exist هذا الـ Limit + +56 +00:04:30,300 --> 00:04:31,640 +غير موجودة + +57 +00:04:41,980 --> 00:04:45,300 +أنا بدرس لك سؤال فيه أن ايه ال function بعد + +58 +00:04:45,300 --> 00:04:50,160 +الثلاثة؟ ما عنديش يبقى هذي does not exist مش موجودة + +59 +00:04:50,160 --> 00:04:56,400 +لأنه لا يوجد عندنا function يبقى كمان هذي does not + +60 +00:04:56,400 --> 00:05:02,470 +exist تمام؟ طيب نجي للي بعدها اللي هو نمرة ست سبعة + +61 +00:05:02,470 --> 00:05:05,690 +بيقول اللي limit ال F of X لما ال X بيطرح ده C + +62 +00:05:05,690 --> 00:05:11,070 +where C موجودة أي نقطة تأخذها في ال interval من + +63 +00:05:11,070 --> 00:05:14,630 +عند الواحد لغاية الثلاثة بشرط الثلاثة مش منهم + +64 +00:05:14,630 --> 00:05:19,750 +والواحد مش منهم يبقى داخل الفترة من واحد إلى ثلاثة + +65 +00:05:19,750 --> 00:05:26,100 +ال limit قداش؟ بينفعش أقول اثنين هنا؟ هذه القيمة + +66 +00:05:26,100 --> 00:05:30,340 +وليس أنا لما أجرب على الاثنين من جهة اليمين ومن + +67 +00:05:30,340 --> 00:05:34,760 +جهة الشمال بلاقي هذا مجرب على مين؟ على واحد يبقى + +68 +00:05:34,760 --> 00:05:41,390 +limit exist وتساوي قداش كلها وتساوي واحد صحيح يبقى + +69 +00:05:41,390 --> 00:05:45,890 +هذه ال limit أوجدناها من خلال الرسم طبعًا أعطيتكم + +70 +00:05:45,890 --> 00:05:50,230 +قبل ذلك سؤال من هذا الموديل هذا تمام؟ وهذا هو + +71 +00:05:50,230 --> 00:05:56,350 +سؤال ثاني طيب ننتقل الآن إلى نوعية أخرى من هذه + +72 +00:05:56,350 --> 00:06:05,930 +المسائل كمان مثال آخر بقول find the following + +73 +00:06:05,930 --> 00:06:09,490 +limits + +74 +00:06:12,350 --> 00:06:20,430 +if it exists إذا موجودة بدنا إياها مش موجودة بلاش نمرة + +75 +00:06:20,430 --> 00:06:27,750 +واحد limit لما ال X بدها تروح ليه ثلاثة ال absolute + +76 +00:06:27,750 --> 00:06:35,830 +value لل X ناقص ثلاثة على X تربيع ناقص X ناقص ستة + +77 +00:06:35,830 --> 00:06:39,930 +لو + +78 +00:06:39,930 --> 00:06:40,990 +جاء تعوض أيوة + +79 +00:06:45,000 --> 00:06:51,320 +بس أنا كدهش ال domain بالله بيقول زميلكوا ال + +80 +00:06:51,320 --> 00:06:54,760 +domain من سالب واحد لغاية ثلاثة + +81 +00:06:59,330 --> 00:07:05,330 +كل الدالة معرفة على جميع ال interval من سالب واحد + +82 +00:07:05,330 --> 00:07:10,090 +لغاية ثلاثة ما في مشكلة تقدر تجيب لي نقطة اللي بيقول + +83 +00:07:10,090 --> 00:07:14,210 +لأ تقدر تجيب لي نقطة الدالة غير معرفة عندها خلال + +84 +00:07:14,210 --> 00:07:18,970 +الفترة من واحد لثلاثة فيه؟ فهبقى أنا بدي أسألك + +85 +00:07:18,970 --> 00:07:23,980 +كمان سؤال ال range اللي هي قداش؟ اسمه عرضين ترويها، + +86 +00:07:23,980 --> 00:07:30,920 +السؤال ايه له؟ من صفر ل اثنين، من عند اثنين مفتوح + +87 +00:07:30,920 --> 00:07:36,300 +أو لا؟ لأ موجودة يبقى هذه closed من zero لغاية + +88 +00:07:36,300 --> 00:07:40,880 +اثنين ليش طلعت عند اثنين قيمة ده لا يساوي اثنين + +89 +00:07:40,880 --> 00:07:44,660 +هي مفتوحة لكن هي موجودة يبقى ال range closed + +90 +00:07:44,660 --> 00:07:49,680 +interval من zero لغاية اثنين ننتقل للسؤال الثاني + +91 +00:07:49,680 --> 00:07:53,760 +بدها limit لهذا المقدار لما ال X بدها تروح ليه ثلاثة + +92 +00:07:53,760 --> 00:07:59,260 +لو جاء تعوض مباشر يبقى البسط ب zero والمقام كذلك + +93 +00:07:59,260 --> 00:08:00,000 +ب zero + +94 +00:08:03,250 --> 00:08:07,730 +بنرجع الآن بالذاكرة إلى الوراء بتذكير فقط + +95 +00:08:07,730 --> 00:08:11,390 +بتعريف ال absolute value كنا نقول ال absolute + +96 +00:08:11,390 --> 00:08:16,190 +value ل X بيساوي X إذا ال X greater than or equal + +97 +00:08:16,190 --> 00:08:22,340 +to 0 وسالب X إذا ال X أقل من 0 خلي هذه المعلومة + +98 +00:08:22,340 --> 00:08:28,120 +هادية في دماغك ونحاول نقيص عليها يبقى إذا X موجبة + +99 +00:08:28,120 --> 00:08:33,460 +تبقى لابسولية فلل X هي X إذا X سالبة يبقى لابسولية + +100 +00:08:33,460 --> 00:08:38,050 +فلل X ساوية كده؟ سالب X طيب أنا الآن بدي أحسب هذه + +101 +00:08:38,050 --> 00:08:42,030 +ال limit بدي أجرب آخذ ال limit لما ال X بدها تروح + +102 +00:08:42,030 --> 00:08:46,570 +لثلاثة من جهة الشمال لل absolute value لل X ناقص + +103 +00:08:46,570 --> 00:08:51,110 +ثلاثة على X تربيع ناقص X ناقص ستة ويساوي ال limit + +104 +00:08:51,110 --> 00:08:55,800 +لما ال X بدها تروح لثلاثة من جهة الشمال طلع عليك + +105 +00:08:55,800 --> 00:08:59,860 +كويس، الآن أنا لما أروح لثلاثة من جهة الشمال، يعني + +106 +00:08:59,860 --> 00:09:04,680 +لما أقول هذا ال real line وهذا عند الثلاثة وأنا + +107 +00:09:04,680 --> 00:09:09,840 +رايح للثلاثة من جهة الشمال، يبقى أقل من ثلاثة ولا + +108 +00:09:09,840 --> 00:09:15,420 +أكثر؟ أقل من ثلاثة لما نطرحها من ثلاثة بتظهر كمية + +109 +00:09:15,420 --> 00:09:19,960 +سالبة يبقى مادام كمية سالبة إذا إن تعريفها ده + +110 +00:09:19,960 --> 00:09:24,600 +بتظهر الجزء زي ما هو بس بإشارة سالبة يبقى هذا بدي + +111 +00:09:24,600 --> 00:09:30,180 +يصير السالب ال X ناقص ثلاثة يبقى هي اتخلصت من ال + +112 +00:09:30,180 --> 00:09:33,580 +absolute value إذا ال X بتروح لثلاثة من جهة اليسار + +113 +00:09:33,580 --> 00:09:41,060 +والمقام بدي أحلله يبقى هاي X هاي X هنا اثنين + +114 +00:09:41,060 --> 00:09:46,700 +هنا ثلاثة هنا ناقص هنا زاد هاي زائد اثنين X + +115 +00:09:46,700 --> 00:09:50,880 +وناقص ثلاثة X بيبقى ناقص X بتحليلنا سليم مائة + +116 +00:09:50,880 --> 00:09:55,760 +بالمائة الجُث هذا بيروح مع الجُث هذا بتقول المسألة + +117 +00:09:55,760 --> 00:09:59,840 +إلى limit لما ال X بيروح لثلاثة من جهة اليسار + +118 +00:09:59,840 --> 00:10:06,020 +لسالب واحد على X زائد اثنين يبقى limit ال constant + +119 +00:10:06,020 --> 00:10:11,160 +بال constant itself هذا متعدد خطي يبقى تعويض مباشر + +120 +00:10:11,160 --> 00:10:17,220 +يبقى النتيجة تساوي كده؟ سالب خمسة طب تعال نشوف هنا + +121 +00:10:17,220 --> 00:10:22,760 +limit من اليمين يبقى limit لما ال X بدها تروح لثلاثة + +122 +00:10:22,760 --> 00:10:28,420 +من جهة اليمين لل absolute value لل X ناقص ثلاثة على + +123 +00:10:28,420 --> 00:10:33,680 +ال X تربيع ناقص X ناقص ستة يبقى limit لما ال X بدها + +124 +00:10:33,680 --> 00:10:37,240 +تروح لثلاثة من جهة اليمين + +125 +00:10:39,560 --> 00:10:45,280 +ثلاثة من جهة اليمين يبقى احنا هنا أكثر من ثلاثة + +126 +00:10:45,280 --> 00:10:51,200 +ثلاثة وكسر ناقص ثلاثة بدل هذا الكسر يبقى هذا دائمًا + +127 +00:10:51,200 --> 00:10:56,420 +وأبدًا قيمة موجبة مادام قيمة موجبة يبقى ال absolute + +128 +00:10:56,420 --> 00:11:03,360 +value للمقدار بالمقدار itself على من على X زائد + +129 +00:11:03,360 --> 00:11:09,100 +اثنين في X ناقص ثلاثة بالشكل اللي عندنا هذاتمام؟ + +130 +00:11:09,100 --> 00:11:14,460 +نختصر يبقى هنا هذا الجزء مع هذا الجزء ويساوي ال + +131 +00:11:14,460 --> 00:11:19,320 +limit لما ال X بدها تروح إلى ثلاثة من جهة اليمين + +132 +00:11:19,320 --> 00:11:25,800 +لواحد على X زائد اثنين تعويض مباشر واحد على ثلاثة + +133 +00:11:25,800 --> 00:11:30,640 +زائد اثنين يساوي قداش خمسة يبقى هل ال limit exist + +134 +00:11:30,640 --> 00:11:35,100 +ولا does not exist لأن ال limit من اليمين لا تساوي + +135 +00:11:35,100 --> 00:11:40,440 +ال limit من الشمال يبقى بروح بقول لسه limit لما ال + +136 +00:11:40,440 --> 00:11:46,300 +x بدها تروح لثلاثة absolute value ل x ناقص ثلاثة x + +137 +00:11:46,300 --> 00:11:56,790 +تربيع ناقص x ناقص ستة does not exist السبب because + +138 +00:11:56,790 --> 00:12:03,870 +أن ال limit من الشمال لا تساوي ال limit من اليمين + +139 +00:12:03,870 --> 00:12:08,370 +سالب خمسة لا تساوي خمسة وبالتالي ال limit ما لها + +140 +00:12:08,370 --> 00:12:10,370 +does not exist + +141 +00:12:12,930 --> 00:12:19,850 +المثال الثاني أمر اثنين لما + +142 +00:12:19,850 --> 00:12:26,010 +ال X بدها تروح إلى ثلاثة كذلك لمين؟ للجذر التربيعي + +143 +00:12:26,010 --> 00:12:33,090 +لثلاثة X في X ناقص ثلاثة على absolute value لل + +144 +00:12:33,090 --> 00:12:38,230 +X ناقص ثلاثة أنا بهمنيّش ال absolute في البسط ولا + +145 +00:12:38,230 --> 00:12:43,150 +في المقام بأثرّش عندي أنا بهمني النتيجة تبعتها + +146 +00:12:43,150 --> 00:12:47,450 +بأجي بقول برضه بدي آخذ ال limit من اليمين وال + +147 +00:12:47,450 --> 00:12:53,230 +limit من الشمال ونشوف شو النتج يبقى هاي limit لما + +148 +00:12:53,230 --> 00:12:58,650 +ال X بدها تروح لثلاثة من جهة اليسار للجذر التربيعي + +149 +00:12:58,650 --> 00:13:04,450 +لثلاثة X في X ناقص ثلاثة على absolute value لل X + +150 +00:13:04,450 --> 00:13:09,930 +ناقص ثلاثة يبقى limit لما ال X بتروح لثلاثة من جهتي + +151 +00:13:09,930 --> 00:13:16,170 +اليسار الآن الجذر التربيعي لثلاثة X ما له دعوة X + +152 +00:13:16,170 --> 00:13:19,930 +ناقص ثلاثة ما له دعوة نيجي هذا لما ال X بتروح + +153 +00:13:19,930 --> 00:13:24,590 +لثلاثة من جهتي الشمال هذه قيمة سالبة إذا بتخلص من + +154 +00:13:24,590 --> 00:13:29,180 +ال absolute value بحط مكانها ال X ناقص ثلاثة + +155 +00:13:29,180 --> 00:13:33,240 +بإشارة سالب، القوس هذا مع القوس هذا الله سهّل عليه + +156 +00:13:33,240 --> 00:13:37,900 +يبقى limit لما ال X بدها تروح لثلاثة من جهة اليسار + +157 +00:13:37,900 --> 00:13:44,020 +لسالب الجذر التربيعي لمين؟ لثلاثة X الآن ثلاثة في + +158 +00:13:44,020 --> 00:13:50,020 +ثلاثة بتسعة تحت الجذر بسالب ثلاثة نروح نأخذ ال + +159 +00:13:50,020 --> 00:13:54,820 +limit لما ال X بدها تروح إلى ثلاثة من جهة اليمين + +160 +00:13:54,820 --> 00:14:01,340 +لثلاثة X ناقص ثلاثة على absolute value لل X ناقص + +161 +00:14:01,340 --> 00:14:05,940 +ثلاثة يبقى limit لما ال X بدها تروح لثلاثة من جهة + +162 +00:14:05,940 --> 00:14:11,960 +اليمين لجذر ثلاثة X في X ناقص ثلاثة على ال X بيذهب + +163 +00:14:11,960 --> 00:14:16,800 +لـ 3 من جهة اليمين، يبقى هذه القيمة قيمة موجبة، + +164 +00:14:16,800 --> 00:14:23,120 +إذا نزيل ال absolute value ونكتبها كما هي بدون + +165 +00:14:23,120 --> 00:14:27,940 +absolute لأنها قيمة موجبة، بروح القوس هذا مع القوس + +166 +00:14:27,940 --> 00:14:33,320 +هذا، آلة المسألة إلى limit، لما ال X بيذهب لـ 3 + +167 +00:14:33,320 --> 00:14:40,550 +من جهة اليمين لجذر ثلاثة X يبقى النتيجة تساوي كده؟ + +168 +00:14:40,550 --> 00:14:45,630 +تساوي ثلاثة برضه ال limit من اليمين لا تساوي ال + +169 +00:14:45,630 --> 00:14:50,790 +limit من الشمال يبقى سا limit لما ال X بدها تروح + +170 +00:14:50,790 --> 00:14:57,230 +لثلاثة لجذر ثلاثة X في X ناقص ثلاثة على absolute + +171 +00:14:57,230 --> 00:14:59,590 +value ل X ناقص ثلاثة + +172 +00:15:07,730 --> 00:15:17,410 +ما هيّش موجودة طيب النقطة الثالثة بدنا limit لما + +173 +00:15:17,410 --> 00:15:25,280 +ال X كذلك بدها تروح ليه ثلاثة كلها ثلاثات اليوم X + +174 +00:15:25,280 --> 00:15 + +201 +00:18:30,240 --> 00:18:36,120 +أقول له ال limit لما الـ X بده يروح لـ 3 للـ X + +202 +00:18:36,120 --> 00:18:42,120 +ناقص دالة الأرض للـ X دالة السقف للـ X ناقص 2 + +203 +00:18:42,120 --> 00:18:50,580 +does not exist does not exist + +204 +00:18:53,440 --> 00:18:59,140 +السبب because أن ال limit من اليمين لا تساوي ال + +205 +00:18:59,140 --> 00:19:05,020 +limit من من من الشمال طيب دي أعطيك مثال زي هذا + +206 +00:19:05,020 --> 00:19:10,920 +شبهه وأشوف مارشو رأيك في الموضوع يبقى بدنا نيجي + +207 +00:19:10,920 --> 00:19:19,160 +ناخد limit لما الـ X بدها تروح لـ 3.6 لدالة + +208 +00:19:19,160 --> 00:19:21,940 +السقف لـ X على X itself + +209 +00:19:24,940 --> 00:19:31,020 +بتروح آخد limit لما الـ X بيروح لـ 3.6 + +210 +00:19:31,020 --> 00:19:40,720 +من جهة الشمال لمين؟ لدالة السقف على X ويسمى 3 + +211 +00:19:40,720 --> 00:19:45,320 +و 6 من 10 يعني قبل 3.6 يعني قداش + +212 +00:19:45,320 --> 00:19:53,180 +مثلا 3.5 3.5 ارفع على السقف 4 بصير + +213 +00:19:53,180 --> 00:19:59,000 +هذه 4 على 3.6 يعني قداش يعني + +214 +00:19:59,000 --> 00:20:07,480 +40 على 36 مظبوط يعني 10 على 9 + +215 +00:20:07,480 --> 00:20:14,840 +على 9 طب آخد لل limit لما الـ X بده يروح لـ 3.6 + +216 +00:20:14,840 --> 00:20:20,360 +من عشرة من جهة اليمين لدالة السقف لـ X على X و + +217 +00:20:20,360 --> 00:20:26,720 +يساوي 3.6 بده ياخد بعدها، إيه يعني؟ 3 و + +218 +00:20:26,720 --> 00:20:33,220 +7 من عشرة، نرفع على السقف هيبقى 4 على 3 و + +219 +00:20:33,220 --> 00:20:39,410 +6 من عشرة، هيها هاديبقى قداش الجواب 10 على + +220 +00:20:39,410 --> 00:20:46,290 +9 من الاتنين هدول مش بتقدر تستنتج أن ال limit + +221 +00:20:46,290 --> 00:20:52,490 +لما الـ X بده يروح لـ 3.6 لدالة + +222 +00:20:52,490 --> 00:20:58,530 +السقف على X يساوي قداش 10 على 9 طيب استنى شوية + +223 +00:20:58,530 --> 00:21:04,980 +احنا عندنا مثالين المثال الأول طلعت النتيجة عنده + +224 +00:21:04,980 --> 00:21:10,160 +قداش does not exist هنا 1 وفوق 0 صارت does + +225 +00:21:10,160 --> 00:21:16,520 +not exist وهي هذه دالة صحيح X هنا كمان دالة صحيح X + +226 +00:21:16,520 --> 00:21:21,320 +لكن طلعت النتيجة exist إيش ملاحظاتنا على هذا + +227 +00:21:21,320 --> 00:21:25,380 +الكلام؟ اتفضل الخطران الصحيح يكون في نقاط تحول في + +228 +00:21:25,380 --> 00:21:28,540 +جدر الـ .. و يكون عضو الصحيح يكون نقطة تحول و يكون + +229 +00:21:28,540 --> 00:21:31,700 +الـ .. على ناحية اليمين اللي يختلف على ناحية اليسار + +230 +00:21:31,700 --> 00:21:34,260 +قاعدة أو من النقاط اللي فيها عشاب سنة و 3 و + +231 +00:21:34,260 --> 00:21:37,300 +حصة 6 يكون نقاط داخلية داخل القرار على يمين + +232 +00:21:37,300 --> 00:21:40,210 +المجموعة نفس الـ .. نفس اللي من حياته الكلام صحيح + +233 +00:21:40,210 --> 00:21:45,870 +إذا ال limit عندي في حالة دالة صحيح C إذا ال limit + +234 +00:21:45,870 --> 00:21:50,390 +راحت لرقم صحيح بلق ال limit مازالت موجودة بس إذا + +235 +00:21:50,390 --> 00:21:54,530 +راحت لـ كثر بلق ال limit مالها موجودة في الغالب + +236 +00:21:54,530 --> 00:21:59,890 +ليش؟ لأن هذه الدالة اسمها step function دالة + +237 +00:21:59,890 --> 00:22:04,570 +القفزة أو الدالة الدرجية أو الدالة السلمية عند + +238 +00:22:04,570 --> 00:22:08,630 +العدد الصحيح بيحصل ال discontinuity أو بيحصل منين + +239 +00:22:08,630 --> 00:22:11,610 +القفزة بصير ال limit من اليمين تختلف عن ال limit + +240 +00:22:11,610 --> 00:22:16,110 +من الشمال وبالتالي ال limit ما لها does not exist + +241 +00:22:16,110 --> 00:22:23,350 +طيب نعطيك كمان مثال غير هذه الأمثلة ونشوف شو رأيك + +242 +00:22:23,350 --> 00:22:30,010 +فيه وبعدها بنطرح عدة تساؤلات أو بعض التساؤلات + +243 +00:22:30,010 --> 00:22:37,420 +ونشوف كيف بدنا نجاوب عليه آخذ كمان مثال رقم 5 + +244 +00:22:37,420 --> 00:22:51,720 +بيقول ما يأتي 5 بيقول بده limit للـ F of X لما + +245 +00:22:51,720 --> 00:23:00,900 +الـ X بدها تروح لـ 3 where الـ F of X أحد أمرين + +246 +00:23:02,380 --> 00:23:10,580 +الأمر الأول X تربيع ناقص 5 لما الـ X أقل من أو + +247 +00:23:10,580 --> 00:23:17,660 +يساوي 3 أو الجذر التربيعي لـ X زائد 13 لما + +248 +00:23:17,660 --> 00:23:20,360 +الـ X greater than 3 + +249 +00:23:44,700 --> 00:23:50,980 +هذا السؤال طبعا شكله يختلف عن شكل الـ 4 السابقة + +250 +00:23:50,980 --> 00:23:55,880 +أول سؤالين كانوا بيشتملوا على ال absolute value + +251 +00:23:55,880 --> 00:24:01,460 +القيمة المطلقة والسؤالين التانية كانوا بيشتملوا + +252 +00:24:01,460 --> 00:24:06,780 +على دالة العدد الصحيح سواء كانت integer floor + +253 +00:24:06,780 --> 00:24:11,820 +function أو integer ceiling function هذا السؤال + +254 +00:24:11,820 --> 00:24:17,100 +بيكون من جزئين يعني هذه piecewise function تبقى + +255 +00:24:17,100 --> 00:24:23,160 +مكونة منها من جزئين طيب بلاحظ أن الجزئين هدول + +256 +00:24:23,160 --> 00:24:29,290 +بيختلفوا عن بعض وين عند العدد رقم 3 إذا عندي + +257 +00:24:29,290 --> 00:24:33,570 +الـ 3 هذه ممكن آخد ال limit من اليمين ولا آخد ال + +258 +00:24:33,570 --> 00:24:36,530 +limit من الشمال بل إجباري لازم آخد ال limit من + +259 +00:24:36,530 --> 00:24:41,230 +اليمين و ال limit من الشمال إذا بدأت آخد limit + +260 +00:24:41,230 --> 00:24:47,090 +لما الـ X بده تروح لـ 3 من جهة الشمال للـ F of X + +261 +00:24:47,090 --> 00:24:51,450 +يبقى limit لما الـ X بده تروح لـ 3 من جهة الشمال + +262 +00:24:52,000 --> 00:24:56,940 +3 من جهة الشمال يعني احنا مالها أقل من 3 + +263 +00:24:56,940 --> 00:25:02,100 +وقد تساوي، إذا بيكون شكل الدالة هو من X تربيع + +264 +00:25:02,100 --> 00:25:06,880 +ناقص 5، يبقى X تربيع ناقص 5، هذه + +265 +00:25:06,880 --> 00:25:12,050 +polynomial من الدرجة الثانية يبقى تعويض مباشر يبقى + +266 +00:25:12,050 --> 00:25:16,510 +هذه بيصير 3 لكل تربيع ناقص 5 اللي هو قداش + +267 +00:25:16,510 --> 00:25:22,570 +4 بعد هيك بدنا نروح آخد limit الـ F of X لما الـ + +268 +00:25:22,570 --> 00:25:30,770 +X بده يروح لمن؟ لـ 3 من جهة اليمين Limit لما الـ X + +269 +00:25:30,770 --> 00:25:35,230 +بده يروح لـ 3 من جهة اليمين 3 من جهة اليمين + +270 +00:25:35,230 --> 00:25:39,950 +معناته الـ X مالها أكبر من 3 بيكون ال function + +271 +00:25:39,950 --> 00:25:45,950 +هي عبارة عن الجذر التربيعي لـ X زائد 13 + +272 +00:25:45,950 --> 00:25:51,370 +الآن لما آخدنا قوانين ال limit في ال section قبل + +273 +00:25:51,370 --> 00:25:57,770 +الماضي قالت هذا ال limit مالها الصلاحيات وبتدخل تحت + +274 +00:25:57,770 --> 00:26:02,710 +الجذر لما تدخل تحت الجذر اللي تحت الجذر دالة خطية + +275 +00:26:02,710 --> 00:26:08,490 +مدام دالة خطية يبقى تعويض مباشر يبقى النتيجة تساوي + +276 +00:26:08,490 --> 00:26:14,810 +الجذر لـ 3 زائد 13 اللي هو قداش 4 مدام + +277 +00:26:14,810 --> 00:26:18,930 +4 يبقى صارت النتيجة من اليمين اللي بلعب في + +278 +00:26:18,930 --> 00:26:23,840 +الجوال يرمي الجوال وإلا يبقى صارت ال limit من + +279 +00:26:23,840 --> 00:26:28,700 +اليمين زي ال limit من الشمال وبالتالي أصبح عندنا + +280 +00:26:28,700 --> 00:26:34,780 +ال limit للـ F of X لما الـ X بتروح لـ 3 exist وتساوي + +281 +00:26:34,780 --> 00:26:40,120 +كده؟ تساوي 4 يبقى ال limit في هذه الحالة يساوي 4 + +282 +00:26:40,120 --> 00:26:44,900 +بدنا نعطي كمان مثال على ال piecewise function بس + +283 +00:26:44,900 --> 00:26:59,620 +بشكل آخر المثال بيقول ما يأتي نمرة 6 ستة بيقولي أو + +284 +00:26:59,620 --> 00:27:03,940 +بيخلي example لحاله example جديد باعتباره يبقى هذا + +285 +00:27:03,940 --> 00:27:08,120 +example بيقول + +286 +00:27:08,120 --> 00:27:17,070 +لما الـ F of X يساوي أحد أمرين يا إما AX plus 1 + +287 +00:27:17,070 --> 00:27:23,230 +لما الـ X less than or equal to 3 يا إما AX + +288 +00:27:23,230 --> 00:27:29,890 +تربيع ناقص 1 لما الـ X greater than 3 find + +289 +00:27:29,890 --> 00:27:34,690 +the value + +290 +00:27:37,490 --> 00:27:49,230 +Find the value of the constant A + +291 +00:27:49,230 --> 00:28:00,530 +هات المقدار الثابت A such that بحيث أن limit + +292 +00:28:23,840 --> 00:28:30,940 +سؤال هذا زي السؤال اللي قبله لكن بفكرة جديدة طبعا + +293 +00:28:30,940 --> 00:28:35,140 +زي ما أنت شايف هو piecewise function دل مجزئي + +294 +00:28:35,140 --> 00:28:39,840 +لجزئين بدنا نقرأ هذا السؤال ونفهم ما هو المطلوب + +295 +00:28:39,840 --> 00:28:44,100 +منه السؤال ميعطيني الـ F of X على الشكل اللي قدامنا + +296 +00:28:44,100 --> 00:28:49,920 +X plus 1 لما X أقل من أو يساوي 3 و X تربيع + +297 +00:28:49,920 --> 00:28:54,710 +ناقص 1 لما X greater than 3 واللي هاتلي + +298 +00:28:54,710 --> 00:29:00,390 +مقبار ثابت A بحيث ال limit هذه مالها exist سؤال + +299 +00:29:00,390 --> 00:29:03,510 +اللي يقبله ماكنتش عارف أنا exist ولا لأ حسبت ال + +300 +00:29:03,510 --> 00:29:05,590 +limit من اليمين و ال limit من الشمال اللي جيتنا مع + +301 +00:29:05,590 --> 00:29:08,650 +بعضك وقلت لو exist what ساوي 4 هنا بقول لي لأ + +302 +00:29:08,650 --> 00:29:13,310 +ال limit exist بس هو مش عارفها ومن خلال هذا الكلام + +303 +00:29:13,310 --> 00:29:16,250 +بيقول لي هاتلي قيمة الثابت A بقول له مادام ال + +304 +00:29:16,250 --> 00:29:20,110 +limit exist إذا ال limit من اليمين تساوي ال limit + +305 +00:29:20,110 --> 00:29:24,610 +من الشمال يبقى أنا بده أحسب ال two limits وبعدين + +306 +00:29:24,610 --> 00:29:29,170 +بسويهم بعض وبجيب قيمة الثابت A أصبح يبقى بناء + +307 +00:29:29,170 --> 00:29:36,090 +عليه بدهجي أقول له بدهجي آخد limit الـ F of X لما + +308 +00:29:36,090 --> 00:29:42,790 +الـ X بده يروح لـ 3 من جهة الشمال يبقى هذا ال + +309 +00:29:42,790 --> 00:29:48,010 +limit لما الـ X بده يروح لـ 3 من جهة اليسار من + +310 +00:29:48,010 --> 00:29:53,550 +جهة اليسار يبقى X أقل من أو يساوي 3 يبقى الدالة + +311 +00:29:53,550 --> 00:30:01,430 +عبارة عن إيش؟ AX plus 1 يبقى AX plus 1 ويساوي + +312 +00:30:01,430 --> 00:30:07,050 +هذه الدالة دالة خطية يبقى عند حساب الليمت عوّض + +313 +00:30:07,050 --> 00:30:14,240 +تعويضا مباشرا يبقى دي بيصير 3A plus 1 بعد + +314 +00:30:14,240 --> 00:30:18,800 +هيك بروح آخد ال limit لما الـ X بده يروح لـ 3 من + +315 +00:30:18,800 --> 00:30:25,360 +جهة اليمين للـ F of X يبقى limit لما الـ X بده تروح + +316 +00:30:25,360 --> 00:30:32,220 +لـ 3 من جهة اليمين لمن للـ AX تربيع ناقص 1 X + +317 +00:30:32,220 --> 00:30:37,320 +أكبر من 3 يبقى تروح لـ 3 من جهة اليمين يبقى + +318 +00:30:37,320 --> 00:30:42,720 +بتكون هذه هيبالا، هذه البرنامج من الدرجة + +319 +00:30:42,720 --> 00:30:49,000 +الثانية، إذا تعويض مباشر يبقى A في 3 لكل تربيع + +320 +00:30:49,000 --> 00:30:56,080 +ناقص 1، يبقى 9A ناقص 1، من الاتنين هدول، + +321 +00:30:56,080 --> 00:31:01,730 +جال ال limit exists، يبقى باجي بقول له since بما أن + +322 +00:31:01,730 --> 00:31:09,990 +limit للـ F of X لما الـ X بيروح ليه 3 exists we + +323 +00:31:09,990 --> 00:31:15,190 +have إيش + +324 +00:31:15,190 --> 00:31:21,890 +بيحصل أن 3A زائد 1 بتساوي 9A ناقص + +325 +00:31:21,890 --> 00:31:26,730 +الـ 1 بنجيب الـ Aهات عن بعض و ال constants عن بعض + +326 +00:31:26,730 --> 00:31:32,530 +بيصير 6A يساوي 2 ومنها A يساوي قداش + +327 +00:31:32,530 --> 00:31:38,330 +1/3 إذا A لما تكون 1/3 هي اللي خلت ال limit + +328 +00:31:38,330 --> 00:31:42,750 +مالها exist يبقى فكرة السؤال مثل فكرة السؤال اللي + +329 +00:31:42,750 --> 00:31:49,100 +جاب له لكن فيها شغلة فنية جديدة شوية خلّينا نوقف + +330 +00:31:49,100 --> 00:31:56,140 +وقفة محاسبة مع النفس ونسأل بعض التسوئلات ونشوف كيف + +331 +00:31:56,140 --> 00:32:00,920 +بدنا نجاوب عليها احنا سابقا قبل أن آخذ هذا ال + +332 +00:32:00,920 --> 00:32:04,460 +section لا كنا بناخد نهاية من اليمين ولا نهاية من + +333 +00:32:04,460 --> 00:32:09,240 +الشمال اللي بيعطيني هذا السؤال وتك بضرب في المرافق بحلل + +334 +00:32:09,240 --> 00:32:15,020 +واختصر بمش عارف أعمل شغل زي هيك إيه لو بيطلع عياش + +335 +00:32:15,020 --> 00:32:16,480 +الجواب أن + +336 +00:32:19,360 --> 00:32:26,440 +السؤال هو متى نأخذ النهاية من اليمين والنهاية من + +337 +00:32:26,440 --> 00:32:29,620 +اليسار لل function اللي عندنا؟ + +338 +00:32:35,560 --> 00:32:40,740 +يعني قصدك لو كانت الدالة غير معرفة عندها نقطة، + +339 +00:32:40,740 --> 00:32:47,300 +كلام كويس، أيوة، + +340 +00:32:47,300 --> 00:32:51,980 +ماشي وجهة نظر سليمة، + +341 +00:32:51,980 --> 00:32:55,960 +نقاط تحول، كلام كويس + +342 +00:32:59,820 --> 00:33:06,680 +يبقى هذه الأمثلة اللي أعطناها اتعمد أجيبها أمثلة + +343 +00:33:06,680 --> 00:33:10,480 +على الحالات اللي بدنا نروح آخذ فيها ال limit من + +344 +00:33:10,480 --> 00:33:15,600 +اليمين و ال limit من اليسار لذلك بدنا نخليك تكتبها + +345 +00:33:15,600 --> 00:33:19,280 +بالعربي حتى وين ما تشوف مسألة من هذا القبيل تعرف + +346 +00:33:19,280 --> 00:33:24,460 +كيف نتجاوب عليها اكتب لي بالعربي متى نأخذ النهاية + +347 +00:33:24,460 --> 00:33:26,760 +من اليمين ومن اليسار + +348 +00:33:29,340 --> 00:33:35,300 +متى نأخذ أو نحسب النهاية من اليمين ومن اليسار + +349 +00:33:35,300 --> 00:33:43,780 +الإجابة في الحالات التالية في الحالات الـ 4 + +350 +00:33:43,780 --> 00:33:49,260 +التالية الحالة + +351 +00:33:49,260 --> 00:33:56,800 +الأولى إذا احتوت المسألة على + +352 +00:33:56,800 --> 00:33:58,560 +القيمة المطلقة + +353 +00:34:06,030 --> 00:34:17,470 +إذا احتوت المسألة على دالة صحيح سين ولا صحيح إكس + +354 +00:34:17,470 --> 00:34:24,150 +صحيح إكس بنجو سين بتقدر تكتب دالة السقف ودالة + +355 +00:34:24,150 --> 00:34:34,030 +الأرض دالة السقف ودالة الأرض للعدد الصحيح نمر + +356 +00:34:34,030 --> 00:34:45,940 +3 إذا كانت الدالة مجزئة إلى عدة أجزاء زي + +357 +00:34:45,940 --> 00:34:51,840 +السؤالين الاثنين الأخيرين هؤلاء اللي بقى نقولها + +358 +00:34:51,840 --> 00:34:58,800 +piecewise function دالة مجزئة إلى أجزاء نمر 4 + +359 +00:34:58,800 --> 00:35:06,380 +إذا كانت الدالة غير معرفة + +360 +00:35:08,580 --> 00:35:24,680 +عند النقطة المراد إيجاد النهاية عندها تمام؟ طبعا + +361 +00:35:24,680 --> 00:35:28,420 +هذه إن شاء الله هنتعرض لها في ال section مش القادم + +362 +00:35:28,420 --> 00:35:33,480 +اللي بعده هنرجع للنقطة الرابعة هذه الأخيرة إن شاء + +363 +00:35:33,480 --> 00:35:37,160 +الله ونعطي عليها أمثلة كثيرة أيضا + +364 +00:35:39,840 --> 00:35:47,580 +هي عندك مثال إيه؟ كيف؟ الأول ليش ما فنتوش؟ ليش ما + +365 +00:35:47,580 --> 00:35:52,560 +قلت إن أنا من هنا؟ ليه ولا هدى؟ أنت عندك X بتروح + +366 +00:35:52,560 --> 00:35:57,660 +لرقم، آخدت من الشمال قبل الرقم هذا، آخدت من اليمين + +367 +00:35:57,660 --> 00:36:02,280 +يعني بعد الرقم هذا، قبل الرقم هذا، لا السقف، بطلع + +368 +00:36:02,280 --> 00:36:05,980 +للرقم الصحيح اللي فوق، ده للأرض، بنزل للرقم الصحيح + +369 +00:36:05,980 --> 00:36:08,040 +اللي من تحت وكذا، الله بالسر علينا + +370 +00:36:21,870 --> 00:36:24,670 +خالصة طيب + +371 +00:36:37,650 --> 00:36:43,170 +الآن زي ما أنت شايف أعطيناك بدل المثال 5 وكلها + +372 +00:36:43,170 --> 00:36:47,270 +ما جبناش فيها سيرة النسب + +401 +00:40:50,350 --> 00:40:55,170 +بتنزل عند السالب by أكثر، بعدك بتصير أقل، أقل و + +402 +00:40:55,170 --> 00:40:59,750 +هكذا، و من الناحية الثانية بنفس الـ main بنفس الطريقة + +403 +00:40:59,750 --> 00:41:04,780 +اللي عندنا طيب الآن من الرسم اللي قدامنا هذه لو + +404 +00:41:04,780 --> 00:41:09,540 +روحت أخدت الـ limit من الشمال و الـ limit من اليمين + +405 +00:41:09,540 --> 00:41:17,040 +يبقى الـ limit لـ sin θ على θ لما θ بدأت تروح لـ zero من + +406 +00:41:17,040 --> 00:41:23,190 +جهة الشمال لو احنا روحنا لـ zero من جهة الشمال يبقى + +407 +00:41:23,190 --> 00:41:28,430 +الدالة بتروح للواحد يبقى هذه بتساوي واحد and + +408 +00:41:28,430 --> 00:41:36,150 +لو روحنا أخدنا الـ limit لـ sin θ على θ لما θ راحت لل + +409 +00:41:36,150 --> 00:41:44,720 +zero من جهة اليمين يبقى يساوي كمان؟ يساوي واحد يبقى + +410 +00:41:44,720 --> 00:41:50,060 +بناء عليه الـ limit اللي فوق هذا يبقى كم؟ واحد يبقى + +411 +00:41:50,060 --> 00:41:56,220 +هذا بده يعطيك دائما و أبدا أن الـ limit لمين؟ ل + +412 +00:41:56,220 --> 00:42:01,400 +sin theta على theta لما theta بدها تروح لل zero + +413 +00:42:01,400 --> 00:42:07,470 +بدها تساوي واحد رغم أنه عشان عند ال zero الدالة is + +414 +00:42:07,470 --> 00:42:12,950 +undefined ماهياش معرفة لأنه sin zero بـ zero صار + +415 +00:42:12,950 --> 00:42:16,590 +zero على zero كمية غير معينة وبالتالي الدالة هذه + +416 +00:42:16,590 --> 00:42:22,910 +مالها غير معرفة بهمنا الآن كيفية استخدام هذه + +417 +00:42:22,910 --> 00:42:29,750 +النظرية في حل المسائل المختلفة يبقى بنيجي نقولك + +418 +00:42:29,750 --> 00:42:39,650 +احسب للنهايات التالية إذا كانت موجودة example find + +419 +00:42:39,650 --> 00:42:45,970 +the following limits + +420 +00:42:45,970 --> 00:42:50,750 +النهايات + +421 +00:42:50,750 --> 00:42:57,130 +التالية نمرة واحد بعد ذلك بدنا الـ limit لما الـ X بدها + +422 +00:42:57,130 --> 00:43:04,190 +تروح لـ zero للـ sin X على 2 على X + +423 +00:43:11,440 --> 00:43:17,320 +طلع لهنا تاني للنظرية الـ limit sin θ على θ لما θ + +424 +00:43:17,320 --> 00:43:22,640 +بتروح للزيرو يساوي واحد، بدي الزاوية، هي نفسها + +425 +00:43:22,640 --> 00:43:27,400 +اللي هنا، هي نفسها اللي بدها تروح لمين، للزيرو + +426 +00:43:28,620 --> 00:43:34,000 +بعدين بطلع في مثلث هنا X على 2 وهنا X وهنا X بدي + +427 +00:43:34,000 --> 00:43:38,240 +هدي X على 2 و بدي هدي X على 2 وبالتالي بقدر أستخدم + +428 +00:43:38,240 --> 00:43:42,800 +النظرية مباشرة يعني كأنه ثيتا صارت في الجداش ثيتا + +429 +00:43:42,800 --> 00:43:48,880 +على 2 بقوله بسيطة يعني هنا لو هدي كانت X على 2 كان + +430 +00:43:48,880 --> 00:43:53,980 +المشكلة انحلت صحيح ولا لا؟ يبقى بقول أضرب في نص و + +431 +00:43:53,980 --> 00:44:02,830 +أقسم على نص ما بتتغير القيمة يبقى بناء عليه هذي بدها + +432 +00:44:02,830 --> 00:44:09,110 +تساوي الـ limit لما الـ X بدها تروح لمين؟ لـ Zero ل + +433 +00:44:09,110 --> 00:44:19,100 +نص sin X على 2 على X على 2 صارت هذه الزاوية هي + +434 +00:44:19,100 --> 00:44:24,820 +اللي تحت، بس هذه لأ، بقول أضرب هذه في نص، بصير نص + +435 +00:44:24,820 --> 00:44:31,000 +في X، نص في X، نص في Zero، بـ Zero، يبقى هذا الكلام + +436 +00:44:31,000 --> 00:44:37,920 +يساوي، النص هذا بدي أخليه برا هيوهذا الـ limit هذي + +437 +00:44:37,920 --> 00:44:46,300 +بتصير نص الـ X والله الـ X على 2 الـ X على 2 تروح لل Zero لمن؟ + +438 +00:44:46,300 --> 00:44:53,630 +لـ sin X على 2 على X على 2 صارت الزاوية اللي هنا هي + +439 +00:44:53,630 --> 00:44:59,230 +اللي هنا هي اللي هنا يبقى نص في واحد يبقى الجواب + +440 +00:44:59,230 --> 00:45:04,710 +يساوي قداش يساوي نص يعني المطلوب منك إنك تحور + +441 +00:45:04,710 --> 00:45:09,270 +المسألة تبعتها تكون على شكل النظرية وبالتالي + +442 +00:45:09,270 --> 00:45:10,850 +باستخدام النظرية أيضا + +443 +00:45:30,660 --> 00:45:33,460 +مثال اثنين + +444 +00:45:40,820 --> 00:45:46,020 +مثال اثنين بنحسب الـ limit لما الـ X بدها تروح لل zero + +445 +00:45:46,020 --> 00:45:57,840 +لـ tan خمسة X على من؟ على ثلاثة X أول + +446 +00:45:57,840 --> 00:46:05,720 +شيء هدي tan وليست sin اثنين اثنين الزاوية عندي + +447 +00:46:05,720 --> 00:46:13,690 +خمسة X واللي تحت مالها ثلاثة X مضروبة في ايش؟ ولا + +448 +00:46:13,690 --> 00:46:17,670 +مدي مضروبة في خمسة أو ثلاثة ولا عادي بس اسمعني كويس + +449 +00:46:17,670 --> 00:46:24,650 +اسمع كويس بس بدنا نمشي step by step خطوة بخطوة أنا + +450 +00:46:24,650 --> 00:46:28,890 +بقول بدل الثلاثة هذه لو كانت خمسة كانت مشكلتي + +451 +00:46:28,890 --> 00:46:33,570 +محلولة يبقى يا تلف بدها تخليك برا وبعدك بدنا نضرب في + +452 +00:46:33,570 --> 00:46:38,130 +خمسة ونقسم على خمسة أو على رأيكم نضرب في خمسة على + +453 +00:46:38,130 --> 00:46:43,230 +ثلاثة ونقسم على خمسة على ثلاثة كلام مظبوط وماحدش + +454 +00:46:43,230 --> 00:46:48,560 +له اعتراض على ذلك اسمه يا ابن ايه؟ يبقى أنا بدي + +455 +00:46:48,560 --> 00:46:53,460 +أخلي هذه بدل ثلاثة بدي أخليها خمسة يبقى بدنا + +456 +00:46:53,460 --> 00:46:57,460 +نضرب في خمسة على ثلاثة وهنا نضرب في خمسة على ثلاثة + +457 +00:46:57,460 --> 00:47:02,740 +بيصير الكلام صحيح يعني هذه بدها تصير الـ limit هاي + +458 +00:47:02,740 --> 00:47:12,440 +خمسة على ثلاثة الـ tan عبارة عن sin خمسة X على هذه + +459 +00:47:12,440 --> 00:47:17,860 +صارت ثلاثة مع ثلاثة صارت خمسة X وهنا cos + +460 +00:47:17,860 --> 00:47:25,620 +خمسة X يبقى 10 عملتها sin على cos ضربت في + +461 +00:47:25,620 --> 00:47:29,640 +خمسة على ثلاثة وأنا ضربت في خمسة على ثلاثة راحت + +462 +00:47:29,640 --> 00:47:36,300 +الثلاثة مع ثلاثة ضلت كدهش ضلت خمسة بقول كويس هذه + +463 +00:47:36,300 --> 00:47:43,320 +الـ X بدها تروح لوين لـ zero الآن هذا مقدار ثابت، بقوله + +464 +00:47:43,320 --> 00:47:48,660 +شرفنا برا، يبقى هذا مقدار ثابت خليك برا، وهذا + +465 +00:47:48,660 --> 00:47:58,130 +الـ limit، وهذا sin خمسة X على خمسة X هذا يا شباب لما + +466 +00:47:58,130 --> 00:48:03,910 +تبقى الـ X بدها تروح لل Zero لو ضربتها في خمسة + +467 +00:48:03,910 --> 00:48:08,250 +بيصير خمسة X بتروح لـ Zero في خمسة ليه بيبقى داشت؟ + +468 +00:48:08,250 --> 00:48:14,470 +Zero يبقى الذي يكافئ هذه هي خمسة X بدها تروح لمين؟ + +469 +00:48:14,470 --> 00:48:21,370 +لل Zero By للـ مين؟ الـ limit لما الـ X بدها تروح لـ Zero + +470 +00:48:21,370 --> 00:48:30,670 +لواحد على Cos 5X يعني جزأتي الـ limit لمن؟ الـ limit للدالة + +471 +00:48:30,670 --> 00:48:34,510 +الأولى هذه اللي عندنا و الـ limit للدالة الثانية + +472 +00:48:34,510 --> 00:48:40,450 +الأولى ضربت الساهم هذا في خمسة والثاني خليته زي ما + +473 +00:48:40,450 --> 00:48:44,950 +هو يبقى النتيجة بتساوي هذه الخمسة اعتلتها اللي برا + +474 +00:48:44,950 --> 00:48:50,720 +بالداخل هذه أليست في صيغة النظرية اللي قدامي هذه + +475 +00:48:50,720 --> 00:48:56,200 +إذا بقدر أشيلها وأكتب لها قداش واحد صحيح بيبقى + +476 +00:48:56,200 --> 00:49:03,680 +هذه واحد على عوض تعد ماش الـ cos صفر بواحد يبقى + +477 +00:49:03,680 --> 00:49:09,480 +على واحد إذا النتيجة بتساوي ايش خمسة على ثلاثة + +478 +00:49:18,340 --> 00:49:24,300 +بتسمعش بيقول من هنا بدي أقسم البسط والمقام على + +479 +00:49:24,300 --> 00:49:29,120 +X بصير الثلث برا وبصير tan خمسة X على X + +480 +00:49:33,460 --> 00:49:38,540 +يعني أنت بصير المقام شيلته وصار كله في البسط والبسط + +481 +00:49:38,540 --> 00:49:42,560 +بسط على مقام مكانك لم تأتي بجديد + +482 +00:49:55,270 --> 00:50:01,370 +أنا بديش حفظ الهفظ، أنا بدي تفهم كيف توصل مسألتك + +483 +00:50:01,370 --> 00:50:06,150 +إلى صيغة النظرية، وهذا هو الشغل الرياضي، اسمع + +484 +00:50:06,150 --> 00:50:10,120 +كويس، افهمني كويس أنا ما أريد منك حفظ، أنا أريد منك + +485 +00:50:10,120 --> 00:50:14,380 +فهم، أريد منك تفهم كيف اجت، بقول أخذنا فتنة، بقولك + +486 +00:50:14,380 --> 00:50:17,760 +صح، اللي أخذته في ثانوية عامة صح، بس هذا أنت حفظت + +487 +00:50:17,760 --> 00:50:21,280 +حفظت، من حد ما تشوف الرقم X بالرقم على الرقم وامشي، + +488 +00:50:21,280 --> 00:50:26,000 +لو عملت في الجامعة بنحطلك علامة استفهام من أين لك + +489 +00:50:26,000 --> 00:50:30,160 +هذا، وده السؤال عليه أربع علامة يمكن نحطلك علامة، + +490 +00:50:30,160 --> 00:50:34,400 +بس والثلاثة بتطيروا في الجامعة يا شباب justify + +491 +00:50:34,400 --> 00:50:39,240 +your answer يعني بتبين إجابتك من وين جبتها، ما هو + +492 +00:50:39,240 --> 00:50:42,840 +جبتها إذا حطيت الإجابة دغري أنا أفهم أنه أحد + +493 +00:50:42,840 --> 00:50:48,620 +أمرين، يا إما عندك الـ fox تبعك هذا اللي هو على + +494 +00:50:48,620 --> 00:50:52,560 +الحاسبة، من نوع fox بتعطيك الإجابة دغري، بتعطيكش + +495 +00:50:52,560 --> 00:50:56,850 +خطوات، يا إما الـ radar جابها يمين أو شمال أو واحدة + +496 +00:50:56,850 --> 00:51:00,710 +من الاثنين، مالهاش تفيدنا من غير هيك، ولذلك تاخدش + +497 +00:51:00,710 --> 00:51:05,570 +عليها شيء، لأ أنا بقولك خلّي كل خطوة وتختصرش، و + +498 +00:51:05,570 --> 00:51:09,270 +أنت بتحل إياك أن تختصر، خليني كل خطوة أتسلم + +499 +00:51:09,270 --> 00:51:13,090 +للتانية، لأن احنا بنحط علامات على الخطوات وليس على + +500 +00:51:13,090 --> 00:51:16,610 +الإجابة النهائية، يعني ممكن تبقى خطواتك صح وأنت + +501 +00:51:16,610 --> 00:51:21,450 +غلط بس في الإجابة النهائية، بنحطلك مش أقل من تسعين + +502 +00:51:21,450 --> 00:51:26,190 +في المئة من الدرجة لكن أنا بتحطلي جواب بعطيك درجة، + +503 +00:51:26,190 --> 00:51:31,550 +بعطيك عشرين في المئة بس، اه؟ هو بعد هيك في أسئلة + +504 +00:51:31,550 --> 00:51:35,710 +في الليل في الزوايا المثلثية في المعدد، أحل الصلاة + +505 +00:51:35,710 --> 00:51:38,870 +صفحات لغير ما كنتوا حتى الحاجات حتتوا، قبل ما توصل + +506 +00:51:38,870 --> 00:51:42,430 +لقميها اللي بطبصي، الحل حيكون صفحة. فأنت شو قلتلك + +507 +00:51:42,430 --> 00:51:47,600 +هنا؟ بهمنا .. أنا بهميش اللي هو الجامعة، بهمني + +508 +00:51:47,600 --> 00:51:51,400 +الخطوات الرياضية، طريقة الحل، هي اللي أنا بتهمني + +509 +00:51:51,400 --> 00:51:56,320 +وأنا بوزع الدرجات على خطوات الحل، الخطوة ما ألاقيش + +510 +00:51:56,320 --> 00:52:00,920 +بطيب درجتها، هي كاننا في الجامعة، يعني بدنا الطالب + +511 +00:52:00,920 --> 00:52:05,840 +يطلع فاهم مش حافظ، أنك تطلع فاهم، كويس، هي سؤال، + +512 +00:52:05,840 --> 00:52:06,080 +اه + +513 +00:52:10,830 --> 00:52:15,430 +فهمتش؟ أقولك اشتغل رياضي صح، ما أقولش لك أي حاجة، + +514 +00:52:15,430 --> 00:52:19,010 +لكن تيجي من فوق تقلب غربة النصارى، اغلب الوجهة + +515 +00:52:19,010 --> 00:52:22,170 +تقول لك يالا بدك تنزلي تحت الأعمارة، من الشباب + +516 +00:52:22,170 --> 00:52:26,090 +فطيت ونزلتي تحت طب وأنت ممكن تنكسر، هذا إذا ما + +517 +00:52:26,090 --> 00:52:30,290 +موتتش، وممكن تنزلي مع الدرجة، وممكن تنزلي مع + +518 +00:52:30,290 --> 00:52:34,090 +اللصان صغير، أنا بدي تمشي لي ماشية صحية، ماحدش + +519 +00:52:34,090 --> 00:52:40,770 +يقول لك كده غلط، واضح؟ أيوة في اختيارات اضطرارية، يجب + +520 +00:52:40,770 --> 00:52:44,850 +أن تحولها للصيغة الـ x² على الـ x بدي الصيغة هذه + +521 +00:52:44,850 --> 00:52:48,470 +لتطبيق النظرية، بدي الصيغة على الشكل هذا أو الشكل + +522 +00:52:48,470 --> 00:52:55,450 +هذا؟ بدي أكتب له السؤال أنه بده هذه الصيغة؟ لأ + +523 +00:52:55,450 --> 00:52:59,630 +بكتبش لك، بكتب لك هاتين ليموت وبسكت، وأنت لعلك و + +524 +00:52:59,630 --> 00:53:04,080 +أنت تحطها في الصيغة هذه وتحطها للجواب طيب السؤال + +525 +00:53:04,080 --> 00:53:07,940 +اللي بعده لسه أسئلة فنية كتير هي بس هذا أنا لسه + +526 +00:53:07,940 --> 00:53:12,360 +بفتحلك الخيط شوية شوية لسه .. لسه .. لسه في أسئلة + +527 +00:53:12,360 --> 00:53:20,940 +كتير خد السؤال اللي بعده ثلاثة بدي الـ limit لما الـ X + +528 +00:53:20,940 --> 00:53:30,680 +بدها تروح لـ zero لـ X زي الـ X في cos X على sin X في + +529 +00:53:30,680 --> 00:53:31,900 +cos X + +530 +00:53:36,220 --> 00:53:43,560 +سؤال بقول X زائد X في cos X على sin X في cos X مقترح + +531 +00:53:43,560 --> 00:53:49,380 +بيقول نوزع البسط على المقام بيقول لك خير نجرب نوزع + +532 +00:53:49,380 --> 00:53:54,260 +نشوف نوصل لنتيجة ولا بنوصلش لنتيجة يبقى هذه ال + +533 +00:53:54,260 --> 00:54:01,660 +limit لما الـ X بدها تروح لل zero لل X على sin X cos + +534 +00:54:01,660 --> 00:54:14,550 +X زائد X في cos X على sin X في cos X بقوله تبعرح + +535 +00:54:14,550 --> 00:54:20,530 +قال لي وزع الـ limits قلنا له ماشي high limit لما + +536 +00:54:20,530 --> 00:54:29,110 +الـ X بدها تروح لل zero لل X على sin X في الـ limit لما + +537 +00:54:29,110 --> 00:54:35,370 +الـ X بدها تروح لـ zero لواحد على cos X زائد + +538 +00:54:35,370 --> 00:54:40,930 +الـ limit لما الـ X بدها تروح لـ zero اختصرنا هذه مع هذه + +539 +00:54:40,930 --> 00:54:49,350 +وصارت X على sin X قول له تمام هذه كلها بقداش؟ + +540 +00:54:49,350 --> 00:54:53,410 +بواحد مضروبة + +541 +00:54:53,410 --> 00:55:00,930 +فيه هذه واحد على cos صفر بقداش؟ بواحد زائد هذه كمان + +542 +00:55:00,930 --> 00:55:07,150 +بواحد يبقى الجواب يساوي قداش؟ اثنين واحد ثاني قال لي + +543 +00:55:07,150 --> 00:55:11,280 +لا لا لا أنا ما بديش الطريقة هذه قلت له أيوة قال لي + +544 +00:55:11,280 --> 00:55:14,580 +بدي أروح أضرب البسط كله في اثنين والمقام في + +545 +00:55:14,580 --> 00:55:19,320 +اثنين بس أنا شغل العساب المثلثات شوية صار تعطينا + +546 +00:55:19,320 --> 00:55:33,800 +اثنين sin X cos X بـ sin اثنين X بـ sin + +547 +00:55:33,800 --> 00:55:45,660 +اثنين X بـ sin اثنين X بـ sin اثنين X + +548 +00:55:45,750 --> 00:55:51,530 +يبقى ليحل بالحل الأول سليم وليحل بالحل الثاني سليم + +549 +00:55:51,530 --> 00:56:01,730 +كذلك ما عندي مشكلة في هذه الحالة مثال + +550 +00:56:01,730 --> 00:56:06,050 +رقم أربعة بقول + +551 +00:56:06,050 --> 00:56:14,720 +الـ limit لما الـ X بدها تروح لل Zero لـ tan ثلاثة X على + +552 +00:56:14,720 --> 00:56:23,400 +sin ثمانية X سؤال كذلك من أسئلة الكتاب هذا كنا + +553 +00:56:23,400 --> 00:56:26,760 +بناخده زي في التوجيه يبقى الجواب ثلاثة على ثمانية مش + +554 +00:56:26,760 --> 00:56:35,470 +هيك طبعا؟ ايش بدك تقول؟ ما + +555 +00:56:35,470 --> 00:56:40,510 +شبهتش فيها نهاية أنا حللت والساعة ثانية حولت + +556 +00:56:40,510 --> 00:56:44,550 +القصايل على القصايل وحللت هذه نتيجة على نظرية أنت + +557 +00:56:44,550 --> 00:56:48,790 +أخذتها بس أنا ما بعرفش فاهم لما أقول لك أنا ما بعرفش؟ أنا + +558 +00:56:48,790 --> 00:56:55,140 +كمصحح بدأت أغلي باللي أعطيته لكمش يعني ايه؟ لأن + +559 +00:56:55,140 --> 00:56:57,940 +السؤال ممكن ما تجيش وورقتك معايا، ممكن تيجي مع + +560 +00:56:57,940 --> 00:57:04,340 +غيري، ما مر علي الكلام هذا، اه مثلا يعني، طيب، على + +561 +00:57:04,340 --> 00:57:08,680 +أي حال، بعدين بطلع في مسألة هذه، أنا عندي كل اللي + +562 +00:57:08,680 --> 00:57:12,120 +بعرفه صح، يمكن تحول المسألة بدلالة sin وتكون sin + +563 +00:57:12,610 --> 00:57:19,750 +يبقى هذه المثلث بتساوي الـ limit لما الـ x يروح لـ zero ل + +564 +00:57:19,750 --> 00:57:32,210 +sin 3x على sin 8x في 1 على cos 3x يبقى شيلنا الـ tan + +565 +00:57:32,210 --> 00:57:37,770 +وحطينا قيمتها وبعدين بوزع الـ limit على كل منها + +566 +00:57:37,770 --> 00:57:45,290 +يبقى هذا بيساوي الـ limit لما الـ x بيذهب لوين؟ لـ 0 ل + +567 +00:57:45,290 --> 00:5 + +601 +01:01:30,110 --> 01:01:34,290 +جرادة يبقى تمر جرادة لم تأتِ بجديد أنت قررت ما + +602 +01:01:34,290 --> 01:01:38,910 +قاله محمد العشي بس بدلت خطوة مكان خطوة ولم تأتِ + +603 +01:01:38,910 --> 01:01:44,210 +بأي جديد صحيح؟ اللي بده يرفع يده يعطيني فكرة جميلة + +604 +01:01:44,210 --> 01:01:49,650 +لم تخطر على بالنا مثلًا أو ما استوعبت خطوة وبسأل عليها + +605 +01:01:49,650 --> 01:01:52,710 +هي اللي بدنا مش بدنا نكرر نفس الكلام أيوة + +606 +01:02:04,540 --> 01:02:11,150 +الحل اللي بيكون عندك x بدها تروح لـ 0 تمام؟ لو + +607 +01:02:11,150 --> 01:02:14,830 +ضربتها في ثلاثة بيصير ثلاثة X بتروح ثلاثة في Zero + +608 +01:02:14,830 --> 01:02:19,970 +بقدّاش Zero طب اللي هو العكس أنا عندي ثلاثة X بتروح + +609 +01:02:19,970 --> 01:02:25,810 +لـ Zero ضربتها في ثلاثة إيش بيصير؟ يبقى هيها ولا لا؟ + +610 +01:02:25,810 --> 01:02:31,890 +ما عنديش مشكلة فيها اه أنت الـ X لما .. لما خذتها + +611 +01:02:31,890 --> 01:02:37,130 +ثمانية؟ قل سؤالك أترحب؟ اه + +612 +01:02:42,990 --> 01:02:48,470 +تعال هي بشوف لا + +613 +01:02:48,470 --> 01:02:52,970 +ممكن بس كده سؤال احنا مش ماخذين تعال تفضل شباب أنا + +614 +01:02:52,970 --> 01:02:56,990 +مش شايف إن أنا مصطلح أش كتب من هنا اه على حين جامب + +615 +01:02:56,990 --> 01:03:01,690 +بوز إن هي ثانية في خاعد أخذناها بالأول ثمانية و ثلاثة + +616 +01:03:01,690 --> 01:03:04,710 +x على x ثلاثة قدر من هنا ثمانية و ثمانية x على + +617 +01:03:04,710 --> 01:03:08,290 +x ثمانية أنا كتاب ثلاثة x على x بيساوي واحد + +618 +01:03:08,290 --> 01:03:11,690 +دغري لأ بيساوي ثلاثة مش واحد + +619 +01:03:13,950 --> 01:03:18,750 +ما فيش تطلع إجابتك بقى في الكلام sound + +620 +01:03:18,750 --> 01:03:21,810 +ثلاثة x على x صوت ثلاثة مباشرة مين اللي قال هذا + +621 +01:03:21,810 --> 01:03:25,970 +الكلام يبقى خلاص بدّه نمسح النظرية ونقول الكلمة + +622 +01:03:25,970 --> 01:03:29,910 +أخذناه في التلوية يا زلمة كلامك غلط أنت فاهم غلط + +623 +01:03:29,910 --> 01:03:35,750 +لماذا؟ هكذا طب هي الثلاث احتمالية لا لا لا يا + +624 +01:03:35,750 --> 01:03:39,550 +ابني ما بدّيش تحفظ حفظ ما بتفهم الخطوات هذه كم فرق + +625 +01:03:39,550 --> 01:03:42,730 +ما بتفهمش نظرية خدام ما بتفهمش نظرية خدام ما بتفهمش + +626 +01:03:46,370 --> 01:03:51,490 +x على x بيساوي الأرض اللي هو الأرض اللي هنا فاكر + +627 +01:03:51,490 --> 01:03:57,410 +أكثر من الأرض ساين الأرض لأنه عدد يعني ماشي فاكر + +628 +01:03:57,410 --> 01:04:01,510 +أكثر من الأرض الـ x على x بيساوي الأرض هذا نفسه مين + +629 +01:04:01,510 --> 01:04:03,810 +قال هذا لو كانت البعض الشيخ أستاذ مواطن أنا جابت + +630 +01:04:03,810 --> 01:04:07,910 +عليه يعني أنا ما أدوش شمالي + +631 +01:04:20,520 --> 01:04:25,460 +هذا نص النظرية هيك؟ اللي أخذناها توّ هيك بنص؟ لأ، + +632 +01:04:25,460 --> 01:04:29,080 +ممتاز جدا، يبقى هذا كلام خطأ، لو أحطه، بحط لك عليه + +633 +01:04:29,080 --> 01:04:33,880 +سفر، لأن الزاوية اللي فوق هي زاوية تحت، بدّي يكون + +634 +01:04:33,880 --> 01:04:39,620 +هذا هيك، شوف يا بداية جيت على الجامعة بنا نسخل + +635 +01:04:39,620 --> 01:04:44,200 +عقليتك و نفهمك تفهم صحيح بقول لك من أول مرة ما بدّيش + +636 +01:04:44,200 --> 01:04:49,940 +ياك تبقى صاميم بدّيك تبقى فاهم حتى تقدر بعد أربع + +637 +01:04:49,940 --> 01:04:54,240 +سنين توقف مكان هنا و تبقى معيد و تفهم الطلاب هذا + +638 +01:04:54,240 --> 01:04:57,620 +اللي بدّيك إيّاه، ما بدّيش تبقى حافظ و تقوله خدها و امشي + +639 +01:04:57,620 --> 01:05:04,000 +و خدها و امشي، لا يا عم تفضل لما ناخذ الاشتراك من + +640 +01:05:04,000 --> 01:05:07,840 +اللي نحكي، ليه السادسين الاشتراك بصراحة للاستعجال + +641 +01:05:07,840 --> 01:05:14,160 +الشباب؟ كل حديثة حديثة، أيوة صارت + +642 +01:05:14,160 --> 01:05:18,840 +سلسلة تعوي، تنعوض، تبت x و y + +643 +01:05:30,210 --> 01:05:34,610 +ما فيش مشكلة بس تتعود و تشيل شغلة و تبدّل كلهم كانوا + +644 +01:05:34,610 --> 01:05:39,150 +ما فيش مشكلة عادي جدا ما فيش أيّ إشكالية عادي جدا أنا + +645 +01:05:39,150 --> 01:05:43,870 +بيهمني يظل الشكل العام للنظرية مهما كانت كانت x + +646 +01:05:43,870 --> 01:05:48,490 +كانت ثلاثة x كانت ناقص x بدّي اللي دي الزاوية هي + +647 +01:05:48,490 --> 01:05:54,030 +اللي تحت هي اللي بتروح لـ zero تمام؟ دي ربّع لك اه + +648 +01:05:54,030 --> 01:05:57,870 +كل بدّه يكتب صح مش يكتب لي هيكده مثلًا زي ما كان + +649 +01:05:57,870 --> 01:06:01,990 +كاتب جبل والد تسوي n ما فيش حاجة تسوي هنا، لك تكتب + +650 +01:06:01,990 --> 01:06:05,910 +limit بدون limit لها معنى لها، أنت طالب جامعي طب + +651 +01:06:05,910 --> 01:06:12,650 +غلط، بدون limit غلط، ما علمت بدّك و أقول لك ليش، يا + +652 +01:06:12,650 --> 01:06:17,290 +ابني أفلك تعلم بطريقة صحيحة، بشأن بكرا تعلم الطلاب + +653 +01:06:17,290 --> 01:06:27,040 +بطريقة صحية، طب السؤال الخامس، ببنى limit لما الـ x + +654 +01:06:27,040 --> 01:06:35,020 +بدّه تروح لـ واحد للـ sign x ناقص واحد على x تربيع + +655 +01:06:35,020 --> 01:06:44,300 +zx ناقص اثنين كده + +656 +01:06:44,300 --> 01:06:52,060 +شهد يا ماجي ده؟ حط واحد و خلاص؟ طيب إيه بتطلع في + +657 +01:06:52,060 --> 01:06:57,050 +مثلتي؟ الزاوية x نقص واحد هذه polynomial من الدرجة + +658 +01:06:57,050 --> 01:07:02,150 +الثانية هذه x بتروح للواحد يعني ما هيش شكل النظرية + +659 +01:07:02,150 --> 01:07:07,490 +أصل نظرية x بتروح لـ zero لكن لما أطلع هذه x نقص + +660 +01:07:07,490 --> 01:07:12,070 +واحد بدّي أخلق هنا x نقص واحد و بدّي أخلق هذه هنا x + +661 +01:07:12,070 --> 01:07:17,580 +نقص واحد قصة تبصيفة جدا ضيف سالب واحد للطرفين يعني + +662 +01:07:17,580 --> 01:07:22,200 +نابقوا نخلقنا هنا وهذه من حلّة نابقوا نخلقنا x ناقص + +663 +01:07:22,200 --> 01:07:27,120 +واحد وبعدين الله بفرجها يبقى باجي بقوله هذه بدّه + +664 +01:07:27,120 --> 01:07:32,840 +تبقى الـ limit x ناقص واحد بدّه تروح لمين؟ لـ zero + +665 +01:07:32,840 --> 01:07:41,180 +وهذه الـ sign x ناقص واحد هذه بنحللها | قوسين | x و + +666 +01:07:41,180 --> 01:07:46,160 +| x و | واحد و | اثنين تمام عند الإشارة هذه + +667 +01:07:46,160 --> 01:07:52,060 +بالموجب يبقى هذه بالموجب وهذه بالسالب يبقى تحليلنا + +668 +01:07:52,060 --> 01:07:57,980 +سليم مائة بالمئة هذه الآن ممكن أجزيءها إلى limit + +669 +01:07:57,980 --> 01:08:04,800 +لحاصل ضرب دليل t لو جيت هنا قلت هذه الـ limit لمن x + +670 +01:08:04,800 --> 01:08:11,320 +ناقص واحد كلها بتروح لـ zero للـ sine x ناقص واحد + +671 +01:08:12,560 --> 01:08:17,800 +بعد max ناقص واحد تمام في مين في الـ limit ضال + +672 +01:08:17,800 --> 01:08:24,340 +عندي واحد على x زيد اثنين هذه لو خليتها قلت x بدها + +673 +01:08:24,340 --> 01:08:28,360 +تروح للواحد بدل max ناقص واحد تروح لـ zero يبقى x + +674 +01:08:28,360 --> 01:08:32,920 +بدها تروح لمين للواحد يبقى جزاية الـ limit إلى two + +675 +01:08:32,920 --> 01:08:38,890 +limits سؤالهذه كلها بقدرش لأن الزاوية هذه هي هذه + +676 +01:08:38,890 --> 01:08:42,450 +هي هذه يا محمود أول ساعة بيقول لو قدّلت يعني لو + +677 +01:08:42,450 --> 01:08:47,330 +أنا شيلت x ناقصها و حاطيت فِدالها y شو بيصير؟ y y y + +678 +01:08:47,330 --> 01:08:51,030 +هيها يعني بقى أنا بيهمني إن الزاوية هذه هو المقدر + +679 +01:08:51,030 --> 01:08:55,090 +هذا هو المقدر هذا الجيش ما يكون شغل تحط الـ x تحط الـ y + +680 +01:08:55,090 --> 01:08:58,930 +تحط الـ z تحط قصة تحط إن شاء الله ثلاثة كميات جوا + +681 +01:08:58,930 --> 01:09:02,630 +ما عندي معناه بدّي ازاي هذه تكون هي هذه هي اللي هنا + +682 +01:09:02,630 --> 01:09:08,670 +تمام يبقى هذا كله بقدّاش بواحد صحيح فيه هذا الآن + +683 +01:09:08,670 --> 01:09:15,030 +تعويض مباشر لأن المقدار الثابت هو هنا واحد زائد + +684 +01:09:15,030 --> 01:09:20,850 +اثنين يبقى الجواب قدّاش يساوي طوله يعني بدّي أتفرج + +685 +01:09:20,850 --> 01:09:25,170 +المثال اللي عندك بحيث تحطه في صيغة النظرية وبالتالي + +686 +01:09:25,170 --> 01:09:32,010 +نطبق النظرية بدون مشاكل نَبقى ستة نمرة 6 بالـ + +687 +01:09:32,010 --> 01:09:41,310 +delimit لما الـ x بدها تروح لـ 0 لمن؟ للـ sin واحد + +688 +01:09:41,310 --> 01:09:48,410 +ناقص cosine الـ x على من؟ على x لما الـ x بدها + +689 +01:09:48,410 --> 01:09:54,850 +تروح لـ 0 طالع + +690 +01:09:54,850 --> 01:10:00,440 +ليه كويس هنا؟ يقول limit اللي بين قوسين كلها هي + +691 +01:10:00,440 --> 01:10:05,860 +الزاوية تبعت الـ sign كل اللي بين قوسين هو الزاوية + +692 +01:10:05,860 --> 01:10:10,820 +تبعت الـ sign تمام؟ يبقى أنا مش هنقدر نطبق النظرية + +693 +01:10:10,820 --> 01:10:16,380 +بدّي يكون عند هنا واحد ناقص cosine الـ x و بدّي هنا + +694 +01:10:16,380 --> 01:10:20,680 +واحد ناقص cosine x يروح لمين؟ يروح لـ zero نسمع + +695 +01:10:31,970 --> 01:10:35,830 +يعني تضربت في واحد نقص كوسين وجسمت على واحد نقص + +696 +01:10:35,830 --> 01:10:41,370 +كوسين ما عناه مشكلة زميلكوا بيقترح ما يأتي بيقول + +697 +01:10:41,370 --> 01:10:46,050 +المثال هذه بدّه أكتبها على الشكل التالي limit لما + +698 +01:10:46,050 --> 01:10:52,090 +الـ x بيروح لـ zero لـ sine واحد ناقص cosine الـ x + +699 +01:10:52,090 --> 01:10:58,070 +على x هي الأصل تبعه بيروح اضرب في واحد ناقص cosine + +700 +01:10:58,070 --> 01:11:03,770 +الـ x و أجسم على واحد ناقص cosine الـ x بيقول ماشي + +701 +01:11:03,770 --> 01:11:09,300 +اضرب في واحد صحيح وبالتالي المثال تبقى كما هي طيب + +702 +01:11:09,300 --> 01:11:13,280 +قال لي هذه بدّه أعملها بالشكل التالي هذا الـ limit + +703 +01:11:13,280 --> 01:11:18,920 +لما الـ x بدها تروح لـ zero و قال لي أيّ sine واحد + +704 +01:11:18,920 --> 01:11:29,130 +ناقص cosine الـ x على واحد ناقص كو صين الـ x طبعًا و + +705 +01:11:29,130 --> 01:11:36,490 +كده إيش ضلّ عندنا ضلّ إن واحد على x أو واحد ناقص + +706 +01:11:36,490 --> 01:11:45,150 +كو صين الـ x كل غد على مين على x طبعًا قلنا اللي + +707 +01:11:45,150 --> 01:11:50,710 +بدّنا نيجي للدالة هذه الدالة صار الزاوية اللي عندنا + +708 +01:11:50,710 --> 01:11:56,530 +هي اللي تحت باجي بقولها هذه بتشوف كيف بدّي أعملها + +709 +01:11:56,530 --> 01:12:02,230 +شوف يا سيدي الأول لما أقوله الـ x بدها تروح لـ Zero + +710 +01:12:02,230 --> 01:12:09,750 +خذ الـ cosine للطرفين بيصير cosine الـ x بدّه يروح لـ + +711 +01:12:09,750 --> 01:12:16,130 +cosine الـ Zero قدّاش cosine الـ Zero؟ واحد يبقى صار + +712 +01:12:16,130 --> 01:12:20,820 +cosine الـ x بدّه يروح للواحد هتوا على الشجة + +713 +01:12:20,820 --> 01:12:26,960 +الثانية أو ضيف سالب واحد للطرفين بيصير cosine الـ x + +714 +01:12:26,960 --> 01:12:29,320 +سالب واحد يروح لمين؟ + +715 +01:12:34,370 --> 01:12:41,190 +اضرب الطرفين في شرط السالب بيصير واحد ناقص cosine + +716 +01:12:41,190 --> 01:12:47,930 +الـ x بيروح لمين؟ Zero في السالب ما هو Zero طيب إذا + +717 +01:12:47,930 --> 01:12:53,570 +الـ x بيروح إلى Zero بيكافئها واحد ناقص cosine الـ x + +718 +01:12:53,570 --> 01:12:59,820 +بيروح لوين؟ لـ zero إذا هذه بدها تساوي limit لما + +719 +01:12:59,820 --> 01:13:05,620 +الـ x بدّي روح لـ zero لـ sin واحد ناقص cosine الـ x + +720 +01:13:05,620 --> 01:13:11,040 +على واحد ناقص cosine الـ x في الـ limit لما الـ x + +721 +01:13:11,040 --> 01:13:18,920 +بدها تروح لـ zero لواحد ناقص cosine الـ x طيب + +722 +01:13:18,920 --> 01:13:25,280 +نعمل هذه بالطريقة اللي عملناها يبقى هذه تساوي high + +723 +01:13:25,280 --> 01:13:31,840 +limit هذه بدّي أستبدلها بمين بواحد ناقص cosine الـ x + +724 +01:13:31,840 --> 01:13:38,100 +كلها بدّه تروح لـ zero للـ sine واحد ناقص cosine الـ + +725 +01:13:38,100 --> 01:13:44,150 +x على مين على واحد ناقص cosine الـ x هذه المقامات + +726 +01:13:44,150 --> 01:13:48,810 +كلها مجدّش تشيلها يابان جوسينة تحطها ثيتا تحطها + +727 +01:13:48,810 --> 01:13:52,690 +واي تحطها زيد معنى مشكلة المهم صارت الزاوية هي + +728 +01:13:52,690 --> 01:13:56,250 +المقام هي المقنرة اللي عندنا نيجي هذا كله بواحد + +729 +01:13:56,250 --> 01:14:02,450 +نيجي نكمل high limit لما الـ x بدأ تروح لـ zero + +730 +01:14:02,450 --> 01:14:07,870 +التعويض المباشر هنا بيجيب لـ zero على zero كمية + +731 +01:14:07,870 --> 01:14:14,570 +غير معينة يبقى تدبّر حالك طبعًا هناك أكثر من طريقة + +732 +01:14:14,570 --> 01:14:21,210 +المرافق بنفع المرافق نضرب في المرافق تبع الـ bus + +733 +01:14:21,210 --> 01:14:25,430 +كلام صحيح و تمشي النتيجة واحد ثاني قال لأ أنا بدّي + +734 +01:14:25,430 --> 01:14:27,110 +أستخدم حساب المثلثات + +735 +01:14:34,470 --> 01:14:39,250 +ماشي الحال يفجر بدّه يشيل واحد نقص ويقول لي اثنين + +736 +01:14:39,250 --> 01:14:41,350 +cosine تربيع x على اثنين + +737 +01:14:46,490 --> 01:14:51,950 +يبقى لو ضربنا في المرافق الحل الصحيح مرافق الـ bus + +738 +01:14:51,950 --> 01:14:55,670 +لو روحنا شيلنا الواحد ناقص cosine الـ x و كتبنا + +739 +01:14:55,670 --> 01:14:59,930 +بدله اثنين sin تربيع x على اثنين برضه كلام سليم + +740 +01:14:59,930 --> 01:15:03,870 +100% وما حدا مقدر يقول إن هذا غلط يبقى على شِكتين + +741 +01:15:03,870 --> 01:15:10,330 +صح أمامك طريق طريق الأول أشيل واحد ناقص cosine + +742 +01:15:10,330 --> 01:15:15,050 +الـ x وأكتبها اثنين sin تربيع x على اثنين يا إما + +743 +01:15:15,050 --> 01:15:20,050 +أروح اضرب البسط المقام في المرافق تبع البسط اللي + +744 +01:15:20,050 --> 01:15:25,370 +هو واحد زائد cosine الـ x تحب نضرب في المرافق و + +745 +01:15:25,370 --> 01:15:32,350 +الله حساب المثلثات مرافق المرافق ماشي طيب يبقى high + +746 +01:15:32,350 --> 01:15:39,470 +limit لمن؟ لواحد ناقص cosine x على x واحد زائد + +747 +01:15:39,470 --> 01:15:46,190 +cosine x واحد زائد cosine x هذا الكلام يساوي، هذا + +748 +01:15:46,190 --> 01:15:52,080 +كله بواحد صحيح يبقى هذا بواحد صحيح مضروب هذا الآن + +749 +01:15:52,080 --> 01:15:57,620 +بيصير limit لما الـ x بدها تروح لـ zero البسط فرق + +750 +01:15:57,620 --> 01:16:03,860 +بين المربعين يبقى واحد ناقص cosine تربيع الـ x على + +751 +01:16:03,860 --> 01:16:12,250 +x في واحد على واحد زائد cosine الـ x هذا الكلام بدّه + +752 +01:16:12,250 --> 01:16:17,890 +يساوي limit لما الـ x بدّه يروح لـ 0 بدّاك اللي هتبعت + +753 +01:16:17,890 --> 01:16:22,070 +البسط اللي هو واحد ناقص cosine تربيع ليه كوسين + +754 +01:16:22,070 --> 01:16:29,350 +تربيع يبقى limit للـ sin تربيع الـ x على x في limit + +755 +01:16:29,350 --> 01:16:35,970 +لما الـ x بدّه يروح لـ 0 للواحد على واحد زاد cosine + +756 +01:16:35,970 --> 01:16:46,030 +الـ x هذا الكلام بدّه يساوي limit لما الـ x بدها تروح + +757 +01:16:46,030 --> 01:16:53,350 +لـ zero تمام؟ بدّي اخذ sin x على x في limit لما الـ + +758 +01:16:53,350 --> 01:16:59,590 +x بدها تروح لـ zero لـ sin x في limit لما الـ x بدها + +759 +01:16:59,590 --> 01:17:07,070 +تروح لـ zero لـ 1 على 1 زاد cosine x هذي بقدّاش؟ + +760 +01:17:07,820 --> 01:17:15,800 +وهذا هو قيمة واحد + +761 +01:17:15,800 --> 01:17:21,520 +على واحد زائد واحد يبقى النتيجة تساوي صفر يبقى + +762 +01:17:21,520 --> 01:17:27,160 +limit لهذه الـ function تساوي صفر عليك انتهى هذا + +763 +01:17:27,160 --> 01:17:33,220 +الـ section وإليكم أرقام المسائل ولحد هنا داخل في + +764 +01:17:33,220 --> 01:17:41,860 +الامتحان يبقى exercises اثنين أربعة المسائل التالية + +765 +01:17:41,860 --> 01:17:50,400 +exercises اثنين أربعة المسائل من واحد لغاية واحد + +766 +01:17:50,400 --> 01:17:54,580 +و أربعين القدر + +767 +01:17:54,580 --> 01:18:02, \ No newline at end of file diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OuNt_E3bc1Y_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/OuNt_E3bc1Y_raw.json new file mode 100644 index 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بدي", "probability": 0.966064453125}, {"start": 149.58, "end": 150.24, "word": " أسألها", "probability": 0.86611328125}, {"start": 150.24, "end": 150.6, "word": " أنا", "probability": 0.849609375}, {"start": 150.6, "end": 151.86, "word": " وسنجاوب", "probability": 0.8505859375}, {"start": 151.86, "end": 152.44, "word": " عليها", "probability": 0.990966796875}, {"start": 152.44, "end": 153.16, "word": " بعد", "probability": 0.9541015625}, {"start": 153.16, "end": 154.32, "word": " قليل،", "probability": 0.9462890625}, {"start": 154.32, "end": 154.5, "word": " بس", "probability": 0.99267578125}, {"start": 154.5, "end": 154.86, "word": " ناخد", "probability": 0.990234375}, {"start": 154.86, "end": 155.24, "word": " بعض", "probability": 0.982421875}, {"start": 155.24, "end": 155.94, "word": " الأمثلة", "probability": 0.9859619140625}], "temperature": 1.0}, {"id": 7, "seek": 18680, "start": 157.32, "end": 186.8, "text": "على الـ graph of a function as shown in the following figure رسمى اللى قدامنا هذه بيقول احسب لل limit إذا كانت موجودة و إذا مش موجودة مسامحينك فيها ال limit الأولى بيقول اللى limit ال F of X لما ال X بده تروح لسالب واحد من جهة اليمين يبقى باجي لسالب واحد هي السالب واحد أنا رايحله من جهة مين؟ من جهة اليمين يبقى الدالة كل ما اقترب من سالب واحد من جهة اليمين الدالة طالعة لمين؟", "tokens": [3615, 23942, 2423, 39184, 4295, 295, 257, 2445, 382, 4898, 294, 264, 3480, 2573, 12602, 38251, 7578, 13672, 7578, 12174, 3215, 10943, 8315, 29538, 4724, 1829, 39648, 1975, 5016, 35457, 24976, 4948, 11933, 15730, 25961, 2655, 3714, 29245, 23328, 3660, 4032, 11933, 15730, 37893, 3714, 29245, 23328, 3660, 47524, 10943, 5016, 9957, 4117, 8978, 11296, 2423, 4948, 16247, 12610, 7578, 4724, 1829, 39648, 13672, 7578, 4948, 2423, 479, 295, 1783, 5296, 15042, 2423, 1783, 47525, 3224, 6055, 32887, 5016, 5296, 3794, 6027, 3555, 36764, 24401, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 5296, 3794, 6027, 3555, 36764, 24401, 39896, 21136, 6027, 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دالة", "probability": 0.9518229166666666}, {"start": 238.3, "end": 239.02, "word": " رايحة", "probability": 0.8792724609375}, {"start": 239.02, "end": 239.64, "word": " لوين؟", "probability": 0.9637044270833334}], "temperature": 1.0}, {"id": 10, "seek": 26339, "start": 239.82, "end": 263.4, "text": "يبقى النتيجة تساوي واحد بناء عليه من جهة اليمين بواحد من جهة الشمال باتنين اختلفت القيمتان يبقى ال limit ما لها does not exist يبقى هذه بقوله does not exist", "tokens": [1829, 3555, 4587, 7578, 2423, 29399, 1829, 7435, 3660, 6055, 3794, 995, 45865, 36764, 24401, 44945, 16606, 47356, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 4724, 14407, 24401, 9154, 10874, 3224, 3660, 25124, 2304, 6027, 4724, 9307, 1863, 9957, 1975, 46456, 46538, 2655, 25062, 32640, 2655, 7649, 7251, 3555, 4587, 7578, 2423, 4948, 19446, 5296, 11296, 775, 406, 2514, 7251, 3555, 4587, 7578, 29538, 4724, 39648, 3224, 775, 406, 2514], "avg_logprob": -0.25044014336357656, "compression_ratio": 1.6493506493506493, 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"probability": 0.9853515625}, {"start": 252.24, "end": 252.84, "word": " الشمال", "probability": 0.9723307291666666}, {"start": 252.84, "end": 253.44, "word": " باتنين", "probability": 0.888427734375}, {"start": 253.44, "end": 254.62, "word": " اختلفت", "probability": 0.90576171875}, {"start": 254.62, "end": 255.54, "word": " القيمتان", "probability": 0.9681396484375}, {"start": 255.54, "end": 256.1, "word": " يبقى", "probability": 0.9630126953125}, {"start": 256.1, "end": 256.14, "word": " ال", "probability": 0.31494140625}, {"start": 256.14, "end": 256.32, "word": " limit", "probability": 0.66650390625}, {"start": 256.32, "end": 256.58, "word": " ما", "probability": 0.54638671875}, {"start": 256.58, "end": 256.9, "word": " لها", "probability": 0.83447265625}, {"start": 256.9, "end": 257.62, "word": " does", "probability": 0.76123046875}, {"start": 257.62, "end": 258.02, "word": " not", "probability": 0.96630859375}, {"start": 258.02, "end": 258.68, "word": " exist", "probability": 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سؤال ثاني طيب ننتقل الآن إلى نوية أخرى من هذه المسائل كمان مثال أخر بقول find the following limits", "tokens": [1829, 3555, 4587, 7578, 29538, 2423, 4948, 5551, 29245, 3215, 1863, 11296, 9154, 16490, 1211, 6027, 34892, 38251, 23032, 3555, 3615, 995, 5551, 3615, 9566, 36081, 24793, 12174, 36150, 29910, 23275, 8608, 33604, 6027, 9154, 23758, 9673, 2407, 16254, 1211, 23758, 46811, 10943, 22807, 4032, 23758, 31439, 8608, 33604, 6027, 38637, 7649, 1829, 23032, 1829, 3555, 8717, 29399, 4587, 1211, 6024, 48506, 30731, 8717, 2407, 10632, 5551, 34740, 7578, 9154, 29538, 9673, 3794, 16373, 1211, 9122, 2304, 7649, 50113, 6027, 5551, 34740, 4724, 39648, 915, 264, 3480, 10406], "avg_logprob": -0.18117977929918955, "compression_ratio": 1.5942028985507246, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 340.87, "end": 341.39, "word": "يبقى", "probability": 0.853271484375}, {"start": 341.39, "end": 341.83, "word": " هذه", "probability": 0.84814453125}, {"start": 341.83, "end": 342.33, 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{"id": 17, "seek": 41476, "start": 405.0, "end": 414.76, "text": "بس أنا كدهش ال domain بالله بيقول زميلكوا ال domain من سالب واحد لغاية تلاتة", "tokens": [3555, 3794, 41850, 9122, 3215, 3224, 8592, 2423, 9274, 20666, 43761, 4724, 1829, 39648, 30767, 2304, 26895, 4117, 14407, 2423, 9274, 9154, 8608, 6027, 3555, 36764, 24401, 5296, 17082, 995, 10632, 6055, 1211, 9307, 3660], "avg_logprob": -0.191406255794896, "compression_ratio": 1.26, "no_speech_prob": 7.450580596923828e-06, "words": [{"start": 405.0, "end": 405.88, "word": "بس", "probability": 0.75341796875}, {"start": 405.88, "end": 406.04, "word": " أنا", "probability": 0.85888671875}, {"start": 406.04, "end": 406.48, "word": " كدهش", "probability": 0.68951416015625}, {"start": 406.48, "end": 406.56, "word": " ال", "probability": 0.93115234375}, {"start": 406.56, "end": 406.76, "word": " domain", "probability": 0.96142578125}, {"start": 406.76, "end": 407.18, "word": " بالله", "probability": 0.724853515625}, {"start": 407.18, "end": 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بيكون ال function هي عبارة عن الجدر التربية ل X زائد 100 زائد 13 الآن لما ناخدنا قوانين ال limit في ال section قبل الماضي", "tokens": [43, 332, 270, 5296, 15042, 2423, 1783, 47525, 3224, 7251, 32887, 5016, 5296, 2655, 1211, 9307, 3660, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 6055, 1211, 9307, 3660, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 20449, 8315, 47395, 2423, 1783, 20449, 1211, 11296, 5551, 4117, 26890, 9154, 6055, 1211, 9307, 3660, 4724, 1829, 30544, 2423, 2445, 39896, 6225, 3555, 9640, 3660, 18871, 25724, 3215, 2288, 16712, 25513, 10632, 5296, 1783, 30767, 16373, 3215, 2319, 30767, 16373, 3215, 3705, 6024, 48506, 5296, 15042, 8717, 47283, 3215, 8315, 12174, 2407, 7649, 9957, 2423, 4948, 8978, 2423, 3541, 12174, 36150, 9673, 46958, 1829], "avg_logprob": -0.21271658415841585, "compression_ratio": 1.7129186602870814, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1529.35, "end": 1530.09, "word": "Limit", "probability": 0.6124267578125}, {"start": 1530.09, 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exist سؤال اللي يقبله ماكنتش عارف انا exist ولا لأ حسبت ال limit من اليمين و ال limit من الشمال اللي جيتنا مع بعضك وقلت لو exist what ساوي أربع هنا بقول لي لأ ال limit exist بس هو مش عارفها", "tokens": [2407, 6027, 20292, 8032, 9307, 20292, 3714, 4587, 3555, 9640, 38637, 16758, 2655, 1975, 1829, 3224, 4724, 5016, 1829, 12984, 2423, 4948, 29538, 3714, 6027, 11296, 2514, 8608, 33604, 6027, 13672, 1829, 7251, 4587, 36150, 3224, 19446, 19452, 2655, 8592, 6225, 9640, 5172, 1975, 8315, 2514, 49429, 5296, 10721, 11331, 35457, 2655, 2423, 4948, 9154, 45595, 2304, 9957, 4032, 2423, 4948, 9154, 25124, 2304, 6027, 13672, 1829, 10874, 36081, 8315, 20449, 45030, 11242, 4117, 4032, 4587, 1211, 2655, 45164, 2514, 437, 8608, 995, 45865, 5551, 25513, 3615, 34105, 4724, 39648, 32239, 5296, 10721, 2423, 4948, 2514, 4724, 3794, 31439, 37893, 6225, 9640, 5172, 11296], "avg_logprob": -0.3193452312832787, "compression_ratio": 1.8829268292682926, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 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limit", "probability": 0.92822265625}, {"start": 2466.94, "end": 2467.28, "word": " من", "probability": 0.9560546875}, {"start": 2467.28, "end": 2467.98, "word": " الشمال", "probability": 0.9671223958333334}, {"start": 2467.98, "end": 2468.18, "word": " و", "probability": 0.58203125}, {"start": 2468.18, "end": 2468.26, "word": " ال", "probability": 0.5224609375}, {"start": 2468.26, "end": 2468.56, "word": " limit", "probability": 0.95751953125}, {"start": 2468.56, "end": 2468.88, "word": " من", "probability": 0.9931640625}, {"start": 2468.88, "end": 2469.54, "word": " اليمين", "probability": 0.88330078125}, {"start": 2469.54, "end": 2470.6, "word": " يبقى", "probability": 0.9754638671875}, {"start": 2470.6, "end": 2471.06, "word": " limit", "probability": 0.9873046875}, {"start": 2471.06, "end": 2471.78, "word": " ل", "probability": 0.91357421875}, {"start": 2471.78, "end": 2472.34, "word": " sin", "probability": 0.253662109375}, {"start": 2472.34, "end": 2472.9, "word": " θ", "probability": 0.61669921875}, {"start": 2472.9, "end": 2473.72, "word": " على", "probability": 0.80908203125}, {"start": 2473.72, "end": 2474.22, "word": " θ", "probability": 0.70361328125}, {"start": 2474.22, "end": 2475.1, "word": " لما", "probability": 0.9423828125}, {"start": 2475.1, "end": 2475.5, "word": " θ", "probability": 0.74755859375}, {"start": 2475.5, "end": 2475.86, "word": " بدأ", "probability": 0.7099609375}, {"start": 2475.86, "end": 2476.26, "word": " تروح", "probability": 0.822021484375}, {"start": 2476.26, "end": 2476.44, "word": " ل", "probability": 0.60400390625}, {"start": 2476.44, "end": 2476.78, "word": " zero", "probability": 0.45947265625}, {"start": 2476.78, "end": 2477.04, "word": " من", "probability": 0.99267578125}, {"start": 2477.04, "end": 2477.48, "word": " جهة", "probability": 0.986328125}, {"start": 2477.48, "end": 2478.06, "word": " الشمال", "probability": 0.99267578125}, {"start": 2478.06, "end": 2478.74, "word": " لو", "probability": 0.69970703125}, {"start": 2478.74, "end": 2479.06, "word": " احنا", "probability": 0.8753255208333334}, {"start": 2479.06, "end": 2479.48, "word": " روحنا", "probability": 0.9769287109375}, {"start": 2479.48, "end": 2479.68, "word": " ل", "probability": 0.8984375}, {"start": 2479.68, "end": 2480.0, "word": " zero", "probability": 0.77294921875}, {"start": 2480.0, "end": 2480.3, "word": " من", "probability": 0.9931640625}, {"start": 2480.3, "end": 2480.74, "word": " جهة", "probability": 0.9933268229166666}, {"start": 2480.74, "end": 2481.34, "word": " الشمال", "probability": 0.9933268229166666}], "temperature": 1.0}, {"id": 103, "seek": 249907, "start": 2482.65, "end": 2499.07, "text": "يبقى الدالة الطائحة للواحد يبقى هذه بدل ساعة واحد and لو روحنا أخدنا limit ل sin θ على θ لما θ راحت لل zero من جهة اليمين", "tokens": [1829, 3555, 4587, 7578, 32748, 6027, 3660, 41950, 16373, 5016, 3660, 24976, 14407, 24401, 7251, 3555, 4587, 7578, 29538, 47525, 1211, 8608, 995, 27884, 36764, 24401, 293, 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0.8058268229166666}, {"start": 2487.49, "end": 2487.77, "word": " واحد", "probability": 0.975341796875}, {"start": 2487.77, "end": 2488.43, "word": " and", "probability": 0.57861328125}, {"start": 2488.43, "end": 2489.37, "word": " لو", "probability": 0.8857421875}, {"start": 2489.37, "end": 2489.77, "word": " روحنا", "probability": 0.74542236328125}, {"start": 2489.77, "end": 2490.37, "word": " أخدنا", "probability": 0.8719482421875}, {"start": 2490.37, "end": 2490.87, "word": " limit", "probability": 0.95654296875}, {"start": 2490.87, "end": 2491.57, "word": " ل", "probability": 0.90380859375}, {"start": 2491.57, "end": 2492.17, "word": " sin", "probability": 0.35546875}, {"start": 2492.17, "end": 2492.73, "word": " θ", "probability": 0.488037109375}, {"start": 2492.73, "end": 2493.55, "word": " على", "probability": 0.84033203125}, {"start": 2493.55, "end": 2494.09, "word": " θ", "probability": 0.58349609375}, {"start": 2494.09, "end": 2495.03, "word": " لما", "probability": 0.895751953125}, {"start": 2495.03, "end": 2495.37, "word": " θ", "probability": 0.303955078125}, {"start": 2495.37, "end": 2495.89, "word": " راحت", "probability": 0.7802734375}, {"start": 2495.89, "end": 2496.15, "word": " لل", "probability": 0.72265625}, {"start": 2496.15, "end": 2496.81, "word": " zero", "probability": 0.58447265625}, {"start": 2496.81, "end": 2497.65, "word": " من", "probability": 0.9921875}, {"start": 2497.65, "end": 2498.33, "word": " جهة", "probability": 0.9806315104166666}, {"start": 2498.33, "end": 2499.07, "word": " اليمين", "probability": 0.8434244791666666}], "temperature": 1.0}, {"id": 104, "seek": 252356, "start": 2500.2, "end": 2523.56, "text": "يبقى يساوي كمان؟ يساوي واحد يبقى بناء عليه ال limit اللي فوق هذا يبقى كم؟ واحد يبقى هذا بدي يعطيك دائما و أبدا ان ال limit لمين؟ ل sign theta على theta لما theta بده تروح لل zero بده تساوي واحد", "tokens": [1829, 3555, 4587, 7578, 7251, 3794, 995, 45865, 9122, 2304, 7649, 22807, 7251, 3794, 995, 45865, 36764, 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0.8837890625}, {"start": 2503.76, "end": 2504.72, "word": " يبقى", "probability": 0.9168701171875}, {"start": 2504.72, "end": 2505.1, "word": " بناء", "probability": 0.93115234375}, {"start": 2505.1, "end": 2505.7, "word": " عليه", "probability": 0.459228515625}, {"start": 2505.7, "end": 2506.4, "word": " ال", "probability": 0.55322265625}, {"start": 2506.4, "end": 2506.7, "word": " limit", "probability": 0.908203125}, {"start": 2506.7, "end": 2506.9, "word": " اللي", "probability": 0.8125}, {"start": 2506.9, "end": 2507.18, "word": " فوق", "probability": 0.98193359375}, {"start": 2507.18, "end": 2507.4, "word": " هذا", "probability": 0.394287109375}, {"start": 2507.4, "end": 2507.62, "word": " يبقى", "probability": 0.75360107421875}, {"start": 2507.62, "end": 2508.24, "word": " كم؟", "probability": 0.6787109375}, {"start": 2508.24, "end": 2509.28, "word": " واحد", "probability": 0.9033203125}, {"start": 2509.28, "end": 2510.06, "word": " يبقى", "probability": 0.9075927734375}, {"start": 2510.06, "end": 2510.3, "word": " هذا", "probability": 0.7578125}, {"start": 2510.3, "end": 2510.68, "word": " بدي", "probability": 0.408203125}, {"start": 2510.68, "end": 2511.24, "word": " يعطيك", "probability": 0.9569091796875}, {"start": 2511.24, "end": 2511.86, "word": " دائما", "probability": 0.91552734375}, {"start": 2511.86, "end": 2512.1, "word": " و", "probability": 0.62646484375}, {"start": 2512.1, "end": 2512.8, "word": " أبدا", "probability": 0.8167317708333334}, {"start": 2512.8, "end": 2513.74, "word": " ان", "probability": 0.77685546875}, {"start": 2513.74, "end": 2514.0, "word": " ال", "probability": 0.294677734375}, {"start": 2514.0, "end": 2514.48, "word": " limit", "probability": 0.9765625}, {"start": 2514.48, "end": 2516.08, "word": " لمين؟", "probability": 0.6343587239583334}, {"start": 2516.08, "end": 2516.22, "word": " ل", "probability": 0.85205078125}, {"start": 2516.22, "end": 2516.8, "word": " sign", "probability": 0.21240234375}, {"start": 2516.8, "end": 2517.54, "word": " theta", "probability": 0.2281494140625}, {"start": 2517.54, "end": 2518.32, "word": " على", "probability": 0.740234375}, {"start": 2518.32, "end": 2518.98, "word": " theta", "probability": 0.63916015625}, {"start": 2518.98, "end": 2519.78, "word": " لما", "probability": 0.8583984375}, {"start": 2519.78, "end": 2520.18, "word": " theta", "probability": 0.3984375}, {"start": 2520.18, "end": 2520.46, "word": " بده", "probability": 0.5421142578125}, {"start": 2520.46, "end": 2520.76, "word": " تروح", "probability": 0.9728190104166666}, {"start": 2520.76, "end": 2520.98, "word": " لل", "probability": 0.53759765625}, {"start": 2520.98, "end": 2521.4, "word": " zero", "probability": 0.70166015625}, {"start": 2521.4, "end": 2522.14, "word": " بده", "probability": 0.64306640625}, {"start": 2522.14, "end": 2522.94, "word": " تساوي", "probability": 0.9642333984375}, {"start": 2522.94, "end": 2523.56, "word": " واحد", "probability": 0.982177734375}], "temperature": 1.0}, {"id": 105, "seek": 254367, "start": 2523.87, "end": 2543.67, "text": "رغم انه عشان عند ال zero الدالة is undefined ماهياش معرف لإنه sign zero ب zero صار zero على zero كمية غير معينة وبالتالي الدالة هذه مالها غير معرفة بهمنا الآن كيفية استخدام هذه النظرية", "tokens": [2288, 17082, 2304, 16472, 3224, 6225, 8592, 7649, 43242, 2423, 4018, 32748, 6027, 3660, 307, 674, 5666, 2001, 19446, 3224, 1829, 33599, 20449, 28480, 5296, 28814, 1863, 3224, 1465, 4018, 4724, 4018, 20328, 9640, 4018, 15844, 4018, 9122, 2304, 10632, 32771, 13546, 20449, 9957, 3660, 46599, 6027, 2655, 6027, 1829, 32748, 6027, 3660, 29538, 19446, 1211, 11296, 32771, 13546, 20449, 28480, 3660, 4724, 16095, 8315, 6024, 48506, 9122, 33911, 10632, 44713, 9778, 3215, 10943, 29538, 28239, 19913, 2288, 10632], "avg_logprob": -0.250585949793458, "compression_ratio": 1.6428571428571428, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2523.87, "end": 2524.33, "word": "رغم", "probability": 0.73095703125}, {"start": 2524.33, "end": 2524.75, "word": " انه", "probability": 0.38751220703125}, {"start": 2524.75, "end": 2525.43, "word": " عشان", "probability": 0.5068766276041666}, {"start": 2525.43, "end": 2525.87, "word": " عند", "probability": 0.65283203125}, {"start": 2525.87, "end": 2526.07, "word": " ال", "probability": 0.62060546875}, {"start": 2526.07, "end": 2526.33, "word": " zero", "probability": 0.274658203125}, {"start": 2526.33, "end": 2527.01, "word": " الدالة", "probability": 0.7887369791666666}, {"start": 2527.01, "end": 2527.47, "word": " is", "probability": 0.79931640625}, {"start": 2527.47, "end": 2529.13, "word": " undefined", "probability": 0.8741861979166666}, {"start": 2529.13, "end": 2530.11, "word": " ماهياش", "probability": 0.8709716796875}, {"start": 2530.11, "end": 2530.49, "word": " معرف", "probability": 0.95068359375}, {"start": 2530.49, "end": 2530.99, "word": " لإنه", "probability": 0.6719970703125}, {"start": 2530.99, "end": 2531.59, "word": " sign", "probability": 0.30859375}, {"start": 2531.59, "end": 2532.13, "word": " zero", "probability": 0.59765625}, {"start": 2532.13, "end": 2532.25, "word": " ب", "probability": 0.83203125}, {"start": 2532.25, "end": 2532.61, "word": " zero", "probability": 0.6162109375}, {"start": 2532.61, "end": 2532.95, "word": " صار", "probability": 0.93798828125}, {"start": 2532.95, "end": 2533.23, "word": " zero", "probability": 0.7470703125}, {"start": 2533.23, "end": 2533.47, "word": " على", "probability": 0.6572265625}, {"start": 2533.47, "end": 2533.77, "word": " zero", "probability": 0.77490234375}, {"start": 2533.77, "end": 2534.45, "word": " كمية", "probability": 0.9801432291666666}, {"start": 2534.45, "end": 2535.05, "word": " غير", "probability": 0.994384765625}, {"start": 2535.05, "end": 2535.51, "word": " معينة", "probability": 0.9664713541666666}, {"start": 2535.51, "end": 2535.97, "word": " وبالتالي", "probability": 0.948828125}, {"start": 2535.97, "end": 2536.35, "word": " الدالة", "probability": 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التالية إذا كانت موجودة example find the following limits النهايات التالية نمرة واحد", "tokens": [41185, 11331, 1211, 9673, 3794, 16373, 1211, 9673, 46456, 46538, 3660, 7251, 3555, 4587, 7578, 44945, 1829, 7435, 1829, 8717, 39648, 4117, 1975, 5016, 35457, 24976, 1863, 11296, 1829, 9307, 16712, 6027, 10632, 11933, 15730, 25961, 2655, 3714, 29245, 23328, 3660, 1365, 915, 264, 3480, 10406, 28239, 11296, 1829, 9307, 16712, 6027, 10632, 8717, 2304, 25720, 36764, 24401], "avg_logprob": -0.19584216101694915, "compression_ratio": 1.486842105263158, "no_speech_prob": 0.0, "words": [{"start": 2543.99, "end": 2544.25, "word": "في", "probability": 0.322265625}, {"start": 2544.25, "end": 2544.97, "word": " حل", "probability": 0.933349609375}, {"start": 2544.97, "end": 2546.23, "word": " المسائل", "probability": 0.9361572265625}, {"start": 2546.23, "end": 2548.05, "word": " المختلفة", "probability": 0.9942626953125}, {"start": 2548.05, "end": 2548.97, "word": " يبقى", "probability": 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following", "probability": 0.88916015625}, {"start": 2562.47, "end": 2565.97, "word": " limits", "probability": 0.95166015625}, {"start": 2565.97, "end": 2570.75, "word": " النهايات", "probability": 0.706512451171875}, {"start": 2570.75, "end": 2571.41, "word": " التالية", "probability": 0.9949544270833334}, {"start": 2571.41, "end": 2572.67, "word": " نمرة", "probability": 0.6951497395833334}, {"start": 2572.67, "end": 2573.21, "word": " واحد", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 107, "seek": 258419, "start": 2573.81, "end": 2584.19, "text": "بعد ذلك بدنا limit لما ال X بده تروح ل zero لل sign X على 2 على X", "tokens": [3555, 22488, 29910, 23275, 47525, 8315, 4948, 5296, 15042, 2423, 1783, 47525, 3224, 6055, 32887, 5016, 5296, 4018, 24976, 1465, 1783, 15844, 568, 15844, 1783], "avg_logprob": -0.5552884477835435, "compression_ratio": 1.0909090909090908, "no_speech_prob": 0.0, "words": [{"start": 2573.81, "end": 2574.17, "word": "بعد", "probability": 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هذا في خمسة والتاني خليته زي ما هو يبقى النتيجة تساوية هذه الخمسة اعتلتها اللي برا بالداخل هذه", "tokens": [40228, 22653, 10874, 11622, 10721, 31371, 4948, 5296, 27842, 22807, 4948, 24976, 3215, 6027, 3660, 16247, 12610, 7578, 29538, 13672, 1829, 43242, 8315, 4032, 4948, 24976, 3215, 6027, 3660, 16712, 7649, 10632, 16247, 12610, 7578, 48812, 25513, 2655, 21136, 995, 16095, 23758, 8978, 16490, 2304, 3794, 3660, 16070, 2655, 7649, 1829, 16490, 20292, 47395, 30767, 1829, 19446, 31439, 7251, 3555, 4587, 7578, 28239, 31371, 7435, 3660, 6055, 3794, 995, 2407, 10632, 29538, 33962, 2304, 3794, 3660, 1975, 34268, 1211, 2655, 11296, 13672, 1829, 4724, 23557, 20666, 3215, 47283, 1211, 29538], "avg_logprob": -0.2058722455422957, "compression_ratio": 1.9147727272727273, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2905.57, "end": 2906.19, "word": "يعني", "probability": 0.8916015625}, {"start": 2906.19, "end": 2907.17, "word": " جزأتي", "probability": 0.74249267578125}, {"start": 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إيش خمسة على تلتة", "tokens": [10721, 20292, 14851, 8978, 20328, 1829, 17082, 3660, 28239, 19913, 2288, 10632, 13672, 1829, 12174, 3215, 10943, 1829, 29538, 11933, 15730, 4724, 28543, 2288, 5551, 8592, 26895, 11296, 4032, 5551, 4117, 2655, 3555, 5296, 11296, 12174, 3215, 33599, 36764, 24401, 20328, 5016, 1829, 5016, 4724, 1829, 3555, 4587, 7578, 29538, 36764, 24401, 15844, 6225, 2407, 11242, 6055, 22488, 2304, 33599, 2423, 23565, 20328, 5172, 2288, 4724, 14407, 24401, 7251, 3555, 4587, 7578, 15844, 36764, 24401, 11933, 15730, 28239, 31371, 7435, 3660, 6055, 3794, 995, 45865, 11933, 1829, 8592, 16490, 2304, 3794, 3660, 15844, 6055, 1211, 2655, 3660], "avg_logprob": -0.25892856473825415, "compression_ratio": 1.7119565217391304, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2927.74, "end": 2928.5, "word": "أليست", "probability": 0.4853922526041667}, {"start": 2928.5, "end": 2928.72, "word": " في", "probability": 0.892578125}, {"start": 2928.72, "end": 2929.18, "word": " 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+section 1 لغاية section 3 لم ناخد في اي يوم من + +4 +00:00:32,540 --> 00:00:36,100 +الأيام ال limit من اليمين او ال limit من الشمال + +5 +00:00:36,100 --> 00:00:39,540 +وانما بجأنا ناخد limit سعالية بدلا من محكمة limit + +6 +00:00:39,540 --> 00:00:44,220 +ثم limit سعادية ثم ال section الماضى كان بواسط + +7 +00:00:44,220 --> 00:00:48,240 +epsilon و delta definitionالنظرية بتقول ليش؟ + +8 +00:00:48,240 --> 00:00:52,220 +بالبلدي قبل ما نقراها روح ناخد ال limit للدالة من + +9 +00:00:52,220 --> 00:00:56,380 +اليمين وال limit للدالة من الشمال إذا اتنين تساووا + +10 +00:00:56,380 --> 00:00:59,140 +يبقى ال limit exist و تساوى القيم اللي بتطلع هذا + +11 +00:00:59,140 --> 00:01:03,220 +باختصار، تمام؟ الكلام اللي سمعته هى مكتوب جبنانا، + +12 +00:01:03,220 --> 00:01:07,340 +بنقول a function f of x has a limit as x + +13 +00:01:07,340 --> 00:01:12,140 +approaches c لها limit لما ال x بتروح ل c and only + +14 +00:01:12,140 --> 00:01:16,970 +fإذا و فقط إذا كان it has a left hand and right + +15 +00:01:16,970 --> 00:01:20,390 +hand limits إذا ال limit من اليمين موجودة و ال + +16 +00:01:20,390 --> 00:01:24,570 +limit من الشمال موجودة عند تلك النقطة there يعني + +17 +00:01:24,570 --> 00:01:29,710 +هناك عند النقطة اللي عندنا هذه اللي هي c and these + +18 +00:01:29,710 --> 00:01:33,690 +limits are equal و ال two limits هدول بيكونوا + +19 +00:01:33,690 --> 00:01:35,290 +متساويتين ذاتي + +20 +00:01:39,000 --> 00:01:42,480 +في السطرة و بدأت صيغة مرياضيا بالسطرة اللى قدامنا + +21 +00:01:42,480 --> 00:01:46,020 +هذه فبجب اقول limit ال F of X لما ال X بده تروح + +22 +00:01:46,020 --> 00:01:52,340 +الى C يساوي ال L if and only if limit ال F of X + +23 +00:01:52,340 --> 00:01:56,440 +لما ال X بده تروح الى C من جهة اليسار بده تساوي L + +24 +00:01:56,440 --> 00:01:59,620 +وفي نفس الوقت limit ال F of X لما ال X بده تروح + +25 +00:01:59,620 --> 00:02:04,620 +الى C من جهة اليامين بده يساوي نفس النتيجة اللى هى + +26 +00:02:04,620 --> 00:02:08,690 +Lيبقى إذا تساوت النتيجة للـ function من اليمين + +27 +00:02:08,690 --> 00:02:14,110 +والنتيجة من اليسار يبقى ال limit exists وتساوي هذه + +28 +00:02:14,110 --> 00:02:18,730 +القيمة اللي طلعت أنا بنا نبدأ ناخد أمثلة مختلفة + +29 +00:02:18,730 --> 00:02:23,780 +على ميم على الكلام اللي قلنا هذاطبعا أنا عارف أنه + +30 +00:02:23,780 --> 00:02:28,660 +بعض الأسئلة بتدور في دماكه، لكن هذه الأسئلة بدي + +31 +00:02:28,660 --> 00:02:34,500 +أجاوبها، بدي أسألها أنا وسنجاوب عليها بعد قليل، بس + +32 +00:02:34,500 --> 00:02:39,320 +ناخد بعض الأمثلةعلى الـ graph of a function as + +33 +00:02:39,320 --> 00:02:42,280 +shown in the following figure رسمى اللى قدامنا هذه + +34 +00:02:42,280 --> 00:02:46,860 +بيقول احسب لل limit إذا كانت موجودة و إذا مش + +35 +00:02:46,860 --> 00:02:50,880 +موجودة مسامحينك فيها ال limit الأولى بيقول اللى + +36 +00:02:50,880 --> 00:02:54,240 +limit ال F of X لما ال X بده تروح لسالب واحد من + +37 +00:02:54,240 --> 00:02:58,900 +جهة اليمين يبقى باجي لسالب واحد هي السالب واحد أنا + +38 +00:02:58,900 --> 00:03:03,180 +رايحله من جهة مين؟ من جهة اليمين يبقى الدالة كل ما + +39 +00:03:03,180 --> 00:03:06,200 +اقترب من سالب واحد من جهة اليمين الدالة طالعة + +40 +00:03:06,200 --> 00:03:12,300 +لمين؟للواحد يبقى هذه ال limit تساوي واحد صحيح نجي + +41 +00:03:12,300 --> 00:03:16,140 +لبعدها limit ال f of x لما ال x بده تروح ل zero + +42 +00:03:16,140 --> 00:03:21,160 +إذا روحت ل zero من جهة الشمال بلاقي هذه نزل أوين ل + +43 +00:03:21,160 --> 00:03:25,540 +zero وإذا روحت ل zero من جهة اليمين بلاقي هذه نزل + +44 +00:03:25,540 --> 00:03:29,380 +أوين ل zero يبقى ال limit من اليمين بده تساوي ال + +45 +00:03:29,380 --> 00:03:33,500 +limit من الشمال يبقى بتساوي قداش zeroالان بنا + +46 +00:03:33,500 --> 00:03:36,740 +limit لل F of X لما ال X بده تروح لل واحد من جهة + +47 +00:03:36,740 --> 00:03:40,600 +اليسار يبقى احنا رايحين لل واحد من جهة اليسار + +48 +00:03:40,600 --> 00:03:44,600 +الدالة طالعة لوين؟ لل اتنين يبقى ال limit هنا + +49 +00:03:44,600 --> 00:03:50,660 +تساوي كده ايش؟ تساوي اتنين بنا limit لل F of X لما + +50 +00:03:50,660 --> 00:03:54,620 +ال X بده تروح لل واحد من جهة اليمين يبقى احنا + +51 +00:03:54,620 --> 00:03:59,020 +رايحين لل واحد من جهة اليمين بدي اقول دالة رايحة + +52 +00:03:59,020 --> 00:04:09,800 +لوين؟يبقى النتيجة تساوي واحد بناء عليه من جهة + +53 +00:04:09,800 --> 00:04:15,540 +اليمين بواحد من جهة الشمال باتنين اختلفت القيمتان + +54 +00:04:15,540 --> 00:04:20,760 +يبقى ال limit ما لها does not exist يبقى هذه بقوله + +55 +00:04:20,760 --> 00:04:30,300 +does not existهذا الـ Limit + +56 +00:04:30,300 --> 00:04:31,640 +غير موجودة + +57 +00:04:41,980 --> 00:04:45,300 +أنا بدرسلك سؤال فيه أن إيه ال function بعد + +58 +00:04:45,300 --> 00:04:50,160 +التلاتة؟ ماعنديش يبقى هذي does not exist مش موجودة + +59 +00:04:50,160 --> 00:04:56,400 +لأنه لا يوجد عندنا function يبقى كمان هذي does not + +60 +00:04:56,400 --> 00:05:02,470 +existتمام؟ طيب نيجي للي بعدها اللي هو نمرة ست سبعة + +61 +00:05:02,470 --> 00:05:05,690 +بيقول اللي limit ال F of X لما ال X بيطرح ده C + +62 +00:05:05,690 --> 00:05:11,070 +where C موجودة أي نقطة تاخدها في ال interval من + +63 +00:05:11,070 --> 00:05:14,630 +عند الواحد لغاية التلاتة بشرط التلاتة مش منهم + +64 +00:05:14,630 --> 00:05:19,750 +والواحد مش منهم يبقى داخل الفترة من واحد إلى تلاتة + +65 +00:05:19,750 --> 00:05:26,100 +ال limit جداش؟ بينفعش اقول اتنين هنا؟هذه القيمة + +66 +00:05:26,100 --> 00:05:30,340 +وليس انا لما اجرب على الاتنين من جهة اليمين ومن + +67 +00:05:30,340 --> 00:05:34,760 +جهة الشمال بلاقي هذا مجرب على مين؟ على واحد يبقى + +68 +00:05:34,760 --> 00:05:41,390 +limit exist وتساوي جداش كلها وتساوي واحد صحيحيبقى + +69 +00:05:41,390 --> 00:05:45,890 +هذه ال limit أوجدنها من خلال الرسم طبعا أعطيتكم + +70 +00:05:45,890 --> 00:05:50,230 +قبل ذلك سؤال من هذا الموديل هذا تمام؟ و هذا هو + +71 +00:05:50,230 --> 00:05:56,350 +سؤال ثاني طيب ننتقل الآن إلى نوية أخرى من هذه + +72 +00:05:56,350 --> 00:06:05,930 +المسائل كمان مثال أخر بقول find the following + +73 +00:06:05,930 --> 00:06:09,490 +limits + +74 +00:06:12,350 --> 00:06:20,430 +if it exists إذا موجودة بدناها مش موجودة بلاش نمرة + +75 +00:06:20,430 --> 00:06:27,750 +واحد limit لما ال X بده تروح ليه تلاتة ال absolute + +76 +00:06:27,750 --> 00:06:35,830 +value لل X ناقص تلاتة على X تربية ناقص X ناقص ستة + +77 +00:06:35,830 --> 00:06:39,930 +لو + +78 +00:06:39,930 --> 00:06:40,990 +جه تعوض أيوة + +79 +00:06:45,000 --> 00:06:51,320 +بس أنا كدهش ال domain بالله بيقول زميلكوا ال + +80 +00:06:51,320 --> 00:06:54,760 +domain من سالب واحد لغاية تلاتة + +81 +00:06:59,330 --> 00:07:05,330 +كل الدالة معرفة على جميع ال interval من سالب واحد + +82 +00:07:05,330 --> 00:07:10,090 +لغاية تلاتة مافي مشكلة تقدر تجيبلي نقطة اللي بيقول + +83 +00:07:10,090 --> 00:07:14,210 +لأ تقدر تجيبلي نقطة الدالة غير معرفة عندها خلال + +84 +00:07:14,210 --> 00:07:18,970 +الفترة من واحد لتلاتة فيه؟ فهبقى أنا بدي أسألك + +85 +00:07:18,970 --> 00:07:23,980 +كمان سؤال ال range اللي هيقداش؟اسمه عرضين ترويها، + +86 +00:07:23,980 --> 00:07:30,920 +السؤال إيه له؟ من صفر لأ اتنين، من عند اتنين مفتوح + +87 +00:07:30,920 --> 00:07:36,300 +أو لا؟لأ موجودة يبقى هذه clause من zero لغاية + +88 +00:07:36,300 --> 00:07:40,880 +اتنين ليش اتطلع عند اتنين قيمة ده لا يساوي اتنين + +89 +00:07:40,880 --> 00:07:44,660 +هي مفتوحة لكن هي موجودة يبقى ال range clause + +90 +00:07:44,660 --> 00:07:49,680 +interval من zero لغاية اتنين ننتقل للسؤال الثاني + +91 +00:07:49,680 --> 00:07:53,760 +بده limit لهذا المقدار لما ال X بده يروح ليه تلاتة + +92 +00:07:53,760 --> 00:07:59,260 +لو جاء تعاود مباشر يبقى البسط ب zero والمقام كذلك + +93 +00:07:59,260 --> 00:08:00,000 +ب zero + +94 +00:08:03,250 --> 00:08:07,730 +بنرجع الآن بالذاكرة الى الوراء بذاكر تذكير فقط + +95 +00:08:07,730 --> 00:08:11,390 +بتعريف ال absolute value كنا نقول ال absolute + +96 +00:08:11,390 --> 00:08:16,190 +value ل X بيسوي X إذا ال X greater than or equal + +97 +00:08:16,190 --> 00:08:22,340 +to 0 و سلب X إذا ال X أقل من 100خلّي هذه المعلومة + +98 +00:08:22,340 --> 00:08:28,120 +هادى فى دماغك ونحاول نقيص عليها يبقى إذا X موجبة + +99 +00:08:28,120 --> 00:08:33,460 +تبقى لأبسولية فلل X هي X إذا X سالبة يبقى لأبسولية + +100 +00:08:33,460 --> 00:08:38,050 +فلل X ساوية كده؟ سالب Xطيب أنا الأن بدي أحسب هذه + +101 +00:08:38,050 --> 00:08:42,030 +ال limit بدي أجرب أخد ال limit لما ال X بده تروح + +102 +00:08:42,030 --> 00:08:46,570 +لتلاتة من جهة الشمال لل absolute value لل X ناقص + +103 +00:08:46,570 --> 00:08:51,110 +تلاتة على X تربية ناقص X ناقص ستة ويسوي ال limit + +104 +00:08:51,110 --> 00:08:55,800 +لما ال X بده تروح لتلاتة من جهة الشمالطلع عليك + +105 +00:08:55,800 --> 00:08:59,860 +كويس، الآن أنا لما أروح لتلاتة من جهة الشمال، يعني + +106 +00:08:59,860 --> 00:09:04,680 +لما أقول هذا ال real line وهذا عند التلاتة وأنا + +107 +00:09:04,680 --> 00:09:09,840 +رايح للتلاتة من جهة الشمال، يبقى أقل من تلاتة ولا + +108 +00:09:09,840 --> 00:09:15,420 +أكثر؟أقل من تلاتة لما نطرحها من تلاتة بتظهر كمية + +109 +00:09:15,420 --> 00:09:19,960 +سالبة يبقى مادام كمية سالبة إذا ان تعريفها ده + +110 +00:09:19,960 --> 00:09:24,600 +بتظهر جزء زي ما هو بس بإشارة سالبة يبقى هذا بدي + +111 +00:09:24,600 --> 00:09:30,180 +يصير السالب ال X ناقص تلاتة يبقى هي اتخلص من ال + +112 +00:09:30,180 --> 00:09:33,580 +absolute value إذا ال X بتروح لتلتة من جهات اليسار + +113 +00:09:33,580 --> 00:09:41,060 +والمقام بدي أحللهيبقى هاي اكس هاي اكس هنا اتنين + +114 +00:09:41,060 --> 00:09:46,700 +هنا تلاتة هنا ناقص هنا زاد هاي زائد اتنين اكس + +115 +00:09:46,700 --> 00:09:50,880 +وناقص تلاتة اكس بيبقى ناقص اكس بتحليلنا سليم مائة + +116 +00:09:50,880 --> 00:09:55,760 +بالمائة الجث هذا بيروح مع الجث هذا تقول المسألة + +117 +00:09:55,760 --> 00:09:59,840 +الى limit لما ال X بيروح لتلاتة من جهة اليسار + +118 +00:09:59,840 --> 00:10:06,020 +لسالب واحد على X زائد اتنينيبقى limit ال constant + +119 +00:10:06,020 --> 00:10:11,160 +بال constant itself هذا متضال خطي يبقى تعويض مباشر + +120 +00:10:11,160 --> 00:10:17,220 +يبقى النتيجة تساوي كده؟ سالب خمس طب تعالى نشوف هنا + +121 +00:10:17,220 --> 00:10:22,760 +limit من اليمين يبقى limit لما ال X بده تروح لتلتة + +122 +00:10:22,760 --> 00:10:28,420 +من جهة اليمين لل absolute value لل X ناقص تلتة على + +123 +00:10:28,420 --> 00:10:33,680 +ال X تربية ناقص X ناقص ستة يبقى limit لما ال X بده + +124 +00:10:33,680 --> 00:10:37,240 +تروحالى تلاتة من جهة اليمين + +125 +00:10:39,560 --> 00:10:45,280 +تلاتة من جهة اليمين يبقى احنا هنا اكثر من تلاتة + +126 +00:10:45,280 --> 00:10:51,200 +تلاتة وكسر ناقص تلاتة بدل هذا الكسر يبقى هذا دائما + +127 +00:10:51,200 --> 00:10:56,420 +وابدا قيمة موجبة مدام قيمة موجبة يبقى ال absolute + +128 +00:10:56,420 --> 00:11:03,360 +value للمقدر بالمقدر itself على من على x زائد + +129 +00:11:03,360 --> 00:11:09,100 +اتنين في x ناقص تلاتة بالشكل اللي عندنا هذاتمام؟ + +130 +00:11:09,100 --> 00:11:14,460 +نختصر يبقى هنا هذا الجزء مع هذا الجزء ويساوي ال + +131 +00:11:14,460 --> 00:11:19,320 +limit لما ال X بدها تروح إلى تلاتة من جهة اليمين + +132 +00:11:19,320 --> 00:11:25,800 +لواحد على X زائد اتنين تعويض مباشر واحد ع تلاتة + +133 +00:11:25,800 --> 00:11:30,640 +زائد اتنين يساوي جداش خمسيبقى هل ال limit exist + +134 +00:11:30,640 --> 00:11:35,100 +ولا does not exist لأن ال limit من اليمين لا تساوي + +135 +00:11:35,100 --> 00:11:40,440 +ال limit من الشمال يبقى بروح بقول لسه limit لما ال + +136 +00:11:40,440 --> 00:11:46,300 +x بدها تروح لتلاتة absolute value ل x ناقص ثلاثة x + +137 +00:11:46,300 --> 00:11:56,790 +تربية ناقص x ناقص ستة does not existالسبب because + +138 +00:11:56,790 --> 00:12:03,870 +ان ال limit من الشمال لا تساوي ال limit من اليمين + +139 +00:12:03,870 --> 00:12:08,370 +سالب خمس لا يساوي خمس وبالتالي ال limit ما لها + +140 +00:12:08,370 --> 00:12:10,370 +does not exist + +141 +00:12:12,930 --> 00:12:19,850 +المثال الثاني امر اتنين لما + +142 +00:12:19,850 --> 00:12:26,010 +ال X بدأ تروح الى تلاتة كذلك لمين؟ للجذر التربية + +143 +00:12:26,010 --> 00:12:33,090 +اللي تلاتة X في X ناقص تلاتة على absolute value لل + +144 +00:12:33,090 --> 00:12:38,230 +X ناقص تلاتةأنا بهمنيش ال absolute في البقعة و + +145 +00:12:38,230 --> 00:12:43,150 +الله في المقام بأثرش عندي أنا بهمني النتيجة تبعتها + +146 +00:12:43,150 --> 00:12:47,450 +باجي بقول برضه بدي أخد ال limit من اليمين و ال + +147 +00:12:47,450 --> 00:12:53,230 +limit من الشمال و نشوف شو النتج يبقى هاي limit لما + +148 +00:12:53,230 --> 00:12:58,650 +ال X بده تروح لتلاتة من جهة اليسار للجذر التربيه + +149 +00:12:58,650 --> 00:13:04,450 +لتلاتة X في X ناقص تلاتة على absolute value لل X + +150 +00:13:04,450 --> 00:13:09,930 +ناقص تلاتةيبقى limit لما ال X بتروح لتلاتة من جهتي + +151 +00:13:09,930 --> 00:13:16,170 +اليسار الان الجدر التربية لتلاتة X مالوش دعوة X + +152 +00:13:16,170 --> 00:13:19,930 +ناقص تلاتة مالوش دعوة نيجي هذا لما ال X بتروح + +153 +00:13:19,930 --> 00:13:24,590 +لتلاتة من جهتي الشمال هذه قيمة سالبة اذا بتخلص من + +154 +00:13:24,590 --> 00:13:29,180 +ال absolute value بحق مكانهاالـ X ناقص تلاتة + +155 +00:13:29,180 --> 00:13:33,240 +بإشارة سالب، القوس هذا مع القوس هذا الله سهل عليه + +156 +00:13:33,240 --> 00:13:37,900 +يبقى limit لما ال X بدي روح لتلاتة من جهات اليسار + +157 +00:13:37,900 --> 00:13:44,020 +لسالب الجذري التربية لمين لتلاتة Xالان تلاتة في + +158 +00:13:44,020 --> 00:13:50,020 +تلاتة بتسعة تحت الجدر بسالب تلاتة نروح ناخد ال + +159 +00:13:50,020 --> 00:13:54,820 +limit لما ال X بده تروح إلى تلاتة من جهة اليمين + +160 +00:13:54,820 --> 00:14:01,340 +لتلاتة X ناقص تلاتة على absolute value لل X ناقص + +161 +00:14:01,340 --> 00:14:05,940 +تلاتة يبقى limit لما ال X بده يروح لتلاتة من جهة + +162 +00:14:05,940 --> 00:14:11,960 +اليمين لجدر تلاتة X في X ناقص تلاتة علىالـ X بيذهب + +163 +00:14:11,960 --> 00:14:16,800 +لـ 3 من جهة اليمين، يبقى هذه القيمة قيمة موجبة، + +164 +00:14:16,800 --> 00:14:23,120 +إذا نزيل الـ absolute value ونكتبها كما هي بدون + +165 +00:14:23,120 --> 00:14:27,940 +absolute لأنها قيمة موجبة، بروح القوس هذا مع القوس + +166 +00:14:27,940 --> 00:14:33,320 +هذا، آلة المسألة إلى limit، لما الـ X بيذهب لـ 3 + +167 +00:14:33,320 --> 00:14:40,550 +من جهة اليمينلجدر تلاتة X يبقى النتيجة تساوي كده؟ + +168 +00:14:40,550 --> 00:14:45,630 +تساوي تلاتة برضه ال limit من اليمين لا تساوي ال + +169 +00:14:45,630 --> 00:14:50,790 +limit من الشمال يبقى سا limit لما ال X بدي روح + +170 +00:14:50,790 --> 00:14:57,230 +لتلاتة لجدر تلاتة X في X ناقص تلاتة على absolute + +171 +00:14:57,230 --> 00:14:59,590 +value ل X ناقص تلاتة + +172 +00:15:07,730 --> 00:15:17,410 +ما هيش موجودة طيب النقطة التالتة بدنا limit لما + +173 +00:15:17,410 --> 00:15:25,280 +ال X كذلك بدها تروح ليه تلاتة كلها تلاتات اليومX + +174 +00:15:25,280 --> 00:15:35,640 +بدأ تروح لـ 3 لمن؟ لـ X ناقص دلة صحيح X على دالة + +175 +00:15:35,640 --> 00:15:38,800 +السقف لـ X ناقص 2 + +176 +00:16:02,990 --> 00:16:08,690 +خلّيني أقول لك يا عزيزي مرة تذهب تخطيط يمين للشمال + +177 +00:16:08,690 --> 00:16:15,190 +و تدقق معاه كويس تذهب تخطيط لما تذهب ال X تلاتة من + +178 +00:16:15,190 --> 00:16:24,270 +جهة اليسار لل X ناقص دالةلور انتجر فانكشن دالة + +179 +00:16:24,270 --> 00:16:31,570 +الأرض على دالة السقف X ناقص اتنين ويساوي طلع لينا + +180 +00:16:31,570 --> 00:16:37,130 +كويس احنا رايحين لتلاتة من جهة الشمال يبقى هذا + +181 +00:16:37,130 --> 00:16:42,450 +الخط اللي عندي هذا تلاتة قبله اتنين بعده اربعة + +182 +00:16:42,760 --> 00:16:48,620 +رايحين لتلاتة من جهة اليسار يبقى هذه تلاتة ما فيها + +183 +00:16:48,620 --> 00:16:52,440 +مشكلة هذه اللي بدها تساوي اللي انا احنا رايحين + +184 +00:16:52,440 --> 00:16:57,680 +لتلاتة من جهة اليسار يعني احنا اقل من تلاتة اقل من + +185 +00:16:57,680 --> 00:17:01,620 +تلاتة يعني اتنين وحط الكثر اللي بدك هي اتنين وواحد + +186 +00:17:01,620 --> 00:17:06,220 +من عشرة اتنين ونص اتنين وتسعة من عشرة اتنين وتسعة + +187 +00:17:06,220 --> 00:17:09,320 +وتسعين من المئة زي الانتخابات العربية زي ما بدك + +188 +00:17:09,790 --> 00:17:13,350 +ماعناش مشكلة يا بني لما تقولي 92 و تسعية من المية + +189 +00:17:13,350 --> 00:17:19,880 +ماكت نزلها للأرض مازاش تصيرأتنين يبقى تلاتة ناقص + +190 +00:17:19,880 --> 00:17:24,980 +اتنين على اتنين وكسر يعني اتنين و تسعة و تسعين من + +191 +00:17:24,980 --> 00:17:28,780 +الميان ناقص اتنين و تسعة و تسعين من الميان ارفع + +192 +00:17:28,780 --> 00:17:34,400 +على السقف بقداش اب واحد تلاتة ناقص اتنين اب واحد + +193 +00:17:34,400 --> 00:17:40,020 +يساوي قداش واحد بدنا نروح ناخد ال limit لما ال X + +194 +00:17:40,020 --> 00:17:49,320 +بدها تروح لتلاتة من جهة اليمين لل X ناقصدالة الأرض + +195 +00:17:49,320 --> 00:17:57,560 +لل X على دالة السقف X ناقص اتنين يبقى هذه تساوي + +196 +00:17:57,560 --> 00:18:04,260 +هذه تلاتة ناقص هذه تلاتة من جهة اليامين معناته + +197 +00:18:04,260 --> 00:18:10,700 +تلاتة وكسر تلاتة وكسر نزلها للأرض جديش بصير تلاتة + +198 +00:18:12,420 --> 00:18:18,880 +تلاتة وكسر نقص اتنين يبقى بضال واحد وكسر نرفع على + +199 +00:18:18,880 --> 00:18:25,660 +السجن بصير اتنينيبقى الجواب كده؟ Zero طلع هنا واحد + +200 +00:18:25,660 --> 00:18:30,240 +و هنا Zero يبقى ال limit ممتاز جدا يبقى بالدرجة + +201 +00:18:30,240 --> 00:18:36,120 +أقوله ال limit لما ال X بده يروح ليه تلاتة لل X + +202 +00:18:36,120 --> 00:18:42,120 +ناقص دالة الأرض لل X دالة السقف لل X ناقص اتنين + +203 +00:18:42,120 --> 00:18:50,580 +does not exist does not exist + +204 +00:18:53,440 --> 00:18:59,140 +السبب because ان ال limit من اليمين لا تساوي ال + +205 +00:18:59,140 --> 00:19:05,020 +limit من من من الشمال طيب دي اعطيك مثال زي هذا + +206 +00:19:05,020 --> 00:19:10,920 +شبهه واشوف مارشو رأيك في الموضوع يبقى بدنا نيجي + +207 +00:19:10,920 --> 00:19:19,160 +ناخد limit لما ال X بدها تروح ل 3 و 6 من 10 لدالة + +208 +00:19:19,160 --> 00:19:21,940 +السقف ل X على X itself + +209 +00:19:24,940 --> 00:19:31,020 +بتروح اخد limit لما ال X بيروح لتلاتة وستة من عشرة + +210 +00:19:31,020 --> 00:19:40,720 +من جهة الشمال لمين؟ لدالة السقف على X ويسمى تلاتة + +211 +00:19:40,720 --> 00:19:45,320 +وستة من عشرة يعني قبل تلاتة وستة من عشرة يعني قداش + +212 +00:19:45,320 --> 00:19:53,180 +مثلاتلاتة و نص تلاتة و نص ارفع على السقف اربع بصير + +213 +00:19:53,180 --> 00:19:59,000 +هذه اربعة على تلاتة و ستة من عشرة يعني قداش يعني + +214 +00:19:59,000 --> 00:20:07,480 +اربعين على ستة و تلاتين مظبوط يعني عشر اتساع عشرة + +215 +00:20:07,480 --> 00:20:14,840 +على تسعة طب خد لل limitلما ال X بده يروح ل 3 و 6 + +216 +00:20:14,840 --> 00:20:20,360 +من عشرة من جهة اليمين لدالة السقف ل X على X و + +217 +00:20:20,360 --> 00:20:26,720 +يساوي 3 و 6 من عشرة بده ياخد بعدها، إيه يعني؟ 3 و + +218 +00:20:26,720 --> 00:20:33,220 +7 من عشرة، نرفع على السقف الجبيهش، هيبقى 4 على 3 و + +219 +00:20:33,220 --> 00:20:39,410 +6 من عشرة، هيها هادييبقى قداشي الجواب عشرة على + +220 +00:20:39,410 --> 00:20:46,290 +تسعة من الاتنين هدول مش بتقدر تستنتج ان ال limit + +221 +00:20:46,290 --> 00:20:52,490 +لما ال X بده يروح لتلاتة أو ستة من عشرة لدالة + +222 +00:20:52,490 --> 00:20:58,530 +السقف على X يساوي قداشي عشرة تسعة طيب استنى شوية + +223 +00:20:58,530 --> 00:21:04,980 +احنا عندنا مثالينالمثال الأول طلعت النتيجة عنده + +224 +00:21:04,980 --> 00:21:10,160 +جداش does not exist هنا واحد وفوق زيرو صارت does + +225 +00:21:10,160 --> 00:21:16,520 +not exist وهي هذه دالة صحيح X هنا كمان دالة صحيح X + +226 +00:21:16,520 --> 00:21:21,320 +لكن طلعت النتيجة exist ايش ملاحظاتنا على هذا + +227 +00:21:21,320 --> 00:21:25,380 +الكلام؟ اتفضلالخطران الصحيح يكون في نقاط تحول في + +228 +00:21:25,380 --> 00:21:28,540 +جدر ال .. و يكون عضو الصحيح يكون نقطة تحول و يكون + +229 +00:21:28,540 --> 00:21:31,700 +ال .. على ناحية اليمين اللي يختلف على ناحية اليسار + +230 +00:21:31,700 --> 00:21:34,260 +قاعدة او من النقاط اللي فيها عشاب سنة و ثلاثة و + +231 +00:21:34,260 --> 00:21:37,300 +حصة ستة يكون نقاط داخلية داخل القرار على يمين + +232 +00:21:37,300 --> 00:21:40,210 +المجموعة نفس ال .. نفس اللي من حياتهالكلام صحيح + +233 +00:21:40,210 --> 00:21:45,870 +إذا ال limit عندي في حالة دالة صحيح C إذا ال limit + +234 +00:21:45,870 --> 00:21:50,390 +راحت لرقم صحيح بلق ال limit مازالت موجودة بس إذا + +235 +00:21:50,390 --> 00:21:54,530 +راحت لي كثر بلق ال limit مالها موجودة في الغالب + +236 +00:21:54,530 --> 00:21:59,890 +ليش؟ لأن هذه الدالة اسمها step function دالة + +237 +00:21:59,890 --> 00:22:04,570 +القفزة أو الدالة الدرجية أو الدالة السلمية عند + +238 +00:22:04,570 --> 00:22:08,630 +العدد الصحيحبيحصل ال discontinuity أو بيحصل منين + +239 +00:22:08,630 --> 00:22:11,610 +القفزة بصير ال limit من اليمين تختلف عن ال limit + +240 +00:22:11,610 --> 00:22:16,110 +من الشمال وبالتالي ال limit ما لها does not exist + +241 +00:22:16,110 --> 00:22:23,350 +طيب نعطيك كمان مثال غير هذه الأمثلة ونشوف شو رأيك + +242 +00:22:23,350 --> 00:22:30,010 +فيه وبعدها بنطرح عدة تساؤلات أو بعض التساؤلات + +243 +00:22:30,010 --> 00:22:37,420 +ونشوف كيف بدنا نجاوب عليهاناخد كمان مثال رقم خمسة + +244 +00:22:37,420 --> 00:22:51,720 +بيقول ما يأتي خمسة بيقول بده limit لل F of X لما + +245 +00:22:51,720 --> 00:23:00,900 +ال X بدها تروح لثلاثة where ال F of X أحد أمرين + +246 +00:23:02,380 --> 00:23:10,580 +الأمر الأول X تربية ناقص خمسة لما ال X أقل من أو + +247 +00:23:10,580 --> 00:23:17,660 +يسوى تلاتة أو الجذر التربية إلى X زائد تلتاشر لما + +248 +00:23:17,660 --> 00:23:20,360 +ال X greater than تلاتة + +249 +00:23:44,700 --> 00:23:50,980 +هذا السؤال طبعا شكله يختلف عن شكل الأربعة السابقة + +250 +00:23:50,980 --> 00:23:55,880 +أول سؤالين كانوا بيشتملوا على ال absolute value + +251 +00:23:55,880 --> 00:24:01,460 +القيمة المطلقة والسؤالين التانية كانوا بيشتملوا + +252 +00:24:01,460 --> 00:24:06,780 +على دالة العدد الصحيح سواء كانت integer floor + +253 +00:24:06,780 --> 00:24:11,820 +function أو integer ceiling functionهذا السؤال + +254 +00:24:11,820 --> 00:24:17,100 +بيكون من جزئين يعني هذه piecewise function تبقى + +255 +00:24:17,100 --> 00:24:23,160 +مكونة منها من جزئين طيب بلاحظ ان الجزئين هدول + +256 +00:24:23,160 --> 00:24:29,290 +بيختلفوا عن بعض وين عند العدد رقم تلاتةإذا عندى + +257 +00:24:29,290 --> 00:24:33,570 +التلاتة هذه ممكن أخد ال limit من اليمين ولا اخد ال + +258 +00:24:33,570 --> 00:24:36,530 +limit من الشمال بل إجباري لازم أخد ال limit من + +259 +00:24:36,530 --> 00:24:41,230 +اليمين و ال limit من الشمال إذا بدأت ياخد limit + +260 +00:24:41,230 --> 00:24:47,090 +لما ال X بده تروح لتلاتة من جهة الشمال لل F of X + +261 +00:24:47,090 --> 00:24:51,450 +يبقى limit لما ال X بده تروح لتلاتة من جهة الشمال + +262 +00:24:52,000 --> 00:24:56,940 +تلاتة من جهة الشمال يعني احنا ماله اقل من تلاتة + +263 +00:24:56,940 --> 00:25:02,100 +وقد تساوي، اذا بيكون شكل الدالة هو من اكس تربية + +264 +00:25:02,100 --> 00:25:06,880 +ناقص خمسة، يبقى اكس تربية ناقص خمسة، هذه + +265 +00:25:06,880 --> 00:25:12,050 +polynomial من الدرجة الثانية يبقى تعويض مباشريبقى + +266 +00:25:12,050 --> 00:25:16,510 +هذه بيصير تلاتة لكل تربيع ناقص خمسة اللي هو جداش + +267 +00:25:16,510 --> 00:25:22,570 +أربع بعد هيك بدنا نروح ناخد limit ال F of X لما ال + +268 +00:25:22,570 --> 00:25:30,770 +X بده يروح لمن؟ لتلاتة من جهة اليمينLimit لما ال X + +269 +00:25:30,770 --> 00:25:35,230 +بده يروح لتلاتة من جهة اليمين تلاتة من جهة اليمين + +270 +00:25:35,230 --> 00:25:39,950 +معناته ال X معلها أكبر من تلاتة بيكون ال function + +271 +00:25:39,950 --> 00:25:45,950 +هي عبارة عن الجدر التربية ل X زائد 100 زائد 13 + +272 +00:25:45,950 --> 00:25:51,370 +الآن لما ناخدنا قوانين ال limit في ال section قبل + +273 +00:25:51,370 --> 00:25:57,770 +الماضيقلنا هذا ال limit معاها الصلاحيات وبتدخل تحت + +274 +00:25:57,770 --> 00:26:02,710 +الجدر لما تدخل تحت الجدر اللي تحت الجدر دالة خطية + +275 +00:26:02,710 --> 00:26:08,490 +مدام دالة خطية يبقى تعويض مباشر يبقى النتيجة تساوي + +276 +00:26:08,490 --> 00:26:14,810 +الجدر لتلاتة زائد تلتاشر اللي هو جدات أربعة مدام + +277 +00:26:14,810 --> 00:26:18,930 +أربعة يبقى صارت النتيجة من اليمن اللي بلعب في + +278 +00:26:18,930 --> 00:26:23,840 +الجوال يرمي الجوال وإلايبقى صارت ال limit من + +279 +00:26:23,840 --> 00:26:28,700 +اليمين زي ال limit من الشمال وبالتالي أصبح عندنا + +280 +00:26:28,700 --> 00:26:34,780 +ال limit لل F of X لما ال X بتروح ل 3 exist وتساوي + +281 +00:26:34,780 --> 00:26:40,120 +كده؟ تساوي 4 يبقى ال limit في هذه الحالة يساوي 4 + +282 +00:26:40,120 --> 00:26:44,900 +بدنا نعطي كمان مثال على ال piecewise function بس + +283 +00:26:44,900 --> 00:26:59,620 +بشكل آخر المثال بيقول ما يأتي نمرة 6ستة بيقولي او + +284 +00:26:59,620 --> 00:27:03,940 +بيخلي example لحاله example جديد باعتباره يبقى هذا + +285 +00:27:03,940 --> 00:27:08,120 +example بيقول + +286 +00:27:08,120 --> 00:27:17,070 +لاتالـ F of X يسوى أحد أمرين يا إما AX plus one + +287 +00:27:17,070 --> 00:27:23,230 +لما الـ X less than or equal to three يا إما AX + +288 +00:27:23,230 --> 00:27:29,890 +square minus one لما الـ X greater than three find + +289 +00:27:29,890 --> 00:27:34,690 +the value + +290 +00:27:37,490 --> 00:27:49,230 +Find the value of the constant A + +291 +00:27:49,230 --> 00:28:00,530 +هات المقدار الثابت A such that بحيث أن limit + +292 +00:28:23,840 --> 00:28:30,940 +سؤال هذا زي السؤال اللي قبله لكن بفكرة جديدةطبعا + +293 +00:28:30,940 --> 00:28:35,140 +زي ما انت شايف هو piecewise function دل مجزئي + +294 +00:28:35,140 --> 00:28:39,840 +لجزئين بدنا نقرأ هذا السؤال و نفهم ما هو المطلوب + +295 +00:28:39,840 --> 00:28:44,100 +منه السؤال ميعطيني ال F of X على الشكل اللي قدامنا + +296 +00:28:44,100 --> 00:28:49,920 +X plus one لما X أقل من أو يسوى تلاتة و X square + +297 +00:28:49,920 --> 00:28:54,710 +minus one لما X greater than تلاتةواللي هاتلي + +298 +00:28:54,710 --> 00:29:00,390 +مقبار ثابت ايه بحيث ال limit هذه مالها exist سؤال + +299 +00:29:00,390 --> 00:29:03,510 +اللي يقبله ماكنتش عارف انا exist ولا لأ حسبت ال + +300 +00:29:03,510 --> 00:29:05,590 +limit من اليمين و ال limit من الشمال اللي جيتنا مع + +301 +00:29:05,590 --> 00:29:08,650 +بعضك وقلت لو exist what ساوي أربع هنا بقول لي لأ + +302 +00:29:08,650 --> 00:29:13,310 +ال limit exist بس هو مش عارفهاو من خلال هذا الكلام + +303 +00:29:13,310 --> 00:29:16,250 +بيقوللي هاتلي قيمة الثابت ايه بقولله مادام ال + +304 +00:29:16,250 --> 00:29:20,110 +limit exist إذا ال limit من اليامين تسوي ال limit + +305 +00:29:20,110 --> 00:29:24,610 +من الشمال يبقى أنا بده أحسب ال two limits وبعدين + +306 +00:29:24,610 --> 00:29:29,170 +بسويهم بعض و بجيب قيمة الثابت ايه أصبح يبقى بناء + +307 +00:29:29,170 --> 00:29:36,090 +عليه بدهجي أقوله بدهجي أاخد limitالـ F of X لما + +308 +00:29:36,090 --> 00:29:42,790 +الـ X بده يروح لتلاتة من جهة الشمال يبقى هذا ال + +309 +00:29:42,790 --> 00:29:48,010 +limit لما الـ X بده يروح لتلاتة من جهة اليسار من + +310 +00:29:48,010 --> 00:29:53,550 +جهة اليسار يبقى X أقل من أو يسوى تلاتةيبقى الدالة + +311 +00:29:53,550 --> 00:30:01,430 +عبارة عن ايش؟ ax plus one يبقى ax plus one ويساوي + +312 +00:30:01,430 --> 00:30:07,050 +هذه الدالة دالة خطية يبقى عند حساب الليمت عوّب + +313 +00:30:07,050 --> 00:30:14,240 +تعويضا مباشرا يبقى دي بيصير تلاتة a plus oneبعد + +314 +00:30:14,240 --> 00:30:18,800 +هيك بروح اخد ال limit لما ال X بده يروح لتلاتة من + +315 +00:30:18,800 --> 00:30:25,360 +جهة اليمين لل F of X يبقى limit لما ال X بده تروح + +316 +00:30:25,360 --> 00:30:32,220 +لتلاتة من جهة اليمين لمن لل A X square minus one X + +317 +00:30:32,220 --> 00:30:37,320 +أكبر من تلاتة يبقى تروح للتلاتة من جهة اليمين يبقى + +318 +00:30:37,320 --> 00:30:42,720 +بتكون هذه هيبالا، هذه البرنامج المن الدرجة + +319 +00:30:42,720 --> 00:30:49,000 +الثانية، إذا تعويض مباشر يبقى ا في تلاتة لكل تربيع + +320 +00:30:49,000 --> 00:30:56,080 +ناقص واحد، يبقى تسعة ا ناقص واحد، من الاتنين هدول، + +321 +00:30:56,080 --> 00:31:01,730 +جال ال limit exists، يبقى باجي بقوله sinceبما ان + +322 +00:31:01,730 --> 00:31:09,990 +limit لل F of X لما ال X بيروح ليه تلاتة exists we + +323 +00:31:09,990 --> 00:31:15,190 +have ايش + +324 +00:31:15,190 --> 00:31:21,890 +بيحصل انها تلاتة A زائد واحد بتسوى تسعة A ناقص + +325 +00:31:21,890 --> 00:31:26,730 +الواحدبنجيب الإيهات عن بعض و ال constants عن بعض + +326 +00:31:26,730 --> 00:31:32,530 +بيصير ستة ايه يساوي اتنين و منها ايه يساوي قداش + +327 +00:31:32,530 --> 00:31:38,330 +تلت اذا ايه لما تكون تلت هي اللي خلت ال limit + +328 +00:31:38,330 --> 00:31:42,750 +مالها exist يبقى فكرة السؤال مثل فكرة السؤال اللي + +329 +00:31:42,750 --> 00:31:49,100 +جابله لكن فيها شغلة فنية جديدة شويةخلّينا نوقف + +330 +00:31:49,100 --> 00:31:56,140 +وقفة محاسبة مع النفس ونسأل بعض التسوئلات ونشوف كيف + +331 +00:31:56,140 --> 00:32:00,920 +بدنا نجاوب عليها احنا سابقا قبل أن ناخد هذا ال + +332 +00:32:00,920 --> 00:32:04,460 +section لا كنا بناخد نهاية من اليمين ولا نهامش + +333 +00:32:04,460 --> 00:32:09,240 +واللي بيعطيني هذا السؤال و تك بضرب في المرافق بحلل + +334 +00:32:09,240 --> 00:32:15,020 +و اختصر بمش عارف اعمل شغل زي هيك ايه لو بيطلع عياش + +335 +00:32:15,020 --> 00:32:16,480 +الجواب ان + +336 +00:32:19,360 --> 00:32:26,440 +السؤال هو متى نأخذ النهاية من اليمين والنهاية من + +337 +00:32:26,440 --> 00:32:29,620 +اليسار لل function اللي عندنا؟ + +338 +00:32:35,560 --> 00:32:40,740 +يعني قصدك لو كانت الدالة غير معرفة عندها نقطة، + +339 +00:32:40,740 --> 00:32:47,300 +كلام كويس، ايوة، + +340 +00:32:47,300 --> 00:32:51,980 +ماشي وجهة نظر سليمة، + +341 +00:32:51,980 --> 00:32:55,960 +نقاط تحول، كلام كويس + +342 +00:32:59,820 --> 00:33:06,680 +يبقى هذه الأمثلة اللي أعطناها اتعمد أجيبها أمثلة + +343 +00:33:06,680 --> 00:33:10,480 +على الحالات اللي بدنا نروح ناخد فيها ال limit من + +344 +00:33:10,480 --> 00:33:15,600 +اليمين و ال limit من اليسار لذلك بدنا نخليك تكتبها + +345 +00:33:15,600 --> 00:33:19,280 +بالعربي حتى وين ما تشوف مسألة من هذا القبيل تعرف + +346 +00:33:19,280 --> 00:33:24,460 +كيف نتجاوب عليها اكتبلي بالعربي متى ناخد النهاية + +347 +00:33:24,460 --> 00:33:26,760 +من اليمين و من اليسار + +348 +00:33:29,340 --> 00:33:35,300 +متى ناخذ أو نحسب النهاية من اليمين ومن اليسار + +349 +00:33:35,300 --> 00:33:43,780 +الإجابة في الحالات التالية في الحالات الأربعة + +350 +00:33:43,780 --> 00:33:49,260 +التالية الحالة + +351 +00:33:49,260 --> 00:33:56,800 +الأولى إذا احتوت المسألة على + +352 +00:33:56,800 --> 00:33:58,560 +القيمة المطلقة + +353 +00:34:06,030 --> 00:34:17,470 +إذا احتوت المسألة على دالة صحيح سين ولا صحيح إكس + +354 +00:34:17,470 --> 00:34:24,150 +صحيح إكس بنجو سين بتقدر تكتب دالة السقف ودالة + +355 +00:34:24,150 --> 00:34:34,030 +الأرض دالة السقف ودالة الأرض للعدد الصحيح نمر + +356 +00:34:34,030 --> 00:34:45,940 +تلاتةإذا كانت الدالة مجزئة إلى عدة أجزاء زي + +357 +00:34:45,940 --> 00:34:51,840 +السؤالين الأثنين الأخيرين هؤلاء اللي بقى نقولها + +358 +00:34:51,840 --> 00:34:58,800 +piecewise function دالة مجزئة إلى أجزاء نمر أربعة + +359 +00:34:58,800 --> 00:35:06,380 +إذا كانت الدالة غير معرفة + +360 +00:35:08,580 --> 00:35:24,680 +عند النقطة المراد إيجاد النهاية عندها تمام؟ طبعا + +361 +00:35:24,680 --> 00:35:28,420 +هذه ان شاء الله هنتعرضلها في ال section مش القادم + +362 +00:35:28,420 --> 00:35:33,480 +اللي بعده هنرجع للنقطة الرابعة هذه الأخيرة ان شاء + +363 +00:35:33,480 --> 00:35:37,160 +الله ونعطي عليها أمثلة كثيرة أيضا + +364 +00:35:39,840 --> 00:35:47,580 +هي عندك مثال ايه؟ كيف؟ الأول ليش ما فنتوش؟ ليش ما + +365 +00:35:47,580 --> 00:35:52,560 +قلت إن أنا من هنا؟ ليه ولا هدى؟ أنت عندك X بتروح + +366 +00:35:52,560 --> 00:35:57,660 +لرقم، أخدت من الشمال قبل الرقم هذا، أخدت من اليمين + +367 +00:35:57,660 --> 00:36:02,280 +يعني بعد الرقم هذا، قبل الرقم هذا، لا السقف، بطلع + +368 +00:36:02,280 --> 00:36:05,980 +للرقم الصحيح اللي فوق، ده للأرض، بنزل للرقم الصحيح + +369 +00:36:05,980 --> 00:36:08,040 +اللي من التحت وكذا، الله بالسر علينا + +370 +00:36:21,870 --> 00:36:24,670 +خالصة طيب + +371 +00:36:37,650 --> 00:36:43,170 +الان زي ما انت شايف اعطيناك بدل المثال خمسة وكلها + +372 +00:36:43,170 --> 00:36:47,270 +ماجيبناش فيها سيرة النسب المثلثية على الأطلاق + +373 +00:36:47,270 --> 00:36:53,850 +ولذلك بنحاول نربط القديم بالجديد ندخل النسب + +374 +00:36:53,850 --> 00:36:59,590 +المثلثية في موضوع ال limits بنذكرك بنظرية، النظرية + +375 +00:36:59,590 --> 00:37:05,500 +هذه أخدتها في الثانوية العامة بنذكر بتذكركنت + +376 +00:37:05,500 --> 00:37:12,820 +بتقولوا ما يأتي اسمع انت وياه limit جا سين على سين + +377 +00:37:12,820 --> 00:37:18,760 +لما سين بتروح ل zero بيبقى تساوي واحد مظبوط او + +378 +00:37:18,760 --> 00:37:23,440 +limit لضع سين على سين لما سين بتروح ل zero برضه + +379 +00:37:23,440 --> 00:37:29,740 +تساومين يبقى هذه النظرية بدنا نكتبها و نشتغل عليها + +380 +00:37:29,740 --> 00:37:32,280 +العديد من الأمثلة + +381 +00:37:36,390 --> 00:37:42,030 +يبقى بتيجي تقولي ال limits involving + +382 +00:37:42,030 --> 00:37:45,470 +sin + +383 +00:37:45,470 --> 00:37:57,630 +θ على θ لأ لأ نفس ال section نظرية + +384 +00:37:57,630 --> 00:38:09,590 +limitلـsin θ على θ لما θ بدها تروح للـ0 يسوى 1 and + +385 +00:38:09,590 --> 00:38:19,450 +limit لما θ بدها تروح للـ0 لـθ على sin θ يسوى 1 + +386 +00:38:19,450 --> 00:38:20,230 +كذلك + +387 +00:38:35,490 --> 00:38:36,330 +عشان يبقى سهل + +388 +00:39:44,960 --> 00:39:49,720 +اللي بقى لك هناطبعا هذه اللي أخدته في التنوية + +389 +00:39:49,720 --> 00:39:54,660 +العامة بنذكر بها تذكير لسؤالها لكن بهمنا كيفية + +390 +00:39:54,660 --> 00:39:58,840 +استخدامهاطبعا الكتاب رايح انبرهان احنا بننشط برهين + +391 +00:39:58,840 --> 00:40:02,700 +بس الله يعطيك العافية عرفنا ياها وبنقولك ما هو + +392 +00:40:02,700 --> 00:40:07,980 +السبب اللي خلى ال limit لها تساوي واحد صحيح يبقى + +393 +00:40:07,980 --> 00:40:11,840 +limit لصين ثيتا على ثيتا لما ثيتا تساوي zero بده + +394 +00:40:11,840 --> 00:40:17,320 +يساوي واحد لو رحنا جلبناها جلبنا ثيتا فوق والصين + +395 +00:40:17,320 --> 00:40:22,970 +تحتيبقى بتعطيك نفس النتيجة اللي هي واحد يبقى limit + +396 +00:40:22,970 --> 00:40:26,830 +لثيتا على sin ثيتا لما ثيتا بتروح على zero بتسوي + +397 +00:40:26,830 --> 00:40:31,110 +قداش واحد هذه الرسمة اللي احنا رسمينها اللي هي + +398 +00:40:31,110 --> 00:40:39,070 +رسمة main sin theta على thetaالمنحنة عند الـ zero + +399 +00:40:39,070 --> 00:40:46,190 +ده اللي غير معرفة، طبعا، طيب، هذه بتنزل عند الـ + +400 +00:40:46,190 --> 00:40:50,350 +zero، يعني عند الـ zero بتكون وصلت أقصى ما يمكن، + +401 +00:40:50,350 --> 00:40:55,170 +بتنزل عند السلب by أكتر، بعدك بتصير أقل، أقل و + +402 +00:40:55,170 --> 00:40:59,750 +هكذا، و من الناحية التانية بنفس main بنفس الطريقة + +403 +00:40:59,750 --> 00:41:04,780 +اللي عندناطيب الآن من الرسم اللى قدامنا هذه لو + +404 +00:41:04,780 --> 00:41:09,540 +روحت أخدت ال limit من الشمال و ال limit من اليمين + +405 +00:41:09,540 --> 00:41:17,040 +يبقى limit ل sin θ على θ لما θ بدأ تروح ل zero من + +406 +00:41:17,040 --> 00:41:23,190 +جهة الشمال لو احنا روحنا ل zero من جهة الشماليبقى + +407 +00:41:23,190 --> 00:41:28,430 +الدالة الطائحة للواحد يبقى هذه بدل ساعة واحد and + +408 +00:41:28,430 --> 00:41:36,150 +لو روحنا أخدنا limit ل sin θ على θ لما θ راحت لل + +409 +00:41:36,150 --> 00:41:44,720 +zero من جهة اليمينيبقى يساوي كمان؟ يساوي واحد يبقى + +410 +00:41:44,720 --> 00:41:50,060 +بناء عليه ال limit اللي فوق هذا يبقى كم؟ واحد يبقى + +411 +00:41:50,060 --> 00:41:56,220 +هذا بدي يعطيك دائما و أبدا ان ال limit لمين؟ ل + +412 +00:41:56,220 --> 00:42:01,400 +sign theta على theta لما theta بده تروح لل zero + +413 +00:42:01,400 --> 00:42:07,470 +بده تساوي واحدرغم انه عشان عند ال zero الدالة is + +414 +00:42:07,470 --> 00:42:12,950 +undefined ماهياش معرف لإنه sign zero ب zero صار + +415 +00:42:12,950 --> 00:42:16,590 +zero على zero كمية غير معينة وبالتالي الدالة هذه + +416 +00:42:16,590 --> 00:42:22,910 +مالها غير معرفة بهمنا الآن كيفية استخدام هذه + +417 +00:42:22,910 --> 00:42:29,750 +النظريةفي حل المسائل المختلفة يبقى بنيجي نقولك + +418 +00:42:29,750 --> 00:42:39,650 +احسب للنهايات التالية إذا كانت موجودة example find + +419 +00:42:39,650 --> 00:42:45,970 +the following limits + +420 +00:42:45,970 --> 00:42:50,750 +النهايات + +421 +00:42:50,750 --> 00:42:57,130 +التالية نمرة واحدبعد ذلك بدنا limit لما ال X بده + +422 +00:42:57,130 --> 00:43:04,190 +تروح ل zero لل sign X على 2 على X + +423 +00:43:11,440 --> 00:43:17,320 +طلع لهنا تاني للنظرية limit sin θ على θ لما θ + +424 +00:43:17,320 --> 00:43:22,640 +بتروح للزيرو يساوي واحد، بدي الزاوية، هي نفسها + +425 +00:43:22,640 --> 00:43:27,400 +اللي هنا، هي نفسها اللي بدها تروح لمين، للزيرو + +426 +00:43:28,620 --> 00:43:34,000 +بعدين باطلع في مثلة هنا X على 2 وهنا X وهنا X بدي + +427 +00:43:34,000 --> 00:43:38,240 +هدي X على 2 و بدي هدي X على 2 وبالتالي بقدر استخدم + +428 +00:43:38,240 --> 00:43:42,800 +النظرية مباشرة يعني كأنه ثيتا صارت في الجداش ثيتا + +429 +00:43:42,800 --> 00:43:48,880 +على 2 بقوله بسيطة يعني هنا لو هدي كانت X على 2 كان + +430 +00:43:48,880 --> 00:43:53,980 +المشكلة انحلت صحيح ولا لا؟ يبقى بقول اضرب في نص و + +431 +00:43:53,980 --> 00:44:02,830 +اجسم على نصلا تتغير القيمة يبقى بناء عليه هذي بدها + +432 +00:44:02,830 --> 00:44:09,110 +تساوي ال limit لما ال X بدها تروح لمين؟ ل Zero ل + +433 +00:44:09,110 --> 00:44:19,100 +نص Sign X على 2 على X على 2صارت هذه الزاوية هي + +434 +00:44:19,100 --> 00:44:24,820 +اللي تحت، بس هذه لأ، بقول أضرب هذه في نص، بصير نص + +435 +00:44:24,820 --> 00:44:31,000 +في X، نص في X، نص في Zero، ب Zero، يبقى هذا الكلام + +436 +00:44:31,000 --> 00:44:37,920 +يساوي، النص هذا بدي أخليه برا هيوهذا ال limit هذي + +437 +00:44:37,920 --> 00:44:46,300 +بتصير نص X والله X على 2 X على 2 تروح لل Zero لمن؟ + +438 +00:44:46,300 --> 00:44:53,630 +لصين X على 2 على X على 2صارت الزاوية اللي هنا هي + +439 +00:44:53,630 --> 00:44:59,230 +اللي هنا هي اللي هنا يبقى نص في واحد يبقى الجواب + +440 +00:44:59,230 --> 00:45:04,710 +يساوي قداش يساوي نص يعني المطلوب منك إنك تحور + +441 +00:45:04,710 --> 00:45:09,270 +المسألة تبعتها تكون على شكل النظرية وبالتالي + +442 +00:45:09,270 --> 00:45:10,850 +باستخدم النظرية أيضا + +443 +00:45:30,660 --> 00:45:33,460 +مثال اتنين + +444 +00:45:40,820 --> 00:45:46,020 +مثال اتنين بيبنى ال limit لما ال X بدى روح لل zero + +445 +00:45:46,020 --> 00:45:57,840 +لتان خمسة X على من؟ على تلاتة X اول + +446 +00:45:57,840 --> 00:46:05,720 +شي هدى تان و ليست ساعة اتنين اتنين الزاوية عندى + +447 +00:46:05,720 --> 00:46:13,690 +خمسة X و اللى تحت مالها تلاتة Xمضرو في ايش؟ ولا + +448 +00:46:13,690 --> 00:46:17,670 +مدي أضرو في خمسة أو تلاتة ولا عادي بس اسمعني كويس + +449 +00:46:17,670 --> 00:46:24,650 +اسمع كويس بس بدأ نمشي step by step خطوة بخطوة أنا + +450 +00:46:24,650 --> 00:46:28,890 +بقول بدلي التلاتة هذه لو كانت خمسة كان مشكلتي + +451 +00:46:28,890 --> 00:46:33,570 +محلولةيبقى يا تلف بده يخليك برا وبعدك بده نضغط في + +452 +00:46:33,570 --> 00:46:38,130 +خمسة ونقسم على خمسة أو على رأيكوا نضغط في خمسة على + +453 +00:46:38,130 --> 00:46:43,230 +تلاتة ونقسم على خمسة على تلاتة كلام مظبوط وماحدش + +454 +00:46:43,230 --> 00:46:48,560 +إله اعتراب على ذلك اسمه يا ابن ايه؟يبقى أنا بدّى + +455 +00:46:48,560 --> 00:46:53,460 +أخلّي هذه بدل تلاتة بدّى أخلّيها خمسة يبقى بدأ + +456 +00:46:53,460 --> 00:46:57,460 +أضرب في خمسة على تلاتة وهنا أضرب في خمسة على تلاتة + +457 +00:46:57,460 --> 00:47:02,740 +بيصير الكلام صحيح يعني هذه بدها أصير ال limit هاي + +458 +00:47:02,740 --> 00:47:12,440 +خمسة على تلاتة التان عبارة عن signخمسة اكس على هذه + +459 +00:47:12,440 --> 00:47:17,860 +صارت تلاتة مع تلاتة صارت خمسة اكس و هنا cosine + +460 +00:47:17,860 --> 00:47:25,620 +خمسة اكسيبقى 10 عملتها sign على cosine ضربت في + +461 +00:47:25,620 --> 00:47:29,640 +خمسة على تلاتة وانا ضربت في خمسة على تلاتة راحت + +462 +00:47:29,640 --> 00:47:36,300 +التلاتة مع تلاتة ضلت كدهش ضلت خمسة بقول كويس هذه + +463 +00:47:36,300 --> 00:47:43,320 +ال X بدي روح لوين ل zeroالان هذا مقدار ثابت، بقوله + +464 +00:47:43,320 --> 00:47:48,660 +شرفنا برا، يبقى هذا مقدار ثابت خليك برا، وهذا + +465 +00:47:48,660 --> 00:47:58,130 +limit، وهذا sign خمسة X على خمسة Xهذا يا شباب لما + +466 +00:47:58,130 --> 00:48:03,910 +تبقى ال X بدها تروح لل Zero لو ضربتها في خمسة + +467 +00:48:03,910 --> 00:48:08,250 +بيصير خمسة X بتروح ل Zero في خمسة ليه بيبقى داشت؟ + +468 +00:48:08,250 --> 00:48:14,470 +Zero يبقى الذي يكافئ هذه هي خمسة X بدها تروح لمين؟ + +469 +00:48:14,470 --> 00:48:21,370 +لل Zero By للمين؟ Limit لما ال X بدها تروح ل Zero + +470 +00:48:21,370 --> 00:48:30,670 +لواحد على Cos 5Xيعني جزأتي limit لمن؟ limit للدالة + +471 +00:48:30,670 --> 00:48:34,510 +الأولى هذه اللي عندنا و limit للدالة التانية + +472 +00:48:34,510 --> 00:48:40,450 +الأولى ضربت الساهم هذا في خمسة والتاني خليته زي ما + +473 +00:48:40,450 --> 00:48:44,950 +هو يبقى النتيجة تساوية هذه الخمسة اعتلتها اللي برا + +474 +00:48:44,950 --> 00:48:50,720 +بالداخل هذهأليست في صيغة النظرية اللي قدامي هذه + +475 +00:48:50,720 --> 00:48:56,200 +إذا بقدر أشيلها و أكتب لها قداش واحد صحيح بيبقى + +476 +00:48:56,200 --> 00:49:03,680 +هذه واحد على عوض تعدماش ال cosine صفر بواحد يبقى + +477 +00:49:03,680 --> 00:49:09,480 +على واحد إذا النتيجة تساوي إيش خمسة على تلتة + +478 +00:49:18,340 --> 00:49:24,300 +بتسمعش بيقول من هنا بدي أقسم البصد و المقام على + +479 +00:49:24,300 --> 00:49:29,120 +إكس بصير التلت برا و بصير تان خمس إكس على إكس + +480 +00:49:33,460 --> 00:49:38,540 +يعني انت بصير المقام شيلته وصار كله في البص و البص + +481 +00:49:38,540 --> 00:49:42,560 +بص على مقام مكانك لم تأتي بجديد + +482 +00:49:55,270 --> 00:50:01,370 +أنا بديش تحفظ الهفظ، أنا بدي تفهم كيف توصل مسألتك + +483 +00:50:01,370 --> 00:50:06,150 +إلى صيغة النظرية، وهذا هو الشغل الرياضي، اسمع + +484 +00:50:06,150 --> 00:50:10,120 +كويس، افهمني كويسأنا ماأريد منك حفيظ، انا اريد منك + +485 +00:50:10,120 --> 00:50:14,380 +فهم، اريد منك تفهم كيف أجت، بقول أخدنا فتنة، بقولك + +486 +00:50:14,380 --> 00:50:17,760 +صح، اللي أخدته في ثانوية صحية، بس هاد انت حفظت + +487 +00:50:17,760 --> 00:50:21,280 +حفظت، من حد ما تشوف الرقم X بالرقم ع الرقم وامشي، + +488 +00:50:21,280 --> 00:50:26,000 +لو عملت في الجامعة بنحطلك علامة استفهام من أين لك + +489 +00:50:26,000 --> 00:50:30,160 +هذا، و ده السؤال عليه أربع علامة يمكن نحطلك علامة، + +490 +00:50:30,160 --> 00:50:34,400 +بس و التلاتة بتطيروافي الجامعة يا شباب justify + +491 +00:50:34,400 --> 00:50:39,240 +your answer يعني بتبين إجابتك من وين جبتها، ما هو + +492 +00:50:39,240 --> 00:50:42,840 +جبتها إذا حطيت الإجابة دغري أنا أفهم إنه أحد + +493 +00:50:42,840 --> 00:50:48,620 +أمرين، يا إما عندك ال fox تبعك هذا اللي هو على + +494 +00:50:48,620 --> 00:50:52,560 +الحاسبة، من نوع fox بتعطيك الإجابة دغري، بتعطيكش + +495 +00:50:52,560 --> 00:50:56,850 +خطوات، يا إما ال radar جابها يمين أو شمالأو واحدة + +496 +00:50:56,850 --> 00:51:00,710 +من الاتنين، مالهاش تفتينا من غير هيك، ولذلك تاخدش + +497 +00:51:00,710 --> 00:51:05,570 +عليها شيء، لأ أنا بقولك خلّي كل خطوة و تختصرش، و + +498 +00:51:05,570 --> 00:51:09,270 +أنت بتحل إياك أن تختصر، خلّيني كل خطوة أتسلم + +499 +00:51:09,270 --> 00:51:13,090 +للتانية، لإن احنا بحط علامات على الخطوات و ليس على + +500 +00:51:13,090 --> 00:51:16,610 +الإجابة النهائية، يعني ممكن تبقى خطواتك صح و أنت + +501 +00:51:16,610 --> 00:51:21,450 +غلط بس في الإجابة النهائية، بحطلك مش أقل من تسعين + +502 +00:51:21,450 --> 00:51:26,190 +في المية من الدرجةلكن انا بتحطقني جواب بعطيك درجة، + +503 +00:51:26,190 --> 00:51:31,550 +بعطيك عشرين في المية بس، اه؟ هو بعد هيك في أسئلة + +504 +00:51:31,550 --> 00:51:35,710 +في الليل في الزوايا المثلثية في المعدد، أحل الصلاة + +505 +00:51:35,710 --> 00:51:38,870 +صفحات لغير ما كنتوا حتى الحاجات هتتوا، قبل ما توصل + +506 +00:51:38,870 --> 00:51:42,430 +لقميها اللي بطبصي، الحل هيكون صفحة. فانت شو قلتلك + +507 +00:51:42,430 --> 00:51:47,600 +هنا؟بهمنا .. انا بهمنيش اللي هو الجامعة، بهمني + +508 +00:51:47,600 --> 00:51:51,400 +الخطوات الرياضية، طريقة الحل، هي اللي انا بتبقىها + +509 +00:51:51,400 --> 00:51:56,320 +وانا بوزع الدرجات على خطوات الحل، الخطوة مالاقاش + +510 +00:51:56,320 --> 00:52:00,920 +بطيب درجتها، هي كاننا في الجامعة، يعني بدنا الطالب + +511 +00:52:00,920 --> 00:52:05,840 +يطلع فاهم مش حافظ، انك تطلع فاهم، كويس، هاي سؤال، + +512 +00:52:05,840 --> 00:52:06,080 +اه + +513 +00:52:10,830 --> 00:52:15,430 +فهمتش؟ أقولك اشتغل رياضي صح، ماقولش لك أي حاجة، + +514 +00:52:15,430 --> 00:52:19,010 +لكن تيجي من فوق اقلب غربة النصارى، اغلب الوجهة + +515 +00:52:19,010 --> 00:52:22,170 +تقولتلك يالا بدك تنزلي تحت الأعمارة، من الشباب + +516 +00:52:22,170 --> 00:52:26,090 +فطيت و نزلتي تحت طب و أنت ممكن تنكسر، هذا إذا ما + +517 +00:52:26,090 --> 00:52:30,290 +موتتش، و ممكن تنزلي مع الدرجة، و ممكن تنزلي مع + +518 +00:52:30,290 --> 00:52:34,090 +اللصان صغير، أنا بدي تمشي لي ماشية صحية، ماحدش + +519 +00:52:34,090 --> 00:52:40,770 +يقولك كده غلط، واضح؟ ايوةفي إخترانات مضطراتية، يجب + +520 +00:52:40,770 --> 00:52:44,850 +أن تحولها للصيغة الـx² على الـx بدي الصيغة هذه + +521 +00:52:44,850 --> 00:52:48,470 +تطبيق النظرية، بدي الصيغة على الشكل هذا أو الشكل + +522 +00:52:48,470 --> 00:52:55,450 +هذا؟ بدي أكتب له السؤال إنه بده هذه الصيغة؟ لأ + +523 +00:52:55,450 --> 00:52:59,630 +بكتبش لك، بكتب لك هاتين ليموت و بسكت، و أنت لعلك و + +524 +00:52:59,630 --> 00:53:04,080 +أنت تحطها في الصيغة هذه و تحطها للجوابطيب السؤال + +525 +00:53:04,080 --> 00:53:07,940 +اللي بعده لسه أسئلة فنية كتير هي بس هذا أنا لسه + +526 +00:53:07,940 --> 00:53:12,360 +بفتحلك الخيطة شوية شوية لسه .. لسه .. لسه في أسئلة + +527 +00:53:12,360 --> 00:53:20,940 +كتير خد السؤال اللي بعده تلاتة بدي limit لما ال X + +528 +00:53:20,940 --> 00:53:30,680 +بدي أروح ل zero ل X زي ال X في Cos X على Sin X في + +529 +00:53:30,680 --> 00:53:31,900 +Cos X + +530 +00:53:36,220 --> 00:53:43,560 +سؤال بقول X زاد X في Cos X على Sin X في Cos Xمقترح + +531 +00:53:43,560 --> 00:53:49,380 +بيقول نوزع البسط على المقال بيقولك خير نجرب نوزع + +532 +00:53:49,380 --> 00:53:54,260 +نشوف نوصل لنتيجة ولا بنوصلش لنتيجة يبقى هذه ال + +533 +00:53:54,260 --> 00:54:01,660 +limit لما ال X بده يروح لل zero لل X على sin X cos + +534 +00:54:01,660 --> 00:54:14,550 +X زائد X في cos X على sin X في cos Xأقوله تبعرح + +535 +00:54:14,550 --> 00:54:20,530 +قال لي وزع ال limits قلنا له ماشي high limit لما + +536 +00:54:20,530 --> 00:54:29,110 +ال X بدها تروح لل zero لل X على sin X في limit لما + +537 +00:54:29,110 --> 00:54:35,370 +ال X بدها تروح ل zero ل واحد على cosine X زائد + +538 +00:54:35,370 --> 00:54:40,930 +limit لما ال X بدها تروح ل zero اختصرنا هذه مع هذه + +539 +00:54:40,930 --> 00:54:49,350 +وصرت Xعلى صين الـ X قول له تمام هذه كلها بقداش؟ + +540 +00:54:49,350 --> 00:54:53,410 +بواحد مضوبة + +541 +00:54:53,410 --> 00:55:00,930 +فيه هذه واحد قصين صفر بقداش؟ بواحد زائد هذه كمان + +542 +00:55:00,930 --> 00:55:07,150 +بواحد يبقى الجواب يساوي قداش؟ نه واحد تاني قال لي + +543 +00:55:07,150 --> 00:55:11,280 +لا لا لا أنا ماديش الطريقة هذه قولت له أيوةقال لي + +544 +00:55:11,280 --> 00:55:14,580 +بدي اروح اضرب ال bus كله في اتنين و المقام في + +545 +00:55:14,580 --> 00:55:19,320 +اتنين بس انا شغل العساب المثلثات شويه صار تدى + +546 +00:55:19,320 --> 00:55:33,800 +اتنين sin X cos Xبصين اتنين اكس بصين + +547 +00:55:33,800 --> 00:55:45,660 +اتنين اكس بصين اتنين اكس بصين اتنين اكس + +548 +00:55:45,750 --> 00:55:51,530 +يبقى ليحل بالحل الأول سليم وليحل بالحل الثاني سليم + +549 +00:55:51,530 --> 00:56:01,730 +كذلك ماعندي مشكلة في هذه الحالة مثال + +550 +00:56:01,730 --> 00:56:06,050 +رقم أربعة بقول + +551 +00:56:06,050 --> 00:56:14,720 +limitلما ال X بدها تروح لل Zero لتان تلاتة X على + +552 +00:56:14,720 --> 00:56:23,400 +سين تمانية X سؤال كذلك من أسلة الكتاب هذا كنا + +553 +00:56:23,400 --> 00:56:26,760 +بناخد زي في التوجيه يبقى الجواب تلاتة ع تمانية مش + +554 +00:56:26,760 --> 00:56:35,470 +هيكطبعا؟ إيش بدك تقول؟ ما + +555 +00:56:35,470 --> 00:56:40,510 +شبهتش فيها نهاية أنا حللت و الساعة تانية حولت + +556 +00:56:40,510 --> 00:56:44,550 +القصايل على القصايل و حللت هذه نتيجة على نظرية انت + +557 +00:56:44,550 --> 00:56:48,790 +خدتها بس أنا بعرفاش فاهم لما أقولك أنا بعرفاش؟ أنا + +558 +00:56:48,790 --> 00:56:55,140 +كمصحح بدتش تغلي باللي أعطيته لكمش يعني ايه؟ لإن + +559 +00:56:55,140 --> 00:56:57,940 +السؤال ممكن ماتجيش ووركتك معايا، ممكن تيجي مع + +560 +00:56:57,940 --> 00:57:04,340 +غيري، مامرش علي الكلام هذا، اه مثلا يعني، طيب، على + +561 +00:57:04,340 --> 00:57:08,680 +اي حال، بعدين باطلع في مسألة هذه، انا عندي كل اللي + +562 +00:57:08,680 --> 00:57:12,120 +بعرفه صح، يمكن تحول المسألة بدلالة صين و تكون صين + +563 +00:57:12,610 --> 00:57:19,750 +يبقى هذه المثلة تساوي limit لما ال x يروح ل zero ل + +564 +00:57:19,750 --> 00:57:32,210 +sin 3x على sin 8x في 1 على cos 3xيبقى شيلنا التان + +565 +00:57:32,210 --> 00:57:37,770 +و حطينا قيمتها و بعدين بوزع ال limit على كل منها + +566 +00:57:37,770 --> 00:57:45,290 +يبقى هذا يسوى ال limit لما ال x بيذهب لين؟ ل 0 ل + +567 +00:57:45,290 --> 00:57:54,710 +sin 3x على sin 8x في ال limit لما ال x بيذهب ل 0 ل + +568 +00:57:54,710 --> 00:58:02,980 +1 على cos 3xطيب باجي بتطلع هذه ال sign على ال sign + +569 +00:58:02,980 --> 00:58:09,600 +مش النظرية اللي عندناطب ايش بدى اعمل مشان احطها في + +570 +00:58:09,600 --> 00:58:14,920 +صفر ايوة بدنا نقسم كل من البسط والمقام علي مين علي + +571 +00:58:14,920 --> 00:58:20,360 +x اذا لو قسمنا كل من البسط والمقام علي x بيصير + +572 +00:58:20,360 --> 00:58:28,140 +limit لما ال x بيروح لل zero ل sin 3x علي x كله ل + +573 +00:58:28,140 --> 00:58:35,500 +sin 8x علي x وهدى ال cosine سفر بقداشواحد اللي + +574 +00:58:35,500 --> 00:58:42,840 +يجيبش واحد ماعنده مشكلة يساوي هذه لو كانت تلاتة + +575 +00:58:42,840 --> 00:58:47,240 +كانت حلت مشكلتناوهنا لو كان تمانية لان حلت + +576 +00:58:47,240 --> 00:58:51,160 +مشكلتنا، اذا اننا حضروا في تلاتة ع تلاتة وهنا + +577 +00:58:51,160 --> 00:58:56,140 +تمانية ع تمانية يبقى وزع ال limit يبقى هذه ال + +578 +00:58:56,140 --> 00:59:04,180 +limit واي تلاتة لل sign تلاتة X على تلاتة X واي + +579 +00:59:04,180 --> 00:59:11,070 +تلاتة X بدأ تروح لل zeroعلى limit طيب يبقى بروح + +580 +00:59:11,070 --> 00:59:16,190 +نكمل مثل هذه او نضرب في تمانية و بنجسم على تمانية + +581 +00:59:16,190 --> 00:59:25,630 +يبقى limit لتمانية X على sign تمانية X sign + +582 +00:59:25,630 --> 00:59:31,850 +لتمانية X بدي هنا تمانية يبقى بضرب في تمانية و + +583 +00:59:31,850 --> 00:59:40,120 +بجسم على تمانية و هنا تمانية X بتروح لوينالان هاي + +584 +00:59:40,120 --> 00:59:46,540 +تلاتة برا limit وهي limit لمن؟ لتلاتة اكس بدها + +585 +00:59:46,540 --> 00:59:52,680 +تروح لل zero لل sign تلاتة اكس على تلاتة اكس + +586 +00:59:52,680 --> 00:59:59,200 +تمانية limit ل تمانية اكس بدها تروح لل zero لل + +587 +00:59:59,200 --> 01:00:05,590 +sign تمانية اكس على تمانية اكساللي هاللاحظ تلاتة + +588 +01:00:05,590 --> 01:00:09,570 +اكس تلاتة اكس تلاتة اكس يبقى ال limit لهذه بقداش + +589 +01:00:09,570 --> 01:00:14,110 +بواحد تمانية اكس تمانية اكس تمانية اكس يبقى ال + +590 +01:00:14,110 --> 01:00:18,950 +limit له في قداش بواحد يبقى هذه صارت تلاتة في واحد + +591 +01:00:18,950 --> 01:00:24,810 +على تمانية في واحد ويسوي قداش تلاتة اتمان بالشكل + +592 +01:00:24,810 --> 01:00:33,230 +اللي عنها دهعشان أول من بدأوا يسمعوا 8x، 8x حصلوا + +593 +01:00:33,230 --> 01:00:42,670 +وقعوا، صارت 8، صارت هذه 10 ثلاثة x ع تمانية x + +594 +01:00:52,500 --> 01:00:58,140 +سؤال إيه لك؟ شو اسمك انت؟ محمد العشي مشان اتعشى + +595 +01:00:58,140 --> 01:01:03,700 +جيبتنا شي جديد؟ انا .. و لا هذا مش طريقة انا، نفس + +596 +01:01:03,700 --> 01:01:08,680 +الطريقة و نفس الفكرة أنا بدي جيبلي شغل هيك من + +597 +01:01:08,680 --> 01:01:11,960 +بينك، تمام؟ يبغي اخليك مع الملاعب + +598 +01:01:15,210 --> 01:01:19,970 +ومن منعك؟ ابدا + +599 +01:01:19,970 --> 01:01:23,270 +انت بدلت خطوة مكان خطوة وخليت كل شي زي ما هو صحيح + +600 +01:01:23,270 --> 01:01:29,550 +ولا لا؟ فإيه صاحبنا محمد العايش؟ وانت شسمك؟ تامر؟ + +601 +01:01:30,110 --> 01:01:34,290 +جرادة يبقى تمر جرادة لم تأتي بجديد انت قررت ما + +602 +01:01:34,290 --> 01:01:38,910 +قاله محمد العشي بس بدلت خطوة مكان خطوة ولم تأتي + +603 +01:01:38,910 --> 01:01:44,210 +بأي جديد صحيح؟ اللي بده يرفع يدي يعطيني فكرة جميلة + +604 +01:01:44,210 --> 01:01:49,650 +لم تخطر عبالنا مثلا او ما استوعبش خطوة وبسأل عليها + +605 +01:01:49,650 --> 01:01:52,710 +هي اللي بدنا مش بدنا نكرر نفس الكلام ايوة + +606 +01:02:04,540 --> 01:02:11,150 +الحل اللي بيكون عندك x بدها تروح ل 0تمام؟ لو + +607 +01:02:11,150 --> 01:02:14,830 +ضربتها في تلتة بيصير تلتة X بتروح تلتة في Zero + +608 +01:02:14,830 --> 01:02:19,970 +بقداش Zero طب اللي هو العكس أنا عندي تلتة X بتروح + +609 +01:02:19,970 --> 01:02:25,810 +ل Zero ضربتها في تلت ايش بيصير؟ يبقى هيها ولا لا؟ + +610 +01:02:25,810 --> 01:02:31,890 +ماعنديش مشكلة فيها اه انت ال X لما .. لما خدتها + +611 +01:02:31,890 --> 01:02:37,130 +ثمانية؟ قول سؤالك اترحب؟ اه + +612 +01:02:42,990 --> 01:02:48,470 +تعال هى بشوف لا + +613 +01:02:48,470 --> 01:02:52,970 +ممكن بس كده سؤال احنا مش ماخده تعال اتفضل شباب انا + +614 +01:02:52,970 --> 01:02:56,990 +مش شايف ان انا مصطلح اش كتب من هنا اه على حين جامب + +615 +01:02:56,990 --> 01:03:01,690 +بوزة انها تانه في خاعد اخدناها بالاول ثمان و تلاتة + +616 +01:03:01,690 --> 01:03:04,710 +اكس على اكس تلاتة قدر من هنا ثمان و تمانية اكس على + +617 +01:03:04,710 --> 01:03:08,290 +اكس تمانية انا كتاب تلاتة اكس على اكس بساوي واحد + +618 +01:03:08,290 --> 01:03:11,690 +دغري لأ بساوي تلاتة مش واحد + +619 +01:03:13,950 --> 01:03:18,750 +مافعش تطلع إجابتك بقى في الكلام صاند + +620 +01:03:18,750 --> 01:03:21,810 +تلاتة X على X صوت تلاتة مباشرة مين اللي قال هذا + +621 +01:03:21,810 --> 01:03:25,970 +الكلام يبقى خلاص بده نمسح النظرية وقول الكلامة + +622 +01:03:25,970 --> 01:03:29,910 +أخدناه في التلوية يا زلمة كلامك غلط أنت فاهمان غلط + +623 +01:03:29,910 --> 01:03:35,750 +لماذا؟ هكذا طب هاي التلاتة احتمالية لا لا لا يا + +624 +01:03:35,750 --> 01:03:39,550 +ابني مابديش تحفظ حفظ مابتفهم الخطوات هذه كم فرق + +625 +01:03:39,550 --> 01:03:42,730 +مابتفهمش نظرية خدام مابتفهمش نظرية خدام مابتفهمش + +626 +01:03:42,730 --> 01:03:42,730 +نظرية خدام + +627 +01:03:46,370 --> 01:03:51,490 +X على X بيساوي الأرض اللي هو الأرض اللي هنا فاكر + +628 +01:03:51,490 --> 01:03:57,410 +أكتر من الأرض ساين الأرض لأنه عدد يعني ماشي فاكر + +629 +01:03:57,410 --> 01:04:01,510 +أكتر من الأرض ال X على X بيساوي الأرض هذا نفسه مين + +630 +01:04:01,510 --> 01:04:03,810 +قال هذا لو كانت البعض الشيخ أستاذ مواطن انا جابت + +631 +01:04:03,810 --> 01:04:07,910 +عليه يعني انا مادوش شمالي + +632 +01:04:20,520 --> 01:04:25,460 +هذا نص النظرية هيك؟ اللي خدناها تو هيك بنص؟ لأ، + +633 +01:04:25,460 --> 01:04:29,080 +ممتاز جدا، يبقى هذا كلام خطأ، لو أحطه، بحطلك عليه + +634 +01:04:29,080 --> 01:04:33,880 +سفر، لإن الزاوية اللي فوق هي زاوية تحت، بدي يكون + +635 +01:04:33,880 --> 01:04:39,620 +هذا هيك، شوف يا بدايةجيت على الجامعة بنا نسخل + +636 +01:04:39,620 --> 01:04:44,200 +عقليتك و نفهمك تفهم صحيح بقولتلك من أول مرة بديش + +637 +01:04:44,200 --> 01:04:49,940 +ياك تبقى صاميم بديك تبقى فاهم حتى تقدر بعد أربع + +638 +01:04:49,940 --> 01:04:54,240 +سنين توقف مكان هنا و تبقى معيد و تفهم الطلاب هذا + +639 +01:04:54,240 --> 01:04:57,620 +اللي بديكي ياه، بديش تبقى حافظ و تقوله خدها و امشي + +640 +01:04:57,620 --> 01:05:04,000 +و خدها و امشي، لا يا عم اتفضللما ناخد الاشتراك من + +641 +01:05:04,000 --> 01:05:07,840 +اللي نحكي، ليه السادسين الاشتراك بصرا للاستعجال + +642 +01:05:07,840 --> 01:05:14,160 +الشباب؟ كل حديثة حديثة، ايوة صارت + +643 +01:05:14,160 --> 01:05:18,840 +سلسلة تعوي، تنعوض، تبت X و Y + +644 +01:05:30,210 --> 01:05:34,610 +مافيش مشكلة بس تتعود و تشيل شغلة و تبدل كلهم كانوا + +645 +01:05:34,610 --> 01:05:39,150 +مافيش مشكلة عادي جدامافيش اي اشكالية عادي جدا انا + +646 +01:05:39,150 --> 01:05:43,870 +بيهمني يظل الشكل العام للنظرية مهما كانت كانت X + +647 +01:05:43,870 --> 01:05:48,490 +كانت تلاتة X كانت ناقص X بدى اللى دى الزاوية هى + +648 +01:05:48,490 --> 01:05:54,030 +اللى تحت هى اللى بتروح لل zero تمام؟ دى ربالك اه + +649 +01:05:54,030 --> 01:05:57,870 +كل بدى هيكتب صح مش هيكتبلى هيكده مثلا زى ما كان + +650 +01:05:57,870 --> 01:06:01,990 +كاتب جبل والد تسوي Nمافيش حاجة تسوي هنا، لك تكتب + +651 +01:06:01,990 --> 01:06:05,910 +limit بدون limit لها معنى لها، انت طالب جامعي طب + +652 +01:06:05,910 --> 01:06:12,650 +غلط، بدون limit غلط، ما علمت بدك و تقولك ليش، يا + +653 +01:06:12,650 --> 01:06:17,290 +ابني افلك تعلم بطريقة صحيحة، بشان بكرا تعلم الطلاب + +654 +01:06:17,290 --> 01:06:27,040 +بطريقة صحية، طب السؤال الخامس، ببنى limitلما ال X + +655 +01:06:27,040 --> 01:06:35,020 +بده تروح لل واحد لل sign X ناقص واحد على X تربيع + +656 +01:06:35,020 --> 01:06:44,300 +ZX ناقص اتنين كده + +657 +01:06:44,300 --> 01:06:52,060 +شهد يا ماجي ده؟ حط واحد و خلاص؟ طيب ايه بتطلع في + +658 +01:06:52,060 --> 01:06:57,050 +مثلتي؟الزاوية X نقص واحد هذه polynomial من الدرجة + +659 +01:06:57,050 --> 01:07:02,150 +الثانية هذه X بتروح للواحد يعني ما هيش شكل النظرية + +660 +01:07:02,150 --> 01:07:07,490 +أصل نظرية X بتروح ل zero لكن لما أطلع هذه X نقص + +661 +01:07:07,490 --> 01:07:12,070 +واحد بدي أخلق هنا X نقص واحد و بدي أخلق هذه هنا X + +662 +01:07:12,070 --> 01:07:17,580 +نقص واحدقصة تبصيفة جدا ضيف سالب واحد للطرفين يعني + +663 +01:07:17,580 --> 01:07:22,200 +نبقوا نخلقنا هنا وهذه من حللة نبقوا نخلقنا X ناقص + +664 +01:07:22,200 --> 01:07:27,120 +واحد وبعدين الله بفرجهايبقى باجي بقوله هذه بده + +665 +01:07:27,120 --> 01:07:32,840 +تبقى ال limit X ناقص واحد بده تروح لمين؟ لل zero + +666 +01:07:32,840 --> 01:07:41,180 +وهذه ال sign X ناقص واحد هذه بنحللها I قوسين I X و + +667 +01:07:41,180 --> 01:07:46,160 +I X و I واحد و I اتنين تمام عند الإشارة هذه + +668 +01:07:46,160 --> 01:07:52,060 +بالموجب يبقى هذه بالموجب وهذه بالسالب يبقى تحليلنا + +669 +01:07:52,060 --> 01:07:57,980 +سليم مائة بالمائةهذه الان ممكن اجزئها الى limit + +670 +01:07:57,980 --> 01:08:04,800 +لحاصل ضرب دليل T لو جيت هنا قلت هذه ال limit لمن X + +671 +01:08:04,800 --> 01:08:11,320 +ناقص واحد كلها بتروح لل zero لل sine X ناقص واحد + +672 +01:08:12,560 --> 01:08:17,800 +بعد ماكس ناقص واحد تمام فى مين فى ال limit ضال + +673 +01:08:17,800 --> 01:08:24,340 +عندى واحد على X زيدي اتنين هذه لو خلتها قلت X بدها + +674 +01:08:24,340 --> 01:08:28,360 +تروح للواحد بدل ماكس ناقص واحد تروح لزيره يبقى X + +675 +01:08:28,360 --> 01:08:32,920 +بدها تروح لمين للواحد يبقى جزاية ال limit الى two + +676 +01:08:32,920 --> 01:08:38,890 +limits سؤالهذه كلها بقدرش لإن الزاوية هذه هي هذه + +677 +01:08:38,890 --> 01:08:42,450 +هي هذه يا محمود أول ساعة بيقول لو قدّلت يعني لو + +678 +01:08:42,450 --> 01:08:47,330 +أنا شيلت X ناقصها و حاطيت فدالها Y شو بيصير؟ Y Y Y + +679 +01:08:47,330 --> 01:08:51,030 +هيها يعني بقى أنا بيهم إن الزاوية هذه هو المقدر + +680 +01:08:51,030 --> 01:08:55,090 +هذا هو المقدر هذا جيش مايكون شغل تحط ال X تحط ال Y + +681 +01:08:55,090 --> 01:08:58,930 +تحط ال Z تحط قصه تحط ان شاء الله تلت كميات جوا + +682 +01:08:58,930 --> 01:09:02,630 +ماعندي معناهبدي ازاى هذه تكون هى هذه هى اللى هنا + +683 +01:09:02,630 --> 01:09:08,670 +تمام يبقى هذا كله بقداش بواحد صحيح فيه هذا الان + +684 +01:09:08,670 --> 01:09:15,030 +تعويض مباشر لإن المقدار الثابت هو هنا واحد زائد + +685 +01:09:15,030 --> 01:09:20,850 +اتنين يبقى الجواب قداش يساوي طوله يعني بدي اتفرج + +686 +01:09:20,850 --> 01:09:25,170 +المثل اللى عندك بحيث تحطه في صيغة النظرية وبالتالي + +687 +01:09:25,170 --> 01:09:32,010 +نطبق النظرية بدون مشاكل نبقى ستةنمرى 6 بالـ + +688 +01:09:32,010 --> 01:09:41,310 +delimit لما الـ X بدها تروح للـ 0 لمن؟ للصين واحد + +689 +01:09:41,310 --> 01:09:48,410 +ناقص cosine الـ X على من؟ على X لما الـ X بدها + +690 +01:09:48,410 --> 01:09:54,850 +تروح للـ 0 طالع + +691 +01:09:54,850 --> 01:10:00,440 +ليه كويس هنا؟يقول limit اللي بين قصين كلها هي + +692 +01:10:00,440 --> 01:10:05,860 +الزاوية تبعت ال sign كل اللي بين قصين هو الزاوية + +693 +01:10:05,860 --> 01:10:10,820 +تبعت ال sign تمام؟ يبقى انا مش هنقدر اطبق النظرية + +694 +01:10:10,820 --> 01:10:16,380 +بدي يكون عند هنا واحد ناقص cosine ال X و بدي هنا + +695 +01:10:16,380 --> 01:10:20,680 +واحد ناقص cosine X يروح لمين؟ يروح ل zero نسمع + +696 +01:10:31,970 --> 01:10:35,830 +يعني اتضربت في واحد نقص كوصين و جسمت على واحد نقص + +697 +01:10:35,830 --> 01:10:41,370 +كوصين ماعناه مشكلة زميلكوا بيقترح ما يأتيبيقول + +698 +01:10:41,370 --> 01:10:46,050 +المثل هذه بيدا اكتبها على الشكل التالي limit لما + +699 +01:10:46,050 --> 01:10:52,090 +ال X بيروح لل zero ل sine واحد ناقص cosine ال X + +700 +01:10:52,090 --> 01:10:58,070 +على X هي الاصل تبعه بيروح اضرب في واحد ناقص cosine + +701 +01:10:58,070 --> 01:11:03,770 +ال X و اجسم على واحد ناقص cosine ال X بيقول ماشي + +702 +01:11:03,770 --> 01:11:09,300 +اضرب في واحدصحيح وبالتالي المثالة تبقى كما هي طيب + +703 +01:11:09,300 --> 01:11:13,280 +قال لي هذه بدى اعملها بالشكل التالي هذا ال limit + +704 +01:11:13,280 --> 01:11:18,920 +لما ال x بدها تروح ل zero و قال لي اي sine واحد + +705 +01:11:18,920 --> 01:11:29,130 +ناقص cosine ال x على واحد ناقصكو صين ال X طبعا و + +706 +01:11:29,130 --> 01:11:36,490 +كده ايش ضلة عندنا ضلة ان واحد على X او واحد ناقص + +707 +01:11:36,490 --> 01:11:45,150 +كو صين ال X كل غد على مين على X طبعا قلنا اللي + +708 +01:11:45,150 --> 01:11:50,710 +بدنا نيجي للدالة هذه الدالة صار الزاوية اللي عندنا + +709 +01:11:50,710 --> 01:11:56,530 +هي اللي تحت باجي بقولها هذهبتشوف كيف بدي أعملها + +710 +01:11:56,530 --> 01:12:02,230 +شوف يا سيدي الأول لما أقوله ال X بدها تروح ل Zero + +711 +01:12:02,230 --> 01:12:09,750 +خد ال cosine للطرفين بصير cosine ال X بده يروح ل + +712 +01:12:09,750 --> 01:12:16,130 +cosine ال Zero قداش cosine ال Zero؟ واحد يبقى صار + +713 +01:12:16,130 --> 01:12:20,820 +cosine ال X بده يروح لل واحدهاتوا على الشجة + +714 +01:12:20,820 --> 01:12:26,960 +التانية او ضيف سالب واحد للطرفين بيصير cosine ال X + +715 +01:12:26,960 --> 01:12:29,320 +سالب واحد يروح لمين؟ + +716 +01:12:34,370 --> 01:12:41,190 +أضرب الطرفين في شرط السالب بصير واحد ناقص cosine + +717 +01:12:41,190 --> 01:12:47,930 +ال X بيروح لمين؟ Zero في السالب ما هو Zero طيب إذا + +718 +01:12:47,930 --> 01:12:53,570 +ال X بيروح إلى Zero بيكافئها واحد ناقص cosine ال X + +719 +01:12:53,570 --> 01:12:59,820 +بيروح لوين؟للـ zero إذا هذه بدها تساوي limit لما + +720 +01:12:59,820 --> 01:13:05,620 +ال X بدي روح لل zero ل sin واحد ناقص cosine ال X + +721 +01:13:05,620 --> 01:13:11,040 +على واحد ناقص cosine ال X في ال limit لما ال X + +722 +01:13:11,040 --> 01:13:18,920 +بدها تروح لل zero لواحد ناقص cosine ال X على Xطيب + +723 +01:13:18,920 --> 01:13:25,280 +نعمل هذه بالطريقة اللى عملناها يبقى هذه تساوي high + +724 +01:13:25,280 --> 01:13:31,840 +limit هذه بدي استبدلها بمين بواحد ناقص cosine ال X + +725 +01:13:31,840 --> 01:13:38,100 +كلها بده تروح لل zero لل sine واحد ناقص cosine ال + +726 +01:13:38,100 --> 01:13:44,150 +X على مين على واحد ناقص cosine ال Xهذه المقامات + +727 +01:13:44,150 --> 01:13:48,810 +كلها مجددش تشيلها يابان جوسينة تحطها ثيتا تحطها + +728 +01:13:48,810 --> 01:13:52,690 +واي تحطها زيد معنى مشكلة المهم صارت الزاوية هي + +729 +01:13:52,690 --> 01:13:56,250 +المقام هي المقنرة اللي عندنا نيجي هذا كله بواحد + +730 +01:13:56,250 --> 01:14:02,450 +نيجي نكملhigh limit لما ال X بدأ تروح لل zero + +731 +01:14:02,450 --> 01:14:07,870 +التعويض المباشر هنا بيجيب لل zero على zero كمية + +732 +01:14:07,870 --> 01:14:14,570 +غير معينة يبقى تدبر حالك طبعا هناك أكثر من طريقة + +733 +01:14:14,570 --> 01:14:21,210 +المرافق بنفع المرافق نضرب في المرافق تبع ال bus + +734 +01:14:21,210 --> 01:14:25,430 +كلام صحيح و تمشي النتيجة واحد تاني قال لأ انا بدي + +735 +01:14:25,430 --> 01:14:27,110 +استخدم حساب المثلثات + +736 +01:14:34,470 --> 01:14:39,250 +ماشي الحال يفجر بده يشيل واحد نقص ويقول لي اتنين + +737 +01:14:39,250 --> 01:14:41,350 +cosine تربيه X ع اتنين + +738 +01:14:46,490 --> 01:14:51,950 +يبقى لو ضربنا في المرافق الحل الصحيح مرافق ال bus + +739 +01:14:51,950 --> 01:14:55,670 +لو روحنا شيلنا الواحد ناقص cosine ال X و كتبنا + +740 +01:14:55,670 --> 01:14:59,930 +بدلة اتنين sin تربيه X على اتنين برضه كلام سليم + +741 +01:14:59,930 --> 01:15:03,870 +100% و ماحدش مقدر يقول ان هذا غلط يبقى على شكتين + +742 +01:15:03,870 --> 01:15:10,330 +صح امامك طريقاطريق الاول اشيل واحد ناقص cosine + +743 +01:15:10,330 --> 01:15:15,050 +الاكس واكتبها اتنين sin تروية X على اتنين يا اما + +744 +01:15:15,050 --> 01:15:20,050 +اروح اضرب البصط المقام في المرافق تبع البصط اللي + +745 +01:15:20,050 --> 01:15:25,370 +هو واحد زائد cosine الاكس تحب نضرب في المرافق و + +746 +01:15:25,370 --> 01:15:32,350 +الله حساب المثلثات مرافق المرافق ماشيطيب يبقى high + +747 +01:15:32,350 --> 01:15:39,470 +limit لمن؟ لواحد ناقص cosine X على X واحد زائد + +748 +01:15:39,470 --> 01:15:46,190 +cosine X واحد زائد cosine X هذا الكلام يساوي، هذا + +749 +01:15:46,190 --> 01:15:52,080 +كله بواحد صحيحيبقى هذا بواعي صحيح مضروب هذا الآن + +750 +01:15:52,080 --> 01:15:57,620 +بيصير limit لما ال X بدها تروح ل zero البسط فرق + +751 +01:15:57,620 --> 01:16:03,860 +بين المربعين يبقى واحد ناقص cosine تربيع ال X على + +752 +01:16:03,860 --> 01:16:12,250 +X في واحد على واحد زائد cosine ال Xهذا الكلام بده + +753 +01:16:12,250 --> 01:16:17,890 +يساوي limit لما ال X بده يروح لل 0 بداك اللي هتبعت + +754 +01:16:17,890 --> 01:16:22,070 +البصر اللي هو واحد ناقص cosine تربيع ليه بصين + +755 +01:16:22,070 --> 01:16:29,350 +تربيع يبقى limit للصين تربيع ال X على X في limit + +756 +01:16:29,350 --> 01:16:35,970 +لما ال X بده تروح لل 0 للواحد على واحد زاد cosine + +757 +01:16:35,970 --> 01:16:46,030 +ال Xهذا الكلام بده يساوي limit لما ال X بدها تروح + +758 +01:16:46,030 --> 01:16:53,350 +لل zero تمام؟ بدي أخد sin X على X في limit لما ال + +759 +01:16:53,350 --> 01:16:59,590 +X بدها تروح لل zero ل sin X في limit لما ال X بدها + +760 +01:16:59,590 --> 01:17:07,070 +تروح لل zero ل 1 على 1 زاد cosine X هذي بقدراش؟ + +761 +01:17:07,820 --> 01:17:15,800 +وهذا هو قيمة واحد + +762 +01:17:15,800 --> 01:17:21,520 +على واحد زائد واحد يبقى النتيجة تساوي زيرو يبقى + +763 +01:17:21,520 --> 01:17:27,160 +limit لهذه ال function تساوي زيرو عليك انتهى هذا + +764 +01:17:27,160 --> 01:17:33,220 +ال section وإليكم أرقام المسائل ولحد هنا داخل في + +765 +01:17:33,220 --> 01:17:41,860 +الامتحانيبقى exercises اتنين اربعة المسائل التالية + +766 +01:17:41,860 --> 01:17:50,400 +exercises اتنين اربعة المسائل من واحد لغاية واحد + +767 +01:17:50,400 --> 01:17:54,580 +واربعين القدر + +768 +01:17:54,580 --> 01:18:02,720 +ومن تلاتة واربعين لغاية ستة واربعين + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RLVHplY4UgE.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RLVHplY4UgE.srt new file mode 100644 index 0000000000000000000000000000000000000000..9abdc8e96d07786e12896f2f9563e441e8db45c2 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RLVHplY4UgE.srt @@ -0,0 +1,3539 @@ +1 +00:00:21,190 --> 00:00:26,950 +بسم الله الرحمن الرحيم المرة الماضية بدأنا بعنوان + +2 +00:00:26,950 --> 00:00:32,630 +اللي هو بعض أنواع الدوال العادية واخدنا أول نوع من + +3 +00:00:32,630 --> 00:00:37,410 +هذه الأنواع وهي الـ linear function يعني الدالة + +4 +00:00:37,410 --> 00:00:42,430 +الخطية وشوفنا أن رسمته هو خط مستقيم وشفنا + +5 +00:00:42,430 --> 00:00:47,140 +الخطوط المستقيمة في حالات مختلفة مثل موازية لمحور + +6 +00:00:47,140 --> 00:00:53,380 +X أو عمودية على محور X أو مائلة على محور X أو + +7 +00:00:53,380 --> 00:00:58,180 +الخطوط المستقيمة تمر بنقطة الأصل أو لا تمر بنقطة + +8 +00:00:58,180 --> 00:01:03,410 +الأصل كل هذه رسمناها واخدنا المعادلات التابعة لها. نجي + +9 +00:01:03,410 --> 00:01:07,010 +للنوع الثاني اللي هو the power functions دوال + +10 +00:01:07,010 --> 00:01:13,530 +القوة يعني الدالة المرفوعة لمين؟ لأس معين. بنعطيها + +11 +00:01:13,530 --> 00:01:18,790 +التعريف كتالي: the function f of x يساوي x to the + +12 +00:01:18,790 --> 00:01:23,750 +power a where الـ a is constant حيث الـ a مقدار ثابت + +13 +00:01:23,750 --> 00:01:26,670 +is called a power function. + +14 +00:01:29,820 --> 00:01:35,920 +الدالة اللي عندنا هذه الأساس متغير والأس ثابت. جالي + +15 +00:01:35,920 --> 00:01:41,080 +الـ a is constant الآن الـ a هذا ما حطيتش قيود عليه + +16 +00:01:41,080 --> 00:01:46,450 +إلا أنه مقدار ثابت. يبقى مدام مقدار ثابت يعني real + +17 +00:01:46,450 --> 00:01:53,770 +number قد يكون صفر قد يكون موجب قد يكون سالب قد + +18 +00:01:53,770 --> 00:01:59,650 +يكون كسري. طبعا لو كان الصفر لأصبح X و Zero بواحدة + +19 +00:01:59,650 --> 00:02:04,750 +له الخط المستقيم الموازي لمحور X واللي بيبقى بعنه + +20 +00:02:04,750 --> 00:02:08,250 +مسافة مقدرة واحد. وهذه رسمناها وهي في الـ linear + +21 +00:02:08,250 --> 00:02:12,070 +function يبقى الـ a عندي بدنا نستبعد الصفر. بدنا + +22 +00:02:12,070 --> 00:02:19,890 +ناخد positive negative بالسالب وهكذا أو كسري ونشوف + +23 +00:02:19,890 --> 00:02:23,890 +الحالات المختلفة. مثلا لو بدنا ناخد أمثلة + +24 +00:02:23,890 --> 00:02:29,570 +مختلفة على هذه و بدنا ناخد لو كانت الـ a موجبة. فمثلا + +25 +00:02:29,570 --> 00:02:36,370 +لو جيت أخدت الـ F of X تساوي X يبقى الـ A عندي هنا + +26 +00:02:36,370 --> 00:02:42,250 +قداش بتكون؟ واحد صحيح. طبعا رسمناها قبل هيك وقلنا + +27 +00:02:42,250 --> 00:02:48,910 +هذا محور X هذا محور Y هذا نقطة الأصل اللي هي Zero + +28 +00:02:50,280 --> 00:02:55,600 +هذا الخط الذي يمثل هذه الدالة هو الخط المستقيم + +29 +00:02:55,600 --> 00:03:00,960 +اللي عندنا هذا باللون الأزرق. وقولنا هذا معادلة Y + +30 +00:03:00,960 --> 00:03:05,120 +تساوي X الزاوية اللي عندنا هذه جد الزاوية عندنا + +31 +00:03:05,120 --> 00:03:09,980 +هذه. وكل واحدة فيهم خمسة وأربعين درجة. وسميناها في + +32 +00:03:09,980 --> 00:03:13,960 +حالة الـ linear functions الـ identity function اللي + +33 +00:03:13,960 --> 00:03:19,410 +دالة الواحد. هذا لو كان A تساوي واحد. نجي لو كان الـ + +34 +00:03:19,410 --> 00:03:26,770 +F of X يساوي مثلا X تربيع وبدنا نرسم هذه الدالة + +35 +00:03:26,770 --> 00:03:31,910 +يبقى هذا محور X هذا محور Y هذا نقطة الأصل اللي هي + +36 +00:03:31,910 --> 00:03:36,170 +Zero يبقى هذا الـ problem المشهورة اللي بنرفع طول + +37 +00:03:36,170 --> 00:03:41,050 +دراستنا في المرحلة الثانوية. يبقى القطع المكافئ + +38 +00:03:41,050 --> 00:03:45,730 +اللي على الشكل اللي عندنا هذا. يبقى هذا Y تساوي X + +39 +00:03:45,730 --> 00:03:51,190 +تربيع والـ A عندي تساوي كم؟ تساوي اثنين. طيب لو جينا + +40 +00:03:51,190 --> 00:03:57,190 +قلنا الـ F of X بدها تساوي X تكعيب يبقى الـ A عندي + +41 +00:03:57,190 --> 00:04:02,990 +هنا كم؟ ثلاثة. برضه الرسم هذه رسمناها كثيرا في + +42 +00:04:02,990 --> 00:04:09,810 +المرحلة الثانوية وكان رسمتها على الشكل التالي. نذكر + +43 +00:04:09,810 --> 00:04:17,380 +بها تذكير ليس إلا. يبقى هذا رسمة المنحنى اللي عندنا + +44 +00:04:17,380 --> 00:04:24,580 +هذا الـ Y تساوي X تكعيب. هذه نقطة الأصل اللي هي Zero + +45 +00:04:24,580 --> 00:04:30,120 +والـ A عندي تساوي ثلاثة. طب لو كانت الـ A تساوي + +46 +00:04:30,120 --> 00:04:36,320 +أربعة يبقى بصير عند الـ F of X يساوي X أس أربعة. + +47 +00:04:36,320 --> 00:04:42,120 +يبقى الـ A تساوي أربعة. لو حبينا نرسم الرسمة هذه + +48 +00:04:42,120 --> 00:04:48,820 +يبقى هي المحاور. هذا محور X هذا محور Y هذه نقطة + +49 +00:04:48,820 --> 00:04:56,340 +الأصل اللي هي Zero. رسمتها تشبه X تربيعها لكن مع بعض + +50 +00:04:56,340 --> 00:05:03,520 +الفوارق البسيطة كالتالي. يبقى هاي رسمتها بتجيني هيك + +51 +00:05:06,950 --> 00:05:11,150 +بتجي بالشكل اللي عندنا هنا. يبقى هذا رسمة Y F of X + +52 +00:05:11,150 --> 00:05:17,870 +يساوي X أس 4 أو Y تساوي X أس 4. بنجي لو كانت F of X + +53 +00:05:17,870 --> 00:05:25,470 +يساوي X أس 5 يبقى الـ A تساوي 5. يبقى رسمتها تشبه + +54 +00:05:25,470 --> 00:05:32,030 +لـ F of X يساوي X تكعيب مع الفارق. يبقى هي المحاور. هذا + +55 +00:05:32,030 --> 00:05:39,950 +محور X هذا محور Y هذا نقطة الأصل اللي هي Zero. يبقى + +56 +00:05:39,950 --> 00:05:44,290 +المنحنى بيجينا بالشكل اللي عندنا هذا هيك. يبقى هذا + +57 +00:05:44,290 --> 00:05:47,090 +بيجينا هيك. + +58 +00:05:53,820 --> 00:05:59,740 +لا مش نفسها، هذه يا دوب تقاطع تقاطع هذه كأنها + +59 +00:05:59,740 --> 00:06:05,160 +تمسح وركز ولا تشبيه يعني، يعني بتفتح شوية عند ال + +60 +00:06:05,160 --> 00:06:10,000 +zero، بتلاقيها أفتح شوية. طيب هذا لو كانت الأسس + +61 +00:06:10,000 --> 00:06:16,820 +موجبة. طب لو كانت الأسس سالبة زي ايش مثلا؟ زي f of x + +62 +00:06:16,820 --> 00:06:22,640 +يساوي x سالب واحد يعني قداش؟ واحد على x يبقى ال + +63 +00:06:22,640 --> 00:06:27,680 +a تساوي قداش؟ سالب واحد. لو روحنا رسمنا الرسمة هذه + +64 +00:06:27,680 --> 00:06:33,520 +فبجي بقول هذا محور x هذا محور y هذا نقطة الأصل + +65 +00:06:33,520 --> 00:06:35,100 +اللي هي zero. + +66 +00:06:41,950 --> 00:06:46,990 +الدالة معرفة على طول القط. يبقى على يمين الـ zero + +67 +00:06:46,990 --> 00:06:51,830 +بتاخد قيم موجبة على طول الشكل اللي عندنا هذا هيك + +68 +00:06:51,830 --> 00:06:57,250 +وعلى شمال الـ zero بتاخد قيم سالبة بالشكل اللي + +69 +00:06:57,250 --> 00:07:03,910 +عندنا هذا هيك. يبقى هذه اللي هي ده الـ F of X يساوي + +70 +00:07:03,910 --> 00:07:10,450 +واحد على X والـ X الأس تبعه بده يساوي سالب واحد. لو + +71 +00:07:10,450 --> 00:07:16,270 +جينا الأس يساوي سالب اثنين يبقى الـ F of X يساوي X + +72 +00:07:16,270 --> 00:07:23,350 +أس سالب اثنين يعني واحد على X تربيع. يبقى هذا محور X + +73 +00:07:23,350 --> 00:07:30,540 +هذا محور Y هذه نقطة الأصل اللي هي Zero. هل يمكن لهذه + +74 +00:07:30,540 --> 00:07:36,320 +الدالة أن تأخذ القيمة صفر أبدا؟ هل يمكن + +75 +00:07:36,320 --> 00:07:42,050 +أن تأخذ قيمة سالبة؟ يبقى على الشجرتين القيم موجبة + +76 +00:07:42,050 --> 00:07:45,690 +سواء كان على يمين الـ zero ولا على شمالي الـ zero + +77 +00:07:45,690 --> 00:07:51,290 +القيم موجبة. يبقى المنحنى بيجيلك كده أو من هنا + +78 +00:07:51,290 --> 00:07:56,770 +بيجي جوس بالشكل الثاني. هذا الـ data is undefined + +79 +00:07:56,770 --> 00:08:01,150 +عند الـ zero لاحظ بالنسبة للـ data الأولى الـ domain + +80 +00:08:01,150 --> 00:08:07,030 +يساوي الـ range يساوي كل الـ real line معها ده زيرو. هنا + +81 +00:08:07,030 --> 00:08:14,850 +الـ domain كل الـ real line ما عدا زيرو الـ range من + +82 +00:08:14,850 --> 00:08:20,310 +zero لـ infinity as an open interval. تمام. طيب هذا + +83 +00:08:20,310 --> 00:08:25,730 +رسمتنا لو كانت الأسس سالبة. طب لو كانت الأسس كسرية + +84 +00:08:25,730 --> 00:08:32,170 +فالرسم على الشكل التالي. افترض أن f of x يساوي جذر + +85 +00:08:32,170 --> 00:08:37,970 +الـ X يعني X أس قداش؟ أس نص. لو حبينا نرسم الرسم اللي + +86 +00:08:37,970 --> 00:08:42,570 +عندنا هذه يبقى بصير على الشكل التالي. هذا محور X + +87 +00:08:42,570 --> 00:08:50,310 +هذا محور Y هذه نقطة الأصل اللي هي Zero. يبقى مجوس + +88 +00:08:50,310 --> 00:08:56,890 +بالشكل اللي عندنا هذا هيك. يبقى هذا رسمة الدالة Y + +89 +00:08:56,890 --> 00:09:03,330 +تساوي جذر الـ X الـ domain يساوي الـ range يساوي + +90 +00:09:03,330 --> 00:09:08,110 +الفترة من عند الـ zero لغاية infinity طبعا مغلقة من + +91 +00:09:08,110 --> 00:09:16,790 +عند الـ zero. لو جينا للـ Y تساوي X أس ثلث يعني الجذر + +92 +00:09:16,790 --> 00:09:22,810 +الثالث لـ X وحبنا نرسم الرسمة هذه فبجي بقول هذا محور + +93 +00:09:22,810 --> 00:09:30,110 +X هذا محور Y هذه النقطة الأصل اللي هي Zero. بدنا + +94 +00:09:30,110 --> 00:09:34,990 +هذا الجذر يبقى الجذر هيجيك بالشكل الثالث لأن منحنى + +95 +00:09:34,990 --> 00:09:38,410 +هيجيك هيك ويجي من ناحية تانية هيك. + +96 +00:09:42,100 --> 00:09:50,540 +يبقى هذا Y يساوي الجذر الثالث لـ X أو X أس ثلث. بعد + +97 +00:09:50,540 --> 00:09:59,540 +هيك بدنا نيجي للرسمة Y تساوي Y تساوي X أس ثلتين + +98 +00:09:59,540 --> 00:10:08,670 +مثلا يعني مين؟ يعني الجذر الثالث للـ X تربيع. طبعا + +99 +00:10:08,670 --> 00:10:14,590 +هذه الرسمة دائما وأبدا معرفة للـ X الموجبة + +100 +00:10:14,590 --> 00:10:20,930 +والسلبية والصفر يعني الـ domain كله الـ real line + +101 +00:10:20,930 --> 00:10:25,890 +لكن الـ range بياخد قيمة سالبة. طب بياخد القيمة + +102 +00:10:25,890 --> 00:10:32,750 +الصفر؟ بياخد صفر. لو روحت رسمتها هتاخد الشكل التالي. + +103 +00:10:32,750 --> 00:10:39,720 +هذا محور X هذا محور Y هذا نقطة الأصل اللي هي Zero + +104 +00:10:39,720 --> 00:10:45,460 +يبقى حيجيك جزء من المنحنى بالشكل هذا والجزء الثاني + +105 +00:10:45,460 --> 00:10:51,700 +بالشكل هذا. يبقى هذه اللي هي X أس ثلتين أو الجذر + +106 +00:10:51,700 --> 00:10:58,940 +الثالث لـ X تربيع. بقيت أن أخر رسمة وهي Y تساوي بدل + +107 +00:10:58,940 --> 00:11:05,720 +X أس ثلتين X أس ثلاثة على اثنين. يعني مين؟ يعني الجذر + +108 +00:11:05,720 --> 00:11:11,680 +التربيعي لمن؟ للـ X تكعيب، لو روحنا رسمنا المنحنى + +109 +00:11:11,680 --> 00:11:18,280 +يبقى هذا محور X، هذا محور Y، هذه نقطة الأصل اللي + +110 +00:11:18,280 --> 00:11:25,260 +هي Zero. طبعا لا يمكن يكون الجذر معرف لقيمة سالب. إذا + +111 +00:11:25,260 --> 00:11:29,080 +الـ domain هيكون من where لـ where من Zero لـ + +112 +00:11:29,080 --> 00:11:34,020 +infinity و الـ range كذلك من Zero لـ infinity. يبقى + +113 +00:11:34,020 --> 00:11:39,400 +المنحنى هيطلع عندك بمين؟ بالشكل اللي عندك هنا. يبقى + +114 +00:11:39,400 --> 00:11:43,880 +هذا اللي هو x أس 3 على 2 الـ domain يساوي الـ range + +115 +00:11:49,790 --> 00:11:55,870 +يبقى الرسومات هذه هي الرسومات الأساسية التي ستتكرر + +116 +00:11:55,870 --> 00:12:01,690 +معك كثيرا جدا خلال دراستنا هذا في Calculus A يبقى + +117 +00:12:01,690 --> 00:12:06,730 +مطلوب منك أن تكون ملما بهذه الرسومات. + +118 +00:12:10,620 --> 00:12:15,720 +طيب ننتقل الآن إلى النوع الثاني من أنواع الدوال + +119 +00:12:15,720 --> 00:12:21,920 +يبقى انتهينا من الـ linear functions ومن الـ power + +120 +00:12:21,920 --> 00:12:30,400 +functions بدنا نروح للنوع الثالث من هذه الدوال + +121 +00:12:30,400 --> 00:12:36,400 +يبقى النوع الثالث اللي هو عبارة عن كثيرات الحدود + +122 +00:12:36,400 --> 00:12:37,800 +اللي هي الـ polynomial + +123 +00:12:40,400 --> 00:12:46,260 +يبقى النوع الثالث polynomials + +124 +00:12:46,260 --> 00:12:54,620 +اللي هو كثيرات الحدود. نعطيها تعريف definition a + +125 +00:12:54,620 --> 00:13:05,480 +polynomial كثيرة الحدود is a function يبقى هي + +126 +00:13:05,480 --> 00:13:15,910 +عبارة عن الـ in the form في الشكل التالي الـ P of X + +127 +00:13:15,910 --> 00:13:18,250 +يساوي AN + +128 +00:13:36,450 --> 00:13:41,290 +لحظة الأس يتدرج من أعلى إلى أسفل. + +129 +00:13:44,390 --> 00:13:51,690 +في عندنا الـ N هذا اللي بتبدأ يبقى هذا عدد صحيح غير + +130 +00:13:51,690 --> 00:13:57,690 +سالب يعني ممكن يكون موجب وممكن يكون صفر. يبقى لا + +131 +00:13:57,690 --> 00:14:02,130 +يمكن أن يكون سالب. الـ A N والـ A N minus one والـ A + +132 +00:14:02,130 --> 00:14:06,530 +two والـ A one والـ A node كل الـ A هيهات هدول ثوابت a + +133 +00:14:06,530 --> 00:14:10,750 +reconnaissance أو a real number. نكتب لك هذا الكلام + +134 +00:14:12,740 --> 00:14:25,560 +حيث الـ N is a non negative + +135 +00:14:25,560 --> 00:14:29,760 +integer عدد + +136 +00:14:29,760 --> 00:14:32,120 +صحيح غير سالب. + +137 +00:14:38,340 --> 00:14:46,560 +numbers والأرقام اللي هو a n و a n minus الـ one ونظل + +138 +00:14:46,560 --> 00:14:54,340 +ماشيين لغاية ما نوصل للـ a two a one a naught هدول + +139 +00:14:54,340 --> 00:15:02,860 +كلهم are real are real numbers. + +140 +00:15:05,780 --> 00:15:14,120 +أعداد حقيقية. بنسميها called the coefficients + +141 +00:15:14,120 --> 00:15:21,300 +المعاملات + +142 +00:15:21,300 --> 00:15:30,220 +of the polynomial معاملات + +143 +00:15:30,220 --> 00:15:33,900 +كثيرة الحدود and + +144 +00:15:37,730 --> 00:15:49,330 +الـ N is called the degree of + +145 +00:15:49,330 --> 00:15:52,850 +the polynomial. + +146 +00:16:25,360 --> 00:16:30,900 +يبقى مرة ثانية أو النوع الثالث من الدوال اللي هو من + +147 +00:16:30,900 --> 00:16:35,900 +كثيرات الحدود. لما أقول كثيرات الحدود يعني عندي + +148 +00:16:35,900 --> 00:16:40,580 +مجموعة من الحدود وجمعناهم جمع. طب الحدود هدول في + +149 +00:16:40,580 --> 00:16:45,120 +عليهم قيود؟ أه، في عليهم قيود. تعالى نشوف كثيرة + +150 +00:16:45,120 --> 00:16:49,760 +الحدود هي عبارة عن دالة في الشكل التالي. بديها الرمز + +151 +00:16:49,760 --> 00:16:54,980 +اللي هو P of X الحرف الأول من كلمة polynomial وهو + +152 +00:16:54,980 --> 00:16:59,670 +function فقولنا P of X هي constant في الـ X to the + +153 +00:16:59,670 --> 00:17:03,430 +power N constant تاني في X to the power N minus + +154 +00:17:03,430 --> 00:17:07,410 +one constant ثالث في X to the power N minus two و + +155 +00:17:07,410 --> 00:17:12,150 +هكذا الأس بيبينزل N الناقص واحد الناقص اثنين + +156 +00:17:12,150 --> 00:17:16,910 +الناقص ثلاثة and so on لغاية ما نصل إلى A2 X تربيع + +157 +00:17:16,910 --> 00:17:25,690 +A1 X زائد الـ A0. الرقم N قد يكون صفرا وقد يكون عددا + +158 +00:17:25,690 --> 00:17:32,150 +موجبا لا يمكن أن يكون كسريا ولا يمكن أن يكون سالبا. + +159 +00:17:32,150 --> 00:17:37,090 +ولما قلت N is a non negative integer يبقى عدد + +160 +00:17:37,090 --> 00:17:42,770 +صحيح والعدد الصحيح غير سالب إذا لم يبقى إلا zero أو + +161 +00:17:42,770 --> 00:17:48,320 +عدد صحيح موجب. هذه النقطة الأولى. الآن الأرقام اللي + +162 +00:17:48,320 --> 00:17:53,400 +عندنا الـ a هات هذول a0 و a1 و a2 و a3 و a4 و aN + +163 +00:17:53,400 --> 00:17:58,200 +minus 1 و aN هذول ثوابت بسميهم معاملات الـ + +164 +00:17:58,200 --> 00:18:02,800 +polynomial يبقى هذول بسميهم the coefficients + +165 +00:18:02,800 --> 00:18:09,240 +المعاملات لكثيرات الحدود. طيب الـ N اللي هو أعلى قوة + +166 +00:18:09,240 --> 00:18:14,520 +موجودة عندنا هنا بسميها برجة الـ polynomial يبقى + +167 +00:18:14,520 --> 00:18:20,240 +كثيرة الحدود هذه من الدرجة N-ية يعني من الدرجة + +168 +00:18:20,240 --> 00:18:28,500 +الرقم N. نعطي شغلة توضيحية على ذلك for example + +169 +00:18:28,500 --> 00:18:32,500 +كمثال على ذلك + +170 +00:18:36,520 --> 00:18:42,580 +فمثال على ذلك الآن لو جيت قلت اثنين X أس أربعة + +171 +00:18:42,580 --> 00:18:51,560 +زائد ثلاثة X تربيع زائد عشرة X ناقص واحد + +172 +00:18:53,020 --> 00:18:57,660 + +201 +00:21:39,360 --> 00:21:44,820 +الدوال النسبية أو بعض الترجمات العربية بتقول الدوال + +202 +00:21:44,820 --> 00:21:48,720 +الجذرية الدوال الجذرية ولا الدوال النسبية بِهَمهنّ + +203 +00:21:48,720 --> 00:21:55,500 +المعنى الرياضي فبأجي بقول له the rational function + +204 +00:21:55,500 --> 00:21:58,580 +is + +205 +00:21:58,580 --> 00:22:10,710 +an expression هي صيغة in the form في الشكل التالي + +206 +00:22:10,710 --> 00:22:20,930 +الـ F of X بده يساوي P of X مقسومة على الـ Q of X + +207 +00:22:20,930 --> 00:22:33,610 +where حيث الـ P of X and الـ Q of X are polynomials + +208 +00:22:41,130 --> 00:22:51,310 +Polynomials P of + +209 +00:22:51,310 --> 00:22:57,410 +X على Q of X يعني الـ domain تبع الـ polynomial + +210 +00:23:00,980 --> 00:23:05,080 +هو كل الـ real number ماعدا الأرقام اللي بتخلي + +211 +00:23:05,080 --> 00:23:11,440 +المقام بأصفار يبقى the set of all element x such + +212 +00:23:11,440 --> 00:23:22,600 +that q of x does not equal to zero for example لو + +213 +00:23:22,600 --> 00:23:23,460 +بدي domain + +214 +00:23:27,660 --> 00:23:37,060 +مثلاً X أُس أربع ثلاثة X تكعيب زائد X ناقص ستاشر + +215 +00:23:37,060 --> 00:23:47,320 +كله مقسومًا على X في X زائد ثلاثة مش بنفع هذه + +216 +00:23:47,320 --> 00:23:51,500 +polynomial ولا لا؟ X تربيع زائد ثلاثة X يبقى + +217 +00:23:51,500 --> 00:23:58,780 +polynomial يبقى الـ domain اللي هو كل الـ real + +218 +00:23:58,780 --> 00:24:03,820 +number بده يشيل منها الأرقام اللي بتخلي المقام + +219 +00:24:03,820 --> 00:24:11,230 +يساوي zero وهي ناقص تلاتة و Zero يعني كأنه من سالب + +220 +00:24:11,230 --> 00:24:15,930 +Infinity لغاية سالب تلاتة اتحاد سالب تلاتة و Zero + +221 +00:24:15,930 --> 00:24:21,670 +اتحاد Zero و Infinity كلها فترات مفتوحة يبقى هذا + +222 +00:24:21,670 --> 00:24:26,510 +الـ domain يعني ممكن أصيغها بصياغة أخرى وأقول من + +223 +00:24:26,510 --> 00:24:32,270 +سالب Infinity لسالب تلاتة اتحاد سالب تلاتة و Zero + +224 +00:24:32,270 --> 00:24:39,390 +اتحاد Zero و Infinity بالشكل اللي قدامنا هذا طيب + +225 +00:24:39,390 --> 00:24:45,330 +ننتقل الآن إلى الدالة الخامسة وهي الـ algebraic + +226 +00:24:45,330 --> 00:24:56,410 +function الـ algebraic functions الدوال الجبرية it + +227 +00:24:56,410 --> 00:25:02,190 +is a function يبقى الدالة الجبرية it is a + +228 +00:25:02,190 --> 00:25:12,830 +function هي عبارة عن دالة that can be constructed + +229 +00:25:12,830 --> 00:25:22,190 +يمكن أن تنشأ أو يمكن أن تتكون using باستخدام + +230 +00:25:22,190 --> 00:25:24,510 +algebraic operations + +231 +00:25:33,780 --> 00:25:43,220 +إيش العمليات الجبرية زي addition subtraction + +232 +00:25:43,220 --> 00:25:48,760 +عملية + +233 +00:25:48,760 --> 00:25:59,300 +الطرح multiplication عملية الضرب multiplication + +234 +00:25:59,300 --> 00:26:01,200 +division + +235 +00:26:02,640 --> 00:26:11,020 +عملية القسمة taking roots + +236 +00:26:11,020 --> 00:26:16,300 +عملية + +237 +00:26:16,300 --> 00:26:26,720 +أخذ الجذور for example the + +238 +00:26:26,720 --> 00:26:33,930 +functions مثلاً يعني بينجل الدوال الجبرية ما هي + +239 +00:26:33,930 --> 00:26:39,330 +الدوال الجبرية بيقول الدوال الجبرية هي الدوال + +240 +00:26:39,330 --> 00:26:45,130 +التي يمكن أن تنشأ أو تتكون can be constructed + +241 +00:26:45,130 --> 00:26:50,750 +using algebraic operations يعني تنشأ نتيجة + +242 +00:26:50,750 --> 00:26:54,750 +للعمليات الجبرية العمليات الجبرية هي الجمع + +243 +00:26:54,750 --> 00:27:01,570 +والطرح والضرب والقسمة وكذلك أخذ الجذور ونحو ذلك + +244 +00:27:01,570 --> 00:27:05,590 +يبقى كل هذه المقول عليها عمليات رياضية أو عمليات + +245 +00:27:05,590 --> 00:27:12,570 +جبرية زي إيش مثلاً يبقى هنا الـ function f of x بدها + +246 +00:27:12,570 --> 00:27:18,970 +تساوي مثلاً الجذر التربيعي لـ x تربيع زائد 5 كم + +247 +00:27:18,970 --> 00:27:27,140 +عملية جبرية عملنا هنا تلات عمليات ضربنا الـ X في + +248 +00:27:27,140 --> 00:27:32,300 +نفسها لـ product أو الـ multiple كده وصارت X تربيع، + +249 +00:27:32,300 --> 00:27:36,940 +عضفنا إليها خمسة يبقى عملية الجمع عيتين تاني، + +250 +00:27:36,940 --> 00:27:42,020 +التالت أخذنا الجذر يبقى تلت عمليات في نفس الوقت، + +251 +00:27:42,020 --> 00:27:50,160 +مثلاً لو جينا قولنا الـ G of X يساوي X زائد تلاتة في + +252 +00:27:50,160 --> 00:27:59,520 +الجذر التالت مثلاً للـ X ناقص واحد زائد X على X + +253 +00:27:59,520 --> 00:28:07,060 +تربيع زائد خمسة وعشرين كل العمليات الجبرية موجودة + +254 +00:28:07,060 --> 00:28:10,380 +الحمد لله كل اللي ذكرناها موجودة في السؤال يمكن هذه كمان + +255 +00:28:10,380 --> 00:28:11,280 +algebraic + +256 +00:28:15,880 --> 00:28:20,020 +هل الـ rational function اللي فوق الـ algebraic + +257 +00:28:20,020 --> 00:28:25,160 +function؟ الـ algebraic لإنه جمع وبعدها قسمة، + +258 +00:28:25,160 --> 00:28:32,940 +مظبوط؟ يبقى and الـ rational functions + +259 +00:28:32,940 --> 00:28:36,440 +are algebraic function + +260 +00:28:42,040 --> 00:28:51,000 +يبقى هذه كذلك اللي هو دوال جبرية مالها؟ + +261 +00:28:51,000 --> 00:28:54,160 +متأكد؟ + +262 +00:28:54,160 --> 00:28:59,100 +طب وأنا زيك هاي، + +263 +00:28:59,100 --> 00:29:05,520 +بدي أقول عبارة هيك وشوفولي إياها صحيحة ولا لأ Any + +264 +00:29:05,520 --> 00:29:12,470 +algebraic function is a rational function خطأ طب + +265 +00:29:12,470 --> 00:29:16,510 +نشوف العكس any rational function is an algebraic + +266 +00:29:16,510 --> 00:29:24,410 +function صح؟ any real أو any linear function is an + +267 +00:29:24,410 --> 00:29:31,200 +algebraic function أي دالة تربيعية هي الـ algebraic + +268 +00:29:31,200 --> 00:29:35,300 +function يعني إيه f of x يساوي X تربيع؟ عملية ضرب + +269 +00:29:35,300 --> 00:29:41,460 +طيب بدي أسأل السؤال التالي وشوفولي كلامي صح ولا لأ + +270 +00:29:41,460 --> 00:29:45,660 +any polynomial is a rational function + +271 +00:29:47,940 --> 00:29:54,760 +أي كثيرة حدود is a rational function. لأ مدام هي + +272 +00:29:54,760 --> 00:29:59,220 +كانت في قضية خلافية بين الفقهاء بدنا جواب محدد + +273 +00:29:59,220 --> 00:30:01,480 +ونناقش ليش أيوة يا أخي العرب. + +274 +00:30:05,170 --> 00:30:10,270 +مية المية كلامه صحيح أنا أي polynomial عبارة عن + +275 +00:30:10,270 --> 00:30:14,710 +مين؟ عبارة عن نفسي الـ polynomial مقسومة على واحد، + +276 +00:30:14,710 --> 00:30:18,810 +الواحد هو polynomial من الدرجة الصفرية وإن اشترط + +277 +00:30:18,810 --> 00:30:21,510 +في الـ rational function تبقى polynomial في الوسط و + +278 +00:30:21,510 --> 00:30:25,550 +polynomial في المقام إذا كلامه صح حط على واحد مظبوط + +279 +00:30:25,550 --> 00:30:29,810 +مية المية يبقى any polynomial is a rational + +280 +00:30:29,810 --> 00:30:34,430 +function وبالتالي any polynomial is an algebraic + +281 +00:30:34,430 --> 00:30:38,580 +function مظبوط ولا لا؟ إنها rational function وأنا + +282 +00:30:38,580 --> 00:30:41,880 +بقول any rational function is an algebraic + +283 +00:30:41,880 --> 00:30:45,000 +function and so on وها كده دي الواقع الكلمة + +284 +00:30:45,000 --> 00:30:50,240 +بيقول لك ممكن نجيبه صح أو خطأ أو خيارات متعددة + +285 +00:30:50,240 --> 00:30:55,080 +وتختار الإجابة الصحيحة أو الإجابة الخاطئة ممكن + +286 +00:30:55,080 --> 00:30:59,290 +أعطيك تلت إجابات صحيحة وواحدة خاطئة ويقول لك طلع + +287 +00:30:59,290 --> 00:31:03,210 +للإجابة الخاطئة وليس الإجابة الصحيحة والعكس ممكن + +288 +00:31:03,210 --> 00:31:06,310 +يكون مثلًا إجابة خاطئة وواحدة صحيحة وطلع للإجابة + +289 +00:31:06,310 --> 00:31:10,070 +الصحيحة يعني السؤال ممكن يأتي هكذا أو هكذا أو حط + +290 +00:31:10,070 --> 00:31:14,250 +صح أو خطأ على العبارات الرياضية التالية ده ماكنتش + +291 +00:31:14,250 --> 00:31:16,790 +فاهم الكلام اللي قدامي على اللوحة معناته مش هتعرف + +292 +00:31:16,790 --> 00:31:22,810 +تشتغل يبقى هداني بفتح ذهنك بأسئلة مختلفة من خلال + +293 +00:31:22,810 --> 00:31:25,770 +التعريف اللي مكتوب عندي على اللوحة ما جبتش زيادة ولا + +294 +00:31:25,770 --> 00:31:29,170 +كلمة جبتش زيادة كله من خلال التعريف اللي موجود بس + +295 +00:31:29,170 --> 00:31:34,710 +بربطها مع بعضها بمين بالمسائل اللي أنت رسمتها طيب + +296 +00:31:34,710 --> 00:31:41,670 +نيجي للدالة السادسة والأخيرة يبقى الدالة رقم ستة للـ + +297 +00:31:41,670 --> 00:31:45,210 +Transcendental function يبقى + +298 +00:31:57,350 --> 00:32:04,890 +transcendental functions الدوال السامية it is the + +299 +00:32:04,890 --> 00:32:14,170 +functions السامية it is the functions هي الدوال + +300 +00:32:14,170 --> 00:32:22,090 +that are not algebraic + +301 +00:32:27,180 --> 00:32:30,940 +Trigonometric functions هي الدوال اللي ماهيّاش دوال + +302 +00:32:30,940 --> 00:32:39,260 +جبرية as زي إيش؟ نمرة واحد Trigonometric + +303 +00:32:39,260 --> 00:32:44,820 +functions Trigonometric + +304 +00:32:44,820 --> 00:32:52,020 +functions نمرة اتنين الـ exponential + +305 +00:32:59,130 --> 00:33:08,550 +f of x يساوي a to the power x والـ a greater than + +306 +00:33:08,550 --> 00:33:17,630 +zero and a does not equal to one نمرة تلاتة الـ + +307 +00:33:17,630 --> 00:33:18,950 +logarithmic + +308 +00:33:23,400 --> 00:33:32,960 +الدوال اللوغاريتمية زي إيش؟ زي الـ F of X يساوي + +309 +00:33:32,960 --> 00:33:43,740 +لوغاريتم X للأساس A والـ A greater than zero and A + +310 +00:33:43,740 --> 00:33:46,400 +does not equal to one + +311 +00:34:02,400 --> 00:34:03,020 +حسناً؟ + +312 +00:34:18,780 --> 00:34:24,020 +طبعاً هنرسم كل دالة من الدوال السامية اللي عندّه، + +313 +00:34:24,020 --> 00:34:30,500 +طبعاً في غيرهم كمان هنشرّح لها بعد قليل ونرسم هذه + +314 +00:34:30,500 --> 00:34:38,160 +الدوال للـ Transcendental function الدوال السامية + +315 +00:34:46,460 --> 00:34:52,180 +يبقى الدوال السامية عدة أنواع من هذه الأنواع نمرة + +316 +00:34:52,180 --> 00:34:56,940 +واحد هي ما تكونش دوال جبرية من هذه الأنواع اللي هي + +317 +00:34:56,940 --> 00:35:02,180 +الـ trigonometric functions يعني الدوال المثلثية + +318 +00:35:02,180 --> 00:35:06,980 +الدوال المثلثية كام واحدة؟ ستة الجيب، جيب تمام، + +319 +00:35:06,980 --> 00:35:12,720 +ظل تمام، قاطع، قاطع تمام الزاوية وهي الجيب اللي هي + +320 +00:35:12,720 --> 00:35:24,540 +Sin الـ X جيب التمام Cosine الـ X، الظل هي Tan الـ X، + +321 +00:35:24,540 --> 00:35:33,180 +ظل التمام Cotan الـ X، قاطع الزاوية يبقى Sec الـ X، + +322 +00:35:33,180 --> 00:35:40,600 +قاطع تمام الزاوية Cosecant الـ X، يبقى هذه الدولة + +323 +00:35:40,600 --> 00:35:46,700 +المثلثية الستة مرة تانية Sin X يعني جيب الزاوية X + +324 +00:35:46,700 --> 00:35:55,580 +Cos X يبقى جيب تمام الزاوية X Tan X يبقى ظل X ضا + +325 +00:35:55,580 --> 00:36:04,940 +X Cotan X ظل تمام الزاوية X Sec X قا X قاطعي + +326 +00:36:04,940 --> 00:36:11,830 +الزاوية Cosequent X قاطع تمام الزاوية X يبقى هذه + +327 +00:36:11,830 --> 00:36:17,910 +النسب المثلثية الستة إن شاء الله الست هذول هنرسمهم + +328 +00:36:17,910 --> 00:36:23,070 +وناخذ الـ domain والـ range والمتطابقات المثلثية + +329 +00:36:23,070 --> 00:36:26,560 +المتعلقة بهم بس مش في الـ section الجاي هذا الـ + +330 +00:36:26,560 --> 00:36:31,000 +section اللي بعده section واحد تلاتة منفرد كله + +331 +00:36:31,000 --> 00:36:34,340 +للدوال المثلثية أو مين إيه في نُوْمين أو الـ domain + +332 +00:36:34,340 --> 00:36:37,520 +مقدار الـ period لكل واحدة فيهم كل هذا الموضوع + +333 +00:36:37,520 --> 00:36:44,260 +section واحد تلاتة ورسوماتهم كمان تمام؟ يبقى هذه + +334 +00:36:44,260 --> 00:36:47,460 +اللي لما إليها عودة إن شاء الله في section واحد + +335 +00:36:47,460 --> 00:36:51,460 +تلاتة طيب نجي للدالة الثانية الـ exponential + +336 +00:36:51,460 --> 00:36:57,650 +function طبعاً في فرق ما بين الـ power function وبين + +337 +00:36:57,650 --> 00:37:01,770 +الـ exponential function الـ power function الأساس + +338 +00:37:01,770 --> 00:37:06,910 +متغير والأُس ثابت لكن الـ exponential function + +339 +00:37:06,910 --> 00:37:14,300 +الأساس ثابت والأُس متغير يعني مقدار ثابت هناك الـ + +340 +00:37:14,300 --> 00:37:19,160 +power function قبل قليل كانت x أُس a هنا جلبنا + +341 +00:37:19,160 --> 00:37:23,860 +خلّينا الأساس a والأس ماله x سمّيناها الـ + +342 +00:37:23,860 --> 00:37:30,730 +exponential functions الدوال الأسية F of X يساوي A + +343 +00:37:30,730 --> 00:37:35,870 +to the power X اتنين بدّ الـ A تبقى أكبر من الـ zero + +344 +00:37:35,870 --> 00:37:40,790 +دائماً وأبداً والـ A لا تساوي واحد طب ليش الـ + +345 +00:37:40,790 --> 00:37:46,690 +condition هذا لحاجة في نفس يعقوب سنعرّفكم بعضها بعد + +346 +00:37:46,690 --> 00:37:51,470 +قليل والبعض الآخر لـ calculus B إن شاء الله لما + +347 +00:37:51,470 --> 00:37:56,750 +تدرسوا calculus B في الفصل القادم أو في ثالث + +348 +00:37:56,750 --> 00:38:01,420 +section من الفصل القادم طيب يبقى بدنا نيجي للدالة + +349 +00:38:01,420 --> 00:38:06,560 +هذه a to the power x بدنا نروح نرسم رسمة هذه + +350 +00:38:06,560 --> 00:38:11,400 +الدالة ونشوف شو الـ domain إلها وشو الـ range إلها + +351 +00:38:11,400 --> 00:38:17,880 +وشكلها هذه فبأجي بقول الشكل كالتالي خلي بالك معايا + +352 +00:38:17,880 --> 00:38:24,460 +كويس هذا محور x هذا محور y هذه النقطة اللي هي Zero + +353 +00:38:25,930 --> 00:38:31,350 +قبل برسم قبل a أكبر من Zero يبقى a بتأخذ قيمة + +354 +00:38:31,350 --> 00:38:38,490 +دائماً لو أبقى القيمة موجبة اتنين قبل a لا تساوي + +355 +00:38:38,490 --> 00:38:44,370 +الواحد لإن لو كانت الـ a تساوي واحد بصير واحد قص أي + +356 +00:38:44,370 --> 00:38:50,270 +رقم بواحد يبقى هذه الـ linear function أو الدالة + +357 +00:38:50,270 --> 00:38:54,330 +الثابتة لرسمتها خط مستقيم يعني كأنه ما كانك سر + +358 +00:38:54,330 --> 00:38:59,630 +ماسويناش شيبس في كمان سبب آخر خليه للقلاص بيه + +359 +00:38:59,630 --> 00:39:03,070 +إن شاء الله لما تأخذ القلاص يبقى نقول لك يام طيب + +360 +00:39:03,070 --> 00:39:09,330 +يبقى بدنا نروح نرسم هذه يبقى لو قلت لك واحد أُس x + +361 +00:39:09,330 --> 00:39:14,930 +بده يطلع خط مستقيم صحيح ولا لا؟ يبقى هذا الواحد أُس + +362 +00:39:14,930 --> 00:39:20,990 +x هذا عندك هنا الواحد وهذا هذا هذا هيك هذا + +363 +00:39:20,990 --> 00:39:32,140 +الواحد أُس x لو كان اتنين أُس x يبقى اتنين + +364 +00:39:32,140 --> 00:39:40,860 +أُس x يبقى اتنين أُس x يبقى اتنين + +365 +00:39:40,860 --> 00:39:48,600 +أُس x يبقى اتنين أُس x يبقى + +366 +00:39:48,600 --> 00:39:55,210 +اتنين أُس x يبقى اتنين أُس x بنفس الطريقة جوز زيّه + +367 +00:39:55,210 --> 00:40:01,330 +بدّها تمر بنفس النقطة هذه طيب ليش؟ لأنه x أُس لو + +368 +00:40:01,330 --> 00:40:07,470 +كانت الـ X بـ Zero فـ اتنين أُس Zero تلاتة أُس Zero مية + +369 +00:40:07,470 --> 00:40:13,890 +أُس Zero يبقى كله بدّها تمر بالنقطة هذه هي الإحداث + +370 +00:40:13,890 --> 00:40:20,140 +ياتها Zero واحد كله لازم يمر بالنقطة هذه إذا لو قلت + +371 +00:40:20,140 --> 00:40:23,540 +أربعة أُس x هل تجي منها وفوق ولا منها وتحت؟ + +372 +00:40:23,540 --> 00:40:28,460 +منها وفوق وتعالى نقول لك ليش لو جيت قلت هذه رسمة + +373 +00:40:28,460 --> 00:40:35,800 +الدالة أربعة أُس x مثلاً لو أخذت الـ X عندي بواحد + +374 +00:40:35,800 --> 00:40:42,630 +يبقى واحد أُس واحد اللي هي الواحد تجي كنقطة هذه طيب + +375 +00:40:42,630 --> 00:40:47,930 +لو قلت اتنين أُس واحد يعني باتنين بدّها تجيك النقطة + +376 +00:40:47,930 --> 00:40:53,410 +هذه لو قلت لك أربعة أُس واحد يبقى بتطلع بدّها تجيلك + +377 +00:40:53,410 --> 00:40:57,950 +النقطة هذه وهكذا يبقى من + +401 +00:43:21,720 --> 00:43:27,160 +أي قيمة سالبة يبقى بناء عليه بقدر أحط القاعدة و أنا + +402 +00:43:27,160 --> 00:43:35,200 +مرتاح a to the power x أكبر من 0 for all x بس + +403 +00:43:35,200 --> 00:43:40,300 +الشرط هذا موجود عندي ههه ال a أكبر من ال 0 و ال a + +404 +00:43:40,300 --> 00:43:44,620 +ممنوع تساوي واحد يبقى ال a to the power x positive + +405 +00:43:44,620 --> 00:43:51,240 +دائما و always يعني لن يكسر هذا القانون ولو مرة + +406 +00:43:52,830 --> 00:43:59,490 +أكبر من 100 من 0 لا بيساوي 0 ولا بيساوي قيمة سالبة + +407 +00:43:59,490 --> 00:44:06,270 +هذا هي ال exponential function a to the power x + +408 +00:44:06,270 --> 00:44:13,020 +نجي لل logarithmic function الدالة اللوغاريتمية طبعا + +409 +00:44:13,020 --> 00:44:17,200 +أخذت لوغاريتمات الأعداد والأعداد المقابلة للوغاريتمات + +410 +00:44:17,200 --> 00:44:21,580 +في المرحلة الثانوية، مظبوط؟ السؤال مرة ثانية، مدام + +411 +00:44:21,580 --> 00:44:25,860 +أخذناها أبدأ أسأل السؤال التالي، هل أخذت في يوم من + +412 +00:44:25,860 --> 00:44:33,060 +الأيام لوغاريتم لكمية سالبة؟ لأ، يعني ما أخذناش + +413 +00:44:33,060 --> 00:44:38,800 +لوغاريتم لعدد سالب، أخذت في الكيمياء لوغاريتم لعدد + +414 +00:44:38,800 --> 00:44:46,210 +سالب؟ يا رجل اتقي الله يا رجل تقرأ بالدالة في سالب + +415 +00:44:46,210 --> 00:44:49,930 +ماعنديش مشكلة، لكن أنا بقول هل أخذت له غريتم كمية + +416 +00:44:49,930 --> 00:44:55,130 +سالبة؟ السؤال اللي بعده هل أخذت له غريتم للزيرو؟ + +417 +00:45:00,430 --> 00:45:06,410 +لوغاريتم الواحد بصفر، مش لوغاريتم صفر بواحد، يبقى لوغاريتم + +418 +00:45:06,410 --> 00:45:10,410 +صفر Undefined، لوغاريتم الكمية السلبية Undefined، + +419 +00:45:10,410 --> 00:45:16,390 +بتداسة للسؤال الثالث، قداش domain لوغاريتم X للأساس + +420 +00:45:16,390 --> 00:45:22,990 +إيه قبل أن أرسمها؟ من صفر لإنفينيتي مفتوح على أن + +421 +00:45:22,990 --> 00:45:27,030 +اللغة الرسمية ليست معرفة للازرع ولا للثالث يبقى + +422 +00:45:27,030 --> 00:45:31,750 +مضلووش اللي هي القيامة الموجبة يبقى ال domain للغة + +423 +00:45:31,750 --> 00:45:38,650 +الرسمية تبع ال X من صفر إلى إنفتاح يعني لما أرسم + +424 +00:45:38,650 --> 00:45:44,190 +الرسمة بدها تطلع عيمين محور Y وعلى الشمال ولا بس + +425 +00:45:44,190 --> 00:45:49,070 +عيمينه؟ عيمينه عيمينه طيب قبل ما أرسمها بدي أسأل + +426 +00:45:49,070 --> 00:45:54,410 +كمان سؤال قداش ال domain لل A to the power X + +427 +00:45:54,410 --> 00:46:00,410 +domain ال + +428 +00:46:00,410 --> 00:46:07,490 +A to the power X ما هي قدامي هي هذه بتاخد الموجب + +429 +00:46:07,490 --> 00:46:12,370 +وهي هذه بتاخد السالب وهذه زيها يبقى من سالب + +430 +00:46:12,370 --> 00:46:18,170 +infinity ل infinity كل real number طيب السؤال + +431 +00:46:18,170 --> 00:46:23,370 +الثاني ال range ما هي مكتوب قدامك ومرسوم يبقى من + +432 +00:46:23,370 --> 00:46:28,610 +زيرو، من واحد، يعني هذه الرسومات من هذه الشخصيات + +433 +00:46:30,180 --> 00:46:36,920 +يبقى الـ Range للـ A to the power X من Zero + +434 +00:46:36,920 --> 00:46:42,280 +لإنفينيتي as an open interval خلي المعلومتين هذول + +435 +00:46:42,280 --> 00:46:48,340 +عندك، بدي أرجع أسئلك فيهم سؤال، بدي أرجع أسئلك في + +436 +00:46:48,340 --> 00:46:53,480 +هذول سؤال طيب نجي للدالة اللوغاريتمية الدالة اللوغاريتمية + +437 +00:46:53,480 --> 00:46:58,700 +اللوغاريتمية لو روحت رسمت هذه المحاور يبقى هذا محور X + +438 +00:46:58,700 --> 00:47:04,160 +هذا محور Y هذه النقطة اللي هي main اللي هي zero لو + +439 +00:47:04,160 --> 00:47:07,440 +روحنا رسمنا ال function تفاجئنا وياك والسالب + +440 +00:47:07,440 --> 00:47:12,820 +والصفر يبعد الله يبقى بتاخدش إلا أو غير معرفة إلا + +441 +00:47:12,820 --> 00:47:20,720 +للقيم الموجبة يبقى هذا الخط الأزرق اللي هو Y تساوي + +442 +00:47:20,720 --> 00:47:24,560 +logarithm X للأساس A + +443 +00:47:36,180 --> 00:47:44,280 +طيب تمام النقطة هذه لحدثي تبعها واحد وزيرو زي ما + +444 +00:47:44,280 --> 00:47:48,900 +النقطة اللي فوق زيرو واحد طيب الآن ال domain + +445 +00:47:48,900 --> 00:47:52,420 +لللوغاريتم + +446 +00:47:52,420 --> 00:47:55,700 +ال X للأساس ايه؟ + +447 +00:47:58,690 --> 00:48:04,890 +من صفر لغاية infinity as an open interval بد ال + +448 +00:48:04,890 --> 00:48:14,410 +range للوغاريتم ال X للأساس هذا بياخد القيم الموجبة + +449 +00:48:14,410 --> 00:48:23,770 +هذا بياخد ال zero هذا بياخد القيم من سالب + +450 +00:48:23,770 --> 00:48:31,770 +infinity لغاية infinity يعني لوغاريتم الرقم قد يكون + +451 +00:48:31,770 --> 00:48:37,750 +موجبا و قد يكون صفرا و قد يكون سالبا لكن ال domain + +452 +00:48:37,750 --> 00:48:43,870 +دائما و أبدا موجب طيب النوع الثالث النوع الرابع + +453 +00:48:44,130 --> 00:48:47,790 +اللي أنا ما كتبتش من ال Transcendental function + +454 +00:48:47,790 --> 00:48:55,350 +اللي هو ال inverse function اللي هو معكوس الدالة، + +455 +00:48:55,350 --> 00:49:00,740 +معكوس الدالة ما لكوش علاقة فيه في هذا الفصل لكن + +456 +00:49:00,740 --> 00:49:05,260 +الفصل الجاي إن شاء الله الفصل الثاني Calculus بأول + +457 +00:49:05,260 --> 00:49:10,160 +section في أول محاضرة inverse function معكوس + +458 +00:49:10,160 --> 00:49:15,680 +الدالة تمام؟ يبقى هدول الأربعة أصناف هم اللي + +459 +00:49:15,680 --> 00:49:20,240 +بنسميهم ال Transcendental functions اللي هيمروا + +460 +00:49:20,240 --> 00:49:23,380 +علينا خلال دراستنا سواء كان في Calculus A أو + +461 +00:49:23,380 --> 00:49:29,910 +Calculus B بدنا نغششك معلومة ل Calculus B إن الـ A + +462 +00:49:29,910 --> 00:49:34,690 +to the power X ولوغاريتم الـ X to the power A كل + +463 +00:49:34,690 --> 00:49:39,130 +واحدة فيهم معكوسة للتانية يبقى the inverse + +464 +00:49:39,130 --> 00:49:43,630 +function of A to the power X is لوغاريتم الـ X + +465 +00:49:43,630 --> 00:49:49,010 +للأساس A والعكس بالعكس معكوسة دالة لوغاريتم X للأساس + +466 +00:49:49,010 --> 00:49:53,570 +A هي A to the power X ولاحظ السؤال اللي قلناه القوله + +467 +00:49:53,570 --> 00:49:59,620 +ال domain هنا هو ال range هنا والـ Range هنا هو ال + +468 +00:49:59,620 --> 00:50:04,460 +domain لما كتبتيها عكس مظبوط يبقى الدوام لما تبقى + +469 +00:50:04,460 --> 00:50:07,520 +واحدة معكوسة للثانية بيكون ال domain الأولى هو ال + +470 +00:50:07,520 --> 00:50:12,060 +range الثانية و ال range الأولى هو domain الثانية + +471 +00:50:12,060 --> 00:50:16,660 +و رسمة كل واحدة فيهم إن شاء الله هتلاقيها is + +472 +00:50:16,660 --> 00:50:19,560 +symmetric about the line Y تساوي X + +473 +00:50:32,370 --> 00:50:37,970 +ولو واحد يجاوز، الزلمة سأل سؤاله، بدي يفهم، تيجي + +474 +00:50:37,970 --> 00:50:43,670 +على لوحك شوية نتفهن احنا معاك؟ يلا تعالي هنا، طبعا + +475 +00:50:43,670 --> 00:50:49,080 +في أمور تبسط على شو اسمك أنت؟ حسن الكحول يالا يا + +476 +00:50:49,080 --> 00:50:56,700 +حسن أسألك ولا كده مرة ثانية مظبوط + +477 +00:50:56,700 --> 00:51:00,680 +صحيح يعني لا سالب ولا صفر يعني ال X هذه دائما و + +478 +00:51:00,680 --> 00:51:06,220 +أبدا موجبة طلع هنا من هنا لهنا أخذنا صفر ولا أخذنا + +479 +00:51:06,220 --> 00:51:13,410 +سالب ليبقى تفاجئنا على القطة هذه النقطة الثانية هذه + +480 +00:51:13,410 --> 00:51:18,390 +domain والله range، يعني احنا لما أخذنا القيم + +481 +00:51:18,390 --> 00:51:25,050 +الموجبة فلعنا هنا قيم موجبة وطلعتنا صفر وطلعتنا + +482 +00:51:25,050 --> 00:51:31,540 +قيم سالبة يعني ال range بتجيب الموجب والسالب، بس ال + +483 +00:51:31,540 --> 00:51:37,820 +domain للموجب، واضح؟ في مشكلة؟ ايوة، اتخربطش من ال + +484 +00:51:37,820 --> 00:51:46,580 +domain واتكترني، حاجة بت .. ايوة ايه تتطارق، صح؟ + +485 +00:51:46,580 --> 00:51:50,780 +صحيح؟ + +486 +00:51:50,780 --> 00:51:53,860 +لنسمع + +487 +00:51:53,860 --> 00:51:58,510 +سؤاله، أشوف سؤاله مرة ثانية، ايوة؟ بحكي ال A أُس X + +488 +00:51:58,510 --> 00:52:01,730 +هي اللي احنا أخذناها ها والسين اللي هي قيمة أولها + +489 +00:52:01,730 --> 00:52:06,410 +لإيه؟ يعني مش عارف الشيء اللي أخذتها أنت وبعدين + +490 +00:52:06,410 --> 00:52:10,870 +عالم والله عارف شيء اللي بدويا شوف يا سيدي في عندك + +491 +00:52:10,870 --> 00:52:17,270 +حاجة اسم A أُس X وفي E أُس X E أُس X اللي عدده + +492 +00:52:17,270 --> 00:52:22,670 +اثنين وسبعة من عشرة تقريبا بس a to the power x هذه + +493 +00:52:22,670 --> 00:52:28,610 +ال a أي رقم من صفر ل infinity عدل واحد الصحيح يعني + +494 +00:52:28,610 --> 00:52:32,070 +ال a to the power x اللي هو العدد اللي أنت بتقصده + +495 +00:52:32,070 --> 00:52:37,870 +هو حالة خاصة من a to the power x لما تكون a فقط + +496 +00:52:37,870 --> 00:52:44,410 +اثنين وسبعة من عشرة أو كاشر بخلصش تمام؟ خلاصنا؟ + +497 +00:52:44,410 --> 00:52:44,810 +ايوة + +498 +00:52:51,140 --> 00:52:55,820 +ممتاز جدا، بيسأل صاحبنا السؤال التالي والسؤال + +499 +00:52:55,820 --> 00:53:00,900 +وجهه، مع الحق، بيقول احنا رسمنا اللوغاريتم هذه لـ A + +500 +00:53:00,900 --> 00:53:05,460 +to the power X، هذه even والله odd، بيقول والله + +501 +00:53:05,460 --> 00:53:10,560 +إذا متمثلة بالنسبة لمحور A وI فهي even هل هي + +502 +00:53:10,560 --> 00:53:15,720 +متماثلة؟ يبقى not even صف على شجة نجي هل متماثلة + +503 +00:53:15,720 --> 00:53:19,520 +بالنسبة لمحور X؟ يعني هل أي نقطة هنا فيك بالها + +504 +00:53:19,520 --> 00:53:24,200 +نقطة هنا؟ يبقى ماهياش متماثلة بالنسبة لمحور X و + +505 +00:53:24,200 --> 00:53:28,180 +بضيفله عليها ولا حتى symmetric بالنسبة لل origin + +506 +00:53:28,180 --> 00:53:32,860 +الثلاثة كلها لا يبقى ما عنديش symmetry بالنسبة لها + +507 +00:53:32,860 --> 00:53:40,720 +بتاتا خلصنا؟ طيب لحد هنا stop بدنا في الحل تروح + +508 +00:53:40,720 --> 00:53:46,340 +تمرن يدك في ال exercises تبعد واحد واحد من + +509 +00:53:46,340 --> 00:53:53,840 +المسائل من واحد لسبعة وخمسين ال odd numbers طبعا + +510 +00:53:53,840 --> 00:53:58,620 +و بقولك odd ليش إن الإجابات عندك في الكتاب مش + +511 +00:53:58,620 --> 00:54:03,750 +هنتعرف أنت بتشتغل صح ولا بتشتغل غلط، تمام؟ ولا يصعب + +512 +00:54:03,750 --> 00:54:08,950 +عليك بتروح على ال discussion وانت جاهز مش تروح على + +513 +00:54:08,950 --> 00:54:12,790 +ال discussion وانت مش محلل ولا سؤال بصير انت مجمعي + +514 +00:54:12,790 --> 00:54:17,310 +شوية أما محلل، بتروح وانت موطن نفسك وفاهمي كويس، + +515 +00:54:17,310 --> 00:54:21,910 +okay؟ يبقى هنا يعني، يبقى المسألة بتروح تحلها، نبغى + +516 +00:54:21,910 --> 00:54:24,190 +بك تروح على ال discussion وإذا ما لحقتش في ال + +517 +00:54:24,190 --> 00:54:27,760 +discussion ورحت للميضة على الغرفة وما لقيتش و + +518 +00:54:27,760 --> 00:54:31,160 +بتجيني في الساعات المكتبية أهلا وسهلا و راحت بالكل + +519 +00:54:31,160 --> 00:54:34,780 +اللي بيجي يسأله و اللي بيجي يسأله حرف ده اللي هو + +520 +00:54:34,780 --> 00:54:39,700 +على جنبه طب الآن ننتقل إلى ال section الثاني اللي + +521 +00:54:39,700 --> 00:54:47,220 +يليه هو section 1-2 اللي بتكون من ثلاث نقاط رئيسة + +522 +00:54:47,790 --> 00:54:53,450 +النقطة الأولى لل combining functions بدنا نكون + +523 +00:54:53,450 --> 00:54:59,890 +دالة جديدة من دوال موجودة والنقطة الثانية ال + +524 +00:54:59,890 --> 00:55:05,010 +shifting of functions بدنا نرسم الدول ونعمل لها + +525 +00:55:05,010 --> 00:55:12,560 +إزاحات ذات اليمين أو ذات الشمال وإلى أعلى وإلى أسفل + +526 +00:55:12,560 --> 00:55:18,420 +كذلك والنقطة الثالثة ال scaling graphs إذا بنرسم + +527 +00:55:18,420 --> 00:55:24,660 +الرسمة بنسب معينة تصغير أو تكبير للرسمة الكلام + +528 +00:55:24,660 --> 00:55:31,320 +اللي سمعته هو مختصر section 1-2 يبقى section 1-2 + +529 +00:55:31,320 --> 00:55:33,680 +بتكلم عن ما يأتي + +530 +00:55:37,890 --> 00:55:45,130 +combining functions النقطة الأولى النقطة الثانية + +531 +00:55:45,130 --> 00:55:53,110 +shiftings shiftings + +532 +00:55:53,110 --> 00:56:00,170 +الإزاحات and scaling graphs + +533 +00:56:05,720 --> 00:56:10,340 +نبدأ بالنقطة الأولى اللي في ال combining functions + +534 +00:56:10,340 --> 00:56:18,400 +بإننا ناخد ال sums و ال differences الطرح أو + +535 +00:56:18,400 --> 00:56:26,520 +الفروقات و ال products اللي هو عملية الضرب and + +536 +00:56:26,520 --> 00:56:32,480 +quotients عملية القسمة + +537 +00:56:37,900 --> 00:56:44,640 +كل هدول بإننا نعطيهم تعريف فبجي بقول definition if + +538 +00:56:44,640 --> 00:57:02,810 +ال if and ال g are two functions and if ال x موجودة + +539 +00:57:02,810 --> 00:57:11,830 +في domain ال F تقاطع مع domain ال G we define + +540 +00:57:11,830 --> 00:57:16,090 +بالروح + +541 +00:57:16,560 --> 00:57:25,640 +نعرف تعريفات التالية نمرة واحد f زائد أو ناقص g as + +542 +00:57:25,640 --> 00:57:32,820 +a function of x بدي يساوي ال f of x زائد أو ناقص g + +543 +00:57:32,820 --> 00:57:41,220 +of x نمرة اثنين ال f في g of x بدي يساوي ال f of x + +544 +00:57:41,220 --> 00:57:45,640 +مضروب في ال g of x and + +545 +00:57:47,780 --> 00:57:54,200 +الـCF as a function of X بدي يساوي C في الـF of X + +546 +00:57:54,200 --> 00:58:07,200 +والـC is constant نمرة ثلاثة بدنا ال F على G كله as + +547 +00:58:07,200 --> 00:58:15,320 +a function of X بديه يساوي ال F of X على G of X + +548 +00:58:15,320 --> 00:58:25,640 +وبشرط أن ال G of X ممنوع يتساوي Zero لأن + +549 +00:58:25,640 --> 00:58:33,850 +كل هدول functions جديدة بدنا domain لمام لل F زائد + +550 +00:58:33,850 --> 00:58:43,110 +ال G هو ال domain لل F ناقص ال G هو ال domain لل F + +551 +00:58:43,110 --> 00:58:54,450 +في G هو ال domain لل F تقاطع مع domain لل G and + +552 +00:58:54,450 --> 00:59:02,550 +وزيادة على ذلك ال domain لل C في ال F + +553 +00:59:06,800 --> 00:59:13,280 +النقطة الثالثة والأخيرة domain ال F على G + +554 +00:59:17,790 --> 00:59:26,930 +Domain الـ F تقاطع مع Domain الـ G كل هذا بتشيل كل + +555 +00:59:26,930 --> 00:59:37,670 +العناصر اللي بتخللي G of X يساوي Zero for example + +556 +00:59:37,670 --> 00:59:38,270 +let + +557 +00:59:47,290 --> 00:59:55,150 +الـ F of X يساوي جذر التربيع إلى X زائد أربعة and + +558 +00:59:55,150 --> 01:00:04,090 +الـ G of X يساوي جذر التربيع إلى X تربيع ناقص أربعة + +559 +01:00:04,090 --> 01:00:16,110 +find بدنا كل من نمرة A بدنا + +560 +01:00:16,830 --> 01:00:34,510 +ال F زيدي الجي و ال F في جي و ال F على جي + +561 +01:00:34,510 --> 01:00:47,000 +نمرة B بدنا domain ال F زيدي الجي domain الـ F في + +562 +01:00:47,000 --> 01:00:58,460 +G and domain ال F على G نمرة C + +563 +01:00:58,460 --> 01:01:08,340 +بدنا ال F على G as a function of one and ال F على + +564 +01:01:08,340 --> 01:01:12,140 +G as a function of three + +565 +01:01:20,840 --> 01:01:26,660 +لما أقول combining functions يبقى احنا عندنا + +566 +01:01:26,660 --> 01:01:32,820 +دالتين أو أكثر بدنا نعملهم عملية تجميع عملية تجميع + +567 +01:01:32,820 --> 01:01:37,580 +قد يكون جمع قد يكون طرح قد يكون ضرب قد يكون قسمة + +568 +01:01:37,580 --> 01:01:43,140 +قد يكون عملية تركيبية بس التركيبية أجلناها لك إلى + +569 +01:01:43,140 --> 01:01:47,900 +ما بعد قليل قلنا نشوف الشغلات اللي بيبقى أول شغلة + +570 +01:01:47,900 --> 01:01:53,560 +بدنا نكون دالة جديدة من دالتين موجودتين إما + +571 +01:01:53,560 --> 01:01:58,360 +بعملية الجمع أو عملية الطرح أو عملية الضرب أو + +572 +01:01:58,360 --> 01:02:04,020 +عملية القسمة وبعد ما نكون هذه الدوال بدنا ندور على + +573 +01:02:04,020 --> 01:02:08,560 +ال domain تبعها ما هي علاقة ال domain لهذه الدوال + +574 +01:02:08 + +601 +01:04:36,250 --> 01:04:40,410 +بين الاتنين يبقى أنا بدأ آخذ الضرب بدل الـ F أو الـ + +602 +01:04:40,410 --> 01:04:45,250 +G بدأ أحط مقدار ثابت هو الـ F of X لما تساوي مقدار + +603 +01:04:45,250 --> 01:04:49,860 +ثابت جدّيش الـ domain تبعها كل real number من سالب + +604 +01:04:49,860 --> 01:04:54,480 +infinity إلى infinity بـ gene مين الـ domain الـ F يبقى + +605 +01:04:54,480 --> 01:04:58,040 +تقاطع ما بين الـ domain الـ F وما بين الـ set of real + +606 +01:04:58,040 --> 01:05:02,240 +numbers الـ domain الـ F itself ومن هنا نروح نقول دومين + +607 +01:05:02,240 --> 01:05:08,250 +ال constant F هو مين هو الـ domain الـ F itself طبقنا + +608 +01:05:08,250 --> 01:05:12,850 +الـ domain تبع حاصل الضرب هذا قولنا الـ intersection + +609 +01:05:12,850 --> 01:05:18,730 +ما بين الـ two domains طيب الـ domain خارج القسمة يبقى + +610 +01:05:18,730 --> 01:05:22,690 +الـ intersection ما بين الـ two domains بدي أشيل منه + +611 +01:05:22,690 --> 01:05:27,760 +النقاط اللي بتخليه للمقام ما له ساوي زي هو يبقى + +612 +01:05:27,760 --> 01:05:33,180 +ناقص كل العناصر X اللي صورتها بدها تكون صفر لأن + +613 +01:05:33,180 --> 01:05:37,960 +القسم عند هذه النقاط بيصير ما له and five طب هذا + +614 +01:05:37,960 --> 01:05:44,060 +كلام نظري بدنا نشوفه على أرض الواقع معطيني دالتين و + +615 +01:05:44,060 --> 01:05:49,080 +قال لي للجمع والضرب والقسمة وبعد هيك الـ domains + +616 +01:05:49,080 --> 01:05:52,520 +اللي لهم وبعدين احسب لي الـ domains القسمة عنده + +617 +01:05:52,520 --> 01:05:58,500 +رقمين بقوله ماشي بدي آجي للنقطة الأولى بدي آخذ له f + +618 +01:05:58,500 --> 01:06:04,160 +زائد g as a function of x بدي أعرف شو شكل الجمع + +619 +01:06:04,540 --> 01:06:08,900 +بنطبق التعريف اللي أنا قايليه يبقى لما أطبق التعريف + +620 +01:06:08,900 --> 01:06:15,720 +هذه عبارة عن f of x زائد g of x f of x معروفة + +621 +01:06:15,720 --> 01:06:22,140 +عند اللي هي جذر تربيعي لـ x زائد 4 زائد + +622 +01:06:22,140 --> 01:06:28,400 +الـ g of x اللي هي جذر تربيعي لـ x تربيع ناقص 4 + +623 +01:06:28,400 --> 01:06:36,950 +بقدر هذول أجمعهم أكثر من هيك خلاص؟ يبقى خلاص؟ بقدرش + +624 +01:06:36,950 --> 01:06:40,410 +أجمع أكثر من هيك، يبقى هيوم، كل اللي بقدر أعمله أن + +625 +01:06:40,410 --> 01:06:44,770 +أضرب في المرافق وبالتالي أحطهم في شكل جديد، + +626 +01:06:44,770 --> 01:06:48,530 +كالكعزيزة ما لهاش لزوم، يبقى خلاص وصل لحد هنا، + +627 +01:06:48,530 --> 01:06:53,200 +والله يعطيك العافية بعد هيك بندجي لمين؟ للنقطة + +628 +01:06:53,200 --> 01:06:58,760 +الثانية اللي هي الـ FG as a function of X يبقى الـ F + +629 +01:06:58,760 --> 01:07:04,840 +of X في الـ G of X يبقى جذر تربيعي للـ X اللي + +630 +01:07:04,840 --> 01:07:10,920 +عندنا هذه للـ X زائد الـ 4 مضروبة في جذر + +631 +01:07:10,920 --> 01:07:16,220 +تربيعي لـ X تربيع ناقص 4 هذه صحيحة بقدر + +632 +01:07:16,220 --> 01:07:21,700 +أخليها جذر واحد مظبوط بقدر أقول هذا جذر واحد، + +633 +01:07:21,700 --> 01:07:27,260 +مظبوط لمين؟ للـ X زائد 4 بالـ X تربيع نقص + +634 +01:07:27,260 --> 01:07:31,320 +4 بقدر واحد وأخليه جذر واحد أكثر من هيك، + +635 +01:07:31,320 --> 01:07:36,910 +وصل لحد هنا والله يعطيك العافية بندجي لمن؟ لـ الـ F + +636 +01:07:36,910 --> 01:07:43,510 +على G as a function of X يبقى الـ F of X على الـ G + +637 +01:07:43,510 --> 01:07:49,710 +of X يبقى جذر تربيعي للـ X زائد 4 على من على + +638 +01:07:49,710 --> 01:07:54,290 +جذر تربيعي لـ X تربيع ناقص 4 هو اللي بقدر أخليه + +639 +01:07:54,290 --> 01:07:54,870 +كذلك + +640 +01:08:04,710 --> 01:08:11,790 +خلصنا المطلوب الأول بدنا نيجي للمطلوب الثاني نجيب + +641 +01:08:11,790 --> 01:08:17,120 +الـ domain للأولى والـ domain للثانية مش هنجيب الـ two + +642 +01:08:17,120 --> 01:08:22,840 +domains لازم أعرف قدّيش الـ domain الـ F والـ domain الـ G و + +643 +01:08:22,840 --> 01:08:26,840 +تقاطعه فيما بينهما لأن هذا أساسي في شغلنا صحيح + +644 +01:08:26,840 --> 01:08:32,020 +ولا لأ يبقى باجي بقوله بدي أجيب له في الأول domain + +645 +01:08:32,020 --> 01:08:38,600 +ده الـ F هو كل العناصر X بحيث أنه بيرجع للـ F صح + +646 +01:08:38,600 --> 01:08:45,260 +بيتنا هذه تمام؟ بدي الـ domain تبعها بدي القيمة اللي + +647 +01:08:45,260 --> 01:08:49,720 +تحت الجذر تبقى دائماً وأبداً أكبر من أو تساوي الـ + +648 +01:08:49,720 --> 01:08:54,160 +zero يبقى الـ X زائد 4 greater than or equal to + +649 +01:08:54,160 --> 01:08:59,060 +zero يبقى الـ X زائد 4 greater than or equal to + +650 +01:08:59,060 --> 01:09:06,500 +zero يبقى كل العناصر X بحيث أن الـ X تكون أكبر من + +651 +01:09:06,500 --> 01:09:12,080 +أو تساوي قدّيش سالب 4 يعني من سالب 4 ثم فوق + +652 +01:09:12,080 --> 01:09:18,350 +يعني من ولا وين سالب 4 لغاية infinity يبقى هذا + +653 +01:09:18,350 --> 01:09:23,850 +كل الـ interval مغلقة من عند السالب 4 ولغاية الـ + +654 +01:09:23,850 --> 01:09:28,330 +infinity مفتوحة بالشكل اللي قدامنا هنا تمام هي + +655 +01:09:28,330 --> 01:09:33,690 +جيبنا الـ domain الـ F بدنا نجيب domain الـ G + +656 +01:09:33,690 --> 01:09:39,170 +domain الـ G كل العناصر X بحيث برضه صاحبنا هذا + +657 +01:09:39,170 --> 01:09:44,610 +جذر يبقى بدي كل الكمية اللي تحت الجذر تبقى أكبر من + +658 +01:09:44,610 --> 01:09:49,870 +أو تساوي الـ zero بحيث إن X squared minus four + +659 +01:09:49,870 --> 01:09:54,750 +greater than or equal to zero يبقى كل العناصر X + +660 +01:09:54,750 --> 01:10:01,290 +نضيف 4 للطرفين يبقى بحيث إن X تربيع greater + +661 +01:10:01,290 --> 01:10:07,310 +than or equal to من الـ 4 أنا ما بدي X تربيع بدي + +662 +01:10:07,310 --> 01:10:12,970 +X يبقى شو بعمل؟ بأخذ الجذر التربيعي للطرفين، يبقى + +663 +01:10:12,970 --> 01:10:19,370 +هذا كل العناصر X بحيث إن absolute value لـ X أكبر + +664 +01:10:19,370 --> 01:10:24,130 +من أو تساوي absolute value للـ 2 اللي همّين + +665 +01:10:24,130 --> 01:10:32,380 +بالـ 2 صح؟ سكت الشعب جذر تربيعي على X تربيع + +666 +01:10:32,380 --> 01:10:35,180 +هو absolute value لـ X يبقى absolute value لـ X + +667 +01:10:35,180 --> 01:10:38,000 +جذر تربيعي على 4 هو absolute value للـ 2 + +668 +01:10:38,000 --> 01:10:43,940 +اللي هي بـ 2 itself طبعاً فبدي أعبر عن هذه بصياغة + +669 +01:10:43,940 --> 01:10:51,260 +أخرى فبجي بقول هذه كل العناصر X such that هذه إمّا + +670 +01:10:51,260 --> 01:10:54,260 +الـ X greater than or equal to + +671 +01:11:03,630 --> 01:11:07,610 +بس اسمع اسمع ليش إيش؟ وهي + +672 +01:11:21,220 --> 01:11:28,020 +هذا الكلام يسمى كلمة or تعني اتحاد + +673 +01:11:30,080 --> 01:11:35,140 +يبقى باجي بقول جال الـ X أكبر من أو تساوي 2 يعني من + +674 +01:11:35,140 --> 01:11:39,680 +عند 2 لوين للمالها نهاية جال الـ X أقل من أو + +675 +01:11:39,680 --> 01:11:44,620 +تساوي سالب 2 يعني بدك ترجع من سالب 2 لوين لكن الفترة + +676 +01:11:44,620 --> 01:11:49,020 +الصغيرة بنحطها في الأول والكبيرة بنحطها في الآخر + +677 +01:11:49,020 --> 01:11:54,460 +يبقى كل الـ interval من سالب infinity لغاية سالب + +678 +01:11:54,460 --> 01:12:01,530 +2 مغلقة من عند السالب 2 بسبب اليساوي اتحاد + +679 +01:12:01,530 --> 01:12:05,490 +الفترة من 2 لغاية infinity + +680 +01:12:08,010 --> 01:12:12,170 +طيب حتى الآن جيب بس الـ domain الـ F والـ domain الـ G، + +681 +01:12:12,170 --> 01:12:17,750 +أصبر عليّ بس نخلص الآن أنا بدي الـ domain المشترك ما + +682 +01:12:17,750 --> 01:12:23,750 +بين الاثنين لأنه عند التعريف قال X موجودة وين في + +683 +01:12:23,750 --> 01:12:27,610 +التقاطع ولمن حسبنا الـ domain قال اللي موجود في + +684 +01:12:27,610 --> 01:12:32,970 +تقاطع الاثنين يبقى إحنا بدنا نروح نجيب تقاطع + +685 +01:12:32,970 --> 01:12:39,410 +الفترتين domain الـ F مع domain الـ G إذا بقوله بدي + +686 +01:12:39,410 --> 01:12:47,290 +domain الدالة F تقاطع مع domain الدالة G يساوي وما + +687 +01:12:47,290 --> 01:12:52,510 +أدركي ما له يساوي وكيف بدنا نعزّبه استغلنا شوية بقى + +688 +01:12:52,510 --> 01:12:58,340 +أصبّر الله ما أخلق الآن بدي أعلمك كيف تحسبه بطريقة ما + +689 +01:12:58,340 --> 01:13:05,000 +تخرّش الميه تمام؟ بدك تروح تلصق راسم كيف الرسم؟ + +690 +01:13:05,000 --> 01:13:11,740 +بقوله هذا الـ real life بتدهش للفترة الأولى تبع الـ + +691 +01:13:11,740 --> 01:13:15,680 +domain ده اللي بيطلع من وين؟ من عند السالب 4 + +692 +01:13:15,680 --> 01:13:22,120 +لغاية؟ يعني لو قلت هذا الـ zero بده تجينا سالب 4 + +693 +01:13:22,120 --> 01:13:27,160 +هنا مظبوط؟ نبعدها شوية مشان الكل يشوف جول هنا، + +694 +01:13:27,160 --> 01:13:32,900 +هي سالب 4 يبقى من وين لوين؟ من عند السالب 4 + +695 +01:13:32,900 --> 01:13:39,780 +بدي أبقى ماشي لما لا نهاية سهم يعني قال فالله + +696 +01:13:39,780 --> 01:13:43,960 +سهّل عليها إلى نيرة الله الأرض ومن عليها خلاصنا + +697 +01:13:43,960 --> 01:13:49,020 +مين؟ هذا مين اللي رسمته؟ domain الـ F بدي أروح لـ + +698 +01:13:49,020 --> 01:13:53,320 +domain الـ G domain الـ G جاله من سالب infinity + +699 +01:13:53,320 --> 01:13:58,320 +لغاية سالب 2 سالب 2 وين بيجينا؟ هنا سالب + +700 +01:13:58,320 --> 01:14:04,710 +2 وبتدّك ترجع لوين؟ لسالب infinity وبعد هيك من + +701 +01:14:04,710 --> 01:14:09,830 +عند 2 للـ infinity يبقى 2 تجينا بعد الـ zero + +702 +01:14:09,830 --> 01:14:15,230 +يبقى هي 2 وللـ infinity بالشكل اللي عندنا هذا + +703 +01:14:16,480 --> 01:14:20,860 +الآن التقاطع بتاعهم هو المنطقة المشتركة ما بين + +704 +01:14:20,860 --> 01:14:24,880 +الاثنين وإن الاثنين موجودين مع بعض بتكون هي المنطقة + +705 +01:14:24,880 --> 01:14:30,560 +المشتركة اطلع لي هذه أظنّ هذه المنطقة المشتركة ما + +706 +01:14:30,560 --> 01:14:35,800 +بين الاثنين هنا وهنا هذه المنطقة المشتركة ما بين + +707 +01:14:35,800 --> 01:14:41,190 +الاثنين صحيح ولا لأ؟ يبقى بناء عليه بقدر الـ domain + +708 +01:14:41,190 --> 01:14:47,910 +من سالب 4 لسالب 2 من سالب 4 لسالب + +709 +01:14:47,910 --> 01:14:54,590 +2 as an closed interval بسبب وجود اليساوي بدي + +710 +01:14:54,590 --> 01:15:00,230 +أحط عليها كمان الفترة من ولا وام من 2 مغلقة + +711 +01:15:00,230 --> 01:15:06,190 +لغاية infinity يبقى يا شباب إن رسمت زيها في عمرك ما + +712 +01:15:06,190 --> 01:15:11,010 +هتغلط بس تجي تقدرها بدل الرسم احتمال الخطأ وارد + +713 +01:15:11,010 --> 01:15:17,380 +بنسبة 150% هذا للبعض والبعض الآخر قد يكون نسبة نجاح + +714 +01:15:17,380 --> 01:15:22,540 +150% واما ما ده فيه اختلاف في العقول إذا حتى ما + +715 +01:15:22,540 --> 01:15:28,860 +نغلطش بنحاول نرسم طيب رسمنا وحددنا الفترة الحين + +716 +01:15:28,860 --> 01:15:33,120 +بدنا نيجي لمين؟ لنمبر 2 في المثال نحسب الـ domain + +717 +01:15:33,120 --> 01:15:38,020 +اللي بدنا إياه بعد ما اشتغلنا الشغل هذه كلها + +718 +01:15:52,810 --> 01:15:58,970 +نمسك نمبر بي لأن هي نمبر بي نمبر بي قال لي + +719 +01:15:58,970 --> 01:16:02,190 +domain الـ F زي دي الـ G وdomain الـ F في G هذول زي + +720 +01:16:02,190 --> 01:16:06,870 +بعض مش فيهم مشكلة مظبوط؟ يبقى بقى جيبقى أقول له + +721 +01:16:06,870 --> 01:16:15,980 +domain الـ F زائد الـ G هو domain الـ F في G هو + +722 +01:16:15,980 --> 01:16:23,020 +domain الـ F تقاطعه مع domain الـ G مش هيك؟ يبقى + +723 +01:16:23,020 --> 01:16:27,650 +هذا جاهز حسبته بجيبها زي ما هي وبقعدها بسلامتها + +724 +01:16:27,650 --> 01:16:35,330 +يبقى هذه تساوي سالب 4 وسالب 2 اتحاد 2 + +725 +01:16:35,330 --> 01:16:39,450 +و infinity بقى اللي عندنا في نمبر بي إيجاد domain + +726 +01:16:39,450 --> 01:16:44,010 +خارج القسمة بقوله and + +727 +01:16:46,520 --> 01:16:52,740 +الـ domain بتبع الـ F على G اللي هو domain الـ F + +728 +01:16:52,740 --> 01:17:02,980 +تقاطعه مع domain الـ G بدي أشيل منه كل الـ X's اللي + +729 +01:17:02,980 --> 01:17:10,090 +بدها تخليه لـ G of X يساوي Zero مش هيك التعريف طيب + +730 +01:17:10,090 --> 01:17:15,030 +الـ intersection جاهز هيّه فوق يبقى سالب 2 + +731 +01:17:15,030 --> 01:17:23,090 +سالب 4 لغاية سالب 2 اتحاد 2 و + +732 +01:17:23,090 --> 01:17:29,370 +infinity بدي أشيل منه كل القيم اللي بدها تخلي + +733 +01:17:29,370 --> 01:17:35,470 +المقام بـ zero من القيم اللي بتخلي جي بـ zero هي جي + +734 +01:17:36,000 --> 01:17:40,000 +ما هو اللي بيخليها zero؟ 2 وسالب 2 هل + +735 +01:17:40,000 --> 01:17:47,340 +يوجد غيرهم؟ بنكتبهم as a set سالب 2 و2، + +736 +01:17:47,340 --> 01:17:51,700 +يبقى بدنا نجي على الفترة هذه بدي أشيل منها سالب + +737 +01:17:51,700 --> 01:17:56,460 +2 و2 اللي عندنا يبقى بدل ما تلت بخليها + +738 +01:17:56,460 --> 01:18:02,020 +مفتوحة بيقول خلصنا حلّينا مشكلتنا يبقى هذه تساوي + +739 +01:18:02,020 --> 01:18:09,540 +سالب 4 مغلقة سالب 2 بنخليها مفتوحة اتحاد + +740 +01:18:09,540 --> 01:18:15,140 +كمان مفتوحة 2 و infinity يبقى استبعدنا سالب + +741 +01:18:15,140 --> 01:18:16,300 +2 و2 + +742 +01:18:27,360 --> 01:18:30,980 +المشكلة في حساب الـ domain مش في الشكل إذا في + +743 +01:18:30,980 --> 01:18:36,340 +اختصارات باختصرها المقال فيش اختصارات X ناقص + +744 +01:18:36,340 --> 01:18:41,980 +2 في X زي 2 فرق من المربعين هدف اللي فوق + +745 +01:18:41,980 --> 01:18:45,680 +X زي 4 لأ لأ اجى في باله X ناقص 4 X زي + +746 +01:18:45,680 --> 01:18:47,360 +4 تم اختصار فيش اختصار + +747 +01:18:55,340 --> 01:19:00,800 +هي الـ F في الـ bus ولا في المقام مظبوط؟ يبقى بيخلي + +748 +01:19:00,800 --> 01:19:04,360 +اللي في المقام هو اللي يساوي دي لأصفار المقام مش + +749 +01:19:04,360 --> 01:19:07,520 +أصفار البسط أصفار البسط ده اللي معرفة عندها + +750 +01:19:07,520 --> 01:19:10,960 +ماعنديش مشكلة المشكلة لو وقعت الأصفار في المقام + +751 +01:19:10,960 --> 01:19:16,320 +عارف ليش؟ لأنه لا يمكن في علم الرياضيات إنك تقسم + +752 +01:19:16,320 --> 01:19:21,680 +على صفر خارج نطاق العقل البشري مش ممكن يتصورها + +753 +01:19:21,680 --> 01:19:25,320 +العقل البشري في يوم من الأيام ماشي ليومنا هذا + +754 +01:19:25,320 --> 01:19:30,340 +طبعاً تمام؟ يبقى خلاصنا من وين؟ نمبر بي خلاصنا منها + +755 +01:19:30,340 --> 01:19:36,960 +كلها جيبنا الـ domain طبعاً أيوة كيف؟ تعال هنا إيه + +756 +01:19:36,960 --> 01:19:41,040 +الحدّ؟ + +757 +01:19:41,040 --> 01:19:51,280 +إنيّات اللي بتنعد لحد هنا؟ وين اللي ما فهمتوش؟ ممتاز + +758 +01:19:51,280 --> 01:19:57,420 +جداً طيب إذا الـ domain دولة F1 وF2 هيّها هل الجذر معرف + +759 +01:19:57,420 --> 01:20:04,100 +لقيمة سالبة يعني بدي أكبر أو يساوي ها إيه أكبر من + +760 +01:20:04,100 --> 01:20:08,140 +أو يساوي زيّه تعرف تحلّي المتباينة هنا يعني بنضيف + +761 +01:20:08,140 --> 01:20:12,980 +سالب 4 على الطرفين بيصير X أكبر من سالب 4 + +762 +01:20:12,980 --> 01:20:16,580 +أو يساوي يعني من سالب 4 والله سهّل عليك لوين؟ + +763 +01:20:18,220 --> 01:20:22,200 +أكبر منها سالب 3 سالب 2 سالب 1 زيرو 1 + +764 +01:20:22,200 --> 01:20:25,680 +2 لغاية ما يبقى هذه خلاصة من هذه الثانية + +765 +01:20:25,680 --> 01:20:29,260 +واختها هي الجذر التربيعي لـ X تربيع ناقص 4 بدنا + +766 +01:20:29,260 --> 01:20:34,140 +ياها أكبر من أو تساوي مين الـ zero نضيف 4 على + +767 +01:20:34,140 --> 01:20:38,700 +الطرفين بيصير X تربيع أكبر نأخذ الجذر التربيعي + +768 +01:20:38,700 --> 01:20:43,800 +للطرفين موافق؟ لحد هنا تمام؟ بدنا نفسر هذه هذه + +769 +01:20:43,800 --> + +801 +01:23:57,460 --> 01:24:00,040 +وهي very important + +802 +01:24:06,110 --> 01:24:10,190 +هي النقطة الثانية لل composition of functions + +803 +01:24:10,190 --> 01:24:18,290 +اللي كنتوا بتسموها f circle g أو f بعد g أيوة تمامًا + +804 +01:24:18,290 --> 01:24:24,530 +الـ f على الـ g ما له أبداً تمامًا الـ f التقاطع تبع الـ + +805 +01:24:24,530 --> 01:24:29,090 +اثنين اللي كتبنا تحت بده الشيء القيم اللي بتخلي الـ g + +806 +01:24:29,090 --> 01:24:33,950 +تساوي صفر الجذر التربيعي لـ x تربيع ناقص 4 أو اكتشف + +807 +01:24:33,950 --> 01:24:40,360 +بيساوي صفر عند x اثنين و سالب اثنين لأنه 4 ناقص + +808 +01:24:40,360 --> 01:24:43,580 +4 بصفر ناقص 2 كل تربيع 4 ناقص 4 + +809 +01:24:43,580 --> 01:24:47,020 +بصفر يبقى بدنا نشيل 2 و سالب 2 من الـ + +810 +01:24:47,020 --> 01:24:51,040 +interval سالب 4 لغاية سالب 2 اتحاد 2 و + +811 +01:24:51,040 --> 01:24:54,760 +infinity يعني بصير مفتوح عند سالب 2 و 2 + +812 +01:24:54,760 --> 01:25:03,070 +ليس الأفضل نجي الآن لتكملة النقطة الأولى اللي هي + +813 +01:25:03,070 --> 01:25:08,450 +الـ composite functions يبقى بالدالي لحاجة اسمها الـ + +814 +01:25:08,450 --> 01:25:12,130 +composite functions + +815 +01:25:12,130 --> 01:25:15,250 +definition + +816 +01:25:15,250 --> 01:25:18,310 +F + +817 +01:25:18,310 --> 01:25:25,130 +الـ F عند الـ G R + +818 +01:25:26,470 --> 01:25:34,830 +two functions recomposite + +819 +01:25:34,830 --> 01:25:38,430 +function + +820 +01:25:38,430 --> 01:25:45,410 +الدالة التركيبية أو الدالة المحصلة للـ F composition + +821 +01:25:45,410 --> 01:25:49,670 +G is defined by + +822 +01:25:55,990 --> 01:26:02,750 +إذا كانت الـ composition جي كمعاملة من X يساوي F + +823 +01:26:02,750 --> 01:26:20,990 +للـ جي من X بحيث أن X موجودة في Domain الجي مرة + +824 +01:26:20,990 --> 01:26:21,370 +ثانية + +825 +01:26:24,890 --> 01:26:29,170 +الـ composite function الدالة المحاصلة أو الدالة + +826 +01:26:29,170 --> 01:26:34,890 +التركيبية يعني أنا عندي دالتين بدي أركب منهم دالة + +827 +01:26:34,890 --> 01:26:39,050 +جديدة دالة واحدة دي من الدالتين اللي موجودة أو ثلاث + +828 +01:26:39,050 --> 01:26:42,410 +دول بدي أركب منهم دالة أو أربعة أو ما إلى ذلك + +829 +01:26:48,990 --> 01:26:54,130 +الدالة التركيبية أو الدالة المحصلة بدي أعطيها رمز + +830 +01:26:54,130 --> 01:26:59,890 +F circle G كنتوا بتقراوها في الثانوي F بعد G أو F + +831 +01:26:59,890 --> 01:27:08,950 +circle G في علمنا F composition G F composition G + +832 +01:27:08,950 --> 01:27:12,390 +Circle بس عشانها دائرة صغيرة بنقول Circle أما في + +833 +01:27:12,390 --> 01:27:17,550 +الحقيقة بنقول F composition G is defined by + +834 +01:27:17,550 --> 01:27:24,670 +بنعرفها كالتالي F composition G of X يساوي F of G of + +835 +01:27:24,670 --> 01:27:29,470 +X بحيث أن X موجودة وين في Domain الـ G خلي بالك + +836 +01:27:29,470 --> 01:27:34,200 +معايا هنا الآن أنا بقول if composition D of X مين + +837 +01:27:34,200 --> 01:27:39,740 +أقرب واحد على X؟ if والله جي جي يبقى جي هتأثر على + +838 +01:27:39,740 --> 01:27:45,780 +X يبقى X لازم تكون وين من الـ G حتى تقدر تأثر + +839 +01:27:45,780 --> 01:27:52,730 +عليها طيب أثرنا بـ G على X صارت مين؟ G of X إذاً G + +840 +01:27:52,730 --> 01:27:58,610 +of X صار element جديد في Domain الدالة F حتى + +841 +01:27:58,610 --> 01:28:03,810 +تقدر F تأثر عليها نوضح لك هذا الكلام بالرسم لو + +842 +01:28:03,810 --> 01:28:11,250 +عندي هنا Set والست سميتها A والست الثانية سميتها B + +843 +01:28:11,250 --> 01:28:19,800 +والست الثالثة سميتها C خلي بالك معايا كويس الآن من A + +844 +01:28:19,800 --> 01:28:29,960 +إلى B في عندي دالة اسمها G من B إلى C في عندي دالة + +845 +01:28:29,960 --> 01:28:39,330 +اسمها F الآن لو كان عندي element هنا اسمه X يبقى + +846 +01:28:39,330 --> 01:28:44,250 +هذا الـ element موجود في Domain إذا جي بتأثر + +847 +01:28:44,250 --> 01:28:49,270 +على كل عناصر A إذا هتأثر على هذا الـ element يبقى + +848 +01:28:49,270 --> 01:28:55,230 +جي لما تحث .. لما تأثر على X بده يظهر له صورة في B + +849 +01:28:55,230 --> 01:29:02,650 +اسمها G of X هي صورة الـ Element X اللي موجود + +850 +01:29:02,650 --> 01:29:09,410 +في A صورتها ظهرت في B بي هو Domain مين يبقى الـ F + +851 +01:29:09,410 --> 01:29:14,170 +هتأثر على هذا الـ element اللي موجود في Domainها + +852 +01:29:14,170 --> 01:29:21,630 +اللي موجود في Domainها وتخلي صورته هنا F of الـ + +853 +01:29:21,630 --> 01:29:26,710 +element اللي موجود في Domainها اللي هو G of X + +854 +01:29:26,710 --> 01:29:34,270 +وكأنه بيه مهّدّي مش هتظهر كأنه بده يصير الـ X بده + +855 +01:29:34,270 --> 01:29:39,390 +يجي للـ element اللي عندنا هذا اللي اسمه F of + +856 +01:29:39,390 --> 01:29:47,110 +G of X وبالتالي F composition G of X بده يسوي F of + +857 +01:29:47,110 --> 01:29:59,300 +G of X طيب سؤال هل الـ F composition G يساوي G + +858 +01:29:59,300 --> 01:30:04,600 +composition F؟ فرقة السما على الأرض هنا الـ element + +859 +01:30:04,600 --> 01:30:06,840 +بيكون في الـ Domain الـ G هنا الـ element في الـ + +860 +01:30:06,840 --> 01:30:14,640 +Domain الـ F يبقى هذه اللي لا يمكن أن تساوي هذه يبقى + +861 +01:30:14,640 --> 01:30:19,940 +بقوله هنا in general على وجه العموم الـ F + +862 +01:30:19,940 --> 01:30:23,920 +composition G لا يساوي G composition F السؤال + +863 +01:30:23,920 --> 01:30:30,790 +الثاني احنا جبنا دالة جديدة من الدالتين الأصليتين + +864 +01:30:30,790 --> 01:30:35,650 +زي ما كنا قبل قليل بنضيف دالة جديدة إذا بدنا الـ + +865 +01:30:35,650 --> 01:30:40,570 +Domain تبعها وافتح لي كويس لإن كتير من الشباب بيضلوا + +866 +01:30:40,570 --> 01:30:44,690 +يسألوا فيها كتير عملية سهلة جدا بس مش عارف ليش + +867 +01:30:44,690 --> 01:30:49,990 +بيكتروا فيها السؤال الآن بدنا نيجي للـ Domain بتابع + +868 +01:30:49,990 --> 01:30:56,690 +الـ F composition G بدي أعرفه تعريف مين هو الآن هذه + +869 +01:30:56,690 --> 01:31:02,920 +مشان تأثر على element بدي أقول كل العناصر X يبقى X + +870 +01:31:02,920 --> 01:31:07,400 +وهوين بده يكون موجود؟ في Domain الجي يبقى كل + +871 +01:31:07,400 --> 01:31:14,580 +العناصر X بحيث أن X موجود في Domain الجي وفي نفس + +872 +01:31:14,580 --> 01:31:20,840 +الوقت and الـ G of X هوين بده يكون موجود؟ في Domain + +873 +01:31:20,840 --> 01:31:26,760 +الـ F موجود في Domain الـ F يبقى هذا تعريف تبع + +874 +01:31:26,760 --> 01:31:32,240 +الـ composition ولا رئاسة منها كل العناصر اللي موجود في + +875 +01:31:32,240 --> 01:31:36,420 +Domain الـ G صار عنده G of X يبقى G of X بدها تكون + +876 +01:31:36,420 --> 01:31:41,820 +وأن موجودة في Domain الـ F خلص التعريف بالمهم مش + +877 +01:31:41,820 --> 01:31:46,480 +التعريف هو كيف اتطبق لمين التعريف إذا سنذهب إلى + +878 +01:31:46,480 --> 01:31:52,800 +مثال مباشرة example عادي + +879 +01:31:52,800 --> 01:31:58,590 +نثبت المعلومة هذه قبل ما نمشي المثال بيقول ما يأتي + +880 +01:31:58,590 --> 01:32:05,250 +let فبرض هأعطيك على هذه النقطة بدل المثال ثلاثة وكل + +881 +01:32:05,250 --> 01:32:11,550 +واحد فني بيختلف عن الثاني فافتحه كويس ودقق معه let + +882 +01:32:11,550 --> 01:32:25,910 +اللي هو الـ f of x بدل يساوي x تربيع ناقص 1 and الـ G of X بدي + +883 +01:32:25,910 --> 01:32:42,290 +أساوي الـ Square Root لمين؟ للخمسة ناقص الـ X نمرا + +884 +01:32:42,290 --> 01:32:50,790 +A بدي الـ F composition G نمرا B بدي الـ G + +885 +01:32:50,790 --> 01:32:59,780 +composition F نمرة C بدي الـ G composition G نمرة D + +886 +01:32:59,780 --> 01:33:09,900 +بدي الـ Domain الـ F composition G and Domain الـ G + +887 +01:33:09,900 --> 01:33:11,620 +composition G + +888 +01:33:40,400 --> 01:33:45,080 +هلا مالك هنا افتح معايا كويس مش هشوف كيف بنحسب + +889 +01:33:45,080 --> 01:33:52,760 +الشغلات هذه الآن بدنا F composition g as a + +890 +01:33:52,760 --> 01:34:01,240 +function of x شو شكله؟ فبجي بقول شكله كالتالي F of G + +891 +01:34:01,240 --> 01:34:08,380 +of X طبعا الآن G of X موجودة عندي يبقى بشيل G of X + +892 +01:34:08,380 --> 01:34:15,240 +و بحط قيمة مكانها يبقى F of الـ G of X هي عبارة عن + +893 +01:34:15,240 --> 01:34:22,680 +الجذر التربيعي لمين؟ لـ 5 ناقص الـ X بعدك اسمع + +894 +01:34:22,680 --> 01:34:29,540 +شوية هنا بيقول الـ F لما تأثر على العنصر يساوي مربع + +895 +01:34:29,540 --> 01:34:34,860 +العنصر مطروح منه 1 يبقى F لما تأثر على هذا العنصر + +896 +01:34:34,860 --> 01:34:42,020 +مربع هذا العنصر مطروح منه 1 يبقى هذا الكلام بده + +897 +01:34:42,020 --> 01:34:49,440 +يصير 5 ناقص X تحت الجذر الكل تربيع بده أشيل منه + +898 +01:34:49,440 --> 01:34:56,580 +1 تمام؟ يبقى هذا شو بده يساوي؟ هذا 5 ناقص X + +899 +01:34:56,580 --> 01:35:02,080 +ناقص 1 يبقى النتيجة 4 ناقص X + +900 +01:35:05,260 --> 01:35:09,560 +بنفس الطريقة نجيب جي جي جي جي جي جي جي جي جي جي + +901 +01:35:09,560 --> 01:35:22,360 +جي جي جي جي جي جي جي جي جي جي + +902 +01:35:22,360 --> 01:35:25,980 +جي + +903 +01:35:34,480 --> 01:35:39,840 +الآن جي لما تأثر على العنصر يساوي الجذر التربيعي + +904 +01:35:39,840 --> 01:35:45,860 +لـ 5 ناقص هذا العنصر يبقى هذا بده يساوي الجذر + +905 +01:35:45,860 --> 01:35:53,760 +التربيعي لـ 5 ناقص هذا العنصر لـ X تربيع ناقص + +906 +01:35:53,760 --> 01:36:02,260 +1 هذا بده يصير الجذر التربيعي لـ 5 ناقص X تربيع + +907 +01:36:02,260 --> 01:36:10,200 +زائد 1 يبقى الجذر التربيعي لـ 6 ناقص X تربيع اللي + +908 +01:36:10,200 --> 01:36:16,560 +ما فهمش يتابع معاه نمرة C بدي جي composition جي + +909 +01:36:16,560 --> 01:36:23,070 +كذلك بعد هيك بيضلّ هو يضرب ولا لوحده، بدل السؤال ثلاثة + +910 +01:36:23,070 --> 01:36:32,170 +على نفس المفهوم يبقى هذا G لـ G of X يبقى G لأ، + +911 +01:36:32,170 --> 01:36:35,670 +بدي أشيل الـ G of X و أحط قيمته اللي هو الجذر + +912 +01:36:35,670 --> 01:36:44,560 +التربيعي للخمسة ناقص X وكأن هذا الـ element كله أصبح + +913 +01:36:44,560 --> 01:36:50,000 +عنصر في Domain الـ G جي لما اتأثر على عنصر + +914 +01:36:50,000 --> 01:36:54,180 +اللي في Domainها بده يساوي الجذر التربيعي لـ 5 + +915 +01:36:54,180 --> 01:37:00,420 +ناقص هذا العنصر يبقى هذا بده يساوي الجذر التربيعي + +916 +01:37:00,420 --> 01:37:09,240 +لـ 5 ناقص هذا العنصر 5 ناقص X واضح؟ هاي بدل + +917 +01:37:09,240 --> 01:37:12,980 +سؤال اثنين ثلاثة حلّينا لك كيف تحسب F الـ + +918 +01:37:12,980 --> 01:37:18,500 +composition وبالتالي خلصنا A و B و C الآن بدنا نجيب + +919 +01:37:18,500 --> 01:37:22,820 +الـ Domain بشان نجيب الـ Domain بدنا Domain كل واحدة + +920 +01:37:22,820 --> 01:37:28,320 +فيهم في الأول يبقى قبل ما نيجي للباقي بدي Domain + +921 +01:37:28,320 --> 01:37:36,670 +الـ F يساوي R كفاية في نقطة لفها دي مش معرفة عندها + +922 +01:37:36,670 --> 01:37:42,590 +يبقى معناها كل الـ Real Number يبقى من سالب + +923 +01:37:42,590 --> 01:37:51,010 +Infinity إلى Infinity ماشي بدنا Domain الـ جي كل + +924 +01:37:51,010 --> 01:37:56,770 +العناصر X بحيث R بدي كل القيم اللي تحت الجذرة + +925 +01:37:56,770 --> 01:38:03,550 +تبقى مالها أكبر من أو تساوي الـ Zero بدي كل الخمسة + +926 +01:38:03,550 --> 01:38:10,010 +ناقص X greater than or equal to Zero يعني كل + +927 +01:38:10,010 --> 01:38:22,820 +العناصر X بحيث أن يبقى X أقل + +928 +01:38:22,820 --> 01:38:30,340 +من أو تساوي 5 من سالب Infinity لغاية 5 + +929 +01:38:37,960 --> 01:38:42,280 +تمام؟ جبنا الـ two Domains يبقى حلينا المعضلة و + +930 +01:38:42,280 --> 01:38:46,840 +بلش عندي إلا أحسب كده الـ Domain تبع كل واحدة فيهم + +931 +01:38:46,840 --> 01:38:53,100 +إذا بنجي لنمرة D بدي الـ Domain بتبع الـ F + +932 +01:38:53,100 --> 01:38:56,380 +composition G ولا الـ G composition .. الـ F + +933 +01:38:56,380 --> 01:39:04,470 +composition G التعريف بيقول لك كل العناصر X بحيث أن X + +934 +01:39:04,470 --> 01:39:11,790 +موجودة في Domain الـ G and الـ G of X موجودة في Domain + +935 +01:39:11,790 --> 01:39:17,630 +الـ F مش هيك التعريف بدنا نبدأ نطبق التعريف افتحه + +936 +01:39:17,630 --> 01:39:23,570 +كيف بدنا نطبق التعريف الـ X هذه موجودة في Domain + +937 +01:39:23,570 --> 01:39:30,210 +الـ جي وين Domain الـ جي؟ أيّه؟ يبقى من سالب Infinity + +938 +01:39:30,210 --> 01:39:38,180 +لغاية 5 وفي نفس الوقت and الـ G of X هي + +939 +01:39:38,180 --> 01:39:44,440 +اللي عندنا اللي هي الجذر التربيعي لـ 5 ناقص X + +940 +01:39:44,440 --> 01:39:49,380 +موجودة في Domain الـ F Domain الـ F من وين لأ وين من + +941 +01:39:49,380 --> 01:39:57,400 +سالب Infinity إلى Infinity خلصنا هذا التطبيق حرفي + +942 +01:39:57,400 --> 01:40:01,860 +بعد ما خلصنا التطبيق الحرفي بدّه المخ يبدأ يشتغل + +943 +01:40:02,300 --> 01:40:08,840 +بنشوف كيف بده يشتغل هذا يا شباب بنزلها زي ما هيّ X + +944 +01:40:08,840 --> 01:40:12,360 +موجودة من سالب Infinity لغاية أخرى هذا ما فيش مشكلة + +945 +01:40:12,360 --> 01:40:18,500 +المشكلة هو هنا مدام X هنا بدي أطلع X هنا موجودة في + +946 +01:40:18,500 --> 01:40:23,670 +فترة وبعد هيك بجيب التقاطع بين الفترتين بيكون خلصنا، + +947 +01:40:23,670 --> 01:40:29,090 +مظبوط؟ طيب مشان نخلص هذا الجذر فيه قبله إشارة + +948 +01:40:29,090 --> 01:40:35,530 +سالب؟ ما فيش قبله إشارة سالب إذا هذا فيه جزء موجب + +949 +01:40:35,530 --> 01:40:42,030 +و جزء سالب إذا لا يمكن لهذا ياخذ لي أي قيمة قبل الـ + +950 +01:40:42,030 --> 01:40:47,770 +Zero صح ولا لا؟ بس ممكن يكون Zero مظبوط؟ يعني + +951 +01:40:47,770 --> 01:40:55,230 +معنى هذا الكلام and الجذر التربيعي لـ 5 ناقص X + +952 +01:40:55,230 --> 01:41:03,830 +بدّه يكون أكبر من أو يساوي الـ Zero سكت الشعب وسكت + +953 +01:41:03,830 --> 01:41:10,020 +أهل الكهف طيب خليكم معاه مرة ثانية بقول مرة ثانية + +954 +01:41:10,020 --> 01:41:14,380 +صح صح هذه very important بتجيبها لامتحانات كتير صح + +955 +01:41:14,380 --> 01:41:20,460 +صح معايا كويس الحين هذه نزلت كما هي تمام هذه + +956 +01:41:20,460 --> 01:41:25,180 +الـ G of X بدها تكون موجودة في Domain الـ F كتبنا + +957 +01:41:25,180 --> 01:41:31,800 +Domain الـ F هل الجذر مسبوق بإشارة سالب؟ لا يعني + +958 +01:41:31,800 --> 01:41:37,040 +هذا الجذر اللي لا ياخذ إلا قيمًا يبقى من سالب + +959 +01:41:37,040 --> 01:41:41,620 +Infinity لغاية Zero يبعث لك الله صح؟ يعني يبدو + +960 +01:41:41,620 --> 01:41:47,860 +يكون موجود من وين؟ من Zero إلى Infinity يعني هه، + +961 +01:41:47,860 --> 01:41:54,220 +نعملها كخطوط موجود في الفترة من Zero لغاية + +962 +01:41:54,220 --> 01:42:00,450 +Infinity أظن ما فيش مشكلة هنا؟ خلصنا؟ يعني هذا الجذر + +963 +01:42:00,450 --> 01:42:06,610 +فلو كان قبله إشارة سالب بروح بأخذ الفترة من سالب + +964 +01:42:06,610 --> 01:42:10,410 +Infinity إلى وين؟ لغاية Zero و بحثت هذه؟ + +965 +01:42:14,690 --> 01:42:20,690 +بنزلها زي ما هي مش هغير فيها ولا حاجة إن هذا + +966 +01:42:20,690 --> 01:42:26,150 +معناه إن الجذر التربيعي لـ 5 ناقص X أكبر من أو + +967 +01:42:26,150 --> 01:42:31,700 +تساوي الـ Zero مظهر؟ مش عارف معناها؟ طيب هذه بدأ + +968 +01:42:31,700 --> 01:42:39,360 +تنزل كما هي وهي الآن نربع للطرفين بصير عندك 5 + +969 +01:42:39,360 --> 01:42:46,000 +ناقص X greater than or equal to Zero نزل هذه زي ما + +970 +01:42:46,000 --> 01:42:54,800 +هيّ and هات لي X للطرفين بصير مالها 5 أكبر من أو + +971 +01:42:54,800 --> 01:43:00,290 +تساوي الـ X يعني مين؟ نفس الفترة اللي عندنا هذه يعني + +972 +01:4 + +1001 +01:46:17,990 --> 01:46:21,290 +السالب X أقل من أو يساوي + +1002 +01:46:33,500 --> 01:46:39,400 +طيب هادي بالصير تنزل هادي زي ما هي هادي إن اضرب + +1003 +01:46:39,400 --> 01:46:46,410 +كله في شر السلب لأن أنا بدي أكسب الموجب خمسة أكبر + +1004 +01:46:46,410 --> 01:46:55,830 +من X أكبر من سالب عشرين وجفلنا تمام؟ يبقى هذه + +1005 +01:46:55,830 --> 01:47:02,550 +صارت كل العناصر X بحيث أن X موجودة من سالب + +1006 +01:47:02,550 --> 01:47:06,910 +Infinity لغاية خمسة and + +1007 +01:47:09,950 --> 01:47:15,990 +الـ X موجودة طلع هذه بتظبطها أكبر من أو يساوي سالب + +1008 +01:47:15,990 --> 01:47:19,950 +عشرين وأقل من أو يساوي خمسة صغيرة بنكتبها في الأول + +1009 +01:47:19,950 --> 01:47:28,850 +يبقى هذه سالب عشرين وهذه ما لها أقل من أو يساوي X + +1010 +01:47:28,850 --> 01:47:45,470 +وهذه أقل من أو يساوي خمسة جلبت بس الوضع X موجودة + +1011 +01:47:45,470 --> 01:47:54,890 +في الفترة من سالب عشرين لغاية خمسة يبقى أنا عند هذا + +1012 +01:47:54,890 --> 01:48:02,570 +الـ real line هذا من عند الخمسة بدأ ترجع لين؟ لل + +1013 +01:48:02,570 --> 01:48:08,150 +infinity وهذا بيجينا قبلها هنا الـ zero هذا بيقول X + +1014 +01:48:08,150 --> 01:48:13,310 +موجودة من سالب عشرين لغاية خمسة سالب عشرين وين بدأ + +1015 +01:48:13,310 --> 01:48:19,010 +تجينا؟ تجينا هنا سالب عشرين يعني على الفترة اللي + +1016 +01:48:19,010 --> 01:48:26,830 +عندنا هذه فقط لا غير هذه من هنا هك لهنا أين الفترة + +1017 +01:48:26,830 --> 01:48:32,710 +المشتركة بينهم؟ سالب عشرين دغاية خمسة يعني كأن هذه + +1018 +01:48:32,710 --> 01:48:42,150 +X موجودة في سالب Infinity وخمسة تقاطع الفترة سالب + +1019 +01:48:42,150 --> 01:48:50,850 +عشرين وخمسة اللي هو بده يساوي عنه سالب عشرين ولغاية + +1020 +01:48:50,850 --> 01:48:56,530 +خمسة، سالب عشرين لغاية خمسة، خلاص؟ واضح عظم الشغل + +1021 +01:48:56,530 --> 01:49:02,090 +هيك؟ طيب، لسه لا يزال عندنا مثالين فكرتهم في نفس + +1022 +01:49:02,090 --> 01:49:05,810 +الموضوع بس بأفكار مختلفة، هعطيكوا العزف diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RLVHplY4UgE_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RLVHplY4UgE_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..ca2318f36c912bbb26910b9c10130d35e18399fc --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RLVHplY4UgE_postprocess.srt @@ -0,0 +1,4088 @@ +1 +00:00:21,190 --> 00:00:26,950 +بسم الله الرحمن الرحيم المرة الماضية بدأنا بعنوان + +2 +00:00:26,950 --> 00:00:32,630 +اللي هو بعض أنواع الدوال العادية واخدنا أول نوع من + +3 +00:00:32,630 --> 00:00:37,410 +هذه الأنواع وهي ال linear function يعني الدالة + +4 +00:00:37,410 --> 00:00:42,430 +الخطية وشوفنا ان هذا رسمته هو خط مستقيم وشفنا + +5 +00:00:42,430 --> 00:00:47,140 +الخطوط المستقيمةفي حالات المختلفة مثل موازية لمحور + +6 +00:00:47,140 --> 00:00:53,380 +X أو عمودية على محور X أو مائلة على محور X أو + +7 +00:00:53,380 --> 00:00:58,180 +الخطوط المستقيمة تمر بنقطة الأصل أو لا تمر بنقطة + +8 +00:00:58,180 --> 00:01:03,410 +الأصل كل هذه رسمناها واخدنا المعادلات تبعتهابنجي + +9 +00:01:03,410 --> 00:01:07,010 +للنوع الثاني اللي هو the power functions دوال + +10 +00:01:07,010 --> 00:01:13,530 +القوة يعني الدالة المرفوعة لمين لأس معين بنعطيها + +11 +00:01:13,530 --> 00:01:18,790 +التعريف كتالي the function f of x يساوي x to the + +12 +00:01:18,790 --> 00:01:23,750 +power a where ال a is constant حيث ال a مقدار ثابت + +13 +00:01:23,750 --> 00:01:26,670 +is called a power function + +14 +00:01:29,820 --> 00:01:35,920 +الدالة اللي عندنا هذه الاساس متغير والأس ثابت جالي + +15 +00:01:35,920 --> 00:01:41,080 +ال a is constant الآن ال a هذا ما حطيتش قيود عليه + +16 +00:01:41,080 --> 00:01:46,450 +إلا أنه مقدارا ثابتايبقى مدام مقدار ثابت يعني real + +17 +00:01:46,450 --> 00:01:53,770 +number قد يكون صفر قد يكون موجب قد يكون سالب قد + +18 +00:01:53,770 --> 00:01:59,650 +يكون كاسري طبعا لو كان الصفر لأصبح X و Zero بواحدة + +19 +00:01:59,650 --> 00:02:04,750 +له الخط المستقيم الموازي لمحور Xواللي بيبقى بعنه + +20 +00:02:04,750 --> 00:02:08,250 +مسافة مقدرة واحد وهذه رسمناها وهي في ال linear + +21 +00:02:08,250 --> 00:02:12,070 +function يبقى ال a عندي بدنا نستبعد الصفر بدنا + +22 +00:02:12,070 --> 00:02:19,890 +ناخد positive negative بالسالب و هكذا أو كثري و + +23 +00:02:19,890 --> 00:02:23,890 +نشوف الحالات المختلفة مثلا لو بدنا ناخد أمثلة + +24 +00:02:23,890 --> 00:02:29,570 +مختلفة على هذه و بدنا ناخد لو كانت ال a موجةفمثلا + +25 +00:02:29,570 --> 00:02:36,370 +لو جيت أخدت ال F of X تساوي X يبقى ال A عندي هنا + +26 +00:02:36,370 --> 00:02:42,250 +قداش بتكون واحد صحيح طبعا رسمناها قبل هيك وقلنا + +27 +00:02:42,250 --> 00:02:48,910 +هذا محور X هذا محور Y هذا نقطة الأصل اللي هي Zero + +28 +00:02:50,280 --> 00:02:55,600 +هذا الخط الذي يمثل هذه الدالة هو الخط المستقيم + +29 +00:02:55,600 --> 00:03:00,960 +اللى عندنا هذا باللون الأزرق وقولنا هذا معادلة Y + +30 +00:03:00,960 --> 00:03:05,120 +تساوي X الزاوية اللى عندنا هذه جد الزاوية عندنا + +31 +00:03:05,120 --> 00:03:09,980 +هذه وكل واحدة فيهم خمسة واربعين درجة وسميناها في + +32 +00:03:09,980 --> 00:03:13,960 +حالة ال linear functions ال identity function اللى + +33 +00:03:13,960 --> 00:03:19,410 +دالت الواحدةهذا لو كان A تساوي واحد نجي لو كان ال + +34 +00:03:19,410 --> 00:03:26,770 +F of X يساوي مثلا X تربية و بدنا نرسم هذه الدالة + +35 +00:03:26,770 --> 00:03:31,910 +يبقى هذا محور X هذا محور Y هذا نقطة الاصل اللي هي + +36 +00:03:31,910 --> 00:03:36,170 +Zero يبقى هذا ال problem المشهورة اللي بنرفع طول + +37 +00:03:36,170 --> 00:03:41,050 +دراستنا في المرحلة الثانوية يبقى القطة المكافئة + +38 +00:03:41,050 --> 00:03:45,730 +اللي على الشكل اللي عندنا هذايبقى هذا Y تساوي X + +39 +00:03:45,730 --> 00:03:51,190 +تربيع والـA عندي تساوي كم؟ تساوي اتنين طيب لو جينا + +40 +00:03:51,190 --> 00:03:57,190 +قولنا ال F of X بدها تساوي X تكييم يبقى الـA عندي + +41 +00:03:57,190 --> 00:04:02,990 +هنا كم؟ تلاتة برضه الرسم هذه رسمناها كثيرا في + +42 +00:04:02,990 --> 00:04:09,810 +المرحلة الثانوية وكان رسمتها على الشكل التالي نذكر + +43 +00:04:09,810 --> 00:04:17,380 +بها تذكير ليس الايبقى هذا رسمة المنحنى اللى عندنا + +44 +00:04:17,380 --> 00:04:24,580 +هذا ال Y تساوي X تكعيبهذه نقطة الأصل اللي هي Zero + +45 +00:04:24,580 --> 00:04:30,120 +والـ A عندي تساوي تلتة طب لو كانت الـ A تساوي + +46 +00:04:30,120 --> 00:04:36,320 +أربعة يبقى بصير عند ال F of X يساوي X أُص أربعة + +47 +00:04:36,320 --> 00:04:42,120 +يبقى الـ A تساوي أربعة لو حبينا نرسم الرسم هذه + +48 +00:04:42,120 --> 00:04:48,820 +يبقى هي المحاور هذا محور X هذا محور Y هذه نقطة + +49 +00:04:48,820 --> 00:04:56,340 +الأصل اللي هي Zeroرسمتها تشبه X تربيها لكن مع بعض + +50 +00:04:56,340 --> 00:05:03,520 +الفوارق البسيطة كالتالي يبقى هاي رسمتها بتجيني هيك + +51 +00:05:06,950 --> 00:05:11,150 +بتجي بالشكل اللي عندنا هنا يبقى هذا رسمة Y F of X + +52 +00:05:11,150 --> 00:05:17,870 +يسوى X أس 4 او Y تسوى X أس 4 بنجي لو كانت F of X + +53 +00:05:17,870 --> 00:05:25,470 +يسوى X أس 5 يبقى ال A تسوى 5يبقى رسمتها تشبه + +54 +00:05:25,470 --> 00:05:32,030 +لفوفكس يساوي X تكيب مع الفارق يبقى هي المحاور هذا + +55 +00:05:32,030 --> 00:05:39,950 +محور X هذا محور Y هذا نقطة الأصل اللي هي Zero يبقى + +56 +00:05:39,950 --> 00:05:44,290 +المنحنة بيجينا بالشكل اللي عندنا هذا هيك يبقى هذا + +57 +00:05:44,290 --> 00:05:47,090 +بيجينا هيك + +58 +00:05:53,820 --> 00:05:59,740 +لا مش نفسها، هذه يا دوب تقاطع تقاطع هذه كأنها + +59 +00:05:59,740 --> 00:06:05,160 +تمسمح و ركز ولا تشبيه يعني، يعني بتفتح شوية عند ال + +60 +00:06:05,160 --> 00:06:10,000 +zero، بتلاقيها أفتح شويةطيب هذا لو كانت الأسس + +61 +00:06:10,000 --> 00:06:16,820 +موجبة طب لو كانت الأسس سالبة زي ايش مثلا زي f of x + +62 +00:06:16,820 --> 00:06:22,640 +يسوى x السالب واحد يعني قداش واحد ع الاكس يبقى ال + +63 +00:06:22,640 --> 00:06:27,680 +a تسوى قداش سالب واحد لو روحنا رسمنا الرسمة هذه + +64 +00:06:27,680 --> 00:06:33,520 +فبجي بقول هذا محور x هذا محور y هذا نقطة الأصل + +65 +00:06:33,520 --> 00:06:35,100 +اللي هي zero + +66 +00:06:41,950 --> 00:06:46,990 +الدالة المعرفة على طول القط يبقى على يمين الـ zero + +67 +00:06:46,990 --> 00:06:51,830 +بتاخد قيم موجبة على طول الشكل اللي عندنا هذا هيك + +68 +00:06:51,830 --> 00:06:57,250 +وعلى شمال الـ zero بتاخدش قيم سالبة بالشكل اللي + +69 +00:06:57,250 --> 00:07:03,910 +عندنا هذا هيكيبقى هذه اللي هي ده ال F of X يسوى + +70 +00:07:03,910 --> 00:07:10,450 +واحد على X وال X الأس تبعها بده يسوى سالب واحد لو + +71 +00:07:10,450 --> 00:07:16,270 +جينا الأس يسوى سالب اتنين يبقى ال F of X يسوى X + +72 +00:07:16,270 --> 00:07:23,350 +أسالي باتنين يعني واحد على X تربيع يبقى هذا محور X + +73 +00:07:23,350 --> 00:07:30,540 +هذا محور Y هذه نقطة الأصل اللي هي Zeroهل يمكن لهذه + +74 +00:07:30,540 --> 00:07:36,320 +الدالة أن تأخذ القيمة صفر يبعد على اتنين؟ هل يمكن + +75 +00:07:36,320 --> 00:07:42,050 +أن تأخذ قيمة سالبة؟يبقى على الشجتين القيام موجبة + +76 +00:07:42,050 --> 00:07:45,690 +سواء كان على يمين ال zero ولا على شمالي ال zero + +77 +00:07:45,690 --> 00:07:51,290 +القيام موجبة يبقى المنحنى بيجيلك كده او من هنا + +78 +00:07:51,290 --> 00:07:56,770 +بيجي جوس بالشكل التاني هذا ال data is undefined + +79 +00:07:56,770 --> 00:08:01,150 +عند ال zero لاحظ بالنسبة لل data الأولى ال domain + +80 +00:08:01,150 --> 00:08:07,030 +يسوى ال rain يسوى كل ال real line معاها دهزيرو هنا + +81 +00:08:07,030 --> 00:08:14,850 +ال domain كل ال real line ما عدا زيرو ال range من + +82 +00:08:14,850 --> 00:08:20,310 +zero ل infinity as an open interval تمام طيب هذا + +83 +00:08:20,310 --> 00:08:25,730 +رسمتنا لو كانت الأسس سالبة طب لو كانت الأسس كثور + +84 +00:08:25,730 --> 00:08:32,170 +فالرسم على الشكل التاليأفترض أن f of x يساوي جذر + +85 +00:08:32,170 --> 00:08:37,970 +ال X يعني X أس قداش أس نص لو حبينا نرسم الرسم اللي + +86 +00:08:37,970 --> 00:08:42,570 +عندنا هذه يبقى بصير على الشكل التالي هذا محور X + +87 +00:08:42,570 --> 00:08:50,310 +هذا محور Y هذه نقطة الأصل اللي هي Zero يبقى مجوس + +88 +00:08:50,310 --> 00:08:56,890 +بالشكل اللي عندنا هذا هيكيبقى هذا رسمة الدالة Y + +89 +00:08:56,890 --> 00:09:03,330 +تساوي جذر ال X ال domain يساوي ال range يساوي + +90 +00:09:03,330 --> 00:09:08,110 +الفترة من عند ال zero لغاية infinity طبعا مغلقة من + +91 +00:09:08,110 --> 00:09:16,790 +عند ال zeroلو جينا لل Y تساوي X أس طلت يعني الجذر + +92 +00:09:16,790 --> 00:09:22,810 +التالت ل X وحبنا نرسم الرسم هذه فبجي بقول هذا محور + +93 +00:09:22,810 --> 00:09:30,110 +X هذا محور Y هذه النقطة الأصل اللي هي Zero بدنا + +94 +00:09:30,110 --> 00:09:34,990 +هذا الجذر يبقى الجذر هيجيك بالشكل التالت لأن منحنى + +95 +00:09:34,990 --> 00:09:38,410 +هيجيك هيك ويجي من ناحية تانية هيك + +96 +00:09:42,100 --> 00:09:50,540 +يبقى هذا Y يساوي الجذر التالت ل X أو X أُس طول بعد + +97 +00:09:50,540 --> 00:09:59,540 +هيك بدنا نيجي للرسمة Y تساوي Y تساوي X أُس طول تين + +98 +00:09:59,540 --> 00:10:08,670 +مثلا يعني مين؟ يعني الجذر التالت لل X تربيةطبعا + +99 +00:10:08,670 --> 00:10:14,590 +هذه الرسمة دائما و أبدا معرفة لل X الموجبة + +100 +00:10:14,590 --> 00:10:20,930 +والسالبة والصفر يعني ال domain كله ال real line + +101 +00:10:20,930 --> 00:10:25,890 +لكن ال range بياخد قيمة سالبة طب بياخد القيمة + +102 +00:10:25,890 --> 00:10:32,750 +الصفر بياخد صفر لو روحت رسمتها هتاخد الشكل التالي + +103 +00:10:32,750 --> 00:10:39,720 +هذا محور X هذا محور Yهذا نقطة الأصل اللي هي Zero + +104 +00:10:39,720 --> 00:10:45,460 +يبقى حيجيك جزء من المنحنة بالشكل هذا والجزء التاني + +105 +00:10:45,460 --> 00:10:51,700 +بالشكل هذا يبقى هذه اللي هي X أس تلتين أو الجذر + +106 +00:10:51,700 --> 00:10:58,940 +التالت ل X تربية بقيت أن أخر رسمة وهي Y تساوي بدل + +107 +00:10:58,940 --> 00:11:05,720 +X أس تلتين X أس تلتة على اتنينيعني مين؟ يعني الجذر + +108 +00:11:05,720 --> 00:11:11,680 +التربيهي لمن؟ لل X تكيب، لو روحنا رسمنا المنحنة + +109 +00:11:11,680 --> 00:11:18,280 +يبقى هذا محور X، هذا محور Y، هذه نقطة الأصل اللي + +110 +00:11:18,280 --> 00:11:25,260 +هي Zeroطبعا لا يمكن يكون الجدر معرف لقيمة سالب إذا + +111 +00:11:25,260 --> 00:11:29,080 +ال domain هيكون من where ل where من zero ل + +112 +00:11:29,080 --> 00:11:34,020 +infinity و ال range كذلك من zero ل infinity يبقى + +113 +00:11:34,020 --> 00:11:39,400 +المنحنة هيطلع عندك بمين؟ بالشكل اللي عندك هنا يبقى + +114 +00:11:39,400 --> 00:11:43,880 +هذا اللي هو x أس 3 على 2 ال domain يساوي ال range + +115 +00:11:49,790 --> 00:11:55,870 +يبقى الرسومات هذه هي الرسومات الأساسية التي ستتكرر + +116 +00:11:55,870 --> 00:12:01,690 +معاك كثيرا جدا خلال دراستنا هذا في Calculus A يبقى + +117 +00:12:01,690 --> 00:12:06,730 +مطلوب منك أن تكون ملمن بهذه الرسومات + +118 +00:12:10,620 --> 00:12:15,720 +طيب ننتقل الآن إلى النوع الثاني من أنواع الدوالة + +119 +00:12:15,720 --> 00:12:21,920 +يبقى انتهينا من ال linear functions و من ال power + +120 +00:12:21,920 --> 00:12:30,400 +functions بدنا نروح للنوع الثالث من هذه الدوالة + +121 +00:12:30,400 --> 00:12:36,400 +يبقى النوع التالت اللي هو عبارة عن كثيرات الحدود + +122 +00:12:36,400 --> 00:12:37,800 +اللي هي ال polynomial + +123 +00:12:40,400 --> 00:12:46,260 +يبقى النوع التالت polynomials + +124 +00:12:46,260 --> 00:12:54,620 +اللي هو كثيرات الحدود نعطيها تعريف definition a + +125 +00:12:54,620 --> 00:13:05,480 +polynomial كثيرة الحدود is a function يبقى هي + +126 +00:13:05,480 --> 00:13:15,910 +عبارة عن ال in the formفي الشكل التالي ال P of X + +127 +00:13:15,910 --> 00:13:18,250 +يساوي AN + +128 +00:13:36,450 --> 00:13:41,290 +لحظة الأس يتدرج من أعلى إلى أسفل + +129 +00:13:44,390 --> 00:13:51,690 +في عندنا ال N هذا اللي بتبدأ يبقى هذا عدد صحيح غير + +130 +00:13:51,690 --> 00:13:57,690 +سالب يعني ممكن يكون موجب و ممكن يكون صفر يبقى لا + +131 +00:13:57,690 --> 00:14:02,130 +يمكن أن يكون سالب ال A N و ال A N minus one و ال A + +132 +00:14:02,130 --> 00:14:06,530 +two و ال A one و ال A node كل الإيهات هدول ثوابت a + +133 +00:14:06,530 --> 00:14:10,750 +reconnaissance او a real number نكتب لك هذا الكلام + +134 +00:14:12,740 --> 00:14:25,560 +حيث ال N is a non negative + +135 +00:14:25,560 --> 00:14:29,760 +integer عدد + +136 +00:14:29,760 --> 00:14:32,120 +صحيح غير سالب + +137 +00:14:38,340 --> 00:14:46,560 +نمبرز والأرقام اللي هو a n و a n minus ال one ونظل + +138 +00:14:46,560 --> 00:14:54,340 +ماشيين لغاية ما نوصل لل a two a one a naught هدول + +139 +00:14:54,340 --> 00:15:02,860 +كلهم are real are real numbers + +140 +00:15:05,780 --> 00:15:14,120 +أعداد حقيقية بنسميها called the coefficients + +141 +00:15:14,120 --> 00:15:21,300 +المعاملات + +142 +00:15:21,300 --> 00:15:30,220 +of the polynomial معاملات + +143 +00:15:30,220 --> 00:15:33,900 +كثيرة الحدود and + +144 +00:15:37,730 --> 00:15:49,330 +الـ N is called the degree of + +145 +00:15:49,330 --> 00:15:52,850 +the polynomial + +146 +00:16:25,360 --> 00:16:30,900 +يبقى مرة تانيةأو النوع الثالث من الدوال اللي هو من + +147 +00:16:30,900 --> 00:16:35,900 +كثيرات الحدود لما أقول كثيرات الحدود يعني عندي + +148 +00:16:35,900 --> 00:16:40,580 +مجموعة من الحدود وجمعناهم جمع طب الحدود هدول في + +149 +00:16:40,580 --> 00:16:45,120 +عليهم قيود أه في عليهم قيود تعالى نشوف الكثيرة + +150 +00:16:45,120 --> 00:16:49,760 +الحدود هي عبارة عن دلة في الشكل التالي بديها الرمز + +151 +00:16:49,760 --> 00:16:54,980 +اللي هو P of X الحرف الأول من كلمة polynomial وهو + +152 +00:16:54,980 --> 00:16:59,670 +function فقولنا P of Xهي constant في ال X to the + +153 +00:16:59,670 --> 00:17:03,430 +power N constant تاني في X to the power N minus + +154 +00:17:03,430 --> 00:17:07,410 +one constant تالت في X to the power N minus two و + +155 +00:17:07,410 --> 00:17:12,150 +هكذا الأسبيب ينزل N الناقص واحد الناقص اتنين + +156 +00:17:12,150 --> 00:17:16,910 +الناقص ثلاثة and so on لغاية ما نصل إلى A2 X تربية + +157 +00:17:16,910 --> 00:17:25,690 +A1 X زائد ال A9الرقم N قد يكون صفرا و قد يكون عددا + +158 +00:17:25,690 --> 00:17:32,150 +موجبا لا يمكن أن يكون كاسري ولا يمكن أن يكون سالبي + +159 +00:17:32,150 --> 00:17:37,090 +و لما قلت N is a non negative integer يبقى عدد + +160 +00:17:37,090 --> 00:17:42,770 +صحيح و العدد صحيح غير سالب إذا لم يبقى إلا zero أو + +161 +00:17:42,770 --> 00:17:48,320 +عدد صحيح موجبهذه النقطة الأولى الآن الأرقام اللي + +162 +00:17:48,320 --> 00:17:53,400 +عندنا ال a هات هذول a0 و a1 و a2 و a3 و a4 و aN + +163 +00:17:53,400 --> 00:17:58,200 +minus 1 و aN هذول ثوابت بسميهم معاملات ال + +164 +00:17:58,200 --> 00:18:02,800 +polynomial يبقى هذول بسميهم the coefficients + +165 +00:18:02,800 --> 00:18:09,240 +المعاملات لكثيرات الحدود طيب ان اللي هو أعلى قوة + +166 +00:18:09,240 --> 00:18:14,520 +موجودة عندنا هنا بسميها برجة ال polynomialيبقى + +167 +00:18:14,520 --> 00:18:20,240 +كثيرة الحدود هذه من الدرجة النونية يعني من الدرجة + +168 +00:18:20,240 --> 00:18:28,500 +الرقم N نعطي شغلة توضيحية على ذلك مثلا for example + +169 +00:18:28,500 --> 00:18:32,500 +كمثال على ذلك + +170 +00:18:36,520 --> 00:18:42,580 +فمثال على ذلك الان لو جيت قلت اتنين اكس اص اربعة + +171 +00:18:42,580 --> 00:18:51,560 +زائد تلاتة اكس ترابيع زائد عشرة اكس ناقص واحد + +172 +00:18:53,020 --> 00:18:57,660 +ملاحظين ان الأساس بتنزل اربعة اتنين يعني التلاتة + +173 +00:18:57,660 --> 00:19:03,180 +ماله مفقود مش موجود شو اللي ضيعوا المعامل تبعه + +174 +00:19:03,180 --> 00:19:08,980 +المعامل تبعه عبارة عن ايه؟ Zero هلجل ممنوعالمعامل + +175 +00:19:08,980 --> 00:19:12,920 +يكون Zero وما جليش، إذا ممكن للمعامل أن يكون صفر + +176 +00:19:12,920 --> 00:19:18,500 +وبالتالي يفقد term او اتنين او تلاتة او عشرة من ال + +177 +00:19:18,500 --> 00:19:23,600 +polynomial ماعناه مشكلة المهم أعلى أس موجود، يبقى + +178 +00:19:23,600 --> 00:19:30,360 +هذه polynomial من الدرجة الرابعةاللي هو أعلى أس أو + +179 +00:19:30,360 --> 00:19:38,220 +أعلى قوة موجودة عند الأمين للعدد X يبقى هذه as a + +180 +00:19:38,220 --> 00:19:42,940 +polynomial of + +181 +00:19:42,940 --> 00:19:46,280 +degree + +182 +00:19:46,280 --> 00:19:49,220 +4 + +183 +00:19:52,490 --> 00:19:56,050 +طيب خلّيني أسأل السؤال التالي أول دل الخطية اللي + +184 +00:19:56,050 --> 00:20:01,410 +أخدناها المرة الماضية دل الخطية دل الخطية بلونوميا + +185 +00:20:01,410 --> 00:20:06,810 +ولا لا؟ ومن أي درجة؟ من ال first degree من الدرجة + +186 +00:20:06,810 --> 00:20:11,610 +الأولى يبقى any linear function is a polynomial of + +187 +00:20:11,610 --> 00:20:16,410 +the first degree طيب لو قلت لك F of X سوى constant + +188 +00:20:18,830 --> 00:20:23,950 +بولنوميل من الدرجة الصفرية يعني X to the power + +189 +00:20:23,950 --> 00:20:27,670 +zero يعني ممكن يكون عندي بولنوميل من الدرجة + +190 +00:20:27,670 --> 00:20:31,070 +الصفرية بولنوميل من الدرجة الأولى بولنوميل من + +191 +00:20:31,070 --> 00:20:40,190 +الدرجة الثانية و هكذا يبقى هنا and ال P of X يساوي + +192 +00:20:40,190 --> 00:20:46,070 +تلاتة مثلا is a polynomial + +193 +00:20:48,550 --> 00:20:58,670 +of degree أو of zero degree يبقى + +194 +00:20:58,670 --> 00:21:01,610 +من الدرجة الصفرية وهكذا + +195 +00:21:04,460 --> 00:21:09,060 +بننتقل الان الى النوع الرابع من هذه ال functions + +196 +00:21:09,060 --> 00:21:15,040 +وهي ال rational functions الدوال النسبية الدوال + +197 +00:21:15,040 --> 00:21:21,070 +النسبية هي دلاخر قسم فسط و مقامبس كل دا اللي في + +198 +00:21:21,070 --> 00:21:26,330 +البصد ونظرتها في المقام التنتين are polynomials مش + +199 +00:21:26,330 --> 00:21:30,130 +أي دوال يبقى بالدالي للنقطة الرابعة اللي هي + +200 +00:21:30,130 --> 00:21:37,610 +rational functions الرابعة صحيح اللي هي rational + +201 +00:21:39,360 --> 00:21:44,820 +الدوال النسبية او بعض التراجم العربية بتقول الدوال + +202 +00:21:44,820 --> 00:21:48,720 +الجذرية الدوال الجذرية و لا الدوال النسبية بهمن + +203 +00:21:48,720 --> 00:21:55,500 +المعنى الرياضي فباجي بقوله the rational function + +204 +00:21:55,500 --> 00:21:58,580 +is + +205 +00:21:58,580 --> 00:22:10,710 +an expression هي صيغة in the formفي الشكل التالي + +206 +00:22:10,710 --> 00:22:20,930 +ال F of X بده يساوي P of X مقسومة على ال Q of X + +207 +00:22:20,930 --> 00:22:33,610 +where حيث ال P of X and ال Q of X are polynomials + +208 +00:22:41,130 --> 00:22:51,310 +Polynomials P of + +209 +00:22:51,310 --> 00:22:57,410 +X على Q of X يعني ال domain تبع ال polynomial + +210 +00:23:00,980 --> 00:23:05,080 +هو كل ال real number ما يعدى الأرقام اللى بتخلى + +211 +00:23:05,080 --> 00:23:11,440 +المقام بأصفار يبقى the set of all element x such + +212 +00:23:11,440 --> 00:23:22,600 +that q of x does not equal to zero for example لو + +213 +00:23:22,600 --> 00:23:23,460 +بدي domain + +214 +00:23:27,660 --> 00:23:37,060 +مثلا X أُص أربع ثلاثة X تكييب زائد X ناقص ستاشر + +215 +00:23:37,060 --> 00:23:47,320 +كله مقسوما على X في X زائد ثلاثة مش بنفع هذه + +216 +00:23:47,320 --> 00:23:51,500 +polynomial ولا لا؟ X ترمية زائد ثلاثة X يبقى + +217 +00:23:51,500 --> 00:23:58,780 +polynomial يبقى ال domain الهدىاللي هو كل ال real + +218 +00:23:58,780 --> 00:24:03,820 +number بده يشيل منها الأرقام اللي بتخلي المقام + +219 +00:24:03,820 --> 00:24:11,230 +يساوي zero وهي ناقص تلاتة وزيريعني كأنه من سالب + +220 +00:24:11,230 --> 00:24:15,930 +Infinity لغاية سالب تلاتة اتحاد سالب تلاتة و Zero + +221 +00:24:15,930 --> 00:24:21,670 +اتحاد Zero و Infinity كلها فترات مفتوحة يبقى هذا + +222 +00:24:21,670 --> 00:24:26,510 +ال domain يعني ممكن أصيغها بصياغة أخرى و أقول من + +223 +00:24:26,510 --> 00:24:32,270 +سالب Infinity لسالب تلاتة اتحاد سالب تلاتة و Zero + +224 +00:24:32,270 --> 00:24:39,390 +اتحاد Zero و Infinity بالشكل اللي قدامنا هذاطيب + +225 +00:24:39,390 --> 00:24:45,330 +ننتقل الأن إلى الدالة الخامسة وهي ال algebraic + +226 +00:24:45,330 --> 00:24:56,410 +function ال algebraic functions الدوال الجابرية it + +227 +00:24:56,410 --> 00:25:02,190 +is a function يبقى الدالة الجابرية it is a + +228 +00:25:02,190 --> 00:25:12,830 +function هي عبارة عن دالة thatcan be constructed + +229 +00:25:12,830 --> 00:25:22,190 +يمكن أن تنشأ أو يمكن أن تتكون using باستخدام + +230 +00:25:22,190 --> 00:25:24,510 +algebraic operations + +231 +00:25:33,780 --> 00:25:43,220 +ايش العمليات الجابرية زي addition subtraction + +232 +00:25:43,220 --> 00:25:48,760 +عملية + +233 +00:25:48,760 --> 00:25:59,300 +الطرح multiplication عملية الدرب multiplication + +234 +00:25:59,300 --> 00:26:01,200 +division + +235 +00:26:02,640 --> 00:26:11,020 +عملية القسمة taking roots + +236 +00:26:11,020 --> 00:26:16,300 +عملية + +237 +00:26:16,300 --> 00:26:26,720 +أخذ الجذور for example the + +238 +00:26:26,720 --> 00:26:33,930 +functions مثلايعني بينجل الدوال الجابرية ما هي + +239 +00:26:33,930 --> 00:26:39,330 +الدوال الجابرية بيقول الدوال الجابرية هي الدوال + +240 +00:26:39,330 --> 00:26:45,130 +التي يمكن أن تنشأ أو تتكون can be constructed + +241 +00:26:45,130 --> 00:26:50,750 +using algebraic operations يعني تنشأ نتيجة + +242 +00:26:50,750 --> 00:26:54,750 +للعمليات الجابرية العمليات الجابرية هي الجمع + +243 +00:26:54,750 --> 00:27:01,570 +والطرح والضربوالقسمة و كذلك اخذ الجذور و نحو ذلك + +244 +00:27:01,570 --> 00:27:05,590 +يبقى كل هذه المقول عليها عمليات رياضية او عمليات + +245 +00:27:05,590 --> 00:27:12,570 +جبرية زي ايش مثلا يبقى هنا ال function f of x بدها + +246 +00:27:12,570 --> 00:27:18,970 +تساوي مثلا الجدر التربيعي ل x تربية زائد 5 كم + +247 +00:27:18,970 --> 00:27:27,140 +عملية جبرية عملنا هناتلت عمليات، ضربنا ال X في + +248 +00:27:27,140 --> 00:27:32,300 +نفسها ل product أو ال multiple كده و صارت X تربية، + +249 +00:27:32,300 --> 00:27:36,940 +عضفنا إلها خمسة، يبقى عملية الجامعة عيتين تان، + +250 +00:27:36,940 --> 00:27:42,020 +التالت أخدنا الجذر، يبقى تلت عمليات في نفس الوقت، + +251 +00:27:42,020 --> 00:27:50,160 +مثلالو جينا قولنا الـ G of X يساوي X زائد تلاتة في + +252 +00:27:50,160 --> 00:27:59,520 +الجذر التالت مثلاً للـ X ناقص واحد وزائد X على X + +253 +00:27:59,520 --> 00:28:07,060 +تربية زائد خمسة وعشرين كل العمليات الجبرية موجودة + +254 +00:28:07,060 --> 00:28:10,380 +الحمد لله كل ذكرضها موجودة في السؤال يمكن هذه كمان + +255 +00:28:10,380 --> 00:28:11,280 +algebraic + +256 +00:28:15,880 --> 00:28:20,020 +هل الـ rational function اللي فوق ال algebraic + +257 +00:28:20,020 --> 00:28:25,160 +function؟ ال algebraic لإنه جامع وبعدها قسمة، + +258 +00:28:25,160 --> 00:28:32,940 +مظبوط؟ يبقى and ال rational functions + +259 +00:28:32,940 --> 00:28:36,440 +are algebraic function + +260 +00:28:42,040 --> 00:28:51,000 +يبقى هذه كذلك اللي هو دوال جابرية مالها؟ + +261 +00:28:51,000 --> 00:28:54,160 +متأكد؟ + +262 +00:28:54,160 --> 00:28:59,100 +طب وانا زيك هاي، + +263 +00:28:59,100 --> 00:29:05,520 +بدي أقول عبارة هيك وشوفوليها صحيحة ولا لأ Any + +264 +00:29:05,520 --> 00:29:12,470 +algebraic function is a rational function خطأطب + +265 +00:29:12,470 --> 00:29:16,510 +نشوف العكس، any rational function is an algebraic + +266 +00:29:16,510 --> 00:29:24,410 +function صح؟ any real أو any linear function is an + +267 +00:29:24,410 --> 00:29:31,200 +algebraic functionأي دالة تربيعية هي الـ algebraic + +268 +00:29:31,200 --> 00:29:35,300 +function يعني ايه فوكس يساوي X تربيع؟ عملية ضرب + +269 +00:29:35,300 --> 00:29:41,460 +طيب بدأ أسأل السؤال التالي وشوفولي كلامي صح ولا لأ + +270 +00:29:41,460 --> 00:29:45,660 +any polynomial is a rational function + +271 +00:29:47,940 --> 00:29:54,760 +أي كثيرة حدود is a rational function. لأ، مدام هي + +272 +00:29:54,760 --> 00:29:59,220 +كانت في قضية خلافية بين الفقهاء، بدنا جواب محدد + +273 +00:29:59,220 --> 00:30:01,480 +ونناقش ليش، أيوة يا أخي العرب. + +274 +00:30:05,170 --> 00:30:10,270 +مية المية كلامه صحيح انا اي polynomial عبارة عن + +275 +00:30:10,270 --> 00:30:14,710 +مين؟ عبارة عن نفسي ال polynomial مجسومة على واحد، + +276 +00:30:14,710 --> 00:30:18,810 +الواحد هو polynomial من الدرجة الصفرية وان اشترط + +277 +00:30:18,810 --> 00:30:21,510 +في ال rational function تبقى polynomial في الوسط و + +278 +00:30:21,510 --> 00:30:25,550 +polynomial في المقامإذا كلامه صح حط على واحد مظبوط + +279 +00:30:25,550 --> 00:30:29,810 +مية لمية يبقى any polynomial is a rational + +280 +00:30:29,810 --> 00:30:34,430 +function وبالتالي any polynomial is an algebraic + +281 +00:30:34,430 --> 00:30:38,580 +functionمصبوط ولا لا؟ انها rational function وانا + +282 +00:30:38,580 --> 00:30:41,880 +بقول any rational function is an algebraic + +283 +00:30:41,880 --> 00:30:45,000 +function and so on وها كده دي الواقع الكلمة + +284 +00:30:45,000 --> 00:30:50,240 +بيقولولك ممكن نجيبه صح او خطأ او خيارات متعددة + +285 +00:30:50,240 --> 00:30:55,080 +وتختار الإجابة الصحيحة او الإجابة الخاطئة ممكن + +286 +00:30:55,080 --> 00:30:59,290 +اعطيك تلت إجابات صحيحةووحدة خاطئة ويقولك طلع + +287 +00:30:59,290 --> 00:31:03,210 +للإجابة الخاطئة وليس الإجابة الصحيحة والعكس ممكن + +288 +00:31:03,210 --> 00:31:06,310 +يكون مثلة إجابة خاطئة وواحدة صحيحة وطلع للإجابة + +289 +00:31:06,310 --> 00:31:10,070 +الصحيحة يعني السؤال ممكن يأتي هكذا أو هكذا أو حط + +290 +00:31:10,070 --> 00:31:14,250 +صح أو خطأ على العبارات الرياضية التالية ده ماكنتش + +291 +00:31:14,250 --> 00:31:16,790 +فاهم الكلام اللي قدامي على اللوحة معناته مش هتعرف + +292 +00:31:16,790 --> 00:31:22,810 +تشتغل يبقى هداني بفتح ذهنك بأسئلة مختلفة من خلال + +293 +00:31:22,810 --> 00:31:25,770 +التعريف اللي مكتوب عندي على اللوحة ماجبتش زيدة ولا + +294 +00:31:25,770 --> 00:31:29,170 +كلمة جبتش زيدةكله من خلال التعريف اللي موجود بس + +295 +00:31:29,170 --> 00:31:34,710 +بربطها مع بعضها بمين بالمسائل اللي انت ارتسمها طيب + +296 +00:31:34,710 --> 00:31:41,670 +نيجي للدالة سادسة والاخيرة يبقى الدالة رقم ستة لل + +297 +00:31:41,670 --> 00:31:45,210 +Transcendental function يبقى + +298 +00:31:57,350 --> 00:32:04,890 +transcendental functions الدوال السامية it is the + +299 +00:32:04,890 --> 00:32:14,170 +functions السامية it is the functions هي الدوال + +300 +00:32:14,170 --> 00:32:22,090 +that are not algebraic + +301 +00:32:27,180 --> 00:32:30,940 +Trigonometric functions هي الدوال اللي ماهياش دوال + +302 +00:32:30,940 --> 00:32:39,260 +جابريا as زي ايش؟ نمرة واحد Trigonometric + +303 +00:32:39,260 --> 00:32:44,820 +functions Trigonometric + +304 +00:32:44,820 --> 00:32:52,020 +functions نمرة اتنين ال exponential + +305 +00:32:59,130 --> 00:33:08,550 +f of x يساوي a to the power x و ال a greater than + +306 +00:33:08,550 --> 00:33:17,630 +zero and a does not equal to one نمرة تلاتة ال + +307 +00:33:17,630 --> 00:33:18,950 +logarithmic + +308 +00:33:23,400 --> 00:33:32,960 +الدوال اللغاريتمية زي ايش؟ زي ال F of X يساوي + +309 +00:33:32,960 --> 00:33:43,740 +لغاريتم X للأساس A وال A greater than zero and A + +310 +00:33:43,740 --> 00:33:46,400 +does not equal to one + +311 +00:34:02,400 --> 00:34:03,020 +حسنا؟ + +312 +00:34:18,780 --> 00:34:24,020 +طبعا هنرسم كل دوالة من الدوال السامية اللي عنده، + +313 +00:34:24,020 --> 00:34:30,500 +طبعا في غيرهم كمان، هشرلها بعد قليل ونرسم هذه + +314 +00:34:30,500 --> 00:34:38,160 +الدوالة لل Transcendental function الدوال السامية + +315 +00:34:46,460 --> 00:34:52,180 +يبقى الدوال السامية عدة أنواع من هذه الأنواع نمرة + +316 +00:34:52,180 --> 00:34:56,940 +واحد هي ما تكونش دوال جبرية من هذه الأنواع اللي هي + +317 +00:34:56,940 --> 00:35:02,180 +الـ trigonometric functions يعني الدوال المثلثية + +318 +00:35:02,180 --> 00:35:06,980 +الدوال المثلثية كام واحدة؟ ستة الجيب، جيب تمام، + +319 +00:35:06,980 --> 00:35:12,720 +غلط تمام، قاطع قاطع تمام الزاوية وهي الجيب اللي هي + +320 +00:35:12,720 --> 00:35:24,540 +صين ال Xجب التمام cosine ال X، الظل هي tan ال X، + +321 +00:35:24,540 --> 00:35:33,180 +ظل التمام كتان ال X، قاطع الزاوية يبقى سك ال X، + +322 +00:35:33,180 --> 00:35:40,600 +قاطع تمام الزاوية كsecant ال X، يبقى هذه الدولة + +323 +00:35:40,600 --> 00:35:46,700 +المثلثية الستة مرة تانيةSin X يعني جيب الزاوية X + +324 +00:35:46,700 --> 00:35:55,580 +Cos X يبقى جيب تمامي الزاوية X Tan X يبقى ضل X ضا + +325 +00:35:55,580 --> 00:36:04,940 +X كتان X ضل تمامي الزاوية X سك X قا X قاطعي + +326 +00:36:04,940 --> 00:36:11,830 +الزاوية Consequent X قاطع تمامي الزاوية Xيبقى هذه + +327 +00:36:11,830 --> 00:36:17,910 +النسب المثلثية الستة ان شاء الله الست هذول هنرسمهم + +328 +00:36:17,910 --> 00:36:23,070 +وناخد ال domain و ال range و المتطابقات المثلثية + +329 +00:36:23,070 --> 00:36:26,560 +المتعلقة بهمبس مش في ال section الجاي هذا ال + +330 +00:36:26,560 --> 00:36:31,000 +section اللي بعده section واحد تلاتة منفرد كله + +331 +00:36:31,000 --> 00:36:34,340 +للدوالي المثلثي او مين ايه في نومين او الدومين + +332 +00:36:34,340 --> 00:36:37,520 +مقدش ال period لكل واحدة فيهم كل هذا الموضوع + +333 +00:36:37,520 --> 00:36:44,260 +section واحد تلاتة ورسوماتهم كمان تمام؟ يبقى هذه + +334 +00:36:44,260 --> 00:36:47,460 +اللي لما إليها عودة ان شاء الله في section واحد + +335 +00:36:47,460 --> 00:36:51,460 +تلاتة طيب نجي للدالة الثانية ال exponential + +336 +00:36:51,460 --> 00:36:57,650 +functionطبعا في فرق ما بين ال power function و بين + +337 +00:36:57,650 --> 00:37:01,770 +ال exponential function ال power function الأساس + +338 +00:37:01,770 --> 00:37:06,910 +متغير و الأوس ثابت لكن ال exponential function + +339 +00:37:06,910 --> 00:37:14,300 +الأساس ثابت و الأوس متغير يعنيمقدار ثابت هناك ال + +340 +00:37:14,300 --> 00:37:19,160 +power function قبل قليل كانت x أس a هنا جلبنا + +341 +00:37:19,160 --> 00:37:23,860 +خلّينا الأساس أس والأس ماله أساسه سمناها ال + +342 +00:37:23,860 --> 00:37:30,730 +exponential functions الدوال الأسيةF of X يساوي A + +343 +00:37:30,730 --> 00:37:35,870 +to the power X اتنين بد ال A تبقى أكبر من ال zero + +344 +00:37:35,870 --> 00:37:40,790 +دائما و أبدا و ال A لا تساوي واحد طب ليش ال + +345 +00:37:40,790 --> 00:37:46,690 +condition هذا لحاجة في نفس يعقوب سنعرفكم بعضها بعد + +346 +00:37:46,690 --> 00:37:51,470 +قليل والبعض الآخر ل calculus B ان شاء الله لما + +347 +00:37:51,470 --> 00:37:56,750 +تدرسوا calculus B في الفصل القادم او في ثالث + +348 +00:37:56,750 --> 00:38:01,420 +section من الفصل القادمطيب يبقى بدنا نيجي للدالة + +349 +00:38:01,420 --> 00:38:06,560 +هذه a to the power x بدنا نروح نرسم رسمة هذه + +350 +00:38:06,560 --> 00:38:11,400 +الدالة و نشوف شو ال domain إلها وش ال range إلها + +351 +00:38:11,400 --> 00:38:17,880 +وش شكلها هذه فبقى بقول الشكل كتالي خلي بالك معايا + +352 +00:38:17,880 --> 00:38:24,460 +كويس هذا محور x هذا محور y هذا النقطة اللي هي zero + +353 +00:38:25,930 --> 00:38:31,350 +قبل برسم قبل a أكبر من zero يبقى a بتاخدش قيمة + +354 +00:38:31,350 --> 00:38:38,490 +دائما لو أبقى القيمة موجبة اتنين قبل a لا تساوي + +355 +00:38:38,490 --> 00:38:44,370 +الواحد لإن لو كانت ال a تساوي واحد بصير واحد قص أي + +356 +00:38:44,370 --> 00:38:50,270 +رقم بواحد يبقى هذه ال linear function أو الدالة + +357 +00:38:50,270 --> 00:38:54,330 +الثابتة لرسمتها خط مستغرب يعني كأنه ماكانك سر + +358 +00:38:54,330 --> 00:38:59,630 +ماسويناش اشيبس في كمان سبب اخر خليه لك القلاص بيه + +359 +00:38:59,630 --> 00:39:03,070 +ان شاء الله لما تاخد القلاص يبقى نقولك يام طيب + +360 +00:39:03,070 --> 00:39:09,330 +يبقى بدنا نروح نرسم هذه يبقى لو قلتلك واحد أس اكس + +361 +00:39:09,330 --> 00:39:14,930 +بده يطلع خط مستقيم صحيح ولا لا؟ يبقى هذا الواحد أس + +362 +00:39:14,930 --> 00:39:20,990 +اكس، هذا عندك هنا الواحد، وهذا هذا، هذا هيك، هذا + +363 +00:39:20,990 --> 00:39:32,140 +الواحد أس اكسلو كان اتنين اص اكس يبقى اتنين + +364 +00:39:32,140 --> 00:39:40,860 +اص اكس يبقى اتنين اص اكس يبقى اتنين + +365 +00:39:40,860 --> 00:39:48,600 +اص اكس يبقى اتنين اص اكس يبقى + +366 +00:39:48,600 --> 00:39:55,210 +اتنين اص اكس يبقى اتنين اص اكسبنفس الطريقة جوز زيه + +367 +00:39:55,210 --> 00:40:01,330 +بدي مر بنفس النقطة هذه طيب ليش؟ لأنه إكس أس لو + +368 +00:40:01,330 --> 00:40:07,470 +كانت ال X ب Zero فتنين أز Zero تلاتة أز Zero مية + +369 +00:40:07,470 --> 00:40:13,890 +أز Zero يبقى كله بدي مر بالنقطة هذهها اللي الإحداث + +370 +00:40:13,890 --> 00:40:20,140 +تبعها Zero واحدكله لازم يمر بالنقطة هذه إذا لو قلت + +371 +00:40:20,140 --> 00:40:23,540 +أربعة أس إكس هل تجي منها و فوق ولا منها و تحت؟ + +372 +00:40:23,540 --> 00:40:28,460 +منها و فوق و تعالى نقولك ليش لو جيت قلت هذه رسمة + +373 +00:40:28,460 --> 00:40:35,800 +الدالة أربعة أس إكس مثلا لو خدت ال X عندي بواحد + +374 +00:40:35,800 --> 00:40:42,630 +يبقى واحد أس واحد اللي هي الواحد تجي كنقطة هذهطيب + +375 +00:40:42,630 --> 00:40:47,930 +لو قلت اتنين أس واحد يعني باتنين بدها تجيك النقطة + +376 +00:40:47,930 --> 00:40:53,410 +هذه لو قلت لك أربعة أس واحد يبقى بتطلع بدها تجيلك + +377 +00:40:53,410 --> 00:40:57,950 +النقطة هذه و هكذا يبقى من هنا تجي منها و فوق و + +378 +00:40:57,950 --> 00:41:02,870 +هكذا مادام رقم أكبر من الواحدة الصحية يعني الجزء + +379 +00:41:02,870 --> 00:41:06,410 +اللي على اليمين بده يجي من الخط واحد هو ال six و + +380 +00:41:06,410 --> 00:41:13,500 +فوقطب لو كان محصور بين الصفر والواحد الصحيح مص طول + +381 +00:41:13,500 --> 00:41:19,210 +تلات اربع الاخرى ومدنيجي هذابدي يجي هنا تحت بس هنا + +382 +00:41:19,210 --> 00:41:25,910 +بدي يطلع فوق نوريك كده يبقى لو أجينا للخط هذا هيك + +383 +00:41:25,910 --> 00:41:34,150 +بالشكل اللي عندنا هنا هذا بيصير نص أس X تمام؟ يعني + +384 +00:41:34,150 --> 00:41:40,960 +نص اتنين هذي لو طلعتها فهو بيصير اتنين أس سالب1 في + +385 +00:41:40,960 --> 00:41:49,880 +1 ب2 أس سالب 1 يعني 2 أس سالب 1 في x يعني 2 أس + +386 +00:41:49,880 --> 00:41:57,780 +سالب x إذا مص أس x يساوي 2 أس سالب xلو كان الرقم + +387 +00:41:57,780 --> 00:42:02,700 +أكبر من الواحد الصحيح اتنين تلاتة أربعة ورفعة إلى + +388 +00:42:02,700 --> 00:42:07,940 +أسالب الرسم هذه بتجيه من وين؟ من الشجة التانية، من + +389 +00:42:07,940 --> 00:42:11,640 +اليمين لوين؟ لليشمال يبقى هذه رسمة + +390 +00:42:17,390 --> 00:42:22,570 +يبقى هذه رسمة a to the power x in general سواء كان + +391 +00:42:22,570 --> 00:42:29,370 +الأس موجب أو سالب أو زيرو طيب السؤال هو a to the + +392 +00:42:29,370 --> 00:42:35,030 +power x هل عمرها بتاخد القيمة الصيفر و أي رسومات + +393 +00:42:35,030 --> 00:42:41,350 +قدامك؟سفر بتاخد واحد مأمنين وقل من واحد مأمنين + +394 +00:42:41,350 --> 00:42:46,450 +كمان السؤال الثاني هل يمكن A to the power X ان + +395 +00:42:46,450 --> 00:42:52,290 +تاخد قيمة سالبة؟ مش ممكنية لإن كلها رسمتها فوق + +396 +00:42:52,290 --> 00:42:56,870 +محوركها لكن تعالي برضه نحسبها عدديا لو قلتك اتنين + +397 +00:42:56,870 --> 00:43:02,070 +أس سالب تلاتة يعني واحد على اتنين أس ثلاثة + +398 +00:43:06,220 --> 00:43:12,080 +إذا قلت اتنين والثلاثة يبقى تمانية ملموقة واتنين + +399 +00:43:12,080 --> 00:43:16,740 +والزيرو واحد يعني موجة إذا ال exponential function + +400 +00:43:16,740 --> 00:43:21,720 +لا يمكن في يوم من الأيام أن تأخذ القيمة الصفر أو + +401 +00:43:21,720 --> 00:43:27,160 +أي قيمة سلبة يبقى بناء عليهبقدر أحط القاعدة و أنا + +402 +00:43:27,160 --> 00:43:35,200 +مرتاح a to the power x أكبر من 0 for all x بس + +403 +00:43:35,200 --> 00:43:40,300 +الشرط هذا موجود عندي ههه ال a أكبر من ال 0 و ال a + +404 +00:43:40,300 --> 00:43:44,620 +ممنوع تساوي واحد يبقى ال a to the power x positive + +405 +00:43:44,620 --> 00:43:51,240 +دائما و always يعني لن يكسر هذا القانون ولو مرة + +406 +00:43:52,830 --> 00:43:59,490 +أكبر من 100 من 0 لا بيساوي 0 ولا بيساوي قيمة سالفة + +407 +00:43:59,490 --> 00:44:06,270 +هذا الهي ال exponential function a to the power x + +408 +00:44:06,270 --> 00:44:13,020 +نجي لل logarithmic function الدالة اللغريةطبعا + +409 +00:44:13,020 --> 00:44:17,200 +أخدت لغارتمات الأعداد والأعداد المقابلة لللغارتمات + +410 +00:44:17,200 --> 00:44:21,580 +في المرحلة الثانوية، مظبوط؟ السؤال مرة تانية، مدام + +411 +00:44:21,580 --> 00:44:25,860 +أخدناها بدأ أسأل السؤال التالي، هل أخدت في يوم من + +412 +00:44:25,860 --> 00:44:33,060 +الأيام لغارتم لكمية سالبة؟ لأ، يعني ما أخدناش + +413 +00:44:33,060 --> 00:44:38,800 +لغارتم لعدد سالب، أخدت في الكيميا لغارتم لعدد + +414 +00:44:38,800 --> 00:44:46,210 +سالب؟يا راجل اتجه الله يا راجل تقرأ بالدالة في سلب + +415 +00:44:46,210 --> 00:44:49,930 +ماعنديش مشكلة، لكن انا بقول هل أخدت له غريتم كمية + +416 +00:44:49,930 --> 00:44:55,130 +سالبة؟ السؤال اللي بعده هل أخدت له غريتم لزيرو؟ + +417 +00:45:00,430 --> 00:45:06,410 +لغرتم الواحد بصفر، مش لغرتم صفر بواحد، يبقى لغرتم + +418 +00:45:06,410 --> 00:45:10,410 +صفر Undefined، لغرتم الكمية السلبية Undefined، + +419 +00:45:10,410 --> 00:45:16,390 +بتداسة للسؤال التالت، قداش domain لغرتم X للأساس + +420 +00:45:16,390 --> 00:45:22,990 +إيه قبل أن أرسمها؟من صفر لإنفينيتي مفتوح على أن + +421 +00:45:22,990 --> 00:45:27,030 +اللغة الرسمية ليست معرفة للازرع ولا للثالث يبقى + +422 +00:45:27,030 --> 00:45:31,750 +مضلوش اللي هي القيامة الموجبة يبقى ال domain لللغة + +423 +00:45:31,750 --> 00:45:38,650 +الرسمية تبع ال Xمن صفر إلى انفتاح يعني لما أرسم + +424 +00:45:38,650 --> 00:45:44,190 +الرسمة بدها تطلع عيمين محور Y وعلى الشمال ولا بس + +425 +00:45:44,190 --> 00:45:49,070 +عيمينه؟ عيمينه عيمينه طيب قبل ما أرسمها بدي أسأل + +426 +00:45:49,070 --> 00:45:54,410 +كمان سؤال قداشي ال domain لل A to the power X + +427 +00:45:54,410 --> 00:46:00,410 +domain ال + +428 +00:46:00,410 --> 00:46:07,490 +A to the power Xما هي قدامي هي هذه بتاخد الموجب + +429 +00:46:07,490 --> 00:46:12,370 +وهي هذه بتاخد السالب وهذه زيها يبقى من سالب + +430 +00:46:12,370 --> 00:46:18,170 +infinity ل infinity كل real number طيب السؤال + +431 +00:46:18,170 --> 00:46:23,370 +الثاني ال range ما هي مكتوب قندك ومرسوم يبقى من + +432 +00:46:23,370 --> 00:46:28,610 +زير، من واحد، يعني هذه الرسومات من هذه الشخصيات + +433 +00:46:30,180 --> 00:46:36,920 +يبقى الـ Range للـ A to the power X من Zero + +434 +00:46:36,920 --> 00:46:42,280 +لإنفينيتي as an open interval خلّي المعلومتين هذول + +435 +00:46:42,280 --> 00:46:48,340 +عندك، بدي أرجع أسئلك فيهم سؤال، بدي أرجع أسئلك في + +436 +00:46:48,340 --> 00:46:53,480 +هذول سؤالطيب نجي للدالة اللغة الرثمية الدالة اللغة + +437 +00:46:53,480 --> 00:46:58,700 +الرثمية لو روحت رسمت هذه المحاور يبقى هذا محور X + +438 +00:46:58,700 --> 00:47:04,160 +هذا محور Y هذا النقطة اللي هي main اللي هي zero لو + +439 +00:47:04,160 --> 00:47:07,440 +روحنا رسمنا ال function تفاج نحنا وياك والسالب + +440 +00:47:07,440 --> 00:47:12,820 +والصفر يبعد الله يبقى بتاخدش إلا أو غير معرفة إلا + +441 +00:47:12,820 --> 00:47:20,720 +للقيم الموجبةيبقى هذا الخط الأزرق اللي هو Y تساوي + +442 +00:47:20,720 --> 00:47:24,560 +logarithm X للأساس A + +443 +00:47:36,180 --> 00:47:44,280 +طيب تمام النقطة هذه لحدثي تبعها واحد وزيرو زي ما + +444 +00:47:44,280 --> 00:47:48,900 +النقطة اللي فوق زيرو واحد طيب الآن ال domain + +445 +00:47:48,900 --> 00:47:52,420 +للورتم + +446 +00:47:52,420 --> 00:47:55,700 +ال X للأساس ايه؟ + +447 +00:47:58,690 --> 00:48:04,890 +من صفر لغاية infinity as an open interval بد ال + +448 +00:48:04,890 --> 00:48:14,410 +range للغرتم ال X للأساس هذا بياخد القيام الموجب + +449 +00:48:14,410 --> 00:48:23,770 +هذا بياخد ال zero هذا بياخد القيام من سالب + +450 +00:48:23,770 --> 00:48:31,770 +infinity لغاية infinityيعني لغارتما الرقم قد يكون + +451 +00:48:31,770 --> 00:48:37,750 +موجبا و قد يكون صفرا و قد يكون سالبا لكن ال domain + +452 +00:48:37,750 --> 00:48:43,870 +دائما و أبدا موجب طيب النوع الثالث النوع الرابع + +453 +00:48:44,130 --> 00:48:47,790 +اللي أنا ما كتبتش من ال Transcendental function + +454 +00:48:47,790 --> 00:48:55,350 +اللي هو ال inverse function اللي هو معاكوس الدالة، + +455 +00:48:55,350 --> 00:49:00,740 +معاكوس الدالة ما لكوش علاقة فيه في هذا الفصللكن + +456 +00:49:00,740 --> 00:49:05,260 +الفصل الجاي ان شاء الله الفصل التاني Calculus بأول + +457 +00:49:05,260 --> 00:49:10,160 +section في أول محاضرة inverse function معكوس + +458 +00:49:10,160 --> 00:49:15,680 +الدالة تمام؟ يبقى هدول الأربعة أصناف هم اللي + +459 +00:49:15,680 --> 00:49:20,240 +بنسميهم ال Transcendental functions اللي هيمروا + +460 +00:49:20,240 --> 00:49:23,380 +علينا خلال دراستنا سواء كان في Calculus A أو + +461 +00:49:23,380 --> 00:49:29,910 +Calculus B بدنا نغششك معلومة لCalculus Bإن الـ A + +462 +00:49:29,910 --> 00:49:34,690 +to the power X ولغرتم الـ X to the power A كل + +463 +00:49:34,690 --> 00:49:39,130 +واحدة فيهم معكوسة للتانية يبقى the inverse + +464 +00:49:39,130 --> 00:49:43,630 +function of A to the power X is لغرتم الـ X + +465 +00:49:43,630 --> 00:49:49,010 +للأساسي والعكس بالعكس معكوسة دالة لغرتم X للأساسي + +466 +00:49:49,010 --> 00:49:53,570 +هي A to the power X ولاحظ السؤال اللي قلناه القوله + +467 +00:49:53,570 --> 00:49:59,620 +ال domain هنا هو ال range هناوالـ Range هنا هو ال + +468 +00:49:59,620 --> 00:50:04,460 +domain لما كتبتيها عكس مظبوط يبقى الدوام لما تبقى + +469 +00:50:04,460 --> 00:50:07,520 +واحدة معكوسة للدنيا بيكون ال domain الأولى هو ال + +470 +00:50:07,520 --> 00:50:12,060 +range التانية و ال range الأولى هو domain التانية + +471 +00:50:12,060 --> 00:50:16,660 +و رسمة كل واحدة فيهم ان شاء الله هتلاقيها is + +472 +00:50:16,660 --> 00:50:19,560 +symmetric about the line Y تساوي X + +473 +00:50:32,370 --> 00:50:37,970 +ولو واحد يجاوز، الزلمة سأل سؤاله، بدي يفهم، تيجي + +474 +00:50:37,970 --> 00:50:43,670 +على لوحك شويه نتفهن احنا معاك؟ يلا تعالي هنا، طبعا + +475 +00:50:43,670 --> 00:50:49,080 +في أمور تبسط على شو اسمك انت؟حسن الكحول يالا يا + +476 +00:50:49,080 --> 00:50:56,700 +حسن اسألك و لا كده مرة تانية مظبوط + +477 +00:50:56,700 --> 00:51:00,680 +صحيح يعني لا سالب ولا صفر يعني ال X هذه دائما و + +478 +00:51:00,680 --> 00:51:06,220 +أبدا موجبة طلع هنا من هنا لهنا أخدنا صفر ولا أخدنا + +479 +00:51:06,220 --> 00:51:13,410 +سالب ليبقى تفاجنا على القطة هذا النقطة التانيةهذا + +480 +00:51:13,410 --> 00:51:18,390 +domain والله range، يعني احنا لما أخذنا القيم + +481 +00:51:18,390 --> 00:51:25,050 +الموجبة فلعتنا هنا قيم موجبة وطلعتنا صفر وطلعتنا + +482 +00:51:25,050 --> 00:51:31,540 +قيم سالبةيعني ال range بتجيب الموجب والسالب، بس ال + +483 +00:51:31,540 --> 00:51:37,820 +domain للموجب، واضح؟ في مشكلة؟ ايوة، اتخربطش من ال + +484 +00:51:37,820 --> 00:51:46,580 +domain و اتكترنى، حاجة بت .. ايوة ايه تتطارق، صح؟ + +485 +00:51:46,580 --> 00:51:50,780 +صحيح؟ + +486 +00:51:50,780 --> 00:51:53,860 +لنسمع + +487 +00:51:53,860 --> 00:51:58,510 +سؤاله، اشوف سؤاله مرة تانية، ايوة؟بحكي ال A أُس X + +488 +00:51:58,510 --> 00:52:01,730 +هي اللي احنا أخدناها ها والسين اللي هي قيمة أولها + +489 +00:52:01,730 --> 00:52:06,410 +لإيه؟ يعني مش عارف الشي اللي أخدتها أنت و بعدين + +490 +00:52:06,410 --> 00:52:10,870 +عالم والله عارف أشي اللي بدويا شوف يا سيدي في عندك + +491 +00:52:10,870 --> 00:52:17,270 +حاجة اسم A أُس X وفي E أُس X E أُس X اللي عدده + +492 +00:52:17,270 --> 00:52:22,670 +اتنين وسبعة من عشرة تقريبابس a to the power x هذه + +493 +00:52:22,670 --> 00:52:28,610 +ال a أي رقم من صفر ل infinity عدل واحد الصحيح يعني + +494 +00:52:28,610 --> 00:52:32,070 +ال a to the power x اللي هو العدد اللي انت بتقصده + +495 +00:52:32,070 --> 00:52:37,870 +هو حالة خاصة من a to the power x لما تكون a فقط + +496 +00:52:37,870 --> 00:52:44,410 +اتنين وسبعة من عشرة أو كاشر بخلصش تمام؟ خلاصنا؟ + +497 +00:52:44,410 --> 00:52:44,810 +ايوة + +498 +00:52:51,140 --> 00:52:55,820 +ممتاز جدا، بيسأل صاحبنا السؤال التالي والسؤال + +499 +00:52:55,820 --> 00:53:00,900 +وجهه، مع الحق، بيقول احنا رسمنا اللغارتم هذه لـA + +500 +00:53:00,900 --> 00:53:05,460 +to the power X، هذه even والله odd، بيقول والله + +501 +00:53:05,460 --> 00:53:10,560 +إذا متمثلة بالنسبة لمحور A وI فهي evenهل هي + +502 +00:53:10,560 --> 00:53:15,720 +متماثلة؟ يبقى not even صف على شجة نجي هل متماثلة + +503 +00:53:15,720 --> 00:53:19,520 +بالنسبة لمحور X؟ يعني هل اي نقطة هنا فيك بالها + +504 +00:53:19,520 --> 00:53:24,200 +نقطة هنا؟ يبقى ماهياش متماثلة بالنسبة لمحور X و + +505 +00:53:24,200 --> 00:53:28,180 +بضيفله عليها ولا حتى symmetric بالنسبة لل origin + +506 +00:53:28,180 --> 00:53:32,860 +التلاتة كلها لا يبقى ماعنديش symmetry بالنسبة لها + +507 +00:53:32,860 --> 00:53:40,720 +بتاتا خلصنا؟طيب لحد هنا stop بدنا في الحل تروح + +508 +00:53:40,720 --> 00:53:46,340 +تمرن إيدك في ال exercises تبعد واحد واحد من + +509 +00:53:46,340 --> 00:53:53,840 +المسائل من واحد لسبعة و خمسين ال odd numbers طبعا + +510 +00:53:53,840 --> 00:53:58,620 +و بقولك odd ليش ان الإيجابات عندك في الكتاب مش + +511 +00:53:58,620 --> 00:54:03,750 +هنتعرف أنت بتشتغل صحولا بتشتغل غلط، تمام؟ ولا يصعب + +512 +00:54:03,750 --> 00:54:08,950 +عليك بتروح على ال discussion وانت جاهز مش تروح على + +513 +00:54:08,950 --> 00:54:12,790 +ال discussion وانت مش حلل ولا سؤال بصير انت مجمعي + +514 +00:54:12,790 --> 00:54:17,310 +شوية أما حلل، بتروح وانت موطن نفسك وفاهمي كويس، + +515 +00:54:17,310 --> 00:54:21,910 +okay؟ يبقى هنا يعني، يبقى المسال بتروح تحلوا، نبغى + +516 +00:54:21,910 --> 00:54:24,190 +بك تروح على ال discussion وإذا ملهجتش في ال + +517 +00:54:24,190 --> 00:54:27,760 +discussionو رحت للميضة على الغرفة و مالقتش و + +518 +00:54:27,760 --> 00:54:31,160 +بتجيني في الساعات المكتبية أهلا وسهلا وراحت بالكل + +519 +00:54:31,160 --> 00:54:34,780 +اللي بيجي يسأله و اللي بيجي يسأله حرف ده اللي هو + +520 +00:54:34,780 --> 00:54:39,700 +على جنهه طب الأن ننتقل إلى ال section الثاني اللي + +521 +00:54:39,700 --> 00:54:47,220 +يليه هو section 1-2 اللي بتكون من ثلاث نقاط رئيسة + +522 +00:54:47,790 --> 00:54:53,450 +النقطة الأولى لل combining functions بدنا نكوّن + +523 +00:54:53,450 --> 00:54:59,890 +دالة جديدة من دوال موجودة والنقطة الثانية ال + +524 +00:54:59,890 --> 00:55:05,010 +shifting of functions بدنا نرسم الدول و نعمل لها + +525 +00:55:05,010 --> 00:55:12,560 +إذاحاتذات اليمين أو ذات الشمال وإلى أعلى وإلى أسفل + +526 +00:55:12,560 --> 00:55:18,420 +كذلك والنقطة التالتة ال scaling graphs اذا بنرسم + +527 +00:55:18,420 --> 00:55:24,660 +الرسمة بنسب معينة تصغير أو تكبير للرسمة الكلام + +528 +00:55:24,660 --> 00:55:31,320 +اللي سمعته هو مختصر section 1-2 يبقى section 1-2 + +529 +00:55:31,320 --> 00:55:33,680 +بتكلم عن ما يأتي + +530 +00:55:37,890 --> 00:55:45,130 +combining functions النقطة الأولى النقطة التانية + +531 +00:55:45,130 --> 00:55:53,110 +shiftings shiftings + +532 +00:55:53,110 --> 00:56:00,170 +الإزاحات and scaling graphs + +533 +00:56:05,720 --> 00:56:10,340 +نبدأ بالنقطة الأولى اللى فى ال combining functions + +534 +00:56:10,340 --> 00:56:18,400 +بإننا ناخد ال sums و ال differences الطرح أو + +535 +00:56:18,400 --> 00:56:26,520 +الفروقات و ال products اللى هو عملية الدرب and + +536 +00:56:26,520 --> 00:56:32,480 +quotients عملية القسمة + +537 +00:56:37,900 --> 00:56:44,640 +كل هدول بإننا نعطيهم تعريف فبجي بقول definition if + +538 +00:56:44,640 --> 00:57:02,810 +ال if and ال g are two functions and if ال xموجودة + +539 +00:57:02,810 --> 00:57:11,830 +في domain ال F تقاطع مع domain ال G we define + +540 +00:57:11,830 --> 00:57:16,090 +بالروح + +541 +00:57:16,560 --> 00:57:25,640 +نعرف تعريفات التالية نمرة واحد f زائد او ناقص g as + +542 +00:57:25,640 --> 00:57:32,820 +a function of x بدي يساوي ال f of x زائد او ناقص g + +543 +00:57:32,820 --> 00:57:41,220 +of x نمرة اتنين ال f في g of x بدي يساوي ال f of x + +544 +00:57:41,220 --> 00:57:45,640 +مضروب في ال g of x and + +545 +00:57:47,780 --> 00:57:54,200 +الـCF as a function of X بدي الساوي C في الـF of X + +546 +00:57:54,200 --> 00:58:07,200 +والـC is constant نمرة تلاتةبدنا ال F على G كله as + +547 +00:58:07,200 --> 00:58:15,320 +a function of X بديه ساوي ال F of X على G of X + +548 +00:58:15,320 --> 00:58:25,640 +وبشرط ان ال G of X ممنوع يتساوي Zero لان + +549 +00:58:25,640 --> 00:58:33,850 +كل هدول functions جديدة بدنا domain لمام لل Fزائد + +550 +00:58:33,850 --> 00:58:43,110 +ال G هو ال domain لل F ناقص ال G هو ال domain لل F + +551 +00:58:43,110 --> 00:58:54,450 +في G هو ال domain لل F تقاطع مع domain لل G and + +552 +00:58:54,450 --> 00:59:02,550 +وزيادة على ذلك ال domain لل C في ال F + +553 +00:59:06,800 --> 00:59:13,280 +النقطة التالتة والاخيرة domain ال F على G + +554 +00:59:17,790 --> 00:59:26,930 +Domain الـ F تقاطم مع Domain الـ G كل هذا بتشيل كل + +555 +00:59:26,930 --> 00:59:37,670 +العناصر اللي بتخللي G of X يساوي Zero for example + +556 +00:59:37,670 --> 00:59:38,270 +let + +557 +00:59:47,290 --> 00:59:55,150 +الـ F of X ساول جدر التربيع إلى X زائد أربعة and + +558 +00:59:55,150 --> 01:00:04,090 +الـ G of X ساول جدر التربيع إلى X تربيع ناقص أربعة + +559 +01:00:04,090 --> 01:00:16,110 +find بدنا كل من نمرا A بدنا + +560 +01:00:16,830 --> 01:00:34,510 +ال F زيدي الجي و ال F في جي و ال F على جي + +561 +01:00:34,510 --> 01:00:47,000 +نمر بين بدنا domain ال F زيدي الجي domainالـ F في + +562 +01:00:47,000 --> 01:00:58,460 +G and domain ال F على G نمرسى + +563 +01:00:58,460 --> 01:01:08,340 +بدنا ال F على G as a function of one and ال F على + +564 +01:01:08,340 --> 01:01:12,140 +G as a function of three + +565 +01:01:20,840 --> 01:01:26,660 +لما اقول combining functions يبقى احنا عندنا + +566 +01:01:26,660 --> 01:01:32,820 +دالتين او اكثر بدنا نعملهم عملية تجميع عملية تجميع + +567 +01:01:32,820 --> 01:01:37,580 +قد يكون جمع قد يكون طرح قد يكون طرب قد يكون قسمة + +568 +01:01:37,580 --> 01:01:43,140 +قد يكون عملية تركيبيةبس التركيبية أجلناها لك إلى + +569 +01:01:43,140 --> 01:01:47,900 +ما بعد قليل قلينا نشوف الشغلات اللي بيبقى أول شغلة + +570 +01:01:47,900 --> 01:01:53,560 +بدنا نكوّن دالة جديدة من دالتين موجودتين إما + +571 +01:01:53,560 --> 01:01:58,360 +بعملية الجامعة أو عملية الطرح أو عملية الضرب أو + +572 +01:01:58,360 --> 01:02:04,020 +عملية القسمة وبعد ما نكوّن هذه الدول بدنا ندور على + +573 +01:02:04,020 --> 01:02:08,560 +ال domain تبعهاما هي علاقة الـ domain لهذه الدوال + +574 +01:02:08,560 --> 01:02:16,180 +بالـ domains للدلتين الأصليتين بقول التعريف كتل + +575 +01:02:16,180 --> 01:02:22,160 +افترض ان عندك دلتين f و g are two functions وخدنا + +576 +01:02:22,160 --> 01:02:28,420 +element x موجود في تقاطع two domains domain ال f + +577 +01:02:28,420 --> 01:02:33,560 +intersection domain ال g يعني انا جبت domain ال fو + +578 +01:02:33,560 --> 01:02:38,720 +جبت domain الـ G و أخدت النقاط المشتركة بين ال two + +579 +01:02:38,720 --> 01:02:43,020 +domains تمام؟ يبقى هذا اللي سمنا ال intersection + +580 +01:02:43,020 --> 01:02:49,340 +أو تقاطع ال two domains أخدت element موجود في هذا + +581 +01:02:49,340 --> 01:02:55,280 +و جيت بدي أخد F زائد G أو F ناقصي لما اتأثر على + +582 +01:02:55,280 --> 01:03:00,060 +هذا ال elementبعرفها هي عبارة عن تأثير ال F على X + +583 +01:03:00,060 --> 01:03:07,520 +مضافا إليه أو مقروحا منه تأثير ال G على X الأن لو + +584 +01:03:07,520 --> 01:03:13,480 +أخدت حاصل ضرب FG as a function of X يسوى تأثير ال + +585 +01:03:13,480 --> 01:03:18,780 +F على X مضروبا في تأثير ال G على X الأن لو دالها + +586 +01:03:18,780 --> 01:03:22,760 +دي أخدتها مقدار ثابت مضروبة في الدالة تانية ممكن + +587 +01:03:22,760 --> 01:03:29,070 +أقولمقدار ثابت مضروب في F كله بيؤثر على X يساوي C + +588 +01:03:29,070 --> 01:03:34,230 +itself نفسها ماتغيرتاش في تأثير ال F على X حيث ال + +589 +01:03:34,230 --> 01:03:40,270 +C constant مقدار ثابت بدنا ال F على G لما تأثر على + +590 +01:03:40,270 --> 01:03:44,650 +X يساوي تأثير ال F على X مقسوما على تأثير ال G على + +591 +01:03:44,650 --> 01:03:49,830 +X بحيث انالجيوبكس ممنوع يتساوي zero لإن لو سوى + +592 +01:03:49,830 --> 01:03:55,310 +zero عند هذه النقطة بصير القسمة is undefined غير + +593 +01:03:55,310 --> 01:04:02,470 +معرفة إذا أنشأنا دوال جديدة من الدالتين الأصليتين + +594 +01:04:02,470 --> 01:04:06,970 +بد ال domain لكل واحدة منهم الحمد لله domain + +595 +01:04:06,970 --> 01:04:12,100 +الجامع هو domain الطرح هو domainاللي هو الضرب هو + +596 +01:04:12,100 --> 01:04:17,140 +التقاطة بين ال two domains زي ما هشوف عمليا بعد + +597 +01:04:17,140 --> 01:04:21,760 +قليل طيب بيجيني ال domain main المقدار الثابت في F + +598 +01:04:21,760 --> 01:04:26,420 +بيقول هو ال domain تبع ال F تعالى نشوف ليش قاللي + +599 +01:04:26,420 --> 01:04:31,590 +domain ال Fالسؤال اللى جابلى و قاللى ال domain + +600 +01:04:31,590 --> 01:04:36,250 +الجامع و الطرح و الضرب اللى هو ال intersection ما + +601 +01:04:36,250 --> 01:04:40,410 +بين الاتنين يبقى انا بدأ اخد الضرب بدل ال F او ال + +602 +01:04:40,410 --> 01:04:45,250 +G بدأ احط مقدار ثابت هو ال F of X لما تسوى مقدار + +603 +01:04:45,250 --> 01:04:49,860 +ثابت جديش ال domain تبعهاكل real number من سالب + +604 +01:04:49,860 --> 01:04:54,480 +infinity إلى infinity ب gene مين domain ال F يبقى + +605 +01:04:54,480 --> 01:04:58,040 +تقاطع ما بين domain ال F وما بين ال set of real + +606 +01:04:58,040 --> 01:05:02,240 +numbers domain ال F itself ومن هنا روح نقول دومين + +607 +01:05:02,240 --> 01:05:08,250 +ال constant F هو مينهو domain الـ F itself طبقنا + +608 +01:05:08,250 --> 01:05:12,850 +ال domain تبع حاصل الطرب هذا قولنا ال intersection + +609 +01:05:12,850 --> 01:05:18,730 +ما بين ال two domains طيب domain خارج القسمة يبقى + +610 +01:05:18,730 --> 01:05:22,690 +ال intersection ما بين ال two domains بدي أشيل منه + +611 +01:05:22,690 --> 01:05:27,760 +النقاطاللي بتخليه للمقام ما لها ساوي زي هو يبقى + +612 +01:05:27,760 --> 01:05:33,180 +ناقص كل العناصر X اللي صورتها بدها تكون صفر لإن + +613 +01:05:33,180 --> 01:05:37,960 +القسم عند هذه النقاط بصير ما لها and five طب هذا + +614 +01:05:37,960 --> 01:05:44,060 +كلام نظري بدنا نشوفه على أرض الواقعمعطيني دلتين و + +615 +01:05:44,060 --> 01:05:49,080 +قليلات للجمع و الضرب و القسمة و بعد هيك ال domains + +616 +01:05:49,080 --> 01:05:52,520 +اللي لهم و بعدين تحسبلي ال domains القسمة عنده + +617 +01:05:52,520 --> 01:05:58,500 +رقمين بقوله ماشي بدي اجي للنقطة الأولى بدي اخدله f + +618 +01:05:58,500 --> 01:06:04,160 +زائد g as a function of x بدي اعرف شو شكل الجمع + +619 +01:06:04,540 --> 01:06:08,900 +بنطبق التعريف اللي أنا قايله يبقى لما أطبق التعريف + +620 +01:06:08,900 --> 01:06:15,720 +هذه عبارة عن f of x زائد main g of x f of x معروفة + +621 +01:06:15,720 --> 01:06:22,140 +عند اللي هي main الجذر التربية إلى x زائد 4 زائد + +622 +01:06:22,140 --> 01:06:28,400 +ال g of x اللي هي الجذر التربية إلى x تربية ناقص 4 + +623 +01:06:28,400 --> 01:06:36,950 +بقدر هدولة جمعهم أكتر من هيخلاص؟ يبقى خلاص؟ بقدرش + +624 +01:06:36,950 --> 01:06:40,410 +أجمع أكثر منك، يبقى هايوم، كل اللي بقدر أعمله أن + +625 +01:06:40,410 --> 01:06:44,770 +أضرب في المرافق وبالتالي أحطهم في شكل جديد، + +626 +01:06:44,770 --> 01:06:48,530 +كالكعزيزة، مالهاش لزوم، يبقى خلاص، وصل لحد هنا، + +627 +01:06:48,530 --> 01:06:53,200 +والله يعطيك العافيةبعد هيك بداجي لمين؟ للنقطة + +628 +01:06:53,200 --> 01:06:58,760 +التانية اللي هي ال FG as a function of X يبقى ال F + +629 +01:06:58,760 --> 01:07:04,840 +of X في ال G of X يبقى الجدر التربيعي لل X اللي + +630 +01:07:04,840 --> 01:07:10,920 +عندنا هذه لل X زائد الأربعة مضروبة في الجدر + +631 +01:07:10,920 --> 01:07:16,220 +التربيعي لل X تربيع ناقص أربعةهذه صحيحه بقدر + +632 +01:07:16,220 --> 01:07:21,700 +أخليها جذر واحد، مظبوط، بقدر أقول هذا جذر واحد، + +633 +01:07:21,700 --> 01:07:27,260 +مظبوط، لمين؟ لل X زائد أربعة، بال X تربية نقص + +634 +01:07:27,260 --> 01:07:31,320 +أربعة، بقدر واحد و أخليه جذر واحد، أكتر من هيك، + +635 +01:07:31,320 --> 01:07:36,910 +وصل لحد هنا، والله يعطيك العافيةبتداجي لمن؟ ل ال F + +636 +01:07:36,910 --> 01:07:43,510 +على G as a function of X يبقى ال F of X على ال G + +637 +01:07:43,510 --> 01:07:49,710 +of X يبقى الجدرى التربية لل X زائد 4 على من على + +638 +01:07:49,710 --> 01:07:54,290 +الجدرى التربية ل X تربية ناقص 4 هو اللي بقدر أخليه + +639 +01:07:54,290 --> 01:07:54,870 +كذلك + +640 +01:08:04,710 --> 01:08:11,790 +خلصنا المطلوب الأول بدنا نيجي للمطلوب التاني نجلب + +641 +01:08:11,790 --> 01:08:17,120 +الدميل للأولى و الدميل للتانىمش هنجيب ال two + +642 +01:08:17,120 --> 01:08:22,840 +domains لازم أعرف قداش domain ال F و domain ال G و + +643 +01:08:22,840 --> 01:08:26,840 +التقاطة فيما بينهما لأن هذا أساسي في شغلنا صحيح + +644 +01:08:26,840 --> 01:08:32,020 +ولا لأ يبقى باجي بقوله بدي أجيبله في الأول domain + +645 +01:08:32,020 --> 01:08:38,600 +ده ال F هو كل العناصر X بحيث هو أنه برجع لل F صح + +646 +01:08:38,600 --> 01:08:45,260 +بيتنا هذه تمام؟ بدي ال domain تبعهابدى القيمة اللى + +647 +01:08:45,260 --> 01:08:49,720 +تحت الجدر تبقى دائما و أبدا أكبر من أو تساوي ال + +648 +01:08:49,720 --> 01:08:54,160 +zero يبقى ال X زائد أربعة greater than or equal to + +649 +01:08:54,160 --> 01:08:59,060 +zero يبقى ال X زائد أربعة greater than or equal to + +650 +01:08:59,060 --> 01:09:06,500 +zero يبقى كل العناصر X بحيث أن ال X تكون أكبر من + +651 +01:09:06,500 --> 01:09:12,080 +أو تساوي جداش سلب أربعة يعني من سلب أربعة ثم فوق + +652 +01:09:12,080 --> 01:09:18,350 +يعني من و لا وينسالب أربعة لغاية infinity يبقى هذا + +653 +01:09:18,350 --> 01:09:23,850 +كل ال interval مغلقة من عند السلب أربعة و لغاية ال + +654 +01:09:23,850 --> 01:09:28,330 +infinity مفتوحة بالشكل اللي قدامنا هنا تمام هاي + +655 +01:09:28,330 --> 01:09:33,690 +جيبنا domain ال F بدنا نجيب main domain ال G + +656 +01:09:33,690 --> 01:09:39,170 +domain ال G كل العناصر X بحيث رانا برضه صاحبنا هذا + +657 +01:09:39,170 --> 01:09:44,610 +جذريبقى بدى كل الكمية اللى تحت الجدرد تبقى أكبر من + +658 +01:09:44,610 --> 01:09:49,870 +أو تساوي ال zero بحيث ان X squared minus four + +659 +01:09:49,870 --> 01:09:54,750 +greater than or equal to zero يبقى كل العناصر X + +660 +01:09:54,750 --> 01:10:01,290 +أضيف أربعة للطرفين يبقى بحيث أن X تربية greater + +661 +01:10:01,290 --> 01:10:07,310 +than or equal to من للأربعة انا مابدى X تربية بدى + +662 +01:10:07,310 --> 01:10:12,970 +X يبقى شو بعمل؟بأخد الجذر التربيهي للطرفين، يبقى + +663 +01:10:12,970 --> 01:10:19,370 +هذا كل العناصر X بحيث أن absolute value ل X أكبر + +664 +01:10:19,370 --> 01:10:24,130 +من أو تسوى absolute value لاتنين اللي همين + +665 +01:10:24,130 --> 01:10:32,380 +بالاتنين، صح؟ سكت الشعبالجدر التربية على اكس تربية + +666 +01:10:32,380 --> 01:10:35,180 +هو absolute value لكس يبقى absolute value لكس + +667 +01:10:35,180 --> 01:10:38,000 +الجدر التربية على اربعة هو absolute value لاتنين + +668 +01:10:38,000 --> 01:10:43,940 +اللي هي باتنين itself طبعا فبدي اعبر عن هذه بصياغة + +669 +01:10:43,940 --> 01:10:51,260 +اخرى فبجي بقول هذه كل العناصر X such that هذه اما + +670 +01:10:51,260 --> 01:10:54,260 +ال X greater than or equal to + +671 +01:11:03,630 --> 01:11:07,610 +بس اسمع اسمع ليش ايش؟ وهي + +672 +01:11:21,220 --> 01:11:28,020 +هذا الكلام يسمى كلمة or تعني اتحاد + +673 +01:11:30,080 --> 01:11:35,140 +يبقى باجي بقول جال ال X أكبر من أو تساوي 2 يعني من + +674 +01:11:35,140 --> 01:11:39,680 +عند اتنين لوان للمالة نهاية جال ال X أقل من أو + +675 +01:11:39,680 --> 01:11:44,620 +يسالب يعني بدك ترجع من سالب اتنين لوان لكن الفترة + +676 +01:11:44,620 --> 01:11:49,020 +الصغيرة بنحطها في الأول و الكبيرة بنحطها بالاخر + +677 +01:11:49,020 --> 01:11:54,460 +يبقى كل ال interval من سالب infinity لغاية سالب + +678 +01:11:54,460 --> 01:12:01,530 +اتنينمغلقة من عند السلب اتنين بسبب اليساوي اتحاد + +679 +01:12:01,530 --> 01:12:05,490 +الفترة من اتنين لغاية infinity + +680 +01:12:08,010 --> 01:12:12,170 +طيب، حتى الآن جيب بس domain ال F و domain ال G، + +681 +01:12:12,170 --> 01:12:17,750 +أصبر عليا بس نخلص، الآن أنا بدي domain المشترك ما + +682 +01:12:17,750 --> 01:12:23,750 +بين الأثنين، لأنه عند التعريف قال X موجودة وين في + +683 +01:12:23,750 --> 01:12:27,610 +التقاطة، ولمن حسبنا ال domain قال اللي موجود في + +684 +01:12:27,610 --> 01:12:32,970 +تقاطة الأثنينيبقى احنا بدنا نروح نجيب تقاطع + +685 +01:12:32,970 --> 01:12:39,410 +الفترتين domain ال F مع domain ال G إذا بقوله بدي + +686 +01:12:39,410 --> 01:12:47,290 +domain الدلة F تقاطع مع domain الدلة G يساوي وما + +687 +01:12:47,290 --> 01:12:52,510 +أدركى مالي يساوي وكيف بدنا نعزبه استغلنا شوية بقى + +688 +01:12:52,510 --> 01:12:58,340 +أصب الله ما أخلصالان بدى أعلمك كيف تحسبه بطريقة ما + +689 +01:12:58,340 --> 01:13:05,000 +تخرش الميه تمام؟ بدك تروح تلصم راسم كيف الرسم؟ + +690 +01:13:05,000 --> 01:13:11,740 +بقوله هذا ال real lifeبتدهش للفترة الأولى تبع ال + +691 +01:13:11,740 --> 01:13:15,680 +domain ده اللي يفجل من وين؟ من عند السلب أربعة + +692 +01:13:15,680 --> 01:13:22,120 +لغاية؟ يعني لو قلت هذا ال zero بده تجينا سلب أربعة + +693 +01:13:22,120 --> 01:13:27,160 +هنا، مظبوط؟ نبعدها شوية مشان الكل يشوف جول هنا، + +694 +01:13:27,160 --> 01:13:32,900 +هاي سلب أربعة يبقى من وين لوين، من عند السلب أربعة + +695 +01:13:32,900 --> 01:13:39,780 +بدي أبقى الماشي إلى ما لا نهايةسهم يعني قال فالله + +696 +01:13:39,780 --> 01:13:43,960 +سهل عليها إلى نيرة الله الأرض ومن عليها خلاصنا + +697 +01:13:43,960 --> 01:13:49,020 +مين؟ هذا مين اللي رسمته؟ domain ال F بدي أروح ل + +698 +01:13:49,020 --> 01:13:53,320 +domain ال G domain ال G جاله من سالب infinity + +699 +01:13:53,320 --> 01:13:58,320 +لغاية سالب اتنين سالب اتنين وين بيجينا؟ هنا سالب + +700 +01:13:58,320 --> 01:14:04,710 +اتنين و بتدك ترجع لوين؟ لسالب infinity و بعد هيكمن + +701 +01:14:04,710 --> 01:14:09,830 +عند اتنين لل infinity يبقى اتنين تجينا بعد ال zero + +702 +01:14:09,830 --> 01:14:15,230 +يبقى هاي اتنين ولل infinity بالشكل اللي عندنا هذا + +703 +01:14:16,480 --> 01:14:20,860 +الان التقاط اتباعهم هو المنطقة المشتركة ما بين + +704 +01:14:20,860 --> 01:14:24,880 +الاتنين وإن اتنين موجودين مع بعض تكون هي المنطقة + +705 +01:14:24,880 --> 01:14:30,560 +المشتركة اطلعلي هذه اظن هذه المنطقة المشتركة ما + +706 +01:14:30,560 --> 01:14:35,800 +بين الاتنين هنا وهنا هذه المنطقة المشتركة ما بين + +707 +01:14:35,800 --> 01:14:41,190 +الاتنينصحيح ولا لأ؟ يبقى بناء عليه بقدر ال domain + +708 +01:14:41,190 --> 01:14:47,910 +من سالب أربعة لسالب اتنين من سالب أربعة لسالب + +709 +01:14:47,910 --> 01:14:54,590 +اتنين as an closed interval بسبب وجود اليساوي بدا + +710 +01:14:54,590 --> 01:15:00,230 +أحب عليها كمان الفترة من و لا و ام من اتنين مغلقة + +711 +01:15:00,230 --> 01:15:06,190 +لغاية infinityيبقى يا شباب إن رسمت زيها في عمرك ما + +712 +01:15:06,190 --> 01:15:11,010 +هتغلط، بس تجي تقدرها بدور الرسم، احتمال الخطأ وارد + +713 +01:15:11,010 --> 01:15:17,380 +بنسبة 150%هذا للبعض والبعض الاخر قد يكون نسبة نجاح + +714 +01:15:17,380 --> 01:15:22,540 +150% واما ما ده فيه اختلاف في العقول إذا حتى ما + +715 +01:15:22,540 --> 01:15:28,860 +نغلطش بنحاول نرسم طيب رسمنا وحددنا الفترة الحين + +716 +01:15:28,860 --> 01:15:33,120 +بدنا نيجي لمين لنمربيه في المثلة نحسب ال domain + +717 +01:15:33,120 --> 01:15:38,020 +اللي بدناه بعد ما اشتغلنا الشغل هذه كلها + +718 +01:15:52,810 --> 01:15:58,970 +نمسك نمرة بي لان، هاي نمرة بي، نمرة بي قال لي + +719 +01:15:58,970 --> 01:16:02,190 +domain ال F زي دي ال G و domain ال F في G هدول زي + +720 +01:16:02,190 --> 01:16:06,870 +بعض، مش فيهم مشكلة، مظبوط؟ يبقى بقى جيبقى أقول له + +721 +01:16:06,870 --> 01:16:15,980 +domainالـ F زائد الـ G هو domain الـ F في G هو + +722 +01:16:15,980 --> 01:16:23,020 +domain الـ F تقاطعه مع domain الـ G، مش هيك؟ يبقى + +723 +01:16:23,020 --> 01:16:27,650 +هذا جاهز، حسبتهبجيبها زي ما هي و بقعدها بسلامتها + +724 +01:16:27,650 --> 01:16:35,330 +يبقى هذه يساوي سالب أربعة و سالب اتنين اتحاد اتنين + +725 +01:16:35,330 --> 01:16:39,450 +و infinity بقى اللي عندنا في نمرة بيه ايجاد domain + +726 +01:16:39,450 --> 01:16:44,010 +خارج القسمة بقوله and + +727 +01:16:46,520 --> 01:16:52,740 +الـ domain بتبع ال F على G اللي هو domain ال F + +728 +01:16:52,740 --> 01:17:02,980 +تقعقه مع domain ال G بدي أشيل منه كل ال X's اللي + +729 +01:17:02,980 --> 01:17:10,090 +بدها تخليه ليه G of X يساوي Zeroمش هيك التعريف طيب + +730 +01:17:10,090 --> 01:17:15,030 +ال intersection جاهز هيه فوق يبقى سالي باتنين + +731 +01:17:15,030 --> 01:17:23,090 +أسالف أربع لغاية سالي باتنين اتحاد اتنين و + +732 +01:17:23,090 --> 01:17:29,370 +infinity بدي أشيل منه كل القيم اللي بدها تخلي + +733 +01:17:29,370 --> 01:17:35,470 +المقام ب zero من القيم اللي بتخلي جي ب zero هي جي + +734 +01:17:36,000 --> 01:17:40,000 +ما هو اللي يجعلها zero؟ إتنان و سالب إتنان، هل + +735 +01:17:40,000 --> 01:17:47,340 +يوجد غيرهم؟ بكتبهم as a set سالب إتنين و إتنين، + +736 +01:17:47,340 --> 01:17:51,700 +يبقى بدا يجي على الفترة هذه، بدي أشيل منها سالب + +737 +01:17:51,700 --> 01:17:56,460 +إتنين و إتنان اللي عندنا، يبقى بدل ما يتلت، بخليها + +738 +01:17:56,460 --> 01:18:02,020 +مفتوحة، يقول خلصنا، حلنا مشكلتنايبقى هذه يساوي + +739 +01:18:02,020 --> 01:18:09,540 +سالب أربعة مغلقة سالب اتنين بنخليها مفتوحة اتحاد + +740 +01:18:09,540 --> 01:18:15,140 +كمان مفتوحة اتنين و infinity يبقى استبعدنا سالب + +741 +01:18:15,140 --> 01:18:16,300 +اتنين و اتنين + +742 +01:18:27,360 --> 01:18:30,980 +المشكلة في حساب ال domain مش في الشكل إذا في + +743 +01:18:30,980 --> 01:18:36,340 +اختصارات باختصرها بالمقال فيش اختصارات X ناقص + +744 +01:18:36,340 --> 01:18:41,980 +اتنين في X زي اتنين فرق من المربعين هدفش اللي فوق + +745 +01:18:41,980 --> 01:18:45,680 +X زي اتاربعة لأ لأ اجى في باله X ناقص اربعة X زي + +746 +01:18:45,680 --> 01:18:47,360 +اتاربعة تم اختصار فيش اختصار + +747 +01:18:55,340 --> 01:19:00,800 +هي ال F في ال bus و لا في المقاممصبوط؟ يبقى بيخلى + +748 +01:19:00,800 --> 01:19:04,360 +اللى فى المقام هو اللى يساوي دى لأصفار المقام مش + +749 +01:19:04,360 --> 01:19:07,520 +أصفار البطل أصفار البطل ده اللى معرفة عندها + +750 +01:19:07,520 --> 01:19:10,960 +ماعنديش مشكلة المشكلة لو وقعت الأصفار فى المقام + +751 +01:19:10,960 --> 01:19:16,320 +عارف ليش؟ لأنه لا يمكن في علم الرياضية إنك تقسم + +752 +01:19:16,320 --> 01:19:21,680 +على صفر خارج نطاقة العقل البشري مش ممكن يتصورها + +753 +01:19:21,680 --> 01:19:25,320 +العقل البشري في يوم من الأيامماشي الى يومنا هذا + +754 +01:19:25,320 --> 01:19:30,340 +طبعا تمام؟ يبقى خلاصنا منين؟ نمرة بيخلاصنا منها + +755 +01:19:30,340 --> 01:19:36,960 +كلها جيبنا ال domain طبعا ايوة كيف؟ تعال هنا، ايه + +756 +01:19:36,960 --> 01:19:41,040 +الحد؟ + +757 +01:19:41,040 --> 01:19:51,280 +انيات اللي بتنعد، لحد هنا؟ وين اللي مافهمتوش؟ممتاز + +758 +01:19:51,280 --> 01:19:57,420 +جدا طيب اذا دمية دولة F1 و F2 هيها هل الجلر معرف + +759 +01:19:57,420 --> 01:20:04,100 +لقيمة سالبة يعني بدي اكبر او يساوي ها ايه اكبر من + +760 +01:20:04,100 --> 01:20:08,140 +او يساوي زيه تعرف تحلي المتباينة هنا يعني بنضيف + +761 +01:20:08,140 --> 01:20:12,980 +سالب اربعة على الطرفين بصير X اكبر من سالب اربعة + +762 +01:20:12,980 --> 01:20:16,580 +او يساوي يعني من سالب اربعة والله سهل عليك لوين؟ + +763 +01:20:18,220 --> 01:20:22,200 +أكبر منها سالب ثلاثة سالب اتنين سالب واحد زير واحد + +764 +01:20:22,200 --> 01:20:25,680 +اتنين لغاية ما يبقى هذه خلاصة من هذه التانية + +765 +01:20:25,680 --> 01:20:29,260 +واختها هاي الجدرى التربية الاكستربية نقصرها + +766 +01:20:29,260 --> 01:20:34,140 +بدناياها اكبر من او تساومين ال zero ضيف اربع على + +767 +01:20:34,140 --> 01:20:38,700 +الطرفين بصير الاكستربية اكبرخد الجدر التربيه + +768 +01:20:38,700 --> 01:20:43,800 +الاطفالي موافق؟ لحد هنا تمام؟ بدنا نفسر هذه، هذه + +769 +01:20:43,800 --> 01:20:47,860 +معناها يا إما ال X أكبر يسوى اتنين، يا إما أقل من + +770 +01:20:47,860 --> 01:20:51,980 +أوي يسوى سالب اتنين، يعني من عند اتنين لما لا + +771 +01:20:51,980 --> 01:20:56,040 +نهاية من سالب اتنين اكترى على سالب ما لا نهاية، + +772 +01:20:56,040 --> 01:21:01,560 +مظبط هك؟ فهمت؟ بدنا التقاط ما بين الفترة هذه و + +773 +01:21:01,560 --> 01:21:07,830 +الفترة هذه هي قدامكخلاص لا؟ ضالي شيء؟ شو اسمك أنت؟ + +774 +01:21:07,830 --> 01:21:12,530 +زهر المناصر، هاي تالث مرة بسأله عن اسمه، مظبوط؟ + +775 +01:21:14,120 --> 01:21:18,260 +يبقى زهرة المناصرة بانها تزهر هك و تفتح اكتر ان + +776 +01:21:18,260 --> 01:21:22,740 +شاء الله هاي خلاصة من المطلوب التاني نمره بيه بدنا + +777 +01:21:22,740 --> 01:21:29,900 +نروح لنمره ال C حد بيقدر يعطيني الجواب مباشرة من + +778 +01:21:29,900 --> 01:21:34,000 +ضل يعوض ولا حاجة F على G of 1 + +779 +01:21:45,180 --> 01:21:50,400 +طلع للـ domain تباعها، وين ال domain؟ ال F على G + +780 +01:21:50,400 --> 01:21:56,610 +اللي هاد، موجود الواحد هناموجود؟ يبقى does not + +781 +01:21:56,610 --> 01:22:01,890 +exist مظبوط ان واحد مش موجود في الفترة هذه يبقى + +782 +01:22:01,890 --> 01:22:05,630 +اوتوماتيكي هذه محلولة خالصة اذا يبقى بالداجي اقوله + +783 +01:22:05,630 --> 01:22:15,390 +ال F على G as a function of one does not does not + +784 +01:22:15,390 --> 01:22:27,190 +existبسبب ان الواحد ليس مستحيل للفترة ناقص اربعة + +785 +01:22:27,190 --> 01:22:32,650 +وناقص اتنين اتحاد اتنين وانفنتي مش موجود في الفترة + +786 +01:22:32,650 --> 01:22:37,110 +هذهيبقى كيف؟ احنا بيجيب قيمة الدالة في element + +787 +01:22:37,110 --> 01:22:40,830 +موجود في domainها، هذا مش موجود في domainها، إذا + +788 +01:22:40,830 --> 01:22:45,290 +لا يمكن لهذه أن يحصل، طب واحد قاللي لا ماجهش في + +789 +01:22:45,290 --> 01:22:49,630 +باله الكلام هذا، اخرج قاللي احنا أخذنا اللي وين + +790 +01:22:49,630 --> 01:22:55,090 +خارج قسمة الاتنين هايه، تمام؟ بقولكوا إيهوقال حطلي + +791 +01:22:55,090 --> 01:22:59,270 +واحد بقوله واحد واربعة خمسة واحد تربيه بواحد نقص + +792 +01:22:59,270 --> 01:23:04,590 +اربعة نقص ثلاثة سالب خمسة ع تلاتة does not exist + +793 +01:23:04,590 --> 01:23:09,210 +كمية تخيلية مظبوط يبقى لا يمكن نقدر يجيب قال لي + +794 +01:23:09,210 --> 01:23:18,800 +بعد هيك هات ليه؟فعل جي جاهز + +795 +01:23:18,800 --> 01:23:26,480 +هي الجدر التربيعي لتلاتة زائد أربعة على تلاتة + +796 +01:23:26,480 --> 01:23:32,320 +تربيع ناقص أربعة مظبوط يعني هذا الجدر التربيعي + +797 +01:23:32,320 --> 01:23:39,900 +لسبعة على تسعة ناقص أربعة سبعة أخمس يبقى existماشي + +798 +01:23:39,900 --> 01:23:48,040 +يا سيدي طيب لحد هنا تمام انتهينا من جزء من النقطة + +799 +01:23:48,040 --> 01:23:52,560 +الأولى اللي هي ال combining functions بدنا ننتقل + +800 +01:23:52,560 --> 01:23:57,460 +إلى النقطة الثانية في نفس ال combining function + +801 +01:23:57,460 --> 01:24:00,040 +وهي very important + +802 +01:24:06,110 --> 01:24:10,190 +هيش النقطة الثانية لل composition of functions + +803 +01:24:10,190 --> 01:24:18,290 +اللي كنتوا بتسموها f circle g او f بعد g ايوة دمان + +804 +01:24:18,290 --> 01:24:24,530 +ال f على g ماله ابدا دمان ال f التقاطة تبع ال + +805 +01:24:24,530 --> 01:24:29,090 +اتنين اللي كتبنا تحت بده الشيء القيم اللي بتخلي g + +806 +01:24:29,090 --> 01:24:33,950 +تساوي صفر الجدر التربية ل x تربية نقص 4 او اكتشف + +807 +01:24:33,950 --> 01:24:40,360 +بيساوي صفرعند x اتنين و سالب اتنين لأنه اربعة ناقص + +808 +01:24:40,360 --> 01:24:43,580 +اربعة بصفر ناقص اتنين كل تربية اربعة ناقص اربعة + +809 +01:24:43,580 --> 01:24:47,020 +بزيرو يبقى بدنا نشيل اتنين و سالب اتنين من ال + +810 +01:24:47,020 --> 01:24:51,040 +interval سالب اربعة لغاية سالب اتنين اتحاد اتنين و + +811 +01:24:51,040 --> 01:24:54,760 +infinity يعني بصير مفتوح ان عند سالب اتنين و اتنين + +812 +01:24:54,760 --> 01:25:03,070 +ليس الاطيب بنيجي الأن لتكملة النقطة الأولى اللي هي + +813 +01:25:03,070 --> 01:25:08,450 +ال composite functions يبقى بالدالي لحاجة اسمها ال + +814 +01:25:08,450 --> 01:25:12,130 +composite functions + +815 +01:25:12,130 --> 01:25:15,250 +definition + +816 +01:25:15,250 --> 01:25:18,310 +F + +817 +01:25:18,310 --> 01:25:25,130 +ال F عند ال G R + +818 +01:25:26,470 --> 01:25:34,830 +two functions recomposite + +819 +01:25:34,830 --> 01:25:38,430 +function + +820 +01:25:38,430 --> 01:25:45,410 +الدلة التركيبية او الدلة المحصلة لل F composition + +821 +01:25:45,410 --> 01:25:49,670 +G is defined by + +822 +01:25:55,990 --> 01:26:02,750 +إذا كانت الـ composition جي كمعاملة من X يساوي F + +823 +01:26:02,750 --> 01:26:20,990 +للجي من X بحيث أن X موجودة في دمين الجي مرة + +824 +01:26:20,990 --> 01:26:21,370 +تانية + +825 +01:26:24,890 --> 01:26:29,170 +الكمبوزيت فانكشن الدالة المحاصلة أو الدالة + +826 +01:26:29,170 --> 01:26:34,890 +التركيبية يعني انا عندى دالتين بدى اركب منهم دالة + +827 +01:26:34,890 --> 01:26:39,050 +جديدة دالة واحدة دى من الدالتين اللى موجودة او تلت + +828 +01:26:39,050 --> 01:26:42,410 +دول بدى اركب منهم دالة او اربعة او ما إلى ذلك + +829 +01:26:48,990 --> 01:26:54,130 +الدالة التركيبية او الدالة المحاصلة بدي اعطيها رمز + +830 +01:26:54,130 --> 01:26:59,890 +F circle G كنتوا بتقراوها في التانوي F بعد G او F + +831 +01:26:59,890 --> 01:27:08,950 +circle Gفي علمنا F composition G F composition G + +832 +01:27:08,950 --> 01:27:12,390 +Circle بس عشانها دائرة صغيرة بنقول Circle أما في + +833 +01:27:12,390 --> 01:27:17,550 +الحقيقة بنقول F composition G is defined by + +834 +01:27:17,550 --> 01:27:24,670 +بنعرفها كتالة F composition G of X يساوي F of G of + +835 +01:27:24,670 --> 01:27:29,470 +X بعيثة X موجودة وين في domain الجي خلّي بالك + +836 +01:27:29,470 --> 01:27:34,200 +معايا هناالان انا بقول if composition D of X مين + +837 +01:27:34,200 --> 01:27:39,740 +اقرب واحد علي X؟ if والله جي جي يبقى جي هتأثر علي + +838 +01:27:39,740 --> 01:27:45,780 +X يبقى X لازم تكون وين ومن الجي حتى تقدر تأثر + +839 +01:27:45,780 --> 01:27:52,730 +عليها طيب أثرنا ب G علي X صارت مين؟G of X إذاً G + +840 +01:27:52,730 --> 01:27:58,610 +of X صار element جديد في domain main الدالة F حتى + +841 +01:27:58,610 --> 01:28:03,810 +تقدر F تأثر عليها نوضح لك هذا الكلام بالرسم لو + +842 +01:28:03,810 --> 01:28:11,250 +عندي هنا ست والست سميتها A والست تانية سميتها B + +843 +01:28:11,250 --> 01:28:19,800 +والست ثالثة سميتها C خلي بالك معايا كويسالان من A + +844 +01:28:19,800 --> 01:28:29,960 +الى B في عندي دالة اسمها G من B الى C في عندي دالة + +845 +01:28:29,960 --> 01:28:39,330 +اسمها F الان لو كان عندي element هنا اسمه Xيبقى + +846 +01:28:39,330 --> 01:28:44,250 +هذا ال element موجود في domain main إذا جي بتأثر + +847 +01:28:44,250 --> 01:28:49,270 +على كل عناصر a إذا هتأثر على هذا ال element يبقى + +848 +01:28:49,270 --> 01:28:55,230 +جي لما تحث .. لما تأثر على x بده يظهرله صورة في بي + +849 +01:28:55,230 --> 01:29:02,650 +اسمها mainG of X هي صورة الـ Element X اللي موجود + +850 +01:29:02,650 --> 01:29:09,410 +في A صورته ظهرت في B بي هو domain مين يبقى ال F + +851 +01:29:09,410 --> 01:29:14,170 +هتأثر على هذا ال element اللي موجود في domainها + +852 +01:29:14,170 --> 01:29:21,630 +اللي موجود في domainها وتخلي صورته هناF of ال + +853 +01:29:21,630 --> 01:29:26,710 +element اللي موجود في domainها اللي هو G of X + +854 +01:29:26,710 --> 01:29:34,270 +وكأنه بيه مهادي مش هتظهر كأنه بده يصير ال X بده + +855 +01:29:34,270 --> 01:29:39,390 +يجي لل element اللي عندنا هذا اللي اسمه main F of + +856 +01:29:39,390 --> 01:29:47,110 +G of X وبالتالي F composition G of X بده يسوي F of + +857 +01:29:47,110 --> 01:29:59,300 +G of Xطيب سؤال هل ال F composition G يساوي G + +858 +01:29:59,300 --> 01:30:04,600 +composition F؟ فرقة السما على الأرض هنا ال element + +859 +01:30:04,600 --> 01:30:06,840 +بيكون في ال domain ال G هنا ال element في ال + +860 +01:30:06,840 --> 01:30:14,640 +domain ال F يبقى هذه اللي لا يمكن أن تساوي هذهيبقى + +861 +01:30:14,640 --> 01:30:19,940 +بقوله هنا in general على وجه العموم ال F + +862 +01:30:19,940 --> 01:30:23,920 +composition G لا يساوي G composition F السؤال + +863 +01:30:23,920 --> 01:30:30,790 +الثاني احنا جبنادالة جديدة من الدالتين الأصليتين + +864 +01:30:30,790 --> 01:30:35,650 +زي ما كنا قبل قليل بنضيف دالة جديدة إذا بدنا ال + +865 +01:30:35,650 --> 01:30:40,570 +domain تبعها وفتحلي كويس لإن كتير من الشباب بضلوا + +866 +01:30:40,570 --> 01:30:44,690 +يسألوا فيها كتير عملية سهلة جدابس مش عارف ليش + +867 +01:30:44,690 --> 01:30:49,990 +بيكتروا فيها السؤال الان بدنا نيجي لل domain بتابع + +868 +01:30:49,990 --> 01:30:56,690 +ال F composition G بدي اعرفه تعريف مين هو الان هذه + +869 +01:30:56,690 --> 01:31:02,920 +مشان تأثر على element بدي اقول كل العناصر Xيبقى x + +870 +01:31:02,920 --> 01:31:07,400 +هوين بده يكون موجود؟ في domain الجي يبقى كل + +871 +01:31:07,400 --> 01:31:14,580 +العناصر x بحيث أن x موجود في domain الجي وفي نفس + +872 +01:31:14,580 --> 01:31:20,840 +الوقت and ال g of x هوين بده يكون موجود؟ في domain + +873 +01:31:20,840 --> 01:31:26,760 +ال F موجود في domain ال F يبقى هذا تعريف تبع + +874 +01:31:26,760 --> 01:31:32,240 +الكوميزيون ولا رياسة منهاكل العناصر اللى موجود فى + +875 +01:31:32,240 --> 01:31:36,420 +domain الـG صار عنده Geobox يبقى Geobox بديها تكون + +876 +01:31:36,420 --> 01:31:41,820 +وان موجودة فى domain الـF خلص التعريف بالمهم مش + +877 +01:31:41,820 --> 01:31:46,480 +التعريف هو كيف اتطبق لمين التعريف إذا سنذهب إلى + +878 +01:31:46,480 --> 01:31:52,800 +مثال مباشرة example عادى + +879 +01:31:52,800 --> 01:31:58,590 +نثبت المعلومة هذه قبل ما نمشيالمثال بيقول ما ياتي + +880 +01:31:58,590 --> 01:32:05,250 +let فبرا هعطيك على هذه النقطة بدل المثال تلاتة وكل + +881 +01:32:05,250 --> 01:32:11,550 +واحد فني بيختلف عن الثاني ففتحه كويس ودجج معاه let + +882 +01:32:11,550 --> 01:32:25,910 +اللي هو ال f of x بدل يسوى x²-1 andالـ G of X بدي + +883 +01:32:25,910 --> 01:32:42,290 +ساوي الـ Square Root لمن؟ للخمسة ناقص الـ X نمرا + +884 +01:32:42,290 --> 01:32:50,790 +A بدي الـ F composition G نمرا B بدي الـ G + +885 +01:32:50,790 --> 01:32:59,780 +composition Fنمرة C بد ال G composition G نمرة D + +886 +01:32:59,780 --> 01:33:09,900 +بد ال domain ال F composition G and domain ال G + +887 +01:33:09,900 --> 01:33:11,620 +composition G + +888 +01:33:40,400 --> 01:33:45,080 +هلا مالك هنافتح معايا كويس مش هشوف كيف بنحسب + +889 +01:33:45,080 --> 01:33:52,760 +الشغلات هذه الان بدنا f composition g as a + +890 +01:33:52,760 --> 01:34:01,240 +function of x شو شكلهفبجي بقول شكله كالتالي F of G + +891 +01:34:01,240 --> 01:34:08,380 +of X طبعا الان G of X موجودة عندي يبقى بشيل G of X + +892 +01:34:08,380 --> 01:34:15,240 +و بحط قيمة مكانها يبقى F of ال G of X هي عبارة عن + +893 +01:34:15,240 --> 01:34:22,680 +الجذر التربية إلى مين لخمسة ناقص ال Xبعدك اسمع + +894 +01:34:22,680 --> 01:34:29,540 +شوية هنا بيقول ال F لما تأثر على العنصر يسوى مربع + +895 +01:34:29,540 --> 01:34:34,860 +العنصر مطروح منه يبقى F لما تأثر على هذا العنصر + +896 +01:34:34,860 --> 01:34:42,020 +مربع هذا العنصر مطروح منه واحد يبقى هذا الكلام بده + +897 +01:34:42,020 --> 01:34:49,440 +يصير خمسة ناقص X تحت الجذر الكل تربية بده أشيل منه + +898 +01:34:49,440 --> 01:34:56,580 +واحدتمام؟ يبقى هذا شو بده يساوي؟ هذا خمسة ناقص X + +899 +01:34:56,580 --> 01:35:02,080 +ناقص واحد يبقى النتيجة أربع ناقص X + +900 +01:35:05,260 --> 01:35:09,560 +بنفس الطريقة يجيب الجي جي جي جي جي جي جي جي جي جي + +901 +01:35:09,560 --> 01:35:22,360 +جي جي جي جي جي جي جي جي جي جي + +902 +01:35:22,360 --> 01:35:25,980 +جي + +903 +01:35:34,480 --> 01:35:39,840 +الان جي لما تأثر على العنصر يساوي الجذري التربيعي + +904 +01:35:39,840 --> 01:35:45,860 +لخمسة ناقص هذا العنصر يبقى هذا بده يساوي الجذري + +905 +01:35:45,860 --> 01:35:53,760 +التربيعي لخمسة ناقص هذا العنصر لإكس تربية ناقص + +906 +01:35:53,760 --> 01:36:02,260 +واحدهذا بده يصير الجدر التربية لخمسة ناقص X تربية + +907 +01:36:02,260 --> 01:36:10,200 +زي واحد يبقى الجدر التربية لستة ناقص X تربية اللي + +908 +01:36:10,200 --> 01:36:16,560 +مافهمش يتابع معاه نمره C بده جي composition جي + +909 +01:36:16,560 --> 01:36:23,070 +كذلكبعد هيك بيضلش هوضر ولا لوحد، بدل السؤال تلاتة + +910 +01:36:23,070 --> 01:36:32,170 +على نفس المفهوم، يبقى هذا G لـG of X يبقى G لأ، + +911 +01:36:32,170 --> 01:36:35,670 +بدي أشيل الـG of X و أحط قيمة اللي هو الجذر + +912 +01:36:35,670 --> 01:36:44,560 +الترفيعي للخمسة ناقص Xوكأن هذا ال element كله أصبح + +913 +01:36:44,560 --> 01:36:50,000 +عنصر في domain main الجي جي لما اتأثر على عنصر + +914 +01:36:50,000 --> 01:36:54,180 +اللي في domainها بده يساوي الجدري التربيعي لخمسة + +915 +01:36:54,180 --> 01:37:00,420 +ناقص هذا العنصر يبقى هذا بده يساوي الجدري التربيعي + +916 +01:37:00,420 --> 01:37:09,240 +لخمسة ناقص هذا العنصر خمسة ناقص Xواضح؟ هاي بدل + +917 +01:37:09,240 --> 01:37:12,980 +سؤال اتنين تلاتة حلنا لك كيف تحسب main ال + +918 +01:37:12,980 --> 01:37:18,500 +composition وبالتالي خلصنا A وB وC الآن بدنا نجيب + +919 +01:37:18,500 --> 01:37:22,820 +ال domain بشان نجيب ال domain بدنا domain كل واحدة + +920 +01:37:22,820 --> 01:37:28,320 +فيهم في الأول يبقى قبل ما نيجي للباقي بدي domain + +921 +01:37:28,320 --> 01:37:36,670 +ال F يسوّن كفايةفى نقطة لفها دى مش معرفة عندها + +922 +01:37:36,670 --> 01:37:42,590 +يبقى معناها كل ال real number يبقى من سالب + +923 +01:37:42,590 --> 01:37:51,010 +infinity إلى infinity ماشي بدنا domain الجى كل + +924 +01:37:51,010 --> 01:37:56,770 +العناصر X بحيث N بدى كل القيمة اللى تحت الجدرة + +925 +01:37:56,770 --> 01:38:03,550 +تبقى مالهاأكبر من أو تساوي الـ zero بدي كل الخمسة + +926 +01:38:03,550 --> 01:38:10,010 +نقص X greater than or equal to zero يعني كل + +927 +01:38:10,010 --> 01:38:22,820 +العناصر X بحيث أنيبقى X أقل + +928 +01:38:22,820 --> 01:38:30,340 +من أو تسوى خمسة بسالب infinity لغاية خمسة + +929 +01:38:37,960 --> 01:38:42,280 +تمام؟ جيبنا ال two domains يبقى حلينا المعضلة و + +930 +01:38:42,280 --> 01:38:46,840 +بلش عندي إلا أحسب كده ال domain تبع كل واحدة فيهم + +931 +01:38:46,840 --> 01:38:53,100 +إذا بيداجي لنمرى D بدي ال domain بتبع ال F + +932 +01:38:53,100 --> 01:38:56,380 +composition G و لا ال G composition .. ال F + +933 +01:38:56,380 --> 01:39:04,470 +composition Gالتعريف بيقولك كل العناصر X بحيث ان X + +934 +01:39:04,470 --> 01:39:11,790 +موجودة في دمين الـG and الـG of X موجودة في دمين + +935 +01:39:11,790 --> 01:39:17,630 +الـF مش هيك التعريف بدنا نبدأ نطبق التعريف فتحه + +936 +01:39:17,630 --> 01:39:23,570 +كيف بدنا نطبق التعريفالـ X هذه موجودة في domain + +937 +01:39:23,570 --> 01:39:30,210 +الجي وين domain الجي؟ أيه؟ يبقى من سالب infinity + +938 +01:39:30,210 --> 01:39:38,180 +لغاية خمسة وفي نفس الوقت andالـ g of x main هي + +939 +01:39:38,180 --> 01:39:44,440 +اللى عندنا اللى هى الجدرى التربية الى خمسة ناقص x + +940 +01:39:44,440 --> 01:39:49,380 +موجودة فى domain ال F domain ال F من وين لأ وين من + +941 +01:39:49,380 --> 01:39:57,400 +سالب infinity الى infinity خلصنا هذا التطبيق حرفى + +942 +01:39:57,400 --> 01:40:01,860 +بعد ما خلصنا التطبيق الحرفى بده المخ يبدأ يشتغل + +943 +01:40:02,300 --> 01:40:08,840 +بنشوف كيف بده يشتغل هاد يا شباب بنزلها زي ما هين X + +944 +01:40:08,840 --> 01:40:12,360 +موجودة من سالب infinity لغاية أخرى هاد مافيش مشكلة + +945 +01:40:12,360 --> 01:40:18,500 +المشكلة هو هنا مدام X هنا بدي أطلع X هنا موجودة في + +946 +01:40:18,500 --> 01:40:23,670 +فترة وبعد هيك بجيب التقاطع بين الفترتينبكون خلصنا، + +947 +01:40:23,670 --> 01:40:29,090 +مظبوط؟ طب مشان نخلص، هذا الجذر فيه قبله إشارة + +948 +01:40:29,090 --> 01:40:35,530 +سالم؟ مافيش قبله إشارة سالم، إذا هذا فيه جزء موجب + +949 +01:40:35,530 --> 01:40:42,030 +و جزء سالم، إذا لا يمكن لهذا يخد لي أي قيمة قبل ال + +950 +01:40:42,030 --> 01:40:47,770 +zero، صح ولا لا؟بس ممكن يكون zero، مظبوط؟ يعني + +951 +01:40:47,770 --> 01:40:55,230 +معنى هذا الكلام and الجذر التربيهي لخمسة ناقص X + +952 +01:40:55,230 --> 01:41:03,830 +بدي يكون أكبر من أو يساوي ال zero سكت الشعب وسكت + +953 +01:41:03,830 --> 01:41:10,020 +أهل الكهف طيب خليكم معاه مرة تانيةبقول مرة تانية + +954 +01:41:10,020 --> 01:41:14,380 +صح صح هذي very important بتجيبها لامتحانات كتير صح + +955 +01:41:14,380 --> 01:41:20,460 +صح معايا كويس الحين هذي نزلت كما هي تمام هذه + +956 +01:41:20,460 --> 01:41:25,180 +الهيجيوفكس بديها تكون موجودة في domain ال F كتبنا + +957 +01:41:25,180 --> 01:41:31,800 +domain ال Fهل الجدر مسبوق بإشارة سالب؟ لا، يعني + +958 +01:41:31,800 --> 01:41:37,040 +هذا الجدر اللي لا يأخذ إلا قيمًا يبقى من سالب + +959 +01:41:37,040 --> 01:41:41,620 +infinity لغاية zero يبعتلك الله، صح؟ يعني يبدو + +960 +01:41:41,620 --> 01:41:47,860 +يكون موجود من وين؟ من zero إلى infinity، يعني هه، + +961 +01:41:47,860 --> 01:41:54,220 +نعملها كخطوطين موجود في الفترة من zero لغاية + +962 +01:41:54,220 --> 01:42:00,450 +infinity، أظن فيش مشكلة هنا؟خلاصنا؟ يعني هذا الجذر + +963 +01:42:00,450 --> 01:42:06,610 +فلو كان قبله إشارة سالم بروح باخد الفترة من سالم + +964 +01:42:06,610 --> 01:42:10,410 +infinity إلى وين لغاية zero، وابحثت هذه؟ + +965 +01:42:14,690 --> 01:42:20,690 +بنزلها زي ما هي مش هغير فيها ولا حاجة ان هذا + +966 +01:42:20,690 --> 01:42:26,150 +معناته ان الجدر التربية لخمسة ناقص x أكبر من أو + +967 +01:42:26,150 --> 01:42:31,700 +تساوي ال zeroمظهر؟ مش عارف معناها؟ طيب هذه بدأ + +968 +01:42:31,700 --> 01:42:39,360 +تنزل كما هي وهي الأن ربع للطرفين بصير عندك خمسة + +969 +01:42:39,360 --> 01:42:46,000 +نقص X greater than or equal to zero نزل هذه زي ما + +970 +01:42:46,000 --> 01:42:54,800 +هي and هاتلي X للطرفين بصير مالها خمسة أكبر من أو + +971 +01:42:54,800 --> 01:43:00,290 +تساوي ال X يعني مين؟نفس الفترة اللي عندنا هذه يعني + +972 +01:43:00,290 --> 01:43:06,590 +كأنه هذه كل العناصر x بحيث أن x موجودة من سلب + +973 +01:43:06,590 --> 01:43:14,630 +infinity لغاية خمسة and ال x موجودة تمام من سلب + +974 +01:43:14,630 --> 01:43:20,080 +infinity لغاية خمسةيبقى موجودة في الفترة التانية + +975 +01:43:20,080 --> 01:43:24,460 +طب ما هي نفس الفترة صح ولا لا إذا انت قاطع الفترة + +976 +01:43:24,460 --> 01:43:30,540 +مع نفسها هي نفس الفترة إذا نفس ال interval من سالب + +977 +01:43:30,540 --> 01:43:38,100 +infinity لغاية خمسة بالشكل اللي عندنا هذا هذه مهما + +978 +01:43:38,100 --> 01:43:43,890 +اتحلل بسيطة تمام طيب بدنا نيجي نشوف التانيةالتانية + +979 +01:43:43,890 --> 01:43:49,650 +يا ترى بدأ تطلع نفس الفترة والله بتختلف عنها هذا + +980 +01:43:49,650 --> 01:43:57,050 +ما سنجيب عليه فورا يبقى مضاجي الآن اخر حاجة domain + +981 +01:43:57,050 --> 01:44:05,390 +الجي composition جي يبقى كل العناصر x بحيث ان x + +982 +01:44:05,390 --> 01:44:13,770 +موجودة في domain الجي andالـ G of X موجودة في دمين + +983 +01:44:13,770 --> 01:44:18,370 +الـ G يبقى + +984 +01:44:18,370 --> 01:44:24,890 +كل العناصر X بحيث ان X موجودة وين دمين الـ G؟ هاي + +985 +01:44:24,890 --> 01:44:29,850 +دمين الـ G من سالب Infinity إلى خمسة من سالب + +986 +01:44:29,850 --> 01:44:37,760 +Infinity إلى خمسة andالـ g of x اللى هى الجدرى + +987 +01:44:37,760 --> 01:44:44,500 +التربية اللى خمسة ماقص x كما هى موجودة فى domain + +988 +01:44:44,500 --> 01:44:49,100 +main فى domain الـ g domain الـ g اللى هى من سالب + +989 +01:44:49,100 --> 01:44:57,980 +infinity لغاية كده لغاية خمسةهذه الآن بنزلها كما + +990 +01:44:57,980 --> 01:45:05,720 +هي وباقي بقول and هذا الجدر مسبوق بإشارة موجب يعني + +991 +01:45:05,720 --> 01:45:10,400 +ماعنديش سلب جابله إذا من سلب infinity لغاية zero + +992 +01:45:10,400 --> 01:45:14,940 +يبعتلك الله زي ما حكينا هنا يبقى وضل من ويل لويلمن + +993 +01:45:14,940 --> 01:45:22,640 +zero لخمسة بس يبقى and الجدر تبع الخمسة ناقص x + +994 +01:45:22,640 --> 01:45:30,640 +موجود في ال closed interval من zero لغاية خمسةليش؟ + +995 +01:45:30,640 --> 01:45:36,340 +لأنه بالموجة بيبقى استبعدنا كل السالب بالمرة طيب + +996 +01:45:36,340 --> 01:45:44,660 +هذه بنزلها زي ما هي and الجدر التربية ل 5-x أقل من + +997 +01:45:44,660 --> 01:45:52,630 +و قد يساوي 5و أكبر من و قد يساوي zero هذه بنزلها + +998 +01:45:52,630 --> 01:46:00,550 +زي ما هي and ربع الطرفين بصير خمسة ناقص x أقل من + +999 +01:46:00,550 --> 01:46:10,190 +أو يساوي 125 هذه بنزلها زي ما هيعشان اضيف السالب + +1000 +01:46:10,190 --> 01:46:17,990 +خمسة للثلاثة اطراف السالب خمسة اقل من او يسوى + +1001 +01:46:17,990 --> 01:46:21,290 +السالب X اقل من او يسوى + +1002 +01:46:33,500 --> 01:46:39,400 +طيب هادي بالصير تنزل هادي زي ما هي هادي ان اضرب + +1003 +01:46:39,400 --> 01:46:46,410 +كله في شر السلب لان انا بدي اكسب الموجةخمسة أكبر + +1004 +01:46:46,410 --> 01:46:55,830 +من X أكبر من سالب عشرين و جفلنا تمام؟ يبقى هذه + +1005 +01:46:55,830 --> 01:47:02,550 +صارت كل العناصر X بحيث أن X موجودة من سالب + +1006 +01:47:02,550 --> 01:47:06,910 +Infinity لغاية خمسة and + +1007 +01:47:09,950 --> 01:47:15,990 +الـ X موجودة طلع هذه بتظبطها أكبر من أو يساوي سالب + +1008 +01:47:15,990 --> 01:47:19,950 +عشرين وأقل من أو يساوي خمسة صغيرة بنكتبها في الأول + +1009 +01:47:19,950 --> 01:47:28,850 +يبقى هذه سالب عشرين وهذه ما لها أقل من أو يساوي X + +1010 +01:47:28,850 --> 01:47:45,470 +وهذه أقل من أو يساوي خمسة جلبت بس الوضعX موجودة + +1011 +01:47:45,470 --> 01:47:54,890 +في الفترة من سالب عشرين لغاية خمسةيبقى انا عند هذا + +1012 +01:47:54,890 --> 01:48:02,570 +ال real line هذا من عند الخمسة بدأ ترجع لين؟ لل + +1013 +01:48:02,570 --> 01:48:08,150 +infinity وهذا بيجينا قبلها هنا ال zero هذا بيقول X + +1014 +01:48:08,150 --> 01:48:13,310 +موجودة من سالب عشرين لغاية خمسة سالب عشرين وين بدأ + +1015 +01:48:13,310 --> 01:48:19,010 +تجينا؟ تجينا هنا سالب عشرينيعني على الفترة اللي + +1016 +01:48:19,010 --> 01:48:26,830 +عندنا هذه فقط لا غير هذه من هنا هك لهنا أين الفترة + +1017 +01:48:26,830 --> 01:48:32,710 +المشتركة بينهم؟ سالب عشرين دغاية خمسة يعني كأن هذه + +1018 +01:48:32,710 --> 01:48:42,150 +X موجودة في سلب Infinity وخمسة تقاطع الفترة سالب + +1019 +01:48:42,150 --> 01:48:50,850 +عشرين وخمسةاللي هو بده يساوي عنه سالب عشرين ولغاية + +1020 +01:48:50,850 --> 01:48:56,530 +خمسة، سالب عشرين لغاية خمسة، خلاص؟ واضح عظم الشغل + +1021 +01:48:56,530 --> 01:49:02,090 +هيك؟ طيب، لسه لا يزال عندنا مثالين فكرتهم في نفس + +1022 +01:49:02,090 --> 01:49:05,810 +الموضوع بس بأفكار مختلفة، هعطيكوا العزف + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RZIGsgvo6gk_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RZIGsgvo6gk_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..6fa39618ca7245f99b20f554613ba5854519ea59 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/RZIGsgvo6gk_postprocess.srt @@ -0,0 +1,3328 @@ +1 +00:00:21,400 --> 00:00:26,060 +بسم الله الرحمن الرحيم فبنكمل الآن ما ابتدأناه في + +2 +00:00:26,060 --> 00:00:30,060 +section خمسة اتنين المرة الماضية اخر حاجة اتكلمناه + +3 +00:00:30,060 --> 00:00:34,600 +هي على الريمان صم ولم نعطي مثال على ذلك وقلنالكوا + +4 +00:00:34,600 --> 00:00:39,860 +المثال بده نص ساعة فهيبنى ناخد من الآن هذا المثال + +5 +00:00:39,860 --> 00:00:42,900 +وبهذا المثال ينتهي هذا ال section وينتقل ال + +6 +00:00:42,900 --> 00:00:48,350 +section اللى وراه اللى يعتمد عليه كذلكيبقى الريمان + +7 +00:00:48,350 --> 00:01:03,030 +صان مهم جدا في خمسة اتنين وخمسة تلاتة + +8 +00:01:03,110 --> 00:01:08,370 +المطلوب الأول يقول هاتلي الصيغة for the remand sum + +9 +00:01:08,370 --> 00:01:13,090 +لمجموع ريمان اللى بنحصل عليه لما نجسم الفترة اللى + +10 +00:01:13,090 --> 00:01:19,010 +عندنا الى n equal sub intervals الى مجموعة عددها n + +11 +00:01:19,290 --> 00:01:26,850 +من الفترات الجزئية المتساوية ثم نستخدم ال right + +12 +00:01:26,850 --> 00:01:32,870 +hand in point for each CK تمام هذا المطلوب الأول + +13 +00:01:32,870 --> 00:01:36,810 +مطلوب الثاني جليهات لل limit للمقدار اللي بيطلع + +14 +00:01:36,810 --> 00:01:40,690 +عندك لما ال N بده تروح للمالة نهايةهذه ال limit + +15 +00:01:40,690 --> 00:01:45,330 +بتعطينا فعلا مساحة الحقيقية المحصورة بين المنحنة + +16 +00:01:45,330 --> 00:01:52,170 +ومحور X على الفترة من 0 لغاية 3 خلّينا نذكر شو كان + +17 +00:01:52,170 --> 00:02:04,900 +ريمان صاممجموع المربع سام او مربع رول او مربع رول + +18 +00:02:04,900 --> 00:02:09,800 +او + +19 +00:02:09,800 --> 00:02:14,350 +مربع رولسب قولنا هو summation من k تساوية 1 لغاية + +20 +00:02:14,350 --> 00:02:19,650 +ال N لل F of Ck Delta Xk وقلنا هو عبارة عن F of C1 + +21 +00:02:19,650 --> 00:02:25,310 +Delta X1 زي F of C2 Delta X2 زي F of Cn Delta Xn + +22 +00:02:25,310 --> 00:02:31,350 +هذا ما قلناه المرة الماضية بدنا نعطي مثال عليهبس + +23 +00:02:31,350 --> 00:02:34,190 +الفرق بين هال مثال وما قولنا المرة الماضية قولنا + +24 +00:02:34,190 --> 00:02:39,130 +لك ال interval لما نعملها partition ليس بالضرورة + +25 +00:02:39,130 --> 00:02:42,810 +ال sub interval يكونوا مالهم متساويات، هذا السؤال + +26 +00:02:42,810 --> 00:02:47,050 +قال لي لأ خدهم متساوياتطيب نتيجة لو أخدها مش + +27 +00:02:47,050 --> 00:02:50,110 +متساويات بيزهجوني في الاحسابات بس لما أخدهم + +28 +00:02:50,110 --> 00:02:55,670 +متساويات بيصير أسهل كتير في عملية الحساب فإيش بقول + +29 +00:02:55,670 --> 00:03:02,530 +يجسم الفترة اللي عندك A إلى N من الفترات الجزئية + +30 +00:03:02,530 --> 00:03:07,690 +المتساوية وخدلي ال CK قولنا المرة اللي فاتت ال CK + +31 +00:03:07,690 --> 00:03:11,350 +بتاخدها داخل ال intervalفي اول interval ماشي داخل + +32 +00:03:11,350 --> 00:03:14,570 +ال interval ماشي في نهاية ال interval ماشي انا + +33 +00:03:14,570 --> 00:03:19,110 +بقول خدها في نهاية main ال end point عشان نشوف هذا + +34 +00:03:19,110 --> 00:03:23,830 +الكلام على الطبيعة بدنا نروح نرسم رسمة المسألة + +35 +00:03:23,830 --> 00:03:27,990 +اللي عندنا يبقى لو جينا يقولنا هذا محور X وهذا + +36 +00:03:27,990 --> 00:03:32,910 +محور Y الدالة اللي عندنا F of X يسوى X تقريبا يبقى + +37 +00:03:32,910 --> 00:03:36,770 +Parabola F of X يسوى X تقريبا زاد واحد shift إلى + +38 +00:03:36,770 --> 00:03:41,160 +أعلى بمقدار واحديبقى بدأجي أقول هي ال parabola + +39 +00:03:41,160 --> 00:03:46,980 +اللي علناها ذلكيبقى هذه النقطة هي واحد وهذه زيرو + +40 +00:03:46,980 --> 00:03:53,380 +وانا بدي على الفترة فقط من غاية واحد لغاية تلاتة + +41 +00:03:53,380 --> 00:03:57,160 +بعد التلاتة ماليش علاقة فيه جابلي ال zero ماليوش + +42 +00:03:57,160 --> 00:04:01,040 +علاقة طبعا لو جميت جيت كملت ال parabola بصير + +43 +00:04:01,040 --> 00:04:04,800 +بالشكل اننا ماليش علاقة فيها احنا بس بدنا نتقيد من + +44 +00:04:04,800 --> 00:04:09,340 +وين لوين من zero إلى تلاتة اذا بدي اجسم الفترة من + +45 +00:04:09,340 --> 00:04:15,320 +zero إلى تلاتة ل in equal subيبقى الـ Zero هذي بده + +46 +00:04:15,320 --> 00:04:21,280 +يسميها mean الـ X non بده ياخد هنا X one هنا بده + +47 +00:04:21,280 --> 00:04:28,720 +ياخد X two اللي هي جدها تماما هنا بده ياخد X three + +48 +00:04:28,720 --> 00:04:36,560 +و هكذا لغاية ما نصل الى XN minus ال one والتلاتة + +49 +00:04:36,560 --> 00:04:43,270 +اللي هي main ال XNيبقى هذه النقطة اللى عندنا جسمنا + +50 +00:04:43,270 --> 00:04:50,050 +هذا مساحة الى الأقسام او ما يشبه المستطيلات اللى + +51 +00:04:50,050 --> 00:04:55,650 +انت شفها وكلها ايه جت بعضها يعني delta x واحد جت + +52 +00:04:55,650 --> 00:04:57,570 +delta x اتنين جت delta x اتنين جت delta x اتنين جت + +53 +00:04:57,570 --> 00:04:57,950 +delta x اتنين جت delta x اتنين جت delta x اتنين جت + +54 +00:04:57,950 --> 00:04:58,410 +delta x اتنين جت delta x اتنين جت delta x اتنين جت + +55 +00:04:58,410 --> 00:04:59,430 +delta x اتنين جت delta x اتنين جت delta x اتنين جت + +56 +00:04:59,430 --> 00:04:59,450 +delta x اتنين جت delta x اتنين جت delta x اتنين جت + +57 +00:04:59,450 --> 00:05:01,730 +delta x اتنين جت delta x اتنين جت delta x اتنين جت + +58 +00:05:01,730 --> 00:05:07,690 +delta x اتنين جت delta x اتنين جت deltaهذه المسافة + +59 +00:05:07,690 --> 00:05:17,210 +Delta X2 هذه المسافة Delta X3 و هكذا تمام؟ طيب + +60 +00:05:17,210 --> 00:05:27,850 +بدنا نيجي ل .. يبقى بالدقج أقول the width of + +61 +00:05:27,850 --> 00:05:33,390 +each sub interval + +62 +00:05:37,340 --> 00:05:42,500 +دلتا اكس بده يساوي طول المسافة كلها على عدد + +63 +00:05:42,500 --> 00:05:47,120 +التقسيمات تلاتة نقص زيرو على ان اللي هو جد ياشي + +64 +00:05:47,120 --> 00:05:52,060 +تلاتة على ان إذا دلتا اكس هذه بتلاتة على ان دلتا + +65 +00:05:52,060 --> 00:05:56,160 +اكس هذه بتلاتة على ان دلتا اكس هذه بتلاتة على ان + +66 +00:05:56,160 --> 00:06:04,170 +إلى آخرينهيجب ان نجسم الفترة الى N من ال equal sub + +67 +00:06:04,170 --> 00:06:06,290 +intervals زى ما انت شايف + +68 +00:06:28,170 --> 00:06:36,750 +X2 هي عبارة عن C2 X3 عبارة عن مين؟ C3 طيب السؤال + +69 +00:06:36,750 --> 00:06:42,590 +هو حد بيقدر أقول يجدش طول تبع C1 Delta X اللي هو 3 + +70 +00:06:42,590 --> 00:06:45,290 +على M طيب C2 + +71 +00:06:50,450 --> 00:06:57,170 +يعني اتنين دلت اكس مظبوط اتنين دلت اكس يبقى ال C1 + +72 +00:06:57,170 --> 00:07:03,450 +هذه بدها تساوي تلاتة على اكس او تساوي دلت اكس + +73 +00:07:03,450 --> 00:07:13,010 +مباشرةC1 بيبقى تساوي Delta X C2 باتنين Delta X من + +74 +00:07:13,010 --> 00:07:18,690 +هنا لهنا اتنين Delta X هي المسافة هذه كلها هذه + +75 +00:07:18,690 --> 00:07:26,090 +اليمين اللي هي C2 طيب C3 تلاتة Delta X يبقى هذه + +76 +00:07:26,090 --> 00:07:29,130 +تلاتة Delta X طيب + +77 +00:07:31,640 --> 00:07:37,900 +ان دلتا اكس ان دلتا اكس يبقى هذه بدها تساوي الـCN + +78 +00:07:37,900 --> 00:07:45,310 +انه الـN في دلتا اكس خليلي هذه المعلومات لزمانيبقى + +79 +00:07:45,310 --> 00:07:48,390 +انا بدي اجيب له الريمان .. من هنا بدأنا اللي هي + +80 +00:07:48,390 --> 00:07:52,870 +النقطة A بدي اجيب له الريمان صم اللي ادناله الرمز + +81 +00:07:52,870 --> 00:07:58,070 +SP يبقى اقول هذا المرة اللي فده الصماش من K to C + +82 +00:07:58,070 --> 00:08:06,510 +واحد لغاية N لمن لل F of C K Delta X Kالان قولنا + +83 +00:08:06,510 --> 00:08:09,830 +Delta X كلهم جات بعضهم يعني Delta X واحد هي نفس + +84 +00:08:09,830 --> 00:08:13,530 +Delta X اتنين هي نفس Delta X تلاتة اذا هذا لو + +85 +00:08:13,530 --> 00:08:20,330 +فاكرتوا ايش بداتي اقول F of C1 في Delta X زائد F + +86 +00:08:20,330 --> 00:08:28,870 +of C2 في Delta X زائد ونظل ماشي لغاية F of CN تمين + +87 +00:08:28,870 --> 00:08:35,090 +في Delta X يبقى هذا مجموع الريمان صممالدالي احطه + +88 +00:08:35,090 --> 00:08:40,210 +على الطبيعة اشوفه قداش يساوي اظن Delta X Delta X + +89 +00:08:40,210 --> 00:08:45,130 +Delta X مقدر اخدها اعمل مشارك من الكل بدل ما كل + +90 +00:08:45,130 --> 00:08:50,870 +مرة ازهجنا لأ لأ انا برا من الكل Delta X بضل جوا + +91 +00:08:50,870 --> 00:08:59,830 +قداش F of C1 C1 يبقى قداش Delta X يبقى هنا F of + +92 +00:08:59,830 --> 00:09:11,050 +Delta Xزي F of C2 C2 بيبقى داش ب2 Delta X يبقى 2 + +93 +00:09:11,050 --> 00:09:23,610 +Delta X F of C3 3 Delta X يبقى F of 3 Delta X زي + +94 +00:09:23,610 --> 00:09:30,290 +ده نظل ماشيل لغاية ما نوصل لآخر حد F of C N يبقى N + +95 +00:09:30,290 --> 00:09:37,820 +في Delta Xيبقى F of N في Delta X بالشكل اللي عندنا + +96 +00:09:37,820 --> 00:09:43,280 +هذا هاي جفالنا لهو طيب تمام هذا الكلام بده يساوي + +97 +00:09:43,280 --> 00:09:50,260 +بدالي اشوف هنا Delta X اللي هو جداش تلاتة على N + +98 +00:09:50,260 --> 00:09:57,800 +يبقى هذه تلاتة على N الان هذه ال F of Delta X اللي + +99 +00:09:57,800 --> 00:10:05,770 +هو تلاتة على Mال F of اتنين Delta X يبجى اتنين في + +100 +00:10:05,770 --> 00:10:15,850 +تلاتة على N زاد ال F of تلاتة بمين في تلاتة على M + +101 +00:10:15,850 --> 00:10:26,270 +زاد زاد ال F of N في تلاتة على N بالشكل العامطبعا + +102 +00:10:26,270 --> 00:10:31,970 +طبعا عندي f of m تساوى جدّا يعني ال f لما تأثر على + +103 +00:10:31,970 --> 00:10:36,130 +ال element يساوي مربع هذا ال element زائد واحد اذا + +104 +00:10:36,130 --> 00:10:40,250 +هذا الكلام بده يساوي تلاتة على ان اللي برا خليها + +105 +00:10:40,250 --> 00:10:44,950 +زي مين يبقى f of هذا ال element يساوي مربع هذا ال + +106 +00:10:44,950 --> 00:10:51,530 +element زائد واحد يبقى تلاتة على ان الكل تربيع + +107 +00:10:51,530 --> 00:10:59,100 +زائد واحدمش اللي بعده زائد مربع هذا يبقى اتنين + +108 +00:10:59,100 --> 00:11:06,700 +تربيع ثلاثة على ان الكل تربيع زائد واحدةليه جلال + +109 +00:11:06,700 --> 00:11:14,000 +يبعدوا؟ مربع هذا تلاتة تربيع تلاتة على إن الكل + +110 +00:11:14,000 --> 00:11:20,960 +تربيع زائد واحد ان تبقى الماشيين يبقى زائد زائد ان + +111 +00:11:20,960 --> 00:11:30,100 +تربيع تلاتة على إن الكل تربيع زائد واحديبقى انا + +112 +00:11:30,100 --> 00:11:34,580 +عوضت عويض مباشر في مين في الدالة الأصلية اللى فوق + +113 +00:11:34,580 --> 00:11:38,400 +هل هي ماضلش عليا اللى احسب الحسابات ده بيقول خلصنا + +114 +00:11:38,400 --> 00:11:45,380 +باجي بقولك كويس يبقى تلاتة على ان ادي برا زي مين + +115 +00:11:45,380 --> 00:11:50,860 +شو رايك في الترمات اللى عندنا هذه طلعلي في هذه و + +116 +00:11:50,860 --> 00:11:57,390 +هذه و هذه و هذهتلاتة على ان الكل تربيع هذا عام + +117 +00:11:57,390 --> 00:12:03,910 +المشترك منهم كلهم يبقى هاي تاخد تلاتة على ان الكل + +118 +00:12:03,910 --> 00:12:09,590 +تربيع عام المشترك فضل عندي جد واحد يعني واحد تربيع + +119 +00:12:09,590 --> 00:12:19,320 +زائد اتنين تربيع زائد تلاتة تربيع زائد ان تربيعايش + +120 +00:12:19,320 --> 00:12:24,860 +ضال عندى؟ واحد زائد واحد زائد واحد زائد واحد يبقى + +121 +00:12:24,860 --> 00:12:31,580 +زائد واحد زائد واحد زائد زائد واحد هى كام مرة هدول + +122 +00:12:31,580 --> 00:12:38,340 +ان عددهم يساوي ان تمام؟ اذا بداتي افك هذا المقار + +123 +00:12:38,340 --> 00:12:44,590 +واشوفه كده يساوي هذا الكلام يساويقال لعلي في هذا + +124 +00:12:44,590 --> 00:12:50,430 +هذا تلاتة تربيع بتسعة في تلاتة سبعة وعشرين على ان + +125 +00:12:50,430 --> 00:12:59,110 +تكعيب يبقى هذا سبعة وعشرين على ان تكعيب فيه هذا من + +126 +00:12:59,110 --> 00:13:05,290 +هو يا جباب؟ مش هذا submission على كتربية؟سكت الشاب + +127 +00:13:05,290 --> 00:13:10,090 +مش هتصمش على كتر بيه واخدنا الوصيه ان فين زي + +128 +00:13:10,090 --> 00:13:14,450 +الواحد في اتنين ان زي الواحد على ستة مظبوط اذا هذا + +129 +00:13:14,450 --> 00:13:22,990 +كله بده اشيله و اكتب بداله ان فين زي الواحد في + +130 +00:13:22,990 --> 00:13:30,750 +اتنين ان زي الواحد على ستة by line دي تلاتة على ان + +131 +00:13:30,750 --> 00:13:42,030 +بده اضربها في مجموع هدولزائد تلاتة على N في N تمام + +132 +00:13:42,030 --> 00:13:46,210 +هذول مجموعة كلهم يساوي N طب تعالوا نختصر + +133 +00:13:46,210 --> 00:13:51,410 +الاكتسارات اللي عندنا و نشوف يبقى أصبح شكل ال S P + +134 +00:13:51,410 --> 00:13:59,250 +على شكل التالت هذه بتروح ال N مع ال N تقريب بظل N + +135 +00:13:59,250 --> 00:14:04,150 +تربيةوالتلاتة فيها اتنين ع التلاتة فيها جداد تسعة + +136 +00:14:04,150 --> 00:14:12,090 +يبقى بظل عند هنا فوق تسعة و بظل عند هنا M زائد + +137 +00:14:12,090 --> 00:14:19,370 +واحد اتنين M زائد واحد على اتنين M تربيع هذا بظل + +138 +00:14:19,370 --> 00:14:23,710 +فيها M تربيع وهذا بظل فيها اتنين وهذا M مع M تصبح + +139 +00:14:23,710 --> 00:14:29,750 +جداد زائد تلاتة بهذا الشكلطيب هذه بدي أحاول أصيغها + +140 +00:14:29,750 --> 00:14:36,330 +صياغة أخرى فبجي بقول هذه تسعة على اتنين ان تربية + +141 +00:14:36,330 --> 00:14:44,990 +فيه اتنين ان تربية زائد تلاتة ان زائد واحد زائد + +142 +00:14:44,990 --> 00:14:51,410 +برة تلاتة يعني يا شباب هذا بالصير كان تاني بالصير + +143 +00:14:51,410 --> 00:14:59,630 +كان تاني هذه تسعة فيههذه بدخلها جوا بصير واحد زائد + +144 +00:14:59,630 --> 00:15:09,270 +ثلاثة ثلاثة على اتنين انتربيع زائد واحد على اتنين + +145 +00:15:09,270 --> 00:15:15,290 +انتربيع اختصارات مافيش يبقى هذه الزائد ثلاثة بده + +146 +00:15:15,290 --> 00:15:22,590 +ادخل التسعة جوا يبقى هذه بصير ايشبصير هذه كلها هي + +147 +00:15:22,590 --> 00:15:28,930 +ثلاثة M هذه ثلاثة M على اتنين M طيب يفجر بيصير + +148 +00:15:28,930 --> 00:15:36,810 +تسعة زائد ثلاثة M زائد بتمر في تسعة له سبعة وعشرين + +149 +00:15:36,810 --> 00:15:43,490 +سبعة وعشرين M زائد تسعة كله على اتنين M تربيع زائد + +150 +00:15:43,490 --> 00:15:50,040 +ثلاثةيبقى النتيجة النهائية بالصيرة معشقة زائد سبعة + +151 +00:15:50,040 --> 00:15:57,450 +وعشرين N زائد تسعة عشرة Nالمطلوب الأول جالي هات + +152 +00:15:57,450 --> 00:16:03,250 +لمين الريمان صم للمجموع اللي هيبقى هذا شكل الريمان + +153 +00:16:03,250 --> 00:16:08,610 +صم اللي هو جداش اتناشر زي سبعة وعشرين N زي تسعة + +154 +00:16:08,610 --> 00:16:14,870 +على اتنين N تربية تمام خلصنا المطلوب الأول المطلوب + +155 +00:16:14,870 --> 00:16:20,420 +التانيبقول هتل ال limit لما ال N بدها تروح لمالة + +156 +00:16:20,420 --> 00:16:25,060 +نهاية للنتيجة اللى حصلت عليها يعني ايش معناه لو + +157 +00:16:25,060 --> 00:16:31,120 +زاد عدد التقسيمات الى مالة نهاية احنا لما خدنا CK + +158 +00:16:31,120 --> 00:16:35,320 +هنا C1 هنا يبقى السعر عندنا المستطيل هنا يا شباب + +159 +00:16:35,810 --> 00:16:40,410 +صار عندك المستطيل هذا، صار عندك المستطيل هذا، يعني + +160 +00:16:40,410 --> 00:16:44,370 +احنا جيبنا المساحة وزيادة شوية، لو زاد عدد + +161 +00:16:44,370 --> 00:16:50,130 +التقسيمات إلى ما لا نهاية، يبقى المساحةبصير تقترب + +162 +00:16:50,130 --> 00:16:53,510 +من المساحة الحقيقية أو هي المساحة الحقيقية بالضبط + +163 +00:16:53,510 --> 00:16:57,710 +وبالتالي كل الزيادات اللي فوق هذه بتبقى راحة + +164 +00:16:57,710 --> 00:17:02,510 +ماضلش، إلها وجود يبقى بدنا نقوله ال area المطلوبة + +165 +00:17:02,510 --> 00:17:11,990 +نمرى بـ ال area المطلوبة تساوي limit لل S P لما ال + +166 +00:17:11,990 --> 00:17:17,640 +N بدها تروح لوين؟ للماء لنهايةيبقى هذه ال limit + +167 +00:17:17,640 --> 00:17:26,280 +لما ال N بدأ تروح للملة نهاية لل 12 زائد 27 N زائد + +168 +00:17:26,280 --> 00:17:31,880 +9 على 2 N ترابيع نهاية المقدار الثابت بالمقدار + +169 +00:17:31,880 --> 00:17:37,290 +الثابت كده نهاية المقدار هذا كله؟0 لأن درجة الـ + +170 +00:17:37,290 --> 00:17:44,730 +Bus أقل من درجة المقام يبقى زائد Zero يسوى كم؟ 12 + +171 +00:17:44,730 --> 00:17:50,690 +يبقى المساحة الحقيقية ما بين الدالة F of X أو X + +172 +00:17:50,690 --> 00:17:57,250 +تربية ومحور السينات أو محور X المساحة يتمثل 12 من + +173 +00:17:57,250 --> 00:18:04,620 +وحدات المساحةهل عندك أي سؤال هنا؟ هعطيك مثال بعد + +174 +00:18:04,620 --> 00:18:09,860 +قليل زيها نفس الفكرة اه طيب انا كنت طالع اعمل كل + +175 +00:18:09,860 --> 00:18:14,200 +هذا؟ ففي طريقة اخرى لو كنت تقولي مثلا سينجر سينجر + +176 +00:18:14,200 --> 00:18:18,600 +تساوي هو أول أنصف زائد فقدر فضلية تلاتة على أنف + +177 +00:18:18,600 --> 00:18:20,960 +كتر كتر كتر كتر كتر كتر كتر كتر كتر + +178 +00:18:35,800 --> 00:18:41,260 +بتجيب كلام غير هذا؟ ولا بسيط ولا حاجة، انت من أول + +179 +00:18:41,260 --> 00:18:46,420 +بدأ حط ال delta X، حط التلت على N بس يا أخويا أنا + +180 +00:18:46,420 --> 00:18:49,440 +بفهم أنت فيه، و بعدين انت تكتبلي أي شروع صح + +181 +00:18:49,440 --> 00:18:54,200 +ماعنديش مشكلةأنا بحللك حلة نموذجيا بحيث مايظلش لا + +182 +00:18:54,200 --> 00:18:58,960 +شيردة ولا وردة انت بعدين حر زي ما بدك تفعل تمام؟ + +183 +00:18:58,960 --> 00:19:02,980 +يبقى لحد هنا بكون انتهى هذا ال section وإليكم + +184 +00:19:02,980 --> 00:19:07,340 +أرقام المسائل ال exercises خمسة اتنين يبقى + +185 +00:19:07,340 --> 00:19:17,060 +exercises خمسة اتنين المسائل التالية من واحد لخمسة + +186 +00:19:17,060 --> 00:19:18,520 +واربعين ال odd + +187 +00:20:08,800 --> 00:20:19,880 +العربية الموجودة في + +188 +00:20:19,880 --> 00:20:20,520 +المدينة العربية السعودية + +189 +00:20:34,590 --> 00:20:40,730 +لتال اف اف اكس بيه function defined on a closed + +190 +00:20:40,730 --> 00:20:47,150 +interval فترة مغلقة a و b + +191 +00:21:00,410 --> 00:21:16,530 +X0 X1 X2 Xn-1 Xn is a partition is a partition of + +192 +00:21:16,530 --> 00:21:24,590 +the closed interval a وb we define the integral we + +193 +00:21:24,590 --> 00:21:28,070 +define the + +194 +00:21:32,920 --> 00:21:43,340 +Integral of F منعرف التكامل على F over ال A و ال B + +195 +00:21:43,340 --> 00:21:52,640 +على الفترة A و B by تكامل + +196 +00:21:52,990 --> 00:22:01,810 +من A الى B ال F of X DX يسوى ال limit لما ال norm + +197 +00:22:01,810 --> 00:22:07,510 +بتابع ال P بده يروح لل Zero ال summation من K بده + +198 +00:22:07,510 --> 00:22:14,810 +تسوى واحد لغاية ال N لل F of C K Delta X K + +199 +00:22:14,810 --> 00:22:20,630 +provided the + +200 +00:22:20,630 --> 00:22:22,690 +limit + +201 +00:22:24,210 --> 00:22:28,950 +exist not + +202 +00:22:28,950 --> 00:22:32,650 +ملاحظة + +203 +00:22:32,650 --> 00:22:38,930 +if we chose if + +204 +00:22:38,930 --> 00:22:48,190 +we chose a partition with + +205 +00:22:48,190 --> 00:22:52,670 +n equal + +206 +00:22:54,130 --> 00:23:07,950 +sub intervals and equal sub intervals then the + +207 +00:23:07,950 --> 00:23:11,810 +width of + +208 +00:23:11,810 --> 00:23:21,090 +each sub interval is + +209 +00:23:23,410 --> 00:23:34,630 +delta X سوى B ناقص ال A على N answer + +210 +00:23:34,630 --> 00:23:39,210 +the + +211 +00:23:39,210 --> 00:23:48,010 +above answer the above definition + +212 +00:23:50,460 --> 00:23:59,200 +بكم بيصبح على الشكل التالي تكامل من a إلى b لل F + +213 +00:23:59,200 --> 00:24:08,180 +of x dx بدي يساوي limit ال norm ل P بدي اروح لل + +214 +00:24:08,180 --> 00:24:15,160 +zero ال summation من K تساوي واحد لغاية ال Nللـ F + +215 +00:24:15,160 --> 00:24:26,060 +of C K Delta X K ويسوي limit لما ال norm بتابع ال + +216 +00:24:26,060 --> 00:24:34,460 +P يروح لل Zero لصميشة من K تسوى واحد لغاية ال N + +217 +00:24:34,460 --> 00:24:38,000 +لمن؟ + +218 +00:24:38,000 --> 00:24:50,530 +لل F of C Kالـ B نقص الـ A على N يساوي الـ B نقص + +219 +00:24:50,530 --> 00:24:57,630 +الـ A في limit لما الـ N tends to infinity للـ + +220 +00:24:57,630 --> 00:25:07,730 +summation من A من K equal one to N لواحد على N F + +221 +00:25:07,730 --> 00:25:11,770 +of C K example + +222 +00:25:18,320 --> 00:25:26,540 +استخدم ريمان صام استخدم + +223 +00:25:26,540 --> 00:25:42,420 +ريمان صام لتطور الانتقال + +224 +00:25:55,120 --> 00:26:03,360 +تكامل من 0 للإتنين لإتنين X زائد واحد DX + +225 +00:26:32,480 --> 00:26:37,360 +هنا نحاول نفهم ما هو مكتوب قدامنا هذا على الصبر + +226 +00:26:37,360 --> 00:26:41,360 +طبعا احنا في نهاية ال chapter الماضي اتكلمنا عن ال + +227 +00:26:41,360 --> 00:26:46,220 +indefinite integral اللي هو التكامل غير المحدود + +228 +00:26:46,220 --> 00:26:50,660 +بنحط اشارة التكامل بدون اللي هو حد علوي للتكامل + +229 +00:26:50,660 --> 00:26:55,020 +وحد السفلي للتكامل وشوفنا كده بنكمل الدوال + +230 +00:26:55,020 --> 00:27:00,790 +المختلفةللـ definite integrals يعني التكاملات + +231 +00:27:00,790 --> 00:27:05,270 +المحدودة تكامل بس من كامل على فترة من كذا إلى كذا + +232 +00:27:05,270 --> 00:27:10,690 +يبقى هذا ما نسميه تكامل محدود نعطي تعريف لهذا + +233 +00:27:10,690 --> 00:27:15,630 +التكامل المحدود فباجي بقول افترض ان f of x هي + +234 +00:27:15,630 --> 00:27:20,910 +عبارة عن ده لو معرف على ال closed interval a وb ال + +235 +00:27:20,910 --> 00:27:24,910 +interval هذه روحنا عملنا لها partitionزي ما انت + +236 +00:27:24,910 --> 00:27:28,230 +شايفين مثل ما كان في السؤال اللي جابله ومثل ما كان + +237 +00:27:28,230 --> 00:27:31,990 +في الجزء النظري اللي جابله ال partition هذا عامل + +238 +00:27:31,990 --> 00:27:36,790 +معاه على الفترة a وb بيقولي we define the integral + +239 +00:27:36,790 --> 00:27:43,710 +or دالة f على الفترة a وb byبنحط إشارة تكمل بالشكل + +240 +00:27:43,710 --> 00:27:50,970 +اللى عندنا لل F of X DX بهذا الشكل ال هدى شوف شو + +241 +00:27:50,970 --> 00:27:54,490 +معنى هدى من ناحية رياضية أو كيف بدنا نربط موضوع + +242 +00:27:54,490 --> 00:27:59,090 +التكمل المحدود بريمان صم الذي أشرنا إليه في نهاية + +243 +00:27:59,090 --> 00:28:04,020 +المحاضرة ماضية و قبل قليل كذلكهذا هو الريمان صم + +244 +00:28:04,020 --> 00:28:08,400 +مظبوط إذا الريمان صم اللي بحصل عليه بدي أخدله ال + +245 +00:28:08,400 --> 00:28:12,440 +limit لما ال norm بتابع ال P بده يروح لوين ل zero + +246 +00:28:12,440 --> 00:28:16,860 +ال norm بتابع ال P المرة اللي فاتت عرفنا انه لما + +247 +00:28:16,860 --> 00:28:20,740 +نيجي نجسم ال interval ايه و بيجسمها إلى مجموعة من + +248 +00:28:20,740 --> 00:28:25,900 +ال sub intervalsأطول واحدة فيهم بنسميها norm ل P + +249 +00:28:25,900 --> 00:28:32,040 +طبعا طيب بيقول هذا بتاخد ال limit لما norm ل P بده + +250 +00:28:32,040 --> 00:28:37,020 +يروح ل zero يعني لما أطول فترة بده تروح ل وين ل + +251 +00:28:37,020 --> 00:28:40,280 +zero طب ما هو اذا أطول فترة لها تروح ل zero يبقى + +252 +00:28:40,280 --> 00:28:44,390 +الفترة الأصغر منها تروح ل zero طبيعيطبعا إذا احنا + +253 +00:28:44,390 --> 00:28:48,590 +متعمدين لما قلنا نور P بدي روح ل Zero يعني لما + +254 +00:28:48,590 --> 00:28:52,070 +أكبر Delta X موجودة عندي بدي تقول ل Zero يبقى + +255 +00:28:52,070 --> 00:28:55,470 +Delta X اللي أصغر منها الأخر هتروح ل Zero من باب + +256 +00:28:55,470 --> 00:29:01,030 +أو لا طبعا طب السؤال هو متى يحدث ذلك يعني ممكنش ال + +257 +00:29:01,030 --> 00:29:04,890 +نور P بدي روح ل Zero في شغل مكافئة لأ نعم في شغل + +258 +00:29:04,890 --> 00:29:08,970 +مكافئة لأهل هى لو قلت norm P في السؤال الماضى في + +259 +00:29:08,970 --> 00:29:13,290 +نهاية المحافظة، قلنا 1 و 1 من عشرة، مظبوط، لو ال N + +260 +00:29:13,290 --> 00:29:19,150 +هذه كل واحدة قسمتها اتنين، بصير نص تقريبا، و + +261 +00:29:19,150 --> 00:29:23,090 +انتقلت نص، لو قسمتها اربعة، بصير ربعة، و هكذا، + +262 +00:29:23,090 --> 00:29:27,670 +يعني كل ما زيد عدد التقسيمات، كل ما المساحة اللى + +263 +00:29:27,670 --> 00:29:33,540 +جبتها زيادةأو المساحة اللي تركتها بتجل مصغور بتجل + +264 +00:29:33,540 --> 00:29:38,140 +يعني بكون انا حصلت لما ال N تكبر بدرجة كبيرة جدا + +265 +00:29:38,140 --> 00:29:42,940 +بحصل على المساحة الحقيقية المحصورة بين المنحنة + +266 +00:29:42,940 --> 00:29:47,980 +ومحور X وهذاما سنشير إليه بعلى أنه هو التكامل لدى + +267 +00:29:47,980 --> 00:29:52,840 +ال F of X على الفترة اللى عدنا من A إلى B إذا لما + +268 +00:29:52,840 --> 00:29:56,920 +نقل يقول تكامل من A إلى B لل F of X DX معناته ال + +269 +00:29:56,920 --> 00:30:01,260 +limit للريمان sum لما ال norm لل P بده يروح ل0 + +270 +00:30:01,260 --> 00:30:05,940 +بشرط إن ال limit هذه ما لها exist طيب هذه لو كانت + +271 +00:30:05,940 --> 00:30:10,440 +التقسيمات غير متساوية لو حدثوكانت التقسيمات + +272 +00:30:10,440 --> 00:30:15,200 +متساوية زي ما في المثال اللي كان قبل قليل يبقى هذا + +273 +00:30:15,200 --> 00:30:19,260 +بدها تصير if we chose لل partition with n equal + +274 +00:30:19,260 --> 00:30:25,610 +sub interval thenأي sub interval بدي يكون الارض + +275 +00:30:25,610 --> 00:30:30,830 +تبعها او الاتساع تبعها ال width هو delta x بدي نقص + +276 +00:30:30,830 --> 00:30:36,290 +a على n يعني طول الفترة اللي لنا مقسومة عالمين على + +277 +00:30:36,290 --> 00:30:41,890 +عدد التقسيمات دي بدي يصير b نقص a على n وبالتالي + +278 +00:30:41,890 --> 00:30:46,030 +التعريف اللي فوق بدي يصبح على الشكل التالي تكمل ما + +279 +00:30:46,030 --> 00:30:51,740 +نشدعه بالتقسيماتLimit f of z كدلتا اكس ك لما النور + +280 +00:30:51,740 --> 00:30:54,720 +بتابع ال P بيكون سواء زير وهذا يبقى مكتوب فوق + +281 +00:30:54,720 --> 00:30:59,760 +مظبوط لكن لما صاروا كلهم جد بعض يبقى دلتا اكس ك + +282 +00:30:59,760 --> 00:31:02,620 +صارت دلتا اكس وان هي دلتا اكس اثنين وان هي دلتا + +283 +00:31:02,620 --> 00:31:08,160 +اكس ثلاث يبقى انا شيلناها وقلنا بدلها دلتا اكس + +284 +00:31:08,160 --> 00:31:14,420 +يبقى هذه ها اللي عندنا هذه بالضبط هذه كأنها + +285 +00:31:18,370 --> 00:31:24,010 +كل واحدة جدت تانية كل واحدة من هدول جدت تانية فصار + +286 +00:31:24,010 --> 00:31:31,470 +F of C كافة Delta X جداشة Delta X هي عبارة عن P + +287 +00:31:31,470 --> 00:31:37,330 +نقص ال A على M هذا الكلام يسمى P نقص A رقم + +288 +00:31:39,720 --> 00:31:42,520 +خلّيك برا ال limit هيطلعنا برا ال limit + +289 +00:31:49,020 --> 00:31:55,420 +هذا المثال يحدث + +290 +00:31:55,420 --> 00:32:00,360 +إذا عدد التقسيمات ألوان لما لا نهاية، يعني عندما + +291 +00:32:00,360 --> 00:32:03,700 +يكون لدي مالة نهاية من التقسيمات بسيرة طول النار + +292 +00:32:03,700 --> 00:32:06,940 +المتبع الـP بيساوي Zero، يبقى النار المتبع الـP + +293 +00:32:06,940 --> 00:32:10,180 +بيساوي Zero، وبالتالي Delta اللي أغر منه بيبدأ + +294 +00:32:10,180 --> 00:32:15,790 +تروح كملمينلـ 0 ومن هنا بقول الصيغة المكافئة لهذه + +295 +00:32:15,790 --> 00:32:20,070 +الصيغة هي B نقص الـ A limit لما ال N بتروح ل المال + +296 +00:32:20,070 --> 00:32:24,750 +انه هي لصة ماشي ل واحد على N F of CK F of CK هي + +297 +00:32:24,750 --> 00:32:28,670 +هذا طلع برا بيبقى اللي عندى هنا جداش واحد على N + +298 +00:32:28,670 --> 00:32:32,710 +يبقى هي الواحد على N وهي ال F of CK وهي ال B نقص + +299 +00:32:32,710 --> 00:32:36,090 +ال A والنور اللي فيه بده يروح ل 0 لكافئة N بده + +300 +00:32:36,090 --> 00:32:39,570 +تروح لمين للمال انه هي في المثال السابق المطموب + +301 +00:32:39,570 --> 00:32:43,430 +الثاني كان في المثال السابققلنا هات ال area وهي ال + +302 +00:32:43,430 --> 00:32:47,390 +limit لما ال N بدها تروح لوين للمالة نهائية بتعطيك + +303 +00:32:47,390 --> 00:32:48,430 +المساحة الحقيقية + +304 +00:32:53,170 --> 00:32:58,250 +المتغير ليس الكرستان، مش بقول زاد عدد التقسيمات + +305 +00:32:58,250 --> 00:33:02,530 +إلى مال نهاية المقدار ثابت هو P ناقص الـA طول + +306 +00:33:02,530 --> 00:33:05,670 +الـInterval من أول الـInterval إلى أخر + +307 +00:33:05,670 --> 00:33:10,630 +الـInterval، A وB يبقى طولها جديد، P ناقص الـA طول + +308 +00:33:10,630 --> 00:33:13,810 +الـInterval، هذا ثابت، لكن التقسيمات أنا بدي + +309 +00:33:13,810 --> 00:33:17,710 +أغيرها و أجعلها تزيد إلى أين؟ ممكن أجسمها لفترة أو + +310 +00:33:17,710 --> 00:33:22,320 +تانيةممكن اقسم ل 3 فترات ممكن ل 4 فترات ممكن ل 100 + +311 +00:33:22,320 --> 00:33:26,520 +فترة ممكن ل مليون فترة او هكذا وبالتالي الان ليست + +312 +00:33:26,520 --> 00:33:31,340 +ثابتة جداش بقسم جداش بتقترب من المساحة الحقيقية + +313 +00:33:31,340 --> 00:33:34,780 +المساحة الحقيقية بحصلها بالضبط وقتاش لما الان بده + +314 +00:33:34,780 --> 00:33:39,640 +تروح لوين يعني اذا زاد عدد التقسيمات ووصلها الى + +315 +00:33:39,640 --> 00:33:43,720 +مالة نهاية يمكن بصير ال limit للريمان صم اللي هو + +316 +00:33:43,720 --> 00:33:47,880 +المقدر هذا وهذا بيعطيني المساحة الحقيقيةوبالتالي + +317 +00:33:47,880 --> 00:33:52,800 +بيعطيني قيمة من؟ قيمة التكامل اللي عندنا الان مثلا + +318 +00:33:52,800 --> 00:33:56,800 +بقول استخدم ريمان صم مشان تحسبلي قداش قيمة التكامل + +319 +00:33:56,800 --> 00:34:03,880 +المحدود من 0 ل 2 ل 2 X زائد 1 ولم يقول خد CK في + +320 +00:34:03,880 --> 00:34:06,920 +نهاية ال interval ولا في نص ال interval ولا في + +321 +00:34:06,920 --> 00:34:12,540 +بداية ال interval يبقى انت لك الحرية خد ال CK وان + +322 +00:34:12,540 --> 00:34:16,030 +ما بدكأذا خدت في أول interval أو في نصف ال + +323 +00:34:16,030 --> 00:34:19,370 +interval أو في نهاية ال interval كله هيعطيك نفس + +324 +00:34:19,370 --> 00:34:22,170 +النتيجة لما تاخد ال limit طبعا هطلع اذا ما بين + +325 +00:34:22,170 --> 00:34:25,590 +الأفر ثم اللي هو ثم هطلع شكلين مختلفين لكن لما + +326 +00:34:25,590 --> 00:34:30,990 +تاخد ال limit لهم تطلع من نفس النتيجة طبعا طيب + +327 +00:34:30,990 --> 00:34:35,570 +يبقى مقيدنيش يبقى أنا لي الحرية كل اللي مقدر أقوله + +328 +00:34:35,570 --> 00:34:40,450 +بده أجيب قداش طول ال delta Xيبقى انا اول ما ببدأ + +329 +00:34:40,450 --> 00:34:46,510 +بجي بقوله انا عندي ال delta x هاي ال delta x بده + +330 +00:34:46,510 --> 00:34:53,270 +يساوي اللي هو b ناقص a على n يبقى اتنين ناقص zero + +331 +00:34:53,270 --> 00:34:58,790 +على n يبقى اتنين ناقص zero على مين على n يبقى + +332 +00:34:58,790 --> 00:35:05,600 +اتنين على n هذا شكل من ال delta xلو جيت قلت هاي + +333 +00:35:05,600 --> 00:35:12,520 +هيك الرسمة و قلنا هذا محور X وهذا محور Y وهذا نقطة + +334 +00:35:12,520 --> 00:35:18,820 +الأصل هذا أصل الدالة و F of X سوى 2X و الواحد ما + +335 +00:35:18,820 --> 00:35:23,040 +هو هذا shift إلى أعلى بالمقدار الواحد تمام يبقى + +336 +00:35:23,040 --> 00:35:28,440 +بداية أقوله ل 2X اللي هو الخط المستقيم لأن لو كانت + +337 +00:35:28,440 --> 00:35:34,160 +X ب Zero فالY بواحد يبقى النقطة اللي عندنا هذهيبقى + +338 +00:35:34,160 --> 00:35:38,840 +هذا النقطة اللي هو واحد هو هذا الخط اللي عندنا y + +339 +00:35:38,840 --> 00:35:46,160 +تساوي اتنين x زائد واحد و بدك تفيه فقط لحد قداشر + +340 +00:35:46,160 --> 00:35:51,500 +لحد اتنين بهذا الشكل من zero للاتنين يبقى انا بدي + +341 +00:35:51,500 --> 00:35:56,350 +بس المساحة اللي تحت المنحنةعلى الفترة من 0 و 2 + +342 +00:35:56,350 --> 00:36:00,190 +يعني المساحة المحصورة بين المنحنة ومحور X على + +343 +00:36:00,190 --> 00:36:05,590 +الفترة من 0 لغاية 2 بدي اعمل تقسيمات عندي يبقى بدي + +344 +00:36:05,590 --> 00:36:13,610 +اقول هذه X1 وهذه X2 وهذه X3 كلهم جد بعض التقسيمات + +345 +00:36:13,610 --> 00:36:18,830 +اللي عندنا لغاية ماوصل لإتنين اللي هي جداش XNوالـ + +346 +00:36:18,830 --> 00:36:25,770 +Zero اليمين X نوت يبقى هذه اليمين Delta X وهذه + +347 +00:36:25,770 --> 00:36:31,050 +Delta X وهذه Delta X + +348 +00:36:33,110 --> 00:36:36,590 +الان بدى احاول مش ان اثبتك معلومة السؤال اللى فات + +349 +00:36:36,590 --> 00:36:40,850 +بدى اعمل هذا السؤال بنفس الطريقة يبقى بداجى اقول + +350 +00:36:40,850 --> 00:36:54,810 +take خدلي اللى هو C1 او CK at the end of H او at + +351 +00:36:54,810 --> 00:37:01,170 +the right end at the right end right + +352 +00:37:02,720 --> 00:37:09,460 +end of each sub interval + +353 +00:37:12,070 --> 00:37:19,070 +يبقى بيصير C1 هذي X1 عبارة عن مين؟ C1 قداش طول C1 + +354 +00:37:19,070 --> 00:37:28,430 +هو Delta X نيجي CX2 بيصير هي C2 قداش C2 المسافة + +355 +00:37:28,430 --> 00:37:35,830 +هذه كلها يبقى 2 Delta X X3 بيبقى تسوى C3 بيبقى + +356 +00:37:35,830 --> 00:37:43,180 +تسوى 3 Delta X وهكذا طيبيبقى لان بقدر اجيب له اللي + +357 +00:37:43,180 --> 00:37:50,140 +هو الريمان صم SP يبقى هذا الكلام بده يساوي F of C1 + +358 +00:37:50,140 --> 00:38:00,610 +في Delta Xزائد F of C2 في Delta X زائد F of C3 في + +359 +00:38:00,610 --> 00:38:11,210 +Delta X زائد زائد F of C N F of C N كله في من؟ في + +360 +00:38:11,210 --> 00:38:18,250 +Delta X طيب هذا الكلام بده يساوي Delta X خليها برا + +361 +00:38:19,280 --> 00:38:24,720 +بدا يجي للفه في C1 C1 هي عبارة عن مين؟ عن Delta X + +362 +00:38:24,720 --> 00:38:30,220 +أو بدنا نسأل صاحبنا اللي تو Delta X بداش عندنا؟ 2 + +363 +00:38:30,220 --> 00:38:37,860 +على N يعني ها دي 2 على N ها دي ايه؟ 2 في 2 على N + +364 +00:38:37,860 --> 00:38:48,090 +ها دي 3 في 2 على N and so onيبجي على طول الخط يبجي + +365 +00:38:48,090 --> 00:38:51,350 +على طول + +366 +00:38:51,350 --> 00:38:53,390 +الخط يبجي على طول الخط يبجي على طول الخط يبجي على + +367 +00:38:53,390 --> 00:38:54,010 +على طول الخط يبجي على طول الخط يبجي على طول الخط + +368 +00:38:54,010 --> 00:38:54,090 +يبجي على طول الخط يبجي على طول الخط يبجي على طول + +369 +00:38:54,090 --> 00:38:54,110 +على طول الخط يبجي على طول الخط يبجي على طول الخط + +370 +00:38:54,110 --> 00:38:59,090 +يبجي على طول الخط يبجي على طول الخط يبجي + +371 +00:38:59,090 --> 00:39:09,730 +على طول الخط يبجي على + +372 +00:39:09,730 --> 00:39:19,060 +طول الخهذه ثلاثة في اتنين + +373 +00:39:19,060 --> 00:39:25,800 +على N وهذه F of N في اتنين على N بالشكل اللي انها + +374 +00:39:25,800 --> 00:39:26,180 +هنا + +375 +00:39:41,820 --> 00:39:48,550 +الان دلتا اكس اخدتها براتمام؟ شيلت الـC1 و الـC2 و + +376 +00:39:48,550 --> 00:39:53,110 +الـC3 و الـCN و حطيت قيمة فالكتاب ده نعم تمام؟ + +377 +00:39:53,110 --> 00:39:57,950 +يبقى هذا الكلام بده يساوي بده يساوي Delta X اللي + +378 +00:39:57,950 --> 00:40:03,210 +هو جداش ب 2 على N وهذا الجزء بده أشوف جداش قيمة + +379 +00:40:03,210 --> 00:40:07,530 +الدالة هنا وين الدالة هيها يبقى بده أشيل كل X و + +380 +00:40:07,530 --> 00:40:13,990 +أحط مكانها 2 على N يبقى هذه 2 اللي برا وهذه 2 على + +381 +00:40:13,990 --> 00:40:21,280 +Nتمام؟ يبقى هذه اتنين اللي برا وهي اتنين .. اه + +382 +00:40:21,280 --> 00:40:26,460 +نشيلها زائد واحد يبقى + +383 +00:40:26,460 --> 00:40:32,140 +هذه زائد واحد، زائد هذه اتنين اللي برا وهذه اتنين + +384 +00:40:32,140 --> 00:40:42,360 +في اتنين على ان زائد واحد، زائدأتنين في تلاتة في + +385 +00:40:42,360 --> 00:40:51,700 +اتنين على ان زائد واحد زائد زائد اخر حاجة اتنين في + +386 +00:40:51,700 --> 00:40:59,980 +ان في اتنين على ان زائد واحد طيب هذا الكلام يساوي + +387 +00:40:59,980 --> 00:41:06,020 +اتنين على ان هي هبرة نيجي لهذه هذه عبارة عن قداش + +388 +00:41:07,110 --> 00:41:15,490 +اربع عالان زاد اتنين في اربع عالانطبعا زيادة واحد + +389 +00:41:15,490 --> 00:41:19,710 +خلّي الواحد الاخر مش مشكلة يبقى يد اتنين في أربعة + +390 +00:41:19,710 --> 00:41:30,790 +على N زائد اللي هو تلاتة في أربعة على N زائد زائد + +391 +00:41:30,790 --> 00:41:39,650 +N في أربعة على N زائد واحد زائد واحد زائد واحد + +392 +00:41:39,650 --> 00:41:45,730 +الشكل اللي عندنا هناهذه كتابة المجموعة كلها هذا + +393 +00:41:45,730 --> 00:41:52,010 +الكلام يساوي 2 على N فى 4 على N بدي أخدها عامل + +394 +00:41:52,010 --> 00:41:59,770 +مشترك بيبقى لدي واحد زائدي اتنين زائد تلاتة زائد N + +395 +00:41:59,770 --> 00:42:09,710 +زائد 2 على N اللي برا هذا المجموعة مجدد كله Nطيب + +396 +00:42:09,710 --> 00:42:16,210 +هذا الكلام بده يساوي اتنين في اربع تمانية على N + +397 +00:42:16,210 --> 00:42:22,550 +ترمية فيه هذا summation على مين على K اول + +398 +00:42:22,550 --> 00:42:26,110 +summation ناخدها واحد زي اتنين زي تلاتة زي N اللي + +399 +00:42:26,110 --> 00:42:30,970 +هو summation على K من K تساوي واحد لغاية ال N وهذا + +400 +00:42:30,970 --> 00:42:36,790 +اللي هو عبارة عن N في N زي واحد كله على اتنين + +401 +00:42:43,240 --> 00:42:47,020 +نختصر الان الان مع الان و اتنين مع هدى بيبقى + +402 +00:42:47,020 --> 00:42:53,920 +الجداش اربعة يبقى واتس ساوي اربعة على ان في جداش + +403 +00:42:53,920 --> 00:43:01,230 +في ان زائد واحدراحت هذه، ضالت أربعة، راحت اتنين، + +404 +00:43:01,230 --> 00:43:07,110 +راحت هذا الان زائد واحد على مين؟ على الان، هذه + +405 +00:43:07,110 --> 00:43:12,350 +أربعة على الان، ضال عندي مين زائدي اتنين، يبقى + +406 +00:43:12,350 --> 00:43:17,030 +نفسيها، هذه لو دخلت الان جوا، بضال عندي قداش، + +407 +00:43:17,030 --> 00:43:24,970 +أربعة فقط لغير، زائد، هذه بصير أربعة على ان، أربعة + +408 +00:43:24,970 --> 00:43:33,980 +على انزائد اتنين طيب تمام يبقى هذا شكل الريمان صام + +409 +00:43:33,980 --> 00:43:41,640 +تمام اللي هو قداش يعني ستة زائد اربع على ان شكل + +410 +00:43:41,640 --> 00:43:48,350 +الريمان صامأنا بدي التكامل من Zero لغاية اتنين + +411 +00:43:48,350 --> 00:43:54,830 +للاتنين X زائد واحد كله دي X يبقى ال limit لما ال + +412 +00:43:54,830 --> 00:43:58,930 +Intensity to infinity للريمان sum اللي بيطلع عندنا + +413 +00:43:58,930 --> 00:44:05,570 +هذا جدوش الريمان sum اللي هو ستة زائد أربعة على N + +414 +00:44:05,570 --> 00:44:10,170 +و يساوي جدوش ستة طب ايش رأيك بيتأكد الحل صح ولا + +415 +00:44:10,170 --> 00:44:17,610 +غلطكامل هذا على السريع تكامل هذا X تربيع وتكامل + +416 +00:44:17,610 --> 00:44:22,290 +هذا ب X X تربيع زائد X عند اتنين باربع زائد اتنين + +417 +00:44:22,290 --> 00:44:25,830 +ناقص Zero Zero يبقى دياشر اربع زائد اتنين و ستة + +418 +00:44:25,830 --> 00:44:28,530 +يبقى كلام سريع مائة بالمئة + +419 +00:44:37,890 --> 00:44:42,430 +يبقى من الأن فصاعدا قيمة التكامل المحدود هو ال + +420 +00:44:42,430 --> 00:44:47,810 +limit لل remansam سواء أخد upper bound ولا lower + +421 +00:44:47,810 --> 00:44:53,490 +bound سيئا هذي والله هذي بتفرقش عنها خد كمان مثال + +422 +00:44:53,490 --> 00:44:55,170 +صغير express + +423 +00:45:12,510 --> 00:45:21,750 +Limit لصميش من K تساوي واحد لغاية ال N ل C K تربيع + +424 +00:45:21,750 --> 00:45:28,450 +ناقص ثلاثة C K في Delta X K + +425 +00:45:31,320 --> 00:45:42,240 +حيث ال P is a partition ال + +426 +00:45:42,240 --> 00:45:54,340 +P is a partition of the interval لناقص + +427 +00:45:54,340 --> 00:45:58,460 +سبعة وخمسة as + +428 +00:46:01,370 --> 00:46:04,170 +Definite Integral + +429 +00:46:17,520 --> 00:46:22,260 +بقول في المثال اعبر عن ال limit لريمان صم اللي + +430 +00:46:22,260 --> 00:46:26,940 +قدامك هذا حيث ال P هي partition على ال interval as + +431 +00:46:26,940 --> 00:46:31,000 +definite integral يعني بديش اشوف الصيغة اللي عنها + +432 +00:46:31,000 --> 00:46:35,320 +دي وانما بدي اشوفها ك ايه ك definite integral + +433 +00:46:35,320 --> 00:46:42,060 +هنقول ببسيطة الان هذا اللي هو ال limit لما ال norm + +434 +00:46:42,060 --> 00:46:49,550 +لل P بدي روح لوين لل zero شكل اللي عنهالمن؟ لـ + +435 +00:46:49,550 --> 00:46:56,470 +summation من K تساوي واحد لغاية N ل C K تربيع ناقص + +436 +00:46:56,470 --> 00:47:03,370 +ثلاثة C K في Delta X K يساوي تكامل من أين لو اننا + +437 +00:47:03,370 --> 00:47:11,380 +شباب؟ من سالب سبعة لغاية خمسةيبقى الفترة من سالب + +438 +00:47:11,380 --> 00:47:18,540 +سبعة لغاية خمسة بدنا ال F of X يبقى ال F of X في + +439 +00:47:18,540 --> 00:47:23,960 +DX يبقى تكامل من ناقص سبعة إلى خمسة من واحد بده + +440 +00:47:23,960 --> 00:47:25,040 +أجيب له ال F of X + +441 +00:47:27,990 --> 00:47:35,610 +يبقى هذه كإنها X تربيع ناقص تلاتة X بس شار لل X + +442 +00:47:35,610 --> 00:47:41,070 +وحط مكانها مين؟ حط مكانها الـ CK يبقى الدالة هذه + +443 +00:47:41,070 --> 00:47:44,990 +هي X تربيع ناقص تلاتة X + +444 +00:47:58,760 --> 00:48:09,900 +بنجي لنظرية theorem بيقول + +445 +00:48:09,900 --> 00:48:10,480 +ال F + +446 +00:48:13,470 --> 00:48:23,130 +is continuous function on the closed interval a و + +447 +00:48:23,130 --> 00:48:35,790 +b then تكامل من a إلى b لل f of x dx exists that + +448 +00:48:35,790 --> 00:48:49,320 +isأي أن الـ F is integrable على + +449 +00:48:49,320 --> 00:49:04,920 +الفترة A وB نعود + +450 +00:49:04,920 --> 00:49:11,320 +للتعريف أو للنظرية التي كتبناهاطبعا لو أخدنا دالة + +451 +00:49:11,320 --> 00:49:15,620 +مع الدالة هذه قد تكون قابلة للاشتقاق و قد لا تكون + +452 +00:49:15,620 --> 00:49:20,910 +قابلة للاشتقاق في المقابل قد تكون قابلة للتكاملوقد + +453 +00:49:20,910 --> 00:49:25,850 +لا تكون قابلة للتكمل الشرط واحد ان تكون قابلة + +454 +00:49:25,850 --> 00:49:30,370 +للتكمل هو الشرط بس تبقى دالة متاصلة continuous + +455 +00:49:30,370 --> 00:49:34,210 +function يبقى بقول ايه؟ لو دالة دالة متاصلة على + +456 +00:49:34,210 --> 00:49:39,150 +الفترة a وb يبقى التكمل على هذه الفترة exist وفي + +457 +00:49:39,150 --> 00:49:42,810 +هذه الحالة بقول ان الدالة قابلة للتكمل على الفترة + +458 +00:49:42,810 --> 00:49:50,050 +a وb يبقى لو سؤال سؤال هل الدالة هذه؟قابلة للتكامل + +459 +00:49:50,050 --> 00:49:55,070 +على فترة ما ولا لا بقى جيبها اتطالع والله إذا كان + +460 +00:49:55,070 --> 00:50:00,030 +الدالة دالة متصلة على هذه الفترة إذا هي دالة قابلة + +461 +00:50:00,030 --> 00:50:05,850 +للتكامل بس ابحث ال continuity لها ماشي طيب نجي + +462 +00:50:05,850 --> 00:50:12,150 +الآن لخواص التكامل المحدود يبقى ال properties + +463 +00:50:14,670 --> 00:50:27,790 +properties of definite integrals + +464 +00:50:27,790 --> 00:50:31,570 +خاصة + +465 +00:50:31,570 --> 00:50:39,030 +كامل المحدود بيقول لو كانت الدالة F و كذلك الدالة + +466 +00:50:39,030 --> 00:50:43,810 +G are integrable + +467 +00:50:45,720 --> 00:50:54,980 +functions دوال قابلة للتكامل functions of a وb + +468 +00:50:54,980 --> 00:51:00,140 +then النقطة + +469 +00:51:00,140 --> 00:51:09,840 +الأولى تكامل من b إلى aلل F of X DX يسوى ناقص + +470 +00:51:09,840 --> 00:51:18,980 +تكامل من A إلى B لل F of X DX نمره اتنين تكامل من + +471 +00:51:18,980 --> 00:51:28,040 +A إلى A لل F of X DX يسوى Zero تلاتة + +472 +00:51:29,830 --> 00:51:38,290 +تكامل من A إلى B للـK في الـF of X DX يساوي K + +473 +00:51:38,290 --> 00:51:45,930 +تكامل من A للـF of X DX where + +474 +00:51:45,930 --> 00:51:54,970 +حيث الـK is constant الفاصية + +475 +00:51:54,970 --> 00:51:55,630 +الرابعة + +476 +00:51:59,410 --> 00:52:07,870 +خاصية الرارة بيقول تكامل من A إلى B لل F of X زائد + +477 +00:52:07,870 --> 00:52:17,150 +أو ناقص G of X كله في DX بيسوي تكامل من A إلى B لل + +478 +00:52:17,150 --> 00:52:27,070 +F of X DX زائد أو ناقص تكامل من A إلى B لل G of X + +479 +00:52:27,070 --> 00:52:27,890 +DX + +480 +00:52:32,150 --> 00:52:43,030 +خاصية الخامسة تكامل من A إلى B لل F of X DX زائد + +481 +00:52:43,030 --> 00:52:51,490 +تكامل من B إلى C لل F of X DX سوى تكامل من A إلى C + +482 +00:52:51,490 --> 00:53:01,750 +لل F of X DX خاصية ما قبل الأخيرة ال minimumلدالة + +483 +00:53:01,750 --> 00:53:10,970 +F في الـ B ناقص الـ A أقل من أو يساوي تكامل من A + +484 +00:53:10,970 --> 00:53:18,430 +إلى B لل F of X DX أقل من أو يساوي ال maximum + +485 +00:53:18,430 --> 00:53:26,110 +لدالة F في الـ B ناقص الـ A قصية السابعة والأخيرة + +486 +00:53:27,240 --> 00:53:35,260 +if f of x greater than or equal to g of x على + +487 +00:53:35,260 --> 00:53:45,680 +الفترة المغلقة a و b then تكامل من a إلى b لل f of + +488 +00:53:45,680 --> 00:53:54,560 +x dx أكبر من أو يسوى تكامل من a إلى b لل g of x dx + +489 +00:53:54,560 --> 00:53:56,360 +also + +490 +00:54:02,610 --> 00:54:10,150 +وكذلك if ال F of X greater than or equal to zero + +491 +00:54:10,150 --> 00:54:21,550 +على الفترة المغلقة A وB then تكامل من A إلى B لل F + +492 +00:54:21,550 --> 00:54:26,990 +of X DX greater than or equal to zero + +493 +00:54:35,370 --> 00:54:41,170 +نزل لخواص التكامل المحدود هذه الخواص نفس الخواص + +494 +00:54:41,170 --> 00:54:46,190 +اللى أخدتها في الثانوية العامة هي هي لم نأتي بجديد + +495 +00:54:46,190 --> 00:54:51,090 +بدنا نوضح هذه الخواص فببدأ بما يأتي بقول لو كان + +496 +00:54:51,090 --> 00:54:56,790 +عندي دلتين F وجيه كل واحدة فيهم قابلة للتكامل على + +497 +00:54:56,790 --> 00:55:03,000 +نفس الفترةيبقى تنتين integrable على الفترة A وB + +498 +00:55:03,000 --> 00:55:07,840 +الدالة الأولى قبل التكامل على فترة A وB الدالة + +499 +00:55:07,840 --> 00:55:13,360 +التانية قبل التكامل على نفس الفترة A وB إن حدث ذلك + +500 +00:55:13,360 --> 00:55:18,700 +فإن تكامل من B إلى A لل F of X DX يسوى السالب + +501 +00:55:18,700 --> 00:55:25,260 +تكامل من A إلى B للF of X DXيعني لو عندك تكامل إذا + +502 +00:55:25,260 --> 00:55:30,040 +لو قلبت حدية تكامل واحد مكان التاني تعطيك نفس + +503 +00:55:30,040 --> 00:55:35,100 +النتيجة بس بإشارة سالبة يبقى نفس النتيجة بس بإشارة + +504 +00:55:35,100 --> 00:55:40,840 +سالبة يبقى إذا قلبنا حد التكامل السفلي عطنا مكان + +505 +00:55:40,840 --> 00:55:44,520 +العلوي والعلوي مكان السفلي بيعطيني نفس النتيجة بس + +506 +00:55:44,520 --> 00:55:49,940 +بإشارة مخالفة يعني لو كانت النتيجة أصلا سالبة بصير + +507 +00:55:49,940 --> 00:55:50,420 +موجبة + +508 +00:55:53,930 --> 00:55:58,270 +النقطة الثانية قال يتكامل من A إلى A ل F of X DX + +509 +00:55:58,270 --> 00:56:03,410 +سوى قدر؟ Zero بالبلد يبقى جينا نقول إذا تساوى حد + +510 +00:56:03,410 --> 00:56:08,110 +التكاملفإن قيمة التكامل تساوي الصفر مش هيكون اقول + +511 +00:56:08,110 --> 00:56:12,110 +في الثانوية يبقى انا الحد السفلي هو نفس الحد + +512 +00:56:12,110 --> 00:56:15,970 +العليا تكامل من اتنين لاتنين ل F of X DX بساوي + +513 +00:56:15,970 --> 00:56:20,170 +Zero تكامل من عشر على عشر ل F of X DX يعني انا + +514 +00:56:20,170 --> 00:56:25,410 +مامشيتش ولا خطوة ضليت في مكاني من A ل A نفس الرقم + +515 +00:56:25,410 --> 00:56:30,890 +ماخدتش فترةيبقى النتيجة تساوي 0 التكامل هذا بيقول + +516 +00:56:30,890 --> 00:56:34,390 +يتكامل مقدار ثابت في دلة يساوي المقدار الثابت في + +517 +00:56:34,390 --> 00:56:35,370 +تكامل الدلة + +518 +00:56:57,050 --> 00:57:00,310 +أبدًا يعني التكامل هخش على الدالة الأولى و يخش على + +519 +00:57:00,310 --> 00:57:04,870 +الدالة التانية في حالة الجامعة و الطرح ياكوا ثم + +520 +00:57:04,870 --> 00:57:09,610 +ياكوا يضربوا الجسم مش صحيح يبقى صحيح فقط في حالة + +521 +00:57:09,610 --> 00:57:14,290 +الجامعة و الطرح فقط لا غير طيب نيجي نقطة الخامس + +522 +00:57:14,290 --> 00:57:19,150 +تكامل A إلى B ال F of X DX زي تكامل B إلى C لل F + +523 +00:57:19,150 --> 00:57:25,720 +of X DX يساوي تكامل من A إلى C لل F of X DXيعني + +524 +00:57:25,720 --> 00:57:31,940 +يمكن تجزية التكامل إلى مجموعة تكاملين يعني لو جيت + +525 +00:57:31,940 --> 00:57:37,340 +قلت على سبيل المثال ان احنا عندنا دالة هذا محور X + +526 +00:57:37,340 --> 00:57:42,960 +وهذا محور ورسمنا منحنى الدالة هذا كان ايه ابتديت + +527 +00:57:42,960 --> 00:57:48,580 +من عند النقطة A وانتهيت على سبيل المثال عند النقطة + +528 +00:57:48,580 --> 00:57:54,810 +Cيبقى لو كان عندي نقطة B في الطريق هكذا يبقى + +529 +00:57:54,810 --> 00:58:01,650 +التكامل من A إلى B يعطي المساحة هذا التكامل من B + +530 +00:58:01,650 --> 00:58:07,250 +إلى C يعطي المساحة هذه إذا هو عبارة عن التكامل من + +531 +00:58:07,250 --> 00:58:14,250 +A إلى C مباشرة يبقى هذا المقصود اللي هو التكامل + +532 +00:58:14,250 --> 00:58:20,850 +اللي عندكالنقطة السادسة وهي المهمة ال minimum تبع + +533 +00:58:20,850 --> 00:58:27,040 +الدالة f لو ضربته في قول ال intervalهيكون اقل من + +534 +00:58:27,040 --> 00:58:32,760 +او يسوي تكامل من a الى b لل f of x dx اقل من يسوي + +535 +00:58:32,760 --> 00:58:38,840 +maximum للدالة f ميا في طول ال interval فمثلا لو + +536 +00:58:38,840 --> 00:58:45,320 +جيه تقولش لك هذا ا هذا محور x وهذا محور y وافترض + +537 +00:58:45,320 --> 00:58:51,270 +الدالة ماشية بالشكل العلن هذايبقى هذا Y تساوي F of + +538 +00:58:51,270 --> 00:59:00,290 +X وهذا Y تساوي F of X تمام؟ الدالة هذه، هذه نقطة A + +539 +00:59:00,290 --> 00:59:05,950 +وهذه Main وهذه نقطة B المنوعة متابعة ده اللي بيحصل + +540 +00:59:05,950 --> 00:59:11,060 +وين؟ براسمتنا هذه، ممكن يكون بهاحاسس الدالة + +541 +00:59:11,060 --> 00:59:15,980 +تزايدية أو تناقصية ممكن يكون نازل من فوق لتحت يبقى + +542 +00:59:15,980 --> 00:59:18,360 +ال maximum بيحصل في الأول و ال minimum بيحصل في + +543 +00:59:18,360 --> 00:59:23,320 +الآخر يختلف من رسمة لأخرى يبقى هذا بيعطيني ال + +544 +00:59:23,320 --> 00:59:27,700 +minimum تبع الدالة F اللي هو ال F في هذا بيعطيني + +545 +00:59:27,700 --> 00:59:31,940 +ال maximum تبع من الدالة فلما يقول ال minimum تبع + +546 +00:59:31,940 --> 00:59:35,500 +الدالة في ال B ناقص اللي هي ال B ناقص اللي هي + +547 +00:59:35,500 --> 00:59:40,660 +للمسافة هذهالمسافة هذه لو جيتها خط من هنا خط أفقي + +548 +00:59:40,660 --> 00:59:45,160 +بالشكل اللي عناها ال minimum تبع الدالة فيه هذا + +549 +00:59:45,160 --> 00:59:51,800 +فمين في P نقص ال A بيعطيني مساحة المستاطيل المضلة + +550 +00:59:51,800 --> 00:59:57,040 +لهذا صحيح ولا لأ طيب لو أخدت ال maximum تبع الدالة + +551 +00:59:57,040 --> 01:00:03,040 +اللي هو مينالبعد هذا كله، لو جيت قلت كمان زي هيك، + +552 +01:00:03,040 --> 01:00:06,080 +الشكل اللي عندها هذا، يبقى هذا هيعطيلي مساحة + +553 +01:00:06,080 --> 01:00:10,730 +المستطيل الكبيرلكن التكامل على المنحنة بيعطيه + +554 +01:00:10,730 --> 01:00:14,770 +المسافة اللي تحته، المسافة هذه أكبر من المستوطين + +555 +01:00:14,770 --> 01:00:19,150 +الصغير وأقل من المستوطين الكبير، إذا صار التكامل + +556 +01:00:19,150 --> 01:00:22,850 +على الدالة اللي عندنا هذه محصور ما بين ال minimum + +557 +01:00:22,850 --> 01:00:27,070 +لدالة F ال B نقص ال A وما بين ال maximum لدالة F + +558 +01:00:27,070 --> 01:00:31,990 +ال B نقص ال Aهذا عليه أسئلة كثيرة عندك في الكتاب + +559 +01:00:31,990 --> 01:00:38,010 +زي ما هنشوف الآن بعض الأمثلة بعد قليل الخاصية + +560 +01:00:38,010 --> 01:00:42,630 +السابعة والاخيرة بيقول لو كانت ال F of X أكبر من G + +561 +01:00:42,630 --> 01:00:47,830 +of X على فترة ما، كيف يعني؟ يعني لو جيت قلت هذا + +562 +01:00:47,830 --> 01:00:54,540 +المنحنةوهذا محور X وهذا محور Y وهذا النقطة الدالية + +563 +01:00:54,540 --> 01:01:00,460 +لـ0 قال لي على الفترة A وB الـF of X أكبر من مين؟ + +564 +01:01:00,460 --> 01:01:06,640 +من الـG of X يبقى لو كان هذا منحنا الدالة وY تساوي + +565 +01:01:06,640 --> 01:01:13,080 +F of X جيت لمنحنا الدالة التانية وليكن بالشكل اللي + +566 +01:01:13,080 --> 01:01:22,680 +عندك هذا يبقى هذا Y تساوي G of Xأخذت فترة من الـA + +567 +01:01:22,680 --> 01:01:28,800 +مثلا لغاية الـB يبقى في هذه الحالة الفترة A وB + +568 +01:01:28,800 --> 01:01:34,300 +دائما و أبدا F of X أكبر من مين؟ من الـG of X بقول + +569 +01:01:34,300 --> 01:01:37,080 +إيه أن أنت كامل عدل، الأولى أكبر من أنت كامل عدل؟ + +570 +01:01:37,310 --> 01:01:40,610 +طبيعي جداً لإن اتكمل على الدلة لو هعطيك المساحة + +571 +01:01:40,610 --> 01:01:43,810 +هذه كلها و اتكمل على الدلة اني اعطيك المساحة دي + +572 +01:01:43,810 --> 01:01:48,350 +يبقى هذا وضع طبيعي تمام يبقى هذه هي الخاصية رقم + +573 +01:01:48,350 --> 01:01:54,430 +سبعة بتاخد حالة خاصة منها لو كان جيوفكس بزيرو يبقى + +574 +01:01:54,430 --> 01:01:59,010 +لو كان الفوفكس أكبر من أو يساوي زيرو على الفترة + +575 +01:01:59,010 --> 01:02:02,400 +اللي عندنايبقى التكامل على الدالة دي أكبر من أو + +576 +01:02:02,400 --> 01:02:06,860 +يساوي مين؟ Zero يعني هذه حالة خاصة من مين؟ من اللي + +577 +01:02:06,860 --> 01:02:11,120 +فوق يعني التكامل على الدالة الموجبة دائما أو أبدا + +578 +01:02:11,120 --> 01:02:18,060 +بيعطيني قيمة موجبة الآن بهمني كيفية استخدام هذه + +579 +01:02:18,060 --> 01:02:22,900 +الخواص كيف أستخدم هذه الخواص عند حل المسائل + +580 +01:02:22,900 --> 01:02:28,520 +المختلفة؟ يبقى هذا اللي بدنا نتعرض له الآنأول مثال + +581 +01:02:28,520 --> 01:02:38,720 +بيقول ما يأتي example one بيقول ما يأتي if ال + +582 +01:02:38,720 --> 01:02:49,900 +if and ال g are integrable functions integrable + +583 +01:02:49,900 --> 01:02:58,320 +functions andوفي نفس الوقت كان تكامل من واحد إلى + +584 +01:02:58,320 --> 01:03:07,680 +اتنين لل F of X DX بده يساوي سالب أربعة وتكامل من + +585 +01:03:07,680 --> 01:03:20,460 +واحد إلى خمسة لل F of X DX بده يساوي ستة and تكامل + +586 +01:03:21,160 --> 01:03:28,840 +من واحد إلى خمسة للـ G of X DX بده يسوى تمانية + +587 +01:03:28,840 --> 01:03:40,420 +Find the value of بدنا قيمة كله مما يأتي + +588 +01:03:58,540 --> 01:04:08,840 +نمر آي بدنا تكامل من اتنين لغاية واحد لثالث اتنين + +589 +01:04:08,840 --> 01:04:17,280 +F of X DX نمر بيه بدنا تكامل من اتنين إلى خمسة + +590 +01:04:17,280 --> 01:04:25,820 +لخمسة F of X DX نمر سيه بدنا تكامل من واحد إلى + +591 +01:04:25,820 --> 01:04:35,890 +خمسةلمن لا تلاتة f of x ناقص g of x كله في dx + +592 +01:05:08,640 --> 01:05:13,360 +طلعلي في المنصلة كويس بيقول لي ده ال F و G دوال + +593 +01:05:13,360 --> 01:05:17,460 +قابل للتكامل ماتيني قيمة التكامل على F من واحد إلى + +594 +01:05:17,460 --> 01:05:21,040 +اتنين بسالف اربعة تكامل واحد إلى خمسة اللي F of X + +595 +01:05:21,040 --> 01:05:24,820 +يساوي ستة تكامل على G of X من واحد إلى خمسة يساوي + +596 +01:05:24,820 --> 01:05:29,040 +تمانية جالي هاتلي قيمة من التكامل كل تكامل من + +597 +01:05:29,040 --> 01:05:34,160 +التكاملات الثلاثة اللي أمامنا انا عندي خواصب ده + +598 +01:05:34,160 --> 01:05:38,990 +حاول استعمل الخواصب بقدر الإمكان باجي بطلعالاندكس + +599 +01:05:38,990 --> 01:05:43,070 +اللي تحت التكامل اللي تحت هو من الكبير واللي فوق + +600 +01:05:43,070 --> 01:05:47,290 +صغير دائما وأبدا بارتب التكامل لحياتي يكون الاندكس + +601 +01:05:47,290 --> 01:05:51,310 +اللي تحت هو الصغير والاندكس اللي فوق هو الكبير + +602 +01:05:51,310 --> 01:05:56,820 +يبقى بناء عليه هدف بقلب حدود التكاملبقول الخاصية + +603 +01:05:56,820 --> 01:06:01,680 +الأولى مسحناها إذا بتقلب حدود التكامل تجيك إشارة + +604 +01:06:01,680 --> 01:06:06,620 +سالم يبقى هذا هو عبارة عن تكمل من 1 لليتنين + +605 +01:06:06,620 --> 01:06:13,560 +لليتنين f of x dxخاصية تالتة بيقول إذا عندك مقدار + +606 +01:06:13,560 --> 01:06:19,300 +ثابت بتطلعه برا تمام يبقى باجي بقوله يا اتنين خليك + +607 +01:06:19,300 --> 01:06:25,060 +برا و تكامل من واحد للي اتنين لل F of X DX يساوي + +608 +01:06:25,060 --> 01:06:28,100 +اتنين اظن معطف تكام واحد للي اتنين ل F of X DX + +609 +01:06:28,100 --> 01:06:33,140 +يساوي اتنين سالب اربعة يبقى سالب اربعة يبقى + +610 +01:06:33,140 --> 01:06:39,480 +النتيجة تساوي كده سالب تمانية نيجي لنمرمينمرة + +611 +01:06:39,480 --> 01:06:45,520 +بيقول بدي تكامل من اتنين لخمسة لخمسة F of X DX + +612 +01:06:45,520 --> 01:06:53,360 +باجي بقوله هيتكامل من اتنين الى خمسة لخمسة F of X + +613 +01:06:53,360 --> 01:06:59,760 +DX يساوي خمسة مقدار ثابت بقوله برا يبجي من اتنين + +614 +01:06:59,760 --> 01:07:05,600 +الى خمسةللـ F of X DX باجي على التكاملات اللي عندي + +615 +01:07:05,600 --> 01:07:11,640 +ماعنديش ولا تكامل من اتنين الى خمسة يبقى استخدم + +616 +01:07:11,640 --> 01:07:17,140 +عجلك بقول له اه استنى شوية خلي هذا على شجرة انا + +617 +01:07:17,140 --> 01:07:25,510 +عندي تكامل من واحد الى خمسةللـ f of x dx معروفة + +618 +01:07:25,510 --> 01:07:31,250 +قيمته صحيح ولا لا لو بسته بقول اه بنقدر نجزق هذا + +619 +01:07:31,250 --> 01:07:36,920 +التكامل لتكاملينلأن أنا عندي تكامل من واحد لإتنين + +620 +01:07:36,920 --> 01:07:41,540 +و اللي مقلوب من إتنين إذا بجهزه تكامل تبعي إلى + +621 +01:07:41,540 --> 01:07:47,480 +تكاملين طبقا للخاصية رقم خمسة إذا بقدر أقول هذا هو + +622 +01:07:47,480 --> 01:07:55,500 +تكامل من واحد للإتنين لل F of X DX زي التكامل من + +623 +01:07:55,500 --> 01:08:01,200 +إتنين للخمسة لل F of X DX صحيح ولا لأ؟ أنا بدي هذا + +624 +01:08:01,200 --> 01:08:06,670 +التكاملمظبوط يبقى باجي بيقول له هذا بده يعطينا ميم + +625 +01:08:06,670 --> 01:08:14,360 +يعطينا ما يأتيالتكامل الأول 6 يبقى هاي 6 U7 + +626 +01:08:14,360 --> 01:08:22,800 +التكامل التاني جداش سالب 4 زي تكامل من 2 إلى 5 لل + +627 +01:08:22,800 --> 01:08:30,460 +F of X DX يبقى هذا بده يعطيلك انه تكامل من 2 إلى 5 + +628 +01:08:30,460 --> 01:08:36,660 +لل F of X DX ضيف 4 على الطرفين يبقى بده يعطيك جداش + +629 +01:08:36,660 --> 01:08:37,560 +10 + +630 +01:08:41,540 --> 01:08:48,220 +ماذا ما عرفناها يبقى هذا بده يعطيك انه تكامل من + +631 +01:08:48,220 --> 01:08:54,700 +اتنين الى خمسة لخمسة F of X DX بده يساوي خمسة اللي + +632 +01:08:54,700 --> 01:09:00,380 +برا في هذا التكامل هذا التكامل قداش عشرة يبقى + +633 +01:09:00,380 --> 01:09:06,160 +يساوي خمسين يبقى قيمة هذا التكامل يساوي خمسين + +634 +01:09:09,220 --> 01:09:14,520 +نمر الـ C يعطيني مجموع تكاملين، إذا بقدر أوزع + +635 +01:09:14,520 --> 01:09:20,980 +التكامل لكل من هما طبق للخاصية رقم أربع، تمام؟ + +636 +01:09:20,980 --> 01:09:26,160 +فباجي بقوله ما يأتي، أنا عندي تكامل من واحد إلى + +637 +01:09:26,160 --> 01:09:34,480 +خمسة لمين؟ لتلاتة، F of X ناقص الـ G of X كل هذا + +638 +01:09:34,480 --> 01:09:41,140 +الكلام DX يساويبدي اوزع التكامل لكل واحد واطلع + +639 +01:09:41,140 --> 01:09:45,820 +التلاتة من التكامل الاول برة يبقى هاي تلاتة برة + +640 +01:09:45,820 --> 01:09:52,040 +وهاي تكامل من واحد الى خمسة لل F of X DX ناقص + +641 +01:09:52,040 --> 01:09:59,020 +تكامل من واحد الى خمسة لل G of X DX Y الساوي هاي + +642 +01:09:59,020 --> 01:10:05,110 +تلاتةتكمل من واحد إلى خمسة عماطة اللي هو جداش ستة + +643 +01:10:05,110 --> 01:10:12,650 +يبقى بصير هذا تلاتة في ستةنقص تكبر واحد الى خمسة + +644 +01:10:12,650 --> 01:10:16,870 +الجيل اللي هو جداش تمانية يبقى تلاتة في ستة في + +645 +01:10:16,870 --> 01:10:21,990 +تمانتاش ناقص تمانية يبقى نتيجة تساوي جداش عشرة + +646 +01:10:21,990 --> 01:10:26,490 +يبقى هذا مثال على كيفية استخدام الخواص المختلفة + +647 +01:10:26,490 --> 01:10:30,630 +لكن حتى اللحظة اللي هي أهم خاصية فيهم لحد تلان ما + +648 +01:10:30,630 --> 01:10:36,710 +استخدمنهاش طبعا طيب ولا يهمك هناك مزيد من الأمثلة + +649 +01:10:36,710 --> 01:10:38,630 +عشان نستخدمها + +650 +01:10:59,890 --> 01:11:09,350 +Example 2 مقول + +651 +01:11:09,350 --> 01:11:18,890 +find and upper bound and + +652 +01:11:18,890 --> 01:11:20,970 +lower bound + +653 +01:11:26,740 --> 01:11:34,400 +Upper bound and lower bound for the integral + +654 +01:11:34,400 --> 01:11:41,080 +لتكامل + +655 +01:11:41,080 --> 01:11:49,380 +تكامل من باية على أربعة لباية على تلاتة لكوصين X + +656 +01:11:49,380 --> 01:11:52,980 +في DX كوصين X في DX + +657 +01:12:03,800 --> 01:12:09,600 +بقول هاتلي حد علوي و حد سفلي للتكامل اللى عندنا + +658 +01:12:09,600 --> 01:12:14,260 +هذا يعني بدي اجيبليه رقامين بحيث قيمة هذا التكامل + +659 +01:12:14,260 --> 01:12:19,540 +تكون محصورة بينهم ولم يقول كامل صح ولا لا طب باجي + +660 +01:12:19,540 --> 01:12:25,280 +بطلع في الخواصة اللى عندى من واحد لغاية سبعةأول + +661 +01:12:25,280 --> 01:12:29,200 +ميجي فالى مين؟ ستة لإن ستة هي اللى بيقول التكوين + +662 +01:12:29,200 --> 01:12:33,800 +محصور بين قيمتين يبقى لما اقول انا بدي تكوينكصور + +663 +01:12:33,800 --> 01:12:36,700 +محصور بين upper bound و lower bound يعني حد عليه + +664 +01:12:36,700 --> 01:12:41,700 +حد simply إذا مليش الخاصية رقم ستة إذا مشان أجيب + +665 +01:12:41,700 --> 01:12:45,820 +الخاصية رقم ستة بدي أشوف ال minimum تبع الدالة F و + +666 +01:12:45,820 --> 01:12:49,740 +طول الفترة سهلبايع ثلاثة نقص بايع على أربع و بدي + +667 +01:12:49,740 --> 01:12:55,420 +اشوف ال maximum تبع الدالة F اه معناته الدالة هذه + +668 +01:12:55,420 --> 01:12:59,160 +بدي اشوف هل هي increasing و الله decreasing و يمكن + +669 +01:12:59,160 --> 01:13:03,400 +ما تكونش الله أعلم نعم نعرف و يمكن increasing و + +670 +01:13:03,400 --> 01:13:08,520 +decreasing الله أعلم يبقى انا كل اللي عندي بقوله + +671 +01:13:08,520 --> 01:13:15,790 +ان ال F of X الهدنمية اللي هي cos Xبدي اشوف على + +672 +01:13:15,790 --> 01:13:18,930 +الفترة اللي عندنا هل اتدى ل increasing و لا + +673 +01:13:18,930 --> 01:13:22,210 +decreasing طب ليش increasing و لا decreasing؟ لأن + +674 +01:13:22,210 --> 01:13:25,590 +إذا تزايدية يبقى ال minimum في الأول و ال maximum + +675 +01:13:25,590 --> 01:13:29,230 +في الآخر و إذا decreasing يبقى ال maximum في الأول + +676 +01:13:29,230 --> 01:13:33,590 +و ال minimum في الآخر، مظبوط او لا؟ طيب يبقى هذا + +677 +01:13:33,590 --> 01:13:41,350 +الكلام بدي اعطيك ان f prime of x يساوي سالب sin x + +678 +01:13:41,350 --> 01:13:48,520 +طب كويسهذه القيمة على الفترة من باية لأربعة لباية + +679 +01:13:48,520 --> 01:13:52,280 +على تلاتة يعني من خمسة واربعين درجة لغاية الستين + +680 +01:13:52,280 --> 01:13:57,420 +في أي الأربعةالأول يعني ال sign هذا موجب دائما و + +681 +01:13:57,420 --> 01:14:02,200 +أبدا وهذا مسوق بمين بشرة سالب يقول ايش بصير سالب + +682 +01:14:02,200 --> 01:14:08,080 +معناه هذا الكلام انه أقل من ال zero لكل ال X اللي + +683 +01:14:08,080 --> 01:14:13,640 +موجودة من πاي على أربعة لغاية جداش لباية تلاتة + +684 +01:14:13,640 --> 01:14:15,560 +معناته ان الدالة هذه مالها + +685 +01:14:27,590 --> 01:14:35,670 +تنقصية على الفترة من Pi على 4 لغاية Pi على 3يبقى + +686 +01:14:35,670 --> 01:14:40,390 +انا استنتاجها رياضيا دون ان انظر الى الرسم تبعها + +687 +01:14:40,390 --> 01:14:44,330 +لكن لو رجعت للرسمة و صحيح بتبدأ من عندي zero و + +688 +01:14:44,330 --> 01:14:47,830 +بتنزل لغاية باي و هى نازلة، مظبوط ولا لا؟ يبقى + +689 +01:14:47,830 --> 01:14:50,510 +احنا في الرابع الأول يبقى هى كانت decreasing + +690 +01:14:50,510 --> 01:14:55,130 +بالفعل كانت decreasingما علينا ممكن تبقى أي دللة + +691 +01:14:55,130 --> 01:14:58,450 +يبقى انستنتجها رياضيا او لو ان انا عارف رسمتها + +692 +01:14:58,450 --> 01:15:02,310 +وسميت حالة مش عارف الرسمة بتاعتها يبقى محصورة بين + +693 +01:15:02,310 --> 01:15:07,790 +باي على اربعة لغاية باي على تلتة مادام decreasing + +694 +01:15:07,790 --> 01:15:14,130 +تناقصية هي decreasing اذا ال maximum بيحصل وين؟عند + +695 +01:15:14,130 --> 01:15:18,410 +البداية عند ال by على أربع و ال minimum بيحصل عند + +696 +01:15:18,410 --> 01:15:26,670 +النهاية يبقى باجي بقوله إذا ال maximum لدلة F هو + +697 +01:15:26,670 --> 01:15:36,990 +عبارة عن ال maximum للقصائم ال Xهذا اوكر بيحدث ات + +698 +01:15:36,990 --> 01:15:43,510 +من اكس يساوي decreasing يعني نازلة من فوق يبقى عند + +699 +01:15:43,510 --> 01:15:49,700 +ال by على اربع عند البداية و ليس عند النهايةهذا + +700 +01:15:49,700 --> 01:15:55,700 +بده يعطيك انه cosine باي على اربع جدش بده يساوي + +701 +01:15:55,700 --> 01:16:02,400 +جتا خمسة واربعين بواحد على جدر اتنين الان بالدج ال + +702 +01:16:02,400 --> 01:16:07,760 +minimum تبع الدلة F هو عبارة عن ال minimum تبع ال + +703 +01:16:07,760 --> 01:16:14,350 +cosine Xوهذا بيحدث عند x يساوي كده؟ بيعة تلاتة هذا + +704 +01:16:14,350 --> 01:16:20,010 +بيقدر يعطيك ان ال cosine بيعة تلاتة جتا تلاتين + +705 +01:16:22,200 --> 01:16:27,180 +جتا ستين اللي هو بنص طبعا الان بدي اقول الخاصية + +706 +01:16:27,180 --> 01:16:33,860 +تبعتنا تبعتنا بتقول ال minimum تبعت ال F في ال B + +707 +01:16:33,860 --> 01:16:40,140 +ناقص ال A اللي هي باية تلاتة ناقص باية على أربع + +708 +01:16:40,140 --> 01:16:46,080 +أقل من أو يسوى تكامل من باية على أربع لباية تلاتة + +709 +01:16:46,080 --> 01:16:54,180 +لكوصين ال X DX أقل من maximumالدالة F في مين؟ في + +710 +01:16:54,180 --> 01:17:00,980 +الـ πايعة تلاتة ناقص الـ πايع على أربع بقوله كويس + +711 +01:17:00,980 --> 01:17:07,680 +ال minimum تبع الدالة F كده إيش؟ نص يبقى هذا نص + +712 +01:17:07,680 --> 01:17:13,900 +وهذه بايع تلاتة ناقص بايع الأربع مضاعف المشترك + +713 +01:17:13,900 --> 01:17:20,020 +أتناش يبقى أربع ناقص تلاتة بيظل بس بايع على أتناش + +714 +01:17:21,280 --> 01:17:25,940 +باية على أتناشر أقل من تكامل من باية على أربع + +715 +01:17:25,940 --> 01:17:33,600 +لغاية باية على تلاتة لكوسين ال X DX وهذه أقل من أو + +716 +01:17:33,600 --> 01:17:38,930 +يساوي ال maximum تبعهاالـ maximum تبعد ده الافة + +717 +01:17:38,930 --> 01:17:44,770 +اللي أنا جدوش واحد على جذري اتنين يبقى واحد على + +718 +01:17:44,770 --> 01:17:51,410 +جذري اتنين في ال by على اتن عشر ايش قال له؟ بدي + +719 +01:17:51,410 --> 01:17:55,550 +upper bound و lower bound لهذا التكامل يبقى باجي + +720 +01:17:55,550 --> 01:18:05,670 +بقوله the upper bound of the integral + +721 +01:18:08,070 --> 01:18:15,850 +القيمة الأولى و الله التانية يبقى باي على اتناشر + +722 +01:18:15,850 --> 01:18:26,510 +جذري اتنين and the lower bound is باي على اربع + +723 +01:18:26,510 --> 01:18:27,290 +وعشرين + +724 +01:18:55,530 --> 01:19:05,810 +طيب نعطيك كمان مثال find + +725 +01:19:05,810 --> 01:19:22,170 +the values of a and b such that بحيث + +726 +01:19:22,170 --> 01:19:30,250 +انالـ A أقل من أو يساوي تكامل من سلب واحد إلى واحد + +727 +01:19:30,250 --> 01:19:37,050 +للجذر التربيهي لواحد زائد X أربعة DX أقل من أو + +728 +01:19:37,050 --> 01:19:50,050 +يساوي من الـ B أظن + +729 +01:19:50,050 --> 01:19:54,900 +نفس فكرة السؤال السابقنفس الفكرة لكن اختلاف في + +730 +01:19:54,900 --> 01:19:59,760 +الشكل و سنجد اختلاف في المضمون و لو انها نفس + +731 +01:19:59,760 --> 01:20:06,120 +الفكرة كيف؟ قال هاتل قيم a و b بحيث a أقل من أو + +732 +01:20:06,120 --> 01:20:10,340 +يسوى التكامل أقل من أو يسوى لم يقل هاتل قيمة + +733 +01:20:10,340 --> 01:20:14,060 +التكامل اتنين ولا واحد هي كبيرة في كامل الدالة هذه + +734 +01:20:14,060 --> 01:20:17,750 +حتى اللحظةوحتى لما تخلص Calculusيا وانت بتعرفش + +735 +01:20:17,750 --> 01:20:23,890 +تكملها كمان لكن بعديك مرحبا بكم تكملها تمام؟ طيب + +736 +01:20:23,890 --> 01:20:28,640 +بهمنيش مجليش كامل جليبييل لي ان هذا التكامل محصور + +737 +01:20:28,640 --> 01:20:33,380 +يعني بدك تجيبلي الرقمين التكامل هذا أبدا دايما + +738 +01:20:33,380 --> 01:20:39,000 +محصور ما بين الاتنين بقوله كويس بدنا نيجي نجيب له + +739 +01:20:39,000 --> 01:20:42,240 +قيمة ا و بمش هنجيب له قيمة ا و ب بدي اشوف زي اللي + +740 +01:20:42,240 --> 01:20:45,080 +جابله هل هي increasing ولا decreasing ولا شو القصة + +741 +01:20:45,080 --> 01:20:50,320 +بالظبط بقوله بسيطة احنا عندنا ال F of X يساوي + +742 +01:20:50,320 --> 01:20:55,760 +الجدر التربية إلى واحد زي دكسوس أربعلو اشتقناها + +743 +01:20:55,760 --> 01:21:00,940 +يبقى هذا بدي اعطيك f prime of x يبقى واحد على + +744 +01:21:00,940 --> 01:21:07,780 +اتنين الجذر التربيعي لواحد زي x أُص أربعة في مشتقة + +745 +01:21:07,780 --> 01:21:14,540 +ما داخل الجذر اربعة x تكييب يبقى اتنين x تكييب على + +746 +01:21:14,540 --> 01:21:20,390 +الجذر التربيعي لواحد زي x أُص أربعةيبقى هذه + +747 +01:21:20,390 --> 01:21:25,030 +المشتقة in general أنا مقيد للفترة من سالب واحد + +748 +01:21:25,030 --> 01:21:28,490 +إلى واحد وماليش دعوة في الباقي، مظبوط؟ بقولك + +749 +01:21:28,490 --> 01:21:34,870 +كويسة، هذا لو جيت قلت هذا ال real line وهذا سالب + +750 +01:21:34,870 --> 01:21:41,990 +واحد وهنا zero وهنا واحد، تمام؟ الآن المقام عمره + +751 +01:21:41,990 --> 01:21:46,110 +بياخد إشارة سالب؟يبقى ال X سالب هو الله موجبة + +752 +01:21:46,110 --> 01:21:48,610 +وموجبة هو الله موجبة وموجبة هو الله موجبة وموجبة + +753 +01:21:48,610 --> 01:21:49,430 +هو الله موجبة وموجبة هو الله موجبة وموجبة هو الله + +754 +01:21:49,430 --> 01:21:50,790 +موجبة وموجبة هو الله موجبة وموجبة هو الله موجبة + +755 +01:21:50,790 --> 01:21:54,510 +وموجبة هو الله موجبة وموجبة هو الله موجبة وموجبة + +756 +01:21:54,510 --> 01:21:55,110 +هو الله موجبة وموجبة هو الله موجبة وموجبة هو الله + +757 +01:21:55,110 --> 01:21:57,250 +موجبة وموجبة هو الله موجبة وموجبة هو الله موجبة + +758 +01:21:57,250 --> 01:21:59,570 +وموجبة هو الله موجبة وموجبة هو الله موجبة وموجبة + +759 +01:21:59,570 --> 01:21:59,630 +هو الله موجبة وموجبة هو الله موجبة وموجبة هو الله + +760 +01:21:59,630 --> 01:22:02,390 +موجبة وموجبة هو الله موجبة وموجبة هو الله موجبة + +761 +01:22:02,390 --> 01:22:07,750 +وموجبة هو الله موجبة وموجبة هو الله موجبة + +762 +01:22:07,750 --> 01:22:17,170 +وموجالـ F' of X أكبر من الـ Zero على الفترة من + +763 +01:22:17,170 --> 01:22:22,150 +عندي الـ Zero لغاية مين؟ لغاية الواحد، معناته الـ + +764 +01:22:22,150 --> 01:22:31,820 +F is decreasingدالة تناقصية on الفترة من سالب واحد + +765 +01:22:31,820 --> 01:22:40,260 +لغاية مين is zero and increasing دالة تزايدية على + +766 +01:22:40,260 --> 01:22:44,890 +الفترة من عند ال zero لغاية مين لغاية الواحدتبقى + +767 +01:22:44,890 --> 01:22:50,290 +في لحظة ما من سالب واحد الى زيرو كانت decreasing + +768 +01:22:50,290 --> 01:22:55,950 +كانت نازلة و بعدها صارت ايه؟ صارت طالع بالشكل اللي + +769 +01:22:55,950 --> 01:23:01,230 +عندنا لكن احنا مقيدين فقط من سالب واحد الى واحد + +770 +01:23:01,230 --> 01:23:06,210 +ماعناش علاقة بعد واحد و ماعناش علاقة قبل واحد بقول + +771 +01:23:06,210 --> 01:23:10,670 +طيب مدام هيك لما تبقى انتباهي بدي اشوف قداش ال F + +772 +01:23:10,670 --> 01:23:15,960 +of واحد وال F of سالب واحدطب اطلع في الدالة هذه ال + +773 +01:23:15,960 --> 01:23:20,980 +F of واحد وال F of سالب واحد يبقى + +774 +01:23:20,980 --> 01:23:28,220 +ال F of سالب واحد هو نفس ال F of واحد هو الجذر + +775 +01:23:28,220 --> 01:23:34,440 +التربيه الواحد زائد واحد يساوي جذر اتنين يبقى عند + +776 +01:23:34,440 --> 01:23:39,020 +اول النقطة هذه قيمة الدالة جذر اتنين وعند النهاية + +777 +01:23:39,020 --> 01:23:44,170 +جذر اتنينيبقى عند السلب واحد تبقى جدر اتنين وعند + +778 +01:23:44,170 --> 01:23:47,790 +الواحد تبقى جدر اتنين يعني كانت فوق كويس بس هذي + +779 +01:23:47,790 --> 01:23:54,010 +نزلت بده يشوف نزلت لوين بده يروح لل F of Zero ال F + +780 +01:23:54,010 --> 01:23:56,730 +of Zero اللي هو الجدر التربية اللي هو واحد زائد + +781 +01:23:56,730 --> 01:24:02,160 +Zero يعني واحد طب جدر اتنين بقداشاحد واربع من + +782 +01:24:02,160 --> 01:24:06,200 +العاشرة تقريبا و الهدى واحد يبقى ال minimum اللى + +783 +01:24:06,200 --> 01:24:11,900 +دالة بيحصل وين و مقداره و ال maximum تبع الدالة + +784 +01:24:11,900 --> 01:24:17,830 +جذرتنه و بيحصل عنده نقطتين عند السلب واحد واحديبقى + +785 +01:24:17,830 --> 01:24:25,390 +باجي بقوله ال maximum لدلة f بده يساوي جذر اتنين + +786 +01:24:25,390 --> 01:24:35,690 +at x يساوي سالب واحد and at x يساوي واحد and ال + +787 +01:24:35,690 --> 01:24:44,110 +minimum لدلة f بده يساوي واحد at x يساوي زيرا اذا + +788 +01:24:44,110 --> 01:24:51,910 +بده ارجع للخاصية تبعتيالـ Minimum لدالة F مضروب في + +789 +01:24:51,910 --> 01:24:58,790 +الـ B ناقص الـ A الـ B اللي هي واحد ناقص لناقص + +790 +01:24:58,790 --> 01:25:04,550 +واحدأقل من أو يسوى تكامل من سلب واحد إلى واحد + +791 +01:25:04,550 --> 01:25:11,330 +للجدر التربية لواحد زي X أس 4DX أقل من أو يسوى ال + +792 +01:25:11,330 --> 01:25:18,780 +maximum لدلة F في الواحد ناقص ناقص واحدطبعا نجي ال + +793 +01:25:18,780 --> 01:25:22,360 +minimum لده ال F ال minimum لده ال F اللي هو جداش + +794 +01:25:22,360 --> 01:25:29,740 +واحد يبقى هنا واحد في اتنين اقل من او يسوى تكامل + +795 +01:25:29,740 --> 01:25:34,700 +من سالب واحد الى واحد للجذر التربيه الواحد زاد X + +796 +01:25:34,700 --> 01:25:39,860 +وصة اربعة DX اقل من او يسوى ال maximum اللي هو جذر + +797 +01:25:39,860 --> 01:25:46,660 +اتنين في جداش في اتنين اتنين جذر اتنينيبقى الصورة + +798 +01:25:46,660 --> 01:25:52,920 +تكون هذه a وهذه مين ال b يبقى هذا معناته ان ال a + +799 +01:25:52,920 --> 01:26:01,680 +تساوي اتنين and ال b يساوي اتنين جدري اتنين نفس + +800 +01:26:01,680 --> 01:26:04,880 +الفكرة بس السؤال اللي جابله كان increasing على قول + +801 +01:26:04,880 --> 01:26:09,160 +او decreasing هذه مرة increasing ومرة decreasing + +802 +01:26:09,160 --> 01:26:14,280 +digital area under + +803 +01:26:16,510 --> 01:26:20,290 +under the + +804 +01:26:20,290 --> 01:26:29,290 +graph of a non-negative + +805 +01:26:29,290 --> 01:26:38,330 +function definition + +806 +01:26:44,030 --> 01:26:57,350 +Y تساوي F of X is non negative and + +807 +01:26:57,350 --> 01:27:00,790 +integrable + +808 +01:27:00,790 --> 01:27:12,990 +وقابلة للتكامل over a closed interval + +809 +01:27:14,790 --> 01:27:26,410 +closed interval a و b then the area then the area + +810 +01:27:26,410 --> 01:27:29,550 +under + +811 +01:27:29,550 --> 01:27:32,690 +the + +812 +01:27:32,690 --> 01:27:50,290 +curve under the curve y تساوي f of xو X + +813 +01:27:50,290 --> 01:28:01,730 +Axis over A و B تكامل + +814 +01:28:01,730 --> 01:28:06,730 +من A إلى B لل F of X DX + +815 +01:28:20,670 --> 01:28:25,250 +لما نرسم ال function قد تكون اعلى ال X axisوقد + +816 +01:28:25,250 --> 01:28:29,910 +تكون أسفل الـ x-axis وقد يكون جزء أعلى الـ x-axis + +817 +01:28:29,910 --> 01:28:35,050 +وجزء أسفل الـ x-axis موضوعنا هنا لو كانت الدالة + +818 +01:28:35,050 --> 01:28:40,070 +أعلى الـ x-axis والباقي له كلام في المحاضرة + +819 +01:28:40,070 --> 01:28:45,310 +القادمة ان شاء الله تعالى أو التي تليها خلينا بس + +820 +01:28:45,310 --> 01:28:47,950 +ال area under the graph of the non negative + +821 +01:28:47,950 --> 01:28:52,290 +function non negative يعني الدالة لا تاخد قيمة إلا + +822 +01:28:54,880 --> 01:29:01,540 +أكبر من مين؟ من الـ Zero طبعا بقول لو كان Y تساوي + +823 +01:29:01,540 --> 01:29:04,800 +F of X is non-negative and integrable على ال + +824 +01:29:04,800 --> 01:29:09,660 +closed interval A وB then the area under the curve + +825 +01:29:09,660 --> 01:29:15,360 +المساحة الموجودة تحت المنحنة Y تساوي F of X بينها + +826 +01:29:15,360 --> 01:29:21,620 +وبين محور X على الفترة من A إلى B هو تكاملمن A إلى + +827 +01:29:21,620 --> 01:29:26,360 +B لل F of X DX يبقى معنى هذا الكلام طبقًا لهذا ال + +828 +01:29:26,360 --> 01:29:31,640 +definition المعنى الهندسي للتكامل من A إلى B لل F + +829 +01:29:31,640 --> 01:29:36,640 +of X DX هو المساحة المحصورة بين المنحنة ومحور X + +830 +01:29:36,640 --> 01:29:42,940 +على الفترة من A إلى B يعني يمكن استخدام المساحة في + +831 +01:29:42,940 --> 01:29:49,490 +معرفة قيمة التكامل دون إجراء عملية التكاملوهذا ما + +832 +01:29:49,490 --> 01:29:53,390 +سنعرفه في الأمثلة في المحاضرة القادمة + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/V5s5yzhBSiY_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/V5s5yzhBSiY_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..7cc7eb7d47abe5bf33564f3adc25ffda2207273a --- /dev/null +++ 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functions يبقى أنا بدي أجيبله الـdy معناته بدي المشتقة واضغفه في من؟ في الـdx بكون حصلنا على المطلوب بقولك كويس", "tokens": [10721, 2407, 9154, 2423, 39184, 29581, 13760, 24976, 39184, 22845, 288, 6055, 3794, 995, 45865, 283, 295, 2031, 9673, 12984, 6027, 4724, 1829, 39648, 32239, 8032, 9307, 20292, 13672, 1829, 31439, 2423, 15756, 14584, 337, 264, 3480, 6828, 7251, 3555, 4587, 7578, 41850, 4724, 16254, 5551, 7435, 1829, 3555, 43761, 2423, 39184, 3173, 20449, 8315, 47395, 4724, 16254, 9673, 8592, 2655, 28671, 4032, 46958, 17082, 5172, 3224, 8978, 9154, 22807, 8978, 2423, 39184, 67, 87, 4724, 30544, 11331, 36520, 8315, 15844, 9673, 9566, 1211, 37746, 4724, 39648, 4117, 9122, 45865, 3794], "avg_logprob": -0.2802309818241907, "compression_ratio": 1.5194805194805194, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1694.91, "end": 1696.39, "word": "أو", "probability": 0.54461669921875}, {"start": 1696.39, "end": 1696.69, "word": " من", "probability": 0.87353515625}, {"start": 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0.77392578125}, {"start": 1711.33, "end": 1711.89, "word": " أجيبله", "probability": 0.88544921875}, {"start": 1711.89, "end": 1712.45, "word": " الـdy", "probability": 0.7021484375}, {"start": 1712.45, "end": 1713.37, "word": " معناته", "probability": 0.88623046875}, {"start": 1713.37, "end": 1713.75, "word": " بدي", "probability": 0.876220703125}, {"start": 1713.75, "end": 1714.57, "word": " المشتقة", "probability": 0.962890625}, {"start": 1714.57, "end": 1715.15, "word": " واضغفه", "probability": 0.61953125}, {"start": 1715.15, "end": 1715.33, "word": " في", "probability": 0.970703125}, {"start": 1715.33, "end": 1715.89, "word": " من؟", "probability": 0.4539794921875}, {"start": 1715.89, "end": 1716.43, "word": " في", "probability": 0.69970703125}, {"start": 1716.43, "end": 1716.99, "word": " الـdx", "probability": 0.7977294921875}, {"start": 1716.99, "end": 1717.29, "word": " بكون", "probability": 0.62744140625}, {"start": 1717.29, "end": 1717.93, "word": " حصلنا", "probability": 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"إتنين الجذر التربيعي لواحد ناقص X تربية في مشتقة ما تحت الجذر له سالب اتنين X تمام؟ هذا الأولى في مشتقة مين؟ الثانية", "tokens": [28814, 2655, 1863, 9957, 25724, 8848, 2288, 16712, 2288, 21292, 3615, 1829, 5296, 14407, 24401, 8717, 995, 4587, 9381, 1783, 6055, 25513, 10632, 8978, 37893, 2655, 28671, 19446, 6055, 33753, 25724, 8848, 2288, 46740, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 1783, 46811, 10943, 22807, 23758, 16247, 12610, 7578, 8978, 37893, 2655, 28671, 3714, 9957, 22807, 6024, 104, 7649, 10632], "avg_logprob": -0.18942110362600106, "compression_ratio": 1.6, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1747.3, "end": 1748.26, "word": "إتنين", "probability": 0.74359130859375}, {"start": 1748.26, "end": 1748.96, "word": " الجذر", "probability": 0.7731119791666666}, {"start": 1748.96, "end": 1750.14, "word": " التربيعي", "probability": 0.8271484375}, {"start": 1750.14, "end": 1751.4, "word": " لواحد", "probability": 0.8907877604166666}, {"start": 1751.4, "end": 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"end": 1760.96, "word": " تمام؟", "probability": 0.6036783854166666}, {"start": 1760.96, "end": 1761.3, "word": " هذا", "probability": 0.8349609375}, {"start": 1761.3, "end": 1761.78, "word": " الأولى", "probability": 0.9529622395833334}, {"start": 1761.78, "end": 1761.9, "word": " في", "probability": 0.9150390625}, {"start": 1761.9, "end": 1762.5, "word": " مشتقة", "probability": 0.97802734375}, {"start": 1762.5, "end": 1763.04, "word": " مين؟", "probability": 0.8251953125}, {"start": 1763.04, "end": 1763.8, "word": " الثانية", "probability": 0.919677734375}], "temperature": 1.0}, {"id": 76, "seek": 178159, "start": 1764.11, "end": 1781.59, "text": "زائد ثانية في مشتقة الأولى واحد ناقص X تربية ومشتقة الأولى واحد يبقى كله هدف في DX نختصر الاختصارات بصير DY يساوي", "tokens": [11622, 16373, 3215, 38637, 7649, 10632, 8978, 37893, 2655, 28671, 16247, 12610, 7578, 36764, 24401, 8717, 995, 4587, 9381, 1783, 6055, 25513, 10632, 4032, 2304, 8592, 2655, 28671, 16247, 12610, 7578, 36764, 24401, 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9566, 10721, 4724, 2304, 28543, 9640, 23758, 9673, 28543, 9640, 12399, 7251, 3555, 4587, 7578, 23758, 33962, 9566, 10721, 31439, 27188, 2288, 4587, 19446, 49374, 2423, 9307, 1863, 9957, 12399, 27188, 2288, 4587, 19446, 49374, 18183, 479, 4032, 35, 479], "avg_logprob": -0.20298549506281102, "compression_ratio": 1.56, "no_speech_prob": 0.0, "words": [{"start": 2802.38, "end": 2802.88, "word": "هل", "probability": 0.914794921875}, {"start": 2802.88, "end": 2803.18, "word": " الـ", "probability": 0.590576171875}, {"start": 2803.18, "end": 2803.68, "word": " Delta", "probability": 0.228271484375}, {"start": 2803.68, "end": 2804.5, "word": " F", "probability": 0.8408203125}, {"start": 2804.5, "end": 2804.88, "word": " هي", "probability": 0.73876953125}, {"start": 2804.88, "end": 2805.2, "word": " D", "probability": 0.29248046875}, {"start": 2805.2, "end": 2806.1, "word": " F؟", "probability": 0.69970703125}, {"start": 2806.1, "end": 2806.5, "word": " لأ،", "probability": 0.66748046875}, 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{"start": 2811.94, "end": 2813.1, "word": " الاتنين،", "probability": 0.7775390625}, {"start": 2813.1, "end": 2813.62, "word": " الفرق", "probability": 0.9671223958333334}, {"start": 2813.62, "end": 2813.78, "word": " ما", "probability": 0.9892578125}, {"start": 2813.78, "end": 2814.08, "word": " بين", "probability": 0.99609375}, {"start": 2814.08, "end": 2814.74, "word": " Delta", "probability": 0.79345703125}, {"start": 2814.74, "end": 2815.44, "word": " F", "probability": 0.9931640625}, {"start": 2815.44, "end": 2816.36, "word": " وD", "probability": 0.76171875}, {"start": 2816.36, "end": 2816.94, "word": " F", "probability": 0.89453125}], "temperature": 1.0}, {"id": 112, "seek": 283368, "start": 2817.48, "end": 2833.68, "text": "مذكرين لما قلنا متوسط معدل التغير ومعدل التغير متوسط معدل التغير ديلتا F على دلتا X لكن معدل التغير هو limit المقدار هذا لما دلتا X بده تروح لوين", "tokens": [2304, 8848, 37983, 9957, 5296, 15042, 12174, 1211, 8315, 44650, 41779, 9566, 20449, 3215, 1211, 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"end": 2863.22, "text": "للـ Zero هذا اللي قلناه يبجى هنا صار فيه خطأ مقدار الخطأ هو الفرق ما بين Delta F و D F اطرح Delta F بده اشيل منها D F بيبقى مقدار الخطأ اللي عندنا لهو هذا اليزرق اخدت Absolute Value لانه ممكن يكون D F أكبر من Delta F لأن ع رسمتنا هنا Delta F أكبر من مين؟ من D F طبعا", "tokens": [1211, 1211, 39184, 17182, 23758, 13672, 1829, 12174, 1211, 8315, 3224, 7251, 3555, 7435, 7578, 34105, 20328, 9640, 8978, 3224, 16490, 9566, 10721, 3714, 28543, 9640, 33962, 9566, 10721, 31439, 27188, 2288, 4587, 19446, 49374, 18183, 479, 4032, 413, 479, 1975, 9566, 2288, 5016, 18183, 479, 47525, 3224, 1975, 8592, 26895, 9154, 11296, 413, 479, 4724, 1829, 3555, 4587, 7578, 3714, 28543, 9640, 33962, 9566, 10721, 13672, 1829, 43242, 8315, 46740, 2407, 23758, 45595, 11622, 2288, 4587, 1975, 9778, 3215, 2655, 43965, 1169, 39352, 5296, 7649, 3224, 3714, 43020, 7251, 30544, 413, 479, 5551, 4117, 26890, 9154, 18183, 479, 5296, 33456, 6225, 12602, 38251, 2655, 8315, 34105, 18183, 479, 5551, 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{"start": 2856.9, "end": 2857.8, "word": " من", "probability": 0.97705078125}, {"start": 2857.8, "end": 2858.28, "word": " Delta", "probability": 0.88623046875}, {"start": 2858.28, "end": 2858.64, "word": " F", "probability": 0.99072265625}, {"start": 2858.64, "end": 2859.14, "word": " لأن", "probability": 0.6707763671875}, {"start": 2859.14, "end": 2859.3, "word": " ع", "probability": 0.5205078125}, {"start": 2859.3, "end": 2859.84, "word": " رسمتنا", "probability": 0.782135009765625}, {"start": 2859.84, "end": 2860.06, "word": " هنا", "probability": 0.8916015625}, {"start": 2860.06, "end": 2860.44, "word": " Delta", "probability": 0.78173828125}, {"start": 2860.44, "end": 2860.84, "word": " F", "probability": 0.994140625}, {"start": 2860.84, "end": 2861.3, "word": " أكبر", "probability": 0.9521484375}, {"start": 2861.3, "end": 2861.5, "word": " من", "probability": 0.97412109375}, {"start": 2861.5, "end": 2862.24, "word": " مين؟", "probability": 0.679931640625}, {"start": 2862.24, 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اربعة مضروب في Zero واحد من عشرة يبقى اضرب في اربعة بصير Zero اربعة من عشرة", "tokens": [2655, 1863, 9957, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 28242, 23758, 2423, 28820, 10943, 3714, 11242, 32887, 3555, 8978, 17182, 36764, 24401, 9154, 6225, 8592, 25720, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 1975, 25513, 27884, 3714, 11242, 32887, 3555, 8978, 17182, 36764, 24401, 9154, 6225, 8592, 25720, 7251, 3555, 4587, 7578, 1975, 11242, 25513, 8978, 1975, 25513, 27884, 4724, 9381, 13546, 17182, 1975, 25513, 27884, 9154, 6225, 8592, 25720], "avg_logprob": -0.1604034847851041, "compression_ratio": 2.0148148148148146, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 3181.0, "end": 3181.48, "word": "تنين", "probability": 0.4557291666666667}, {"start": 3181.48, "end": 3182.2, "word": " زائد", "probability": 0.8391927083333334}, {"start": 3182.2, "end": 3182.96, "word": " اتنين", "probability": 0.9761962890625}, {"start": 3182.96, 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"end": 3199.46, "word": " اربعة", "probability": 0.90234375}, {"start": 3199.46, "end": 3200.36, "word": " بصير", "probability": 0.8595377604166666}, {"start": 3200.36, "end": 3201.08, "word": " Zero", "probability": 0.9091796875}, {"start": 3201.08, "end": 3202.12, "word": " اربعة", "probability": 0.9005533854166666}, {"start": 3202.12, "end": 3202.38, "word": " من", "probability": 0.99658203125}, {"start": 3202.38, "end": 3202.96, "word": " عشرة", "probability": 0.9405924479166666}], "temperature": 1.0}, {"id": 129, "seek": 322779, "start": 3203.29, "end": 3227.79, "text": "تمام جيبنا له قداش مقدار DF الان بدنا نجيب له قداش مقدار ال error يبقى بدأ اروح لنمرسي بداجي اقوله ال error اللي هو delta F ناقص DF absolute value يعني ال error دائما هو انه هيطلع بالموجة لانه ماخدله", "tokens": [2655, 15042, 2304, 10874, 1829, 3555, 8315, 46740, 12174, 3215, 33599, 3714, 28543, 9640, 48336, 2423, 7649, 47525, 8315, 8717, 7435, 1829, 3555, 46740, 12174, 3215, 33599, 3714, 28543, 9640, 2423, 6713, 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هي أبسلوت فاليو Delta F طلعناها في الأول Zero واحد وأربع من مية ناقص DF طلعناها اللي هي Zero وأربعة من عشرة بضل قدوش واحد من مية يبقى Zero Zero", "tokens": [10721, 3555, 3794, 1211, 35473, 6156, 6027, 1829, 2407, 7251, 3555, 4587, 7578, 39896, 5551, 3555, 3794, 1211, 35473, 6156, 6027, 1829, 2407, 18183, 479, 23032, 1211, 3615, 8315, 11296, 8978, 16247, 12610, 17182, 36764, 24401, 36725, 25513, 3615, 9154, 3714, 10632, 8717, 995, 4587, 9381, 48336, 23032, 1211, 3615, 8315, 11296, 13672, 1829, 39896, 17182, 36725, 25513, 27884, 9154, 6225, 8592, 25720, 4724, 11242, 1211, 12174, 3215, 2407, 8592, 36764, 24401, 9154, 3714, 10632, 7251, 3555, 4587, 7578, 17182, 17182], "avg_logprob": -0.2660060935631031, "compression_ratio": 1.694267515923567, "no_speech_prob": 1.3709068298339844e-06, "words": [{"start": 3228.46, "end": 3229.38, "word": "أبسلوت", "probability": 0.625250244140625}, {"start": 3229.38, "end": 3229.9, "word": " فاليو", "probability": 0.7066650390625}, {"start": 3229.9, "end": 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0.89599609375}, {"start": 3573.82, "end": 3574.74, "word": " موجودة", "probability": 0.75616455078125}, {"start": 3574.74, "end": 3575.84, "word": " في", "probability": 0.8037109375}, {"start": 3575.84, "end": 3576.4, "word": " D", "probability": 0.72119140625}], "temperature": 1.0}, {"id": 143, "seek": 361017, "start": 3582.75, "end": 3610.17, "text": "The absolute maximumThe absolute maximum and absolute minimum values are called absolute", "tokens": [2278, 8236, 6674, 2278, 8236, 6674, 293, 8236, 7285, 4190, 366, 1219, 8236], "avg_logprob": -0.40959822705813814, "compression_ratio": 1.4915254237288136, "no_speech_prob": 0.0, "words": [{"start": 3582.75, "end": 3583.09, "word": "The", "probability": 0.0618896484375}, {"start": 3583.09, "end": 3583.85, "word": " absolute", "probability": 0.736328125}, {"start": 3583.85, "end": 3589.37, "word": " maximumThe", "probability": 0.59588623046875}, {"start": 3589.37, "end": 3589.95, "word": " absolute", "probability": 0.9619140625}, {"start": 3589.95, "end": 3591.81, "word": " maximum", "probability": 0.9912109375}, {"start": 3591.81, "end": 3593.69, "word": " and", "probability": 0.841796875}, {"start": 3593.69, "end": 3596.25, "word": " absolute", "probability": 0.802734375}, {"start": 3596.25, "end": 3598.85, "word": " minimum", "probability": 0.98974609375}, {"start": 3598.85, "end": 3601.41, "word": " values", "probability": 0.822265625}, {"start": 3601.41, "end": 3604.43, "word": " are", "probability": 0.92431640625}, {"start": 3604.43, "end": 3605.85, "word": " called", "probability": 0.93505859375}, {"start": 3605.85, "end": 3610.17, "word": " absolute", "probability": 0.83251953125}], "temperature": 1.0}, {"id": 144, "seek": 363643, "start": 3615.05, "end": 3636.43, "text": "extrema salute extrema and ال maximum and ال minimum values are called", "tokens": [3828, 265, 1696, 1845, 1169, 1279, 265, 1696, 293, 2423, 6674, 293, 2423, 7285, 4190, 366, 1219], "avg_logprob": -0.3009982589218352, "compression_ratio": 1.15625, "no_speech_prob": 0.0, "words": [{"start": 3615.0499999999997, "end": 3616.45, "word": "extrema", "probability": 0.658935546875}, {"start": 3616.45, "end": 3617.85, "word": " salute", "probability": 0.444580078125}, {"start": 3617.85, "end": 3619.11, "word": " extrema", "probability": 0.8614908854166666}, {"start": 3619.11, "end": 3620.05, "word": " and", "probability": 0.78759765625}, {"start": 3620.05, "end": 3624.21, "word": " ال", "probability": 0.72705078125}, {"start": 3624.21, "end": 3624.91, "word": " maximum", "probability": 0.93701171875}, {"start": 3624.91, "end": 3627.79, "word": " and", "probability": 0.79931640625}, {"start": 3627.79, "end": 3629.59, "word": " ال", "probability": 0.94482421875}, {"start": 3629.59, "end": 3630.17, "word": " minimum", "probability": 0.98193359375}, {"start": 3630.17, "end": 3633.19, "word": " values", "probability": 0.880859375}, {"start": 3633.19, "end": 3635.61, "word": " are", "probability": 0.927734375}, {"start": 3635.61, "end": 3636.43, "word": " called", "probability": 0.921875}], "temperature": 1.0}, {"id": 145, "seek": 365640, "start": 3643.82, "end": 3656.4, "text": "Extreme values of the function f", "tokens": [36, 734, 5301, 4190, 295, 264, 2445, 283], "avg_logprob": -0.7782118055555556, "compression_ratio": 0.8, "no_speech_prob": 0.0, "words": [{"start": 3643.8199999999997, "end": 3645.22, "word": "Extreme", "probability": 0.642303466796875}, {"start": 3645.22, "end": 3646.62, "word": " values", "probability": 0.8251953125}, {"start": 3646.62, "end": 3652.18, "word": " of", "probability": 0.1529541015625}, {"start": 3652.18, "end": 3653.92, "word": " the", "probability": 0.57763671875}, {"start": 3653.92, "end": 3655.1, "word": " function", "probability": 0.96142578125}, {"start": 3655.1, "end": 3656.4, "word": " f", "probability": 0.431396484375}], "temperature": 1.0}, {"id": 146, "seek": 370326, "start": 3694.04, "end": 3703.26, "text": "طبعا في فرق شاسعة ما بين ال absolute maximum و ال local maximum absolute minimum و local minimum", "tokens": [9566, 3555, 3615, 995, 8978, 6156, 2288, 4587, 13412, 32277, 27884, 19446, 49374, 2423, 8236, 6674, 4032, 2423, 2654, 6674, 8236, 7285, 4032, 2654, 7285], "avg_logprob": -0.29657451579203975, "compression_ratio": 1.2872340425531914, "no_speech_prob": 0.0, "words": [{"start": 3694.04, "end": 3694.92, "word": "طبعا", "probability": 0.7757110595703125}, {"start": 3694.92, "end": 3695.02, "word": " في", "probability": 0.1859130859375}, {"start": 3695.02, "end": 3695.36, "word": " فرق", "probability": 0.9033203125}, {"start": 3695.36, "end": 3695.92, "word": " شاسعة", "probability": 0.9104817708333334}, {"start": 3695.92, "end": 3696.16, "word": " ما", "probability": 0.46240234375}, {"start": 3696.16, "end": 3696.38, "word": " بين", "probability": 0.984375}, {"start": 3696.38, "end": 3696.54, "word": " ال", "probability": 0.73583984375}, {"start": 3696.54, "end": 3696.96, "word": " absolute", "probability": 0.7041015625}, {"start": 3696.96, "end": 3697.84, "word": " maximum", "probability": 0.92431640625}, {"start": 3697.84, "end": 3698.86, "word": " و", "probability": 0.84619140625}, {"start": 3698.86, "end": 3699.02, "word": " ال", "probability": 0.71044921875}, {"start": 3699.02, "end": 3699.4, "word": " local", "probability": 0.869140625}, {"start": 3699.4, "end": 3700.2, "word": " maximum", "probability": 0.92333984375}, {"start": 3700.2, "end": 3701.16, "word": " absolute", "probability": 0.77197265625}, {"start": 3701.16, "end": 3701.88, "word": " minimum", "probability": 0.9716796875}, {"start": 3701.88, "end": 3702.34, "word": " و", "probability": 0.97998046875}, {"start": 3702.34, "end": 3702.74, "word": " local", "probability": 0.8388671875}, {"start": 3702.74, "end": 3703.26, "word": " minimum", "probability": 0.9765625}], "temperature": 1.0}, {"id": 147, "seek": 371398, "start": 3703.94, "end": 3713.98, "text": "زي ما هنشوف اليوم ناخد ال absolute maximum لما نوصل ال local maximum و ال local minimum ستجد الفرق الشاسع ما بين الاتنين", "tokens": [11622, 1829, 19446, 8032, 1863, 8592, 38688, 45595, 20498, 8717, 47283, 3215, 2423, 8236, 6674, 5296, 15042, 8717, 2407, 36520, 2423, 2654, 6674, 4032, 2423, 2654, 7285, 8608, 2655, 7435, 3215, 27188, 2288, 4587, 25124, 32277, 3615, 19446, 49374, 2423, 9307, 1863, 9957], "avg_logprob": -0.21306818147951906, "compression_ratio": 1.376923076923077, "no_speech_prob": 0.0, "words": [{"start": 3703.94, "end": 3704.3, "word": "زي", "probability": 0.440765380859375}, {"start": 3704.3, "end": 3704.38, "word": " ما", "probability": 0.880859375}, {"start": 3704.38, "end": 3704.78, "word": " هنشوف", "probability": 0.7703857421875}, {"start": 3704.78, "end": 3705.1, "word": " اليوم", "probability": 0.9140625}, {"start": 3705.1, "end": 3705.48, "word": " ناخد", "probability": 0.8997395833333334}, {"start": 3705.48, "end": 3705.58, "word": " ال", "probability": 0.603515625}, {"start": 3705.58, "end": 3705.94, "word": " absolute", "probability": 0.8056640625}, {"start": 3705.94, "end": 3706.52, "word": " maximum", "probability": 0.98095703125}, {"start": 3706.52, "end": 3707.36, "word": " لما", "probability": 0.7353515625}, {"start": 3707.36, "end": 3707.92, "word": " نوصل", "probability": 0.9817708333333334}, {"start": 3707.92, "end": 3708.36, "word": " ال", "probability": 0.88720703125}, {"start": 3708.36, "end": 3708.8, "word": " local", "probability": 0.8828125}, {"start": 3708.8, "end": 3709.28, "word": " maximum", "probability": 0.8544921875}, {"start": 3709.28, "end": 3709.4, "word": " و", "probability": 0.72265625}, {"start": 3709.4, "end": 3709.46, "word": " ال", "probability": 0.72998046875}, {"start": 3709.46, "end": 3709.66, "word": " local", "probability": 0.85888671875}, {"start": 3709.66, "end": 3709.98, "word": " minimum", "probability": 0.83056640625}, {"start": 3709.98, "end": 3710.74, "word": " ستجد", "probability": 0.9476318359375}, {"start": 3710.74, "end": 3711.28, "word": " 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قد أجد قيمة الصغرة في أكثر من موقع لكنها ليست قيمة مختلفة بتأخذ ميا نفس القيمة اللي عندنا هذه", "tokens": [3224, 1829, 19446, 41185, 8592, 11933, 15040, 32771, 13546, 11296, 11331, 49975, 4032, 28814, 1863, 25961, 2655, 8978, 5551, 4117, 49115, 11296, 9154, 3714, 30543, 3615, 46811, 10943, 22807, 23032, 1829, 3555, 9122, 2304, 3615, 1863, 7578, 12174, 32640, 3660, 31767, 17082, 25720, 44945, 36178, 41950, 16572, 28671, 12174, 3215, 5551, 7435, 3215, 12174, 32640, 3660, 31767, 17082, 25720, 8978, 5551, 4117, 49115, 9154, 3714, 30543, 3615, 44381, 11296, 32239, 14851, 12174, 32640, 3660, 3714, 46456, 46538, 3660, 39894, 10721, 9778, 8848, 3714, 25528, 8717, 36178, 25062, 32640, 3660, 13672, 1829, 43242, 8315, 29538], "avg_logprob": -0.16241777005948518, "compression_ratio": 1.8971428571428572, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3977.01, "end": 3977.41, "word": "هي", "probability": 0.5811767578125}, {"start": 3977.41, "end": 3977.89, "word": " مافيش", 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1.0}, {"id": 160, "seek": 402162, "start": 3997.36, "end": 4021.62, "text": "النقطة التانية ال absolute maximum وال absolute minimum values بسميهم absolute extrema extrema يعني جمع extreme بدل ما اقول extreme تبقى maximum اول ما بقول extreme وخلاص يبقى called absolute extreme", "tokens": [6027, 1863, 47432, 3660, 16712, 7649, 10632, 2423, 8236, 6674, 16070, 8236, 7285, 4190, 4724, 38251, 1829, 16095, 8236, 1279, 265, 1696, 1279, 265, 1696, 37495, 22653, 10874, 2304, 3615, 8084, 47525, 1211, 19446, 1975, 39648, 8084, 6055, 3555, 4587, 7578, 6674, 1975, 12610, 19446, 4724, 39648, 8084, 4032, 9778, 1211, 33546, 7251, 3555, 4587, 7578, 1219, 8236, 8084], "avg_logprob": -0.34296876440445584, "compression_ratio": 1.6948051948051948, "no_speech_prob": 0.0, "words": [{"start": 3997.36, "end": 3999.34, "word": "النقطة", "probability": 0.777587890625}, {"start": 3999.34, "end": 3999.72, "word": " التانية", "probability": 0.9479166666666666}, {"start": 3999.72, "end": 4000.38, "word": " ال", 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"probability": 0.724212646484375}, {"start": 4018.4, "end": 4019.36, "word": " يبقى", "probability": 0.9453125}, {"start": 4019.36, "end": 4019.98, "word": " called", "probability": 0.78125}, {"start": 4019.98, "end": 4020.76, "word": " absolute", "probability": 0.9482421875}, {"start": 4020.76, "end": 4021.62, "word": " extreme", "probability": 0.468017578125}], "temperature": 1.0}, {"id": 161, "seek": 402768, "start": 4022.32, "end": 4027.68, "text": "absolute maximum او absolute .. يعني مثلا لما نقعد على ده يمكن مالاجيش فيها", "tokens": [17243, 401, 1169, 6674, 1975, 2407, 8236, 4386, 37495, 22653, 50113, 15040, 5296, 15042, 8717, 4587, 22488, 15844, 11778, 3224, 7251, 43020, 3714, 6027, 26108, 1829, 8592, 8978, 11296], "avg_logprob": -0.4190104087193807, "compression_ratio": 1.0980392156862746, "no_speech_prob": 0.0, "words": [{"start": 4022.32, "end": 4022.98, "word": "absolute", "probability": 0.7897135416666666}, {"start": 4022.98, "end": 4023.54, "word": " maximum", 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{"start": 4436.69, "end": 4437.07, "word": " هنا", "probability": 0.6494140625}, {"start": 4437.07, "end": 4437.37, "word": " ال", "probability": 0.62060546875}, {"start": 4437.37, "end": 4437.87, "word": " F", "probability": 0.5751953125}, {"start": 4437.87, "end": 4439.31, "word": " has", "probability": 0.7060546875}, {"start": 4439.31, "end": 4441.29, "word": " absolute", "probability": 0.86669921875}, {"start": 4441.29, "end": 4443.07, "word": " maximum", "probability": 0.9658203125}, {"start": 4443.07, "end": 4444.81, "word": " اتنين", "probability": 0.855224609375}, {"start": 4444.81, "end": 4445.71, "word": " ات", "probability": 0.583984375}, {"start": 4445.71, "end": 4446.29, "word": " اكس", "probability": 0.90185546875}, {"start": 4446.29, "end": 4446.75, "word": " يساوي", "probability": 0.7847900390625}, {"start": 4446.75, "end": 4447.23, "word": " كده", "probability": 0.74853515625}, {"start": 4447.23, "end": 4447.71, "word": " اش؟", "probability": 0.6171061197916666}, {"start": 4447.71, "end": 4448.27, "word": " اربع", "probability": 0.71435546875}, {"start": 4448.27, "end": 4449.21, "word": " في", "probability": 0.5810546875}, {"start": 4449.21, "end": 4449.61, "word": " عندي", "probability": 0.70556640625}, {"start": 4449.61, "end": 4450.11, "word": " absolute", "probability": 0.91162109375}, {"start": 4450.11, "end": 4450.87, "word": " minimum", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 180, "seek": 447347, "start": 4455.95, "end": 4473.47, "text": "ماعنديش absolute minimum لإيش؟ لأن الدلة تنزل إلى أين؟ للثالث بإنفنتاين ال F has no absolute minimum مالهاش مالهاش بلاش", "tokens": [15042, 3615, 1863, 16254, 8592, 8236, 7285, 5296, 28814, 1829, 8592, 22807, 5296, 33456, 32748, 37977, 6055, 1863, 11622, 1211, 30731, 5551, 9957, 22807, 24976, 12984, 6027, 12984, 4724, 28814, 1863, 5172, 29399, 995, 9957, 2423, 479, 575, 572, 8236, 7285, 3714, 6027, 3224, 33599, 3714, 6027, 3224, 33599, 4724, 1211, 33599], "avg_logprob": 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"word": "كونوستانت", "probability": 0.45234375}, {"start": 5526.34, "end": 5527.08, "word": " فانكشن", "probability": 0.9396484375}, {"start": 5527.08, "end": 5528.2, "word": " كونوستانت", "probability": 0.7562052408854166}, {"start": 5528.2, "end": 5528.5, "word": " فانكشن", "probability": 0.99072265625}, {"start": 5528.5, "end": 5535.98, "word": " كونوستانت", "probability": 0.7911783854166666}, {"start": 5535.98, "end": 5537.12, "word": " فانكشن", "probability": 0.98916015625}, {"start": 5537.12, "end": 5537.94, "word": " كونوستانت", "probability": 0.8413492838541666}, {"start": 5537.94, "end": 5538.76, "word": " فانكشن", "probability": 0.99013671875}, {"start": 5538.76, "end": 5539.42, "word": " كونوستانت", "probability": 0.8666585286458334}, {"start": 5539.42, "end": 5540.16, "word": " فانكشن", "probability": 0.99072265625}, {"start": 5540.16, "end": 5541.9, "word": " كونوستانت", "probability": 0.9012451171875}, {"start": 5541.9, "end": 5545.62, "word": " فانكشن", "probability": 0.9923828125}], "temperature": 1.0}, {"id": 218, "seek": 556821, "start": 5545.65, "end": 5568.21, "text": "الـ Absolute maximum ممكن يكون في طرف الدالة وممكن يكون في طرف ال domain تبع الدالة وممكن يكون داخل ال domain تبع هذه الدالة لو نظرنا للرسمة الأولى يبقى ال absolute maximum حصل عند النقطة X1 لكن ال absolute minimum حصل عند نقطة X2", "tokens": [6027, 39184, 43965, 1169, 6674, 3714, 43020, 7251, 30544, 8978, 23032, 28480, 32748, 6027, 3660, 4032, 2304, 43020, 7251, 30544, 8978, 23032, 28480, 2423, 9274, 6055, 3555, 3615, 32748, 6027, 3660, 4032, 2304, 43020, 7251, 30544, 11778, 47283, 1211, 2423, 9274, 6055, 3555, 3615, 29538, 32748, 6027, 3660, 45164, 8717, 19913, 2288, 8315, 24976, 2288, 38251, 3660, 16247, 12610, 7578, 7251, 3555, 4587, 7578, 2423, 8236, 6674, 11331, 36520, 43242, 28239, 47432, 3660, 1783, 16, 44381, 2423, 8236, 7285, 11331, 36520, 43242, 8717, 47432, 3660, 1783, 17], "avg_logprob": -0.18998580222780054, "compression_ratio": 1.988826815642458, "no_speech_prob": 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X1", "probability": 0.60693359375}, {"start": 5565.15, "end": 5565.83, "word": " لكن", "probability": 0.79541015625}, {"start": 5565.83, "end": 5566.03, "word": " ال", "probability": 0.79150390625}, {"start": 5566.03, "end": 5566.69, "word": " absolute", "probability": 0.94482421875}, {"start": 5566.69, "end": 5567.27, "word": " minimum", "probability": 0.9716796875}, {"start": 5567.27, "end": 5567.81, "word": " حصل", "probability": 0.978271484375}, {"start": 5567.81, "end": 5568.15, "word": " عند", "probability": 0.8505859375}, {"start": 5568.15, "end": 5568.15, "word": " نقطة", "probability": 0.8253580729166666}, {"start": 5568.15, "end": 5568.21, "word": " X2", "probability": 0.66796875}], "temperature": 1.0}, {"id": 219, "seek": 558374, "start": 5568.58, "end": 5583.74, "text": "عنده نقطة X2 يبقى من هنا صار إحداث النقطة دي اللي فوق هي X1 و M يبقى ال M هو ال absolute maximum", "tokens": [3615, 41260, 3224, 8717, 47432, 3660, 1783, 17, 7251, 3555, 4587, 7578, 9154, 34105, 20328, 9640, 11933, 24401, 5718, 104, 28239, 47432, 3660, 11778, 1829, 13672, 1829, 6156, 30543, 39896, 1783, 16, 4032, 376, 7251, 3555, 4587, 7578, 2423, 376, 31439, 2423, 8236, 6674], "avg_logprob": -0.2805555502573649, "compression_ratio": 1.2113821138211383, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5568.58, "end": 5568.98, "word": "عنده", "probability": 0.4909871419270833}, {"start": 5568.98, "end": 5569.82, "word": " نقطة", "probability": 0.9278971354166666}, {"start": 5569.82, "end": 5570.88, "word": " X2", "probability": 0.4150390625}, {"start": 5570.88, "end": 5571.94, "word": " يبقى", "probability": 0.851318359375}, {"start": 5571.94, "end": 5572.14, "word": " من", "probability": 0.880859375}, {"start": 5572.14, "end": 5572.58, "word": " هنا", "probability": 0.98876953125}, {"start": 5572.58, "end": 5573.12, "word": " صار", "probability": 0.65185546875}, {"start": 5573.12, "end": 5573.9, "word": " إحداث", "probability": 0.9034423828125}, {"start": 5573.9, "end": 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"start": 5644.04, "end": 5666.9, "text": "وين عند الـ A و الـ B و أجت ال maximum في الطرف الأول و أجت ال minimum وين في الطرف الثاني بلغتنا القديمة ده اللي هذه increasing و الله decreasing ده التناقصية نجي على الدالة اللي عندنا هذه ال absolute minimum", "tokens": [2407, 9957, 43242, 2423, 39184, 316, 4032, 2423, 39184, 363, 4032, 5551, 7435, 2655, 2423, 6674, 8978, 41950, 28480, 16247, 12610, 4032, 5551, 7435, 2655, 2423, 7285, 4032, 9957, 8978, 41950, 28480, 6024, 104, 7649, 1829, 4724, 1211, 17082, 2655, 8315, 25062, 16254, 46007, 11778, 3224, 13672, 1829, 29538, 5662, 4032, 21984, 23223, 11778, 3224, 16712, 8315, 4587, 9381, 10632, 8717, 7435, 1829, 15844, 32748, 6027, 3660, 13672, 1829, 43242, 8315, 29538, 2423, 8236, 7285], "avg_logprob": -0.30921052553151784, "compression_ratio": 1.7912087912087913, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 5644.04, "end": 5644.6, "word": "وين", "probability": 0.16259765625}, {"start": 5644.6, "end": 5645.0, "word": " عند", 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"word": " at", "probability": 0.475830078125}, {"start": 5713.68, "end": 5715.9, "word": " interior", "probability": 0.517578125}, {"start": 5715.9, "end": 5718.34, "word": " point", "probability": 0.98583984375}, {"start": 5718.34, "end": 5719.88, "word": " يبقى", "probability": 0.947265625}, {"start": 5719.88, "end": 5720.22, "word": " عند", "probability": 0.99658203125}, {"start": 5720.22, "end": 5721.22, "word": " النقطة", "probability": 0.9837239583333334}, {"start": 5721.22, "end": 5723.94, "word": " الداخلية", "probability": 0.993408203125}, {"start": 5723.94, "end": 5725.5, "word": " تالر", "probability": 0.7439778645833334}, {"start": 5725.5, "end": 5727.2, "word": " ال", "probability": 0.759765625}, {"start": 5727.2, "end": 5727.68, "word": " minimum", "probability": 0.97705078125}, {"start": 5727.68, "end": 5728.06, "word": " عند", "probability": 0.9921875}, {"start": 5728.06, "end": 5728.48, "word": " النقطة", "probability": 0.9879557291666666}, {"start": 5728.48, "end": 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+differentiation اللي هو التفابل أضمنه ال section + +7 +00:00:52,300 --> 00:00:55,720 +اللي بعده تلاتة و تمانية من شطبه بروح إلى تلاتة + +8 +00:00:55,720 --> 00:01:01,320 +تسعة اللي هو linearizations and differentials طبعا + +9 +00:01:01,320 --> 00:01:04,720 +linearization جاء من كلمة linear + +10 +00:01:11,850 --> 00:01:18,010 +الدالة خطية عند نقطة طيب شو السبب السبب أحيانا ال + +11 +00:01:18,010 --> 00:01:22,530 +function اللي عندنا بيكون صعب التعامل معاها فيمكن + +12 +00:01:22,530 --> 00:01:30,030 +استبدالها عند نقطة مابدالة خطية تكافئها طبعا بيكون + +13 +00:01:30,030 --> 00:01:36,550 +هناك خطأ بسيط جدا يمكن التغاضي عنه ومن هنا سمنها + +14 +00:01:36,550 --> 00:01:41,110 +approximating function الدالة التقريبية + +15 +00:01:41,110 --> 00:01:46,230 +approximating function يبقى الدالة التقريبية تكافئ + +16 +00:01:46,230 --> 00:01:51,330 +الدالة الأصلية مع فارق في الخطأ بسيط جدا يمكن + +17 +00:01:51,330 --> 00:01:57,590 +التغاضي عنهبالمهم كيف نعمل الدالة اللى عندنا دالة + +18 +00:01:57,590 --> 00:02:03,090 +خطية كيف يمكن تحويل هذه الدالة إلى دالة خطية هذا + +19 +00:02:03,090 --> 00:02:08,590 +ما يتحدث عنه التعريف الأول اللى أمامنا التعريف + +20 +00:02:08,590 --> 00:02:14,500 +بيقول ما يأتيإذا الدالة قابلة الاشتقاق عند X يساوي + +21 +00:02:14,500 --> 00:02:19,020 +A، إذا الدالة قابلة الاشتقاق عند X يساوي A، إذا + +22 +00:02:19,020 --> 00:02:20,160 +الدالة قابلة الاشتقاق عند X يساوي A، إذا الدالة + +23 +00:02:20,160 --> 00:02:21,020 +قابلة الاشتقاق عند X يساوي A، إذا الدالة قابلة + +24 +00:02:21,020 --> 00:02:22,160 +الاشتقاق عند X يساوي A، إذا الدالة قابلة الاشتقاق + +25 +00:02:22,160 --> 00:02:22,300 +عند X يساوي A، إذا الدالة قابلة الاشتقاق عند X + +26 +00:02:22,300 --> 00:02:22,300 +يساوي A، إذا الدالة قابلة الاشتقاق عند X يساوي A، + +27 +00:02:22,300 --> 00:02:25,100 +إذا الدالة قابلة الاشتقاق عند X يساوي A، إذا + +28 +00:02:25,100 --> 00:02:28,340 +الدالة قابلة الاشتقاق عند X يساوي A، إذا الدال + +29 +00:02:28,360 --> 00:02:34,560 +يساوي F of A قيمة الدالة عند A زائد قيمة مشتقة + +30 +00:02:34,560 --> 00:02:39,140 +الدالة عند A مضروبة في X ناقص اللي هي طبعا الشباب + +31 +00:02:39,140 --> 00:02:44,500 +هذه قيمة عددية وهذه قيمة عددية X من الدرجة الأولى + +32 +00:02:44,500 --> 00:02:51,200 +يبقى صارت دالة خطية لأنها معدلة من الدرجة الأولى + +33 +00:02:51,200 --> 00:02:56,900 +ومن هنا سمنها Linear Approximation التقريب الخطي + +34 +00:02:57,240 --> 00:03:01,700 +يبقى هذا is the linearization of f at x يساوي إيه + +35 +00:03:01,700 --> 00:03:08,360 +هو جعل الدالة خطية عند النقطة x يساوي إيه ال L of + +36 +00:03:08,360 --> 00:03:11,940 +x بدل منقول linearization of approximating + +37 +00:03:11,940 --> 00:03:15,900 +function اصطد على تسميته the standard linear + +38 +00:03:15,900 --> 00:03:20,700 +approximation يعني هذا متعرف عليه دوليا في كل كتب + +39 +00:03:20,700 --> 00:03:27,480 +الرياضيةللدالة F عند النقطة X يساوي A النقطة X + +40 +00:03:27,480 --> 00:03:32,260 +يساوي A بنسميها مركز التقريب is called the center + +41 +00:03:32,260 --> 00:03:36,480 +of approximation يعني مركز التقريب اللي قربنا فيه + +42 +00:03:36,480 --> 00:03:42,230 +الدالة الأصلية إلى مين؟ إلى الدالة الخاطيةنذهب + +43 +00:03:42,230 --> 00:03:48,870 +لأمثلة كيف نحسب الدالة الخطية لدالة تمها عند نقطة + +44 +00:03:48,870 --> 00:03:53,750 +بقول هاتل ال linearization اللي هو رمز L of X اللي + +45 +00:03:53,750 --> 00:03:59,050 +فوق عنها هذا لمين لكل من الدوال التالي عند النقطة + +46 +00:03:59,080 --> 00:04:04,060 +المعطال F of X يساوي الجدر التربية ل X تربية زائد + +47 +00:04:04,060 --> 00:04:09,560 +تسعة عند النقطة A تساوي سالب أربعة تبلة F of X + +48 +00:04:09,560 --> 00:04:18,030 +يساوي X عند النقطة A يساوي Yيبقى مطلوب حساب قيمة + +49 +00:04:18,030 --> 00:04:22,810 +الدالة عند النقطة المعطاة اتنين بإن قيمة مشتقة + +50 +00:04:22,810 --> 00:04:28,250 +الدالة عند النقطة المعطاة إذا لو جيت للنقطة الأولى + +51 +00:04:28,250 --> 00:04:35,070 +اللي هي A معناته بدي أحسب F of سالب أربعةيبقى هذا + +52 +00:04:35,070 --> 00:04:40,650 +بدي يساوي ل square root لسالب أربعة لكل تربية زائد + +53 +00:04:40,650 --> 00:04:45,670 +تسعة طبعا ستة عشر زائد تسعة خمسة وعشرين تحت الجذر + +54 +00:04:45,670 --> 00:04:51,730 +بتطلع بقدر خمسة بعد هيك بدنا نروح نجيب f prime of + +55 +00:04:51,730 --> 00:04:58,970 +x يبقى مشتقة الجذر بواحد على اتنين الجذر تربية + +56 +00:04:58,970 --> 00:05:05,270 +زائد تسعة في مشتقة ما تحتالجذر X تربيه ب2X ومشتقة + +57 +00:05:05,270 --> 00:05:11,410 +التسعة ب0 لإنها constant يبقى النتيجة X على الجذر + +58 +00:05:11,410 --> 00:05:18,780 +التربيه ل X تربيه زائد تسعة بالشكل اللي أنها دهزي + +59 +00:05:18,780 --> 00:05:25,420 +9 طبعا بيحسب قداش القيمة اللي عندنا هذه f prime of + +60 +00:05:25,420 --> 00:05:48,220 +سالب أربع + +61 +00:05:48,280 --> 00:05:52,560 +يبقى بناء على الـ Linear Approximation أو الدالة + +62 +00:05:52,560 --> 00:05:59,320 +التقريبية L of X بيساوي ال F of سالب أربعة زي F + +63 +00:05:59,320 --> 00:06:08,370 +prime of سالب أربعة في ال X ناقص ناقص أربعةيبقى + +64 +00:06:08,370 --> 00:06:13,390 +بنتيجة F of سلب أربعة اللي هي أنا قداش خمسة بعد + +65 +00:06:13,390 --> 00:06:17,890 +هيك F prime of سلب أربعة اللي هي سلب أربعة أخمس + +66 +00:06:17,890 --> 00:06:25,670 +يبقى سلب أربعة أخمس كله في X زائد من زائد أربعة + +67 +00:06:25,670 --> 00:06:31,830 +يبقى هذا معناه ما يأتي ان ال L of X + +68 +00:06:34,470 --> 00:06:41,590 +بدها تساوي اللي هو الخمسة سالب أربع أخماس X نضرب + +69 +00:06:41,590 --> 00:06:49,590 +هذه جوا بصير سالب ستاشر على خمسة يبقى معناه هذا + +70 +00:06:49,590 --> 00:06:55,990 +الكلام ان ال L of X بدها تساوي الرقم اللي عندنا ده + +71 +00:06:55,990 --> 00:07:01,670 +خمس عدد صحيح بده تسييل منه ناقص ستاشر على خمسة + +72 +00:07:01,670 --> 00:07:07,520 +نقطة تسعة على خمسةيبقى هذا الكلام بتساوي تسعة + +73 +00:07:07,520 --> 00:07:13,980 +أخماس ناقص أربع أخماس X هذا الشكل ال linearization + +74 +00:07:13,980 --> 00:07:19,660 +لهذه الدالة وزي ما انت شايف هي دالة خطية يعني دالة + +75 +00:07:19,660 --> 00:07:24,960 +من الدرجة الأولى بالنسبة لمن؟ بالنسبة للمتغير X + +76 +00:07:24,960 --> 00:07:31,430 +طيب نيجي لنمرى V من السؤالنمر بيه من السؤال قال لي + +77 +00:07:31,430 --> 00:07:38,190 +F of X يساوي تان ال X يبقى احنا ال F of X يساوي + +78 +00:07:38,190 --> 00:07:45,070 +تان ال X هذا معناته ان ال F of Pi بدي يساوي تان ال + +79 +00:07:45,070 --> 00:07:52,420 +Pi تان ال Pi بقدرش0 تمام بدنا نجيب F prime of X + +80 +00:07:52,420 --> 00:07:59,880 +تفاضل التان ب سك Square X بدنا نجيب F prime of Pi + +81 +00:07:59,880 --> 00:08:08,140 +يساوي سك تربيه الـPi تمام بدنا نيجي لسك تربيه + +82 +00:08:08,140 --> 00:08:13,060 +الـPi سك الـPi اللي مقلوب الكوصين يعني كإن واحد + +83 +00:08:13,060 --> 00:08:20,010 +على كوصين كوصين مية تمانين-1 تربيع يبقى النتيجة + +84 +00:08:20,010 --> 00:08:27,630 +تساوي واحد لكل تربيع يعني واحد حسبناها إذا ال L of + +85 +00:08:27,630 --> 00:08:35,750 +X لهذه الدالة بده يساوي F of Pi زائد F prime of Pi + +86 +00:08:35,750 --> 00:08:44,670 +في X ناقص ال Piهذا سيعطينا ان ال L of X يساوي ال F + +87 +00:08:44,670 --> 00:08:50,230 +of Y عندنا هي فوق اللي هي ب Zero و بعدها زاد ال F + +88 +00:08:50,230 --> 00:08:57,210 +prime of Y هو واحد فى قداش فى X ناقص بي يبقى + +89 +00:08:57,210 --> 00:09:03,630 +الجواب X ناقص بي يبقى هى ده اللى خطيه طبعا بيكون + +90 +00:09:03,630 --> 00:09:11,000 +اصلاوبالتالي دالة دالة من الدرجة الأولى السؤال + +91 +00:09:11,000 --> 00:09:19,120 +الثاني نمر أيه؟ بيقول لما يقول show that the + +92 +00:09:19,120 --> 00:09:28,460 +linearization show that the linearization + +93 +00:09:28,460 --> 00:09:32,400 +of + +94 +00:09:34,170 --> 00:09:41,190 +الـ function f of x يساوي واحد زائد الـ x كله to + +95 +00:09:41,190 --> 00:09:53,070 +the power k at x يساوي zero is L of x يساوي واحد + +96 +00:09:53,070 --> 00:09:59,230 +زائد k في x نمرا + +97 +00:09:59,230 --> 00:10:01,970 +بيه use + +98 +00:10:05,860 --> 00:10:14,940 +استخدم النقطة الأولى عندك to find an + +99 +00:10:14,940 --> 00:10:24,100 +approximation to + +100 +00:10:24,100 --> 00:10:30,540 +find an approximation for the following + +101 +00:10:40,310 --> 00:10:50,110 +f of x يساوي واحد على الجذر التربيعي لواحد زائد x + +102 +00:10:50,110 --> 00:11:02,570 +نقطة ثانية f of xيساوي أربع زائد تلاتة X كل هذا + +103 +00:11:02,570 --> 00:11:12,030 +الكلام أسطلت نمرى الـC use + +104 +00:11:12,030 --> 00:11:22,410 +approximation use + +105 +00:11:22,410 --> 00:11:30,630 +approximationواحد زائد X to the power K يساوي + +106 +00:11:30,630 --> 00:11:43,690 +تقريبا يساوي تقريبا اللي هو واحد زائد K X to + +107 +00:11:43,690 --> 00:11:45,990 +estimate + +108 +00:11:54,000 --> 00:12:02,340 +تستمتع الجذر التالت لـ 1.009 + +109 +00:12:02,340 --> 00:12:07,220 +هذا + +110 +00:12:07,220 --> 00:12:16,080 +بتصلي حاليا يا شباب L of X يساوي تقريبا 1 زائد K + +111 +00:12:16,080 --> 00:12:20,140 +في X بدل يساوي يساوي تقريبا + +112 +00:12:23,970 --> 00:12:29,370 +سؤال مرة تانية سؤال عبارة عن ثلاث نقاط النقطة + +113 +00:12:29,370 --> 00:12:33,770 +الأولى بيقول يبين لإن ال linearization لل F of X + +114 +00:12:33,770 --> 00:12:39,190 +تساوي واحد زائد X كله to the power K عند X يساوي + +115 +00:12:39,190 --> 00:12:44,990 +Zero وL of X يساوي واحد زائد X النقطة الثانية + +116 +00:12:44,990 --> 00:12:50,750 +بيقول استخدم الحلق رقم A مشان توجد تقريب لكل دالة + +117 +00:12:50,750 --> 00:12:56,490 +منها تين الدالتينالنقطة تبتدى use approximation + +118 +00:12:56,490 --> 00:13:01,410 +اللى حصلنا عليه فى الحالة اى مش هنجيب قداش قيمة + +119 +00:13:01,410 --> 00:13:06,470 +الجدرى التالت للواحد وتسعة من الف يعنى بنعرف قداش + +120 +00:13:06,470 --> 00:13:11,430 +الجدرى التالت لهذا العدلبنقول له بسيطة هنمسك + +121 +00:13:11,430 --> 00:13:15,630 +المطاليب هذا واحد واحد اول مطلوب الاول بدنا نجيب + +122 +00:13:15,630 --> 00:13:19,150 +ال linearization لهذه الدالة ونثبت انه ال + +123 +00:13:19,150 --> 00:13:25,050 +linearization بده يسوى واحد زائد K X تقريبا بقوله + +124 +00:13:25,050 --> 00:13:33,510 +كويس يبقى اول شيء بدنا نجيب له F of ZeroF of zero + +125 +00:13:33,510 --> 00:13:38,870 +بدها تساوي واحد زائد زيرو كله to the power of K + +126 +00:13:38,870 --> 00:13:43,530 +يعني واحد to the power of K اللي هو بقدرش بواحد + +127 +00:13:43,530 --> 00:13:53,120 +تمام بدنا نجيب F prime of X نشتق الدالة الاسفى + +128 +00:13:53,120 --> 00:14:00,100 +القوس مرفوعة لنفس الاص مطروح من واحد مضروب فى + +129 +00:14:00,100 --> 00:14:06,220 +مشتقة مداخل القوس لو جداش واحد صحيح طب لنحسب جداش + +130 +00:14:06,220 --> 00:14:11,900 +المشتقة عند ال zero هذا بده يعطينا ان ال F prime + +131 +00:14:11,900 --> 00:14:20,520 +of zero كما لهاش دعوة واحد زائد زيرو أس كماقاس + +132 +00:14:20,520 --> 00:14:20,940 +واحد + +133 +00:14:28,350 --> 00:14:34,510 +يبقى هذا الكلام يبدأ يساوي كي في واحد ويبدأ يساوي + +134 +00:14:34,510 --> 00:14:45,530 +كدهشنجي الان لل linearization لل f of x يساوي ال f + +135 +00:14:45,530 --> 00:14:52,270 +of zero زائد ال f prime of zero في ال x ناقص ال + +136 +00:14:52,270 --> 00:14:59,810 +zeroيبقى ال linearization المطلوب L of X يبدو + +137 +00:14:59,810 --> 00:15:06,330 +يساوي F of Zero عندي بواحد يبقى ايه الواحد؟ Y زائد + +138 +00:15:06,330 --> 00:15:12,770 +الان F prime of Zero هيبقى كده ايش؟ ب K يبقى هذا + +139 +00:15:12,770 --> 00:15:18,510 +اللي هو main K K في مين؟ في ال X ناقص ال Zero اللي + +140 +00:15:18,510 --> 00:15:25,830 +هي ب X X أظن و هو المطلوب؟يبقى linearization يبقى + +141 +00:15:25,830 --> 00:15:35,170 +1 زائد KX اللي هو المطلوب الأول نمرة B نمرة + +142 +00:15:35,170 --> 00:15:40,990 +B نقطتين نجي للنقطة الأولى في الأولالنقطة الأولى + +143 +00:15:40,990 --> 00:15:45,950 +بيقول استخدم الجزء الاول ال part a مشان تجيب ال + +144 +00:15:45,950 --> 00:15:49,730 +approximation للدالة اللى عندنا هادى انا مشان + +145 +00:15:49,730 --> 00:15:53,210 +اجيبك درق اللى هو ال approximation لهذه الدالة + +146 +00:15:53,210 --> 00:15:57,540 +معناه ده بدي احط الدالة هادى على مينعلى الصيغة + +147 +00:15:57,540 --> 00:16:02,720 +اللي عندي مشان أستخدمها صحيح ولا لأ يبقى احنا + +148 +00:16:02,720 --> 00:16:09,360 +عندنا ال F of X اللي هي يسوى واحد على الجذر + +149 +00:16:09,360 --> 00:16:16,830 +التربيه إلى مين لقداش لواحد زاد اكساللي بقدر اقول + +150 +00:16:16,830 --> 00:16:23,270 +واحد زائد اكس اوس قداش اوس سالب نص اص نص نطلع فوق + +151 +00:16:23,270 --> 00:16:27,570 +بصير اوس سالب نص الان صارت هذه على الصيغة اللي + +152 +00:16:27,570 --> 00:16:32,470 +هناك بس ال K سالب السالب والله موجب انا لم اشترط + +153 +00:16:32,470 --> 00:16:37,310 +على K سالب والله موجب يبقى اي ريال number يكون + +154 +00:16:37,310 --> 00:16:42,000 +عندنا اذا بناء انا اليسارة الدالي هذي فيلميابنفس + +155 +00:16:42,000 --> 00:16:45,820 +الصيغة اللي عندنا هذه يبقى اللي استخدم هذا علشان + +156 +00:16:45,820 --> 00:16:50,820 +نجيب ال approximation بديرش لسه اشتق و اعوض ان لأ + +157 +00:16:50,820 --> 00:16:55,800 +لأ هي جاهزة الصيغة من part a يبقى باجي بقوله from + +158 +00:16:55,800 --> 00:17:07,660 +part a من الجزء aالـ L of X بده يساوي واحد زائد K + +159 +00:17:07,660 --> 00:17:15,600 +اللي هو ناقص نص في الـ X، بصبوط؟ واحد زائد K X، + +160 +00:17:15,600 --> 00:17:22,220 +الـ K عندي بسالم نص، يبقى النتيجة يساوي واحد ناقص + +161 +00:17:22,220 --> 00:17:26,740 +X على اتنين، يبقى هذا ال linearization دي يعني + +162 +00:17:26,740 --> 00:17:27,340 +الدالة + +163 +00:17:33,830 --> 00:17:41,810 +لو أربعة زائد تلاتة X أربعة زائد تلاتة X كله أسطل + +164 +00:17:50,580 --> 00:17:58,280 +عشان أستخدم ال approximation يعني هذه بدل الأربعة + +165 +00:17:58,280 --> 00:18:04,180 +بديها كم؟ بديها واحد، صحيح إذا المسألة هذه بقدر + +166 +00:18:04,180 --> 00:18:12,740 +أكتبها على الشكل التالي هذا أربعة في واحدزائد تلت + +167 +00:18:12,740 --> 00:18:16,780 +ربع X وهذا كله أس تلت + +168 +00:18:19,250 --> 00:18:24,130 +لو دخلت الارباجي هو بتعود المثلة كما كانت يعني + +169 +00:18:24,130 --> 00:18:30,810 +معناه هذا الكلام هذه أربعة أس طلت في واحد زائد + +170 +00:18:30,810 --> 00:18:38,390 +تلاتة X على أربعة أس قدر أس طلت تمام تمام نجي ال + +171 +00:18:38,390 --> 00:18:44,970 +approximation اللي عندنا يبقى ال L of X يساوي أظن + +172 +00:18:44,970 --> 00:18:49,920 +الأربعة أس طلت مليش دعوةصحيح ولا لأ؟ ال + +173 +00:18:49,920 --> 00:18:55,700 +approximation بتعمل لمين؟ لدالة لأن هذه يبقى هذه + +174 +00:18:55,700 --> 00:19:05,220 +واحد زائد كداش K عندي؟ تلت كداش ال X؟ تلاتة X على + +175 +00:19:05,220 --> 00:19:09,680 +أربعيعني أجاني بدل ال X ثلاثة X على أربعة يبقى + +176 +00:19:09,680 --> 00:19:15,520 +بحطها بكاملها كما هي نجي نشوف في اختصارات ولا + +177 +00:19:15,520 --> 00:19:21,860 +مافيش؟ اه والله في هذه مع هذه يبقى آلة المسألة إلى + +178 +00:19:21,860 --> 00:19:31,730 +أربعة أس تلت في واحد زائد ل X على أربعةهذا هو + +179 +00:19:31,730 --> 00:19:38,230 +الهدف من هذا السؤال كيف تحور مسألتك بحيث تكون على + +180 +00:19:38,230 --> 00:19:41,950 +الصيغة هذه وإذا حورتها وجعلتها على الصيغة هذه + +181 +00:19:41,950 --> 00:19:47,230 +بتقدر تجيب ال linear approximation بالنسبة لها + +182 +00:19:47,230 --> 00:19:51,930 +يبقى انتهينا من المطلوب التاني النمرة B اللي + +183 +00:19:51,930 --> 00:19:58,020 +استخدمنا فيه نمرة Aنمرة C بيقول استخدم نفس ال + +184 +00:19:58,020 --> 00:20:04,420 +approximation مشان تجيبلي الجذري التالت لوحد وتسعة + +185 +00:20:04,420 --> 00:20:10,900 +من عشرة يبقى باجي لنمرة C فكرة نمرة C زي فكرة نمرة + +186 +00:20:10,900 --> 00:20:16,770 +B ببطالةحط المسألة اللى عندك في صيغة اللى هو ال + +187 +00:20:16,770 --> 00:20:21,330 +inner approximation يبقى باجي بقول انا عند الجدر + +188 +00:20:21,330 --> 00:20:34,470 +التالت ل 1009 تمام يعني هذا كأنه 1009 أسطول يبقى + +189 +00:20:34,470 --> 00:20:39,770 +أسكي صار عندي أي أسكي بل ال bingosين بيداكوا تبقى + +190 +00:20:39,770 --> 00:20:46,250 +على صيغة مجموعة كميتيناحدهما واحد صحيح والتانية X + +191 +00:20:46,250 --> 00:20:52,130 +باجي بقول الواحد و التسعة من الف دي بقدر اقول هي + +192 +00:20:52,130 --> 00:20:59,550 +واحد زائد Zero Zero تسعة من الف و هاي كمان Zero + +193 +00:20:59,550 --> 00:21:00,190 +جابلها + +194 +00:21:03,450 --> 00:21:09,550 +أس طلت يبقى هذه الأس طلت يبقى الواحد هو الواحد + +195 +00:21:09,550 --> 00:21:15,430 +وتسعة من الف كانها مين هي ال X بالضبط تماما يبقى + +196 +00:21:15,430 --> 00:21:23,050 +النتيجة هذه بدا ساوي واحد زائد ال K بقداش طلت وال + +197 +00:21:23,050 --> 00:21:30,960 +X زيرو زيرو تسعة بالشكل اللي عندهايبقى هذا الكلام + +198 +00:21:30,960 --> 00:21:36,440 +يبدو يساوي واحد زاد، تلت في هذه بيصير Zero، Zero + +199 +00:21:36,440 --> 00:21:41,090 +تلتتسعة لتلاتة، اللي بتلاتة بيصير بدل ما هي تسعة + +200 +00:21:41,090 --> 00:21:45,370 +من ألف صارت تلاتة من ألف، ان بقى الواحد يبقى + +201 +00:21:45,370 --> 00:21:52,390 +الجواب بيطلع واحد point zero zero تلاتة، إذا + +202 +00:21:52,390 --> 00:21:57,650 +الجدرى التالت لواحد و تسعة من ألف هو واحد و تلاتة + +203 +00:21:57,650 --> 00:22:02,470 +من الف فعلاًهذا الان لو ضربت في نفسها تلت مرات + +204 +00:22:02,470 --> 00:22:06,990 +فتحصل + +205 +00:22:06,990 --> 00:22:15,270 +على واحد و تسعة منك طيب هذا اللي هو مثال تطبيقي + +206 +00:22:15,270 --> 00:22:22,210 +برضه على linearizationحتى الآن كله بناخد أمثلة على + +207 +00:22:22,210 --> 00:22:25,770 +النقطة الأولى من العنوان اللي احنا عارفينه اللي هو + +208 +00:22:25,770 --> 00:22:31,070 +الكون linearization and differentials التفاضلات + +209 +00:22:31,070 --> 00:22:37,090 +يبقى بنجي نعطي تعريف للتفاضلة ثم نروح نحسب بعض + +210 +00:22:37,090 --> 00:22:41,590 +الأمثلة عليها أو ناخد بعض الأمثلة عليها يبقى + +211 +00:22:41,590 --> 00:22:45,550 +definition let + +212 +00:22:46,770 --> 00:22:57,190 +الـ y تساوي f of x بـ a differentiable function + +213 +00:23:10,300 --> 00:23:25,420 +التفاضلة DX تفاضلة DX is an independent variable + +214 +00:23:25,420 --> 00:23:28,460 +متغير + +215 +00:23:28,460 --> 00:23:36,400 +مستقل and the differential + +216 +00:23:43,040 --> 00:24:02,000 +والتفاضة dy is the dependent variable + +217 +00:24:06,560 --> 00:24:16,040 +بدي يساوي f prime of x dx example + +218 +00:24:16,040 --> 00:24:23,980 +find + +219 +00:24:23,980 --> 00:24:33,200 +the differential dy + +220 +00:24:36,380 --> 00:24:37,360 +للعملات التالية + +221 +00:25:31,100 --> 00:25:40,420 +دالة الأولى Y تساوي Xفي الجدرى التربية الى واحد + +222 +00:25:40,420 --> 00:25:49,540 +ناقص X تربية دالة التانية Y تساوي 6 X تربية ناقص + +223 +00:25:49,540 --> 00:26:01,980 +واحد دالة التالتة X Y تربية ناقص أربعة X از تلاتة + +224 +00:26:01,980 --> 00:26:20,760 +على اتنيننقص Y يساوي كده؟ يساوي Zero نرجع + +225 +00:26:20,760 --> 00:26:25,800 +للتعريف اللي قلناه ده مرة ثانية يبقى ال definition + +226 +00:26:25,800 --> 00:26:31,560 +بيقول ما يأتي افترض ان Y تساوي F of X ده لقابل + +227 +00:26:31,560 --> 00:26:40,360 +للاشتقاءالتفاضلة DX هي متغير + +228 +00:26:40,360 --> 00:26:47,900 +مستقل وكذلك التفاضلة DY هي متغير مستقل يعني اتنين + +229 +00:26:47,900 --> 00:26:55,940 +بيعتمدوا على بعض وبالتالي DY بيكون F' of X DX سؤال + +230 +00:26:55,940 --> 00:27:02,720 +من أين لك هذا خلي بالك هناالآن لما نقول y تساوي f + +231 +00:27:02,720 --> 00:27:10,140 +of x و جينا و قولنا لك اشتق ايش بتقولين دي y by دي + +232 +00:27:10,140 --> 00:27:16,580 +x يساوي f prime of x علموك في الثانوية العامة ان + +233 +00:27:16,580 --> 00:27:23,200 +هذا رمز لا يمكن فاصلة يدل على مين يدل على المشتقة + +234 +00:27:23,200 --> 00:27:27,010 +الأولى قلوا لكوا هيك مظبوطقالولكوا لهاك لإن لو + +235 +00:27:27,010 --> 00:27:31,610 +كانت لسه أقول قصيرة شوية و بيخافوايبقى دال مع دال + +236 +00:27:31,610 --> 00:27:39,290 +بيبقى Y على X لكن الحقيقة انه يمكن فصله بقدر اقول + +237 +00:27:39,290 --> 00:27:41,250 +اضرب في DX بيصير + +238 +00:27:59,850 --> 00:28:06,330 +واتنين العلاقة فيما بينهما هو dy يسوى f prime of x + +239 +00:28:06,330 --> 00:28:10,230 +dx هي اللي كتبناها هنا، يريدوا يعرفوا أصلها جاء من + +240 +00:28:10,230 --> 00:28:17,230 +أين؟ أصلها جاء من المشتقة الأولىأو من الـfirst + +241 +00:28:17,230 --> 00:28:23,490 +derivative للـfunction y تساوي f of x المثال بيقول + +242 +00:28:23,490 --> 00:28:28,650 +لي هاتلي اللي هو ال differential dy for the + +243 +00:28:28,650 --> 00:28:32,450 +following functions يبقى أنا بدي أجيبله الـdy + +244 +00:28:32,450 --> 00:28:37,290 +معناته بدي المشتقة واضغفه في من؟ في الـdx بكون + +245 +00:28:37,290 --> 00:28:44,180 +حصلنا على المطلوب بقولك كويسيبقى انا بدى اجيبله dy + +246 +00:28:44,180 --> 00:28:49,140 +الشكل اللى عنه هذا بجيبله الاشتقاق قادر وبعد ما + +247 +00:28:49,140 --> 00:28:54,820 +خلص بضربه في من؟ في الـ x يبقى هذه تعتبر function + +248 +00:28:54,820 --> 00:29:01,100 +وهذه function تانية اذا هذه مشتقة حاصل ضرب دالتين + +249 +00:29:01,100 --> 00:29:08,260 +يبقى الدالة الاولى فى مشتقة الدالة الثانيةإتنين + +250 +00:29:08,260 --> 00:29:16,060 +الجذر التربيعي لواحد ناقص X تربية في مشتقة ما تحت + +251 +00:29:16,060 --> 00:29:22,500 +الجذر له سالب اتنين X تمام؟ هذا الأولى في مشتقة + +252 +00:29:22,500 --> 00:29:30,090 +مين؟ الثانيةزائد ثانية في مشتقة الأولى واحد ناقص X + +253 +00:29:30,090 --> 00:29:38,070 +تربية ومشتقة الأولى واحد يبقى كله هدف في DX نختصر + +254 +00:29:38,070 --> 00:29:44,420 +الاختصارات بصير DY يساويإتنين مع اتنين مع السلامة + +255 +00:29:44,420 --> 00:29:51,260 +بظل سالب X تربية على الجذري التربية لواحد ناقص X + +256 +00:29:51,260 --> 00:29:59,240 +تربية زائد الجذري التربية لواحد ناقص X تربية كل + +257 +00:29:59,240 --> 00:30:04,640 +هذا الكلام بالنسبة إلى مين؟ كل هذاممكن اعملها + +258 +00:30:04,640 --> 00:30:09,960 +توحيد للمقامات وبالتالي ممكن ابسطها اكثر من ذلك + +259 +00:30:09,960 --> 00:30:15,580 +اذا لو قلت كله على الجذر التربية لو واحد ناقص X + +260 +00:30:15,580 --> 00:30:20,960 +تربية بضل عندى هنا ناقص X تربية والجذر مع الجذر + +261 +00:30:20,960 --> 00:30:26,910 +بطير بالشكل اللى عندنا هذا وكله فاهمين؟فى الـDX + +262 +00:30:26,910 --> 00:30:33,630 +يبقى واحد ناقص اتنين X تربيع على الجذر التربيعى + +263 +00:30:33,630 --> 00:30:40,970 +لواحد ناقص X تربيع DX يبقى هذا شكل التفاضلة DY + +264 +00:30:40,970 --> 00:30:47,570 +بدلالة main بدلالة F prime of X وكذلك بدلالة + +265 +00:30:47,570 --> 00:30:55,290 +التفاضلة DX هذا النقطة الأولى نقطة الثانيةالنقطة + +266 +00:30:55,290 --> 00:30:59,090 +الثانية أبداً دالة واحدة مش حصل ضرب دلتين يبقى + +267 +00:30:59,090 --> 00:31:09,050 +باجي بقوله dy يساوي تفاضل السك بسك الزاوية في تاني + +268 +00:31:09,050 --> 00:31:15,870 +الزاوية في تفاضل الزاوية اللي هو جداش بتنين اكس + +269 +00:31:15,870 --> 00:31:21,570 +فاهمين؟ بدي اكس اختصارات مافيش خليها زي ما هي وروح + +270 +00:31:21,570 --> 00:31:30,650 +وخليها نمر تلاتةأه نمرة تلاتة هذا اشتقاق ضمنى، اذا + +271 +00:31:30,650 --> 00:31:37,150 +بدنا نجيبله dy بدلالة x بواسطة الاشتقاق الضمنى، + +272 +00:31:37,150 --> 00:31:42,210 +يبقى بده افضل كل شيء في ما كانه مع مراعاة قواعد + +273 +00:31:42,210 --> 00:31:46,690 +الاشتقاق اللى اتعلمناها قبل العيد في المحاضرة + +274 +00:31:46,690 --> 00:31:51,840 +الماضية، يبقى بده اجي للدلة اللى عندناهي الدالة + +275 +00:31:51,840 --> 00:31:57,700 +مرة تانية x y تربية ناقص أربعة x أس تلاتة على + +276 +00:31:57,700 --> 00:32:03,360 +اتنين ناقص y تساوي زيرو بدنا نبدأ نشتق يبقى هذه + +277 +00:32:03,360 --> 00:32:07,800 +function وهذه function تانية إذا هذه مشتقة حاصل + +278 +00:32:07,800 --> 00:32:15,020 +ضرب دالتين الدالة الأولى في مشتقة الدالة الثانية + +279 +00:32:15,020 --> 00:32:25,480 +اتنين y أيوةفي dy على dx مش هيك اتعلمناها طيب تمام + +280 +00:32:25,480 --> 00:32:31,560 +يبقى هذه الأولى في مشتقة الدالة الثانية زائد + +281 +00:32:31,560 --> 00:32:35,200 +الدالة الثانية في مشتقة الأولى اللي هو الجدية + +282 +00:32:35,790 --> 00:32:43,630 +أقواحاً طيب هذه ناقص اللي هو أربع في تلاتة على + +283 +00:32:43,630 --> 00:32:52,770 +اتنين في اكس أس قداش أس نص ناقص dy على dx يساوي + +284 +00:32:52,770 --> 00:33:01,070 +زين ماخلصناش بدروح أضرب كله في dx من أوله إلى آخره + +285 +00:33:01,580 --> 00:33:10,880 +تبقى لو ضربت في DX بصير اتنين X Y DY زي Y ترابيع + +286 +00:33:10,880 --> 00:33:22,460 +DX تمام ناقص اتنين في تلاتة بستة X أص نص X أص نص + +287 +00:33:22,460 --> 00:33:31,390 +في DX ناقص DY بده ساوي زيرضربت المعادلة من أولها + +288 +00:33:31,390 --> 00:33:38,010 +لآخرها في DX هنا راح ال DX هنا جتني DX هنا جتني من + +289 +00:33:38,010 --> 00:33:44,630 +DX طب اللي فيهم DY دخليهم مع بعض و اللي فيهم DX + +290 +00:33:44,630 --> 00:33:51,710 +دخليهم مع بعضإذا لو جيت أخدت هذه بصير اتنين XY + +291 +00:33:51,710 --> 00:33:58,770 +ناقص واحد في DY هدول هنقولهم عليه الشكة التانية + +292 +00:33:58,770 --> 00:34:08,310 +واخد DX عام المشترك يبقى ستة جذر ال X ناقص Y تربيع + +293 +00:34:08,310 --> 00:34:14,710 +كله في من؟ في DXطب احنا بدنا dy يبقى بنقسم على + +294 +00:34:14,710 --> 00:34:19,410 +مين؟ على المقدار اللي عندنا يبقى بيصير عندنا dy + +295 +00:34:19,410 --> 00:34:29,250 +يسوى ستة جذر ال X ناقص Y تربيع على اتنين XY ناقص + +296 +00:34:29,250 --> 00:34:35,320 +واحد كله في DXيبقى يجسمنا الطرفين على هذا المقطار + +297 +00:34:35,320 --> 00:34:41,260 +وبالتالي جبت التفاضل دي واي بدلالة التفاضل دي إكس + +298 +00:34:41,260 --> 00:34:50,080 +السؤال + +299 +00:34:50,080 --> 00:34:54,400 +و ليه؟ من جل و من يوم بدأت أتعلم اشتقاق في + +300 +00:34:54,400 --> 00:35:01,060 +الثانوية العامة و إلى يومنا هذاهل اخدت ان الدالة + +301 +00:35:01,060 --> 00:35:07,100 +في متغيرين ولا الدالة Y في متغير واحد؟ لكن مرحبا + +302 +00:35:07,100 --> 00:35:12,400 +بك في Calculus C نعطيك الدالة مش في تلت متغيرات في + +303 +00:35:12,400 --> 00:35:18,370 +N من المتغير بدل 1، 10، 15، كده ما بدكتمام؟ يبقى + +304 +00:35:18,370 --> 00:35:23,290 +هذا لسه فيه Calculus B دالة في متغير واحد والـC هو + +305 +00:35:23,290 --> 00:35:28,310 +الدالة في المتغيرات لسه في قدامك مرحلة قبل أن تصل + +306 +00:35:28,310 --> 00:35:34,210 +أو قبل أن نصل إلى الإجابة على سؤالك وهذا نسميه + +307 +00:35:34,210 --> 00:35:41,190 +اشتقاقا جزئيا partial differentiation تمام؟ لسه + +308 +00:35:41,190 --> 00:35:42,310 +بعيد عنك هذا + +309 +00:35:58,710 --> 00:36:13,970 +مارك if y تساوي f of x and if the variable + +310 +00:36:15,740 --> 00:36:22,100 +إذا كلمة x تتغير + +311 +00:36:22,100 --> 00:36:27,280 +تتغير + +312 +00:36:27,280 --> 00:36:43,320 +في نقطة x من نقطة x إلى نقطة x زائد dx ثم + +313 +00:36:47,100 --> 00:36:58,480 +نقطة الأولى مقدرة + +314 +00:36:58,480 --> 00:36:59,700 +التغيير في F + +315 +00:37:14,380 --> 00:37:21,520 +F of X naught زائد Delta X ناقص F of X naught + +316 +00:37:21,520 --> 00:37:24,640 +النقطة + +317 +00:37:24,640 --> 00:37:31,420 +الثانية The value of + +318 +00:37:31,420 --> 00:37:36,600 +The + +319 +00:37:36,600 --> 00:37:40,300 +value of DF + +320 +00:37:42,260 --> 00:37:54,880 +at X node as DF بدي ساوي F prime of X node في DX + +321 +00:37:54,880 --> 00:38:00,460 +نقطة تالتة + +322 +00:38:00,460 --> 00:38:04,600 +approximation + +323 +00:38:04,600 --> 00:38:08,680 +error + +324 +00:38:13,490 --> 00:38:32,310 +is absolute value لدلتا F ناقص DF وكل + +325 +00:38:32,310 --> 00:38:34,370 +هذا وين وانت كاين وين + +326 +00:38:43,890 --> 00:38:47,170 +كل اللي كتبناها دو توقيت كايد اللي بيقول خليا دول + +327 +00:40:02,370 --> 00:40:03,770 +العزيزي + +328 +00:41:48,170 --> 00:41:48,870 +السلام عليكم و رحمه الله + +329 +00:42:58,620 --> 00:43:02,380 +أخر نقطة في ال section اللي بيننا اللي هو remark + +330 +00:43:02,380 --> 00:43:08,660 +اللي قدامنا هذي remark بتقول ما يأتي بيقول لو كانت + +331 +00:43:08,660 --> 00:43:13,120 +ال y ده اللي في x وكان ال variable x اذا it + +332 +00:43:13,120 --> 00:43:19,940 +changed عند النقطة x0 من x0 إلى x0 زائد dxيبقى + +333 +00:43:19,940 --> 00:43:24,640 +المنحنة تغير من عنده نقطة x node إلى نقطة x node + +334 +00:43:24,640 --> 00:43:30,260 +زائد x بمقدار dx يعني لو وصلنا من هذه النقطة إلى + +335 +00:43:30,260 --> 00:43:34,740 +هذه النقطة بيكون مقدار التغير اللي حصل في x node + +336 +00:43:34,740 --> 00:43:38,880 +لأن هذا نقطة الأصل هي zero هذه المسافة اللي كانت + +337 +00:43:38,880 --> 00:43:43,020 +هي x node صارت المسافة هذه كلها من هنا لهنا + +338 +00:43:53,510 --> 00:44:01,450 +يبقى هذه النقطة كإنها اكس نود زائد DX و F of X نود + +339 +00:44:01,450 --> 00:44:07,130 +زائد DX عنا بالشكل هذا و إحداثيات النقطة المين + +340 +00:44:07,130 --> 00:44:10,390 +اللي عندنا بقول ايش then + +341 +00:44:13,680 --> 00:44:19,080 +مقدار التغير في F نظراً لإن تغير X node من X node + +342 +00:44:19,080 --> 00:44:24,400 +إلى X node زائد DX معناته فهذه كانت F of X node + +343 +00:44:29,670 --> 00:44:35,170 +يعني اذا حصل تغير في F مقداره Delta F وين Delta F + +344 +00:44:35,170 --> 00:44:39,690 +المسافة هذه هيا علمتك عليها اقول لك Delta F يبقى + +345 +00:44:39,690 --> 00:44:44,990 +هذه Delta F وهذه Delta X Delta X اعطيتها الرمز مين + +346 +00:44:44,990 --> 00:44:51,810 +DX يعني ال DX صارت هي المسافة من هنا لغاية هنا + +347 +00:44:52,100 --> 00:44:57,940 +المسافة بين النقطتين يبقى DF هي المسافة من هنا + +348 +00:44:57,940 --> 00:45:04,000 +لهنا وهي الفرق بين مين بين المسافتين يبقى Delta F + +349 +00:45:04,000 --> 00:45:10,140 +ل F of X نول زائد DX ناقص F of X نولهذه من هنا + +350 +00:45:10,140 --> 00:45:15,880 +لهنا لل F of X node وهذه من هنا لهنا لل F of X + +351 +00:45:15,880 --> 00:45:22,360 +node وهذه من هنا لهنا لل F of X node لكن هذه كلها + +352 +00:45:22,360 --> 00:45:27,540 +F of X node زائد DX لو طرحنا التنتمة البعض بنحصل + +353 +00:45:27,540 --> 00:45:32,380 +على المسافة هذه اللي قلنا عليها مين Delta F يبقى + +354 +00:45:32,380 --> 00:45:37,440 +Delta F ل F of X node زائد DX ناقص F of X node + +355 +00:45:38,100 --> 00:45:44,280 +بعملك the value of DF مقدار التفابله DF عند ال X + +356 +00:45:44,280 --> 00:45:50,720 +node هي DF يساوي F prime of X node DX على الخريطة + +357 +00:45:50,720 --> 00:45:57,160 +وين ال DF فادت طلع ليههذه المشتقة تعني ميل المماثل + +358 +00:45:57,160 --> 00:46:01,580 +المنحنى يبقى هي المماثل لو جاني عنده النقطة هذه هي + +359 +00:46:01,580 --> 00:46:07,980 +الرأسي إذا بصير هبهها اللي هو ظل الزاوية هذه يعني + +360 +00:46:07,980 --> 00:46:13,460 +قيمة المشتقة لولا إذا صارت هذه المسافة هي ظل + +361 +00:46:13,460 --> 00:46:17,920 +الزاوية اللي عندها هذا الهدف yf prime of x not + +362 +00:46:17,920 --> 00:46:23,720 +whenمضروبة في DX طبعا الزاوية هذه تساوي الزاوية + +363 +00:46:23,720 --> 00:46:28,720 +هذه بالتناظر مظبوط لأن هذا الخط أفقي وهذا الخط + +364 +00:46:28,720 --> 00:46:33,940 +أفقي الزاوية هذه هي الزاوية هذه بالضبط تماما كويس + +365 +00:46:33,940 --> 00:46:38,440 +يبقى مقدار ال DF هي F prime of X not the man في ال + +366 +00:46:38,440 --> 00:46:45,200 +DX طب هل القمتين بتساوي هدول؟هل الـ Delta F هي D + +367 +00:46:45,200 --> 00:46:50,580 +F؟ لأ، في خطأ بمقدار هذا المقدار، يبقى هذا الخطأ + +368 +00:46:50,580 --> 00:46:56,940 +هو الفرق ما بين الاتنين، الفرق ما بين Delta F وD F + +369 +00:46:57,480 --> 00:47:03,060 +مذكرين لما قلنا متوسط معدل التغير ومعدل التغير + +370 +00:47:03,060 --> 00:47:08,900 +متوسط معدل التغير ديلتا F على دلتا X لكن معدل + +371 +00:47:08,900 --> 00:47:13,240 +التغير هو limit المقدار هذا لما دلتا X بده تروح + +372 +00:47:13,240 --> 00:47:18,480 +لوينللـ Zero هذا اللي قلناه يبجى هنا صار فيه خطأ + +373 +00:47:18,480 --> 00:47:25,440 +مقدار الخطأ هو الفرق ما بين Delta F و D F اطرح + +374 +00:47:25,440 --> 00:47:30,520 +Delta F بده اشيل منها D F بيبقى مقدار الخطأ اللي + +375 +00:47:30,520 --> 00:47:35,040 +عندنا لهو هذا اليزرق اخدت Absolute Value لانه ممكن + +376 +00:47:35,040 --> 00:47:40,840 +يكون D F أكبر من Delta F لأن ع رسمتنا هنا Delta F + +377 +00:47:40,840 --> 00:47:44,610 +أكبر من مين؟ من D F طبعاحسب المادة اللى تكون + +378 +00:47:44,610 --> 00:47:49,810 +تزايدية او تناقصية مثلا طب نعطي مثال عددي كيف + +379 +00:47:49,810 --> 00:48:00,770 +بنستخدم الشغلات هذه يبقى example بيقول + +380 +00:48:00,770 --> 00:48:13,220 +let ال F of X بده يساوي X Square زائد 2XX² زائد + +381 +00:48:13,220 --> 00:48:22,180 +اتنين X والـ X ناد يساوي واحد والـ DX يساوي Zero + +382 +00:48:22,180 --> 00:48:28,220 +واحد من عشرة Find + +383 +00:48:28,220 --> 00:48:32,220 +نمرة + +384 +00:48:32,220 --> 00:48:45,430 +A بدنا Delta Fنمر الـB نمر الـC + +385 +00:48:45,430 --> 00:48:52,190 +نمر الـC نمر الـC نمر الـC نمر الـC نمر الـD + +386 +00:49:09,290 --> 00:49:14,790 +سؤال مرة تانية ماعطينا f of x تساوي x squared زائد + +387 +00:49:14,790 --> 00:49:20,570 +اتنين x ماعطينا النقطة x naught تساوي واحد ماعطينا + +388 +00:49:20,570 --> 00:49:27,180 +dx اللي هو واحد من عشرة يعني مقدار التغيرمن x node + +389 +00:49:27,180 --> 00:49:31,260 +إلى x node زاية dx اللي هو جداش واحد من عشره من + +390 +00:49:31,260 --> 00:49:37,000 +مقدار ال dx جاليهات ليه جداش مقدار delta f جداش + +391 +00:49:37,000 --> 00:49:41,960 +مقدار df عند x node يساوي واحد جداش مقدار ال error + +392 +00:49:41,960 --> 00:49:48,400 +في هذه الحالة بقوله بسيطة بنرجع ل delta f معناته + +393 +00:49:48,400 --> 00:49:54,000 +بدي احسب له f of x node زاية dx واطرح منها f of x + +394 +00:49:54,000 --> 00:50:05,120 +nodeأذا بقوله delta F يساوي F of X0 زائد DXنقص ال + +395 +00:50:05,120 --> 00:50:12,080 +F of X node يبقى Delta F اللي احنا بدنا إياها F of + +396 +00:50:12,080 --> 00:50:19,380 +.. كداش ال X node عندنا؟ بواحد، زاد Zero واحد من + +397 +00:50:19,380 --> 00:50:30,780 +عشرة، تمام؟ يعني ناقص ال F of واحد F of X nodeالـ + +398 +00:50:30,780 --> 00:50:39,100 +F of واحد و واحد من عشرة ناقص F of واحد و يساوي F + +399 +00:50:39,100 --> 00:50:43,460 +of واحد و واحد من عشرة بده شيل كل X وحط مكانها + +400 +00:50:43,460 --> 00:50:49,130 +واحد و واحد من عشرةيبقى ده واحد وواحد من عشرة لكل + +401 +00:50:49,130 --> 00:50:55,530 +ترابية زي دي اتنين في واحد وواحد من عشرة هذا كله + +402 +00:50:55,530 --> 00:51:02,850 +لسه مان F of واحد واحد من عشرة ناقص F of واحد ناقص + +403 +00:51:02,850 --> 00:51:09,310 +F of واحد اللي واحد ترابية زي دي اتنين في واحد + +404 +00:51:09,310 --> 00:51:14,470 +يبقى هاي اللي بنطلعهم من بعض يبقى سعر ال delta F + +405 +00:51:14,470 --> 00:51:18,290 +بده يساويواحد وواحد من عشرة يبقى واحد وواحد من + +406 +00:51:18,290 --> 00:51:21,070 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وواحد من + +407 +00:51:21,070 --> 00:51:24,330 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وواحد من + +408 +00:51:24,330 --> 00:51:24,970 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وواحد من + +409 +00:51:24,970 --> 00:51:27,150 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وواحد من + +410 +00:51:27,150 --> 00:51:28,310 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وواحد من + +411 +00:51:28,310 --> 00:51:30,450 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وواحد من + +412 +00:51:30,450 --> 00:51:36,930 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وواحد من + +413 +00:51:36,930 --> 00:51:46,230 +عشرة يبقى واحد وواحد من عشرة يبقى واحد وهذه تلاتة + +414 +00:51:46,230 --> 00:51:52,270 +واحد واربعين من مائة يبقى تلاتة واحد واربعين من + +415 +00:51:52,270 --> 00:51:58,110 +مائة ناقص تلاتة يبقى النتيجة واحد واربعين من مائة + +416 +00:51:58,110 --> 00:52:05,050 +مقدار التغير في Delta F خلصنا المطلوب الأول بدنا + +417 +00:52:05,050 --> 00:52:11,580 +نيجي للمطلوب التاني اللي هو Nemra Bنمر بيه جليهات + +418 +00:52:11,580 --> 00:52:18,620 +لقداش DF عند X node يساوات برجع لل DF يبقى انا عند + +419 +00:52:18,620 --> 00:52:26,610 +ال DF هي عبارة عن F prime of X node في مينفالـDX + +420 +00:52:26,610 --> 00:52:33,090 +هي ال F of X معناته بدي اشتقها و اعوض عند X none + +421 +00:52:33,090 --> 00:52:40,470 +يبقى هذا الكلام بده يساوي اتنين X زائد اتنين كل + +422 +00:52:40,470 --> 00:52:46,110 +هذا الكلام عند X يساوي كده؟ واحد مضروب في مين؟ في + +423 +00:52:46,110 --> 00:52:54,240 +الـDX الـDX ميعطيني يهالي و قداشيبقى هاي zero واحد + +424 +00:52:54,240 --> 00:53:02,200 +من عشرة عوض بهذه يبقى تنين زائد اتنينتنين زائد + +425 +00:53:02,200 --> 00:53:08,940 +اتنين كل هذا الكلام مضروب في Zero واحد من عشرة + +426 +00:53:08,940 --> 00:53:16,480 +يبقى هذا الكلام بده يساوي اربعة مضروب في Zero واحد + +427 +00:53:16,480 --> 00:53:22,960 +من عشرة يبقى اضرب في اربعة بصير Zero اربعة من عشرة + +428 +00:53:23,290 --> 00:53:29,350 +تمام جيبنا له قداش مقدار DF الان بدنا نجيب له قداش + +429 +00:53:29,350 --> 00:53:36,250 +مقدار ال error يبقى بدأ اروح لنمرسي بداجي اقوله ال + +430 +00:53:36,250 --> 00:53:44,650 +error اللي هو delta F ناقص DF absolute value يعني + +431 +00:53:44,650 --> 00:53:47,790 +ال error دائما هو انه هيطلع بالموجة لانه ماخدله + +432 +00:53:48,460 --> 00:53:53,840 +أبسلوت فاليو يبقى هي أبسلوت فاليو Delta F طلعناها + +433 +00:53:53,840 --> 00:54:00,960 +في الأول Zero واحد وأربع من مية ناقص DF طلعناها + +434 +00:54:00,960 --> 00:54:07,980 +اللي هي Zero وأربعة من عشرة بضل قدوش واحد من مية + +435 +00:54:07,980 --> 00:54:16,600 +يبقى Zero Zeroأربعة من أشهر تاني أربعين من مائة + +436 +00:54:16,600 --> 00:54:18,560 +نترحى من واحد من أربعين نترحى من أربعين نترحى من + +437 +00:54:18,560 --> 00:54:18,600 +أربعين نترحى من أربعين نترحى من أربعين نترحى من + +438 +00:54:18,600 --> 00:54:20,180 +أربعين نترحى من أربعين نترحى من أربعين نترحى من + +439 +00:54:20,180 --> 00:54:22,180 +أربعين نترحى من أربعين نترحى من أربعين نترحى من + +440 +00:54:22,180 --> 00:54:26,580 +أربعين نترحى من أربعين نترحى من أربعين نترحى من + +441 +00:54:26,580 --> 00:54:29,300 +أربعين نترحى من أربعين نترحى من أربعين نترحى من + +442 +00:54:29,300 --> 00:54:37,980 +أربعين نترحى من أربعين نترحى من + +443 +00:54:37,980 --> 00:54:48,550 +أربعين نتتلاتة تسعة المسائل التالية من واحد لتلتاش + +444 +00:54:48,550 --> 00:54:52,750 +الأد ومن + +445 +00:54:52,750 --> 00:54:55,170 +اربعتاش لستاش + +446 +00:54:57,860 --> 00:55:08,300 +و كذلك من سبعتاش لغاية تلاتة وتلاتين، سبعتاش لغاية + +447 +00:55:08,300 --> 00:55:10,140 +تلاتين برضه الأد + +448 +00:55:22,600 --> 00:55:27,940 +طيب لحد هنا انتهى هذا section وبانتهاء هذا section + +449 +00:55:27,940 --> 00:55:33,860 +ينتهي هذا chapter والان ننتقل الى ال chapter اللذي + +450 +00:55:33,860 --> 00:55:40,760 +يليه وهو تطبيقات على المشتق الأولى يعني انتهينا من + +451 +00:55:40,760 --> 00:55:46,640 +عملية الاشتقاء والان بدنا نجي لتطبيقات على + +452 +00:55:46,640 --> 00:55:55,700 +المشتقاتهذا ال chapter يتحدث عن الرسم البياني لل + +453 +00:55:55,700 --> 00:56:03,460 +functions بس مش هي نرسم الرسم رسما دقيقا بدنا نعرف + +454 +00:56:03,460 --> 00:56:09,240 +فترات التزايد و فترات التناقص و القيم العظمى و + +455 +00:56:09,240 --> 00:56:13,380 +الصغرى المحلية و قداش ال absolute maximum و ال + +456 +00:56:13,380 --> 00:56:19,150 +absolute minimum لذلكوقال واجتشكن كيف up و واجتشكن + +457 +00:56:19,150 --> 00:56:24,290 +كيف down ووين ال inflection point وكل هالشغلات هذي + +458 +00:56:24,290 --> 00:56:29,610 +هو ما سندرسه في أول ثلاث sessions بعد هيك بنروح + +459 +00:56:29,610 --> 00:56:35,250 +لعملية الرسم يعني مش من البداية بدنا نبدأ نرسم + +460 +00:56:35,250 --> 00:56:40,110 +يبقى chapter أربعة اللي هو applications + +461 +00:56:40,110 --> 00:56:44,690 +applications + +462 +00:56:44,690 --> 00:56:45,890 +of + +463 +00:56:48,460 --> 00:56:54,400 +أيه ال derivatives applications + +464 +00:56:54,400 --> 00:56:59,160 +of derivatives بدنا نيجي لأول section اللي هو + +465 +00:56:59,160 --> 00:57:07,060 +أربعة واحد extreme values + +466 +00:57:07,060 --> 00:57:12,680 +extreme values of functions + +467 +00:57:17,690 --> 00:57:22,130 +بنعطي تعريف للـ Extreme Values وبعدين بنشوف كيف + +468 +00:57:22,130 --> 00:57:27,270 +بنحسبها Definition let + +469 +00:57:27,270 --> 00:57:40,630 +ال F be a function with domain + +470 +00:57:40,630 --> 00:57:43,850 +D + +471 +00:57:49,580 --> 00:57:56,420 +ال F has an + +472 +00:57:56,420 --> 00:58:05,080 +absolute maximum + +473 +00:58:05,080 --> 00:58:15,980 +value + +474 +00:58:18,140 --> 00:58:31,340 +on D at C اللي موجودة الـ interval D if إذا كان ال + +475 +00:58:31,340 --> 00:58:41,160 +F of X أقل من أو يساوي ال F of C ال F of X أقل من + +476 +00:58:41,160 --> 00:58:47,970 +أو يساوي ال F of X for all X اللي موجودة في Dand + +477 +00:58:47,970 --> 00:58:59,490 +has an absolute minimum + +478 +00:58:59,490 --> 00:59:07,850 +value + +479 +00:59:07,850 --> 00:59:10,630 +on + +480 +00:59:23,620 --> 00:59:35,840 +F of X أكبر من أو يساوي F of C for all X موجودة في + +481 +00:59:35,840 --> 00:59:36,400 +D + +482 +00:59:42,750 --> 00:59:49,370 +The absolute maximumThe + +483 +00:59:49,370 --> 01:00:04,430 +absolute maximum and absolute minimum values are + +484 +01:00:04,430 --> 01:00:10,170 +called absolute + +485 +01:00:15,050 --> 01:00:24,210 +extrema salute extrema and ال + +486 +01:00:24,210 --> 01:00:33,190 +maximum and ال minimum values + +487 +01:00:33,190 --> 01:00:36,430 +are called + +488 +01:00:43,820 --> 01:00:52,180 +Extreme values of + +489 +01:00:52,180 --> 01:00:56,400 +the function f + +490 +01:01:34,040 --> 01:01:39,020 +طبعا في فرق شاسعة ما بين ال absolute maximum و ال + +491 +01:01:39,020 --> 01:01:44,300 +local maximum absolute minimum و local minimumزي + +492 +01:01:44,300 --> 01:01:47,920 +ما هنشوف اليوم ناخد ال absolute maximum لما نوصل + +493 +01:01:47,920 --> 01:01:51,280 +ال local maximum و ال local minimum ستجد الفرق + +494 +01:01:51,280 --> 01:01:53,980 +الشاسع ما بين الاتنين + +495 +01:02:04,410 --> 01:02:08,210 +يبقى الشبكة الأربعة اللي بين إيدينا هذا اللي هو + +496 +01:02:08,210 --> 01:02:14,690 +تطبيقات على المشتقات احنا نبدأ أول شي بال extreme + +497 +01:02:14,690 --> 01:02:18,510 +values of functions إيش يعني معناه extreme values + +498 +01:02:18,510 --> 01:02:24,990 +بالعربي؟ القيم + +499 +01:02:24,990 --> 01:02:29,890 +القصوى، قيم القصوى، قيم القصوى، قيم القصوى، قيم + +500 +01:02:29,890 --> 01:02:33,980 +القصوى، قيم القصوى، قيم القصوىقصوة يعني عالية جدا، + +501 +01:02:33,980 --> 01:02:40,380 +مش ممكن نقول قيم الدنيا مثلا قيم + +502 +01:02:40,380 --> 01:02:44,080 +المطلق، absolute يعني مطلق، أنا قولت extreme، إيش + +503 +01:02:44,080 --> 01:02:48,920 +معناها؟ + +504 +01:02:48,920 --> 01:02:57,800 +نقطة لا يمكن منها يتعدى، على أي حالالترجمة الحرفية + +505 +01:02:57,800 --> 01:03:05,180 +إما قصوى أو متطرفة، مش يعني إرهابية، لأ لأ متطرف، + +506 +01:03:05,180 --> 01:03:09,770 +مالاش دعوة بالإرهابيةكويس؟ يبقى ال extreme values + +507 +01:03:09,770 --> 01:03:16,390 +إما قيم قصوى أو قيم متطرفة للدالة، متطرفة مش يعني + +508 +01:03:16,390 --> 01:03:21,530 +مقصودة في الطرفين، قد تكون في الطرفين و قد تكون في + +509 +01:03:21,530 --> 01:03:28,340 +الداخل، احتماليا وردات كما سنرى بعد قليليقول افترض + +510 +01:03:28,340 --> 01:03:33,260 +ان F عبارة عن دالة و ال domain تبع هذه الدالة هو D + +511 +01:03:33,260 --> 01:03:38,240 +يبقى انا مقيد بال domain تبع هذه الدالة هو D ال F + +512 +01:03:38,240 --> 01:03:46,830 +has an absolute maximum value قيمة مطلقة عظمةعلى + +513 +01:03:46,830 --> 01:03:53,090 +مين؟ على الـ domain D at C الموجودة في D إذا كانت + +514 +01:03:53,090 --> 01:03:59,390 +الـ F of X أقل من أو يساوي F of C لكل الـ X + +515 +01:03:59,390 --> 01:04:06,910 +الموجودة في Dيبقى لو أخدت أي قيمة أخرى غير هذه + +516 +01:04:06,910 --> 01:04:14,010 +الـC على كل الـD، بتكون هذه مالها أكبر ما يمكن طيب + +517 +01:04:14,010 --> 01:04:20,170 +التاني بيقول، and has an absolute minimum value + +518 +01:04:20,170 --> 01:04:29,190 +يبقى قيمة همطلقة صغرة أو دنيا أو على الـD and الـC + +519 +01:04:29,190 --> 01:04:35,210 +اللي موجودة في Dالـ F of X أكبر من أي قيمة أخرى + +520 +01:04:35,210 --> 01:04:40,010 +إذا كانت جميع قيم الدالة عند X بتبقى أكبر دائما أو + +521 +01:04:40,010 --> 01:04:44,190 +أبدا من مين من قيمة الدالة عند C يعني قيمة الدالة + +522 +01:04:44,190 --> 01:04:50,370 +عند C أقل من جميع مين القيم الأخرى السؤال اللي بدي + +523 +01:04:50,370 --> 01:04:56,610 +أطرحه من خلال هذا التعريب هل هناك أكثر من absolute + +524 +01:04:56,610 --> 01:04:58,790 +maximum للدالة؟ + +525 +01:05:02,820 --> 01:05:08,000 +بهمنيش الموقع، بهمنيش الموقع يعني لا يوجد غيرها + +526 +01:05:08,000 --> 01:05:13,140 +لإن قال لي for all x اللي موجودة وياه في دي يعني + +527 +01:05:13,140 --> 01:05:17,900 +على كل ال domain تبعي دي بتبقى هذه أكبر واحدة فيهم + +528 +01:05:17,900 --> 01:05:22,180 +بغض النظر سواء أجت في الطرف والله في الداخل، + +529 +01:05:22,180 --> 01:05:26,840 +بهمنيش يعني إن أجت في طرف ال domain من اليمين أو + +530 +01:05:26,840 --> 01:05:31,340 +طرف الشمال أو الداخل، بهمنيش الموقعبهم انه لا توجد + +531 +01:05:31,340 --> 01:05:36,880 +الا absolute maximum عظمة واحدة وكذلك ماعنديش الا + +532 +01:05:36,880 --> 01:05:42,600 +absolute minimum واحدة فقط لا غير كما سنرى بعد + +533 +01:05:42,600 --> 01:05:47,320 +قليل من خلال الأمثلة يبقى التعريف بيقول لما نكون + +534 +01:05:47,320 --> 01:05:52,360 +عندي absolute maximum بدتكون هذه أكبر قيمة للدالة + +535 +01:05:52,360 --> 01:05:57,430 +أي قيمة أخرى للدالة بدتكونولمّا ربنا يحط فيها + +536 +01:05:57,430 --> 01:06:03,210 +البركة بيصير جدها، صح ولا لا؟ يعني ممكن .. ممكن + +537 +01:06:03,210 --> 01:06:08,250 +أجد في موقع آخر absolute maximum، لكن ليه تبقى + +538 +01:06:08,250 --> 01:06:12,190 +نفسي القيمة؟ يبقى ماليش إلا قيمة واحدة، لكن قد + +539 +01:06:12,190 --> 01:06:15,110 +أجدها فيها أكثر من موقع، أجدها أكتر من موقع + +540 +01:06:15,110 --> 01:06:19,690 +ماعنديش مشكلة، لكن بتظلهي مافيش إلا غيرها حتى وإن + +541 +01:06:19,690 --> 01:06:26,130 +كانت في أكثرها من موقع تمام؟ طيب كمعنى قيمة الصغرة + +542 +01:06:26,130 --> 01:06:30,350 +بنفس الطريقة قد أجد قيمة الصغرة في أكثر من موقع + +543 +01:06:30,350 --> 01:06:36,070 +لكنها ليست قيمة مختلفة بتأخذ ميا نفس القيمة اللي + +544 +01:06:36,070 --> 01:06:41,620 +عندنا هذهالنقطة التانية ال absolute maximum وال + +545 +01:06:41,620 --> 01:06:47,200 +absolute minimum values بسميهم absolute extrema + +546 +01:06:47,200 --> 01:06:55,240 +extrema يعني جمع extreme بدل ما اقول extreme تبقى + +547 +01:06:55,240 --> 01:06:59,980 +maximum اول ما بقول extreme وخلاص يبقى called + +548 +01:06:59,980 --> 01:07:04,440 +absolute extremeabsolute maximum او absolute .. + +549 +01:07:04,440 --> 01:07:08,760 +يعني مثلا لما نقعد على ده يمكن مالاجيش فيهالا + +550 +01:07:08,760 --> 01:07:13,200 +أبسلوت ماكسما ولا أبسلونة أقول له has no absolute + +551 +01:07:13,200 --> 01:07:16,140 +maximum and no absolute من الله بقول له has no + +552 +01:07:16,140 --> 01:07:21,820 +absolute extrema وخلاص، بدى أفهم أنه لا عندي قيم + +553 +01:07:21,820 --> 01:07:27,460 +عظمى مطلقة، غولية ولا حتى سفلة، تمام؟ طب النقطة + +554 +01:07:27,460 --> 01:07:31,160 +الثانية، and ال maximum and minimum values are + +555 +01:07:31,160 --> 01:07:35,050 +called extreme valuesالقيم العظمى والقيم الصغراء + +556 +01:07:35,050 --> 01:07:39,070 +دي بسميها اللي هي القيم المتطرفة أو القيم القصوى + +557 +01:07:39,070 --> 01:07:43,090 +لمين لذنها الان بدنا نشوف كيف بدنا ندور على ال + +558 +01:07:43,090 --> 01:07:47,730 +absolute maximum و ال absolute minimum من خلال عدة + +559 +01:07:47,730 --> 01:07:52,010 +أمثلة يبقى find the absolute extrema + +560 +01:08:23,210 --> 01:08:27,610 +على الفترة المعطاعة + +561 +01:08:30,550 --> 01:08:40,470 +أي graph and graph the function رسم لي كذلك الدلة + +562 +01:08:40,470 --> 01:08:53,570 +نمرة واحد F of X يساوي اما واحد على X لما سالب + +563 +01:08:53,570 --> 01:09:02,900 +واحد اقل من او يساوي Xأقل من مين؟ أقل من الـ Zero + +564 +01:09:02,900 --> 01:09:12,140 +النقطة الثانية جذر ال X لما ال X أكبر من أو تساوي + +565 +01:09:12,140 --> 01:09:17,600 +ال Zero وأقل من أو تساوي مين؟ أقل من أو تساوي + +566 +01:09:17,600 --> 01:09:25,410 +أربعةيبقى اما هذه او هذه نمرى بى او النقطة الثانية + +567 +01:09:25,410 --> 01:09:35,630 +ال F of X بدى يساوي اربعة ناقص X تربية لما سالب + +568 +01:09:35,630 --> 01:09:44,630 +تلاتة اقل من او يساوي X اقل من او يساوي واحد نمرى + +569 +01:09:44,630 --> 01:09:55,510 +تلاتة ال F of Xتساوي الجذر التربيعي لاربع ناقص X + +570 +01:09:55,510 --> 01:09:56,390 +تربيع + +571 +01:09:58,790 --> 01:10:05,510 +اربع نقص X تربية نقص اتنين اقل من X اقل من اتنين + +572 +01:10:05,510 --> 01:10:16,550 +يبقى اربع ال F of X بدي ساوي تلاتة sign ال X و ال + +573 +01:10:16,550 --> 01:10:25,090 +X محصورة ما بين ال zero و ما بين اتنين by خمسة F + +574 +01:10:25,090 --> 01:10:39,860 +of X يساويabsolute value ل X ناقص اتنين اقل + +575 +01:10:39,860 --> 01:10:51,740 +من او يساوي X اقل من infinity F of X يساوي X تكعيب + +576 +01:10:51,740 --> 01:10:53,760 +زائد واحد + +577 +01:11:06,980 --> 01:11:11,860 +سؤال يعطيني بدل الدالة الستة وقال للست دول هدول + +578 +01:11:11,860 --> 01:11:18,280 +بدك ترسمهم وعلى ال domain تبعهم المحدد بدك تعرف + +579 +01:11:18,280 --> 01:11:22,840 +ليه ال absolute x مثلا كان absolute maximum أو + +580 +01:11:22,840 --> 01:11:27,520 +absolute minimum لهذه الدالة بقولها بسيطة هي + +581 +01:11:27,520 --> 01:11:35,110 +solution نجلة من لنقطة الأولىيقول F of X يساوي + +582 +01:11:35,110 --> 01:11:42,650 +واحدة، اه هذه دالة مجزقة من جزئين وليس جزءا واحدا + +583 +01:11:42,650 --> 01:11:51,010 +يعني لو رسمنا هذه الدالة بقول له هذه المحور X وهذه + +584 +01:11:51,010 --> 01:12:00,080 +محور Y وهذه نقطة الأصل اللي هي Zeroقبل او الرسم + +585 +01:12:00,080 --> 01:12:03,260 +الجزء الاول من سالب واحد درجة زمان طبعا واحد على + +586 +01:12:03,260 --> 01:12:08,360 +الاكس جزء على اليمين وجزء على الشمال بس الجزء اللي + +587 +01:12:08,360 --> 01:12:12,820 +على اليمين بديه الشياءأنا فقط جددهم من سالب واحد + +588 +01:12:12,820 --> 01:12:17,760 +إلى زيرو وإن السالب واحد هي السالب واحد لو إلا + +589 +01:12:17,760 --> 01:12:21,820 +زيرو خلال الفترة هذه طيب الدالة هذه لو كانت x + +590 +01:12:21,820 --> 01:12:26,780 +بسالب واحد بتكون هذا جداش واحد على سالب واحد اللي + +591 +01:12:26,780 --> 01:12:36,700 +هو بسالب واحديبقى قيمة الدالة بتبقى هنا ب-1 يبقى + +592 +01:12:36,700 --> 01:12:41,100 +هنا المنحنة بيكون جاي في الأصل بالشكل اللي عناها + +593 +01:12:41,100 --> 01:12:48,090 +دايقتمام و بيجي نازل هنا هذا هنا بصير غامق ليش انه + +594 +01:12:48,090 --> 01:12:53,750 +هذا ال domain تبع الدالة و هذا كله مش موجود يبقى + +595 +01:12:53,750 --> 01:12:59,070 +انا اخدت من هنا و جيت نازل بهذا الشكل + +596 +01:13:02,300 --> 01:13:07,280 +بعدين جاء الجزء التاني هو جذر ال X من Zero لغاية + +597 +01:13:07,280 --> 01:13:13,760 +أربعة يبقى لو جيت هنا واحد وهنا اتنين هالمد هذا + +598 +01:13:13,760 --> 01:13:20,760 +على استقالته يكون هنا تلاتة وهنا أربعة جذر ال X + +599 +01:13:20,760 --> 01:13:26,020 +بيكون بالشكل اللي عندنا هذا تمام عند الأربعة بيكون + +600 +01:13:26,020 --> 01:13:31,960 +واجف هنا يبقى هذه النقطة اللي هي أربعة وقدرو اتنين + +601 +01:13:31,960 --> 01:13:36,920 +يبقى هنا بدى يكون اتنين و هنا بدى يكون قداش اللى + +602 +01:13:36,920 --> 01:13:43,480 +هو واحد تمام تمام هى رسم الرسمة رسمنا الرسمة بدي + +603 +01:13:43,480 --> 01:13:47,520 +اجيبله قداش ال absolute maximum و ال absolute + +604 +01:13:47,520 --> 01:13:53,340 +minimum ان وجده قداش اعلى قيمة او اكبر قيمة تقدها + +605 +01:13:53,340 --> 01:13:59,310 +الدالة اللى هو الاتنينيبقى باجي بقوله هنا ال F has + +606 +01:13:59,310 --> 01:14:08,270 +absolute maximum اتنين ات اكس يساوي كده اش؟ اربع + +607 +01:14:08,270 --> 01:14:10,870 +في عندي absolute minimum + +608 +01:14:15,950 --> 01:14:22,130 +ماعنديش absolute minimum لإيش؟ لأن الدلة تنزل إلى + +609 +01:14:22,130 --> 01:14:30,830 +أين؟ للثالث بإنفنتاين ال F has no absolute minimum + +610 +01:14:30,830 --> 01:14:36,810 +مالهاش مالهاش بلاشطيب نجي للدالة التانية الدالة + +611 +01:14:36,810 --> 01:14:41,150 +التانية أربعة ناقص X تربية ومن سالب تلاتة لغاية + +612 +01:14:41,150 --> 01:14:45,950 +واحد طبعا هذه معادلة عياشي شيل الأربعة أو شيل واحد + +613 +01:14:45,950 --> 01:14:49,270 +يبقى فوق الساعة X تربية اللي هي برابط مفتوح إلى + +614 +01:14:49,270 --> 01:14:53,390 +أعلى سالب مجلوب إلى أسفل أربعة بنعمل shift إلى + +615 +01:14:53,390 --> 01:14:59,600 +أعلى بمقدار أربعة يبقى لو جيت للمحاور هذههذا رقم + +616 +01:14:59,600 --> 01:15:07,280 +اتنين لو جيت رسمته بدي اقول هذا محور X هذا محور Y + +617 +01:15:07,280 --> 01:15:12,720 +هذا نقطة الاصل هي Zero وهذا النقطة اليمين هي أربعة + +618 +01:15:13,080 --> 01:15:19,200 +المنحنة بده يجي ننزل هيك ومن هنا بده يجي هي عند + +619 +01:15:19,200 --> 01:15:24,460 +مين اللي هي الواحد يبقى هنا عندنا سالب واحد و هنا + +620 +01:15:24,460 --> 01:15:31,040 +سالب اتنين لإن عند سالب اتنين بصير قيمة الدلج اداش + +621 +01:15:31,410 --> 01:15:37,910 +زيرو يبقى قال لي بدك تبقى ماشي ل Y سالب تلاتة يبقى + +622 +01:15:37,910 --> 01:15:44,670 +هذا سالب تلاتة و أنزل لحد هنا فقط لغاية يبقى كل ال + +623 +01:15:44,670 --> 01:15:50,170 +term اللي تحت ماعنديهش وهنا اللي هو أخر قيمة + +624 +01:15:50,170 --> 01:15:55,350 +بياخدها المنحنة يبقى هذا المنحنة فقط اللي عندي + +625 +01:16:00,960 --> 01:16:05,400 +خطة الغامضة اذا + +626 +01:16:05,400 --> 01:16:11,860 +اقصى قيمة بياخدها وين عند ال zero وهي اربعة و اقل + +627 +01:16:11,860 --> 01:16:19,100 +قيمة بياخدها عند السالب تلاتة وهي سالب خمسة يبقى + +628 +01:16:19,100 --> 01:16:25,830 +باجي بقوله هنا ال Fالـ F has absolute maximum + +629 +01:16:25,830 --> 01:16:33,090 +أربعة at x يساوي زيرو يبقى ال absolute maximum ما + +630 +01:16:33,090 --> 01:16:37,490 +جاش في الطرفين وإنما جواين في الداخل داخل ال + +631 +01:16:37,490 --> 01:16:48,220 +domain ال F has absolute minimumأذا قمنا بإزالة X + +632 +01:16:48,220 --> 01:16:53,700 +وضعها في مكانها سالب ثلاثة تصبح تسعة يبقى أربعة + +633 +01:16:53,700 --> 01:17:02,380 +ناقص تسعة يبقى خمسة اللي هو الأربعة ناقص تلاتة + +634 +01:17:02,380 --> 01:17:11,360 +تربيع هي ناقص تلاتة تربيع ويسوى سالب خمسة at X + +635 +01:17:11,360 --> 01:17:20,820 +يسوى سالب تلاتةالدالة التالتة F of X سوى الجدر + +636 +01:17:20,820 --> 01:17:25,320 +التربية لاربع ناقص X تربية وحصارها من سنة باتنين + +637 +01:17:25,320 --> 01:17:31,320 +لاتنين من هذه الدائرة يبقى هذه دائرة بس موجودة + +638 +01:17:31,320 --> 01:17:37,630 +عنده نصف العلوي لإن الجدر ماقدموش إشارةسالبة يبقى + +639 +01:17:37,630 --> 01:17:43,030 +باجي بقوله لو جيت رسمتها هتاخد الشكل التالي هذا + +640 +01:17:43,030 --> 01:17:50,370 +محور X هذا محور Y وهنا المنحنة بتجينا بالشكل هذا + +641 +01:17:50,370 --> 01:18:01,520 +هيك تمام بس ايش هذاماعنديش يساوي و هنا ماعنديش + +642 +01:18:01,520 --> 01:18:06,680 +يساوي يبقى بالشكل اللي عندنا هذا تمام و هذا zero و + +643 +01:18:06,680 --> 01:18:13,360 +هذه دائرة نصف خطرة كده؟ نين تمام طيب ايش عند هنا؟ + +644 +01:18:13,780 --> 01:18:34,080 +أبسلوت مقسمم اتنين + +645 +01:18:34,200 --> 01:18:43,200 +أت اكس يساوي زير ال F has no absolute minimum + +646 +01:18:43,200 --> 01:18:49,800 +ماعنديش absolute minimum نجي للأربع تلاتة sign ال + +647 +01:18:49,800 --> 01:18:55,060 +X وال X من زير و اتنين يعني كل ال period تبعت ال + +648 +01:18:55,060 --> 01:19:03,610 +sign فجباجي بقوله كويس هذا المنحنةوهذا محور X وهذا + +649 +01:19:03,610 --> 01:19:13,630 +محور Y هذا واحد وهذا اتنين وهذا تلتة وهنا هي سالب + +650 +01:19:13,630 --> 01:19:20,770 +واحد وهنا هي سالب اتنين وهنا له سالب تلتة يبقى هذا + +651 +01:19:20,770 --> 01:19:27,070 +الخط اللي عندنا وهذا الخط التاني اللي عندناوهو + +652 +01:19:27,070 --> 01:19:32,790 +الخط الوهمي ال sign أصلا محصولة بين مين ومين سالب + +653 +01:19:32,790 --> 01:19:37,570 +واحد وواحد المنظر بقى تلاتة سير من سالب تلاتة زي + +654 +01:19:37,570 --> 01:19:41,040 +السؤال اللي جاكمه في الامتحانبيدّو ال range لإنك + +655 +01:19:41,040 --> 01:19:46,760 +طلعت اتنين من ال sign ال X صلب واحد و واحد تضرب + +656 +01:19:46,760 --> 01:19:50,820 +فيه سلب اتنين صارت من سلب اتنين الاتنين اذا احنا + +657 +01:19:50,820 --> 01:19:56,900 +هنا من سلب تلاتة الى تلاتة يبقى المنحنة هيبدأ من + +658 +01:19:56,900 --> 01:20:03,840 +عند ال zeroو يطلع و يجي نازل تاني اك و يجي طالع بس + +659 +01:20:03,840 --> 01:20:10,080 +لحد اتنين باي يبقى هاي zero هاي باي على اتنين هنا + +660 +01:20:10,080 --> 01:20:17,940 +باي هنا تلاتة باي على اتنين هنا اتنين باي يبقى انا + +661 +01:20:17,940 --> 01:20:25,180 +تقيت بال domain اللي قال عليه تمام؟ اذا هذه هه + +662 +01:20:25,180 --> 01:20:30,300 +اللي هي mainاللي هي النقطة باي على اتنين وهذه + +663 +01:20:30,300 --> 01:20:34,820 +النقطة اللي عندها أخد أقل قيمة عندها اللي هي main + +664 +01:20:34,820 --> 01:20:41,620 +سالب باي على اتنين يبقى فيه عندنا عزيزي absolute + +665 +01:20:41,620 --> 01:20:48,460 +maximum وفيه absolute minimum يبقى باجي بقوله ال F + +666 +01:20:50,080 --> 01:21:01,080 +has absolute maximum تلاتة at x يسوى باى على اتنين + +667 +01:21:01,080 --> 01:21:10,140 +ال F has absolute minimum سالب تلاتة at x يسوى + +668 +01:21:10,140 --> 01:21:13,700 +تلاتة باى على اتنين + +669 +01:21:21,850 --> 01:21:28,010 +ممتاز جدا بدل ما هي من zero ل باى على اتنين لاتنين + +670 +01:21:28,010 --> 01:21:34,030 +باى بتدخليها من zero لاربع باى ماشي او من سالب + +671 +01:21:34,030 --> 01:21:40,150 +اتنين باى لاتنين باى هل ستتغير ال absolute maximum + +672 +01:21:40,150 --> 01:21:44,110 +و ال absolute minimum لما تتغير بصير فيه اكثر من + +673 +01:21:44,110 --> 01:21:49,050 +موقع الاكثر من موقع لكن كله بيجيب نفس النتيجة + +674 +01:22:00,490 --> 01:22:06,830 +وهو الـSin عمره ما يختلفوا؟ كل يعني موجة قصدا، كل + +675 +01:22:06,830 --> 01:22:12,170 +موجة قالعة ونازلة، ممتاز جدا، وين أكبر واحدة فيهم؟ + +676 +01:22:12,170 --> 01:22:16,850 +طبعا هي الـAbsolute maximum، وين أقل واحدة فيهم؟ + +677 +01:22:16,850 --> 01:22:21,180 +بيكون هي الـAbsolute minimumأه طبيعي أه الباقي + +678 +01:22:21,180 --> 01:22:26,440 +بيصير local ان اتكلمتش لسه عن ال local أه كل + +679 +01:22:26,440 --> 01:22:30,540 +absolute maximum ممكن يكون local إن كان في الداخل + +680 +01:22:30,540 --> 01:22:37,520 +لكن العكس مش صحيح ايه نعم طيب نيجي لمين للنقطة + +681 +01:22:37,520 --> 01:22:43,780 +الخامسة يبقى النقطة الخامسةنقطة الخامسة بيقول f of + +682 +01:22:43,780 --> 01:22:48,540 +x سواء absolute بل ال X ناقص اتنين يبقى هذه + +683 +01:22:48,540 --> 01:22:56,500 +المحاولهذا محور X وهذا محور Y absolute value X + +684 +01:22:56,500 --> 01:23:03,680 +نزلها لتحت بالمقدار كم؟ سالي باتنين بس ايش؟ من جهة + +685 +01:23:03,680 --> 01:23:09,180 +اليمين على اطلاقها الله يسهل عليها، موحوين ماتروح، + +686 +01:23:09,180 --> 01:23:15,280 +بس من جهة الشمال لحد وين؟ لحد سالي باتنين بالشكل + +687 +01:23:15,280 --> 01:23:21,200 +اللي قلنا، لا تتعدىلإيش؟ لإن عند سالي باتنين بيصير + +688 +01:23:21,200 --> 01:23:25,320 +موجة باتنين نقظين Zero يبقى بالشكل اللي عندنا هذا، + +689 +01:23:25,320 --> 01:23:32,300 +هاه إيش رأيك؟ فش إيش؟ فش absolute maximum، لكن في + +690 +01:23:32,300 --> 01:23:39,960 +absolute minimum، يبقى ال F هذا absolute minimum + +691 +01:23:39,960 --> 01:23:50,200 +سالي باتنين at x يسوى Zeroالـ F has no absolute + +692 +01:23:50,200 --> 01:23:58,480 +maximum ماعنديش طيب السادسة هذا + +693 +01:23:58,480 --> 01:24:04,200 +محور X هذا محور Y هذه الـ Zero وهذا مين اللي هو + +694 +01:24:04,200 --> 01:24:08,780 +الواحد اتخيل انه عندي خط وهمي بالشكل اللي قالنا + +695 +01:24:10,160 --> 01:24:15,200 +يبقى ده اللي اصلا ال F of X الساوي X تكييب عملنا + +696 +01:24:15,200 --> 01:24:20,700 +له shift الى اعلى بمقدار واحد صحيح يبقى المنحنة + +697 +01:24:20,700 --> 01:24:26,340 +بده يجينا بالشكل هذا يبقى + +698 +01:24:26,340 --> 01:24:28,820 +هذا اللي هو ال F of X + +699 +01:24:32,780 --> 01:24:39,060 +يبدو يساوي اكس تكريب زائد واحد ايش رايك؟ no + +700 +01:24:39,060 --> 01:24:49,680 +absolute extrema يبقى ال F has no absolute extrema + +701 +01:24:49,680 --> 01:24:54,720 +يعني لا عندي absolute maximum ولا عندي absolute + +702 +01:24:54,720 --> 01:24:58,740 +minimum لمين لل function اللي عندنا + +703 +01:25:17,780 --> 01:25:41,520 +أخر نقطة في محاضرة اليوم في RM F + +704 +01:25:41,520 --> 01:25:44,560 +ال + +705 +01:25:44,560 --> 01:25:46,340 +F is + +706 +01:25:51,370 --> 01:26:02,770 +continuous continuous on a closed interval + +707 +01:26:02,770 --> 01:26:12,090 +closed interval a و b then + +708 +01:26:13,840 --> 01:26:18,040 +الـ F attains + +709 +01:26:18,040 --> 01:26:22,340 +attains + +710 +01:26:22,340 --> 01:26:29,300 +both an + +711 +01:26:29,300 --> 01:26:32,940 +absolute + +712 +01:26:32,940 --> 01:26:41,780 +maximum value capital + +713 +01:26:41,780 --> 01:27:00,320 +MAnd an absolute minimum value small m in the + +714 +01:27:00,320 --> 01:27:03,660 +closed interval ARB + +715 +01:27:47,230 --> 01:27:49,130 +Thank you + +716 +01:28:53,590 --> 01:28:54,990 +استخدام البرنامج البرنامج البرنامج + +717 +01:30:29,650 --> 01:30:32,590 +عشان نتمنى من الجواي فينا نعمل أكتر .. أكتر .. + +718 +01:30:32,590 --> 01:30:32,670 +أكتر + +719 +01:31:18,280 --> 01:31:23,220 +بنجد ال extreme value theorem نظرية القيام القصوى + +720 +01:31:23,220 --> 01:31:28,640 +أو القيام المتطرفة بقول لو كانت الدالة دالة متصلة + +721 +01:31:28,640 --> 01:31:35,020 +على closed interval then ال F attains يعني يحرز + +722 +01:31:35,020 --> 01:31:35,720 +بالعربي + +723 +01:31:39,410 --> 01:31:44,550 +يحرز both an absolute maximum value M and an + +724 +01:31:44,550 --> 01:31:49,690 +absolute minimum value M small في الفترة هذه A وB + +725 +01:31:49,690 --> 01:31:54,850 +يبقى لو الدالة دالة متصلة على فترة مغلقة خلال هذه + +726 +01:31:54,850 --> 01:32:00,050 +الفترة ممكن أن تحرز الدالة absolute maximum وكذلك + +727 +01:32:00,050 --> 01:32:06,340 +تحرز main absolute minimum الا إذا كانتكونوستانت + +728 +01:32:06,340 --> 01:32:15,980 +فانكشن كونوستانت فانكشن كونوستانت + +729 +01:32:15,980 --> 01:32:21,900 +فانكشن كونوستانت فانكشن كونوستانت فانكشن كونوستانت + +730 +01:32:21,900 --> 01:32:25,620 +فانكشن + +731 +01:32:25,650 --> 01:32:30,290 +الـ Absolute maximum ممكن يكون في طرف الدالة وممكن + +732 +01:32:30,290 --> 01:32:34,590 +يكون في طرف ال domain تبع الدالة وممكن يكون داخل + +733 +01:32:34,590 --> 01:32:39,210 +ال domain تبع هذه الدالة لو نظرنا للرسمة الأولى + +734 +01:32:39,210 --> 01:32:46,030 +يبقى ال absolute maximum حصل عند النقطة X1 لكن ال + +735 +01:32:46,030 --> 01:32:51,940 +absolute minimum حصل عند نقطة X2عنده نقطة X2 يبقى + +736 +01:32:51,940 --> 01:33:00,120 +من هنا صار إحداث النقطة دي اللي فوق هي X1 و M يبقى + +737 +01:33:00,120 --> 01:33:05,030 +ال M هو ال absolute maximumيبقى ال absolute + +738 +01:33:05,030 --> 01:33:09,090 +maximum و ال absolute .. و هذه النقطة الاهداثي + +739 +01:33:09,090 --> 01:33:15,330 +تبعها x اتنين و M اسمها طبعا ال M هنا السالبة تمام + +740 +01:33:15,330 --> 01:33:19,190 +يبقى ال absolute maximum و ال absolute minimum in + +741 +01:33:19,190 --> 01:33:27,350 +terror points يبقى ال absolute extrema + +742 +01:33:27,350 --> 01:33:32,830 +are at in terror + +743 +01:33:35,080 --> 01:33:43,560 +يبقى عند نقاط داخلية لل domain تبع الدالة هنا ال + +744 +01:33:43,560 --> 01:33:48,360 +absolute maximum وال absolute minimum وين at end + +745 +01:33:48,360 --> 01:33:58,000 +points عند الطرفين يبقى هنا ال absolute extrema at + +746 +01:33:58,000 --> 01:34:02,360 +the end points + +747 +01:34:04,040 --> 01:34:10,300 +وين عند الـ A و الـ B و أجت ال maximum في الطرف + +748 +01:34:10,300 --> 01:34:15,080 +الأول و أجت ال minimum وين في الطرف الثاني بلغتنا + +749 +01:34:15,080 --> 01:34:18,780 +القديمة ده اللي هذه increasing و الله decreasing + +750 +01:34:18,780 --> 01:34:25,460 +ده التناقصية نجي على الدالة اللي عندنا هذه ال + +751 +01:34:25,460 --> 01:34:31,690 +absolute minimumفي بداية الـ interval وال absolute + +752 +01:34:31,690 --> 01:34:41,190 +maximum داخل الفترة يبقى هنا ال absolute minimum M + +753 +01:34:41,190 --> 01:34:48,510 +at interior point + +754 +01:34:48,510 --> 01:34:56,390 +ال absolute minimum لأ مش ال interior point at end + +755 +01:34:56,390 --> 01:34:57,070 +point + +756 +01:35:00,800 --> 01:35:06,000 +at end point اللي في الطرف الشمال و ال absolute + +757 +01:35:06,000 --> 01:35:13,680 +maximum at + +758 +01:35:13,680 --> 01:35:27,200 +interior point يبقى عند النقطة الداخلية تالر ال + +759 +01:35:27,200 --> 01:35:31,870 +minimum عند النقطة الداخلية و ال maximumعن الطرف + +760 +01:35:31,870 --> 01:35:49,450 +تبعها هنا ال absolute minimum at interior point ال + +761 +01:35:49,450 --> 01:35:50,170 +absolute + +762 +01:36:07,770 --> 01:36:14,930 +يختلف الوضع من دالة إلى دالة أخرىقد يكون نقطة + +763 +01:36:14,930 --> 01:36:20,350 +طرفية وقد يكون نقطة داخلية عند الحسابات ان شاء + +764 +01:36:20,350 --> 01:36:25,090 +الله بيصير خير هذا بيفهمنا ايش بيفهمنا انه انا لما + +765 +01:36:25,090 --> 01:36:27,270 +بروح احاسب ال absolute maximum و ال absolute + +766 +01:36:27,270 --> 01:36:32,630 +minimum بدي اجيب قيمة الدالة عند طرفي ال interval + +767 +01:36:32,630 --> 01:36:38,360 +المعرف عليها من هذه ال functionثم اروح ادور على ال + +768 +01:36:38,360 --> 01:36:42,140 +extreme values في الداخل غير الطرفين و هذا ما + +769 +01:36:42,140 --> 01:36:46,840 +سنتحدث عنه ان شاء الله في المحاضرة القادمة + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/X063uSNYJc0.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/X063uSNYJc0.srt new file mode 100644 index 0000000000000000000000000000000000000000..fdd6491a5dd7259a1e34f0a9b07fc924f30de5b2 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/X063uSNYJc0.srt @@ -0,0 +1,3415 @@ +1 +00:00:20,770 --> 00:00:24,530 +بسم الله الرحمن الرحيم بنكمل section واحد اتنين + +2 +00:00:24,530 --> 00:00:29,030 +اللي ابتدينا فيه المرة الماضية طبعًا آخر حاجة + +3 +00:00:29,030 --> 00:00:32,670 +خدناها المرة اللي فاتت ليه كانت scaling و + +4 +00:00:32,670 --> 00:00:36,830 +reflecting graphs تمام آخر نقطة في هذا ال section + +5 +00:00:36,830 --> 00:00:41,670 +اللي هو موضوع ال ellipse يعني القطع الناقص + +6 +00:00:41,670 --> 00:00:48,030 +المخلطية خمسة الخط المستقيم الدائرة القطع المكافئ + +7 +00:00:48,030 --> 00:00:52,670 +القطع الناقص القطع الزائد احنا اليوم بس بنتكلم عن + +8 +00:00:52,670 --> 00:00:59,130 +القطع الناقص معادلة القطع الناقص هي عبارة عن X + +9 +00:00:59,130 --> 00:01:05,450 +تربيع على A تربيع زائد Y تربيع على B تربيع تساوي + +10 +00:01:05,450 --> 00:01:11,860 +واحد بنعرف ما هي الـA وما هي الـB لأنها دي يبقى X + +11 +00:01:11,860 --> 00:01:15,380 +تربيع على A تربيع زي Y تربيع على B تربيع تساوي + +12 +00:01:15,380 --> 00:01:20,750 +واحد اللي هو معادلة القطعة الناقصبنعرف ما هي ال a + +13 +00:01:20,750 --> 00:01:26,750 +و ما هي ال b و كيف ينشأ القطع الناقص يبقى لو جيت + +14 +00:01:26,750 --> 00:01:32,070 +رسمت القطع الناقص رسمته على الشكل التالي هذا محور + +15 +00:01:32,070 --> 00:01:39,570 +x هذا محور y هذه نقطة الأصل اللي هي zero وهي رسمة + +16 +00:01:39,570 --> 00:01:43,330 +ال ellipse بالشكل التالي النقطة هذه الإحداثية + +17 +00:01:43,330 --> 00:01:49,750 +تبعها A و Zero النقطة هذه ناقص A و Zero هذه Zero و + +18 +00:01:49,750 --> 00:01:56,530 +B هذه Zero و سالب B هذه النقطة هي نقطة تلاقي + +19 +00:01:56,530 --> 00:02:02,270 +المحورين بسميها ال center تبع ال ellipse يبقى هذا + +20 +00:02:02,270 --> 00:02:10,690 +بسميه ال center يبقى هذا ال center لل ellipse شوفوا + +21 +00:02:10,690 --> 00:02:16,350 +سيدي، زي ما أنتم شايفين، في عندنا محور كبير و هنا + +22 +00:02:16,350 --> 00:02:21,610 +في محور أصغر منهم، المحور الكبير بنسميه major + +23 +00:02:21,610 --> 00:02:28,250 +axis، المحور الرئيسي، يبقى هذا بسميه المحور اللي + +24 +00:02:28,250 --> 00:02:36,740 +عندنا هذا هيك، بسميه ال major يبقى هذا المحور + +25 +00:02:36,740 --> 00:02:45,740 +الرئيسي هذا الصغير بسميه ال minor axis المحور + +26 +00:02:45,740 --> 00:02:51,790 +الثانوي الـ parabola كان له vertex واحدة لكن ال + +27 +00:02:51,790 --> 00:02:57,550 +ellipse له two vertices يبقى هذه ال vertex الأولى + +28 +00:02:57,550 --> 00:03:02,210 +وهذه ال vertex الثانية هذه ال vertex الإحداثي + +29 +00:03:02,210 --> 00:03:08,870 +تبعها a و 0 هذه السالب a و 0 يبقى a هي المسافة من + +30 +00:03:08,870 --> 00:03:13,970 +ال center لغاية ال vertex و ال a الثانية برضه من ال + +31 +00:03:13,970 --> 00:03:19,810 +center لغاية مين لغاية ال vertex هنا من ال center + +32 +00:03:19,810 --> 00:03:24,330 +لغاية النقطة هذه البعد يساوي بي المسافة تساوي بي + +33 +00:03:24,330 --> 00:03:29,130 +أو من ال zero لغاية النقطة هذه برضه كذلك بي طيب + +34 +00:03:29,130 --> 00:03:35,650 +مُشان يكون عند ال ellipse هذا لازم أحط هنا شرط أن + +35 +00:03:35,650 --> 00:03:41,470 +ال a أكبر من بي يعني الرقم اللي تحت ال x أكبر من + +36 +00:03:41,470 --> 00:03:46,440 +مين من الرقم اللي تحت ال Y حتى يكون ال major axis هو + +37 +00:03:46,440 --> 00:03:51,640 +مين؟ هو محور X السؤال هو طيب أنا من وين بدي أجيب + +38 +00:03:51,640 --> 00:03:56,940 +هذا هو ال ellipse؟ أحد فيكم بيعرف معادلة الدائرة + +39 +00:03:56,940 --> 00:04:01,780 +اللي مركزها نقطة الأصل ونصف قطرها هيساوي ايه؟ ما هي + +40 +00:04:01,780 --> 00:04:07,830 +هذه المعادلة؟ X تربيع زي ال Y تربيع يساوي A تربيع + +41 +00:04:07,830 --> 00:04:12,630 +طيب لو جيت للطرفين من عند المحور X من هنا ومن + +42 +00:04:12,630 --> 00:04:18,430 +الناحية الثانية للدائرة وعملت stretch ايش بيصير؟ + +43 +00:04:18,430 --> 00:04:22,850 +بيصير ال ellipse اللي عندنا هذا تمام؟ يبقى بيصير + +44 +00:04:22,850 --> 00:04:26,170 +ال ellipse اللي عندنا هذا لو عملت له stretch زي ما + +45 +00:04:26,170 --> 00:04:32,170 +قلنا المرة اللي فاتت طيب لو عملت له compress أو + +46 +00:04:32,170 --> 00:04:36,650 +compress أفقي بلاش رأسي horizontal يبقى .. لا + +47 +00:04:36,650 --> 00:04:41,210 +ماهي دائرة أصلا يبقى أنا عند دائرة وبدي أعمل + +48 +00:04:41,210 --> 00:04:47,290 +compress تضاغط أو انكماش للدائرة من طرفيها من جهة + +49 +00:04:47,290 --> 00:04:52,030 +محوري يعني انكماش أفقي compress horizontally يبقى + +50 +00:04:52,030 --> 00:04:57,690 +بيصير استطاليا في اتجاه محور Y يبقى لو صرت في + +51 +00:04:57,690 --> 00:05:02,830 +اتجاه محور Y بيصير شكل ال ellipse بالشكل اللي عندنا + +52 +00:05:02,830 --> 00:05:08,950 +هذا هذا محور X وهذا محور Y وهذه نقطة الأصل بيصير ال + +53 +00:05:08,950 --> 00:05:16,030 +ellipse بالشكل اللي عندنا هذا هيك تمام يبقى هذا شكل + +54 +00:05:16,030 --> 00:05:21,390 +ال ellipse في هذه الحالة طيب ال ellipse اللي عندنا + +55 +00:05:21,390 --> 00:05:26,170 +وين بدها تصير ال a و ال b الكبير هو ال a يبقى + +56 +00:05:26,170 --> 00:05:33,650 +النقطة هذه بتصير Zero و a هذه Zero و سالب a هذه + +57 +00:05:33,650 --> 00:05:40,270 +النقطة اللي هي b و Zero هذه سالب b و Zero من + +58 +00:05:40,270 --> 00:05:43,580 +الناحية الثانية اللي هي النقطة اللي عندنا هذه طيب + +59 +00:05:43,580 --> 00:05:48,580 +السؤال هو هل المعادلة اللي فوق بتبقى كما هي والله + +60 +00:05:48,580 --> 00:05:53,580 +بتتغير بيحصل فيها تغيير يبقى بيصير ال ellipse اللي + +61 +00:05:53,580 --> 00:05:59,900 +عندنا هذا معادلته X تربيع على B تربيع زائد Y تربيع + +62 +00:05:59,900 --> 00:06:05,160 +على A تربيع يساوي واحد وفي نفس الوقت A greater + +63 +00:06:05,160 --> 00:06:12,880 +than B يبقى A أكبر من B كذلك إذا السؤال هو لو + +64 +00:06:12,880 --> 00:06:18,500 +أعطاني سؤال وبدي أميز هل هي الرسمة الأولى ولا + +65 +00:06:18,500 --> 00:06:22,380 +الرسمة الثانية من خلال المعادلة اللي بيعطيها ليه + +66 +00:06:22,380 --> 00:06:28,720 +بروح بطلع في المقام طبعًا في المقام المعادلة اللي + +67 +00:06:28,720 --> 00:06:33,400 +عندنا هنا يعني بدي أطلع في هنا A وB وأطلع في هنا + +68 +00:06:33,400 --> 00:06:38,680 +A وB إذا الرقم اللي في المقام أكبر من الرقم الثاني + +69 +00:06:38,680 --> 00:06:44,000 +يبقى المتغير اللي فوق بيكون هو ال major axis طلع + +70 +00:06:44,000 --> 00:06:50,350 +لي هنا A أكبر من بي و ال A موجودة في مقام ال X يبقى + +71 +00:06:50,350 --> 00:06:55,450 +ال X هو ال major axis فاللي هنا A أكبر من بي و ال A + +72 +00:06:55,450 --> 00:07:01,150 +موجودة في مقام ال Y يبقى Y هو ال major axis + +73 +00:07:01,150 --> 00:07:05,190 +تمام؟ يبقى مُشان أحكم على ال ellipse هل ال major + +74 +00:07:05,190 --> 00:07:09,290 +axis في اتجاه محور Y والله في اتجاه محور X بروح و + +75 +00:07:09,290 --> 00:07:14,940 +بطلع عليه صاحب المقام الرفيع صاحب المقام الكبير يبقى + +76 +00:07:14,940 --> 00:07:18,920 +بيكون المتغير اللي في البسط من فوق بيكون هو ال + +77 +00:07:18,920 --> 00:07:23,480 +major axis والثاني بيكون هو ال minor axis المحور + +78 +00:07:23,480 --> 00:07:28,320 +الثانوي يبقى وبالتالي قدرت أحكم على الرسمة هل هي + +79 +00:07:28,320 --> 00:07:33,260 +الرسمة الأولى أو الرسمة الثانية طبعًا الرسمة الأولى + +80 +00:07:33,260 --> 00:07:37,580 +حصلنا عليها لما نعملها stretch أفقي والرسمة + +81 +00:07:37,580 --> 00:07:40,880 +الثانية حصلنا عليها لما نعملها compress أفقي + +82 +00:07:40,880 --> 00:07:46,640 +للدائرة اللي مركزها نقطة الأصل ونصف قطرها يساوي R + +83 +00:07:46,640 --> 00:07:52,100 +مثلا يبقى عرفنا شكل ال ellipse طب لو ال ellipse هذا + +84 +00:07:52,100 --> 00:07:58,260 +عملت له shift عملت له shift بطلت أخلي ال center 00 + +85 +00:07:58,260 --> 00:08:04,720 +يبقى بدي أعرف ما هو شكل المعادلة فبجي بقوله هنا if + +86 +00:08:04,720 --> 00:08:23,150 +the center of the ellipse is h وk then its equation + +87 +00:08:23,150 --> 00:08:30,430 +is المعادلة تبعته تصبح على الشكل التالي x ناقص h + +88 +00:08:30,430 --> 00:08:33,230 +الكل square على a تربيع + +89 +00:08:36,130 --> 00:08:44,030 +زائد Y ناقص K الكل تربيع على B تربيع يساوي كم؟ يساوي + +90 +00:08:44,030 --> 00:08:47,870 +واحد يبقى لو اتغير ال center تبع ال ellipse من + +91 +00:08:47,870 --> 00:08:53,350 +Zero Zero نقطة الأصل إلى اللي هو النقطة H وK يبقى + +92 +00:08:53,350 --> 00:08:58,130 +بيصير شكل المعادلة X ناقص H الكل تربيع على A تربيع + +93 +00:08:58,130 --> 00:09:02,950 +زائد Y ناقص K الكل تربيع على B تربيع يبقى يساوي كم؟ + +94 +00:09:02,950 --> 00:09:08,720 +يبقى يساوي واحد الإزاحة يمين وأعلى، يمين أسفل، شمال + +95 +00:09:08,720 --> 00:09:13,100 +وأعلى، شمال أسفل، وينما تكون الإزاحة تكون بالنسبة + +96 +00:09:13,100 --> 00:09:19,200 +لمين؟ للرسم فبنعطي بعض الأمثلة التطبيقية على ذلك + +97 +00:09:19,200 --> 00:09:28,000 +أول مثال examples أول + +98 +00:09:28,000 --> 00:09:30,080 +مثل بيقول sketch the ellipse + +99 +00:09:32,960 --> 00:09:42,060 +زي ellipse ارسم لي القطع الناقص X تربيع على أربعة + +100 +00:09:42,060 --> 00:09:50,720 +زائد Y تربيع على خمسة وعشرين يساوي كده؟ يساوي .. + +101 +00:09:50,720 --> 00:09:57,360 +لا لا مش هذا استنى شوية مش هذا يبقى sketch the + +102 +00:09:57,360 --> 00:10:05,100 +ellipse اللي هو من X زائد واحد الكل تربيع زائد + +103 +00:10:05,100 --> 00:10:12,100 +اتنين Y تربيع يساوي أربعة إذا لما يقول يرسم سؤال + +104 +00:10:12,100 --> 00:10:17,380 +مثل هذا السؤال أول خطوة بدي أعملها بدي أحط + +105 +00:10:17,380 --> 00:10:21,740 +المعادلة في ال standard form الشكل اللي عندنا هذا + +106 +00:10:21,740 --> 00:10:25,420 +أو الشكل اللي عندنا هذا أو الشكل اللي عندنا هذا + +107 +00:10:25,790 --> 00:10:30,270 +لذلك في المعادلات التلاتة كلها الطرف اليمين جداش + +108 +00:10:30,270 --> 00:10:34,090 +واحد واحنا في المعادلة اللي أنا الطرف اليمين إذا + +109 +00:10:34,090 --> 00:10:39,810 +بنروح نقسم طرفي المعادلة على أربعة إذا لو روحت قسم + +110 +00:10:39,810 --> 00:10:45,610 +طرفي المعادلة على أربعة بتصبح على الشكل التالي X + +111 +00:10:45,610 --> 00:10:50,750 +زائد واحد الكل تربيع على أربعة زائد Y تربيع على + +112 +00:10:50,750 --> 00:10:56,910 +اثنين يساوي جداش واحد بعد ذلك أنا بدي أميزها للرسمة + +113 +00:10:56,910 --> 00:11:02,570 +الأولى والثانية بطلع على صاحب المقام الكبير يبقى + +114 +00:11:02,570 --> 00:11:08,630 +صاحب المقام الكبير هو مع ال X يبقى المحور هو محور X + +115 +00:11:08,630 --> 00:11:14,570 +أو خط موازٍ له قد يكون محور X وقد يكون الخط + +116 +00:11:14,570 --> 00:11:19,330 +الموازٍ له إذا عملنا shift للمثلة واضح أن هذه + +117 +00:11:19,330 --> 00:11:25,170 +المثلة فيها shift في اتجاه واحد فقط طيب كويس يبقى + +118 +00:11:25,170 --> 00:11:34,710 +هذا ال center تبعه يبقى هذا ellipse with center H + +119 +00:11:34,710 --> 00:11:42,390 +و K بده يساوي كده؟ واحد و Zero و غلط مكتوب ايش اللي + +120 +00:11:42,390 --> 00:11:48,090 +خلى هذه زائد معناته اجتنا هنا اشارة مع اشارة + +121 +00:11:48,090 --> 00:11:54,390 +ناقص يبقى هنا سالب واحد و Zero بالشكل اللي عندنا + +122 +00:11:54,390 --> 00:11:58,330 +هذا بالنسبة ل Y there is no shift ما عنديش shift + +123 +00:11:58,330 --> 00:12:04,870 +لأن Y بقيت كما هي إذا لو حبينا نرسم ال ellipse اللي + +124 +00:12:04,870 --> 00:12:09,850 +عندنا هذا بعدين بقول هي الرسمة هي المحاور هذا محور + +125 +00:12:09,850 --> 00:12:17,870 +X هذا Y هذه نقطة الأصل ال ellipse اللي عندي في + +126 +00:12:17,870 --> 00:12:23,150 +الأساس هي بالشكل اللي عندنا هذا هيك هذا قبل ايه + +127 +00:12:23,150 --> 00:12:27,090 +قبل الإزاحة ال a عندي ك + +128 +00:12:30,990 --> 00:12:36,670 +يبقى عند ال A تساوي اثنين وال B تساوي مان جذر + +129 +00:12:36,670 --> 00:12:41,530 +اثنين، لأن هذا A تربيع وهذا B تربيع، إذا إحداث + +130 +00:12:41,530 --> 00:12:47,350 +النقطة هذه قبل ال shift كان اثنين و Zero وهذه كانت + +131 +00:12:47,350 --> 00:12:53,970 +سالب اثنين و Zero والآن عملنا إزاحة جهة اليمين + +132 +00:12:53,970 --> 00:12:59,790 +بمقدار سالب واحد بمقدار واحد يبقى إذا ال ellipse + +133 +00:12:59,790 --> 00:13:04,510 +بدي يصير ال center بدل ما هو Zero Zero بدي ينتقل + +134 +00:13:04,510 --> 00:13:08,850 +إلى النقطة اللي عندنا هذه اللي الإحداثي تبعها سالب + +135 +00:13:08,850 --> 00:13:15,550 +واحد و Zero إذاً هذه بدها ترجع بمقدار كده؟ واحد Zero + +136 +00:13:15,550 --> 00:13:21,650 +و هذه واحد Zero و هذه ها ها بدها ترجع كمان بمقدار + +137 +00:13:21,650 --> 00:13:26,470 +واحد لوين لعيت النقطة هذه إذاً صار ال ellipse اللي + +138 +00:13:26,470 --> 00:13:32,310 +عندنا بالشكل هذا هيك تمام؟ يبقى بالشكل اللي عندنا + +139 +00:13:32,310 --> 00:13:39,460 +هنا وهذا هو ال center تبعوا للنقطة هذه هي ال center + +140 +00:13:39,460 --> 00:13:43,500 +تبع ال ellipse الجديد الأزرق هذا يبقى صار ellipse + +141 +00:13:43,500 --> 00:13:48,060 +و ال center مع H و K قال لي ارسم هي رسمت + +142 +00:13:48,060 --> 00:13:51,980 +وبالتالي صار ال vertex هذه واحد و Zero طب ال + +143 +00:13:51,980 --> 00:13:56,920 +vertex هذه كده تصير سالب ثلاثة و Zero يبقى هذه + +144 +00:13:56,920 --> 00:14:02,610 +سالب ثلاثة و Zero ال vertex الأخرى وهذا هو ال + +145 +00:14:02,610 --> 00:14:08,310 +major axis بقى هو محور X كما هو وليس الموازي له + +146 +00:14:08,310 --> 00:14:14,500 +وهذا هو ال minor axis المحور الثانوي طب أحد فيكم + +147 +00:14:14,500 --> 00:14:21,720 +بيقدر يقول لي ما هي معادلة المحور الثانوي X + +148 +00:14:21,720 --> 00:14:27,900 +يساوي سالب واحد يبقى X يساوي سالب واحد ننتقل + +149 +00:14:27,900 --> 00:14:33,140 +الآن إلى المثال الثاني المثال الثاني بيقول ما يأتي + +150 +00:14:33,140 --> 00:14:36,960 +نمر اثنين + +151 +00:14:36,960 --> 00:14:47,050 +بيقول write an equation write an equation + +152 +00:14:47,050 --> 00:14:57,170 +اكتب معادلة for the ellipse for the ellipse للـ + +153 +00:14:57,170 --> 00:15:03,290 +ellipse اللي عندنا X تربيع على أربعة زائد Y تربيع + +154 +00:15:03,290 --> 00:15:09,890 +على خمسة وعشرين تساوي واحد that shifted that + +155 +00:15:09,890 --> 00:15:18,330 +shifted اللي عملنا له إزاحة ثلاثة + +156 +00:15:18,330 --> 00:15:32,270 +units ثلاث وحدات to the right يبقى + +157 +00:15:32,270 --> 00:15:41,530 +عملنا له ثلاث وحدات جهة اليمين and two units down و + +158 +00:15:41,530 --> 00:15:49,210 +ثلاث وحدات أو اثنين وحدتين إلى أسفل sketch the ellipse + +159 +00:15:49,210 --> 00:15:52,790 +ارسم لي + +160 +00:15:52,790 --> 00:16:05,550 +هذا ال ellipse and identify وحدد لي + +161 +00:16:05,550 --> 00:16:07,690 +its center + +162 +00:16:10,510 --> 00:16:21,210 +المركز تبعه عند ال major axis وكذلك المحور + +163 +00:16:21,210 --> 00:16:24,370 +الرئيسي لهذا ال ellipse + +164 +00:16:42,260 --> 00:16:47,240 +خليني أقول لك سؤال، اكتب لي معادلة ال Ellipse + +165 +00:16:47,240 --> 00:16:51,000 +اللي عندنا هذا بعد ما عملنا له shift ما هو شكل + +166 +00:16:51,000 --> 00:16:54,860 +ال shift؟ تلك ال shift ثلاث وحدات إلى اليمين يعني + +167 +00:16:54,860 --> 00:17:01,140 +عملنا إذا جهة اليمين بمقدار ثلاثة وعند ثلاث + +168 +00:17:01,140 --> 00:17:06,320 +وحدات وإلى أسفل وحدتين وبعد ذلك بدك ترسم لي ما هو + +169 +00:17:06,320 --> 00:17:11,100 +شكل هذا ال Ellipse And identify the center بدك + +170 +00:17:11,100 --> 00:17:16,880 +تحدد لي قداش إحداثي المركز وما هو ال major axis + +171 +00:17:16,880 --> 00:17:21,780 +لهذا ال ellipse اللي عندنا إذا بدي أرجع لأصل + +172 +00:17:21,780 --> 00:17:24,240 +المعادلة ودقيقة فيها + +173 +00:17:27,510 --> 00:17:31,450 +الرقم هذا أربعة والرقم هذا خمسة واثنين دي اللي + +174 +00:17:31,450 --> 00:17:36,270 +الرقم الكبير تحت مين؟ تحت ال Y يبقى ال major axis + +175 +00:17:36,270 --> 00:17:42,930 +هو محور Y طيب أنا لما أعمله shift بتغير اللي هو + +176 +00:17:42,930 --> 00:17:47,970 +المقامات تبع المعادلة اللي عندنا لا التغير بيصير في + +177 +00:17:47,970 --> 00:17:51,990 +البسط لكن المقام زي ما شفنا قبل قليل لا يتغير + +178 +0 + +201 +00:20:18,380 --> 00:20:25,280 +اللي فوق هذه قداش؟ خمسة بدي أنزلها قداش؟ اثنين إلى + +202 +00:20:25,280 --> 00:20:29,060 +أسفل إلى + +203 +00:20:29,060 --> 00:20:35,200 +اليمين ثلاثة بس أسفل قداش اثنين يبقى ال vertex + +204 +00:20:35,200 --> 00:20:39,460 +اللي فوق بدي أنزلها بمقدار اثنين يبقى بتتّجين هنا + +205 +00:20:40,010 --> 00:20:45,770 +يبقى كم إحداثية النقطة هذه؟ ثلاثة زي ما هي + +206 +00:20:45,770 --> 00:20:49,990 +ما تغيرت وهنا بدأت أصبحت ثلاثة لأن نزلت من فوق + +207 +00:20:49,990 --> 00:20:56,490 +بمقدار اثنين إذا ال vertex هذه ثلاثة وثلاثة وال + +208 +00:20:56,490 --> 00:21:01,430 +center هذا ثلاثة وسالب اثنين يبقى المسافة هذه كلها + +209 +00:21:01,430 --> 00:21:05,410 +كم؟ خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، + +210 +00:21:05,410 --> 00:21:06,690 +خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، + +211 +00:21:06,690 --> 00:21:09,030 +خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، + +212 +00:21:09,030 --> 00:21:11,810 +خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، + +213 +00:21:11,810 --> 00:21:17,250 +خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، خمسة، + +214 +00:21:17,250 --> 00:21:23,850 +خمسة، خمسة، خمسة، خمسة، خمسة حد فيكم بيقدر يقول لي + +215 +00:21:23,850 --> 00:21:32,590 +قداش إحداثيات النقطة اللي عندنا قداش؟ ثلاثة أفقي لم + +216 +00:21:32,590 --> 00:21:38,850 +يتغير يبقى هذا اللي هو من ثلاثة الآن هذه المسافة + +217 +00:21:38,850 --> 00:21:43,470 +اللي هي قداش؟ سالب اثنين وعندك هذه كمان سالب خمسة + +218 +00:21:43,470 --> 00:21:48,820 +إذا سالب سبعة يبقى ثلاثة وسالب سبعة يبقى هي رسمنا + +219 +00:21:48,820 --> 00:21:53,820 +لها من ال ellipse المطلوب يبقى قال لي اكتب المعادلة + +220 +00:21:53,820 --> 00:21:58,320 +لسه ما كتبتهاش لكن قال لي that shifted ثلاثة و + +221 +00:21:58,320 --> 00:22:02,680 +نستدرعي تعملناها واثنين إلى أسفل قال لي سكتش هي + +222 +00:22:02,680 --> 00:22:06,980 +رسمناه معها تمام؟ قال لي identify its center + +223 +00:22:06,980 --> 00:22:12,900 +هيحددناه من ال center فبأجي بقول له the center + +224 +00:22:15,110 --> 00:22:21,170 +of the ellipse is + +225 +00:22:21,170 --> 00:22:24,810 +ثلاثة + +226 +00:22:24,810 --> 00:22:31,970 +وسالب اثنين بعد هيك قال لي هات ال major axis and + +227 +00:22:41,680 --> 00:22:45,180 +الأكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز + +228 +00:22:45,180 --> 00:22:47,940 +أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز + +229 +00:22:47,940 --> 00:22:54,960 +أكسز أكسز أكسز + +230 +00:22:54,960 --> 00:23:00,300 +أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز + +231 +00:23:00,300 --> 00:23:06,360 +أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز + +232 +00:23:06,360 --> 00:23:06,520 +أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز أكسز + +233 +00:23:06,520 --> 00:23:10,890 +أكسز أكسز أكسز طبعًا إذا خلصنا المطلوب لم يبقى علينا + +234 +00:23:10,890 --> 00:23:17,210 +إلا الرسم وقد رسمنا يبقى هي رسمنا له الرسمة هي هي + +235 +00:23:17,210 --> 00:23:21,630 +هي الرسمة جاهزة مش ضايل ولا مطلوب عندنا ضايل علينا + +236 +00:23:21,630 --> 00:23:28,090 +فقط نكتب ما هو شكل المعادلة يبقى المعادلة اللي + +237 +00:23:28,090 --> 00:23:34,060 +عندنا هذه المقامات تبقى زي ما هي ال X والY بس هي + +238 +00:23:34,060 --> 00:23:42,340 +اللي بتغير شكلها فبأجي بقول له the question is X + +239 +00:23:42,340 --> 00:23:49,560 +ناقص ولا زاد؟ ناقص على أنه شفت جهة اليمين يبقى ال X + +240 +00:23:49,560 --> 00:24:00,700 +minus three الكل تربيع تمام على أربعة زائد Y زائد + +241 +00:24:00,700 --> 00:24:07,080 +اثنين تمام زائد اثنين الكل تربيع على خمسة وعشرين + +242 +00:24:07,080 --> 00:24:12,850 +يساوي واحد لأن لما بدي أحطه ناقص ناقص اثنين بيصير + +243 +00:24:12,850 --> 00:24:16,830 +زائد اثنين الكل تربيع يساوي واحد يبقى على هيك + +244 +00:24:16,830 --> 00:24:21,890 +انتهينا من هذا ال section بتروح على ال exercises + +245 +00:24:21,890 --> 00:24:29,790 +هنا عندك exercises واحد اثنين المسائل من واحد + +246 +00:24:29,790 --> 00:24:33,530 +لغاية ستة وثمانين القدر + +247 +00:24:40,410 --> 00:24:45,730 +حد فيكم يتسائل هنا؟ أيوة، + +248 +00:24:45,730 --> 00:24:52,450 +ماسكناها بغاها وحررتنا جاتنا من مقدار ثلاثة و + +249 +00:24:52,450 --> 00:24:58,440 +نزلنا بمقدار اثنين كيف؟ ال center من المركز، طبعًا، + +250 +00:24:58,440 --> 00:25:04,560 +مش المركز، كله بزيحة، لكن ال center بيتحرك من + +251 +00:25:04,560 --> 00:25:08,500 +المركز، تمام؟ ال center حركناه هنا، صار المركز + +252 +00:25:08,500 --> 00:25:11,660 +هنا، نزلناه اثنين، صار ال center هذا الثلاثة، و + +253 +00:25:11,660 --> 00:25:16,380 +السؤال ايه بسالب اثنين؟ حاجة عنده أي سؤال ثاني؟ بننتقل + +254 +00:25:16,380 --> 00:25:21,620 +الآن إلى ال section اللي يليه وهو آخر section في + +255 +00:25:21,620 --> 00:25:25,320 +هذا ال chapter اللي هو section 13 + +256 +00:25:42,490 --> 00:25:48,490 +يبقى الدوال المثلثية قبل ما نبدأ موضوع الدوال + +257 +00:25:48,490 --> 00:25:54,350 +المثلثية بدنا نتكلم في التقدير الستيني والتقدير + +258 +00:25:54,350 --> 00:26:00,050 +الدائري للزوايا كنت بتسموه التقدير الدائري للزوايا + +259 +00:26:00,050 --> 00:26:05,490 +النصف قطرية والتقدير الستيني اللي هو بالدرجات يبقى + +260 +00:26:05,490 --> 00:26:09,010 +بالدرجة أقول هنا Radian + +261 +00:26:15,460 --> 00:26:28,380 +ميجا القياس الدائري and degrees والقياس الستيني لو + +262 +00:26:28,380 --> 00:26:32,260 +جيت سألتك قلت لك بالله اثنين باي قداش تساوي كام + +263 +00:26:32,260 --> 00:26:37,570 +درجة؟ تقول لي قداش؟ ثلاثمائة وستين درجة، إذا + +264 +00:26:37,570 --> 00:26:43,170 +الثلاثمائة وستين درجة هذا هي التقدير الستيني و + +265 +00:26:43,170 --> 00:26:48,610 +اثنين باي هي التقدير الدائري. طب لو قلت لك بالله + +266 +00:26:48,610 --> 00:26:57,730 +واحد radian قداش يساوي بالتقدير الستيني بقول هذا مش + +267 +00:26:57,730 --> 00:27:02,190 +هتخليه واحدة تقسم على اثنين باي يعني بيصير + +268 +00:27:02,190 --> 00:27:08,270 +ثلاثمائة وستين على الاثنين باي ويساوي مئة وثمانين + +269 +00:27:08,270 --> 00:27:14,920 +على باي طب لو جوزك بدي العملية العكسية بدي درجة + +270 +00:27:14,920 --> 00:27:20,180 +واحدة بالتقدير الستيني قداش تساوي بالتقدير الدائري + +271 +00:27:20,180 --> 00:27:25,060 +بتقول له تضرب على ثلاثمائة وستين يبقى بأجي بقول له + +272 +00:27:25,060 --> 00:27:32,080 +اثنين باي على ثلاثمائة وستين ويساوي باي على مئة و + +273 +00:27:32,080 --> 00:27:37,240 +ثمانين إذا بدنا نحط القاعدة الرئيسية لو بدنا نحول + +274 +00:27:37,240 --> 00:27:41,700 +من تقدير ستيني إلى تقدير دائري شو بدنا نعمل والعكس لو + +275 +00:27:41,700 --> 00:27:47,320 +نحول من تقدير دائري إلى ستيني، ايش اللي بدنا نعمله؟ + +276 +00:27:47,320 --> 00:27:50,280 +إذا بدنا نحط القاعدة الأساسية تبعتنا to + +277 +00:27:50,280 --> 00:27:56,440 +change، مشان نحول radian إلى degrees + +278 +00:28:01,440 --> 00:28:10,340 +التقدير الدائري to degrees إلى درجات multiply + +279 +00:28:10,340 --> 00:28:14,900 +multiply + +280 +00:28:14,900 --> 00:28:28,540 +by مئة وثمانين على by to change ال degrees to + +281 +00:28:28,540 --> 00:28:30,460 +radian + +282 +00:28:33,790 --> 00:28:53,530 +multiply by by على 180 هذه + +283 +00:28:53,530 --> 00:28:57,530 +كلها معلومات عتيدة أخذتها في الثانوية بس احنا + +284 +00:28:57,530 --> 00:29:00,710 +بذكر بذكر ليس ال + +285 +00:29:10,780 --> 00:29:17,380 +طب لأن برضه بده يذكرك ببعض الزوايا الخاصة اللي كنت + +286 +00:29:17,380 --> 00:29:22,120 +تستعملها في الثانوية العامة + +287 +00:29:22,120 --> 00:29:29,900 +يبقى + +288 +00:29:29,900 --> 00:29:35,100 +هنا درجات وهنا radian + +289 +00:29:38,030 --> 00:29:43,610 +لو عندي صفر درجة بديها بالتقدير الدائري بتصير هي + +290 +00:29:43,610 --> 00:29:52,680 +صفر لو عندي ثلاثين درجة اللي هي باي على ستة لو + +291 +00:29:52,680 --> 00:29:58,660 +عندي طبعًا هون جبناها من كلام اللي عندنا هذا تمام؟ + +292 +00:29:58,660 --> 00:30:06,260 +لو عندنا خمسة وأربعين درجة ليه الزاوية الخاصة + +293 +00:30:06,260 --> 00:30:13,840 +الثالثة يبقى دي باي على أربعة لو عندنا ستين درجة + +294 +00:30:13,840 --> 00:30:23,270 +يبقى باي على ثلاثة لو عندنا تسعين درجة يبقى باي على + +295 +00:30:23,270 --> 00:30:29,070 +اثنين، لو عندنا مئة وعشرين درجة يعني أقدر ستين + +296 +00:30:29,070 --> 00:30:35,020 +مرتين، يبقى اثنين باي على ثلاثة يبقى اثنين باي على + +297 +00:30:35,020 --> 00:30:40,940 +ثلاثة لو عندنا مئة وخمسة وثلاثين درجة يبقى قد + +298 +00:30:40,940 --> 00:30:47,500 +الخمسة وأربعين ثلاث مرات يبقى ثلاثة باي على أربعة + +299 +00:30:48,790 --> 00:30:54,930 +لو عندنا مئة وخمسين درجة يبقى قد الثلاثين كم مرة؟ + +300 +00:30:54,930 --> 00:30:59,350 +خمس مرات يبقى خمسة باي لأن خمسة في ثلاثين مئة و + +301 +00:30:59,350 --> 00:31:06,670 +خمسين يبقى خمسة باي على ستة لو عندنا مئة وثمانين + +302 +00:31:06,670 --> 00:31:14,840 +درجة يبقى باي طب لو عندنا مئتين وسبعين درجة قد + +303 +00:31:14,840 --> 00:31:19,500 +التسعين كام مرة؟ ثلاث مرات، ثلاثة في تسعين بمئتين + +304 +00:31:19,500 --> 00:31:26,320 +وسبعين يبقى ثلاثة باي على اثنين طيب لو عند اثنين + +305 +00:31:26,320 --> 00:31:32,080 +باي يبقى ثلاثمائة وستين درجة ليه بثنين باي؟ هذه + +306 +00:31:32,080 --> 00:31:36,380 +الزوايا الخاصة اللي في الغالب بتمر معنا خلال + +307 +00:31:36,380 --> 00:31:40,560 +دراستنا طيب هذا النقطة الأولى في هذا ال section + +308 +00:31:40,560 --> 00:31:43,900 +اللي هو العلاقة بين التقدير الدائري والتقدير + +309 +00:31:43,900 --> 00:31:49,060 +الستيني بدنا نيجي الآن لمين؟ لل positive angle وال + +310 +00:31:49,060 --> 00:31:54,120 +negative angle يبقى هذه أول نقطة في هذا ال section + +311 +00:31:54,120 --> 00:31:57,360 +اللي هو العلاقة بين التقدير الستيني والتقدير + +312 +00:31:57,360 --> 00:32:02,000 +الدائري بدنا نيجي للنقطة الثانية من هذا ال section + +313 +00:32:02,000 --> 00:32:13,020 +اللي هو positive and negative angle يبقى الزوايا + +314 +00:32:13,020 --> 00:32:15,000 +الموجبة والزوايا السالبة + +315 +00:32:20,960 --> 00:32:24,140 +إن القلمين الاثنين اللي هدول اللي عندي عبارة عن + +316 +00:32:24,140 --> 00:32:30,940 +خطين مستقيمين متطابقين تمامًا يبقى الزاوية منهم + +317 +00:32:30,940 --> 00:32:37,360 +كذا؟ صفر درجة طيب حقيقة بتدخل القلمين على جهتك + +318 +00:32:37,360 --> 00:32:43,010 +هذه القلم يعني لو جيت ثبت القلم السفلي وحركت + +319 +00:32:43,010 --> 00:32:47,890 +القلم العلوي إلى أعلى بهذا الشكل بيعمل زاوية + +320 +00:32:47,890 --> 00:32:54,510 +لاتجاه اللي حركت فيه القلم الأزرق إلى أعلى إلى أعلى + +321 +00:32:54,510 --> 00:32:58,830 +يعني مع عقارب الساعة ولا ضد عقارب الساعة يبقى + +322 +00:32:58,830 --> 00:33:03,590 +counter clockwise ضد عقارب الساعة الزاوية اللي + +323 +00:33:03,590 --> 00:33:08,940 +اتكونت counter clockwise بسميها positive angle تمام + +324 +00:33:08,940 --> 00:33:13,680 +طيب لو جيت خليتهم تمامًا القلمين بينهم الزاوية + +325 +00:33:13,680 --> 00:33:18,840 +تساوي صفر ثبت القلم العلوي وحركت القلم السفلي + +326 +00:33:18,840 --> 00:33:24,200 +إلى أسفل بهذا الشكل يبقى الزاوية اللي اتكونت مع + +327 +00:33:24,200 --> 00:33:30,880 +عقارب الساعة clockwise يبقى هذه بسميها الكلام اللي + +328 +00:33:30,880 --> 00:33:37,120 +سمعته بدنا نعيده مرة ثانية، لو جيت قلت هذا هو ال + +329 +00:33:37,120 --> 00:33:43,900 +initial ray الشعاع الابتدائي اللي كان القلم + +330 +00:33:43,900 --> 00:33:50,470 +السفلي حركت القلم الثاني إلى أعلى بالشكل اللي + +331 +00:33:50,470 --> 00:33:56,170 +عنده، هيبقى أي اتجاه السهم إلى أعلى عمل لي زاوية، + +332 +00:33:56,170 --> 00:34:00,590 +الزاوية هذه بدي أسميها ثيتا، يبقى هذه ثيتا مكتوبة + +333 +00:34:00,590 --> 00:34:05,050 +ايه؟ positive ولا negative؟ positive يبقى هذه بدي + +334 +00:34:05,050 --> 00:34:10,350 +أختصر كلمة positive إلى زائد وV جنبها، يبقى هذه + +335 +00:34:10,350 --> 00:34:17,610 +اختصار لكلمة positive angle يبقى هذه زاوية موجبة + +336 +00:34:17,610 --> 00:34:22,410 +الاتجاه اللي حركته إلى أعلى بسميه counter + +337 +00:34:22,410 --> 00:34:26,570 +clockwise + +338 +00:34:26,570 --> 00:34:32,790 +بضد عقارب الساعة تمام؟ طيب لو جيت قلت هذا ال + +339 +00:34:32,790 --> 00:34:40,920 +initial ray هذا ال initial ray الشعاع الابتدائي القلم + +340 +00:34:40,920 --> 00:34:44,920 +الثاني السفلي حركته إلى أسفل بهذا الشكل يبقى + +341 +00:34:44,920 --> 00:34:51,020 +الزاوية بتكون سالبة إذا حركت القلم السفلي إلى أسفل + +342 +00:34:51,020 --> 00:34:56,560 +يبقى هذه بسميها negative angle negative هأختصرها + +343 +00:34:56,560 --> 00:35:02,410 +إلى الشكل التالي يبقى negative angle يعني بكتب + +344 +00:35:02,410 --> 00:35:06,570 +الزاوية بإشارة سالب فلو كانت هذه الزاوية خمسة و + +345 +00:35:06,570 --> 00:35:11,650 +أربعين بقول سالب خمسة وأربعين أو سالب باي على + +346 +00:35:11,650 --> 00:35:20,030 +أربعة هذه تكون clockwise Clockwise مع عقارب الساعة + +347 +00:35:20,030 --> 00:35:26,070 +يبقى هذا بالنسبة للزوايا + +348 +00:35:26,070 --> 00:35:29,650 +الموجبة والزوايا السالبة الزوايا الموجبة والزوايا + +349 +00:35:29,650 --> 00:35:34,390 +السالبة بتلعب دور كبير عندنا في حساب المثلثات كما + +350 +00:35:34,390 --> 00:35:40,510 +ستراه خلال هذا ال section وكما ستراه بعد ذلك إن + +351 +00:35:40,510 --> 00:35:45,390 +شاء الله طيب احنا زوايا هنا ضالين ماشيين لغاية + +352 +00:35:45,390 --> 00:35:49,570 +كذا؟ ثلاثمائة وستين ثلاثمائة وستين معناته دورنا + +353 +00:35:49,570 --> 00:35:55,130 +دورة كاملة يعني بتوقف الزاوية عند ثلاثمائة وستين + +354 +00:35:55,130 --> 00:35:59,790 +بيزيدش يعني فيش زاوية الف درجة مثلًا ولا خمسمية + +355 +00:35:59,790 --> 00:36:05,710 +درجة في جد ما بدك إن شاء الله بدك مليون درجة موجودة + +356 +00:36:05,710 --> 00:36:09,990 +طب نتعرف على الشكل كيف بتبقى الزوايا هذه الكبيرة + +357 +00:36:09,990 --> 00:36:15,430 +والزوايا الصغيرة فمثلًا يبقى بالداخل ال angles اللي + +358 +00:36:15,430 --> 00:36:22,450 +أكبر من اثنين باي فمثلًا لو جيت قلت هذه المحاولة + +359 +00:36:22,450 --> 00:36:27,890 +هذا محور X وهذا محور Y وهذه نقطة الأصل اللي هي + +360 +00:36:27,890 --> 00:36:35,730 +صفر لو اتحركت في اتجاه اليمين بالشكل هذا مشيت كذا؟ + +361 +00:36:35,730 --> 00:36:42,930 +بتصير 90 درجة وبإشارة موجبة counter clockwise ضد + +362 +00:36:42,930 --> 00:36:49,650 +عقارب الساعة لو جيت كملت يبقى هذه صار مشيت باي + +363 +00:36:49,650 --> 00:36:57,980 +بتصير 180 درجة لو كملت في نفس الاتجاه يبقى 270 رجعت + +364 +00:36:57,980 --> 00:37:05,020 +لمحور X يبقى هي ال 360 اللي احنا قلنا عليهم لو جيت + +365 +00:37:05,020 --> 00:37:10,240 +مكمل مثلًا لغاية هنا وبده أعرف قداش الزاوية اللي + +366 +00:37:10,240 --> 00:37:16,200 +مشيتها يبقى ثلاثمائة وستين لغاية هنا، بأجي لهم كمان + +367 +00:37:16,200 --> 00:37:21,460 +تسعين بتصير أربعمية وخمسين، أربعمية وخمسين وكمان + +368 +00:37:21,460 --> 00:37:28,440 +تسعين يبقى خمسمية وأربعين، يبقى هذه خمسمية وأربعين + +369 +00:37:28,440 --> 00:37:34,860 +درجة وبالموجبة طبعًا طيب واحد ثاني قال لي لأ ليش نمشي + +370 +00:37:34,860 --> 00:37:38,540 +موجبة بدنا نمشي شمال، بقول له يا رجل خليك مع أهل + +371 +00:37:38,540 --> 00: + +401 +00:40:56,570 --> 00:41:03,730 +زاوية مقدرها theta اللي هو أخدتها as a positive + +402 +00:41:03,730 --> 00:41:10,710 +angle تمام؟ بدنا نيجي للنسب المثلثية الستة أولًا + +403 +00:41:10,710 --> 00:41:18,620 +نسبة من هذه النسب اللي هي الـSin هذه تختصر + +404 +00:41:18,620 --> 00:41:27,940 +إلى كلمة Sin سين ثيتا سين ثيتا اللي هو الجيب كنا + +405 +00:41:27,940 --> 00:41:33,140 +بالعربي بنقول عليه الجيب وهو المقابل على الوتر + +406 +00:41:33,140 --> 00:41:40,360 +يعني إيه؟ Y على R يبقى هذا Y على R بنا نيجي لنمر + +407 +00:41:40,360 --> 00:41:50,720 +اثنين Cos التي تختصر إلى cos θ بقى نقول جيب التمام + +408 +00:41:50,720 --> 00:41:57,740 +هو عبارة عن مجاور على الوتر يبقى x على R يبقى x + +409 +00:41:57,740 --> 00:42:06,870 +على R نمر ثلاثة بدنا الـtangent يبقى الظل تابع + +410 +00:42:06,870 --> 00:42:14,450 +الزاوية يبقى الظل تابع + +411 +00:42:14,450 --> 00:42:14,790 +الزاوية تابع الزاوية تابع الزاوية تابع الزاوية + +412 +00:42:14,790 --> 00:42:15,830 +تابع الزاوية تابع الزاوية تابع الزاوية تابع + +413 +00:42:15,830 --> 00:42:16,430 +الزاوية تابع الزاوية تابع الزاوية تابع الزاوية + +414 +00:42:16,430 --> 00:42:16,550 +تابع الزاوية تابع الزاوية تابع الزاوية تابع + +415 +00:42:16,550 --> 00:42:16,890 +الزاوية تابع الزاوية تابع الزاوية تابع الزاوية + +416 +00:42:16,890 --> 00:42:17,790 +تابع الزاوية تابع الزاوية تابع الزاوية تابع + +417 +00:42:17,790 --> 00:42:23,730 +الزاوية تابع الزاوية تابع الزاوية تابع الزاوية تاب + +418 +00:42:25,560 --> 00:42:30,040 +هل الـY على الـX بنقدر نجيبها من الاثنين اللي فوق + +419 +00:42:30,040 --> 00:42:36,240 +هذول؟ الإجابة نعم بنجيب ونقول لو قسمنا sin على cos + +420 +00:42:36,240 --> 00:42:41,560 +واختصرنا بدرجة دي شنو؟ Y على X إذا بناء عليه + +421 +00:42:41,560 --> 00:42:48,020 +بقدر أستنتج من هذا الكلام معلومة جديدة أن tan θ + +422 +00:42:48,020 --> 00:42:53,040 +بدل ما نقول sin θ على cos θ + +423 +00:43:01,270 --> 00:43:07,610 +طيب كويس نمر أربعة بدنا cotangent + +424 +00:43:08,980 --> 00:43:18,800 +لو مين غلط تمام تختصر إلى cot θ وتنطق كتان ثيتا + +425 +00:43:18,800 --> 00:43:26,180 +كتان عكس التان المجاور على المقابل يبقى الـX على + +426 +00:43:26,180 --> 00:43:35,300 +Y هذا معناه أن cot θ بده يساوي cos على sin + +427 +00:43:35,300 --> 00:43:43,720 +يبقى cos θ على sin θ إذا في علاقة بتربط + +428 +00:43:43,720 --> 00:43:51,200 +بين tan و cot مظبوط يبقى بناء عليه cot θ + +429 +00:43:51,200 --> 00:43:57,890 +يساوي كده واحد على tan الزاوية θ إذا tan + +430 +00:43:57,890 --> 00:44:03,350 +و cot مقلبات لبعضهم cot يساوي واحد على tan θ + +431 +00:44:03,350 --> 00:44:09,170 +أو tan θ تساوي واحد على cot θ بدنا نيجي + +432 +00:44:09,170 --> 00:44:17,570 +لنمرة خمسة sec اللي هو القاطع الزاوية وتختصر + +433 +00:44:17,570 --> 00:44:19,830 +إلى sec θ + +434 +00:44:22,280 --> 00:44:27,880 +sec θ sec θ اللي هو الوتر على مين؟ على + +435 +00:44:27,880 --> 00:44:35,360 +المجاور يبقى مين؟ R على X طيب أنا عندي X على R إذا + +436 +00:44:35,360 --> 00:44:41,100 +الـsec هو مقلوب مين؟ الـcos يبقى بناء عليه قاطع + +437 +00:44:41,100 --> 00:44:47,720 +الزاوية اللي هو sec θ يساوي واحد على cos + +438 +00:44:47,720 --> 00:44:55,400 +الزاوية θ تمام نيجي لآخر حاجة نمرة ستة cosecant + +439 +00:45:03,610 --> 00:45:12,490 +الـcosec تمام الزاوية يبقى هنختصره إلى csc θ وتنطق + +440 +00:45:12,490 --> 00:45:19,870 +cosec θ وهي الوتر على مين؟ على المقابل يبقى + +441 +00:45:19,870 --> 00:45:26,330 +بناء عليه الـcsc θ هو مقلوب مين؟ مقلوب الـsin + +442 +00:45:26,330 --> 00:45:32,630 +يبقى واحد على الـsin الزاوية θ يبقى هذه النسب + +443 +00:45:32,630 --> 00:45:38,810 +المثلثية اللي درسناها الستة وعلاقاتها ببعضها + +444 +00:45:38,810 --> 00:45:45,130 +البعض إذا لو عرفت نسبتين منهم اللي هو الـsin والـ + +445 +00:45:45,130 --> 00:45:48,110 +cos بقدر أجيب الأربعة الباقية + +446 +00:46:03,010 --> 00:46:10,090 +حساب المثلثات مهم جدا وقد اكتشفاه علماء المسلمون + +447 +00:46:10,090 --> 00:46:16,630 +في العصر العباسي الإسلامي احنا سبقنا الشرق والغرب + +448 +00:46:16,630 --> 00:46:22,190 +كمان في هذا المجال كمسلمين والحقيقة حل مشاكل كثيرة + +449 +00:46:22,190 --> 00:46:27,110 +في علم الرياضيات بحب أضيف كمان كلمة بدك تلزقها + +450 +00:46:27,110 --> 00:46:33,710 +في دماغك أن حساب المثلثات بالنسبة للرياضيات مثل + +451 +00:46:33,710 --> 00:46:39,550 +ملح الطعام بالنسبة للأكل حد بيقدر ياكل بدون ما يستخدم + +452 +00:46:39,550 --> 00:46:43,950 +ملح الطعام، بدك تطبخ، بدك تسوي سلطة، بدك تسوي + +453 +00:46:43,950 --> 00:46:49,010 +مشاء الله تعجي الخبز، بده يحط عليه ملعق، يبقى حساب + +454 +00:46:49,010 --> 00:46:54,050 +المثلثات very important for mathematics، مهم جدا + +455 +00:46:54,360 --> 00:47:00,060 +لكل فروع الرياضيات لا يستغنى عنه مش بدنا نفوت + +456 +00:47:00,060 --> 00:47:03,920 +اليوم وبعدين مش بنرجع كل شوية بنرجع له مش على جد + +457 +00:47:03,920 --> 00:47:07,360 +التفاضل والتكامل الميكانيكا بلزم حساب مثلثات + +458 +00:47:07,360 --> 00:47:11,140 +الجبر بلزم حساب مثلثات الهندسة بلزم حساب مثلثات + +459 +00:47:11,140 --> 00:47:16,400 +الهندسة التحليلية مش عارف إيه كل هالشغلات هذه حتى + +460 +00:47:16,400 --> 00:47:20,240 +المصفوفات بلزم بيها حساب المصفوفات، إذا لا يمكن أن + +461 +00:47:20,240 --> 00:47:24,080 +نستغني لا في الجبر العادي ولا في الجبر الخطي ولا + +462 +00:47:24,080 --> 00:47:27,200 +في فروع الرياضية المختلفة، على حسب جيبك اللي + +463 +00:47:27,200 --> 00:47:32,060 +بتاخده معاه، بدك تركز وتفهمه، مش اليوم مش فاهم + +464 +00:47:32,060 --> 00:47:35,880 +خلاص خليه مافيه دروحة، لأ لأ كل يوم يطلع لك جديد، + +465 +00:47:35,880 --> 00:47:41,400 +وبعد شوية بنروح للتفاضل والتكامل وشغلات كثيرة جدا، + +466 +00:47:41,400 --> 00:47:46,710 +هذا very important اللي عرفناه الآن هو النسب + +467 +00:47:46,710 --> 00:47:53,490 +المثلثية الست بالنسبة لحساب المثلثات يبقى هذه اللي + +468 +00:47:53,490 --> 00:47:59,360 +هي النسب المثلثية الأساسية الست السؤال هؤلاء + +469 +00:47:59,360 --> 00:48:04,720 +النسب المثلثة بيأخذوا قيم موجبة على طول والله قيم + +470 +00:48:04,720 --> 00:48:09,620 +سالبة على طول والله أحيانا موجبة وأحيانا سالبة + +471 +00:48:09,620 --> 00:48:15,440 +يبقى أحيان موجب وأحيان سالب وفي الثانوية علموكوا + +472 +00:48:15,440 --> 00:48:23,700 +الأساس نشيد وقالوا كرروها كل جائر أو جبار ظالم + +473 +00:48:23,700 --> 00:48:29,740 +جته نيلة أو جته داهية تمام؟ الأجانب عندهم مقولة زي + +474 +00:48:29,740 --> 00:48:34,380 +مقولتنا بالضبط بدنا نعلمك إياها مشان تعرف وقتاش + +475 +00:48:34,380 --> 00:48:40,840 +النسب المثلثية بتكون موجبة وقتاش بتكون سالبة إذا لو + +476 +00:48:40,840 --> 00:48:48,500 +جيت قسمت المستوى إلى أربعة أرباع لأن هذا محور + +477 +00:48:48,500 --> 00:48:54,720 +X وهذا محور Y وهذه نقطة الأصل اللي هي Zero خلي + +478 +00:48:54,720 --> 00:49:00,180 +بالك معايا يبقى هذا بسميه الربع الأول First + +479 +00:49:00,180 --> 00:49:07,160 +Quadrant نفصل الكلمتين لأنه كلمتين منفصلتين + +480 +00:49:07,160 --> 00:49:18,300 +Quadrant يبقى الربع الأول هذا بسميه Second + +481 +00:49:20,420 --> 00:49:31,840 +Quadrant تمام هذا بسميه Third Quadrant هذا بسميه + +482 +00:49:31,840 --> 00:49:35,840 +Fourth Quadrant + +483 +00:49:35,840 --> 00:49:41,960 +الرابع الرابع نيجي للأعلى بالنسبة للـpositive والـ + +484 +00:49:41,960 --> 00:49:47,740 +negative هنا بروح بقول له كل النسب في الربع الأول + +485 +00:49:47,740 --> 00:49:55,800 +all positive يبقى كل النسب المثلثية بالموجب في الربع + +486 +00:49:55,800 --> 00:50:02,100 +الثاني الـsin ومقلوبه مين؟ الـcsc اللي هي + +487 +00:50:02,100 --> 00:50:10,800 +قصة يبقى هنا الـsin θ و csc θ هذول + +488 +00:50:10,800 --> 00:50:16,820 +اثنين positive وباقي الأربعة ناقصات في الربع الثاني + +489 +00:50:16,820 --> 00:50:21,700 +يعني جيب التمام ناقص ومقلوب الـsec ناقص والـtan وظل + +490 +00:50:21,700 --> 00:50:28,460 +التمام كمان ناقص ابنجي في الربع الثالث tan θ + +491 +00:50:28,460 --> 00:50:33,700 +ومقلوبها cot θ positive وباقي الأربع نسب + +492 +00:50:34,820 --> 00:50:40,580 +الأخرى سالبة. طيب نيجي في الربع الرابع. الربع الرابع الـcos + +493 +00:50:40,580 --> 00:50:47,660 +θ ومقلوبه اللي هو sec θ are positive والباقي + +494 +00:50:47,660 --> 00:50:54,240 +والباقي negative طبعًا يبقى هنا كل النسب المثلثية + +495 +00:50:54,240 --> 00:50:58,540 +بالموجب في الربع الثاني الـsin ومقلوبه اللي هو + +496 +00:50:58,540 --> 00:51:02,980 +الـcos موجب وباقي الأربع نسب سالب هنا الـtan وظل + +497 +00:51:02,980 --> 00:51:07,540 +التمام tan θ و cot θ كله positive وباقي + +498 +00:51:07,540 --> 00:51:12,320 +الأربع نسب negative هنا في الربع الرابع cos θ + +499 +00:51:12,320 --> 00:51:15,080 +ومقلوبه الـsec θ positive وباقي الأربع نسب + +500 +00:51:15,080 --> 00:51:20,370 +معها سالب نيجي الآن نجيب الصيغة اللي بيقولوا عليها + +501 +00:51:20,370 --> 00:51:25,450 +الغرب باللغة الإنجليزية زي صيغتنا العربية اللي قال + +502 +00:51:25,450 --> 00:51:30,230 +لو جينا استعرضنا وضعكم وأنتم هنا كطلاب جامعيين + +503 +00:51:30,230 --> 00:51:34,510 +هلاجي عندنا من طالبة كلية الهندسة ومن طالبة كلية + +504 +00:51:34,510 --> 00:51:41,350 +التربية ومن طالبة كلية تكنولوجيا المعلومات ومنهم + +505 +00:51:41,350 --> 00:51:46,510 +كلية العلوم يبقى الأربع كليات وكمان بنضيف عليهم + +506 +00:51:46,510 --> 00:51:50,010 +كلية العلوم الحياتية اللي هم calculus خاص بهم غير + +507 +00:51:50,010 --> 00:51:54,370 +الـcalculus تبعنا يبقى الآن بنقدر نيجي ونقول + +508 +00:51:54,370 --> 00:52:00,490 +أنتم طلاب جامعيين شو معنى طالب جامعيين student تمام + +509 +00:52:00,490 --> 00:52:10,370 +يبقى باجي بقول all students take كل كلاس كما كلكم + +510 +00:52:10,370 --> 00:52:16,130 +تاخذوا تفاضل وكالكم المظبوط يبقى all الكل students + +511 +00:52:16,130 --> 00:52:20,630 +هي الحرف الأول من كلمة sin والحرف الأول من كلمة + +512 +00:52:20,630 --> 00:52:22,490 +students ومقلبه + +513 +00:52:33,050 --> 00:52:39,830 +أحد الأساتذة كان يقدم دكتوراه هناك وقال له نفسه + +514 +00:52:39,830 --> 00:52:43,710 +اللي هيبقى قال له اه الـstudents take calculus يعني + +515 +00:52:43,710 --> 00:52:49,500 +احنا لما نأتي ببدعة من الرسل وإنما زي الناسي يبقى + +516 +00:52:49,500 --> 00:52:54,200 +هذه العبارة افهم لها all students take calculus + +517 +00:52:54,200 --> 00:52:59,480 +يبقى لكل موجب الـsin ومقلوبها الـtan ومقلوبها الـcos + +518 +00:52:59,480 --> 00:53:03,960 +ومقلوبها كل موجب وباقية الأربعة نسب مالها بتبقى + +519 +00:53:03,960 --> 00:53:09,200 +سالبة طيب بعد معرفة السالب ولو بدنا نعرف شكل الدوال + +520 +00:53:09,200 --> 00:53:13,150 +هذول مش احنا بناخد الدالة والـdomain والـrange و + +521 +00:53:13,150 --> 00:53:16,550 +نرسمها ومش عارف إيه ونعمل الـshift ونعمل الـ + +522 +00:53:16,550 --> 00:53:20,290 +reflecting من الشغلات هذه احنا بدنا نعرف ما هو + +523 +00:53:20,290 --> 00:53:25,190 +الرسم البياني للدوال المثلثية الـset يبقى بدنا نيجي + +524 +00:53:25,190 --> 00:53:31,770 +للنقطة الرابعة من هذا الـsection وهي the graph + +525 +00:53:36,090 --> 00:53:37,990 +Trigonometric functions + +526 +00:53:48,370 --> 00:53:53,210 +يبقى بدنا الرسم البياني للدوال المثلثية الستة طبعًا + +527 +00:53:53,210 --> 00:53:57,210 +في الثانوية رسموها لكم لكن أنا بعتبر لا رسموها + +528 +00:53:57,210 --> 00:54:03,130 +ولا شفتهم بدنا نثبت معلومات من جديد يبقى بد أبدأ + +529 +00:54:03,130 --> 00:54:07,230 +بأول دالة اللي هو منحنى الـsin ليه بنمشي الكتاب + +530 +00:54:07,230 --> 00:54:11,730 +هيك حنمشي فيهم رسم ونكتب كذلك الـdomain والـrange + +531 +00:54:11,730 --> 00:54:17,970 +لكل منها يبقى بداجي لمنحنى الـsin باجي باخد + +532 +00:54:17,970 --> 00:54:24,570 +المستوى هذا محور X هذا محور Y هذا Zero خليني + +533 +00:54:24,570 --> 00:54:30,510 +أسألكم سؤال هكذا حنمشي كده أكبر قيمة بياخدها منحنى + +534 +00:54:30,510 --> 00:54:35,970 +الـsin؟ وكده أقل قيمة؟ إذا المنحنى بيكون محصور بين + +535 +00:54:35,970 --> 00:54:42,500 +واحد لا بيزيد عن واحد ولا بينقص وعلى شكل wave على + +536 +00:54:42,500 --> 00:54:48,400 +شكل موجة مظبوط يبقى أنا لو اتخيلت الخط الوهمي اللي + +537 +00:54:48,400 --> 00:54:54,860 +عندنا هداك هذا اللي هو واحد صحيح وهنا الخط الوهمي + +538 +00:54:54,860 --> 00:55:01,860 +الثاني هذا اللي هو من اللي هو سالب واحد صحيح قداش + +539 +00:55:01,860 --> 00:55:07,900 +جيب الـzero؟ جيب الـzero يا راجل واحد تاج الله + +540 +00:55:07,900 --> 00:55:12,960 +يا راجل يبقى من هون معناته المنحنى بدي يمر بنقطة + +541 +00:55:12,960 --> 00:55:18,020 +الأصل يبقى لو جيت رسمت المنحنى المنحنى بدي يجي + +542 +00:55:18,020 --> 00:55:25,060 +طالع هيك ويجي نازل ويجي طالع وهيك ده تمام؟ ومن + +543 +00:55:25,060 --> 00:55:29,320 +الناحية الثانية بيضل نازل ويجي طالع ونازل + +544 +00:55:29,320 --> 00:55:33,110 +بالشكل اللي عندنا طيب هو بـ result يبقى طلع والله + +545 +00:55:33,110 --> 00:55:42,460 +بشغلات محددة وثابتة، كيف؟ بنقول المنحنى هنا هذه + +546 +00:55:42,460 --> 00:55:49,100 +النقطة π/2 وهذه النقطة π وهذه النقطة + +547 +00:55:49,100 --> 00:55:53,160 +سالب + +548 +00:55:53,160 --> 00:56:01,040 +3π/2 وهذه النقطة 2π على + +549 +00:56:01,040 --> 00:56:07,330 +اثنين ومن الناحية الثانية هذه -π/2 + +550 +00:56:07,330 --> 00:56:15,290 +هذه -π هذه -3π/2 ثلاثة + +551 +00:56:15,290 --> 00:56:21,070 +π/2 هذه -2π and so on وبظل + +552 +00:56:21,070 --> 00:56:26,470 +طالع ونزل إلى أن يرث الله الأرض ومن عليها طبعًا إذا + +553 +00:56:26,470 --> 00:56:31,530 +لو جينا هنا قلنا هذا منحنى الـsin يبقى domain + +554 +00:56:31,530 --> 00:56:38,350 +sin الـX كدهش يساوي كل + +555 +00:56:38,350 --> 00:56:44,170 +الـreal line بلا استثناء يبقى من -∞ + +556 +00:56:44,170 --> 00:56:49,490 +لغاية ∞ بدنا الـrange تبع sin الـX + +557 +00:56:52,560 --> 00:56:57,560 +يبقى الفترة المغلقة من -1 إلى 1 طب لو + +558 +00:56:57,560 --> 00:57:02,300 +جيت سألتك من خلال الرسم كنت قداش تجيب الـπ على + +559 +00:57:02,300 --> 00:57:10,080 +اثنين 1 هي فوق من هذه النقطة إحداثياتها π/2 + +560 +00:57:10,080 --> 00:57:15,480 +و1 لو كده كده كده تجيب الـ180 0 كده + +561 +00:57:15,480 --> 00:57:19,620 +تجيب الـ270 -1 كده تجيب الـ360 π 0 وهكذا إذا أنا من خلال الرسم يمكن + +562 +00:57:19,620 --> 00:57:25,080 +التعرف على مين؟ على اللي هو كل النسب المثلثية قداش + +563 +00:57:25,080 --> 00:57:31,480 +خبطتها الزوايا الخاصة اللي مثل π/2 و + +564 +00:57:31,480 --> 00:57:35,160 +3π/2 وπ الأخرين لو إذا جدية جيب + +565 +00:57:35,160 --> 00:57:38,720 +-π/2 -1 جدية جيب -π 0 + +566 +00:57:38,720 --> 00:57:46,060 +وجدية -3π/2 1 وهكذا تمام + +567 +00:57:46,060 --> 00:57:49,920 +يبقى جبنا الـdomain والـrange بالمثل بدنا نروح + +568 +00:57:49,920 --> 00:57:54,380 +للـcos + +569 +00:57:54,380 --> 00:57:55,360 +الـcos + +570 +00:58:02,380 --> 00:58:10,050 +وأنا اللي بيسأل؟ هذه الرسمة كلكم أخذتوها قبل ذلك أنا + +571 +00:58:10,050 --> 00:58:17,290 +بذكركم بها تذكير ليس إلا فقط لغير لكن بدك تعرفها + +572 +00:58:17,290 --> 00:58:22,830 +وتعرف كل شيء موجود فيها طيب بدوني اجي + +601 +01:01:07,330 --> 01:01:16,950 +ي على 2 وهنا سالب باي على اتنين هذه هناك تلاتة باي + +602 +01:01:16,950 --> 01:01:23,730 +على اتنين إذا بدها تيجي هنا لهمين باي وهكذا بنضال + +603 +01:01:23,730 --> 01:01:31,070 +ماشيين يبقى هنا اتنين باي هنا خمسة باي على اتنين + +604 +01:01:31,070 --> 01:01:36,890 +خمسة باي على اتنين من الناحية الثانية برضه بنفس + +605 +01:01:36,890 --> 01:01:37,710 +الطريقة + +606 +01:01:40,500 --> 01:01:47,880 +هذا هنا هو سالب باي، هنا سالب تلاتة باي على اتنين، + +607 +01:01:47,880 --> 01:01:55,140 +هنا سالب اتنين باي، هنا سالب خمسة باي على اتنين و + +608 +01:01:55,140 --> 01:02:02,940 +هكذا، طلع لي للمنحنى كيف؟ هذه الرسومات مهمة جدا كمال + +609 +01:02:02,940 --> 01:02:11,280 +كالكولاسبيه كمال كالكولاسبيه كمال + +610 +01:02:11,280 --> 01:02:16,180 +كالكولاسبيه + +611 +01:02:16,180 --> 01:02:25,040 +كمال كالكولاسبيه كمال كالكولاسبيه كمال كالكولاسبيه + +612 +01:02:25,040 --> 01:02:28,000 +كمال كالكولاسبيه كمال كالكولاسبيه كمال كالكولاسبيه + +613 +01:02:28,000 --> 01:02:28,040 +كمال كالكولاسبيه كمال كالكولاسبيه كمال كالكولاسبيه + +614 +01:02:28,040 --> 01:02:28,120 +كمال كالكولاسبيه كمال كالكولاسبيه كمال كالكولاسبيه + +615 +01:02:28,120 --> 01:02:28,140 +كمال كالكولاسبيه كمال كالكولاسبيه كمال كالكولاسبيه + +616 +01:02:28,140 --> 01:02:28,160 +كمال كالكولاسبيه كمال كالكولاسبيه كمال كالكولاسبيه + +617 +01:02:28,160 --> 01:02:36,650 +كمالو من هنا بنفس الطريقة هيك و من هنا و من هنا و + +618 +01:02:36,650 --> 01:02:38,690 +من هنا و من هنا و من هنا و من هنا و من هنا و من + +619 +01:02:38,690 --> 01:02:39,790 +هنا و من هنا و من هنا و من هنا و من هنا و من هنا و + +620 +01:02:39,790 --> 01:02:39,850 +هنا و من هنا و من هنا و من هنا و من هنا و من هنا و + +621 +01:02:39,850 --> 01:02:40,350 +من هنا و من هنا و من هنا و من هنا و من هنا و من + +622 +01:02:40,350 --> 01:02:43,410 +من هنا و من هنا ومن هنا ومن هنا ومن هنا ومن هنا + +623 +01:02:43,410 --> 01:02:43,670 +ومن هنا ومن هنا ومن هنا ومن هنا ومن هنا ومن هنا + +624 +01:02:43,670 --> 01:02:44,110 +ومن هنا ومن هنا ومن هنا ومن هنا ومن هنا ومن هنا + +625 +01:02:44,110 --> 01:02:47,070 +ومن هنا ومن هنا ومن هنا ومن هنا ومن هنا ومن هنا + +626 +01:02:47,070 --> 01:02:55,670 +ومن هنا و + +627 +01:03:14,680 --> 01:03:23,820 +بدي آجي ال domain ثاني ال X yourself اه تفضل + +628 +01:03:28,560 --> 01:03:34,360 +أي عدد صحيح؟ طبيعي + +629 +01:03:34,360 --> 01:03:43,720 +والله صحيح فردي odd number تلاتة خمسة سبعة تسعة + +630 +01:03:43,720 --> 01:03:49,680 +الأخرين يبقى هذا شباب بقدر أقول هذا بدي أساوي كل + +631 +01:03:49,680 --> 01:03:58,220 +ال real number بدي أشيل منها ال N by على اتنين + +632 +01:03:58,220 --> 01:04:07,850 +بالزائد أو بالنقص يبقى ناقص هنا زائد أو ناقص in by + +633 +01:04:07,850 --> 01:04:17,730 +على اتنين و ال in is odd على طول عدد فردي، تمام؟ + +634 +01:04:17,730 --> 01:04:22,510 +لاحظ، لو كانت in بواحد، بيصير by على اتنين، هل + +635 +01:04:22,510 --> 01:04:26,610 +الدالة معرفة عند ال by على اتنين؟ لأ، بتطيب لما لا + +636 +01:04:26,610 --> 01:04:31,700 +نهاية عند تلاتة باي على اتنين عند الخمسة باي على اتنين + +637 +01:04:31,700 --> 01:04:35,680 +سبعة باي على اتنين تسعة باي على اتنين بتروح للمعلمة + +638 +01:04:35,680 --> 01:04:40,820 +نعرفش بتبقى undefined غير معرفة لو جينا عند السلب + +639 +01:04:40,820 --> 01:04:45,660 +باي على اتنين بتنخسف لسالب infinity عند سالب تلاتة باي + +640 +01:04:45,660 --> 01:04:49,120 +على اتنين سالب خمسة باي على اتنين and so on كله بتنزل لسالب + +641 +01:04:49,120 --> 01:04:54,080 +infinity يبقى ال domain عرفناه إذا ال domain بده + +642 +01:04:54,080 --> 01:04:55,760 +يشيل كم نقطة منه + +643 +01:04:59,940 --> 01:05:04,940 +مية مية نهاية من النقاط يعني مية نهاية من النقاط + +644 +01:05:04,940 --> 01:05:08,860 +ماقدرش العقل البشري ماقدرش يتصورها فبتداجي لل + +645 +01:05:08,860 --> 01:05:14,580 +range ده + +646 +01:05:14,580 --> 01:05:20,620 +ال gig معايا هنا هي ال zero القيم هذه كلها موجة + +647 +01:05:20,620 --> 01:05:25,600 +بالله سالبة كل ما اجرب على باي على اتنين بتكبر + +648 +01:05:25,600 --> 01:05:31,860 +تبقى من ولا وين بالصفر لغاية ما لنهاية لو بدي آجي + +649 +01:05:31,860 --> 01:05:36,860 +آخذ القيام هذه كل القيام السالبة إذا ال range ماله + +650 +01:05:36,860 --> 01:05:43,400 +كل ال real line بلا ستثناء يبقى يا بكتب R يا بكتب + +651 +01:05:43,400 --> 01:05:47,920 +من سالب infinity إلى infinity بالشكل اللي عندنا + +652 +01:05:47,920 --> 01:05:55,140 +هذا تمام بدنا نيجي الآن لرقم أربعة لكتان ال X + +653 +01:05:58,770 --> 01:06:04,250 +هذا محور X وهذا محور Y وهذه نقطة الأصل اللي هي + +654 +01:06:04,250 --> 01:06:06,350 +Zero هذا Zero + +655 +01:06:17,860 --> 01:06:24,460 +وهذه باي على اتنين وهذه باي هذه تلاتة باي على + +656 +01:06:24,460 --> 01:06:31,500 +اتنين وهذه اتنين باي وهنا ناقص باي على اتنين ناقص + +657 +01:06:31,500 --> 01:06:38,480 +باي ناقص تلاتة باي على اتنين وهنا ناقص اتنين باي + +658 +01:06:38,480 --> 01:06:45,790 +and so on خلّي بالك بالنسبة للتان جاية من اليمين + +659 +01:06:45,790 --> 01:06:52,190 +للشمال هذه هتجيك من الشمال لليمين هذه مرت بنقطة + +660 +01:06:52,190 --> 01:06:58,090 +الأصل هذه undefined عند نقطة الأصل يبقى هتجيك + +661 +01:06:58,090 --> 01:06:59,950 +المنحنى بالشكل هذا هيك + +662 +01:07:18,840 --> 01:07:25,680 +طيب بدنا ال domain و ال range لهذه الدالة يبقى ال + +663 +01:07:25,680 --> 01:07:32,620 +domain لمين؟ لكتان ال X يلا يشوف + +664 +01:07:40,950 --> 01:07:44,790 +طيب تعال نشوف مرة ثانية الكلام اللي جاله و بدنا + +665 +01:07:44,790 --> 01:07:48,510 +نعبر عنه، قول أيوة ال domain بيساوي اللي هو موجة + +666 +01:07:48,510 --> 01:07:55,010 +بالنقص and by one even number يعني odd ماعنديش، + +667 +01:07:55,010 --> 01:08:00,670 +ماعنديش odd طيب + +668 +01:08:00,670 --> 01:08:06,390 +خلّي بالك هنا بنشيل ال zero و ال by و اتنين by و + +669 +01:08:06,390 --> 01:08:10,210 +التلاتة by و الأربعة by يبقى فيش odd و even ال odd + +670 +01:08:10,210 --> 01:08:15,510 +موجود و ال even موجود بدنا نشيله تمام يبقى هنا بجي + +671 +01:08:15,510 --> 01:08:24,070 +بقول كل ال real line بدي أشيل منه زائد أو ناقص n + +672 +01:08:24,070 --> 01:08:36,020 +by تمام و ال n any integer و ال n is an integer يبقى + +673 +01:08:36,020 --> 01:08:39,920 +ال N عدد صحيح سواء كان سالب و الله موجب ماعنديش + +674 +01:08:39,920 --> 01:08:45,480 +مشكلة في هذه الحالة يبقى هذا بالاسم لتان والكتان + +675 +01:08:45,480 --> 01:08:50,920 +دي ربالك الرسمة هذه هنرجعلها بعد قليل مرسومة عندك ف + +676 +01:08:50,920 --> 01:08:57,260 +ال range ال range واضح أن كله ال real number ال + +677 +01:08:57,260 --> 01:09:03,910 +range لكتان ال x من سالب infinity ل infinity لأن + +678 +01:09:03,910 --> 01:09:08,530 +هي بياخد كل القيم الموجبة وهنا بياخد كل القيم + +679 +01:09:08,530 --> 01:09:10,190 +السالبة + +680 +01:09:35,890 --> 01:09:45,930 +طيب نجي للرسمة رقم خمسة اللي هي رسمة ال second هذا + +681 +01:09:45,930 --> 01:09:50,950 +محور X هذا محور Y هذا نقطة الأصل + +682 +01:09:54,580 --> 01:09:59,940 +نعمل التقاطعات تابعة التان بالضبط هاي باي على + +683 +01:09:59,940 --> 01:10:08,260 +اتنين وهذا سالب باي على اتنين بعد هيك هذا تلاتة + +684 +01:10:08,260 --> 01:10:17,050 +باي على اتنين وهنا باي وهكذا and so on هنا كمان + +685 +01:10:17,050 --> 01:10:26,190 +تعمل نفس الجثة هنا اتنين باي و هنا خمسة باي على + +686 +01:10:26,190 --> 01:10:34,210 +الاتنين من ناحية ثانية بنفس الطريقة وهكذا يبقى + +687 +01:10:34,210 --> 01:10:42,270 +هنا سالب باي و هنا سالب تلاتة باي على اتنين + +688 +01:10:45,410 --> 01:10:51,710 +و هنا سالب اتنين by و هنا سالب خمسة by على اتنين + +689 +01:10:51,710 --> 01:11:00,190 +and so on تخيل أنه عندك خط وهمي هذا هيك بهذا الشكل + +690 +01:11:00,190 --> 01:11:08,910 +اللي هو واحد و من هنا بنفس الطريقة الخط اللي عندك + +691 +01:11:08,910 --> 01:11:16,350 +هذا اللي هو main سالب واحد بعدين نرسم ال function + +692 +01:11:16,350 --> 01:11:22,830 +اللي عندنا خلي بالك معايا كويس يبقى بيجيك المنحنى + +693 +01:11:22,830 --> 01:11:28,730 +بالشكل هذا هيك وجهه طالع بالشكل زي شكله زي شكل + +694 +01:11:28,730 --> 01:11:40,470 +البرابولة بالضبط تماما تمام و من هنا بيجي تحت و + +695 +01:11:40,470 --> 01:11:42,410 +من هنا بعود بطلع فوق + +696 +01:11:48,170 --> 01:11:50,630 +من ناحية ثانية بنفس الطريقة + +697 +01:12:06,170 --> 01:12:12,430 +جوز فوق وجوز تحت وجوز فوق وجوز تحت وهكذا طبعا؟ طيب + +698 +01:12:12,430 --> 01:12:18,190 +لو جيت سؤالتك وقلت لك قداش بالله ال domain لسك ال + +699 +01:12:18,190 --> 01:12:22,970 +X بسألك السؤال التالف بيختلف عن ال domain تبع + +700 +01:12:22,970 --> 01:12:29,370 +التان؟ ولا حاجة يبقى هذا بده يساوي نفس ال domain + +701 +01:12:29,370 --> 01:12:36,060 +بتبع تان ال X طبعا ال x طبعا مسحناه قبل شوية هذا + +702 +01:12:36,060 --> 01:12:39,840 +ال quotient تمام يبقى نفس ال domain اللي هو ال + +703 +01:12:39,840 --> 01:12:44,180 +real line بدنا نشيل منه n by على اتنين حيث أن و + +704 +01:12:44,180 --> 01:12:45,240 +the integer + +705 +01:12:57,000 --> 01:13:03,060 +هذه؟ هذه؟ هذه + +706 +01:13:03,060 --> 01:13:11,900 +بس غلطنا فيها، صحيح. هذه لك حق فيها. لا بس لحد + +707 +01:13:11,900 --> 01:13:14,080 +الآن تنزل شكل أقل من واحد. + +708 +01:13:26,730 --> 01:13:35,790 +و هذه نزلت كمان و هذه لأ يعني + +709 +01:13:35,790 --> 01:13:46,290 +بين الواحد و السالب واحد مابتاخدش أي قيمة الشكل + +710 +01:13:46,290 --> 01:13:46,890 +اللي عندنا هذا + +711 +01:13:53,030 --> 01:14:05,790 +طبعا يجب أن ندخل لل range كل + +712 +01:14:05,790 --> 01:14:09,310 +رياضيين + +713 +01:14:09,310 --> 01:14:14,270 +يجب أن يتم إزالة للفترة من سالب واحد إلى واحد + +714 +01:14:20,820 --> 01:14:28,340 +و لم يبقى هذه من سالب infinity لغاية سالب واحد + +715 +01:14:28,340 --> 01:14:36,240 +اتحاد واحد و infinity أو بتقولي كل ال real line + +716 +01:14:36,240 --> 01:14:43,100 +بدي أشيل منه الفترة من سالب واحد إلى واحد open + +717 +01:14:43,100 --> 01:14:48,400 +interval و ليس ك close interval تمام؟ الآن وصلنا + +718 +01:14:48,400 --> 01:14:54,840 +لنمرة ستة آخر حاجة اللي هو main cosecant ال X هذا + +719 +01:14:54,840 --> 01:15:01,160 +good exercise اليك هتروح تفتحها الكتاب وترسمها أنت + +720 +01:15:01,160 --> 01:15:06,560 +تتمرن حالك هارسمتك بدل واحدة خمسة طبعا شبه بهذه بس + +721 +01:15:06,560 --> 01:15:10,400 +بيجي تعملها إزاحة بمقدار باي على اتنين جهة اليمين + +722 +01:15:10,400 --> 01:15:16,580 +و ال domain تبعها هو domain الكتان هذا بالضبط تماما + +723 +01:15:16,580 --> 01:15:17,540 +خلاص؟ + +724 +01:15:19,660 --> 01:15:26,500 +طيب من خلال الرسم هذا بدنا نيجي لحاجة اسمها ال + +725 +01:15:26,500 --> 01:15:34,930 +period قداشي الفترة تبعت اللي هو النسب الثلاثية لو + +726 +01:15:34,930 --> 01:15:38,030 +توضح هنا إيش معناه قاطة؟ إيش يعني بنصف الزاوية و + +727 +01:15:38,030 --> 01:15:42,250 +لا بي .. يعني بيسمها؟ اسمه قاطة الزاوية و قاطة + +728 +01:15:42,250 --> 01:15:46,630 +تمام الزاوية وظل الزاوية وظل تمام الزاوية و جيب + +729 +01:15:46,630 --> 01:15:51,550 +الزاوية و جيب تمام، تمام؟ أنا بهمني على الرسم، شو + +730 +01:15:51,550 --> 01:15:56,210 +شكله؟ يعني .. يعني ليش سميناها قاطة؟ مثلا، لو جيت + +731 +01:15:56,210 --> 01:16:02,920 +رسمت دائرة و جيت قطعتها بوتر، إيش بسميها ده؟ القاطع + +732 +01:16:02,920 --> 01:16:08,100 +الدائرة يبقى بيسميه second لكن لو جيت مسة في نقطة، + +733 +01:16:08,100 --> 01:16:12,940 +إيش بيسميه؟ tangent يبقى هاي الفرق بين المماس + +734 +01:16:12,940 --> 01:16:18,700 +و القطع طيب، نرجع إيش؟ نرجع لموضوعنا، في عندنا هنا + +735 +01:16:18,700 --> 01:16:23,960 +ال period إيش ال period؟ يعني وقت إيش الدالة بتكرر + +736 +01:16:23,960 --> 01:16:31,600 +دورتها من جديد فمثلا، لو جيت لكتان ال كتان كل قداش + +737 +01:16:31,600 --> 01:16:37,420 +بتتكرر الدورة من جديد كل by يبقى ال period للكتان + +738 +01:16:37,420 --> 01:16:39,440 +هي by و ال period للتان + +739 +01:16:41,500 --> 01:16:48,660 +لأ نفس القصة باي طيب هي عندك ال second هذا جزء و + +740 +01:16:48,660 --> 01:16:53,800 +هذا جزء كل هذا بيحضر دورة كاملة يبقى من التقل بعدها + +741 +01:16:53,800 --> 01:16:58,700 +بتبدأ من جديد يبقى ال period اللي عندك من هنا لهنا + +742 +01:16:58,700 --> 01:17:05,620 +كده هذه اتنين باي يبقى اتنين باي كل اتنين باي + +743 +01:17:05,620 --> 01:17:08,880 +بتبدأ دورة من جديد لو رحت لمنحنى ال sine و ال + +744 +01:17:08,880 --> 01:17:14,140 +cosine كمان البرو دول كده؟ نعم طيب، بدنا نيجي + +745 +01:17:14,140 --> 01:17:33,680 +للعنوان الجديد اللي هو رقم خمسة هذا + +746 +01:17:33,680 --> 01:17:35,220 +خلاص انتهينا منه؟ + +747 +01:17:38,480 --> 01:17:42,300 +طيب العنوان اللي جاي اسمه periodicity الدورية + +748 +01:17:42,300 --> 01:17:57,700 +definition + +749 +01:17:57,700 --> 01:18:02,200 +a + +750 +01:18:02,200 --> 01:18:07,700 +function f of x is + +751 +01:18:09,000 --> 01:18:12,980 +call periodic + +752 +01:18:12,980 --> 01:18:24,420 +بقالة دورية if there is if + +753 +01:18:24,420 --> 01:18:32,240 +there is a positive number + +754 +01:18:32,240 --> 01:18:35,580 +P + +755 +01:18:35,580 --> 01:18:38,380 +such that + +756 +01:18:41,390 --> 01:18:54,110 +بحيث أن ال F of X زي ال P يساوي F of X for all X + +757 +01:18:54,110 --> 01:18:58,010 +النقطة + +758 +01:18:58,010 --> 01:19:05,850 +المهمة The smallest such + +759 +01:19:05,850 --> 01:19:08,870 +value + +760 +01:19:10,670 --> 01:19:23,010 +of P when such value of P is the period of + +761 +01:19:23,010 --> 01:19:23,670 +F + +762 +01:19:57,360 --> 01:20:05,640 +الآن نقدر نعطي تعريف لتكرار دورة الرسم كل قد تتكرر + +763 +01:20:05,640 --> 01:20:09,920 +الرسمة التابعة لل trigonometric function فبعدين + +764 +01:20:09,920 --> 01:20:12,940 +باعطي تعريف أي function سواء كان trigonometric + +765 +01:20:12,940 --> 01:20:15,480 +ولا غيره يعني ليه السبب ضروري أن تكون ال + +766 +01:20:15,480 --> 01:20:18,180 +trigonometric أنا بعدين احكي لأي function و بعدين + +767 +01:20:18,180 --> 01:20:21,880 +بروح أركز على ال trigonometric function يبقى a + +768 +01:20:21,880 --> 01:20:25,920 +function f of x is called periodic بسميها دالة + +769 +01:20:25,920 --> 01:20:31,820 +دورية if there is a positive number P لو قدرت + +770 +01:20:31,820 --> 01:20:35,980 +ألاقي رقم موجب P such that + +771 +01:20:48,930 --> 01:20:57,560 +أي رقم تحطه هنا بنقول f x زي هذا رقم يعطيني f of x + +772 +01:20:57,560 --> 01:21:02,520 +itself إن كان هذا الأمر صحيح بسمي هذه مالها + +773 +01:21:02,520 --> 01:21:09,620 +periodic function طب ال P هذه رقم محدد والله بنفع + +774 +01:21:09,620 --> 01:21:15,360 +أي رقم بنفع كل دول لا إلها رقم محدد بيختلف عن + +775 +01:21:15,360 --> 01:21:21,060 +الثاني مظبوط طيب يبقى ال P هذه يمكن أنا أحطها + +776 +01:21:21,060 --> 01:21:25,600 +باتنين والله فعلا طلعت نفس الدي الأصلية و واحد + +777 +01:21:25,600 --> 01:21:30,100 +ثاني حطها ستة لقيتها طلعت نفس الدالة وقعتها تحطها + +77 + +801 +01:24:10,960 --> 01:24:17,240 +للتان والكتان طيب هذا نمر اتنين the period + +802 +01:24:33,960 --> 01:24:39,950 +طلعلي في الرأس ما اللي عندك كله اتنين باى يعني امسك + +803 +01:24:39,950 --> 01:24:42,790 +الـ period بتاعة الـ sign طلعلي فى رسمة الـ sign + +804 +01:24:42,790 --> 01:24:49,970 +بدأنا من عند الـ zero طلعنا نزلنا باى نزلنا تحته و + +805 +01:24:49,970 --> 01:24:54,190 +طلعنا لنفس النقطة اللى جبالي الـ zero اتنين باى و + +806 +01:24:54,190 --> 01:24:58,100 +من عند اتنين باى تبدأ دورة جديدة و هكذا يبقى اتنين + +807 +01:24:58,100 --> 01:25:02,660 +باى الصين والكوسين والسكاند والكوسيكاند اللي هو + +808 +01:25:02,660 --> 01:25:07,380 +اتنين باى الأربع نسب هدول الـ period تبعها قداش + +809 +01:25:07,380 --> 01:25:08,760 +اتنين باى + +810 +01:25:11,860 --> 01:25:21,840 +ساين X زائد اتنين باي ساين + +811 +01:25:21,840 --> 01:25:25,940 +X + +812 +01:25:25,940 --> 01:25:27,800 +ناقص اتنين باي + +813 +01:25:31,460 --> 01:25:37,940 +سين اكس ناقص اتنين باى زد ولا ناقص شو بتفرج انت + +814 +01:25:37,940 --> 01:25:43,460 +عندك دورة كاملة بقولك اعظفتها ولا طلعت بتذرش يبقى + +815 +01:25:43,460 --> 01:25:48,600 +شيلناها او خلناها لا تأثير عليها على القيمة اتنين + +816 +01:25:48,600 --> 01:25:52,940 +باى اربعة باى ستة باى اضعفها ولا طرحت كله بيبقى + +817 +01:25:52,940 --> 01:25:54,060 +سين ال X + +818 +01:25:57,980 --> 01:26:11,860 +Sin X ناقص اتنين باى يساوي Sin X تمام طيب Cos X + +819 +01:26:11,860 --> 01:26:17,180 +زيادة اتنين باى يساوي Cos X + +820 +01:26:33,110 --> 01:26:40,690 +يبقى الدورات الكاملة بتأثرش عندي جدها مرتين جدها + +821 +01:26:40,690 --> 01:26:41,350 +also + +822 +01:26:45,070 --> 01:26:54,810 +Sin X زي عشرة Y خمس دورات هدول مظبوط يبقى هدف Sin + +823 +01:26:54,810 --> 01:27:04,330 +X على طول and so on و هكذا طيب بدنا نعطي مثال عملي + +824 +01:27:04,330 --> 01:27:09,530 +على هالشغل هدى كيف بدنا نحسب الـ period لمين الـ + +825 +01:27:09,530 --> 01:27:12,390 +function example + +826 +01:27:20,550 --> 01:27:35,790 +Find the period of the following functions + +827 +01:27:44,710 --> 01:28:03,290 +F of X يساوي كتان باي X على تلاتة نمر ب F of X بده + +828 +01:28:03,290 --> 01:28:17,130 +يساوي صين خمسة X أو صين خمسة X خليها زي مين نمرى C + +829 +01:28:17,130 --> 01:28:26,110 +F of X بدأ تساوي Cos + +830 +01:28:26,110 --> 01:28:30,510 +2X + +831 +01:28:30,510 --> 01:28:48,680 +زائد Pi على 2 نمرى D F of X بدي أساوي تان تلاتة + +832 +01:28:48,680 --> 01:29:09,480 +X على اتنين زائد تلاتة بيقول + +833 +01:29:09,480 --> 01:29:17,250 +لي هت للفترة لكل دالة من الدوال التالية كتان باي + +834 +01:29:17,250 --> 01:29:21,570 +اكس على تلاتة إذا هذا كتابة مكتوبة على غير العادة + +835 +01:29:21,570 --> 01:29:26,450 +مش زي ما كتبنا فوق هيك طبعا سؤال التاني F of X + +836 +01:29:26,450 --> 01:29:32,070 +يساوي ساين خمسة X سؤال التالت كوصين اتنين X زائد + +837 +01:29:32,070 --> 01:29:37,270 +باي على اتنين سؤال الرابع F of X يساوي تان تلاتة X + +838 +01:29:37,270 --> 01:29:43,190 +على اتنين زائد تلاتة طيب نبدأ بالدالة الأولى نمرأ + +839 +01:29:43,190 --> 01:29:51,530 +ايه؟ بدي قداش الـ period لهذه الدالة بجى بسأل نفسى + +840 +01:29:51,530 --> 01:29:59,310 +سؤال هو الـ period للكتان قداش؟ للكتان؟ by واحدة + +841 +01:29:59,310 --> 01:30:03,890 +الكتان والتان by واحدة مشان أجيب الـ period لهذه + +842 +01:30:03,890 --> 01:30:11,520 +الدالة بجى لهذا المقدر كله و بسويه بال by بطلع قداش + +843 +01:30:11,520 --> 01:30:17,740 +قيمة X بتبقى هي الـ period المطلوبة يبقى باجي بقوله + +844 +01:30:17,740 --> 01:30:29,400 +هنا what حطلي ال همين باي X على تلاتة تساوي مين؟ + +845 +01:30:29,400 --> 01:30:39,620 +تساوي باي الـ period تبعت مين؟ تبعت الكتانة بناء + +846 +01:30:39,620 --> 01:30:45,540 +عليه اقسم على باى بيصير اكس على تلاتة يسوى كدهش + +847 +01:30:45,540 --> 01:30:52,320 +واحد اضرب كله فيه تلاتة يبقى الاكس يسوى كدهش تلاتة + +848 +01:30:52,320 --> 01:30:59,470 +فبعدين بقوله the period P تساوي تلاتة مش يعني كل + +849 +01:30:59,470 --> 01:31:05,010 +اللي ساوي تلاتة؟ يعني بدي أخد تلات وحدات من الطول + +850 +01:31:05,010 --> 01:31:09,650 +مش تلاتة by تلات وحدات من الطول بدي أرسم فيهم + +851 +01:31:09,650 --> 01:31:15,290 +منحنى الكتان اللي عندي اللي هو هذا، تمام؟ بعرفش + +852 +01:31:15,290 --> 01:31:19,330 +التلاتة دي تطلع أكتر من by و الله أقل منه، هو by + +853 +01:31:19,330 --> 01:31:27,380 +قديش؟ تقريبا تقريبا تقريبا تقريبا تقريبا + +854 +01:31:27,380 --> 01:31:32,500 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +855 +01:31:32,500 --> 01:31:32,600 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +856 +01:31:32,600 --> 01:31:32,620 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +857 +01:31:32,620 --> 01:31:32,700 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +858 +01:31:32,700 --> 01:31:33,620 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +859 +01:31:33,620 --> 01:31:41,250 +تقريبا تقريبا تقريبا تقريبا تقريبا النقطة بيه قال + +860 +01:31:41,250 --> 01:31:47,370 +اللي يبدو الـ period للصين خمسة X باجي بسأل نفسي + +861 +01:31:47,370 --> 01:31:53,330 +قداش الـ period للصين؟ اتنين باي يبقى باجي بقوله + +862 +01:31:53,330 --> 01:31:54,710 +the period + +863 +01:32:04,660 --> 01:32:11,400 +خمسة X يبقى بالي بقول خمسة X بده يساوي كده؟ تنين + +864 +01:32:11,400 --> 01:32:18,120 +باي يبقى بناء عليه ال X بده يساوي تنين باي على + +865 +01:32:18,120 --> 01:32:23,780 +خمسة تنين باى أنا جديش تلاتمية و ستين على خمسة يبقى + +866 +01:32:23,780 --> 01:32:28,020 +بيصير هذه الـ period الـ period اللي هياصل تنين باى + +867 +01:32:28,020 --> 01:32:32,180 +يبقى صارت عندي تنين باى و بدي اجسمها كمان على خمسة + +868 +01:32:32,180 --> 01:32:37,100 +يعني معناته ديجت الرسمة والله يعني عملت compress + +869 +01:32:37,100 --> 01:32:44,250 +ولا stretch يعني طلعت و نزلت في فترة بسيطة مش في + +870 +01:32:44,250 --> 01:32:49,490 +احد اتنين يبقى هنا انا ضغط الرسم هذا الـ period لما + +871 +01:32:49,490 --> 01:32:52,350 +اقول الـ period يعني قداش المسافر اللى بدك تطلع + +872 +01:32:52,350 --> 01:33:01,870 +فيها و تنزل طيب نجلس و نمرى الـ C الـ period هذه + +873 +01:33:01,870 --> 01:33:07,110 +cosine الـ period تبع الـ cosine قداش اتنين يبقى هنا + +874 +01:33:09,810 --> 01:33:19,010 +Period of cosine of X is 2π يبقى بجي بقوله put احط + +875 +01:33:19,010 --> 01:33:24,710 +قداش يساوي 2π هنا احط + +876 +01:33:24,710 --> 01:33:33,430 +قداش يعني احط 2X زي الـπ ع 2 يساوي 2π ولا بس 2X طب + +877 +01:33:33,430 --> 01:33:36,790 +و الـπ ع 2 هذي كيف؟ + +878 +01:33:38,920 --> 01:33:44,020 +أيوه، شوف يا سيدي، بدي أسألكوا السؤال التالي، + +879 +01:33:44,020 --> 01:33:48,120 +طلعلي فيه الورق اللي بين إيدي، هيحطيتها على + +880 +01:33:48,120 --> 01:33:55,170 +الطاولة أخدت period معين، مظبوط؟ قداش بتحركها، هل + +881 +01:33:55,170 --> 01:33:58,730 +تتغير الـ period تبعتها؟ يعني انا لو جهة الدلة + +882 +01:33:58,730 --> 01:34:03,330 +عملتلها الـ shift هل تتغير الـ period؟ لأ، يبقى الـ + +883 +01:34:03,330 --> 01:34:07,010 +بايع اتنين هذا مش يعتبر shift لدلة جهة اليمين + +884 +01:34:07,010 --> 01:34:11,430 +بمقدار اتنين، جهة الشمال بمقدار اتنين، و لو كانت + +885 +01:34:11,430 --> 01:34:15,450 +سالب جهة اليمين بمقدار بايع اتنين، إذا الـ shift لا + +886 +01:34:15,450 --> 01:34:21,300 +يؤثر على الـ period تبعت الـ function واضح كلام ايه؟ + +887 +01:34:21,300 --> 01:34:26,200 +يبقى مرة تانية بقول هذا الآن أنا عند الورقة اللي + +888 +01:34:26,200 --> 01:34:30,400 +بقى اللي ورا تطلع كويس هنا الورقة شغلتلي مسافة من + +889 +01:34:30,400 --> 01:34:34,680 +النقطة هذه لغاية النقطة هذه عملت shift للورقة + +890 +01:34:34,680 --> 01:34:39,940 +للامام او للخلف او يمين او شمال هل الـ period تبعت + +891 +01:34:39,940 --> 01:34:45,950 +اختلفت؟ لأ يا عم الفيريو اتضلت هي الكلام تتغير يبقى + +892 +01:34:45,950 --> 01:34:50,970 +نتيجة الـ shift للـ function الـ period لن تتغير + +893 +01:34:50,970 --> 01:34:56,710 +مطلقا يبقى بروحش بكتب 2x زائد بي ع 2 يساوي 2 بي + +894 +01:34:56,710 --> 01:35:03,390 +بكسَب جدية 2x لإن هذا يعتبر shift لميم shift لدالة + +895 +01:35:03,390 --> 01:35:07,430 +لإن ماليش علاقة فيش shift لا بيغير ولا بيقدم ولا + +896 +01:35:07,430 --> 01:35:12,680 +بيأخر من قيمة الـ period يبقى بتروح اكتبله هنا اتنين + +897 +01:35:12,680 --> 01:35:19,360 +X يساوي قداش اتنين Pi ومنها ال X يساوي قداش Pi + +898 +01:35:19,360 --> 01:35:29,960 +يبقى ده period P تساوي Pi فقط يعني القوساين هذه + +899 +01:35:29,960 --> 01:35:34,940 +تبعت الدالة لأن هذه بدل مرسومها من صفر لاتنين باي + +900 +01:35:34,940 --> 01:35:41,240 +اطلع وانزل لأ بدي اضغطها بس من صفر لباي مسافة اطلع + +901 +01:35:41,240 --> 01:35:46,660 +وانزل في خلالها هذه تمام هاي المقصود فيها هذا يعني + +902 +01:35:46,660 --> 01:35:53,140 +لدلع رقم C ونجي لنمرة D نمرة D بيقول F of X ساوية + +903 +01:35:53,140 --> 01:35:57,720 +ثانية ثلاثة X زي اتنين والثلاثة لعالها ملاعق + +904 +01:35:57,720 --> 01:36:01,400 +بالزاوية يبقى ملاعق بالزاوية هذه الزاوية اللي + +905 +01:36:01,400 --> 01:36:07,620 +عندنا هذه ثلاثة مضغوطة للـ function ككل ما رأيك؟ + +906 +01:36:07,620 --> 01:36:12,940 +تلاتة هدا أو هدا؟ لأ هدا الـ shift لدالة إلى أعلى + +907 +01:36:12,940 --> 01:36:16,560 +بمقدار تلاتة، يعني لو رسمت الرسمة الأصلية، بدي + +908 +01:36:16,560 --> 01:36:18,980 +أعملها إزاحة إلى أعلى بمقدار تلاتة، يبقى التلاتة + +909 +01:36:18,980 --> 01:36:23,540 +دي لا تأثيرة لها على الـ period يبقى بدك تحط في + +910 +01:36:23,540 --> 01:36:27,900 +دماغك المعلومة هذه ان الـ shift للـ function لا + +911 +01:36:27,900 --> 01:36:32,360 +تأثير له على الـ period على الإطلاق يبقى بدي أجيب + +912 +01:36:32,360 --> 01:36:38,580 +الـ period لنمرة D فبعدين بقول لنمرة D part بنروح + +913 +01:36:38,580 --> 01:36:45,000 +نحط اللي هو تلاتة X على اتنين يساوي برجع قداش الـ + +914 +01:36:45,000 --> 01:36:52,160 +period للتان و باي يبقى back to pie و منها ال X + +915 +01:36:52,160 --> 01:36:57,960 +يساوي اتنين باي على تلاتة يعني كام درجة + +916 +01:37:01,330 --> 01:37:08,310 +لأ يا راجل، مائة و عشرين درجة، يعني بدلي التان هذه + +917 +01:37:08,310 --> 01:37:13,210 +ما كنت برسمها من صفر إلى باى، يعني في مسافة مائة و + +918 +01:37:13,210 --> 01:37:19,370 +تمانين درجة لأ، بتضايق لو أرسمها في مسافة، و هكذا، + +919 +01:37:19,370 --> 01:37:23,290 +تمام؟ طيب إذا الـ period؟ + +920 +01:37:26,510 --> 01:37:32,870 +فيه يساوي اللي هو اتنين by على تلاتة في هذه العرض + +921 +01:37:32,870 --> 01:37:36,670 +طب السؤال في المسائل هدول أنا بلاحظ ان الـ period + +922 +01:37:36,670 --> 01:37:42,470 +بنديقها طب ممكن نوسع الـ period تطلع مسافة اكبر اه + +923 +01:37:42,470 --> 01:37:48,770 +ممكن ليش لأ اذا لو اعتبرت كمان عندي سؤال تابع + +924 +01:37:48,770 --> 01:37:49,450 +لهدول + +925 +01:37:54,470 --> 01:38:01,590 +مش حاجة أقولنا A وB وC وD؟ خدلي E يبقى E F of X + +926 +01:38:01,590 --> 01:38:08,090 +يساوي بالدجاج أقول هنا X على تلاتة + +927 +01:38:13,660 --> 01:38:18,820 +خيص؟ يبقى الواحد هذا shift مالهوش دعوة طبعا؟ يبقى + +928 +01:38:18,820 --> 01:38:22,740 +.. اه ما قلناش الدالة sign ولا cosine يبقى خد اللي + +929 +01:38:22,740 --> 01:38:29,260 +بدك إياها، قداش؟ sign؟ هاي sign X على تلت، بلاش + +930 +01:38:29,260 --> 01:38:32,360 +واحد، واحد تلت عاملة، شفت وشفت، تسويش وشفت يبقى + +931 +01:38:32,360 --> 01:38:37,200 +بداجي اقوله، مش هنجيب الـ period part حطلي X على + +932 +01:38:37,200 --> 01:38:43,920 +تلت يسوي قداش؟ اتنين باي يبقى ال X بيسوي قداش؟ ستة + +933 +01:38:43,920 --> 01:38:47,260 +باى يبقى ده period + +934 +01:38:50,080 --> 01:38:58,220 +أز ستة باى بدل ما طلعنا و نزلنا في مسافة بس اتنين + +935 +01:38:58,220 --> 01:39:03,840 +باى يعني الرسم يبدأ يصير scaling جدها تلات مرات + +936 +01:39:03,840 --> 01:39:09,180 +يعني عملنا stretch بعد الرسم صار جد قبل تلات مرات + +937 +01:39:09,180 --> 01:39:14,560 +يبقى مغطناها شوية رسمها يعني لو حبيت اتعرف عليها + +938 +01:39:14,560 --> 01:39:22,570 +بس لمجرد العلم ليس الاقلنا هذا X وهذا Y وهذا + +939 +01:39:22,570 --> 01:39:29,550 +القيمة الواحد وهذا Zero وهذا اللي عندك اليمين سالب + +940 +01:39:29,550 --> 01:39:39,820 +واحد بدي أقول هذا باي وهذا اتنين باي هذه هنا تلاتة + +941 +01:39:39,820 --> 01:39:47,320 +باى وهذه هنا أربعة باى وهذه هنا خمسة باى وهذه هنا + +942 +01:39:47,320 --> 01:39:53,400 +ستة باى بالشكل اللي عنها ده أيوه يبقى الدالة + +943 +01:39:53,400 --> 01:39:58,840 +الأصلية في مسافة اتنين باى بدأت تكون طلعت ونزلت + +944 +01:39:58,840 --> 01:40:02,140 +يعني الدالة الأصلية كانت بالشكلها ديك + +945 +01:40:06,370 --> 01:40:15,890 +مظبوط؟ هذا من الصفر لآية اتنين باقي الآن أنا بداجي + +946 +01:40:15,890 --> 01:40:23,890 +من صفر ل ستة باى يبقى هذه بده تبدأ من ال zero تمام + +947 +01:40:23,890 --> 01:40:30,150 +و عند التلاتة باى بده تكون نزلت لغاية هنا و عند + +948 +01:40:30,150 --> 01:40:35,990 +الستة باى بده تبقى طالع يبقى نص المسافة هنا بده + +949 +01:40:35,990 --> 01:40:45,660 +تجي كدالة هيك تمام؟ و بتيجي نازله هيك الشكل هذا هيك + +950 +01:40:45,660 --> 01:40:54,180 +يبقى السودة هذه هي رسمة sine اتنين X هذه اللي هي + +951 +01:40:54,180 --> 01:41:03,660 +sine ال X تمام؟ هذه الآن ستة باي يبقى هذه رسمة + +952 +01:41:03,660 --> 01:41:12,030 +sine X على تلتة تعرف كده؟ يبقى كأن عملنا لها + +953 +01:41:12,030 --> 01:41:17,650 +stretch يبقى هاي الفرق ما بين الرسمات اللي لازلنا + +954 +01:41:17,650 --> 01:41:22,690 +في نفس الـ section ولما ننتهي بعد لسه في كلام يبقى + +955 +01:41:22,690 --> 01:41:29,810 +نعرف مين even ومين odd وناخد السمثل عليهم بالإضافة + +956 +01:41:29,810 --> 01:41:32,490 +للمتطابقات المثلثية diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Xku1FOAUcfU_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Xku1FOAUcfU_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..11cb9dc217425a6c3b64847c413b3ecc8459c24c --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Xku1FOAUcfU_postprocess.srt @@ -0,0 +1,3248 @@ +1 +00:00:20,650 --> 00:00:25,190 +بسم الله الرحمن الرحيم المرة اللى فاتت انتهينا من + +2 +00:00:25,190 --> 00:00:30,550 +section 4.2 اللى هو ال main value theorem والاسئلة + +3 +00:00:30,550 --> 00:00:35,510 +اللى عليها والان بننتقل الى section 4.3 وهو ال + +4 +00:00:35,510 --> 00:00:39,170 +monotonic functions and the first derivative test + +5 +00:00:39,170 --> 00:00:46,250 +يعني الدوال الرتيبة وكذلك اللى هو اختبار المشتقة + +6 +00:00:46,250 --> 00:00:50,770 +الأولىتعريف الـ monotonic function أو الدالة + +7 +00:00:50,770 --> 00:00:55,610 +الرتيبة فبجي بقول الدالة f of x اللى بتبقى تزايدية + +8 +00:00:55,610 --> 00:01:00,990 +أو تناقصية على فترة ما بسميها monotonic function + +9 +00:01:00,990 --> 00:01:05,260 +على تلك الفترةيبقى أنا بدي أحد أمرين، يا إما + +10 +00:01:05,260 --> 00:01:11,340 +تزايدية، يا إما مش الأثنين مع بعض، واحد بس، كاتب + +11 +00:01:11,340 --> 00:01:18,240 +or طلع هي or، هذه أو تلك، يا إما تزايدية على كل + +12 +00:01:18,240 --> 00:01:23,360 +الفترة، يبدأ بقول عليها monotonic أو تناقصية على + +13 +00:01:23,360 --> 00:01:27,510 +كل الفترةبقول عنها monotonic لكن تزاديه وتنقصيه في + +14 +00:01:27,510 --> 00:01:33,070 +نفس الفترة ليست monotonic نعطي مثال توضيح على ذلك + +15 +00:01:33,070 --> 00:01:38,430 +لو خدت الدالة F of X يساوي من X تربية الدالة هذه + +16 +00:01:38,430 --> 00:01:43,470 +معروفة ورسمناها قبل ذلك عدة مرات فلو قلت هذا محور + +17 +00:01:43,470 --> 00:01:51,000 +X وهذا محور Y وجيت رسمت الدالة Y تساوي X تربيةهذا + +18 +00:01:51,000 --> 00:01:56,020 +الـ Zero لو جيت من سالب Infinity لغاية Zero ده + +19 +00:01:56,020 --> 00:02:01,940 +لمالها يجب نزول يبقى Decreasing يبقى على هذا الجزء + +20 +00:02:01,940 --> 00:02:07,660 +ده Decreasing يبقى معناته Monotonic على الفترة من + +21 +00:02:07,660 --> 00:02:13,680 +سالب Infinity لغايةزيرو بعد ذلك الان لو جيت من ال + +22 +00:02:13,680 --> 00:02:19,600 +zero لغاية infinity بلاجي الدالة تزايدية يبقى هنا + +23 +00:02:19,600 --> 00:02:24,440 +increasing يبقى الدالة decreasing على الفترة من + +24 +00:02:24,440 --> 00:02:29,260 +سلب infinity إلى zero و increasing على الفترة من + +25 +00:02:29,260 --> 00:02:34,220 +zero لغاية infinity اذا على الفترة من سلب infinity + +26 +00:02:34,220 --> 00:02:38,280 +إلى zero بقدر اقول عنها monotonic functionعلى + +27 +00:02:38,280 --> 00:02:42,700 +الفترة من 0 إلى infinity بقدر أقول عنها monotonic + +28 +00:02:42,700 --> 00:02:46,480 +function لكن على الفترة كلها من سلب infinity إلى + +29 +00:02:46,480 --> 00:02:51,980 +infinity not monotonic لأن شوية عليها increasing و + +30 +00:02:51,980 --> 00:02:55,060 +شوية decreasing احنا نقول انها increasing على طول + +31 +00:02:55,060 --> 00:03:00,700 +او decreasing على طولالدالة F of X يساوي تربية + +32 +00:03:00,700 --> 00:03:04,980 +مونوتونك من سالب Infinity لغاية Zero وكذلك + +33 +00:03:04,980 --> 00:03:09,000 +مونوتونك على الفترة من Zero إلى Infinity لكنها + +34 +00:03:09,000 --> 00:03:13,340 +ليست مونوتونك على الفترة من وين من سالب Infinity + +35 +00:03:13,340 --> 00:03:17,960 +إلى Infinity يبقى هذا تعريف المونوتونك ب function + +36 +00:03:17,960 --> 00:03:19,380 +ومثال بسيط + +37 +00:03:23,490 --> 00:03:27,090 +نعود لـ Crawler الثلاثة طبعا اللى خدنا المرة اللى + +38 +00:03:27,090 --> 00:03:29,870 +فات نظرية ال mean value theorem و two crawlers + +39 +00:03:29,870 --> 00:03:34,470 +عليها تمام هذه ال crawlery رقم ثلاثة مشان طبق ال + +40 +00:03:34,470 --> 00:03:37,570 +mean value theorem قلنا بدنا دلة تبقى دلة متصلة + +41 +00:03:37,570 --> 00:03:40,910 +على ال closed interval و قبل اشتقاق على ال open + +42 +00:03:40,910 --> 00:03:44,720 +interval a و bمن هنا نجوى للافتراض أن الدالة + +43 +00:03:44,720 --> 00:03:49,680 +فبإستمر على الـClosed Interval وقابلة للاشتقاء على + +44 +00:03:49,680 --> 00:03:53,120 +الفترة المفتوحة أي وبيها الشروط الـMean Value + +45 +00:03:53,120 --> 00:03:59,150 +Theorem، إن حدث ذلك يبقى في هذه الحالةإذا الـ F' + +46 +00:03:59,490 --> 00:04:05,510 +of X أكبر من Zero على كل الفترة بقول الدالة دالة + +47 +00:04:05,510 --> 00:04:09,590 +تزايدية يبقى على كل ال X اللي موجودة في ال + +48 +00:04:09,590 --> 00:04:14,370 +interval A وB يبقى ال F دالة تزايدية على كل closed + +49 +00:04:14,370 --> 00:04:18,870 +interval A وB يعني كأن ال domain تبعهالـ closed + +50 +00:04:18,870 --> 00:04:24,010 +interval او continuous على الفترة المغلقة ا و بيو + +51 +00:04:24,010 --> 00:04:26,370 +differentiable على ال open interval + +52 +00:04:35,010 --> 00:04:39,130 +وإذا كانت f prime أقل من 0 يبقى سالب يبقى الدالة + +53 +00:04:39,130 --> 00:04:43,210 +مالها تناقصي يبقى decreasing function على الفترة + +54 +00:04:43,210 --> 00:04:49,510 +اللي لنا مية a وb يبقى أنا الآن جيب تعريف جديد غير + +55 +00:04:49,510 --> 00:04:52,470 +اللي أخدناه في ال chapter الأول في ال chapter + +56 +00:04:52,470 --> 00:04:55,450 +الأول مش هنجيب الدالة increasing على الفترة اللي + +57 +00:04:55,450 --> 00:05:01,820 +بتاخد two elements عشوائيةإذا كان X1 أقل من X2 إذا + +58 +00:05:01,820 --> 00:05:08,380 +كان X1 أقل من X2 إذا كان + +59 +00:05:08,380 --> 00:05:13,940 +X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل + +60 +00:05:13,940 --> 00:05:15,820 +من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل من X2 + +61 +00:05:15,820 --> 00:05:17,900 +إذا كان X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان + +62 +00:05:17,900 --> 00:05:19,060 +X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل + +63 +00:05:19,060 --> 00:05:20,880 +X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل + +64 +00:05:20,880 --> 00:05:26,470 +من X2 إذا كان X1 أقل من X2 إذا كان Xأذا لما جيت + +65 +00:05:26,470 --> 00:05:31,310 +أستخدم المشتقة في هذه الحالة بقول إذا المشتقة موجب + +66 +00:05:31,310 --> 00:05:34,270 +يبقى الدالة تزايدية وإذا المشتقة سلب يبقى يقول + +67 +00:05:34,270 --> 00:05:39,870 +الدالة تناقصية نعطي مثال توضيحي بيقول لو كان f of + +68 +00:05:39,870 --> 00:05:44,570 +x يساوي x plus 4 نقص 4x تكيب زي 4x تربية بدى + +69 +00:05:44,570 --> 00:05:49,030 +شغلتين الشغلة الأولى بدى ال critical points لهذه + +70 +00:05:49,030 --> 00:05:53,970 +الدالة f النقاط الحرجة وبدى فترات التزيد والتناقص + +71 +00:05:53,970 --> 00:06:00,330 +لمينلهذه الدالة يبقى الدالة الأساسية اللى عندنا f + +72 +00:06:00,330 --> 00:06:07,490 +of x يساوي x to the power 4 minus 4x to the power + +73 +00:06:07,490 --> 00:06:14,890 +3 زائد 4x square لو جينا نشتق هذه الدالة يبقى ال f + +74 +00:06:14,890 --> 00:06:21,690 +prime of x يساويأربعة إكس تكييب ناقص اتناشر إكس + +75 +00:06:21,690 --> 00:06:27,270 +تربية زائد تمانية إكس هذه المشتقة تبعتها لكن بدي + +76 +00:06:27,270 --> 00:06:31,870 +أشوف هل بقدر أحللها و لا بقدرش تعالوا نشوف واضح + +77 +00:06:31,870 --> 00:06:36,290 +أنه في عامل مشترك اللي همين أربعة إكس إذا لو جينا + +78 +00:06:36,290 --> 00:06:42,910 +أخدنا أربعة إكس عامل مشترك بيظل عندي إكس تربية + +79 +00:06:42,910 --> 00:06:50,070 +ناقص تلاتة إكسزائد اتنين اللي بين قوسين إذا ممكن + +80 +00:06:50,070 --> 00:06:56,230 +نحلله بنروح نحلله اللي حاصل ضرب قوسين يبقى هاي اكس + +81 +00:06:56,230 --> 00:07:01,010 +هاي اكس هاي واحد هاي اتنين هاي ناقص ناقص تلاتة اكس + +82 +00:07:01,010 --> 00:07:06,210 +يبقى التحليل سليم مائة بالمائةيبقى اشتقانا، من + +83 +00:07:06,210 --> 00:07:10,510 +خلال هذا الاشتقاق بدأ أجيب ال critical points ال + +84 +00:07:10,510 --> 00:07:15,550 +critical points هي قيم X اللي بتخلي المشتقة صفر أو + +85 +00:07:15,550 --> 00:07:21,130 +المشتقة غير معرفة، هذه المشتقة polynomial إذا لا + +86 +00:07:21,130 --> 00:07:25,960 +يمكن أن تكون غير معرفة في يوم من الأيامصحيح؟ إذا + +87 +00:07:25,960 --> 00:07:30,040 +ما بضلش عندي إلا أسويها بالـ 0 وبالتالي أطلع ال + +88 +00:07:30,040 --> 00:07:35,560 +critical points إذا لو جيت سويت هذه بالـ 0 بصير + +89 +00:07:35,560 --> 00:07:43,100 +عندنا ميم ان ال X تسوي 0 و X يسوي 1 و X يسوي 2 + +90 +00:07:43,100 --> 00:07:48,380 +هدول هم من are the critical + +91 +00:07:50,820 --> 00:07:56,420 +يبقى هذه النقاط الحرجة لمين لهذه ال function وهو + +92 +00:07:56,420 --> 00:08:00,740 +المطلوب الأول من المسألة اللي عندنا بعدين جليتلي + +93 +00:08:00,740 --> 00:08:05,560 +فترات التزايد والتناقص مشان أجيب فترات التزايد + +94 +00:08:05,560 --> 00:08:10,460 +والتناقص بدي أروح أدرس إشارة المشتقة اللي عندنا + +95 +00:08:10,460 --> 00:08:14,640 +مشان أدرس إشارة المشتقة بدي أروح أدرس إشارة كل + +96 +00:08:14,640 --> 00:08:19,200 +term من ال termات التلاتةاللي عندنا هذه يبقى بتروح + +97 +00:08:19,200 --> 00:08:25,280 +هاجي اقوله بدي إشارة ال term الأول اللي هو قداش 4x + +98 +00:08:25,280 --> 00:08:31,320 +هذا بياخد الصفر وين عند x السفر قداش؟ Zero بعد ال + +99 +00:08:31,320 --> 00:08:36,090 +zero positiveوالله خلّيها نجيب ال zero اللي هنا + +100 +00:08:36,090 --> 00:08:40,710 +شوية خلّي هذا ال zero هنا و قبل ال zero ماله + +101 +00:08:40,710 --> 00:08:46,710 +negative بعد هيك بدأ أروح أخد إشارة ال terminal x + +102 +00:08:46,710 --> 00:08:52,210 +ناقص واحد بياخد ال zero تبع وين؟ عند ال واحد بعد + +103 +00:08:52,210 --> 00:08:57,310 +ال واحد كذلك positive و قبل ال واحد ماله negative + +104 +00:08:57,790 --> 00:09:03,150 +لو جيت اخد اشارة الجوس التالت لول اكس ناقص اتنين + +105 +00:09:03,150 --> 00:09:08,690 +يبقى بياخد زيرو تبع وين عند اتنين بعد اتنين زي + +106 +00:09:08,690 --> 00:09:13,050 +تلاتة اربعة خمسة بلاقي قيمة القوس بالموجب وقبل + +107 +00:09:13,050 --> 00:09:18,830 +اتنين بلاقي كل قيمة الجوس ماله بالسالب بعدك بداجي + +108 +00:09:18,830 --> 00:09:24,660 +اخد اشارة حصل ضرب اربعة اكسفي اكس ناقص واحد في اكس + +109 +00:09:24,660 --> 00:09:30,220 +ناقص اتنين واجي اقول هذا ال real line واروح احدد + +110 +00:09:30,220 --> 00:09:36,940 +الحدود الإقليمية اللي موجودة عندنا يبقى لو جيت هذا + +111 +00:09:36,940 --> 00:09:42,230 +الخط اللي هو اتنينوهذا الخط الراسي الـ X عنده + +112 +00:09:42,230 --> 00:09:47,530 +بواحد وهذا الخط اللي عندنا الـ X عنده بقداش بزيرو + +113 +00:09:47,530 --> 00:09:52,130 +الثلاثة تقوس مضروبة في بعض يبقى بدي أضرب الإشارات + +114 +00:09:52,130 --> 00:09:59,710 +التلاتة في بعض ضرب يبقى هنا بالموجة هنا سالم هنا + +115 +00:09:59,710 --> 00:10:06,650 +موجة هنا سالميبقى ضغط الإشارات سالب في سالب بموجب + +116 +00:10:06,650 --> 00:10:10,490 +في سالب بسالب موجب في سالب بسالب سالب في سالب + +117 +00:10:10,490 --> 00:10:15,570 +بموجب موجب في موجب بموجب في سالب بسالب كل موجب + +118 +00:10:15,570 --> 00:10:21,570 +يبقى كل موجب، ممتاز، يبقى هذه إشارة مين؟إشارة + +119 +00:10:21,570 --> 00:10:27,050 +المشتقة طلع هنا المشتقة ما لها سالي بيبقى الدالة + +120 +00:10:27,050 --> 00:10:34,010 +كانت decreasing دناقصية يعني الدالة نزلة إلى أسفل + +121 +00:10:34,010 --> 00:10:39,550 +الإشارة صارت موجة بيبقى increasing الدالة صعدة إلى + +122 +00:10:39,550 --> 00:10:44,390 +أعلى سالي بيبقى decreasing إلى أسفل موجة بيبقى + +123 +00:10:44,390 --> 00:10:49,410 +increasing إلى أعلىإذا بقدر أحدد فترات التزايد + +124 +00:10:49,410 --> 00:10:54,650 +والتناقص لمين لدالة العلم هدفه بروح بقول لما ياتي + +125 +00:10:54,650 --> 00:11:02,810 +ال F is increasing دالة تزايدية on على الفترة + +126 +00:11:02,810 --> 00:11:11,650 +الأولى من صفر لغاية واحد وكذلك على الفترة من اندي + +127 +00:11:11,650 --> 00:11:18,650 +اتنين لغاية كدهش infinity بعد ايه؟الـ F is + +128 +00:11:18,650 --> 00:11:25,630 +decreasing دالة تناقصية على الفترة من سالب + +129 +00:11:25,630 --> 00:11:33,430 +infinity لغاية الـ zero and on وعلى الفترة من أند + +130 +00:11:33,430 --> 00:11:39,470 +الواحد لغاية كداش لغاية اتنين يبقى هذا مثال بسيط + +131 +00:11:39,470 --> 00:11:44,460 +حسبنا من خلاله ال critical points لدالة همهوحسبنا + +132 +00:11:44,460 --> 00:11:48,780 +فترات التزايد والتناقص وطبقنا التعريف اللي لنا + +133 +00:11:48,780 --> 00:11:55,660 +تطبيقا مباشرا يعني الدالة على هذه الفترة كانت + +134 +00:11:55,660 --> 00:12:00,860 +مونوتونك على الفترة هذه مونوتونك على الفترة هذه + +135 +00:12:00,860 --> 00:12:04,640 +مونوتونك على الفترة هذه مونوتونك لكن ال domain + +136 +00:12:04,640 --> 00:12:12,850 +تبعها كلها not monotonicننتقل الأن إلى نقطة ثانية + +137 +00:12:12,850 --> 00:12:15,630 +وأخيرة في هذا ال section + +138 +00:12:30,950 --> 00:12:34,330 +النقطة بين حدد ال first derivative test لل local + +139 +00:12:34,330 --> 00:12:43,810 +extreme values يبقى ال first derivative test + +140 +00:12:43,810 --> 00:12:57,150 +for local extrema يعني ال local extreme values + +141 +00:13:02,410 --> 00:13:13,590 +بيقول هذا ما يأتي suppose that افترض انه ال c is a + +142 +00:13:13,590 --> 00:13:24,950 +critical point افترض ان ال c هي نقطة حريجة of a + +143 +00:13:24,950 --> 00:13:26,570 +continuous + +144 +00:13:28,780 --> 00:13:42,280 +فنكشن F لدالة F and ال F is differentiable + +145 +00:13:42,280 --> 00:13:54,920 +دالة قابلة الاشتراك at every point عند كل نقطة in + +146 +00:13:54,920 --> 00:13:56,980 +some + +147 +00:13:59,100 --> 00:14:06,480 +interval in some interval containing + +148 +00:14:06,480 --> 00:14:20,040 +C except possibly except + +149 +00:14:20,040 --> 00:14:24,180 +possibly at C itself + +150 +00:14:30,630 --> 00:14:45,090 +مرة واحد if ال if prime it change from negative + +151 +00:14:45,090 --> 00:14:54,470 +to positive at c then + +152 +00:14:56,470 --> 00:15:08,950 +الـ F لديه مقاومة مقاومة في الـ C نمرة + +153 +00:15:08,950 --> 00:15:15,030 +اتنين F F برايم تتغير من مقاومة مقاومة مقاومة + +154 +00:15:15,030 --> 00:15:24,170 +مقاومة في الـ C فالـ F لديه مقاومة مقاومة مقاومة + +155 +00:15:24,170 --> 00:15:25,550 +في الـ C + +156 +00:15:28,460 --> 00:15:39,960 +نقطة الثالثة والاخيرة F ال F prime does not change + +157 +00:15:39,960 --> 00:15:46,980 +does not change its + +158 +00:15:46,980 --> 00:15:49,200 +sign + +159 +00:15:51,680 --> 00:16:08,920 +at C then ال F has no local extrema at C + +160 +00:16:57,180 --> 00:16:58,760 +السلام عليكم + +161 +00:17:58,290 --> 00:17:59,310 +حسناً + +162 +00:18:41,000 --> 00:18:47,160 +عليه بركلةبنجي نقل ال test derivative test اختبار + +163 +00:18:47,160 --> 00:18:51,340 +المشتقة الأولى لل local extreme values لمواقع + +164 +00:18:51,340 --> 00:18:57,600 +النهايات العظمى والصغرى المحلية بقول يفترض ان C is + +165 +00:18:57,600 --> 00:19:02,960 +a critical point يبقى C هذه النقطة حرجة لدالة من + +166 +00:19:02,960 --> 00:19:08,160 +لدالة متصلة F ونفترض ان الدالة F قابل اشتراء + +167 +00:19:08,160 --> 00:19:17,050 +للاشتقاق عند كل نقطة in someinterval containing z + +168 +00:19:17,050 --> 00:19:21,130 +يبقى ليس بالضرورة على كل ال domain وإنما عالميا + +169 +00:19:21,130 --> 00:19:26,870 +على جزء من ال domain containing z except possibly + +170 +00:19:26,870 --> 00:19:31,690 +at z itself معدى عند z itself إيش يعني معدى z + +171 +00:19:31,690 --> 00:19:36,630 +itself يعني ده لو ممكن تكون غير قابلة للاشتقاق عند + +172 +00:19:36,630 --> 00:19:40,960 +z ممكن تكون قابلة للاشتقاقأو ممكن تكون غير قابلة + +173 +00:19:40,960 --> 00:19:44,740 +لإشتقاء عند الـC لأن الـcritical point هي النقطة + +174 +00:19:44,740 --> 00:19:46,740 +التي في الـprime موجودة أو لا موجودة في الـprime + +175 +00:19:46,740 --> 00:19:52,620 +بس بحيث النقطة تكون موجودة في دميان الدالة يبقى + +176 +00:19:52,620 --> 00:19:56,380 +هذه المقصود ما عدا عند الـC itself يعني عند الـC + +177 +00:19:56,380 --> 00:20:00,480 +itself ممكن الدالة تكون غير قابلة للإشتقاء ابن + +178 +00:20:00,480 --> 00:20:06,000 +جلان إذا والله المشتقة الأولى غيرت إشارتها من سالب + +179 +00:20:06,000 --> 00:20:11,930 +إلى موجبمن negative إلى positive عند النقطة C يبقى + +180 +00:20:11,930 --> 00:20:16,690 +ال F has a local minimum تعالى نشوف هذا على + +181 +00:20:16,690 --> 00:20:20,090 +الطبيعة قبل ما نتقل إلى النقطة الثانية الدالة + +182 +00:20:20,090 --> 00:20:24,450 +بتغير إشارتها من negative إلى positive بعدين بتطلع + +183 +00:20:24,450 --> 00:20:29,710 +على الدالة الدالة هنا تزايدية بلت هنا كما المالها + +184 +00:20:29,710 --> 00:20:36,370 +تزايدية ماتغيرتشيبقى هنا في هذه المنطقة F أكبر من + +185 +00:20:36,370 --> 00:20:42,850 +الـ 0 و هنا F أكبر من الـ 0 لو جيت على المنطقة من + +186 +00:20:42,850 --> 00:20:50,330 +هنا لغاية هنا يبقى F أقل من الـ 0يبقى هنا ال F' + +187 +00:20:51,130 --> 00:20:56,730 +أقل من ال 0 لو جيت على المنطقة هذه بلاقي أن F' + +188 +00:20:57,350 --> 00:21:02,450 +أكبر من ال 0 لو جيت على المنطقة هذه بلاقي F' أقل + +189 +00:21:02,450 --> 00:21:07,510 +من ال 0 لأنه تناقصية لو جيت على الجزء من هنا لهنا + +190 +00:21:07,510 --> 00:21:13,570 +كمان F' مالها أقل من ال 0 إيش بقوله هنا إذا F' + +191 +00:21:13,970 --> 00:21:18,800 +غيرت شرطها من negative إلى positiveكانت دالة + +192 +00:21:18,800 --> 00:21:25,660 +تناقصية و رجعة الطلاقة التزاودية Local Minimum + +193 +00:21:25,660 --> 00:21:32,260 +يبقى Local Minimum عند الـ C يبقى عندنا Local + +194 +00:21:32,260 --> 00:21:40,360 +Minimum في هذه الحالة الـ F' of C تلاتة بده يساوي + +195 +00:21:40,360 --> 00:21:46,330 +مين؟ بده يساوي Zero في عندي غيرها Local Minimum؟من + +196 +00:21:46,330 --> 00:21:52,150 +خلال الرسم في local minimum اللي هي مين هذه النقطة + +197 +00:21:52,150 --> 00:21:58,450 +يبقى هنا هذه كمان local minimum بس مافيش تغيير + +198 +00:21:58,450 --> 00:22:04,930 +عندها تمام؟ يبقى رغم أنها نقطة بداية من البداية + +199 +00:22:04,930 --> 00:22:11,550 +يبقى هذه local minimum اتا كويس؟ لكن هذه ليست نقطة + +200 +00:22:11,550 --> 00:22:14,990 +موجودة في الداخل انت تقول غيرت إشرتها من كذا إلى + +201 +00:22:14,990 --> 00:22:19,570 +كذايبقى لو كانت نقطة في الداخل وتغيرت من سالب إلى + +202 +00:22:19,570 --> 00:22:23,790 +موجة بقول هنا local minimum هذه local minimum ليش؟ + +203 +00:22:23,790 --> 00:22:29,550 +لأنها أقل قيمة بتاخدها للدالة من عند أول نقطة + +204 +00:22:29,550 --> 00:22:35,310 +لغاية مين لو جيت قلت هذه افترض ان هذه أول نقطة في + +205 +00:22:35,310 --> 00:22:41,420 +ال interval A وهذه أخر نقطة في ال interval Bلو جيت + +206 +00:22:41,420 --> 00:22:45,880 +حوالين الـA لقيت هذه أقل قيمة لدى اللي يبقى هذه + +207 +00:22:45,880 --> 00:22:49,180 +الـlocal minimum من أول section أخدناه اللي هو + +208 +00:22:49,180 --> 00:22:54,820 +section 4-1 طيب في عندي كمان local minimum تاني + +209 +00:22:54,820 --> 00:23:02,940 +ماعنديش لكن هذه هو كمان local minimum بس إيش هذه + +210 +00:23:02,940 --> 00:23:07,420 +نقطة طرفية in point تمام؟ أيوة + +211 +00:23:10,080 --> 00:23:14,880 +لا local minimum ولا local maximum، لا بقدرش ولا + +212 +00:23:14,880 --> 00:23:18,960 +حاجة، ايوة نقدر من هذا الاتباه نعرف اي واحدة هي ال + +213 +00:23:18,960 --> 00:23:22,220 +absolute و ال local minimum؟ هنجي لل absolute، بس + +214 +00:23:22,220 --> 00:23:27,170 +استغلني شوية، هنقول، نشير إليهاطيب بس خلص ال local + +215 +00:23:27,170 --> 00:23:31,090 +بعدين بروح لل absolute لسه احنا اتكلمنا على النقطة + +216 +00:23:31,090 --> 00:23:36,390 +الأولى بدنا نجل أعلى من إذا ال F prime غيرت شريطها + +217 +00:23:36,390 --> 00:23:40,910 +من positive إلى negative يعني كانت الدالة تزايدية + +218 +00:23:40,910 --> 00:23:47,850 +ثم راجعت أصبحت تناقصية بقى هنا تزايدية هنا تزايدية + +219 +00:23:48,160 --> 00:23:52,720 +هذه الاصطناعات المهمة لكنها ليست لوكال ماكسيممم + +220 +00:23:52,720 --> 00:23:58,360 +ولا حتى لوكال مينيما يبقى بقدر أقول لا إكستريما + +221 +00:23:58,360 --> 00:24:04,140 +ماعنديش في هذه يبقى هذه عند هذه النقطة بقول لا + +222 +00:24:04,140 --> 00:24:07,460 +إكستريما + +223 +00:24:23,260 --> 00:24:27,600 +الدالة كانت تزايدية positive و رجعت negative + +224 +00:24:31,460 --> 00:24:37,200 +local maximum اذا هذه النقطة ال local maximum + +225 +00:24:37,200 --> 00:24:44,860 +بيحصل عندها وعندي f prime of c2 بده يساوي قداش بده + +226 +00:24:44,860 --> 00:24:51,340 +يساوي zero تمام في كمان اه في هي الدالة التزايدية + +227 +00:24:51,340 --> 00:24:55,840 +ورجعت صارت تنقصية كانت positive ورجعت negative + +228 +00:24:55,840 --> 00:25:00,240 +يبقى عند النقطة هذه ايش في عندي local + +229 +00:25:02,020 --> 00:25:08,760 +حسب التعريف النقطة هذه كانت تناقصية وظلت تناقصية + +230 +00:25:08,760 --> 00:25:12,680 +يبقى ماعنديش لا local maximum ولا local minimum + +231 +00:25:12,680 --> 00:25:17,700 +نجي للنقطة التانية إذا f prime ماعيرتش إشارتها عند + +232 +00:25:17,700 --> 00:25:23,280 +c يبقى ماعنديش has no local extrema يعني ماعنديش + +233 +00:25:23,280 --> 00:25:27,960 +لا local maximum ولا local minimum طب إيش رأيك عند + +234 +00:25:27,960 --> 00:25:39,230 +النقطة هذه؟الـ F' of C4 is undefined يبقى ماهياش + +235 +00:25:39,230 --> 00:25:45,410 +معرفة لأن عندي أكاسب هنا طيب إذا النقطة هذه بيقول + +236 +00:25:45,410 --> 00:25:50,690 +إذا F ماغيرتش إشارتها يبقى no local extrema يبقى + +237 +00:25:50,690 --> 00:25:58,170 +هاي no local extrema وهنا كذلك no local extrema + +238 +00:25:59,890 --> 00:26:05,890 +يبقى ماعنديش كذا لك رغم انه f prime of c خمسة بده + +239 +00:26:05,890 --> 00:26:11,030 +يساوي قداش بده يساوي zero يبقى صار local minimum + +240 +00:26:11,030 --> 00:26:16,310 +local minimum local minimum local maximum local + +241 +00:26:16,310 --> 00:26:22,750 +maximum no local extrema no local extrema خلصنا من + +242 +00:26:22,750 --> 00:26:26,230 +قصة ال local واحد سأل قال طيب ال absolute بقوله + +243 +00:26:26,230 --> 00:26:30,890 +بدنا نرجع بالذاكرة إلى section 4-1بتداجي على الـ + +244 +00:26:30,890 --> 00:26:35,510 +Interval كلها من A إلى B أقل قيمة بيقول عنها + +245 +00:26:35,510 --> 00:26:40,830 +Absolute minimum أكبر قيمة Absolute maximum إذا + +246 +00:26:40,830 --> 00:26:47,290 +هذه كمان إيش بيكون Absolute minimum لإيش إن هذه + +247 +00:26:47,290 --> 00:26:53,330 +أقل قيمة؟ هذه هنا كمان ما لها Absolute maximum + +248 +00:26:53,330 --> 00:26:58,860 +لإيش؟ لأن أكبر قيمة موجودة لويا للدالةحد له اي + +249 +00:26:58,860 --> 00:27:03,040 +تساؤل اخر؟ ايوة. الدكتور بالنسبة ليه مثل التعريف + +250 +00:27:03,040 --> 00:27:06,540 +الأول؟ مش هو حاجات اللي نفترانها؟ monotonic + +251 +00:27:06,540 --> 00:27:10,560 +التعريف الأول. لأ هذا اللي مكتوب يعني. هذا اللي + +252 +00:27:10,560 --> 00:27:14,220 +التالي يعني. ايوة، هذا، ايوة. قصد اللي هو ال + +253 +00:27:14,220 --> 00:27:17,940 +support يعني ال .. ال support. طيب انا كنت ريوز + +254 +00:27:17,940 --> 00:27:21,520 +على ال closed و differential على ال open. طب ليش + +255 +00:27:21,520 --> 00:27:25,080 +قال in some terms و لا كنتاني؟مش قولناها يا شباب؟ + +256 +00:27:25,080 --> 00:27:29,500 +قولناها و هنقولها كمان مرة مش أنا خاطر، شو اسمك + +257 +00:27:29,500 --> 00:27:40,370 +أنت؟تبقى ادم زائد اذا كان ادم زائد تبقى ادم + +258 +00:27:40,370 --> 00:27:43,970 +زائد + +259 +00:27:43,970 --> 00:27:47,870 +اذا كان ادم زائد تبقى ادم زائد اذا كان ادم زائد + +260 +00:27:47,870 --> 00:27:48,590 +تبقى ادم زائد اذا كان ادم زائد تبقى ادم زائد اذا + +261 +00:27:48,590 --> 00:27:49,430 +كان ادم زائد تبقى ادم زائد تبقى ادم زائد تبقى ادم + +262 +00:27:49,430 --> 00:27:54,190 +زائد تبقى ادم زائد تبقى ادم زائد تبقى ادم زائد + +263 +00:27:54,190 --> 00:28:01,960 +تبقى ادم زائد تبقى ادم زائد تبقىواضحة هي مكتوبة + +264 +00:28:01,960 --> 00:28:05,600 +مكتوبة انا بدي اياها differentiable على ال open + +265 +00:28:05,600 --> 00:28:10,340 +interval هذه مقعدة عندها C تسيلفي ممكن ما تبقاش + +266 +00:28:10,340 --> 00:28:14,960 +differentiable هي لو جيت حولها differentiable + +267 +00:28:14,960 --> 00:28:19,100 +اتدالى مقعدة من مقعدة عند ال C4 عند ال C4 اتدالى + +268 +00:28:19,100 --> 00:28:23,340 +غير قابل الاشتقال واضحة تمام طيب حاجة ضالة بدي + +269 +00:28:23,340 --> 00:28:28,880 +اسأل تاني طب بنروح الآن لالامثلة + +270 +00:28:33,820 --> 00:28:37,440 +طيب قبل الامثلة شاية الكلام اللي قلته هنا بدي أحطه + +271 +00:28:37,440 --> 00:28:41,740 +لك هنا على الطبيعة السؤال أيه قبله؟ اتطلع ليه هنا + +272 +00:28:41,740 --> 00:28:46,100 +المشتقة كانت نازله بعد هيك اتطلعتيه بيه عند ال + +273 +00:28:46,100 --> 00:28:52,180 +zero إيش بدي أكون؟ الان كانت الصعادة مشتقة أكبر من + +274 +00:28:52,180 --> 00:28:55,520 +zero صارت أقل من ال zero يبقى عند الواحد local + +275 +00:28:55,520 --> 00:29:01,220 +maximum الان عند اتنان مشتقة كانت سالفة صارت موجة + +276 +00:29:01,220 --> 00:29:05,310 +بيبقى local minimum و هكذايبقى هايه على الطبيعة من + +277 +00:29:05,310 --> 00:29:10,390 +خلال المثال أسرع يعني أنا مافضيش أمسحها متعمد حتى + +278 +00:29:10,390 --> 00:29:14,510 +أحاول أربط لك هذه فيها والآن بدنا نعطي أمثلة + +279 +00:29:14,510 --> 00:29:20,270 +مختلفة على الكلام الذي تعرضنا له فضل + +280 +00:29:28,700 --> 00:29:35,440 +مش عنده نقطة هادى، شطة الـ C4 مش معرفة؟ مش معرفة + +281 +00:29:35,440 --> 00:29:40,240 +الـ C4؟ المشتقة مش معرفة، الدالة معرفة، الدالة + +282 +00:29:40,240 --> 00:29:43,780 +متصلة لكن المشتقة غير موجودة عشان هيكون ال local + +283 +00:29:43,780 --> 00:29:49,530 +maximum؟ ال local maximum طبيعي لإنها معرفةالمشتقة + +284 +00:29:49,530 --> 00:29:54,350 +ليه مش معرفة الدالة معرفة يعني الدالة دالة متصلة + +285 +00:29:54,350 --> 00:30:00,550 +لكنها غير قابلة لاشتقاق بسبب وجود التأسباب خلاص؟ + +286 +00:30:00,550 --> 00:30:07,190 +حد بيسأل تاني؟ هذه رسمة + +287 +00:30:07,190 --> 00:30:14,490 +F of X لكن لو أخدت الفترة هذه بلقى ال F Prime أكبر + +288 +00:30:14,490 --> 00:30:18,930 +من Zero عليهالو أخدت الفترة التانية هذه بلاج ال F' + +289 +00:30:19,370 --> 00:30:23,290 +أكبر من ال zero لو أخدت الفترة التالتة بلاج ال F' + +290 +00:30:23,790 --> 00:30:28,230 +أقل من ال zero يعني ليش ان الدالة تناقصية طبق + +291 +00:30:28,230 --> 00:30:33,810 +التعريف اللي احنا جاي ليله طبعا؟ طيب نرجع الآن + +292 +00:30:33,810 --> 00:30:36,150 +ناخد مثال example + +293 +00:30:41,420 --> 00:30:47,140 +for the following functions for the following + +294 +00:30:47,140 --> 00:30:59,360 +functions لكل من الدوالة التالية نمرأة a find find + +295 +00:30:59,360 --> 00:31:06,500 +the intervals of + +296 +00:31:06,500 --> 00:31:17,340 +the intervalsin which the function in which the + +297 +00:31:17,340 --> 00:31:24,660 +function is increasing + +298 +00:31:24,660 --> 00:31:28,180 +and + +299 +00:31:28,180 --> 00:31:35,500 +decreasing بدنا فترات التزايد والتناقص + +300 +00:31:43,000 --> 00:31:53,600 +identify the local extreme values the + +301 +00:31:53,600 --> 00:32:03,220 +local extrema وخلصنا بالاختصار هيكد if any if + +302 +00:32:03,220 --> 00:32:05,680 +any saying + +303 +00:32:09,010 --> 00:32:14,710 +saying where they + +304 +00:32:14,710 --> 00:32:20,910 +occur نمرسي + +305 +00:32:20,910 --> 00:32:31,450 +which if any of + +306 +00:32:31,450 --> 00:32:33,610 +the + +307 +00:32:51,100 --> 00:33:01,800 +F of X يساوي 2X تكييب ناقص 18X + +308 +00:33:36,970 --> 00:33:41,970 +سؤال مرة ثانية نعطي مجموعة من الدوال بدل الدالة + +309 +00:33:41,970 --> 00:33:46,970 +أربعة دوال و لكل دالة من هذه الدوال نحسب تلت شغلات + +310 +00:33:46,970 --> 00:33:52,390 +الشغلة الأولى نجيب فترات التزايد والتناقص لكل دالة + +311 +00:33:52,390 --> 00:33:56,890 +من هذه الدوال الشغلة المطموبة تانية identified a + +312 +00:33:56,890 --> 00:34:03,250 +local extraتحددني النهايات العظمة والصغرة المحلية + +313 +00:34:03,250 --> 00:34:09,750 +لهذه الدوال if any ان وجدت مش موجودة مسامحينك فيها + +314 +00:34:09,750 --> 00:34:13,830 +saying where they occur وين بتحصل هذه يعني بتقولي + +315 +00:34:13,830 --> 00:34:18,610 +نهاية العظمة مثلا كذا عند النقطة الفلانية النهاية + +316 +00:34:18,610 --> 00:34:21,570 +الصغرة كذا عند النقطة الفلانية يعني بنحدد مواضع + +317 +00:34:21,570 --> 00:34:28,070 +نهايات العظمة والصغرةبعد ذلك which if any in if + +318 +00:34:28,070 --> 00:34:32,710 +any يعني إيه النوجبات of the extreme values are + +319 +00:34:32,710 --> 00:34:35,430 +absolute mean من ال extreme values اللي بتبقى + +320 +00:34:35,430 --> 00:34:39,810 +absolute maximum أو absolute minimum يعطيني أول + +321 +00:34:39,810 --> 00:34:45,290 +دالة من هذه الدوالة اللي هو 2x كب نقص 18x قداشة ال + +322 +00:34:45,290 --> 00:34:50,700 +domain تبعها هذهكل real number يبقى أنا بقوله هنا + +323 +00:34:50,700 --> 00:34:57,080 +domain ال F يساوي من سالب infinity ل infinity يعني + +324 +00:34:57,080 --> 00:35:02,720 +ماعنديش end points ال domain كله على طاقم، بقوله + +325 +00:35:02,720 --> 00:35:10,060 +كويسيبقى بدي ابدا بال F prime of X 6X تربيه ناقص + +326 +00:35:10,060 --> 00:35:17,440 +تمانتاش يعني 6 بضل X تربيه ناقص تلاتة يعني 6 في X + +327 +00:35:17,440 --> 00:35:24,210 +ناقص جدر تلاتة في X زائد جدر تلاتةيبقى هذا الشكل + +328 +00:35:24,210 --> 00:35:29,430 +المشتقة بالشكل اللي عندنا هذا روحنا حللنا حللنا + +329 +00:35:29,430 --> 00:35:33,690 +إلى حاصل ضرب قوسين زي ما انت شايف المشتقة + +330 +00:35:33,690 --> 00:35:37,810 +polynomial يبقى ال domain تبعها كمان مين كل ال + +331 +00:35:37,810 --> 00:35:42,810 +real line بالاستثناء تمام يبقى حكاية انا غير معرف + +332 +00:35:42,810 --> 00:35:46,810 +احطها ع شجريبقى ما أقدرش أجيب ال critical points + +333 +00:35:46,810 --> 00:35:51,130 +إلا إذا سويتها بالصفر فقط لا غير ماعنديش غير هيك + +334 +00:35:51,130 --> 00:35:56,090 +يبقى بالي بقوله هذا الكلام يساوي Zero إذا لما + +335 +00:35:56,090 --> 00:36:02,090 +يساوي Zero هذا بده يعطيلك إن X يساوي سالب جذر + +336 +00:36:02,090 --> 00:36:10,990 +تلاتة and ال X بده يساوي جذر تلاتة are the only + +337 +00:36:10,990 --> 00:36:12,850 +critical + +338 +00:36:17,890 --> 00:36:22,330 +يبقى انا جبتله الـ critical بس حتى الآن ماجبتلهش + +339 +00:36:22,330 --> 00:36:27,610 +فترات التزايد والتناقص يبقى بده ياخد إشارة الأقواص + +340 +00:36:27,610 --> 00:36:33,470 +اللي عندنا يبقى بده يروح ويقوله بده ياخد إشارة 6 + +341 +00:36:33,470 --> 00:36:39,790 +في X ناقص جذر 3 ويغيرني الله يعني بتاخد ال zero + +342 +00:36:39,790 --> 00:36:45,270 +تبعها وين؟عن جذر التلاتة، لو جيت بعد جذر التلاتة، + +343 +00:36:45,270 --> 00:36:50,410 +الجثة ده بيكون بعد جذر التلاتة، يعني أكبر من جذر + +344 +00:36:50,410 --> 00:36:59,670 +التلاتة بيكون موجب وقبله بصير سالمالان لو جيت اخدت + +345 +00:36:59,670 --> 00:37:06,650 +اشارة ال X زائد جذر تلاتة بياخد ال zero تبع وين + +346 +00:37:06,650 --> 00:37:15,210 +عند سالب جذر تلاتة بعدها موجب و قبلها سالب الان + +347 +00:37:15,210 --> 00:37:21,940 +انا بدي اشارة حاصل ضرب القوسينX ناقص جدر تلاتة في + +348 +00:37:21,940 --> 00:37:28,700 +ستة في X زائد جدر تلاتة وادى ال real line وبدنا + +349 +00:37:28,700 --> 00:37:35,420 +نيجي نحدد الحدود الإقليمية يبقى انقسم ال domain + +350 +00:37:35,420 --> 00:37:42,280 +إلى ثلاثة مناطقهذه جذرية تلاتة وهنا سالب جذرية + +351 +00:37:42,280 --> 00:37:46,820 +تلاتة الجثين مضربات في بعض ضرب يبقى نضرب الإشارات + +352 +00:37:46,820 --> 00:37:53,380 +ضرب سالب في سالب بموجب سالب في موجب بسالب موجب في + +353 +00:37:53,380 --> 00:37:59,380 +موجب بموجب يبقى هنا الدالة المشتقة موجبة يبقى + +354 +00:37:59,380 --> 00:38:05,240 +الدالة كانتincreasing يبقى تدلع الصعيدة الى اعلى + +355 +00:38:05,240 --> 00:38:10,720 +هنا السالبة يبقى صارت مالها decreasing هنا موجة + +356 +00:38:10,720 --> 00:38:17,780 +بيبقى عادة طلعت الى اعلى اذا المطلوب الاول نمر ايه + +357 +00:38:17,780 --> 00:38:23,580 +بقول ال F is increasing + +358 +00:38:25,440 --> 00:38:30,480 +on الفترة من سالب infinity لأن ال domain كل ال + +359 +00:38:30,480 --> 00:38:36,440 +real line بيلاسق الفترة لأن من سالب infinity لغاية + +360 +00:38:36,440 --> 00:38:45,060 +سالب جذر تلاتة and on كذلك اللي هو جذر تلاتة + +361 +00:38:45,060 --> 00:38:51,180 +closed ومن هنا closed من جذر تلاتة لغاية infinity + +362 +00:38:52,070 --> 00:38:57,710 +يبقى حددنا فترة التزايد ضايلة فترة التناقص يبقى + +363 +00:38:57,710 --> 00:39:06,430 +باجي بقوله ان ال F is decreasing يبقى دالة تناقصية + +364 +00:39:06,430 --> 00:39:13,410 +على الفترة من سالف جذر تلاتة إلى جذر تلاتة بالضبط + +365 +00:39:13,410 --> 00:39:18,990 +تماما خلصنا المطلوب الأول بدنا نيجي لمطلوب التاني + +366 +00:39:18,990 --> 00:39:25,070 +نمر بيههو حدد لي ال local extreme values واضح انه + +367 +00:39:25,070 --> 00:39:30,620 +عندى هنا localتغيرت الإشارة من positive إلى + +368 +00:39:30,620 --> 00:39:35,500 +negative يبقى maximum هنا تغيرت من negative إلى + +369 +00:39:35,500 --> 00:39:43,420 +positive يبقى minimum تمام إذا بدنا نحسب F of سالب + +370 +00:39:43,420 --> 00:39:51,380 +جذر تلاتة ويساوي 2 في سالب جذر تلاتة لكل تكيب سالب + +371 +00:39:51,380 --> 00:39:58,970 +تمانتاشر في سالب جذر تلاتة ويساويهذه بتعطيني اللي + +372 +00:39:58,970 --> 00:40:06,230 +هو السالب ستة جذر تلاتة وهذه بتعطيني تمانتاشر جذر + +373 +00:40:06,230 --> 00:40:13,570 +تلاتة ويساوي اتناشر جذر تلاتة بدنا نحسبله ال F of + +374 +00:40:13,570 --> 00:40:20,330 +جذر تلاتة يبقى هذه بدها تساوي اتنين في جذر تلاتة + +375 +00:40:20,330 --> 00:40:29,890 +لكل تكيب نقص تمانتاشر في جذر تلاتةالجواب يساوي ستة + +376 +00:40:29,890 --> 00:40:36,570 +جذر تلاتة ناقص تمانتاشر جذر تلاتة ويساوي ناقص + +377 +00:40:36,570 --> 00:40:39,210 +اتناشر جذر تلاتة + +378 +00:40:44,240 --> 00:40:55,240 +الـ F has a local maximum 12 جدر تلاتة at x يساوي + +379 +00:40:55,240 --> 00:40:57,280 +سالف جدر تلاتة + +380 +00:41:05,890 --> 00:41:10,830 +الجذر ثلاثة انتهينا من المطلوب الثاني يبقى يا شباب + +381 +00:41:10,830 --> 00:41:15,630 +أنا بكتب هذا اللي بالأحمر بناء على النتاج اللي + +382 +00:41:15,630 --> 00:41:20,130 +عندي مش عند القيمة حسب ما هو في الجدول هنا قلنا + +383 +00:41:20,130 --> 00:41:25,050 +local maximum هنا local minimum وبناء عليه قلت + +384 +00:41:25,050 --> 00:41:29,110 +local maximum عند السالب تلاتة وlocal minimum عند + +385 +00:41:29,110 --> 00:41:35,540 +الجذر تلاتةالمطلوب نمرى c قال which if any of the + +386 +00:41:35,540 --> 00:41:39,920 +extreme values are absolute يبقى انا عندي قيمتين + +387 +00:41:39,920 --> 00:41:45,320 +ممن هم absolute ولا واحدة لأنه ماعنديش end points + +388 +00:41:45,320 --> 00:41:50,020 +interval ماشية لغاية سلب infinity و لغاية موجة ب + +389 +00:41:50,020 --> 00:42:00,320 +infinity يبقى نمرى c ال f has no absolute + +390 +00:42:01,440 --> 00:42:06,540 +extrema because + +391 +00:42:06,540 --> 00:42:17,860 +ال F has no end points او ال domain تبع ال F has + +392 +00:42:17,860 --> 00:42:24,800 +no end points عليك انتهى السؤال نروح ناخد السؤال + +393 +00:42:24,800 --> 00:42:28,960 +الثاني السؤال + +394 +00:42:28,960 --> 00:42:37,310 +الثانيالـ F of X تساوي اللي هو مين؟ X تربيع ناقص + +395 +00:42:37,310 --> 00:42:45,250 +تلاتة على X ناقص اتنين والـ X لا تساوي اتنين + +396 +00:42:58,950 --> 00:43:03,570 +طبعا الدالة غير معرفة عند اتنين لكن الدمين بيصير + +397 +00:43:03,570 --> 00:43:07,630 +من سالب infinity لغاية اتنين و من اتنين ل infinity + +398 +00:43:07,630 --> 00:43:13,770 +يبقى باجي بقوله domain الدالة F من سالب infinity + +399 +00:43:13,770 --> 00:43:21,460 +لغاية اتنين اتحاد اتنين و infinityطب بنجيب ال + +400 +00:43:21,460 --> 00:43:25,940 +interval of increasing and decreasing ممكن اشتق + +401 +00:43:25,940 --> 00:43:29,900 +المقام في مشتقة ال bus لكن في واحد يقولي انا بسش + +402 +00:43:29,900 --> 00:43:34,900 +لأ اسهل من هناك بقولتله كده بقالي بقسم جسمه مطولة + +403 +00:43:34,900 --> 00:43:38,660 +و بعد هيك بروح بشتق بقوله والله كلامك مظهر بقسم + +404 +00:43:38,660 --> 00:43:43,500 +جسمه مطولة ماجتيش اذا درجة ال bus اكبر من او تساوي + +405 +00:43:43,500 --> 00:43:49,790 +درجاتأذا هذه المثالة بقدر أقول x تربيع ناقص تلاتة + +406 +00:43:49,790 --> 00:43:56,630 +بدي أجسمها عمليا على x ناقص اتنين فيها x بx تربيع + +407 +00:43:56,630 --> 00:44:02,250 +ناقص اتنين x زاد بصير ناقص وهذه زاد هذه مع السلامة + +408 +00:44:02,250 --> 00:44:07,810 +بضل اتنين x ناقص تلاتةالباقي من الدرجة الأولى + +409 +00:44:07,810 --> 00:44:12,190 +والمقسم عليه من الدرجة الأولى بنواصل عملية القسمة + +410 +00:44:12,190 --> 00:44:19,690 +يبقى 2x على x فيها جداش 2 2 في x ب2x وناقص هنا + +411 +00:44:19,690 --> 00:44:26,070 +جداشأربعة هذي زاد و هذي زاد هذول مع السلامة بيظل + +412 +00:44:26,070 --> 00:44:30,170 +جداش واحد يبقى خلاص طب الله يعطيك العافية لإن + +413 +00:44:30,170 --> 00:44:33,530 +الباقي من الدرجة الصفرية و المقصوم عليها من الدرجة + +414 +00:44:33,530 --> 00:44:40,560 +الثانية يبقى باجي بقوله ال F of Xيقول اكس تربيه + +415 +00:44:40,560 --> 00:44:46,280 +ناقص تلاتة على اكس ناقص اتنين بدي اكتبها بشكل اخر + +416 +00:44:46,280 --> 00:44:52,200 +اكس زائد اتنين زائد واحد على اكس ناقص اتنين يبقى + +417 +00:44:52,200 --> 00:44:56,800 +هذه اسهلة في الشغل منين من الشكل اللي عندنا هذا + +418 +00:44:56,800 --> 00:45:01,500 +يبقى خلاص باشتغل دوري الحين طبعا هذا شباب ايش كنا + +419 +00:45:01,500 --> 00:45:10,750 +بنسميه ابلاج السمتت وهذا ايش كنا بنسميهأكس يساوى + +420 +00:45:10,750 --> 00:45:14,990 +اتنين، Vertical بس بعد ما تفحصوا، طب فيه + +421 +00:45:14,990 --> 00:45:19,970 +horizontal أسمت؟ لأ لإن ضررية ال bus أعلى من ضررية + +422 +00:45:19,970 --> 00:45:24,210 +المقام ال limit بتعطيني infinity وبالتالي نقبلك، + +423 +00:45:24,210 --> 00:45:28,410 +طب احنا هذا بدنا إيش نرسم اليوم، مش شغلتنا الرسم + +424 +00:45:28,410 --> 00:45:33,400 +اليوم، تمام؟شغلتنا بس بيجي فترات التزايد والتناقص + +425 +00:45:33,400 --> 00:45:40,000 +إذا بدي أجي للنقطة A بدي ال F prime of X مشتاقة + +426 +00:45:40,000 --> 00:45:46,460 +هذه بواحد واتنين مع السلامة وهذه X ناقص اتنين لكل + +427 +00:45:46,460 --> 00:45:56,370 +تربيةبنوحد المقامات يبقى x ناقص اتنين لكل تربية + +428 +00:45:56,370 --> 00:46:04,770 +بيصير x ناقص اتنين لكل تربية ناقص واحد طيب نفك هذا + +429 +00:46:04,770 --> 00:46:11,330 +البص بيصير x تربيةناقص أربعة X زائد أربعة ناقص + +430 +00:46:11,330 --> 00:46:18,210 +واحد على X ناقص اتنين لكل تربية يعني X تربية ناقص + +431 +00:46:18,210 --> 00:46:25,450 +أربعة X زائد تلاتة على X ناقص اتنين لكل تربية هذه + +432 +00:46:25,450 --> 00:46:32,710 +يمكن تحليلها يبقى صار ال F prime of X هو X ناقص + +433 +00:46:32,710 --> 00:46:41,310 +واحدفي x ناقص تلاتة على x ناقص اتنين الكل تربيع + +434 +00:46:43,800 --> 00:46:49,360 +الان باجي بقوله ال X تساوي واحد وال X تساوي تلاتة + +435 +00:46:49,360 --> 00:46:52,820 +هما مين ال critical بس ماقالليش هات ال critical + +436 +00:46:52,820 --> 00:46:56,460 +قاللي هاتلي ال interval إذا مافيش داعي أقلب حالي و + +437 +00:46:56,460 --> 00:46:59,020 +أقول له هذا ال critical لو لأ بدي أشوف إشارات + +438 +00:46:59,020 --> 00:47:04,620 +الأقواص دغري مباشرة تمام؟ إذا باجي بقوله بيداجي + +439 +00:47:04,620 --> 00:47:12,060 +أخد إشارة القوس الأول X ناقص واحدهذا الـ real line + +440 +00:47:12,060 --> 00:47:17,720 +بياخد الـ zero تبعه عند الواحد بعد الواحد positive + +441 +00:47:17,720 --> 00:47:25,980 +و قبل الواحد negative بدا ياخد إشارة اللي هو ال X + +442 +00:47:25,980 --> 00:47:31,940 +ناقص تلاتة هذا الخط اللي عندنا هذا هو بياخد ال + +443 +00:47:31,940 --> 00:47:38,080 +zero تبعه أين؟ عند التلاتة بعد التلاتة موجب و قبله + +444 +00:47:38,080 --> 00:47:45,030 +ما شاء الله negativeبدأ ياخد إشارة ال X ناقص اتنين + +445 +00:47:45,030 --> 00:47:50,370 +لكل تربيع، بعدين بقول له هذا بياخد ال zero تبقى + +446 +00:47:50,370 --> 00:47:58,530 +وين؟ عند اتنين، بعد اتنين موجب و جابلهموجب كمال + +447 +00:47:58,530 --> 00:48:05,690 +انه كمية مربع تمام؟ بعد هيك بدنا إشارة اللي هو X + +448 +00:48:05,690 --> 00:48:11,410 +ناقص واحد في ال X ناقص تلاتة على X ناقص اتنين لكل + +449 +00:48:11,410 --> 00:48:18,450 +تربية وهذا ال line اللي عندنا و جينا نحدد الحدود + +450 +00:48:18,450 --> 00:48:26,870 +الإقليمية فيما بينهما بالشكل اللي عندنا هذاتمام؟ + +451 +00:48:26,870 --> 00:48:34,770 +طيب هي التلاتة وهي اتنين وهي الواحد طلعله هنا كلها + +452 +00:48:34,770 --> 00:48:42,830 +موجب وهنا سالب وهنا سالب وهنا موجب يعني الدالة + +453 +00:48:42,830 --> 00:48:49,710 +كانت increasing صارت decreasing بقيت decreasing + +454 +00:48:49,710 --> 00:48:53,970 +صارت increasing بالشكل اللي لدينا هنا + +455 +00:49:15,640 --> 00:49:24,920 +يبقى باجي بقولله ال F is increasing دلتة زيودية on + +456 +00:49:24,920 --> 00:49:32,320 +الفترة من سالب infinity لغاية الواحد و closed عند + +457 +00:49:32,320 --> 00:49:40,580 +الواحد and on و كذلك من عند التلاتة لغاية infinity + +458 +00:49:41,780 --> 00:49:51,620 +بعدها ال F is decreasing on دالة تناقصية على + +459 +00:49:51,620 --> 00:49:55,960 +الفترة من عند الواحد لغاية اتنين مفتوحة من عند + +460 +00:49:55,960 --> 00:50:01,440 +اتنين ليش ان الدالة غير معرفة عند اتنين اتحاد + +461 +00:50:01,440 --> 00:50:10,000 +اتنين و تلاتة بالشكل اللي عندنا هنا مين + +462 +00:50:10,000 --> 00:50:10,680 +اللي بيحكي + +463 +00:50:30,910 --> 00:50:34,090 +طيب نمر بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر + +464 +00:50:34,090 --> 00:50:37,910 +بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر + +465 +00:50:37,910 --> 00:50:40,630 +بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر + +466 +00:50:40,630 --> 00:50:44,820 +بيه نمر بيه نمر بيه نمر بيه نمر بيههنا فيه لأ هنا + +467 +00:50:44,820 --> 00:50:50,860 +local minimum إذا بدنا نحسبله فقط F of واحد و F of + +468 +00:50:50,860 --> 00:50:58,240 +تلاتة يبقى بادي باخدله F of واحد F of واحد يساوي + +469 +00:50:58,240 --> 00:51:04,180 +هاي واحد تربيع ناقص تلاتة على واحد ناقص اتنين + +470 +00:51:04,180 --> 00:51:08,720 +بيبقى لنا ناقص اتنين على ناقص واحد يساوي اتنين + +471 +00:51:09,070 --> 00:51:16,690 +وبدنا ال F of تلاتة ويسوي تلاتة تربيع ناقص تلاتة + +472 +00:51:16,690 --> 00:51:23,510 +على تلاتة ناقص اتنين يبقى تسعة ناقص تلاتة لهو ستة + +473 +00:51:23,510 --> 00:51:33,830 +على واحد ويسوي ستة يبقى ال F has local maximum + +474 +00:51:35,620 --> 00:51:44,680 +local maximum يتنين at x يساوي واحد and local + +475 +00:51:44,680 --> 00:51:52,340 +minimum ستة at x يساوي تلاتة واحد يقول طب هو ال + +476 +00:51:52,340 --> 00:51:58,300 +minimum ستة و ال maximum بنفع يكون اتنينانا هذه + +477 +00:51:58,300 --> 00:52:03,600 +قيم ليش منحنا ممكن يكون جوس تحت و جوس فوق صحيح انا + +478 +00:52:03,600 --> 00:52:07,520 +بيبقى صارت اللي فوق هذه local maximum و هذه اللي + +479 +00:52:07,520 --> 00:52:12,960 +تحت local minimum بهمناش يبقى انا بكتب نتاج مثل ما + +480 +00:52:12,960 --> 00:52:18,720 +بطلعها ايه تماما نجي لنمرى دى، نمرى دى بيقول مين + +481 +00:52:18,720 --> 00:52:21,360 +من ال local maximum و ال local minimum تبقى + +482 +00:52:21,360 --> 00:52:26,340 +absolute بيقولوا الله تعالى هنا جايين من وين احنا؟ + +483 +00:52:29,660 --> 00:52:32,740 +ماعنديش end point، سواء عندي اتنين الدالة غير + +484 +00:52:32,740 --> 00:52:42,820 +معرفة يبقى باجي بقول ال F has no absolute extrema + +485 +00:52:42,820 --> 00:52:49,380 +because domain + +486 +00:52:51,500 --> 00:53:03,500 +الـ F has no end points ماعنديش طب السؤال التالت + +487 +00:53:03,500 --> 00:53:12,620 +السؤال التالت بيقول F of X يساوي + +488 +00:53:12,620 --> 00:53:20,140 +X أسطل تين فمين في X زائد خمسة + +489 +00:53:24,460 --> 00:53:31,140 +كويس طب إيه إيش رأيك؟ هذه بدل ما هي حاصل ضرب دلت + +490 +00:53:31,140 --> 00:53:38,360 +خلنا نفكها وخلاص يعني هذه بيصير X أس جديش خمسة ع + +491 +00:53:38,360 --> 00:53:48,930 +تلاتة زي خمسة X أس طولتينبدنا ال F prime of X يبقى + +492 +00:53:48,930 --> 00:53:59,530 +يساوي خمس أتلات X أس تلتين زائد عشر أتلات X أساليب + +493 +00:53:59,530 --> 00:54:05,890 +تلتمظبوط هيك؟ طب بدنا نجيب ال critical points او + +494 +00:54:05,890 --> 00:54:10,690 +بدي اكتب هذه الشكلة كويس مشان اقدر احدد الإشارات + +495 +00:54:10,690 --> 00:54:17,030 +بقولوا هذه بسيطة يبقى هذه خمسة على تلاتة X أس + +496 +00:54:17,030 --> 00:54:24,320 +طولتين زائد عشرة على تلاتة X أس طولتينأكس أس سالب + +497 +00:54:24,320 --> 00:54:30,920 +تلت نزلتها تحت صارت مين بالمعجب إذا هذا كله بقدر + +498 +00:54:30,920 --> 00:54:37,440 +أقول تلاتة أكس أس تلت عامل مشترك من الكل على تلاتة + +499 +00:54:37,440 --> 00:54:43,060 +بضلش اللي عندي خمسة أكس أس تلت في أكس أس تلتين بضل + +500 +00:54:43,060 --> 00:54:50,950 +خمسة أكسفقط لغاية تلتين زائد تلت تلاتة ع تلاتة + +501 +00:54:50,950 --> 00:54:59,550 +يعني واحد صحيح وهنا زائد عشرة او خمسة في X زائد + +502 +00:54:59,550 --> 00:55:07,750 +اتنين على تلاتة X قص تلت طب يبقى ال critical + +503 +00:55:07,750 --> 00:55:14,060 +points من و من؟ساوي باتنين ومين؟ و Zero لأن عند ال + +504 +00:55:14,060 --> 00:55:18,780 +Zero المشتقة غير معرفة يبقى لو سويت بال Zero البص + +505 +00:55:18,780 --> 00:55:21,660 +هو بالساوي Zero وبالتالي ال critical point CX ساوي + +506 +00:55:21,660 --> 00:55:28,660 +ساوي باتنين وكذلك X يساوي Zero أيضا ماحطيتش ان هذا + +507 +00:55:28,660 --> 00:55:34,050 +السؤال اللي جابله انا قلت ال A6 local maximumأنا + +508 +00:55:34,050 --> 00:55:39,410 +قلت و حكيتها بس أنت كنت في مجال آخر و بده أعيدها + +509 +00:55:39,410 --> 00:55:44,330 +برضه مش هانخطك، شو اسمك أنت؟ تامر جرادة، احنا في + +510 +00:55:44,330 --> 00:55:48,670 +السؤال السابق و ليس في السؤال هذا طيب، على أي حال، + +511 +00:55:48,670 --> 00:55:53,710 +شوفت الرسمة إيش كانت عندك هنا؟ إيش في عند الواحد؟ + +512 +00:55:53,710 --> 00:56:01,500 +F' غيرت إشرتها من موجة بيها السلبية، إيش عندك؟هنا + +513 +00:56:01,500 --> 00:56:07,580 +لف ويرش من سالب لأ موجة بيبقاش عندك عندك تلاتة + +514 +00:56:07,580 --> 00:56:12,500 +طلعت ستة مظبوط ولا من عشان هذه اتنين و هذه ستة ستة + +515 +00:56:12,500 --> 00:56:17,460 +مستقلة مش جزلك هذا في عندك أبلجز سم تطلع ورا سم + +516 +00:56:17,460 --> 00:56:21,460 +تجوز بتطلع فوقو جوس بيطلع تحت يبقى هذه local + +517 +00:56:21,460 --> 00:56:25,500 +maximum و هذه اللي فوق بيصير local minimum + +518 +00:56:25,500 --> 00:56:30,180 +قاعدناها كمان مرة عليها اللي عند الرسم برضه في ال + +519 +00:56:30,180 --> 00:56:34,280 +section القادم اللي سنبدأه بعد قليل هتشوف شغلات زي + +520 +00:56:34,280 --> 00:56:38,670 +كدهتشوف شغلات عملية نرجع لسؤالنا يا شباب احنا + +521 +00:56:38,670 --> 00:56:42,350 +جيبنا المشتقة الأولى و أصبحت المشتقة الأولى على + +522 +00:56:42,350 --> 00:56:46,850 +الشكل خمسة في X زائد اتنين على تلاتة X أس طول تبقى + +523 +00:56:46,850 --> 00:56:51,130 +ال critical point يسالب اتنين و Zero إذا بتشوف + +524 +00:56:51,130 --> 00:56:57,170 +إشارة كل term من هدين ال termينإذا لو جيت Gulf بدى + +525 +00:56:57,170 --> 00:57:04,210 +أخد إشارة خمسة في X زائد اتنين هذا ال real line + +526 +00:57:04,210 --> 00:57:10,270 +بياخد ال zero تبع وين؟ عند السالب اتنين بعد السالب + +527 +00:57:10,270 --> 00:57:19,050 +اتنين ايش بتكون القيمة؟ و قبله؟طيب بدل ياخد إشارة + +528 +00:57:19,050 --> 00:57:26,050 +اللي هو تلاتة إكسوس طول بياخد ال zero تبع وين؟ عند + +529 +00:57:26,050 --> 00:57:31,710 +ال zero بعد ال zero و قبل ال zero طيب الدمين تبع + +530 +00:57:31,710 --> 00:57:37,560 +ده اللي هد مين؟كل الار بلا استثناء يبقى لا عندي + +531 +00:57:37,560 --> 00:57:43,820 +مشكلة في هذه الحالة إذا بدي إشارة خمسة في إكس زائد + +532 +00:57:43,820 --> 00:57:49,860 +اتنين على تلاتة إكس أس طول و هذا ال real line و + +533 +00:57:49,860 --> 00:57:57,480 +بدي نيجي نحدد الحدود الإقليمية أي سالب اتنين أو أي + +534 +00:57:57,480 --> 00:58:04,780 +زيرو هنا موجب هنا سالب هنا موجبسالب على سالب + +535 +00:58:04,780 --> 00:58:09,340 +بموجب، موجب على سالب بسالب، موجب على موجب بموجب. + +536 +00:58:09,760 --> 00:58:16,640 +يبقى الدالة كانت increasing. إيش صارت؟ decreasing. + +537 +00:58:17,020 --> 00:58:23,320 +إيش رجعت؟ increasing. يبقى يا تمر يا جرادة إيش + +538 +00:58:23,320 --> 00:58:28,910 +رأيك؟ عندي السالب اتنين هنا، إيش فيه؟وعندي zero + +539 +00:58:28,910 --> 00:58:34,710 +بدنا نحسب قيمة ده لو جد ما تطلع تطلع بهمناش طبعا + +540 +00:58:34,710 --> 00:58:40,310 +اذا بدنا نروح نحسب F of سالي باتنين يبقى بدنا نيجي + +541 +00:58:40,310 --> 00:58:45,790 +ناخد F of سالي باتنين يبقى هذا الكلام بده يساوي + +542 +00:58:45,790 --> 00:58:53,400 +سالي باتنين أس تلتين في سالي باتنين زائد خمسةطب + +543 +00:58:53,400 --> 00:58:59,780 +كويس هذا بده يعطينا مين؟ بده يعطينا تلاتة هذا + +544 +00:58:59,780 --> 00:59:05,400 +الجذر التالت لسلب اتنين تربية سلب اتنين تربية + +545 +00:59:05,400 --> 00:59:10,940 +مافقداش، يبقى الجذر التالت لاربعة، يبقى تلاتة + +546 +00:59:10,940 --> 00:59:21,340 +الجذر تلاتة الجذر تالتلأربعة تمام بدنا نيجي نحسب F + +547 +00:59:21,340 --> 00:59:28,480 +of Zero Background Zero يبقى بعدي بقوله ال F has + +548 +00:59:28,480 --> 00:59:37,480 +local maximum تلاتة الجدرى التالت لأربعة X يساوي + +549 +00:59:37,480 --> 00:59:43,100 +سالي باتنين ال F has local minimum Zero + +550 +00:59:46,710 --> 00:59:53,870 +السؤال هو في عندي absolute maximum او minimum؟ لأ + +551 +00:59:53,870 --> 00:59:55,990 +لان ماعنديش end points + +552 +01:00:13,680 --> 01:00:26,240 +طيب نجلع نمسي if has no absolute extrema because + +553 +01:00:26,240 --> 01:00:37,040 +ال domain بتبع ال if has no end points + +554 +01:00:39,260 --> 01:00:45,260 +طيب نيجي هذا السؤال التالت نيجي لهذا السؤال الرابع + +555 +01:00:45,260 --> 01:00:52,060 +والاخير في هذا ال section ايه السؤال؟ طيب مثلا لو + +556 +01:00:52,060 --> 01:00:55,700 +انا افتراض ال minimum او ال maximum ساعدنا هي أفضل + +557 +01:00:55,700 --> 01:01:01,420 +حاجة، كيف؟ لو ايه؟ ال minimum القيمة ال minimum + +558 +01:01:01,420 --> 01:01:04,400 +value أو ال absolute مثلا + +559 +01:01:12,440 --> 01:01:17,400 +مش رايك تصبر شوية بس ناخد المثال الأخير هذا، بس + +560 +01:01:17,400 --> 01:01:20,500 +خليك محتفظ بالسؤال، يمكن نجاوب عليه في السؤال + +561 +01:01:20,500 --> 01:01:29,410 +الأخيرقبل التكمل يالا اكتبلي هذا f of x بده يساوي + +562 +01:01:29,410 --> 01:01:38,490 +اللي هو ال X تكيب ناقص تلاتة X تربيع و سالب + +563 +01:01:38,490 --> 01:01:44,770 +infinity اقل من ال X اقل من او يساوي تلاتة + +564 +01:01:51,740 --> 01:01:59,800 +بنجيب الـ f prime of x يبقى تلاتة x تربيه ناقص ستة + +565 +01:01:59,800 --> 01:02:07,180 +x في عندي عامل مشترك اللي هو قداش تلاتة x بيظل x + +566 +01:02:07,180 --> 01:02:15,700 +ناقص اتنين يبقى ال critical points هي zero و اتنين + +567 +01:02:15,700 --> 01:02:21,930 +فقط لا غير مظبوط يبقى احنا بدنا نبحث الإشاراتيبقى + +568 +01:02:21,930 --> 01:02:30,330 +بد إشارة 3x بقوله بتاخد ال zero تبعه أين؟ عند ال + +569 +01:02:30,330 --> 01:02:35,990 +zero و بعد ال zero؟ موجب و قبل ال zero؟ طب على + +570 +01:02:35,990 --> 01:02:42,140 +إطلاق هو الله محدودةبدي اقضى فعندي التلاتة ممنوع + +571 +01:02:42,140 --> 01:02:47,240 +تتحدى التلاتة تتعدى ماعنديش بعد التلاتة دلها تمام + +572 +01:02:47,240 --> 01:02:52,100 +بجهة دي ليست طبعا بس من عن جهة الشمال على إطلاقها + +573 +01:02:52,100 --> 01:02:55,640 +الله سهل علينا نجلب من سالب infinity لغاية مين + +574 +01:02:55,640 --> 01:03:03,140 +لغاية التلاتة بعد هيك بدي إشارة X ناقص 2 تاخد ال + +575 +01:03:03,140 --> 01:03:10,490 +zero تبعها وين عند 2 بعد 2و تلاتة بدي اوقف و قبل + +576 +01:03:10,490 --> 01:03:16,970 +هي set بالشكل اللي انها ده بعد هيك بدي اشارة تلاتة + +577 +01:03:16,970 --> 01:03:24,410 +x في x ناقص اتنين و بنيجي الى الحدود الاقليمية + +578 +01:03:24,410 --> 01:03:31,950 +يبقى هي zeroهو اي اتنين وهو اي مين تلاتة بعد + +579 +01:03:31,950 --> 01:03:36,550 +التلاتة ماعنديش يبقى هذا الجثيم مضربات في بعض ضرب + +580 +01:03:36,550 --> 01:03:42,770 +يبقى سالب يبقى موجب اتدالة increasing صارت + +581 +01:03:42,770 --> 01:03:48,650 +decreasing رجعت increasing يبقى بقدر اقول ماتي + +582 +01:03:48,650 --> 01:03:58,850 +نمرة ايه ال F is increasing onمن سالب infinity + +583 +01:03:58,850 --> 01:04:07,150 +لغاية من ال zero and on وكذلك من الاتنين لغاية + +584 +01:04:07,150 --> 01:04:07,950 +التلاتة + +585 +01:04:11,680 --> 01:04:20,360 +الآن ال F is decreasing ده لتناقصية على الفترة من + +586 +01:04:20,360 --> 01:04:24,940 +Zero لغاية كده اش لغاية اتنين خلصنا المطلوب الأول + +587 +01:04:24,940 --> 01:04:32,160 +بنالي جه نحسبله ال F of نمرة بي ال F of Zero ال F + +588 +01:04:32,160 --> 01:04:39,120 +of Zero تساوي Zero والتانية ال F of اتنينF of + +589 +01:04:39,120 --> 01:04:46,560 +اتنين يساوي اتنين تكعيب ناقص تلاتة في اتنين ترابيع + +590 +01:04:48,150 --> 01:04:54,550 +تمام؟ طيب هذه بتصير تمانية ناقص اتناشر و يساوي + +591 +01:04:54,550 --> 01:05:03,110 +قداشر؟ ناقص اربع اذا عندي zero في عندي ايش؟ في + +592 +01:05:03,110 --> 01:05:09,430 +عندي zero في local maximum يبقى if has local + +593 +01:05:09,430 --> 01:05:19,510 +maximum0 at x يساوي 0 تمام؟ طب إيش رأيك عند + +594 +01:05:19,510 --> 01:05:28,290 +التلاتة؟ طيب عند التلاتة بدنا نجيبله كمان F of + +595 +01:05:28,290 --> 01:05:34,390 +تلاتة يبقى بصير عندي يساوي تلاتة + +596 +01:05:40,050 --> 01:05:49,440 +تلاتة في تلاتة تكيب ناقص تلاتة في تلاتة تربيعفى + +597 +01:05:49,440 --> 01:05:57,400 +اشتلاتها الصحية يبقى النتيجة كده؟ Zero كذلك يبقى + +598 +01:05:57,400 --> 01:06:01,140 +بعد يبقى يقول الـ F has a local maximum Zero at X + +599 +01:06:01,140 --> 01:06:08,440 +يساوي Zero and ال X يساوي تلاتة يبقى موقعين فيهم + +600 +01:06:08,440 --> 01:06:15,060 +local maximum طيب ال F has local + +601 +01:06:21,070 --> 01:06:30,110 +لوكال مينيمم عندي اتنين سالب اربع ات اكس يسمى + +602 +01:06:30,110 --> 01:06:35,550 +لقداش اتنين يبقى جيبنا ال local maximum يبقى لل + +603 +01:06:35,550 --> 01:06:43,090 +absolute نمرسى في absolute maximum؟ فيه + +604 +01:06:44,640 --> 01:06:51,120 +تلاتة ولا لا؟ لأن هذه الدلجة من تحت increasing + +605 +01:06:51,120 --> 01:06:58,600 +صعدت لغاية zero نزلت عند اتنين لمين لسالب اربعة + +606 +01:06:58,600 --> 01:07:04,540 +تحت رجعت طلعت لمين؟ ايش رايك بال zero هذه بالصير؟ + +607 +01:07:05,680 --> 01:07:11,240 +absolute maximum يبقى عندي موقعين لل absolute + +608 +01:07:11,240 --> 01:07:20,160 +maximum برضه بجي بقول ال F has absolute maximum + +609 +01:07:21,920 --> 01:07:29,900 +أت اكس يساوي زيرو and ال X يساوي تلاتة فيه عندي + +610 +01:07:29,900 --> 01:07:34,620 +absolute minimum لإنه جاي من وين من تحت من سالب + +611 +01:07:34,620 --> 01:07:38,820 +infinity وضله طالع على ال zero نزلت لسالب أربع + +612 +01:07:38,820 --> 01:07:42,880 +ورجع طالع لتلتر يعني عندي absolute maximum ولا + +613 +01:07:42,880 --> 01:07:49,080 +يوجد absolute minimum يبقى ال F has + +614 +01:08:10,240 --> 01:08:17,420 +أجابنا سؤالك؟ و لا لسه؟ وصلت؟ الحمد لله ذلك ما كنا + +615 +01:08:17,420 --> 01:08:17,920 +نبغي + +616 +01:08:46,510 --> 01:08:50,450 +السلام عليكم ورحمة الله وبركاته + +617 +01:08:55,470 --> 01:08:59,330 +بعدها نجي ل exercises أربعة تلاتة هكتب عليك فوق + +618 +01:08:59,330 --> 01:09:07,750 +هنا يبقى exercises أربعة تلاتة المسائل التالية + +619 +01:09:07,750 --> 01:09:13,350 +اللي من واحد لتسعة وتلاتين الأد من واحد لتسعة + +620 +01:09:13,350 --> 01:09:21,500 +وتلاتين الأدو من واحد و أربعين لواحد و خمسين من + +621 +01:09:21,500 --> 01:09:29,260 +واحد و أربعين لواحد و خمسين كمان ال odd و part + +622 +01:09:29,260 --> 01:09:39,660 +part a و b a و b فقط لا غيرو من تلاتة و خمسين + +623 +01:09:39,660 --> 01:09:49,320 +لتسعة و خمسين من تلاتة و خمسين لتسعة و خمسين الاد + +624 +01:09:49,320 --> 01:09:59,220 +part F فقط لغير و من واحد و ستين لسبعين من واحد و + +625 +01:09:59,220 --> 01:10:03,580 +ستين لسبعين كلهم بلا استثناء + +626 +01:10:06,940 --> 01:10:15,120 +طيب ننتقل الان الى ال section اللى يليه وهو + +627 +01:10:15,120 --> 01:10:22,660 +section اربعة اربعة يبقى section اربعة اربعة بتحدث + +628 +01:10:22,660 --> 01:10:33,760 +عن شغلتين ال concavity concavity and ال curve + +629 +01:10:33,760 --> 01:10:35,280 +sketching + +630 +01:10:37,400 --> 01:10:45,260 +الرسم البياني للمنحنيات نعطي تعريف لل Concavity في + +631 +01:10:45,260 --> 01:10:53,240 +الأول وبعد ذلك بروح للباقي The graph of + +632 +01:10:53,240 --> 01:11:04,200 +a differentiable function Y تساوي F of X is + +633 +01:11:06,500 --> 01:11:23,060 +المرة واحد Concave up on an open interval I + +634 +01:11:23,060 --> 01:11:35,980 +if ال F' is increasing on I + +635 +01:11:38,360 --> 01:11:47,100 +نمره اتنين concave down على ال open interval I فال + +636 +01:11:47,100 --> 01:11:56,440 +F' is decreasing on I that + +637 +01:11:56,440 --> 01:12:03,160 +is I N نمره + +638 +01:12:03,160 --> 01:12:13,020 +احد Fالـ F double prime greater than zero on I + +639 +01:12:13,020 --> 01:12:17,400 +then + +640 +01:12:17,400 --> 01:12:37,610 +the graph of Fثم graph of F over I is concave up + +641 +01:12:37,610 --> 01:12:40,670 +نمره + +642 +01:12:40,670 --> 01:12:48,890 +اتنين F ال F double prime اقل من ال zero on I ثم + +643 +01:12:48,890 --> 01:12:55,710 +graph of F is concave + +644 +01:12:55,710 --> 01:12:56,490 +down + +645 +01:13:14,380 --> 01:13:24,560 +if ال F is continuous on an open interval + +646 +01:13:24,560 --> 01:13:28,680 +containing + +647 +01:13:28,680 --> 01:13:31,900 +X + +648 +01:13:31,900 --> 01:13:39,440 +node and if ال F + +649 +01:13:44,090 --> 01:13:51,790 +تتغير الاتجاه من + +650 +01:13:51,790 --> 01:13:54,930 +الهيئة + +651 +01:13:54,930 --> 01:14:03,330 +الهيئة الهيئة الهيئة الهيئة الهيئة + +652 +01:14:03,330 --> 01:14:08,750 +الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة + +653 +01:14:12,330 --> 01:14:26,770 +و F of X0 is called an inflection + +654 +01:14:26,770 --> 01:14:30,610 +point + +655 +01:14:30,610 --> 01:14:34,010 +of F + +656 +01:15:17,390 --> 01:15:20,190 +ماذا بحق الجحيم + +657 +01:15:30,110 --> 01:15:30,750 +يا رجل .. + +658 +01:17:57,300 --> 01:18:01,760 +الجد هو يبقى اتراك فترة يكون من يمين و من اليسار، + +659 +01:18:01,760 --> 01:18:04,840 +اي جد يكون من يمين و من اليسار، لكن يكون closed + +660 +01:18:16,440 --> 01:18:23,340 +هذا المتقبل دالة مجزة صح ولا لأ؟ اه لأ، المتقبل + +661 +01:18:23,340 --> 01:18:27,900 +دالة مجزة إلى جزئين، المتقبل دالة مجزة إلى جزئين، + +662 +01:18:27,900 --> 01:18:33,440 +منقول عن طرفين الفترة الدالة غير معرفة، صحيح ولا + +663 +01:18:33,440 --> 01:18:37,960 +لأ؟ منقول مشتقة، المشتقة غير معرفة، مظبوط؟ من + +664 +01:18:37,960 --> 01:18:42,860 +استبعد الطرفين، لأنه لما أوقف عنده احتمال يكون + +665 +01:18:42,860 --> 01:18:47,100 +كبير فيه discontinuityعن طرفين الفترة احتمالها + +666 +01:18:47,100 --> 01:18:50,980 +تمام وبالتالي انا باستبعد الطرفين حتى ماوجعش في + +667 +01:18:50,980 --> 01:18:57,000 +مشاكل مظبوط اسمه + +668 +01:18:57,000 --> 01:18:57,440 +يا راجل + +669 +01:19:05,870 --> 01:19:10,990 +لو كانت دالة عزيزي polynomial فمعرفة عليها كل real + +670 +01:19:10,990 --> 01:19:14,710 +line دخلت الطرفين و الله قلت الطرفين مش سببش عندي + +671 +01:19:14,710 --> 01:19:19,730 +مشكلة خالص بس لما تبقى دالة مجزلة احتمال المشكلة + +672 +01:19:19,730 --> 01:19:21,790 +تكون موجودة احتمال كبير كمان + +673 +01:19:25,440 --> 01:19:29,400 +أف و فكس يساوي كده؟ أف و فكس يساوي اكس تربيع اكس + +674 +01:19:29,400 --> 01:19:33,780 +تربيع ماشية الله هاي بها ال domain كل ال real line + +675 +01:19:33,780 --> 01:19:37,080 +والله انت حجزت عند الواحد و اتنين عند الواحد و + +676 +01:19:37,080 --> 01:19:39,660 +اتنين عند الواحد و اتنين ممتاز جدا يبقى السارات + +677 +01:19:39,660 --> 01:19:42,620 +تلاتة اكس تربيع تلاتة اكس تربيع يبقى السارة عند + +678 +01:19:42,620 --> 01:19:46,260 +الواحد معرفة و عند اتنين معرفة وبالتالي دخلت في ال + +679 +01:19:46,260 --> 01:19:50,240 +interview والله والله قررتها لا يؤثر عندي بصير + +680 +01:19:50,240 --> 01:19:54,640 +المشتقة معرفة عند الواحد و عند اتنينهذا كله مثلا + +681 +01:19:54,640 --> 01:19:58,720 +ماعنديش مشكلة بس لما تبقى دالة مجزة إلى جزءين بصير + +682 +01:19:58,720 --> 01:20:01,400 +اللي احتمال المشاكل او ثلاثة جزء او اربع تصير + +683 +01:20:01,400 --> 01:20:05,240 +المشاكل عند الأطراف ممكنك لايستبعد الأطراف ورايا + +684 +01:20:05,240 --> 01:20:12,020 +دماغك هذا كل ما في الأمر طب نرجع لسؤالنا هذا ال + +685 +01:20:12,020 --> 01:20:16,180 +section اللي بين ادينا اللي هو section 4 4 con kvt + +686 +01:20:16,180 --> 01:20:24,250 +اللي هو mainالتقاعر او التحدب للمنحنة تمام؟ and ال + +687 +01:20:24,250 --> 01:20:28,550 +curve sketching ورسم المنحنيات يبقى احنا في هذا + +688 +01:20:28,550 --> 01:20:34,190 +section بنستخدم كل ما سبق الدراسة وفي section 4.1 + +689 +01:20:34,190 --> 01:20:41,210 +و4.2 و4.3 في رسم المنحنيات وخاصةلـ critical points + +690 +01:20:41,210 --> 01:20:48,290 +وفترات التزايد والتناقص وكذلك ال local maximum و + +691 +01:20:48,290 --> 01:20:53,490 +ال local minimum يبقى احنا بنستخدم كل ما سبق + +692 +01:20:53,490 --> 01:20:59,450 +دراسته في الرسمبنذهب فقط للأول ونعرف الـ Concavity + +693 +01:20:59,450 --> 01:21:03,950 +لمنحنة كيف بدي أحصل عليه وبعد ذلك نشوف كيف بدنا + +694 +01:21:03,950 --> 01:21:07,150 +نعملها فبعدين بقول graph of a differentiable + +695 +01:21:07,150 --> 01:21:14,200 +function y تساوي f of x isconcave up على فترة I + +696 +01:21:14,200 --> 01:21:19,500 +ولم اقول انها مقفلة او مفتوحة او مفتوحة او مفتوحة + +697 +01:21:19,500 --> 01:21:19,780 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +698 +01:21:19,780 --> 01:21:21,340 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +699 +01:21:21,340 --> 01:21:22,920 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +700 +01:21:22,920 --> 01:21:24,760 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +701 +01:21:24,760 --> 01:21:33,120 +او مفتوحة او مفتوحة او مفتوو بقول لك ده لكن cave + +702 +01:21:33,120 --> 01:21:37,640 +up if ال if increasing بحاجة تضيق المشتقة يبقى + +703 +01:21:37,640 --> 01:21:42,120 +كلامي صح ولا غلط؟ غلط يبقى صح صح وخد بالك من + +704 +01:21:42,120 --> 01:21:47,280 +النقطة هذه إذا المشتقة كانت تزايدية يعني إيش؟ يعني + +705 +01:21:47,280 --> 01:21:51,080 +المشتقة الثانية بتكون أكبر من ال zero صح ولا .. + +706 +01:21:51,080 --> 01:21:55,120 +بقول لك ده لا increasing إذا المشتقة تبعتها كانت + +707 +01:21:55,120 --> 01:21:57,960 +أكبر من ال zero يبقى ال if prime increasing إذا + +708 +01:21:57,960 --> 01:22:02,590 +مشتقتهااللي صارت المشتقة الثانية بتبقى أكبر من مين + +709 +01:22:02,590 --> 01:22:07,150 +من ال zero يبقى الدالة بيقول هيكون curve up + +710 +01:22:07,150 --> 01:22:12,890 +المنحنة مفتوح إلى أعلى إذا كانت ال F prime + +711 +01:22:12,890 --> 01:22:17,410 +increasing إذا كانت الدالة إذا كانت مشتقة هذه + +712 +01:22:17,410 --> 01:22:21,630 +الدالة خلال هذه الفترة كانت المشتقة تزايد مش + +713 +01:22:21,630 --> 01:22:28,220 +الدالة مشتقة الدالة كانت تزايدياconcave down يعني + +714 +01:22:28,220 --> 01:22:34,740 +إلى أسفل إذا كانت المشتقة خلالها decreasing يبقى + +715 +01:22:34,740 --> 01:22:40,920 +إذا كانت مشتقة الدالة تناقصية وليست الدالة مشتقة + +716 +01:22:40,920 --> 01:22:46,180 +الدالة تناقصية طيب بدي أعيد صياغة الكلام اللي قلته + +717 +01:22:46,180 --> 01:22:50,960 +بناحية رياضية ثانيةفبعدين بقول ايه ده اللي بتبقى + +718 +01:22:50,960 --> 01:22:56,140 +cone curve up اذا المشتق الثاني اكبر من مين من ال + +719 +01:22:56,140 --> 01:23:00,380 +zero ما هي هذه الترجمة ان ال F prime increasing صح + +720 +01:23:00,380 --> 01:23:05,200 +ولا لأ مش قبل شوية اخدنا اذا المش F prime اكبر من + +721 +01:23:05,200 --> 01:23:10,030 +ال zero يبقى ال F increasingهنا إذا الـ f double + +722 +01:23:10,030 --> 01:23:14,730 +prime أكبر من 0 يبقى الـ f prime increasing يبقى + +723 +01:23:14,730 --> 01:23:19,710 +أكبر من الـ 0 الـ graph of f over a is concave up + +724 +01:23:19,710 --> 01:23:24,930 +يبقى مفتوح إلى أعلى الآن لو كانت المشتقة الثانية + +725 +01:23:24,930 --> 01:23:29,090 +أقل من الـ 0 على الفترة I يبقى ال graph of it + +726 +01:23:29,090 --> 01:23:35,600 +بديكون ماله concave downالكتاب بيسمي الشرطين هدول + +727 +01:23:35,600 --> 01:23:41,760 +هيك بيسميهم second derivative + +728 +01:23:41,760 --> 01:23:44,820 +test + +729 +01:23:44,820 --> 01:23:49,340 +for concavity + +730 +01:23:53,590 --> 01:23:59,170 +يبقى المشتاقة الثانية لقياس تقار و تحدب المنحنة + +731 +01:23:59,170 --> 01:24:03,910 +لكن ال first derivative تستخدم لمن؟ لتحديد ال + +732 +01:24:03,910 --> 01:24:07,710 +local maximum و ال local من فوق ال local extreme + +733 +01:24:07,710 --> 01:24:13,150 +value أيه الفرق في ما بينهما؟ طيب إذا المنحنة + +734 +01:24:13,150 --> 01:24:19,450 +بالشكل إن هذا طلع إن هذا كنك يابوينهذا concave + +735 +01:24:19,450 --> 01:24:25,810 +وين؟ فعندي النقطة اللي عندنا هذه انتقل من concave + +736 +01:24:25,810 --> 01:24:30,490 +up إلى concave من concave down إلى concave up + +737 +01:24:30,490 --> 01:24:36,710 +النقطة اللي هذه بنسميها نقطة انقلاب للمنحنةيبقى + +738 +01:24:36,710 --> 01:24:40,330 +inflection point يبقى ال inflection point بدي + +739 +01:24:40,330 --> 01:24:46,790 +شرطين لها حتى تتحقق أول شي بدي تبقى دالة متاصلة + +740 +01:24:46,790 --> 01:24:51,550 +عند هذه النقطة الشرط الثاني بدي اتجاه ال concavity + +741 +01:24:51,550 --> 01:24:56,850 +يتغير من down إلى up أو من up إلى down طلع عند + +742 +01:24:56,850 --> 01:25:02,330 +النقطة الثانية هذه كان concave up صار concave down + +743 +01:25:02,590 --> 01:25:06,690 +يبقى بادلة تاني بيقول إذا ال F كانت دالة متاصلة + +744 +01:25:06,690 --> 01:25:12,230 +على ال open interval التي تحتوي على مين؟ على X0 + +745 +01:25:12,230 --> 01:25:17,590 +يبقى أنا عندي في فترة تحتوي على نقطة زي النقطة + +746 +01:25:17,590 --> 01:25:23,510 +هذه، كويس؟ تمام، إيش حصل؟ دالة دالة متاصلةand if + +747 +01:25:23,510 --> 01:25:28,130 +it changes the direction of its concavity under X0 + +748 +01:25:28,130 --> 01:25:33,470 +عند X0 الدالة غيرت اتجاه الconcavity تبعها يبقى في + +749 +01:25:33,470 --> 01:25:36,970 +هذه الحالة بقول النقطة X0 و F of X0 بسميها + +750 +01:25:36,970 --> 01:25:40,870 +inflection point دي ما كان ممكن ماتلاقيش التعريف + +751 +01:25:40,870 --> 01:25:43,750 +تبعي هو اللي منصوص عالي في الكتاب يكون الكتاب + +752 +01:25:43,750 --> 01:25:48,250 +ماتلاقي كتبه من نص آخر لكن هذا أدق نص لايمكن يخر + +753 +01:25:48,250 --> 01:25:52,600 +منه الميه زي ما بقولهيبقى انا عشان يكون عندي + +754 +01:25:52,600 --> 01:25:56,060 +inflection point على المنحنة بدي اتحقق شرطين + +755 +01:25:56,060 --> 01:26:00,320 +الاتصال تبع الدلة عند هذه النقطة اتنين بدي اتغير + +756 +01:26:00,320 --> 01:26:05,040 +اتجاه ال connectivity لهذه الدلة ال inflection + +757 +01:26:05,040 --> 01:26:11,240 +point بتحصل وين؟بتدور عليها وين يعني؟ في مكانين + +758 +01:26:11,240 --> 01:26:14,760 +اللي المشتقة الثاني عنده يساوي zero او المشتقة + +759 +01:26:14,760 --> 01:26:18,460 +الثانية تبقى غير معرفة زي ال local maximum و ال + +760 +01:26:18,460 --> 01:26:23,720 +local minimum بدور عليها وين؟ اذا المشتقة الأولى + +761 +01:26:23,720 --> 01:26:26,860 +صفر او المشتقة الأولى غير معرفة؟ اذا المشتقة + +762 +01:26:26,860 --> 01:26:32,550 +الثانية بدل من المشتقة الأولى طيب السؤال هولو كانت + +763 +01:26:32,550 --> 01:26:37,150 +المشتقة ثانية تساوي zero او المشتقة الثانية ما هي + +764 +01:26:37,150 --> 01:26:45,850 +معروفة يعني ضروري الاقي inflection point لأ لأ ليس + +765 +01:26:45,850 --> 01:26:50,890 +بالضرورة يبقى ليس بالضرورة اذا بتطلع بقى قبل ما + +766 +01:26:50,890 --> 01:26:56,370 +نكمل هنالو جيت الفترة من هنا لهنا الفترة اللي + +767 +01:26:56,370 --> 01:27:01,830 +عندنا هذه مفتوح الى أعلى والله الى أسفل الى أعلى + +768 +01:27:01,830 --> 01:27:07,710 +يبقى هذه المرحلة بقول عليها كن كبط + +769 +01:27:08,580 --> 01:27:15,640 +طيب هذه من هنا لغاية هنا concave down يبقى مفتوح + +770 +01:27:15,640 --> 01:27:24,540 +لها لفترة هذه concave up هذه concave down + +771 +01:27:28,820 --> 01:27:34,660 +هذه النقطة وهذه النقطة وهذه النقطة اكس واحد و اكس + +772 +01:27:34,660 --> 01:27:39,040 +اتنين و اكس تلاتة عندهم في انفليكشن point يبقى هذه + +773 +01:27:44,070 --> 01:27:49,890 +point يبقى هدول نقاط انقلاب للمنحنى مين هما اللي + +774 +01:27:49,890 --> 01:27:56,230 +هي النقطة اللي عندك هذه و النقطة هذه و النقطة هذه + +775 +01:27:56,230 --> 01:28:04,050 +و كذلك النقطة اللي عندك مين النقطة هذه طبعا هذه + +776 +01:28:04,050 --> 01:28:09,770 +بقدرش أتأكد منها لأن ماعنديش منحنى بعدها يبقى هذه + +777 +01:28:09,770 --> 01:28:15,680 +بقدرش أتأكد منها بالضبط الآنإلا إذا خلّيت القوس + +778 +01:28:15,680 --> 01:28:18,780 +ينزل شوية ماشي الحال، لكن أنا بقول هاي كل اللي + +779 +01:28:18,780 --> 01:28:22,420 +بقدر أقوله، هدول واحدة، اتين، اتين، تلاتة متأكد + +780 +01:28:22,420 --> 01:28:25,860 +منهم، هد مش متأكد منها، يبقى بقول عندي النقطة + +781 +01:28:25,860 --> 01:28:30,300 +التلاتة هدول فيها عندي main inflection pointهي + +782 +01:28:30,300 --> 01:28:34,720 +concave up، concave down، concave up، concave down + +783 +01:28:34,720 --> 01:28:38,800 +يبقى هذه الفترة جسمت عليها التقسيمات هذه السؤال هو + +784 +01:28:38,800 --> 01:28:45,340 +لو كانت المشتقة تساوي zero المشتقة الثانية هل من + +785 +01:28:45,340 --> 01:28:50,300 +الضروري يكون في عندي inflection point الإجابة ليس + +786 +01:28:50,300 --> 01:28:56,080 +بالضرورة نعطيك هالملاحظة هذه وبها ننهي المحاضرة + +787 +01:28:56,080 --> 01:28:57,680 +الملاحظة بتقول ما يأتي + +788 +01:29:07,390 --> 01:29:15,890 +إذا yw' تساوي 0 فهو + +789 +01:29:15,890 --> 01:29:20,430 +ليس صحيح + +790 +01:29:22,840 --> 01:29:33,260 +through that must there is + +791 +01:29:33,260 --> 01:29:42,260 +an inflection point + +792 +01:29:42,260 --> 01:29:48,160 +there is an inflection point for example + +793 +01:29:50,680 --> 01:29:57,540 +كشغلة توضيحية على ذلك ال Y تساوي X أُص أربعة لو + +794 +01:29:57,540 --> 01:30:03,580 +بدى تجيب المشتقة الأولى بتعطيك أربعة X تكيب مشتقة + +795 +01:30:03,580 --> 01:30:12,360 +ثانية بتساوي اتناشر X تربيع وهذه تساوي Zero at X + +796 +01:30:12,360 --> 01:30:20,620 +يساوي Zeroلو جينا رسمنا هذه بقول هي المنحنة كويس + +797 +01:30:20,620 --> 01:30:25,960 +يبقى هذا محور X و هذا Y طبعا رسمناها قبل هيك يبقى + +798 +01:30:25,960 --> 01:30:33,780 +المنحنة بدي أجيلك هيك هذا Y تساوي X أُص أربع + +799 +01:30:33,780 --> 01:30:40,220 +المشكلة عن وين عند ال zero الآن قبل ال zero + +800 +01:30:40,220 --> 01:30:46,530 +المنحنة كانت كيف وين؟بعد الـ zero مغيرش يبقى هذه + +801 +01:30:46,530 --> 01:30:52,150 +هذا الجزء مفتوح + +802 +01:30:52,150 --> 01:30:57,850 +الى أعلى و هذا كمان concave up يعني الدالة عند ال + +803 +01:30:57,850 --> 01:31:01,990 +zero صحيح دالة متصلة بس لم تغير اتجاه ال concavity + +804 +01:31:01,990 --> 01:31:08,190 +يبقى وبالتالي ليست inflection point يبقى ساوي zero + +805 +01:31:08,190 --> 01:31:19,830 +butالاكس تساوي زيرو مالها + +806 +01:31:19,830 --> 01:31:25,490 +is + +807 +01:31:25,490 --> 01:31:30,550 +not + +808 +01:31:30,550 --> 01:31:38,370 +an inflection point + +809 +01:31:44,950 --> 01:31:55,090 +لأن الـ wireprime لا يتغير + +810 +01:31:55,090 --> 01:31:56,570 +صورتها + +811 +01:32:06,310 --> 01:32:10,870 +يبقى مفيش handy inflection point وصلنا ل الأمثلة + +812 +01:32:10,870 --> 01:32:14,990 +خلّي الأمثلة للمرة القادمة ان شاء الله + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Xku1FOAUcfU_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Xku1FOAUcfU_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..952a27599aa9ac0f4d523abc81c303c1de42714f --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/Xku1FOAUcfU_raw.srt @@ -0,0 +1,3264 @@ +1 +00:00:20,650 --> 00:00:25,190 +بسم الله الرحمن الرحيم المرة اللى فاتت انتهينا من + +2 +00:00:25,190 --> 00:00:30,550 +section 4.2 اللى هو ال main value theorem والاسئلة + +3 +00:00:30,550 --> 00:00:35,510 +اللى عليها والان بننتقل الى section 4.3 وهو ال + +4 +00:00:35,510 --> 00:00:39,170 +monotonic functions and the first derivative test + +5 +00:00:39,170 --> 00:00:46,250 +يعني الدوال الرتيبة وكذلك اللى هو اختبار المشتقة + +6 +00:00:46,250 --> 00:00:50,770 +الأولىتعريف الـ monotonic function أو الدالة + +7 +00:00:50,770 --> 00:00:55,610 +الرتيبة فبجي بقول الدالة f of x اللى بتبقى تزايدية + +8 +00:00:55,610 --> 00:01:00,990 +أو تناقصية على فترة ما بسميها monotonic function + +9 +00:01:00,990 --> 00:01:05,260 +على تلك الفترةيبقى أنا بدي أحد أمرين، يا إما + +10 +00:01:05,260 --> 00:01:11,340 +تزايدية، يا إما مش الأثنين مع بعض، واحد بس، كاتب + +11 +00:01:11,340 --> 00:01:18,240 +or طلع هي or، هذه أو تلك، يا إما تزايدية على كل + +12 +00:01:18,240 --> 00:01:23,360 +الفترة، يبدأ بقول عليها monotonic أو تناقصية على + +13 +00:01:23,360 --> 00:01:27,510 +كل الفترةبقول عنها monotonic لكن تزاديه وتنقصيه في + +14 +00:01:27,510 --> 00:01:33,070 +نفس الفترة ليست monotonic نعطي مثال توضيح على ذلك + +15 +00:01:33,070 --> 00:01:38,430 +لو خدت الدالة F of X يساوي من X تربية الدالة هذه + +16 +00:01:38,430 --> 00:01:43,470 +معروفة ورسمناها قبل ذلك عدة مرات فلو قلت هذا محور + +17 +00:01:43,470 --> 00:01:51,000 +X وهذا محور Y وجيت رسمت الدالة Y تساوي X تربيةهذا + +18 +00:01:51,000 --> 00:01:56,020 +الـ Zero لو جيت من سالب Infinity لغاية Zero ده + +19 +00:01:56,020 --> 00:02:01,940 +لمالها يجب نزول يبقى Decreasing يبقى على هذا الجزء + +20 +00:02:01,940 --> 00:02:07,660 +ده Decreasing يبقى معناته Monotonic على الفترة من + +21 +00:02:07,660 --> 00:02:13,680 +سالب Infinity لغايةزيرو بعد ذلك الان لو جيت من ال + +22 +00:02:13,680 --> 00:02:19,600 +zero لغاية infinity بلاجي الدالة تزايدية يبقى هنا + +23 +00:02:19,600 --> 00:02:24,440 +increasing يبقى الدالة decreasing على الفترة من + +24 +00:02:24,440 --> 00:02:29,260 +سلب infinity إلى zero و increasing على الفترة من + +25 +00:02:29,260 --> 00:02:34,220 +zero لغاية infinity اذا على الفترة من سلب infinity + +26 +00:02:34,220 --> 00:02:38,280 +إلى zero بقدر اقول عنها monotonic functionعلى + +27 +00:02:38,280 --> 00:02:42,700 +الفترة من 0 إلى infinity بقدر أقول عنها monotonic + +28 +00:02:42,700 --> 00:02:46,480 +function لكن على الفترة كلها من سلب infinity إلى + +29 +00:02:46,480 --> 00:02:51,980 +infinity not monotonic لأن شوية عليها increasing و + +30 +00:02:51,980 --> 00:02:55,060 +شوية decreasing احنا نقول انها increasing على طول + +31 +00:02:55,060 --> 00:03:00,700 +او decreasing على طولالدالة F of X يساوي تربية + +32 +00:03:00,700 --> 00:03:04,980 +مونوتونك من سالب Infinity لغاية Zero وكذلك + +33 +00:03:04,980 --> 00:03:09,000 +مونوتونك على الفترة من Zero إلى Infinity لكنها + +34 +00:03:09,000 --> 00:03:13,340 +ليست مونوتونك على الفترة من وين من سالب Infinity + +35 +00:03:13,340 --> 00:03:17,960 +إلى Infinity يبقى هذا تعريف المونوتونك ب function + +36 +00:03:17,960 --> 00:03:19,380 +ومثال بسيط + +37 +00:03:23,490 --> 00:03:27,090 +نعود لـ Crawler الثلاثة طبعا اللى خدنا المرة اللى + +38 +00:03:27,090 --> 00:03:29,870 +فات نظرية ال mean value theorem و two crawlers + +39 +00:03:29,870 --> 00:03:34,470 +عليها تمام هذه ال crawlery رقم ثلاثة مشان طبق ال + +40 +00:03:34,470 --> 00:03:37,570 +mean value theorem قلنا بدنا دلة تبقى دلة متصلة + +41 +00:03:37,570 --> 00:03:40,910 +على ال closed interval و قبل اشتقاق على ال open + +42 +00:03:40,910 --> 00:03:44,720 +interval a و bمن هنا نجوى للافتراض أن الدالة + +43 +00:03:44,720 --> 00:03:49,680 +فبإستمر على الـClosed Interval وقابلة للاشتقاء على + +44 +00:03:49,680 --> 00:03:53,120 +الفترة المفتوحة أي وبيها الشروط الـMean Value + +45 +00:03:53,120 --> 00:03:59,150 +Theorem، إن حدث ذلك يبقى في هذه الحالةإذا الـ F' + +46 +00:03:59,490 --> 00:04:05,510 +of X أكبر من Zero على كل الفترة بقول الدالة دالة + +47 +00:04:05,510 --> 00:04:09,590 +تزايدية يبقى على كل ال X اللي موجودة في ال + +48 +00:04:09,590 --> 00:04:14,370 +interval A وB يبقى ال F دالة تزايدية على كل closed + +49 +00:04:14,370 --> 00:04:18,870 +interval A وB يعني كأن ال domain تبعهالـ closed + +50 +00:04:18,870 --> 00:04:24,010 +interval او continuous على الفترة المغلقة ا و بيو + +51 +00:04:24,010 --> 00:04:26,370 +differentiable على ال open interval + +52 +00:04:35,010 --> 00:04:39,130 +وإذا كانت f prime أقل من 0 يبقى سالب يبقى الدالة + +53 +00:04:39,130 --> 00:04:43,210 +مالها تناقصي يبقى decreasing function على الفترة + +54 +00:04:43,210 --> 00:04:49,510 +اللي لنا مية a وb يبقى أنا الآن جيب تعريف جديد غير + +55 +00:04:49,510 --> 00:04:52,470 +اللي أخدناه في ال chapter الأول في ال chapter + +56 +00:04:52,470 --> 00:04:55,450 +الأول مش هنجيب الدالة increasing على الفترة اللي + +57 +00:04:55,450 --> 00:05:01,820 +بتاخد two elements عشوائيةإذا كان X1 أقل من X2 إذا + +58 +00:05:01,820 --> 00:05:08,380 +كان X1 أقل من X2 إذا كان + +59 +00:05:08,380 --> 00:05:13,940 +X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل + +60 +00:05:13,940 --> 00:05:15,820 +من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل من X2 + +61 +00:05:15,820 --> 00:05:17,900 +إذا كان X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان + +62 +00:05:17,900 --> 00:05:19,060 +X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل + +63 +00:05:19,060 --> 00:05:19,060 +من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل من X2 + +64 +00:05:19,060 --> 00:05:19,060 +إذا كان X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان + +65 +00:05:19,060 --> 00:05:20,880 +X1 أقل من X2 إذا كان X1 أقل من X2 إذا كان X1 أقل + +66 +00:05:20,880 --> 00:05:26,470 +من X2 إذا كان X1 أقل من X2 إذا كان Xأذا لما جيت + +67 +00:05:26,470 --> 00:05:31,310 +أستخدم المشتقة في هذه الحالة بقول إذا المشتقة موجب + +68 +00:05:31,310 --> 00:05:34,270 +يبقى الدالة تزايدية وإذا المشتقة سلب يبقى يقول + +69 +00:05:34,270 --> 00:05:39,870 +الدالة تناقصية نعطي مثال توضيحي بيقول لو كان f of + +70 +00:05:39,870 --> 00:05:44,570 +x يساوي x plus 4 نقص 4x تكيب زي 4x تربية بدى + +71 +00:05:44,570 --> 00:05:49,030 +شغلتين الشغلة الأولى بدى ال critical points لهذه + +72 +00:05:49,030 --> 00:05:53,970 +الدالة f النقاط الحرجة وبدى فترات التزيد والتناقص + +73 +00:05:53,970 --> 00:06:00,330 +لمينلهذه الدالة يبقى الدالة الأساسية اللى عندنا f + +74 +00:06:00,330 --> 00:06:07,490 +of x يساوي x to the power 4 minus 4x to the power + +75 +00:06:07,490 --> 00:06:14,890 +3 زائد 4x square لو جينا نشتق هذه الدالة يبقى ال f + +76 +00:06:14,890 --> 00:06:21,690 +prime of x يساويأربعة إكس تكييب ناقص اتناشر إكس + +77 +00:06:21,690 --> 00:06:27,270 +تربية زائد تمانية إكس هذه المشتقة تبعتها لكن بدي + +78 +00:06:27,270 --> 00:06:31,870 +أشوف هل بقدر أحللها و لا بقدرش تعالوا نشوف واضح + +79 +00:06:31,870 --> 00:06:36,290 +أنه في عامل مشترك اللي همين أربعة إكس إذا لو جينا + +80 +00:06:36,290 --> 00:06:42,910 +أخدنا أربعة إكس عامل مشترك بيظل عندي إكس تربية + +81 +00:06:42,910 --> 00:06:50,070 +ناقص تلاتة إكسزائد اتنين اللي بين قوسين إذا ممكن + +82 +00:06:50,070 --> 00:06:56,230 +نحلله بنروح نحلله اللي حاصل ضرب قوسين يبقى هاي اكس + +83 +00:06:56,230 --> 00:07:01,010 +هاي اكس هاي واحد هاي اتنين هاي ناقص ناقص تلاتة اكس + +84 +00:07:01,010 --> 00:07:06,210 +يبقى التحليل سليم مائة بالمائةيبقى اشتقانا، من + +85 +00:07:06,210 --> 00:07:10,510 +خلال هذا الاشتقاق بدأ أجيب ال critical points ال + +86 +00:07:10,510 --> 00:07:15,550 +critical points هي قيم X اللي بتخلي المشتقة صفر أو + +87 +00:07:15,550 --> 00:07:21,130 +المشتقة غير معرفة، هذه المشتقة polynomial إذا لا + +88 +00:07:21,130 --> 00:07:25,960 +يمكن أن تكون غير معرفة في يوم من الأيامصحيح؟ إذا + +89 +00:07:25,960 --> 00:07:30,040 +ما بضلش عندي إلا أسويها بالـ 0 وبالتالي أطلع ال + +90 +00:07:30,040 --> 00:07:35,560 +critical points إذا لو جيت سويت هذه بالـ 0 بصير + +91 +00:07:35,560 --> 00:07:43,100 +عندنا ميم ان ال X تسوي 0 و X يسوي 1 و X يسوي 2 + +92 +00:07:43,100 --> 00:07:48,380 +هدول هم من are the critical + +93 +00:07:50,820 --> 00:07:56,420 +يبقى هذه النقاط الحرجة لمين لهذه ال function وهو + +94 +00:07:56,420 --> 00:08:00,740 +المطلوب الأول من المسألة اللي عندنا بعدين جليتلي + +95 +00:08:00,740 --> 00:08:05,560 +فترات التزايد والتناقص مشان أجيب فترات التزايد + +96 +00:08:05,560 --> 00:08:10,460 +والتناقص بدي أروح أدرس إشارة المشتقة اللي عندنا + +97 +00:08:10,460 --> 00:08:14,640 +مشان أدرس إشارة المشتقة بدي أروح أدرس إشارة كل + +98 +00:08:14,640 --> 00:08:19,200 +term من ال termات التلاتةاللي عندنا هذه يبقى بتروح + +99 +00:08:19,200 --> 00:08:25,280 +هاجي اقوله بدي إشارة ال term الأول اللي هو قداش 4x + +100 +00:08:25,280 --> 00:08:31,320 +هذا بياخد الصفر وين عند x السفر قداش؟ Zero بعد ال + +101 +00:08:31,320 --> 00:08:36,090 +zero positiveوالله خلّيها نجيب ال zero اللي هنا + +102 +00:08:36,090 --> 00:08:40,710 +شوية خلّي هذا ال zero هنا و قبل ال zero ماله + +103 +00:08:40,710 --> 00:08:46,710 +negative بعد هيك بدأ أروح أخد إشارة ال terminal x + +104 +00:08:46,710 --> 00:08:52,210 +ناقص واحد بياخد ال zero تبع وين؟ عند ال واحد بعد + +105 +00:08:52,210 --> 00:08:57,310 +ال واحد كذلك positive و قبل ال واحد ماله negative + +106 +00:08:57,790 --> 00:09:03,150 +لو جيت اخد اشارة الجوس التالت لول اكس ناقص اتنين + +107 +00:09:03,150 --> 00:09:08,690 +يبقى بياخد زيرو تبع وين عند اتنين بعد اتنين زي + +108 +00:09:08,690 --> 00:09:13,050 +تلاتة اربعة خمسة بلاقي قيمة القوس بالموجب وقبل + +109 +00:09:13,050 --> 00:09:18,830 +اتنين بلاقي كل قيمة الجوس ماله بالسالب بعدك بداجي + +110 +00:09:18,830 --> 00:09:24,660 +اخد اشارة حصل ضرب اربعة اكسفي اكس ناقص واحد في اكس + +111 +00:09:24,660 --> 00:09:30,220 +ناقص اتنين واجي اقول هذا ال real line واروح احدد + +112 +00:09:30,220 --> 00:09:36,940 +الحدود الإقليمية اللي موجودة عندنا يبقى لو جيت هذا + +113 +00:09:36,940 --> 00:09:42,230 +الخط اللي هو اتنينوهذا الخط الراسي الـ X عنده + +114 +00:09:42,230 --> 00:09:47,530 +بواحد وهذا الخط اللي عندنا الـ X عنده بقداش بزيرو + +115 +00:09:47,530 --> 00:09:52,130 +الثلاثة تقوس مضروبة في بعض يبقى بدي أضرب الإشارات + +116 +00:09:52,130 --> 00:09:59,710 +التلاتة في بعض ضرب يبقى هنا بالموجة هنا سالم هنا + +117 +00:09:59,710 --> 00:10:06,650 +موجة هنا سالميبقى ضغط الإشارات سالب في سالب بموجب + +118 +00:10:06,650 --> 00:10:10,490 +في سالب بسالب موجب في سالب بسالب سالب في سالب + +119 +00:10:10,490 --> 00:10:15,570 +بموجب موجب في موجب بموجب في سالب بسالب كل موجب + +120 +00:10:15,570 --> 00:10:21,570 +يبقى كل موجب، ممتاز، يبقى هذه إشارة مين؟إشارة + +121 +00:10:21,570 --> 00:10:27,050 +المشتقة طلع هنا المشتقة ما لها سالي بيبقى الدالة + +122 +00:10:27,050 --> 00:10:34,010 +كانت decreasing دناقصية يعني الدالة نزلة إلى أسفل + +123 +00:10:34,010 --> 00:10:39,550 +الإشارة صارت موجة بيبقى increasing الدالة صعدة إلى + +124 +00:10:39,550 --> 00:10:44,390 +أعلى سالي بيبقى decreasing إلى أسفل موجة بيبقى + +125 +00:10:44,390 --> 00:10:49,410 +increasing إلى أعلىإذا بقدر أحدد فترات التزايد + +126 +00:10:49,410 --> 00:10:54,650 +والتناقص لمين لدالة العلم هدفه بروح بقول لما ياتي + +127 +00:10:54,650 --> 00:11:02,810 +ال F is increasing دالة تزايدية on على الفترة + +128 +00:11:02,810 --> 00:11:11,650 +الأولى من صفر لغاية واحد وكذلك على الفترة من اندي + +129 +00:11:11,650 --> 00:11:18,650 +اتنين لغاية كدهش infinity بعد ايه؟الـ F is + +130 +00:11:18,650 --> 00:11:25,630 +decreasing دالة تناقصية على الفترة من سالب + +131 +00:11:25,630 --> 00:11:33,430 +infinity لغاية الـ zero and on وعلى الفترة من أند + +132 +00:11:33,430 --> 00:11:39,470 +الواحد لغاية كداش لغاية اتنين يبقى هذا مثال بسيط + +133 +00:11:39,470 --> 00:11:44,460 +حسبنا من خلاله ال critical points لدالة همهوحسبنا + +134 +00:11:44,460 --> 00:11:48,780 +فترات التزايد والتناقص وطبقنا التعريف اللي لنا + +135 +00:11:48,780 --> 00:11:55,660 +تطبيقا مباشرا يعني الدالة على هذه الفترة كانت + +136 +00:11:55,660 --> 00:12:00,860 +مونوتونك على الفترة هذه مونوتونك على الفترة هذه + +137 +00:12:00,860 --> 00:12:04,640 +مونوتونك على الفترة هذه مونوتونك لكن ال domain + +138 +00:12:04,640 --> 00:12:12,850 +تبعها كلها not monotonicننتقل الأن إلى نقطة ثانية + +139 +00:12:12,850 --> 00:12:15,630 +وأخيرة في هذا ال section + +140 +00:12:30,950 --> 00:12:34,330 +النقطة بين حدد ال first derivative test لل local + +141 +00:12:34,330 --> 00:12:43,810 +extreme values يبقى ال first derivative test + +142 +00:12:43,810 --> 00:12:57,150 +for local extrema يعني ال local extreme values + +143 +00:13:02,410 --> 00:13:13,590 +بيقول هذا ما يأتي suppose that افترض انه ال c is a + +144 +00:13:13,590 --> 00:13:24,950 +critical point افترض ان ال c هي نقطة حريجة of a + +145 +00:13:24,950 --> 00:13:26,570 +continuous + +146 +00:13:28,780 --> 00:13:42,280 +فنكشن F لدالة F and ال F is differentiable + +147 +00:13:42,280 --> 00:13:54,920 +دالة قابلة الاشتراك at every point عند كل نقطة in + +148 +00:13:54,920 --> 00:13:56,980 +some + +149 +00:13:59,100 --> 00:14:06,480 +interval in some interval containing + +150 +00:14:06,480 --> 00:14:20,040 +C except possibly except + +151 +00:14:20,040 --> 00:14:24,180 +possibly at C itself + +152 +00:14:30,630 --> 00:14:45,090 +مرة واحد if ال if prime it change from negative + +153 +00:14:45,090 --> 00:14:54,470 +to positive at c then + +154 +00:14:56,470 --> 00:15:08,950 +الـ F لديه مقاومة مقاومة في الـ C نمرة + +155 +00:15:08,950 --> 00:15:15,030 +اتنين F F برايم تتغير من مقاومة مقاومة مقاومة + +156 +00:15:15,030 --> 00:15:24,170 +مقاومة في الـ C فالـ F لديه مقاومة مقاومة مقاومة + +157 +00:15:24,170 --> 00:15:25,550 +في الـ C + +158 +00:15:28,460 --> 00:15:39,960 +نقطة الثالثة والاخيرة F ال F prime does not change + +159 +00:15:39,960 --> 00:15:46,980 +does not change its + +160 +00:15:46,980 --> 00:15:49,200 +sign + +161 +00:15:51,680 --> 00:16:08,920 +at C then ال F has no local extrema at C + +162 +00:16:57,180 --> 00:16:58,760 +السلام عليكم + +163 +00:17:58,290 --> 00:17:59,310 +حسناً + +164 +00:18:41,000 --> 00:18:47,160 +عليه بركلةبنجي نقل ال test derivative test اختبار + +165 +00:18:47,160 --> 00:18:51,340 +المشتقة الأولى لل local extreme values لمواقع + +166 +00:18:51,340 --> 00:18:57,600 +النهايات العظمى والصغرى المحلية بقول يفترض ان C is + +167 +00:18:57,600 --> 00:19:02,960 +a critical point يبقى C هذه النقطة حرجة لدالة من + +168 +00:19:02,960 --> 00:19:08,160 +لدالة متصلة F ونفترض ان الدالة F قابل اشتراء + +169 +00:19:08,160 --> 00:19:17,050 +للاشتقاق عند كل نقطة in someinterval containing z + +170 +00:19:17,050 --> 00:19:21,130 +يبقى ليس بالضرورة على كل ال domain وإنما عالميا + +171 +00:19:21,130 --> 00:19:26,870 +على جزء من ال domain containing z except possibly + +172 +00:19:26,870 --> 00:19:31,690 +at z itself معدى عند z itself إيش يعني معدى z + +173 +00:19:31,690 --> 00:19:36,630 +itself يعني ده لو ممكن تكون غير قابلة للاشتقاق عند + +174 +00:19:36,630 --> 00:19:40,960 +z ممكن تكون قابلة للاشتقاقأو ممكن تكون غير قابلة + +175 +00:19:40,960 --> 00:19:44,740 +لإشتقاء عند الـC لأن الـcritical point هي النقطة + +176 +00:19:44,740 --> 00:19:46,740 +التي في الـprime موجودة أو لا موجودة في الـprime + +177 +00:19:46,740 --> 00:19:52,620 +بس بحيث النقطة تكون موجودة في دميان الدالة يبقى + +178 +00:19:52,620 --> 00:19:56,380 +هذه المقصود ما عدا عند الـC itself يعني عند الـC + +179 +00:19:56,380 --> 00:20:00,480 +itself ممكن الدالة تكون غير قابلة للإشتقاء ابن + +180 +00:20:00,480 --> 00:20:06,000 +جلان إذا والله المشتقة الأولى غيرت إشارتها من سالب + +181 +00:20:06,000 --> 00:20:11,930 +إلى موجبمن negative إلى positive عند النقطة C يبقى + +182 +00:20:11,930 --> 00:20:16,690 +ال F has a local minimum تعالى نشوف هذا على + +183 +00:20:16,690 --> 00:20:20,090 +الطبيعة قبل ما نتقل إلى النقطة الثانية الدالة + +184 +00:20:20,090 --> 00:20:24,450 +بتغير إشارتها من negative إلى positive بعدين بتطلع + +185 +00:20:24,450 --> 00:20:29,710 +على الدالة الدالة هنا تزايدية بلت هنا كما المالها + +186 +00:20:29,710 --> 00:20:36,370 +تزايدية ماتغيرتشيبقى هنا في هذه المنطقة F أكبر من + +187 +00:20:36,370 --> 00:20:42,850 +الـ 0 و هنا F أكبر من الـ 0 لو جيت على المنطقة من + +188 +00:20:42,850 --> 00:20:50,330 +هنا لغاية هنا يبقى F أقل من الـ 0يبقى هنا ال F' + +189 +00:20:51,130 --> 00:20:56,730 +أقل من ال 0 لو جيت على المنطقة هذه بلاقي أن F' + +190 +00:20:57,350 --> 00:21:02,450 +أكبر من ال 0 لو جيت على المنطقة هذه بلاقي F' أقل + +191 +00:21:02,450 --> 00:21:07,510 +من ال 0 لأنه تناقصية لو جيت على الجزء من هنا لهنا + +192 +00:21:07,510 --> 00:21:13,570 +كمان F' مالها أقل من ال 0 إيش بقوله هنا إذا F' + +193 +00:21:13,970 --> 00:21:18,800 +غيرت شرطها من negative إلى positiveكانت دالة + +194 +00:21:18,800 --> 00:21:25,660 +تناقصية و رجعة الطلاقة التزاودية Local Minimum + +195 +00:21:25,660 --> 00:21:32,260 +يبقى Local Minimum عند الـ C يبقى عندنا Local + +196 +00:21:32,260 --> 00:21:40,360 +Minimum في هذه الحالة الـ F' of C تلاتة بده يساوي + +197 +00:21:40,360 --> 00:21:46,330 +مين؟ بده يساوي Zero في عندي غيرها Local Minimum؟من + +198 +00:21:46,330 --> 00:21:52,150 +خلال الرسم في local minimum اللي هي مين هذه النقطة + +199 +00:21:52,150 --> 00:21:58,450 +يبقى هنا هذه كمان local minimum بس مافيش تغيير + +200 +00:21:58,450 --> 00:22:04,930 +عندها تمام؟ يبقى رغم أنها نقطة بداية من البداية + +201 +00:22:04,930 --> 00:22:11,550 +يبقى هذه local minimum اتا كويس؟ لكن هذه ليست نقطة + +202 +00:22:11,550 --> 00:22:14,990 +موجودة في الداخل انت تقول غيرت إشرتها من كذا إلى + +203 +00:22:14,990 --> 00:22:19,570 +كذايبقى لو كانت نقطة في الداخل وتغيرت من سالب إلى + +204 +00:22:19,570 --> 00:22:23,790 +موجة بقول هنا local minimum هذه local minimum ليش؟ + +205 +00:22:23,790 --> 00:22:29,550 +لأنها أقل قيمة بتاخدها للدالة من عند أول نقطة + +206 +00:22:29,550 --> 00:22:35,310 +لغاية مين لو جيت قلت هذه افترض ان هذه أول نقطة في + +207 +00:22:35,310 --> 00:22:41,420 +ال interval A وهذه أخر نقطة في ال interval Bلو جيت + +208 +00:22:41,420 --> 00:22:45,880 +حوالين الـA لقيت هذه أقل قيمة لدى اللي يبقى هذه + +209 +00:22:45,880 --> 00:22:49,180 +الـlocal minimum من أول section أخدناه اللي هو + +210 +00:22:49,180 --> 00:22:54,820 +section 4-1 طيب في عندي كمان local minimum تاني + +211 +00:22:54,820 --> 00:23:02,940 +ماعنديش لكن هذه هو كمان local minimum بس إيش هذه + +212 +00:23:02,940 --> 00:23:07,420 +نقطة طرفية in point تمام؟ أيوة + +213 +00:23:10,080 --> 00:23:14,880 +لا local minimum ولا local maximum، لا بقدرش ولا + +214 +00:23:14,880 --> 00:23:18,960 +حاجة، ايوة نقدر من هذا الاتباه نعرف اي واحدة هي ال + +215 +00:23:18,960 --> 00:23:22,220 +absolute و ال local minimum؟ هنجي لل absolute، بس + +216 +00:23:22,220 --> 00:23:27,170 +استغلني شوية، هنقول، نشير إليهاطيب بس خلص ال local + +217 +00:23:27,170 --> 00:23:31,090 +بعدين بروح لل absolute لسه احنا اتكلمنا على النقطة + +218 +00:23:31,090 --> 00:23:36,390 +الأولى بدنا نجل أعلى من إذا ال F prime غيرت شريطها + +219 +00:23:36,390 --> 00:23:40,910 +من positive إلى negative يعني كانت الدالة تزايدية + +220 +00:23:40,910 --> 00:23:47,850 +ثم راجعت أصبحت تناقصية بقى هنا تزايدية هنا تزايدية + +221 +00:23:48,160 --> 00:23:52,720 +هذه الاصطناعات المهمة لكنها ليست لوكال ماكسيممم + +222 +00:23:52,720 --> 00:23:58,360 +ولا حتى لوكال مينيما يبقى بقدر أقول لا إكستريما + +223 +00:23:58,360 --> 00:24:04,140 +ماعنديش في هذه يبقى هذه عند هذه النقطة بقول لا + +224 +00:24:04,140 --> 00:24:07,460 +إكستريما + +225 +00:24:23,260 --> 00:24:27,600 +الدالة كانت تزايدية positive و رجعت negative + +226 +00:24:31,460 --> 00:24:37,200 +local maximum اذا هذه النقطة ال local maximum + +227 +00:24:37,200 --> 00:24:44,860 +بيحصل عندها وعندي f prime of c2 بده يساوي قداش بده + +228 +00:24:44,860 --> 00:24:51,340 +يساوي zero تمام في كمان اه في هي الدالة التزايدية + +229 +00:24:51,340 --> 00:24:55,840 +ورجعت صارت تنقصية كانت positive ورجعت negative + +230 +00:24:55,840 --> 00:25:00,240 +يبقى عند النقطة هذه ايش في عندي local + +231 +00:25:02,020 --> 00:25:08,760 +حسب التعريف النقطة هذه كانت تناقصية وظلت تناقصية + +232 +00:25:08,760 --> 00:25:12,680 +يبقى ماعنديش لا local maximum ولا local minimum + +233 +00:25:12,680 --> 00:25:17,700 +نجي للنقطة التانية إذا f prime ماعيرتش إشارتها عند + +234 +00:25:17,700 --> 00:25:23,280 +c يبقى ماعنديش has no local extrema يعني ماعنديش + +235 +00:25:23,280 --> 00:25:27,960 +لا local maximum ولا local minimum طب إيش رأيك عند + +236 +00:25:27,960 --> 00:25:39,230 +النقطة هذه؟الـ F' of C4 is undefined يبقى ماهياش + +237 +00:25:39,230 --> 00:25:45,410 +معرفة لأن عندي أكاسب هنا طيب إذا النقطة هذه بيقول + +238 +00:25:45,410 --> 00:25:50,690 +إذا F ماغيرتش إشارتها يبقى no local extrema يبقى + +239 +00:25:50,690 --> 00:25:58,170 +هاي no local extrema وهنا كذلك no local extrema + +240 +00:25:59,890 --> 00:26:05,890 +يبقى ماعنديش كذا لك رغم انه f prime of c خمسة بده + +241 +00:26:05,890 --> 00:26:11,030 +يساوي قداش بده يساوي zero يبقى صار local minimum + +242 +00:26:11,030 --> 00:26:16,310 +local minimum local minimum local maximum local + +243 +00:26:16,310 --> 00:26:22,750 +maximum no local extrema no local extrema خلصنا من + +244 +00:26:22,750 --> 00:26:26,230 +قصة ال local واحد سأل قال طيب ال absolute بقوله + +245 +00:26:26,230 --> 00:26:30,890 +بدنا نرجع بالذاكرة إلى section 4-1بتداجي على الـ + +246 +00:26:30,890 --> 00:26:35,510 +Interval كلها من A إلى B أقل قيمة بيقول عنها + +247 +00:26:35,510 --> 00:26:40,830 +Absolute minimum أكبر قيمة Absolute maximum إذا + +248 +00:26:40,830 --> 00:26:47,290 +هذه كمان إيش بيكون Absolute minimum لإيش إن هذه + +249 +00:26:47,290 --> 00:26:53,330 +أقل قيمة؟ هذه هنا كمان ما لها Absolute maximum + +250 +00:26:53,330 --> 00:26:58,860 +لإيش؟ لأن أكبر قيمة موجودة لويا للدالةحد له اي + +251 +00:26:58,860 --> 00:27:03,040 +تساؤل اخر؟ ايوة. الدكتور بالنسبة ليه مثل التعريف + +252 +00:27:03,040 --> 00:27:06,540 +الأول؟ مش هو حاجات اللي نفترانها؟ monotonic + +253 +00:27:06,540 --> 00:27:10,560 +التعريف الأول. لأ هذا اللي مكتوب يعني. هذا اللي + +254 +00:27:10,560 --> 00:27:14,220 +التالي يعني. ايوة، هذا، ايوة. قصد اللي هو ال + +255 +00:27:14,220 --> 00:27:17,940 +support يعني ال .. ال support. طيب انا كنت ريوز + +256 +00:27:17,940 --> 00:27:21,520 +على ال closed و differential على ال open. طب ليش + +257 +00:27:21,520 --> 00:27:25,080 +قال in some terms و لا كنتاني؟مش قولناها يا شباب؟ + +258 +00:27:25,080 --> 00:27:29,500 +قولناها و هنقولها كمان مرة مش أنا خاطر، شو اسمك + +259 +00:27:29,500 --> 00:27:40,370 +أنت؟تبقى ادم زائد اذا كان ادم زائد تبقى ادم + +260 +00:27:40,370 --> 00:27:43,970 +زائد + +261 +00:27:43,970 --> 00:27:47,870 +اذا كان ادم زائد تبقى ادم زائد اذا كان ادم زائد + +262 +00:27:47,870 --> 00:27:48,590 +تبقى ادم زائد اذا كان ادم زائد تبقى ادم زائد اذا + +263 +00:27:48,590 --> 00:27:49,430 +كان ادم زائد تبقى ادم زائد تبقى ادم زائد تبقى ادم + +264 +00:27:49,430 --> 00:27:49,430 +زائد تبقى ادم زائد تبقى ادم زائد تبقى ادم زائد + +265 +00:27:49,430 --> 00:27:49,430 +تبقى ادم زائد تبقى ادم زائد تبقى ادم زائد تبقى ادم + +266 +00:27:49,430 --> 00:27:54,190 +زائد تبقى ادم زائد تبقى ادم زائد تبقى ادم زائد + +267 +00:27:54,190 --> 00:28:01,960 +تبقى ادم زائد تبقى ادم زائد تبقىواضحة هي مكتوبة + +268 +00:28:01,960 --> 00:28:05,600 +مكتوبة انا بدي اياها differentiable على ال open + +269 +00:28:05,600 --> 00:28:10,340 +interval هذه مقعدة عندها C تسيلفي ممكن ما تبقاش + +270 +00:28:10,340 --> 00:28:14,960 +differentiable هي لو جيت حولها differentiable + +271 +00:28:14,960 --> 00:28:19,100 +اتدالى مقعدة من مقعدة عند ال C4 عند ال C4 اتدالى + +272 +00:28:19,100 --> 00:28:23,340 +غير قابل الاشتقال واضحة تمام طيب حاجة ضالة بدي + +273 +00:28:23,340 --> 00:28:28,880 +اسأل تاني طب بنروح الآن لالامثلة + +274 +00:28:33,820 --> 00:28:37,440 +طيب قبل الامثلة شاية الكلام اللي قلته هنا بدي أحطه + +275 +00:28:37,440 --> 00:28:41,740 +لك هنا على الطبيعة السؤال أيه قبله؟ اتطلع ليه هنا + +276 +00:28:41,740 --> 00:28:46,100 +المشتقة كانت نازله بعد هيك اتطلعتيه بيه عند ال + +277 +00:28:46,100 --> 00:28:52,180 +zero إيش بدي أكون؟ الان كانت الصعادة مشتقة أكبر من + +278 +00:28:52,180 --> 00:28:55,520 +zero صارت أقل من ال zero يبقى عند الواحد local + +279 +00:28:55,520 --> 00:29:01,220 +maximum الان عند اتنان مشتقة كانت سالفة صارت موجة + +280 +00:29:01,220 --> 00:29:05,310 +بيبقى local minimum و هكذايبقى هايه على الطبيعة من + +281 +00:29:05,310 --> 00:29:10,390 +خلال المثال أسرع يعني أنا مافضيش أمسحها متعمد حتى + +282 +00:29:10,390 --> 00:29:14,510 +أحاول أربط لك هذه فيها والآن بدنا نعطي أمثلة + +283 +00:29:14,510 --> 00:29:20,270 +مختلفة على الكلام الذي تعرضنا له فضل + +284 +00:29:28,700 --> 00:29:35,440 +مش عنده نقطة هادى، شطة الـ C4 مش معرفة؟ مش معرفة + +285 +00:29:35,440 --> 00:29:40,240 +الـ C4؟ المشتقة مش معرفة، الدالة معرفة، الدالة + +286 +00:29:40,240 --> 00:29:43,780 +متصلة لكن المشتقة غير موجودة عشان هيكون ال local + +287 +00:29:43,780 --> 00:29:49,530 +maximum؟ ال local maximum طبيعي لإنها معرفةالمشتقة + +288 +00:29:49,530 --> 00:29:54,350 +ليه مش معرفة الدالة معرفة يعني الدالة دالة متصلة + +289 +00:29:54,350 --> 00:30:00,550 +لكنها غير قابلة لاشتقاق بسبب وجود التأسباب خلاص؟ + +290 +00:30:00,550 --> 00:30:07,190 +حد بيسأل تاني؟ هذه رسمة + +291 +00:30:07,190 --> 00:30:14,490 +F of X لكن لو أخدت الفترة هذه بلقى ال F Prime أكبر + +292 +00:30:14,490 --> 00:30:18,930 +من Zero عليهالو أخدت الفترة التانية هذه بلاج ال F' + +293 +00:30:19,370 --> 00:30:23,290 +أكبر من ال zero لو أخدت الفترة التالتة بلاج ال F' + +294 +00:30:23,790 --> 00:30:28,230 +أقل من ال zero يعني ليش ان الدالة تناقصية طبق + +295 +00:30:28,230 --> 00:30:33,810 +التعريف اللي احنا جاي ليله طبعا؟ طيب نرجع الآن + +296 +00:30:33,810 --> 00:30:36,150 +ناخد مثال example + +297 +00:30:41,420 --> 00:30:47,140 +for the following functions for the following + +298 +00:30:47,140 --> 00:30:59,360 +functions لكل من الدوالة التالية نمرأة a find find + +299 +00:30:59,360 --> 00:31:06,500 +the intervals of + +300 +00:31:06,500 --> 00:31:17,340 +the intervalsin which the function in which the + +301 +00:31:17,340 --> 00:31:24,660 +function is increasing + +302 +00:31:24,660 --> 00:31:28,180 +and + +303 +00:31:28,180 --> 00:31:35,500 +decreasing بدنا فترات التزايد والتناقص + +304 +00:31:43,000 --> 00:31:53,600 +identify the local extreme values the + +305 +00:31:53,600 --> 00:32:03,220 +local extrema وخلصنا بالاختصار هيكد if any if + +306 +00:32:03,220 --> 00:32:05,680 +any saying + +307 +00:32:09,010 --> 00:32:14,710 +saying where they + +308 +00:32:14,710 --> 00:32:20,910 +occur نمرسي + +309 +00:32:20,910 --> 00:32:31,450 +which if any of + +310 +00:32:31,450 --> 00:32:33,610 +the + +311 +00:32:51,100 --> 00:33:01,800 +F of X يساوي 2X تكييب ناقص 18X + +312 +00:33:36,970 --> 00:33:41,970 +سؤال مرة ثانية نعطي مجموعة من الدوال بدل الدالة + +313 +00:33:41,970 --> 00:33:46,970 +أربعة دوال و لكل دالة من هذه الدوال نحسب تلت شغلات + +314 +00:33:46,970 --> 00:33:52,390 +الشغلة الأولى نجيب فترات التزايد والتناقص لكل دالة + +315 +00:33:52,390 --> 00:33:56,890 +من هذه الدوال الشغلة المطموبة تانية identified a + +316 +00:33:56,890 --> 00:34:03,250 +local extraتحددني النهايات العظمة والصغرة المحلية + +317 +00:34:03,250 --> 00:34:09,750 +لهذه الدوال if any ان وجدت مش موجودة مسامحينك فيها + +318 +00:34:09,750 --> 00:34:13,830 +saying where they occur وين بتحصل هذه يعني بتقولي + +319 +00:34:13,830 --> 00:34:18,610 +نهاية العظمة مثلا كذا عند النقطة الفلانية النهاية + +320 +00:34:18,610 --> 00:34:21,570 +الصغرة كذا عند النقطة الفلانية يعني بنحدد مواضع + +321 +00:34:21,570 --> 00:34:28,070 +نهايات العظمة والصغرةبعد ذلك which if any in if + +322 +00:34:28,070 --> 00:34:32,710 +any يعني إيه النوجبات of the extreme values are + +323 +00:34:32,710 --> 00:34:35,430 +absolute mean من ال extreme values اللي بتبقى + +324 +00:34:35,430 --> 00:34:39,810 +absolute maximum أو absolute minimum يعطيني أول + +325 +00:34:39,810 --> 00:34:45,290 +دالة من هذه الدوالة اللي هو 2x كب نقص 18x قداشة ال + +326 +00:34:45,290 --> 00:34:50,700 +domain تبعها هذهكل real number يبقى أنا بقوله هنا + +327 +00:34:50,700 --> 00:34:57,080 +domain ال F يساوي من سالب infinity ل infinity يعني + +328 +00:34:57,080 --> 00:35:02,720 +ماعنديش end points ال domain كله على طاقم، بقوله + +329 +00:35:02,720 --> 00:35:10,060 +كويسيبقى بدي ابدا بال F prime of X 6X تربيه ناقص + +330 +00:35:10,060 --> 00:35:17,440 +تمانتاش يعني 6 بضل X تربيه ناقص تلاتة يعني 6 في X + +331 +00:35:17,440 --> 00:35:24,210 +ناقص جدر تلاتة في X زائد جدر تلاتةيبقى هذا الشكل + +332 +00:35:24,210 --> 00:35:29,430 +المشتقة بالشكل اللي عندنا هذا روحنا حللنا حللنا + +333 +00:35:29,430 --> 00:35:33,690 +إلى حاصل ضرب قوسين زي ما انت شايف المشتقة + +334 +00:35:33,690 --> 00:35:37,810 +polynomial يبقى ال domain تبعها كمان مين كل ال + +335 +00:35:37,810 --> 00:35:42,810 +real line بالاستثناء تمام يبقى حكاية انا غير معرف + +336 +00:35:42,810 --> 00:35:46,810 +احطها ع شجريبقى ما أقدرش أجيب ال critical points + +337 +00:35:46,810 --> 00:35:51,130 +إلا إذا سويتها بالصفر فقط لا غير ماعنديش غير هيك + +338 +00:35:51,130 --> 00:35:56,090 +يبقى بالي بقوله هذا الكلام يساوي Zero إذا لما + +339 +00:35:56,090 --> 00:36:02,090 +يساوي Zero هذا بده يعطيلك إن X يساوي سالب جذر + +340 +00:36:02,090 --> 00:36:10,990 +تلاتة and ال X بده يساوي جذر تلاتة are the only + +341 +00:36:10,990 --> 00:36:12,850 +critical + +342 +00:36:17,890 --> 00:36:22,330 +يبقى انا جبتله الـ critical بس حتى الآن ماجبتلهش + +343 +00:36:22,330 --> 00:36:27,610 +فترات التزايد والتناقص يبقى بده ياخد إشارة الأقواص + +344 +00:36:27,610 --> 00:36:33,470 +اللي عندنا يبقى بده يروح ويقوله بده ياخد إشارة 6 + +345 +00:36:33,470 --> 00:36:39,790 +في X ناقص جذر 3 ويغيرني الله يعني بتاخد ال zero + +346 +00:36:39,790 --> 00:36:45,270 +تبعها وين؟عن جذر التلاتة، لو جيت بعد جذر التلاتة، + +347 +00:36:45,270 --> 00:36:50,410 +الجثة ده بيكون بعد جذر التلاتة، يعني أكبر من جذر + +348 +00:36:50,410 --> 00:36:59,670 +التلاتة بيكون موجب وقبله بصير سالمالان لو جيت اخدت + +349 +00:36:59,670 --> 00:37:06,650 +اشارة ال X زائد جذر تلاتة بياخد ال zero تبع وين + +350 +00:37:06,650 --> 00:37:15,210 +عند سالب جذر تلاتة بعدها موجب و قبلها سالب الان + +351 +00:37:15,210 --> 00:37:21,940 +انا بدي اشارة حاصل ضرب القوسينX ناقص جدر تلاتة في + +352 +00:37:21,940 --> 00:37:28,700 +ستة في X زائد جدر تلاتة وادى ال real line وبدنا + +353 +00:37:28,700 --> 00:37:35,420 +نيجي نحدد الحدود الإقليمية يبقى انقسم ال domain + +354 +00:37:35,420 --> 00:37:42,280 +إلى ثلاثة مناطقهذه جذرية تلاتة وهنا سالب جذرية + +355 +00:37:42,280 --> 00:37:46,820 +تلاتة الجثين مضربات في بعض ضرب يبقى نضرب الإشارات + +356 +00:37:46,820 --> 00:37:53,380 +ضرب سالب في سالب بموجب سالب في موجب بسالب موجب في + +357 +00:37:53,380 --> 00:37:59,380 +موجب بموجب يبقى هنا الدالة المشتقة موجبة يبقى + +358 +00:37:59,380 --> 00:38:05,240 +الدالة كانتincreasing يبقى تدلع الصعيدة الى اعلى + +359 +00:38:05,240 --> 00:38:10,720 +هنا السالبة يبقى صارت مالها decreasing هنا موجة + +360 +00:38:10,720 --> 00:38:17,780 +بيبقى عادة طلعت الى اعلى اذا المطلوب الاول نمر ايه + +361 +00:38:17,780 --> 00:38:23,580 +بقول ال F is increasing + +362 +00:38:25,440 --> 00:38:30,480 +on الفترة من سالب infinity لأن ال domain كل ال + +363 +00:38:30,480 --> 00:38:36,440 +real line بيلاسق الفترة لأن من سالب infinity لغاية + +364 +00:38:36,440 --> 00:38:45,060 +سالب جذر تلاتة and on كذلك اللي هو جذر تلاتة + +365 +00:38:45,060 --> 00:38:51,180 +closed ومن هنا closed من جذر تلاتة لغاية infinity + +366 +00:38:52,070 --> 00:38:57,710 +يبقى حددنا فترة التزايد ضايلة فترة التناقص يبقى + +367 +00:38:57,710 --> 00:39:06,430 +باجي بقوله ان ال F is decreasing يبقى دالة تناقصية + +368 +00:39:06,430 --> 00:39:13,410 +على الفترة من سالف جذر تلاتة إلى جذر تلاتة بالضبط + +369 +00:39:13,410 --> 00:39:18,990 +تماما خلصنا المطلوب الأول بدنا نيجي لمطلوب التاني + +370 +00:39:18,990 --> 00:39:25,070 +نمر بيههو حدد لي ال local extreme values واضح انه + +371 +00:39:25,070 --> 00:39:30,620 +عندى هنا localتغيرت الإشارة من positive إلى + +372 +00:39:30,620 --> 00:39:35,500 +negative يبقى maximum هنا تغيرت من negative إلى + +373 +00:39:35,500 --> 00:39:43,420 +positive يبقى minimum تمام إذا بدنا نحسب F of سالب + +374 +00:39:43,420 --> 00:39:51,380 +جذر تلاتة ويساوي 2 في سالب جذر تلاتة لكل تكيب سالب + +375 +00:39:51,380 --> 00:39:58,970 +تمانتاشر في سالب جذر تلاتة ويساويهذه بتعطيني اللي + +376 +00:39:58,970 --> 00:40:06,230 +هو السالب ستة جذر تلاتة وهذه بتعطيني تمانتاشر جذر + +377 +00:40:06,230 --> 00:40:13,570 +تلاتة ويساوي اتناشر جذر تلاتة بدنا نحسبله ال F of + +378 +00:40:13,570 --> 00:40:20,330 +جذر تلاتة يبقى هذه بدها تساوي اتنين في جذر تلاتة + +379 +00:40:20,330 --> 00:40:29,890 +لكل تكيب نقص تمانتاشر في جذر تلاتةالجواب يساوي ستة + +380 +00:40:29,890 --> 00:40:36,570 +جذر تلاتة ناقص تمانتاشر جذر تلاتة ويساوي ناقص + +381 +00:40:36,570 --> 00:40:39,210 +اتناشر جذر تلاتة + +382 +00:40:44,240 --> 00:40:55,240 +الـ F has a local maximum 12 جدر تلاتة at x يساوي + +383 +00:40:55,240 --> 00:40:57,280 +سالف جدر تلاتة + +384 +00:41:05,890 --> 00:41:10,830 +الجذر ثلاثة انتهينا من المطلوب الثاني يبقى يا شباب + +385 +00:41:10,830 --> 00:41:15,630 +أنا بكتب هذا اللي بالأحمر بناء على النتاج اللي + +386 +00:41:15,630 --> 00:41:20,130 +عندي مش عند القيمة حسب ما هو في الجدول هنا قلنا + +387 +00:41:20,130 --> 00:41:25,050 +local maximum هنا local minimum وبناء عليه قلت + +388 +00:41:25,050 --> 00:41:29,110 +local maximum عند السالب تلاتة وlocal minimum عند + +389 +00:41:29,110 --> 00:41:35,540 +الجذر تلاتةالمطلوب نمرى c قال which if any of the + +390 +00:41:35,540 --> 00:41:39,920 +extreme values are absolute يبقى انا عندي قيمتين + +391 +00:41:39,920 --> 00:41:45,320 +ممن هم absolute ولا واحدة لأنه ماعنديش end points + +392 +00:41:45,320 --> 00:41:50,020 +interval ماشية لغاية سلب infinity و لغاية موجة ب + +393 +00:41:50,020 --> 00:42:00,320 +infinity يبقى نمرى c ال f has no absolute + +394 +00:42:01,440 --> 00:42:06,540 +extrema because + +395 +00:42:06,540 --> 00:42:17,860 +ال F has no end points او ال domain تبع ال F has + +396 +00:42:17,860 --> 00:42:24,800 +no end points عليك انتهى السؤال نروح ناخد السؤال + +397 +00:42:24,800 --> 00:42:28,960 +الثاني السؤال + +398 +00:42:28,960 --> 00:42:37,310 +الثانيالـ F of X تساوي اللي هو مين؟ X تربيع ناقص + +399 +00:42:37,310 --> 00:42:45,250 +تلاتة على X ناقص اتنين والـ X لا تساوي اتنين + +400 +00:42:58,950 --> 00:43:03,570 +طبعا الدالة غير معرفة عند اتنين لكن الدمين بيصير + +401 +00:43:03,570 --> 00:43:07,630 +من سالب infinity لغاية اتنين و من اتنين ل infinity + +402 +00:43:07,630 --> 00:43:13,770 +يبقى باجي بقوله domain الدالة F من سالب infinity + +403 +00:43:13,770 --> 00:43:21,460 +لغاية اتنين اتحاد اتنين و infinityطب بنجيب ال + +404 +00:43:21,460 --> 00:43:25,940 +interval of increasing and decreasing ممكن اشتق + +405 +00:43:25,940 --> 00:43:29,900 +المقام في مشتقة ال bus لكن في واحد يقولي انا بسش + +406 +00:43:29,900 --> 00:43:34,900 +لأ اسهل من هناك بقولتله كده بقالي بقسم جسمه مطولة + +407 +00:43:34,900 --> 00:43:38,660 +و بعد هيك بروح بشتق بقوله والله كلامك مظهر بقسم + +408 +00:43:38,660 --> 00:43:43,500 +جسمه مطولة ماجتيش اذا درجة ال bus اكبر من او تساوي + +409 +00:43:43,500 --> 00:43:49,790 +درجاتأذا هذه المثالة بقدر أقول x تربيع ناقص تلاتة + +410 +00:43:49,790 --> 00:43:56,630 +بدي أجسمها عمليا على x ناقص اتنين فيها x بx تربيع + +411 +00:43:56,630 --> 00:44:02,250 +ناقص اتنين x زاد بصير ناقص وهذه زاد هذه مع السلامة + +412 +00:44:02,250 --> 00:44:07,810 +بضل اتنين x ناقص تلاتةالباقي من الدرجة الأولى + +413 +00:44:07,810 --> 00:44:12,190 +والمقسم عليه من الدرجة الأولى بنواصل عملية القسمة + +414 +00:44:12,190 --> 00:44:19,690 +يبقى 2x على x فيها جداش 2 2 في x ب2x وناقص هنا + +415 +00:44:19,690 --> 00:44:26,070 +جداشأربعة هذي زاد و هذي زاد هذول مع السلامة بيظل + +416 +00:44:26,070 --> 00:44:30,170 +جداش واحد يبقى خلاص طب الله يعطيك العافية لإن + +417 +00:44:30,170 --> 00:44:33,530 +الباقي من الدرجة الصفرية و المقصوم عليها من الدرجة + +418 +00:44:33,530 --> 00:44:40,560 +الثانية يبقى باجي بقوله ال F of Xيقول اكس تربيه + +419 +00:44:40,560 --> 00:44:46,280 +ناقص تلاتة على اكس ناقص اتنين بدي اكتبها بشكل اخر + +420 +00:44:46,280 --> 00:44:52,200 +اكس زائد اتنين زائد واحد على اكس ناقص اتنين يبقى + +421 +00:44:52,200 --> 00:44:56,800 +هذه اسهلة في الشغل منين من الشكل اللي عندنا هذا + +422 +00:44:56,800 --> 00:45:01,500 +يبقى خلاص باشتغل دوري الحين طبعا هذا شباب ايش كنا + +423 +00:45:01,500 --> 00:45:10,750 +بنسميه ابلاج السمتت وهذا ايش كنا بنسميهأكس يساوى + +424 +00:45:10,750 --> 00:45:14,990 +اتنين، Vertical بس بعد ما تفحصوا، طب فيه + +425 +00:45:14,990 --> 00:45:19,970 +horizontal أسمت؟ لأ لإن ضررية ال bus أعلى من ضررية + +426 +00:45:19,970 --> 00:45:24,210 +المقام ال limit بتعطيني infinity وبالتالي نقبلك، + +427 +00:45:24,210 --> 00:45:28,410 +طب احنا هذا بدنا إيش نرسم اليوم، مش شغلتنا الرسم + +428 +00:45:28,410 --> 00:45:33,400 +اليوم، تمام؟شغلتنا بس بيجي فترات التزايد والتناقص + +429 +00:45:33,400 --> 00:45:40,000 +إذا بدي أجي للنقطة A بدي ال F prime of X مشتاقة + +430 +00:45:40,000 --> 00:45:46,460 +هذه بواحد واتنين مع السلامة وهذه X ناقص اتنين لكل + +431 +00:45:46,460 --> 00:45:56,370 +تربيةبنوحد المقامات يبقى x ناقص اتنين لكل تربية + +432 +00:45:56,370 --> 00:46:04,770 +بيصير x ناقص اتنين لكل تربية ناقص واحد طيب نفك هذا + +433 +00:46:04,770 --> 00:46:11,330 +البص بيصير x تربيةناقص أربعة X زائد أربعة ناقص + +434 +00:46:11,330 --> 00:46:18,210 +واحد على X ناقص اتنين لكل تربية يعني X تربية ناقص + +435 +00:46:18,210 --> 00:46:25,450 +أربعة X زائد تلاتة على X ناقص اتنين لكل تربية هذه + +436 +00:46:25,450 --> 00:46:32,710 +يمكن تحليلها يبقى صار ال F prime of X هو X ناقص + +437 +00:46:32,710 --> 00:46:41,310 +واحدفي x ناقص تلاتة على x ناقص اتنين الكل تربيع + +438 +00:46:43,800 --> 00:46:49,360 +الان باجي بقوله ال X تساوي واحد وال X تساوي تلاتة + +439 +00:46:49,360 --> 00:46:52,820 +هما مين ال critical بس ماقالليش هات ال critical + +440 +00:46:52,820 --> 00:46:56,460 +قاللي هاتلي ال interval إذا مافيش داعي أقلب حالي و + +441 +00:46:56,460 --> 00:46:59,020 +أقول له هذا ال critical لو لأ بدي أشوف إشارات + +442 +00:46:59,020 --> 00:47:04,620 +الأقواص دغري مباشرة تمام؟ إذا باجي بقوله بيداجي + +443 +00:47:04,620 --> 00:47:12,060 +أخد إشارة القوس الأول X ناقص واحدهذا الـ real line + +444 +00:47:12,060 --> 00:47:17,720 +بياخد الـ zero تبعه عند الواحد بعد الواحد positive + +445 +00:47:17,720 --> 00:47:25,980 +و قبل الواحد negative بدا ياخد إشارة اللي هو ال X + +446 +00:47:25,980 --> 00:47:31,940 +ناقص تلاتة هذا الخط اللي عندنا هذا هو بياخد ال + +447 +00:47:31,940 --> 00:47:38,080 +zero تبعه أين؟ عند التلاتة بعد التلاتة موجب و قبله + +448 +00:47:38,080 --> 00:47:45,030 +ما شاء الله negativeبدأ ياخد إشارة ال X ناقص اتنين + +449 +00:47:45,030 --> 00:47:50,370 +لكل تربيع، بعدين بقول له هذا بياخد ال zero تبقى + +450 +00:47:50,370 --> 00:47:58,530 +وين؟ عند اتنين، بعد اتنين موجب و جابلهموجب كمال + +451 +00:47:58,530 --> 00:48:05,690 +انه كمية مربع تمام؟ بعد هيك بدنا إشارة اللي هو X + +452 +00:48:05,690 --> 00:48:11,410 +ناقص واحد في ال X ناقص تلاتة على X ناقص اتنين لكل + +453 +00:48:11,410 --> 00:48:18,450 +تربية وهذا ال line اللي عندنا و جينا نحدد الحدود + +454 +00:48:18,450 --> 00:48:26,870 +الإقليمية فيما بينهما بالشكل اللي عندنا هذاتمام؟ + +455 +00:48:26,870 --> 00:48:34,770 +طيب هي التلاتة وهي اتنين وهي الواحد طلعله هنا كلها + +456 +00:48:34,770 --> 00:48:42,830 +موجب وهنا سالب وهنا سالب وهنا موجب يعني الدالة + +457 +00:48:42,830 --> 00:48:49,710 +كانت increasing صارت decreasing بقيت decreasing + +458 +00:48:49,710 --> 00:48:53,970 +صارت increasing بالشكل اللي لدينا هنا + +459 +00:49:15,640 --> 00:49:24,920 +يبقى باجي بقولله ال F is increasing دلتة زيودية on + +460 +00:49:24,920 --> 00:49:32,320 +الفترة من سالب infinity لغاية الواحد و closed عند + +461 +00:49:32,320 --> 00:49:40,580 +الواحد and on و كذلك من عند التلاتة لغاية infinity + +462 +00:49:41,780 --> 00:49:51,620 +بعدها ال F is decreasing on دالة تناقصية على + +463 +00:49:51,620 --> 00:49:55,960 +الفترة من عند الواحد لغاية اتنين مفتوحة من عند + +464 +00:49:55,960 --> 00:50:01,440 +اتنين ليش ان الدالة غير معرفة عند اتنين اتحاد + +465 +00:50:01,440 --> 00:50:10,000 +اتنين و تلاتة بالشكل اللي عندنا هنا مين + +466 +00:50:10,000 --> 00:50:10,680 +اللي بيحكي + +467 +00:50:30,910 --> 00:50:34,090 +طيب نمر بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر + +468 +00:50:34,090 --> 00:50:37,910 +بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر + +469 +00:50:37,910 --> 00:50:40,630 +بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر بيه نمر + +470 +00:50:40,630 --> 00:50:44,820 +بيه نمر بيه نمر بيه نمر بيه نمر بيههنا فيه لأ هنا + +471 +00:50:44,820 --> 00:50:50,860 +local minimum إذا بدنا نحسبله فقط F of واحد و F of + +472 +00:50:50,860 --> 00:50:58,240 +تلاتة يبقى بادي باخدله F of واحد F of واحد يساوي + +473 +00:50:58,240 --> 00:51:04,180 +هاي واحد تربيع ناقص تلاتة على واحد ناقص اتنين + +474 +00:51:04,180 --> 00:51:08,720 +بيبقى لنا ناقص اتنين على ناقص واحد يساوي اتنين + +475 +00:51:09,070 --> 00:51:16,690 +وبدنا ال F of تلاتة ويسوي تلاتة تربيع ناقص تلاتة + +476 +00:51:16,690 --> 00:51:23,510 +على تلاتة ناقص اتنين يبقى تسعة ناقص تلاتة لهو ستة + +477 +00:51:23,510 --> 00:51:33,830 +على واحد ويسوي ستة يبقى ال F has local maximum + +478 +00:51:35,620 --> 00:51:44,680 +local maximum يتنين at x يساوي واحد and local + +479 +00:51:44,680 --> 00:51:52,340 +minimum ستة at x يساوي تلاتة واحد يقول طب هو ال + +480 +00:51:52,340 --> 00:51:58,300 +minimum ستة و ال maximum بنفع يكون اتنينانا هذه + +481 +00:51:58,300 --> 00:52:03,600 +قيم ليش منحنا ممكن يكون جوس تحت و جوس فوق صحيح انا + +482 +00:52:03,600 --> 00:52:07,520 +بيبقى صارت اللي فوق هذه local maximum و هذه اللي + +483 +00:52:07,520 --> 00:52:12,960 +تحت local minimum بهمناش يبقى انا بكتب نتاج مثل ما + +484 +00:52:12,960 --> 00:52:18,720 +بطلعها ايه تماما نجي لنمرى دى، نمرى دى بيقول مين + +485 +00:52:18,720 --> 00:52:21,360 +من ال local maximum و ال local minimum تبقى + +486 +00:52:21,360 --> 00:52:26,340 +absolute بيقولوا الله تعالى هنا جايين من وين احنا؟ + +487 +00:52:29,660 --> 00:52:32,740 +ماعنديش end point، سواء عندي اتنين الدالة غير + +488 +00:52:32,740 --> 00:52:42,820 +معرفة يبقى باجي بقول ال F has no absolute extrema + +489 +00:52:42,820 --> 00:52:49,380 +because domain + +490 +00:52:51,500 --> 00:53:03,500 +الـ F has no end points ماعنديش طب السؤال التالت + +491 +00:53:03,500 --> 00:53:12,620 +السؤال التالت بيقول F of X يساوي + +492 +00:53:12,620 --> 00:53:20,140 +X أسطل تين فمين في X زائد خمسة + +493 +00:53:24,460 --> 00:53:31,140 +كويس طب إيه إيش رأيك؟ هذه بدل ما هي حاصل ضرب دلت + +494 +00:53:31,140 --> 00:53:38,360 +خلنا نفكها وخلاص يعني هذه بيصير X أس جديش خمسة ع + +495 +00:53:38,360 --> 00:53:48,930 +تلاتة زي خمسة X أس طولتينبدنا ال F prime of X يبقى + +496 +00:53:48,930 --> 00:53:59,530 +يساوي خمس أتلات X أس تلتين زائد عشر أتلات X أساليب + +497 +00:53:59,530 --> 00:54:05,890 +تلتمظبوط هيك؟ طب بدنا نجيب ال critical points او + +498 +00:54:05,890 --> 00:54:10,690 +بدي اكتب هذه الشكلة كويس مشان اقدر احدد الإشارات + +499 +00:54:10,690 --> 00:54:17,030 +بقولوا هذه بسيطة يبقى هذه خمسة على تلاتة X أس + +500 +00:54:17,030 --> 00:54:24,320 +طولتين زائد عشرة على تلاتة X أس طولتينأكس أس سالب + +501 +00:54:24,320 --> 00:54:30,920 +تلت نزلتها تحت صارت مين بالمعجب إذا هذا كله بقدر + +502 +00:54:30,920 --> 00:54:37,440 +أقول تلاتة أكس أس تلت عامل مشترك من الكل على تلاتة + +503 +00:54:37,440 --> 00:54:43,060 +بضلش اللي عندي خمسة أكس أس تلت في أكس أس تلتين بضل + +504 +00:54:43,060 --> 00:54:50,950 +خمسة أكسفقط لغاية تلتين زائد تلت تلاتة ع تلاتة + +505 +00:54:50,950 --> 00:54:59,550 +يعني واحد صحيح وهنا زائد عشرة او خمسة في X زائد + +506 +00:54:59,550 --> 00:55:07,750 +اتنين على تلاتة X قص تلت طب يبقى ال critical + +507 +00:55:07,750 --> 00:55:14,060 +points من و من؟ساوي باتنين ومين؟ و Zero لأن عند ال + +508 +00:55:14,060 --> 00:55:18,780 +Zero المشتقة غير معرفة يبقى لو سويت بال Zero البص + +509 +00:55:18,780 --> 00:55:21,660 +هو بالساوي Zero وبالتالي ال critical point CX ساوي + +510 +00:55:21,660 --> 00:55:28,660 +ساوي باتنين وكذلك X يساوي Zero أيضا ماحطيتش ان هذا + +511 +00:55:28,660 --> 00:55:34,050 +السؤال اللي جابله انا قلت ال A6 local maximumأنا + +512 +00:55:34,050 --> 00:55:39,410 +قلت و حكيتها بس أنت كنت في مجال آخر و بده أعيدها + +513 +00:55:39,410 --> 00:55:44,330 +برضه مش هانخطك، شو اسمك أنت؟ تامر جرادة، احنا في + +514 +00:55:44,330 --> 00:55:48,670 +السؤال السابق و ليس في السؤال هذا طيب، على أي حال، + +515 +00:55:48,670 --> 00:55:53,710 +شوفت الرسمة إيش كانت عندك هنا؟ إيش في عند الواحد؟ + +516 +00:55:53,710 --> 00:56:01,500 +F' غيرت إشرتها من موجة بيها السلبية، إيش عندك؟هنا + +517 +00:56:01,500 --> 00:56:07,580 +لف ويرش من سالب لأ موجة بيبقاش عندك عندك تلاتة + +518 +00:56:07,580 --> 00:56:12,500 +طلعت ستة مظبوط ولا من عشان هذه اتنين و هذه ستة ستة + +519 +00:56:12,500 --> 00:56:17,460 +مستقلة مش جزلك هذا في عندك أبلجز سم تطلع ورا سم + +520 +00:56:17,460 --> 00:56:21,460 +تجوز بتطلع فوقو جوس بيطلع تحت يبقى هذه local + +521 +00:56:21,460 --> 00:56:25,500 +maximum و هذه اللي فوق بيصير local minimum + +522 +00:56:25,500 --> 00:56:30,180 +قاعدناها كمان مرة عليها اللي عند الرسم برضه في ال + +523 +00:56:30,180 --> 00:56:34,280 +section القادم اللي سنبدأه بعد قليل هتشوف شغلات زي + +524 +00:56:34,280 --> 00:56:38,670 +كدهتشوف شغلات عملية نرجع لسؤالنا يا شباب احنا + +525 +00:56:38,670 --> 00:56:42,350 +جيبنا المشتقة الأولى و أصبحت المشتقة الأولى على + +526 +00:56:42,350 --> 00:56:46,850 +الشكل خمسة في X زائد اتنين على تلاتة X أس طول تبقى + +527 +00:56:46,850 --> 00:56:51,130 +ال critical point يسالب اتنين و Zero إذا بتشوف + +528 +00:56:51,130 --> 00:56:57,170 +إشارة كل term من هدين ال termينإذا لو جيت Gulf بدى + +529 +00:56:57,170 --> 00:57:04,210 +أخد إشارة خمسة في X زائد اتنين هذا ال real line + +530 +00:57:04,210 --> 00:57:10,270 +بياخد ال zero تبع وين؟ عند السالب اتنين بعد السالب + +531 +00:57:10,270 --> 00:57:19,050 +اتنين ايش بتكون القيمة؟ و قبله؟طيب بدل ياخد إشارة + +532 +00:57:19,050 --> 00:57:26,050 +اللي هو تلاتة إكسوس طول بياخد ال zero تبع وين؟ عند + +533 +00:57:26,050 --> 00:57:31,710 +ال zero بعد ال zero و قبل ال zero طيب الدمين تبع + +534 +00:57:31,710 --> 00:57:37,560 +ده اللي هد مين؟كل الار بلا استثناء يبقى لا عندي + +535 +00:57:37,560 --> 00:57:43,820 +مشكلة في هذه الحالة إذا بدي إشارة خمسة في إكس زائد + +536 +00:57:43,820 --> 00:57:49,860 +اتنين على تلاتة إكس أس طول و هذا ال real line و + +537 +00:57:49,860 --> 00:57:57,480 +بدي نيجي نحدد الحدود الإقليمية أي سالب اتنين أو أي + +538 +00:57:57,480 --> 00:58:04,780 +زيرو هنا موجب هنا سالب هنا موجبسالب على سالب + +539 +00:58:04,780 --> 00:58:09,340 +بموجب، موجب على سالب بسالب، موجب على موجب بموجب. + +540 +00:58:09,760 --> 00:58:16,640 +يبقى الدالة كانت increasing. إيش صارت؟ decreasing. + +541 +00:58:17,020 --> 00:58:23,320 +إيش رجعت؟ increasing. يبقى يا تمر يا جرادة إيش + +542 +00:58:23,320 --> 00:58:28,910 +رأيك؟ عندي السالب اتنين هنا، إيش فيه؟وعندي zero + +543 +00:58:28,910 --> 00:58:34,710 +بدنا نحسب قيمة ده لو جد ما تطلع تطلع بهمناش طبعا + +544 +00:58:34,710 --> 00:58:40,310 +اذا بدنا نروح نحسب F of سالي باتنين يبقى بدنا نيجي + +545 +00:58:40,310 --> 00:58:45,790 +ناخد F of سالي باتنين يبقى هذا الكلام بده يساوي + +546 +00:58:45,790 --> 00:58:53,400 +سالي باتنين أس تلتين في سالي باتنين زائد خمسةطب + +547 +00:58:53,400 --> 00:58:59,780 +كويس هذا بده يعطينا مين؟ بده يعطينا تلاتة هذا + +548 +00:58:59,780 --> 00:59:05,400 +الجذر التالت لسلب اتنين تربية سلب اتنين تربية + +549 +00:59:05,400 --> 00:59:10,940 +مافقداش، يبقى الجذر التالت لاربعة، يبقى تلاتة + +550 +00:59:10,940 --> 00:59:21,340 +الجذر تلاتة الجذر تالتلأربعة تمام بدنا نيجي نحسب F + +551 +00:59:21,340 --> 00:59:28,480 +of Zero Background Zero يبقى بعدي بقوله ال F has + +552 +00:59:28,480 --> 00:59:37,480 +local maximum تلاتة الجدرى التالت لأربعة X يساوي + +553 +00:59:37,480 --> 00:59:43,100 +سالي باتنين ال F has local minimum Zero + +554 +00:59:46,710 --> 00:59:53,870 +السؤال هو في عندي absolute maximum او minimum؟ لأ + +555 +00:59:53,870 --> 00:59:55,990 +لان ماعنديش end points + +556 +01:00:13,680 --> 01:00:26,240 +طيب نجلع نمسي if has no absolute extrema because + +557 +01:00:26,240 --> 01:00:37,040 +ال domain بتبع ال if has no end points + +558 +01:00:39,260 --> 01:00:45,260 +طيب نيجي هذا السؤال التالت نيجي لهذا السؤال الرابع + +559 +01:00:45,260 --> 01:00:52,060 +والاخير في هذا ال section ايه السؤال؟ طيب مثلا لو + +560 +01:00:52,060 --> 01:00:55,700 +انا افتراض ال minimum او ال maximum ساعدنا هي أفضل + +561 +01:00:55,700 --> 01:01:01,420 +حاجة، كيف؟ لو ايه؟ ال minimum القيمة ال minimum + +562 +01:01:01,420 --> 01:01:04,400 +value أو ال absolute مثلا + +563 +01:01:12,440 --> 01:01:17,400 +مش رايك تصبر شوية بس ناخد المثال الأخير هذا، بس + +564 +01:01:17,400 --> 01:01:20,500 +خليك محتفظ بالسؤال، يمكن نجاوب عليه في السؤال + +565 +01:01:20,500 --> 01:01:29,410 +الأخيرقبل التكمل يالا اكتبلي هذا f of x بده يساوي + +566 +01:01:29,410 --> 01:01:38,490 +اللي هو ال X تكيب ناقص تلاتة X تربيع و سالب + +567 +01:01:38,490 --> 01:01:44,770 +infinity اقل من ال X اقل من او يساوي تلاتة + +568 +01:01:51,740 --> 01:01:59,800 +بنجيب الـ f prime of x يبقى تلاتة x تربيه ناقص ستة + +569 +01:01:59,800 --> 01:02:07,180 +x في عندي عامل مشترك اللي هو قداش تلاتة x بيظل x + +570 +01:02:07,180 --> 01:02:15,700 +ناقص اتنين يبقى ال critical points هي zero و اتنين + +571 +01:02:15,700 --> 01:02:21,930 +فقط لا غير مظبوط يبقى احنا بدنا نبحث الإشاراتيبقى + +572 +01:02:21,930 --> 01:02:30,330 +بد إشارة 3x بقوله بتاخد ال zero تبعه أين؟ عند ال + +573 +01:02:30,330 --> 01:02:35,990 +zero و بعد ال zero؟ موجب و قبل ال zero؟ طب على + +574 +01:02:35,990 --> 01:02:42,140 +إطلاق هو الله محدودةبدي اقضى فعندي التلاتة ممنوع + +575 +01:02:42,140 --> 01:02:47,240 +تتحدى التلاتة تتعدى ماعنديش بعد التلاتة دلها تمام + +576 +01:02:47,240 --> 01:02:52,100 +بجهة دي ليست طبعا بس من عن جهة الشمال على إطلاقها + +577 +01:02:52,100 --> 01:02:55,640 +الله سهل علينا نجلب من سالب infinity لغاية مين + +578 +01:02:55,640 --> 01:03:03,140 +لغاية التلاتة بعد هيك بدي إشارة X ناقص 2 تاخد ال + +579 +01:03:03,140 --> 01:03:10,490 +zero تبعها وين عند 2 بعد 2و تلاتة بدي اوقف و قبل + +580 +01:03:10,490 --> 01:03:16,970 +هي set بالشكل اللي انها ده بعد هيك بدي اشارة تلاتة + +581 +01:03:16,970 --> 01:03:24,410 +x في x ناقص اتنين و بنيجي الى الحدود الاقليمية + +582 +01:03:24,410 --> 01:03:31,950 +يبقى هي zeroهو اي اتنين وهو اي مين تلاتة بعد + +583 +01:03:31,950 --> 01:03:36,550 +التلاتة ماعنديش يبقى هذا الجثيم مضربات في بعض ضرب + +584 +01:03:36,550 --> 01:03:42,770 +يبقى سالب يبقى موجب اتدالة increasing صارت + +585 +01:03:42,770 --> 01:03:48,650 +decreasing رجعت increasing يبقى بقدر اقول ماتي + +586 +01:03:48,650 --> 01:03:58,850 +نمرة ايه ال F is increasing onمن سالب infinity + +587 +01:03:58,850 --> 01:04:07,150 +لغاية من ال zero and on وكذلك من الاتنين لغاية + +588 +01:04:07,150 --> 01:04:07,950 +التلاتة + +589 +01:04:11,680 --> 01:04:20,360 +الآن ال F is decreasing ده لتناقصية على الفترة من + +590 +01:04:20,360 --> 01:04:24,940 +Zero لغاية كده اش لغاية اتنين خلصنا المطلوب الأول + +591 +01:04:24,940 --> 01:04:32,160 +بنالي جه نحسبله ال F of نمرة بي ال F of Zero ال F + +592 +01:04:32,160 --> 01:04:39,120 +of Zero تساوي Zero والتانية ال F of اتنينF of + +593 +01:04:39,120 --> 01:04:46,560 +اتنين يساوي اتنين تكعيب ناقص تلاتة في اتنين ترابيع + +594 +01:04:48,150 --> 01:04:54,550 +تمام؟ طيب هذه بتصير تمانية ناقص اتناشر و يساوي + +595 +01:04:54,550 --> 01:05:03,110 +قداشر؟ ناقص اربع اذا عندي zero في عندي ايش؟ في + +596 +01:05:03,110 --> 01:05:09,430 +عندي zero في local maximum يبقى if has local + +597 +01:05:09,430 --> 01:05:19,510 +maximum0 at x يساوي 0 تمام؟ طب إيش رأيك عند + +598 +01:05:19,510 --> 01:05:28,290 +التلاتة؟ طيب عند التلاتة بدنا نجيبله كمان F of + +599 +01:05:28,290 --> 01:05:34,390 +تلاتة يبقى بصير عندي يساوي تلاتة + +600 +01:05:40,050 --> 01:05:49,440 +تلاتة في تلاتة تكيب ناقص تلاتة في تلاتة تربيعفى + +601 +01:05:49,440 --> 01:05:57,400 +اشتلاتها الصحية يبقى النتيجة كده؟ Zero كذلك يبقى + +602 +01:05:57,400 --> 01:06:01,140 +بعد يبقى يقول الـ F has a local maximum Zero at X + +603 +01:06:01,140 --> 01:06:08,440 +يساوي Zero and ال X يساوي تلاتة يبقى موقعين فيهم + +604 +01:06:08,440 --> 01:06:15,060 +local maximum طيب ال F has local + +605 +01:06:21,070 --> 01:06:30,110 +لوكال مينيمم عندي اتنين سالب اربع ات اكس يسمى + +606 +01:06:30,110 --> 01:06:35,550 +لقداش اتنين يبقى جيبنا ال local maximum يبقى لل + +607 +01:06:35,550 --> 01:06:43,090 +absolute نمرسى في absolute maximum؟ فيه + +608 +01:06:44,640 --> 01:06:51,120 +تلاتة ولا لا؟ لأن هذه الدلجة من تحت increasing + +609 +01:06:51,120 --> 01:06:58,600 +صعدت لغاية zero نزلت عند اتنين لمين لسالب اربعة + +610 +01:06:58,600 --> 01:07:04,540 +تحت رجعت طلعت لمين؟ ايش رايك بال zero هذه بالصير؟ + +611 +01:07:05,680 --> 01:07:11,240 +absolute maximum يبقى عندي موقعين لل absolute + +612 +01:07:11,240 --> 01:07:20,160 +maximum برضه بجي بقول ال F has absolute maximum + +613 +01:07:21,920 --> 01:07:29,900 +أت اكس يساوي زيرو and ال X يساوي تلاتة فيه عندي + +614 +01:07:29,900 --> 01:07:34,620 +absolute minimum لإنه جاي من وين من تحت من سالب + +615 +01:07:34,620 --> 01:07:38,820 +infinity وضله طالع على ال zero نزلت لسالب أربع + +616 +01:07:38,820 --> 01:07:42,880 +ورجع طالع لتلتر يعني عندي absolute maximum ولا + +617 +01:07:42,880 --> 01:07:49,080 +يوجد absolute minimum يبقى ال F has + +618 +01:08:10,240 --> 01:08:17,420 +أجابنا سؤالك؟ و لا لسه؟ وصلت؟ الحمد لله ذلك ما كنا + +619 +01:08:17,420 --> 01:08:17,920 +نبغي + +620 +01:08:46,510 --> 01:08:50,450 +السلام عليكم ورحمة الله وبركاته + +621 +01:08:55,470 --> 01:08:59,330 +بعدها نجي ل exercises أربعة تلاتة هكتب عليك فوق + +622 +01:08:59,330 --> 01:09:07,750 +هنا يبقى exercises أربعة تلاتة المسائل التالية + +623 +01:09:07,750 --> 01:09:13,350 +اللي من واحد لتسعة وتلاتين الأد من واحد لتسعة + +624 +01:09:13,350 --> 01:09:21,500 +وتلاتين الأدو من واحد و أربعين لواحد و خمسين من + +625 +01:09:21,500 --> 01:09:29,260 +واحد و أربعين لواحد و خمسين كمان ال odd و part + +626 +01:09:29,260 --> 01:09:39,660 +part a و b a و b فقط لا غيرو من تلاتة و خمسين + +627 +01:09:39,660 --> 01:09:49,320 +لتسعة و خمسين من تلاتة و خمسين لتسعة و خمسين الاد + +628 +01:09:49,320 --> 01:09:59,220 +part F فقط لغير و من واحد و ستين لسبعين من واحد و + +629 +01:09:59,220 --> 01:10:03,580 +ستين لسبعين كلهم بلا استثناء + +630 +01:10:06,940 --> 01:10:15,120 +طيب ننتقل الان الى ال section اللى يليه وهو + +631 +01:10:15,120 --> 01:10:22,660 +section اربعة اربعة يبقى section اربعة اربعة بتحدث + +632 +01:10:22,660 --> 01:10:33,760 +عن شغلتين ال concavity concavity and ال curve + +633 +01:10:33,760 --> 01:10:35,280 +sketching + +634 +01:10:37,400 --> 01:10:45,260 +الرسم البياني للمنحنيات نعطي تعريف لل Concavity في + +635 +01:10:45,260 --> 01:10:53,240 +الأول وبعد ذلك بروح للباقي The graph of + +636 +01:10:53,240 --> 01:11:04,200 +a differentiable function Y تساوي F of X is + +637 +01:11:06,500 --> 01:11:23,060 +المرة واحد Concave up on an open interval I + +638 +01:11:23,060 --> 01:11:35,980 +if ال F' is increasing on I + +639 +01:11:38,360 --> 01:11:47,100 +نمره اتنين concave down على ال open interval I فال + +640 +01:11:47,100 --> 01:11:56,440 +F' is decreasing on I that + +641 +01:11:56,440 --> 01:12:03,160 +is I N نمره + +642 +01:12:03,160 --> 01:12:13,020 +احد Fالـ F double prime greater than zero on I + +643 +01:12:13,020 --> 01:12:17,400 +then + +644 +01:12:17,400 --> 01:12:37,610 +the graph of Fثم graph of F over I is concave up + +645 +01:12:37,610 --> 01:12:40,670 +نمره + +646 +01:12:40,670 --> 01:12:48,890 +اتنين F ال F double prime اقل من ال zero on I ثم + +647 +01:12:48,890 --> 01:12:55,710 +graph of F is concave + +648 +01:12:55,710 --> 01:12:56,490 +down + +649 +01:13:14,380 --> 01:13:24,560 +if ال F is continuous on an open interval + +650 +01:13:24,560 --> 01:13:28,680 +containing + +651 +01:13:28,680 --> 01:13:31,900 +X + +652 +01:13:31,900 --> 01:13:39,440 +node and if ال F + +653 +01:13:44,090 --> 01:13:51,790 +تتغير الاتجاه من + +654 +01:13:51,790 --> 01:13:54,930 +الهيئة + +655 +01:13:54,930 --> 01:14:03,330 +الهيئة الهيئة الهيئة الهيئة الهيئة + +656 +01:14:03,330 --> 01:14:08,750 +الهيئة الهيئة الهيئة الهيئة الهيئة الهيئة + +657 +01:14:12,330 --> 01:14:26,770 +و F of X0 is called an inflection + +658 +01:14:26,770 --> 01:14:30,610 +point + +659 +01:14:30,610 --> 01:14:34,010 +of F + +660 +01:15:17,390 --> 01:15:20,190 +ماذا بحق الجحيم + +661 +01:15:30,110 --> 01:15:30,750 +يا رجل .. + +662 +01:17:57,300 --> 01:18:01,760 +الجد هو يبقى اتراك فترة يكون من يمين و من اليسار، + +663 +01:18:01,760 --> 01:18:04,840 +اي جد يكون من يمين و من اليسار، لكن يكون closed + +664 +01:18:16,440 --> 01:18:23,340 +هذا المتقبل دالة مجزة صح ولا لأ؟ اه لأ، المتقبل + +665 +01:18:23,340 --> 01:18:27,900 +دالة مجزة إلى جزئين، المتقبل دالة مجزة إلى جزئين، + +666 +01:18:27,900 --> 01:18:33,440 +منقول عن طرفين الفترة الدالة غير معرفة، صحيح ولا + +667 +01:18:33,440 --> 01:18:37,960 +لأ؟ منقول مشتقة، المشتقة غير معرفة، مظبوط؟ من + +668 +01:18:37,960 --> 01:18:42,860 +استبعد الطرفين، لأنه لما أوقف عنده احتمال يكون + +669 +01:18:42,860 --> 01:18:47,100 +كبير فيه discontinuityعن طرفين الفترة احتمالها + +670 +01:18:47,100 --> 01:18:50,980 +تمام وبالتالي انا باستبعد الطرفين حتى ماوجعش في + +671 +01:18:50,980 --> 01:18:57,000 +مشاكل مظبوط اسمه + +672 +01:18:57,000 --> 01:18:57,440 +يا راجل + +673 +01:19:05,870 --> 01:19:10,990 +لو كانت دالة عزيزي polynomial فمعرفة عليها كل real + +674 +01:19:10,990 --> 01:19:14,710 +line دخلت الطرفين و الله قلت الطرفين مش سببش عندي + +675 +01:19:14,710 --> 01:19:19,730 +مشكلة خالص بس لما تبقى دالة مجزلة احتمال المشكلة + +676 +01:19:19,730 --> 01:19:21,790 +تكون موجودة احتمال كبير كمان + +677 +01:19:25,440 --> 01:19:29,400 +أف و فكس يساوي كده؟ أف و فكس يساوي اكس تربيع اكس + +678 +01:19:29,400 --> 01:19:33,780 +تربيع ماشية الله هاي بها ال domain كل ال real line + +679 +01:19:33,780 --> 01:19:37,080 +والله انت حجزت عند الواحد و اتنين عند الواحد و + +680 +01:19:37,080 --> 01:19:39,660 +اتنين عند الواحد و اتنين ممتاز جدا يبقى السارات + +681 +01:19:39,660 --> 01:19:42,620 +تلاتة اكس تربيع تلاتة اكس تربيع يبقى السارة عند + +682 +01:19:42,620 --> 01:19:46,260 +الواحد معرفة و عند اتنين معرفة وبالتالي دخلت في ال + +683 +01:19:46,260 --> 01:19:50,240 +interview والله والله قررتها لا يؤثر عندي بصير + +684 +01:19:50,240 --> 01:19:54,640 +المشتقة معرفة عند الواحد و عند اتنينهذا كله مثلا + +685 +01:19:54,640 --> 01:19:58,720 +ماعنديش مشكلة بس لما تبقى دالة مجزة إلى جزءين بصير + +686 +01:19:58,720 --> 01:20:01,400 +اللي احتمال المشاكل او ثلاثة جزء او اربع تصير + +687 +01:20:01,400 --> 01:20:05,240 +المشاكل عند الأطراف ممكنك لايستبعد الأطراف ورايا + +688 +01:20:05,240 --> 01:20:12,020 +دماغك هذا كل ما في الأمر طب نرجع لسؤالنا هذا ال + +689 +01:20:12,020 --> 01:20:16,180 +section اللي بين ادينا اللي هو section 4 4 con kvt + +690 +01:20:16,180 --> 01:20:24,250 +اللي هو mainالتقاعر او التحدب للمنحنة تمام؟ and ال + +691 +01:20:24,250 --> 01:20:28,550 +curve sketching ورسم المنحنيات يبقى احنا في هذا + +692 +01:20:28,550 --> 01:20:34,190 +section بنستخدم كل ما سبق الدراسة وفي section 4.1 + +693 +01:20:34,190 --> 01:20:41,210 +و4.2 و4.3 في رسم المنحنيات وخاصةلـ critical points + +694 +01:20:41,210 --> 01:20:48,290 +وفترات التزايد والتناقص وكذلك ال local maximum و + +695 +01:20:48,290 --> 01:20:53,490 +ال local minimum يبقى احنا بنستخدم كل ما سبق + +696 +01:20:53,490 --> 01:20:59,450 +دراسته في الرسمبنذهب فقط للأول ونعرف الـ Concavity + +697 +01:20:59,450 --> 01:21:03,950 +لمنحنة كيف بدي أحصل عليه وبعد ذلك نشوف كيف بدنا + +698 +01:21:03,950 --> 01:21:07,150 +نعملها فبعدين بقول graph of a differentiable + +699 +01:21:07,150 --> 01:21:14,200 +function y تساوي f of x isconcave up على فترة I + +700 +01:21:14,200 --> 01:21:19,500 +ولم اقول انها مقفلة او مفتوحة او مفتوحة او مفتوحة + +701 +01:21:19,500 --> 01:21:19,780 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +702 +01:21:19,780 --> 01:21:21,340 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +703 +01:21:21,340 --> 01:21:22,920 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +704 +01:21:22,920 --> 01:21:24,760 +او مفتوحة او مفتوحة او مفتوحة او مفتوحة او مفتوحة + +705 +01:21:24,760 --> 01:21:33,120 +او مفتوحة او مفتوحة او مفتوو بقول لك ده لكن cave + +706 +01:21:33,120 --> 01:21:37,640 +up if ال if increasing بحاجة تضيق المشتقة يبقى + +707 +01:21:37,640 --> 01:21:42,120 +كلامي صح ولا غلط؟ غلط يبقى صح صح وخد بالك من + +708 +01:21:42,120 --> 01:21:47,280 +النقطة هذه إذا المشتقة كانت تزايدية يعني إيش؟ يعني + +709 +01:21:47,280 --> 01:21:51,080 +المشتقة الثانية بتكون أكبر من ال zero صح ولا .. + +710 +01:21:51,080 --> 01:21:55,120 +بقول لك ده لا increasing إذا المشتقة تبعتها كانت + +711 +01:21:55,120 --> 01:21:57,960 +أكبر من ال zero يبقى ال if prime increasing إذا + +712 +01:21:57,960 --> 01:22:02,590 +مشتقتهااللي صارت المشتقة الثانية بتبقى أكبر من مين + +713 +01:22:02,590 --> 01:22:07,150 +من ال zero يبقى الدالة بيقول هيكون curve up + +714 +01:22:07,150 --> 01:22:12,890 +المنحنة مفتوح إلى أعلى إذا كانت ال F prime + +715 +01:22:12,890 --> 01:22:17,410 +increasing إذا كانت الدالة إذا كانت مشتقة هذه + +716 +01:22:17,410 --> 01:22:21,630 +الدالة خلال هذه الفترة كانت المشتقة تزايد مش + +717 +01:22:21,630 --> 01:22:28,220 +الدالة مشتقة الدالة كانت تزايدياconcave down يعني + +718 +01:22:28,220 --> 01:22:34,740 +إلى أسفل إذا كانت المشتقة خلالها decreasing يبقى + +719 +01:22:34,740 --> 01:22:40,920 +إذا كانت مشتقة الدالة تناقصية وليست الدالة مشتقة + +720 +01:22:40,920 --> 01:22:46,180 +الدالة تناقصية طيب بدي أعيد صياغة الكلام اللي قلته + +721 +01:22:46,180 --> 01:22:50,960 +بناحية رياضية ثانيةفبعدين بقول ايه ده اللي بتبقى + +722 +01:22:50,960 --> 01:22:56,140 +cone curve up اذا المشتق الثاني اكبر من مين من ال + +723 +01:22:56,140 --> 01:23:00,380 +zero ما هي هذه الترجمة ان ال F prime increasing صح + +724 +01:23:00,380 --> 01:23:05,200 +ولا لأ مش قبل شوية اخدنا اذا المش F prime اكبر من + +725 +01:23:05,200 --> 01:23:10,030 +ال zero يبقى ال F increasingهنا إذا الـ f double + +726 +01:23:10,030 --> 01:23:14,730 +prime أكبر من 0 يبقى الـ f prime increasing يبقى + +727 +01:23:14,730 --> 01:23:19,710 +أكبر من الـ 0 الـ graph of f over a is concave up + +728 +01:23:19,710 --> 01:23:24,930 +يبقى مفتوح إلى أعلى الآن لو كانت المشتقة الثانية + +729 +01:23:24,930 --> 01:23:29,090 +أقل من الـ 0 على الفترة I يبقى ال graph of it + +730 +01:23:29,090 --> 01:23:35,600 +بديكون ماله concave downالكتاب بيسمي الشرطين هدول + +731 +01:23:35,600 --> 01:23:41,760 +هيك بيسميهم second derivative + +732 +01:23:41,760 --> 01:23:44,820 +test + +733 +01:23:44,820 --> 01:23:49,340 +for concavity + +734 +01:23:53,590 --> 01:23:59,170 +يبقى المشتاقة الثانية لقياس تقار و تحدب المنحنة + +735 +01:23:59,170 --> 01:24:03,910 +لكن ال first derivative تستخدم لمن؟ لتحديد ال + +736 +01:24:03,910 --> 01:24:07,710 +local maximum و ال local من فوق ال local extreme + +737 +01:24:07,710 --> 01:24:13,150 +value أيه الفرق في ما بينهما؟ طيب إذا المنحنة + +738 +01:24:13,150 --> 01:24:19,450 +بالشكل إن هذا طلع إن هذا كنك يابوينهذا concave + +739 +01:24:19,450 --> 01:24:25,810 +وين؟ فعندي النقطة اللي عندنا هذه انتقل من concave + +740 +01:24:25,810 --> 01:24:30,490 +up إلى concave من concave down إلى concave up + +741 +01:24:30,490 --> 01:24:36,710 +النقطة اللي هذه بنسميها نقطة انقلاب للمنحنةيبقى + +742 +01:24:36,710 --> 01:24:40,330 +inflection point يبقى ال inflection point بدي + +743 +01:24:40,330 --> 01:24:46,790 +شرطين لها حتى تتحقق أول شي بدي تبقى دالة متاصلة + +744 +01:24:46,790 --> 01:24:51,550 +عند هذه النقطة الشرط الثاني بدي اتجاه ال concavity + +745 +01:24:51,550 --> 01:24:56,850 +يتغير من down إلى up أو من up إلى down طلع عند + +746 +01:24:56,850 --> 01:25:02,330 +النقطة الثانية هذه كان concave up صار concave down + +747 +01:25:02,590 --> 01:25:06,690 +يبقى بادلة تاني بيقول إذا ال F كانت دالة متاصلة + +748 +01:25:06,690 --> 01:25:12,230 +على ال open interval التي تحتوي على مين؟ على X0 + +749 +01:25:12,230 --> 01:25:17,590 +يبقى أنا عندي في فترة تحتوي على نقطة زي النقطة + +750 +01:25:17,590 --> 01:25:23,510 +هذه، كويس؟ تمام، إيش حصل؟ دالة دالة متاصلةand if + +751 +01:25:23,510 --> 01:25:28,130 +it changes the direction of its concavity under X0 + +752 +01:25:28,130 --> 01:25:33,470 +عند X0 الدالة غيرت اتجاه الconcavity تبعها يبقى في + +753 +01:25:33,470 --> 01:25:36,970 +هذه الحالة بقول النقطة X0 و F of X0 بسميها + +754 +01:25:36,970 --> 01:25:40,870 +inflection point دي ما كان ممكن ماتلاقيش التعريف + +755 +01:25:40,870 --> 01:25:43,750 +تبعي هو اللي منصوص عالي في الكتاب يكون الكتاب + +756 +01:25:43,750 --> 01:25:48,250 +ماتلاقي كتبه من نص آخر لكن هذا أدق نص لايمكن يخر + +757 +01:25:48,250 --> 01:25:52,600 +منه الميه زي ما بقولهيبقى انا عشان يكون عندي + +758 +01:25:52,600 --> 01:25:56,060 +inflection point على المنحنة بدي اتحقق شرطين + +759 +01:25:56,060 --> 01:26:00,320 +الاتصال تبع الدلة عند هذه النقطة اتنين بدي اتغير + +760 +01:26:00,320 --> 01:26:05,040 +اتجاه ال connectivity لهذه الدلة ال inflection + +761 +01:26:05,040 --> 01:26:11,240 +point بتحصل وين؟بتدور عليها وين يعني؟ في مكانين + +762 +01:26:11,240 --> 01:26:14,760 +اللي المشتقة الثاني عنده يساوي zero او المشتقة + +763 +01:26:14,760 --> 01:26:18,460 +الثانية تبقى غير معرفة زي ال local maximum و ال + +764 +01:26:18,460 --> 01:26:23,720 +local minimum بدور عليها وين؟ اذا المشتقة الأولى + +765 +01:26:23,720 --> 01:26:26,860 +صفر او المشتقة الأولى غير معرفة؟ اذا المشتقة + +766 +01:26:26,860 --> 01:26:32,550 +الثانية بدل من المشتقة الأولى طيب السؤال هولو كانت + +767 +01:26:32,550 --> 01:26:37,150 +المشتقة ثانية تساوي zero او المشتقة الثانية ما هي + +768 +01:26:37,150 --> 01:26:45,850 +معروفة يعني ضروري الاقي inflection point لأ لأ ليس + +769 +01:26:45,850 --> 01:26:50,890 +بالضرورة يبقى ليس بالضرورة اذا بتطلع بقى قبل ما + +770 +01:26:50,890 --> 01:26:56,370 +نكمل هنالو جيت الفترة من هنا لهنا الفترة اللي + +771 +01:26:56,370 --> 01:27:01,830 +عندنا هذه مفتوح الى أعلى والله الى أسفل الى أعلى + +772 +01:27:01,830 --> 01:27:07,710 +يبقى هذه المرحلة بقول عليها كن كبط + +773 +01:27:08,580 --> 01:27:15,640 +طيب هذه من هنا لغاية هنا concave down يبقى مفتوح + +774 +01:27:15,640 --> 01:27:24,540 +لها لفترة هذه concave up هذه concave down + +775 +01:27:28,820 --> 01:27:34,660 +هذه النقطة وهذه النقطة وهذه النقطة اكس واحد و اكس + +776 +01:27:34,660 --> 01:27:39,040 +اتنين و اكس تلاتة عندهم في انفليكشن point يبقى هذه + +777 +01:27:44,070 --> 01:27:49,890 +point يبقى هدول نقاط انقلاب للمنحنى مين هما اللي + +778 +01:27:49,890 --> 01:27:56,230 +هي النقطة اللي عندك هذه و النقطة هذه و النقطة هذه + +779 +01:27:56,230 --> 01:28:04,050 +و كذلك النقطة اللي عندك مين النقطة هذه طبعا هذه + +780 +01:28:04,050 --> 01:28:09,770 +بقدرش أتأكد منها لأن ماعنديش منحنى بعدها يبقى هذه + +781 +01:28:09,770 --> 01:28:15,680 +بقدرش أتأكد منها بالضبط الآنإلا إذا خلّيت القوس + +782 +01:28:15,680 --> 01:28:18,780 +ينزل شوية ماشي الحال، لكن أنا بقول هاي كل اللي + +783 +01:28:18,780 --> 01:28:22,420 +بقدر أقوله، هدول واحدة، اتين، اتين، تلاتة متأكد + +784 +01:28:22,420 --> 01:28:25,860 +منهم، هد مش متأكد منها، يبقى بقول عندي النقطة + +785 +01:28:25,860 --> 01:28:30,300 +التلاتة هدول فيها عندي main inflection pointهي + +786 +01:28:30,300 --> 01:28:34,720 +concave up، concave down، concave up، concave down + +787 +01:28:34,720 --> 01:28:38,800 +يبقى هذه الفترة جسمت عليها التقسيمات هذه السؤال هو + +788 +01:28:38,800 --> 01:28:45,340 +لو كانت المشتقة تساوي zero المشتقة الثانية هل من + +789 +01:28:45,340 --> 01:28:50,300 +الضروري يكون في عندي inflection point الإجابة ليس + +790 +01:28:50,300 --> 01:28:56,080 +بالضرورة نعطيك هالملاحظة هذه وبها ننهي المحاضرة + +791 +01:28:56,080 --> 01:28:57,680 +الملاحظة بتقول ما يأتي + +792 +01:29:07,390 --> 01:29:15,890 +إذا yw' تساوي 0 فهو + +793 +01:29:15,890 --> 01:29:20,430 +ليس صحيح + +794 +01:29:22,840 --> 01:29:33,260 +through that must there is + +795 +01:29:33,260 --> 01:29:42,260 +an inflection point + +796 +01:29:42,260 --> 01:29:48,160 +there is an inflection point for example + +797 +01:29:50,680 --> 01:29:57,540 +كشغلة توضيحية على ذلك ال Y تساوي X أُص أربعة لو + +798 +01:29:57,540 --> 01:30:03,580 +بدى تجيب المشتقة الأولى بتعطيك أربعة X تكيب مشتقة + +799 +01:30:03,580 --> 01:30:12,360 +ثانية بتساوي اتناشر X تربيع وهذه تساوي Zero at X + +800 +01:30:12,360 --> 01:30:20,620 +يساوي Zeroلو جينا رسمنا هذه بقول هي المنحنة كويس + +801 +01:30:20,620 --> 01:30:25,960 +يبقى هذا محور X و هذا Y طبعا رسمناها قبل هيك يبقى + +802 +01:30:25,960 --> 01:30:33,780 +المنحنة بدي أجيلك هيك هذا Y تساوي X أُص أربع + +803 +01:30:33,780 --> 01:30:40,220 +المشكلة عن وين عند ال zero الآن قبل ال zero + +804 +01:30:40,220 --> 01:30:46,530 +المنحنة كانت كيف وين؟بعد الـ zero مغيرش يبقى هذه + +805 +01:30:46,530 --> 01:30:52,150 +هذا الجزء مفتوح + +806 +01:30:52,150 --> 01:30:57,850 +الى أعلى و هذا كمان concave up يعني الدالة عند ال + +807 +01:30:57,850 --> 01:31:01,990 +zero صحيح دالة متصلة بس لم تغير اتجاه ال concavity + +808 +01:31:01,990 --> 01:31:08,190 +يبقى وبالتالي ليست inflection point يبقى ساوي zero + +809 +01:31:08,190 --> 01:31:19,830 +butالاكس تساوي زيرو مالها + +810 +01:31:19,830 --> 01:31:25,490 +is + +811 +01:31:25,490 --> 01:31:30,550 +not + +812 +01:31:30,550 --> 01:31:38,370 +an inflection point + +813 +01:31:44,950 --> 01:31:55,090 +لأن الـ wireprime لا يتغير + +814 +01:31:55,090 --> 01:31:56,570 +صورتها + +815 +01:32:06,310 --> 01:32:10,870 +يبقى مفيش handy inflection point وصلنا ل الأمثلة + +816 +01:32:10,870 --> 01:32:14,990 +خلّي الأمثلة للمرة القادمة ان شاء الله + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/a29rwypicLY_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/a29rwypicLY_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..b013995891e02b75935163db8b6c8b038e39a931 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/a29rwypicLY_postprocess.srt @@ -0,0 +1,4160 @@ +1 +00:00:20,860 --> 00:00:26,020 +بسم الله الرحمن الرحيمهذه تعتبر المحاضرة الأولى + +2 +00:00:26,020 --> 00:00:31,340 +بالنسبةلكوا طبعا الغالبية العظمى منكم طلاب جدد + +3 +00:00:31,340 --> 00:00:38,840 +فنهنئكم بقابولكم في الجامعة الإسلامية و كذلك ببدء + +4 +00:00:38,840 --> 00:00:45,280 +الفصل الدراسى الجديد لذلك أول شغلة سنشير اليها + +5 +00:00:45,280 --> 00:00:53,310 +الفرق بين التعليم المدرسى والتعليم الجامعىطبعا + +6 +00:00:53,310 --> 00:01:01,390 +هنتناول هذا الكتاب القاعة المدرس طريقة الدراسة + +7 +00:01:01,390 --> 00:01:06,290 +تمام؟ بعد هيك ننتقل إلى النقطة الثانية في هذه + +8 +00:01:06,290 --> 00:01:15,740 +المحاضرةوهي طريقة التدريس والمنهج الذي سيدرس خلال + +9 +00:01:15,740 --> 00:01:21,840 +هذا الفصل النقطة اللي بعدها لساعة ثانية من هذه + +10 +00:01:21,840 --> 00:01:27,260 +المحاضرة سندخل فيصل بالموضوع وهي النقطة الأولى من + +11 +00:01:27,260 --> 00:01:33,320 +أول section في المقرر تمام؟ نبدأ أول حاجة بالكتاب + +12 +00:01:33,320 --> 00:01:38,130 +الكتاباللي انت في المرحلة الثانوية والإعدادية + +13 +00:01:38,130 --> 00:01:41,910 +والابتدائية، اللي هو كتاب الوزارة، لابتقدر تطلع + +14 +00:01:41,910 --> 00:01:47,790 +عنه لايمين ولا إشمال، ولو أجى موجهي المادة ولاقي + +15 +00:01:47,790 --> 00:01:52,810 +عندك كتاب على الطاولة غير الكتاب المقرر، بيبقى + +16 +00:01:52,810 --> 00:01:56,330 +دليل مدرس، احنا بيقولك ان شاء الله تجيب خمس كتب + +17 +00:01:56,330 --> 00:02:00,750 +بالإضافة لكتاب المقرر وتحطها قدامك ونكون مبسوطين، + +18 +00:02:00,750 --> 00:02:06,290 +معناته ان انت بالذاكر وبتطلع، تمام؟لكننا سنسمي + +19 +00:02:06,290 --> 00:02:11,890 +كتابا واحدا هو العمودي الفقري أثناء تدريسنا اللي + +20 +00:02:11,890 --> 00:02:15,670 +هنكون ماشيين على هوا هذا الكتاب لكن اللي جينا + +21 +00:02:15,670 --> 00:02:19,810 +معلومة أخرى زيادة على ما هي موجودة في الكتاب + +22 +00:02:19,810 --> 00:02:25,010 +بنجيبها و بنعطيهاكوا كمان لإن احنا في مرحلة جامعية + +23 +00:02:25,010 --> 00:02:31,310 +مرحلة صقل العقول و بناء الشخصيات العلمية و + +24 +00:02:31,310 --> 00:02:35,980 +الأكاديميةلأن لو عدتكوا بعد أربع سنين و إذا كنت من + +25 +00:02:35,980 --> 00:02:40,340 +الهندسة بعد خمس سنين ممكن توقف مكاني في هذا المكان + +26 +00:02:40,340 --> 00:02:45,800 +و تدرس للطلاب وبالتالي في الأربع سنين أو الخمس + +27 +00:02:45,800 --> 00:02:50,000 +سنين هم اللي بيبنوا شخصيتك العلمية و شخصيتك + +28 +00:02:50,000 --> 00:02:56,760 +الأكاديمية و يؤهلوك لإنك تكمل بعد ذلك الكتاب اللي + +29 +00:02:56,760 --> 00:03:01,280 +بين إيدينا اللي هندرسه المرة هذه اسمه Calculus + +30 +00:03:06,300 --> 00:03:11,140 +طبعا في calculus B و في calculus C هذا حوالي ثلث + +31 +00:03:11,140 --> 00:03:16,820 +الكتاب تبع كتاب ال calculus المؤلف اسمه Thomas + +32 +00:03:19,380 --> 00:03:24,600 +طبعا في كتب calculus كتيرة لمؤلفين اخرين احده من + +33 +00:03:24,600 --> 00:03:29,960 +الكتاب اللى المؤلف تبعه اسمه Thomas الطبعة تبعت + +34 +00:03:29,960 --> 00:03:37,160 +هذا الكتاب هي رقم اتناشر اتناشر editionيعني + +35 +00:03:37,160 --> 00:03:43,660 +الطابعة ثانية عشرة كل سنتين أو ثلاث سنوات بيطبق + +36 +00:03:43,660 --> 00:03:48,660 +بطابعة جديدة بيعمل فيها بعض التغييرات إضافات نقصان + +37 +00:03:48,660 --> 00:03:53,400 +حسب التطور العلمي إلى آخرى هذا هو الكتاب اللي + +38 +00:03:53,400 --> 00:03:59,080 +هندرس منه أي كتاب كالقلاس آخر يعتبر مرجع عندك + +39 +00:03:59,080 --> 00:04:05,290 +تقتني كتاب الأزهرإذا كان كتاب القدس المفتوحة، إذا + +40 +00:04:05,290 --> 00:04:09,310 +كان أي كتاب كالكلس آخر، ما عندنا مشكلة، هذا لو + +41 +00:04:09,310 --> 00:04:13,690 +جيته بيكون مارجع بالنسبة لك، لكن هذا هو كتابنا + +42 +00:04:13,690 --> 00:04:19,970 +الأصلي الذي سندرس عليه وإذا في معلومة مش موجودة ان + +43 +00:04:19,970 --> 00:04:24,430 +شاء الله بنجيبها و بنحطها، بنضيف لهذه المعلومة + +44 +00:04:24,430 --> 00:04:29,540 +اللي موجودةفي هذا الكتاب، لكن في المدارس بيكون + +45 +00:04:29,540 --> 00:04:32,880 +كتاب واحد مافيش غيره اللي هو كتاب الوزراء وفي + +46 +00:04:32,880 --> 00:04:38,080 +توجيهه بتروح تشتريلك كتاب تاني وما إلى ذاك بيسميها + +47 +00:04:38,080 --> 00:04:43,460 +كتب تجارية وليست مراجعة، تمام؟ يبقى هذا الفرق بين + +48 +00:04:43,460 --> 00:04:48,640 +كتابناوكتاب ميم وكتاب المدارس، اتنين، بالنسبة + +49 +00:04:48,640 --> 00:04:54,040 +للقاعة، انت كل محاضرة بتقعد في كرسي، هاي الشباب + +50 +00:04:54,040 --> 00:04:56,820 +الأربع هدول قاعدين في الكرسي الأول او في المقعد + +51 +00:04:56,820 --> 00:05:00,040 +الأول، المرة جاية ممكن يكونوا في المقعد الأخير، + +52 +00:05:00,040 --> 00:05:02,740 +المرة اللي بعدين يكونوا في المقعد ده نصف، يعني ان + +53 +00:05:02,740 --> 00:05:07,700 +القاعة ده شرية الجمعة لمن سبقاللي بيسبق هو اللي + +54 +00:05:07,700 --> 00:05:11,520 +بيقعد قدام، بيذهبك وبعدين بيقعد ورا، لكن في + +55 +00:05:11,520 --> 00:05:15,820 +المدارس مقعد ثابت، بتظلك طول السنة وانت قاعد في + +56 +00:05:15,820 --> 00:05:20,400 +نفس المكان، يا بيزهج منك المقعد، يا انت بتزهج، يا + +57 +00:05:20,400 --> 00:05:25,060 +انا مابتزهجوش، بيصيروا صحبة مع بعض، تمام؟ هاي كمان + +58 +00:05:25,060 --> 00:05:28,620 +فرق بين التعليم المدرسي والتعليم الجامعي من ناحية + +59 +00:05:28,620 --> 00:05:33,740 +وجودك في القاعة، لن تسمع جرس في الجامعة، نهائيبس + +60 +00:05:33,740 --> 00:05:39,220 +هناك كل 45 دقيقة بتسمع ايش؟ بتسمع جرس و المدرس + +61 +00:05:39,220 --> 00:05:42,280 +بيطلع و بيجي مدرس اخر و انت قاعد في نفس المكان لأ + +62 +00:05:42,280 --> 00:05:47,040 +هنا ممكن يتغير المدرس و تتغير القاعة هاي توجب + +63 +00:05:47,040 --> 00:05:51,500 +انكوا من وين؟ من الطابق الأرضي في مبنى القدس الى + +64 +00:05:51,500 --> 00:05:55,880 +الطابق السادس في مبنى طيبة تمام؟ و بعد ما تخلصي + +65 +00:05:55,880 --> 00:05:59,860 +ممكن تروح على المختبرات في مبنى Pو بعد هيك مش + +66 +00:05:59,860 --> 00:06:05,880 +عارفة تروح على قاعة و هيكذا المحاضرة تبعتك ساعتين + +67 +00:06:05,880 --> 00:06:10,640 +لو كانت ساعة من حق المدرسة يطلع آخر عشر دقايق + +68 +00:06:10,640 --> 00:06:14,320 +وبالتالي لما تكون المحاضرة ساعتين من حق يطلع آخر + +69 +00:06:14,320 --> 00:06:19,820 +تلت ساعة لكن هذا مستحيل بالنسبالي انطلعت سريع بطلع + +70 +00:06:19,820 --> 00:06:23,980 +آخر ربع ساعة و يمكن آخر عشر دقايق و يمكن آخر سبعة + +71 +00:06:23,980 --> 00:06:28,610 +دقايقانت و أختك حسب الموضوع اللي في بين إيدينا خلص + +72 +00:06:28,610 --> 00:06:33,290 +و الله ماخلصش تمام؟ يبقى هذا بتقعد هنا و بتنسى + +73 +00:06:33,290 --> 00:06:39,150 +حكاية الوجد تمام يا سيدي؟ لن تسمع جراس؟ طب ليش + +74 +00:06:39,150 --> 00:06:43,710 +بيخلونا أخر عشر دقايق و أخر وقت نطلع؟ ايوة انت + +75 +00:06:43,710 --> 00:06:48,770 +نعست بتروح تغسل وجهك، عطشت بتروح تشرب، بدك تنتقل + +76 +00:06:48,770 --> 00:06:52,650 +من قاع إلى قاع، بتغير النشاط تبعك حتى بيتغير + +77 +00:06:52,650 --> 00:06:57,210 +تفكيركوهذا شيء ضروري جدك، لكن ضليت، قعد في نفس + +78 +00:06:57,210 --> 00:07:01,470 +المكان أربع ساعات، بتقرا في حالك طول اليوم، مش + +79 +00:07:01,470 --> 00:07:06,510 +هيك؟ لكن في الجامعة لأ، فيش مقعد ثابت، فيش هذا + +80 +00:07:06,510 --> 00:07:09,550 +المكان، إيه لك بتغيرهش طول السنة؟ لأ لأ يا عم، + +81 +00:07:09,550 --> 00:07:13,590 +بتقدر تغيره كل محاضرة، أنت و بخلق، وين ما تيجي + +82 +00:07:13,590 --> 00:07:19,670 +تيجي، تمام؟ يبقى هذا بالنسبة ليه؟ بالنسبة للمكان + +83 +00:07:20,220 --> 00:07:27,000 +ضرورة التواجد في القاعة قبل المدرس لماذا او + +84 +00:07:27,000 --> 00:07:31,020 +للمحاضرة الساعة اتناشى الساعة اتناشى الا دقيقة + +85 +00:07:31,020 --> 00:07:35,780 +يمكن تلاقيني عندك جوا هنا تمام باتخرش ابدا باذن + +86 +00:07:35,780 --> 00:07:40,280 +الله الا اذا ضعت ضرورة واتخرت دقيقتين او تلاتة + +87 +00:07:40,280 --> 00:07:46,680 +وهذا نادرا دائما وبحاول التزمبالموعد بالضبط و يمكن + +88 +00:07:46,680 --> 00:07:51,600 +قبل الموعد، تمام؟ فاحرص أن تكون قبل الموعد موجود + +89 +00:07:51,600 --> 00:07:55,600 +في قاعة المحاضرة حتى ت .. سواء كنت قبل دقيقتين + +90 +00:07:55,600 --> 00:08:01,340 +تلاتة تتأهل نفسيا مشان .. مشان تاخد معلومات و تبدأ + +91 +00:08:01,340 --> 00:08:04,840 +تسجل من الأول لكن اللي بيجي متأخر دقيقتين تلاتة + +92 +00:08:04,840 --> 00:08:08,700 +خمس دقايق بيصير زي اللي بيشعلك في السيارة و هي + +93 +00:08:08,700 --> 00:08:12,810 +ماشية أو في القطاريمكن يوجع، يمكن ينكسر، يمكن + +94 +00:08:12,810 --> 00:08:16,570 +ينكسر ضلعينه الزاوية، الله أعلم، مايعرفش، المهم + +95 +00:08:16,570 --> 00:08:22,630 +لازم يحصل فيه عنده خلال ما، لذلك احصر، احرص على + +96 +00:08:22,630 --> 00:08:29,830 +الحضور مبكرا، ولا تتأخر، والتزم بالقاعة بمجرد + +97 +00:08:29,830 --> 00:08:34,910 +حضورك تمام يا سيدي؟ يبقى هذا بالنسبة ليش؟ للقاعة + +98 +00:08:34,910 --> 00:08:40,270 +والالتزام في القاعة، نجي لفرق آخرفي المدارس بتلاقي + +99 +00:08:40,270 --> 00:08:45,570 +المدرس هو النظر معاه عصاه، لن تجد مدرس في الجامعة + +100 +00:08:45,570 --> 00:08:48,990 +معاه عصاه ولا حتى رئيس الجامعة ولا نواب، مافيش + +101 +00:08:48,990 --> 00:08:53,890 +حاجة اسمه معاه عصاه، هذا للصغاريبقى حاول تسجل اي + +102 +00:08:53,890 --> 00:08:58,690 +معلومة جديدة بالنسبة اليك بيتشعر حكمة مقولة اللي + +103 +00:08:58,690 --> 00:09:03,490 +بدكيها تمام؟ في هذه الحالة بصير عندك حصيلة اكتر من + +104 +00:09:03,490 --> 00:09:07,470 +زميلك اللي اندخلت انت ويا الجامعة في نفس ايه؟ في + +105 +00:09:07,470 --> 00:09:12,390 +نفس المستوى طيب الان نجي اليك كيف بدى ادرس بطريقة + +106 +00:09:12,390 --> 00:09:16,390 +صحيحة الان انا بدأ اشرحلك اليوم موضوع ال functions + +107 +00:09:16,390 --> 00:09:20,790 +يعني الدوال او الاقتراناتبدى يا جبل تيجى على + +108 +00:09:20,790 --> 00:09:24,810 +المحاضرة تتطلع عليها جراية زى جراية الجريدة جراية + +109 +00:09:24,810 --> 00:09:26,890 +الجريدة البعض ما خلاص بيكون فى دماغنا بس فى + +110 +00:09:26,890 --> 00:09:30,510 +العناوين الرئيسى لكن التفاصيلات ابنى نساها إلا إذا + +111 +00:09:30,510 --> 00:09:34,350 +كان فى تفصيل مثير بيظل ملزق فى دماغنا يبقى انا + +112 +00:09:34,350 --> 00:09:37,910 +بديك تجراها مش تقعد تحل بس تجراها زى جراية الجريدة + +113 +00:09:37,910 --> 00:09:42,290 +هي تتطلع انه اه هذا ال functions بدي اتكلم عنهال + +114 +00:09:42,290 --> 00:09:45,730 +domain و ال range يعني عن المجال و المدى و ما .. + +115 +00:09:45,730 --> 00:09:48,730 +خلاص بدي أروح أجرى الكلمة بس يكون في دماغك إيش بدي + +116 +00:09:48,730 --> 00:09:51,950 +أحكي قبل ما أحكي يبقى هذا التحضير مش بديك تروح + +117 +00:09:51,950 --> 00:09:55,550 +تجرى و تحل و تجرى .. لا لا لا بديش هذا الكلام بدي + +118 +00:09:55,550 --> 00:09:59,390 +بس يكون عندك خلفية زي اللي بيحلم حلم لما يصحب و + +119 +00:09:59,390 --> 00:10:03,270 +يصير عارف إيش بعض الأشياء الرئيسية و يمكن ينسى كل + +120 +00:10:03,270 --> 00:10:07,330 +الحلم أما ماعندي مشكلة المهم يصير في دماغك خلفية + +121 +00:10:07,330 --> 00:10:11,350 +عن الموضوع اللي بدنا نشرها نامدخلنا القاعدة بيبقى + +122 +00:10:11,350 --> 00:10:16,590 +بدنا نتابع المدرس و هو بيشرح و بدنا نكتب كل كلمة + +123 +00:10:16,590 --> 00:10:20,950 +بيكتبها او بيقولها اه مشان هذه بصير مرجع اننا في + +124 +00:10:20,950 --> 00:10:25,010 +الدار لما نروح بدنا .. بدنا نذاكرطب كتبنا و الحمد + +125 +00:10:25,010 --> 00:10:29,210 +لله وناقشنا طبعا أنا بطرح أسئلة و بطلب منك إجابة + +126 +00:10:29,210 --> 00:10:35,630 +منك بدك تشارك ليها بالإجابة هذه بتولد تفكير عندك و + +127 +00:10:35,630 --> 00:10:40,950 +بتولد أسئلة لم تكن تخطر على بلق قبل أنا مطرحها قبل + +128 +00:10:40,950 --> 00:10:45,430 +ما مطرح السؤال الأسئلة اللي بطرحها تجيب على كثير + +129 +00:10:45,430 --> 00:10:48,870 +من التساؤلات اللي ممكن هي تطرق على دماغك و أنت + +130 +00:10:48,870 --> 00:10:53,330 +قاعد فلا تستعجلإذا أنا خلصت و ماحدش سأل بقول مين + +131 +00:10:53,330 --> 00:10:57,450 +بده يحب يسأل سؤال، مين عنده أي سؤال، تبخلش على + +132 +00:10:57,450 --> 00:11:02,490 +نفسك، ماحدش بسمع من ساكن، اسأل ولو كان سؤالك غلط، + +133 +00:11:02,490 --> 00:11:06,170 +واسأل كمان مرة ولو كان سؤالك غلط، المرة التالتة + +134 +00:11:06,170 --> 00:11:11,350 +بصير تسأل صح، يعني عود نفسك السؤال، والعلم لن يثبت + +135 +00:11:11,540 --> 00:11:15,820 +إلا بالتساؤل، بالتساؤل اللي بثبت العلم في دماغك و + +136 +00:11:15,820 --> 00:11:19,880 +بصير من أهل الدراية و العلم، ما سألتش بصير زي ما + +137 +00:11:19,880 --> 00:11:24,520 +فهمت ركبت المعلومات في دماغي زميل صح و لا غلط زي + +138 +00:11:24,520 --> 00:11:29,860 +ما فهمت، و طبعا العقول متفاوتة و هو من هنا فإن + +139 +00:11:29,860 --> 00:11:36,140 +الأفهام تكون متفاوتةممكن تكون فهمت خطأ و ممكن تكون + +140 +00:11:36,140 --> 00:11:40,340 +فهمت صح لكن اذا روحت سؤالة المدرس بصير تفهم صح + +141 +00:11:40,340 --> 00:11:45,800 +تمام؟ يبقى احنا سجلنا و تابعنا و ماصرحناش برا + +142 +00:11:45,800 --> 00:11:50,960 +أثناء المحاضرة ماصرناش من بني سرحان لأ نصرنا من + +143 +00:11:50,960 --> 00:11:56,600 +بني علم اه من تابعنا مش صرحنا برا اه كويس؟ يبقى + +144 +00:11:56,600 --> 00:12:01,820 +كنا هنا قاعدين بالجسم والعقل مش بالجسم والعقل + +145 +00:12:01,820 --> 00:12:06,060 +سرحان براأصحى درباك أنت وياه طيب تابعنا و سجلنا + +146 +00:12:06,060 --> 00:12:09,940 +محاضرتنا و كلش تمام طيب اللي ضال يتابع من أول + +147 +00:12:09,940 --> 00:12:14,460 +المحاضرة إلى آخره قداش حصل من المعلومات بقولك + +148 +00:12:14,460 --> 00:12:18,700 +والله أنا طلعت فاهم أنا بطنه طلع فاهم بس خمسين في + +149 +00:12:18,700 --> 00:12:23,640 +المية بس أجعص واحد بطلع خمسين في المية طب و من وين + +150 +00:12:23,640 --> 00:12:28,550 +بدنا نجيب الخمسين التانية؟ بقولك بسيطة جدابتروح + +151 +00:12:28,550 --> 00:12:32,930 +على الدار بتقرا المحاضرة من جديد ان روحت قريتها في + +152 +00:12:32,930 --> 00:12:37,450 +نفس اليوم في نص ساعة بتقراها ويمكن أقل كمان واذي + +153 +00:12:37,450 --> 00:12:42,610 +بتخليها لبكرا بدها ساعة اه لان بصير تحلم و تتذكر + +154 +00:12:42,610 --> 00:12:46,530 +ايش جال من بارحه و ايش كان جصده تمام؟ واذي بتخليها + +155 +00:12:46,530 --> 00:12:49,750 +الأخر الأسبوع لخميس والجمعة لإنه عندنا اجازة + +156 +00:12:49,750 --> 00:12:55,870 +امساها بدها أربع ساعات ليه ربالك؟ ولذلك بدك تقرا + +157 +00:12:55,870 --> 00:13:00,610 +أولا بأولوبحب أطمنك لامتحان الأول بنعطيكوا + +158 +00:13:00,610 --> 00:13:04,850 +امتحانين لامتحان الأول يوم تسعة عشرة يعني بنبقى + +159 +00:13:04,850 --> 00:13:09,090 +عليكوا من اليوم بعد تمانية وثلاثين يوم من الآن في + +160 +00:13:09,090 --> 00:13:14,630 +عندك لمتحان النصف الأول بنعطى نمتحانين نصفين + +161 +00:13:14,630 --> 00:13:19,950 +لمتحان النصف الأول في تسعة عشرة ولمتحان الثاني بعد + +162 +00:13:19,950 --> 00:13:23,730 +ما تاخد الأول بنقولك لمتحان لكن اختصارا بعده + +163 +00:13:23,730 --> 00:13:28,130 +باربعين يوم يعني كل اربعين يومابن يعطيك امتحان + +164 +00:13:28,130 --> 00:13:32,330 +وبالتالي امتحاني وبعد ذلك الامتحان النهائي وسأرجع + +165 +00:13:32,330 --> 00:13:37,370 +إلى هذه النقطة بعد قليل طبعا لما أقولك سأرجع إلى + +166 +00:13:37,370 --> 00:13:41,990 +هذه النقطة بعد قليل هذا أسلوب نسميه أسلوب تشويق + +167 +00:13:41,990 --> 00:13:46,030 +يعني إيش بده يقول في هذا الموضوع هذا بعد قليل بتظل + +168 +00:13:46,030 --> 00:13:53,310 +أنت مشدود هذا أحد أساليب التعليم طيب الآنحضرنا + +169 +00:13:53,310 --> 00:13:57,450 +المحاضرة تابعنا سجلنا المعلومات روحنا قريناها في + +170 +00:13:57,450 --> 00:14:01,590 +نفس اليوم خلال نص ساعة خلصنا قراها بعدين بدك تبدأ + +171 +00:14:01,590 --> 00:14:05,590 +تحل مساعدة لما قريت المحاضرة جيبت كمان عشرين في + +172 +00:14:05,590 --> 00:14:10,370 +المية صار قداش عندك؟ سبعين اه مليح نجحنا وزيادة + +173 +00:14:10,370 --> 00:14:15,190 +شوية كويس؟طيب بنروح ان .. بعد ما نحلي .. بنروح + +174 +00:14:15,190 --> 00:14:19,010 +نحلي التمرين تبعات ال .. ال .. ال section اللي + +175 +00:14:19,010 --> 00:14:22,850 +احنا كلفناكي بهم لما تحل بيكون جيبك كمان عشرين في + +176 +00:14:22,850 --> 00:14:26,010 +المية يعني مقدش صار عندك؟ تسعين في المضايق اللي + +177 +00:14:26,010 --> 00:14:29,430 +عنينا و ايه؟ عشرة في المية العشرة في المية بنروح + +178 +00:14:29,430 --> 00:14:33,370 +على وين؟ على الساعة تبع ال discussion لإن انت لما + +179 +00:14:33,370 --> 00:14:38,350 +تحل مسألة التمرين لازم تواجك صعابماحدش فضحى او نزل + +180 +00:14:38,350 --> 00:14:42,650 +عالما كله بيتعلم ومدام يتعلم لازم يتجابلك صعوبة + +181 +00:14:42,650 --> 00:14:46,350 +واللي بيتجابلهوش صعوبة معناته هو مش فاهم اللي بين + +182 +00:14:46,350 --> 00:14:51,810 +أيديه كل واحد بيتعلم لازم يقابل صعوبة مافيش + +183 +00:14:51,810 --> 00:14:55,130 +إمكانية اللي يتجابل الصعوبة و بعد هيك تتغلب على + +184 +00:14:55,130 --> 00:14:59,610 +هذه الصعوبة إما بالذهاب إلى ساعة تبعة المناقشة مع + +185 +00:14:59,610 --> 00:15:03,700 +المدرس الآخربتقول وصيب علينا السؤال الفلاني و هو + +186 +00:15:03,700 --> 00:15:06,500 +السؤال اللي بيجيب .. بيحلك السؤال الفلاني وبالتالي + +187 +00:15:06,500 --> 00:15:10,900 +بيجيبك اللغة اللي انت ايه ماكنتش قادر تفهمها طيب + +188 +00:15:10,900 --> 00:15:14,480 +هذا جابله سؤالين و هذا جابله سؤالين غيرهم و هذا + +189 +00:15:14,480 --> 00:15:17,560 +جابله سؤالين .. و كل واحد جابله سؤالين مختلفه عن + +190 +00:15:17,560 --> 00:15:22,700 +بعضطبعا هذا كلام غير معقول لإن هو التمرين قداش كله + +191 +00:15:22,700 --> 00:15:26,760 +و بنطلبش المسائل كلها، تمام؟ إذا هذا غير معقول لكن + +192 +00:15:26,760 --> 00:15:31,220 +قد يكون بقى السؤال أو اتنين من التمرين غالبية انت + +193 +00:15:31,220 --> 00:15:35,440 +مش فاهمينه يا أخي أنا موجود تعالي بعطيلك بعد قليل + +194 +00:15:35,440 --> 00:15:38,120 +هقولك أنا عند الساعة المكتبية هذه بكون قاعد في + +195 +00:15:38,120 --> 00:15:42,910 +المكتب باستنىك تيجي تسألنيتمام؟ ان جيت سؤالني + +196 +00:15:42,910 --> 00:15:46,490 +بتبقى استفدت منها، جيت سؤالني بتضلك ما انتش عارف + +197 +00:15:46,490 --> 00:15:49,990 +الإجابة على السؤال أو السؤالين أو التلاتة اللي + +198 +00:15:49,990 --> 00:15:54,670 +ضايلات عندك، اذا جيت سؤالني بعد المناقشة معناته + +199 +00:15:54,670 --> 00:15:59,510 +انت صرت بتفهم في المادة مية بالمية، لكن اذا + +200 +00:15:59,510 --> 00:16:05,060 +ماحليتش مسائل و روحت على المناقشةبتروح وانت ايش + +201 +00:16:05,060 --> 00:16:11,300 +فاتح ثمه وقعد ايش ما يقول بصير تكتب بصير انت مجمع + +202 +00:16:11,300 --> 00:16:17,340 +حلول وليس بتعرف تحلزي ايش؟ زي واحد كتاب الوزارة + +203 +00:16:17,340 --> 00:16:20,840 +اللى معاه كان في الثانوية طابع احد المدرسين لحل + +204 +00:16:20,840 --> 00:16:24,360 +المسائل وطابع كتاب العلوم وشارك كتاب العلوم ويقولك + +205 +00:16:24,360 --> 00:16:28,200 +والله اي سؤال بحله، بحله ليه؟ لإنه بيبدأ يفكر، اول + +206 +00:16:28,200 --> 00:16:32,740 +يجي اتنين مثلة .. اه بنقلب وقوم بونجل الحل، صار + +207 +00:16:32,740 --> 00:16:37,080 +عنده حل، عرف الفكرة، لكن لو جاء السؤال وغيطله فيه + +208 +00:16:37,080 --> 00:16:41,710 +رقامبقدر يمشي و بقدرش يمشي لأن هذا مااشتغلش هذا + +209 +00:16:41,710 --> 00:16:47,830 +النجل نجل الحل إذا مطلوب تمسك جلمك و تحل بنفسك حتى + +210 +00:16:47,830 --> 00:16:52,450 +تثبت هذه المعلومات ذيك بصير انت مية لمية و ماعنا + +211 +00:16:52,450 --> 00:16:57,550 +مشكلة و احنا هنا انا لما اعرضلك الموضوع اخلصه + +212 +00:16:57,550 --> 00:17:00,570 +المحاضرة الجاية بقولك شرحنا في المحاضرة الماضية + +213 +00:17:00,570 --> 00:17:04,370 +كذا كذا في حدود دقيقتين و اليوم بدنا ناخد كذا كذا + +214 +00:17:04,370 --> 00:17:10,750 +تمام؟ و ببدأ أشرح جديدوالباقي بيضل عليه، بتمشي، + +215 +00:17:10,750 --> 00:17:15,370 +بتمشي، تمشيش، تمشيش، بعض الطلاب إيش بيسويه؟ قال + +216 +00:17:15,370 --> 00:17:20,110 +بيقرا الشرح اللي أنا شرحته تمام و بيقرا الأمثلة، + +217 +00:17:20,110 --> 00:17:23,930 +بيقول أخو الله أنا فهمت الموضوعهذا اللي بروحش يحل + +218 +00:17:23,930 --> 00:17:28,890 +مثال ويكتفي بالأمثلة بقول يمكن ينجح ويجيب علامة + +219 +00:17:28,890 --> 00:17:32,450 +نجاح اللي هي ستين مش خمسين، خمسين في الثانوية + +220 +00:17:32,450 --> 00:17:35,890 +العامة، عندنا في الجامعة ستين، عشان تنجح تجيب ستين + +221 +00:17:35,890 --> 00:17:40,450 +.. بقول يمكن يجيب علامة نجاح ويمكن يرصف، لكن لن + +222 +00:17:40,450 --> 00:17:44,050 +يتعد علامة نجاح، لكن اللي بحل مثال automatically + +223 +00:17:44,050 --> 00:17:48,150 +بترفت على درجته وبيجيب فوق الستين، فوق السبعين، + +224 +00:17:48,150 --> 00:17:53,480 +فوق الثمانينو بعض الطلاب والله بطبق المية بجيب مية + +225 +00:17:53,480 --> 00:17:57,180 +من مية في الجامعة و بقول إنه جاب مية بحطها له مية + +226 +00:17:57,180 --> 00:18:00,300 +زي ما هي و بعضهم بجيب تسعة و تسعين و بعضهم بجيب + +227 +00:18:00,300 --> 00:18:03,580 +تمانية و تسعين و دي لباقي الكلمات ده أربع ساعات + +228 +00:18:03,580 --> 00:18:07,700 +إذا جيبت من التسعين فمطق بظل معدلك في ال top حتى + +229 +00:18:07,700 --> 00:18:12,140 +لو مديتين تلاتة نزل بظل مرتع لإن هذه أربع ساعات مش + +230 +00:18:12,140 --> 00:18:15,420 +تلاتة والله ساعة يعني كنت في القرآن مية من مية + +231 +00:18:15,420 --> 00:18:19,860 +القرآن ساعةبس هاد المادة اربع ساعات لو جيت فوقها + +232 +00:18:19,860 --> 00:18:24,660 +فوق التسعين بتضل معدلكيهش عالى حتى لو نزل في مواد + +233 +00:18:24,660 --> 00:18:30,660 +اخرى يبقى احرص على هذه النقطة تمام طيب وصلنا الان + +234 +00:18:30,660 --> 00:18:36,670 +الى توزيع الدرجات كيف تتوزع الدرجات؟المادة عليها + +235 +00:18:36,670 --> 00:18:41,250 +مائة درجة بنجسمها الى امتحان اول امتحان ثاني + +236 +00:18:41,250 --> 00:18:47,530 +بنسميهم اعمال الفصل وامتحان النهائي الامتحان الاول + +237 +00:18:47,530 --> 00:18:51,870 +بنجيبه جاب الامتحان متطلبات الجامعة يعني يوم تسعة + +238 +00:18:51,870 --> 00:18:56,760 +عشرةبتكون لسه مادخلتش امتحانات متطلبات الجامعة + +239 +00:18:56,760 --> 00:19:01,780 +عليها عشرين او خمسة وعشرين درجة حسب ما نتفق ان + +240 +00:19:01,780 --> 00:19:05,580 +احنا ولا ساتذة الاخرون اللي بدرسوا معانا نفس المدة + +241 +00:19:05,580 --> 00:19:09,800 +الامتحان الثاني زي عشرين او خمسة وعشرين ان كان + +242 +00:19:09,800 --> 00:19:13,040 +خمسة وعشرين خمسة وعشرين هي خمسين يبقى النهائي + +243 +00:19:13,040 --> 00:19:18,200 +خمسين تمام ان كان عشرين عشرين بتظل عشرة العشرة + +244 +00:19:18,200 --> 00:19:22,930 +ممكن تخليها فيدي المناقش اللي بحل معاك أسئلةهذا + +245 +00:19:22,930 --> 00:19:27,090 +بيعطيكو الذات بيحطها على الحضور و يقولوا زي ما يحط + +246 +00:19:27,090 --> 00:19:32,290 +يحط لا نتدخل فيه، فيه عشر علامات بنقوله زي ما + +247 +00:19:32,290 --> 00:19:36,910 +جبتنا صفر بنحطها على الجهاز صفر و ان جبتنا عشرة + +248 +00:19:36,910 --> 00:19:40,910 +بنحطها عشرة، لكن احنا ان في الامتحان الأول و + +249 +00:19:40,910 --> 00:19:46,580 +الثاني و الأخيرواضح كلامي؟ طيب فيه انا حاجة اسمها + +250 +00:19:46,580 --> 00:19:50,360 +الساعات المكتبية الساعات المكتبية هذه اللي + +251 +00:19:50,360 --> 00:19:55,160 +وعدناكوا فيها قبل قليل انا بكون موجود في المكتب + +252 +00:19:55,160 --> 00:20:00,960 +جاعد فى انتظارك اذا عندك حاجة بتحب تسأل فيها انا + +253 +00:20:00,960 --> 00:20:08,780 +جاعد يوم السبت والأحد والاربعاء من ال 11 الى ال 12 + +254 +00:20:08,780 --> 00:20:17,940 +السبت أحدأربعاء من الأحداش للاتناش ويوم الأثنين + +255 +00:20:17,940 --> 00:20:23,840 +قاعد من الأتناش لساعة واحدة أي واحد بيجيني في + +256 +00:20:23,840 --> 00:20:29,400 +الأربع ساعات بيجدني موجود في المكتب طيب المكتب وين + +257 +00:20:29,400 --> 00:20:35,060 +موجود هذا؟ موجود في الطابق الثاني في مبنى الإدارة + +258 +00:20:35,060 --> 00:20:41,970 +الطابق الثاني في مبنى الإدارةرقم الغرفة تلاتمية و + +259 +00:20:41,970 --> 00:20:48,990 +تلاتة و عشرين رقم الغرفة تلاتة اتنين تلاتة تلاتمية + +260 +00:20:48,990 --> 00:20:54,530 +و تلاتة و عشرين رقم التليفون الداخلي الفين و ستمية + +261 +00:20:54,530 --> 00:20:59,410 +و تسعة عشر يعني من اي تليفون داخل الجامعة اضرب على + +262 +00:20:59,410 --> 00:21:03,170 +الفين و ستمية و تسعة عشر يابا ارد عليك انا يابا + +263 +00:21:03,170 --> 00:21:06,230 +ارد عليك الدكتور محمد الاشجار لان احنا اتنين + +264 +00:21:06,230 --> 00:21:12,110 +جاعدين مع بعض في نفس الغرفةوالتاني كذلك رياضية، + +265 +00:21:12,110 --> 00:21:16,070 +تمام؟ يبقى هذا بالنسبة للساعات المكتبية، لو جاتني + +266 +00:21:16,070 --> 00:21:20,890 +في وقت غير هذه الساعات ولا جاتني، برضه بجاوبك، + +267 +00:21:20,890 --> 00:21:24,370 +ماجوشلك تعالي في الساعات المكتبية، يعني بس هدول + +268 +00:21:24,370 --> 00:21:29,620 +ملتزم أني أكون موجود في المكتباللي هو في الغرفة + +269 +00:21:29,620 --> 00:21:34,820 +تلاتمية وتلاتة وعشرين هذا بالنسبة للساعات المكتبية + +270 +00:21:34,820 --> 00:21:39,800 +ونظار المتحانات وتوزيع الدرجات وكيفية الدراسة ورقم + +271 +00:21:39,800 --> 00:21:45,740 +الغرفة ورقم التليفون حد فيكوا إيه أي تساول حتى هذه + +272 +00:21:45,740 --> 00:21:51,120 +المحظة قبل ما ندخل في الموضوع اللي بدنا نشرحه؟ حد + +273 +00:21:51,120 --> 00:21:53,140 +بيحب يسأل أي سؤال اتفضل + +274 +00:21:56,720 --> 00:22:02,260 +بعض الخلافات، بعض الاختلافات، في عدد الأسئلة وبعض + +275 +00:22:02,260 --> 00:22:05,640 +المواضيع، بعض المواضيع شالها وبعض المواضيع دمجها، + +276 +00:22:05,640 --> 00:22:12,160 +إذا احنا بيقولنا تقيد بالطبعة الثانية عشرة، تمام؟ + +277 +00:22:12,160 --> 00:22:18,280 +طيب اتفضل كيف؟ + +278 +00:22:18,280 --> 00:22:21,820 +لغة الكتاب اللغة الإنجليزية، لكن زي ما انت شايف + +279 +00:22:21,820 --> 00:22:26,940 +انا بكتب بالإنجليزي و بشرح بالعربيبحيث مش هخليك + +280 +00:22:26,940 --> 00:22:31,220 +ترجع للا الكمبيوتر وللا القاموس كل كلمة انجليزي + +281 +00:22:31,220 --> 00:22:36,080 +بقولك إيش معناها بالعربي تمام؟ وبالتالي و بدّيش + +282 +00:22:36,080 --> 00:22:39,920 +إياك تروح تجرى من الكتاب بديك بس تروح تحل مسائل من + +283 +00:22:39,920 --> 00:22:44,780 +الكتاب أنا بلخصلك بحيث أريحك من قراية الكتاب و + +284 +00:22:44,780 --> 00:22:48,400 +ياريت كانوا بيعملونا زي ما عملوكوا هنا والله بجينا + +285 +00:22:48,400 --> 00:22:50,680 +نخاف نسأله أيوة تفضل + +286 +00:22:54,330 --> 00:22:59,150 +في ايش؟ الملخصات الملخصات هنا على اللوح يعني هذا + +287 +00:22:59,150 --> 00:23:02,910 +اللي انت شايفها بتلاقينه كاتب السؤال و مش كاتب حل + +288 +00:23:02,910 --> 00:23:07,770 +تمام؟ وبالتالي انت بدك الحل، مصبوط ولا لا؟ يبقى + +289 +00:23:07,770 --> 00:23:14,150 +الملخص تجده هنا تفصيليا على اللوح خلاص؟ ايوة، حد + +290 +00:23:14,150 --> 00:23:18,880 +بدي أسأل تاني؟اسأل اي حاجة حتى لو كان سؤال غلط + +291 +00:23:18,880 --> 00:23:23,140 +تعود انك تسأل و تناقش و تاخد و تعطي المثل هنا + +292 +00:23:23,140 --> 00:23:27,660 +اخويا انا اصار باللي بيسأل اكتر من اللي بيسألش لان + +293 +00:23:27,660 --> 00:23:31,200 +اللي بيسأل معناته فكر معناته اجا في باله حاجة بدي + +294 +00:23:31,200 --> 00:23:35,160 +يقولها ويمكن يقول ان حاجة احنا نستفيد منها كلها + +295 +00:23:35,160 --> 00:23:38,680 +ماتستغربش ه ان شاء الله نكتة مثلا قولنا للي بدي + +296 +00:23:38,680 --> 00:23:42,040 +يقول نكتة قولي اخي نكتة واش فيه مافيش عندهوش مشكلة + +297 +00:23:42,240 --> 00:23:47,080 +بنغير فيها الجو وإذا قلت نقطة برد عليك بنقطة أخرها + +298 +00:23:47,080 --> 00:23:50,300 +وبالتالي غيرنا اليوم نرجع لموضوع نفيد جيج تان + +299 +00:23:50,300 --> 00:23:54,440 +تلاتة ونرجع لموضوع نتانى احنا بدى نسأل اي تساؤل + +300 +00:23:54,440 --> 00:24:00,960 +بدخل في الموضوع اهدروا بالكم خلاص ندخل في الموضوع + +301 +00:24:00,960 --> 00:24:09,220 +طيب الشبتر هذا اسمه functions شبتر واحديبقى هذا + +302 +00:24:09,220 --> 00:24:18,060 +اللي هو chapter one اسمه functions functions يعني + +303 +00:24:18,060 --> 00:24:25,260 +ايه؟ يعني الدوال بنجي لأول section هذا مقسم إلى + +304 +00:24:25,260 --> 00:24:31,280 +ثلاث سكاشف تمام؟ او بدل ما نشرح نقول محتوى المادة + +305 +00:24:31,280 --> 00:24:37,700 +في الأول يا شباب وبعد هيك بروح نعطي تفصيلفالعشر + +306 +00:24:37,700 --> 00:24:41,160 +دقيقة اللي ضايلة بنقولك شو اللي بدنا ندرسه في هذا + +307 +00:24:41,160 --> 00:24:45,920 +المنهج اول chapter اللي هو ال functions بدنا ندرس + +308 +00:24:45,920 --> 00:24:53,160 +في ال functions حاجة اسمها ال domain domain يعني + +309 +00:24:53,160 --> 00:24:59,880 +المجال function يعني دالة او اقتران يبقى الدوال او + +310 +00:24:59,880 --> 00:25:05,820 +الاقترانات ال domain يعني المجال بدنا حاجة اسمها + +311 +00:25:05,820 --> 00:25:14,350 +ال rangerange يعني المدى code domain المجال + +312 +00:25:14,350 --> 00:25:20,230 +المناظر او المجال المصاحب او المجال المرافق يبقى + +313 +00:25:20,230 --> 00:25:25,650 +كمان ال code domain بعد هيك بدنا نيجي لالي graph + +314 +00:25:25,650 --> 00:25:34,950 +of a function الرسم البياني لدالة فاختصر كلمة + +315 +00:25:34,950 --> 00:25:41,930 +function إلى fn تمام؟يبقى graph of a function يبقى + +316 +00:25:41,930 --> 00:25:50,110 +الرسم البياني لمين لدالة ما بعد الرسم بننتقل حاجة + +317 +00:25:50,110 --> 00:25:55,030 +اسمها shift او + +318 +00:25:55,030 --> 00:26:02,950 +shifting ازاحةمش إزاحة احنا عندنا رسم ما بدنا + +319 +00:26:02,950 --> 00:26:08,470 +نزيحه جهة اليمين او جهة اليسار او الى اعلى او + +320 +00:26:08,470 --> 00:26:13,710 +الاسفل او جهة اليمين و اعلى او جهة اليمين واسفل او + +321 +00:26:13,710 --> 00:26:17,970 +جهة الشمال و اعلى و جهة الشمال واسفل شو بده يكون + +322 +00:26:17,970 --> 00:26:22,190 +شكل الدلة في هذه الحالة اللى عملنا لها shift او + +323 +00:26:22,190 --> 00:26:27,910 +إزاحة هذا الموضوع اللى هندرسه بعد ال shiftingبدنا + +324 +00:26:27,910 --> 00:26:36,310 +نيجي لحاجة متعلقة فيها اللي حاجة اسمة combining of + +325 +00:26:36,310 --> 00:26:40,130 +functions + +326 +00:26:40,130 --> 00:26:43,610 +إيش + +327 +00:26:43,610 --> 00:26:48,490 +يعني combining؟ combine يعني تجميع، تجميع هذا قد + +328 +00:26:48,490 --> 00:26:56,350 +يكون بالجمعأو الطرح أو الضرب أو القسمة أو التركيب + +329 +00:26:56,350 --> 00:27:01,390 +ال composition of functions تحصيل الدوال أو تركيب + +330 +00:27:01,390 --> 00:27:06,730 +الدوال اللي كنتوا بترمزوله if composition G أو if + +331 +00:27:06,730 --> 00:27:11,590 +circle G أو if بعد G زي ما كانوا بنتقلها لكم في + +332 +00:27:11,590 --> 00:27:15,610 +الثانويةيبقى اي اي تعبير من هذه التعبيرات اللي + +333 +00:27:15,610 --> 00:27:19,930 +ذكرناها يدل على ال composition of functions يبقى + +334 +00:27:19,930 --> 00:27:24,850 +اختصارا combining of functions تجميع الدوام جمع + +335 +00:27:24,850 --> 00:27:29,170 +طرح ضرب قسمة تركيب كله بنسميه combining of + +336 +00:27:29,170 --> 00:27:37,290 +functions بضل عندنا حاجة اسمها trigonometric + +337 +00:27:37,290 --> 00:27:39,350 +functions + +338 +00:27:41,390 --> 00:27:47,150 +ماذا يعني تريجونومتريك فانكشنز تريجونومتريك سمعتوا + +339 +00:27:47,150 --> 00:27:55,090 +فيها الدوال المثلثية كم واحد الدوال المثلثية لقدهم + +340 +00:27:55,090 --> 00:28:02,950 +في الثانوية ثلاثة بسقداش؟ ستة بس تلاتة مقلبات + +341 +00:28:02,950 --> 00:28:07,950 +التلاتة الأخرى التلاتة الأولانية reciprocal يعني + +342 +00:28:07,950 --> 00:28:14,210 +مقلب لمن؟ لدول الأخرى الجيب، جيب التمام، الظل، ظل + +343 +00:28:14,210 --> 00:28:18,550 +التمام، قاطع، قاطع تمامي الزاوية هي اللي خدهم + +344 +00:28:18,550 --> 00:28:21,990 +العربي في التانية، في غيرهم الستة دول؟ مافيش + +345 +00:28:21,990 --> 00:28:28,630 +غيرهم، الآن لو جت الظل مقلبه ظل التماملو جيت للجيب + +346 +00:28:28,630 --> 00:28:33,250 +مقلبه قاطع التمام، لو جيت لجيب التمام مقلبه + +347 +00:28:33,250 --> 00:28:37,990 +القاطع، هاي الدول المثلثية الستة، بدنا نرسم الدول + +348 +00:28:37,990 --> 00:28:44,170 +المثلثية الستةونعرف قداش ال period لكل functions + +349 +00:28:44,170 --> 00:28:49,310 +من ال functions الستة ونرسمهم و بعد ذلك لو عملنا + +350 +00:28:49,310 --> 00:28:56,770 +لهم إذاعة كيف بيحدث هذا و بعد ذلك بنجي للمتطابقات + +351 +00:28:56,770 --> 00:29:02,060 +المثلثية و هذا اللي كنا بنخاف منهامن حد ما ييجي + +352 +00:29:02,060 --> 00:29:07,600 +برتفعنا درجة الحرارة وربما النبض تمام؟ لكن هذه + +353 +00:29:07,600 --> 00:29:13,480 +المطابقة التي سأعرضها لكم بطريقة سهلة وبسيطة تصير + +354 +00:29:13,480 --> 00:29:17,860 +تستثفى حالك في الاشي اللي كنت تفكر به في الثانوية + +355 +00:29:17,860 --> 00:29:23,520 +أشياء بسيطة لكن بهمنا كيفية استخدامها مش القانون + +356 +00:29:23,520 --> 00:29:28,020 +أو المتطابقة كشغلة جامدة لا لا فيش حاجة سما جامدة + +357 +00:29:28,310 --> 00:29:32,930 +انت الان في جامعة يعني بيجي تشغل مخك وكيف تلعب + +358 +00:29:32,930 --> 00:29:37,370 +بالقانون حسب طبيعة السؤال اللى موجودة عندك وعارف + +359 +00:29:37,370 --> 00:29:41,990 +تلاقيه بسيط ومن أبسط ما يكون ان شاء الله يبقى هذا + +360 +00:29:41,990 --> 00:29:46,210 +كل ما يتعلق بال chapter الأول بنروح لل chapter + +361 +00:29:46,210 --> 00:29:51,770 +التانى chapter التانى بيناخد فيه limits and + +362 +00:29:51,770 --> 00:29:55,010 +continuity + +363 +00:29:58,700 --> 00:30:05,500 +النهايات والاتصال يبقى limits النهايات continuity + +364 +00:30:05,500 --> 00:30:13,160 +الاتصال اول ما بدنا نبدأ بدنا نبدأ نفهمك شو يعني + +365 +00:30:13,160 --> 00:30:18,300 +معنى limit ايش معنى نهاية يبقى بنبدأ لك الأول حاجة + +366 +00:30:18,300 --> 00:30:25,640 +the concept of a limit يبقى the concept of + +367 +00:30:26,720 --> 00:30:32,280 +A limit نسأل + +368 +00:30:32,280 --> 00:30:36,640 +السؤال اليومها مش اليومها بس بدنا نسأل اليوم هل + +369 +00:30:36,640 --> 00:30:42,300 +هناك فرق بين نهاية الدالة عند نقطة وقيمة الدالة + +370 +00:30:42,300 --> 00:30:48,200 +عند تلك النقطة الإجابة سنعرفها في chapter 2 ومسبق + +371 +00:30:48,200 --> 00:30:52,780 +ما أقولك اه في فروق لكن ان نفهم ان نهاية الدالة + +372 +00:30:52,780 --> 00:30:56,910 +عند نقطة قيمتها عند تلك النقطة هذا مفهومقد قد يحدث + +373 +00:30:56,910 --> 00:31:02,030 +و قد لا يحدث بس in general ما هواش صحيح تمام يبقى + +374 +00:31:02,030 --> 00:31:07,310 +هذا بنفهمكيا قبل ما نبدأ في قواعد النهايات او + +375 +00:31:07,310 --> 00:31:13,670 +قوانين النهايات بعد هيك بنروح ل limit laws او + +376 +00:31:13,670 --> 00:31:21,050 +limit formulas يبقى limit laws قوانين النهايات + +377 +00:31:21,050 --> 00:31:25,660 +اللي خدتها في الثانويةنهاية المجموع الجبري لدالتين + +378 +00:31:25,660 --> 00:31:31,200 +نهاية حصل ضرب دالتين نهاية حصل ضرب مقدار ثابت فيه + +379 +00:31:31,200 --> 00:31:38,940 +دالة نهاية دالة فيها جذر هيك و نضرب في المرافق و + +380 +00:31:38,940 --> 00:31:43,400 +نظرية sandwich theorem نظرية sandwich أو squeezing + +381 +00:31:43,400 --> 00:31:47,180 +theorem و كل هالشغلات إذا أخدتها في الثانوية بدا + +382 +00:31:47,180 --> 00:31:52,900 +أن أدهلك من جديد و كأنها جديدة بالنسبة إلى تمام؟ + +383 +00:31:53,180 --> 00:31:59,040 +بعد هذا هنجي نشوف أحيانا سنضطر نأخد النهاية من + +384 +00:31:59,040 --> 00:32:04,060 +اليمين و النهاية من الشمال right limit و left + +385 +00:32:04,060 --> 00:32:08,460 +limit تمام و نجي نعرف و اكتشف بدي أخد ال limit من + +386 +00:32:08,460 --> 00:32:13,180 +اليمين و ال limit مين هي الدوال هذه ما هي الأنواع + +387 +00:32:13,180 --> 00:32:16,520 +من الدوال اللي بدنا ناخدلها ال limit من اليمين و + +388 +00:32:16,520 --> 00:32:19,620 +ال limit من الشمال كل الدوال و الله بعضها الإجابة + +389 +00:32:19,620 --> 00:32:25,030 +بعضها مين هي هذا ما ستعرفه يومهاأربعة أنواع من + +390 +00:32:25,030 --> 00:32:28,110 +الدوالة هذا اللي بدنا ناخدلها ال limit من اليمين + +391 +00:32:28,110 --> 00:32:31,710 +وال limit مش مماخة لذلك limit عادية وامشي + +392 +00:32:31,710 --> 00:32:36,190 +بالقوانين وما إلى ذلك زيادة على ذلك بدنا ناخد ال + +393 +00:32:36,190 --> 00:32:43,090 +limit لما سين بدها تروح للمالة نهاية كويس أو نهاية + +394 +00:32:43,090 --> 00:32:47,670 +لدالة القيمة اللتي تقولها سين بتخلي الدالة تروح + +395 +00:32:47,670 --> 00:32:54,110 +لوينللمالانها in finite limits هذا كمان بدنا نعرفه + +396 +00:32:54,110 --> 00:33:00,190 +بنعرف حاجة اسمها ال asymptotes خطوط التقارب خط + +397 +00:33:00,190 --> 00:33:04,670 +تقارب للمنحنة كله داخل وين؟ داخل في هذا الموضوع + +398 +00:33:04,670 --> 00:33:08,410 +اللي هو limits, laws و limits and continuum بعد ما + +399 +00:33:08,410 --> 00:33:12,650 +نخلص ال limits اللي بتاخدها حوالي أربعة secation + +400 +00:33:12,650 --> 00:33:18,710 +بنروح لمين؟ بنروح لل continuity اللي بيعتمداعتمادا + +401 +00:33:18,710 --> 00:33:23,770 +كليا على مين؟ على ال limits لإن إذا كانت نهاية + +402 +00:33:23,770 --> 00:33:27,670 +الدالة عند نقطة تساوي قيمة الدالة عند تلك النقطة + +403 +00:33:27,670 --> 00:33:33,690 +بنقول إذا الدالة دالة متاصلة عند تلك النقطة ويمكن + +404 +00:33:33,690 --> 00:33:38,430 +أن نصل هذا التريف إلى three conditions سنعرفه كذلك + +405 +00:33:38,430 --> 00:33:43,070 +يومهامش اليوم يبقى هذا بالنسبة لل limits and + +406 +00:33:43,070 --> 00:33:48,070 +continuity هناخد الاتصال عند نقطة و بعد هيك + +407 +00:33:48,070 --> 00:33:55,090 +الاتصال على فترة على interval بعد هيك بنجي لشبتر + +408 +00:33:55,090 --> 00:34:03,870 +تلاتة الشبتر تلاتة اللي هو differentiation ايش + +409 +00:34:03,870 --> 00:34:09,210 +يعني differentiationالاشتقاء التفاضل يعني + +410 +00:34:09,210 --> 00:34:13,590 +derivatives التفاضل ال differentiation اللي هو + +411 +00:34:13,590 --> 00:34:20,070 +الاشتقاء بدنا أول حاجة ناخد ال derivative of a + +412 +00:34:20,070 --> 00:34:25,830 +function كيه مشتق ده لما؟ شو المفهوم تبعها؟ يبقى + +413 +00:34:25,830 --> 00:34:32,490 +بدي أخد ال derivative of + +414 +00:34:32,490 --> 00:34:35,010 +a function + +415 +00:34:38,800 --> 00:34:43,980 +بعد هك اذا انا ايجي اخد قوانين الاشتقاق او قواعد + +416 +00:34:43,980 --> 00:34:49,780 +الاشتقاق ال differentiation rules + +417 +00:34:49,780 --> 00:34:56,300 +كلمة differentiation هختصرها الى d i double f هي + +418 +00:34:56,300 --> 00:35:00,140 +قدامها يبجد ال differentiation rules قواعد + +419 +00:35:00,140 --> 00:35:07,620 +الاشتقاق بعد هكبدنا نيجي مشتقة الدول المثلثية مش + +420 +00:35:07,620 --> 00:35:13,440 +هالنا دول مثلثية ستة بدي أعرف ما هي مشتقاتها يبقى + +421 +00:35:13,440 --> 00:35:19,300 +هنا بدي أجي لليه derivative of + +422 +00:35:19,300 --> 00:35:27,280 +the trigonometric functions + +423 +00:35:30,550 --> 00:35:37,330 +يعني مشتقة الدوال المثلثية بعد مشتقة الدوال + +424 +00:35:37,330 --> 00:35:44,050 +المثلثية بداجة لحاجة اسمة chain rule يعني ايش + +425 +00:35:44,050 --> 00:35:50,870 +قاعدة السلسلة او مشتقة دالة الدالة بجدنا نسميها + +426 +00:35:50,870 --> 00:35:56,750 +هيك يا اما قاعدة السلسلة يا اما مشتقة دالة الدالة + +427 +00:35:57,150 --> 00:36:01,870 +بعد ما ناخد share role بدنا نروح لحاجة اسمها + +428 +00:36:01,870 --> 00:36:06,710 +implicit differentiation + +429 +00:36:06,710 --> 00:36:10,390 +يعني + +430 +00:36:10,390 --> 00:36:17,390 +إيش implicit differentiation؟ يعني الاشتقاق بنيإيش + +431 +00:36:17,390 --> 00:36:21,590 +الاشتقاق الدمني هذا؟ طب ما أحنا عارفين الصاد تساوي + +432 +00:36:21,590 --> 00:36:24,410 +سين تربية يبقى ده الصاد اللي لديه السين باتنين + +433 +00:36:24,410 --> 00:36:29,630 +سين، مظبوط؟ أه هذا اسمه اشتقاق صريح، إيش يعني + +434 +00:36:29,630 --> 00:36:33,550 +صريح؟ إذا الصاد في شجة و السينات كلهم في شجة + +435 +00:36:33,550 --> 00:36:38,690 +واحدة، هذا اسمه اشتقاق صريح لكن إذا كان صاد و + +436 +00:36:38,690 --> 00:36:43,730 +السين مشربكات مع بعض فقدر شخص الواحدة فيهم عند + +437 +00:36:43,730 --> 00:36:47,920 +تانية ومطلوب اشتقاقهمهذا بسميه اشتقاق ضمن .. يعني + +438 +00:36:47,920 --> 00:36:54,520 +زي ايه؟ زي صد تربيع زائد سين تكعيب صد أس أربعة + +439 +00:36:54,520 --> 00:37:00,260 +زائد جذر سين صد أس تلاتة على اتنين يسوى خمسة + +440 +00:37:00,260 --> 00:37:06,120 +وعشرين شربك مبالغ لاقدر اجيب صد بدلالة سين ولاقدر + +441 +00:37:06,120 --> 00:37:10,720 +اجيب سين بدلالة صد ومطلوب يوجد اشتقاق يبقى هذا + +442 +00:37:10,720 --> 00:37:15,870 +اسمه اشتقاق ضمن implicit differentiationهنشتق + +443 +00:37:15,870 --> 00:37:22,410 +ونبيّلك كيف قواعد الاشتقاء في هذه العالم تمام يبقى + +444 +00:37:22,410 --> 00:37:26,210 +هذا بالنسبة أنا بعطيك الخطوط العريضة لل chapter + +445 +00:37:26,210 --> 00:37:30,450 +وليست التفاصيلات الدقيقة التفاصيلات الدقيقة في هنا + +446 +00:37:30,450 --> 00:37:33,970 +لإن أنا بقولك الخطوط العريضة اللي موجودة وين في + +447 +00:37:33,970 --> 00:37:38,710 +هذا ال chapter بعد chapter تلاتة بيجينا ل chapter + +448 +00:37:38,710 --> 00:37:42,770 +أربع chapter أربع له applications + +449 +00:37:46,160 --> 00:37:56,580 +applications of derivatives تطبيقات + +450 +00:37:56,580 --> 00:38:03,200 +على المشتقات ايش + +451 +00:38:03,200 --> 00:38:08,820 +التطبيقات على المشتقات؟ هنبدأ أول حاجة بشيء اسمه + +452 +00:38:08,820 --> 00:38:12,780 +extreme values + +453 +00:38:15,320 --> 00:38:25,480 +extreme values ايش يعني extreme values القيم + +454 +00:38:25,480 --> 00:38:31,290 +المتطرفة شو القيم المتطرفة؟يعني القيام اللي فيها + +455 +00:38:31,290 --> 00:38:35,950 +ال local maximum و local minimum و ال end points + +456 +00:38:35,950 --> 00:38:41,450 +تمام او بمعنى اخر ل critical points زائد ال end + +457 +00:38:41,450 --> 00:38:45,930 +points نقاط الطرفين تبعات الفترة و النقاط اللي في + +458 +00:38:45,930 --> 00:38:49,790 +الداخل اللي تبقى نقاط حرجة يبقى هادر يبقى عليها + +459 +00:38:49,790 --> 00:38:54,670 +extreme values تمام بعد ما ناخد extreme values + +460 +00:38:54,670 --> 00:39:01,650 +بدنا نروح ناخدabsolute في الأول absolute maximum و + +461 +00:39:01,650 --> 00:39:11,390 +absolute minimum يبقى absolute maximum + +462 +00:39:11,390 --> 00:39:23,370 +and absolute minimum القيم + +463 +00:39:24,050 --> 00:39:29,350 +المطلقة العظمة والقيم المطلقة الصغيرة بتختلف عن ال + +464 +00:39:29,350 --> 00:39:33,790 +local maximum و ال local minimum بعد ذلك بنيجي لل + +465 +00:39:33,790 --> 00:39:42,990 +local maximum local maximum and local + +466 +00:39:42,990 --> 00:39:44,430 +minimum + +467 +00:39:46,880 --> 00:39:51,780 +القيم العظمى المحلية والقيم الصغرى المحلية طبعا في + +468 +00:39:51,780 --> 00:39:55,800 +فرق ما بين الاتنين هنعطيك الفرق يومها من عشان + +469 +00:39:55,800 --> 00:40:00,800 +نستعجل اليوم عليك ونقولك الفروقات كذا وكذا تمام + +470 +00:40:00,800 --> 00:40:04,540 +بعد ما ناخد ال local maximum و ال local minimum + +471 +00:40:04,540 --> 00:40:10,260 +نجي لحاجة اسمة concave up and concave down يبقى + +472 +00:40:10,260 --> 00:40:22,840 +concave up andconcave down التحدب + +473 +00:40:22,840 --> 00:40:27,740 +إلى أعلى أو إلى أسفل أو التحدب اللي بيسميه تقعر + +474 +00:40:27,740 --> 00:40:32,180 +وده كما بيسميه التحدب ما علينا اللي هو ال concave + +475 +00:40:32,180 --> 00:40:38,940 +up و ال concave down بضلنا نقطة انقلاب للمنحنة لل + +476 +00:40:38,940 --> 00:40:43,800 +inflection point يبقى inflection + +477 +00:40:46,000 --> 00:40:54,370 +pointيبقى نقطة الانقلاب أو نقطة الانعطاف للمنحنة + +478 +00:40:54,370 --> 00:41:00,790 +تمام المعلومات اللي عندنا هذه معلومات أساسية لرسم + +479 +00:41:00,790 --> 00:41:07,350 +المنحنة هذه هتشغل منها حوالي تلت سكاتشن at least + +480 +00:41:07,350 --> 00:41:14,030 +بعدين بنجي ل curve sketching بنجي لحاجة اسمها + +481 +00:41:14,030 --> 00:41:17,230 +curve sketching + +482 +00:41:19,880 --> 00:41:27,840 +curve يعني منحنى sketch رسم يبقى رسم المنحنيات كل + +483 +00:41:27,840 --> 00:41:32,220 +المعلومات اللى عرفناها فى السطرين هدول بدنا + +484 +00:41:32,220 --> 00:41:37,500 +نستخدمها فى رسم من المنحنيات طبعا هنا إيش جايلينا + +485 +00:41:37,500 --> 00:41:43,020 +إحنا هنا جايلينا graph of a function شو الفرق بين + +486 +00:41:43,020 --> 00:41:49,450 +هذه و هذهفرق شاسة، فرق الشاسة أنه هذا رسم لدول + +487 +00:41:49,450 --> 00:41:54,030 +بسيطة، يعني سالة standard اتكرر معاك دائما و أبدا + +488 +00:41:54,030 --> 00:41:58,690 +طيلة في الكتاب سواء كان بكالة قلصية أو B أو C، بس + +489 +00:41:58,690 --> 00:42:03,110 +هذه لا، هذه بدا شغل كتير حتى نقدر نقول ده اللي في + +490 +00:42:03,110 --> 00:42:06,380 +البسط و ده اللي في المقامأو ده اللي في المقام على + +491 +00:42:06,380 --> 00:42:10,280 +طوله بدي أشوف كيف ده رسمها عملية مش سهلة يبقى بدي + +492 +00:42:10,280 --> 00:42:14,360 +أدرس الشغلات كلها عشان أقدر أرسم ملحانة هذا يعني + +493 +00:42:14,360 --> 00:42:21,540 +هذه رسومات بسيطة و هذه رسومات أصعب من هذه بكثير + +494 +00:42:21,540 --> 00:42:27,740 +تمام؟ يبقى هذا هو chapter من أربعة إجمالة بنجي ل + +495 +00:42:27,740 --> 00:42:32,120 +chapter خمسة chapter خمسة اللي هو ال integration + +496 +00:42:35,850 --> 00:42:41,530 +Integration يعني إيه؟ تكامل، ممتاز، هنجسمه إلى + +497 +00:42:41,530 --> 00:42:46,650 +نوعين، النوع الأول indefinite integral و definite + +498 +00:42:46,650 --> 00:42:52,970 +integral بس قبل هيك بدنا نقول ال existence لتكامل، + +499 +00:42:52,970 --> 00:42:56,610 +هل التكامل هذا exist ولا لازم لا exist؟ زي ما في + +500 +00:42:56,610 --> 00:43:00,690 +حالة ال differentiation هنا، هل الدالة قابلة + +501 +00:43:00,690 --> 00:43:04,480 +للاشتراك ولا غير قابلة للاشتراك؟هنا بنقول هل + +502 +00:43:04,480 --> 00:43:09,680 +الدالة قابلة للتكامل والله غير قابلة للتكامل وما + +503 +00:43:09,680 --> 00:43:14,660 +هو الشرط انها تبقى قابلة للتكامل نفترض انها قابلة + +504 +00:43:14,660 --> 00:43:19,880 +للتكامل يبقى في عندي نوعين mini تكامل النوع الأول + +505 +00:43:19,880 --> 00:43:25,020 +اسمه definite integrals + +506 +00:43:26,870 --> 00:43:35,070 +التكاملات محدودة والنوع الثاني اسمه indefinite + +507 +00:43:35,070 --> 00:43:44,790 +integrals التكاملات غير المحدودة بالنسبة + +508 +00:43:44,790 --> 00:43:50,230 +للdefinite integrals يبقى احنا بنكامله مقولش زائد + +509 +00:43:50,230 --> 00:43:54,950 +مقدار ثابت بكون تكامل محدود من كذا إلى كذابنعوض + +510 +00:43:54,950 --> 00:44:01,470 +بحدود التكامل لكن على هذا الموضوع في نظرية مشهورة + +511 +00:44:01,470 --> 00:44:06,290 +وهي very important بنسميها ال fundamental theorem + +512 +00:44:06,290 --> 00:44:10,550 +of calculus النظرية الأساسية لحساب التفاضل + +513 +00:44:10,550 --> 00:44:16,890 +والتكامل يبقى في هنا حاجة اسمها fundamental + +514 +00:44:16,890 --> 00:44:19,950 +theorem + +515 +00:44:22,810 --> 00:44:25,450 +Ave Calculus + +516 +00:44:27,240 --> 00:44:32,100 +يبقى النظرية الأساسية لحساب التفاضل والتكامل في + +517 +00:44:32,100 --> 00:44:36,100 +الـ indefinite integral فهنا حاجة very important + +518 +00:44:36,100 --> 00:44:41,100 +كمان اللي هو استخدام التكامل بالتعويد يعني كيف ده + +519 +00:44:41,100 --> 00:44:45,160 +اللي مكلك ع هيك وشكلها مخيف بنقدر نبسطها ونخلي + +520 +00:44:45,160 --> 00:44:49,700 +شكلها لطيف ونقدر نكملها بسهولة يبقى ده اسم + +521 +00:44:49,700 --> 00:44:55,660 +integration by substitution يبقى هنا integration + +522 +00:45:00,160 --> 00:45:06,100 +by substitution يبقى + +523 +00:45:06,100 --> 00:45:10,900 +التكامل بالتعويض كيف نستخدم التعويض فإننا نقدر + +524 +00:45:10,900 --> 00:45:17,420 +نكامل ده لشكل غريب أو مكلقع بعد هيك بنيجي للمساحة + +525 +00:45:17,420 --> 00:45:27,000 +بين منحنيين يبقى ال area between curves + +526 +00:45:28,400 --> 00:45:32,940 +المساحة بين منحنا يعني احنا رسمنا دالة و رسمنا + +527 +00:45:32,940 --> 00:45:37,700 +دالة تانية دلتين حصروا بين بينهم في المستوى مساحة + +528 +00:45:37,700 --> 00:45:43,060 +بدنا نعرف كيف بدنا نحسب هذه المساحة بنجي لأخر حاجة + +529 +00:45:43,060 --> 00:45:48,840 +رقم ستة تطبيقات على التكامل زي ما في تطبيقات على + +530 +00:45:48,840 --> 00:45:55,120 +التفاضل فينا تطبيقات على التكامل يبقى بنجي لهنا ل + +531 +00:45:55,120 --> 00:45:55,960 +applications + +532 +00:45:59,710 --> 00:46:07,210 +of integrals ايش ال applications of integrals + +533 +00:46:07,210 --> 00:46:14,950 +تطبيقات على التكامل هروح نستخدم التكامل في حساب ال + +534 +00:46:14,950 --> 00:46:25,770 +volume حجم مجسم تمام بعد هيك ال surface area + +535 +00:46:28,370 --> 00:46:39,950 +المساحة السطحية لمجسم ما بعد هيك ال arc length of + +536 +00:46:39,950 --> 00:46:42,210 +a curve + +537 +00:46:45,030 --> 00:46:49,690 +يبقى هذه المحاورة الرئيسية في الشبتر السادس + +538 +00:46:49,690 --> 00:46:56,370 +والاخير بان نجي حجوم الأجسام الدورانية حجم مجسم في + +539 +00:46:56,370 --> 00:47:02,190 +الفراغ قداش المساحة السطحية لهذا المجسم لاحظ هنا + +540 +00:47:02,190 --> 00:47:07,210 +قولنا اه قولنا ال area between two curves في مستوى + +541 +00:47:07,790 --> 00:47:11,530 +منحنيا تقاطعوا بدنا المساحة اللي بينهم في مستوى + +542 +00:47:11,530 --> 00:47:18,110 +لكن هذه مساحة في الفراغ مجسم في الفراغ بد المساحة + +543 +00:47:18,110 --> 00:47:23,870 +السطحية لهذا المجسم arc length طول القوس او طول + +544 +00:47:23,870 --> 00:47:31,400 +جزء من منحنة arc length of a curveيبقى طول منحنة + +545 +00:47:31,400 --> 00:47:35,480 +في مرسوم عندى، بدى أعرف قداش الطول هذا كل هذا + +546 +00:47:35,480 --> 00:47:41,000 +بنستخدمله مين؟ التكامل هذا هو ايه المواضيع + +547 +00:47:41,000 --> 00:47:46,980 +الرئيسية التي سندرسها خلال هذا الفصل في calculus A + +548 +00:47:46,980 --> 00:47:53,000 +ونغير لكم الجو بأبيات من الشعر على التفاضل + +549 +00:47:53,000 --> 00:47:57,570 +والتكامليعني التفاضل و التكامل هذول زي الطوم، + +550 +00:47:57,570 --> 00:48:00,510 +شفتوا الطوم دايما أو أبدا بتناجروا مع بعض و دايما + +551 +00:48:00,510 --> 00:48:05,490 +بتكاتلوا و دايما صحبوا مع بعض في المقابل، تمام؟ + +552 +00:48:05,490 --> 00:48:12,610 +قال التفاضل شامتا أنا للتكامل معبره، أنا فاضل + +553 +00:48:12,610 --> 00:48:21,850 +متفضل، أنا يا تكامل أكبر، انظر على متكالاتيmy long + +554 +00:48:21,850 --> 00:48:25,770 +يطولوا ويقصروا تفضل ويقولوا شوف علامتك اللي هي + +555 +00:48:25,770 --> 00:48:32,760 +زادلة طبعا زي التكاملهبت تكامل هائجا أسكت أنا + +556 +00:48:32,760 --> 00:48:40,660 +متحرر أنا لم أقعد لك تابعا لا و لست منك أسطر أنا + +557 +00:48:40,660 --> 00:48:49,800 +للمساحة حاسب حتى الحجوم أصوره أنا بحسب المساحات و + +558 +00:48:49,800 --> 00:48:53,940 +الحجوم و أنت ما تقدرش تحسبها و أنا مش مشتاق منك + +559 +00:48:53,940 --> 00:49:00,500 +أنا منفصل لعاليبهذا بيقول هذا هو المقرر، الآن الذي + +560 +00:49:00,500 --> 00:49:05,300 +سندرسه طيلة هذا الفصل، حد بدي يسأل أي سؤال، فيما + +561 +00:49:05,300 --> 00:49:12,840 +سيدرس في هذا الفصل؟ بس + +562 +00:49:12,840 --> 00:49:20,300 +بنوسع شويةأو بنأسسك لما سيأتي فيما بعد يعني بنخليك + +563 +00:49:20,300 --> 00:49:30,760 +تتأسس تأسيسا سليما صحيحا مش تحفيظا لفهما ايوة + +564 +00:49:30,760 --> 00:49:34,780 +تفتسأل؟ والله بس الكلام جاي ال هيك طيب حد بتسأل + +565 +00:49:34,780 --> 00:49:43,420 +تاني؟ اذا ندخل في صميم الموضوعنبدأ بأول موضوع اللي + +566 +00:49:43,420 --> 00:49:46,140 +هو موضوع main ال functions + +567 +00:50:18,110 --> 00:50:27,330 +يبقى أول سيكشن لو سيكشن واحد واحد functions and + +568 +00:50:27,330 --> 00:50:37,710 +their graphs الدوال + +569 +00:50:37,710 --> 00:50:44,150 +والرسومات البيانية بدنا نبدأ أول شي ان نعطي تعريف + +570 +00:50:44,150 --> 00:50:49,900 +لل functionونحاول نفهم هذا التعريف التعريف بيقول + +571 +00:50:49,900 --> 00:51:08,440 +ما يأتي a function f from a set D to a set Y + +572 +00:51:08,440 --> 00:51:20,660 +وبينجو سلم نقول f من D إلى Yالشكل هذا is a role + +573 +00:51:20,660 --> 00:51:28,560 +that ascends to + +574 +00:51:28,560 --> 00:51:40,380 +each element x in D a unique element + +575 +00:51:47,630 --> 00:51:52,990 +Ionic element F + +576 +00:51:52,990 --> 00:52:04,170 +of X and Y Ionic element F of X and Y انتهى + +577 +00:52:04,170 --> 00:52:16,570 +التعريف The set D is called the + +578 +00:52:17,800 --> 00:52:34,140 +domain of F ال Y is called the codomain of F the + +579 +00:52:34,140 --> 00:52:37,380 +codomain + +580 +00:52:37,380 --> 00:52:43,620 +of F and + +581 +00:52:45,800 --> 00:52:53,500 +the collection of + +582 +00:52:53,500 --> 00:53:10,840 +all f of x is called the range of f + +583 +00:53:16,650 --> 00:53:21,370 +الان هذا التعريف اللى بين ادينا نحاول نقرأ هذا + +584 +00:53:21,370 --> 00:53:27,930 +التعريف من جديد نحاول نفهم كل كلمة من هذا التعريف + +585 +00:53:27,930 --> 00:53:33,490 +نحاول نحط هذا التعريف بالرسم على أرض الواقع بقى + +586 +00:53:33,490 --> 00:53:37,890 +فعلا نفهم شو الكلام اللى احنا كاتبينه يعني احنا + +587 +00:53:37,890 --> 00:53:43,690 +بنصمش صم احنا بنفهم فاهماذا فهمنا فهمنا صحيحا يبقى + +588 +00:53:43,690 --> 00:53:49,880 +بصير معنا مشكلة بعد هيك بنبني ازاي ما بدناهنرجع + +589 +00:53:49,880 --> 00:53:55,500 +لهذا التعريف نقرأه من جديد نحاول نفسر كل كلمة + +590 +00:53:55,500 --> 00:54:02,920 +موجودة أو كل عبارة هنا ما هو المقصود بها تمام؟ طيب + +591 +00:54:02,920 --> 00:54:07,480 +بدنا ننجل التعريف من بدايته اللي بين أدينا هو + +592 +00:54:07,480 --> 00:54:13,300 +تعريف ال function اللي بالعربي الاغتران أو الدلة + +593 +00:54:13,300 --> 00:54:16,960 +فإيش بيقولين؟ a function f + +594 +00:54:26,800 --> 00:54:31,300 +السطر هذا ممكن اختصره كله بالكلام اللي بينجوز هنا + +595 +00:54:36,160 --> 00:54:42,720 +is a role هو عبارة عن صيغة ما للصيغة هذه that + +596 +00:54:42,720 --> 00:54:52,540 +ascends تعين أو تحدد أو تخصص لكل عنصر X موجود في D + +597 +00:54:52,540 --> 00:55:00,620 +عنصرا وحيدا a unique element عنصر وحيد اسمه F of X + +598 +00:55:00,620 --> 00:55:06,090 +موجود وين؟ موجود في الست Yيبقى هذا هو ايه التعريف + +599 +00:55:06,090 --> 00:55:11,570 +يبقى مرة تانية دالة F هي عبارة عن الدالة F من ال + +600 +00:55:11,570 --> 00:55:17,070 +set D إلى ال set Y هي عبارة عن صيغة هذه الصيغة + +601 +00:55:17,070 --> 00:55:22,970 +تحدد لكل عنصر في ال set D عنصرا واحدا في ال set Y + +602 +00:55:22,970 --> 00:55:28,730 +تمام؟ يبقى هذا الترجمة العربية للتعريف احنا بناشي + +603 +00:55:28,730 --> 00:55:35,130 +الترجمة العربية من الترجمة الفهميةلمن؟ لالتعريف + +604 +00:55:35,130 --> 00:55:39,250 +قبل ما نجي للترجمة الفهمية انواصل بيقول ال 6D + +605 +00:55:39,250 --> 00:55:46,230 +بسميها المجال تبع الدالة F ال 6Y بسميها المجال + +606 +00:55:46,230 --> 00:55:53,740 +المرافق ال code domain للدالة Fكل f of x اللى + +607 +00:55:53,740 --> 00:55:59,020 +عندنا كل العناصر اللى ظهرت كصور لعناصر دى + +608 +00:55:59,020 --> 00:56:05,820 +collection جمعناها بنسميها المدى تبع الدالة f تمام + +609 +00:56:07,190 --> 00:56:11,430 +نرجع الأن للتريف من أول و جديد و كأننا ما سمعنا + +610 +00:56:11,430 --> 00:56:17,910 +شيئا و بدنا نعرض الموضوع بطريقة الرسم بيقول يتدلف + +611 +00:56:17,910 --> 00:56:23,870 +من 6D إلى 6Y يبقى أنا بدروح أرسم رسمة زي هيك و + +612 +00:56:23,870 --> 00:56:30,350 +أقول هذه 6D بدي أرسم رسمة تانية مثلا و أقول هذه ال + +613 +00:56:30,350 --> 00:56:35,810 +6 اللي عندنا اللي هي capital Yهذه الستة افترض فيها + +614 +00:56:35,810 --> 00:56:42,150 +عنصر وفيها كمان عنصر وفيها عنصر بس تلت عناصر هذه + +615 +00:56:42,150 --> 00:56:45,830 +الستة اللي جيت فيها ما شاء الله عليه هاي عنصر وهاي + +616 +00:56:45,830 --> 00:56:51,170 +اتنين وهاي تلاتة وهاي اربعة وهاي خمسة وهاي ستة ولا + +617 +00:56:51,170 --> 00:56:58,480 +يهمكطلع فيها عناصر كتير كويس ال F هي عبارة عن ده + +618 +00:56:58,480 --> 00:57:07,720 +لمن ال 6D ل6Y اديتها الرمز F يبقى هاي F من D الى Y + +619 +00:57:07,720 --> 00:57:13,360 +ايش بتسوي هذه في دنياتها جال هذه بتيجي تخصص لكل + +620 +00:57:13,360 --> 00:57:21,120 +عنصر X موجود في دي يبقى انا لو جيت سميت هذا Xموجود + +621 +00:57:21,120 --> 00:57:26,800 +في دي ايش بيحصل له هذه F بتخلي لهذا العنصر صورة في + +622 +00:57:26,800 --> 00:57:34,140 +ال 6Y الصورة هذه اسمها ايش اسمها F of X يبقى هذا + +623 +00:57:34,140 --> 00:57:40,660 +العنصر صار من F of X يبقى X في D صارتله صورة تحت + +624 +00:57:40,660 --> 00:57:46,250 +تأثير ال Fيعني F لما انأثرت على X صارت الصورة main + +625 +00:57:46,250 --> 00:57:52,110 +F of X موجودة وين؟ موجودة في ال set Y يبقى الكلام + +626 +00:57:52,110 --> 00:57:57,270 +اللي قلناه النظري روح نحطناه على شكل ايه؟ على شكل + +627 +00:57:57,270 --> 00:58:03,930 +رسم بيانلكن حتى الآن مافهمناش التعريف فهما دقيقة + +628 +00:58:03,930 --> 00:58:09,390 +لذلك هاطرح مجموعة من الأسئلة المجموعة من الأسئلة + +629 +00:58:09,390 --> 00:58:15,110 +هذه هي التي ستفهمنا التعريف و لذلك تعالوا مع + +630 +00:58:15,110 --> 00:58:22,340 +التعريففمن D الى Y هي F من D الى Y ماشي لها ايش + +631 +00:58:22,340 --> 00:58:27,420 +بتسوي هذه قال لي هي الصيغة الصيغة هذه انا اعطيتها + +632 +00:58:27,420 --> 00:58:32,720 +الرمز اللي هو F ايش بتسوي هذه قال لي that ascends + +633 +00:58:32,720 --> 00:58:39,380 +to each element X in D لكل عنصر X من D طب استنى + +634 +00:58:39,380 --> 00:58:47,870 +شويةمن هذه العبارة أفهم إن F هذه هتأثر على بعض + +635 +00:58:47,870 --> 00:58:53,230 +عناصر دي و الله عليها كلها على البعض مش على الكل + +636 +00:58:53,230 --> 00:59:01,210 +يعني دي باختلفة الروايات اختلف الفقهاء مش هيكخلفوا + +637 +00:59:01,210 --> 00:59:05,070 +في الفهم وهذه طبيعة البشر أنهم يختلفوا في الأفام + +638 +00:59:05,070 --> 00:59:09,090 +لكن تطلع للناس الناس بيقولوا that's essence to + +639 +00:59:09,090 --> 00:59:16,110 +each element in D كل عنصر في D إذا متأثر على بعض + +640 +00:59:16,110 --> 00:59:21,540 +العناصر و الله عليهم كلهمعليهم كلهم بلا استثناء لن + +641 +00:59:21,540 --> 00:59:27,280 +تستثني عنصر تمام؟ ليش؟ لأنه جالي to each element x + +642 +00:59:27,280 --> 00:59:32,760 +in D يعني مثلاته هتأثر على x و هتأثر على x1 و + +643 +00:59:32,760 --> 00:59:37,660 +هتأثر على x2 كلهم هتأثر عليهمتمام؟ لأنه قال لي to + +644 +00:59:37,660 --> 00:59:42,560 +each element X and Y شو بدى تعمله؟ بدى تخصص لكل + +645 +00:59:42,560 --> 00:59:50,960 +واحد منهم عنصرا وحيدا في ال set Y ممتاز جدا طيب + +646 +00:59:50,960 --> 00:59:56,240 +تعال مع عنصرا وحيدا في ال set Y استنى شوية السؤال + +647 +00:59:56,240 --> 01:00:03,220 +هو هل للعنصر X ستظهر صورة واحدة فقط ولا ممكن صوتين + +648 +01:00:03,220 --> 01:00:08,920 +او تلاتة؟سورة واحد لان جالي unique element يبقى + +649 +01:00:08,920 --> 01:00:16,520 +العنصر هذا X لن تظهر له الا صورة واحدة فقط في الست + +650 +01:00:16,520 --> 01:00:23,140 +Y الهمين ب F of X فقط ده غير يبقى العنصر الواحد له + +651 +01:00:23,140 --> 01:00:30,200 +ايه؟ له صورة واحدةنجي نكمل نسأل السؤال اللي بعده + +652 +01:00:30,200 --> 01:00:39,460 +هل يمكن لعنصرين أن يشترك في نفس الصورة؟ + +653 +01:00:43,900 --> 01:00:49,860 +يمكن لأنه مشراتش ممكن لعنصرين يشتركوا في نفسه + +654 +01:00:49,860 --> 01:00:54,320 +بصورة هذا العنصر له صورة واحدة والعنصر التاني له + +655 +01:00:54,320 --> 01:00:59,520 +صورة واحدة صحيح ولا لأ يبقى هدول محدش هداك يعني + +656 +01:00:59,520 --> 01:01:06,780 +يمكن لعنصرين أن يعني هذا X F خلت صورة F of X واخدت + +657 +01:01:06,780 --> 01:01:13,920 +X واحد وخلت صورته من F of X يعني أصارf of x هو + +658 +01:01:13,920 --> 01:01:20,600 +نفسه من f of x one اه ممكن لعنصرين وممكن التلاتة + +659 +01:01:20,600 --> 01:01:24,780 +يشتركوا في نفس الصورة كمان تمام احنا خل اتنين + +660 +01:01:24,780 --> 01:01:28,560 +يشتركوا في نفس الصورة اذا ماعنا مشكلة السؤال اللي + +661 +01:01:28,560 --> 01:01:34,120 +بعده يعني ممكن لعنصرين ان يشتركوا في نفس الصورة + +662 +01:01:34,120 --> 01:01:40,420 +لكن لايمكن للعنصر تظهرله صورتين ممنوه منع بات + +663 +01:01:40,840 --> 01:01:47,740 +السؤال اللي بعده هل الدالة F لما اتأثر على عناصر D + +664 +01:01:47,740 --> 01:01:51,880 +التفاقنة ما اتأثر عليهم كلهم بلا استثناء ستغطي + +665 +01:01:51,880 --> 01:01:59,160 +جميع عناصر Y سؤال بطريقة اخرى هل جميع عناصر Y + +666 +01:01:59,160 --> 01:02:06,860 +ستظهر كصور لعناصر D؟ مش ممكنممكن .. ممكن كلهم + +667 +01:02:06,860 --> 01:02:12,110 +يظهروا صحيح وارد، لكن in general لأ مش صحيحكويس + +668 +01:02:12,110 --> 01:02:17,950 +يعني ال range ممكن يسوي ال code main لكن in + +669 +01:02:17,950 --> 01:02:22,670 +general بيسويهوش طب هش بيسويه بيكون مجموعة جزئية + +670 +01:02:22,670 --> 01:02:29,170 +منه طبعا يعني x اتنين هذه لو أثرت عليها f بدها + +671 +01:02:29,170 --> 01:02:33,010 +تجيبه على العنصر اللي عندنا هنا وبالتالي يظل عندي + +672 +01:02:33,010 --> 01:02:38,830 +عنصر اتنين تلات مظهروش كصورعناصر في ال code domain + +673 +01:02:38,830 --> 01:02:45,010 +لكنها لم تظهر كصورة تمام؟ إذا ال range شو بيكون يا + +674 +01:02:45,010 --> 01:02:56,110 +شباب؟ بس F of X وهذه F of X2 هذه F of X2 يبقى سعر + +675 +01:02:56,110 --> 01:03:01,450 +ال range بيتبعد أوي خلينا نكتبهم كلهم ال domain و + +676 +01:03:01,450 --> 01:03:08,930 +ال range و ما إلى ذلكيبقى سعر domain هاختصرها DOM + +677 +01:03:08,930 --> 01:03:15,290 +الـ DLF بده يساوي من العناصر تبع كل اللي موجودة في + +678 +01:03:15,290 --> 01:03:25,730 +دي X و X1 و X2 بالاستثناء طيب بده ال range بتابع + +679 +01:03:25,730 --> 01:03:36,970 +ال DLF من هما عنصرين فقط يأمف of Xو f of x2 مافيش + +680 +01:03:36,970 --> 01:03:41,570 +غيرهم طب و f of x واحد ماهي f of x بثنانهم بيسووا + +681 +01:03:41,570 --> 01:03:46,370 +بعض يبقى مكتوب hash بتكرر يبقى في ال set لو تكرر + +682 +01:03:46,370 --> 01:03:50,730 +عنصرين تلاتة هذا بيعتبر كل عنصر واحد فقط لغيره + +683 +01:03:50,730 --> 01:03:56,030 +وبالتالي هذا صار ال range طب ما علاقة ال range بال + +684 +01:03:56,030 --> 01:04:04,170 +code mainمجموعة جزئية منه يبقى صار ال range لدالة + +685 +01:04:04,170 --> 01:04:16,720 +F هو مجموعة جزئية من ال code من اللي هو Y ممكنيغطي + +686 +01:04:16,720 --> 01:04:20,320 +كل عناصر وايد، ده اللي غطيها، إذا غطتها بسميها + +687 +01:04:20,320 --> 01:04:25,800 +دالة فوقية، on to function، هذي مشلكو، هذي بس + +688 +01:04:25,800 --> 01:04:28,680 +للناس اللي بتخصصوا رياضيات، بعدين في المستوى + +689 +01:04:28,680 --> 01:04:31,320 +التاني، فما فوق، يعني المعلومة اللي قلتها مش + +690 +01:04:31,320 --> 01:04:34,380 +الحين، هياخدوها السنة الجاية ان شاء الله اللي + +691 +01:04:34,380 --> 01:04:37,660 +بتخصصوا رياضيات، سواء كان من كلية التربية أو كلية + +692 +01:04:37,660 --> 01:04:41,040 +العلم، هندس أو تكنولوجيا، مالهمش دعوة في الموضوع، + +693 +01:04:41,040 --> 01:04:47,410 +تمام؟يبقى دائما وابدا هذه تقرأ مجموعة جزئية أقل من + +694 +01:04:47,410 --> 01:04:51,530 +.. مش أقل subset من أو تساوي لكن in general بقولش + +695 +01:04:51,530 --> 01:04:56,650 +subset من أو تساوي بقول subset من مجموعة جزئية من + +696 +01:04:56,650 --> 01:05:02,060 +اللي هو من ال Y اللي عندنا هذهطيب حتى اللحظة أظن + +697 +01:05:02,060 --> 01:05:07,560 +التعريف انفهم الآن ده لا بتخصص لعنصر من هنا صورة + +698 +01:05:07,560 --> 01:05:11,940 +واحدة لا يمكن لعنصر يظهرله صورتين ممكن لعنصر + +699 +01:05:11,940 --> 01:05:17,160 +يشتركها في نفس الصورة ال range هو جزء من ال code + +700 +01:05:17,160 --> 01:05:21,680 +domain خلصنا هذا كل الكلام اللي قلناه قدامنا هذا + +701 +01:05:21,680 --> 01:05:26,240 +على اللوح حد إله أي تساول قبل أن ندخل إلى أمثلة + +702 +01:05:26,240 --> 01:05:31,730 +توضيحية لكيفية إيجاد ال domain و ال rangeعشان لو + +703 +01:05:31,730 --> 01:05:39,230 +تسأل ايه اتفضل ال domain اف .. ده من فوق يعني ال + +704 +01:05:39,230 --> 01:05:47,610 +domain هو كل عناصر دي يعني هذا بده يساوي دي itself + +705 +01:05:47,610 --> 01:05:52,590 +ماشي؟ يعني كل العناصر اللي موجودة في دي لإنه جالي + +706 +01:05:52,590 --> 01:05:58,190 +to each element كل عنصر موجود في دي لن استثني فيهم + +707 +01:05:58,190 --> 01:06:06,860 +أحدا ماشي يا سيدي؟عناصر متشابهة في D لو في كان + +708 +01:06:06,860 --> 01:06:09,800 +عناصر متشابهة .. عناصر متشابهة في D ممكن نحطها في + +709 +01:06:09,800 --> 01:06:12,400 +.. مافيش يا سيدي في مفهومنا في ال groups يعني في + +710 +01:06:12,400 --> 01:06:16,980 +المجموعات ان العناصر متشابهة تعتبر عنصر عن واحدة + +711 +01:06:16,980 --> 01:06:20,580 +مثلا لو قلت لي مثلا انا عند الست اتنين و تلاتة و + +712 +01:06:20,580 --> 01:06:24,840 +تلاتة و تلاتة و تلاتة و خمسة يبقى ده مش الا تلاتة + +713 +01:06:24,840 --> 01:06:29,580 +عناصر هو اتنين و تلاتة و خمسة فقط لغاية ماشي؟ حد + +714 +01:06:29,580 --> 01:06:35,280 +بدي أسأل أي سؤال تاني؟طيب خش على الأمثلة المثال + +715 +01:06:35,280 --> 01:06:42,320 +بيقول ما يأتي example find + +716 +01:06:42,320 --> 01:07:00,840 +the domain and range of the following functions + +717 +01:07:11,930 --> 01:07:20,870 +هنا الـ function F هنا الـ domain تبع الدالة F هنا + +718 +01:07:20,870 --> 01:07:29,650 +ال range تبع الدالة F نجي لأول دالة من هذه الدوالة + +719 +01:07:29,650 --> 01:07:36,330 +لل F of X يساوي X تربيع زائد تلاتة + +720 +01:07:41,960 --> 01:07:47,060 +خلّي بالك معناه بنفهمك كيف بنحسب ال domain ثم كيف + +721 +01:07:47,060 --> 01:07:52,440 +بنحسب ال range لدالة ما الدالة اللي عندنا f of x + +722 +01:07:52,440 --> 01:07:57,540 +سوى x تربية زائد تلاتية ال domain يا شباب كل القيم + +723 +01:07:57,540 --> 01:08:04,420 +اللي بتاخذها x حتى تكون الدالة معرفة هذا بدوء + +724 +01:08:04,420 --> 01:08:09,660 +خلّيني أطرح السؤال التالي هل هناك قيمة ال x على كل + +725 +01:08:09,660 --> 01:08:15,720 +ال real lineبتخلّي القيمة هذه ماهياش معرفة في .. + +726 +01:08:15,720 --> 01:08:22,160 +في .. يعني معنى هذا ال domain من وين لوين من سالب + +727 +01:08:22,160 --> 01:08:27,540 +infinity إلى .. يعني كل ال real line يبقى هذه كل + +728 +01:08:27,540 --> 01:08:33,580 +مجموعة الأعداد الحقيقية the set of real numbers أو + +729 +01:08:33,580 --> 01:08:38,200 +انشي تفقل من سالب infinity إلى infinity ان قلت هذه + +730 +01:08:38,200 --> 01:08:42,940 +ماشي، ان قلت هذه ماشي تمام؟يبقى ال domain كل القيم + +731 +01:08:42,940 --> 01:08:47,560 +اللى بتاخدها x حتى تكون الدالة معرفة، بدي ال range + +732 +01:08:47,560 --> 01:08:55,300 +ال range هي كل قيم f of x يعني ايش؟ يعني بدي أخد + +733 +01:08:55,300 --> 01:09:01,440 +قيم من الفترة هذهوأعوض بها هنا شو بيطلع بيكون هذا + +734 +01:09:01,440 --> 01:09:05,760 +ال range ومشان يكون شغلي صح بدي أمسك من ال zero و + +735 +01:09:05,760 --> 01:09:08,960 +أتحرك على اليمين و بعدين أمسك من ال zero و أتحرك + +736 +01:09:08,960 --> 01:09:13,040 +على الشمال بحيث أغطي كل ال real life طيب بدي أبدأ + +737 +01:09:13,040 --> 01:09:17,560 +من عند ال zero من عند ال zero قدرش بتاخد تلاتة طيب + +738 +01:09:17,560 --> 01:09:23,920 +بعد ال zero إيش بيجيني واحد مربع و تلاتة يبقى من + +739 +01:09:23,920 --> 01:09:29,940 +تلاتة طالع نهوين لاربع لو قلتلك خمسةتربية و تلاتة + +740 +01:09:29,940 --> 01:09:35,620 +ثمانوية و اف طلعين لو قلتلك مية يبقى عشر تلاف و + +741 +01:09:35,620 --> 01:09:39,760 +تلاتة اف طلعين يعني انا بدأت من عند التلاتة وجيت + +742 +01:09:39,760 --> 01:09:45,420 +طالع تمام هذا لو ايش لو اخدت بعد مين بعد ال zero + +743 +01:09:45,420 --> 01:09:51,520 +طب لو جيت قبل ال zero سالب واحد تربية بصير بالموجة + +744 +01:09:51,520 --> 01:09:55,360 +بزاية التلاتة بصير اربعة يبقى انا بنزل رايح جهة + +745 +01:09:55,360 --> 01:10:00,950 +سالب infinity ورغم ذلكالقيم طالع القيم هذه هي ال + +746 +01:10:00,950 --> 01:10:08,110 +range يبقى ال range من ويل لويل من تلاتة تلاتة + +747 +01:10:08,110 --> 01:10:12,130 +موجودة قبل الأربع تلاتة اربع خمسة ستة مية الف + +748 +01:10:12,130 --> 01:10:18,910 +مليون الاخرين يبقى من عند التلاتة لغاية ال + +749 +01:10:18,910 --> 01:10:23,890 +infinityسواه نخدتها السالب و الله موجبة لما تربعها + +750 +01:10:23,890 --> 01:10:28,910 +بيصير موجبة إذا لا يمكن لل range أن ياخد أي قيمة + +751 +01:10:28,910 --> 01:10:32,110 +سالبة ولا حتى واحد ولا اتنين ولا اتنين و نص ولا + +752 +01:10:32,110 --> 01:10:36,210 +اتنين و تسعة من عشرة من تلات .. أقل قيمة بياخدها + +753 +01:10:36,210 --> 01:10:41,030 +ال range ثلاثة و بعدين بيبدأ يطالع واضح هذا الظن؟ + +754 +01:10:41,030 --> 01:10:47,610 +طيب هذه من أبسط أنواع الأمثلةانتجلي شوية يبقى + +755 +01:10:47,610 --> 01:10:53,130 +السؤال بعده لو جينا قولنا نمرة اتنين ال F of X + +756 +01:10:53,130 --> 01:11:00,170 +يساوي جذر X ناقص تلاتة مش + +757 +01:11:00,170 --> 01:11:04,770 +زي التلاتة جذر ال X ناقص تلاتة بدي ال domain من + +758 +01:11:04,770 --> 01:11:11,610 +وين لوين اه استنى شوية سيبك من السلب تلاتة برجع + +759 +01:11:11,610 --> 01:11:17,030 +لجذر ال X هو معرفي وين لوينعمر الجدر معرف لقيمة + +760 +01:11:17,030 --> 01:11:22,990 +سالبة إذا استثنى كل القيم السالبة معرف لل zeroجدر + +761 +01:11:22,990 --> 01:11:27,630 +ال zero جدر ال zero ب zero معرف يبقى من وين لوين + +762 +01:11:27,630 --> 01:11:33,030 +من عند ال zero لغاية ما لا نهاية يبقى من عند ال + +763 +01:11:33,030 --> 01:11:38,750 +zero لغاية مفتوحة و هنا مغلقة لإن عند ال zero + +764 +01:11:38,750 --> 01:11:42,370 +معرفة لكن لو كان عند ال zero مش معرفة بخليها + +765 +01:11:42,370 --> 01:11:48,630 +مفتوحة بالشكل اللي قدامنا هذا تمام إذا هذا هو ال + +766 +01:11:48,630 --> 01:11:52,990 +domain طب دي ال rangeبدي أبدأ أخد من ال domain + +767 +01:11:52,990 --> 01:11:58,900 +معوض هناحط zero بيظل قداش اذا سالب تلاتة في ال + +768 +01:11:58,900 --> 01:12:03,360 +range بدي امشي بعد zero بمشيش قبله انا باخد بس من + +769 +01:12:03,360 --> 01:12:06,300 +الفترة برا الفترة هذه ماليش علاقة ماليش علاقات + +770 +01:12:06,300 --> 01:12:09,600 +فيها قانف يبقى انا بتقيد علاقة بيجي بعدها قداش + +771 +01:12:09,600 --> 01:12:14,280 +واحد يبقى لو أخدت واحد في جدر واحد واحد سالب تلاتة + +772 +01:12:14,280 --> 01:12:18,780 +بيظل سالب اتنين مين اللي اكبر سالب تلاتة ولا سالب + +773 +01:12:18,780 --> 01:12:22,860 +اتنين سالب اتنين اكبر يعني معناه ان انا قاعد باطلع + +774 +01:12:24,320 --> 01:12:29,100 +أنا بطلع فى الدمين و بطلع فى ال rain طب بعد اللى + +775 +01:12:29,100 --> 01:12:36,600 +هو الواحد لو أخدت تسعة بصير تلاتة ناقص تلاتة يساوي + +776 +01:12:36,600 --> 01:12:42,260 +zero سالف تلاتة سالف اتنين سالف واحد zero طيب بدل + +777 +01:12:42,260 --> 01:12:47,960 +التسعة بدي أخد ميةجذر المية بعشرة ناقص تلاتة بسبعة + +778 +01:12:47,960 --> 01:12:52,780 +يبقى من السلب صار نموج وماشيين لو أخدت مثلا مليون + +779 +01:12:52,780 --> 01:12:58,340 +جذر المليون بألف ناقص تلاتة تسعة تسعة سبعة زي + +780 +01:12:58,340 --> 01:13:01,700 +الانتخابات العربية السابقة طبعا مش اللي الحين .. + +781 +01:13:01,700 --> 01:13:05,080 +الحين خلاص بدأوا يمشوا صح او ما رجعوا الانتخابات + +782 +01:13:05,080 --> 01:13:10,100 +مظورة طيب يبقى هنا جداش تسعة تسعة سبعة اخر بدأنا + +783 +01:13:10,100 --> 01:13:16,120 +نطلع هنبقى ماشي إلى ويناذا كم سيكون ال range؟ سالف + +784 +01:13:16,120 --> 01:13:20,900 +تلاتة لغاية infinity يبقى closed من عند السالف + +785 +01:13:20,900 --> 01:13:26,140 +تلاتة لغاية كم؟ لغاية infinity انت قلك شوية كمان + +786 +01:13:26,140 --> 01:13:33,820 +لو جيت الجذري التربيعي تلاتة f of x بيساوي الجذري + +787 +01:13:33,820 --> 01:13:42,010 +التربيعي لتلاتة ناقص x يالا يجب أن يكون صفر صفراه + +788 +01:13:42,010 --> 01:13:47,210 +استنى شوية يعنى هنا اوقف شوية احنا بنلقون الجدر + +789 +01:13:47,210 --> 01:13:52,750 +اللى ليس معرفا الا لقيمة اذا ممنوع لسالبة اما عند + +790 +01:13:52,750 --> 01:13:57,890 +الصفر مرحبا بواهلا وسهلا اذا بدي كل القيمة اللى + +791 +01:13:57,890 --> 01:14:03,750 +تحت الجدر تبقى اكبر من أو تساوي zero باجى فى الهمش + +792 +01:14:03,750 --> 01:14:12,420 +هامش هامش هكو يقول انا بدي تلاتة ناقص ال X تبقى + +793 +01:14:12,420 --> 01:14:16,700 +greater than or equal to zero صحيح؟ بدنا الحل + +794 +01:14:16,700 --> 01:14:23,560 +المتبين هذي بقوله بسيطة اضيف X للطرفين يبقى بيضل + +795 +01:14:23,560 --> 01:14:29,860 +هنا قداشر تلاتة و هنا بصير X صح ولا لا؟هو زمان كنا + +796 +01:14:29,860 --> 01:14:33,020 +بنقول البلدي on كل X على الشجرة التانية احنا + +797 +01:14:33,020 --> 01:14:37,200 +مابنقولش X رياضية مابنقول بنضيف للطرفين اللي هو ال + +798 +01:14:37,200 --> 01:14:42,860 +X اللي عندنا بيصير X ونقص X ب Zero واضفنا X زائد + +799 +01:14:42,860 --> 01:14:48,660 +Zero له ب X يبقى تلاتة أكبر تساوي X أو X أقل من أو + +800 +01:14:48,660 --> 01:14:54,620 +تساوي جداش تلاتة يعني أكبر قيمة بياخدها جداش وبعد + +801 +01:14:54,620 --> 01:14:57,180 +هيك يعني بيصير من وين لوين + +802 +01:15:00,020 --> 01:15:07,520 +بس قوللي بسير من ورا إلى ورا و بعدين بنرجعلك جديش + +803 +01:15:07,520 --> 01:15:13,550 +من ورا؟من سالب infinity لغاية التلاتة اذا بصير هذا + +804 +01:15:13,550 --> 01:15:19,770 +ال domain من سالب infinity لغاية التلاتة closed من + +805 +01:15:19,770 --> 01:15:25,630 +هنا و من هنا open هلحين لو اخدت اي رقم من هنا + +806 +01:15:25,630 --> 01:15:31,510 +بتلاقي هذا الجذر معرف مرة تانية يا شباب مرة تانية + +807 +01:15:31,510 --> 01:15:35,150 +بقول انا بدي كل الكمية اللي تحت اليدر تبقى اكبر من + +808 +01:15:35,150 --> 01:15:37,790 +او تساوي zero هذه + +809 +01:16:02,600 --> 01:16:09,320 +هذا يجعلني أسأل السؤال التالي متى تقلب المتباينةفي + +810 +01:16:09,320 --> 01:16:16,400 +حالتين ثالثة لهم إذا ضربت المتبينة في كمية سالبة + +811 +01:16:16,400 --> 01:16:22,120 +والأمر الثاني إذا قلبت المتبينة بالشرط أن يكون + +812 +01:16:22,120 --> 01:16:26,180 +الإشارتين في الطرفين زي بعض وإلا بصير كلامنا مش + +813 +01:16:26,180 --> 01:16:30,990 +صحيح، مظبوط؟يبقى أنا بقلب المتباينة إذا الطرفين + +814 +01:16:30,990 --> 01:16:37,330 +بنفس الإشارة بقلب الطرفين وفي هذه أو أضرب الطرفين + +815 +01:16:37,330 --> 01:16:42,230 +في قيمة سالبة فتنقلب الأقل من إلى أكبر منه وعكسه + +816 +01:16:42,230 --> 01:16:42,850 +بالعكس + +817 +01:16:47,260 --> 01:16:51,220 +انا مش عرفت ان ال X موجبة، ال U في الساعة، ان اش + +818 +01:16:51,220 --> 01:16:54,680 +ما تكون ال X تكون، موجة و لا ساعة، اضفت للطرفين، + +819 +01:16:54,680 --> 01:17:00,380 +الإضافة، بس رد عليك، الإضافة أو الطرح أو الضرب في + +820 +01:17:00,380 --> 01:17:05,240 +قيمة موجبة لا تغير و بقى ال inequality، نهائي، + +821 +01:17:05,240 --> 01:17:06,740 +بتظل ال inequality كما هي، اه + +822 +01:17:12,430 --> 01:17:16,950 +تانى تانى تانى تانى الصياغة عبّر ..قول أشوف، اعتبر + +823 +01:17:16,950 --> 01:17:24,990 +سؤالك كله غلط وحكي براعتك عادي جدا، ردش عليك تلقية + +824 +01:17:24,990 --> 01:17:25,830 +اللقاء صح + +825 +01:17:29,370 --> 01:17:35,130 +من سالب عشرة الى تلاتة من سالب عشرة الى تلاتة + +826 +01:17:35,130 --> 01:17:39,070 +والله من تلاتة لسالب عشرة دائما من الصغرة بنخليها + +827 +01:17:39,070 --> 01:17:43,310 +في الأول والكبرى بالآخر يبقى هنا من سلب infinity + +828 +01:17:43,310 --> 01:17:49,540 +لغايةلغاية تلاتة تمام؟ هذه الصيغة أو الصيغة هذه + +829 +01:17:49,540 --> 01:17:53,320 +الاتنين are the same هنا X أقل من أوي سوى تلاتة + +830 +01:17:53,320 --> 01:17:56,820 +هنا X أقل من أوي سوى تلاتة لكن كنا بنكتب انجليزي + +831 +01:17:56,820 --> 01:18:00,740 +بقال صح نكتب بالشكل اللي عندنا ده ما عليناطيب + +832 +01:18:00,740 --> 01:18:05,420 +جيبنا ال domain بدنا نروح نجيب main الرين يبقى بده + +833 +01:18:05,420 --> 01:18:11,440 +اشيل ال X و احط مكانها تالتة بيصير قد صفر طيب ارجع + +834 +01:18:11,440 --> 01:18:17,680 +قبل التلاتة لو حطيت X باتنين بيصير تلاتة ناقص + +835 +01:18:17,680 --> 01:18:20,400 +اتنين اللي هو بواحديبقى احد يبقى من اتنين رجعنا + +836 +01:18:20,400 --> 01:18:26,040 +لوين لواحد من صفر طلعنا قصدي لواحد طيب لو جينا + +837 +01:18:26,040 --> 01:18:33,360 +لصفر مضطري قداش جدر تلاتة لو جينا لسالب واحد سالب + +838 +01:18:33,360 --> 01:18:36,960 +سالب واحد بيصير مجبرة تلاتة اربعة يعني قداش يبقى + +839 +01:18:36,960 --> 01:18:41,720 +من الصفر وصلنا لاتنين طيب ارجع كمان لو قلت هنا + +840 +01:18:41,720 --> 01:18:50,260 +سالب ستةبصير موجة ب 6 و 3 9 يبقى 3 طالعين طب لو + +841 +01:18:50,260 --> 01:18:57,800 +قلت لك إن السالب 97 بصير موجة ب 97 و 3 جدر ال 110 + +842 +01:18:57,800 --> 01:19:03,340 +يبقى من صفر و احنا طالعين يبقى كدش يا رياني من + +843 +01:19:03,340 --> 01:19:10,980 +الصفر مافيش سالب عندي نهائي يبقى من عند ال zero + +844 +01:19:10,980 --> 01:19:17,130 +لغاية ال infinityحد يلو يتسول حتى الآن، يعني واضح + +845 +01:19:17,130 --> 01:19:20,870 +هذا، كل مرة بتقل شوية ها في شكل الدلقاء، اه يا + +846 +01:19:20,870 --> 01:19:26,770 +ابني بتحط قسم، بتحط .. مفتوح، مفتوح، مفتوح، مفتوح، + +847 +01:19:26,770 --> 01:19:28,330 +مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، + +848 +01:19:28,330 --> 01:19:28,990 +مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، + +849 +01:19:28,990 --> 01:19:30,370 +مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، + +850 +01:19:30,370 --> 01:19:36,260 +مفتوح، مفتوح، مفتوح، ملا نلجأ إلا مالها إلا مصير + +851 +01:19:36,260 --> 01:19:40,760 +عنها عاجز رياضي يعني إذا قولتك معاك شكل و بيتقسمه + +852 +01:19:40,760 --> 01:19:44,820 +بين اتنين أه بقسمه بعطي كل واحد نص شكل و لو كانوا + +853 +01:19:44,820 --> 01:19:48,900 +عشرة بعطي كل واحد أجورة لكن لما يكون معاك شكل و + +854 +01:19:48,900 --> 01:19:57,060 +عندك صفر من البشر هل يمكن أن تتم هذه العملية مطلوب + +855 +01:19:57,060 --> 01:20:02,920 +إنك توزعهم و إلا بتنطخيبقى العقل البشري خارج + +856 +01:20:02,920 --> 01:20:06,860 +نطاقه، رياضيا بقدرش يعمل العملية هذه فاحنا لما + +857 +01:20:06,860 --> 01:20:10,160 +نتحرك من هذا الشغل هتقول ما لنا، يعني خارج نطاقة + +858 +01:20:10,160 --> 01:20:16,300 +العقل البشري، ماشي؟ اه يا ابن ايه؟ + +859 +01:20:16,300 --> 01:20:23,860 +مانا؟ شوف يا زيد، لما أقول لك قوس هيك، يبقى هذه + +860 +01:20:23,860 --> 01:20:30,130 +closed intervalهذه فترة مغلقة نقول لك لجثين + +861 +01:20:30,130 --> 01:20:35,950 +زعلانين مع بعض واحد موجه هيك والتاني موجه هيك إيش + +862 +01:20:35,950 --> 01:20:41,650 +كنت تقولوا عليها هذه؟ إحنا عندنا هذه تكافئ تماما + +863 +01:20:41,650 --> 01:20:45,550 +جثين صغير موجهات على بعض يبقى هذه فترة .. هذه + +864 +01:20:45,550 --> 01:20:49,470 +بتلاقيهاش في كتابنا لكن بتلاقي هذه .. هذه هي هذه + +865 +01:20:49,470 --> 01:20:54,430 +بالضبط تماماممكن تلاقي من جهة مقفلة ومن جهة تانية + +866 +01:20:54,430 --> 01:20:59,410 +مفتوحة من عند ال infinity أو السالب infinity دائما + +867 +01:20:59,410 --> 01:21:04,010 +و أبدا مطول مغلقة يعني التلاتة من ضمن الفترة + +868 +01:21:04,010 --> 01:21:10,330 +مفتوحة يعني التلاتة ليست من الفترة ماشي ايوة اتفضل + +869 +01:21:10,330 --> 01:21:14,130 +في المثال الثالث اماله + +870 +01:21:18,490 --> 01:21:23,110 +الـ Range من سالب مالة نهائية لصرف يعني كلها بتاخد + +871 +01:21:23,110 --> 01:21:29,430 +قيم سالبة جزدك طيب انا باسألك هل يعني كل القيم + +872 +01:21:29,430 --> 01:21:34,530 +اللي من تحت الجدر بتطلع سالبة مش هي الجزدك؟ بس + +873 +01:21:34,530 --> 01:21:41,030 +هتبطى الهاء الهاء بتامسك من هنا تلاتة نقص تلاتة + +874 +01:21:41,030 --> 01:21:47,890 +نقص نقص تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص + +875 +01:21:47,890 --> 01:21:47,930 +تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص + +876 +01:21:47,930 --> 01:21:48,290 +تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص + +877 +01:21:48,290 --> 01:21:50,510 +تلاتة نقص تلاتة نقص تلاتة نيبقى بسيط تلاتة نقصت + +878 +01:21:50,510 --> 01:21:56,190 +هنا بقداش؟ بواحد، يبقى بواحد، بدي أرجع تاني وصلت + +879 +01:21:56,190 --> 01:22:02,470 +الصفر، بصير هنا جزر تلاتة، بدي أرجع قبل الصفر مين؟ + +880 +01:22:02,470 --> 01:22:06,950 +سالب واحد، وقال هنا سالب، بصير موجة بواحد تلاتة + +881 +01:22:07,820 --> 01:22:12,400 +يبقى اتنين من اين تأتي السالب؟ جيبك ارجع كمان سالب + +882 +01:22:12,400 --> 01:22:17,120 +سبعة وتسعين وهنا سالب في الموجة بيبقى سعرات مية من + +883 +01:22:17,120 --> 01:22:21,480 +اين تأتي السالب؟ اذا لا يمكن ان تكون النتيجة سالبة + +884 +01:22:21,480 --> 01:22:26,980 +على الإطلاق دائما الموجة بإيجابية طيب نعطي مثال + +885 +01:22:26,980 --> 01:22:34,440 +اخر لو قلتك نمره اربعة F of X يساوي الجدر التربيه + +886 +01:22:34,440 --> 01:22:41,170 +للست عشر ناقص X تربيهأصلا هادى زى هادى بس هادى X + +887 +01:22:41,170 --> 01:22:46,490 +هادى X تربية لكن تعالى شوف ماهى الفوارق الشاسعة + +888 +01:22:46,490 --> 01:22:52,750 +بين السؤالين بدي أمشي زى ما مشيت هنا هاي في الهامش + +889 +01:22:52,750 --> 01:22:58,850 +هاي ال 16 ناقص X تربية بديها تبقى أكبر من أو تساوي + +890 +01:22:58,850 --> 01:23:04,380 +Zero مظبوط هيك؟يبقى هنا لو أضفنا X تربية للطرفين + +891 +01:23:04,380 --> 01:23:11,620 +بيصير 16 أكبر من أو تساوي X تربية لو قعدت صياغتها + +892 +01:23:11,620 --> 01:23:19,980 +يبقى X تربية أقل من أو تساوي 16 مظبوط انا مابدي X + +893 +01:23:19,980 --> 01:23:26,400 +تربية بدي X شو بعمل باخد الجذر التربيهي للطرفين + +894 +01:23:26,400 --> 01:23:33,080 +الجذر التربيهي ل X تربية هو كدهabsolute value of x + +895 +01:23:33,080 --> 01:23:40,260 +دي بالك تمام أقل من أو يساوي جدر التربيه على ال 16 + +896 +01:23:40,260 --> 01:23:46,390 +و 4 خدها قاعدة دائما و أبدا ايه بكتبها لكالجذر + +897 +01:23:46,390 --> 01:23:50,290 +التربية إلى x تربية دائما و أبدا هي absolute value + +898 +01:23:50,290 --> 01:23:56,610 +لزادة أو ناقص x لأن مربع ال x بx تربية و مربع ناقص + +899 +01:23:56,610 --> 01:24:01,510 +x برضه بx تربية إذا زادة أو ناقص هي absolute value + +900 +01:24:01,510 --> 01:24:08,890 +إذا صار absolute value ل x أقل من أو تساوي 4طباش + +901 +01:24:08,890 --> 01:24:14,210 +معناها رياضيا كذلك معناها هذه لو بدى فك ال + +902 +01:24:14,210 --> 01:24:21,170 +absolute ان ال X هذه اما اقل من او يساوي اربعة او + +903 +01:24:21,170 --> 01:24:26,870 +اكبر من او يساوي جداشيبقى من وين لوين من سالب + +904 +01:24:26,870 --> 01:24:32,850 +أربعة لأربعة فقط لغير شايف هذه قداش كانت وهذه قداش + +905 +01:24:32,850 --> 01:24:39,370 +صارت يبقى من سالب أربعة إلى أربعة as any closed + +906 +01:24:39,370 --> 01:24:45,890 +interval لو مافيش يساوي هنا بكتبها فترة مفتوحة لكن + +907 +01:24:45,890 --> 01:24:50,690 +نظرا لإنه فيه يساوي بروح بكتبها فترة مغلقة أو + +908 +01:24:50,690 --> 01:24:56,900 +closed intervalهذا هو ال domain الان بناجي لل + +909 +01:24:56,900 --> 01:25:05,960 +range طيب بده احط هنا سالب اربعة مربعها موجب ستة + +910 +01:25:05,960 --> 01:25:10,240 +عشر بسرعة ستة عشر نقص ستة عشر يساوي Zero لو حطيت + +911 +01:25:10,240 --> 01:25:14,560 +الاربعة هذه تانية بصير كمان قداش Zero يعني ال + +912 +01:25:14,560 --> 01:25:21,790 +range يساوي Zeroلأ مش صحيح شوف يا سيدى ان جيت على + +913 +01:25:21,790 --> 01:25:26,290 +الفترة و لجيت القيمة الأولى و القيمة الأخيرة عطتني + +914 +01:25:26,290 --> 01:25:31,610 +نفس النتيجة بتروح على نص ال interval من الرقم اللى + +915 +01:25:31,610 --> 01:25:36,490 +فى نص ال interval اللى هو ال zero حط x ب zero بصير + +916 +01:25:36,490 --> 01:25:42,950 +جدر سطحش اللى و جداش يبقى من zero لغاية أربعة فقط + +917 +01:25:42,950 --> 01:25:48,760 +لا غيريبقى النتيجة من عند ال zero لغاية أربعة as + +918 +01:25:48,760 --> 01:25:54,760 +any closed interval هلحين أي رقم أخر ييجي في بالك + +919 +01:25:54,760 --> 01:25:59,780 +في هذا الفترة عوضه بدي يطلع هنا سواء كان كثري ولا + +920 +01:25:59,780 --> 01:26:03,180 +مش كثري تستخدم ال calculator ما تستخدم كله بدي + +921 +01:26:03,180 --> 01:26:11,320 +يطلع موجود هنا طيب ايه المثال الخامسالمثال الخامس + +922 +01:26:11,320 --> 01:26:20,700 +انتقل شوية ب the f of x يسوى مية على x ناقص ثلاثة + +923 +01:26:20,700 --> 01:26:28,220 +x ناقص ثلاثة يالا شوف مالها؟ + +924 +01:26:28,220 --> 01:26:34,220 +كدهش لما تحط x سالب أربع كدهش بتطلع النتيجة؟و لما + +925 +01:26:34,220 --> 01:26:39,480 +تحطها باربع صفر لما نتيجة عن نص ال interval اللي + +926 +01:26:39,480 --> 01:26:45,000 +هو قداش صفر قداش بطلع جدر الستاش اللي هو قداش اذا + +927 +01:26:45,000 --> 01:26:48,840 +من صفر لاربع اي رقم يجي في بالك من سالب اربع لاربع + +928 +01:26:48,840 --> 01:26:53,320 +بتجي محصور النتيجة تبعته من صفر لغاية اربع ايوا + +929 +01:26:58,260 --> 01:27:06,660 +النتيجة الطرف الأول نفس النتيجة بروح نص الفترة طيب + +930 +01:27:06,660 --> 01:27:15,240 +الان عندنا سؤال تاني مية على اكس ناقص تلاتة ماعدد + +931 +01:27:15,240 --> 01:27:20,870 +تلاتة يعني كل real number ماعدد تلاتةيبقى يا بقوله + +932 +01:27:20,870 --> 01:27:28,370 +R ناقص التلاتة و بحطها as a ستة بشكل مش تلاتة + +933 +01:27:28,370 --> 01:27:32,030 +لحالة في الخلة تلاتة معناه تعنصر بس تلاتة بين + +934 +01:27:32,030 --> 01:27:37,850 +قوسين عبارة عن ستة مطروحة منها ستة أخرى أو بقدر + +935 +01:27:37,850 --> 01:27:43,670 +أقوله هذه من سالب infinity لغاية التلاتة اتحاد + +936 +01:27:43,670 --> 01:27:51,500 +تلاتة و infinity الشكل اللي عندناطيب يالا هذا هو + +937 +01:27:51,500 --> 01:28:00,120 +ال domain بده ال range ال range ايش يعني يعني مالة + +938 +01:28:00,120 --> 01:28:05,220 +نهاية عنصر يعني يالا + +939 +01:28:05,220 --> 01:28:09,580 +يعطوني فكر ويعطيني نتيجة انا بدي طبعا هناقشك فيها + +940 +01:28:09,580 --> 01:28:15,520 +بس يعطيني نتيجة ايوة يعني + +941 +01:28:15,520 --> 01:28:20,100 +ارشيلك على حال ماعدد التلاتة ولا ماعدد السفارةمعدى + +942 +01:28:20,100 --> 01:28:24,040 +التلاتة و بعدين انت و اياه لما يجيك الدور بتجاوز + +943 +01:28:24,040 --> 01:28:28,360 +بشان نستفيد كله يصغل لرجل اللي بيجاوز يمكن بيجاوب + +944 +01:28:28,360 --> 01:28:32,060 +صحي و يمكن بيجاوب غلط معدى التلاتة معدى التلاتة + +945 +01:28:32,060 --> 01:28:34,900 +يعني كل ال real life معدى التلاتة في نفس الدور + +946 +01:28:34,900 --> 01:28:39,940 +يعني او كما قال يعني اوش اتنس بسبب ادران اصلا مش + +947 +01:28:39,940 --> 01:28:44,440 +من الدور يعني انا مش مصدر دران مافيش x4 انا اناقش + +948 +01:28:44,440 --> 01:28:52,590 +تلاتة او ستةعيد الصقر تاني يعني + +949 +01:28:52,590 --> 01:28:56,850 +كفترة و لا كرقامين؟ اه يعني من الريال الله يمكنك + +950 +01:28:56,850 --> 01:29:00,970 +تشيله التلاتة و تشيله الزفر و هي وجهة نظر أخرى، هل + +951 +01:29:00,970 --> 01:29:06,030 +صار عني وجهتين نظر، في غيرهم؟ أيوة تاني من النهاية + +952 +01:29:06,030 --> 01:29:12,480 +إلى تلات مفتوح اتحادالثلاثة مفتوحة لأمالها. أو كما + +953 +01:29:12,480 --> 01:29:16,260 +قال يعني. ما جبتش جديد. بدنا .. فيه جديد؟ والله + +954 +01:29:16,260 --> 01:29:20,580 +مافيش. أيوة. جميع الأعداد الحقيقية بين ما فيها + +955 +01:29:20,580 --> 01:29:24,980 +التلاتة اللي بيقول عليها. واي. هاي كمان إجابة غير + +956 +01:29:24,980 --> 01:29:30,300 +شكلة أو جرت شكلة. كمان زي نجمتهم. أه. ال domain هو + +957 +01:29:30,300 --> 01:29:30,980 +ايش؟ + +958 +01:29:33,450 --> 01:29:40,310 +يعني زي ما قالوا في جديد و لا فيش جديد يعني + +959 +01:29:40,310 --> 01:29:46,610 +سحبت التلاتة هذه هذه فقط الإجابة الصحيحة كل اللي + +960 +01:29:46,610 --> 01:29:53,230 +فات كله خطأ يبقى هذه من سالب infinity لغاية ال + +961 +01:29:53,230 --> 01:29:59,870 +zero اتحاد zero و infinity أو إن شئت فقول كل ال R + +962 +01:29:59,870 --> 01:30:01,890 +بدي أشيل منها ال zero + +963 +01:30:04,770 --> 01:30:11,050 +طيب، ثانى شوية بس، ثانى شوية، من أين لك هذا؟ اذا + +964 +01:30:11,050 --> 01:30:15,210 +نفهم، من وين هذا يا عزيزي؟ طلعلي كويس انت و ايه، + +965 +01:30:15,210 --> 01:30:21,730 +هذا ال real life و هذا الرقم ثلاثة، ثلاثة ليس من + +966 +01:30:21,730 --> 01:30:26,470 +ال domain يبقى بعد الثلاثة كله من ال domain و قبل + +967 +01:30:26,470 --> 01:30:31,950 +الثلاثة كله من ال domain تعالى نشوف كيف بدنا .. + +968 +01:30:31,980 --> 01:30:37,900 +اعرفنا هذه تمام؟ انا بديش نقعد انحذر بدي افهمكيا + +969 +01:30:37,900 --> 01:30:41,680 +step by step بدي اتحرك على يمين التلاتة و بعدين + +970 +01:30:41,680 --> 01:30:46,000 +اتحرك على شمال التلاتة اشوف ايش بتجيبلي لو اتحركت + +971 +01:30:46,000 --> 01:30:49,820 +على يمين التلاتة بصير ايش بيجيبلك؟ مثلا اربع بصير + +972 +01:30:49,820 --> 01:30:55,970 +اربع ناقص تلاتة بواحد يبقى الجواب قداش مية طيبجبت + +973 +01:30:55,970 --> 01:31:01,770 +خمسة خمسة نقص تلاتة اتنين مية على اتنين صار خمسين + +974 +01:31:01,770 --> 01:31:08,290 +يبقى نزلت من مية نزلت لوين لخمسين طيب ها بدي امشي + +975 +01:31:08,290 --> 01:31:13,610 +بعد التلاتة انا مشيت اربع ومشيت خمسة وقول مشيت يا + +976 +01:31:13,610 --> 01:31:20,350 +سيدي مية و تلاتة مية و تلاتة نقص تلاتة كده؟ مية + +977 +01:31:20,350 --> 01:31:26,820 +على مية يعني من مية نزلت للواحدطيب امشي كمان امشي + +978 +01:31:26,820 --> 01:31:32,700 +وقاس director وصلت هنا الف و تلاتة ناقص تلاتة، + +979 +01:31:32,700 --> 01:31:38,120 +الف، مية على الف في قدام، عشر، ضال عندي عشرة في + +980 +01:31:38,120 --> 01:31:42,360 +المقام، صحيح ولا لأ؟ يبقى من مين نزلت لعشر، طب + +981 +01:31:42,360 --> 01:31:47,460 +امشي مليون و تلاتة، شيل منهم تلاتة، المليون صار + +982 +01:31:47,460 --> 01:31:52,850 +مية مليونمية على مليون و واحد على عشرة آلاف يعني + +983 +01:31:52,850 --> 01:31:57,210 +القسر قاعد بينخسر كل ما انا طاير لقدام كل ما القسر + +984 +01:31:57,210 --> 01:32:02,170 +نازل على وين؟ على السفر يعني انا لو وصلت لمالة + +985 +01:32:02,170 --> 01:32:06,490 +نهاية ده سمح الله طبعا ولا واحد بقدر يوصل يبقى مية + +986 +01:32:06,490 --> 01:32:11,430 +على مالة نهاية في جدشأى عدد على مالة نهاية بيعطيك + +987 +01:32:11,430 --> 01:32:16,650 +ال zero تمام يبقى انا كل مناطير اللى قدام هذا نازل + +988 +01:32:16,650 --> 01:32:21,850 +لوين نازل لل zero انا موصلش لمالة نهاية اذا لا + +989 +01:32:21,850 --> 01:32:25,970 +يمكن اوصل لل zero يبقى روحنا خليناها مفتوحة من + +990 +01:32:25,970 --> 01:32:31,930 +zero لوين للمالة نهاية هذا لو مشيت باش بارقام + +991 +01:32:31,930 --> 01:32:36,180 +موجبةمن التلاتة فاهمه طيب بده اجي قابل التلاتة + +992 +01:32:36,180 --> 01:32:41,600 +قابل التلاتة زي مين؟ زي اتنين يبقى اتنين ناقص + +993 +01:32:41,600 --> 01:32:49,480 +تلاتة سالب واحد يعني سالب مية تمام طيب سالب مية لو + +994 +01:32:49,480 --> 01:32:54,340 +جيت اخف واحد بدل اتنين بيصير واحد ناقص تلاتة بناقص + +995 +01:32:54,340 --> 01:33:00,340 +اتنين يبقى ناقص خمسين يبقى من سالب مية طالع لسالب + +996 +01:33:00,340 --> 01:33:05,880 +خمسين مظبوط ولا لا؟طيب لو جيتلي قبلها جيتلي ال + +997 +01:33:05,880 --> 01:33:10,540 +zero بيظل مية سالب تلاتة بتلاتة و تلاتين و تلت بس + +998 +01:33:10,540 --> 01:33:15,460 +بالسالب يبقى طالع و هكذا كله لغاية ما وصل ال goal + +999 +01:33:15,460 --> 01:33:20,620 +مثلا هنا سالب سبعة وتسعين سالب تسمى سبعة وتسعين و + +1000 +01:33:20,620 --> 01:33:27,260 +سالب تلاتة سالب جداش مية يبقى هذا كله جداش بسالب + +1001 +01:33:27,260 --> 01:33:32,550 +واحد يبقى من سالب مية طالع انا وصلت لسالب واحديبقى + +1002 +01:33:32,550 --> 01:33:39,090 +كل ما غلط و هكذا وصلت ل-997 + +1003 +01:33:39,090 --> 01:33:47,290 +زي الانتخابات العربية 799 سالب تلاتة بصير سالب ألف + +1004 +01:33:47,290 --> 01:33:52,860 +يبقى صار عندي السالب عشرمظبوط ولا لا؟ انا طالع + +1005 +01:33:52,860 --> 01:33:56,280 +سالب مش عارف اش .. سالب مش عارف اش .. سالب .. طيب + +1006 +01:33:56,280 --> 01:34:00,660 +طالع لوين؟ سالب عشر؟ سالب واحد على مية؟ سالب واحد + +1007 +01:34:00,660 --> 01:34:07,050 +على الف؟ سالب واحد على مليون؟ يعني لوين رايح؟لزيرو + +1008 +01:34:07,050 --> 01:34:12,950 +لزيرو رايح مش طالع انا طالع لكن كلها بسالب مش قادر + +1009 +01:34:12,950 --> 01:34:17,150 +اوصل للموجب يبقى كله رايح لوين رايح على ال zero + +1010 +01:34:17,150 --> 01:34:21,930 +طيب هذا لو اخدت ارقام طب بده جرب على التلاتة من + +1011 +01:34:21,930 --> 01:34:26,610 +الناحيتين لو جيت قولتلك اني بده اجرب على تلاتة + +1012 +01:34:26,610 --> 01:34:31,910 +واحد من عشرةيبقى تلاتة و واحد من عشرة ناقص تلاتة + +1013 +01:34:31,910 --> 01:34:35,770 +يبقى واحد من عشر يعني عشر العشرة بتنقل فوق بصير + +1014 +01:34:35,770 --> 01:34:40,050 +المية قداش ألف كل ما أجرب على التلاتة باجهها دي + +1015 +01:34:40,050 --> 01:34:44,690 +الشفقة تترايح لوين للمالة نفسها مثلا لو جيت قولتك + +1016 +01:34:44,690 --> 01:34:52,030 +X ابتلاتة و واحد من ألف تلاتة و واحد من ألف ناقص + +1017 +01:34:52,030 --> 01:34:55,110 +تلاتة بيبقى واحد من ألف يعني واحدة على ألف بصير + +1018 +01:34:55,110 --> 01:34:58,970 +مية ألفكل ما اجرب على تلاتة بيلاقيها شخطة لوين + +1019 +01:34:58,970 --> 01:35:02,890 +للمال انها وكل مابعد عن التلاتة بيلاقيها نزل لوين + +1020 +01:35:02,890 --> 01:35:07,410 +لزيرو طب تعا أسحبها من الناحية التانية بدي أبدأ + +1021 +01:35:07,410 --> 01:35:12,210 +أجرب على مين على التلاتة من جهة الشمال أنا جربتها + +1022 +01:35:12,210 --> 01:35:16,640 +في الأول من جهة اليمينبدي اقول اتنين وتسعة من عشرة + +1023 +01:35:16,640 --> 01:35:22,020 +موجة اتنين وتسعة من عشرة نقص تلاتة بظهر سالب او شر + +1024 +01:35:22,020 --> 01:35:28,100 +يعني بصير سالب الف مصغور كل ما اجرب اتلاقي هنزلت + +1025 +01:35:28,100 --> 01:35:35,520 +اكتر يعني لو كان الفرق بينها وبين التلاتةاللي هو + +1026 +01:35:35,520 --> 01:35:42,060 +سالب واحد من مية بصير سالب عشرة آلاف الفرق بينه + +1027 +01:35:42,060 --> 01:35:47,200 +وبينها سالب واحد على الف يبقى سالب ميت ألف يبقى + +1028 +01:35:47,200 --> 01:35:51,640 +نازل لوين لسه يعني إذا اتحركت جربت للتلاتة من جهة + +1029 +01:35:51,640 --> 01:35:55,980 +اليمين بلاقي طاير لما لنهايةجربت ليه تلاتة من جهة + +1030 +01:35:55,980 --> 01:35:59,920 +الشمال بلاقي حالي رايح لوين لسلب infinity ابعت عني + +1031 +01:35:59,920 --> 01:36:03,820 +التلاتة بلاقي حالي نازل لل zero جربت على التلاتة + +1032 +01:36:03,820 --> 01:36:07,120 +.. ابعت عني التلاتة من الناحية التانية بلاقي حالي + +1033 +01:36:07,120 --> 01:36:12,040 +رايح لل zero كذلك إذا من zero إلى infinity و من + +1034 +01:36:12,040 --> 01:36:16,020 +سلب infinity إلى من؟ إلى ال zero هذه الإجابة + +1035 +01:36:16,020 --> 01:36:21,620 +الأخيرة اللي قالها صاحبي شو اسمك أنت؟ شامي + +1036 +01:36:23,160 --> 01:36:27,340 +اللي بين الوالد إيش يعني؟ من السنة أن يذكر الرجل + +1037 +01:36:27,340 --> 01:36:32,820 +اسم بيه عند التعارف لأن هذا يعتبر صلة رحم فإن + +1038 +01:36:32,820 --> 01:36:37,520 +تنويت ذلك تؤجر علي اسمه هشام إسماعيل ياغي هو الذي + +1039 +01:36:37,520 --> 01:36:42,040 +أعطانا الإجابة آه الصحيحة طبعا حتى الآن نكتفي + +1040 +01:36:42,040 --> 01:36:44,180 +واخدنا أكثر من وقتنا + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/a29rwypicLY_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/a29rwypicLY_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..b013995891e02b75935163db8b6c8b038e39a931 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/a29rwypicLY_raw.srt @@ -0,0 +1,4160 @@ +1 +00:00:20,860 --> 00:00:26,020 +بسم الله الرحمن الرحيمهذه تعتبر المحاضرة الأولى + +2 +00:00:26,020 --> 00:00:31,340 +بالنسبةلكوا طبعا الغالبية العظمى منكم طلاب جدد + +3 +00:00:31,340 --> 00:00:38,840 +فنهنئكم بقابولكم في الجامعة الإسلامية و كذلك ببدء + +4 +00:00:38,840 --> 00:00:45,280 +الفصل الدراسى الجديد لذلك أول شغلة سنشير اليها + +5 +00:00:45,280 --> 00:00:53,310 +الفرق بين التعليم المدرسى والتعليم الجامعىطبعا + +6 +00:00:53,310 --> 00:01:01,390 +هنتناول هذا الكتاب القاعة المدرس طريقة الدراسة + +7 +00:01:01,390 --> 00:01:06,290 +تمام؟ بعد هيك ننتقل إلى النقطة الثانية في هذه + +8 +00:01:06,290 --> 00:01:15,740 +المحاضرةوهي طريقة التدريس والمنهج الذي سيدرس خلال + +9 +00:01:15,740 --> 00:01:21,840 +هذا الفصل النقطة اللي بعدها لساعة ثانية من هذه + +10 +00:01:21,840 --> 00:01:27,260 +المحاضرة سندخل فيصل بالموضوع وهي النقطة الأولى من + +11 +00:01:27,260 --> 00:01:33,320 +أول section في المقرر تمام؟ نبدأ أول حاجة بالكتاب + +12 +00:01:33,320 --> 00:01:38,130 +الكتاباللي انت في المرحلة الثانوية والإعدادية + +13 +00:01:38,130 --> 00:01:41,910 +والابتدائية، اللي هو كتاب الوزارة، لابتقدر تطلع + +14 +00:01:41,910 --> 00:01:47,790 +عنه لايمين ولا إشمال، ولو أجى موجهي المادة ولاقي + +15 +00:01:47,790 --> 00:01:52,810 +عندك كتاب على الطاولة غير الكتاب المقرر، بيبقى + +16 +00:01:52,810 --> 00:01:56,330 +دليل مدرس، احنا بيقولك ان شاء الله تجيب خمس كتب + +17 +00:01:56,330 --> 00:02:00,750 +بالإضافة لكتاب المقرر وتحطها قدامك ونكون مبسوطين، + +18 +00:02:00,750 --> 00:02:06,290 +معناته ان انت بالذاكر وبتطلع، تمام؟لكننا سنسمي + +19 +00:02:06,290 --> 00:02:11,890 +كتابا واحدا هو العمودي الفقري أثناء تدريسنا اللي + +20 +00:02:11,890 --> 00:02:15,670 +هنكون ماشيين على هوا هذا الكتاب لكن اللي جينا + +21 +00:02:15,670 --> 00:02:19,810 +معلومة أخرى زيادة على ما هي موجودة في الكتاب + +22 +00:02:19,810 --> 00:02:25,010 +بنجيبها و بنعطيهاكوا كمان لإن احنا في مرحلة جامعية + +23 +00:02:25,010 --> 00:02:31,310 +مرحلة صقل العقول و بناء الشخصيات العلمية و + +24 +00:02:31,310 --> 00:02:35,980 +الأكاديميةلأن لو عدتكوا بعد أربع سنين و إذا كنت من + +25 +00:02:35,980 --> 00:02:40,340 +الهندسة بعد خمس سنين ممكن توقف مكاني في هذا المكان + +26 +00:02:40,340 --> 00:02:45,800 +و تدرس للطلاب وبالتالي في الأربع سنين أو الخمس + +27 +00:02:45,800 --> 00:02:50,000 +سنين هم اللي بيبنوا شخصيتك العلمية و شخصيتك + +28 +00:02:50,000 --> 00:02:56,760 +الأكاديمية و يؤهلوك لإنك تكمل بعد ذلك الكتاب اللي + +29 +00:02:56,760 --> 00:03:01,280 +بين إيدينا اللي هندرسه المرة هذه اسمه Calculus + +30 +00:03:06,300 --> 00:03:11,140 +طبعا في calculus B و في calculus C هذا حوالي ثلث + +31 +00:03:11,140 --> 00:03:16,820 +الكتاب تبع كتاب ال calculus المؤلف اسمه Thomas + +32 +00:03:19,380 --> 00:03:24,600 +طبعا في كتب calculus كتيرة لمؤلفين اخرين احده من + +33 +00:03:24,600 --> 00:03:29,960 +الكتاب اللى المؤلف تبعه اسمه Thomas الطبعة تبعت + +34 +00:03:29,960 --> 00:03:37,160 +هذا الكتاب هي رقم اتناشر اتناشر editionيعني + +35 +00:03:37,160 --> 00:03:43,660 +الطابعة ثانية عشرة كل سنتين أو ثلاث سنوات بيطبق + +36 +00:03:43,660 --> 00:03:48,660 +بطابعة جديدة بيعمل فيها بعض التغييرات إضافات نقصان + +37 +00:03:48,660 --> 00:03:53,400 +حسب التطور العلمي إلى آخرى هذا هو الكتاب اللي + +38 +00:03:53,400 --> 00:03:59,080 +هندرس منه أي كتاب كالقلاس آخر يعتبر مرجع عندك + +39 +00:03:59,080 --> 00:04:05,290 +تقتني كتاب الأزهرإذا كان كتاب القدس المفتوحة، إذا + +40 +00:04:05,290 --> 00:04:09,310 +كان أي كتاب كالكلس آخر، ما عندنا مشكلة، هذا لو + +41 +00:04:09,310 --> 00:04:13,690 +جيته بيكون مارجع بالنسبة لك، لكن هذا هو كتابنا + +42 +00:04:13,690 --> 00:04:19,970 +الأصلي الذي سندرس عليه وإذا في معلومة مش موجودة ان + +43 +00:04:19,970 --> 00:04:24,430 +شاء الله بنجيبها و بنحطها، بنضيف لهذه المعلومة + +44 +00:04:24,430 --> 00:04:29,540 +اللي موجودةفي هذا الكتاب، لكن في المدارس بيكون + +45 +00:04:29,540 --> 00:04:32,880 +كتاب واحد مافيش غيره اللي هو كتاب الوزراء وفي + +46 +00:04:32,880 --> 00:04:38,080 +توجيهه بتروح تشتريلك كتاب تاني وما إلى ذاك بيسميها + +47 +00:04:38,080 --> 00:04:43,460 +كتب تجارية وليست مراجعة، تمام؟ يبقى هذا الفرق بين + +48 +00:04:43,460 --> 00:04:48,640 +كتابناوكتاب ميم وكتاب المدارس، اتنين، بالنسبة + +49 +00:04:48,640 --> 00:04:54,040 +للقاعة، انت كل محاضرة بتقعد في كرسي، هاي الشباب + +50 +00:04:54,040 --> 00:04:56,820 +الأربع هدول قاعدين في الكرسي الأول او في المقعد + +51 +00:04:56,820 --> 00:05:00,040 +الأول، المرة جاية ممكن يكونوا في المقعد الأخير، + +52 +00:05:00,040 --> 00:05:02,740 +المرة اللي بعدين يكونوا في المقعد ده نصف، يعني ان + +53 +00:05:02,740 --> 00:05:07,700 +القاعة ده شرية الجمعة لمن سبقاللي بيسبق هو اللي + +54 +00:05:07,700 --> 00:05:11,520 +بيقعد قدام، بيذهبك وبعدين بيقعد ورا، لكن في + +55 +00:05:11,520 --> 00:05:15,820 +المدارس مقعد ثابت، بتظلك طول السنة وانت قاعد في + +56 +00:05:15,820 --> 00:05:20,400 +نفس المكان، يا بيزهج منك المقعد، يا انت بتزهج، يا + +57 +00:05:20,400 --> 00:05:25,060 +انا مابتزهجوش، بيصيروا صحبة مع بعض، تمام؟ هاي كمان + +58 +00:05:25,060 --> 00:05:28,620 +فرق بين التعليم المدرسي والتعليم الجامعي من ناحية + +59 +00:05:28,620 --> 00:05:33,740 +وجودك في القاعة، لن تسمع جرس في الجامعة، نهائيبس + +60 +00:05:33,740 --> 00:05:39,220 +هناك كل 45 دقيقة بتسمع ايش؟ بتسمع جرس و المدرس + +61 +00:05:39,220 --> 00:05:42,280 +بيطلع و بيجي مدرس اخر و انت قاعد في نفس المكان لأ + +62 +00:05:42,280 --> 00:05:47,040 +هنا ممكن يتغير المدرس و تتغير القاعة هاي توجب + +63 +00:05:47,040 --> 00:05:51,500 +انكوا من وين؟ من الطابق الأرضي في مبنى القدس الى + +64 +00:05:51,500 --> 00:05:55,880 +الطابق السادس في مبنى طيبة تمام؟ و بعد ما تخلصي + +65 +00:05:55,880 --> 00:05:59,860 +ممكن تروح على المختبرات في مبنى Pو بعد هيك مش + +66 +00:05:59,860 --> 00:06:05,880 +عارفة تروح على قاعة و هيكذا المحاضرة تبعتك ساعتين + +67 +00:06:05,880 --> 00:06:10,640 +لو كانت ساعة من حق المدرسة يطلع آخر عشر دقايق + +68 +00:06:10,640 --> 00:06:14,320 +وبالتالي لما تكون المحاضرة ساعتين من حق يطلع آخر + +69 +00:06:14,320 --> 00:06:19,820 +تلت ساعة لكن هذا مستحيل بالنسبالي انطلعت سريع بطلع + +70 +00:06:19,820 --> 00:06:23,980 +آخر ربع ساعة و يمكن آخر عشر دقايق و يمكن آخر سبعة + +71 +00:06:23,980 --> 00:06:28,610 +دقايقانت و أختك حسب الموضوع اللي في بين إيدينا خلص + +72 +00:06:28,610 --> 00:06:33,290 +و الله ماخلصش تمام؟ يبقى هذا بتقعد هنا و بتنسى + +73 +00:06:33,290 --> 00:06:39,150 +حكاية الوجد تمام يا سيدي؟ لن تسمع جراس؟ طب ليش + +74 +00:06:39,150 --> 00:06:43,710 +بيخلونا أخر عشر دقايق و أخر وقت نطلع؟ ايوة انت + +75 +00:06:43,710 --> 00:06:48,770 +نعست بتروح تغسل وجهك، عطشت بتروح تشرب، بدك تنتقل + +76 +00:06:48,770 --> 00:06:52,650 +من قاع إلى قاع، بتغير النشاط تبعك حتى بيتغير + +77 +00:06:52,650 --> 00:06:57,210 +تفكيركوهذا شيء ضروري جدك، لكن ضليت، قعد في نفس + +78 +00:06:57,210 --> 00:07:01,470 +المكان أربع ساعات، بتقرا في حالك طول اليوم، مش + +79 +00:07:01,470 --> 00:07:06,510 +هيك؟ لكن في الجامعة لأ، فيش مقعد ثابت، فيش هذا + +80 +00:07:06,510 --> 00:07:09,550 +المكان، إيه لك بتغيرهش طول السنة؟ لأ لأ يا عم، + +81 +00:07:09,550 --> 00:07:13,590 +بتقدر تغيره كل محاضرة، أنت و بخلق، وين ما تيجي + +82 +00:07:13,590 --> 00:07:19,670 +تيجي، تمام؟ يبقى هذا بالنسبة ليه؟ بالنسبة للمكان + +83 +00:07:20,220 --> 00:07:27,000 +ضرورة التواجد في القاعة قبل المدرس لماذا او + +84 +00:07:27,000 --> 00:07:31,020 +للمحاضرة الساعة اتناشى الساعة اتناشى الا دقيقة + +85 +00:07:31,020 --> 00:07:35,780 +يمكن تلاقيني عندك جوا هنا تمام باتخرش ابدا باذن + +86 +00:07:35,780 --> 00:07:40,280 +الله الا اذا ضعت ضرورة واتخرت دقيقتين او تلاتة + +87 +00:07:40,280 --> 00:07:46,680 +وهذا نادرا دائما وبحاول التزمبالموعد بالضبط و يمكن + +88 +00:07:46,680 --> 00:07:51,600 +قبل الموعد، تمام؟ فاحرص أن تكون قبل الموعد موجود + +89 +00:07:51,600 --> 00:07:55,600 +في قاعة المحاضرة حتى ت .. سواء كنت قبل دقيقتين + +90 +00:07:55,600 --> 00:08:01,340 +تلاتة تتأهل نفسيا مشان .. مشان تاخد معلومات و تبدأ + +91 +00:08:01,340 --> 00:08:04,840 +تسجل من الأول لكن اللي بيجي متأخر دقيقتين تلاتة + +92 +00:08:04,840 --> 00:08:08,700 +خمس دقايق بيصير زي اللي بيشعلك في السيارة و هي + +93 +00:08:08,700 --> 00:08:12,810 +ماشية أو في القطاريمكن يوجع، يمكن ينكسر، يمكن + +94 +00:08:12,810 --> 00:08:16,570 +ينكسر ضلعينه الزاوية، الله أعلم، مايعرفش، المهم + +95 +00:08:16,570 --> 00:08:22,630 +لازم يحصل فيه عنده خلال ما، لذلك احصر، احرص على + +96 +00:08:22,630 --> 00:08:29,830 +الحضور مبكرا، ولا تتأخر، والتزم بالقاعة بمجرد + +97 +00:08:29,830 --> 00:08:34,910 +حضورك تمام يا سيدي؟ يبقى هذا بالنسبة ليش؟ للقاعة + +98 +00:08:34,910 --> 00:08:40,270 +والالتزام في القاعة، نجي لفرق آخرفي المدارس بتلاقي + +99 +00:08:40,270 --> 00:08:45,570 +المدرس هو النظر معاه عصاه، لن تجد مدرس في الجامعة + +100 +00:08:45,570 --> 00:08:48,990 +معاه عصاه ولا حتى رئيس الجامعة ولا نواب، مافيش + +101 +00:08:48,990 --> 00:08:53,890 +حاجة اسمه معاه عصاه، هذا للصغاريبقى حاول تسجل اي + +102 +00:08:53,890 --> 00:08:58,690 +معلومة جديدة بالنسبة اليك بيتشعر حكمة مقولة اللي + +103 +00:08:58,690 --> 00:09:03,490 +بدكيها تمام؟ في هذه الحالة بصير عندك حصيلة اكتر من + +104 +00:09:03,490 --> 00:09:07,470 +زميلك اللي اندخلت انت ويا الجامعة في نفس ايه؟ في + +105 +00:09:07,470 --> 00:09:12,390 +نفس المستوى طيب الان نجي اليك كيف بدى ادرس بطريقة + +106 +00:09:12,390 --> 00:09:16,390 +صحيحة الان انا بدأ اشرحلك اليوم موضوع ال functions + +107 +00:09:16,390 --> 00:09:20,790 +يعني الدوال او الاقتراناتبدى يا جبل تيجى على + +108 +00:09:20,790 --> 00:09:24,810 +المحاضرة تتطلع عليها جراية زى جراية الجريدة جراية + +109 +00:09:24,810 --> 00:09:26,890 +الجريدة البعض ما خلاص بيكون فى دماغنا بس فى + +110 +00:09:26,890 --> 00:09:30,510 +العناوين الرئيسى لكن التفاصيلات ابنى نساها إلا إذا + +111 +00:09:30,510 --> 00:09:34,350 +كان فى تفصيل مثير بيظل ملزق فى دماغنا يبقى انا + +112 +00:09:34,350 --> 00:09:37,910 +بديك تجراها مش تقعد تحل بس تجراها زى جراية الجريدة + +113 +00:09:37,910 --> 00:09:42,290 +هي تتطلع انه اه هذا ال functions بدي اتكلم عنهال + +114 +00:09:42,290 --> 00:09:45,730 +domain و ال range يعني عن المجال و المدى و ما .. + +115 +00:09:45,730 --> 00:09:48,730 +خلاص بدي أروح أجرى الكلمة بس يكون في دماغك إيش بدي + +116 +00:09:48,730 --> 00:09:51,950 +أحكي قبل ما أحكي يبقى هذا التحضير مش بديك تروح + +117 +00:09:51,950 --> 00:09:55,550 +تجرى و تحل و تجرى .. لا لا لا بديش هذا الكلام بدي + +118 +00:09:55,550 --> 00:09:59,390 +بس يكون عندك خلفية زي اللي بيحلم حلم لما يصحب و + +119 +00:09:59,390 --> 00:10:03,270 +يصير عارف إيش بعض الأشياء الرئيسية و يمكن ينسى كل + +120 +00:10:03,270 --> 00:10:07,330 +الحلم أما ماعندي مشكلة المهم يصير في دماغك خلفية + +121 +00:10:07,330 --> 00:10:11,350 +عن الموضوع اللي بدنا نشرها نامدخلنا القاعدة بيبقى + +122 +00:10:11,350 --> 00:10:16,590 +بدنا نتابع المدرس و هو بيشرح و بدنا نكتب كل كلمة + +123 +00:10:16,590 --> 00:10:20,950 +بيكتبها او بيقولها اه مشان هذه بصير مرجع اننا في + +124 +00:10:20,950 --> 00:10:25,010 +الدار لما نروح بدنا .. بدنا نذاكرطب كتبنا و الحمد + +125 +00:10:25,010 --> 00:10:29,210 +لله وناقشنا طبعا أنا بطرح أسئلة و بطلب منك إجابة + +126 +00:10:29,210 --> 00:10:35,630 +منك بدك تشارك ليها بالإجابة هذه بتولد تفكير عندك و + +127 +00:10:35,630 --> 00:10:40,950 +بتولد أسئلة لم تكن تخطر على بلق قبل أنا مطرحها قبل + +128 +00:10:40,950 --> 00:10:45,430 +ما مطرح السؤال الأسئلة اللي بطرحها تجيب على كثير + +129 +00:10:45,430 --> 00:10:48,870 +من التساؤلات اللي ممكن هي تطرق على دماغك و أنت + +130 +00:10:48,870 --> 00:10:53,330 +قاعد فلا تستعجلإذا أنا خلصت و ماحدش سأل بقول مين + +131 +00:10:53,330 --> 00:10:57,450 +بده يحب يسأل سؤال، مين عنده أي سؤال، تبخلش على + +132 +00:10:57,450 --> 00:11:02,490 +نفسك، ماحدش بسمع من ساكن، اسأل ولو كان سؤالك غلط، + +133 +00:11:02,490 --> 00:11:06,170 +واسأل كمان مرة ولو كان سؤالك غلط، المرة التالتة + +134 +00:11:06,170 --> 00:11:11,350 +بصير تسأل صح، يعني عود نفسك السؤال، والعلم لن يثبت + +135 +00:11:11,540 --> 00:11:15,820 +إلا بالتساؤل، بالتساؤل اللي بثبت العلم في دماغك و + +136 +00:11:15,820 --> 00:11:19,880 +بصير من أهل الدراية و العلم، ما سألتش بصير زي ما + +137 +00:11:19,880 --> 00:11:24,520 +فهمت ركبت المعلومات في دماغي زميل صح و لا غلط زي + +138 +00:11:24,520 --> 00:11:29,860 +ما فهمت، و طبعا العقول متفاوتة و هو من هنا فإن + +139 +00:11:29,860 --> 00:11:36,140 +الأفهام تكون متفاوتةممكن تكون فهمت خطأ و ممكن تكون + +140 +00:11:36,140 --> 00:11:40,340 +فهمت صح لكن اذا روحت سؤالة المدرس بصير تفهم صح + +141 +00:11:40,340 --> 00:11:45,800 +تمام؟ يبقى احنا سجلنا و تابعنا و ماصرحناش برا + +142 +00:11:45,800 --> 00:11:50,960 +أثناء المحاضرة ماصرناش من بني سرحان لأ نصرنا من + +143 +00:11:50,960 --> 00:11:56,600 +بني علم اه من تابعنا مش صرحنا برا اه كويس؟ يبقى + +144 +00:11:56,600 --> 00:12:01,820 +كنا هنا قاعدين بالجسم والعقل مش بالجسم والعقل + +145 +00:12:01,820 --> 00:12:06,060 +سرحان براأصحى درباك أنت وياه طيب تابعنا و سجلنا + +146 +00:12:06,060 --> 00:12:09,940 +محاضرتنا و كلش تمام طيب اللي ضال يتابع من أول + +147 +00:12:09,940 --> 00:12:14,460 +المحاضرة إلى آخره قداش حصل من المعلومات بقولك + +148 +00:12:14,460 --> 00:12:18,700 +والله أنا طلعت فاهم أنا بطنه طلع فاهم بس خمسين في + +149 +00:12:18,700 --> 00:12:23,640 +المية بس أجعص واحد بطلع خمسين في المية طب و من وين + +150 +00:12:23,640 --> 00:12:28,550 +بدنا نجيب الخمسين التانية؟ بقولك بسيطة جدابتروح + +151 +00:12:28,550 --> 00:12:32,930 +على الدار بتقرا المحاضرة من جديد ان روحت قريتها في + +152 +00:12:32,930 --> 00:12:37,450 +نفس اليوم في نص ساعة بتقراها ويمكن أقل كمان واذي + +153 +00:12:37,450 --> 00:12:42,610 +بتخليها لبكرا بدها ساعة اه لان بصير تحلم و تتذكر + +154 +00:12:42,610 --> 00:12:46,530 +ايش جال من بارحه و ايش كان جصده تمام؟ واذي بتخليها + +155 +00:12:46,530 --> 00:12:49,750 +الأخر الأسبوع لخميس والجمعة لإنه عندنا اجازة + +156 +00:12:49,750 --> 00:12:55,870 +امساها بدها أربع ساعات ليه ربالك؟ ولذلك بدك تقرا + +157 +00:12:55,870 --> 00:13:00,610 +أولا بأولوبحب أطمنك لامتحان الأول بنعطيكوا + +158 +00:13:00,610 --> 00:13:04,850 +امتحانين لامتحان الأول يوم تسعة عشرة يعني بنبقى + +159 +00:13:04,850 --> 00:13:09,090 +عليكوا من اليوم بعد تمانية وثلاثين يوم من الآن في + +160 +00:13:09,090 --> 00:13:14,630 +عندك لمتحان النصف الأول بنعطى نمتحانين نصفين + +161 +00:13:14,630 --> 00:13:19,950 +لمتحان النصف الأول في تسعة عشرة ولمتحان الثاني بعد + +162 +00:13:19,950 --> 00:13:23,730 +ما تاخد الأول بنقولك لمتحان لكن اختصارا بعده + +163 +00:13:23,730 --> 00:13:28,130 +باربعين يوم يعني كل اربعين يومابن يعطيك امتحان + +164 +00:13:28,130 --> 00:13:32,330 +وبالتالي امتحاني وبعد ذلك الامتحان النهائي وسأرجع + +165 +00:13:32,330 --> 00:13:37,370 +إلى هذه النقطة بعد قليل طبعا لما أقولك سأرجع إلى + +166 +00:13:37,370 --> 00:13:41,990 +هذه النقطة بعد قليل هذا أسلوب نسميه أسلوب تشويق + +167 +00:13:41,990 --> 00:13:46,030 +يعني إيش بده يقول في هذا الموضوع هذا بعد قليل بتظل + +168 +00:13:46,030 --> 00:13:53,310 +أنت مشدود هذا أحد أساليب التعليم طيب الآنحضرنا + +169 +00:13:53,310 --> 00:13:57,450 +المحاضرة تابعنا سجلنا المعلومات روحنا قريناها في + +170 +00:13:57,450 --> 00:14:01,590 +نفس اليوم خلال نص ساعة خلصنا قراها بعدين بدك تبدأ + +171 +00:14:01,590 --> 00:14:05,590 +تحل مساعدة لما قريت المحاضرة جيبت كمان عشرين في + +172 +00:14:05,590 --> 00:14:10,370 +المية صار قداش عندك؟ سبعين اه مليح نجحنا وزيادة + +173 +00:14:10,370 --> 00:14:15,190 +شوية كويس؟طيب بنروح ان .. بعد ما نحلي .. بنروح + +174 +00:14:15,190 --> 00:14:19,010 +نحلي التمرين تبعات ال .. ال .. ال section اللي + +175 +00:14:19,010 --> 00:14:22,850 +احنا كلفناكي بهم لما تحل بيكون جيبك كمان عشرين في + +176 +00:14:22,850 --> 00:14:26,010 +المية يعني مقدش صار عندك؟ تسعين في المضايق اللي + +177 +00:14:26,010 --> 00:14:29,430 +عنينا و ايه؟ عشرة في المية العشرة في المية بنروح + +178 +00:14:29,430 --> 00:14:33,370 +على وين؟ على الساعة تبع ال discussion لإن انت لما + +179 +00:14:33,370 --> 00:14:38,350 +تحل مسألة التمرين لازم تواجك صعابماحدش فضحى او نزل + +180 +00:14:38,350 --> 00:14:42,650 +عالما كله بيتعلم ومدام يتعلم لازم يتجابلك صعوبة + +181 +00:14:42,650 --> 00:14:46,350 +واللي بيتجابلهوش صعوبة معناته هو مش فاهم اللي بين + +182 +00:14:46,350 --> 00:14:51,810 +أيديه كل واحد بيتعلم لازم يقابل صعوبة مافيش + +183 +00:14:51,810 --> 00:14:55,130 +إمكانية اللي يتجابل الصعوبة و بعد هيك تتغلب على + +184 +00:14:55,130 --> 00:14:59,610 +هذه الصعوبة إما بالذهاب إلى ساعة تبعة المناقشة مع + +185 +00:14:59,610 --> 00:15:03,700 +المدرس الآخربتقول وصيب علينا السؤال الفلاني و هو + +186 +00:15:03,700 --> 00:15:06,500 +السؤال اللي بيجيب .. بيحلك السؤال الفلاني وبالتالي + +187 +00:15:06,500 --> 00:15:10,900 +بيجيبك اللغة اللي انت ايه ماكنتش قادر تفهمها طيب + +188 +00:15:10,900 --> 00:15:14,480 +هذا جابله سؤالين و هذا جابله سؤالين غيرهم و هذا + +189 +00:15:14,480 --> 00:15:17,560 +جابله سؤالين .. و كل واحد جابله سؤالين مختلفه عن + +190 +00:15:17,560 --> 00:15:22,700 +بعضطبعا هذا كلام غير معقول لإن هو التمرين قداش كله + +191 +00:15:22,700 --> 00:15:26,760 +و بنطلبش المسائل كلها، تمام؟ إذا هذا غير معقول لكن + +192 +00:15:26,760 --> 00:15:31,220 +قد يكون بقى السؤال أو اتنين من التمرين غالبية انت + +193 +00:15:31,220 --> 00:15:35,440 +مش فاهمينه يا أخي أنا موجود تعالي بعطيلك بعد قليل + +194 +00:15:35,440 --> 00:15:38,120 +هقولك أنا عند الساعة المكتبية هذه بكون قاعد في + +195 +00:15:38,120 --> 00:15:42,910 +المكتب باستنىك تيجي تسألنيتمام؟ ان جيت سؤالني + +196 +00:15:42,910 --> 00:15:46,490 +بتبقى استفدت منها، جيت سؤالني بتضلك ما انتش عارف + +197 +00:15:46,490 --> 00:15:49,990 +الإجابة على السؤال أو السؤالين أو التلاتة اللي + +198 +00:15:49,990 --> 00:15:54,670 +ضايلات عندك، اذا جيت سؤالني بعد المناقشة معناته + +199 +00:15:54,670 --> 00:15:59,510 +انت صرت بتفهم في المادة مية بالمية، لكن اذا + +200 +00:15:59,510 --> 00:16:05,060 +ماحليتش مسائل و روحت على المناقشةبتروح وانت ايش + +201 +00:16:05,060 --> 00:16:11,300 +فاتح ثمه وقعد ايش ما يقول بصير تكتب بصير انت مجمع + +202 +00:16:11,300 --> 00:16:17,340 +حلول وليس بتعرف تحلزي ايش؟ زي واحد كتاب الوزارة + +203 +00:16:17,340 --> 00:16:20,840 +اللى معاه كان في الثانوية طابع احد المدرسين لحل + +204 +00:16:20,840 --> 00:16:24,360 +المسائل وطابع كتاب العلوم وشارك كتاب العلوم ويقولك + +205 +00:16:24,360 --> 00:16:28,200 +والله اي سؤال بحله، بحله ليه؟ لإنه بيبدأ يفكر، اول + +206 +00:16:28,200 --> 00:16:32,740 +يجي اتنين مثلة .. اه بنقلب وقوم بونجل الحل، صار + +207 +00:16:32,740 --> 00:16:37,080 +عنده حل، عرف الفكرة، لكن لو جاء السؤال وغيطله فيه + +208 +00:16:37,080 --> 00:16:41,710 +رقامبقدر يمشي و بقدرش يمشي لأن هذا مااشتغلش هذا + +209 +00:16:41,710 --> 00:16:47,830 +النجل نجل الحل إذا مطلوب تمسك جلمك و تحل بنفسك حتى + +210 +00:16:47,830 --> 00:16:52,450 +تثبت هذه المعلومات ذيك بصير انت مية لمية و ماعنا + +211 +00:16:52,450 --> 00:16:57,550 +مشكلة و احنا هنا انا لما اعرضلك الموضوع اخلصه + +212 +00:16:57,550 --> 00:17:00,570 +المحاضرة الجاية بقولك شرحنا في المحاضرة الماضية + +213 +00:17:00,570 --> 00:17:04,370 +كذا كذا في حدود دقيقتين و اليوم بدنا ناخد كذا كذا + +214 +00:17:04,370 --> 00:17:10,750 +تمام؟ و ببدأ أشرح جديدوالباقي بيضل عليه، بتمشي، + +215 +00:17:10,750 --> 00:17:15,370 +بتمشي، تمشيش، تمشيش، بعض الطلاب إيش بيسويه؟ قال + +216 +00:17:15,370 --> 00:17:20,110 +بيقرا الشرح اللي أنا شرحته تمام و بيقرا الأمثلة، + +217 +00:17:20,110 --> 00:17:23,930 +بيقول أخو الله أنا فهمت الموضوعهذا اللي بروحش يحل + +218 +00:17:23,930 --> 00:17:28,890 +مثال ويكتفي بالأمثلة بقول يمكن ينجح ويجيب علامة + +219 +00:17:28,890 --> 00:17:32,450 +نجاح اللي هي ستين مش خمسين، خمسين في الثانوية + +220 +00:17:32,450 --> 00:17:35,890 +العامة، عندنا في الجامعة ستين، عشان تنجح تجيب ستين + +221 +00:17:35,890 --> 00:17:40,450 +.. بقول يمكن يجيب علامة نجاح ويمكن يرصف، لكن لن + +222 +00:17:40,450 --> 00:17:44,050 +يتعد علامة نجاح، لكن اللي بحل مثال automatically + +223 +00:17:44,050 --> 00:17:48,150 +بترفت على درجته وبيجيب فوق الستين، فوق السبعين، + +224 +00:17:48,150 --> 00:17:53,480 +فوق الثمانينو بعض الطلاب والله بطبق المية بجيب مية + +225 +00:17:53,480 --> 00:17:57,180 +من مية في الجامعة و بقول إنه جاب مية بحطها له مية + +226 +00:17:57,180 --> 00:18:00,300 +زي ما هي و بعضهم بجيب تسعة و تسعين و بعضهم بجيب + +227 +00:18:00,300 --> 00:18:03,580 +تمانية و تسعين و دي لباقي الكلمات ده أربع ساعات + +228 +00:18:03,580 --> 00:18:07,700 +إذا جيبت من التسعين فمطق بظل معدلك في ال top حتى + +229 +00:18:07,700 --> 00:18:12,140 +لو مديتين تلاتة نزل بظل مرتع لإن هذه أربع ساعات مش + +230 +00:18:12,140 --> 00:18:15,420 +تلاتة والله ساعة يعني كنت في القرآن مية من مية + +231 +00:18:15,420 --> 00:18:19,860 +القرآن ساعةبس هاد المادة اربع ساعات لو جيت فوقها + +232 +00:18:19,860 --> 00:18:24,660 +فوق التسعين بتضل معدلكيهش عالى حتى لو نزل في مواد + +233 +00:18:24,660 --> 00:18:30,660 +اخرى يبقى احرص على هذه النقطة تمام طيب وصلنا الان + +234 +00:18:30,660 --> 00:18:36,670 +الى توزيع الدرجات كيف تتوزع الدرجات؟المادة عليها + +235 +00:18:36,670 --> 00:18:41,250 +مائة درجة بنجسمها الى امتحان اول امتحان ثاني + +236 +00:18:41,250 --> 00:18:47,530 +بنسميهم اعمال الفصل وامتحان النهائي الامتحان الاول + +237 +00:18:47,530 --> 00:18:51,870 +بنجيبه جاب الامتحان متطلبات الجامعة يعني يوم تسعة + +238 +00:18:51,870 --> 00:18:56,760 +عشرةبتكون لسه مادخلتش امتحانات متطلبات الجامعة + +239 +00:18:56,760 --> 00:19:01,780 +عليها عشرين او خمسة وعشرين درجة حسب ما نتفق ان + +240 +00:19:01,780 --> 00:19:05,580 +احنا ولا ساتذة الاخرون اللي بدرسوا معانا نفس المدة + +241 +00:19:05,580 --> 00:19:09,800 +الامتحان الثاني زي عشرين او خمسة وعشرين ان كان + +242 +00:19:09,800 --> 00:19:13,040 +خمسة وعشرين خمسة وعشرين هي خمسين يبقى النهائي + +243 +00:19:13,040 --> 00:19:18,200 +خمسين تمام ان كان عشرين عشرين بتظل عشرة العشرة + +244 +00:19:18,200 --> 00:19:22,930 +ممكن تخليها فيدي المناقش اللي بحل معاك أسئلةهذا + +245 +00:19:22,930 --> 00:19:27,090 +بيعطيكو الذات بيحطها على الحضور و يقولوا زي ما يحط + +246 +00:19:27,090 --> 00:19:32,290 +يحط لا نتدخل فيه، فيه عشر علامات بنقوله زي ما + +247 +00:19:32,290 --> 00:19:36,910 +جبتنا صفر بنحطها على الجهاز صفر و ان جبتنا عشرة + +248 +00:19:36,910 --> 00:19:40,910 +بنحطها عشرة، لكن احنا ان في الامتحان الأول و + +249 +00:19:40,910 --> 00:19:46,580 +الثاني و الأخيرواضح كلامي؟ طيب فيه انا حاجة اسمها + +250 +00:19:46,580 --> 00:19:50,360 +الساعات المكتبية الساعات المكتبية هذه اللي + +251 +00:19:50,360 --> 00:19:55,160 +وعدناكوا فيها قبل قليل انا بكون موجود في المكتب + +252 +00:19:55,160 --> 00:20:00,960 +جاعد فى انتظارك اذا عندك حاجة بتحب تسأل فيها انا + +253 +00:20:00,960 --> 00:20:08,780 +جاعد يوم السبت والأحد والاربعاء من ال 11 الى ال 12 + +254 +00:20:08,780 --> 00:20:17,940 +السبت أحدأربعاء من الأحداش للاتناش ويوم الأثنين + +255 +00:20:17,940 --> 00:20:23,840 +قاعد من الأتناش لساعة واحدة أي واحد بيجيني في + +256 +00:20:23,840 --> 00:20:29,400 +الأربع ساعات بيجدني موجود في المكتب طيب المكتب وين + +257 +00:20:29,400 --> 00:20:35,060 +موجود هذا؟ موجود في الطابق الثاني في مبنى الإدارة + +258 +00:20:35,060 --> 00:20:41,970 +الطابق الثاني في مبنى الإدارةرقم الغرفة تلاتمية و + +259 +00:20:41,970 --> 00:20:48,990 +تلاتة و عشرين رقم الغرفة تلاتة اتنين تلاتة تلاتمية + +260 +00:20:48,990 --> 00:20:54,530 +و تلاتة و عشرين رقم التليفون الداخلي الفين و ستمية + +261 +00:20:54,530 --> 00:20:59,410 +و تسعة عشر يعني من اي تليفون داخل الجامعة اضرب على + +262 +00:20:59,410 --> 00:21:03,170 +الفين و ستمية و تسعة عشر يابا ارد عليك انا يابا + +263 +00:21:03,170 --> 00:21:06,230 +ارد عليك الدكتور محمد الاشجار لان احنا اتنين + +264 +00:21:06,230 --> 00:21:12,110 +جاعدين مع بعض في نفس الغرفةوالتاني كذلك رياضية، + +265 +00:21:12,110 --> 00:21:16,070 +تمام؟ يبقى هذا بالنسبة للساعات المكتبية، لو جاتني + +266 +00:21:16,070 --> 00:21:20,890 +في وقت غير هذه الساعات ولا جاتني، برضه بجاوبك، + +267 +00:21:20,890 --> 00:21:24,370 +ماجوشلك تعالي في الساعات المكتبية، يعني بس هدول + +268 +00:21:24,370 --> 00:21:29,620 +ملتزم أني أكون موجود في المكتباللي هو في الغرفة + +269 +00:21:29,620 --> 00:21:34,820 +تلاتمية وتلاتة وعشرين هذا بالنسبة للساعات المكتبية + +270 +00:21:34,820 --> 00:21:39,800 +ونظار المتحانات وتوزيع الدرجات وكيفية الدراسة ورقم + +271 +00:21:39,800 --> 00:21:45,740 +الغرفة ورقم التليفون حد فيكوا إيه أي تساول حتى هذه + +272 +00:21:45,740 --> 00:21:51,120 +المحظة قبل ما ندخل في الموضوع اللي بدنا نشرحه؟ حد + +273 +00:21:51,120 --> 00:21:53,140 +بيحب يسأل أي سؤال اتفضل + +274 +00:21:56,720 --> 00:22:02,260 +بعض الخلافات، بعض الاختلافات، في عدد الأسئلة وبعض + +275 +00:22:02,260 --> 00:22:05,640 +المواضيع، بعض المواضيع شالها وبعض المواضيع دمجها، + +276 +00:22:05,640 --> 00:22:12,160 +إذا احنا بيقولنا تقيد بالطبعة الثانية عشرة، تمام؟ + +277 +00:22:12,160 --> 00:22:18,280 +طيب اتفضل كيف؟ + +278 +00:22:18,280 --> 00:22:21,820 +لغة الكتاب اللغة الإنجليزية، لكن زي ما انت شايف + +279 +00:22:21,820 --> 00:22:26,940 +انا بكتب بالإنجليزي و بشرح بالعربيبحيث مش هخليك + +280 +00:22:26,940 --> 00:22:31,220 +ترجع للا الكمبيوتر وللا القاموس كل كلمة انجليزي + +281 +00:22:31,220 --> 00:22:36,080 +بقولك إيش معناها بالعربي تمام؟ وبالتالي و بدّيش + +282 +00:22:36,080 --> 00:22:39,920 +إياك تروح تجرى من الكتاب بديك بس تروح تحل مسائل من + +283 +00:22:39,920 --> 00:22:44,780 +الكتاب أنا بلخصلك بحيث أريحك من قراية الكتاب و + +284 +00:22:44,780 --> 00:22:48,400 +ياريت كانوا بيعملونا زي ما عملوكوا هنا والله بجينا + +285 +00:22:48,400 --> 00:22:50,680 +نخاف نسأله أيوة تفضل + +286 +00:22:54,330 --> 00:22:59,150 +في ايش؟ الملخصات الملخصات هنا على اللوح يعني هذا + +287 +00:22:59,150 --> 00:23:02,910 +اللي انت شايفها بتلاقينه كاتب السؤال و مش كاتب حل + +288 +00:23:02,910 --> 00:23:07,770 +تمام؟ وبالتالي انت بدك الحل، مصبوط ولا لا؟ يبقى + +289 +00:23:07,770 --> 00:23:14,150 +الملخص تجده هنا تفصيليا على اللوح خلاص؟ ايوة، حد + +290 +00:23:14,150 --> 00:23:18,880 +بدي أسأل تاني؟اسأل اي حاجة حتى لو كان سؤال غلط + +291 +00:23:18,880 --> 00:23:23,140 +تعود انك تسأل و تناقش و تاخد و تعطي المثل هنا + +292 +00:23:23,140 --> 00:23:27,660 +اخويا انا اصار باللي بيسأل اكتر من اللي بيسألش لان + +293 +00:23:27,660 --> 00:23:31,200 +اللي بيسأل معناته فكر معناته اجا في باله حاجة بدي + +294 +00:23:31,200 --> 00:23:35,160 +يقولها ويمكن يقول ان حاجة احنا نستفيد منها كلها + +295 +00:23:35,160 --> 00:23:38,680 +ماتستغربش ه ان شاء الله نكتة مثلا قولنا للي بدي + +296 +00:23:38,680 --> 00:23:42,040 +يقول نكتة قولي اخي نكتة واش فيه مافيش عندهوش مشكلة + +297 +00:23:42,240 --> 00:23:47,080 +بنغير فيها الجو وإذا قلت نقطة برد عليك بنقطة أخرها + +298 +00:23:47,080 --> 00:23:50,300 +وبالتالي غيرنا اليوم نرجع لموضوع نفيد جيج تان + +299 +00:23:50,300 --> 00:23:54,440 +تلاتة ونرجع لموضوع نتانى احنا بدى نسأل اي تساؤل + +300 +00:23:54,440 --> 00:24:00,960 +بدخل في الموضوع اهدروا بالكم خلاص ندخل في الموضوع + +301 +00:24:00,960 --> 00:24:09,220 +طيب الشبتر هذا اسمه functions شبتر واحديبقى هذا + +302 +00:24:09,220 --> 00:24:18,060 +اللي هو chapter one اسمه functions functions يعني + +303 +00:24:18,060 --> 00:24:25,260 +ايه؟ يعني الدوال بنجي لأول section هذا مقسم إلى + +304 +00:24:25,260 --> 00:24:31,280 +ثلاث سكاشف تمام؟ او بدل ما نشرح نقول محتوى المادة + +305 +00:24:31,280 --> 00:24:37,700 +في الأول يا شباب وبعد هيك بروح نعطي تفصيلفالعشر + +306 +00:24:37,700 --> 00:24:41,160 +دقيقة اللي ضايلة بنقولك شو اللي بدنا ندرسه في هذا + +307 +00:24:41,160 --> 00:24:45,920 +المنهج اول chapter اللي هو ال functions بدنا ندرس + +308 +00:24:45,920 --> 00:24:53,160 +في ال functions حاجة اسمها ال domain domain يعني + +309 +00:24:53,160 --> 00:24:59,880 +المجال function يعني دالة او اقتران يبقى الدوال او + +310 +00:24:59,880 --> 00:25:05,820 +الاقترانات ال domain يعني المجال بدنا حاجة اسمها + +311 +00:25:05,820 --> 00:25:14,350 +ال rangerange يعني المدى code domain المجال + +312 +00:25:14,350 --> 00:25:20,230 +المناظر او المجال المصاحب او المجال المرافق يبقى + +313 +00:25:20,230 --> 00:25:25,650 +كمان ال code domain بعد هيك بدنا نيجي لالي graph + +314 +00:25:25,650 --> 00:25:34,950 +of a function الرسم البياني لدالة فاختصر كلمة + +315 +00:25:34,950 --> 00:25:41,930 +function إلى fn تمام؟يبقى graph of a function يبقى + +316 +00:25:41,930 --> 00:25:50,110 +الرسم البياني لمين لدالة ما بعد الرسم بننتقل حاجة + +317 +00:25:50,110 --> 00:25:55,030 +اسمها shift او + +318 +00:25:55,030 --> 00:26:02,950 +shifting ازاحةمش إزاحة احنا عندنا رسم ما بدنا + +319 +00:26:02,950 --> 00:26:08,470 +نزيحه جهة اليمين او جهة اليسار او الى اعلى او + +320 +00:26:08,470 --> 00:26:13,710 +الاسفل او جهة اليمين و اعلى او جهة اليمين واسفل او + +321 +00:26:13,710 --> 00:26:17,970 +جهة الشمال و اعلى و جهة الشمال واسفل شو بده يكون + +322 +00:26:17,970 --> 00:26:22,190 +شكل الدلة في هذه الحالة اللى عملنا لها shift او + +323 +00:26:22,190 --> 00:26:27,910 +إزاحة هذا الموضوع اللى هندرسه بعد ال shiftingبدنا + +324 +00:26:27,910 --> 00:26:36,310 +نيجي لحاجة متعلقة فيها اللي حاجة اسمة combining of + +325 +00:26:36,310 --> 00:26:40,130 +functions + +326 +00:26:40,130 --> 00:26:43,610 +إيش + +327 +00:26:43,610 --> 00:26:48,490 +يعني combining؟ combine يعني تجميع، تجميع هذا قد + +328 +00:26:48,490 --> 00:26:56,350 +يكون بالجمعأو الطرح أو الضرب أو القسمة أو التركيب + +329 +00:26:56,350 --> 00:27:01,390 +ال composition of functions تحصيل الدوال أو تركيب + +330 +00:27:01,390 --> 00:27:06,730 +الدوال اللي كنتوا بترمزوله if composition G أو if + +331 +00:27:06,730 --> 00:27:11,590 +circle G أو if بعد G زي ما كانوا بنتقلها لكم في + +332 +00:27:11,590 --> 00:27:15,610 +الثانويةيبقى اي اي تعبير من هذه التعبيرات اللي + +333 +00:27:15,610 --> 00:27:19,930 +ذكرناها يدل على ال composition of functions يبقى + +334 +00:27:19,930 --> 00:27:24,850 +اختصارا combining of functions تجميع الدوام جمع + +335 +00:27:24,850 --> 00:27:29,170 +طرح ضرب قسمة تركيب كله بنسميه combining of + +336 +00:27:29,170 --> 00:27:37,290 +functions بضل عندنا حاجة اسمها trigonometric + +337 +00:27:37,290 --> 00:27:39,350 +functions + +338 +00:27:41,390 --> 00:27:47,150 +ماذا يعني تريجونومتريك فانكشنز تريجونومتريك سمعتوا + +339 +00:27:47,150 --> 00:27:55,090 +فيها الدوال المثلثية كم واحد الدوال المثلثية لقدهم + +340 +00:27:55,090 --> 00:28:02,950 +في الثانوية ثلاثة بسقداش؟ ستة بس تلاتة مقلبات + +341 +00:28:02,950 --> 00:28:07,950 +التلاتة الأخرى التلاتة الأولانية reciprocal يعني + +342 +00:28:07,950 --> 00:28:14,210 +مقلب لمن؟ لدول الأخرى الجيب، جيب التمام، الظل، ظل + +343 +00:28:14,210 --> 00:28:18,550 +التمام، قاطع، قاطع تمامي الزاوية هي اللي خدهم + +344 +00:28:18,550 --> 00:28:21,990 +العربي في التانية، في غيرهم الستة دول؟ مافيش + +345 +00:28:21,990 --> 00:28:28,630 +غيرهم، الآن لو جت الظل مقلبه ظل التماملو جيت للجيب + +346 +00:28:28,630 --> 00:28:33,250 +مقلبه قاطع التمام، لو جيت لجيب التمام مقلبه + +347 +00:28:33,250 --> 00:28:37,990 +القاطع، هاي الدول المثلثية الستة، بدنا نرسم الدول + +348 +00:28:37,990 --> 00:28:44,170 +المثلثية الستةونعرف قداش ال period لكل functions + +349 +00:28:44,170 --> 00:28:49,310 +من ال functions الستة ونرسمهم و بعد ذلك لو عملنا + +350 +00:28:49,310 --> 00:28:56,770 +لهم إذاعة كيف بيحدث هذا و بعد ذلك بنجي للمتطابقات + +351 +00:28:56,770 --> 00:29:02,060 +المثلثية و هذا اللي كنا بنخاف منهامن حد ما ييجي + +352 +00:29:02,060 --> 00:29:07,600 +برتفعنا درجة الحرارة وربما النبض تمام؟ لكن هذه + +353 +00:29:07,600 --> 00:29:13,480 +المطابقة التي سأعرضها لكم بطريقة سهلة وبسيطة تصير + +354 +00:29:13,480 --> 00:29:17,860 +تستثفى حالك في الاشي اللي كنت تفكر به في الثانوية + +355 +00:29:17,860 --> 00:29:23,520 +أشياء بسيطة لكن بهمنا كيفية استخدامها مش القانون + +356 +00:29:23,520 --> 00:29:28,020 +أو المتطابقة كشغلة جامدة لا لا فيش حاجة سما جامدة + +357 +00:29:28,310 --> 00:29:32,930 +انت الان في جامعة يعني بيجي تشغل مخك وكيف تلعب + +358 +00:29:32,930 --> 00:29:37,370 +بالقانون حسب طبيعة السؤال اللى موجودة عندك وعارف + +359 +00:29:37,370 --> 00:29:41,990 +تلاقيه بسيط ومن أبسط ما يكون ان شاء الله يبقى هذا + +360 +00:29:41,990 --> 00:29:46,210 +كل ما يتعلق بال chapter الأول بنروح لل chapter + +361 +00:29:46,210 --> 00:29:51,770 +التانى chapter التانى بيناخد فيه limits and + +362 +00:29:51,770 --> 00:29:55,010 +continuity + +363 +00:29:58,700 --> 00:30:05,500 +النهايات والاتصال يبقى limits النهايات continuity + +364 +00:30:05,500 --> 00:30:13,160 +الاتصال اول ما بدنا نبدأ بدنا نبدأ نفهمك شو يعني + +365 +00:30:13,160 --> 00:30:18,300 +معنى limit ايش معنى نهاية يبقى بنبدأ لك الأول حاجة + +366 +00:30:18,300 --> 00:30:25,640 +the concept of a limit يبقى the concept of + +367 +00:30:26,720 --> 00:30:32,280 +A limit نسأل + +368 +00:30:32,280 --> 00:30:36,640 +السؤال اليومها مش اليومها بس بدنا نسأل اليوم هل + +369 +00:30:36,640 --> 00:30:42,300 +هناك فرق بين نهاية الدالة عند نقطة وقيمة الدالة + +370 +00:30:42,300 --> 00:30:48,200 +عند تلك النقطة الإجابة سنعرفها في chapter 2 ومسبق + +371 +00:30:48,200 --> 00:30:52,780 +ما أقولك اه في فروق لكن ان نفهم ان نهاية الدالة + +372 +00:30:52,780 --> 00:30:56,910 +عند نقطة قيمتها عند تلك النقطة هذا مفهومقد قد يحدث + +373 +00:30:56,910 --> 00:31:02,030 +و قد لا يحدث بس in general ما هواش صحيح تمام يبقى + +374 +00:31:02,030 --> 00:31:07,310 +هذا بنفهمكيا قبل ما نبدأ في قواعد النهايات او + +375 +00:31:07,310 --> 00:31:13,670 +قوانين النهايات بعد هيك بنروح ل limit laws او + +376 +00:31:13,670 --> 00:31:21,050 +limit formulas يبقى limit laws قوانين النهايات + +377 +00:31:21,050 --> 00:31:25,660 +اللي خدتها في الثانويةنهاية المجموع الجبري لدالتين + +378 +00:31:25,660 --> 00:31:31,200 +نهاية حصل ضرب دالتين نهاية حصل ضرب مقدار ثابت فيه + +379 +00:31:31,200 --> 00:31:38,940 +دالة نهاية دالة فيها جذر هيك و نضرب في المرافق و + +380 +00:31:38,940 --> 00:31:43,400 +نظرية sandwich theorem نظرية sandwich أو squeezing + +381 +00:31:43,400 --> 00:31:47,180 +theorem و كل هالشغلات إذا أخدتها في الثانوية بدا + +382 +00:31:47,180 --> 00:31:52,900 +أن أدهلك من جديد و كأنها جديدة بالنسبة إلى تمام؟ + +383 +00:31:53,180 --> 00:31:59,040 +بعد هذا هنجي نشوف أحيانا سنضطر نأخد النهاية من + +384 +00:31:59,040 --> 00:32:04,060 +اليمين و النهاية من الشمال right limit و left + +385 +00:32:04,060 --> 00:32:08,460 +limit تمام و نجي نعرف و اكتشف بدي أخد ال limit من + +386 +00:32:08,460 --> 00:32:13,180 +اليمين و ال limit مين هي الدوال هذه ما هي الأنواع + +387 +00:32:13,180 --> 00:32:16,520 +من الدوال اللي بدنا ناخدلها ال limit من اليمين و + +388 +00:32:16,520 --> 00:32:19,620 +ال limit من الشمال كل الدوال و الله بعضها الإجابة + +389 +00:32:19,620 --> 00:32:25,030 +بعضها مين هي هذا ما ستعرفه يومهاأربعة أنواع من + +390 +00:32:25,030 --> 00:32:28,110 +الدوالة هذا اللي بدنا ناخدلها ال limit من اليمين + +391 +00:32:28,110 --> 00:32:31,710 +وال limit مش مماخة لذلك limit عادية وامشي + +392 +00:32:31,710 --> 00:32:36,190 +بالقوانين وما إلى ذلك زيادة على ذلك بدنا ناخد ال + +393 +00:32:36,190 --> 00:32:43,090 +limit لما سين بدها تروح للمالة نهاية كويس أو نهاية + +394 +00:32:43,090 --> 00:32:47,670 +لدالة القيمة اللتي تقولها سين بتخلي الدالة تروح + +395 +00:32:47,670 --> 00:32:54,110 +لوينللمالانها in finite limits هذا كمان بدنا نعرفه + +396 +00:32:54,110 --> 00:33:00,190 +بنعرف حاجة اسمها ال asymptotes خطوط التقارب خط + +397 +00:33:00,190 --> 00:33:04,670 +تقارب للمنحنة كله داخل وين؟ داخل في هذا الموضوع + +398 +00:33:04,670 --> 00:33:08,410 +اللي هو limits, laws و limits and continuum بعد ما + +399 +00:33:08,410 --> 00:33:12,650 +نخلص ال limits اللي بتاخدها حوالي أربعة secation + +400 +00:33:12,650 --> 00:33:18,710 +بنروح لمين؟ بنروح لل continuity اللي بيعتمداعتمادا + +401 +00:33:18,710 --> 00:33:23,770 +كليا على مين؟ على ال limits لإن إذا كانت نهاية + +402 +00:33:23,770 --> 00:33:27,670 +الدالة عند نقطة تساوي قيمة الدالة عند تلك النقطة + +403 +00:33:27,670 --> 00:33:33,690 +بنقول إذا الدالة دالة متاصلة عند تلك النقطة ويمكن + +404 +00:33:33,690 --> 00:33:38,430 +أن نصل هذا التريف إلى three conditions سنعرفه كذلك + +405 +00:33:38,430 --> 00:33:43,070 +يومهامش اليوم يبقى هذا بالنسبة لل limits and + +406 +00:33:43,070 --> 00:33:48,070 +continuity هناخد الاتصال عند نقطة و بعد هيك + +407 +00:33:48,070 --> 00:33:55,090 +الاتصال على فترة على interval بعد هيك بنجي لشبتر + +408 +00:33:55,090 --> 00:34:03,870 +تلاتة الشبتر تلاتة اللي هو differentiation ايش + +409 +00:34:03,870 --> 00:34:09,210 +يعني differentiationالاشتقاء التفاضل يعني + +410 +00:34:09,210 --> 00:34:13,590 +derivatives التفاضل ال differentiation اللي هو + +411 +00:34:13,590 --> 00:34:20,070 +الاشتقاء بدنا أول حاجة ناخد ال derivative of a + +412 +00:34:20,070 --> 00:34:25,830 +function كيه مشتق ده لما؟ شو المفهوم تبعها؟ يبقى + +413 +00:34:25,830 --> 00:34:32,490 +بدي أخد ال derivative of + +414 +00:34:32,490 --> 00:34:35,010 +a function + +415 +00:34:38,800 --> 00:34:43,980 +بعد هك اذا انا ايجي اخد قوانين الاشتقاق او قواعد + +416 +00:34:43,980 --> 00:34:49,780 +الاشتقاق ال differentiation rules + +417 +00:34:49,780 --> 00:34:56,300 +كلمة differentiation هختصرها الى d i double f هي + +418 +00:34:56,300 --> 00:35:00,140 +قدامها يبجد ال differentiation rules قواعد + +419 +00:35:00,140 --> 00:35:07,620 +الاشتقاق بعد هكبدنا نيجي مشتقة الدول المثلثية مش + +420 +00:35:07,620 --> 00:35:13,440 +هالنا دول مثلثية ستة بدي أعرف ما هي مشتقاتها يبقى + +421 +00:35:13,440 --> 00:35:19,300 +هنا بدي أجي لليه derivative of + +422 +00:35:19,300 --> 00:35:27,280 +the trigonometric functions + +423 +00:35:30,550 --> 00:35:37,330 +يعني مشتقة الدوال المثلثية بعد مشتقة الدوال + +424 +00:35:37,330 --> 00:35:44,050 +المثلثية بداجة لحاجة اسمة chain rule يعني ايش + +425 +00:35:44,050 --> 00:35:50,870 +قاعدة السلسلة او مشتقة دالة الدالة بجدنا نسميها + +426 +00:35:50,870 --> 00:35:56,750 +هيك يا اما قاعدة السلسلة يا اما مشتقة دالة الدالة + +427 +00:35:57,150 --> 00:36:01,870 +بعد ما ناخد share role بدنا نروح لحاجة اسمها + +428 +00:36:01,870 --> 00:36:06,710 +implicit differentiation + +429 +00:36:06,710 --> 00:36:10,390 +يعني + +430 +00:36:10,390 --> 00:36:17,390 +إيش implicit differentiation؟ يعني الاشتقاق بنيإيش + +431 +00:36:17,390 --> 00:36:21,590 +الاشتقاق الدمني هذا؟ طب ما أحنا عارفين الصاد تساوي + +432 +00:36:21,590 --> 00:36:24,410 +سين تربية يبقى ده الصاد اللي لديه السين باتنين + +433 +00:36:24,410 --> 00:36:29,630 +سين، مظبوط؟ أه هذا اسمه اشتقاق صريح، إيش يعني + +434 +00:36:29,630 --> 00:36:33,550 +صريح؟ إذا الصاد في شجة و السينات كلهم في شجة + +435 +00:36:33,550 --> 00:36:38,690 +واحدة، هذا اسمه اشتقاق صريح لكن إذا كان صاد و + +436 +00:36:38,690 --> 00:36:43,730 +السين مشربكات مع بعض فقدر شخص الواحدة فيهم عند + +437 +00:36:43,730 --> 00:36:47,920 +تانية ومطلوب اشتقاقهمهذا بسميه اشتقاق ضمن .. يعني + +438 +00:36:47,920 --> 00:36:54,520 +زي ايه؟ زي صد تربيع زائد سين تكعيب صد أس أربعة + +439 +00:36:54,520 --> 00:37:00,260 +زائد جذر سين صد أس تلاتة على اتنين يسوى خمسة + +440 +00:37:00,260 --> 00:37:06,120 +وعشرين شربك مبالغ لاقدر اجيب صد بدلالة سين ولاقدر + +441 +00:37:06,120 --> 00:37:10,720 +اجيب سين بدلالة صد ومطلوب يوجد اشتقاق يبقى هذا + +442 +00:37:10,720 --> 00:37:15,870 +اسمه اشتقاق ضمن implicit differentiationهنشتق + +443 +00:37:15,870 --> 00:37:22,410 +ونبيّلك كيف قواعد الاشتقاء في هذه العالم تمام يبقى + +444 +00:37:22,410 --> 00:37:26,210 +هذا بالنسبة أنا بعطيك الخطوط العريضة لل chapter + +445 +00:37:26,210 --> 00:37:30,450 +وليست التفاصيلات الدقيقة التفاصيلات الدقيقة في هنا + +446 +00:37:30,450 --> 00:37:33,970 +لإن أنا بقولك الخطوط العريضة اللي موجودة وين في + +447 +00:37:33,970 --> 00:37:38,710 +هذا ال chapter بعد chapter تلاتة بيجينا ل chapter + +448 +00:37:38,710 --> 00:37:42,770 +أربع chapter أربع له applications + +449 +00:37:46,160 --> 00:37:56,580 +applications of derivatives تطبيقات + +450 +00:37:56,580 --> 00:38:03,200 +على المشتقات ايش + +451 +00:38:03,200 --> 00:38:08,820 +التطبيقات على المشتقات؟ هنبدأ أول حاجة بشيء اسمه + +452 +00:38:08,820 --> 00:38:12,780 +extreme values + +453 +00:38:15,320 --> 00:38:25,480 +extreme values ايش يعني extreme values القيم + +454 +00:38:25,480 --> 00:38:31,290 +المتطرفة شو القيم المتطرفة؟يعني القيام اللي فيها + +455 +00:38:31,290 --> 00:38:35,950 +ال local maximum و local minimum و ال end points + +456 +00:38:35,950 --> 00:38:41,450 +تمام او بمعنى اخر ل critical points زائد ال end + +457 +00:38:41,450 --> 00:38:45,930 +points نقاط الطرفين تبعات الفترة و النقاط اللي في + +458 +00:38:45,930 --> 00:38:49,790 +الداخل اللي تبقى نقاط حرجة يبقى هادر يبقى عليها + +459 +00:38:49,790 --> 00:38:54,670 +extreme values تمام بعد ما ناخد extreme values + +460 +00:38:54,670 --> 00:39:01,650 +بدنا نروح ناخدabsolute في الأول absolute maximum و + +461 +00:39:01,650 --> 00:39:11,390 +absolute minimum يبقى absolute maximum + +462 +00:39:11,390 --> 00:39:23,370 +and absolute minimum القيم + +463 +00:39:24,050 --> 00:39:29,350 +المطلقة العظمة والقيم المطلقة الصغيرة بتختلف عن ال + +464 +00:39:29,350 --> 00:39:33,790 +local maximum و ال local minimum بعد ذلك بنيجي لل + +465 +00:39:33,790 --> 00:39:42,990 +local maximum local maximum and local + +466 +00:39:42,990 --> 00:39:44,430 +minimum + +467 +00:39:46,880 --> 00:39:51,780 +القيم العظمى المحلية والقيم الصغرى المحلية طبعا في + +468 +00:39:51,780 --> 00:39:55,800 +فرق ما بين الاتنين هنعطيك الفرق يومها من عشان + +469 +00:39:55,800 --> 00:40:00,800 +نستعجل اليوم عليك ونقولك الفروقات كذا وكذا تمام + +470 +00:40:00,800 --> 00:40:04,540 +بعد ما ناخد ال local maximum و ال local minimum + +471 +00:40:04,540 --> 00:40:10,260 +نجي لحاجة اسمة concave up and concave down يبقى + +472 +00:40:10,260 --> 00:40:22,840 +concave up andconcave down التحدب + +473 +00:40:22,840 --> 00:40:27,740 +إلى أعلى أو إلى أسفل أو التحدب اللي بيسميه تقعر + +474 +00:40:27,740 --> 00:40:32,180 +وده كما بيسميه التحدب ما علينا اللي هو ال concave + +475 +00:40:32,180 --> 00:40:38,940 +up و ال concave down بضلنا نقطة انقلاب للمنحنة لل + +476 +00:40:38,940 --> 00:40:43,800 +inflection point يبقى inflection + +477 +00:40:46,000 --> 00:40:54,370 +pointيبقى نقطة الانقلاب أو نقطة الانعطاف للمنحنة + +478 +00:40:54,370 --> 00:41:00,790 +تمام المعلومات اللي عندنا هذه معلومات أساسية لرسم + +479 +00:41:00,790 --> 00:41:07,350 +المنحنة هذه هتشغل منها حوالي تلت سكاتشن at least + +480 +00:41:07,350 --> 00:41:14,030 +بعدين بنجي ل curve sketching بنجي لحاجة اسمها + +481 +00:41:14,030 --> 00:41:17,230 +curve sketching + +482 +00:41:19,880 --> 00:41:27,840 +curve يعني منحنى sketch رسم يبقى رسم المنحنيات كل + +483 +00:41:27,840 --> 00:41:32,220 +المعلومات اللى عرفناها فى السطرين هدول بدنا + +484 +00:41:32,220 --> 00:41:37,500 +نستخدمها فى رسم من المنحنيات طبعا هنا إيش جايلينا + +485 +00:41:37,500 --> 00:41:43,020 +إحنا هنا جايلينا graph of a function شو الفرق بين + +486 +00:41:43,020 --> 00:41:49,450 +هذه و هذهفرق شاسة، فرق الشاسة أنه هذا رسم لدول + +487 +00:41:49,450 --> 00:41:54,030 +بسيطة، يعني سالة standard اتكرر معاك دائما و أبدا + +488 +00:41:54,030 --> 00:41:58,690 +طيلة في الكتاب سواء كان بكالة قلصية أو B أو C، بس + +489 +00:41:58,690 --> 00:42:03,110 +هذه لا، هذه بدا شغل كتير حتى نقدر نقول ده اللي في + +490 +00:42:03,110 --> 00:42:06,380 +البسط و ده اللي في المقامأو ده اللي في المقام على + +491 +00:42:06,380 --> 00:42:10,280 +طوله بدي أشوف كيف ده رسمها عملية مش سهلة يبقى بدي + +492 +00:42:10,280 --> 00:42:14,360 +أدرس الشغلات كلها عشان أقدر أرسم ملحانة هذا يعني + +493 +00:42:14,360 --> 00:42:21,540 +هذه رسومات بسيطة و هذه رسومات أصعب من هذه بكثير + +494 +00:42:21,540 --> 00:42:27,740 +تمام؟ يبقى هذا هو chapter من أربعة إجمالة بنجي ل + +495 +00:42:27,740 --> 00:42:32,120 +chapter خمسة chapter خمسة اللي هو ال integration + +496 +00:42:35,850 --> 00:42:41,530 +Integration يعني إيه؟ تكامل، ممتاز، هنجسمه إلى + +497 +00:42:41,530 --> 00:42:46,650 +نوعين، النوع الأول indefinite integral و definite + +498 +00:42:46,650 --> 00:42:52,970 +integral بس قبل هيك بدنا نقول ال existence لتكامل، + +499 +00:42:52,970 --> 00:42:56,610 +هل التكامل هذا exist ولا لازم لا exist؟ زي ما في + +500 +00:42:56,610 --> 00:43:00,690 +حالة ال differentiation هنا، هل الدالة قابلة + +501 +00:43:00,690 --> 00:43:04,480 +للاشتراك ولا غير قابلة للاشتراك؟هنا بنقول هل + +502 +00:43:04,480 --> 00:43:09,680 +الدالة قابلة للتكامل والله غير قابلة للتكامل وما + +503 +00:43:09,680 --> 00:43:14,660 +هو الشرط انها تبقى قابلة للتكامل نفترض انها قابلة + +504 +00:43:14,660 --> 00:43:19,880 +للتكامل يبقى في عندي نوعين mini تكامل النوع الأول + +505 +00:43:19,880 --> 00:43:25,020 +اسمه definite integrals + +506 +00:43:26,870 --> 00:43:35,070 +التكاملات محدودة والنوع الثاني اسمه indefinite + +507 +00:43:35,070 --> 00:43:44,790 +integrals التكاملات غير المحدودة بالنسبة + +508 +00:43:44,790 --> 00:43:50,230 +للdefinite integrals يبقى احنا بنكامله مقولش زائد + +509 +00:43:50,230 --> 00:43:54,950 +مقدار ثابت بكون تكامل محدود من كذا إلى كذابنعوض + +510 +00:43:54,950 --> 00:44:01,470 +بحدود التكامل لكن على هذا الموضوع في نظرية مشهورة + +511 +00:44:01,470 --> 00:44:06,290 +وهي very important بنسميها ال fundamental theorem + +512 +00:44:06,290 --> 00:44:10,550 +of calculus النظرية الأساسية لحساب التفاضل + +513 +00:44:10,550 --> 00:44:16,890 +والتكامل يبقى في هنا حاجة اسمها fundamental + +514 +00:44:16,890 --> 00:44:19,950 +theorem + +515 +00:44:22,810 --> 00:44:25,450 +Ave Calculus + +516 +00:44:27,240 --> 00:44:32,100 +يبقى النظرية الأساسية لحساب التفاضل والتكامل في + +517 +00:44:32,100 --> 00:44:36,100 +الـ indefinite integral فهنا حاجة very important + +518 +00:44:36,100 --> 00:44:41,100 +كمان اللي هو استخدام التكامل بالتعويد يعني كيف ده + +519 +00:44:41,100 --> 00:44:45,160 +اللي مكلك ع هيك وشكلها مخيف بنقدر نبسطها ونخلي + +520 +00:44:45,160 --> 00:44:49,700 +شكلها لطيف ونقدر نكملها بسهولة يبقى ده اسم + +521 +00:44:49,700 --> 00:44:55,660 +integration by substitution يبقى هنا integration + +522 +00:45:00,160 --> 00:45:06,100 +by substitution يبقى + +523 +00:45:06,100 --> 00:45:10,900 +التكامل بالتعويض كيف نستخدم التعويض فإننا نقدر + +524 +00:45:10,900 --> 00:45:17,420 +نكامل ده لشكل غريب أو مكلقع بعد هيك بنيجي للمساحة + +525 +00:45:17,420 --> 00:45:27,000 +بين منحنيين يبقى ال area between curves + +526 +00:45:28,400 --> 00:45:32,940 +المساحة بين منحنا يعني احنا رسمنا دالة و رسمنا + +527 +00:45:32,940 --> 00:45:37,700 +دالة تانية دلتين حصروا بين بينهم في المستوى مساحة + +528 +00:45:37,700 --> 00:45:43,060 +بدنا نعرف كيف بدنا نحسب هذه المساحة بنجي لأخر حاجة + +529 +00:45:43,060 --> 00:45:48,840 +رقم ستة تطبيقات على التكامل زي ما في تطبيقات على + +530 +00:45:48,840 --> 00:45:55,120 +التفاضل فينا تطبيقات على التكامل يبقى بنجي لهنا ل + +531 +00:45:55,120 --> 00:45:55,960 +applications + +532 +00:45:59,710 --> 00:46:07,210 +of integrals ايش ال applications of integrals + +533 +00:46:07,210 --> 00:46:14,950 +تطبيقات على التكامل هروح نستخدم التكامل في حساب ال + +534 +00:46:14,950 --> 00:46:25,770 +volume حجم مجسم تمام بعد هيك ال surface area + +535 +00:46:28,370 --> 00:46:39,950 +المساحة السطحية لمجسم ما بعد هيك ال arc length of + +536 +00:46:39,950 --> 00:46:42,210 +a curve + +537 +00:46:45,030 --> 00:46:49,690 +يبقى هذه المحاورة الرئيسية في الشبتر السادس + +538 +00:46:49,690 --> 00:46:56,370 +والاخير بان نجي حجوم الأجسام الدورانية حجم مجسم في + +539 +00:46:56,370 --> 00:47:02,190 +الفراغ قداش المساحة السطحية لهذا المجسم لاحظ هنا + +540 +00:47:02,190 --> 00:47:07,210 +قولنا اه قولنا ال area between two curves في مستوى + +541 +00:47:07,790 --> 00:47:11,530 +منحنيا تقاطعوا بدنا المساحة اللي بينهم في مستوى + +542 +00:47:11,530 --> 00:47:18,110 +لكن هذه مساحة في الفراغ مجسم في الفراغ بد المساحة + +543 +00:47:18,110 --> 00:47:23,870 +السطحية لهذا المجسم arc length طول القوس او طول + +544 +00:47:23,870 --> 00:47:31,400 +جزء من منحنة arc length of a curveيبقى طول منحنة + +545 +00:47:31,400 --> 00:47:35,480 +في مرسوم عندى، بدى أعرف قداش الطول هذا كل هذا + +546 +00:47:35,480 --> 00:47:41,000 +بنستخدمله مين؟ التكامل هذا هو ايه المواضيع + +547 +00:47:41,000 --> 00:47:46,980 +الرئيسية التي سندرسها خلال هذا الفصل في calculus A + +548 +00:47:46,980 --> 00:47:53,000 +ونغير لكم الجو بأبيات من الشعر على التفاضل + +549 +00:47:53,000 --> 00:47:57,570 +والتكامليعني التفاضل و التكامل هذول زي الطوم، + +550 +00:47:57,570 --> 00:48:00,510 +شفتوا الطوم دايما أو أبدا بتناجروا مع بعض و دايما + +551 +00:48:00,510 --> 00:48:05,490 +بتكاتلوا و دايما صحبوا مع بعض في المقابل، تمام؟ + +552 +00:48:05,490 --> 00:48:12,610 +قال التفاضل شامتا أنا للتكامل معبره، أنا فاضل + +553 +00:48:12,610 --> 00:48:21,850 +متفضل، أنا يا تكامل أكبر، انظر على متكالاتيmy long + +554 +00:48:21,850 --> 00:48:25,770 +يطولوا ويقصروا تفضل ويقولوا شوف علامتك اللي هي + +555 +00:48:25,770 --> 00:48:32,760 +زادلة طبعا زي التكاملهبت تكامل هائجا أسكت أنا + +556 +00:48:32,760 --> 00:48:40,660 +متحرر أنا لم أقعد لك تابعا لا و لست منك أسطر أنا + +557 +00:48:40,660 --> 00:48:49,800 +للمساحة حاسب حتى الحجوم أصوره أنا بحسب المساحات و + +558 +00:48:49,800 --> 00:48:53,940 +الحجوم و أنت ما تقدرش تحسبها و أنا مش مشتاق منك + +559 +00:48:53,940 --> 00:49:00,500 +أنا منفصل لعاليبهذا بيقول هذا هو المقرر، الآن الذي + +560 +00:49:00,500 --> 00:49:05,300 +سندرسه طيلة هذا الفصل، حد بدي يسأل أي سؤال، فيما + +561 +00:49:05,300 --> 00:49:12,840 +سيدرس في هذا الفصل؟ بس + +562 +00:49:12,840 --> 00:49:20,300 +بنوسع شويةأو بنأسسك لما سيأتي فيما بعد يعني بنخليك + +563 +00:49:20,300 --> 00:49:30,760 +تتأسس تأسيسا سليما صحيحا مش تحفيظا لفهما ايوة + +564 +00:49:30,760 --> 00:49:34,780 +تفتسأل؟ والله بس الكلام جاي ال هيك طيب حد بتسأل + +565 +00:49:34,780 --> 00:49:43,420 +تاني؟ اذا ندخل في صميم الموضوعنبدأ بأول موضوع اللي + +566 +00:49:43,420 --> 00:49:46,140 +هو موضوع main ال functions + +567 +00:50:18,110 --> 00:50:27,330 +يبقى أول سيكشن لو سيكشن واحد واحد functions and + +568 +00:50:27,330 --> 00:50:37,710 +their graphs الدوال + +569 +00:50:37,710 --> 00:50:44,150 +والرسومات البيانية بدنا نبدأ أول شي ان نعطي تعريف + +570 +00:50:44,150 --> 00:50:49,900 +لل functionونحاول نفهم هذا التعريف التعريف بيقول + +571 +00:50:49,900 --> 00:51:08,440 +ما يأتي a function f from a set D to a set Y + +572 +00:51:08,440 --> 00:51:20,660 +وبينجو سلم نقول f من D إلى Yالشكل هذا is a role + +573 +00:51:20,660 --> 00:51:28,560 +that ascends to + +574 +00:51:28,560 --> 00:51:40,380 +each element x in D a unique element + +575 +00:51:47,630 --> 00:51:52,990 +Ionic element F + +576 +00:51:52,990 --> 00:52:04,170 +of X and Y Ionic element F of X and Y انتهى + +577 +00:52:04,170 --> 00:52:16,570 +التعريف The set D is called the + +578 +00:52:17,800 --> 00:52:34,140 +domain of F ال Y is called the codomain of F the + +579 +00:52:34,140 --> 00:52:37,380 +codomain + +580 +00:52:37,380 --> 00:52:43,620 +of F and + +581 +00:52:45,800 --> 00:52:53,500 +the collection of + +582 +00:52:53,500 --> 00:53:10,840 +all f of x is called the range of f + +583 +00:53:16,650 --> 00:53:21,370 +الان هذا التعريف اللى بين ادينا نحاول نقرأ هذا + +584 +00:53:21,370 --> 00:53:27,930 +التعريف من جديد نحاول نفهم كل كلمة من هذا التعريف + +585 +00:53:27,930 --> 00:53:33,490 +نحاول نحط هذا التعريف بالرسم على أرض الواقع بقى + +586 +00:53:33,490 --> 00:53:37,890 +فعلا نفهم شو الكلام اللى احنا كاتبينه يعني احنا + +587 +00:53:37,890 --> 00:53:43,690 +بنصمش صم احنا بنفهم فاهماذا فهمنا فهمنا صحيحا يبقى + +588 +00:53:43,690 --> 00:53:49,880 +بصير معنا مشكلة بعد هيك بنبني ازاي ما بدناهنرجع + +589 +00:53:49,880 --> 00:53:55,500 +لهذا التعريف نقرأه من جديد نحاول نفسر كل كلمة + +590 +00:53:55,500 --> 00:54:02,920 +موجودة أو كل عبارة هنا ما هو المقصود بها تمام؟ طيب + +591 +00:54:02,920 --> 00:54:07,480 +بدنا ننجل التعريف من بدايته اللي بين أدينا هو + +592 +00:54:07,480 --> 00:54:13,300 +تعريف ال function اللي بالعربي الاغتران أو الدلة + +593 +00:54:13,300 --> 00:54:16,960 +فإيش بيقولين؟ a function f + +594 +00:54:26,800 --> 00:54:31,300 +السطر هذا ممكن اختصره كله بالكلام اللي بينجوز هنا + +595 +00:54:36,160 --> 00:54:42,720 +is a role هو عبارة عن صيغة ما للصيغة هذه that + +596 +00:54:42,720 --> 00:54:52,540 +ascends تعين أو تحدد أو تخصص لكل عنصر X موجود في D + +597 +00:54:52,540 --> 00:55:00,620 +عنصرا وحيدا a unique element عنصر وحيد اسمه F of X + +598 +00:55:00,620 --> 00:55:06,090 +موجود وين؟ موجود في الست Yيبقى هذا هو ايه التعريف + +599 +00:55:06,090 --> 00:55:11,570 +يبقى مرة تانية دالة F هي عبارة عن الدالة F من ال + +600 +00:55:11,570 --> 00:55:17,070 +set D إلى ال set Y هي عبارة عن صيغة هذه الصيغة + +601 +00:55:17,070 --> 00:55:22,970 +تحدد لكل عنصر في ال set D عنصرا واحدا في ال set Y + +602 +00:55:22,970 --> 00:55:28,730 +تمام؟ يبقى هذا الترجمة العربية للتعريف احنا بناشي + +603 +00:55:28,730 --> 00:55:35,130 +الترجمة العربية من الترجمة الفهميةلمن؟ لالتعريف + +604 +00:55:35,130 --> 00:55:39,250 +قبل ما نجي للترجمة الفهمية انواصل بيقول ال 6D + +605 +00:55:39,250 --> 00:55:46,230 +بسميها المجال تبع الدالة F ال 6Y بسميها المجال + +606 +00:55:46,230 --> 00:55:53,740 +المرافق ال code domain للدالة Fكل f of x اللى + +607 +00:55:53,740 --> 00:55:59,020 +عندنا كل العناصر اللى ظهرت كصور لعناصر دى + +608 +00:55:59,020 --> 00:56:05,820 +collection جمعناها بنسميها المدى تبع الدالة f تمام + +609 +00:56:07,190 --> 00:56:11,430 +نرجع الأن للتريف من أول و جديد و كأننا ما سمعنا + +610 +00:56:11,430 --> 00:56:17,910 +شيئا و بدنا نعرض الموضوع بطريقة الرسم بيقول يتدلف + +611 +00:56:17,910 --> 00:56:23,870 +من 6D إلى 6Y يبقى أنا بدروح أرسم رسمة زي هيك و + +612 +00:56:23,870 --> 00:56:30,350 +أقول هذه 6D بدي أرسم رسمة تانية مثلا و أقول هذه ال + +613 +00:56:30,350 --> 00:56:35,810 +6 اللي عندنا اللي هي capital Yهذه الستة افترض فيها + +614 +00:56:35,810 --> 00:56:42,150 +عنصر وفيها كمان عنصر وفيها عنصر بس تلت عناصر هذه + +615 +00:56:42,150 --> 00:56:45,830 +الستة اللي جيت فيها ما شاء الله عليه هاي عنصر وهاي + +616 +00:56:45,830 --> 00:56:51,170 +اتنين وهاي تلاتة وهاي اربعة وهاي خمسة وهاي ستة ولا + +617 +00:56:51,170 --> 00:56:58,480 +يهمكطلع فيها عناصر كتير كويس ال F هي عبارة عن ده + +618 +00:56:58,480 --> 00:57:07,720 +لمن ال 6D ل6Y اديتها الرمز F يبقى هاي F من D الى Y + +619 +00:57:07,720 --> 00:57:13,360 +ايش بتسوي هذه في دنياتها جال هذه بتيجي تخصص لكل + +620 +00:57:13,360 --> 00:57:21,120 +عنصر X موجود في دي يبقى انا لو جيت سميت هذا Xموجود + +621 +00:57:21,120 --> 00:57:26,800 +في دي ايش بيحصل له هذه F بتخلي لهذا العنصر صورة في + +622 +00:57:26,800 --> 00:57:34,140 +ال 6Y الصورة هذه اسمها ايش اسمها F of X يبقى هذا + +623 +00:57:34,140 --> 00:57:40,660 +العنصر صار من F of X يبقى X في D صارتله صورة تحت + +624 +00:57:40,660 --> 00:57:46,250 +تأثير ال Fيعني F لما انأثرت على X صارت الصورة main + +625 +00:57:46,250 --> 00:57:52,110 +F of X موجودة وين؟ موجودة في ال set Y يبقى الكلام + +626 +00:57:52,110 --> 00:57:57,270 +اللي قلناه النظري روح نحطناه على شكل ايه؟ على شكل + +627 +00:57:57,270 --> 00:58:03,930 +رسم بيانلكن حتى الآن مافهمناش التعريف فهما دقيقة + +628 +00:58:03,930 --> 00:58:09,390 +لذلك هاطرح مجموعة من الأسئلة المجموعة من الأسئلة + +629 +00:58:09,390 --> 00:58:15,110 +هذه هي التي ستفهمنا التعريف و لذلك تعالوا مع + +630 +00:58:15,110 --> 00:58:22,340 +التعريففمن D الى Y هي F من D الى Y ماشي لها ايش + +631 +00:58:22,340 --> 00:58:27,420 +بتسوي هذه قال لي هي الصيغة الصيغة هذه انا اعطيتها + +632 +00:58:27,420 --> 00:58:32,720 +الرمز اللي هو F ايش بتسوي هذه قال لي that ascends + +633 +00:58:32,720 --> 00:58:39,380 +to each element X in D لكل عنصر X من D طب استنى + +634 +00:58:39,380 --> 00:58:47,870 +شويةمن هذه العبارة أفهم إن F هذه هتأثر على بعض + +635 +00:58:47,870 --> 00:58:53,230 +عناصر دي و الله عليها كلها على البعض مش على الكل + +636 +00:58:53,230 --> 00:59:01,210 +يعني دي باختلفة الروايات اختلف الفقهاء مش هيكخلفوا + +637 +00:59:01,210 --> 00:59:05,070 +في الفهم وهذه طبيعة البشر أنهم يختلفوا في الأفام + +638 +00:59:05,070 --> 00:59:09,090 +لكن تطلع للناس الناس بيقولوا that's essence to + +639 +00:59:09,090 --> 00:59:16,110 +each element in D كل عنصر في D إذا متأثر على بعض + +640 +00:59:16,110 --> 00:59:21,540 +العناصر و الله عليهم كلهمعليهم كلهم بلا استثناء لن + +641 +00:59:21,540 --> 00:59:27,280 +تستثني عنصر تمام؟ ليش؟ لأنه جالي to each element x + +642 +00:59:27,280 --> 00:59:32,760 +in D يعني مثلاته هتأثر على x و هتأثر على x1 و + +643 +00:59:32,760 --> 00:59:37,660 +هتأثر على x2 كلهم هتأثر عليهمتمام؟ لأنه قال لي to + +644 +00:59:37,660 --> 00:59:42,560 +each element X and Y شو بدى تعمله؟ بدى تخصص لكل + +645 +00:59:42,560 --> 00:59:50,960 +واحد منهم عنصرا وحيدا في ال set Y ممتاز جدا طيب + +646 +00:59:50,960 --> 00:59:56,240 +تعال مع عنصرا وحيدا في ال set Y استنى شوية السؤال + +647 +00:59:56,240 --> 01:00:03,220 +هو هل للعنصر X ستظهر صورة واحدة فقط ولا ممكن صوتين + +648 +01:00:03,220 --> 01:00:08,920 +او تلاتة؟سورة واحد لان جالي unique element يبقى + +649 +01:00:08,920 --> 01:00:16,520 +العنصر هذا X لن تظهر له الا صورة واحدة فقط في الست + +650 +01:00:16,520 --> 01:00:23,140 +Y الهمين ب F of X فقط ده غير يبقى العنصر الواحد له + +651 +01:00:23,140 --> 01:00:30,200 +ايه؟ له صورة واحدةنجي نكمل نسأل السؤال اللي بعده + +652 +01:00:30,200 --> 01:00:39,460 +هل يمكن لعنصرين أن يشترك في نفس الصورة؟ + +653 +01:00:43,900 --> 01:00:49,860 +يمكن لأنه مشراتش ممكن لعنصرين يشتركوا في نفسه + +654 +01:00:49,860 --> 01:00:54,320 +بصورة هذا العنصر له صورة واحدة والعنصر التاني له + +655 +01:00:54,320 --> 01:00:59,520 +صورة واحدة صحيح ولا لأ يبقى هدول محدش هداك يعني + +656 +01:00:59,520 --> 01:01:06,780 +يمكن لعنصرين أن يعني هذا X F خلت صورة F of X واخدت + +657 +01:01:06,780 --> 01:01:13,920 +X واحد وخلت صورته من F of X يعني أصارf of x هو + +658 +01:01:13,920 --> 01:01:20,600 +نفسه من f of x one اه ممكن لعنصرين وممكن التلاتة + +659 +01:01:20,600 --> 01:01:24,780 +يشتركوا في نفس الصورة كمان تمام احنا خل اتنين + +660 +01:01:24,780 --> 01:01:28,560 +يشتركوا في نفس الصورة اذا ماعنا مشكلة السؤال اللي + +661 +01:01:28,560 --> 01:01:34,120 +بعده يعني ممكن لعنصرين ان يشتركوا في نفس الصورة + +662 +01:01:34,120 --> 01:01:40,420 +لكن لايمكن للعنصر تظهرله صورتين ممنوه منع بات + +663 +01:01:40,840 --> 01:01:47,740 +السؤال اللي بعده هل الدالة F لما اتأثر على عناصر D + +664 +01:01:47,740 --> 01:01:51,880 +التفاقنة ما اتأثر عليهم كلهم بلا استثناء ستغطي + +665 +01:01:51,880 --> 01:01:59,160 +جميع عناصر Y سؤال بطريقة اخرى هل جميع عناصر Y + +666 +01:01:59,160 --> 01:02:06,860 +ستظهر كصور لعناصر D؟ مش ممكنممكن .. ممكن كلهم + +667 +01:02:06,860 --> 01:02:12,110 +يظهروا صحيح وارد، لكن in general لأ مش صحيحكويس + +668 +01:02:12,110 --> 01:02:17,950 +يعني ال range ممكن يسوي ال code main لكن in + +669 +01:02:17,950 --> 01:02:22,670 +general بيسويهوش طب هش بيسويه بيكون مجموعة جزئية + +670 +01:02:22,670 --> 01:02:29,170 +منه طبعا يعني x اتنين هذه لو أثرت عليها f بدها + +671 +01:02:29,170 --> 01:02:33,010 +تجيبه على العنصر اللي عندنا هنا وبالتالي يظل عندي + +672 +01:02:33,010 --> 01:02:38,830 +عنصر اتنين تلات مظهروش كصورعناصر في ال code domain + +673 +01:02:38,830 --> 01:02:45,010 +لكنها لم تظهر كصورة تمام؟ إذا ال range شو بيكون يا + +674 +01:02:45,010 --> 01:02:56,110 +شباب؟ بس F of X وهذه F of X2 هذه F of X2 يبقى سعر + +675 +01:02:56,110 --> 01:03:01,450 +ال range بيتبعد أوي خلينا نكتبهم كلهم ال domain و + +676 +01:03:01,450 --> 01:03:08,930 +ال range و ما إلى ذلكيبقى سعر domain هاختصرها DOM + +677 +01:03:08,930 --> 01:03:15,290 +الـ DLF بده يساوي من العناصر تبع كل اللي موجودة في + +678 +01:03:15,290 --> 01:03:25,730 +دي X و X1 و X2 بالاستثناء طيب بده ال range بتابع + +679 +01:03:25,730 --> 01:03:36,970 +ال DLF من هما عنصرين فقط يأمف of Xو f of x2 مافيش + +680 +01:03:36,970 --> 01:03:41,570 +غيرهم طب و f of x واحد ماهي f of x بثنانهم بيسووا + +681 +01:03:41,570 --> 01:03:46,370 +بعض يبقى مكتوب hash بتكرر يبقى في ال set لو تكرر + +682 +01:03:46,370 --> 01:03:50,730 +عنصرين تلاتة هذا بيعتبر كل عنصر واحد فقط لغيره + +683 +01:03:50,730 --> 01:03:56,030 +وبالتالي هذا صار ال range طب ما علاقة ال range بال + +684 +01:03:56,030 --> 01:04:04,170 +code mainمجموعة جزئية منه يبقى صار ال range لدالة + +685 +01:04:04,170 --> 01:04:16,720 +F هو مجموعة جزئية من ال code من اللي هو Y ممكنيغطي + +686 +01:04:16,720 --> 01:04:20,320 +كل عناصر وايد، ده اللي غطيها، إذا غطتها بسميها + +687 +01:04:20,320 --> 01:04:25,800 +دالة فوقية، on to function، هذي مشلكو، هذي بس + +688 +01:04:25,800 --> 01:04:28,680 +للناس اللي بتخصصوا رياضيات، بعدين في المستوى + +689 +01:04:28,680 --> 01:04:31,320 +التاني، فما فوق، يعني المعلومة اللي قلتها مش + +690 +01:04:31,320 --> 01:04:34,380 +الحين، هياخدوها السنة الجاية ان شاء الله اللي + +691 +01:04:34,380 --> 01:04:37,660 +بتخصصوا رياضيات، سواء كان من كلية التربية أو كلية + +692 +01:04:37,660 --> 01:04:41,040 +العلم، هندس أو تكنولوجيا، مالهمش دعوة في الموضوع، + +693 +01:04:41,040 --> 01:04:47,410 +تمام؟يبقى دائما وابدا هذه تقرأ مجموعة جزئية أقل من + +694 +01:04:47,410 --> 01:04:51,530 +.. مش أقل subset من أو تساوي لكن in general بقولش + +695 +01:04:51,530 --> 01:04:56,650 +subset من أو تساوي بقول subset من مجموعة جزئية من + +696 +01:04:56,650 --> 01:05:02,060 +اللي هو من ال Y اللي عندنا هذهطيب حتى اللحظة أظن + +697 +01:05:02,060 --> 01:05:07,560 +التعريف انفهم الآن ده لا بتخصص لعنصر من هنا صورة + +698 +01:05:07,560 --> 01:05:11,940 +واحدة لا يمكن لعنصر يظهرله صورتين ممكن لعنصر + +699 +01:05:11,940 --> 01:05:17,160 +يشتركها في نفس الصورة ال range هو جزء من ال code + +700 +01:05:17,160 --> 01:05:21,680 +domain خلصنا هذا كل الكلام اللي قلناه قدامنا هذا + +701 +01:05:21,680 --> 01:05:26,240 +على اللوح حد إله أي تساول قبل أن ندخل إلى أمثلة + +702 +01:05:26,240 --> 01:05:31,730 +توضيحية لكيفية إيجاد ال domain و ال rangeعشان لو + +703 +01:05:31,730 --> 01:05:39,230 +تسأل ايه اتفضل ال domain اف .. ده من فوق يعني ال + +704 +01:05:39,230 --> 01:05:47,610 +domain هو كل عناصر دي يعني هذا بده يساوي دي itself + +705 +01:05:47,610 --> 01:05:52,590 +ماشي؟ يعني كل العناصر اللي موجودة في دي لإنه جالي + +706 +01:05:52,590 --> 01:05:58,190 +to each element كل عنصر موجود في دي لن استثني فيهم + +707 +01:05:58,190 --> 01:06:06,860 +أحدا ماشي يا سيدي؟عناصر متشابهة في D لو في كان + +708 +01:06:06,860 --> 01:06:09,800 +عناصر متشابهة .. عناصر متشابهة في D ممكن نحطها في + +709 +01:06:09,800 --> 01:06:12,400 +.. مافيش يا سيدي في مفهومنا في ال groups يعني في + +710 +01:06:12,400 --> 01:06:16,980 +المجموعات ان العناصر متشابهة تعتبر عنصر عن واحدة + +711 +01:06:16,980 --> 01:06:20,580 +مثلا لو قلت لي مثلا انا عند الست اتنين و تلاتة و + +712 +01:06:20,580 --> 01:06:24,840 +تلاتة و تلاتة و تلاتة و خمسة يبقى ده مش الا تلاتة + +713 +01:06:24,840 --> 01:06:29,580 +عناصر هو اتنين و تلاتة و خمسة فقط لغاية ماشي؟ حد + +714 +01:06:29,580 --> 01:06:35,280 +بدي أسأل أي سؤال تاني؟طيب خش على الأمثلة المثال + +715 +01:06:35,280 --> 01:06:42,320 +بيقول ما يأتي example find + +716 +01:06:42,320 --> 01:07:00,840 +the domain and range of the following functions + +717 +01:07:11,930 --> 01:07:20,870 +هنا الـ function F هنا الـ domain تبع الدالة F هنا + +718 +01:07:20,870 --> 01:07:29,650 +ال range تبع الدالة F نجي لأول دالة من هذه الدوالة + +719 +01:07:29,650 --> 01:07:36,330 +لل F of X يساوي X تربيع زائد تلاتة + +720 +01:07:41,960 --> 01:07:47,060 +خلّي بالك معناه بنفهمك كيف بنحسب ال domain ثم كيف + +721 +01:07:47,060 --> 01:07:52,440 +بنحسب ال range لدالة ما الدالة اللي عندنا f of x + +722 +01:07:52,440 --> 01:07:57,540 +سوى x تربية زائد تلاتية ال domain يا شباب كل القيم + +723 +01:07:57,540 --> 01:08:04,420 +اللي بتاخذها x حتى تكون الدالة معرفة هذا بدوء + +724 +01:08:04,420 --> 01:08:09,660 +خلّيني أطرح السؤال التالي هل هناك قيمة ال x على كل + +725 +01:08:09,660 --> 01:08:15,720 +ال real lineبتخلّي القيمة هذه ماهياش معرفة في .. + +726 +01:08:15,720 --> 01:08:22,160 +في .. يعني معنى هذا ال domain من وين لوين من سالب + +727 +01:08:22,160 --> 01:08:27,540 +infinity إلى .. يعني كل ال real line يبقى هذه كل + +728 +01:08:27,540 --> 01:08:33,580 +مجموعة الأعداد الحقيقية the set of real numbers أو + +729 +01:08:33,580 --> 01:08:38,200 +انشي تفقل من سالب infinity إلى infinity ان قلت هذه + +730 +01:08:38,200 --> 01:08:42,940 +ماشي، ان قلت هذه ماشي تمام؟يبقى ال domain كل القيم + +731 +01:08:42,940 --> 01:08:47,560 +اللى بتاخدها x حتى تكون الدالة معرفة، بدي ال range + +732 +01:08:47,560 --> 01:08:55,300 +ال range هي كل قيم f of x يعني ايش؟ يعني بدي أخد + +733 +01:08:55,300 --> 01:09:01,440 +قيم من الفترة هذهوأعوض بها هنا شو بيطلع بيكون هذا + +734 +01:09:01,440 --> 01:09:05,760 +ال range ومشان يكون شغلي صح بدي أمسك من ال zero و + +735 +01:09:05,760 --> 01:09:08,960 +أتحرك على اليمين و بعدين أمسك من ال zero و أتحرك + +736 +01:09:08,960 --> 01:09:13,040 +على الشمال بحيث أغطي كل ال real life طيب بدي أبدأ + +737 +01:09:13,040 --> 01:09:17,560 +من عند ال zero من عند ال zero قدرش بتاخد تلاتة طيب + +738 +01:09:17,560 --> 01:09:23,920 +بعد ال zero إيش بيجيني واحد مربع و تلاتة يبقى من + +739 +01:09:23,920 --> 01:09:29,940 +تلاتة طالع نهوين لاربع لو قلتلك خمسةتربية و تلاتة + +740 +01:09:29,940 --> 01:09:35,620 +ثمانوية و اف طلعين لو قلتلك مية يبقى عشر تلاف و + +741 +01:09:35,620 --> 01:09:39,760 +تلاتة اف طلعين يعني انا بدأت من عند التلاتة وجيت + +742 +01:09:39,760 --> 01:09:45,420 +طالع تمام هذا لو ايش لو اخدت بعد مين بعد ال zero + +743 +01:09:45,420 --> 01:09:51,520 +طب لو جيت قبل ال zero سالب واحد تربية بصير بالموجة + +744 +01:09:51,520 --> 01:09:55,360 +بزاية التلاتة بصير اربعة يبقى انا بنزل رايح جهة + +745 +01:09:55,360 --> 01:10:00,950 +سالب infinity ورغم ذلكالقيم طالع القيم هذه هي ال + +746 +01:10:00,950 --> 01:10:08,110 +range يبقى ال range من ويل لويل من تلاتة تلاتة + +747 +01:10:08,110 --> 01:10:12,130 +موجودة قبل الأربع تلاتة اربع خمسة ستة مية الف + +748 +01:10:12,130 --> 01:10:18,910 +مليون الاخرين يبقى من عند التلاتة لغاية ال + +749 +01:10:18,910 --> 01:10:23,890 +infinityسواه نخدتها السالب و الله موجبة لما تربعها + +750 +01:10:23,890 --> 01:10:28,910 +بيصير موجبة إذا لا يمكن لل range أن ياخد أي قيمة + +751 +01:10:28,910 --> 01:10:32,110 +سالبة ولا حتى واحد ولا اتنين ولا اتنين و نص ولا + +752 +01:10:32,110 --> 01:10:36,210 +اتنين و تسعة من عشرة من تلات .. أقل قيمة بياخدها + +753 +01:10:36,210 --> 01:10:41,030 +ال range ثلاثة و بعدين بيبدأ يطالع واضح هذا الظن؟ + +754 +01:10:41,030 --> 01:10:47,610 +طيب هذه من أبسط أنواع الأمثلةانتجلي شوية يبقى + +755 +01:10:47,610 --> 01:10:53,130 +السؤال بعده لو جينا قولنا نمرة اتنين ال F of X + +756 +01:10:53,130 --> 01:11:00,170 +يساوي جذر X ناقص تلاتة مش + +757 +01:11:00,170 --> 01:11:04,770 +زي التلاتة جذر ال X ناقص تلاتة بدي ال domain من + +758 +01:11:04,770 --> 01:11:11,610 +وين لوين اه استنى شوية سيبك من السلب تلاتة برجع + +759 +01:11:11,610 --> 01:11:17,030 +لجذر ال X هو معرفي وين لوينعمر الجدر معرف لقيمة + +760 +01:11:17,030 --> 01:11:22,990 +سالبة إذا استثنى كل القيم السالبة معرف لل zeroجدر + +761 +01:11:22,990 --> 01:11:27,630 +ال zero جدر ال zero ب zero معرف يبقى من وين لوين + +762 +01:11:27,630 --> 01:11:33,030 +من عند ال zero لغاية ما لا نهاية يبقى من عند ال + +763 +01:11:33,030 --> 01:11:38,750 +zero لغاية مفتوحة و هنا مغلقة لإن عند ال zero + +764 +01:11:38,750 --> 01:11:42,370 +معرفة لكن لو كان عند ال zero مش معرفة بخليها + +765 +01:11:42,370 --> 01:11:48,630 +مفتوحة بالشكل اللي قدامنا هذا تمام إذا هذا هو ال + +766 +01:11:48,630 --> 01:11:52,990 +domain طب دي ال rangeبدي أبدأ أخد من ال domain + +767 +01:11:52,990 --> 01:11:58,900 +معوض هناحط zero بيظل قداش اذا سالب تلاتة في ال + +768 +01:11:58,900 --> 01:12:03,360 +range بدي امشي بعد zero بمشيش قبله انا باخد بس من + +769 +01:12:03,360 --> 01:12:06,300 +الفترة برا الفترة هذه ماليش علاقة ماليش علاقات + +770 +01:12:06,300 --> 01:12:09,600 +فيها قانف يبقى انا بتقيد علاقة بيجي بعدها قداش + +771 +01:12:09,600 --> 01:12:14,280 +واحد يبقى لو أخدت واحد في جدر واحد واحد سالب تلاتة + +772 +01:12:14,280 --> 01:12:18,780 +بيظل سالب اتنين مين اللي اكبر سالب تلاتة ولا سالب + +773 +01:12:18,780 --> 01:12:22,860 +اتنين سالب اتنين اكبر يعني معناه ان انا قاعد باطلع + +774 +01:12:24,320 --> 01:12:29,100 +أنا بطلع فى الدمين و بطلع فى ال rain طب بعد اللى + +775 +01:12:29,100 --> 01:12:36,600 +هو الواحد لو أخدت تسعة بصير تلاتة ناقص تلاتة يساوي + +776 +01:12:36,600 --> 01:12:42,260 +zero سالف تلاتة سالف اتنين سالف واحد zero طيب بدل + +777 +01:12:42,260 --> 01:12:47,960 +التسعة بدي أخد ميةجذر المية بعشرة ناقص تلاتة بسبعة + +778 +01:12:47,960 --> 01:12:52,780 +يبقى من السلب صار نموج وماشيين لو أخدت مثلا مليون + +779 +01:12:52,780 --> 01:12:58,340 +جذر المليون بألف ناقص تلاتة تسعة تسعة سبعة زي + +780 +01:12:58,340 --> 01:13:01,700 +الانتخابات العربية السابقة طبعا مش اللي الحين .. + +781 +01:13:01,700 --> 01:13:05,080 +الحين خلاص بدأوا يمشوا صح او ما رجعوا الانتخابات + +782 +01:13:05,080 --> 01:13:10,100 +مظورة طيب يبقى هنا جداش تسعة تسعة سبعة اخر بدأنا + +783 +01:13:10,100 --> 01:13:16,120 +نطلع هنبقى ماشي إلى ويناذا كم سيكون ال range؟ سالف + +784 +01:13:16,120 --> 01:13:20,900 +تلاتة لغاية infinity يبقى closed من عند السالف + +785 +01:13:20,900 --> 01:13:26,140 +تلاتة لغاية كم؟ لغاية infinity انت قلك شوية كمان + +786 +01:13:26,140 --> 01:13:33,820 +لو جيت الجذري التربيعي تلاتة f of x بيساوي الجذري + +787 +01:13:33,820 --> 01:13:42,010 +التربيعي لتلاتة ناقص x يالا يجب أن يكون صفر صفراه + +788 +01:13:42,010 --> 01:13:47,210 +استنى شوية يعنى هنا اوقف شوية احنا بنلقون الجدر + +789 +01:13:47,210 --> 01:13:52,750 +اللى ليس معرفا الا لقيمة اذا ممنوع لسالبة اما عند + +790 +01:13:52,750 --> 01:13:57,890 +الصفر مرحبا بواهلا وسهلا اذا بدي كل القيمة اللى + +791 +01:13:57,890 --> 01:14:03,750 +تحت الجدر تبقى اكبر من أو تساوي zero باجى فى الهمش + +792 +01:14:03,750 --> 01:14:12,420 +هامش هامش هكو يقول انا بدي تلاتة ناقص ال X تبقى + +793 +01:14:12,420 --> 01:14:16,700 +greater than or equal to zero صحيح؟ بدنا الحل + +794 +01:14:16,700 --> 01:14:23,560 +المتبين هذي بقوله بسيطة اضيف X للطرفين يبقى بيضل + +795 +01:14:23,560 --> 01:14:29,860 +هنا قداشر تلاتة و هنا بصير X صح ولا لا؟هو زمان كنا + +796 +01:14:29,860 --> 01:14:33,020 +بنقول البلدي on كل X على الشجرة التانية احنا + +797 +01:14:33,020 --> 01:14:37,200 +مابنقولش X رياضية مابنقول بنضيف للطرفين اللي هو ال + +798 +01:14:37,200 --> 01:14:42,860 +X اللي عندنا بيصير X ونقص X ب Zero واضفنا X زائد + +799 +01:14:42,860 --> 01:14:48,660 +Zero له ب X يبقى تلاتة أكبر تساوي X أو X أقل من أو + +800 +01:14:48,660 --> 01:14:54,620 +تساوي جداش تلاتة يعني أكبر قيمة بياخدها جداش وبعد + +801 +01:14:54,620 --> 01:14:57,180 +هيك يعني بيصير من وين لوين + +802 +01:15:00,020 --> 01:15:07,520 +بس قوللي بسير من ورا إلى ورا و بعدين بنرجعلك جديش + +803 +01:15:07,520 --> 01:15:13,550 +من ورا؟من سالب infinity لغاية التلاتة اذا بصير هذا + +804 +01:15:13,550 --> 01:15:19,770 +ال domain من سالب infinity لغاية التلاتة closed من + +805 +01:15:19,770 --> 01:15:25,630 +هنا و من هنا open هلحين لو اخدت اي رقم من هنا + +806 +01:15:25,630 --> 01:15:31,510 +بتلاقي هذا الجذر معرف مرة تانية يا شباب مرة تانية + +807 +01:15:31,510 --> 01:15:35,150 +بقول انا بدي كل الكمية اللي تحت اليدر تبقى اكبر من + +808 +01:15:35,150 --> 01:15:37,790 +او تساوي zero هذه + +809 +01:16:02,600 --> 01:16:09,320 +هذا يجعلني أسأل السؤال التالي متى تقلب المتباينةفي + +810 +01:16:09,320 --> 01:16:16,400 +حالتين ثالثة لهم إذا ضربت المتبينة في كمية سالبة + +811 +01:16:16,400 --> 01:16:22,120 +والأمر الثاني إذا قلبت المتبينة بالشرط أن يكون + +812 +01:16:22,120 --> 01:16:26,180 +الإشارتين في الطرفين زي بعض وإلا بصير كلامنا مش + +813 +01:16:26,180 --> 01:16:30,990 +صحيح، مظبوط؟يبقى أنا بقلب المتباينة إذا الطرفين + +814 +01:16:30,990 --> 01:16:37,330 +بنفس الإشارة بقلب الطرفين وفي هذه أو أضرب الطرفين + +815 +01:16:37,330 --> 01:16:42,230 +في قيمة سالبة فتنقلب الأقل من إلى أكبر منه وعكسه + +816 +01:16:42,230 --> 01:16:42,850 +بالعكس + +817 +01:16:47,260 --> 01:16:51,220 +انا مش عرفت ان ال X موجبة، ال U في الساعة، ان اش + +818 +01:16:51,220 --> 01:16:54,680 +ما تكون ال X تكون، موجة و لا ساعة، اضفت للطرفين، + +819 +01:16:54,680 --> 01:17:00,380 +الإضافة، بس رد عليك، الإضافة أو الطرح أو الضرب في + +820 +01:17:00,380 --> 01:17:05,240 +قيمة موجبة لا تغير و بقى ال inequality، نهائي، + +821 +01:17:05,240 --> 01:17:06,740 +بتظل ال inequality كما هي، اه + +822 +01:17:12,430 --> 01:17:16,950 +تانى تانى تانى تانى الصياغة عبّر ..قول أشوف، اعتبر + +823 +01:17:16,950 --> 01:17:24,990 +سؤالك كله غلط وحكي براعتك عادي جدا، ردش عليك تلقية + +824 +01:17:24,990 --> 01:17:25,830 +اللقاء صح + +825 +01:17:29,370 --> 01:17:35,130 +من سالب عشرة الى تلاتة من سالب عشرة الى تلاتة + +826 +01:17:35,130 --> 01:17:39,070 +والله من تلاتة لسالب عشرة دائما من الصغرة بنخليها + +827 +01:17:39,070 --> 01:17:43,310 +في الأول والكبرى بالآخر يبقى هنا من سلب infinity + +828 +01:17:43,310 --> 01:17:49,540 +لغايةلغاية تلاتة تمام؟ هذه الصيغة أو الصيغة هذه + +829 +01:17:49,540 --> 01:17:53,320 +الاتنين are the same هنا X أقل من أوي سوى تلاتة + +830 +01:17:53,320 --> 01:17:56,820 +هنا X أقل من أوي سوى تلاتة لكن كنا بنكتب انجليزي + +831 +01:17:56,820 --> 01:18:00,740 +بقال صح نكتب بالشكل اللي عندنا ده ما عليناطيب + +832 +01:18:00,740 --> 01:18:05,420 +جيبنا ال domain بدنا نروح نجيب main الرين يبقى بده + +833 +01:18:05,420 --> 01:18:11,440 +اشيل ال X و احط مكانها تالتة بيصير قد صفر طيب ارجع + +834 +01:18:11,440 --> 01:18:17,680 +قبل التلاتة لو حطيت X باتنين بيصير تلاتة ناقص + +835 +01:18:17,680 --> 01:18:20,400 +اتنين اللي هو بواحديبقى احد يبقى من اتنين رجعنا + +836 +01:18:20,400 --> 01:18:26,040 +لوين لواحد من صفر طلعنا قصدي لواحد طيب لو جينا + +837 +01:18:26,040 --> 01:18:33,360 +لصفر مضطري قداش جدر تلاتة لو جينا لسالب واحد سالب + +838 +01:18:33,360 --> 01:18:36,960 +سالب واحد بيصير مجبرة تلاتة اربعة يعني قداش يبقى + +839 +01:18:36,960 --> 01:18:41,720 +من الصفر وصلنا لاتنين طيب ارجع كمان لو قلت هنا + +840 +01:18:41,720 --> 01:18:50,260 +سالب ستةبصير موجة ب 6 و 3 9 يبقى 3 طالعين طب لو + +841 +01:18:50,260 --> 01:18:57,800 +قلت لك إن السالب 97 بصير موجة ب 97 و 3 جدر ال 110 + +842 +01:18:57,800 --> 01:19:03,340 +يبقى من صفر و احنا طالعين يبقى كدش يا رياني من + +843 +01:19:03,340 --> 01:19:10,980 +الصفر مافيش سالب عندي نهائي يبقى من عند ال zero + +844 +01:19:10,980 --> 01:19:17,130 +لغاية ال infinityحد يلو يتسول حتى الآن، يعني واضح + +845 +01:19:17,130 --> 01:19:20,870 +هذا، كل مرة بتقل شوية ها في شكل الدلقاء، اه يا + +846 +01:19:20,870 --> 01:19:26,770 +ابني بتحط قسم، بتحط .. مفتوح، مفتوح، مفتوح، مفتوح، + +847 +01:19:26,770 --> 01:19:28,330 +مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، + +848 +01:19:28,330 --> 01:19:28,990 +مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، + +849 +01:19:28,990 --> 01:19:30,370 +مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، مفتوح، + +850 +01:19:30,370 --> 01:19:36,260 +مفتوح، مفتوح، مفتوح، ملا نلجأ إلا مالها إلا مصير + +851 +01:19:36,260 --> 01:19:40,760 +عنها عاجز رياضي يعني إذا قولتك معاك شكل و بيتقسمه + +852 +01:19:40,760 --> 01:19:44,820 +بين اتنين أه بقسمه بعطي كل واحد نص شكل و لو كانوا + +853 +01:19:44,820 --> 01:19:48,900 +عشرة بعطي كل واحد أجورة لكن لما يكون معاك شكل و + +854 +01:19:48,900 --> 01:19:57,060 +عندك صفر من البشر هل يمكن أن تتم هذه العملية مطلوب + +855 +01:19:57,060 --> 01:20:02,920 +إنك توزعهم و إلا بتنطخيبقى العقل البشري خارج + +856 +01:20:02,920 --> 01:20:06,860 +نطاقه، رياضيا بقدرش يعمل العملية هذه فاحنا لما + +857 +01:20:06,860 --> 01:20:10,160 +نتحرك من هذا الشغل هتقول ما لنا، يعني خارج نطاقة + +858 +01:20:10,160 --> 01:20:16,300 +العقل البشري، ماشي؟ اه يا ابن ايه؟ + +859 +01:20:16,300 --> 01:20:23,860 +مانا؟ شوف يا زيد، لما أقول لك قوس هيك، يبقى هذه + +860 +01:20:23,860 --> 01:20:30,130 +closed intervalهذه فترة مغلقة نقول لك لجثين + +861 +01:20:30,130 --> 01:20:35,950 +زعلانين مع بعض واحد موجه هيك والتاني موجه هيك إيش + +862 +01:20:35,950 --> 01:20:41,650 +كنت تقولوا عليها هذه؟ إحنا عندنا هذه تكافئ تماما + +863 +01:20:41,650 --> 01:20:45,550 +جثين صغير موجهات على بعض يبقى هذه فترة .. هذه + +864 +01:20:45,550 --> 01:20:49,470 +بتلاقيهاش في كتابنا لكن بتلاقي هذه .. هذه هي هذه + +865 +01:20:49,470 --> 01:20:54,430 +بالضبط تماماممكن تلاقي من جهة مقفلة ومن جهة تانية + +866 +01:20:54,430 --> 01:20:59,410 +مفتوحة من عند ال infinity أو السالب infinity دائما + +867 +01:20:59,410 --> 01:21:04,010 +و أبدا مطول مغلقة يعني التلاتة من ضمن الفترة + +868 +01:21:04,010 --> 01:21:10,330 +مفتوحة يعني التلاتة ليست من الفترة ماشي ايوة اتفضل + +869 +01:21:10,330 --> 01:21:14,130 +في المثال الثالث اماله + +870 +01:21:18,490 --> 01:21:23,110 +الـ Range من سالب مالة نهائية لصرف يعني كلها بتاخد + +871 +01:21:23,110 --> 01:21:29,430 +قيم سالبة جزدك طيب انا باسألك هل يعني كل القيم + +872 +01:21:29,430 --> 01:21:34,530 +اللي من تحت الجدر بتطلع سالبة مش هي الجزدك؟ بس + +873 +01:21:34,530 --> 01:21:41,030 +هتبطى الهاء الهاء بتامسك من هنا تلاتة نقص تلاتة + +874 +01:21:41,030 --> 01:21:47,890 +نقص نقص تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص + +875 +01:21:47,890 --> 01:21:47,930 +تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص + +876 +01:21:47,930 --> 01:21:48,290 +تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص تلاتة نقص + +877 +01:21:48,290 --> 01:21:50,510 +تلاتة نقص تلاتة نقص تلاتة نيبقى بسيط تلاتة نقصت + +878 +01:21:50,510 --> 01:21:56,190 +هنا بقداش؟ بواحد، يبقى بواحد، بدي أرجع تاني وصلت + +879 +01:21:56,190 --> 01:22:02,470 +الصفر، بصير هنا جزر تلاتة، بدي أرجع قبل الصفر مين؟ + +880 +01:22:02,470 --> 01:22:06,950 +سالب واحد، وقال هنا سالب، بصير موجة بواحد تلاتة + +881 +01:22:07,820 --> 01:22:12,400 +يبقى اتنين من اين تأتي السالب؟ جيبك ارجع كمان سالب + +882 +01:22:12,400 --> 01:22:17,120 +سبعة وتسعين وهنا سالب في الموجة بيبقى سعرات مية من + +883 +01:22:17,120 --> 01:22:21,480 +اين تأتي السالب؟ اذا لا يمكن ان تكون النتيجة سالبة + +884 +01:22:21,480 --> 01:22:26,980 +على الإطلاق دائما الموجة بإيجابية طيب نعطي مثال + +885 +01:22:26,980 --> 01:22:34,440 +اخر لو قلتك نمره اربعة F of X يساوي الجدر التربيه + +886 +01:22:34,440 --> 01:22:41,170 +للست عشر ناقص X تربيهأصلا هادى زى هادى بس هادى X + +887 +01:22:41,170 --> 01:22:46,490 +هادى X تربية لكن تعالى شوف ماهى الفوارق الشاسعة + +888 +01:22:46,490 --> 01:22:52,750 +بين السؤالين بدي أمشي زى ما مشيت هنا هاي في الهامش + +889 +01:22:52,750 --> 01:22:58,850 +هاي ال 16 ناقص X تربية بديها تبقى أكبر من أو تساوي + +890 +01:22:58,850 --> 01:23:04,380 +Zero مظبوط هيك؟يبقى هنا لو أضفنا X تربية للطرفين + +891 +01:23:04,380 --> 01:23:11,620 +بيصير 16 أكبر من أو تساوي X تربية لو قعدت صياغتها + +892 +01:23:11,620 --> 01:23:19,980 +يبقى X تربية أقل من أو تساوي 16 مظبوط انا مابدي X + +893 +01:23:19,980 --> 01:23:26,400 +تربية بدي X شو بعمل باخد الجذر التربيهي للطرفين + +894 +01:23:26,400 --> 01:23:33,080 +الجذر التربيهي ل X تربية هو كدهabsolute value of x + +895 +01:23:33,080 --> 01:23:40,260 +دي بالك تمام أقل من أو يساوي جدر التربيه على ال 16 + +896 +01:23:40,260 --> 01:23:46,390 +و 4 خدها قاعدة دائما و أبدا ايه بكتبها لكالجذر + +897 +01:23:46,390 --> 01:23:50,290 +التربية إلى x تربية دائما و أبدا هي absolute value + +898 +01:23:50,290 --> 01:23:56,610 +لزادة أو ناقص x لأن مربع ال x بx تربية و مربع ناقص + +899 +01:23:56,610 --> 01:24:01,510 +x برضه بx تربية إذا زادة أو ناقص هي absolute value + +900 +01:24:01,510 --> 01:24:08,890 +إذا صار absolute value ل x أقل من أو تساوي 4طباش + +901 +01:24:08,890 --> 01:24:14,210 +معناها رياضيا كذلك معناها هذه لو بدى فك ال + +902 +01:24:14,210 --> 01:24:21,170 +absolute ان ال X هذه اما اقل من او يساوي اربعة او + +903 +01:24:21,170 --> 01:24:26,870 +اكبر من او يساوي جداشيبقى من وين لوين من سالب + +904 +01:24:26,870 --> 01:24:32,850 +أربعة لأربعة فقط لغير شايف هذه قداش كانت وهذه قداش + +905 +01:24:32,850 --> 01:24:39,370 +صارت يبقى من سالب أربعة إلى أربعة as any closed + +906 +01:24:39,370 --> 01:24:45,890 +interval لو مافيش يساوي هنا بكتبها فترة مفتوحة لكن + +907 +01:24:45,890 --> 01:24:50,690 +نظرا لإنه فيه يساوي بروح بكتبها فترة مغلقة أو + +908 +01:24:50,690 --> 01:24:56,900 +closed intervalهذا هو ال domain الان بناجي لل + +909 +01:24:56,900 --> 01:25:05,960 +range طيب بده احط هنا سالب اربعة مربعها موجب ستة + +910 +01:25:05,960 --> 01:25:10,240 +عشر بسرعة ستة عشر نقص ستة عشر يساوي Zero لو حطيت + +911 +01:25:10,240 --> 01:25:14,560 +الاربعة هذه تانية بصير كمان قداش Zero يعني ال + +912 +01:25:14,560 --> 01:25:21,790 +range يساوي Zeroلأ مش صحيح شوف يا سيدى ان جيت على + +913 +01:25:21,790 --> 01:25:26,290 +الفترة و لجيت القيمة الأولى و القيمة الأخيرة عطتني + +914 +01:25:26,290 --> 01:25:31,610 +نفس النتيجة بتروح على نص ال interval من الرقم اللى + +915 +01:25:31,610 --> 01:25:36,490 +فى نص ال interval اللى هو ال zero حط x ب zero بصير + +916 +01:25:36,490 --> 01:25:42,950 +جدر سطحش اللى و جداش يبقى من zero لغاية أربعة فقط + +917 +01:25:42,950 --> 01:25:48,760 +لا غيريبقى النتيجة من عند ال zero لغاية أربعة as + +918 +01:25:48,760 --> 01:25:54,760 +any closed interval هلحين أي رقم أخر ييجي في بالك + +919 +01:25:54,760 --> 01:25:59,780 +في هذا الفترة عوضه بدي يطلع هنا سواء كان كثري ولا + +920 +01:25:59,780 --> 01:26:03,180 +مش كثري تستخدم ال calculator ما تستخدم كله بدي + +921 +01:26:03,180 --> 01:26:11,320 +يطلع موجود هنا طيب ايه المثال الخامسالمثال الخامس + +922 +01:26:11,320 --> 01:26:20,700 +انتقل شوية ب the f of x يسوى مية على x ناقص ثلاثة + +923 +01:26:20,700 --> 01:26:28,220 +x ناقص ثلاثة يالا شوف مالها؟ + +924 +01:26:28,220 --> 01:26:34,220 +كدهش لما تحط x سالب أربع كدهش بتطلع النتيجة؟و لما + +925 +01:26:34,220 --> 01:26:39,480 +تحطها باربع صفر لما نتيجة عن نص ال interval اللي + +926 +01:26:39,480 --> 01:26:45,000 +هو قداش صفر قداش بطلع جدر الستاش اللي هو قداش اذا + +927 +01:26:45,000 --> 01:26:48,840 +من صفر لاربع اي رقم يجي في بالك من سالب اربع لاربع + +928 +01:26:48,840 --> 01:26:53,320 +بتجي محصور النتيجة تبعته من صفر لغاية اربع ايوا + +929 +01:26:58,260 --> 01:27:06,660 +النتيجة الطرف الأول نفس النتيجة بروح نص الفترة طيب + +930 +01:27:06,660 --> 01:27:15,240 +الان عندنا سؤال تاني مية على اكس ناقص تلاتة ماعدد + +931 +01:27:15,240 --> 01:27:20,870 +تلاتة يعني كل real number ماعدد تلاتةيبقى يا بقوله + +932 +01:27:20,870 --> 01:27:28,370 +R ناقص التلاتة و بحطها as a ستة بشكل مش تلاتة + +933 +01:27:28,370 --> 01:27:32,030 +لحالة في الخلة تلاتة معناه تعنصر بس تلاتة بين + +934 +01:27:32,030 --> 01:27:37,850 +قوسين عبارة عن ستة مطروحة منها ستة أخرى أو بقدر + +935 +01:27:37,850 --> 01:27:43,670 +أقوله هذه من سالب infinity لغاية التلاتة اتحاد + +936 +01:27:43,670 --> 01:27:51,500 +تلاتة و infinity الشكل اللي عندناطيب يالا هذا هو + +937 +01:27:51,500 --> 01:28:00,120 +ال domain بده ال range ال range ايش يعني يعني مالة + +938 +01:28:00,120 --> 01:28:05,220 +نهاية عنصر يعني يالا + +939 +01:28:05,220 --> 01:28:09,580 +يعطوني فكر ويعطيني نتيجة انا بدي طبعا هناقشك فيها + +940 +01:28:09,580 --> 01:28:15,520 +بس يعطيني نتيجة ايوة يعني + +941 +01:28:15,520 --> 01:28:20,100 +ارشيلك على حال ماعدد التلاتة ولا ماعدد السفارةمعدى + +942 +01:28:20,100 --> 01:28:24,040 +التلاتة و بعدين انت و اياه لما يجيك الدور بتجاوز + +943 +01:28:24,040 --> 01:28:28,360 +بشان نستفيد كله يصغل لرجل اللي بيجاوز يمكن بيجاوب + +944 +01:28:28,360 --> 01:28:32,060 +صحي و يمكن بيجاوب غلط معدى التلاتة معدى التلاتة + +945 +01:28:32,060 --> 01:28:34,900 +يعني كل ال real life معدى التلاتة في نفس الدور + +946 +01:28:34,900 --> 01:28:39,940 +يعني او كما قال يعني اوش اتنس بسبب ادران اصلا مش + +947 +01:28:39,940 --> 01:28:44,440 +من الدور يعني انا مش مصدر دران مافيش x4 انا اناقش + +948 +01:28:44,440 --> 01:28:52,590 +تلاتة او ستةعيد الصقر تاني يعني + +949 +01:28:52,590 --> 01:28:56,850 +كفترة و لا كرقامين؟ اه يعني من الريال الله يمكنك + +950 +01:28:56,850 --> 01:29:00,970 +تشيله التلاتة و تشيله الزفر و هي وجهة نظر أخرى، هل + +951 +01:29:00,970 --> 01:29:06,030 +صار عني وجهتين نظر، في غيرهم؟ أيوة تاني من النهاية + +952 +01:29:06,030 --> 01:29:12,480 +إلى تلات مفتوح اتحادالثلاثة مفتوحة لأمالها. أو كما + +953 +01:29:12,480 --> 01:29:16,260 +قال يعني. ما جبتش جديد. بدنا .. فيه جديد؟ والله + +954 +01:29:16,260 --> 01:29:20,580 +مافيش. أيوة. جميع الأعداد الحقيقية بين ما فيها + +955 +01:29:20,580 --> 01:29:24,980 +التلاتة اللي بيقول عليها. واي. هاي كمان إجابة غير + +956 +01:29:24,980 --> 01:29:30,300 +شكلة أو جرت شكلة. كمان زي نجمتهم. أه. ال domain هو + +957 +01:29:30,300 --> 01:29:30,980 +ايش؟ + +958 +01:29:33,450 --> 01:29:40,310 +يعني زي ما قالوا في جديد و لا فيش جديد يعني + +959 +01:29:40,310 --> 01:29:46,610 +سحبت التلاتة هذه هذه فقط الإجابة الصحيحة كل اللي + +960 +01:29:46,610 --> 01:29:53,230 +فات كله خطأ يبقى هذه من سالب infinity لغاية ال + +961 +01:29:53,230 --> 01:29:59,870 +zero اتحاد zero و infinity أو إن شئت فقول كل ال R + +962 +01:29:59,870 --> 01:30:01,890 +بدي أشيل منها ال zero + +963 +01:30:04,770 --> 01:30:11,050 +طيب، ثانى شوية بس، ثانى شوية، من أين لك هذا؟ اذا + +964 +01:30:11,050 --> 01:30:15,210 +نفهم، من وين هذا يا عزيزي؟ طلعلي كويس انت و ايه، + +965 +01:30:15,210 --> 01:30:21,730 +هذا ال real life و هذا الرقم ثلاثة، ثلاثة ليس من + +966 +01:30:21,730 --> 01:30:26,470 +ال domain يبقى بعد الثلاثة كله من ال domain و قبل + +967 +01:30:26,470 --> 01:30:31,950 +الثلاثة كله من ال domain تعالى نشوف كيف بدنا .. + +968 +01:30:31,980 --> 01:30:37,900 +اعرفنا هذه تمام؟ انا بديش نقعد انحذر بدي افهمكيا + +969 +01:30:37,900 --> 01:30:41,680 +step by step بدي اتحرك على يمين التلاتة و بعدين + +970 +01:30:41,680 --> 01:30:46,000 +اتحرك على شمال التلاتة اشوف ايش بتجيبلي لو اتحركت + +971 +01:30:46,000 --> 01:30:49,820 +على يمين التلاتة بصير ايش بيجيبلك؟ مثلا اربع بصير + +972 +01:30:49,820 --> 01:30:55,970 +اربع ناقص تلاتة بواحد يبقى الجواب قداش مية طيبجبت + +973 +01:30:55,970 --> 01:31:01,770 +خمسة خمسة نقص تلاتة اتنين مية على اتنين صار خمسين + +974 +01:31:01,770 --> 01:31:08,290 +يبقى نزلت من مية نزلت لوين لخمسين طيب ها بدي امشي + +975 +01:31:08,290 --> 01:31:13,610 +بعد التلاتة انا مشيت اربع ومشيت خمسة وقول مشيت يا + +976 +01:31:13,610 --> 01:31:20,350 +سيدي مية و تلاتة مية و تلاتة نقص تلاتة كده؟ مية + +977 +01:31:20,350 --> 01:31:26,820 +على مية يعني من مية نزلت للواحدطيب امشي كمان امشي + +978 +01:31:26,820 --> 01:31:32,700 +وقاس director وصلت هنا الف و تلاتة ناقص تلاتة، + +979 +01:31:32,700 --> 01:31:38,120 +الف، مية على الف في قدام، عشر، ضال عندي عشرة في + +980 +01:31:38,120 --> 01:31:42,360 +المقام، صحيح ولا لأ؟ يبقى من مين نزلت لعشر، طب + +981 +01:31:42,360 --> 01:31:47,460 +امشي مليون و تلاتة، شيل منهم تلاتة، المليون صار + +982 +01:31:47,460 --> 01:31:52,850 +مية مليونمية على مليون و واحد على عشرة آلاف يعني + +983 +01:31:52,850 --> 01:31:57,210 +القسر قاعد بينخسر كل ما انا طاير لقدام كل ما القسر + +984 +01:31:57,210 --> 01:32:02,170 +نازل على وين؟ على السفر يعني انا لو وصلت لمالة + +985 +01:32:02,170 --> 01:32:06,490 +نهاية ده سمح الله طبعا ولا واحد بقدر يوصل يبقى مية + +986 +01:32:06,490 --> 01:32:11,430 +على مالة نهاية في جدشأى عدد على مالة نهاية بيعطيك + +987 +01:32:11,430 --> 01:32:16,650 +ال zero تمام يبقى انا كل مناطير اللى قدام هذا نازل + +988 +01:32:16,650 --> 01:32:21,850 +لوين نازل لل zero انا موصلش لمالة نهاية اذا لا + +989 +01:32:21,850 --> 01:32:25,970 +يمكن اوصل لل zero يبقى روحنا خليناها مفتوحة من + +990 +01:32:25,970 --> 01:32:31,930 +zero لوين للمالة نهاية هذا لو مشيت باش بارقام + +991 +01:32:31,930 --> 01:32:36,180 +موجبةمن التلاتة فاهمه طيب بده اجي قابل التلاتة + +992 +01:32:36,180 --> 01:32:41,600 +قابل التلاتة زي مين؟ زي اتنين يبقى اتنين ناقص + +993 +01:32:41,600 --> 01:32:49,480 +تلاتة سالب واحد يعني سالب مية تمام طيب سالب مية لو + +994 +01:32:49,480 --> 01:32:54,340 +جيت اخف واحد بدل اتنين بيصير واحد ناقص تلاتة بناقص + +995 +01:32:54,340 --> 01:33:00,340 +اتنين يبقى ناقص خمسين يبقى من سالب مية طالع لسالب + +996 +01:33:00,340 --> 01:33:05,880 +خمسين مظبوط ولا لا؟طيب لو جيتلي قبلها جيتلي ال + +997 +01:33:05,880 --> 01:33:10,540 +zero بيظل مية سالب تلاتة بتلاتة و تلاتين و تلت بس + +998 +01:33:10,540 --> 01:33:15,460 +بالسالب يبقى طالع و هكذا كله لغاية ما وصل ال goal + +999 +01:33:15,460 --> 01:33:20,620 +مثلا هنا سالب سبعة وتسعين سالب تسمى سبعة وتسعين و + +1000 +01:33:20,620 --> 01:33:27,260 +سالب تلاتة سالب جداش مية يبقى هذا كله جداش بسالب + +1001 +01:33:27,260 --> 01:33:32,550 +واحد يبقى من سالب مية طالع انا وصلت لسالب واحديبقى + +1002 +01:33:32,550 --> 01:33:39,090 +كل ما غلط و هكذا وصلت ل-997 + +1003 +01:33:39,090 --> 01:33:47,290 +زي الانتخابات العربية 799 سالب تلاتة بصير سالب ألف + +1004 +01:33:47,290 --> 01:33:52,860 +يبقى صار عندي السالب عشرمظبوط ولا لا؟ انا طالع + +1005 +01:33:52,860 --> 01:33:56,280 +سالب مش عارف اش .. سالب مش عارف اش .. سالب .. طيب + +1006 +01:33:56,280 --> 01:34:00,660 +طالع لوين؟ سالب عشر؟ سالب واحد على مية؟ سالب واحد + +1007 +01:34:00,660 --> 01:34:07,050 +على الف؟ سالب واحد على مليون؟ يعني لوين رايح؟لزيرو + +1008 +01:34:07,050 --> 01:34:12,950 +لزيرو رايح مش طالع انا طالع لكن كلها بسالب مش قادر + +1009 +01:34:12,950 --> 01:34:17,150 +اوصل للموجب يبقى كله رايح لوين رايح على ال zero + +1010 +01:34:17,150 --> 01:34:21,930 +طيب هذا لو اخدت ارقام طب بده جرب على التلاتة من + +1011 +01:34:21,930 --> 01:34:26,610 +الناحيتين لو جيت قولتلك اني بده اجرب على تلاتة + +1012 +01:34:26,610 --> 01:34:31,910 +واحد من عشرةيبقى تلاتة و واحد من عشرة ناقص تلاتة + +1013 +01:34:31,910 --> 01:34:35,770 +يبقى واحد من عشر يعني عشر العشرة بتنقل فوق بصير + +1014 +01:34:35,770 --> 01:34:40,050 +المية قداش ألف كل ما أجرب على التلاتة باجهها دي + +1015 +01:34:40,050 --> 01:34:44,690 +الشفقة تترايح لوين للمالة نفسها مثلا لو جيت قولتك + +1016 +01:34:44,690 --> 01:34:52,030 +X ابتلاتة و واحد من ألف تلاتة و واحد من ألف ناقص + +1017 +01:34:52,030 --> 01:34:55,110 +تلاتة بيبقى واحد من ألف يعني واحدة على ألف بصير + +1018 +01:34:55,110 --> 01:34:58,970 +مية ألفكل ما اجرب على تلاتة بيلاقيها شخطة لوين + +1019 +01:34:58,970 --> 01:35:02,890 +للمال انها وكل مابعد عن التلاتة بيلاقيها نزل لوين + +1020 +01:35:02,890 --> 01:35:07,410 +لزيرو طب تعا أسحبها من الناحية التانية بدي أبدأ + +1021 +01:35:07,410 --> 01:35:12,210 +أجرب على مين على التلاتة من جهة الشمال أنا جربتها + +1022 +01:35:12,210 --> 01:35:16,640 +في الأول من جهة اليمينبدي اقول اتنين وتسعة من عشرة + +1023 +01:35:16,640 --> 01:35:22,020 +موجة اتنين وتسعة من عشرة نقص تلاتة بظهر سالب او شر + +1024 +01:35:22,020 --> 01:35:28,100 +يعني بصير سالب الف مصغور كل ما اجرب اتلاقي هنزلت + +1025 +01:35:28,100 --> 01:35:35,520 +اكتر يعني لو كان الفرق بينها وبين التلاتةاللي هو + +1026 +01:35:35,520 --> 01:35:42,060 +سالب واحد من مية بصير سالب عشرة آلاف الفرق بينه + +1027 +01:35:42,060 --> 01:35:47,200 +وبينها سالب واحد على الف يبقى سالب ميت ألف يبقى + +1028 +01:35:47,200 --> 01:35:51,640 +نازل لوين لسه يعني إذا اتحركت جربت للتلاتة من جهة + +1029 +01:35:51,640 --> 01:35:55,980 +اليمين بلاقي طاير لما لنهايةجربت ليه تلاتة من جهة + +1030 +01:35:55,980 --> 01:35:59,920 +الشمال بلاقي حالي رايح لوين لسلب infinity ابعت عني + +1031 +01:35:59,920 --> 01:36:03,820 +التلاتة بلاقي حالي نازل لل zero جربت على التلاتة + +1032 +01:36:03,820 --> 01:36:07,120 +.. ابعت عني التلاتة من الناحية التانية بلاقي حالي + +1033 +01:36:07,120 --> 01:36:12,040 +رايح لل zero كذلك إذا من zero إلى infinity و من + +1034 +01:36:12,040 --> 01:36:16,020 +سلب infinity إلى من؟ إلى ال zero هذه الإجابة + +1035 +01:36:16,020 --> 01:36:21,620 +الأخيرة اللي قالها صاحبي شو اسمك أنت؟ شامي + +1036 +01:36:23,160 --> 01:36:27,340 +اللي بين الوالد إيش يعني؟ من السنة أن يذكر الرجل + +1037 +01:36:27,340 --> 01:36:32,820 +اسم بيه عند التعارف لأن هذا يعتبر صلة رحم فإن + +1038 +01:36:32,820 --> 01:36:37,520 +تنويت ذلك تؤجر علي اسمه هشام إسماعيل ياغي هو الذي + +1039 +01:36:37,520 --> 01:36:42,040 +أعطانا الإجابة آه الصحيحة طبعا حتى الآن نكتفي + +1040 +01:36:42,040 --> 01:36:44,180 +واخدنا أكثر من وقتنا + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc.srt new file mode 100644 index 0000000000000000000000000000000000000000..682b99217da80de34ab3ce99b3b037dcbf0da194 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc.srt @@ -0,0 +1,3582 @@ +1 +00:00:21,020 --> 00:00:25,220 +بسم الله الرحمن الرحيم نواصل الآن ما ابتدأنا به + +2 +00:00:25,220 --> 00:00:30,160 +المحاضرة الماضية بدأنا بأول مثال + +3 +00:00:30,160 --> 00:00:34,740 +على الـ function أعطيناكوا صيغ مختلفة لـ functions + +4 +00:00:34,740 --> 00:00:39,140 +مختلفة و طلبنا الـ domain والـ range والآن بنواصل + +5 +00:00:39,140 --> 00:00:42,950 +في نفس الموضوع المثال كان معناه المرة اللي فاتت + +6 +00:00:42,950 --> 00:00:45,210 +find the domain and range of the following + +7 +00:00:45,210 --> 00:00:51,050 +functions بدنا المجال والمدى لكل من الدوال التالية + +8 +00:00:51,050 --> 00:00:57,130 +دالة رقم ستة F of X يساوي X زائد absolute value لـ + +9 +00:00:57,130 --> 00:01:00,990 +X ذكرنا المرة الماضية أن الـ domain تبع الدالة هو + +10 +00:01:00,990 --> 00:01:07,550 +القيم التي تأخذها X حتى تكون الدالة معرفة سؤالنا + +11 +00:01:07,550 --> 00:01:13,380 +هو هل هناك قيمة لـ X بتجعل F of X ماهياش معرفة هنا + +12 +00:01:13,380 --> 00:01:19,140 +على الـ real line يعني لو أخدنا أي real number أي + +13 +00:01:19,140 --> 00:01:24,160 +عدد حقيقي وعوضنا به هنا بتطلع لا معرفة ولا لا + +14 +00:01:24,160 --> 00:01:28,120 +معرفة مادام معرفة إذا الـ domain تبقى الدالة من وين + +15 +00:01:28,120 --> 00:01:33,880 +لوين؟ كل الـ R أو من سالب infinity إلى infinity كتبت + +16 +00:01:33,880 --> 00:01:38,920 +R ماشي الحال of real numbers كتبتلي من سالب + +17 +00:01:38,920 --> 00:01:43,060 +infinity لـ infinity معناه مشكلة هذه الصيغة وهذه + +18 +00:01:43,060 --> 00:01:47,700 +الصيغة الاتنين are the same طيب هذا الـ domain بدنا + +19 +00:01:47,700 --> 00:01:52,560 +الـ range المرة الماضية ذكرنا أنه الـ range بدي أخد + +20 +00:01:52,560 --> 00:01:56,080 +من الـ domain و أعوض في الدالة القيم اللي بتطلع + +21 +00:01:56,080 --> 00:02:00,640 +بتكون هي الـ range تبع هذه الدالة يبقى بنفضل نبدأ + +22 +00:02:00,640 --> 00:02:04,280 +من عند zero نتحرك على اليمين ثم نبدأ من عند zero + +23 +00:02:04,280 --> 00:02:08,960 +نتحرك اللي بيطلع عنا بيكون هو الـ real number فلو + +24 +00:02:08,960 --> 00:02:15,340 +أخدت X بـ Zero يبقى الناتج كده؟ Zero يبقى Zero من + +25 +00:02:15,340 --> 00:02:21,920 +ضمن الـ range اتحرك على اليمين خدلي واحد مثلا اثنين، طب + +26 +00:02:21,920 --> 00:02:30,590 +خدلي ثلاثة ونص، سبع، تمام، خدلي مئة، ميتين، ألف، ألفين، + +27 +00:02:30,590 --> 00:02:34,490 +مليون، اثنين، إيه؟ يبقى رايحين لوين؟ للمالا نهاية + +28 +00:02:34,490 --> 00:02:40,570 +فبنمشي العكس بالسالب لو أخدنا سالب واحد سالب واحد + +29 +00:02:40,570 --> 00:02:45,270 +زائد absolute value لسالب واحد absolute value لسالب + +30 +00:02:45,270 --> 00:02:50,410 +واحد، واحد، وفيه قبل سالب واحد؟ Zero طيب + +31 +00:02:50,410 --> 00:02:57,750 +absolute value لسالب مئة، مية وسالب مية، إذا كل + +32 +00:02:57,750 --> 00:03:02,550 +القيم السالبة، الـ range تبعها مين؟ يعني أنا عندي + +33 +00:03:02,550 --> 00:03:08,750 +من سالب infinity لغاية قبل zero، كل النتيجة + +34 +00:03:08,750 --> 00:03:13,250 +بتعطيني zero، حتى عند الـ zero بـ zero، تمام؟ إذا الـ + +35 +00:03:13,250 --> 00:03:18,110 +range لكل القيم السالبة، يعني كل القيم السالبة لها + +36 +00:03:18,110 --> 00:03:24,040 +صورة واحدة فقط، وهلّكن اللي بعدها الله يسهل عليها + +37 +00:03:24,040 --> 00:03:27,480 +رايحة لمالها نهائيا، إذا من وين لوين؟ من Zero + +38 +00:03:27,480 --> 00:03:31,440 +لغاية النهائي. Closed من عند الـ Zero هي Infinity + +39 +00:03:31,440 --> 00:03:41,340 +Open من عند المالها نهائيا. السؤال السابع F of X + +40 +00:03:41,340 --> 00:03:46,740 +يساوي الجذر التربيعي لـ X تربيع ناقص 3X + +41 +00:03:49,480 --> 00:03:54,460 +خلاص، بدأ أدور على الـ domain، الآن بتنعلمك طريقة + +42 +00:03:54,460 --> 00:04:00,420 +سهلة وميسورة بحيث تجيب اللي هو المنطقة المعرفة + +43 +00:04:00,420 --> 00:04:05,340 +الدال عليها بدون أي مشاكل، خلي بالك معايا هنا هل + +44 +00:04:05,340 --> 00:04:10,580 +الجذر معرف لقيمة السالبة؟ لأ، يبقى الجذر مش معرف + +45 +00:04:10,580 --> 00:04:16,700 +إلا لقيمة، إذا بدي كل القيمة اللي تحت الجذر تبقى + +46 +00:04:16,700 --> 00:04:21,680 +أكبر من أو تساوي Zero، يقول خليني نشتغل في الهامش، + +47 +00:04:21,680 --> 00:04:26,560 +يبقى أنا بدي X تربيع ناقص ثلاثة X greater than or + +48 +00:04:26,560 --> 00:04:33,190 +equal to zero أو بمعنى آخر لو أخدت X عامل مشترك بظل + +49 +00:04:33,190 --> 00:04:38,060 +X ناقص ثلاثة greater than or equal to zero مظبوط + +50 +00:04:38,060 --> 00:04:43,720 +هكذا؟ طيب، الآن نعلمك الطريقة كيف بدي أجيب على الـ + +51 +00:04:43,720 --> 00:04:49,880 +real line الأعداد التي تحقق هذه الـ inequality يعني + +52 +00:04:49,880 --> 00:04:54,620 +ما هي الأعداد الحقيقية التي تحقق هذه المتباينة يبقى + +53 +00:04:54,620 --> 00:05:00,780 +هنا بدي أقول بدي أخد إشارة الـ X الأولانية لحالة و + +54 +00:05:00,780 --> 00:05:06,410 +برسم الـ real line الـ X هذه بتاخد الـ 0 تبعها وين؟ + +55 +00:05:06,410 --> 00:05:10,450 +عند الـ 0، لو جيت بعد الـ 0، الـ X موجبة ولا + +56 +00:05:10,450 --> 00:05:16,310 +سالبة، يبقى لا تأخذ إلا قيما موجبة بعد مين؟ بعد + +57 +00:05:16,310 --> 00:05:22,040 +الـ 0، لو رجعت قبل الـ 0 بتاخد كلها قيم سالبة بعد + +58 +00:05:22,040 --> 00:05:28,100 +هيك بدنا نيجي ناخد إشارة sign X minus three يعني + +59 +00:05:28,100 --> 00:05:32,760 +إشارة X نقص ثلاثة بياخد القيمة الصفر عند X + +60 +00:05:32,760 --> 00:05:36,640 +تساوي ثلاثة وبتيجي على يمين الـ zero يعني + +61 +00:05:36,640 --> 00:05:42,400 +الثلاثة هتجي هنا، إذا بعد الثلاثة زي أربعة، الجث + +62 +00:05:42,400 --> 00:05:46,850 +بيكون مالها أربعة وخمسة وستة ومية وكذا يبقى كله + +63 +00:05:46,850 --> 00:05:50,650 +positive زي ما أنت شايف، لو جيت قبل الثلاثة زي + +64 +00:05:50,650 --> 00:05:55,930 +اثنين وواحد وزيرو وسالب خمسة وسالب مية وكله قيم + +65 +00:05:55,930 --> 00:06:01,690 +مالها؟ سالبة، يبقى كله قبلها قيم سالبة، أنا ما بدء + +66 +00:06:01,690 --> 00:06:05,770 +أشارة كل واحد لحالة، بدأ إشارة اثنين مضربين في بعض + +67 +00:06:05,770 --> 00:06:11,750 +ضرب إذا بروح بقوله بدي أخد إشارة X مضروبة في الـ X + +68 +00:06:11,750 --> 00:06:16,350 +minus three و أقول له هي الـ real line وهذه الحدود + +69 +00:06:16,350 --> 00:06:22,170 +الإقليمية هذا zero وهذا ثلاثة اثنين هذول مضربين في + +70 +00:06:22,170 --> 00:06:25,870 +بعض يبقى بدي أضرب الإشارات في بعض موجب في موجب + +71 +00:06:25,870 --> 00:06:32,430 +موجب، موجب في سالب سالب، سالب في سالب موجب ممتاز جدا + +72 +00:06:32,970 --> 00:06:38,890 +هي فسرنا حاصل الضرب للمقدار يوم ما يكون موجب ويوم + +73 +00:06:38,890 --> 00:06:43,790 +ما يكون سالب برجع للمتباينة الأصلية اللي عندها بدي + +74 +00:06:43,790 --> 00:06:48,790 +حاصل الضرب يكون مالها؟ أكبر من أو يساوي زيرو يعني يا + +75 +00:06:48,790 --> 00:06:52,850 +زيرو يا إما قيمة موجب، طلع وين القيم الموجب، + +76 +00:06:52,850 --> 00:06:56,830 +اللي هي المنطقة هذه والمنطقة هذه، إذا الجواب هو من + +77 +00:06:56,830 --> 00:07:02,790 +سالب infinity لغاية الـ zero وكذلك من ثلاثة لغاية + +78 +00:07:02,790 --> 00:07:07,770 +infinity إذا الـ domain بيصير عندنا من سالب infinity + +79 +00:07:07,770 --> 00:07:12,810 +لغاية الـ zero طبعا من عند الـ zero مغلقة بسبب + +80 +00:07:12,810 --> 00:07:19,590 +اليساوي اتحاد ثلاثة و infinity كتبنا الفترة مغلقة + +81 +00:07:19,590 --> 00:07:25,330 +من عند الـ zero والثلاثة بسبب اليساوي، لو ما عنديش + +82 +00:07:25,330 --> 00:07:30,450 +يساوي بكتب هذه إيه؟ open، بكتب الفترة هذه فترة + +83 +00:07:30,450 --> 00:07:35,790 +إيه؟ مفتوحة طيب احنا الآن كل اللي عملناه حسبنا من + +84 +00:07:35,790 --> 00:07:42,390 +أين؟ حسبنا الـ interval اللي دالة معرف عليها يعني + +85 +00:07:42,390 --> 00:07:47,470 +استبعدنا الفترة من أين لوين؟ من زيرو لثلاثة طيب + +86 +00:07:47,470 --> 00:07:52,270 +يعني لو أخدت رقم من زيرو لثلاثة بحق لك في الـ link ولا + +87 +00:07:52,270 --> 00:07:57,170 +لا تهادي نقولك الله جرب خد الرقم اللي يعجبك كداش + +88 +00:07:57,170 --> 00:08:01,670 +يعني من زيرو لثلاثة اثنين مثلا يبقى لو جات لليه + +89 +00:08:01,670 --> 00:08:06,750 +اثنين، اثنين تربيع ناقص ثلاثة في اثنين فظل سالب واحد في + +90 +00:08:06,750 --> 00:08:10,430 +اثنين سالب اثنين هل السالب اثنين أكبر من الـ zero + +91 +00:08:10,890 --> 00:08:14,490 +يبقى لا يمكن يبقى لا اثنين ولا الواحد ولا واحد و + +92 +00:08:14,490 --> 00:08:18,370 +نص ولا الواحد وثلث ربع ولا واحد كل هذه الأرقام + +93 +00:08:18,370 --> 00:08:21,910 +لا تحقق الـ inequality قبل الـ zero جاهزين بعد الـ + +94 +00:08:21,910 --> 00:08:26,570 +zero مجول برضه، طب خلي قبل الـ zero خلي أي رقم سالب + +95 +00:08:27,210 --> 00:08:32,310 +ناخد ناقص اثنين اللي قلت عليه هذا ناقص اثنين أي + +96 +00:08:32,310 --> 00:08:37,530 +ناقص اثنين تربيع ناقص ثلاثة في ناقص خمسة، ناقص خمسة وهنا + +97 +00:08:37,530 --> 00:08:42,890 +ناقص اثنين، زي عشرة أكبر من زيرو هذا لو أخدت سالم طب + +98 +00:08:42,890 --> 00:08:49,800 +لو أخدت موجب اي رقم كود اللي هو الأربعة ففاجئي بقوله + +99 +00:08:49,800 --> 00:08:53,760 +أربعة تربيع وأربعة ناقص ثلاثة اللي هو واحد فيه أربعة بأربعة + +100 +00:08:53,760 --> 00:08:57,840 +أكبر من الـ zero إذا كلامنا صحيح يبقى بناء عليها + +101 +00:08:57,840 --> 00:09:01,920 +إذا بعدنا فقط الفترة من zero لغاية ثلاثة هذا الـ + +102 +00:09:01,920 --> 00:09:05,510 +domain بدنا الـ range الـ Range بدك تروح تأخذ من + +103 +00:09:05,510 --> 00:09:09,530 +الفترة اللي عندك هذه وتعوض في الدالة وتشوف إيش + +104 +00:09:09,530 --> 00:09:12,910 +اللي بيطلع يلا أشوف مين الشاطرة فيك واللي حسبها + +105 +00:09:12,910 --> 00:09:18,770 +دوري هيك يعطيني إجابة أيوة من صفر لـ Infinity من + +106 +00:09:18,770 --> 00:09:22,950 +Zero لغاية Infinity مفتوحة أو هنا مغلقة ولا + +107 +00:09:22,950 --> 00:09:31,920 +مفتوحة؟ مغلقة، تمشي اسمك أنت عبدالهاد إيش؟ عبدالهاد + +108 +00:09:31,920 --> 00:09:38,160 +أزميلي، عبدالهاد أزميلي هذا من الرفع شجعية + +109 +00:09:38,160 --> 00:09:44,940 +من الدرج طب كويس هي عبدالهاد أزميلي من منطقة الدرج + +110 +00:09:44,940 --> 00:09:49,400 +الدرج وأعطانا إجابة صحيحة تمام؟ يعني الدرج في + +111 +00:09:49,400 --> 00:09:53,260 +الطريق الصحيح إلى أن وصل إلى الإجابة الصحيحة، حد + +112 +00:09:53,260 --> 00:10:02,120 +عنده إجابة غير الإجابة هذه؟ فيه؟ إذا فيه قولونا طيب + +113 +00:10:02,120 --> 00:10:05,460 +نقولكوا يا عبدالله كيف استدل على هذه النتيجة + +114 +00:10:05,460 --> 00:10:10,240 +بطريقة صحيحة، إذا قال بدأ أحط zero بتطلع جداش الـ + +115 +00:10:10,240 --> 00:10:13,680 +zero، جذر الـ zero في zero، هاي مغلقة من عند الـ zero + +116 +00:10:13,680 --> 00:10:17,800 +قال بدأ ارجع بعد الـ zero قلنا له جداش؟ جداش سالب + +117 +00:10:17,800 --> 00:10:21,940 +واحد وسالب خمسة وسالب عشرين والأخرين يبقى لما + +118 +00:10:21,940 --> 00:10:27,660 +انحطّ سالب خمسة صار هذه كده؟ خمسة عشر وهذه سالب + +119 +00:10:27,660 --> 00:10:30,340 +خمسة تربيع خمسة وعشرين وخمسة عشر أربعين جدر + +120 +00:10:30,340 --> 00:10:35,880 +الأربعين موجب يعني بعد الـ zero مظبوط وقال لو رجعت + +121 +00:10:35,880 --> 00:10:40,460 +إن شاء الله لغاية سالب عشرة يبقى بصير هنا مئة وهنا + +122 +00:10:40,460 --> 00:10:45,440 +كده؟ ثلاثين يبقى مئة وثلاثين يبقى أكبر من اللي + +123 +00:10:45,440 --> 00:10:49,560 +جابله وهكذا يبقى كلام صحيح، قال لي طيب انتقل على + +124 +00:10:49,560 --> 00:10:53,900 +الفترة الثانية هوب طلعت بتطلع تسعة ناقص تسعة بـ + +125 +00:10:53,900 --> 00:10:59,300 +zero، هايم تمام؟ بعد الثلاثة بجنم اثنين، أربعة، خمسة عشر + +126 +00:10:59,300 --> 00:11:04,940 +عشرة مثلا عشرة في عشرة بمئة ثلاثة في عشرة بتلاتين + +127 +00:11:04,940 --> 00:11:08,800 +مئة ناقص ثلاثين سبعين تحت الجذر قيمة بعد الصفر وهكذا + +128 +00:11:08,800 --> 00:11:12,840 +إذا قال لي على كل الأمر يعني الفترة هذه + +129 +00:11:12,840 --> 00:11:16,180 +هتجيبلي الفترة من zero لـ infinity والفترة هذه + +130 +00:11:16,180 --> 00:11:20,140 +هتجيبلي نفس الفترة كمان من zero لوين؟ إلى infinity + +131 +00:11:20,140 --> 00:11:25,480 +نقولك كلام مضبوط والإجابة صحيحة لا غبارة عليها + +132 +00:11:25,650 --> 00:11:30,910 +ننتقل الآن إلى السؤال الثامن أو الدالة رقم ثمانية + +133 +00:11:30,910 --> 00:11:39,430 +F of X يساوي absolute value لـ X تمام الـ absolute + +134 +00:11:39,430 --> 00:11:43,630 +value لـ X أخدته تعريفه في الثانوية بدي أحب أذكر + +135 +00:11:43,630 --> 00:11:48,290 +بتعريفه مرة ثانية يبقى الـ absolute value لـ X بدها + +136 +00:11:48,290 --> 00:11:52,570 +تساوي X إذا كانت الـ X greater than or equal to + +137 +00:11:52,570 --> 00:11:58,910 +zero وتساوي سالب X إذا كانت الـ X أقل من الـ zero + +138 +00:11:58,910 --> 00:12:06,320 +اللي كنتوا سميوها القيمة المطلقة لـ سين القيمة + +139 +00:12:06,320 --> 00:12:10,400 +المطلقة لسين يبقى احنا هنا بقول absolute value of + +140 +00:12:10,400 --> 00:12:14,620 +X هي اللي كنت تقول عليها القيمة المطلقة للعدد سين + +141 +00:12:14,620 --> 00:12:19,380 +طيب هذه بدها تساوي X إذا X أكبر من أو تساوي Zero + +142 +00:12:19,380 --> 00:12:24,480 +وتساوي سالب X إذا كان X أقل من Zero هذا الـ + +143 +00:12:24,480 --> 00:12:29,270 +definition أو التعريف تبع القيمة المطلقة. إيه + +144 +00:12:29,270 --> 00:12:34,430 +الخاطر؟ أسأل السؤال التالي وفكر قبل ما تعطينا + +145 +00:12:34,430 --> 00:12:38,490 +الإجابة السؤال هو هاي تعريف الـ absolute value + +146 +00:12:38,490 --> 00:12:44,590 +السؤال هو هل الـ absolute value لـ X بتطلع قيمة + +147 +00:12:44,590 --> 00:12:50,150 +موجبة ولا ممكن موجبة وممكن سالبة زي ما أنت كاتب؟ + +148 +00:13:00,640 --> 00:13:05,880 +ممكن تكون سالب إذا كان السالب كان جديد؟ أنا مش فاهم + +149 +00:13:05,880 --> 00:13:14,540 +again مرة ثانية لا لا لا أنا بتكلم خليك معايا أنا + +150 +00:13:14,540 --> 00:13:18,680 +بتكلم داخل الـ absolute مالي ولا اللي برا مالي ولا + +151 +00:13:18,680 --> 00:13:22,060 +اللي برا أنا بس absolute لو كان الأمر كما أقول + +152 +00:13:22,060 --> 00:13:26,400 +سأقول لك سالب absolute بالعكس بتكلم زميلكوا عنه لو + +153 +00:13:26,400 --> 00:13:29,640 +كان فيه إشارة سالب برا الـ absolute ماليش علاقة + +154 +00:13:29,640 --> 00:13:37,010 +فيها أنا بتكلم هل بيطلع قيمة موجبة وقيمة سالبة؟ + +155 +00:13:37,010 --> 00:13:40,210 +والله موجبة بس، والله سالبة بس فقط لا غير + +156 +00:13:49,930 --> 00:13:54,350 +ممتاز جدا يعني يا شباب لما تأخذ التعريف مش تأخذ + +157 +00:13:54,350 --> 00:13:58,370 +شوية منه وتسيب الباقي بآخذه كاملا لما قال لي + +158 +00:13:58,370 --> 00:14:03,130 +absolute بالـ X يستوي X اشترط أن X يا إما موجبة يا + +159 +00:14:03,130 --> 00:14:06,850 +إما صفر يبقى ما عندي مشكلة بتطلع أن أنا موجبة تعني + +160 +00:14:06,850 --> 00:14:11,090 +موجبة صفر تعني صفر لكن لما قال لي هنا سالب x قال لي + +161 +00:14:11,090 --> 00:14:17,270 +إذا كانت x أقل من الـ zero يعني لو كان x قيمة سالبة + +162 +00:14:17,270 --> 00:14:21,490 +يبقى الجوا بتحط نفس القيمة وقبلها إنشرط مين سالب + +163 +00:14:21,490 --> 00:14:25,750 +بصير سالب سالب اللي هو الرقم اللي عندك يبقى بصير + +164 +00:14:26,240 --> 00:14:29,860 +إذا الـ absolute value ما بتطلعش إلا قيمة موجبة + +165 +00:14:29,860 --> 00:14:38,080 +فمثلا absolute value لسالب ثلاثة يساوي + +166 +00:14:38,080 --> 00:14:43,840 +سالب لسالب ثلاثة أي السالب والـ X بسالب ثلاثة أي + +167 +00:14:43,840 --> 00:14:48,500 +السالب ثلاثة يبقى النتيجة ثلاثة إذا ما بتطلعش إلا + +168 +00:14:48,500 --> 00:14:52,900 +قيمة موجبة ما علينا أنا الآن بتدور على الـ domain + +169 +00:14:52,900 --> 00:14:57,000 +تبع هذه الدالة بعد ما أعطيتها التعريف فيه في + +170 +00:14:57,000 --> 00:15:00,520 +الهامش ذكرتك ابو تذكرنا أن أنت أخدته في الثانوية + +171 +00:15:00,520 --> 00:15:07,000 + +201 +00:17:38,410 --> 00:17:42,990 +يعني كل الـ X الموجبة بزيادة الصفر وهنا كل الـ X السالبة + +202 +00:17:42,990 --> 00:17:47,550 +الشكلتين مع بعض بيعطيني كل الـ real number + +203 +00:17:47,550 --> 00:17:57,400 +بلا ستنة من سالب infinity إلى infinity فبالتالي نفس + +204 +00:17:57,400 --> 00:18:02,420 +هذه يعني اللي جاب لها نفس عرفيا؟ هل خطر تغير؟ + +205 +00:18:03,740 --> 00:18:08,400 +يعني أو كما قيل، في أحد عنده إجابة غير حكاية الـ + +206 +00:18:08,400 --> 00:18:12,940 +zero و infinity؟ إذا في إجابة، أعطوني إياها، أحد ما + +207 +00:18:12,940 --> 00:18:13,840 +نتناقش فيها. + +208 +00:18:17,820 --> 00:18:23,440 +يبقى من zero كل الـ R ولا نصفها؟ كل الـ R + +209 +00:18:34,930 --> 00:18:41,510 +يعني أو كما قيل طيب يلا موافقين نفس النتيجة اللي + +210 +00:18:41,510 --> 00:18:48,810 +فوق من Zero لغاية Infinity طيب السؤال العاشر بدنا + +211 +00:18:48,810 --> 00:18:57,650 +الـ F of X تساوي absolute value لـ X على X وشوف ليها + +212 +00:18:57,650 --> 00:19:01,370 +هي X على absolute value لـ X ولا لا؟ + +213 +00:19:07,570 --> 00:19:13,410 +هل هذه هي هذه يا شباب؟ بيختلفوا عن بعض يعني متأكدين + +214 +00:19:13,410 --> 00:19:17,470 +الدالة + +215 +00:19:17,470 --> 00:19:23,430 +هذه هي نفس الدالة هذه بالحرف الواحد تمام؟ الآن + +216 +00:19:23,430 --> 00:19:28,100 +بوريك كيف هذا طلع لي هنا لما أنا قاعد بقول absolute + +217 +00:19:28,100 --> 00:19:33,620 +value لـ X على X بدي أعطيها التعريف تبعها يبقى هذي + +218 +00:19:33,620 --> 00:19:39,720 +X على X إذا الـ X أكبر من الـ 0 هحط يساوي + +219 +00:19:42,310 --> 00:19:46,370 +زيرو على زيرو هذا ممنوع، ما في إمكانية يبقى حكاية + +220 +00:19:46,370 --> 00:19:55,130 +زيرو استبعدناها وهنا تساوي سالب X على X إذا الـ X + +221 +00:19:55,130 --> 00:20:02,570 +greater than 0 طب هدى علي هدى بقداش وهدى علي هدى + +222 +00:20:02,570 --> 00:20:08,970 +بقداش سالب واحد إذا كان الـ X greater than zero إذا + +223 +00:20:08,970 --> 00:20:15,190 +كان الـ X less than zero لو أخدت الثانية اللي تحت + +224 +00:20:15,190 --> 00:20:22,090 +بصير X على X و X على سالب X يبقى هي ولا لا؟ إذا الـ + +225 +00:20:22,090 --> 00:20:26,150 +function هذه إن كتبتها بالشكل هذا أو بالشكل هذا + +226 +00:20:26,150 --> 00:20:32,090 +الاثنين بعرف ده same الاثنين نفس الشيء طيب سؤالنا هو + +227 +00:20:32,090 --> 00:20:35,850 +قداش الـ domain وشوف اللي موجود هنا على اللوح ولا + +228 +00:20:35,850 --> 00:20:44,440 +لا؟ كل الـ real number ما عدا الـ zero يبقى بقول له كل + +229 +00:20:44,440 --> 00:20:50,340 +الـ real number ما عدا الـ zero as except يا إما من + +230 +00:20:50,340 --> 00:20:56,340 +سالب infinity لـ zero اتحاد zero و infinite طيب بدنا + +231 +00:20:56,340 --> 00:21:00,760 +نيجي للـ range بس + +232 +00:21:00,760 --> 00:21:05,620 +اسمع شوية وبده أغششك الـ range على اللوح كمان موجودة + +233 +00:21:08,210 --> 00:21:12,970 +استنى شوية استنى شوية سمعت فيه خلافات؟ أيوه سالب + +234 +00:21:12,970 --> 00:21:19,550 +واحد واحد كفترة ولا رقمين بس؟ رقمين رقمين + +235 +00:21:19,550 --> 00:21:29,410 +يعني آه رقمين يعني رقمين بس ممتازة يبقى لا يوجد + +236 +00:21:29,410 --> 00:21:34,940 +صورة للما لا نهاية من الأرقام اللي عندي إلا صورة لو + +237 +00:21:34,940 --> 00:21:40,660 +سالب واحد وواحد فقط لغير as a set يبقى بعملها set + +238 +00:21:40,660 --> 00:21:45,680 +وبقول سالب واحد وواحد لما نكتب جثين بالشكل هذا + +239 +00:21:45,680 --> 00:21:51,490 +مجموعة يعني هذه مجموعة تحتوي على عنصرين فقط هو + +240 +00:21:51,490 --> 00:21:55,510 +العنصر سالب واحد وواحد هي الـ range اللي طالع عندي + +241 +00:21:55,510 --> 00:22:00,910 +واحد وسالب واحد لكن الـ domain هو x أكبر من الـ + +242 +00:22:00,910 --> 00:22:04,970 +zero و x أقل من الـ zero يعني كل الـ real number ما + +243 +00:22:04,970 --> 00:22:11,250 +عدا main ما عدا الـ zero تمشي + +244 +00:22:11,250 --> 00:22:15,870 +الحالة تحط الفترة المغلقة وتقولي ناقص الـ zero هاي + +245 +00:22:15,870 --> 00:22:22,000 +كتبنا R هنا ناقص الـ zero هل هذا سؤالك؟ مهم أنت عارف + +246 +00:22:22,000 --> 00:22:27,220 +هي كتبناها لك قبل ما تحكي طيب أبنجي الآن للرسم + +247 +00:22:27,220 --> 00:22:31,420 +البياني لـ functions زي ما وعدناك وأحد بدي يسأل؟ + +248 +00:22:31,420 --> 00:22:35,440 +أيوه فقط + +249 +00:22:35,440 --> 00:22:42,580 +لا غير تاني + +250 +00:22:42,580 --> 00:22:43,920 +تاني ايش بتقول؟ + +251 +00:22:46,620 --> 00:22:51,960 +أنا ما سمعتش كويسة، إذا ما كوه يعني + +252 +00:22:51,960 --> 00:22:56,080 +كفترة من سالب واحد واحد معادا zero؟ لأ لأ لأ مش + +253 +00:22:56,080 --> 00:23:01,160 +صحيح، قلت رقمين فقط لغير اللي هم سالب واحد واحد + +254 +00:23:37,230 --> 00:23:46,950 +طيب نحط عنوان جانبي graph of a function graph of a + +255 +00:23:46,950 --> 00:23:53,270 +function الرسم البياني للدالة بدنا نعرف الرسم + +256 +00:23:53,270 --> 00:24:00,590 +البياني للدالة definition graph of + +257 +00:24:00,590 --> 00:24:02,070 +a function + +258 +00:24:04,190 --> 00:24:16,670 +فلذلك ف with domain D is the set + +259 +00:24:19,380 --> 00:24:28,720 +of points هو مجموعة النقاط اللي على الشكل X و F of + +260 +00:24:28,720 --> 00:24:36,440 +X such that الـ X موجودة في الـ domain D example + +261 +00:24:36,440 --> 00:24:41,700 +find + +262 +00:24:41,700 --> 00:24:42,500 +the domain + +263 +00:24:48,980 --> 00:24:59,440 +and then a graph and then graph the following + +264 +00:24:59,440 --> 00:25:03,500 +functions + +265 +00:25:03,500 --> 00:25:08,580 +نمر + +266 +00:25:08,580 --> 00:25:19,350 +أيه الـ F of X تساوي ثلاثة والله سالب ثلاثة نمر ب + +267 +00:25:19,350 --> 00:25:26,490 +الـ F of X يساوي الجذر التربيعي لـ absolute value لـ + +268 +00:25:26,490 --> 00:25:36,130 +X نمر ج الـ F of X يساوي X على absolute value لـ X + +269 +00:25:36,130 --> 00:25:46,790 +نمر د الـ F of X يساوي X تربيع ناقص 9 على X ناقص 3 + +270 +00:26:08,040 --> 00:26:12,200 +يبقى اللون اللي احنا كاتبينه لـ graph of a function + +271 +00:26:12,200 --> 00:26:17,600 +الرسم البياني للاقتراب أو الرسم البياني للدالة بدنا + +272 +00:26:17,600 --> 00:26:22,060 +نعطيله تعريف وبعد هيك بنروح نطبق هذا التعريف + +273 +00:26:22,060 --> 00:26:26,540 +التعريف بيقول the graph of a function f الرسم + +274 +00:26:26,540 --> 00:26:32,000 +البياني للدالة f اللي الـ domain تبعها دي هو عبارة + +275 +00:26:32,000 --> 00:26:37,630 +عن مجموعة نقاط is the set of points مجموعة النقاط + +276 +00:26:37,630 --> 00:26:44,050 +اللي على الشكل التالي كله كزوج مرتب أو كإحداثيات + +277 +00:26:44,050 --> 00:26:49,330 +نقط X و F of X بحيث الـ X هذه لازم تكون موجودة في الـ + +278 +00:26:49,330 --> 00:26:55,610 +domain تبع الـ D النقاط هدول كلهم لما نرسمهم + +279 +00:26:55,610 --> 00:27:01,360 +بيكونوا على ايش؟ الشكل العام لمنحنى اتعلمنا في + +280 +00:27:01,360 --> 00:27:06,540 +الثانوية وفي الاعدادية بترسم جدول وبتحط فيه قيم + +281 +00:27:06,540 --> 00:27:10,320 +سين وبعدين قيم الصاد وبتيجي على الرسم البياني + +282 +00:27:10,320 --> 00:27:14,520 +بتحط إحداثيات النقط وتوصل منهم وبتطلع المنحنى + +283 +00:27:14,520 --> 00:27:18,140 +مظبوط هذا اللي احنا بنقول عليه الـ igraph of a + +284 +00:27:18,140 --> 00:27:23,560 +function يعني نحن هنا لم نأتِ بجديد بدنا نروح نطبق + +285 +00:27:23,560 --> 00:27:28,200 +هذا الكلام على أرض الواقع فقلنا هات لي الـ domain و + +286 +00:27:28,200 --> 00:27:33,480 +كذلك ارسم كل من الدوال التالية يعني كل دالة من هذه + +287 +00:27:33,480 --> 00:27:37,660 +الدوال بدي أعرف قداش الـ domain بالنسبة لها name + +288 +00:27:37,660 --> 00:27:41,900 +بدي أرسمها بعدين بقول لك قويس بدي أمسك السؤال الأول + +289 +00:27:42,660 --> 00:27:48,200 +اللي هو الـ F of X يساوي ناقص ثلاثة هذا دي ايش + +290 +00:27:48,200 --> 00:27:53,900 +بنسميها شباب الدالة ثابتة يبقى الـ constant + +291 +00:27:53,900 --> 00:28:02,460 +function دالة ثابتة يبقى هنا constant function + +292 +00:28:02,460 --> 00:28:09,750 +يعني دالة ثابتة ماذا يعني دالة ثابتة؟ يعني مهما + +293 +00:28:09,750 --> 00:28:16,330 +تغيرت X بيبقى قيمة الدالة هي القيمة الثابتة أو + +294 +00:28:16,330 --> 00:28:22,670 +بمعنى آخر جميع قيم X لها صورة واحدة هي غير اليمين + +295 +00:28:22,670 --> 00:28:30,390 +سالب ثلاثة يعني كأن Y تساوي سالب أو ص تساوي سالب + +296 +00:28:30,390 --> 00:28:36,520 +ثلاثة طيب هذه معادلة ايش؟ معادلة مستقيم ماله موازي + +297 +00:28:36,520 --> 00:28:43,380 +لمحور السينات وأسفله بمقدار ثلاثة يعني لو جيت + +298 +00:28:43,380 --> 00:28:50,360 +سألت قداش الـ domain بتاع الدالة F بتقول X اللي + +299 +00:28:50,360 --> 00:28:56,000 +هدعو بالسالب ثلاثة لقداش بتتغير X نتيجة السلب بتغيري + +300 +00:28:56,000 --> 00:29:01,750 +بتغير X زي ما بدك من سالب infinity إلى infinity يبقى + +301 +00:29:01,750 --> 00:29:07,450 +هذا من سالب infinity إلى infinity بدنا نرسم الرسمة + +302 +00:29:07,450 --> 00:29:13,050 +يبقى بجي بقول له هاي المحاور هذا محور X وهذا محور Y + +303 +00:29:13,050 --> 00:29:18,490 +وهذه نقطة الأصل اللي هي Zero اللي كنت بتقول له محور + +304 +00:29:18,490 --> 00:29:25,530 +السينات ومحور الصاد احنا هنقول محور X ومحور Y هذا + +305 +00:29:25,530 --> 00:29:30,730 +خط مستقيم يوازي السينات ويبعد عنه مسافة مقدارها + +306 +00:29:30,730 --> 00:29:36,690 +ثلاثة من وحدات المسافة يبقى لو رسمنا الخط اللي + +307 +00:29:36,690 --> 00:29:43,620 +عندنا هذا يكون هذا الخط هذه النقطة سالب ثلاثة وهذا + +308 +00:29:43,620 --> 00:29:48,520 +النقطة سالب اثنين وهذا النقطة سالب واحد وهذا + +309 +00:29:48,520 --> 00:29:54,640 +النقطة السابقة هي zero يبقى هذا f of x يساوي كم؟ + +310 +00:29:54,640 --> 00:30:00,540 +يساوي سالب ثلاثة طبعا طب لو سألتك السؤال اللي قلت + +311 +00:30:00,540 --> 00:30:08,970 +لك f of x بده يساوي ثلاثة يبقى بيمدي يطلع فوق بس + +312 +00:30:08,970 --> 00:30:16,570 +موازية وها كده طيب نرجع نرجع مين اللي بيسأل؟ عمود + +313 +00:30:16,570 --> 00:30:20,550 +على الصناعة عمود على الصناعة بدل ما أقول Y تساوي + +314 +00:30:20,550 --> 00:30:24,470 +سالب ثلاثة بقول لك X يساوي سالب ثلاثة و X يساوي سالب + +315 +00:30:24,470 --> 00:30:30,270 +ثلاثة يعني الخط هنا X يساوي ثلاثة هنا X يساوي سالب + +316 +00:30:30,270 --> 00:30:36,190 +ثلاثة ماشي واضح أظن طيب نجرب من السؤال اللي بعده + +317 +00:30:36,190 --> 00:30:41,680 +نمر ب نمر ب لخاطر ارسم absolute value لـ X جاب لي + +318 +00:30:41,680 --> 00:30:45,680 +للجذر التربيعي لـ absolute value لـ X يبقى أنا بدي + +319 +00:30:45,680 --> 00:30:51,720 +أبدأ بـ absolute value لـ X اتفقنا على أنها X إذا + +320 +00:30:51,720 --> 00:30:57,520 +كانت الـ X أكبر من أو تساوي الـ zero اتفقنا سالب X + +321 +00:30:57,520 --> 00:31:02,520 +إذا الـ X أقل من الـ zero جالي هات للـ domain الـ + +322 +00:31:02,520 --> 00:31:06,780 +domain حسبناه قبل قليل وقلنا كل الـ real line + +323 +00:31:06,780 --> 00:31:14,000 +مظبوط يبقى هنا الـ domain بتاع الـ F كل الـ real line + +324 +00:31:14,000 --> 00:31:18,800 +من سالب infinity إلى infinity بدنا نرسمها يبقى لو + +325 +00:31:18,800 --> 00:31:23,520 +روحنا رسمناها بنقول هذه المحاولة هذا محور X هذا + +326 +00:31:23,520 --> 00:31:30,760 +محور Y هذه نقطة الأصل اللي هي الـ zero الدالة هذه لو + +327 +00:31:30,760 --> 00:31:36,140 +قلت لك Y تساوي absolute value لـ X يبقى Y بدها + +328 +00:31:36,140 --> 00:31:42,740 +تساوي X أظن معروف فده خط ينصف الربع الأول والربع + +329 +00:31:42,740 --> 00:31:48,660 +الثالث يبقى هذا الخط أخذناه قبل هيك كتير وبروح + +330 +00:31:48,660 --> 00:31:53,200 +بمدّه على استقامة ويبقى هذا الخط اللي هو Y يساوي + +331 +00:31:53,200 --> 00:32:01,090 +منهم يساوي X بس أصبر شوية الخط الثاني Y تساوي مين؟ + +332 +00:32:01,090 --> 00:32:07,550 +سالب X يبقى بدنا الربع الرابع الثاني والرابع الشكل + +333 +00:32:07,550 --> 00:32:13,230 +اللي عندنا هذا يبقى هاي Y يساوي سالب X هذا لو كان + +334 +00:32:13,230 --> 00:32:25,840 +على إطلاق لكن حط لي هنا condition يبقى + +335 +00:32:25,840 --> 00:32:32,600 +الخط هذا الله يسّهل عليه مش موجود قال لي Y تساوي + +336 +00:32:32,600 --> 00:32:37,620 +السالب X إذا X أقل من الـ Zero يبقى على اليمين هذا + +337 +00:32:37,620 --> 00:32:44,380 +ماله مش موجود يبقى اللي بظل عندي هو رسمة main رسمة + +338 +00:32:44,380 --> 00:32:49,220 +absolute value لـ X على شكل سبعة بالعربي أو ثمانية + +339 +00:32:49,220 --> 00:32:55,800 +مقلوبة يبقى هذا معرف عند نقطة الأصل لإن absolute + +340 +00:32:55,800 --> 00:33:03,080 +value للـ 0 في 0 يبقى هذه رسمة absolute أو Y أو F + +341 +00:33:03,080 --> 00:33:08,880 +of X يساوي absolute value لـ X مش هذه اللي بدنا + +342 +00:33:08,880 --> 00:33:13,430 +إياها بدنا الجذر التربيعي لـ absolute value لـ X + +343 +00:33:13,430 --> 00:33:17,290 +بقول له آه احنا عندنا هنا الجذر التربيعي لـ + +344 +00:33:17,290 --> 00:33:21,750 +absolute value لـ X أحد أمرين يا إما الجذر التربيعي + +345 +00:33:21,750 --> 00:33:26,630 +لـ X إذا الـ X أكبر من أو تساوي Zero يا إما الجذر + +346 +00:33:26,630 --> 00:33:32,790 +التربيعي لـ سالب X إذا X أقل من مين أقل من Zero طب + +347 +00:33:32,790 --> 00:33:36,650 +خليني أسألكم السؤال التالي قبل ما ارسم الرسمة هذه + +348 +00:33:36,650 --> 00:33:40,970 +الدالة الأولى اللي هي absolute value لـ X من خلال + +349 +00:33:40,970 --> 00:33:46,950 +الرسم قداش الـ domain تبعها من الرسم طلع في الرسم + +350 +00:33:46,950 --> 00:33:53,070 +هي كل X اللي على اليمين الدالة معرفة كل X اللي على + +351 +00:33:53,070 --> 00:33:56,710 +الشمال الدالة معرفة يبقى الـ domain من وين من + +352 +00:33:56,710 --> 00:34:01,550 +سالب infinity إلى infinity فبقدرش أقل القيمة + +353 +00:34:01,550 --> 00:34:05,370 +بتاخذها الـ absolute من خلال الـ zero وبعد هيك تطلع + +354 +00:34:05,370 --> 00:34:10,480 +يبقى من وين من وين يبقى الكلام اللي أنا بحكي لك هذا + +355 +00:34:10,480 --> 00:34:14,740 +شوفه مكتوب عندك جبريا قبل قليل في الجدول ولا لا + +356 +00:34:14,740 --> 00:34:18,220 +طلع للـ absolute value of X بتلاقي الـ domain من سلب + +357 +00:34:18,220 --> 00:34:21,280 +infinity لـ infinity والـ range من zero إلى + +358 +00:34:21,280 --> 00:34:25,600 +infinity يبقى هي جبريا قلناه هي بيانيا طلعناه من + +359 +00:34:25,600 --> 00:34:30,200 +خلال ايه؟ من خلال الرسم بدنا نيجي لمسألتنا هذه + +360 +00:34:41,140 --> 00:34:47,080 +يبقى لو روحت رسمت بذكر بالرسمة تذكير اللي ليس إلا + +361 +00:34:47,080 --> 00:34:55,770 +هذا X وهذا Y وهذا رسمة Y تساوي جذر الـ X يعني ص + +362 +00:34:55,770 --> 00:35:02,250 +تساوي الجذر التربيعي لـ X هذا لما X مالها أكبر من + +363 +00:35:02,250 --> 00:35:08,330 +الـ 0 أو تساوي طيب لما أقل من الـ 0 لو كانت الـ X + +364 +00:35:08,330 --> 00:35:14,420 +بسالب أو سبقت بإشارة بالسلب موجب يعني النتيجة هذه + +365 +00:35:14,420 --> 00:35:19,580 +نفس النتيجة اللي فوق الموجبة يبقى بده يظهر قوس زيه + +366 +00:35:19,580 --> 00:35:24,040 +بس من وين من الناحية الثانية يبقى Y يساوي الجذر + +367 +00:35:24,040 --> 00:35:29,400 +التربيعي لـ -X لأنه كل ما كانت X سالبة وسبقت بإشارة + +368 +00:35:29,400 --> 00:35:34,000 +سالب بصير سالب سالب موجب يبقى نفس البعد اللي هنا + +369 +00:35:34,000 --> 00:35:38,140 +هو اللي يعني صورة الواحد هي واحد صورة السالب واحد + +370 +00:35:38,140 --> 00:35:44,890 +هي واحد صورة مثلا الأربعة اثنين صورة السالب أربعة + +371 +00:35:44,890 --> 00:35:49,930 +هي اثنين وهكذا إذا من خلال الرسم قداش الـ domain + +372 +00:35:49,930 --> 00:35:58,270 +تبع الدالة هذه الـ domain سالب infinity لـ طب والـ + +373 +00:35:58,270 --> 0 + +401 +00:38:33,500 --> 00:38:40,690 +بدنا نيجي لمن؟ للنمرى يبقى بالداجي لـD وهذه C دي + +402 +00:38:40,690 --> 00:38:46,630 +بيقول الـ F of X يساوي X تربيع ناقص 9 على X ناقص 3 + +403 +00:38:46,630 --> 00:38:53,190 +سؤالي هو هل الدالة معرفة عند الثلاث؟لأن عندي + +404 +00:38:53,190 --> 00:38:57,830 +الثلاث بصير Zero على Zero كمية غير معينة، تمام؟ + +405 +00:38:57,830 --> 00:39:03,430 +إذا لا يمكن لهذه الدالة أن تكون معرفة عند الثلاث، + +406 +00:39:03,430 --> 00:39:08,090 +لكن أنا بدي أحاول أرسمها، إذا مشان أرسمها لازم + +407 +00:39:08,090 --> 00:39:14,310 +أبسطها إذا باجي بقوله هذا كفرق بين المربعين x-3 في + +408 +00:39:14,310 --> 00:39:20,810 +x plus 3 على x minus 3 بتروح هذه مع هذه وبظل اليوم + +409 +00:39:20,810 --> 00:39:27,290 +x زائد ثلاث بس بشرط إن x ما لها ممنوعة تساوي + +410 +00:39:27,290 --> 00:39:33,050 +ثلاث لإن عندي الثلاث غير معرفة يبقى المرسمتنا + +411 +00:39:33,050 --> 00:39:41,120 +عبارة عن خط مستقيم والخط المستقيم بدي يكون خالي عند x + +412 +00:39:41,120 --> 00:39:46,080 +يساوي 3 يعني هذه النقطة فرعة على الخط المستقيم عند + +413 +00:39:46,080 --> 00:39:52,200 +x يساوي 3 بقوله بسيطة إذا إحنا لو جينا نرسم هذا + +414 +00:39:52,200 --> 00:39:56,500 +الخط المستقيم بالشكل اللي عندنا هذا وقلنا هذا + +415 +00:39:56,500 --> 00:40:02,420 +محور x هذا محور y هذه النقطة الأصل اللي هي عندنا + +416 +00:40:02,420 --> 00:40:08,800 +zero الآن عشان ارسم أي خط مستقيم في الدنيا بيكفيني + +417 +00:40:08,800 --> 00:40:13,320 +نقطتين موجودتين عليه إذا عرفت النقطتين بجيبها + +418 +00:40:13,320 --> 00:40:16,520 +المصدر وبرسمها الخط بيصير هذا اللي هو الخط + +419 +00:40:16,520 --> 00:40:22,280 +المستقيم اللي عندنا فمثلا لو كانت X بـ Zero فـ F of + +420 +00:40:22,280 --> 00:40:26,900 +Zero بقداش؟ بثلاث يعني معنى هذا الكلام أن النقطة + +421 +00:40:26,900 --> 00:40:33,850 +Zero ثلاث تقع على الخط المستقيم هذه Zero ثلاث لو + +422 +00:40:33,850 --> 00:40:39,950 +كانت f of x كلها بـ0 يبقى x بدها تساوي جدّها إذا + +423 +00:40:39,950 --> 00:40:46,230 +سالب 3 و 0 تقع على الخط المستقيم سالب 3 و 0 بدها + +424 +00:40:46,230 --> 00:40:47,690 +تجيلك النقطة هذه + +425 +00:40:50,790 --> 00:40:56,430 +إذا احنا صار أن هذا الخط المستقيم بقدر ارسمه بدون + +426 +00:40:56,430 --> 00:41:02,250 +مشاكل يبقى بوصل بين النقطتين و بمد الخط على + +427 +00:41:02,250 --> 00:41:07,070 +استقامته من الناحيتين بصير هذا هو الخط المستقيم + +428 +00:41:07,070 --> 00:41:12,170 +لأن y تساوي x زائد الثلاث أو f of x يساوي x زائد + +429 +00:41:12,170 --> 00:41:17,330 +الثلاث بس استنى شوية لما تيجي عند الواحد وعند + +430 +00:41:17,330 --> 00:41:22,290 +اثنين وعند الثلاث ونيجي طالعين مشان قبل الخط + +431 +00:41:22,290 --> 00:41:28,830 +المستقيم بيصير الخط المستقيم في تجويف هنا وبالتالي + +432 +00:41:28,830 --> 00:41:36,070 +عند x يساوي ثلاث الـ function is undefined يبقى + +433 +00:41:36,070 --> 00:41:41,390 +عند x يساوي ثلاث بيظهر تجويف أو ثقب في الخط + +434 +00:41:41,390 --> 00:41:46,870 +المستقيم بمعنى آخر النقطة ثلاث وستة لا تقع على + +435 +00:41:46,870 --> 00:41:51,790 +الخط المستقيم، لو حطيت ثلاث زائد ثلاث بيصير ستة، + +436 +00:41:51,790 --> 00:41:56,290 +يبقى ثلاث وستة هذه مش موجودة على الخط المستقيم، + +437 +00:41:56,290 --> 00:42:03,630 +يبقى فراغ، تمام؟ طيب، لخاطر أسأل سؤال ثاني، لو + +438 +00:42:03,630 --> 00:42:08,450 +احنا رسمنا وقلت لك خد لك هالرسمة، وشوف ليها دي رسمة + +439 +00:42:08,450 --> 00:42:14,220 +function والله مش function، كيف بدي أعرف؟ رسمت لك + +440 +00:42:14,220 --> 00:42:17,500 +رسمة على اللوحة وقلت لك اتفضل هي رسمة وشوف لي هي + +441 +00:42:17,500 --> 00:42:21,020 +الرسمة هذه رسمة function والله ماهيّاش function + +442 +00:42:21,020 --> 00:42:27,240 +القضية بسيطة ولا بتحققها القضية من أبسط وأسهل ما + +443 +00:42:27,240 --> 00:42:31,870 +يكون كيف؟ المحاضرة اللي فاتت بتتذكروا لما جينا + +444 +00:42:31,870 --> 00:42:37,650 +عرفنا تعريف الـ function وجينا قولنا لا يمكن + +445 +00:42:37,650 --> 00:42:42,130 +للعنصر الواحد أن تكون له صورتين أو أكثر مظبوط صورة + +446 +00:42:42,130 --> 00:42:45,990 +واحدة على انوراس بس أكثر بتبطل يصير function إذا + +447 +00:42:45,990 --> 00:42:51,970 +أنا لو أعطيتك رسمة هل هذه رسمة دالة ولا لا؟ بقوله + +448 +00:42:51,970 --> 00:42:56,410 +بسيطة بدي آخذ أي نقطة في دمنا وأشوف عند النقطة هذه + +449 +00:42:56,410 --> 00:43:00,590 +بلاقي صورتين ولا لا إذا لاقيت صورتين ما بتبطل تصير + +450 +00:43:00,590 --> 00:43:07,390 +function مظبوط؟ أي vertical line أي خط رأسي ممنوع + +451 +00:43:07,390 --> 00:43:12,500 +يقطع المنحنى إلا في لو قطع في نقطتين بيصير بطل يصير + +452 +00:43:12,500 --> 00:43:17,720 +function لأن X بيصير لها صورتين على الرسم مظبوط + +453 +00:43:17,720 --> 00:43:22,700 +الكلام اللي أنا بقوله اسمه الـ vertical line test + +454 +00:43:22,700 --> 00:43:29,640 +for a function اختبار الخط الرأسي لمين؟ للدالة إذا لو + +455 +00:43:29,640 --> 00:43:33,860 +أعطاني رسمة وقال لي شوف لي هذه تمثل دالة ولا لا + +456 +00:43:33,860 --> 00:43:39,440 +تمثل دالة بدون معرف شكلة بجيبها لمصر بحاول أرسم أي + +457 +00:43:39,440 --> 00:43:43,860 +خط رأسي إذا الخط الرأسي قطع المنحنى في نقطتين ليست + +458 +00:43:43,860 --> 00:43:47,880 +function لكن إذا كل الخطوط الرأسية ما قدرتش تقطعوا + +459 +00:43:47,880 --> 00:43:52,360 +إلا في نقطة واحدة يبقى هذا إيش؟ vertical line يبقى + +460 +00:43:52,360 --> 00:43:57,200 +هذه تمثل معنى دالة الكلام اللي سمعته بدنا نروح + +461 +00:43:57,200 --> 00:44:19,680 +نكتبه الآن ونشوف كيف انطبقه على أرض الواقع عنوان + +462 +00:44:19,680 --> 00:44:20,420 +جانبي + +463 +00:44:24,040 --> 00:44:37,600 +vertical line test test for a function if + +464 +00:44:37,600 --> 00:44:50,860 +الـ if is a function then no vertical + +465 +00:45:00,260 --> 00:45:13,040 +ممكن أن يقطع الرسم + +466 +00:45:13,040 --> 00:45:18,760 +البياني للدالة if more than + +467 +00:45:19,670 --> 00:45:31,150 +once أكثر من مرة واحدة that is if الـ + +468 +00:45:31,150 --> 00:45:46,090 +a موجودة في دومين الدالة if then the vertical line + +469 +00:45:46,090 --> 00:45:57,230 +الخط الرأسي x بدها تساوي a will intersect + +470 +00:45:57,230 --> 00:46:00,410 +the + +471 +00:46:00,410 --> 00:46:07,030 +graph of + +472 +00:46:07,030 --> 00:46:16,810 +f at the single point + +473 +00:46:19,920 --> 00:46:23,800 +و F of A + +474 +00:46:39,750 --> 00:46:44,690 +يبقى هذا الاختبار اسمه اختبار الخط الرأسي للدالة + +475 +00:46:44,690 --> 00:46:52,570 +vertical line خط رأسي فيه كلمة perpendicular عمودي + +476 +00:46:52,570 --> 00:46:55,710 +يعني خطين لما يكونوا عمودين على بعض بقول + +477 +00:46:55,710 --> 00:47:00,310 +perpendicular line لكن لما أقول vertical line يبقى + +478 +00:47:00,310 --> 00:47:03,870 +هذا بسميه خط رأسي بغض النظر هل هو عمودي على غيره + +479 +00:47:03,870 --> 00:47:08,740 +ولا مش عمودي على غيره يبقى باجي بقول لو كانت الـ F + +480 +00:47:08,740 --> 00:47:12,720 +function يبقى لو كانت الدالة الرسمة اللي عندي هي + +481 +00:47:12,720 --> 00:47:18,800 +رسمة function إذا لا يمكن أقدر ألاقي خط مستقيم + +482 +00:47:18,800 --> 00:47:24,180 +رأسي يقطع منحنى الدالة في أكثر من نقطة لكن لو + +483 +00:47:24,180 --> 00:47:28,300 +ما كانتش function ممكن في اثنين أو في ثلاث أو في + +484 +00:47:28,300 --> 00:47:32,770 +أربعة زي ما بدك مرة ثانية لو كنت لـ function then + +485 +00:47:32,770 --> 00:47:38,230 +no vertical line لا يمكن تقدر تلاقي خط رأسي ممكن + +486 +00:47:38,230 --> 00:47:44,390 +يقطع المنحنى في أكثر من مرة more than once يعني + +487 +00:47:44,390 --> 00:47:48,790 +أكثر من مرة واحدة مش هتلاقي ولا خط إذا لو المنحنى + +488 +00:47:48,790 --> 00:47:53,870 +منحنى ده لأ الخط الرأسي لا يمكن أن يقطع المنحنى إلا + +489 +00:47:54,400 --> 00:47:59,420 +في نقطة واحدة فقط الآن الكلام اللي قلته هيك بدي أروح + +490 +00:47:59,420 --> 00:48:06,160 +أصيغه بمفهوم آخر فقولت that is أي أنه لو كان الـ a + +491 +00:48:06,160 --> 00:48:10,280 +موجود في domain الـ F لو كانت النقطة a موجودة في + +492 +00:48:10,280 --> 00:48:17,830 +domain الـ F والخط الرئيسي X يساوي الـA وينترسج في + +493 +00:48:17,830 --> 00:48:21,430 +نقطة + +494 +00:48:21,430 --> 00:48:28,550 +واحدة A و F of A كيف هذا الكلام؟ بجي بقول لو كان + +495 +00:48:28,550 --> 00:48:33,670 +عندنا محاور مثلا بالشكل هذا وقلنا هذا محور X وهذا + +496 +00:48:33,670 --> 00:48:38,680 +محور Y ورسمنا منحنى وكان المنحنى بالشكل هذا فكان + +497 +00:48:38,680 --> 00:48:46,400 +هذا منحنى Y تساوي F of X يعني الـ y تساوي دالة الـ x + +498 +00:48:46,400 --> 00:48:52,020 +روحنا أخدنا أي نقطة في domain الدالة هذه ولتكن + +499 +00:48:52,020 --> 00:48:58,060 +النقطة هذه مالها A يبقى هذه X يساوي A وهذه Zero + +500 +00:48:58,060 --> 00:49:05,920 +جينا رسمنا خط رأسي يمر بالنقطة A يبقى الخط الرأسي + +501 +00:49:05,920 --> 00:49:10,980 +بالشكل اللي عندنا هذا يبقى الخط الرأسي هذا معادلته + +502 +00:49:10,980 --> 00:49:16,720 +X يساوي A زي مثال بعض الشباب قبل قليل قال لو كان + +503 +00:49:16,720 --> 00:49:21,740 +عمودي على محور الصادات يعني الخط المستقيم الموازي + +504 +00:49:21,740 --> 00:49:26,340 +لمحور الصادات Y تساوي رقم، موجب، سالب، صفر، + +505 +00:49:26,340 --> 00:49:30,800 +ما تفرجش عليها، لكن لو كان عمودي على محور الصادات فـ + +506 +00:49:30,800 --> 00:49:36,220 +X يساوي رقم، يعني X يساوي A أو سالب A عندها أو X + +507 +00:49:36,220 --> 00:49:41,260 +يساوي Zero أظن X يساوي Zero هو محور الصادات، محور + +508 +00:49:41,260 --> 00:49:46,120 +Y، X يساوي ثلاث على اليمين بثلاث X يساوي سالب + +509 +00:49:46,120 --> 00:49:50,440 +ثلاث يبقى على الشمال بمقدار ثلاث يبقى هنا بقول + +510 +00:49:50,440 --> 00:49:56,600 +لو كان الـ A element موجود في دومين الدالة F يبقى أي + +511 +00:49:56,600 --> 00:50:05,040 +خط رأسي يمر بالنقطة هذه اللي إحداثياتها A و F of A + +512 +00:50:05,040 --> 00:50:10,940 +اللي هما الخط X يساوي A لا يمكن أن يقطع المنحنى + +513 +00:50:10,940 --> 00:50:19,200 +إلا في نقطة واحدة اللي هي A و F of A تمام يبقى + +514 +00:50:19,200 --> 00:50:24,560 +هاللي بقوله الآن أنا بروح أستخدم الاختبار هذا في + +515 +00:50:24,560 --> 00:50:29,500 +معرفة بعض الرسومات هل تمثل functions ولا لا تمثل + +516 +00:50:29,500 --> 00:50:34,780 +functions إذا بدنا نروح نأخذ المثال التالي يبقى + +517 +00:50:34,780 --> 00:50:35,360 +example + +518 +00:50:55,160 --> 00:51:09,900 +describe the graph of the following equations + +519 +00:51:21,840 --> 00:51:41,100 +undetermined whether the graph is + +520 +00:51:41,100 --> 00:51:41,500 +that + +521 +00:51:44,780 --> 00:51:53,880 +of a function or not + +522 +00:51:53,880 --> 00:52:00,200 +نمرة + +523 +00:52:00,200 --> 00:52:10,430 +a f of x يساوي x زائد absolute value لـ x نمرة b X + +524 +00:52:10,430 --> 00:52:16,910 +تربيع زائد Y تربيع يساوي تسعة و X أكبر من أو يساوي + +525 +00:52:16,910 --> 00:52:23,870 +زيرو نمرة C X تربيع زائد Y تربيع يساوي تسعة و Y + +526 +00:52:23,870 --> 00:52:32,270 +greater than or equal to zero نمرة D نمرة دي X تربيع + +527 +00:52:32,270 --> 00:52:38,890 +يساوي Y تربيع نمرة A absolute value لـ X زائد + +528 +00:52:38,890 --> 00:52:43,150 +absolute value لـ Y يساوي مين؟ يساوي واحد + +529 +00:52:52,350 --> 00:52:57,290 +نرجع لسؤالنا مرة ثانية بيقول describe the graph of + +530 +00:52:57,290 --> 00:53:01,830 +the following equations ايه وصف لي الرسم البياني + +531 +00:53:01,830 --> 00:53:06,930 +لكل من المعادلات التالية هذه يا شباب اختصار لكلمة + +532 +00:53:06,930 --> 00:53:11,170 +EQUATIONS + +533 +00:53:11,170 --> 00:53:14,630 +equations يعني معادلات + +534 +00:53:16,450 --> 00:53:21,730 +أنا بأختصرها إلى EQUN و S تبعت الإضافة أو تبعت + +535 +00:53:21,730 --> 00:53:27,090 +الجامعة يبقى هنا أوصف لي كل من المعادلات التالية و + +536 +00:53:27,090 --> 00:53:31,810 +أتعمد أقول معادلات لأن المعادلة قد تكون function و + +537 +00:53:31,810 --> 00:53:35,730 +قد لا تكون function أما لو قلت لك function يبقى + +538 +00:53:35,730 --> 00:53:39,850 +خلاص مضمونة لكن معادلة ممكن تبقى function و ممكن + +539 +00:53:39,850 --> 00:53:44,730 +ما تكونش function حدد لي هل الرسم + +540 +00:53:44,730 --> 00:53:52,270 +البياني يمثل دالة أو لا يمثل دالة Undetermined حدد + +541 +00:53:52,270 --> 00:53:56,830 +ليه whether the graph L الرسم البياني يمثل + +542 +00:53:56,830 --> 00:54:03,450 +function or not بنقوله بسيطة يبقى بدنا نيجي للدالة + +543 +00:54:03,450 --> 00:54:07,890 +الأولى الـ F of X يساوي X زائد absolute value لـ X + +544 +00:54:07,890 --> 00:54:13,610 +يبقى نمرة A الدالة F of X يساوي X زائد absolute + +545 +00:54:13,610 --> 00:54:20,670 +value لـ X هذه سوف أعرفها لكي أرسمها يبقى هذه أحد + +546 +00:54:20,670 --> 00:54:24,490 +أمرين يا شباب بدي أستخدم تعريف الـ absolute value + +547 +00:54:24,490 --> 00:54:31,170 +يبقى x زائد x إذا الـ x أكبر من أو يساوي zero و x + +548 +00:54:31,170 --> 00:54:37,490 +ناقص x إذا الـ x أقل من الـ zero صحيح ولا لا؟ مظبوط؟ + +549 +00:54:37,930 --> 00:54:45,830 +طيب هذه هي عبارة عن مين؟ 2X إذا الـ X أكبر من + +550 +00:54:45,830 --> 00:54:53,390 +أو يساوي Zero و Zero إذا الـ X أقل من Zero واضح أن + +551 +00:54:53,390 --> 00:54:59,530 +الـ domain قداش؟ كل الـ real line وطلعنا في الجزء + +552 +00:54:59,530 --> 00:55:03,590 +النظري قبل قليل قلنا كل الـ real line وقلنا الـ + +553 +00:55:03,590 --> 00:55:07,870 +range إيه اللي من وين لوين؟ من صفر لغاية ما نوصل + +554 +00:55:07,870 --> 00:55:10,870 +الكلام اللي قلناه بنروح نبينه الآن على الرسم + +555 +00:55:10,870 --> 00:55:16,070 +كلامنا صحيح ولا لأ؟ إذا بدنا نروح نرسم المحاور يبقى + +556 +00:55:16,070 --> 00:55:22,030 +هذه المحاور اللي عندنا هذا محور X هذا Y هذا Zero + +557 +00:55:23,620 --> 00:55:30,960 +يبقى احنا عندنا f of x يساوي zero إذا x أقل من الـ + +558 +00:55:30,960 --> 00:55:35,780 +zero يبقى لكل الـ x اللي أقل من الـ zero قيمة الدالة + +559 +00:55:35,780 --> 00:55:42,440 +قداش؟ تساوي صفر يبقى هنا هذا بيكون كل المنطقة اللي + +560 +00:55:42,440 --> 00:55:47,860 +عندنا هنا لغاية ما نصل إلى سالب الـ infinity بما + +561 +00:55:47,860 --> 00:55:52,490 +فيها الـ zero طب الـ zero جيبته من وين؟ جيبته من اللي + +562 +00:55:52,490 --> 00:55:57,370 +قبلها لو كانت x تساوي zero بصير اثنين في zero بـ + +563 +00:55:57,370 --> 00:56:03,130 +zero طيب لما أقول لك y تساوي اثنين سين هذه خطية + +564 +00:56:03,130 --> 00:56:07,550 +ولا لأ؟ خطية لأنها من أي درجة؟ من الدرجة الأولى + +565 +00:56:07,550 --> 00:56:11,170 +يبقى لما أقول لك y تساوي اثنين x معادلة من الدرجة + +566 +00:56:11,170 --> 00:56:15,830 +الأولى يعني معادلة خط مستقيم إذا يكفيني من الخط + +567 +00:56:15,830 --> 00:56:22,670 +المستقيم نقطتين تقعان عليه يبقى هذه إحداهما بدي + +568 +00:56:22,670 --> 00:56:27,390 +أجيب النقطة الثانية، لو كانت X بواحد يبقى هاي + +569 +00:56:27,390 --> 00:56:32,130 +واحد وهي اثنين يبقى بدها تجينا النقطة وين؟ اللي + +570 +00:56:32,130 --> 00:56:36,570 +عندنا هذا يبقى بدي أمسك الخط المستقيم بالمسطرة أو + +571 +00:56:36,570 --> 00:56:41,360 +القلم وأوصل الخط المستقيم اللي عندنا هذا يبقى هذا + +572 +00:56:41,360 --> 00:56:46,760 +الخط y تساوي اثنين x الخطين الاثنين مع بعض + +573 +00:56:46,760 --> 00:56:51,640 +يمثلون معادلة الدالة لأن f of x زائد absolute value + +574 +00:56:51,640 --> 00: + +601 +00:59:04,650 --> 00:59:10,670 +هو هذه معادلة إيش يا شباب؟ دائرة مدرجات ثانية + +602 +00:59:10,670 --> 00:59:13,190 +معادلة دائرة مركزها + +603 +00:59:14,730 --> 00:59:20,690 +نقطة الأصل (0,0) نصف قطرها ثلاثة. ممتاز جداً، يبقى هذا + +604 +00:59:20,690 --> 00:59:24,730 +أنتم مذاكرين كويس على كل الأحوال. ريحت هنا شوية يبقى + +605 +00:59:24,730 --> 00:59:31,150 +لو جئت للدائرة هذه ورحت قلت هذا محور X وهذا محور + +606 +00:59:31,150 --> 00:59:36,250 +Y وهذا نقطة الأصل وحبيت أرسم الدائرة بدي أرسمها + +607 +00:59:36,250 --> 00:59:41,150 +منقطة في الأول لأنّه مش عارف هذه هي دائرة كاملة ولا + +608 +00:59:41,150 --> 00:59:45,410 +نص دائرة ولا ربع دائرة ولا سدس دائرة، الله أعلم + +609 +00:59:45,410 --> 00:59:50,330 +يبقى لو جئت لدائرة هذه مركزها نقطة الأصل ونص قطرها + +610 +00:59:50,330 --> 00:59:58,300 +يساوي ثلاثة بالشكل اللي عنها تمام؟ اه، في condition + +611 +00:59:58,300 --> 01:00:03,660 +حاطط ليه؟ قال لي ممنوع الـ X تأخذ قيمة سالبة دائماً و + +612 +01:00:03,660 --> 01:00:10,080 +أبدأً. X يا إما بـ Zero يا إما بقيمة موجبة. من وين هي + +613 +01:00:10,080 --> 01:00:15,100 +المنطقة تمام؟ إذاً الدائرة الجزء هذا يبقى الجزء اللي + +614 +01:00:15,100 --> 01:00:18,810 +على اليمين يبقى عقلك الله ما فيش عندي دائرة على + +615 +01:00:18,810 --> 01:00:23,030 +الجزء الشمالي، يبقى هذا الله يساهل عليه مع السلامة + +616 +01:00:23,030 --> 01:00:28,830 +غير مأسوف عليه، يبقى ما ضلّش عندي إلاّ مين؟ إلاّ نصف + +617 +01:00:28,830 --> 01:00:32,550 +الدائرة اللي على اليمين، الشكل اللي عندنا هذا + +618 +01:00:32,550 --> 01:00:37,190 +تمام؟ بما فيها النقطة اللي عندنا هذه والنقطة اللي + +619 +01:00:37,190 --> 01:00:42,640 +عندنا هذه. خليني أسألك سؤال: النقطة الـ Zero هذه اللي + +620 +01:00:42,640 --> 01:00:48,880 +قال لي X أكبر من أو تساوي Zero، كم صورة لها تنتقل + +621 +01:00:48,880 --> 01:00:53,600 +لفوق ولتحت؟ يبقى هذه ليست Function، صح؟ + +622 +01:01:01,210 --> 01:01:07,290 +على اليمين. يبقى أي نقطة من Zero لغاية ثلاثة نصف + +623 +01:01:07,290 --> 01:01:12,910 +القطر اللي هو ثلاثة وهنا ثلاثة وهنا سالب ثلاثة + +624 +01:01:12,910 --> 01:01:18,010 +هذه سالب ثلاثة و Zero وهذه ثلاثة و Zero + +625 +01:01:18,010 --> 01:01:29,120 +وهذه ثلاثة و Zero و 3 و 3 و 0. اتحرك أي خط على + +626 +01:01:29,120 --> 01:01:34,340 +اليمين هتلاقي يقطع المنحنى معها في نقطتين. يبقى هذه + +627 +01:01:34,340 --> 01:01:40,400 +Function، يبقى هذه Not a function. يبقى هذه ليست + +628 +01:01:40,400 --> 01:01:49,250 +دالة. Not a function، يبقى هذه المعادلة لا تمثل دالة + +629 +01:01:49,250 --> 01:01:54,450 +بأي حال من الأحوال. ليش؟ لأن الـ vertical line test + +630 +01:01:54,450 --> 01:01:59,730 +بيقول: لو عملت خط رأسي بدّو يقطعها إلاّ وين؟ في نقطة + +631 +01:01:59,730 --> 01:02:05,810 +واحدة. طيب، نمرة C نفس المعادلة: X تربيع زائد Y تربيع + +632 +01:02:05,810 --> 01:02:11,980 +يساوي 9، و Y greater than or equal to 0 بنقول له تعالى + +633 +01:02:11,980 --> 01:02:18,700 +نشوف هذه المحاور وهذا محور X وهذا محور Y وهذا نقطة + +634 +01:02:18,700 --> 01:02:22,740 +الأصل اللي هي Zero، وبدنا نروح للدائرة اللي قلنا + +635 +01:02:22,740 --> 01:02:27,940 +عليها هيها ما اتغيرت بالشكل اللي عندنا هنا، تمام؟ + +636 +01:02:27,940 --> 01:02:31,720 +بس بدي أعرف هل هي دائرة كاملة والله شوية منها راح + +637 +01:02:31,720 --> 01:02:35,500 +قلّش يبقى Y أكبر من Y أقل من Y أقل من Y أقل من Y أقل + +638 +01:02:35,500 --> 01:02:37,060 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +639 +01:02:37,060 --> 01:02:40,800 +أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل + +640 +01:02:40,800 --> 01:02:43,000 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +641 +01:02:43,000 --> 01:02:44,260 +أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل + +642 +01:02:44,260 --> 01:02:47,960 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +643 +01:02:47,960 --> 01:02:53,070 +أقل من ما عنديش إلاّ النصف العلوي وبالتالي بيصير عندك + +644 +01:02:53,070 --> 01:02:57,530 +النصف العلوي بهذا الشكل، نصف القطر يساوي ثلاثة يبقى + +645 +01:02:57,530 --> 01:03:02,930 +هذه ثلاثة و Zero هذه سالب ثلاثة و Zero هذه Zero و + +646 +01:03:02,930 --> 01:03:07,580 +ثلاثة، يبقى نصف الدائرة العلوي، السؤال هو هل هذه + +647 +01:03:07,580 --> 01:03:13,560 +الرسمة تمثل Function؟ اه لأنّ ارسم أي خط رأسي وين + +648 +01:03:13,560 --> 01:03:20,560 +ما بدّك بتلاقيه بيقطعها بس وين؟ في نقطة واحدة فقط لا + +649 +01:03:20,560 --> 01:03:27,500 +غير. إذاً هذه تمثل Function، تمام؟ بدنا نيجي للسؤال + +650 +01:03:27,500 --> 01:03:32,200 +الثالث اللي هو D + +651 +01:03:33,770 --> 01:03:39,990 +بدي أجي لـ D، قال لي X تربيع بدها تساوي Y تربيع، + +652 +01:03:39,990 --> 01:03:45,670 +اه، معادلة إيش هذه؟ الشهادة يقول الله وعلا، مش عارفين، + +653 +01:03:45,670 --> 01:03:50,410 +لكن أرتّبها شوية يقولوا: ارتّبها كيف؟ خذ الجذر + +654 +01:03:50,410 --> 01:03:55,010 +التربيعي يا أخي للطرفين، يبقى أنا لو جئت أخذت الجذر + +655 +01:03:55,010 --> 01:03:59,550 +التربيعي للطرفين، الجذر التربيعي يلاّ Y تربيع بمين؟ + +656 +01:03:59,960 --> 01:04:04,940 +absolute value لـ Y، الجذر التربيعي لـ X بـ absolute + +657 +01:04:04,940 --> 01:04:12,960 +value لـ X، طيب شو رأيك؟ بدي أستبدل هذه المعادلة + +658 +01:04:12,960 --> 01:04:19,340 +بمعادلة أخرى وشوف كلامي صح ولا غلط، هذه بدي + +659 +01:04:19,340 --> 01:04:25,800 +أستبدلها فقط بالمعادلة Y تساوي زائد أو ناقص X، بنفع + +660 +01:04:25,800 --> 01:04:26,360 +هيك؟ + +661 +01:04:31,130 --> 01:04:35,290 +طيب، أنا شايف فيها غبش في وجوه البعض فيكم، شايف + +662 +01:04:35,290 --> 01:04:40,030 +فيها غبش يعني مش واضحة الصورة في ذهنه، تمام؟ يبقى + +663 +01:04:40,030 --> 01:04:44,690 +أنا بدي أمشي بعقلية اللي عندهم الغبش هذا ونشوف + +664 +01:04:44,690 --> 01:04:48,870 +النزيلة الغبش هذا والله يبقى هذه المعادلة لو رحت + +665 +01:04:48,870 --> 01:04:53,090 +شيلت لبس الـ absolute بدي أقول زائد أو ناقص Y تساوي زائد + +666 +01:04:53,090 --> 01:04:57,870 +أو ناقص X، أظن لو كتبت هيك ما حدا بيزعل، طب هذه كم + +667 +01:04:57,870 --> 01:05:06,200 +معادلة؟ أربع معادلات: Y تساوي X، هي Y تساوي X بالزائد، Y + +668 +01:05:06,200 --> 01:05:13,560 +تساوي ناقص X، هي Y تساوي ناقص X، بضل عندنا Y بالموجب + +669 +01:05:13,560 --> 01:05:20,520 +يساوي X وناقص X، خلصنا منها. بدي اخذ من ناقص Y، ناقص + +670 +01:05:20,520 --> 01:05:26,880 +Y تساوي X، اضرب في السالب يعني Y تساوي ناقص X يبقى + +671 +01:05:26,880 --> 01:05:31,630 +نفس المعادلة ولا لا؟ تمام. طيب، بدا أخذ الثانية: ناقص + +672 +01:05:31,630 --> 01:05:37,330 +Y تساوي ناقص X، لو ضربنا في السالب يعني Y تساوي X، مظبوط؟ + +673 +01:05:37,330 --> 01:05:42,730 +يبقى هذه الأربع معادلات هذي كالكزيدة، والحقيقة هي + +674 +01:05:42,730 --> 01:05:48,990 +معادلتين وليست أربع معادلات، مظبوط هيك؟ يبقى أزلنا + +675 +01:05:48,990 --> 01:05:54,450 +اللبس أو الغبش، يبقى هدول معادلتين فقط لغاية، طب + +676 +01:05:54,450 --> 01:06:01,990 +السؤال هو: لما أقول Y تساوي X، معادلة إيش؟ خط مستقيم، و + +677 +01:06:01,990 --> 01:06:12,500 +لما أقول Y تساوي سالب X، خط مستقيم، يبقى + +678 +01:06:12,500 --> 01:06:17,500 +خط مستقيم على طول الخط، لو جئت ارسم الخط اللي اتنين + +679 +01:06:17,500 --> 01:06:24,700 +هدول، يبقى هذا محور X وهذا محور Y، الخط الأول Y + +680 +01:06:24,700 --> 01:06:30,980 +تساوي X بنصف الربع الأول والربع الثالث، يعني هذا + +681 +01:06:30,980 --> 01:06:39,500 +الخط Y تساوي X، الخط الغامق هذا، أيوه تمام، يبقى هذا + +682 +01:06:39,500 --> 01:06:48,480 +الخط Y تساوي X، كويس. + +683 +01:06:50,210 --> 01:06:54,490 +طبعاً الزاوية هذه قد الزاوية هذه بالضبط تماماً، كل + +684 +01:06:54,490 --> 01:07:00,410 +واحدة فيهم خمسة وأربعين، يبقى هذا Y تساوي زائد X، + +685 +01:07:00,410 --> 01:07:05,850 +يعني Y تساوي X، الآن Y تساوي ناقص X، بنص في الربع الثاني + +686 +01:07:05,850 --> 01:07:11,370 +والربع الرابع، يبقى بدا نرسم هنا بهذا الشكل. + +687 +01:07:12,060 --> 01:07:19,520 +يبقى هذا Y تساوي سالب X، تمام تمام، ما عندوش قيود، + +688 +01:07:19,520 --> 01:07:24,240 +يبقى كل واحد ضد والد مستمر لـ Infinity. السؤال هو: + +689 +01:07:24,240 --> 01:07:29,940 +هل الرسم البياني هذا يمثل Function؟ أيوة Not + +690 +01:07:29,940 --> 01:07:37,030 +Function، ليش؟ لأن أي خط رأسي بده يقطع وين؟ نقطتين. + +691 +01:07:37,030 --> 01:07:41,390 +أي خط رأسي بدي أقطعه في نقطتين. طب، واحد يقول لي: طب + +692 +01:07:41,390 --> 01:07:45,530 +هاي واي بس قطع اتنين في نقطة واحدة، بقول لك مصبور لأنّ + +693 +01:07:45,530 --> 01:07:52,520 +أنا ما قلتش بس خط واحد، قلت لك أي خط رأسي إذا قطعه في + +694 +01:07:52,520 --> 01:07:56,820 +أكثر من نقطة يبقى ليست Functional حتى وإن حدث مش + +695 +01:07:56,820 --> 01:07:59,940 +مرة قطع في نقطة مرتين وثلاثة بس في نقطة، لكن + +696 +01:07:59,940 --> 01:08:04,460 +الباقي كله في نقطة ثانية يبقى ليست Functional. لازم + +697 +01:08:04,460 --> 01:08:09,940 +ولا مرة يقطع في نقطة واحدة، يبقى كله أي خط vertical line + +698 +01:08:09,940 --> 01:08:17,160 +يقطع في نقطة واحدة يبقى هادئ Function، يبقى + +699 +01:08:17,160 --> 01:08:22,400 +هذه ليست Function، تمام. هذه نمرة D. نيجي لنمرة C، دير + +700 +01:08:22,400 --> 01:08:26,660 +بالك، هذه أسئلة موجودة في الكتاب، من أسئلة التمرين + +701 +01:08:26,660 --> 01:08:32,320 +اللي في الكتاب، طيب، نيجي لنمرة E، نمرة E قال لي + +702 +01:08:32,320 --> 01:08:36,780 +absolute value لـ X، absolute value لـ Y تساوي واحد، + +703 +01:08:36,780 --> 01:08:42,930 +بدنا نرسم الرسم البياني لهذه الدالة. بدا نجي أشيل الـ + +704 +01:08:42,930 --> 01:08:46,890 +absolute value وأضع زائد أو ناقص زي ما حطينا هنا. + +705 +01:08:46,890 --> 01:08:52,410 +يبقى أنا عندي زائد أو ناقص X، زائد أو ناقص Y تساوي + +706 +01:08:52,410 --> 01:08:58,250 +واحد. هنا قلنا هدول مش أربع معادلات، هدول بس معادلة + +707 +01:08:58,250 --> 01:09:03,790 +سؤالنا هو هنا هدول أربع معادلات، والله معادلتين. + +708 +01:09:03,790 --> 01:09:10,630 +تعال نشوف المعادلة الأولى: X زائد Y تساوي واحد. + +709 +01:09:11,110 --> 01:09:16,410 +المعادلة الثانية: X ناقص Y تساوي واحد، المعادلة + +710 +01:09:16,410 --> 01:09:21,850 +الثالثة: ناقص X زائد Y تساوي واحد، المعادلة الرابعة + +711 +01:09:21,850 --> 01:09:29,770 +ناقص X ناقص Y يساوي كده؟ يساوي واحد، ولا واحدة فيهم + +712 +01:09:29,770 --> 01:09:36,970 +زي الثانية؟ طيب هذه الـ Y زائد X يساوي واحد، هذه + +713 +01:09:36,970 --> 01:09:40,990 +والله خليها بنفس الترتيب بلاش تقول لي بدلتهم، X + +714 +01:09:40,990 --> 01:09:48,030 +زائد Y يساوي واحد، وهذه X ناقص Y يساوي من؟ يساوي + +715 +01:09:48,030 --> 01:09:52,700 +واحد. شو رأيك هذه لو ضربتها في إشارة سالب؟ ما هو + +716 +01:09:52,700 --> 01:09:58,200 +بالضبط؟ X ناقص Y يساوي من؟ يساوي سالب واحد، هذا لو + +717 +01:09:58,200 --> 01:10:03,020 +ضربت بإشارة السالب X زائد Y يساوي سالب واحد، هتطلع + +718 +01:10:03,020 --> 01:10:07,620 +لهذه، وهذه بيختلفوا عن بعض، مظبوط؟ النتيجة هنا واحد + +719 +01:10:07,620 --> 01:10:11,040 +وهنا سالب واحد، رغم أن الطرف اليمين زي بعضه، لكن + +720 +01:10:11,040 --> 01:10:15,560 +الشمال لا. هذه وهذه طرف الشمال زي بعضه بالسالب؟ لا، + +721 +01:10:15,560 --> 01:10:20,920 +يبقى هذول أربع معادلات منفصلات، كل واحدة فيهم تمثل + +722 +01:10:22,570 --> 01:10:29,790 +بنرسم هذه الخطوط المستقيمة فبنقول هذا محور X هذا + +723 +01:10:29,790 --> 01:10:35,490 +محور Y، هذا نقطة الأصل اللي هي Zero، بدي أمسك الخط + +724 +01:10:35,490 --> 01:10:43,720 +الأول، لو كانت X بـ 0، Y بقد إيش؟ واحد، يبقى النقطة Zero + +725 +01:10:43,720 --> 01:10:50,740 +واحد، يبقى هذه النقطة Zero واحد، لو كانت Y بـ Zero، X + +726 +01:10:50,740 --> 01:10:55,080 +بقد إيش؟ واحد، يعني واحد و Zero، اللي هي النقطة اللي + +727 +01:10:55,080 --> 01:11:01,000 +عندنا هذه واحد و Zero، تمام؟ إذاً النقطتين تقعان على + +728 +01:11:01,000 --> 01:11:07,590 +الخط المستقيم الأول، يبقى ما عليّ إلاّ أجيب من هناك و + +729 +01:11:07,590 --> 01:11:12,750 +أوصل وأمد على استقامته يبقى هذا الخط المستقيم + +730 +01:11:12,750 --> 01:11:19,170 +الأول. طيب، نيجي للخط المستقيم الثاني: لو كانت Y بـ + +731 +01:11:19,170 --> 01:11:23,950 +Zero، X بقد إيش؟ يعني واحد و Zero اللي هي النقطة اللي + +732 +01:11:23,950 --> 01:11:31,180 +عندنا هذه، ما تغيرتش، مظبوط؟ طيب، لو كانت X بـ 0، و Y بـ + +733 +01:11:31,180 --> 01:11:35,960 +سالب واحد، لما تبقى X بـ 0، و Y بـ سالب واحد اللي هي + +734 +01:11:35,960 --> 01:11:41,120 +النقطة اللي هنا يبقى سالب واحد و Zero وسالب واحد + +735 +01:11:41,590 --> 01:11:48,310 +Zero وسالب واحد، تمام؟ يبقى النقطتين الاتنين تقعان + +736 +01:11:48,310 --> 01:11:53,890 +على الخط المستقيم يبقى روحنا رسمنا الخط المستقيم + +737 +01:11:53,890 --> 01:12:00,590 +بالشكل هذا يبقى هذا X زائد Y يساوي واحد، هذا X ناقص + +738 +01:12:00,590 --> 01:12:06,400 +Y يساوي واحد، خلصنا من هذا، نيجي لمستقيم الثالث، لو + +739 +01:12:06,400 --> 01:12:14,520 +كانت Y بـ 0، X سالب واحد يعني سالب واحد و Zero، سالب + +740 +01:12:14,520 --> 01:12:20,160 +واحد و Zero اللي هي النقطة هذه سالب واحد و Zero، يبقى + +741 +01:12:20,160 --> 01:12:25,840 +هنا، لو كانت Y بـ Zero، X بسالب واحد. طب لو كانت X + +742 +01:12:25,840 --> 01:12:32,170 +بـ Zero، Y بواحد، لو كانت X بـ Zero و Y بواحد اللي هي وين + +743 +01:12:32,170 --> 01:12:37,730 +النقطة اللي عندنا هذه فوق يبقى لأ بروح بوصل بين + +744 +01:12:37,730 --> 01:12:44,550 +النقطتين وأمدّ هذا على استقامته إذاً هذا X ناقص Y + +745 +01:12:44,550 --> 01:12:49,990 +يساوي ناقص واحد. بعد هيك بدا أقول هنا لو كانت X + +746 +01:12:49,990 --> 01:12:59,690 +بـ Zero و Y بسالب واحد، نقطة هذه، لو كانت Y بـ 0، X بسالب + +747 +01:12:59,690 --> 01:13:04,930 +واحد، Y بالنقطة هذه، بوصل بينهم بالشكل اللي عندنا + +748 +01:13:04,930 --> 01:13:10,570 +هذا بيصير هذا X زائد Y يساوي سالب واحد، يبقى الرسم + +749 +01:13:10,570 --> 01:13:17,170 +اللي قدامنا هذي تمام، طيب تمثل Function، أي خط + +750 +01:13:17,170 --> 01:13:22,530 +مستقيم أقل ما فيه سيقطع في نقطتين ما كانش في أربع، + +751 +01:13:22,970 --> 01:13:25,650 +لأنّ الخطوط المستقيمة ماشية على اطلاع ماشية يعني + +752 +01:13:25,650 --> 01:13:32,250 +ما هيّش مقيدة بفترة معينة، يبقى هذه Not a Function. + +753 +01:13:32,250 --> 01:13:37,290 +ما هيّش ده لأ بسبب الـ vertical line test، أي خط + +754 +01:13:37,290 --> 01:13:46,220 +مستقيم من فوق لتحت لو كانت إيش؟ + +755 +01:13:46,220 --> 01:13:51,740 +كمعادلة، ممتاز جداً، بتعتبرها كـ Function ولا لا؟ + +756 +01:13:51,740 --> 01:13:57,960 +إيش رأيك؟ أنا بقول لا، عارف ليش؟ لأنّ بيصير العنصر + +757 +01:13:57,960 --> 01:14:03,480 +الواحد له ما له نهاية من الصور. سؤال يا سميركو بيقول: ما + +758 +01:14:03,480 --> 01:14:08,740 +يأتي لو أنا أخذت الخط اللي عندنا هي المحاور وقلت + +759 +01:14:08,740 --> 01:14:14,400 +هذا X وهذا Y وأخذت الخط هذا مثلاً وهو vertical + +760 +01:14:14,400 --> 01:14:18,360 +line، باعتبرها Function ولا لا؟ بنقول له لا، + +761 +01:14:18,360 --> 01:14:22,390 +لماذا؟ لأنّ القيمة تبعت الـ X دا إلها ما شاء الله + +762 +01:14:22,390 --> 01:14:26,530 +صور جد ما بدّك فوق وبتاع يعني الصور اللي هو نفس + +76 + +801 +01:18:43,410 --> 01:18:46,850 +الواحد، وممكن ما يلتجئوا عند الواحد، يمكن أو يمكن + +802 +01:18:46,850 --> 01:18:52,450 +لأ، مظبوط ولا لأ؟ لكن جالي يساوي ويساوي معناته في + +803 +01:18:52,450 --> 01:18:57,610 +التقاء لازم يكون في التقاء، صحيح ولا لأ؟ الالتقاء + +804 +01:18:57,610 --> 01:19:01,730 +هذا، بدي أشوف هل بيحصل ولا بيحصلش؟ + +805 +01:19:03,730 --> 01:19:07,730 +المشكلة وين؟ عند الواحد، مش هنا هي الواحد، أكبر + +806 +01:19:07,730 --> 01:19:11,730 +وساقه واحد، يعني المنحنى ممكن تقول هذا جاي خط + +807 +01:19:11,730 --> 01:19:14,790 +مستقيم وهذا جاي قَصّ والتقوا عند النقطة هذه اللي هي + +808 +01:19:14,790 --> 01:19:17,650 +واحد، إذا المشكلة بتكون عند واحد، يمكن يكون في + +809 +01:19:17,650 --> 01:19:21,730 +اتصال وممكن يكون فيش اتصال، صحيح ولا لا؟ يمكن عند + +810 +01:19:21,730 --> 01:19:25,510 +الواحد تبقى الدالة معرفة وممكن ما تكونش معرفة كل + +811 +01:19:25,510 --> 01:19:29,390 +الاحتمالات واردة الدالة قابلة للاشتقاق ويمكن مش + +812 +01:19:29,390 --> 01:19:32,790 +قابلة للاشتقاق زي ما احنا بناخد بعد ذلك الدالة + +813 +01:19:32,790 --> 01:19:37,110 +متصلة أو ويرمى كل الاحتمالات بيصير واردة كويس احنا + +814 +01:19:37,110 --> 01:19:41,390 +ما بناش نبحث هذا احنا بنبحث بس هل الدالة معرفة عند + +815 +01:19:41,390 --> 01:19:45,550 +هذه النقطة أو لا إذا معرفة تمام مش معرفة خلاص ليست + +816 +01:19:45,550 --> 01:19:51,190 +function صحيح ولا لأ؟ إذا مشان هيك بتروح أجيبله F + +817 +01:19:51,190 --> 01:19:57,160 +of واحد يبقى f of واحد يساوي أقل من إذا يساوي واحد + +818 +01:19:57,160 --> 01:20:02,980 +يبقى بنعوض في الأولى يبقى 2 ناقص 3 في 1 + +819 +01:20:02,980 --> 01:20:12,050 +تكعيب اللي هو قداش؟ ناقص 1 بط ولكن كذلك f of واحد + +820 +01:20:12,050 --> 01:20:17,810 +لأنها معرفة عند الواحد يساوي كده يبقى يساوي 3 في + +821 +01:20:17,810 --> 01:20:24,110 +واحد، آه 4 ناقص 3 يساوي 0 هذا العنصر + +822 +01:20:24,110 --> 01:20:28,710 +الواحد كم صورة؟ جينا له صورتين يبقى هذه function + +823 +01:20:28,710 --> 01:20:38,850 +يبقى not a function يبقى هذا بده يعطيلك أنه given + +824 +01:20:38,850 --> 01:20:47,990 +expression الصيغة المعطاة دي مالها؟ is not a + +825 +01:20:47,990 --> 01:20:58,090 +function because السبب أنه سالب واحد بدأ لا تساوي + +826 +01:20:58,090 --> 01:21:04,110 +zero بس هنا طلعت بتساوي بعض وهذا كلام ماله؟ مرفوض + +827 +01:21:07,980 --> 01:21:14,440 +بنجي للمثال الثاني example two + +828 +01:21:14,440 --> 01:21:18,960 +بقول sketch the graph of the function + +829 +01:21:28,510 --> 01:21:36,010 +ارسم لرسمة الدالة f of x يساوي أحد ثلاثة أمور يا + +830 +01:21:36,010 --> 01:21:43,110 +إما 4 لما الـ X أقل من سالب 2 يا إما X + +831 +01:21:43,110 --> 01:21:50,700 +تربيع لما سالب 2 أقل من أو يساوي X أقل من أو + +832 +01:21:50,700 --> 01:21:57,680 +يساوي 0 يا إما X لما الـ X greater than Zero + +833 +01:22:00,770 --> 01:22:05,330 +يقول احنا عندنا piecewise function مش جزئين ثلاثة + +834 +01:22:05,330 --> 01:22:11,050 +أجزاء قال لي ارسملي هذه الدالة بقوله تعال نشوف + +835 +01:22:11,050 --> 01:22:18,630 +كيف بدنا نرسم هذه الدالة بقوله هذه المحاور وهذا + +836 +01:22:18,630 --> 01:22:28,030 +محور X وهذا محور Y وهذا نقطة الأصل اللي هي Zero إذا + +837 +01:22:28,030 --> 01:22:34,570 +X أقل من سالب 2 قيمة الدالة كده يبقى هذه Zero + +838 +01:22:34,570 --> 01:22:41,410 +وهذا سالب 1 وهذه سالب 2 وهذه سالب 3 عند + +839 +01:22:41,410 --> 01:22:45,230 +السالب 2 وقبل السالب 2 قيمة الدالة كده + +840 +01:22:45,230 --> 01:22:52,790 +يبقى أنا بدي اطلع فوق وهي اللي عندنا من هنا اللي هي + +841 +01:22:52,790 --> 01:22:59,770 +الـ 4 يبقى قبل السالب 2 خط مستقيم دالة ثابتة + +842 +01:22:59,770 --> 01:23:06,770 +قيمتها تساوي قداش؟ 4 وما فيش يساوي عندما تساوي + +843 +01:23:06,770 --> 01:23:09,670 +سالب 2 الدالة قداش بتكون؟ + +844 +01:23:15,730 --> 01:23:22,770 +بس أنا مقيد بمين؟ بالفترة من سالب 2 لغاية zero + +845 +01:23:22,770 --> 01:23:28,250 +فقط غير يبقى الـ parabola بديجي هيك وممنوع يطلع + +846 +01:23:28,250 --> 01:23:32,470 +وممنوع يفوت هيك لإيش؟ لأن عند السالب 2 تربيع + +847 +01:23:32,470 --> 01:23:38,760 +بصير 4 يبقى بديبدأ من عند النقطة هذه ويكون قاس + +848 +01:23:38,760 --> 01:23:46,490 +بهذا الشكل مغلقة عند سالب 2 بالسبب أن هذه تساوي 4 + +849 +01:23:46,490 --> 01:23:51,510 +مش بالسبب الأول مغلقة بالشكل اللي إن هذا تمام + +850 +01:23:51,510 --> 01:23:58,150 +وصلنا لـ 0 وخلصنا لغاية 0 كمان يساوي 0 تربيع بـ 0 + +851 +01:23:58,150 --> 01:24:05,930 +إذا من هنا كمان مغلقة تماماً يبقى هذا هو الـ 4 + +852 +01:24:05,930 --> 01:24:11,620 +وهذا هو الـ X تربيع قال لي بعد هيك بعد الـ zero + +853 +01:24:11,620 --> 01:24:17,620 +فالدالة تساوي من X يعني Y تساوي يعني الـ X تساوي + +854 +01:24:17,620 --> 01:24:24,360 +بنرسم خط قبل شوية يعني خط ينصف من الربع الأول + +855 +01:24:24,360 --> 01:24:31,000 +بهذا الشكل خط مستقيم يبقى هذا Y تساوي X هذا Y + +856 +01:24:31,000 --> 01:24:37,680 +تساوي X تربيع هذا Y تساوي 4 يبقى هذه دالة مكونة + +857 +01:24:37,680 --> 01:24:45,960 +من ثلاثة أجزاء خط مستقيم أفقي خط مائل قوس Y تساوي + +858 +01:24:45,960 --> 01:24:51,260 +X تربيع طبعاً هذه أمثلة سهلة ننتقل شوية + +859 +01:25:00,040 --> 01:25:04,620 +بالنسبة للنقطة الأولى بتكون مفتوحة هنا لكن لما + +860 +01:25:04,620 --> 01:25:08,340 +جاب لي يساوي للسالب 2 إذا عندي السالب 2 + +861 +01:25:08,340 --> 01:25:13,780 +بدا تبقى مغلقة فرحنا أغلقناها من هنا يساوي ال + +862 +01:25:13,780 --> 01:25:19,500 +zero يبقى أغلقناها من عن الـ zero الباقي مفتوحة طيب + +863 +01:25:19,500 --> 01:25:25,690 +بنجي لمثال رقم 3 ثلاثة حاجة اسمه إلى نقطة إيه؟ + +864 +01:25:25,690 --> 01:25:33,590 +لأنه very important يبقى example 3 حاجة اسمه + +865 +01:25:33,590 --> 01:25:38,910 +إلى نقطة إيه؟ في الأول the integer floor function + +866 +01:25:38,910 --> 01:25:49,030 +integer floor function دالة الأرض is the function + +867 +01:25:49,030 --> 01:25:52,010 +whose + +868 +01:25:55,840 --> 01:26:05,860 +value with value at with + +869 +01:26:05,860 --> 01:26:18,820 +value at any real number x is + +870 +01:26:18,820 --> 01:26:23,680 +the greatest + +871 +01:26:28,030 --> 01:26:41,650 +integer less than or equal less than or equal to x + +872 +01:27:08,850 --> 01:27:14,030 +مرة ثانية نقرأ الكلام اللي مكتوب نحاول نفهم ما هو + +873 +01:27:14,030 --> 01:27:19,410 +مكتوب لنروح نطبقه على أرض الواقع بأمثلة مختلفة + +874 +01:27:19,410 --> 01:27:24,450 +إيش بقول the integer floor function قبل المبدأ + +875 +01:27:24,450 --> 01:27:30,950 +سمعته بالثانوية بدالة صحيح C هي دالة صحيح C بس بدي + +876 +01:27:30,950 --> 01:27:37,540 +أجزاءها لإيش؟ إلى جزءين دالة الأرض ودالة السقف، دالة + +877 +01:27:37,540 --> 01:27:41,960 +الأرض لأنها بنزل العدد الكسري للأرض ودالة السقف + +878 +01:27:41,960 --> 01:27:47,320 +بنطلع العدد الكسري للأعلى للسقف يعني للعدد الصحيح + +879 +01:27:47,320 --> 01:27:50,980 +اللي بيجي بعده أو اللي بيجي قبله حسب طبيعة المثال + +880 +01:27:51,510 --> 01:27:55,630 +the integer of lower function يعني دالة مين؟ يعني + +881 +01:27:55,630 --> 01:27:57,990 +بالبلدي إن قلت لك 2.9، ممكن + +882 +01:27:57,990 --> 01:28:03,030 +تنزلها لوين؟ لـ 2 ممتاز يبقى is the function هي + +883 +01:28:03,030 --> 01:28:08,470 +دالة whose value اللي قيمته at any real number X + +884 +01:28:08,470 --> 01:28:14,550 +ما قالتش عدد صحيح، real صحيح، والله الكسري is the + +885 +01:28:14,550 --> 01:28:22,260 +greatest integer أكبر رقم less than يكون أقل من أو + +886 +01:28:22,260 --> 01:28:27,880 +يكون مساوياً لـ X يبقى إيش قال هنا is the greatest + +887 +01:28:27,880 --> 01:28:35,340 +integer أكبر رقم يكون مساوياً أو أقل منه فمثلاً لما + +888 +01:28:35,340 --> 01:28:40,760 +قلت لك 2.9 إيش الرقم الصحيح اللي أقل + +889 +01:28:40,760 --> 01:28:48,300 +منه؟ 2 لما قلت لك 2 2 لأنه قال لي أقل منه + +890 +01:28:48,300 --> 01:28:53,920 +أو مساوياً له إذا بيساوي يبقى بنأخذ عليه for example + +891 +01:28:53,920 --> 01:29:05,040 +بديها الرمز اللي هو F of X يساوي هيك وبقول X تمام + +892 +01:29:05,040 --> 01:29:09,340 +زي اللي قاعد على كرسي يبقى هذه هي دالة اللي هو + +893 +01:29:09,340 --> 01:29:15,080 +الأرض يبقى for example لو جيت قلت لك لـ 2 إيش + +894 +01:29:15,080 --> 01:29:23,020 +بدك تقول؟ لـ 2 لو قلت لك هنا دالة الأرض لـ 2 + +895 +01:29:23,020 --> 01:29:30,050 +و.99 من مين؟ 2 برضه يبقى هذه اللي هو + +896 +01:29:30,050 --> 01:29:39,830 +الـ 2 لو قلت لك قداش 2.01 من + +897 +01:29:39,830 --> 01:29:44,790 +عشر من مية برضه 2 يعني هدول 2 بيساوي بعض + +898 +01:29:44,790 --> 01:29:51,430 +وبيساوي هذا يساوي 2 طيب بلاش دالة الأرض لـ zero + +899 +01:29:52,510 --> 01:30:01,910 +0 زي ما هي طيب دالة الأرض لمين؟ لسالب 3.1 + +900 +01:30:01,910 --> 01:30:07,870 +من العشرة قول يا ابني سالب 4 سالب 4 هي + +901 +01:30:07,870 --> 01:30:11,350 +الإجابة اللي بقول عليها حد إيه اللي اعتراض على هذه + +902 +01:30:11,350 --> 01:30:17,230 +الإجابة؟ سالب 4 أقل من سالب 3.1 من عشر، + +903 +01:30:17,230 --> 01:30:22,450 +واحنا قلنا بأول رقم أقل منه يبقى هذه إجابة صحيحة + +904 +01:30:22,450 --> 01:30:29,290 +وما عداها فهي إجابة خاطئة طيب لو جيت قلت لك هذه يا + +905 +01:30:29,290 --> 01:30:34,030 +سيد العزيز سالب + +906 +01:30:34,030 --> 01:30:40,530 +3.99 برضه طيب ماشي الحال + +907 +01:30:40,530 --> 01:30:48,310 +طيب بدي أقول لك سالب 0.3 من عشر سالب 1 + +908 +01:30:48,310 --> 01:30:53,990 +يعني كمان طيب سالب 1 ماشي سالب 1 وهكذا يبقى + +909 +01:30:53,990 --> 01:30:58,850 +هذه كلها إجابات صحيحة طيب هذه خلصنا إيه؟ بدنا نروح + +910 +01:30:58,850 --> 01:31:03,230 +لنمرة 5 طبعاً هرسم لك إياها بعد قليل بس خلينا ناخد + +911 +01:31:03,230 --> 01:31:08,370 +نمرة 5 يبقى بيننا بـ a the integer ceiling function + +912 +01:31:08,370 --> 01:31:14,230 +هي دالة السقف the integer ceiling + +913 +01:31:14,230 --> 01:31:18,110 +function + +914 +01:31:18,110 --> 01:31:27,230 +is the function whose value is the function whose + +915 +01:31:27,230 --> 01:31:36,290 +value القيمة بتاعتها at any real number at any real + +916 +01:31:36,290 --> 01:31:51,750 +number x is the smallest is the smallest is + +917 +01:31:51,750 --> 01:31:58,070 +the smallest integer greater + +918 +01:31:58,070 --> 01:31:58,970 +than + +919 +01:32:03,570 --> 01:32:10,210 +Greater than or equal to + +920 +01:32:10,210 --> 01:32:11,270 +X + +921 +01:32:42,620 --> 01:32:49,700 +العدد الصحيح تبع السقف وليس تبع الأرض هو عبارة عن + +922 +01:32:49,700 --> 01:32:54,800 +الدالة whose value قيمتها number X عند أي عدد + +923 +01:32:54,800 --> 01:33:02,040 +حقيقي X هو أصغر + +924 +01:33:02,040 --> 01:33:08,150 +رقم يكون greater than or equal to X يعني بدل ما كنت + +925 +01:33:08,150 --> 01:33:13,430 +بتنزل للأرض هتطلع لوين؟ للسقف تمام؟ طيب بدي + +926 +01:33:13,430 --> 01:33:18,650 +أمسك الأعداد هذه وأشوف إذا لو أنا بدي دالة السقف + +927 +01:33:18,650 --> 01:33:23,630 +للـ 2 قداش بتساوي؟ 2 طيب يعني لاحظ السقف + +928 +01:33:23,630 --> 01:33:28,330 +والأرض للعدد الصحيح 2 are equal طب لو جيت + +929 +01:33:28,330 --> 01:33:36,970 +قلت لك دالة السقف للـ 2.01 يبقى 3 بدي + +930 +01:33:36,970 --> 01:33:42,650 +دالة السقف لـ 2.99 يبقى 3 + +931 +01:33:42,650 --> 01:33:48,030 +برضه كله بطلع للعدد الصحيح اللي بيجي بعده هذه + +932 +01:33:48,030 --> 01:33:54,150 +قلناها لو جيت قلت لك دالة السقف لمين؟ لـ zero يبقى + +933 +01:33:54,150 --> 01:34:03,990 +zero بده دالة السقف لسالب 3.1 من عشر كملة + +934 +01:34:03,990 --> 01:34:07,130 +الروايات زي المرض اللي فاتت + +935 +01:34:09,750 --> 01:34:15,470 +سالب 3 سالب 3 أكبر من سالب 3.1 من + +936 +01:34:15,470 --> 01:34:21,150 +عشرة يبقى هذه السالب ركزي كويس من جيبها هذه كرناها + +937 +01:34:21,150 --> 01:34:25,370 +بدل المرة مرات في الخيارات المتعددة هذه اللي + +938 +01:34:25,370 --> 01:34:30,710 +بتسبب لك أشكالية بنحط السؤال فيها في الغالب تمام؟ طيب + +939 +01:34:30,710 --> 01:34:38,210 +لو جيت قلت لك دالة الصفر السالب 0.3 من + +940 +01:34:38,210 --> 01:34:46,730 +عشرة 0 ممتاز جداً يبقى 0 خلاصنا هي يبقى كل الأرقام + +941 +01:34:46,730 --> 01:34:53,130 +اللي موجودة عندنا طيب بنحاول نرسم A شكل الدالة يا + +942 +01:34:53,130 --> 01:34:58,910 +شباب نكتب هيك Y أو F of X يساوي دالة السقف لـ X + +943 +01:34:58,910 --> 01:35:04,550 +بالشكل هذا هنا هنا هي كرسي هنا بنعملها سقف بالشكل + +944 +01:35:04,550 --> 01:35:08,510 +اللي عندنا بدا نرسم كل function من ال functions + +945 +01:35:08,510 --> 01:35:15,010 +هدول بدا نيجي لرسمة الدالة الأولى يبقى هذا محور X + +946 +01:35:15,010 --> 01:35:22,450 +هذا محور Y خلي بالك هنا بدا تخيل عند الخط الوهمي هذا + +947 +01:35:22,450 --> 01:35:26,890 +مش من ضمن الرسمة مالوش دعوة بالرسمة هذا الخط + +948 +01:35:26,890 --> 01:35:28,730 +الوهمي اللي عندك أكثر + +949 +01:35:31,740 --> 01:35:40,060 +هذا الخط اللي هو Y تساوي X شوف يا سيدي نبدأ من عند + +950 +01:35:40,060 --> 01:35:46,380 +الـ Zero هذا Zero وهذا 1 وهذا 2 وهذا + +951 +01:35:46,380 --> 01:35:53,660 +3 وهنا 1 وهنا 2 وهنا 3 وهنا + +952 +01:35:53,660 --> 01:36:00,750 +سالب 1 وهنا سالب 2 وهنا سالب 3 وهنا + +953 +01:36:00,750 --> 01:36:06,810 +سالب 1 ثم سالب 2 ثم سالب 3 ثم سالب 4 + +954 +01:36:06,810 --> 01:36:07,870 +ثم سالب 5 ثم سالب 5 ثم سالب 5 ثم سالب + +955 +01:36:07,870 --> 01:36:09,470 +5 ثم سالب 5 ثم سالب 5 ثم سالب 5 ثم + +956 +01:36:09,470 --> 01:36:10,370 +سالب 5 ثم سالب 5 ثم سالب 5 ثم سالب 5 + +957 +01:36:10,370 --> 01:36:11,310 +ثم سالب 5 ثم سالب 5 ثم سالب 5 ثم سالب + +958 +01:36:11,310 --> 01:36:17,690 +5 ثم سالب 5 ثم سالب 5 ثم سالب 5 ثم + +959 +01:36:17,690 --> 01:36:28,760 +سالب 5 ثم سالب 5 ثم سالب 5 فوق 2 + +960 +01:36:28,760 --> 01:36:33,980 +هنسميها الدالة الدرجية أو الدالة السلمية يبقى هنا + +961 +01:36:33,980 --> 01:36:39,600 +بديجي لك اللي هو الـ 2 مغلقة وهي 3 لفوق وهي + +962 +01:36:39,600 --> 01:36:47,060 +3 تمام؟ يبقى مغلقة وبعد هيك تمشي لقبال الـ 3 + +963 +01:36:47,360 --> 01:36:53,040 +و بتكون مفتوحة وهكذا تمام؟ من الناحية هذه برضه + +964 +01:36:53,040 --> 01:36:58,840 +بنفس الطريقة بتيجي لتحت السالب 1 مغلقة وبتيجي + +965 +01:36:58,840 --> 01:37:05,080 +عند السالب 1 مفتوحة الآن بتيجي عند 2 تحت + +966 +01:37:05,080 --> 01:37:14,050 +السالب 2 مغلقة وهيك بتيجي مفتوحة هنا تحت السالب + +967 +01:37:14,050 --> 01:37:24,270 +3 دوري مغلقة وهنا مفتوحة يبقى هذا رسم تمين الـ + +968 +01:37:24,270 --> 01:37:31,030 +function الأولى اللي هو Y تساوي دالة الأرض لمين؟ للـ + +969 +01:37:31,030 --> 01:37:36,760 +X نجي للدالة الثانية اللي هي دالة السقف يبقى دالة + +970 +01:37:36,760 --> 01:37:43,340 +السقف هذا محور X هذا محور Y هذه نقطة الأصل اللي هي + +971 +01:37:43,340 --> 01:37:50,100 +Zero بدا أتخيل الخط الوهمي نفسه اللي هو Y تساوي X + +972 +01:37:50,100 --> 01:37:55,780 +Y + +1001 +01:40:53,830 --> 01:40:58,930 +الرسمة؟ هذي تعالَ هذي هذي تبقى تطلع على فوق تمام + +1002 +01:40:58,930 --> 01:41:04,110 +عند ال zero ب zero عند ال واحدة من العشرة تطلع + +1003 +01:41:04,110 --> 01:41:08,050 +للواحد عند تسعة من العشرة تطلع للواحد عند الواحد + +1004 +01:41:08,050 --> 01:41:12,190 +بواحد عند الواحد واحد من العشرة تطلع للاتنين و + +1005 +01:41:12,190 --> 01:41:16,210 +هكذا، وبالتالي الجزء السليم زي ذلك عرفنا كيف الرأس + +1006 +01:41:16,210 --> 01:41:20,950 +مجد مش حيال الله يخبط ويمشي لأ لأ هذه جت بناء على + +1007 +01:41:20,950 --> 01:41:27,690 +فهمنا اللي موجود هناك بدي أسأل سؤال جداش إيه ال + +1008 +01:41:27,690 --> 01:41:34,650 +domain لدالة الأرض هذه؟ + +1009 +01:41:36,310 --> 01:41:41,490 +الأولى كداش ال domain لها؟ هل هناك نقطة دالة غير + +1010 +01:41:41,490 --> 01:41:48,090 +معرفة عندها؟ لأ يعني لكل ال real line طيب هل هذا + +1011 +01:41:48,090 --> 01:41:56,910 +هو domain الدالة الثانية تبعت السقف؟ هو نفسه ولا + +1012 +01:41:56,910 --> 01:42:02,630 +لأ؟ يعني ويسوي كداش؟ من سالب infinity إلى infinity + +1013 +01:42:02,630 --> 01:42:10,630 +لكل real line طب بدّ ال range لدالة + +1014 +01:42:10,630 --> 01:42:18,290 +الأرض بدّ ال range كل + +1015 +01:42:18,290 --> 01:42:23,530 +الأعداد معنى إيش؟ ال range يعني أستفيد الأعداد + +1016 +01:42:23,530 --> 01:42:24,250 +الصحيحة + +1017 +01:42:29,140 --> 01:42:34,920 +كل الأعداد، كل الـ real، يعني هدول؟ طيب، في الإجابة، + +1018 +01:42:34,920 --> 01:42:38,260 +استنى شوية، في الصورة اللي عندك هذا اللي أنت + +1019 +01:42:38,260 --> 01:42:44,300 +شايفها، في كسر موجود؟ يبقى الإجابة بس اللي عدده + +1020 +01:42:44,300 --> 01:42:48,100 +صحيح، مش هستفيد اللي عدده الصحيح، بس تبعد كل + +1021 +01:42:48,100 --> 01:42:55,970 +الكسور، يبقى هتلاقي ال range لهذه هو نفس ال range + +1022 +01:42:55,970 --> 01:43:06,080 +لدالة السقف اللي عندنا هذه هو منهو الـ zero زاد أو + +1023 +01:43:06,080 --> 01:43:12,720 +ناقص واحد، زاد أو ناقص اتنين، زاد أو ناقص تلاتة، + +1024 +01:43:12,720 --> 01:43:19,500 +وفاصلة، وتظلك ماشي إلى أي شيء الله، يبقى عارفين + +1025 +01:43:19,500 --> 01:43:20,980 +الست هذه جسمها؟ + +1026 +01:43:23,210 --> 01:43:28,550 +مجموعة الأعداد الصحيحة the set of integers يبقى + +1027 +01:43:28,550 --> 01:43:36,830 +هذه بدل سوى set Z عندنا اللي هي the set of + +1028 +01:43:36,830 --> 01:43:43,930 +integers يبقى هذه عبارة عن مجموعة الأعداد الصحيحة + +1029 +01:43:43,930 --> 01:43:48,770 +بلا استثناء تمام؟ + +1030 +01:43:50,990 --> 01:43:54,630 +ركزي عليه الشغل هذه يبقى domain الدالة الأولى هو + +1031 +01:43:54,630 --> 01:43:58,950 +domain الدالة الثانية the set of all real numbers + +1032 +01:43:58,950 --> 01:44:03,390 +ضال مين عندنا؟ ضال ال range ال range هنا بيعطينيش + +1033 +01:44:03,390 --> 01:44:09,190 +إلا أعداد صحيحة هذا الخط كله يعتبر قداش اتنين، هنا + +1034 +01:44:09,190 --> 01:44:14,420 +اتنين، هنا اتنين، هنا اتنين، كله اتنين هنا واحد هنا + +1035 +01:44:14,420 --> 01:44:19,520 +صفر هنا سالب واحد يبقى عندي zero واحد اتنين تلاتة + +1036 +01:44:19,520 --> 01:44:22,400 +اربعة خمسة سالب واحد سالب اتنين يبقى مجموعة + +1037 +01:44:22,400 --> 01:44:26,600 +الاعداد الصحية وهكذا بالنسبة للرسم الثاني ال + +1038 +01:44:26,600 --> 01:44:29,140 +domain الدالة الأولى هو domain الدالة الثانية هو + +1039 +01:44:29,140 --> 01:44:32,400 +the set of all real numbers ال range تبع الدالة + +1040 +01:44:32,400 --> 01:44:35,020 +الأولى هو ال range تبع الدالة الثانية هو مجموعة + +1041 +01:44:35,020 --> 01:44:41,180 +الاعداد الصحية لا يزال عندنا كلام كثير يبقى بنكتفي + +1042 +01:44:41,180 --> 01:44:46,240 +هذا اليوم أو في هذه المحاضرة وسنعود إلى ال + +1043 +01:44:46,240 --> 01:44:51,200 +piecewise function بمثال جديد المحاضرة القادمة إن + +1044 +01:44:51,200 --> 01:44:51,700 +شاء الله diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..b87d2b8afec1d45ebf672fed113e93dc754d0220 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc_postprocess.srt @@ -0,0 +1,4176 @@ +1 +00:00:21,020 --> 00:00:25,220 +بسم الله الرحمن الرحيم نواصل الآن ما ابتدأنا به + +2 +00:00:25,220 --> 00:00:30,160 +المحاضرة الماضية المحاضرة الماضية بدأنا بأول مثال + +3 +00:00:30,160 --> 00:00:34,740 +على ال function أعطيناكوا صيغ مختلفة ل functions + +4 +00:00:34,740 --> 00:00:39,140 +مختلفة و طلبنا ال domain و ال range و الآن بنواصل + +5 +00:00:39,140 --> 00:00:42,950 +في نفس الموضوعالمثال كان معناه المرة اللي فاتت + +6 +00:00:42,950 --> 00:00:45,210 +find the domain and range of the following + +7 +00:00:45,210 --> 00:00:51,050 +functions بدنا المجال والمدى لكل من الدوال التالية + +8 +00:00:51,050 --> 00:00:57,130 +دالة رقم ستة F of X يساوي X زائد absolute value ل + +9 +00:00:57,130 --> 00:01:00,990 +X ذكرنا المرة الماضية ان ال domain تبع الدالة هو + +10 +00:01:00,990 --> 00:01:07,550 +القيم التي تأخذها X حتى تكون الدالة معرفة سؤالنا + +11 +00:01:07,550 --> 00:01:13,380 +هوهل هناك قيمة ال X بتجعل F of X ماهياش معرفة هنا + +12 +00:01:13,380 --> 00:01:19,140 +على ال real line يعني لو أخدنا أي real number أي + +13 +00:01:19,140 --> 00:01:24,160 +عدد حقيقي وعوض مابو هنا بتطلع ده لا معرفة ولا لا + +14 +00:01:24,160 --> 00:01:28,120 +معرفة مادام معرفة إذا ال domain تبقى الدالة من وين + +15 +00:01:28,120 --> 00:01:33,880 +لوين كل ال R أو من سلب infinity إلى infinite كتبت + +16 +00:01:33,880 --> 00:01:38,920 +R ماشي الحال6 of real numbers كتبتلي من سالب + +17 +00:01:38,920 --> 00:01:43,060 +infinity ل infinity معناه مشكلة هذا الصيغة و هذا + +18 +00:01:43,060 --> 00:01:47,700 +الصيغة الاتنين are the same طيب هذا ال domain بدنا + +19 +00:01:47,700 --> 00:01:52,560 +ال range المرة الماضية ذكرنا انه ال range بدي اخد + +20 +00:01:52,560 --> 00:01:56,080 +من ال domain و اعوض في الدالة القيم اللي بتطلع + +21 +00:01:56,080 --> 00:02:00,640 +بتكون هي ال range تبع هذه الدالة يبقى بنفضل نبدأ + +22 +00:02:00,640 --> 00:02:04,280 +من عند zero نتحرك على اليمين ثم نبدأ من عند zero + +23 +00:02:04,280 --> 00:02:08,960 +نتحركاللي بيطلع عنا بيكون هو ال real number فلو + +24 +00:02:08,960 --> 00:02:15,340 +أخدت X ب Zero يبقى الناتج كده؟ Zero يبقى Zero من + +25 +00:02:15,340 --> 00:02:21,920 +ضمن الرين اتحرك على اليمين خدلي واحد مثلا اتمين طب + +26 +00:02:21,920 --> 00:02:30,590 +خدلي تلاتة و نص سبع تمام خدلي ميةمتين، ألف، ألفين، + +27 +00:02:30,590 --> 00:02:34,490 +مليون، اتنين، ايه؟ يبقى رايحين لوين؟ للمالة نهاية + +28 +00:02:34,490 --> 00:02:40,570 +فبنمشي العكس بالسالب لو أخدنا سالب واحد سالب واحد + +29 +00:02:40,570 --> 00:02:45,270 +زيد absolute value لسالب واحد absolute value لسالب + +30 +00:02:45,270 --> 00:02:50,410 +واحد مقداش؟ واحد وفيه قبل سالب واحد؟ Zero طيب + +31 +00:02:50,410 --> 00:02:57,750 +absolute value لسالب ميةمية و سالب مية، إذا كل + +32 +00:02:57,750 --> 00:03:02,550 +القيم السالبة، ال range تبعها مين؟ يعني أنا عندي + +33 +00:03:02,550 --> 00:03:08,750 +من سالب infinity لغاية قبل zero، كل النتيجة + +34 +00:03:08,750 --> 00:03:13,250 +بتعطيني zero، حتى عند ال zero ب zero، تمام؟ إذا ال + +35 +00:03:13,250 --> 00:03:18,110 +range لكل القيم السالبة، يعني كل القيم السالبة لها + +36 +00:03:18,110 --> 00:03:24,040 +صورة واحدة فقط وهيلكن اللي بعدها الله يسهل عليها + +37 +00:03:24,040 --> 00:03:27,480 +رايحة لمالها نهائيا، إذا من وين لوين؟ من Zero + +38 +00:03:27,480 --> 00:03:31,440 +لغاية النهائي. Closed من عند ال Zero هي Infinity + +39 +00:03:31,440 --> 00:03:41,340 +Open من عند المالها نهائيا. السؤال السابع F of X + +40 +00:03:41,340 --> 00:03:46,740 +يساوي الجذر التربية لX تربية ناقص 3X + +41 +00:03:49,480 --> 00:03:54,460 +خلاص، بدأ أدور على ال domain، الآن بتنعلمك طريقة + +42 +00:03:54,460 --> 00:04:00,420 +سهلة وميسورة بحيث تجيب اللي هو المنطقة المعرفة + +43 +00:04:00,420 --> 00:04:05,340 +الدال عليها بدون أي مشاكل، خلي بالك معايا هناهل + +44 +00:04:05,340 --> 00:04:10,580 +الجذر معرف لقيمة السالبة؟ لأ، يبقى الجذر مش معرف + +45 +00:04:10,580 --> 00:04:16,700 +إلا لقيمة، إذا بدي كل القيمة اللي تحت الجذر تبقى + +46 +00:04:16,700 --> 00:04:21,680 +أكبر من أو تساوي Zero، يقول خليني نشتغل في الهامش، + +47 +00:04:21,680 --> 00:04:26,560 +يبقى أنا بدي X تربية ناقص تلاتة X greater than or + +48 +00:04:26,560 --> 00:04:33,190 +equal to zeroأو بمعنى آخر لو أخدت X عامل مشترك بظل + +49 +00:04:33,190 --> 00:04:38,060 +X ناقص تلاتة greater than or equal to zeroمظبوط + +50 +00:04:38,060 --> 00:04:43,720 +هكذا؟ طيب، الأن نعلمك الطريقة كيف بدي أجيب على ال + +51 +00:04:43,720 --> 00:04:49,880 +real line الأعداد التي تحقق هذه ال inequality يعني + +52 +00:04:49,880 --> 00:04:54,620 +ما هي الأعداد الحقيقية التي تحقق هذه المتبانة يبقى + +53 +00:04:54,620 --> 00:05:00,780 +هنا بدي أقول بدي أخد إشارة ال X الأولانية لحالة و + +54 +00:05:00,780 --> 00:05:06,410 +برسم ال real lineالـ X هذه بتاخد الـ 0 تبعها وين؟ + +55 +00:05:06,410 --> 00:05:10,450 +عند الـ 0، لو جيت بعد الـ 0، الـ X موجبة و لا + +56 +00:05:10,450 --> 00:05:16,310 +سالبة، يبقى لا تاخد إلا قيما موجبة بعد مين؟ بعد + +57 +00:05:16,310 --> 00:05:22,040 +الـ 0، لو رجعت قبل الـ 0 بتاخد كلها قيم سالبةبعد + +58 +00:05:22,040 --> 00:05:28,100 +هيك بدنا نيجي ناخد إشارة sign X minus three يعني + +59 +00:05:28,100 --> 00:05:32,760 +إشارة الجث X نقص تلاتة بياخد القيمة الصفر عند X + +60 +00:05:32,760 --> 00:05:36,640 +تساوي و التلاتة بتيجي على يمين ال zero يعني + +61 +00:05:36,640 --> 00:05:42,400 +التلاتة هتجي هنا إذا بعد التلاتة زي أربع الجث + +62 +00:05:42,400 --> 00:05:46,850 +بيكون مالهأربعة وخمسة وستة ومية وكذا يبقى كله + +63 +00:05:46,850 --> 00:05:50,650 +positive زي ما انت شايف، لو جيت قبل التلاتة زي + +64 +00:05:50,650 --> 00:05:55,930 +اتنين وواحد وزيرو سالب خمسة وسالب مية وكله قيم + +65 +00:05:55,930 --> 00:06:01,690 +مالها؟ سالبة، يبقى كله قبلها قيم سالبة، انا مابدأ + +66 +00:06:01,690 --> 00:06:05,770 +اشارة كل واحد لحالة بدأ اشارة اتنين مضربين في بعض + +67 +00:06:05,770 --> 00:06:11,750 +ضربإذا بروح بقوله بدي أخد إشارة X مضروبة في الـ X + +68 +00:06:11,750 --> 00:06:16,350 +minus three و أقول له هي ال real line و هذه الحدود + +69 +00:06:16,350 --> 00:06:22,170 +الإقليمية هذا zero وهذا تلاتة اتنين هذول مضربين في + +70 +00:06:22,170 --> 00:06:25,870 +بعض يبقى بدي أضرب الإشارات في بعض موجب في موجب + +71 +00:06:25,870 --> 00:06:32,430 +موجب موجب في سالب سالب سالب في سالب موجب ممتاز جدا + +72 +00:06:32,970 --> 00:06:38,890 +هي فسرنا حاصل الضرب للمقدار يوم ما يكون موجب و يوم + +73 +00:06:38,890 --> 00:06:43,790 +ما يكون سالب برجع للمتباينة الأصلية اللى عنده بدى + +74 +00:06:43,790 --> 00:06:48,790 +حاصل الضرب يكون ماله أكبر من أو يساوي زيرو يعني يا + +75 +00:06:48,790 --> 00:06:52,850 +زيرو يا إما قيمةموجب ضد طلع وين القيام الموجب، + +76 +00:06:52,850 --> 00:06:56,830 +اللي هي المنطقة هذه والمنطقة هذه إذا الجواب هو من + +77 +00:06:56,830 --> 00:07:02,790 +سلب infinity لغاية ال zero وكذلك من تلاتة لغاية + +78 +00:07:02,790 --> 00:07:07,770 +infinity إذا ال domain بيصير عندنا من سلب infinity + +79 +00:07:07,770 --> 00:07:12,810 +لغاية ال zero طبعا من عند ال zero مغلقة بسبب + +80 +00:07:12,810 --> 00:07:19,590 +اليساوي اتحاد تلاتة و infinityكتبنا الفترة مغلقة + +81 +00:07:19,590 --> 00:07:25,330 +من عند الـ zero والتلاتة بسبب ال يساوي، لو ماعنديش + +82 +00:07:25,330 --> 00:07:30,450 +يساوي بكتب هذه ايه؟ open، بكتب الفترة هذه فترة + +83 +00:07:30,450 --> 00:07:35,790 +ايه؟ مختوها طيب احنا الان كل اللي عملناه حسبنا من + +84 +00:07:35,790 --> 00:07:42,390 +اين؟ حسبنا ال interval اللي داله معرف عليها يعني + +85 +00:07:42,390 --> 00:07:47,470 +استبعدنا الفترة من اين لوين؟من زيرو لتلاتة طيب + +86 +00:07:47,470 --> 00:07:52,270 +يعني لو أخدت رقم من زيرو لتلاتة بحقك في ال link و + +87 +00:07:52,270 --> 00:07:57,170 +لا تهادي نقولك الله جرب خد الرقم اللي يعجبك كداش + +88 +00:07:57,170 --> 00:08:01,670 +يعني من زيرو لتلاتة اتنين مثلا يبقى لو جات لليه + +89 +00:08:01,670 --> 00:08:06,750 +اتنين اتنين اتنين ناقص تلاتة فظل سالب واحد في + +90 +00:08:06,750 --> 00:08:10,430 +اتنين سالب اتنين هل السلب اتنين اكبر من ال zero + +91 +00:08:10,890 --> 00:08:14,490 +يبقى لا يمكن يبقى لا اتنين ولا الواحد ولا واحد و + +92 +00:08:14,490 --> 00:08:18,370 +نص ولا الواحد و تلت اربع ولا واحد كل هذه الأرقام + +93 +00:08:18,370 --> 00:08:21,910 +لا تحقق ال inequality قبل ال zero جاهزين بعد ال + +94 +00:08:21,910 --> 00:08:26,570 +zero مجول برضه طب خلي قبل ال zero خلي اي رقم سالب + +95 +00:08:27,210 --> 00:08:32,310 +ناخد ناقص اتنين اللي قلت عليه هذا ناقص اتنين اي + +96 +00:08:32,310 --> 00:08:37,530 +ناقص اتنين هو ناقص ثلاثة ناقص خمسة ناقص خمسة و هنا + +97 +00:08:37,530 --> 00:08:42,890 +ناقص اتنين زي عشرة اكبر من زير هذا لو أخدت سلم طب + +98 +00:08:42,890 --> 00:08:49,800 +لو أخدت هموجبايرام كود اللي هو الاربع ففاجئي بقوله + +99 +00:08:49,800 --> 00:08:53,760 +اربع واربع ناقص تلاتة اللي هو احد فيه اربع باربع + +100 +00:08:53,760 --> 00:08:57,840 +اكبر من ال zero إذا كلامنا صحيح يبقى بناء عليها + +101 +00:08:57,840 --> 00:09:01,920 +إذا بعدنا فقط الفترة من zero لغاية تلاتة هذا ال + +102 +00:09:01,920 --> 00:09:05,510 +domain بدنا ال rangeالـ Range بدك تروح تاخد من + +103 +00:09:05,510 --> 00:09:09,530 +الفترة اللي عندك هذه و تعوض في الدالة و تشوف إيش + +104 +00:09:09,530 --> 00:09:12,910 +اللي بطلع يلا أشوف مين الشاطرة فيك و اللي حسبها + +105 +00:09:12,910 --> 00:09:18,770 +دوري هيك يعطيني إجابة أيوة من سفر ل Infinity من + +106 +00:09:18,770 --> 00:09:22,950 +Zero لغاية Infinity مفتوحة أو هنا مغلقة ولا + +107 +00:09:22,950 --> 00:09:31,920 +مفتوحة؟ مغلقة تمشي اسمك انت عبدالهاد ايش؟عبدالهاد + +108 +00:09:31,920 --> 00:09:38,160 +ازميلي عبدالهاد ازميلي هذا من الرفع شجعية + +109 +00:09:38,160 --> 00:09:44,940 +من الدرج طب كويس هي عبدالهاد ازميلي من منطقة الدرج + +110 +00:09:44,940 --> 00:09:49,400 +الدرج و أعطانا إجابة صحيحة تمام؟ يعني درج في + +111 +00:09:49,400 --> 00:09:53,260 +الطريق الصحيح إلى أن وصل إلى الإجابة الصحيحة حد + +112 +00:09:53,260 --> 00:10:02,120 +عنده إجابة غير الإجابة هذه؟ فيه؟ إذا فيه قولوناطيب + +113 +00:10:02,120 --> 00:10:05,460 +نقولكوا يا عبدالله كيف استدل على هذه النتيجة + +114 +00:10:05,460 --> 00:10:10,240 +بطريقة صحيحة اذا قال بدأ احط zero بتطلع جداش ال + +115 +00:10:10,240 --> 00:10:13,680 +zero جدر ال zero في zero هاي مغلقة من عند ال zero + +116 +00:10:13,680 --> 00:10:17,800 +قال بدأ ارجع بعد ال zero قلنا له جداش جداش سالب + +117 +00:10:17,800 --> 00:10:21,940 +واحد و سالب خمسة و سالب عشرين الاخرينيبقى لما + +118 +00:10:21,940 --> 00:10:27,660 +انحطني سالب خمسة صار هذه كده؟ خمستاشر وهذه سالب + +119 +00:10:27,660 --> 00:10:30,340 +خمسة تربية خمسة وعشرين وخمستاشر اربعين جدر + +120 +00:10:30,340 --> 00:10:35,880 +الاربعين موجب يعني بعد ال zero مظبوط وقال لو رجعت + +121 +00:10:35,880 --> 00:10:40,460 +ان شاء الله لغاية سالب عشرة يبقى بصير هنا مية وهنا + +122 +00:10:40,460 --> 00:10:45,440 +كده؟ تلاتين يبقى مية و تلاتين يبقى اكبر من اللي + +123 +00:10:45,440 --> 00:10:49,560 +جابله وهكذا يبقى كلام صحيحقال لي طيب انتقل على + +124 +00:10:49,560 --> 00:10:53,900 +الفترة التانية هوب طلعت بتطلع تسعة ناقص تسعة ب + +125 +00:10:53,900 --> 00:10:59,300 +zero هايمتمام؟ بعد التلاتة بجنمين اربعة خمسة عشر + +126 +00:10:59,300 --> 00:11:04,940 +عشرة مثلا عشرة في عشرة بمية تلاتة في عشرة بتلاتين + +127 +00:11:04,940 --> 00:11:08,800 +مية ناقص تلاتين سبعين تحت الجذر قيمة بعد الصفر و + +128 +00:11:08,800 --> 00:11:12,840 +هكذا إذا قال لي على كل الأمر يعني الفترة هذه + +129 +00:11:12,840 --> 00:11:16,180 +هتجيبلي الفترة من zero ل infinity و الفترة هذه + +130 +00:11:16,180 --> 00:11:20,140 +هتجيبلي نفس الفترة كمان من zero ل وين الى infinity + +131 +00:11:20,140 --> 00:11:25,480 +نقولك كلام مصبوط والإجابة صحيحة لا غبارة عليها + +132 +00:11:25,650 --> 00:11:30,910 +ننتقل الآن إلى السؤال الثامن أو الدالة رقم تمانية + +133 +00:11:30,910 --> 00:11:39,430 +F of X يسوى absolute value ل Xتمام ال absolute + +134 +00:11:39,430 --> 00:11:43,630 +value ل X أخدته تعريفه في الثانوية بدي أحب أذكر + +135 +00:11:43,630 --> 00:11:48,290 +بتعريفه مرة تانية يبقى ال absolute value ل X بدها + +136 +00:11:48,290 --> 00:11:52,570 +تساوي X إذا كانت ال X greater than or equal to + +137 +00:11:52,570 --> 00:11:58,910 +zero وتساوي سالب X إذا كانت ال X أقل من ال zero + +138 +00:11:58,910 --> 00:12:06,320 +اللي كنتوا سميوها القيمة المطلقة ل سينالقيمة + +139 +00:12:06,320 --> 00:12:10,400 +المطلقة لسين يبقى احنا هنا بقول absolute value of + +140 +00:12:10,400 --> 00:12:14,620 +X هي اللي كنت تقول عليها القيمة المطلقة للعدد سين + +141 +00:12:14,620 --> 00:12:19,380 +طيب هذه بدها تساوي X إذا X أكبر من أو تساوي Zero + +142 +00:12:19,380 --> 00:12:24,480 +وتساوي سالب X إذا كان X أقل من Zero هذا ال + +143 +00:12:24,480 --> 00:12:29,270 +definitionأو التعريف تبع القيمة المطلقة. إيه + +144 +00:12:29,270 --> 00:12:34,430 +الخاطر؟ أسأل السؤال التالي وافكر قبل ما تعطينا + +145 +00:12:34,430 --> 00:12:38,490 +الإجابة السؤال هو هاي تعريف ال absolute value + +146 +00:12:38,490 --> 00:12:44,590 +السؤال هو هل ال absolute value ل X بتطلع قيمة + +147 +00:12:44,590 --> 00:12:50,150 +موجبة و لا ممكن موجبة و ممكن سالبة زي ما انت كاتب؟ + +148 +00:13:00,640 --> 00:13:05,880 +ممكن تكون سالب إذا كان السالب كان جديد؟أنا مش فاهم + +149 +00:13:05,880 --> 00:13:14,540 +again مرة تانية لا لا لا انا بتكلم خليك معايا انا + +150 +00:13:14,540 --> 00:13:18,680 +بتكلم داخل ال absolute مالي ولا اللي برا مالي ولا + +151 +00:13:18,680 --> 00:13:22,060 +اللي برا انا بس absolute لو كان الأمر كما اقول + +152 +00:13:22,060 --> 00:13:26,400 +سأقول لك سالب absolute بالعكس بتكلم زميلكوا عنه لو + +153 +00:13:26,400 --> 00:13:29,640 +كان فيه إشارة سالب برا ال absolute ماليش علاقة + +154 +00:13:29,640 --> 00:13:37,010 +فيها انا بتكلمهل بيطلع قيمة موجبة وقيمة سالبة؟ + +155 +00:13:37,010 --> 00:13:40,210 +والله موجبة بس والله سالبة بس فقط لا غير + +156 +00:13:49,930 --> 00:13:54,350 +ممتاز جدا يعني يا شباب لما تاخد التعريف مش تاخد + +157 +00:13:54,350 --> 00:13:58,370 +شوية منه و تسيب الباقي باخده كاملا لما قال لي + +158 +00:13:58,370 --> 00:14:03,130 +absolute بال X يستوي X اشترق ان X يا اما موجبة يا + +159 +00:14:03,130 --> 00:14:06,850 +اما صفر يبقى ماعندي مشكلة بتطلع ان انا موجبة تعني + +160 +00:14:06,850 --> 00:14:11,090 +موجبة صفر تعني صفرلكن لما قال لي هنا سالب x قال لي + +161 +00:14:11,090 --> 00:14:17,270 +إذا كانت x أقل من ال zero يعني لو كان x قيمة سالبة + +162 +00:14:17,270 --> 00:14:21,490 +يبقى الجوا بتحط نفس القيمة و قبلها انشرت مين سالب + +163 +00:14:21,490 --> 00:14:25,750 +بصير سالب سالب اللي هو الرقم اللي عندك يبقاش بصير + +164 +00:14:26,240 --> 00:14:29,860 +إذا ال absolute value مابتطلعش إلا قيمة موجبة + +165 +00:14:29,860 --> 00:14:38,080 +فمثلا absolute value لسالب تلاتة يساوي + +166 +00:14:38,080 --> 00:14:43,840 +سالب لسالب تلاتة أي السالب وال X بسالب تلاتة أي + +167 +00:14:43,840 --> 00:14:48,500 +السالب تلاتة يبقى النتيجة 11تلاتة إذا مبطلعش إلا + +168 +00:14:48,500 --> 00:14:52,900 +قيمة موجبة ما علينا أنا الآن بتدور على ال domain + +169 +00:14:52,900 --> 00:14:57,000 +تبع هذه الدالة بعد ما أعطيتها التعريف فيه في + +170 +00:14:57,000 --> 00:15:00,520 +الهامش ذكرتك ابو تذكرنا ان انت أخدته في الثانوية + +171 +00:15:00,520 --> 00:15:07,000 +العامة السؤال هو هل هناك قيمة ال X بتخلي الدالة + +172 +00:15:07,000 --> 00:15:13,700 +غير معرفة؟لا يمكن أن يبقى الـ domain كل الـ real + +173 +00:15:13,700 --> 00:15:19,100 +line بلا ستنة يبقى هذه يا اما R يا اما من سلب + +174 +00:15:19,100 --> 00:15:24,220 +infinity إلى infinity.الان بدنا نروح على ال range + +175 +00:15:27,010 --> 00:15:30,690 +نحن أعطينا الجواب من ثانية كلامنا اللي سألناه قبل + +176 +00:15:30,690 --> 00:15:34,870 +قليل.قلت لك بتطلع قيمة سالمة؟ قلت لأ.يبقى السبعة + +177 +00:15:34,870 --> 00:15:39,010 +مسالمة.شو ضال عندي؟ Zero والموجب.إذا من Zero إلى + +178 +00:15:39,010 --> 00:15:45,490 +Infinity.يبقى من Zero لغاية Infinity.بعد قليل ان + +179 +00:15:45,490 --> 00:15:49,920 +شاء الله هرسملكم إياها هذه.سأرسم لكم رسمة الدالة و + +180 +00:15:49,920 --> 00:15:54,240 +ارسم كمان الدالة هذه كمان و هكذا خلّوه للمحاضرة ان + +181 +00:15:54,240 --> 00:16:00,980 +شاء الله طيب بدنا نروح للسؤال 9 ال F of X يساوي + +182 +00:16:00,980 --> 00:16:07,380 +الجذر التربيهي ل absolute value ل Xبنعرف ال domain + +183 +00:16:07,380 --> 00:16:14,280 +تبع هذه الدالة وبعد قليل كمان نرسمها مش عاجبك طبعا + +184 +00:16:14,280 --> 00:16:19,380 +لو جيت الجذر التربية ل absolute value ل X شو + +185 +00:16:19,380 --> 00:16:24,440 +يساوي؟ يبقى طبقا لتعريف ال absolute value لفوق بدي + +186 +00:16:24,440 --> 00:16:29,780 +يكون الجذر التربية ل X إذا ال X greater than or + +187 +00:16:29,780 --> 00:16:35,710 +equal to zeroو يساوي الجذر التربية إلى سالم X إذا + +188 +00:16:35,710 --> 00:16:41,310 +الـ X أقل من الـ Zero، مظبوط ولا لا؟ طيب السؤال هو + +189 +00:16:41,310 --> 00:16:47,250 +قدش ال domain لهذه الدالة؟ من صفر لما لنهاية، يعني + +190 +00:16:47,250 --> 00:16:53,550 +النصر يا الله، اسمع يا شباب واحد واحد، بس تانا + +191 +00:16:53,550 --> 00:16:57,070 +شوية، اللي بيجاوب من ليها، اللي بنسأله بيجاوب من + +192 +00:16:57,070 --> 00:17:00,330 +ليها حتى وإن كان جاوبه خطأ، بتعود بعد ذلك الآية، + +193 +00:17:00,330 --> 00:17:06,310 +واتفضلكل ال number من سالب infinity لغاية ال + +194 +00:17:06,310 --> 00:17:12,670 +infinity بلا استثناء طيب سؤالي هو هل أنا كاتب ال + +195 +00:17:12,670 --> 00:17:16,790 +domain قدامك على اللوح هنا ولا لا؟ مكتوب ال + +196 +00:17:16,790 --> 00:17:22,010 +domain؟ في التعريف اللي أنا كاتبه مبين موجود ال + +197 +00:17:22,010 --> 00:17:28,090 +domain؟مش ال domain هي قيم X؟ ايش كتب هنا؟ X أكبر + +198 +00:17:28,090 --> 00:17:31,770 +و أساوي زينو، ايش كتب هنا؟ يعني كل ال real number + +199 +00:17:31,770 --> 00:17:34,550 +مظبوط يبقى هاي ال domain مكتوب قدامي على اللوح + +200 +00:17:34,550 --> 00:17:38,410 +يعني بدي أنجله نقل ليس الا يبقى من سالب infinity + +201 +00:17:38,410 --> 00:17:42,990 +يعني كل ال X الموجة بزايد الصفر و هنا كل ال X زي + +202 +00:17:42,990 --> 00:17:47,550 +السالب الشكتين مع بعض بيعطيني كل ال real number + +203 +00:17:47,550 --> 00:17:57,400 +بلا ستنة من سالب infinity إلى infinityفبرينج. نفس + +204 +00:17:57,400 --> 00:18:02,420 +هذه يعني اللي جابلها؟ نفس عرفيا؟ إلك خطر تغير. + +205 +00:18:03,740 --> 00:18:08,400 +يعني أو كما قال، في حد عنده إجابة غير حكاية ال + +206 +00:18:08,400 --> 00:18:12,940 +zero و infinity؟ إذا في إجابة، أعطوني إياها، حد ما + +207 +00:18:12,940 --> 00:18:13,840 +نتناقش فيها. + +208 +00:18:17,820 --> 00:18:23,440 +يبقى من zero كل ال R ولا نصها؟ كل ال R + +209 +00:18:34,930 --> 00:18:41,510 +يعني أو كما قيل طيب يالا موافقين نفس النتيجة اللي + +210 +00:18:41,510 --> 00:18:48,810 +فوق من Zero لغاية Infinity طيب السؤال العاشر بدنا + +211 +00:18:48,810 --> 00:18:57,650 +ال F of X تساوي absolute value ل X على X وشوف ليها + +212 +00:18:57,650 --> 00:19:01,370 +هي X على absolute value ل X ولا لا؟ + +213 +00:19:07,570 --> 00:19:13,410 +هل هذه هي هذه يا شباب؟ بختلفوا عن بعض يعني متأكدين + +214 +00:19:13,410 --> 00:19:17,470 +الدالة + +215 +00:19:17,470 --> 00:19:23,430 +هذه هي نفس الدالة هذه بالحرف الواحد تمام؟ الآن + +216 +00:19:23,430 --> 00:19:28,100 +بوريك كيف هذا طلعلي هنالما أنا قاعد يقول absolute + +217 +00:19:28,100 --> 00:19:33,620 +value ل X على X بدي اعطيها التعريف تبعها يبقى هذي + +218 +00:19:33,620 --> 00:19:39,720 +X على X إذا ال X أكبر من ال 0 هحط يساوي + +219 +00:19:42,310 --> 00:19:46,370 +زيروا على زيروا هذا ممنوع، مافي إمكانية يبقى حكاية + +220 +00:19:46,370 --> 00:19:55,130 +زيروا استبعدناها وهنا تساوي سالب X على X إذا الـ X + +221 +00:19:55,130 --> 00:20:02,570 +greater than 0طب هدى علي هدى بقداش و هدى علي هدى + +222 +00:20:02,570 --> 00:20:08,970 +بقداش سالف واحد إذا كان ال X greater than zero إذا + +223 +00:20:08,970 --> 00:20:15,190 +كان ال X less than zero لو أخدت التانية اللى تحت + +224 +00:20:15,190 --> 00:20:22,090 +بصير X على Xو X على سالب X يبقى هيه ولا لا؟ اذا ال + +225 +00:20:22,090 --> 00:20:26,150 +function هذه ان كتبتها بالشكل هذا او بالشكل هذا + +226 +00:20:26,150 --> 00:20:32,090 +الاتنين اعرف ده same اتنين نفس الشيء طيب سؤالنا هو + +227 +00:20:32,090 --> 00:20:35,850 +جداش ال domain وشوف اللي موجود هنا على اللوح ولا + +228 +00:20:35,850 --> 00:20:44,440 +لا؟كل ال real number ما عدا ال zero يبقى بقوله كل + +229 +00:20:44,440 --> 00:20:50,340 +ال real number ما عدا ال zero as except يا اما من + +230 +00:20:50,340 --> 00:20:56,340 +سلب infinity ل zero اتحاد zero و infinite طيب بدنا + +231 +00:20:56,340 --> 00:21:00,760 +نيجي لل range بس + +232 +00:21:00,760 --> 00:21:05,620 +اسمع شوية و بده اغششك ال range ع اللوح كمان موجودة + +233 +00:21:08,210 --> 00:21:12,970 +استنى شوية استنى شوية سمعت فيه خلافات؟ ايوه سالب + +234 +00:21:12,970 --> 00:21:19,550 +واحد واحد كفترة ولا رقمين بس؟ رقمين رقمين + +235 +00:21:19,550 --> 00:21:29,410 +يعني اه رقمين يعني رقمين بس ممتازة يبقى لا يوجد + +236 +00:21:29,410 --> 00:21:34,940 +صورة للمال نهية من الأرقام اللى عندي الا صورةلو + +237 +00:21:34,940 --> 00:21:40,660 +سالب واحد و واحد فقط لغير as a set يبقى بعملهم set + +238 +00:21:40,660 --> 00:21:45,680 +و بقول سالب واحد و واحد لما نكتب جثين بالشكل هذا + +239 +00:21:45,680 --> 00:21:51,490 +متوسطات يعني هذه مجموعة تحتوي على عنصرين فقطهو + +240 +00:21:51,490 --> 00:21:55,510 +العنصر سالب واحد و واحد هي ال range اللي طالع عندي + +241 +00:21:55,510 --> 00:22:00,910 +واحد و سالب واحد لكن ال domain هو x أكبر من ال + +242 +00:22:00,910 --> 00:22:04,970 +zero و x أقل من ال zero يعني كل ال real number ما + +243 +00:22:04,970 --> 00:22:11,250 +عدا main ما عدا ال zero تمشي + +244 +00:22:11,250 --> 00:22:15,870 +الحالة تحط الفترة المغلقة وتقولي ناقص ال zero هاي + +245 +00:22:15,870 --> 00:22:22,000 +كتبنا Rهنا ناقص ال zero هل هذا سؤالك؟ مهم انت عارف + +246 +00:22:22,000 --> 00:22:27,220 +هي كتبناه لك قبل ما تحكي طيب ابنجي الآن للرسم + +247 +00:22:27,220 --> 00:22:31,420 +البياني ل functions زي ما وعدناك و حد بدي يسأل؟ + +248 +00:22:31,420 --> 00:22:35,440 +ايوة فقط + +249 +00:22:35,440 --> 00:22:42,580 +لا غير تاني + +250 +00:22:42,580 --> 00:22:43,920 +تاني ايش بتقول؟ + +251 +00:22:46,620 --> 00:22:51,960 +أنا ماسمعتش كويسة، إذا ما كوه يعني + +252 +00:22:51,960 --> 00:22:56,080 +كفترة من سالب واحد واحد معادا zero؟ لأ لأ لأ مش + +253 +00:22:56,080 --> 00:23:01,160 +صحيح، قلت رقامين فقط لغير اللي هم سالب واحد واحد + +254 +00:23:37,230 --> 00:23:46,950 +طيب نحط عنوان جانبي graph of a function graph of a + +255 +00:23:46,950 --> 00:23:53,270 +function الرسم البياني لدله بدنا نعرف الرسم + +256 +00:23:53,270 --> 00:24:00,590 +البياني لدله definition graph of + +257 +00:24:00,590 --> 00:24:02,070 +a function + +258 +00:24:04,190 --> 00:24:16,670 +ف لذال ف with domain D is the set + +259 +00:24:19,380 --> 00:24:28,720 +of points هو مجموعة النقاط اللي على الشكل X وF of + +260 +00:24:28,720 --> 00:24:36,440 +X such that ال X موجودة في ال domain D example + +261 +00:24:36,440 --> 00:24:41,700 +find + +262 +00:24:41,700 --> 00:24:42,500 +the domain + +263 +00:24:48,980 --> 00:24:59,440 +and then a graph and then graph the following + +264 +00:24:59,440 --> 00:25:03,500 +functions + +265 +00:25:03,500 --> 00:25:08,580 +نمر + +266 +00:25:08,580 --> 00:25:19,350 +ايه ال F of X تساوي تلاتة والله سالب تلاتةنمر بي + +267 +00:25:19,350 --> 00:25:26,490 +ال F of X يساوي الجذر التربية ال absolute value ل + +268 +00:25:26,490 --> 00:25:36,130 +X نمر سي ال F of X يساوي X على absolute value ل X + +269 +00:25:36,130 --> 00:25:46,790 +نمر دي ال F of X يساوي X تربية ناقص 9 على X ناقص 3 + +270 +00:26:08,040 --> 00:26:12,200 +يبقى اللون اللي احنا كاتبينه ل graph of a function + +271 +00:26:12,200 --> 00:26:17,600 +الرسم البياني للاقتران او الرسم البياني لدالة بدنا + +272 +00:26:17,600 --> 00:26:22,060 +نعطيله تعريف و بعد هيك بنروح نطبق هذا التعريف + +273 +00:26:22,060 --> 00:26:26,540 +التعريف بيقول the graph of a function f الرسم + +274 +00:26:26,540 --> 00:26:32,000 +البياني لدالة f اللي ال domain تبعها دي هو عبارة + +275 +00:26:32,000 --> 00:26:37,630 +عن مجموعة نقطis the set of points مجموعة النقاط + +276 +00:26:37,630 --> 00:26:44,050 +اللي على الشكل التالي كله كزوج مرتب أو كإحداثيات + +277 +00:26:44,050 --> 00:26:49,330 +نقط X وF of X بحيث ال X هذه لازم تكون موجودة في ال + +278 +00:26:49,330 --> 00:26:55,610 +domain تبعد ال D النقاط هدول كلهم لما نرسمهم + +279 +00:26:55,610 --> 00:27:01,360 +بيكونوا ليش؟الشكل العام لمنحنة اتبالى كنتوا في + +280 +00:27:01,360 --> 00:27:06,540 +الثانوية وفي الاعدادية بترسم جدول وبتحط فيه قيم + +281 +00:27:06,540 --> 00:27:10,320 +سين وبعدين قيم الصادر وبتيجي على الرسم البياني + +282 +00:27:10,320 --> 00:27:14,520 +بتحط احداثيات النقط وتغسل منهم وبتطلع المنحنة + +283 +00:27:14,520 --> 00:27:18,140 +مظبوط هذا اللي احنا بنقول عليه الigraph of a + +284 +00:27:18,140 --> 00:27:23,560 +function يعني نحن هنا لم نأتي بجديد بدنا نروح نطبق + +285 +00:27:23,560 --> 00:27:28,200 +هذا الكلام على أرض الواقع فقولناهات لي ال domain و + +286 +00:27:28,200 --> 00:27:33,480 +كذلك أرسم كل من الدوال التالية يعني كل دالة من هذه + +287 +00:27:33,480 --> 00:27:37,660 +الدوال بدي أعرف قداش ال domain بالنسبة لها name + +288 +00:27:37,660 --> 00:27:41,900 +بدي أرسمها بعدين بقولك قويس بدي أمسك السؤال الأول + +289 +00:27:42,660 --> 00:27:48,200 +اللي هو ال F of X يسوى ناقص تلاتة هذا دي ايش + +290 +00:27:48,200 --> 00:27:53,900 +بنسميها شباب الدالة ثابتة يبقى ال constant + +291 +00:27:53,900 --> 00:28:02,460 +function دالة ثابتة يبقى هنا constant function + +292 +00:28:02,460 --> 00:28:09,750 +يعني دالة ثابتةماذا يعني دالة ثابتة؟يعني مهما + +293 +00:28:09,750 --> 00:28:16,330 +تغيرت X بيبقى قيمة الدالة هي القيمة الثابتة او + +294 +00:28:16,330 --> 00:28:22,670 +بمعنى اخر جميع قيم X لها صورة واحدة في شغير اليمين + +295 +00:28:22,670 --> 00:28:30,390 +سالب تلاتة يعني كأن Y تساوي سالب او صد تساوي سالب + +296 +00:28:30,390 --> 00:28:36,520 +تلاتة طيب هذه معادلة ايه؟فاط مستقيم ماله موازي + +297 +00:28:36,520 --> 00:28:43,380 +لمحور الصينات و أسفله بمقدار تلاتة يعني لو جيت + +298 +00:28:43,380 --> 00:28:50,360 +سألت قداش ال domain بتابع الدالة F بتقول X اللي + +299 +00:28:50,360 --> 00:28:56,000 +هدعو بالسلب تلاتة لقداش بتتغير X نتيجة السلب تغيري + +300 +00:28:56,000 --> 00:29:01,750 +بتغير X زي ما بدك من سلب infinity إلى infinityيبقى + +301 +00:29:01,750 --> 00:29:07,450 +هذا من سالب infinity إلى infinity بدنا نرسم الرسمة + +302 +00:29:07,450 --> 00:29:13,050 +يبقى بجي بقوله هاي المحاور هذا محور X وهذا محور Y + +303 +00:29:13,050 --> 00:29:18,490 +وهذا نقطة الأصل اللي هي Zero اللي كنت بتقوله محور + +304 +00:29:18,490 --> 00:29:25,530 +الصينات ومحور الصدر احنا هنقول محور X ومحور Yهذا + +305 +00:29:25,530 --> 00:29:30,730 +خط مستقيم يوازي السينات ويبعد عنه مسافة مقدارها + +306 +00:29:30,730 --> 00:29:36,690 +تلاتة من وحدات المسافة، يبقى لو رسمنا الخط اللي + +307 +00:29:36,690 --> 00:29:43,620 +عندنا هذا، يكون هذا الخطهذا النقطة سالب تلاتة وهذا + +308 +00:29:43,620 --> 00:29:48,520 +النقطة سالب اتنين وهذا النقطة سالب واحد وهذا + +309 +00:29:48,520 --> 00:29:54,640 +النقطة السابقة هي zero يبقى هذا f of x يسوى كم؟ + +310 +00:29:54,640 --> 00:30:00,540 +يسوى سالب تلاتة طبعا طب لو سألتك السؤال اللي قلت + +311 +00:30:00,540 --> 00:30:08,970 +لك f of x بده يسوى تلاتةيبقى مودي يطلع فوق بس + +312 +00:30:08,970 --> 00:30:16,570 +موازيه وها كده طيب نرجع نرجع مين اللي بيسأل؟عمود + +313 +00:30:16,570 --> 00:30:20,550 +على الصناعة عمود على الصناعة بدل ما اقول Y تساوي + +314 +00:30:20,550 --> 00:30:24,470 +سالب تلاتة بقولك X يساوي سالب تلاتة و X يساوي سالب + +315 +00:30:24,470 --> 00:30:30,270 +تلاتة يعني الخط هنا X يساوي تلاتة هنا X يساوي سالب + +316 +00:30:30,270 --> 00:30:36,190 +تلاتة ماشي واضح اظن طيب نجرب من السؤال اللي بعده + +317 +00:30:36,190 --> 00:30:41,680 +نمر بيه نمر بيه لخاطر ارسم absolute value ل Xجابي + +318 +00:30:41,680 --> 00:30:45,680 +للجدر التربية ال absolute value ل X يبقى انا بدي + +319 +00:30:45,680 --> 00:30:51,720 +ابدأ ب absolute value ل X اتفاجنا على انها X اذا + +320 +00:30:51,720 --> 00:30:57,520 +كانت ال X اكبر من او تساوي ال zero اتفاجنا سالب X + +321 +00:30:57,520 --> 00:31:02,520 +اذا ال X اقل من ال zero جالي هات لل domain ال + +322 +00:31:02,520 --> 00:31:06,780 +domain حسبناه قبل قليل و قولنا كل ال real line + +323 +00:31:06,780 --> 00:31:14,000 +مظبوطيبقى هنا ال domain بتابع ال F كل ال real line + +324 +00:31:14,000 --> 00:31:18,800 +من سالب infinity إلى infinity بدنا نرسمها يبقى لو + +325 +00:31:18,800 --> 00:31:23,520 +روحنا رسمناها بنقول هذه المحاولة هذا محور X هذا + +326 +00:31:23,520 --> 00:31:30,760 +محور Y هذه نقطة الأصل اللي هي ال zeroالدالة هذه لو + +327 +00:31:30,760 --> 00:31:36,140 +قلت لك Y تساوي absolute value ل X يبقى Y بدها + +328 +00:31:36,140 --> 00:31:42,740 +تساوي X أظن معروف فده خط ينصف الرابع الأول والرابع + +329 +00:31:42,740 --> 00:31:48,660 +التالت يبقى هذا الخط أخدته قبل هيك كتير و بروح + +330 +00:31:48,660 --> 00:31:53,200 +بمده على استقالة و يبقى هذا الخط اللي هو Y يساوي + +331 +00:31:53,200 --> 00:32:01,090 +منهم يساوي X بس أصبر شويةالخط التاني Y تساوي مين؟ + +332 +00:32:01,090 --> 00:32:07,550 +سالب X يبقى بدنا الصفر الرابع التاني والرابع الشكل + +333 +00:32:07,550 --> 00:32:13,230 +اللي عندنا هذا يبقى هاي Y يساوي سالب X هذا لو كان + +334 +00:32:13,230 --> 00:32:25,840 +على إطلاقلكن حط لي هنا condition يبقى + +335 +00:32:25,840 --> 00:32:32,600 +الخط هذا الله سهل عليه مش موجودقال لي Y تساوي + +336 +00:32:32,600 --> 00:32:37,620 +السلب X إذا X أقل من الـ Zero يبقى على اليمين هذا + +337 +00:32:37,620 --> 00:32:44,380 +ماله مش موجود يبقى اللي بظل عندي هو رسمة main رسمة + +338 +00:32:44,380 --> 00:32:49,220 +absolute value ل X على شكل سبعة بالعربي أو تمانية + +339 +00:32:49,220 --> 00:32:55,800 +مقلوبةيبقى هذا معرف عند نقطة الأصل لإن absolute + +340 +00:32:55,800 --> 00:33:03,080 +value للـ 0 في 0 يبقى هذه رسمة absolute أو Y أو F + +341 +00:33:03,080 --> 00:33:08,880 +of X يسوي absolute value لـ X مش هذه اللي بدنا + +342 +00:33:08,880 --> 00:33:13,430 +إياهابدنا الجذر التربيه الى absolute value ل X + +343 +00:33:13,430 --> 00:33:17,290 +بقول له اه احنا عندنا هنا الجذر التربيه الى + +344 +00:33:17,290 --> 00:33:21,750 +absolute value ل X احد امرين يا اما الجذر التربيه + +345 +00:33:21,750 --> 00:33:26,630 +الى X اذا ال X اكبر من او تساوي Zero يا اما الجذر + +346 +00:33:26,630 --> 00:33:32,790 +التربيه الى سلب X اذا X اقل من مين اقل من Zeroطب + +347 +00:33:32,790 --> 00:33:36,650 +خليني أسالكوا السؤال التالي قبل ما أرسم الرسم هذه + +348 +00:33:36,650 --> 00:33:40,970 +الدالة الأولى اللى هي absolute value ل X من خلال + +349 +00:33:40,970 --> 00:33:46,950 +الرسم قدش ال domain تبعهامن الرسم الطلع فى الرسم + +350 +00:33:46,950 --> 00:33:53,070 +هي كل X اللى على اليمين الدالة معرفة كل X اللى على + +351 +00:33:53,070 --> 00:33:56,710 +الشمال الدالة معرفة يبقى ال domain من و لا وين من + +352 +00:33:56,710 --> 00:34:01,550 +سالب infinity الى infinity فبقدرش أقل القيمة + +353 +00:34:01,550 --> 00:34:05,370 +بتاخدها ال absolute من خلال ال zero وبعد هيك تطلع + +354 +00:34:05,370 --> 00:34:10,480 +يبقى من و لا وينيبقى الكلام اللى انا بحكيه لك هذا + +355 +00:34:10,480 --> 00:34:14,740 +شوفه مكتوب عندك جابريا قبل قليل في الجدول ولا لا + +356 +00:34:14,740 --> 00:34:18,220 +طلع لل absolute value of X بتلاقي ال domain من سلب + +357 +00:34:18,220 --> 00:34:21,280 +infinity ل infinity و ال range من zero الى + +358 +00:34:21,280 --> 00:34:25,600 +infinity يبقى هى جابريا قلناه هى بيانيا طلعناه من + +359 +00:34:25,600 --> 00:34:30,200 +خلال ايه؟ من خلال الرسم بدنا نيجي لمسألتنا هذه + +360 +00:34:41,140 --> 00:34:47,080 +يبقى لو روحت رسمت بذكر بالرسمة تذكير اللي ليس الا + +361 +00:34:47,080 --> 00:34:55,770 +هذا X وهذا Y وهذا رسمة Y تساوي جذر ال Xيعني الساعة + +362 +00:34:55,770 --> 00:35:02,250 +تساوي الجذر التربيعي لـC هذا لما X مالها أكبر من + +363 +00:35:02,250 --> 00:35:08,330 +الـ0 أو تساوي طيب لما أقل من الـ0 لو كانت الـX + +364 +00:35:08,330 --> 00:35:14,420 +بسالب أو سبقت بإشارة بالسلبموجب يعني النتيجة هذه + +365 +00:35:14,420 --> 00:35:19,580 +نفس النتيجة اللي فوق الموجبة يبقى بده يظهر قوس زيه + +366 +00:35:19,580 --> 00:35:24,040 +بس من وين من الناحية التانية يبقى Y يساوي الجذر + +367 +00:35:24,040 --> 00:35:29,400 +التربية ل-X لأنه كل ما كانت X سالبة وسبقت بإشارة + +368 +00:35:29,400 --> 00:35:34,000 +سالب بصير سالب سالب موجب يبقى نفس البعد اللي هنا + +369 +00:35:34,000 --> 00:35:38,140 +هو اللي يعني صورة الواحد هي واحد صورة السالب واحد + +370 +00:35:38,140 --> 00:35:44,890 +هي واحدصورة مثلا الأربعة اتنين صورة السالب أربعة + +371 +00:35:44,890 --> 00:35:49,930 +هي اتنين و هكذا إذا من خلال الرسم قدش ال domain + +372 +00:35:49,930 --> 00:35:58,270 +تبع الدالة هذه ال domain سالب infinity لطب و ال + +373 +00:35:58,270 --> 00:36:02,790 +range من zero ل infinity طلع عندك في الجدل شوف هو + +374 +00:36:02,790 --> 00:36:06,950 +الكلام اللي بنحكيه ولا غيرهيعني الكلام اللى بنحكيه + +375 +00:36:06,950 --> 00:36:11,390 +شفه قبل قليل في الأمثلة هو بنقدر نستنتجه من خلال + +376 +00:36:11,390 --> 00:36:16,550 +الرسمة إذا كنا بنعرف الرسمة وبالتالي مافي مشكلة في + +377 +00:36:16,550 --> 00:36:21,890 +هذه الحالة يبقى هذا بالنسبة للسؤال رقم B بدنا نيجي + +378 +00:36:21,890 --> 00:36:28,260 +لل Cالـ C توا كتبناها قبل شوية وقلنا ان ال X على + +379 +00:36:28,260 --> 00:36:34,000 +absolute value ل X هي بالضبط تماما absolute value + +380 +00:36:34,000 --> 00:36:38,840 +ل X على X وقلنا أحد أمرين يا إما واحد إذا ال X + +381 +00:36:38,840 --> 00:36:43,340 +أكبر من ال zero يا إما سالب واحد إذا ال X أقل من + +382 +00:36:43,340 --> 00:36:49,880 +من ال zero وقلنا ال domain كل ال real line مع ده + +383 +00:36:54,140 --> 00:37:01,320 +بسيطة جدا هاي المحاور وهذا محور X وهذا محور Y وهذا + +384 +00:37:01,320 --> 00:37:07,620 +نقطة الأصل اللي هي Zero نجي للجزء الأول يبقى هذي + +385 +00:37:07,620 --> 00:37:14,860 +constant functionجداش بتتغير X موجب تظل قيمة + +386 +00:37:14,860 --> 00:37:18,400 +الدالة واحد، يعني عند الواحد قيمة الدالة واحد، عند + +387 +00:37:18,400 --> 00:37:21,600 +اتنين قيمة واحد، عند المية قيمة واحد، عند الألف + +388 +00:37:21,600 --> 00:37:27,600 +قيمة واحد، وها كده، إذا خط مستقيم يوازي محور + +389 +00:37:27,600 --> 00:37:33,910 +الصينات ويبعد عنه مسافة مقدارهاواحد يبقى هذا البعد + +390 +00:37:33,910 --> 00:37:41,210 +واحد وهذه مجوّفة فراغ لإن عندي ال zero الدالة غير + +391 +00:37:41,210 --> 00:37:47,440 +معرفةالجزء الثاني قيمة الدالة تساوي واحد لكل اكس + +392 +00:37:47,440 --> 00:37:52,060 +السالبة يبقى كل اكس السالبة بسالب واحد يبقى بتجيني + +393 +00:37:52,060 --> 00:37:58,000 +هنا هذا الخط المستقيم بالشكل اللاناني وهنا تجويف + +394 +00:37:58,000 --> 00:38:03,060 +دليل على ان عند هذه النقطة الدالة مالها غير معرفة + +395 +00:38:03,060 --> 00:38:08,080 +مفتوحةالـ domain زي ما انت شايفه كل الـ real الله + +396 +00:38:08,080 --> 00:38:11,220 +إنما عدى الـ zero لأنه عنده zero لأن ده لا معرفة + +397 +00:38:11,220 --> 00:38:15,680 +فوق ولا معرفة تحت كل ال real الله إنما عدى ال zero + +398 +00:38:18,140 --> 00:38:23,520 +القيمة سالب واحد فقط لغير القيمة سالب واحد هذه هنا + +399 +00:38:23,520 --> 00:38:28,240 +النقطة سالب واحد والنقطة هذه واحد يبقى واحد وسالب + +400 +00:38:28,240 --> 00:38:33,500 +واحد ال range لهذه الدلة طيب هذا بالنسبة الى C + +401 +00:38:33,500 --> 00:38:40,690 +بدنا نيجي لمن؟ للنمرى Dيبقى بالداجي لـD وهذه C دي + +402 +00:38:40,690 --> 00:38:46,630 +بيقول ال F of X يساوي X تربية ناقص 9 على X ناقص 3 + +403 +00:38:46,630 --> 00:38:53,190 +سؤالي هو هل الدالة معرفة عند التلاتة؟لأن عندي + +404 +00:38:53,190 --> 00:38:57,830 +التلاتة بصير Zero على Zero كمية غير معينة، تمام؟ + +405 +00:38:57,830 --> 00:39:03,430 +إذا لا يمكن لهذه الدالة أن تكون معرفة عند التلاتة، + +406 +00:39:03,430 --> 00:39:08,090 +لكن أنا بدي أحاول أرسمها، إذا مشان أرسمهالازم + +407 +00:39:08,090 --> 00:39:14,310 +أبسطها إذا باجي بقوله هذا كفرق بين المربعين x-3 في + +408 +00:39:14,310 --> 00:39:20,810 +x plus 3 على x minus 3 بتروح هذه مع هذه وبظل اليوم + +409 +00:39:20,810 --> 00:39:27,290 +x زائد تلاتة بس بشرط إن x ما لها ممنوعة تساوي + +410 +00:39:27,290 --> 00:39:33,050 +تلاتة لإن عندي التلاتة غير معرفة يبقى المرسمتنا + +411 +00:39:33,050 --> 00:39:41,120 +عبارة عن خط مستقيموالخط مستقيم بدي يكون خالي عند x + +412 +00:39:41,120 --> 00:39:46,080 +يساوي 3 يعني هذه النقطة فرعة على الخط المستقيم عند + +413 +00:39:46,080 --> 00:39:52,200 +x يساوي 3 بقوله بسيطة إذا إحنا لو جينا نرسم هذا + +414 +00:39:52,200 --> 00:39:56,500 +الخط المستقيم بالشكل اللي عندنا هذا وقولنا هذا + +415 +00:39:56,500 --> 00:40:02,420 +محور x هذا محور y هذه النقطة الأصل اللي هي عندنا + +416 +00:40:02,420 --> 00:40:08,800 +zeroالان عشان ارسم اي خط مستقيم في الدنيا بيكفيني + +417 +00:40:08,800 --> 00:40:13,320 +نقطتين موجودتين عليه اذا عرفت النقطتين بجيبها + +418 +00:40:13,320 --> 00:40:16,520 +المصدر و برسمها الخط بيصير هذا اللي هو الخط + +419 +00:40:16,520 --> 00:40:22,280 +المستقيم اللي عندنا فمثلا لو كانت X ب Zero ف F of + +420 +00:40:22,280 --> 00:40:26,900 +Zero بقداشي بتلاتة يعني معنى هذا الكلام ان النقطة + +421 +00:40:26,900 --> 00:40:33,850 +Zero تلاتة تقع على الخط المستقيم هذه Zero تلاتةلو + +422 +00:40:33,850 --> 00:40:39,950 +كانت f of x كلها بـ0 يبقى x بدأ تسوى جدّها إذا + +423 +00:40:39,950 --> 00:40:46,230 +سالب 3 و 0 تقع على الخط المستقيم سالب 3 و 0 بدأ + +424 +00:40:46,230 --> 00:40:47,690 +تجيلك النقطة هذه + +425 +00:40:50,790 --> 00:40:56,430 +أذا احنا صار ان هذا الخط المستقيم بقدر ارسمه بدون + +426 +00:40:56,430 --> 00:41:02,250 +مشاكل يبقى بوصل بين النقطتين و بمد الخط على + +427 +00:41:02,250 --> 00:41:07,070 +استقامته من الناحيتين بصير هذا هو الخط المستقيم + +428 +00:41:07,070 --> 00:41:12,170 +لأن y تساوي x زي التلتة او f of x يساوي x زي + +429 +00:41:12,170 --> 00:41:17,330 +التلتة بس استنى شويةلما تيجي عند الواحد و عند + +430 +00:41:17,330 --> 00:41:22,290 +اتنين و عند التلاتة و نيجي طالعين مشان قبل الخط + +431 +00:41:22,290 --> 00:41:28,830 +المستقيم بيصير الخط المستقيم في تجويف هنا وبالتالي + +432 +00:41:28,830 --> 00:41:36,070 +عند x يساوي تلاتة ال function is undefined يبقى + +433 +00:41:36,070 --> 00:41:41,390 +عند x يساوي تلاتة يوهر تجويف او ثقب في الخط + +434 +00:41:41,390 --> 00:41:46,870 +المستقيم بمعنى اخرالنقطة تلاتة وستة لا تقع على + +435 +00:41:46,870 --> 00:41:51,790 +الخط المستقيم، لو حطيت تلاتة زائد تلاتة بيصير ستة، + +436 +00:41:51,790 --> 00:41:56,290 +يبقى تلاتة وستة هذه مش موجودة على الخط المستقيم، + +437 +00:41:56,290 --> 00:42:03,630 +يبقى فراغ، تمام؟ طيب، لخاطر أسأل سؤال تاني، لو + +438 +00:42:03,630 --> 00:42:08,450 +احنا رمض وقلت لك خد لك هالرسمة، وشوف ليها دي رسمة + +439 +00:42:08,450 --> 00:42:14,220 +function والله مش function، كي بدي أعرف؟رسمت لك + +440 +00:42:14,220 --> 00:42:17,500 +رسمة على اللوحة و قلت لك اتفضل هي رسمة و شوف لي هي + +441 +00:42:17,500 --> 00:42:21,020 +الرسمة هذه رسمة function و الله ماهياش function + +442 +00:42:21,020 --> 00:42:27,240 +القضية بسيطة ولا بتحققها القضية من أبسط و أدفه ما + +443 +00:42:27,240 --> 00:42:31,870 +يكون كيف؟المحاضرة اللى فاتت بتتذكروا لما جينا + +444 +00:42:31,870 --> 00:42:37,650 +عرفنا تعريف ال function و جينا قولنا لا يمكن + +445 +00:42:37,650 --> 00:42:42,130 +للعنصر الواحد ان تكون له صورتين او اكتر مظبوط صورة + +446 +00:42:42,130 --> 00:42:45,990 +واحدة علي انوراس بس اكتر بتبطل يصير function اذا + +447 +00:42:45,990 --> 00:42:51,970 +انا لو اعطيتك رسمةهل هذه رسمة دالة ولا لا؟ بقوله + +448 +00:42:51,970 --> 00:42:56,410 +بسيطة بدي اخد اي نقطة في دمنا واشوف عند النقطة هذه + +449 +00:42:56,410 --> 00:43:00,590 +بلاقي صورتين ولا لا إذا لاجئت صورتين ماتبطل أصير + +450 +00:43:00,590 --> 00:43:07,390 +function مظبوط؟ أي vertical line أي قط رأسي ممنوع + +451 +00:43:07,390 --> 00:43:12,500 +يقطع المنحنة إلا فيلو قطع في نقطتين بيصير بطل يصير + +452 +00:43:12,500 --> 00:43:17,720 +function لإن X بيصير لها صورتين على الراسم مظبوط + +453 +00:43:17,720 --> 00:43:22,700 +الكلام اللي أنا بقوله اسمه ال vertical line test + +454 +00:43:22,700 --> 00:43:29,640 +for a function اختبار الخط الرأسي لمين لدالةإذا لو + +455 +00:43:29,640 --> 00:43:33,860 +أعطاني رسمة وقاللي شوف لي هذه تمثل دالة ولا لا + +456 +00:43:33,860 --> 00:43:39,440 +تمثل دالة بدون معرف شكلة بجيبها لمصر بحاول أرسم أي + +457 +00:43:39,440 --> 00:43:43,860 +خط رأسي إذا الخط الرأسي قطع المنحنة في نقطتها ليست + +458 +00:43:43,860 --> 00:43:47,880 +function لكن إذا كل الخطوط الرأسية ماقدرش تقطعوا + +459 +00:43:47,880 --> 00:43:52,360 +إلا في نقطة واحدة يبقى هذا إيش vertical line يبقى + +460 +00:43:52,360 --> 00:43:57,200 +هذه تمثل معنى دالةالكلام اللى سمعته بدنا نروح + +461 +00:43:57,200 --> 00:44:19,680 +نكتبه الآن ونشوف كيف انطبقه على أرض الواقع عنوان + +462 +00:44:19,680 --> 00:44:20,420 +جانبي + +463 +00:44:24,040 --> 00:44:37,600 +vertical line test test for a function if + +464 +00:44:37,600 --> 00:44:50,860 +ال if is a function then no vertical + +465 +00:45:00,260 --> 00:45:13,040 +ممكن ان يقطع الرسم + +466 +00:45:13,040 --> 00:45:18,760 +البياني للدالة if more than + +467 +00:45:19,670 --> 00:45:31,150 +once أكثر من مرة واحدة that is if ال + +468 +00:45:31,150 --> 00:45:46,090 +a موجودة في دمين الدلة if then the vertical line + +469 +00:45:46,090 --> 00:45:57,230 +الخط الرأسيx بدى يساوي a will intersect + +470 +00:45:57,230 --> 00:46:00,410 +the + +471 +00:46:00,410 --> 00:46:07,030 +graph of + +472 +00:46:07,030 --> 00:46:16,810 +f at the single point + +473 +00:46:19,920 --> 00:46:23,800 +و F of A + +474 +00:46:39,750 --> 00:46:44,690 +يبقى هذا الاختبار اسمه اختبار الخط الرأسي لدالة + +475 +00:46:44,690 --> 00:46:52,570 +vertical line خط رأسي فيه كلمة perpendicular عمودي + +476 +00:46:52,570 --> 00:46:55,710 +يعني خطين لما يكونوا عمودين على بعض بقول + +477 +00:46:55,710 --> 00:47:00,310 +perpendicular line لكن لما أقول vertical line يبقى + +478 +00:47:00,310 --> 00:47:03,870 +هذا بسميه خط رأسي بغض النظر هل هو عمودي على غيره + +479 +00:47:03,870 --> 00:47:08,740 +ولا مش عموديعلى غيره يبقى باجي بقول لو كانت ال F + +480 +00:47:08,740 --> 00:47:12,720 +function يبقى لو كانت الدالة الرسمة اللي عندي هي + +481 +00:47:12,720 --> 00:47:18,800 +رسمة function إذا لا يمكن أقدر ألاقي خط مستقيم + +482 +00:47:18,800 --> 00:47:24,180 +رأسي يقطع منحنى الدالة في أكثر من نقطة لكن لو + +483 +00:47:24,180 --> 00:47:28,300 +ماكنتش function ممكن في اتنين أو في تلاتة أو في + +484 +00:47:28,300 --> 00:47:32,770 +أربعة زي ما بدكمرة تانية لو كنت لف function then + +485 +00:47:32,770 --> 00:47:38,230 +no vertical line لا يمكن تقدر تلاقي خط رأسي ممكن + +486 +00:47:38,230 --> 00:47:44,390 +يقطع المنحنة في أكثر من مرة more than once يعني + +487 +00:47:44,390 --> 00:47:48,790 +أكثر من مرة واحدة مش هتلاقي ولا خط إذا لو المنحنة + +488 +00:47:48,790 --> 00:47:53,870 +منحنة ده لأ الخط الرأسي لايمكن أن يقطع المنحنة إلا + +489 +00:47:54,400 --> 00:47:59,420 +في نقطة واحدة فقط الآن الكلام اللي قلته هيك بدروح + +490 +00:47:59,420 --> 00:48:06,160 +أصيغه بمفهوم آخر فقولت that is أي أنه لو كان ال a + +491 +00:48:06,160 --> 00:48:10,280 +موجود في domain ال F لو كانت النقطة a موجودة في + +492 +00:48:10,280 --> 00:48:17,830 +domain ال Fوالخط الرئيسي X يساوي الـA وينترسج في + +493 +00:48:17,830 --> 00:48:21,430 +نقطة + +494 +00:48:21,430 --> 00:48:28,550 +واحدة A و F of A كيف هذا الكلام؟ بجي بقول لو كان + +495 +00:48:28,550 --> 00:48:33,670 +عندنا محاور مثلا بالشكل هذا وقلنا هذا محور X وهذا + +496 +00:48:33,670 --> 00:48:38,680 +محور Y ورسمنا منحنة وكان المنحنة بالشكل هذافكان + +497 +00:48:38,680 --> 00:48:46,400 +هذا منحنا Y تساوي F of X يعني الصواد تساوي دالة C + +498 +00:48:46,400 --> 00:48:52,020 +روحنا أخدنا أي نقطة في domain الدالة هذه ولتكن + +499 +00:48:52,020 --> 00:48:58,060 +النقطة هذه مالها Aيبقى هذه X يساوي A وهذه Zero + +500 +00:48:58,060 --> 00:49:05,920 +جينا رسمنا خط رأسي يمر بالنقطة A يبقى الخط الرأسي + +501 +00:49:05,920 --> 00:49:10,980 +بالشكل اللي عندنا هذا يبقى الخط الرأسي هذا معادلة + +502 +00:49:10,980 --> 00:49:16,720 +X يساوي A زي مثال بعض الشباب قبل قليل قال لو كان + +503 +00:49:16,720 --> 00:49:21,740 +عمودي على مهور الصينيةيعني الخط المستقيم الموازي + +504 +00:49:21,740 --> 00:49:26,340 +لمحور الصينات Y تساوي رقم، موجب، سالب، صفر، + +505 +00:49:26,340 --> 00:49:30,800 +ماتفرجش عنها، لكن لو كان عمودي على محور الصينات ف + +506 +00:49:30,800 --> 00:49:36,220 +X يساوي رقم، يعني X يساوي A أو سالب A عندها أو X + +507 +00:49:36,220 --> 00:49:41,260 +يساوي Zero أظن X يساوي Zero هو محور الصداد، محور + +508 +00:49:41,260 --> 00:49:46,120 +Y، X يساوي تلاتة على اليمن بتلاتةX يسوي تسالب + +509 +00:49:46,120 --> 00:49:50,440 +تلاتة يبقى على الشمال بمقدار تلاتة يبقى هنا بقول + +510 +00:49:50,440 --> 00:49:56,600 +لو كان ال A element موجود في دمين الدالة F يبقى اي + +511 +00:49:56,600 --> 00:50:05,040 +خط رأسي يمر بالنقطة هذه اللي احداثيها A وF of A + +512 +00:50:05,040 --> 00:50:10,940 +اللي همينالخط X يساوي A لا يمكن ان يقطع المنحنى + +513 +00:50:10,940 --> 00:50:19,200 +الا في نقطة واحدة اللي هي A ايا و F of A تمام يبقى + +514 +00:50:19,200 --> 00:50:24,560 +هاللي بقوله الان انا بروح استخدم الاختبار هذا في + +515 +00:50:24,560 --> 00:50:29,500 +معرفة بعض الرسومات هل تمثل functions ولا لا تمثل + +516 +00:50:29,500 --> 00:50:34,780 +functions اذا بدنا نروح ناخد المثال التالي يبقى + +517 +00:50:34,780 --> 00:50:35,360 +example + +518 +00:50:55,160 --> 00:51:09,900 +describe the graph of the following equations + +519 +00:51:21,840 --> 00:51:41,100 +undetermined whether the graph is + +520 +00:51:41,100 --> 00:51:41,500 +that + +521 +00:51:44,780 --> 00:51:53,880 +of a function or not + +522 +00:51:53,880 --> 00:52:00,200 +نمرة + +523 +00:52:00,200 --> 00:52:10,430 +a f of x يساوي x زائد absolute value ل x نمرة bX + +524 +00:52:10,430 --> 00:52:16,910 +تربيع زائد Y تربيع يساوي تسعة و X أكبر من أو تساوي + +525 +00:52:16,910 --> 00:52:23,870 +زيرو نمرة C X تربيع زائد Y تربيع يساوي تسعة و Y + +526 +00:52:23,870 --> 00:52:32,270 +greater than or equal to zero نمرة Dنمر دي X تربيع + +527 +00:52:32,270 --> 00:52:38,890 +يساوي Y تربيع نمر A absolute value ل X زادة + +528 +00:52:38,890 --> 00:52:43,150 +absolute value ل Y يساوي مين؟ يساوي واحد + +529 +00:52:52,350 --> 00:52:57,290 +نرجع لسؤالنا مرة تانية بيقول describe the graph of + +530 +00:52:57,290 --> 00:53:01,830 +the following equations ايه وصفلي الرسم البياني + +531 +00:53:01,830 --> 00:53:06,930 +لكل من المعادلات التالية هذه يا شباب اختصار لكلمة + +532 +00:53:06,930 --> 00:53:11,170 +EQUATIONS + +533 +00:53:11,170 --> 00:53:14,630 +equations يعني معادلات + +534 +00:53:16,450 --> 00:53:21,730 +أنا باختصرها إلى EQUN و S تبعت الإضافة أو تبعت + +535 +00:53:21,730 --> 00:53:27,090 +الجامعة يبقى هنا أوصف لي كل من المعادلات التالية و + +536 +00:53:27,090 --> 00:53:31,810 +أتعمد تقول معادلات لأن المعادلة قد تكون function و + +537 +00:53:31,810 --> 00:53:35,730 +قد لا تكون function أما لو قلت لك function يبقى + +538 +00:53:35,730 --> 00:53:39,850 +خلاص مضمونة لكن معادلة ممكن تبقى function و ممكن + +539 +00:53:39,850 --> 00:53:44,730 +ما تكونش function أندي تامة و حددلي هل الرسم + +540 +00:53:44,730 --> 00:53:52,270 +البيانييمثل دالة أو لا يمثل دالة Undetermined حدد + +541 +00:53:52,270 --> 00:53:56,830 +ليه whether the graph L الرسم البياني يمثل + +542 +00:53:56,830 --> 00:54:03,450 +function or not بنقوله بسيطة يبقى بدنا نيجي للدالة + +543 +00:54:03,450 --> 00:54:07,890 +الأولى ال F of X يساوي X زائد absolute value ل X + +544 +00:54:07,890 --> 00:54:13,610 +يبقى نمرأة A الدالة F of X يساوي X زائد absolute + +545 +00:54:13,610 --> 00:54:20,670 +value ل Xهذه سوف أعرفها لكي أرسمها يبقى هذه أحد + +546 +00:54:20,670 --> 00:54:24,490 +أمرين يا شباب بدي أستخدم تعريف ال absolute value + +547 +00:54:24,490 --> 00:54:31,170 +يبقى x زائد x إذا ال x أكبر من أو تساوي zero و x + +548 +00:54:31,170 --> 00:54:37,490 +ناقص x إذا ال x أقل من ال zero صحيح ولا لا؟ مظبوط؟ + +549 +00:54:37,930 --> 00:54:45,830 +طيب هده هي عبارة عن مين؟ اتنين X إذا ال X أكبر من + +550 +00:54:45,830 --> 00:54:53,390 +أو تساوي Zero و Zero إذا ال X أقل من Zeroواضح ان + +551 +00:54:53,390 --> 00:54:59,530 +ال domain جداش كل ال real line وطوحنا في الجزء + +552 +00:54:59,530 --> 00:55:03,590 +النظري قبل قليل قولنا كل ال real line وقولنا ال + +553 +00:55:03,590 --> 00:55:07,870 +range إيه اللي من وين لوين من صفر لغاية ملانا + +554 +00:55:07,870 --> 00:55:10,870 +الكلام اللي قولناه بنروح نبينه الآن على الرسم + +555 +00:55:10,870 --> 00:55:16,070 +كلامنا صحيح ولا لأ إذا بيدروح أرسم المحاور يبقى + +556 +00:55:16,070 --> 00:55:22,030 +هذه المحاور اللي عندنا هذا محور X هذا Y هذا Zero + +557 +00:55:23,620 --> 00:55:30,960 +يبقى احنا عندنا f of x يساوي zero اذا x اقل من ال + +558 +00:55:30,960 --> 00:55:35,780 +zero يبقى لكل ال x اللي اقل من ال zero قيمة الدلج + +559 +00:55:35,780 --> 00:55:42,440 +اداش تساوي صفر يبقى هنا هذا بيكون كل المنطقة اللي + +560 +00:55:42,440 --> 00:55:47,860 +عندنا هنا لغاية ما نصل إلى سالب ال infinity بما + +561 +00:55:47,860 --> 00:55:52,490 +فيها ال zeroطب ال zero جيبته من وين؟ جيبته من اللي + +562 +00:55:52,490 --> 00:55:57,370 +قبلها لو كانت x يساوي zero بصير اثنين في zero ب + +563 +00:55:57,370 --> 00:56:03,130 +zero طيب لما أقول لك صد تساوي اتنين سين ده لأ خطية + +564 +00:56:03,130 --> 00:56:07,550 +ولا لأ؟ خطية لإنها من أي درجة؟ من الدرجة الأولى + +565 +00:56:07,550 --> 00:56:11,170 +يبقى لما أقول لك y تساوي اتنين x معدلة من الدرجة + +566 +00:56:11,170 --> 00:56:15,830 +الأولى يعني معدلة خط مستقيم إذا يكفيني من الخط + +567 +00:56:15,830 --> 00:56:22,670 +المستقيم نقطتين تقعان عليهيبقى هذه إحداهما، بدى + +568 +00:56:22,670 --> 00:56:27,390 +أجيب النقطة التانية، لو كانت X بواحد، يبقى هاي + +569 +00:56:27,390 --> 00:56:32,130 +واحد وهي اتنين، يبقى بدى تجينا النقطة وين اللي + +570 +00:56:32,130 --> 00:56:36,570 +عندنا هذا، يبقى بدى أمسك الخط المستقيم بالمصطر أو + +571 +00:56:36,570 --> 00:56:41,360 +القلم و أوصل الخط المستقيم اللي عندنا هذايبقى هذا + +572 +00:56:41,360 --> 00:56:46,760 +الخط y تساوي main اتنين x الخطين الاتنين مع بعض + +573 +00:56:46,760 --> 00:56:51,640 +يمثلون main الدالة لأن f of x زائد absolute value + +574 +00:56:51,640 --> 00:56:55,920 +of x يبقى قال لي اوصف للرسم البياني للمعادلة اللي + +575 +00:56:55,920 --> 00:57:00,380 +اواصفته قال لي بعدين شوف لي هذا يمثل دالة ولا لا + +576 +00:57:00,380 --> 00:57:06,380 +بقول له اه ارسم vertical line وين ما يعجبكشوفوا هل + +577 +00:57:06,380 --> 00:57:13,360 +يقطع المنحنة في نقطة ولا اكتر نقطة فقط لا غير اي + +578 +00:57:13,360 --> 00:57:19,920 +خط مستقيم برسم نقطة واحدة يبقى هذه تمثل function + +579 +00:57:19,920 --> 00:57:25,640 +على طول الخط تمام؟ اظن لو جيت اقارن بين ال domain + +580 +00:57:25,640 --> 00:57:29,120 +وال range اللي في الجدول بلاقي ال domain كله ال + +581 +00:57:29,120 --> 00:57:33,620 +real line وال range من zero لوين ل infinity يتفق + +582 +00:57:33,620 --> 00:57:41,310 +تماما كيف؟الرسمة طلعلي هذا يعني ايش بتقول قيمة + +583 +00:57:41,310 --> 00:57:46,170 +الدالة تساوي صفر إذا كانت X سالبة X سالبة يعني كل + +584 +00:57:46,170 --> 00:57:49,990 +المنطقة هذه قداش قيمة الدالة Zero يعني انا بضل على + +585 +00:57:49,990 --> 00:57:53,710 +ما هو رسالة لها بطلع ولا بنزل وحطينا هذه اللي هي + +586 +00:57:53,710 --> 00:57:59,070 +القيمة الثابتة تساوي Zeroلما جينا لان f of x ساوي + +587 +00:57:59,070 --> 00:58:04,710 +2x كلها دي معادلة خطية يعني معادلة خط مستقيم الخط + +588 +00:58:04,710 --> 00:58:08,190 +المستقيم اللي ارسمه بده نقطة تانية عليه طبعا عندي + +589 +00:58:08,190 --> 00:58:10,590 +ال zero ب zero اتنين في zero ب zero يبقى نقطة + +590 +00:58:10,590 --> 00:58:14,610 +الاصل واحدة جاهزة و خالصة بظل مين بدناها نقطة + +591 +00:58:14,610 --> 00:58:18,010 +اتنين انا اخدت واحد انت خد اتنين خد عشرة زي ما بدك + +592 +00:58:18,010 --> 00:58:21,890 +و ضرب في اتنينحطها فوق وامشي كمصدر أواصل بيانه + +593 +00:58:21,890 --> 00:58:26,110 +يبقى رسمنا الجزء الثاني يبقى الخطين الاتنين مع بعض + +594 +00:58:26,110 --> 00:58:31,530 +يمثلوين الرسم البياني اللي ادى ل F of X سوى X زائد + +595 +00:58:31,530 --> 00:58:36,170 +absolute value ل Xيبقى ال domain صار كل ال real + +596 +00:58:36,170 --> 00:58:40,010 +line و ال range من zero ل infinity و رسمنا هذه + +597 +00:58:40,010 --> 00:58:45,190 +تعتبر function لأن لو رسم اي vertical line رأسي لا + +598 +00:58:45,190 --> 00:58:52,010 +يقطع المنحنة الا في نقطة واحدة تمام تمام نمر بي + +599 +00:58:52,010 --> 00:59:00,070 +نمر بي بيقول ايش بيقول x تربيةزائد Y تربية تساوي + +600 +00:59:00,070 --> 00:59:04,650 +تسعة والاكس greater than or equal to zero السؤال + +601 +00:59:04,650 --> 00:59:10,670 +هو هذه معادلة ايش يا شباب دائرة مدرجات تانية + +602 +00:59:10,670 --> 00:59:13,190 +معادلة دائرة مركزها + +603 +00:59:14,730 --> 00:59:20,690 +نقطة الاصل 00 نصف قطرة ثلاثة ممتاز جدا يبقى هذا + +604 +00:59:20,690 --> 00:59:24,730 +انت مذاكرين كويس على كل الحالة ريحت هنا شوية يبقى + +605 +00:59:24,730 --> 00:59:31,150 +لو جيت للدائرة هذه و روحت قلت هذا محور X وهذا محور + +606 +00:59:31,150 --> 00:59:36,250 +Y وهذا نقطة الأصل وحبيت أرسم الدائرة بدي أرسمها + +607 +00:59:36,250 --> 00:59:41,150 +منقطة في الأوللأنه مش عارف هذه هي دائرة كاملة ولا + +608 +00:59:41,150 --> 00:59:45,410 +نص دائرة ولا ربع دائرة ولا سُدس دائرة، الله أعلم + +609 +00:59:45,410 --> 00:59:50,330 +يبقى لو جيت لدائرة هذه مركزها نقطة الأصل ونص قطرها + +610 +00:59:50,330 --> 00:59:58,300 +يساوي تلاتة بالشكل اللي عنهاتمام؟ اه في condition + +611 +00:59:58,300 --> 01:00:03,660 +حاطط ليه قال لي ممنوع ال X تاخد قيمة سلبة دايما و + +612 +01:00:03,660 --> 01:00:10,080 +ابدا X يا اما ب zero يا اما بقيمة موجبة من وين هي + +613 +01:00:10,080 --> 01:00:15,100 +المنطقة تمام؟ اذا الدار الجزء هذا يبقى الجزء اللي + +614 +01:00:15,100 --> 01:00:18,810 +على الشماليبقى عقلك الله مافيش عندي دائرة على + +615 +01:00:18,810 --> 01:00:23,030 +الجزر الشمال، يبقى هذا الله يساهل عليه مع السلام + +616 +01:00:23,030 --> 01:00:28,830 +غير مأسوف عليه يبقى ماضلش عندي إلا مين؟ إلا نصف + +617 +01:00:28,830 --> 01:00:32,550 +الدائرة اللي على اليمين، الشكل اللي عندنا هذا + +618 +01:00:32,550 --> 01:00:37,190 +تمام؟ بما فيها النقطة اللي عندنا هذه والنقطة اللي + +619 +01:00:37,190 --> 01:00:42,640 +عندنا هذه خليني أسألك سؤالالنقطة الـ Zero هذه اللي + +620 +01:00:42,640 --> 01:00:48,880 +قال لي X أكبر من أو تساوي Zero، كام صورة لها تنتقل + +621 +01:00:48,880 --> 01:00:53,600 +لفوق و لتحت؟ يبقى هذه ليست function، صح؟ + +622 +01:01:01,210 --> 01:01:07,290 +على اليمين يبقى اي نقطة من Zero لغاية تلاتة نصف + +623 +01:01:07,290 --> 01:01:12,910 +القطر اللي هو تلاتة وهنا تلاتة وهنا تلاتة بالسالب + +624 +01:01:12,910 --> 01:01:18,010 +تلاتة هذه السالب تلاتة و Zero وهذه تلاتة و Zero + +625 +01:01:18,010 --> 01:01:29,120 +وهذه تلاتة و Zero0 و 3 و 3 و 0 اتحرك اي خط على + +626 +01:01:29,120 --> 01:01:34,340 +اليمين هتلاقي يقطع المنحنى معله في نقطتين يبقى هذه + +627 +01:01:34,340 --> 01:01:40,400 +function يبقى هذه not a function يبقى هذه ليست + +628 +01:01:40,400 --> 01:01:49,250 +دالة not a functionيبقى هذه المعادلة لا تمثل دالة + +629 +01:01:49,250 --> 01:01:54,450 +بأي حال من الأحوال ليش؟ لأن ال vertical line test + +630 +01:01:54,450 --> 01:01:59,730 +بيقول لو عملت خط راسي بدوش يقطعها إلا وين فى نقطة + +631 +01:01:59,730 --> 01:02:05,810 +واحدة طيب نمرى C نفس المعادلة X تربية زد Y تربية + +632 +01:02:05,810 --> 01:02:11,980 +يسوى 9 وY greater than or equal to 0بنقول له تعالى + +633 +01:02:11,980 --> 01:02:18,700 +نشوف هذه المحاور وهذا محور X وهذا محور Y وهذا نقطة + +634 +01:02:18,700 --> 01:02:22,740 +الاصل اللي هي Zero وبدنا نروح الدائرة اللي قلنا + +635 +01:02:22,740 --> 01:02:27,940 +عليها هيها ما اتغيرتش بالشكل اللي عندنا هنا، تمام؟ + +636 +01:02:27,940 --> 01:02:31,720 +بس بدي أعرف هل هي دائرة كاملة و الله شوية منها راح + +637 +01:02:31,720 --> 01:02:35,500 +قلشيبقى Y أكبر من Y أقل من Y أقل من Y أقل من Y أقل + +638 +01:02:35,500 --> 01:02:37,060 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +639 +01:02:37,060 --> 01:02:40,800 +أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل + +640 +01:02:40,800 --> 01:02:43,000 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +641 +01:02:43,000 --> 01:02:44,260 +أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل + +642 +01:02:44,260 --> 01:02:47,960 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +643 +01:02:47,960 --> 01:02:53,070 +أقل منماعنديش الا النصف العلوي وبالتالي بصير عندك + +644 +01:02:53,070 --> 01:02:57,530 +النصف العلوي بهذا الشكل نصف القطر يساوي تلاتة يبقى + +645 +01:02:57,530 --> 01:03:02,930 +هذه تلاتة و Zero هذه سالب تلاتة و Zero هذه Zero و + +646 +01:03:02,930 --> 01:03:07,580 +تلاتة يبقى نصف الدائرة العلوي السؤال هوهل هذه + +647 +01:03:07,580 --> 01:03:13,560 +الرسمة تمثل function؟ اه لأن ارسم اي خط رأسي وين + +648 +01:03:13,560 --> 01:03:20,560 +ما بدك بتلاقيه بيقطعها بس وين في نقطة واحدة فقط لا + +649 +01:03:20,560 --> 01:03:27,500 +غير اذا هذه تمثل function تمام؟ بدنا نيجي للسؤال + +650 +01:03:27,500 --> 01:03:32,200 +التالت اللي هو دي + +651 +01:03:33,770 --> 01:03:39,990 +بدي اجي ل دى، قال لي X تربية بدها تساوي Y تربية، + +652 +01:03:39,990 --> 01:03:45,670 +اه معادلة إيه الشهادة؟ يقول الله وعلا، مش عارفين، + +653 +01:03:45,670 --> 01:03:50,410 +لكن ارتبها شوية، يقولوا ارتبها كيف؟ خد الجذر + +654 +01:03:50,410 --> 01:03:55,010 +التربية يا اخي للطرفين، يبقى انا لو جيت اخدت الجذر + +655 +01:03:55,010 --> 01:03:59,550 +التربية للطرفين، الجذر التربية يلا Y تربية بمين؟ + +656 +01:03:59,960 --> 01:04:04,940 +absolute value ل Y الجدر التربيع ل X ب absolute + +657 +01:04:04,940 --> 01:04:12,960 +value ل X طيب شو رأيك؟ بدي أستبدل هذه المعادلة + +658 +01:04:12,960 --> 01:04:19,340 +بمعادلة أخرى وشوف كلامي صح ولا غلط هذه بدي + +659 +01:04:19,340 --> 01:04:25,800 +أستبدلها فقط بالمعادلة Y تساوي زاد او ناقص X بنفع + +660 +01:04:25,800 --> 01:04:26,360 +هيك؟ + +661 +01:04:31,130 --> 01:04:35,290 +طيب انا شايف فيها غبش في وجوه البعض فيكوا شايف + +662 +01:04:35,290 --> 01:04:40,030 +فيها غبش يعني مش واضحة الصورة في ذهنه تمام يبقى + +663 +01:04:40,030 --> 01:04:44,690 +انا بدي امشي بعقلية اللي عندهم الغبش هذا و نشوف + +664 +01:04:44,690 --> 01:04:48,870 +النزيلة الغبش هذا و الله يبقى هذه المعادلة لو روحت + +665 +01:04:48,870 --> 01:04:53,090 +شيلت لبس الويت باني بدي اقول زاد او ناقص y سوى زاد + +666 +01:04:53,090 --> 01:04:57,870 +او ناقص x اظن لو كتبت هيك ماحدش بيزعل طب هذه كام + +667 +01:04:57,870 --> 01:05:06,200 +معادلة؟أربعة y تساوي x هي y تساوي x بالزايد y + +668 +01:05:06,200 --> 01:05:13,560 +تساوي نقص x هي y تساوي نقص x بضل عندنا y بالموجب + +669 +01:05:13,560 --> 01:05:20,520 +يساوي x و نقص x خلصنا منها بدي اخد من ناقص y ناقص + +670 +01:05:20,520 --> 01:05:26,880 +y تساوي x اضرب في السلب يعني y تساوي ناقص x يبقى + +671 +01:05:26,880 --> 01:05:31,630 +نفس المعادلة ولا لا؟تمام طيب بدأ اخد التانية ناقص + +672 +01:05:31,630 --> 01:05:37,330 +Y تساوي ناقص X لو ضرب ناقص يعني Y تساوي X مظبوط + +673 +01:05:37,330 --> 01:05:42,730 +يبقى هذه الأربع معادلات هذي كالكزيدة والحقيقة هي + +674 +01:05:42,730 --> 01:05:48,990 +معادلتين وليست أربع معادلات مظبوط هيك؟ يبقى أزلنا + +675 +01:05:48,990 --> 01:05:54,450 +اللبس أو الغراش يبقى هدول معادلتين فقط لغية طب + +676 +01:05:54,450 --> 01:06:01,990 +السؤال هولما اقول Y تساوي X معدلتاش فاطم مستقيم و + +677 +01:06:01,990 --> 01:06:12,500 +لما اقول Y تساوي سالب Xخط مستقيم يبقى + +678 +01:06:12,500 --> 01:06:17,500 +خط مستقيم على طول الخط لو جيت ارسم الخط اللي اتنين + +679 +01:06:17,500 --> 01:06:24,700 +هدول يبقى هذا محور X وهذا محور Y الخط الأول Y + +680 +01:06:24,700 --> 01:06:30,980 +تساوي X بنصف الرمال الأول والربعةالتالت يعني هذا + +681 +01:06:30,980 --> 01:06:39,500 +الخط Y تساوي X خط الغامق هذا ايوه تمام يبقى هذا + +682 +01:06:39,500 --> 01:06:48,480 +الخط Y تساوي X كويس + +683 +01:06:50,210 --> 01:06:54,490 +طبعا الزاوية هذه جد الزاوية هذه بالضبط تماما كل + +684 +01:06:54,490 --> 01:07:00,410 +واحدة فيهم خمسة واربعين يبقى هذا Y تساوي زاد X + +685 +01:07:00,410 --> 01:07:05,850 +يعني Y تساوي X الان Y تساوي ناقص X بنص في الرابع + +686 +01:07:05,850 --> 01:07:11,370 +التاني و الرابع الرابع يبقى بدريجي هنا بهذا الشكل + +687 +01:07:12,060 --> 01:07:19,520 +يبقى هذا Y تساوي سالب X تمام تمام ماعندوش قيود + +688 +01:07:19,520 --> 01:07:24,240 +يبقى كل واحد ضد والد مستمر ليه Infinity السؤال هو + +689 +01:07:24,240 --> 01:07:29,940 +هل الرسم البياني هذا يمثل function؟ ايوة not + +690 +01:07:29,940 --> 01:07:37,030 +function ليش؟ لأن اي خط رأسي بده يقطع وين؟نقطتين + +691 +01:07:37,030 --> 01:07:41,390 +اي خط رأسي بدي اقطعه في نقطتين طب واحد يقول لي طب + +692 +01:07:41,390 --> 01:07:45,530 +هاي واي بس قطع اتنين في نقطة واحدة بقولك مصبور لإن + +693 +01:07:45,530 --> 01:07:52,520 +انا ماقلتش بس خط واحد قولتلك اي خط رأسي اذا قطعهفي + +694 +01:07:52,520 --> 01:07:56,820 +اكتر من نقطة يبقى ليست functional حتى وان حدث مش + +695 +01:07:56,820 --> 01:07:59,940 +مرة قضع في نقطة مرتين و تلاتة بس في نقطة لكن + +696 +01:07:59,940 --> 01:08:04,460 +الباقي كله في نقطة تانية يبقى ليست functional لازم + +697 +01:08:04,460 --> 01:08:09,940 +ولا مرة يقطع في نقطة يبقى كله اي خط vertical line + +698 +01:08:09,940 --> 01:08:17,160 +يقطع في نقطة واحدة يبقى هادئ نقطةأي function يبقى + +699 +01:08:17,160 --> 01:08:22,400 +هذه ليست function تمام هذه نمرة D نجلة نمرة C دير + +700 +01:08:22,400 --> 01:08:26,660 +بالك هذه أسئلة موجودة في الكتاب من أسئلة التمرين + +701 +01:08:26,660 --> 01:08:32,320 +اللي في الكتاب طيب نجلة نمرة E نمرة E قال لي + +702 +01:08:32,320 --> 01:08:36,780 +absolute value ل X absolute value ل Y تساوي واحد + +703 +01:08:36,780 --> 01:08:42,930 +بدنا نرسم الرسم البياني لهذه الدالةبدا جي اشيل ال + +704 +01:08:42,930 --> 01:08:46,890 +absolute value و اضع زائد او ناقص زي ما حطينا هنا + +705 +01:08:46,890 --> 01:08:52,410 +يبقى انا عندي زائد او ناقص x زائد او ناقص y يساوي + +706 +01:08:52,410 --> 01:08:58,250 +واحد هنا قولنا هدول مش اربع معادلات هدول بس معادلة + +707 +01:08:58,250 --> 01:09:03,790 +سؤالنا هو هنا هدول اربع معادلات والله معادلتين + +708 +01:09:03,790 --> 01:09:10,630 +تعالى نشوف المعادلة الاولى x زائد y تساوي واحد + +709 +01:09:11,110 --> 01:09:16,410 +المعادلة التانية x ناقص y تساوي واحد المعادلة + +710 +01:09:16,410 --> 01:09:21,850 +التالتة ناقص x زائد y تساوي واحد المعادلة الرابعة + +711 +01:09:21,850 --> 01:09:29,770 +ناقص x ناقص y يساوي كده؟ يساوي واحدولا واحدة فيهم + +712 +01:09:29,770 --> 01:09:36,970 +زي التانية طيب هذه ال Y زائد X يساوي واحد هذه + +713 +01:09:36,970 --> 01:09:40,990 +والله خليها بالنفس الترتيب بلاش تقوليش بدلتهم X + +714 +01:09:40,990 --> 01:09:48,030 +زائد Y يساوي واحد وهذه X ناقص Y يساوي من؟ يساوي + +715 +01:09:48,030 --> 01:09:52,700 +واحد شو رأيك هذه لو ضربتها في إشارة سالم؟ما هو + +716 +01:09:52,700 --> 01:09:58,200 +بالصين؟ X ناقص Y يساوي من؟ ساوي سالب واحد هذا لو + +717 +01:09:58,200 --> 01:10:03,020 +ضربت مشار السالب X زائد Y يساوي سالب واحد هتطلع + +718 +01:10:03,020 --> 01:10:07,620 +لهذه وهذه باختلفوا عن بعض مظبوط النتيجة هنا واحد + +719 +01:10:07,620 --> 01:10:11,040 +وهنا سالب واحد رغم ان الطرف اليمين زي بعضه لكن + +720 +01:10:11,040 --> 01:10:15,560 +الشمال لا هذه وهذه طرف الشمال زي بعضه بالسلمين لأ + +721 +01:10:15,560 --> 01:10:20,920 +يبقى هذول أربع معادلات منفاصلات كل واحدة فيهم تمثل + +722 +01:10:22,570 --> 01:10:29,790 +بنرسم هذه الخطوط المستقيمة فبنقول هذا محور X هذا + +723 +01:10:29,790 --> 01:10:35,490 +محور Y هذا نقطة الاصل اللي هي Zero بدي امسك الخط + +724 +01:10:35,490 --> 01:10:43,720 +الأول لو كانت X ب0Yبقداشي واحد يبقى النقطة Zero + +725 +01:10:43,720 --> 01:10:50,740 +واحد يبقى هذه النقطة Zero واحد لو كانت Y ب Zero X + +726 +01:10:50,740 --> 01:10:55,080 +بقداشي واحد يعني واحد و Zero اللي هي النقطة اللي + +727 +01:10:55,080 --> 01:11:01,000 +عندنا هذه واحد و Zero تمام؟ إذا النقطتين يقعان على + +728 +01:11:01,000 --> 01:11:07,590 +الخط المستقيم الأوليبقى ما علي الا اجيب من هناك و + +729 +01:11:07,590 --> 01:11:12,750 +اوصل و امد على استقبال يبقى هذا الخط المستقيم + +730 +01:11:12,750 --> 01:11:19,170 +الأول طيب نجرى الخط المستقيم الثاني لو كانت Y ب + +731 +01:11:19,170 --> 01:11:23,950 +Zero X بقدرش يعني واحد وزيله اللي هي النقطة اللي + +732 +01:11:23,950 --> 01:11:31,180 +عندنا هذه ماتغيرتشمظبوط طيب لو كانت x ب 0 و y ب + +733 +01:11:31,180 --> 01:11:35,960 +سالب واحد لما تبقى x ب 0 و y ب سالب واحد اللي هي + +734 +01:11:35,960 --> 01:11:41,120 +النقطة اللي هنا يبقى سالب واحد و زير و سالب واحد + +735 +01:11:41,590 --> 01:11:48,310 +زيرو و سالب واحد تمام يبقى النقطتين الاتنين يقعن + +736 +01:11:48,310 --> 01:11:53,890 +على الخط المستقيم يبقى روحنا رسمنا الخط المستقيم + +737 +01:11:53,890 --> 01:12:00,590 +بالشكل هذا يبقى هذا X زائد Y يساوي واحد هذا X ناقص + +738 +01:12:00,590 --> 01:12:06,400 +Y يساوي واحد خلصنا من هذا نجي لمستقيم التالفلو + +739 +01:12:06,400 --> 01:12:14,520 +كانت Y ب0 X سالب واحد يعني سالب واحد وزيرو سالب + +740 +01:12:14,520 --> 01:12:20,160 +واحد وزيرو اللي هي النقطة هذه سالب واحد وزيرو يبقى + +741 +01:12:20,160 --> 01:12:25,840 +هنا لو كانت Y بزيرو X بسالب واحد طب لو كانت X + +742 +01:12:25,840 --> 01:12:32,170 +بزيرو Y بواحدلو كانت x بزير و y بواحد اللي هي وين + +743 +01:12:32,170 --> 01:12:37,730 +النقطة اللي عندنا هذه فوق يبقى لأ بروح بوصل بين + +744 +01:12:37,730 --> 01:12:44,550 +النقطتين و بمد هذا على استقامته إذا هذا x ناقص y + +745 +01:12:44,550 --> 01:12:49,990 +يسوى ناقص واحد بعد هيك بدأت أقول هنا لو كانت x + +746 +01:12:49,990 --> 01:12:59,690 +بزير و y بسالب واحد نقطة هذهلو كانت Y ب0 X بسالب + +747 +01:12:59,690 --> 01:13:04,930 +واحد Y بالنقطة هذه بوصل بينهم بالشكل اللي عندنا + +748 +01:13:04,930 --> 01:13:10,570 +هذا بصير هذا X زائد Y ساوي سالب واحد يبقى الرسم + +749 +01:13:10,570 --> 01:13:17,170 +اللي قدامنا هذي تمام طيب تمثل function أي خط + +750 +01:13:17,170 --> 01:13:22,530 +مستقيم أقل ما فيها سيقطع في نقطتين ماكانش في أربعة + +751 +01:13:22,970 --> 01:13:25,650 +لان الخطوة المستقلية ماشية على اطلاع ماشية يعني + +752 +01:13:25,650 --> 01:13:32,250 +ماهياش مقيدة بفترة معينة يبقى هذه not a function + +753 +01:13:32,250 --> 01:13:37,290 +ماهياش ده لأ بسبب ال vertical line test أي خط + +754 +01:13:37,290 --> 01:13:46,220 +مستقيم من فوق لتحتلو كانت ايش؟ + +755 +01:13:46,220 --> 01:13:51,740 +كمعادلة، ممتاز جدا، بتعتبرها ك function ولا لا؟ + +756 +01:13:51,740 --> 01:13:57,960 +ايش رأيك؟ انا بقول لا، عارف ليش؟ لأن بصير العنصر + +757 +01:13:57,960 --> 01:14:03,480 +واحد له مالة نهاية من الصورسؤال ياسميلكو بيقول ما + +758 +01:14:03,480 --> 01:14:08,740 +يأتي لو أنا أخدت الخط اللي عندنا هي المحاور و قلت + +759 +01:14:08,740 --> 01:14:14,400 +هذا X و هذا Y و أخدت الخط هذا مثلا وهو vertical + +760 +01:14:14,400 --> 01:14:18,360 +line، باعتبر هذا function ولا لأ؟ بنقول له لأ، + +761 +01:14:18,360 --> 01:14:22,390 +لماذا؟لأن القيمة تبعت الـ X دا إلها ما شاء الله + +762 +01:14:22,390 --> 01:14:26,530 +صور جد ما بدك، فوق و بتاع، يعني الصور اللي هو نفس + +763 +01:14:26,530 --> 01:14:29,790 +الواحد له مالة نهية من الصور، مش صورتين، وبالتالي + +764 +01:14:29,790 --> 01:14:36,770 +not function، لكن أي خط مستغيم غير الخط الرأسي لا + +765 +01:14:36,770 --> 01:14:43,710 +يمكن أن يكون إلا دالةلا يمكن أن يكون إلا دا لا مش + +766 +01:14:43,710 --> 01:14:47,770 +لا يمكن أن يكون دا لا إذا هذا لا يمكن أن يكون + +767 +01:14:47,770 --> 01:14:53,470 +function لكن كل الخطوط الأخرى غير الموازية لهذا + +768 +01:14:53,470 --> 01:14:58,210 +الخط كلها function سواء كان مائل أوبليج أو + +769 +01:14:58,210 --> 01:15:02,750 +horizontal أوفقي أوفقي أو مائل ماعرفش بس الخط + +770 +01:15:02,750 --> 01:15:08,110 +الرأسي لا يمكن أن يكون function أو لا يمكن أن يمثل + +771 +01:15:08,110 --> 01:15:13,670 +functionماشي سؤال وجيه هو سؤال في محلي ممتاز جدا + +772 +01:15:13,670 --> 01:15:20,830 +شو اسمك انت؟ زيد ابو زيد ماشي يبقى زيد نهض ابو زيد + +773 +01:15:20,830 --> 01:15:27,170 +كويس يا سيدي نيجي لحاجة جديدة يا شباب اسمها ال + +774 +01:15:27,170 --> 01:15:32,850 +piecewise defined function نيجي لعنوان جديد جانبي + +775 +01:15:32,850 --> 01:15:36,070 +اسمه piece + +776 +01:15:41,290 --> 01:15:48,350 +wise defined defined + +777 +01:15:48,350 --> 01:15:56,170 +functions example + +778 +01:15:56,170 --> 01:16:00,590 +one + +779 +01:16:00,590 --> 01:16:13,220 +اول مثال is the expression isthe exception هل + +780 +01:16:13,220 --> 01:16:24,340 +الصيغة التالية f of x يساوي أحد أمرين اتنين ناقص + +781 +01:16:24,340 --> 01:16:32,620 +تلاتة x تكيب و ال x أقل من أو يساوي الواحد و تلاتة + +782 +01:16:32,620 --> 01:16:42,780 +x أُص أربعناقص تلاتة وال X greater than or equal + +783 +01:16:42,780 --> 01:16:49,360 +to one define a + +784 +01:16:49,360 --> 01:16:53,600 +function والسؤال + +785 +01:16:53,600 --> 01:16:56,660 +لماذا + +786 +01:16:56,660 --> 01:17:02,640 +يالا فكرولي كويس ع بالنا نمسح اللوح ونبحث عن + +787 +01:17:02,640 --> 01:17:04,000 +الإجابة + +788 +01:17:32,390 --> 01:17:35,750 +النقطة الجديدة اللى حضرتنا لان اللى لازلنا في نفس + +789 +01:17:35,750 --> 01:17:39,390 +ال section is piecewise function او piecewise + +790 +01:17:39,390 --> 01:17:44,190 +defined function يبقى الدالة المكونة من اكثر من + +791 +01:17:44,190 --> 01:17:49,730 +جزء عدة جزءين تلاتة كذا piece قطعة فلما اقول + +792 +01:17:49,730 --> 01:17:53,790 +piecewise يعني قطعة piecewise function دالة مكونة + +793 +01:17:53,790 --> 01:17:57,810 +من عدة قطعة يعني من عدة اجزاء لكن هذه الدالة + +794 +01:18:01,950 --> 01:18:07,850 +هل هذه الصيغة التالية بتعرف function ولا لا؟ + +795 +01:18:07,850 --> 01:18:13,230 +الاجابة يا نعم يا لا نقول نعم لماذا ونقول لا لماذا + +796 +01:18:13,230 --> 01:18:20,250 +بدنا الحل في هذه الحالة حد + +797 +01:18:20,250 --> 01:18:24,050 +فيكم يقدر يقول لي هل هذه دالة ولا لا؟ + +798 +01:18:27,890 --> 01:18:30,990 +أنا أنا بدي أجيب فيه من دور الرسم، طب خليني أسأل + +799 +01:18:32,290 --> 01:18:37,790 +هذا الآن منحنى، مظبوط؟ وهذا منحنى عادي جدا، لكن + +800 +01:18:37,790 --> 01:18:43,410 +المشكلة أنه في التقاء فيما بينهما الوين؟ عند + +801 +01:18:43,410 --> 01:18:46,850 +الواحد، وممكن مايلتجوش عند الواحد، يمكن أو يمكن + +802 +01:18:46,850 --> 01:18:52,450 +لأ، مظبوط ولا لأ؟ لكن جالي يساوي ويساوي معناته في + +803 +01:18:52,450 --> 01:18:57,610 +التقاء لازم يكون في التقاء، صحيح ولا لأ؟ الالتقاء + +804 +01:18:57,610 --> 01:19:01,730 +هذا، بدي أشوف هل بيحصل ولا بيحصلش؟ + +805 +01:19:03,730 --> 01:19:07,730 +المشكلة وين؟ عند الواحد، مش هنا هي الواحد، اكبر + +806 +01:19:07,730 --> 01:19:11,730 +وساقه واحد، يعني المنحلة ممكن تقول هذا جاي خط + +807 +01:19:11,730 --> 01:19:14,790 +مستقيم و هذا جاي قص والتقوا عند النقطة هذه اللي هي + +808 +01:19:14,790 --> 01:19:17,650 +واحد، إذا المشكلة تكون عند واحد، يمكن يكون في + +809 +01:19:17,650 --> 01:19:21,730 +اتصال وممكن يكون فيش اتصال، صحيح ولا لا؟ يمكن عند + +810 +01:19:21,730 --> 01:19:25,510 +الواحد تبقى الدالة معرفة وممكن ما تكونش معرفةكل + +811 +01:19:25,510 --> 01:19:29,390 +الاحتمالات واردة الدالة قابلة للاشتقاق ويمكن مش + +812 +01:19:29,390 --> 01:19:32,790 +قابلة للاشتقاق زي ما احنا ناخد بعد ذلك الدالة + +813 +01:19:32,790 --> 01:19:37,110 +متصلة أو ويرمى كل الاحتمالات بيصير واردة كويس احنا + +814 +01:19:37,110 --> 01:19:41,390 +مابناش نبحث هذا احنا نبحث بس هل الدالة معرفة عند + +815 +01:19:41,390 --> 01:19:45,550 +هذه النقطة او لا إذا معرفة كرمى مش معرفة خلاص ليست + +816 +01:19:45,550 --> 01:19:51,190 +function صحيح ولا لأ إذا مشان هيك بتروح أجيبله F + +817 +01:19:51,190 --> 01:19:57,160 +of واحديبقى f of واحد يساوي اقل من اذا يساوي واحد + +818 +01:19:57,160 --> 01:20:02,980 +يبقى بضعوم في الاولى يبقى اتنين ناقص تلاتة في واحد + +819 +01:20:02,980 --> 01:20:12,050 +تكيب اللي هو قداش ناقص واحدبط ولكن كذلك f of واحد + +820 +01:20:12,050 --> 01:20:17,810 +لانه معرف عن الواحد يساوي كده يبقى يساوي تلاتة في + +821 +01:20:17,810 --> 01:20:24,110 +واحد أص أربعة ناقص تلاتة يساوي زيرو هذا العنصر + +822 +01:20:24,110 --> 01:20:28,710 +الواحد أكم صورة لجينا له صورتين يبقى هدى function + +823 +01:20:28,710 --> 01:20:38,850 +يبقى not a function يبقى هذا بده يعطيلك انهgiven + +824 +01:20:38,850 --> 01:20:47,990 +expression الصيغة المعطاها دي مالها is not a + +825 +01:20:47,990 --> 01:20:58,090 +function because السبب انه سالب واحد بدأ لاتساوي + +826 +01:20:58,090 --> 01:21:04,110 +zero بس هنا طلعت بساوي بعض و هذا كلام ماله مرفوض + +827 +01:21:07,980 --> 01:21:14,440 +بنجي المثال الثاني example two + +828 +01:21:14,440 --> 01:21:18,960 +بقول sketch the graph of the function + +829 +01:21:28,510 --> 01:21:36,010 +أرسم لرسمة الدالة f of x يساوي أحد ثلاثة أمور يا + +830 +01:21:36,010 --> 01:21:43,110 +إما أربعة لما ال X أقل من سالب اتنين يا إما X + +831 +01:21:43,110 --> 01:21:50,700 +تربيةلما سالب اتنين اقل من او يسوى X اقل من او + +832 +01:21:50,700 --> 01:21:57,680 +يسوى Zero يا اما X لما الـ X greater than Zero + +833 +01:22:00,770 --> 01:22:05,330 +يقول احنا عندنا piecewise function مش جزئين ثلاثة + +834 +01:22:05,330 --> 01:22:11,050 +اجزاء قال لي ارسملي هذه الدالة بقوله تعالى نشوف + +835 +01:22:11,050 --> 01:22:18,630 +كيف بدنا نرسم هذه الدالة بقوله هذه المحاور وهذا + +836 +01:22:18,630 --> 01:22:28,030 +محور X وهذا محور Y وهذا نقطة الأصل اللي هي Zeroاذا + +837 +01:22:28,030 --> 01:22:34,570 +X أقل من سالب اتنين قيمة الدالة كده يبقى هذه Zero + +838 +01:22:34,570 --> 01:22:41,410 +وهذا سالب واحد وهذه سالب اتنين وهذه سالب تلاتة عند + +839 +01:22:41,410 --> 01:22:45,230 +السالب اتنين وقبل السالب اتنين قيمة الدالة كده + +840 +01:22:45,230 --> 01:22:52,790 +يبقى انا بدي اطلع فوقوهي اللى عندنا من هنا اللى هى + +841 +01:22:52,790 --> 01:22:59,770 +الاربعة يبقى قبل السالب اتنين خط مستقيم دالة ثابتة + +842 +01:22:59,770 --> 01:23:06,770 +قيمتها تساوي قداش اربعة ومافيش يساوي عندما تساوي + +843 +01:23:06,770 --> 01:23:09,670 +سالب اتنين الدالة قداش بتكون + +844 +01:23:15,730 --> 01:23:22,770 +بس انا مقيد بمين بالفترة من سالب اتنين لغاية zero + +845 +01:23:22,770 --> 01:23:28,250 +فقط لغير يبقى ال parabola بديجين هيك و ممنوع يطلع + +846 +01:23:28,250 --> 01:23:32,470 +و ممنوع يفوت هيك لإيش؟ لإن عند السالب اتنين تربية + +847 +01:23:32,470 --> 01:23:38,760 +بصير باربعة يبقى بديبدة من عند النقطة هذهويكون قاس + +848 +01:23:38,760 --> 01:23:46,490 +بهذا الشكلمغلقة عند سالب 2 بالسبب ان هذه تساوي 4 + +849 +01:23:46,490 --> 01:23:51,510 +مش بالسبب الأول مغلقة بالشكل اللي ان هذا تمام + +850 +01:23:51,510 --> 01:23:58,150 +وصلنا ل 0 وخلصنا لغاية 0 كمان يساوي 0 تربيع ب 0 + +851 +01:23:58,150 --> 01:24:05,930 +إذا من هنا كمان مغلقة تماما يبقى هذا هو الأربعة + +852 +01:24:05,930 --> 01:24:11,620 +وهذا هو ال X تربيعقال لي بعد هيك بعد ال zero + +853 +01:24:11,620 --> 01:24:17,620 +فالدلة تساوي من X يعني Y تساوي يعني الساعة تساوي + +854 +01:24:17,620 --> 01:24:24,360 +صين رسمنا خط قبل شوية يعني خط ينصف من الرابع الأول + +855 +01:24:24,360 --> 01:24:31,000 +بهذا الشكل خط مستقيم يبقى هذا Y تساوي X هذا Y + +856 +01:24:31,000 --> 01:24:37,680 +تساوي X تربيع هذا Y تساوي أربعيبقى هذه دالة مكونة + +857 +01:24:37,680 --> 01:24:45,960 +من ثلاثة أجزاء خط مستقيم أوفقي خط مائل قوس Y تساوي + +858 +01:24:45,960 --> 01:24:51,260 +X تربية طبعا هذه أمثلة سهلة ننتقل شوية + +859 +01:25:00,040 --> 01:25:04,620 +بالنسبة للنقطة الأولى بتكون مفتوحة هنا لكن لما + +860 +01:25:04,620 --> 01:25:08,340 +جابلي يساوي السالي باتنين إذا عندي السالي باتنين + +861 +01:25:08,340 --> 01:25:13,780 +بدا تبقى مغلقة فروحنا أغلقناها من هنا يساوي ال + +862 +01:25:13,780 --> 01:25:19,500 +zero يبقى أغلقناها من عن ال zero الباقي مفتوحة طيب + +863 +01:25:19,500 --> 01:25:25,690 +نجي لمثال رقم تلاتةتلاتة حاجة اسمه إلى نقطة ايه؟ + +864 +01:25:25,690 --> 01:25:33,590 +لأنه very important يبقى example تلاتة حاجة اسمه + +865 +01:25:33,590 --> 01:25:38,910 +إلى نقطة ايه؟ في الأول the integer floor function + +866 +01:25:38,910 --> 01:25:49,030 +integer floor function دالة الأرض is the function + +867 +01:25:49,030 --> 01:25:52,010 +whose + +868 +01:25:55,840 --> 01:26:05,860 +value with value at with + +869 +01:26:05,860 --> 01:26:18,820 +value at any real number x is + +870 +01:26:18,820 --> 01:26:23,680 +the greatest + +871 +01:26:28,030 --> 01:26:41,650 +انتجر less than or equal less than or equal to x + +872 +01:27:08,850 --> 01:27:14,030 +مرة تانية نقرأ الكلام اللى مكتوب نحاول نفهم ما هو + +873 +01:27:14,030 --> 01:27:19,410 +مكتوب لنروح على طبقه على أرض الواقع بأمثلة مختلفة + +874 +01:27:19,410 --> 01:27:24,450 +ايش بقول the integer floor function قبل المبدأ + +875 +01:27:24,450 --> 01:27:30,950 +سمعته بالثانوية بدالة صحيح C هى دالة صحيح C بس بدى + +876 +01:27:30,950 --> 01:27:37,540 +جزاياه لإيش إلى جزءيندالة الأرض ودالة السقف، دالة + +877 +01:27:37,540 --> 01:27:41,960 +الأرض لأنه بنزل العدد الكاثري للأرض ودالة السقف + +878 +01:27:41,960 --> 01:27:47,320 +بنطلع العدد الكاثري الأوان للسقف يعني للعدد الصحيح + +879 +01:27:47,320 --> 01:27:50,980 +اللي بيجي بعده أو اللي بيجي قبله حسب طبيعة المثلة + +880 +01:27:51,510 --> 01:27:55,630 +the integer of lower function يعني دالة مين؟ يعني + +881 +01:27:55,630 --> 01:27:57,990 +بالبلد، ان قلت لك اتنين و تسعة من عشرة، ممكن + +882 +01:27:57,990 --> 01:28:03,030 +تنزلها لوين؟ لاتنين، ممتاز يبقى is the function هي + +883 +01:28:03,030 --> 01:28:08,470 +دالة whose value، اللي قيمته at any real number X + +884 +01:28:08,470 --> 01:28:14,550 +ماقلتش عدد صحيح، real صحيح، والله كثري is the + +885 +01:28:14,550 --> 01:28:22,260 +greatest integer، أكبر رقمless than يكون أقل من أو + +886 +01:28:22,260 --> 01:28:27,880 +يكون مساويا ل X يبقى ايش قال هنا is the greatest + +887 +01:28:27,880 --> 01:28:35,340 +integer اكبر رقم يكون مساويا او اقل منه فمثلا لما + +888 +01:28:35,340 --> 01:28:40,760 +قلتك اتنين وتسعة من عشرة ايش الرقم الصحيح اللي اقل + +889 +01:28:40,760 --> 01:28:48,300 +منه اتنين لما نقلتك اتنينإتنين لإنه قال لي أقل منه + +890 +01:28:48,300 --> 01:28:53,920 +أو مساويا له إذا بيساوي يبقى بنان عليه for example + +891 +01:28:53,920 --> 01:29:05,040 +بديها الرمز اللي هو F of X يساوي هيكو بقول X تمام + +892 +01:29:05,040 --> 01:29:09,340 +زي اللي قاعد على كرسي، يبقى هذه هي دالة اللي هو + +893 +01:29:09,340 --> 01:29:15,080 +الأرض، يبقى for example لو جيت قلتلك لإتنين، إيش + +894 +01:29:15,080 --> 01:29:23,020 +بدك تقول؟ لإتنين، لو قلتلك هنا دالة الأرض لإتنين + +895 +01:29:23,020 --> 01:29:30,050 +وتسعة وتسعين من مين؟إتنين برضه يبقى هذه اللي هو + +896 +01:29:30,050 --> 01:29:39,830 +الاتنين لو قلتلك جداش اتنين فاصلة زيرو واحد من + +897 +01:29:39,830 --> 01:29:44,790 +عاشر من مية برضه اتنين يعني هدول اتنين بيساوي بعض + +898 +01:29:44,790 --> 01:29:51,430 +و بيساوي هذا يساوي اتنين طيب بلاش دالة الأرض لزيرو + +899 +01:29:52,510 --> 01:30:01,910 +0 زي ما هي.طيب، دلت الأرض لمين؟ لسالب تلاتة وواحد + +900 +01:30:01,910 --> 01:30:07,870 +من العشرة.قول يا ابني.سالب أربعة.سالب أربعة، هي + +901 +01:30:07,870 --> 01:30:11,350 +الإجابة اللي بقول عليها.حد إيه اللي اعتراض على هذه + +902 +01:30:11,350 --> 01:30:17,230 +الإجابة؟سالب أربعة أقل من سالب تلاتة واحد من عشر، + +903 +01:30:17,230 --> 01:30:22,450 +وإحنا قلنا بأول رقم أقل منه، يبقى هذه إجابة سليمة + +904 +01:30:22,450 --> 01:30:29,290 +وما عداها فهي إجابة خاطية طيب، لو جيت قلتلك هذه يا + +905 +01:30:29,290 --> 01:30:34,030 +سيد العزيز سالب + +906 +01:30:34,030 --> 01:30:40,530 +تلاتة وتسعة وتسعين من الميةبرضه طيب ماشي الحالة + +907 +01:30:40,530 --> 01:30:48,310 +طيب بدي أقولك سالب زيرو و تلاتة من عشر سالب واحد + +908 +01:30:48,310 --> 01:30:53,990 +يعني كمان طيب سالب واحد ماشي سالب واحد و هكذا يبقى + +909 +01:30:53,990 --> 01:30:58,850 +هذه كلها إجابات صحيحة طيب هذه خلصنا إيه بدنا نروح + +910 +01:30:58,850 --> 01:31:03,230 +لنمرة V طبعا هرسملك إياها بعد قليل بس خلينا ناخد + +911 +01:31:03,230 --> 01:31:08,370 +نمرة Vيبقى بيننا بـ a the integer ceiling function + +912 +01:31:08,370 --> 01:31:14,230 +هي دالة السقف the integer ceiling + +913 +01:31:14,230 --> 01:31:18,110 +function + +914 +01:31:18,110 --> 01:31:27,230 +is the function whose value is the function whose + +915 +01:31:27,230 --> 01:31:36,290 +valueالقيمة بتابعة at any real number at any real + +916 +01:31:36,290 --> 01:31:51,750 +number x is the smallest is the smallest is + +917 +01:31:51,750 --> 01:31:58,070 +the smallest integer greater + +918 +01:31:58,070 --> 01:31:58,970 +than + +919 +01:32:03,570 --> 01:32:10,210 +Greater than or equal to + +920 +01:32:10,210 --> 01:32:11,270 +X + +921 +01:32:42,620 --> 01:32:49,700 +العدد الصحيح تبع السقف وليس تبع الأرض هو عبارة عن + +922 +01:32:49,700 --> 01:32:54,800 +الدالة whose value قيمتها number X عند أي عدد + +923 +01:32:54,800 --> 01:33:02,040 +حقيقي X هو أصغر + +924 +01:33:02,040 --> 01:33:08,150 +رقميكون greater than or equal to X يعني بدل ما كنت + +925 +01:33:08,150 --> 01:33:13,430 +بتنزل للأرض، هتطلع لوين؟ للسقف، تمام؟ طيب، بدي + +926 +01:33:13,430 --> 01:33:18,650 +أمسك الإعداد هذه و أشوف إذا لو أنا بدي دلة السقف + +927 +01:33:18,650 --> 01:33:23,630 +للإتنين، قداش بتساوي اتنين؟ طيب، يعني لاحظ السقف + +928 +01:33:23,630 --> 01:33:28,330 +والأرض للعدد الصحيح اتنين are equal طب لو جيت، + +929 +01:33:28,330 --> 01:33:36,970 +قلتلك دلة السقف للإتنينو Zero واحد يبقى تلاتة بدي + +930 +01:33:36,970 --> 01:33:42,650 +دالة السقف لتنين تسعة وتسعين من المية يبقى تلاتة + +931 +01:33:42,650 --> 01:33:48,030 +برضه كله بطل للعدد الصحيح من اللي بيجي بعدههذه + +932 +01:33:48,030 --> 01:33:54,150 +قولناها لو جيت قولتلك دلت السقف لمن؟ لزيرو يبقى + +933 +01:33:54,150 --> 01:34:03,990 +zero بده دلت السقف لسالب تلاتة واحد من عشر كتلة + +934 +01:34:03,990 --> 01:34:07,130 +الروايات زي المرض اللي فاتت + +935 +01:34:09,750 --> 01:34:15,470 +سالب تلاتة سالب تلاتة أكبر من سالب تلاتة واحد من + +936 +01:34:15,470 --> 01:34:21,150 +عشرة يبقى هذه السالب ركزي كويس من جيبها هذه كرناها + +937 +01:34:21,150 --> 01:34:25,370 +بدل المرة مرات في الخيارات المتعددة هذه اللي + +938 +01:34:25,370 --> 01:34:30,710 +بتسببك أشكالية بنحط السؤال فيها في الغالبتمام؟ طيب + +939 +01:34:30,710 --> 01:34:38,210 +لو جيت قولتلك دالة الصفر الزالب Zero و تلاتة من + +940 +01:34:38,210 --> 01:34:46,730 +عشرة0 ممتاز جدا يبقى 0 خلاصنا هي يبقى كل الأرقام + +941 +01:34:46,730 --> 01:34:53,130 +اللي موجودة عندنا طيب بنحاول نرسم A شكل الدالة يا + +942 +01:34:53,130 --> 01:34:58,910 +شباب نكتب هيك Y أو F of X يسوى دالة السقف ل X + +943 +01:34:58,910 --> 01:35:04,550 +بالشكل هذاهنا هنا هي كرسي هنا بنعملها سقف بالشكل + +944 +01:35:04,550 --> 01:35:08,510 +اللي عندنا بدأ نرسم كل function من ال functions + +945 +01:35:08,510 --> 01:35:15,010 +هدول بدأيجي لرسمة الدالة الأولى يبقى هذا محور X + +946 +01:35:15,010 --> 01:35:22,450 +هذا محور Y خلي بالك هنا بدأ تخيل عند الخط وهمي هذا + +947 +01:35:22,450 --> 01:35:26,890 +مش من ضمن الرسمة مالوش دعوة بالرسمة هذا الخط + +948 +01:35:26,890 --> 01:35:28,730 +الوهمي اللي عندك اكتر + +949 +01:35:31,740 --> 01:35:40,060 +هذا الخط اللي هو Y تساوي X شوف يا سيدي نبدأ من عند + +950 +01:35:40,060 --> 01:35:46,380 +الـ Zero هذا Zero و هذا واحد و هذا اتنين و هذا + +951 +01:35:46,380 --> 01:35:53,660 +تلاتة و هنا واحد و هنا اتنين و هنا تلاتة و هنا + +952 +01:35:53,660 --> 01:36:00,750 +سالب واحد و هنا سالب اتنين و هنا سالب تلاتةوهنا + +953 +01:36:00,750 --> 01:36:06,810 +سالب واحد ثم سالب اتنين ثم سالب تلاتة ثم سالب اربع + +954 +01:36:06,810 --> 01:36:07,870 +ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب + +955 +01:36:07,870 --> 01:36:09,470 +خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم + +956 +01:36:09,470 --> 01:36:10,370 +سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة + +957 +01:36:10,370 --> 01:36:11,310 +ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب + +958 +01:36:11,310 --> 01:36:17,690 +خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم + +959 +01:36:17,690 --> 01:36:28,760 +سالب خمسة ثم سالب خمسة ثم سالب خمسة ثفوق اتنين + +960 +01:36:28,760 --> 01:36:33,980 +هبسموها الدالة الدرجية او الدالة السلمية يبقى هنا + +961 +01:36:33,980 --> 01:36:39,600 +بديجيلك اللي هو الاتنين مغلقة وهي تلاتة لفوق وهي + +962 +01:36:39,600 --> 01:36:47,060 +تلاتة تمام؟ يبقى مغلقة وبعد هيك تمشي لقبال التلاتة + +963 +01:36:47,360 --> 01:36:53,040 +و بتكون مفتوحة و هكذا تمام؟ من الناحية هذه برضه + +964 +01:36:53,040 --> 01:36:58,840 +بنفس الطريقة بتيجي لتحت السلب واحد مغلقة و بتيجي + +965 +01:36:58,840 --> 01:37:05,080 +عند السلب واحد مفتوحة الآن بتيجي عند اتنين تحت + +966 +01:37:05,080 --> 01:37:14,050 +السلب اتنين مغلقة و هيك بتيجي مفتوحةهنا تحت السلب + +967 +01:37:14,050 --> 01:37:24,270 +تلاتة دوري مغلقة وهنا مفتوحة يبقى هذا رسم تمين ال + +968 +01:37:24,270 --> 01:37:31,030 +function الاولى اللى هو Y تساوي دالة الأرض لمن؟ لل + +969 +01:37:31,030 --> 01:37:36,760 +X نجى للدالة التانية اللى هى دالة السقفيبقى دالة + +970 +01:37:36,760 --> 01:37:43,340 +السقف هذا محور X هذا محور Y هذه نقطة الأصل اللي هي + +971 +01:37:43,340 --> 01:37:50,100 +Zero بدا أتخيل الخط الوهمي نفسه اللي هو Y تساوي X + +972 +01:37:50,100 --> 01:37:55,780 +Y تساوي X اللي بنص في الرابع الأول والربع التالت + +973 +01:37:55,780 --> 01:38:02,020 +بنفس الطريقة بدا أقول عندي اي واحد اي اتنين اي + +974 +01:38:02,020 --> 01:38:09,750 +تلاتة اي واحدأي اتنين أي تلاتة وهكذا هنا سالب واحد + +975 +01:38:09,750 --> 01:38:16,110 +سالب اتنين سالب تلاتة هنا سالب واحد سالب اتنين + +976 +01:38:16,110 --> 01:38:22,810 +سالب تلاتة وهكذا تمام؟ بدك تتخيل تماما نفس الرسم + +977 +01:38:22,810 --> 01:38:28,730 +بس جلبها عبر الخط Y تساوي X يعني رسمة الدالة + +978 +01:38:28,730 --> 01:38:35,740 +الأولى تحت الخط Y تساوي Xأعلى الخط Y27X يبقى هذه + +979 +01:38:35,740 --> 01:38:42,700 +بدها نقلبها هنا وتجيلك هنا مفتوحة تمام هذه بدها + +980 +01:38:42,700 --> 01:38:52,140 +تجيلك هنا مفتوحة هذه بدها تجيلك هنا مغلقة وتجيلك + +981 +01:38:52,140 --> 01:39:00,090 +هنا مفتوحة أعلى هذا مباشرةهذه بدأت تجيلك هنا مغلقة + +982 +01:39:00,090 --> 01:39:06,250 +وهنا بدأت تجيلك مفتوحة تحتها مباشرة بدأت تجي مغلقة + +983 +01:39:06,250 --> 01:39:16,230 +وهنا تجي مفتوحة وهكذا تمام؟ يبقى هذه رسمة الدالة Y + +984 +01:39:16,230 --> 01:39:21,290 +تساوي دالة صحيح X بس إيش؟ السقف + +985 +01:39:23,930 --> 01:39:30,210 +طيب، واحد بده يسأل وبده يقول السؤال التالي، من أين + +986 +01:39:30,210 --> 01:39:36,930 +لك هذا؟ يعني أنت حافظهم حافظ، والله هذه بدها فاهم، + +987 +01:39:36,930 --> 01:39:41,850 +بيقولك لا، بدنا فاهم وبدنا نتقيد بالتعريف و نيجي + +988 +01:39:41,850 --> 01:39:48,250 +نرسم، كيف؟طلّالي رسمة الدالة الأولى مثلا عند ال + +989 +01:39:48,250 --> 01:39:54,150 +zero دالة الأرض ب zero متفقين طيب لو كانت واحد من + +990 +01:39:54,150 --> 01:39:59,450 +عشرة بتنزل لوين ل zero يبقى عندما أمشي لغاية + +991 +01:39:59,450 --> 01:40:03,850 +الواحدة كلها ب zero هاي الخط الغامق اللي هو هنا ان + +992 +01:40:03,850 --> 01:40:08,510 +شاء الله يكون تسعة من عشرة بدك تنزل لمين ل ال zero + +993 +01:40:08,510 --> 01:40:15,780 +طيب وصلت واحد صحيةتقفز لو هي حاجة صحية، مظلوم؟ طب + +994 +01:40:15,780 --> 01:40:22,450 +واحد و نصواحد صحيح واحد وتسعة من عشرة واحد صحيح + +995 +01:40:22,450 --> 01:40:26,650 +اتنين واحد من عشرة اتنين و هكذا يبقى فاهمنا كيف + +996 +01:40:26,650 --> 01:40:32,290 +هذه تعالى نمشي للجزء السالم يبقى انا هذا بدأتي + +997 +01:40:32,290 --> 01:40:36,830 +لسالب تسعة من عشرة او سالب واحد تنزل لسالب واحد + +998 +01:40:36,830 --> 01:40:42,090 +لكن سالب تسعة من عشرة بدك تنزلها لقل منها لو سالب + +999 +01:40:42,090 --> 01:40:48,570 +واحد هيو سالب واحد من عشرة سالب واحدفبسالب واحد + +1000 +01:40:48,570 --> 01:40:53,830 +واحد من عشرة نزلها للاتنين و هكذا تبقى عارفين كيف + +1001 +01:40:53,830 --> 01:40:58,930 +الرسمة؟ هذي تعالى هذي هذي تبقى تطلع على فوق تمام + +1002 +01:40:58,930 --> 01:41:04,110 +عند ال zero ب zero عند ال واحدة من العشرة تطلع + +1003 +01:41:04,110 --> 01:41:08,050 +للواحد عند تسعة من العشرة تطلع للواحد عند الواحد + +1004 +01:41:08,050 --> 01:41:12,190 +بواحد عند الواحد واحد من العشرة تطلع للاتنين و + +1005 +01:41:12,190 --> 01:41:16,210 +هكذاوبالتالي الجزء السليم زي ذلك عرفنا كيف الرأس + +1006 +01:41:16,210 --> 01:41:20,950 +مجد مش حيال الله يخبط ويمشي لأ لأ هذه جت بناء على + +1007 +01:41:20,950 --> 01:41:27,690 +فهمنا اللي موجود هناك بدي أسأل سؤال جداش ايه ال + +1008 +01:41:27,690 --> 01:41:34,650 +domain لدالة الأرض هذه؟ + +1009 +01:41:36,310 --> 01:41:41,490 +الأولى كداش ال domain لها؟ هل هناك نقطة دالة غير + +1010 +01:41:41,490 --> 01:41:48,090 +معرفة عندها؟ لأ يعني لكل ال real line طيب هل هذا + +1011 +01:41:48,090 --> 01:41:56,910 +هو domain الدالة التانية تبعت السقف؟ هو نفسه ولا + +1012 +01:41:56,910 --> 01:42:02,630 +لأ؟ يعني ويسوي كداش؟ من سالب infinity إلى infinity + +1013 +01:42:02,630 --> 01:42:10,630 +لكل real lineطب بد ال range لدالة + +1014 +01:42:10,630 --> 01:42:18,290 +الأرض بد ال range كل + +1015 +01:42:18,290 --> 01:42:23,530 +الأعداد معنى إيش؟ ال range يعني أستفيد الأعداد + +1016 +01:42:23,530 --> 01:42:24,250 +الصحيحة + +1017 +01:42:29,140 --> 01:42:34,920 +كل الأعداد، كل الريال، يعني هدول؟ طيب، في الإجابة، + +1018 +01:42:34,920 --> 01:42:38,260 +استنى شوية، في الصورة اللي عندك هذا اللي انت + +1019 +01:42:38,260 --> 01:42:44,300 +شايفها، في كسر موجود؟ يبقى الإجابة بس اللي عدده + +1020 +01:42:44,300 --> 01:42:48,100 +صحيح، مش هستفيد اللي عدده الصحيح، بس تبعد كل + +1021 +01:42:48,100 --> 01:42:55,970 +الكسور، يبقىهتلاقي ال range لهذه هو نفس ال range + +1022 +01:42:55,970 --> 01:43:06,080 +لدلة السقف اللي عندنا هذه هو منهو الـ zero زاد أو + +1023 +01:43:06,080 --> 01:43:12,720 +ناقص واحد، زاد أو ناقص اتنين، زاد أو ناقص تلاتة، + +1024 +01:43:12,720 --> 01:43:19,500 +وفاصلة، وتظلك ماشي إلى أي شاء الله، يبقى عارفين + +1025 +01:43:19,500 --> 01:43:20,980 +الست هذه جسمها؟ + +1026 +01:43:23,210 --> 01:43:28,550 +مجموعة الأعداد الصحيحة the set of integers يبقى + +1027 +01:43:28,550 --> 01:43:36,830 +هذه بدل سوى set Z عندنا اللي هي the set of + +1028 +01:43:36,830 --> 01:43:43,930 +integers يبقى هذه عبارة عن مجموعة الأعداد الصحيحة + +1029 +01:43:43,930 --> 01:43:48,770 +بلا استثناء تمام؟ + +1030 +01:43:50,990 --> 01:43:54,630 +ركزي عليه الشغل هذه يبقى domain الدالة الأولى هو + +1031 +01:43:54,630 --> 01:43:58,950 +domain الدالة التانية the set of all real numbers + +1032 +01:43:58,950 --> 01:44:03,390 +ضال مين عندنا؟ ضال ال range ال range هنا بيعطينيش + +1033 +01:44:03,390 --> 01:44:09,190 +إلا أعداد صحية هذا الخط كله يعتبر قداش اتنين، هنا + +1034 +01:44:09,190 --> 01:44:14,420 +اتنين، هنا اتنين، هنا اتنين، كله اتنينهنا واحد هنا + +1035 +01:44:14,420 --> 01:44:19,520 +صفر هنا سالب واحد يبقى عندي zero واحد اتنين تلاتة + +1036 +01:44:19,520 --> 01:44:22,400 +اربعة خمسة سالب واحد سالب اتنين يبقى مجموعة + +1037 +01:44:22,400 --> 01:44:26,600 +الاعداد الصحية وهكذا بالنسبة للرسم التاني ال + +1038 +01:44:26,600 --> 01:44:29,140 +domain الدالة الأولى هو domain الدالة التانية هو + +1039 +01:44:29,140 --> 01:44:32,400 +the set of all real numbers ال range تبع الدالة + +1040 +01:44:32,400 --> 01:44:35,020 +الأولى هو ال range تبع الدالة التانية هو مجموعة + +1041 +01:44:35,020 --> 01:44:41,180 +الاعداد الصحيةلا يزال عندنا كلام كتير يبقى بنكتفي + +1042 +01:44:41,180 --> 01:44:46,240 +هذا اليوم أو في هذه المحاضرة وسنعود الى ال + +1043 +01:44:46,240 --> 01:44:51,200 +piecewise function بمثال جديد المحاضرة القادمة ان + +1044 +01:44:51,200 --> 01:44:51,700 +شاء الله + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..159a065501c30a4312f4be6e636dbf6f3f87956d --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aL-As5ef2Rc_raw.srt @@ -0,0 +1,4184 @@ +1 +00:00:21,020 --> 00:00:25,220 +بسم الله الرحمن الرحيم نواصل الآن ما ابتدأنا به + +2 +00:00:25,220 --> 00:00:30,160 +المحاضرة الماضية المحاضرة الماضية بدأنا بأول مثال + +3 +00:00:30,160 --> 00:00:34,740 +على ال function أعطيناكوا صيغ مختلفة ل functions + +4 +00:00:34,740 --> 00:00:39,140 +مختلفة و طلبنا ال domain و ال range و الآن بنواصل + +5 +00:00:39,140 --> 00:00:42,950 +في نفس الموضوعالمثال كان معناه المرة اللي فاتت + +6 +00:00:42,950 --> 00:00:45,210 +find the domain and range of the following + +7 +00:00:45,210 --> 00:00:51,050 +functions بدنا المجال والمدى لكل من الدوال التالية + +8 +00:00:51,050 --> 00:00:57,130 +دالة رقم ستة F of X يساوي X زائد absolute value ل + +9 +00:00:57,130 --> 00:01:00,990 +X ذكرنا المرة الماضية ان ال domain تبع الدالة هو + +10 +00:01:00,990 --> 00:01:07,550 +القيم التي تأخذها X حتى تكون الدالة معرفة سؤالنا + +11 +00:01:07,550 --> 00:01:13,380 +هوهل هناك قيمة ال X بتجعل F of X ماهياش معرفة هنا + +12 +00:01:13,380 --> 00:01:19,140 +على ال real line يعني لو أخدنا أي real number أي + +13 +00:01:19,140 --> 00:01:24,160 +عدد حقيقي وعوض مابو هنا بتطلع ده لا معرفة ولا لا + +14 +00:01:24,160 --> 00:01:28,120 +معرفة مادام معرفة إذا ال domain تبقى الدالة من وين + +15 +00:01:28,120 --> 00:01:33,880 +لوين كل ال R أو من سلب infinity إلى infinite كتبت + +16 +00:01:33,880 --> 00:01:38,920 +R ماشي الحال6 of real numbers كتبتلي من سالب + +17 +00:01:38,920 --> 00:01:43,060 +infinity ل infinity معناه مشكلة هذا الصيغة و هذا + +18 +00:01:43,060 --> 00:01:47,700 +الصيغة الاتنين are the same طيب هذا ال domain بدنا + +19 +00:01:47,700 --> 00:01:52,560 +ال range المرة الماضية ذكرنا انه ال range بدي اخد + +20 +00:01:52,560 --> 00:01:56,080 +من ال domain و اعوض في الدالة القيم اللي بتطلع + +21 +00:01:56,080 --> 00:02:00,640 +بتكون هي ال range تبع هذه الدالة يبقى بنفضل نبدأ + +22 +00:02:00,640 --> 00:02:04,280 +من عند zero نتحرك على اليمين ثم نبدأ من عند zero + +23 +00:02:04,280 --> 00:02:08,960 +نتحركاللي بيطلع عنا بيكون هو ال real number فلو + +24 +00:02:08,960 --> 00:02:15,340 +أخدت X ب Zero يبقى الناتج كده؟ Zero يبقى Zero من + +25 +00:02:15,340 --> 00:02:21,920 +ضمن الرين اتحرك على اليمين خدلي واحد مثلا اتمين طب + +26 +00:02:21,920 --> 00:02:30,590 +خدلي تلاتة و نص سبع تمام خدلي ميةمتين، ألف، ألفين، + +27 +00:02:30,590 --> 00:02:34,490 +مليون، اتنين، ايه؟ يبقى رايحين لوين؟ للمالة نهاية + +28 +00:02:34,490 --> 00:02:40,570 +فبنمشي العكس بالسالب لو أخدنا سالب واحد سالب واحد + +29 +00:02:40,570 --> 00:02:45,270 +زيد absolute value لسالب واحد absolute value لسالب + +30 +00:02:45,270 --> 00:02:50,410 +واحد مقداش؟ واحد وفيه قبل سالب واحد؟ Zero طيب + +31 +00:02:50,410 --> 00:02:57,750 +absolute value لسالب ميةمية و سالب مية، إذا كل + +32 +00:02:57,750 --> 00:03:02,550 +القيم السالبة، ال range تبعها مين؟ يعني أنا عندي + +33 +00:03:02,550 --> 00:03:08,750 +من سالب infinity لغاية قبل zero، كل النتيجة + +34 +00:03:08,750 --> 00:03:13,250 +بتعطيني zero، حتى عند ال zero ب zero، تمام؟ إذا ال + +35 +00:03:13,250 --> 00:03:18,110 +range لكل القيم السالبة، يعني كل القيم السالبة لها + +36 +00:03:18,110 --> 00:03:24,040 +صورة واحدة فقط وهيلكن اللي بعدها الله يسهل عليها + +37 +00:03:24,040 --> 00:03:27,480 +رايحة لمالها نهائيا، إذا من وين لوين؟ من Zero + +38 +00:03:27,480 --> 00:03:31,440 +لغاية النهائي. Closed من عند ال Zero هي Infinity + +39 +00:03:31,440 --> 00:03:41,340 +Open من عند المالها نهائيا. السؤال السابع F of X + +40 +00:03:41,340 --> 00:03:46,740 +يساوي الجذر التربية لX تربية ناقص 3X + +41 +00:03:49,480 --> 00:03:54,460 +خلاص، بدأ أدور على ال domain، الآن بتنعلمك طريقة + +42 +00:03:54,460 --> 00:04:00,420 +سهلة وميسورة بحيث تجيب اللي هو المنطقة المعرفة + +43 +00:04:00,420 --> 00:04:05,340 +الدال عليها بدون أي مشاكل، خلي بالك معايا هناهل + +44 +00:04:05,340 --> 00:04:10,580 +الجذر معرف لقيمة السالبة؟ لأ، يبقى الجذر مش معرف + +45 +00:04:10,580 --> 00:04:16,700 +إلا لقيمة، إذا بدي كل القيمة اللي تحت الجذر تبقى + +46 +00:04:16,700 --> 00:04:21,680 +أكبر من أو تساوي Zero، يقول خليني نشتغل في الهامش، + +47 +00:04:21,680 --> 00:04:26,560 +يبقى أنا بدي X تربية ناقص تلاتة X greater than or + +48 +00:04:26,560 --> 00:04:33,190 +equal to zeroأو بمعنى آخر لو أخدت X عامل مشترك بظل + +49 +00:04:33,190 --> 00:04:38,060 +X ناقص تلاتة greater than or equal to zeroمظبوط + +50 +00:04:38,060 --> 00:04:43,720 +هكذا؟ طيب، الأن نعلمك الطريقة كيف بدي أجيب على ال + +51 +00:04:43,720 --> 00:04:49,880 +real line الأعداد التي تحقق هذه ال inequality يعني + +52 +00:04:49,880 --> 00:04:54,620 +ما هي الأعداد الحقيقية التي تحقق هذه المتبانة يبقى + +53 +00:04:54,620 --> 00:05:00,780 +هنا بدي أقول بدي أخد إشارة ال X الأولانية لحالة و + +54 +00:05:00,780 --> 00:05:06,410 +برسم ال real lineالـ X هذه بتاخد الـ 0 تبعها وين؟ + +55 +00:05:06,410 --> 00:05:10,450 +عند الـ 0، لو جيت بعد الـ 0، الـ X موجبة و لا + +56 +00:05:10,450 --> 00:05:16,310 +سالبة، يبقى لا تاخد إلا قيما موجبة بعد مين؟ بعد + +57 +00:05:16,310 --> 00:05:22,040 +الـ 0، لو رجعت قبل الـ 0 بتاخد كلها قيم سالبةبعد + +58 +00:05:22,040 --> 00:05:28,100 +هيك بدنا نيجي ناخد إشارة sign X minus three يعني + +59 +00:05:28,100 --> 00:05:32,760 +إشارة الجث X نقص تلاتة بياخد القيمة الصفر عند X + +60 +00:05:32,760 --> 00:05:36,640 +تساوي و التلاتة بتيجي على يمين ال zero يعني + +61 +00:05:36,640 --> 00:05:42,400 +التلاتة هتجي هنا إذا بعد التلاتة زي أربع الجث + +62 +00:05:42,400 --> 00:05:46,850 +بيكون مالهأربعة وخمسة وستة ومية وكذا يبقى كله + +63 +00:05:46,850 --> 00:05:50,650 +positive زي ما انت شايف، لو جيت قبل التلاتة زي + +64 +00:05:50,650 --> 00:05:55,930 +اتنين وواحد وزيرو سالب خمسة وسالب مية وكله قيم + +65 +00:05:55,930 --> 00:06:01,690 +مالها؟ سالبة، يبقى كله قبلها قيم سالبة، انا مابدأ + +66 +00:06:01,690 --> 00:06:05,770 +اشارة كل واحد لحالة بدأ اشارة اتنين مضربين في بعض + +67 +00:06:05,770 --> 00:06:11,750 +ضربإذا بروح بقوله بدي أخد إشارة X مضروبة في الـ X + +68 +00:06:11,750 --> 00:06:16,350 +minus three و أقول له هي ال real line و هذه الحدود + +69 +00:06:16,350 --> 00:06:22,170 +الإقليمية هذا zero وهذا تلاتة اتنين هذول مضربين في + +70 +00:06:22,170 --> 00:06:25,870 +بعض يبقى بدي أضرب الإشارات في بعض موجب في موجب + +71 +00:06:25,870 --> 00:06:32,430 +موجب موجب في سالب سالب سالب في سالب موجب ممتاز جدا + +72 +00:06:32,970 --> 00:06:38,890 +هي فسرنا حاصل الضرب للمقدار يوم ما يكون موجب و يوم + +73 +00:06:38,890 --> 00:06:43,790 +ما يكون سالب برجع للمتباينة الأصلية اللى عنده بدى + +74 +00:06:43,790 --> 00:06:48,790 +حاصل الضرب يكون ماله أكبر من أو يساوي زيرو يعني يا + +75 +00:06:48,790 --> 00:06:52,850 +زيرو يا إما قيمةموجب ضد طلع وين القيام الموجب، + +76 +00:06:52,850 --> 00:06:56,830 +اللي هي المنطقة هذه والمنطقة هذه إذا الجواب هو من + +77 +00:06:56,830 --> 00:07:02,790 +سلب infinity لغاية ال zero وكذلك من تلاتة لغاية + +78 +00:07:02,790 --> 00:07:07,770 +infinity إذا ال domain بيصير عندنا من سلب infinity + +79 +00:07:07,770 --> 00:07:12,810 +لغاية ال zero طبعا من عند ال zero مغلقة بسبب + +80 +00:07:12,810 --> 00:07:19,590 +اليساوي اتحاد تلاتة و infinityكتبنا الفترة مغلقة + +81 +00:07:19,590 --> 00:07:25,330 +من عند الـ zero والتلاتة بسبب ال يساوي، لو ماعنديش + +82 +00:07:25,330 --> 00:07:30,450 +يساوي بكتب هذه ايه؟ open، بكتب الفترة هذه فترة + +83 +00:07:30,450 --> 00:07:35,790 +ايه؟ مختوها طيب احنا الان كل اللي عملناه حسبنا من + +84 +00:07:35,790 --> 00:07:42,390 +اين؟ حسبنا ال interval اللي داله معرف عليها يعني + +85 +00:07:42,390 --> 00:07:47,470 +استبعدنا الفترة من اين لوين؟من زيرو لتلاتة طيب + +86 +00:07:47,470 --> 00:07:52,270 +يعني لو أخدت رقم من زيرو لتلاتة بحقك في ال link و + +87 +00:07:52,270 --> 00:07:57,170 +لا تهادي نقولك الله جرب خد الرقم اللي يعجبك كداش + +88 +00:07:57,170 --> 00:08:01,670 +يعني من زيرو لتلاتة اتنين مثلا يبقى لو جات لليه + +89 +00:08:01,670 --> 00:08:06,750 +اتنين اتنين اتنين ناقص تلاتة فظل سالب واحد في + +90 +00:08:06,750 --> 00:08:10,430 +اتنين سالب اتنين هل السلب اتنين اكبر من ال zero + +91 +00:08:10,890 --> 00:08:14,490 +يبقى لا يمكن يبقى لا اتنين ولا الواحد ولا واحد و + +92 +00:08:14,490 --> 00:08:18,370 +نص ولا الواحد و تلت اربع ولا واحد كل هذه الأرقام + +93 +00:08:18,370 --> 00:08:21,910 +لا تحقق ال inequality قبل ال zero جاهزين بعد ال + +94 +00:08:21,910 --> 00:08:26,570 +zero مجول برضه طب خلي قبل ال zero خلي اي رقم سالب + +95 +00:08:27,210 --> 00:08:32,310 +ناخد ناقص اتنين اللي قلت عليه هذا ناقص اتنين اي + +96 +00:08:32,310 --> 00:08:37,530 +ناقص اتنين هو ناقص ثلاثة ناقص خمسة ناقص خمسة و هنا + +97 +00:08:37,530 --> 00:08:42,890 +ناقص اتنين زي عشرة اكبر من زير هذا لو أخدت سلم طب + +98 +00:08:42,890 --> 00:08:49,800 +لو أخدت هموجبايرام كود اللي هو الاربع ففاجئي بقوله + +99 +00:08:49,800 --> 00:08:53,760 +اربع واربع ناقص تلاتة اللي هو احد فيه اربع باربع + +100 +00:08:53,760 --> 00:08:57,840 +اكبر من ال zero إذا كلامنا صحيح يبقى بناء عليها + +101 +00:08:57,840 --> 00:09:01,920 +إذا بعدنا فقط الفترة من zero لغاية تلاتة هذا ال + +102 +00:09:01,920 --> 00:09:05,510 +domain بدنا ال rangeالـ Range بدك تروح تاخد من + +103 +00:09:05,510 --> 00:09:09,530 +الفترة اللي عندك هذه و تعوض في الدالة و تشوف إيش + +104 +00:09:09,530 --> 00:09:12,910 +اللي بطلع يلا أشوف مين الشاطرة فيك و اللي حسبها + +105 +00:09:12,910 --> 00:09:18,770 +دوري هيك يعطيني إجابة أيوة من سفر ل Infinity من + +106 +00:09:18,770 --> 00:09:22,950 +Zero لغاية Infinity مفتوحة أو هنا مغلقة ولا + +107 +00:09:22,950 --> 00:09:31,920 +مفتوحة؟ مغلقة تمشي اسمك انت عبدالهاد ايش؟عبدالهاد + +108 +00:09:31,920 --> 00:09:38,160 +ازميلي عبدالهاد ازميلي هذا من الرفع شجعية + +109 +00:09:38,160 --> 00:09:44,940 +من الدرج طب كويس هي عبدالهاد ازميلي من منطقة الدرج + +110 +00:09:44,940 --> 00:09:49,400 +الدرج و أعطانا إجابة صحيحة تمام؟ يعني درج في + +111 +00:09:49,400 --> 00:09:53,260 +الطريق الصحيح إلى أن وصل إلى الإجابة الصحيحة حد + +112 +00:09:53,260 --> 00:10:02,120 +عنده إجابة غير الإجابة هذه؟ فيه؟ إذا فيه قولوناطيب + +113 +00:10:02,120 --> 00:10:05,460 +نقولكوا يا عبدالله كيف استدل على هذه النتيجة + +114 +00:10:05,460 --> 00:10:10,240 +بطريقة صحيحة اذا قال بدأ احط zero بتطلع جداش ال + +115 +00:10:10,240 --> 00:10:13,680 +zero جدر ال zero في zero هاي مغلقة من عند ال zero + +116 +00:10:13,680 --> 00:10:17,800 +قال بدأ ارجع بعد ال zero قلنا له جداش جداش سالب + +117 +00:10:17,800 --> 00:10:21,940 +واحد و سالب خمسة و سالب عشرين الاخرينيبقى لما + +118 +00:10:21,940 --> 00:10:27,660 +انحطني سالب خمسة صار هذه كده؟ خمستاشر وهذه سالب + +119 +00:10:27,660 --> 00:10:30,340 +خمسة تربية خمسة وعشرين وخمستاشر اربعين جدر + +120 +00:10:30,340 --> 00:10:35,880 +الاربعين موجب يعني بعد ال zero مظبوط وقال لو رجعت + +121 +00:10:35,880 --> 00:10:40,460 +ان شاء الله لغاية سالب عشرة يبقى بصير هنا مية وهنا + +122 +00:10:40,460 --> 00:10:45,440 +كده؟ تلاتين يبقى مية و تلاتين يبقى اكبر من اللي + +123 +00:10:45,440 --> 00:10:49,560 +جابله وهكذا يبقى كلام صحيحقال لي طيب انتقل على + +124 +00:10:49,560 --> 00:10:53,900 +الفترة التانية هوب طلعت بتطلع تسعة ناقص تسعة ب + +125 +00:10:53,900 --> 00:10:59,300 +zero هايمتمام؟ بعد التلاتة بجنمين اربعة خمسة عشر + +126 +00:10:59,300 --> 00:11:04,940 +عشرة مثلا عشرة في عشرة بمية تلاتة في عشرة بتلاتين + +127 +00:11:04,940 --> 00:11:08,800 +مية ناقص تلاتين سبعين تحت الجذر قيمة بعد الصفر و + +128 +00:11:08,800 --> 00:11:12,840 +هكذا إذا قال لي على كل الأمر يعني الفترة هذه + +129 +00:11:12,840 --> 00:11:16,180 +هتجيبلي الفترة من zero ل infinity و الفترة هذه + +130 +00:11:16,180 --> 00:11:20,140 +هتجيبلي نفس الفترة كمان من zero ل وين الى infinity + +131 +00:11:20,140 --> 00:11:25,480 +نقولك كلام مصبوط والإجابة صحيحة لا غبارة عليها + +132 +00:11:25,650 --> 00:11:30,910 +ننتقل الآن إلى السؤال الثامن أو الدالة رقم تمانية + +133 +00:11:30,910 --> 00:11:39,430 +F of X يسوى absolute value ل Xتمام ال absolute + +134 +00:11:39,430 --> 00:11:43,630 +value ل X أخدته تعريفه في الثانوية بدي أحب أذكر + +135 +00:11:43,630 --> 00:11:48,290 +بتعريفه مرة تانية يبقى ال absolute value ل X بدها + +136 +00:11:48,290 --> 00:11:52,570 +تساوي X إذا كانت ال X greater than or equal to + +137 +00:11:52,570 --> 00:11:58,910 +zero وتساوي سالب X إذا كانت ال X أقل من ال zero + +138 +00:11:58,910 --> 00:12:06,320 +اللي كنتوا سميوها القيمة المطلقة ل سينالقيمة + +139 +00:12:06,320 --> 00:12:10,400 +المطلقة لسين يبقى احنا هنا بقول absolute value of + +140 +00:12:10,400 --> 00:12:14,620 +X هي اللي كنت تقول عليها القيمة المطلقة للعدد سين + +141 +00:12:14,620 --> 00:12:19,380 +طيب هذه بدها تساوي X إذا X أكبر من أو تساوي Zero + +142 +00:12:19,380 --> 00:12:24,480 +وتساوي سالب X إذا كان X أقل من Zero هذا ال + +143 +00:12:24,480 --> 00:12:29,270 +definitionأو التعريف تبع القيمة المطلقة. إيه + +144 +00:12:29,270 --> 00:12:34,430 +الخاطر؟ أسأل السؤال التالي وافكر قبل ما تعطينا + +145 +00:12:34,430 --> 00:12:38,490 +الإجابة السؤال هو هاي تعريف ال absolute value + +146 +00:12:38,490 --> 00:12:44,590 +السؤال هو هل ال absolute value ل X بتطلع قيمة + +147 +00:12:44,590 --> 00:12:50,150 +موجبة و لا ممكن موجبة و ممكن سالبة زي ما انت كاتب؟ + +148 +00:13:00,640 --> 00:13:05,880 +ممكن تكون سالب إذا كان السالب كان جديد؟أنا مش فاهم + +149 +00:13:05,880 --> 00:13:14,540 +again مرة تانية لا لا لا انا بتكلم خليك معايا انا + +150 +00:13:14,540 --> 00:13:18,680 +بتكلم داخل ال absolute مالي ولا اللي برا مالي ولا + +151 +00:13:18,680 --> 00:13:22,060 +اللي برا انا بس absolute لو كان الأمر كما اقول + +152 +00:13:22,060 --> 00:13:26,400 +سأقول لك سالب absolute بالعكس بتكلم زميلكوا عنه لو + +153 +00:13:26,400 --> 00:13:29,640 +كان فيه إشارة سالب برا ال absolute ماليش علاقة + +154 +00:13:29,640 --> 00:13:37,010 +فيها انا بتكلمهل بيطلع قيمة موجبة وقيمة سالبة؟ + +155 +00:13:37,010 --> 00:13:40,210 +والله موجبة بس والله سالبة بس فقط لا غير + +156 +00:13:49,930 --> 00:13:54,350 +ممتاز جدا يعني يا شباب لما تاخد التعريف مش تاخد + +157 +00:13:54,350 --> 00:13:58,370 +شوية منه و تسيب الباقي باخده كاملا لما قال لي + +158 +00:13:58,370 --> 00:14:03,130 +absolute بال X يستوي X اشترق ان X يا اما موجبة يا + +159 +00:14:03,130 --> 00:14:06,850 +اما صفر يبقى ماعندي مشكلة بتطلع ان انا موجبة تعني + +160 +00:14:06,850 --> 00:14:11,090 +موجبة صفر تعني صفرلكن لما قال لي هنا سالب x قال لي + +161 +00:14:11,090 --> 00:14:17,270 +إذا كانت x أقل من ال zero يعني لو كان x قيمة سالبة + +162 +00:14:17,270 --> 00:14:21,490 +يبقى الجوا بتحط نفس القيمة و قبلها انشرت مين سالب + +163 +00:14:21,490 --> 00:14:25,750 +بصير سالب سالب اللي هو الرقم اللي عندك يبقاش بصير + +164 +00:14:26,240 --> 00:14:29,860 +إذا ال absolute value مابتطلعش إلا قيمة موجبة + +165 +00:14:29,860 --> 00:14:38,080 +فمثلا absolute value لسالب تلاتة يساوي + +166 +00:14:38,080 --> 00:14:43,840 +سالب لسالب تلاتة أي السالب وال X بسالب تلاتة أي + +167 +00:14:43,840 --> 00:14:48,500 +السالب تلاتة يبقى النتيجة 11تلاتة إذا مبطلعش إلا + +168 +00:14:48,500 --> 00:14:52,900 +قيمة موجبة ما علينا أنا الآن بتدور على ال domain + +169 +00:14:52,900 --> 00:14:57,000 +تبع هذه الدالة بعد ما أعطيتها التعريف فيه في + +170 +00:14:57,000 --> 00:15:00,520 +الهامش ذكرتك ابو تذكرنا ان انت أخدته في الثانوية + +171 +00:15:00,520 --> 00:15:07,000 +العامة السؤال هو هل هناك قيمة ال X بتخلي الدالة + +172 +00:15:07,000 --> 00:15:13,700 +غير معرفة؟لا يمكن أن يبقى الـ domain كل الـ real + +173 +00:15:13,700 --> 00:15:19,100 +line بلا ستنة يبقى هذه يا اما R يا اما من سلب + +174 +00:15:19,100 --> 00:15:24,220 +infinity إلى infinity.الان بدنا نروح على ال range + +175 +00:15:27,010 --> 00:15:30,690 +نحن أعطينا الجواب من ثانية كلامنا اللي سألناه قبل + +176 +00:15:30,690 --> 00:15:34,870 +قليل.قلت لك بتطلع قيمة سالمة؟ قلت لأ.يبقى السبعة + +177 +00:15:34,870 --> 00:15:39,010 +مسالمة.شو ضال عندي؟ Zero والموجب.إذا من Zero إلى + +178 +00:15:39,010 --> 00:15:45,490 +Infinity.يبقى من Zero لغاية Infinity.بعد قليل ان + +179 +00:15:45,490 --> 00:15:49,920 +شاء الله هرسملكم إياها هذه.سأرسم لكم رسمة الدالة و + +180 +00:15:49,920 --> 00:15:54,240 +ارسم كمان الدالة هذه كمان و هكذا خلّوه للمحاضرة ان + +181 +00:15:54,240 --> 00:16:00,980 +شاء الله طيب بدنا نروح للسؤال 9 ال F of X يساوي + +182 +00:16:00,980 --> 00:16:07,380 +الجذر التربيهي ل absolute value ل Xبنعرف ال domain + +183 +00:16:07,380 --> 00:16:14,280 +تبع هذه الدالة وبعد قليل كمان نرسمها مش عاجبك طبعا + +184 +00:16:14,280 --> 00:16:19,380 +لو جيت الجذر التربية ل absolute value ل X شو + +185 +00:16:19,380 --> 00:16:24,440 +يساوي؟ يبقى طبقا لتعريف ال absolute value لفوق بدي + +186 +00:16:24,440 --> 00:16:29,780 +يكون الجذر التربية ل X إذا ال X greater than or + +187 +00:16:29,780 --> 00:16:35,710 +equal to zeroو يساوي الجذر التربية إلى سالم X إذا + +188 +00:16:35,710 --> 00:16:41,310 +الـ X أقل من الـ Zero، مظبوط ولا لا؟ طيب السؤال هو + +189 +00:16:41,310 --> 00:16:47,250 +قدش ال domain لهذه الدالة؟ من صفر لما لنهاية، يعني + +190 +00:16:47,250 --> 00:16:53,550 +النصر يا الله، اسمع يا شباب واحد واحد، بس تانا + +191 +00:16:53,550 --> 00:16:57,070 +شوية، اللي بيجاوب من ليها، اللي بنسأله بيجاوب من + +192 +00:16:57,070 --> 00:17:00,330 +ليها حتى وإن كان جاوبه خطأ، بتعود بعد ذلك الآية، + +193 +00:17:00,330 --> 00:17:06,310 +واتفضلكل ال number من سالب infinity لغاية ال + +194 +00:17:06,310 --> 00:17:12,670 +infinity بلا استثناء طيب سؤالي هو هل أنا كاتب ال + +195 +00:17:12,670 --> 00:17:16,790 +domain قدامك على اللوح هنا ولا لا؟ مكتوب ال + +196 +00:17:16,790 --> 00:17:22,010 +domain؟ في التعريف اللي أنا كاتبه مبين موجود ال + +197 +00:17:22,010 --> 00:17:28,090 +domain؟مش ال domain هي قيم X؟ ايش كتب هنا؟ X أكبر + +198 +00:17:28,090 --> 00:17:31,770 +و أساوي زينو، ايش كتب هنا؟ يعني كل ال real number + +199 +00:17:31,770 --> 00:17:34,550 +مظبوط يبقى هاي ال domain مكتوب قدامي على اللوح + +200 +00:17:34,550 --> 00:17:38,410 +يعني بدي أنجله نقل ليس الا يبقى من سالب infinity + +201 +00:17:38,410 --> 00:17:42,990 +يعني كل ال X الموجة بزايد الصفر و هنا كل ال X زي + +202 +00:17:42,990 --> 00:17:47,550 +السالب الشكتين مع بعض بيعطيني كل ال real number + +203 +00:17:47,550 --> 00:17:57,400 +بلا ستنة من سالب infinity إلى infinityفبرينج. نفس + +204 +00:17:57,400 --> 00:18:02,420 +هذه يعني اللي جابلها؟ نفس عرفيا؟ إلك خطر تغير. + +205 +00:18:03,740 --> 00:18:08,400 +يعني أو كما قال، في حد عنده إجابة غير حكاية ال + +206 +00:18:08,400 --> 00:18:12,940 +zero و infinity؟ إذا في إجابة، أعطوني إياها، حد ما + +207 +00:18:12,940 --> 00:18:13,840 +نتناقش فيها. + +208 +00:18:17,820 --> 00:18:23,440 +يبقى من zero كل ال R ولا نصها؟ كل ال R + +209 +00:18:34,930 --> 00:18:41,510 +يعني أو كما قيل طيب يالا موافقين نفس النتيجة اللي + +210 +00:18:41,510 --> 00:18:48,810 +فوق من Zero لغاية Infinity طيب السؤال العاشر بدنا + +211 +00:18:48,810 --> 00:18:57,650 +ال F of X تساوي absolute value ل X على X وشوف ليها + +212 +00:18:57,650 --> 00:19:01,370 +هي X على absolute value ل X ولا لا؟ + +213 +00:19:07,570 --> 00:19:13,410 +هل هذه هي هذه يا شباب؟ بختلفوا عن بعض يعني متأكدين + +214 +00:19:13,410 --> 00:19:17,470 +الدالة + +215 +00:19:17,470 --> 00:19:23,430 +هذه هي نفس الدالة هذه بالحرف الواحد تمام؟ الآن + +216 +00:19:23,430 --> 00:19:28,100 +بوريك كيف هذا طلعلي هنالما أنا قاعد يقول absolute + +217 +00:19:28,100 --> 00:19:33,620 +value ل X على X بدي اعطيها التعريف تبعها يبقى هذي + +218 +00:19:33,620 --> 00:19:39,720 +X على X إذا ال X أكبر من ال 0 هحط يساوي + +219 +00:19:42,310 --> 00:19:46,370 +زيروا على زيروا هذا ممنوع، مافي إمكانية يبقى حكاية + +220 +00:19:46,370 --> 00:19:55,130 +زيروا استبعدناها وهنا تساوي سالب X على X إذا الـ X + +221 +00:19:55,130 --> 00:20:02,570 +greater than 0طب هدى علي هدى بقداش و هدى علي هدى + +222 +00:20:02,570 --> 00:20:08,970 +بقداش سالف واحد إذا كان ال X greater than zero إذا + +223 +00:20:08,970 --> 00:20:15,190 +كان ال X less than zero لو أخدت التانية اللى تحت + +224 +00:20:15,190 --> 00:20:22,090 +بصير X على Xو X على سالب X يبقى هيه ولا لا؟ اذا ال + +225 +00:20:22,090 --> 00:20:26,150 +function هذه ان كتبتها بالشكل هذا او بالشكل هذا + +226 +00:20:26,150 --> 00:20:32,090 +الاتنين اعرف ده same اتنين نفس الشيء طيب سؤالنا هو + +227 +00:20:32,090 --> 00:20:35,850 +جداش ال domain وشوف اللي موجود هنا على اللوح ولا + +228 +00:20:35,850 --> 00:20:44,440 +لا؟كل ال real number ما عدا ال zero يبقى بقوله كل + +229 +00:20:44,440 --> 00:20:50,340 +ال real number ما عدا ال zero as except يا اما من + +230 +00:20:50,340 --> 00:20:56,340 +سلب infinity ل zero اتحاد zero و infinite طيب بدنا + +231 +00:20:56,340 --> 00:21:00,760 +نيجي لل range بس + +232 +00:21:00,760 --> 00:21:05,620 +اسمع شوية و بده اغششك ال range ع اللوح كمان موجودة + +233 +00:21:08,210 --> 00:21:12,970 +استنى شوية استنى شوية سمعت فيه خلافات؟ ايوه سالب + +234 +00:21:12,970 --> 00:21:19,550 +واحد واحد كفترة ولا رقمين بس؟ رقمين رقمين + +235 +00:21:19,550 --> 00:21:29,410 +يعني اه رقمين يعني رقمين بس ممتازة يبقى لا يوجد + +236 +00:21:29,410 --> 00:21:34,940 +صورة للمال نهية من الأرقام اللى عندي الا صورةلو + +237 +00:21:34,940 --> 00:21:40,660 +سالب واحد و واحد فقط لغير as a set يبقى بعملهم set + +238 +00:21:40,660 --> 00:21:45,680 +و بقول سالب واحد و واحد لما نكتب جثين بالشكل هذا + +239 +00:21:45,680 --> 00:21:51,490 +متوسطات يعني هذه مجموعة تحتوي على عنصرين فقطهو + +240 +00:21:51,490 --> 00:21:55,510 +العنصر سالب واحد و واحد هي ال range اللي طالع عندي + +241 +00:21:55,510 --> 00:22:00,910 +واحد و سالب واحد لكن ال domain هو x أكبر من ال + +242 +00:22:00,910 --> 00:22:04,970 +zero و x أقل من ال zero يعني كل ال real number ما + +243 +00:22:04,970 --> 00:22:11,250 +عدا main ما عدا ال zero تمشي + +244 +00:22:11,250 --> 00:22:15,870 +الحالة تحط الفترة المغلقة وتقولي ناقص ال zero هاي + +245 +00:22:15,870 --> 00:22:22,000 +كتبنا Rهنا ناقص ال zero هل هذا سؤالك؟ مهم انت عارف + +246 +00:22:22,000 --> 00:22:27,220 +هي كتبناه لك قبل ما تحكي طيب ابنجي الآن للرسم + +247 +00:22:27,220 --> 00:22:31,420 +البياني ل functions زي ما وعدناك و حد بدي يسأل؟ + +248 +00:22:31,420 --> 00:22:35,440 +ايوة فقط + +249 +00:22:35,440 --> 00:22:42,580 +لا غير تاني + +250 +00:22:42,580 --> 00:22:43,920 +تاني ايش بتقول؟ + +251 +00:22:46,620 --> 00:22:51,960 +أنا ماسمعتش كويسة، إذا ما كوه يعني + +252 +00:22:51,960 --> 00:22:56,080 +كفترة من سالب واحد واحد معادا zero؟ لأ لأ لأ مش + +253 +00:22:56,080 --> 00:23:01,160 +صحيح، قلت رقامين فقط لغير اللي هم سالب واحد واحد + +254 +00:23:37,230 --> 00:23:46,950 +طيب نحط عنوان جانبي graph of a function graph of a + +255 +00:23:46,950 --> 00:23:53,270 +function الرسم البياني لدله بدنا نعرف الرسم + +256 +00:23:53,270 --> 00:24:00,590 +البياني لدله definition graph of + +257 +00:24:00,590 --> 00:24:02,070 +a function + +258 +00:24:04,190 --> 00:24:16,670 +ف لذال ف with domain D is the set + +259 +00:24:19,380 --> 00:24:28,720 +of points هو مجموعة النقاط اللي على الشكل X وF of + +260 +00:24:28,720 --> 00:24:36,440 +X such that ال X موجودة في ال domain D example + +261 +00:24:36,440 --> 00:24:41,700 +find + +262 +00:24:41,700 --> 00:24:42,500 +the domain + +263 +00:24:48,980 --> 00:24:59,440 +and then a graph and then graph the following + +264 +00:24:59,440 --> 00:25:03,500 +functions + +265 +00:25:03,500 --> 00:25:08,580 +نمر + +266 +00:25:08,580 --> 00:25:19,350 +ايه ال F of X تساوي تلاتة والله سالب تلاتةنمر بي + +267 +00:25:19,350 --> 00:25:26,490 +ال F of X يساوي الجذر التربية ال absolute value ل + +268 +00:25:26,490 --> 00:25:36,130 +X نمر سي ال F of X يساوي X على absolute value ل X + +269 +00:25:36,130 --> 00:25:46,790 +نمر دي ال F of X يساوي X تربية ناقص 9 على X ناقص 3 + +270 +00:26:08,040 --> 00:26:12,200 +يبقى اللون اللي احنا كاتبينه ل graph of a function + +271 +00:26:12,200 --> 00:26:17,600 +الرسم البياني للاقتران او الرسم البياني لدالة بدنا + +272 +00:26:17,600 --> 00:26:22,060 +نعطيله تعريف و بعد هيك بنروح نطبق هذا التعريف + +273 +00:26:22,060 --> 00:26:26,540 +التعريف بيقول the graph of a function f الرسم + +274 +00:26:26,540 --> 00:26:32,000 +البياني لدالة f اللي ال domain تبعها دي هو عبارة + +275 +00:26:32,000 --> 00:26:37,630 +عن مجموعة نقطis the set of points مجموعة النقاط + +276 +00:26:37,630 --> 00:26:44,050 +اللي على الشكل التالي كله كزوج مرتب أو كإحداثيات + +277 +00:26:44,050 --> 00:26:49,330 +نقط X وF of X بحيث ال X هذه لازم تكون موجودة في ال + +278 +00:26:49,330 --> 00:26:55,610 +domain تبعد ال D النقاط هدول كلهم لما نرسمهم + +279 +00:26:55,610 --> 00:27:01,360 +بيكونوا ليش؟الشكل العام لمنحنة اتبالى كنتوا في + +280 +00:27:01,360 --> 00:27:06,540 +الثانوية وفي الاعدادية بترسم جدول وبتحط فيه قيم + +281 +00:27:06,540 --> 00:27:10,320 +سين وبعدين قيم الصادر وبتيجي على الرسم البياني + +282 +00:27:10,320 --> 00:27:14,520 +بتحط احداثيات النقط وتغسل منهم وبتطلع المنحنة + +283 +00:27:14,520 --> 00:27:18,140 +مظبوط هذا اللي احنا بنقول عليه الigraph of a + +284 +00:27:18,140 --> 00:27:23,560 +function يعني نحن هنا لم نأتي بجديد بدنا نروح نطبق + +285 +00:27:23,560 --> 00:27:28,200 +هذا الكلام على أرض الواقع فقولناهات لي ال domain و + +286 +00:27:28,200 --> 00:27:33,480 +كذلك أرسم كل من الدوال التالية يعني كل دالة من هذه + +287 +00:27:33,480 --> 00:27:37,660 +الدوال بدي أعرف قداش ال domain بالنسبة لها name + +288 +00:27:37,660 --> 00:27:41,900 +بدي أرسمها بعدين بقولك قويس بدي أمسك السؤال الأول + +289 +00:27:42,660 --> 00:27:48,200 +اللي هو ال F of X يسوى ناقص تلاتة هذا دي ايش + +290 +00:27:48,200 --> 00:27:53,900 +بنسميها شباب الدالة ثابتة يبقى ال constant + +291 +00:27:53,900 --> 00:28:02,460 +function دالة ثابتة يبقى هنا constant function + +292 +00:28:02,460 --> 00:28:09,750 +يعني دالة ثابتةماذا يعني دالة ثابتة؟يعني مهما + +293 +00:28:09,750 --> 00:28:16,330 +تغيرت X بيبقى قيمة الدالة هي القيمة الثابتة او + +294 +00:28:16,330 --> 00:28:22,670 +بمعنى اخر جميع قيم X لها صورة واحدة في شغير اليمين + +295 +00:28:22,670 --> 00:28:30,390 +سالب تلاتة يعني كأن Y تساوي سالب او صد تساوي سالب + +296 +00:28:30,390 --> 00:28:36,520 +تلاتة طيب هذه معادلة ايه؟فاط مستقيم ماله موازي + +297 +00:28:36,520 --> 00:28:43,380 +لمحور الصينات و أسفله بمقدار تلاتة يعني لو جيت + +298 +00:28:43,380 --> 00:28:50,360 +سألت قداش ال domain بتابع الدالة F بتقول X اللي + +299 +00:28:50,360 --> 00:28:56,000 +هدعو بالسلب تلاتة لقداش بتتغير X نتيجة السلب تغيري + +300 +00:28:56,000 --> 00:29:01,750 +بتغير X زي ما بدك من سلب infinity إلى infinityيبقى + +301 +00:29:01,750 --> 00:29:07,450 +هذا من سالب infinity إلى infinity بدنا نرسم الرسمة + +302 +00:29:07,450 --> 00:29:13,050 +يبقى بجي بقوله هاي المحاور هذا محور X وهذا محور Y + +303 +00:29:13,050 --> 00:29:18,490 +وهذا نقطة الأصل اللي هي Zero اللي كنت بتقوله محور + +304 +00:29:18,490 --> 00:29:25,530 +الصينات ومحور الصدر احنا هنقول محور X ومحور Yهذا + +305 +00:29:25,530 --> 00:29:30,730 +خط مستقيم يوازي السينات ويبعد عنه مسافة مقدارها + +306 +00:29:30,730 --> 00:29:36,690 +تلاتة من وحدات المسافة، يبقى لو رسمنا الخط اللي + +307 +00:29:36,690 --> 00:29:43,620 +عندنا هذا، يكون هذا الخطهذا النقطة سالب تلاتة وهذا + +308 +00:29:43,620 --> 00:29:48,520 +النقطة سالب اتنين وهذا النقطة سالب واحد وهذا + +309 +00:29:48,520 --> 00:29:54,640 +النقطة السابقة هي zero يبقى هذا f of x يسوى كم؟ + +310 +00:29:54,640 --> 00:30:00,540 +يسوى سالب تلاتة طبعا طب لو سألتك السؤال اللي قلت + +311 +00:30:00,540 --> 00:30:08,970 +لك f of x بده يسوى تلاتةيبقى مودي يطلع فوق بس + +312 +00:30:08,970 --> 00:30:16,570 +موازيه وها كده طيب نرجع نرجع مين اللي بيسأل؟عمود + +313 +00:30:16,570 --> 00:30:20,550 +على الصناعة عمود على الصناعة بدل ما اقول Y تساوي + +314 +00:30:20,550 --> 00:30:24,470 +سالب تلاتة بقولك X يساوي سالب تلاتة و X يساوي سالب + +315 +00:30:24,470 --> 00:30:30,270 +تلاتة يعني الخط هنا X يساوي تلاتة هنا X يساوي سالب + +316 +00:30:30,270 --> 00:30:36,190 +تلاتة ماشي واضح اظن طيب نجرب من السؤال اللي بعده + +317 +00:30:36,190 --> 00:30:41,680 +نمر بيه نمر بيه لخاطر ارسم absolute value ل Xجابي + +318 +00:30:41,680 --> 00:30:45,680 +للجدر التربية ال absolute value ل X يبقى انا بدي + +319 +00:30:45,680 --> 00:30:51,720 +ابدأ ب absolute value ل X اتفاجنا على انها X اذا + +320 +00:30:51,720 --> 00:30:57,520 +كانت ال X اكبر من او تساوي ال zero اتفاجنا سالب X + +321 +00:30:57,520 --> 00:31:02,520 +اذا ال X اقل من ال zero جالي هات لل domain ال + +322 +00:31:02,520 --> 00:31:06,780 +domain حسبناه قبل قليل و قولنا كل ال real line + +323 +00:31:06,780 --> 00:31:14,000 +مظبوطيبقى هنا ال domain بتابع ال F كل ال real line + +324 +00:31:14,000 --> 00:31:18,800 +من سالب infinity إلى infinity بدنا نرسمها يبقى لو + +325 +00:31:18,800 --> 00:31:23,520 +روحنا رسمناها بنقول هذه المحاولة هذا محور X هذا + +326 +00:31:23,520 --> 00:31:30,760 +محور Y هذه نقطة الأصل اللي هي ال zeroالدالة هذه لو + +327 +00:31:30,760 --> 00:31:36,140 +قلت لك Y تساوي absolute value ل X يبقى Y بدها + +328 +00:31:36,140 --> 00:31:42,740 +تساوي X أظن معروف فده خط ينصف الرابع الأول والرابع + +329 +00:31:42,740 --> 00:31:48,660 +التالت يبقى هذا الخط أخدته قبل هيك كتير و بروح + +330 +00:31:48,660 --> 00:31:53,200 +بمده على استقالة و يبقى هذا الخط اللي هو Y يساوي + +331 +00:31:53,200 --> 00:32:01,090 +منهم يساوي X بس أصبر شويةالخط التاني Y تساوي مين؟ + +332 +00:32:01,090 --> 00:32:07,550 +سالب X يبقى بدنا الصفر الرابع التاني والرابع الشكل + +333 +00:32:07,550 --> 00:32:13,230 +اللي عندنا هذا يبقى هاي Y يساوي سالب X هذا لو كان + +334 +00:32:13,230 --> 00:32:25,840 +على إطلاقلكن حط لي هنا condition يبقى + +335 +00:32:25,840 --> 00:32:32,600 +الخط هذا الله سهل عليه مش موجودقال لي Y تساوي + +336 +00:32:32,600 --> 00:32:37,620 +السلب X إذا X أقل من الـ Zero يبقى على اليمين هذا + +337 +00:32:37,620 --> 00:32:44,380 +ماله مش موجود يبقى اللي بظل عندي هو رسمة main رسمة + +338 +00:32:44,380 --> 00:32:49,220 +absolute value ل X على شكل سبعة بالعربي أو تمانية + +339 +00:32:49,220 --> 00:32:55,800 +مقلوبةيبقى هذا معرف عند نقطة الأصل لإن absolute + +340 +00:32:55,800 --> 00:33:03,080 +value للـ 0 في 0 يبقى هذه رسمة absolute أو Y أو F + +341 +00:33:03,080 --> 00:33:08,880 +of X يسوي absolute value لـ X مش هذه اللي بدنا + +342 +00:33:08,880 --> 00:33:13,430 +إياهابدنا الجذر التربيه الى absolute value ل X + +343 +00:33:13,430 --> 00:33:17,290 +بقول له اه احنا عندنا هنا الجذر التربيه الى + +344 +00:33:17,290 --> 00:33:21,750 +absolute value ل X احد امرين يا اما الجذر التربيه + +345 +00:33:21,750 --> 00:33:26,630 +الى X اذا ال X اكبر من او تساوي Zero يا اما الجذر + +346 +00:33:26,630 --> 00:33:32,790 +التربيه الى سلب X اذا X اقل من مين اقل من Zeroطب + +347 +00:33:32,790 --> 00:33:36,650 +خليني أسالكوا السؤال التالي قبل ما أرسم الرسم هذه + +348 +00:33:36,650 --> 00:33:40,970 +الدالة الأولى اللى هي absolute value ل X من خلال + +349 +00:33:40,970 --> 00:33:46,950 +الرسم قدش ال domain تبعهامن الرسم الطلع فى الرسم + +350 +00:33:46,950 --> 00:33:53,070 +هي كل X اللى على اليمين الدالة معرفة كل X اللى على + +351 +00:33:53,070 --> 00:33:56,710 +الشمال الدالة معرفة يبقى ال domain من و لا وين من + +352 +00:33:56,710 --> 00:34:01,550 +سالب infinity الى infinity فبقدرش أقل القيمة + +353 +00:34:01,550 --> 00:34:05,370 +بتاخدها ال absolute من خلال ال zero وبعد هيك تطلع + +354 +00:34:05,370 --> 00:34:10,480 +يبقى من و لا وينيبقى الكلام اللى انا بحكيه لك هذا + +355 +00:34:10,480 --> 00:34:14,740 +شوفه مكتوب عندك جابريا قبل قليل في الجدول ولا لا + +356 +00:34:14,740 --> 00:34:18,220 +طلع لل absolute value of X بتلاقي ال domain من سلب + +357 +00:34:18,220 --> 00:34:21,280 +infinity ل infinity و ال range من zero الى + +358 +00:34:21,280 --> 00:34:25,600 +infinity يبقى هى جابريا قلناه هى بيانيا طلعناه من + +359 +00:34:25,600 --> 00:34:30,200 +خلال ايه؟ من خلال الرسم بدنا نيجي لمسألتنا هذه + +360 +00:34:41,140 --> 00:34:47,080 +يبقى لو روحت رسمت بذكر بالرسمة تذكير اللي ليس الا + +361 +00:34:47,080 --> 00:34:55,770 +هذا X وهذا Y وهذا رسمة Y تساوي جذر ال Xيعني الساعة + +362 +00:34:55,770 --> 00:35:02,250 +تساوي الجذر التربيعي لـC هذا لما X مالها أكبر من + +363 +00:35:02,250 --> 00:35:08,330 +الـ0 أو تساوي طيب لما أقل من الـ0 لو كانت الـX + +364 +00:35:08,330 --> 00:35:14,420 +بسالب أو سبقت بإشارة بالسلبموجب يعني النتيجة هذه + +365 +00:35:14,420 --> 00:35:19,580 +نفس النتيجة اللي فوق الموجبة يبقى بده يظهر قوس زيه + +366 +00:35:19,580 --> 00:35:24,040 +بس من وين من الناحية التانية يبقى Y يساوي الجذر + +367 +00:35:24,040 --> 00:35:29,400 +التربية ل-X لأنه كل ما كانت X سالبة وسبقت بإشارة + +368 +00:35:29,400 --> 00:35:34,000 +سالب بصير سالب سالب موجب يبقى نفس البعد اللي هنا + +369 +00:35:34,000 --> 00:35:38,140 +هو اللي يعني صورة الواحد هي واحد صورة السالب واحد + +370 +00:35:38,140 --> 00:35:44,890 +هي واحدصورة مثلا الأربعة اتنين صورة السالب أربعة + +371 +00:35:44,890 --> 00:35:49,930 +هي اتنين و هكذا إذا من خلال الرسم قدش ال domain + +372 +00:35:49,930 --> 00:35:58,270 +تبع الدالة هذه ال domain سالب infinity لطب و ال + +373 +00:35:58,270 --> 00:36:02,790 +range من zero ل infinity طلع عندك في الجدل شوف هو + +374 +00:36:02,790 --> 00:36:06,950 +الكلام اللي بنحكيه ولا غيرهيعني الكلام اللى بنحكيه + +375 +00:36:06,950 --> 00:36:11,390 +شفه قبل قليل في الأمثلة هو بنقدر نستنتجه من خلال + +376 +00:36:11,390 --> 00:36:16,550 +الرسمة إذا كنا بنعرف الرسمة وبالتالي مافي مشكلة في + +377 +00:36:16,550 --> 00:36:21,890 +هذه الحالة يبقى هذا بالنسبة للسؤال رقم B بدنا نيجي + +378 +00:36:21,890 --> 00:36:28,260 +لل Cالـ C توا كتبناها قبل شوية وقلنا ان ال X على + +379 +00:36:28,260 --> 00:36:34,000 +absolute value ل X هي بالضبط تماما absolute value + +380 +00:36:34,000 --> 00:36:38,840 +ل X على X وقلنا أحد أمرين يا إما واحد إذا ال X + +381 +00:36:38,840 --> 00:36:43,340 +أكبر من ال zero يا إما سالب واحد إذا ال X أقل من + +382 +00:36:43,340 --> 00:36:49,880 +من ال zero وقلنا ال domain كل ال real line مع ده + +383 +00:36:54,140 --> 00:37:01,320 +بسيطة جدا هاي المحاور وهذا محور X وهذا محور Y وهذا + +384 +00:37:01,320 --> 00:37:07,620 +نقطة الأصل اللي هي Zero نجي للجزء الأول يبقى هذي + +385 +00:37:07,620 --> 00:37:14,860 +constant functionجداش بتتغير X موجب تظل قيمة + +386 +00:37:14,860 --> 00:37:18,400 +الدالة واحد، يعني عند الواحد قيمة الدالة واحد، عند + +387 +00:37:18,400 --> 00:37:21,600 +اتنين قيمة واحد، عند المية قيمة واحد، عند الألف + +388 +00:37:21,600 --> 00:37:27,600 +قيمة واحد، وها كده، إذا خط مستقيم يوازي محور + +389 +00:37:27,600 --> 00:37:33,910 +الصينات ويبعد عنه مسافة مقدارهاواحد يبقى هذا البعد + +390 +00:37:33,910 --> 00:37:41,210 +واحد وهذه مجوّفة فراغ لإن عندي ال zero الدالة غير + +391 +00:37:41,210 --> 00:37:47,440 +معرفةالجزء الثاني قيمة الدالة تساوي واحد لكل اكس + +392 +00:37:47,440 --> 00:37:52,060 +السالبة يبقى كل اكس السالبة بسالب واحد يبقى بتجيني + +393 +00:37:52,060 --> 00:37:58,000 +هنا هذا الخط المستقيم بالشكل اللاناني وهنا تجويف + +394 +00:37:58,000 --> 00:38:03,060 +دليل على ان عند هذه النقطة الدالة مالها غير معرفة + +395 +00:38:03,060 --> 00:38:08,080 +مفتوحةالـ domain زي ما انت شايفه كل الـ real الله + +396 +00:38:08,080 --> 00:38:11,220 +إنما عدى الـ zero لأنه عنده zero لأن ده لا معرفة + +397 +00:38:11,220 --> 00:38:15,680 +فوق ولا معرفة تحت كل ال real الله إنما عدى ال zero + +398 +00:38:18,140 --> 00:38:23,520 +القيمة سالب واحد فقط لغير القيمة سالب واحد هذه هنا + +399 +00:38:23,520 --> 00:38:28,240 +النقطة سالب واحد والنقطة هذه واحد يبقى واحد وسالب + +400 +00:38:28,240 --> 00:38:33,500 +واحد ال range لهذه الدلة طيب هذا بالنسبة الى C + +401 +00:38:33,500 --> 00:38:40,690 +بدنا نيجي لمن؟ للنمرى Dيبقى بالداجي لـD وهذه C دي + +402 +00:38:40,690 --> 00:38:46,630 +بيقول ال F of X يساوي X تربية ناقص 9 على X ناقص 3 + +403 +00:38:46,630 --> 00:38:53,190 +سؤالي هو هل الدالة معرفة عند التلاتة؟لأن عندي + +404 +00:38:53,190 --> 00:38:57,830 +التلاتة بصير Zero على Zero كمية غير معينة، تمام؟ + +405 +00:38:57,830 --> 00:39:03,430 +إذا لا يمكن لهذه الدالة أن تكون معرفة عند التلاتة، + +406 +00:39:03,430 --> 00:39:08,090 +لكن أنا بدي أحاول أرسمها، إذا مشان أرسمهالازم + +407 +00:39:08,090 --> 00:39:14,310 +أبسطها إذا باجي بقوله هذا كفرق بين المربعين x-3 في + +408 +00:39:14,310 --> 00:39:20,810 +x plus 3 على x minus 3 بتروح هذه مع هذه وبظل اليوم + +409 +00:39:20,810 --> 00:39:27,290 +x زائد تلاتة بس بشرط إن x ما لها ممنوعة تساوي + +410 +00:39:27,290 --> 00:39:33,050 +تلاتة لإن عندي التلاتة غير معرفة يبقى المرسمتنا + +411 +00:39:33,050 --> 00:39:41,120 +عبارة عن خط مستقيموالخط مستقيم بدي يكون خالي عند x + +412 +00:39:41,120 --> 00:39:46,080 +يساوي 3 يعني هذه النقطة فرعة على الخط المستقيم عند + +413 +00:39:46,080 --> 00:39:52,200 +x يساوي 3 بقوله بسيطة إذا إحنا لو جينا نرسم هذا + +414 +00:39:52,200 --> 00:39:56,500 +الخط المستقيم بالشكل اللي عندنا هذا وقولنا هذا + +415 +00:39:56,500 --> 00:40:02,420 +محور x هذا محور y هذه النقطة الأصل اللي هي عندنا + +416 +00:40:02,420 --> 00:40:08,800 +zeroالان عشان ارسم اي خط مستقيم في الدنيا بيكفيني + +417 +00:40:08,800 --> 00:40:13,320 +نقطتين موجودتين عليه اذا عرفت النقطتين بجيبها + +418 +00:40:13,320 --> 00:40:16,520 +المصدر و برسمها الخط بيصير هذا اللي هو الخط + +419 +00:40:16,520 --> 00:40:22,280 +المستقيم اللي عندنا فمثلا لو كانت X ب Zero ف F of + +420 +00:40:22,280 --> 00:40:26,900 +Zero بقداشي بتلاتة يعني معنى هذا الكلام ان النقطة + +421 +00:40:26,900 --> 00:40:33,850 +Zero تلاتة تقع على الخط المستقيم هذه Zero تلاتةلو + +422 +00:40:33,850 --> 00:40:39,950 +كانت f of x كلها بـ0 يبقى x بدأ تسوى جدّها إذا + +423 +00:40:39,950 --> 00:40:46,230 +سالب 3 و 0 تقع على الخط المستقيم سالب 3 و 0 بدأ + +424 +00:40:46,230 --> 00:40:47,690 +تجيلك النقطة هذه + +425 +00:40:50,790 --> 00:40:56,430 +أذا احنا صار ان هذا الخط المستقيم بقدر ارسمه بدون + +426 +00:40:56,430 --> 00:41:02,250 +مشاكل يبقى بوصل بين النقطتين و بمد الخط على + +427 +00:41:02,250 --> 00:41:07,070 +استقامته من الناحيتين بصير هذا هو الخط المستقيم + +428 +00:41:07,070 --> 00:41:12,170 +لأن y تساوي x زي التلتة او f of x يساوي x زي + +429 +00:41:12,170 --> 00:41:17,330 +التلتة بس استنى شويةلما تيجي عند الواحد و عند + +430 +00:41:17,330 --> 00:41:22,290 +اتنين و عند التلاتة و نيجي طالعين مشان قبل الخط + +431 +00:41:22,290 --> 00:41:28,830 +المستقيم بيصير الخط المستقيم في تجويف هنا وبالتالي + +432 +00:41:28,830 --> 00:41:36,070 +عند x يساوي تلاتة ال function is undefined يبقى + +433 +00:41:36,070 --> 00:41:41,390 +عند x يساوي تلاتة يوهر تجويف او ثقب في الخط + +434 +00:41:41,390 --> 00:41:46,870 +المستقيم بمعنى اخرالنقطة تلاتة وستة لا تقع على + +435 +00:41:46,870 --> 00:41:51,790 +الخط المستقيم، لو حطيت تلاتة زائد تلاتة بيصير ستة، + +436 +00:41:51,790 --> 00:41:56,290 +يبقى تلاتة وستة هذه مش موجودة على الخط المستقيم، + +437 +00:41:56,290 --> 00:42:03,630 +يبقى فراغ، تمام؟ طيب، لخاطر أسأل سؤال تاني، لو + +438 +00:42:03,630 --> 00:42:08,450 +احنا رمض وقلت لك خد لك هالرسمة، وشوف ليها دي رسمة + +439 +00:42:08,450 --> 00:42:14,220 +function والله مش function، كي بدي أعرف؟رسمت لك + +440 +00:42:14,220 --> 00:42:17,500 +رسمة على اللوحة و قلت لك اتفضل هي رسمة و شوف لي هي + +441 +00:42:17,500 --> 00:42:21,020 +الرسمة هذه رسمة function و الله ماهياش function + +442 +00:42:21,020 --> 00:42:27,240 +القضية بسيطة ولا بتحققها القضية من أبسط و أدفه ما + +443 +00:42:27,240 --> 00:42:31,870 +يكون كيف؟المحاضرة اللى فاتت بتتذكروا لما جينا + +444 +00:42:31,870 --> 00:42:37,650 +عرفنا تعريف ال function و جينا قولنا لا يمكن + +445 +00:42:37,650 --> 00:42:42,130 +للعنصر الواحد ان تكون له صورتين او اكتر مظبوط صورة + +446 +00:42:42,130 --> 00:42:45,990 +واحدة علي انوراس بس اكتر بتبطل يصير function اذا + +447 +00:42:45,990 --> 00:42:51,970 +انا لو اعطيتك رسمةهل هذه رسمة دالة ولا لا؟ بقوله + +448 +00:42:51,970 --> 00:42:56,410 +بسيطة بدي اخد اي نقطة في دمنا واشوف عند النقطة هذه + +449 +00:42:56,410 --> 00:43:00,590 +بلاقي صورتين ولا لا إذا لاجئت صورتين ماتبطل أصير + +450 +00:43:00,590 --> 00:43:07,390 +function مظبوط؟ أي vertical line أي قط رأسي ممنوع + +451 +00:43:07,390 --> 00:43:12,500 +يقطع المنحنة إلا فيلو قطع في نقطتين بيصير بطل يصير + +452 +00:43:12,500 --> 00:43:17,720 +function لإن X بيصير لها صورتين على الراسم مظبوط + +453 +00:43:17,720 --> 00:43:22,700 +الكلام اللي أنا بقوله اسمه ال vertical line test + +454 +00:43:22,700 --> 00:43:29,640 +for a function اختبار الخط الرأسي لمين لدالةإذا لو + +455 +00:43:29,640 --> 00:43:33,860 +أعطاني رسمة وقاللي شوف لي هذه تمثل دالة ولا لا + +456 +00:43:33,860 --> 00:43:39,440 +تمثل دالة بدون معرف شكلة بجيبها لمصر بحاول أرسم أي + +457 +00:43:39,440 --> 00:43:43,860 +خط رأسي إذا الخط الرأسي قطع المنحنة في نقطتها ليست + +458 +00:43:43,860 --> 00:43:47,880 +function لكن إذا كل الخطوط الرأسية ماقدرش تقطعوا + +459 +00:43:47,880 --> 00:43:52,360 +إلا في نقطة واحدة يبقى هذا إيش vertical line يبقى + +460 +00:43:52,360 --> 00:43:57,200 +هذه تمثل معنى دالةالكلام اللى سمعته بدنا نروح + +461 +00:43:57,200 --> 00:44:19,680 +نكتبه الآن ونشوف كيف انطبقه على أرض الواقع عنوان + +462 +00:44:19,680 --> 00:44:20,420 +جانبي + +463 +00:44:24,040 --> 00:44:37,600 +vertical line test test for a function if + +464 +00:44:37,600 --> 00:44:50,860 +ال if is a function then no vertical + +465 +00:45:00,260 --> 00:45:13,040 +ممكن ان يقطع الرسم + +466 +00:45:13,040 --> 00:45:18,760 +البياني للدالة if more than + +467 +00:45:19,670 --> 00:45:31,150 +once أكثر من مرة واحدة that is if ال + +468 +00:45:31,150 --> 00:45:46,090 +a موجودة في دمين الدلة if then the vertical line + +469 +00:45:46,090 --> 00:45:57,230 +الخط الرأسيx بدى يساوي a will intersect + +470 +00:45:57,230 --> 00:46:00,410 +the + +471 +00:46:00,410 --> 00:46:07,030 +graph of + +472 +00:46:07,030 --> 00:46:16,810 +f at the single point + +473 +00:46:19,920 --> 00:46:23,800 +و F of A + +474 +00:46:39,750 --> 00:46:44,690 +يبقى هذا الاختبار اسمه اختبار الخط الرأسي لدالة + +475 +00:46:44,690 --> 00:46:52,570 +vertical line خط رأسي فيه كلمة perpendicular عمودي + +476 +00:46:52,570 --> 00:46:55,710 +يعني خطين لما يكونوا عمودين على بعض بقول + +477 +00:46:55,710 --> 00:47:00,310 +perpendicular line لكن لما أقول vertical line يبقى + +478 +00:47:00,310 --> 00:47:03,870 +هذا بسميه خط رأسي بغض النظر هل هو عمودي على غيره + +479 +00:47:03,870 --> 00:47:08,740 +ولا مش عموديعلى غيره يبقى باجي بقول لو كانت ال F + +480 +00:47:08,740 --> 00:47:12,720 +function يبقى لو كانت الدالة الرسمة اللي عندي هي + +481 +00:47:12,720 --> 00:47:18,800 +رسمة function إذا لا يمكن أقدر ألاقي خط مستقيم + +482 +00:47:18,800 --> 00:47:24,180 +رأسي يقطع منحنى الدالة في أكثر من نقطة لكن لو + +483 +00:47:24,180 --> 00:47:28,300 +ماكنتش function ممكن في اتنين أو في تلاتة أو في + +484 +00:47:28,300 --> 00:47:32,770 +أربعة زي ما بدكمرة تانية لو كنت لف function then + +485 +00:47:32,770 --> 00:47:38,230 +no vertical line لا يمكن تقدر تلاقي خط رأسي ممكن + +486 +00:47:38,230 --> 00:47:44,390 +يقطع المنحنة في أكثر من مرة more than once يعني + +487 +00:47:44,390 --> 00:47:48,790 +أكثر من مرة واحدة مش هتلاقي ولا خط إذا لو المنحنة + +488 +00:47:48,790 --> 00:47:53,870 +منحنة ده لأ الخط الرأسي لايمكن أن يقطع المنحنة إلا + +489 +00:47:54,400 --> 00:47:59,420 +في نقطة واحدة فقط الآن الكلام اللي قلته هيك بدروح + +490 +00:47:59,420 --> 00:48:06,160 +أصيغه بمفهوم آخر فقولت that is أي أنه لو كان ال a + +491 +00:48:06,160 --> 00:48:10,280 +موجود في domain ال F لو كانت النقطة a موجودة في + +492 +00:48:10,280 --> 00:48:17,830 +domain ال Fوالخط الرئيسي X يساوي الـA وينترسج في + +493 +00:48:17,830 --> 00:48:21,430 +نقطة + +494 +00:48:21,430 --> 00:48:28,550 +واحدة A و F of A كيف هذا الكلام؟ بجي بقول لو كان + +495 +00:48:28,550 --> 00:48:33,670 +عندنا محاور مثلا بالشكل هذا وقلنا هذا محور X وهذا + +496 +00:48:33,670 --> 00:48:38,680 +محور Y ورسمنا منحنة وكان المنحنة بالشكل هذافكان + +497 +00:48:38,680 --> 00:48:46,400 +هذا منحنا Y تساوي F of X يعني الصواد تساوي دالة C + +498 +00:48:46,400 --> 00:48:52,020 +روحنا أخدنا أي نقطة في domain الدالة هذه ولتكن + +499 +00:48:52,020 --> 00:48:58,060 +النقطة هذه مالها Aيبقى هذه X يساوي A وهذه Zero + +500 +00:48:58,060 --> 00:49:05,920 +جينا رسمنا خط رأسي يمر بالنقطة A يبقى الخط الرأسي + +501 +00:49:05,920 --> 00:49:10,980 +بالشكل اللي عندنا هذا يبقى الخط الرأسي هذا معادلة + +502 +00:49:10,980 --> 00:49:16,720 +X يساوي A زي مثال بعض الشباب قبل قليل قال لو كان + +503 +00:49:16,720 --> 00:49:21,740 +عمودي على مهور الصينيةيعني الخط المستقيم الموازي + +504 +00:49:21,740 --> 00:49:26,340 +لمحور الصينات Y تساوي رقم، موجب، سالب، صفر، + +505 +00:49:26,340 --> 00:49:30,800 +ماتفرجش عنها، لكن لو كان عمودي على محور الصينات ف + +506 +00:49:30,800 --> 00:49:36,220 +X يساوي رقم، يعني X يساوي A أو سالب A عندها أو X + +507 +00:49:36,220 --> 00:49:41,260 +يساوي Zero أظن X يساوي Zero هو محور الصداد، محور + +508 +00:49:41,260 --> 00:49:46,120 +Y، X يساوي تلاتة على اليمن بتلاتةX يسوي تسالب + +509 +00:49:46,120 --> 00:49:50,440 +تلاتة يبقى على الشمال بمقدار تلاتة يبقى هنا بقول + +510 +00:49:50,440 --> 00:49:56,600 +لو كان ال A element موجود في دمين الدالة F يبقى اي + +511 +00:49:56,600 --> 00:50:05,040 +خط رأسي يمر بالنقطة هذه اللي احداثيها A وF of A + +512 +00:50:05,040 --> 00:50:10,940 +اللي همينالخط X يساوي A لا يمكن ان يقطع المنحنى + +513 +00:50:10,940 --> 00:50:19,200 +الا في نقطة واحدة اللي هي A ايا و F of A تمام يبقى + +514 +00:50:19,200 --> 00:50:24,560 +هاللي بقوله الان انا بروح استخدم الاختبار هذا في + +515 +00:50:24,560 --> 00:50:29,500 +معرفة بعض الرسومات هل تمثل functions ولا لا تمثل + +516 +00:50:29,500 --> 00:50:34,780 +functions اذا بدنا نروح ناخد المثال التالي يبقى + +517 +00:50:34,780 --> 00:50:35,360 +example + +518 +00:50:55,160 --> 00:51:09,900 +describe the graph of the following equations + +519 +00:51:21,840 --> 00:51:41,100 +undetermined whether the graph is + +520 +00:51:41,100 --> 00:51:41,500 +that + +521 +00:51:44,780 --> 00:51:53,880 +of a function or not + +522 +00:51:53,880 --> 00:52:00,200 +نمرة + +523 +00:52:00,200 --> 00:52:10,430 +a f of x يساوي x زائد absolute value ل x نمرة bX + +524 +00:52:10,430 --> 00:52:16,910 +تربيع زائد Y تربيع يساوي تسعة و X أكبر من أو تساوي + +525 +00:52:16,910 --> 00:52:23,870 +زيرو نمرة C X تربيع زائد Y تربيع يساوي تسعة و Y + +526 +00:52:23,870 --> 00:52:32,270 +greater than or equal to zero نمرة Dنمر دي X تربيع + +527 +00:52:32,270 --> 00:52:38,890 +يساوي Y تربيع نمر A absolute value ل X زادة + +528 +00:52:38,890 --> 00:52:43,150 +absolute value ل Y يساوي مين؟ يساوي واحد + +529 +00:52:52,350 --> 00:52:57,290 +نرجع لسؤالنا مرة تانية بيقول describe the graph of + +530 +00:52:57,290 --> 00:53:01,830 +the following equations ايه وصفلي الرسم البياني + +531 +00:53:01,830 --> 00:53:06,930 +لكل من المعادلات التالية هذه يا شباب اختصار لكلمة + +532 +00:53:06,930 --> 00:53:11,170 +EQUATIONS + +533 +00:53:11,170 --> 00:53:14,630 +equations يعني معادلات + +534 +00:53:16,450 --> 00:53:21,730 +أنا باختصرها إلى EQUN و S تبعت الإضافة أو تبعت + +535 +00:53:21,730 --> 00:53:27,090 +الجامعة يبقى هنا أوصف لي كل من المعادلات التالية و + +536 +00:53:27,090 --> 00:53:31,810 +أتعمد تقول معادلات لأن المعادلة قد تكون function و + +537 +00:53:31,810 --> 00:53:35,730 +قد لا تكون function أما لو قلت لك function يبقى + +538 +00:53:35,730 --> 00:53:39,850 +خلاص مضمونة لكن معادلة ممكن تبقى function و ممكن + +539 +00:53:39,850 --> 00:53:44,730 +ما تكونش function أندي تامة و حددلي هل الرسم + +540 +00:53:44,730 --> 00:53:52,270 +البيانييمثل دالة أو لا يمثل دالة Undetermined حدد + +541 +00:53:52,270 --> 00:53:56,830 +ليه whether the graph L الرسم البياني يمثل + +542 +00:53:56,830 --> 00:54:03,450 +function or not بنقوله بسيطة يبقى بدنا نيجي للدالة + +543 +00:54:03,450 --> 00:54:07,890 +الأولى ال F of X يساوي X زائد absolute value ل X + +544 +00:54:07,890 --> 00:54:13,610 +يبقى نمرأة A الدالة F of X يساوي X زائد absolute + +545 +00:54:13,610 --> 00:54:20,670 +value ل Xهذه سوف أعرفها لكي أرسمها يبقى هذه أحد + +546 +00:54:20,670 --> 00:54:24,490 +أمرين يا شباب بدي أستخدم تعريف ال absolute value + +547 +00:54:24,490 --> 00:54:31,170 +يبقى x زائد x إذا ال x أكبر من أو تساوي zero و x + +548 +00:54:31,170 --> 00:54:37,490 +ناقص x إذا ال x أقل من ال zero صحيح ولا لا؟ مظبوط؟ + +549 +00:54:37,930 --> 00:54:45,830 +طيب هده هي عبارة عن مين؟ اتنين X إذا ال X أكبر من + +550 +00:54:45,830 --> 00:54:53,390 +أو تساوي Zero و Zero إذا ال X أقل من Zeroواضح ان + +551 +00:54:53,390 --> 00:54:59,530 +ال domain جداش كل ال real line وطوحنا في الجزء + +552 +00:54:59,530 --> 00:55:03,590 +النظري قبل قليل قولنا كل ال real line وقولنا ال + +553 +00:55:03,590 --> 00:55:07,870 +range إيه اللي من وين لوين من صفر لغاية ملانا + +554 +00:55:07,870 --> 00:55:10,870 +الكلام اللي قولناه بنروح نبينه الآن على الرسم + +555 +00:55:10,870 --> 00:55:16,070 +كلامنا صحيح ولا لأ إذا بيدروح أرسم المحاور يبقى + +556 +00:55:16,070 --> 00:55:22,030 +هذه المحاور اللي عندنا هذا محور X هذا Y هذا Zero + +557 +00:55:23,620 --> 00:55:30,960 +يبقى احنا عندنا f of x يساوي zero اذا x اقل من ال + +558 +00:55:30,960 --> 00:55:35,780 +zero يبقى لكل ال x اللي اقل من ال zero قيمة الدلج + +559 +00:55:35,780 --> 00:55:42,440 +اداش تساوي صفر يبقى هنا هذا بيكون كل المنطقة اللي + +560 +00:55:42,440 --> 00:55:47,860 +عندنا هنا لغاية ما نصل إلى سالب ال infinity بما + +561 +00:55:47,860 --> 00:55:52,490 +فيها ال zeroطب ال zero جيبته من وين؟ جيبته من اللي + +562 +00:55:52,490 --> 00:55:57,370 +قبلها لو كانت x يساوي zero بصير اثنين في zero ب + +563 +00:55:57,370 --> 00:56:03,130 +zero طيب لما أقول لك صد تساوي اتنين سين ده لأ خطية + +564 +00:56:03,130 --> 00:56:07,550 +ولا لأ؟ خطية لإنها من أي درجة؟ من الدرجة الأولى + +565 +00:56:07,550 --> 00:56:11,170 +يبقى لما أقول لك y تساوي اتنين x معدلة من الدرجة + +566 +00:56:11,170 --> 00:56:15,830 +الأولى يعني معدلة خط مستقيم إذا يكفيني من الخط + +567 +00:56:15,830 --> 00:56:22,670 +المستقيم نقطتين تقعان عليهيبقى هذه إحداهما، بدى + +568 +00:56:22,670 --> 00:56:27,390 +أجيب النقطة التانية، لو كانت X بواحد، يبقى هاي + +569 +00:56:27,390 --> 00:56:32,130 +واحد وهي اتنين، يبقى بدى تجينا النقطة وين اللي + +570 +00:56:32,130 --> 00:56:36,570 +عندنا هذا، يبقى بدى أمسك الخط المستقيم بالمصطر أو + +571 +00:56:36,570 --> 00:56:41,360 +القلم و أوصل الخط المستقيم اللي عندنا هذايبقى هذا + +572 +00:56:41,360 --> 00:56:46,760 +الخط y تساوي main اتنين x الخطين الاتنين مع بعض + +573 +00:56:46,760 --> 00:56:51,640 +يمثلون main الدالة لأن f of x زائد absolute value + +574 +00:56:51,640 --> 00:56:55,920 +of x يبقى قال لي اوصف للرسم البياني للمعادلة اللي + +575 +00:56:55,920 --> 00:57:00,380 +اواصفته قال لي بعدين شوف لي هذا يمثل دالة ولا لا + +576 +00:57:00,380 --> 00:57:06,380 +بقول له اه ارسم vertical line وين ما يعجبكشوفوا هل + +577 +00:57:06,380 --> 00:57:13,360 +يقطع المنحنة في نقطة ولا اكتر نقطة فقط لا غير اي + +578 +00:57:13,360 --> 00:57:19,920 +خط مستقيم برسم نقطة واحدة يبقى هذه تمثل function + +579 +00:57:19,920 --> 00:57:25,640 +على طول الخط تمام؟ اظن لو جيت اقارن بين ال domain + +580 +00:57:25,640 --> 00:57:29,120 +وال range اللي في الجدول بلاقي ال domain كله ال + +581 +00:57:29,120 --> 00:57:33,620 +real line وال range من zero لوين ل infinity يتفق + +582 +00:57:33,620 --> 00:57:41,310 +تماما كيف؟الرسمة طلعلي هذا يعني ايش بتقول قيمة + +583 +00:57:41,310 --> 00:57:46,170 +الدالة تساوي صفر إذا كانت X سالبة X سالبة يعني كل + +584 +00:57:46,170 --> 00:57:49,990 +المنطقة هذه قداش قيمة الدالة Zero يعني انا بضل على + +585 +00:57:49,990 --> 00:57:53,710 +ما هو رسالة لها بطلع ولا بنزل وحطينا هذه اللي هي + +586 +00:57:53,710 --> 00:57:59,070 +القيمة الثابتة تساوي Zeroلما جينا لان f of x ساوي + +587 +00:57:59,070 --> 00:58:04,710 +2x كلها دي معادلة خطية يعني معادلة خط مستقيم الخط + +588 +00:58:04,710 --> 00:58:08,190 +المستقيم اللي ارسمه بده نقطة تانية عليه طبعا عندي + +589 +00:58:08,190 --> 00:58:10,590 +ال zero ب zero اتنين في zero ب zero يبقى نقطة + +590 +00:58:10,590 --> 00:58:14,610 +الاصل واحدة جاهزة و خالصة بظل مين بدناها نقطة + +591 +00:58:14,610 --> 00:58:18,010 +اتنين انا اخدت واحد انت خد اتنين خد عشرة زي ما بدك + +592 +00:58:18,010 --> 00:58:21,890 +و ضرب في اتنينحطها فوق وامشي كمصدر أواصل بيانه + +593 +00:58:21,890 --> 00:58:26,110 +يبقى رسمنا الجزء الثاني يبقى الخطين الاتنين مع بعض + +594 +00:58:26,110 --> 00:58:31,530 +يمثلوين الرسم البياني اللي ادى ل F of X سوى X زائد + +595 +00:58:31,530 --> 00:58:36,170 +absolute value ل Xيبقى ال domain صار كل ال real + +596 +00:58:36,170 --> 00:58:40,010 +line و ال range من zero ل infinity و رسمنا هذه + +597 +00:58:40,010 --> 00:58:45,190 +تعتبر function لأن لو رسم اي vertical line رأسي لا + +598 +00:58:45,190 --> 00:58:52,010 +يقطع المنحنة الا في نقطة واحدة تمام تمام نمر بي + +599 +00:58:52,010 --> 00:59:00,070 +نمر بي بيقول ايش بيقول x تربيةزائد Y تربية تساوي + +600 +00:59:00,070 --> 00:59:04,650 +تسعة والاكس greater than or equal to zero السؤال + +601 +00:59:04,650 --> 00:59:10,670 +هو هذه معادلة ايش يا شباب دائرة مدرجات تانية + +602 +00:59:10,670 --> 00:59:13,190 +معادلة دائرة مركزها + +603 +00:59:14,730 --> 00:59:20,690 +نقطة الاصل 00 نصف قطرة ثلاثة ممتاز جدا يبقى هذا + +604 +00:59:20,690 --> 00:59:24,730 +انت مذاكرين كويس على كل الحالة ريحت هنا شوية يبقى + +605 +00:59:24,730 --> 00:59:31,150 +لو جيت للدائرة هذه و روحت قلت هذا محور X وهذا محور + +606 +00:59:31,150 --> 00:59:36,250 +Y وهذا نقطة الأصل وحبيت أرسم الدائرة بدي أرسمها + +607 +00:59:36,250 --> 00:59:41,150 +منقطة في الأوللأنه مش عارف هذه هي دائرة كاملة ولا + +608 +00:59:41,150 --> 00:59:45,410 +نص دائرة ولا ربع دائرة ولا سُدس دائرة، الله أعلم + +609 +00:59:45,410 --> 00:59:50,330 +يبقى لو جيت لدائرة هذه مركزها نقطة الأصل ونص قطرها + +610 +00:59:50,330 --> 00:59:58,300 +يساوي تلاتة بالشكل اللي عنهاتمام؟ اه في condition + +611 +00:59:58,300 --> 01:00:03,660 +حاطط ليه قال لي ممنوع ال X تاخد قيمة سلبة دايما و + +612 +01:00:03,660 --> 01:00:10,080 +ابدا X يا اما ب zero يا اما بقيمة موجبة من وين هي + +613 +01:00:10,080 --> 01:00:15,100 +المنطقة تمام؟ اذا الدار الجزء هذا يبقى الجزء اللي + +614 +01:00:15,100 --> 01:00:18,810 +على الشماليبقى عقلك الله مافيش عندي دائرة على + +615 +01:00:18,810 --> 01:00:23,030 +الجزر الشمال، يبقى هذا الله يساهل عليه مع السلام + +616 +01:00:23,030 --> 01:00:28,830 +غير مأسوف عليه يبقى ماضلش عندي إلا مين؟ إلا نصف + +617 +01:00:28,830 --> 01:00:32,550 +الدائرة اللي على اليمين، الشكل اللي عندنا هذا + +618 +01:00:32,550 --> 01:00:37,190 +تمام؟ بما فيها النقطة اللي عندنا هذه والنقطة اللي + +619 +01:00:37,190 --> 01:00:42,640 +عندنا هذه خليني أسألك سؤالالنقطة الـ Zero هذه اللي + +620 +01:00:42,640 --> 01:00:48,880 +قال لي X أكبر من أو تساوي Zero، كام صورة لها تنتقل + +621 +01:00:48,880 --> 01:00:53,600 +لفوق و لتحت؟ يبقى هذه ليست function، صح؟ + +622 +01:01:01,210 --> 01:01:07,290 +على اليمين يبقى اي نقطة من Zero لغاية تلاتة نصف + +623 +01:01:07,290 --> 01:01:12,910 +القطر اللي هو تلاتة وهنا تلاتة وهنا تلاتة بالسالب + +624 +01:01:12,910 --> 01:01:18,010 +تلاتة هذه السالب تلاتة و Zero وهذه تلاتة و Zero + +625 +01:01:18,010 --> 01:01:29,120 +وهذه تلاتة و Zero0 و 3 و 3 و 0 اتحرك اي خط على + +626 +01:01:29,120 --> 01:01:34,340 +اليمين هتلاقي يقطع المنحنى معله في نقطتين يبقى هذه + +627 +01:01:34,340 --> 01:01:40,400 +function يبقى هذه not a function يبقى هذه ليست + +628 +01:01:40,400 --> 01:01:49,250 +دالة not a functionيبقى هذه المعادلة لا تمثل دالة + +629 +01:01:49,250 --> 01:01:54,450 +بأي حال من الأحوال ليش؟ لأن ال vertical line test + +630 +01:01:54,450 --> 01:01:59,730 +بيقول لو عملت خط راسي بدوش يقطعها إلا وين فى نقطة + +631 +01:01:59,730 --> 01:02:05,810 +واحدة طيب نمرى C نفس المعادلة X تربية زد Y تربية + +632 +01:02:05,810 --> 01:02:11,980 +يسوى 9 وY greater than or equal to 0بنقول له تعالى + +633 +01:02:11,980 --> 01:02:18,700 +نشوف هذه المحاور وهذا محور X وهذا محور Y وهذا نقطة + +634 +01:02:18,700 --> 01:02:22,740 +الاصل اللي هي Zero وبدنا نروح الدائرة اللي قلنا + +635 +01:02:22,740 --> 01:02:27,940 +عليها هيها ما اتغيرتش بالشكل اللي عندنا هنا، تمام؟ + +636 +01:02:27,940 --> 01:02:31,720 +بس بدي أعرف هل هي دائرة كاملة و الله شوية منها راح + +637 +01:02:31,720 --> 01:02:35,500 +قلشيبقى Y أكبر من Y أقل من Y أقل من Y أقل من Y أقل + +638 +01:02:35,500 --> 01:02:37,060 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +639 +01:02:37,060 --> 01:02:40,800 +أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل + +640 +01:02:40,800 --> 01:02:43,000 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +641 +01:02:43,000 --> 01:02:44,260 +أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل + +642 +01:02:44,260 --> 01:02:44,260 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +643 +01:02:44,260 --> 01:02:44,260 +أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل + +644 +01:02:44,260 --> 01:02:47,960 +من Y أقل من Y أقل من Y أقل من Y أقل من Y أقل من Y + +645 +01:02:47,960 --> 01:02:53,070 +أقل منماعنديش الا النصف العلوي وبالتالي بصير عندك + +646 +01:02:53,070 --> 01:02:57,530 +النصف العلوي بهذا الشكل نصف القطر يساوي تلاتة يبقى + +647 +01:02:57,530 --> 01:03:02,930 +هذه تلاتة و Zero هذه سالب تلاتة و Zero هذه Zero و + +648 +01:03:02,930 --> 01:03:07,580 +تلاتة يبقى نصف الدائرة العلوي السؤال هوهل هذه + +649 +01:03:07,580 --> 01:03:13,560 +الرسمة تمثل function؟ اه لأن ارسم اي خط رأسي وين + +650 +01:03:13,560 --> 01:03:20,560 +ما بدك بتلاقيه بيقطعها بس وين في نقطة واحدة فقط لا + +651 +01:03:20,560 --> 01:03:27,500 +غير اذا هذه تمثل function تمام؟ بدنا نيجي للسؤال + +652 +01:03:27,500 --> 01:03:32,200 +التالت اللي هو دي + +653 +01:03:33,770 --> 01:03:39,990 +بدي اجي ل دى، قال لي X تربية بدها تساوي Y تربية، + +654 +01:03:39,990 --> 01:03:45,670 +اه معادلة إيه الشهادة؟ يقول الله وعلا، مش عارفين، + +655 +01:03:45,670 --> 01:03:50,410 +لكن ارتبها شوية، يقولوا ارتبها كيف؟ خد الجذر + +656 +01:03:50,410 --> 01:03:55,010 +التربية يا اخي للطرفين، يبقى انا لو جيت اخدت الجذر + +657 +01:03:55,010 --> 01:03:59,550 +التربية للطرفين، الجذر التربية يلا Y تربية بمين؟ + +658 +01:03:59,960 --> 01:04:04,940 +absolute value ل Y الجدر التربيع ل X ب absolute + +659 +01:04:04,940 --> 01:04:12,960 +value ل X طيب شو رأيك؟ بدي أستبدل هذه المعادلة + +660 +01:04:12,960 --> 01:04:19,340 +بمعادلة أخرى وشوف كلامي صح ولا غلط هذه بدي + +661 +01:04:19,340 --> 01:04:25,800 +أستبدلها فقط بالمعادلة Y تساوي زاد او ناقص X بنفع + +662 +01:04:25,800 --> 01:04:26,360 +هيك؟ + +663 +01:04:31,130 --> 01:04:35,290 +طيب انا شايف فيها غبش في وجوه البعض فيكوا شايف + +664 +01:04:35,290 --> 01:04:40,030 +فيها غبش يعني مش واضحة الصورة في ذهنه تمام يبقى + +665 +01:04:40,030 --> 01:04:44,690 +انا بدي امشي بعقلية اللي عندهم الغبش هذا و نشوف + +666 +01:04:44,690 --> 01:04:48,870 +النزيلة الغبش هذا و الله يبقى هذه المعادلة لو روحت + +667 +01:04:48,870 --> 01:04:53,090 +شيلت لبس الويت باني بدي اقول زاد او ناقص y سوى زاد + +668 +01:04:53,090 --> 01:04:57,870 +او ناقص x اظن لو كتبت هيك ماحدش بيزعل طب هذه كام + +669 +01:04:57,870 --> 01:05:06,200 +معادلة؟أربعة y تساوي x هي y تساوي x بالزايد y + +670 +01:05:06,200 --> 01:05:13,560 +تساوي نقص x هي y تساوي نقص x بضل عندنا y بالموجب + +671 +01:05:13,560 --> 01:05:20,520 +يساوي x و نقص x خلصنا منها بدي اخد من ناقص y ناقص + +672 +01:05:20,520 --> 01:05:26,880 +y تساوي x اضرب في السلب يعني y تساوي ناقص x يبقى + +673 +01:05:26,880 --> 01:05:31,630 +نفس المعادلة ولا لا؟تمام طيب بدأ اخد التانية ناقص + +674 +01:05:31,630 --> 01:05:37,330 +Y تساوي ناقص X لو ضرب ناقص يعني Y تساوي X مظبوط + +675 +01:05:37,330 --> 01:05:42,730 +يبقى هذه الأربع معادلات هذي كالكزيدة والحقيقة هي + +676 +01:05:42,730 --> 01:05:48,990 +معادلتين وليست أربع معادلات مظبوط هيك؟ يبقى أزلنا + +677 +01:05:48,990 --> 01:05:54,450 +اللبس أو الغراش يبقى هدول معادلتين فقط لغية طب + +678 +01:05:54,450 --> 01:06:01,990 +السؤال هولما اقول Y تساوي X معدلتاش فاطم مستقيم و + +679 +01:06:01,990 --> 01:06:12,500 +لما اقول Y تساوي سالب Xخط مستقيم يبقى + +680 +01:06:12,500 --> 01:06:17,500 +خط مستقيم على طول الخط لو جيت ارسم الخط اللي اتنين + +681 +01:06:17,500 --> 01:06:24,700 +هدول يبقى هذا محور X وهذا محور Y الخط الأول Y + +682 +01:06:24,700 --> 01:06:30,980 +تساوي X بنصف الرمال الأول والربعةالتالت يعني هذا + +683 +01:06:30,980 --> 01:06:39,500 +الخط Y تساوي X خط الغامق هذا ايوه تمام يبقى هذا + +684 +01:06:39,500 --> 01:06:48,480 +الخط Y تساوي X كويس + +685 +01:06:50,210 --> 01:06:54,490 +طبعا الزاوية هذه جد الزاوية هذه بالضبط تماما كل + +686 +01:06:54,490 --> 01:07:00,410 +واحدة فيهم خمسة واربعين يبقى هذا Y تساوي زاد X + +687 +01:07:00,410 --> 01:07:05,850 +يعني Y تساوي X الان Y تساوي ناقص X بنص في الرابع + +688 +01:07:05,850 --> 01:07:11,370 +التاني و الرابع الرابع يبقى بدريجي هنا بهذا الشكل + +689 +01:07:12,060 --> 01:07:19,520 +يبقى هذا Y تساوي سالب X تمام تمام ماعندوش قيود + +690 +01:07:19,520 --> 01:07:24,240 +يبقى كل واحد ضد والد مستمر ليه Infinity السؤال هو + +691 +01:07:24,240 --> 01:07:29,940 +هل الرسم البياني هذا يمثل function؟ ايوة not + +692 +01:07:29,940 --> 01:07:37,030 +function ليش؟ لأن اي خط رأسي بده يقطع وين؟نقطتين + +693 +01:07:37,030 --> 01:07:41,390 +اي خط رأسي بدي اقطعه في نقطتين طب واحد يقول لي طب + +694 +01:07:41,390 --> 01:07:45,530 +هاي واي بس قطع اتنين في نقطة واحدة بقولك مصبور لإن + +695 +01:07:45,530 --> 01:07:52,520 +انا ماقلتش بس خط واحد قولتلك اي خط رأسي اذا قطعهفي + +696 +01:07:52,520 --> 01:07:56,820 +اكتر من نقطة يبقى ليست functional حتى وان حدث مش + +697 +01:07:56,820 --> 01:07:59,940 +مرة قضع في نقطة مرتين و تلاتة بس في نقطة لكن + +698 +01:07:59,940 --> 01:08:04,460 +الباقي كله في نقطة تانية يبقى ليست functional لازم + +699 +01:08:04,460 --> 01:08:09,940 +ولا مرة يقطع في نقطة يبقى كله اي خط vertical line + +700 +01:08:09,940 --> 01:08:17,160 +يقطع في نقطة واحدة يبقى هادئ نقطةأي function يبقى + +701 +01:08:17,160 --> 01:08:22,400 +هذه ليست function تمام هذه نمرة D نجلة نمرة C دير + +702 +01:08:22,400 --> 01:08:26,660 +بالك هذه أسئلة موجودة في الكتاب من أسئلة التمرين + +703 +01:08:26,660 --> 01:08:32,320 +اللي في الكتاب طيب نجلة نمرة E نمرة E قال لي + +704 +01:08:32,320 --> 01:08:36,780 +absolute value ل X absolute value ل Y تساوي واحد + +705 +01:08:36,780 --> 01:08:42,930 +بدنا نرسم الرسم البياني لهذه الدالةبدا جي اشيل ال + +706 +01:08:42,930 --> 01:08:46,890 +absolute value و اضع زائد او ناقص زي ما حطينا هنا + +707 +01:08:46,890 --> 01:08:52,410 +يبقى انا عندي زائد او ناقص x زائد او ناقص y يساوي + +708 +01:08:52,410 --> 01:08:58,250 +واحد هنا قولنا هدول مش اربع معادلات هدول بس معادلة + +709 +01:08:58,250 --> 01:09:03,790 +سؤالنا هو هنا هدول اربع معادلات والله معادلتين + +710 +01:09:03,790 --> 01:09:10,630 +تعالى نشوف المعادلة الاولى x زائد y تساوي واحد + +711 +01:09:11,110 --> 01:09:16,410 +المعادلة التانية x ناقص y تساوي واحد المعادلة + +712 +01:09:16,410 --> 01:09:21,850 +التالتة ناقص x زائد y تساوي واحد المعادلة الرابعة + +713 +01:09:21,850 --> 01:09:29,770 +ناقص x ناقص y يساوي كده؟ يساوي واحدولا واحدة فيهم + +714 +01:09:29,770 --> 01:09:36,970 +زي التانية طيب هذه ال Y زائد X يساوي واحد هذه + +715 +01:09:36,970 --> 01:09:40,990 +والله خليها بالنفس الترتيب بلاش تقوليش بدلتهم X + +716 +01:09:40,990 --> 01:09:48,030 +زائد Y يساوي واحد وهذه X ناقص Y يساوي من؟ يساوي + +717 +01:09:48,030 --> 01:09:52,700 +واحد شو رأيك هذه لو ضربتها في إشارة سالم؟ما هو + +718 +01:09:52,700 --> 01:09:58,200 +بالصين؟ X ناقص Y يساوي من؟ ساوي سالب واحد هذا لو + +719 +01:09:58,200 --> 01:10:03,020 +ضربت مشار السالب X زائد Y يساوي سالب واحد هتطلع + +720 +01:10:03,020 --> 01:10:07,620 +لهذه وهذه باختلفوا عن بعض مظبوط النتيجة هنا واحد + +721 +01:10:07,620 --> 01:10:11,040 +وهنا سالب واحد رغم ان الطرف اليمين زي بعضه لكن + +722 +01:10:11,040 --> 01:10:15,560 +الشمال لا هذه وهذه طرف الشمال زي بعضه بالسلمين لأ + +723 +01:10:15,560 --> 01:10:20,920 +يبقى هذول أربع معادلات منفاصلات كل واحدة فيهم تمثل + +724 +01:10:22,570 --> 01:10:29,790 +بنرسم هذه الخطوط المستقيمة فبنقول هذا محور X هذا + +725 +01:10:29,790 --> 01:10:35,490 +محور Y هذا نقطة الاصل اللي هي Zero بدي امسك الخط + +726 +01:10:35,490 --> 01:10:43,720 +الأول لو كانت X ب0Yبقداشي واحد يبقى النقطة Zero + +727 +01:10:43,720 --> 01:10:50,740 +واحد يبقى هذه النقطة Zero واحد لو كانت Y ب Zero X + +728 +01:10:50,740 --> 01:10:55,080 +بقداشي واحد يعني واحد و Zero اللي هي النقطة اللي + +729 +01:10:55,080 --> 01:11:01,000 +عندنا هذه واحد و Zero تمام؟ إذا النقطتين يقعان على + +730 +01:11:01,000 --> 01:11:07,590 +الخط المستقيم الأوليبقى ما علي الا اجيب من هناك و + +731 +01:11:07,590 --> 01:11:12,750 +اوصل و امد على استقبال يبقى هذا الخط المستقيم + +732 +01:11:12,750 --> 01:11:19,170 +الأول طيب نجرى الخط المستقيم الثاني لو كانت Y ب + +733 +01:11:19,170 --> 01:11:23,950 +Zero X بقدرش يعني واحد وزيله اللي هي النقطة اللي + +734 +01:11:23,950 --> 01:11:31,180 +عندنا هذه ماتغيرتشمظبوط طيب لو كانت x ب 0 و y ب + +735 +01:11:31,180 --> 01:11:35,960 +سالب واحد لما تبقى x ب 0 و y ب سالب واحد اللي هي + +736 +01:11:35,960 --> 01:11:41,120 +النقطة اللي هنا يبقى سالب واحد و زير و سالب واحد + +737 +01:11:41,590 --> 01:11:48,310 +زيرو و سالب واحد تمام يبقى النقطتين الاتنين يقعن + +738 +01:11:48,310 --> 01:11:53,890 +على الخط المستقيم يبقى روحنا رسمنا الخط المستقيم + +739 +01:11:53,890 --> 01:12:00,590 +بالشكل هذا يبقى هذا X زائد Y يساوي واحد هذا X ناقص + +740 +01:12:00,590 --> 01:12:06,400 +Y يساوي واحد خلصنا من هذا نجي لمستقيم التالفلو + +741 +01:12:06,400 --> 01:12:14,520 +كانت Y ب0 X سالب واحد يعني سالب واحد وزيرو سالب + +742 +01:12:14,520 --> 01:12:20,160 +واحد وزيرو اللي هي النقطة هذه سالب واحد وزيرو يبقى + +743 +01:12:20,160 --> 01:12:25,840 +هنا لو كانت Y بزيرو X بسالب واحد طب لو كانت X + +744 +01:12:25,840 --> 01:12:32,170 +بزيرو Y بواحدلو كانت x بزير و y بواحد اللي هي وين + +745 +01:12:32,170 --> 01:12:37,730 +النقطة اللي عندنا هذه فوق يبقى لأ بروح بوصل بين + +746 +01:12:37,730 --> 01:12:44,550 +النقطتين و بمد هذا على استقامته إذا هذا x ناقص y + +747 +01:12:44,550 --> 01:12:49,990 +يسوى ناقص واحد بعد هيك بدأت أقول هنا لو كانت x + +748 +01:12:49,990 --> 01:12:59,690 +بزير و y بسالب واحد نقطة هذهلو كانت Y ب0 X بسالب + +749 +01:12:59,690 --> 01:13:04,930 +واحد Y بالنقطة هذه بوصل بينهم بالشكل اللي عندنا + +750 +01:13:04,930 --> 01:13:10,570 +هذا بصير هذا X زائد Y ساوي سالب واحد يبقى الرسم + +751 +01:13:10,570 --> 01:13:17,170 +اللي قدامنا هذي تمام طيب تمثل function أي خط + +752 +01:13:17,170 --> 01:13:22,530 +مستقيم أقل ما فيها سيقطع في نقطتين ماكانش في أربعة + +753 +01:13:22,970 --> 01:13:25,650 +لان الخطوة المستقلية ماشية على اطلاع ماشية يعني + +754 +01:13:25,650 --> 01:13:32,250 +ماهياش مقيدة بفترة معينة يبقى هذه not a function + +755 +01:13:32,250 --> 01:13:37,290 +ماهياش ده لأ بسبب ال vertical line test أي خط + +756 +01:13:37,290 --> 01:13:46,220 +مستقيم من فوق لتحتلو كانت ايش؟ + +757 +01:13:46,220 --> 01:13:51,740 +كمعادلة، ممتاز جدا، بتعتبرها ك function ولا لا؟ + +758 +01:13:51,740 --> 01:13:57,960 +ايش رأيك؟ انا بقول لا، عارف ليش؟ لأن بصير العنصر + +759 +01:13:57,960 --> 01:14:03,480 +واحد له مالة نهاية من الصورسؤال ياسميلكو بيقول ما + +760 +01:14:03,480 --> 01:14:08,740 +يأتي لو أنا أخدت الخط اللي عندنا هي المحاور و قلت + +761 +01:14:08,740 --> 01:14:14,400 +هذا X و هذا Y و أخدت الخط هذا مثلا وهو vertical + +762 +01:14:14,400 --> 01:14:18,360 +line، باعتبر هذا function ولا لأ؟ بنقول له لأ، + +763 +01:14:18,360 --> 01:14:22,390 +لماذا؟لأن القيمة تبعت الـ X دا إلها ما شاء الله + +764 +01:14:22,390 --> 01:14:26,530 +صور جد ما بدك، فوق و بتاع، يعني الصور اللي هو نفس + +765 +01:14:26,530 --> 01:14:29,790 +الواحد له مالة نهية من الصور، مش صورتين، وبالتالي + +766 +01:14:29,790 --> 01:14:36,770 +not function، لكن أي خط مستغيم غير الخط الرأسي لا + +767 +01:14:36,770 --> 01:14:43,710 +يمكن أن يكون إلا دالةلا يمكن أن يكون إلا دا لا مش + +768 +01:14:43,710 --> 01:14:47,770 +لا يمكن أن يكون دا لا إذا هذا لا يمكن أن يكون + +769 +01:14:47,770 --> 01:14:53,470 +function لكن كل الخطوط الأخرى غير الموازية لهذا + +770 +01:14:53,470 --> 01:14:58,210 +الخط كلها function سواء كان مائل أوبليج أو + +771 +01:14:58,210 --> 01:15:02,750 +horizontal أوفقي أوفقي أو مائل ماعرفش بس الخط + +772 +01:15:02,750 --> 01:15:08,110 +الرأسي لا يمكن أن يكون function أو لا يمكن أن يمثل + +773 +01:15:08,110 --> 01:15:13,670 +functionماشي سؤال وجيه هو سؤال في محلي ممتاز جدا + +774 +01:15:13,670 --> 01:15:20,830 +شو اسمك انت؟ زيد ابو زيد ماشي يبقى زيد نهض ابو زيد + +775 +01:15:20,830 --> 01:15:27,170 +كويس يا سيدي نيجي لحاجة جديدة يا شباب اسمها ال + +776 +01:15:27,170 --> 01:15:32,850 +piecewise defined function نيجي لعنوان جديد جانبي + +777 +01:15:32,850 --> 01:15:36,070 +اسمه piece + +778 +01:15:41,290 --> 01:15:48,350 +wise defined defined + +779 +01:15:48,350 --> 01:15:56,170 +functions example + +780 +01:15:56,170 --> 01:16:00,590 +one + +781 +01:16:00,590 --> 01:16:13,220 +اول مثال is the expression isthe exception هل + +782 +01:16:13,220 --> 01:16:24,340 +الصيغة التالية f of x يساوي أحد أمرين اتنين ناقص + +783 +01:16:24,340 --> 01:16:32,620 +تلاتة x تكيب و ال x أقل من أو يساوي الواحد و تلاتة + +784 +01:16:32,620 --> 01:16:42,780 +x أُص أربعناقص تلاتة وال X greater than or equal + +785 +01:16:42,780 --> 01:16:49,360 +to one define a + +786 +01:16:49,360 --> 01:16:53,600 +function والسؤال + +787 +01:16:53,600 --> 01:16:56,660 +لماذا + +788 +01:16:56,660 --> 01:17:02,640 +يالا فكرولي كويس ع بالنا نمسح اللوح ونبحث عن + +789 +01:17:02,640 --> 01:17:04,000 +الإجابة + +790 +01:17:32,390 --> 01:17:35,750 +النقطة الجديدة اللى حضرتنا لان اللى لازلنا في نفس + +791 +01:17:35,750 --> 01:17:39,390 +ال section is piecewise function او piecewise + +792 +01:17:39,390 --> 01:17:44,190 +defined function يبقى الدالة المكونة من اكثر من + +793 +01:17:44,190 --> 01:17:49,730 +جزء عدة جزءين تلاتة كذا piece قطعة فلما اقول + +794 +01:17:49,730 --> 01:17:53,790 +piecewise يعني قطعة piecewise function دالة مكونة + +795 +01:17:53,790 --> 01:17:57,810 +من عدة قطعة يعني من عدة اجزاء لكن هذه الدالة + +796 +01:18:01,950 --> 01:18:07,850 +هل هذه الصيغة التالية بتعرف function ولا لا؟ + +797 +01:18:07,850 --> 01:18:13,230 +الاجابة يا نعم يا لا نقول نعم لماذا ونقول لا لماذا + +798 +01:18:13,230 --> 01:18:20,250 +بدنا الحل في هذه الحالة حد + +799 +01:18:20,250 --> 01:18:24,050 +فيكم يقدر يقول لي هل هذه دالة ولا لا؟ + +800 +01:18:27,890 --> 01:18:30,990 +أنا أنا بدي أجيب فيه من دور الرسم، طب خليني أسأل + +801 +01:18:32,290 --> 01:18:37,790 +هذا الآن منحنى، مظبوط؟ وهذا منحنى عادي جدا، لكن + +802 +01:18:37,790 --> 01:18:43,410 +المشكلة أنه في التقاء فيما بينهما الوين؟ عند + +803 +01:18:43,410 --> 01:18:46,850 +الواحد، وممكن مايلتجوش عند الواحد، يمكن أو يمكن + +804 +01:18:46,850 --> 01:18:52,450 +لأ، مظبوط ولا لأ؟ لكن جالي يساوي ويساوي معناته في + +805 +01:18:52,450 --> 01:18:57,610 +التقاء لازم يكون في التقاء، صحيح ولا لأ؟ الالتقاء + +806 +01:18:57,610 --> 01:19:01,730 +هذا، بدي أشوف هل بيحصل ولا بيحصلش؟ + +807 +01:19:03,730 --> 01:19:07,730 +المشكلة وين؟ عند الواحد، مش هنا هي الواحد، اكبر + +808 +01:19:07,730 --> 01:19:11,730 +وساقه واحد، يعني المنحلة ممكن تقول هذا جاي خط + +809 +01:19:11,730 --> 01:19:14,790 +مستقيم و هذا جاي قص والتقوا عند النقطة هذه اللي هي + +810 +01:19:14,790 --> 01:19:17,650 +واحد، إذا المشكلة تكون عند واحد، يمكن يكون في + +811 +01:19:17,650 --> 01:19:21,730 +اتصال وممكن يكون فيش اتصال، صحيح ولا لا؟ يمكن عند + +812 +01:19:21,730 --> 01:19:25,510 +الواحد تبقى الدالة معرفة وممكن ما تكونش معرفةكل + +813 +01:19:25,510 --> 01:19:29,390 +الاحتمالات واردة الدالة قابلة للاشتقاق ويمكن مش + +814 +01:19:29,390 --> 01:19:32,790 +قابلة للاشتقاق زي ما احنا ناخد بعد ذلك الدالة + +815 +01:19:32,790 --> 01:19:37,110 +متصلة أو ويرمى كل الاحتمالات بيصير واردة كويس احنا + +816 +01:19:37,110 --> 01:19:41,390 +مابناش نبحث هذا احنا نبحث بس هل الدالة معرفة عند + +817 +01:19:41,390 --> 01:19:45,550 +هذه النقطة او لا إذا معرفة كرمى مش معرفة خلاص ليست + +818 +01:19:45,550 --> 01:19:51,190 +function صحيح ولا لأ إذا مشان هيك بتروح أجيبله F + +819 +01:19:51,190 --> 01:19:57,160 +of واحديبقى f of واحد يساوي اقل من اذا يساوي واحد + +820 +01:19:57,160 --> 01:20:02,980 +يبقى بضعوم في الاولى يبقى اتنين ناقص تلاتة في واحد + +821 +01:20:02,980 --> 01:20:12,050 +تكيب اللي هو قداش ناقص واحدبط ولكن كذلك f of واحد + +822 +01:20:12,050 --> 01:20:17,810 +لانه معرف عن الواحد يساوي كده يبقى يساوي تلاتة في + +823 +01:20:17,810 --> 01:20:24,110 +واحد أص أربعة ناقص تلاتة يساوي زيرو هذا العنصر + +824 +01:20:24,110 --> 01:20:28,710 +الواحد أكم صورة لجينا له صورتين يبقى هدى function + +825 +01:20:28,710 --> 01:20:38,850 +يبقى not a function يبقى هذا بده يعطيلك انهgiven + +826 +01:20:38,850 --> 01:20:47,990 +expression الصيغة المعطاها دي مالها is not a + +827 +01:20:47,990 --> 01:20:58,090 +function because السبب انه سالب واحد بدأ لاتساوي + +828 +01:20:58,090 --> 01:21:04,110 +zero بس هنا طلعت بساوي بعض و هذا كلام ماله مرفوض + +829 +01:21:07,980 --> 01:21:14,440 +بنجي المثال الثاني example two + +830 +01:21:14,440 --> 01:21:18,960 +بقول sketch the graph of the function + +831 +01:21:28,510 --> 01:21:36,010 +أرسم لرسمة الدالة f of x يساوي أحد ثلاثة أمور يا + +832 +01:21:36,010 --> 01:21:43,110 +إما أربعة لما ال X أقل من سالب اتنين يا إما X + +833 +01:21:43,110 --> 01:21:50,700 +تربيةلما سالب اتنين اقل من او يسوى X اقل من او + +834 +01:21:50,700 --> 01:21:57,680 +يسوى Zero يا اما X لما الـ X greater than Zero + +835 +01:22:00,770 --> 01:22:05,330 +يقول احنا عندنا piecewise function مش جزئين ثلاثة + +836 +01:22:05,330 --> 01:22:11,050 +اجزاء قال لي ارسملي هذه الدالة بقوله تعالى نشوف + +837 +01:22:11,050 --> 01:22:18,630 +كيف بدنا نرسم هذه الدالة بقوله هذه المحاور وهذا + +838 +01:22:18,630 --> 01:22:28,030 +محور X وهذا محور Y وهذا نقطة الأصل اللي هي Zeroاذا + +839 +01:22:28,030 --> 01:22:34,570 +X أقل من سالب اتنين قيمة الدالة كده يبقى هذه Zero + +840 +01:22:34,570 --> 01:22:41,410 +وهذا سالب واحد وهذه سالب اتنين وهذه سالب تلاتة عند + +841 +01:22:41,410 --> 01:22:45,230 +السالب اتنين وقبل السالب اتنين قيمة الدالة كده + +842 +01:22:45,230 --> 01:22:52,790 +يبقى انا بدي اطلع فوقوهي اللى عندنا من هنا اللى هى + +843 +01:22:52,790 --> 01:22:59,770 +الاربعة يبقى قبل السالب اتنين خط مستقيم دالة ثابتة + +844 +01:22:59,770 --> 01:23:06,770 +قيمتها تساوي قداش اربعة ومافيش يساوي عندما تساوي + +845 +01:23:06,770 --> 01:23:09,670 +سالب اتنين الدالة قداش بتكون + +846 +01:23:15,730 --> 01:23:22,770 +بس انا مقيد بمين بالفترة من سالب اتنين لغاية zero + +847 +01:23:22,770 --> 01:23:28,250 +فقط لغير يبقى ال parabola بديجين هيك و ممنوع يطلع + +848 +01:23:28,250 --> 01:23:32,470 +و ممنوع يفوت هيك لإيش؟ لإن عند السالب اتنين تربية + +849 +01:23:32,470 --> 01:23:38,760 +بصير باربعة يبقى بديبدة من عند النقطة هذهويكون قاس + +850 +01:23:38,760 --> 01:23:46,490 +بهذا الشكلمغلقة عند سالب 2 بالسبب ان هذه تساوي 4 + +851 +01:23:46,490 --> 01:23:51,510 +مش بالسبب الأول مغلقة بالشكل اللي ان هذا تمام + +852 +01:23:51,510 --> 01:23:58,150 +وصلنا ل 0 وخلصنا لغاية 0 كمان يساوي 0 تربيع ب 0 + +853 +01:23:58,150 --> 01:24:05,930 +إذا من هنا كمان مغلقة تماما يبقى هذا هو الأربعة + +854 +01:24:05,930 --> 01:24:11,620 +وهذا هو ال X تربيعقال لي بعد هيك بعد ال zero + +855 +01:24:11,620 --> 01:24:17,620 +فالدلة تساوي من X يعني Y تساوي يعني الساعة تساوي + +856 +01:24:17,620 --> 01:24:24,360 +صين رسمنا خط قبل شوية يعني خط ينصف من الرابع الأول + +857 +01:24:24,360 --> 01:24:31,000 +بهذا الشكل خط مستقيم يبقى هذا Y تساوي X هذا Y + +858 +01:24:31,000 --> 01:24:37,680 +تساوي X تربيع هذا Y تساوي أربعيبقى هذه دالة مكونة + +859 +01:24:37,680 --> 01:24:45,960 +من ثلاثة أجزاء خط مستقيم أوفقي خط مائل قوس Y تساوي + +860 +01:24:45,960 --> 01:24:51,260 +X تربية طبعا هذه أمثلة سهلة ننتقل شوية + +861 +01:25:00,040 --> 01:25:04,620 +بالنسبة للنقطة الأولى بتكون مفتوحة هنا لكن لما + +862 +01:25:04,620 --> 01:25:08,340 +جابلي يساوي السالي باتنين إذا عندي السالي باتنين + +863 +01:25:08,340 --> 01:25:13,780 +بدا تبقى مغلقة فروحنا أغلقناها من هنا يساوي ال + +864 +01:25:13,780 --> 01:25:19,500 +zero يبقى أغلقناها من عن ال zero الباقي مفتوحة طيب + +865 +01:25:19,500 --> 01:25:25,690 +نجي لمثال رقم تلاتةتلاتة حاجة اسمه إلى نقطة ايه؟ + +866 +01:25:25,690 --> 01:25:33,590 +لأنه very important يبقى example تلاتة حاجة اسمه + +867 +01:25:33,590 --> 01:25:38,910 +إلى نقطة ايه؟ في الأول the integer floor function + +868 +01:25:38,910 --> 01:25:49,030 +integer floor function دالة الأرض is the function + +869 +01:25:49,030 --> 01:25:52,010 +whose + +870 +01:25:55,840 --> 01:26:05,860 +value with value at with + +871 +01:26:05,860 --> 01:26:18,820 +value at any real number x is + +872 +01:26:18,820 --> 01:26:23,680 +the greatest + +873 +01:26:28,030 --> 01:26:41,650 +انتجر less than or equal less than or equal to x + +874 +01:27:08,850 --> 01:27:14,030 +مرة تانية نقرأ الكلام اللى مكتوب نحاول نفهم ما هو + +875 +01:27:14,030 --> 01:27:19,410 +مكتوب لنروح على طبقه على أرض الواقع بأمثلة مختلفة + +876 +01:27:19,410 --> 01:27:24,450 +ايش بقول the integer floor function قبل المبدأ + +877 +01:27:24,450 --> 01:27:30,950 +سمعته بالثانوية بدالة صحيح C هى دالة صحيح C بس بدى + +878 +01:27:30,950 --> 01:27:37,540 +جزاياه لإيش إلى جزءيندالة الأرض ودالة السقف، دالة + +879 +01:27:37,540 --> 01:27:41,960 +الأرض لأنه بنزل العدد الكاثري للأرض ودالة السقف + +880 +01:27:41,960 --> 01:27:47,320 +بنطلع العدد الكاثري الأوان للسقف يعني للعدد الصحيح + +881 +01:27:47,320 --> 01:27:50,980 +اللي بيجي بعده أو اللي بيجي قبله حسب طبيعة المثلة + +882 +01:27:51,510 --> 01:27:55,630 +the integer of lower function يعني دالة مين؟ يعني + +883 +01:27:55,630 --> 01:27:57,990 +بالبلد، ان قلت لك اتنين و تسعة من عشرة، ممكن + +884 +01:27:57,990 --> 01:28:03,030 +تنزلها لوين؟ لاتنين، ممتاز يبقى is the function هي + +885 +01:28:03,030 --> 01:28:08,470 +دالة whose value، اللي قيمته at any real number X + +886 +01:28:08,470 --> 01:28:14,550 +ماقلتش عدد صحيح، real صحيح، والله كثري is the + +887 +01:28:14,550 --> 01:28:22,260 +greatest integer، أكبر رقمless than يكون أقل من أو + +888 +01:28:22,260 --> 01:28:27,880 +يكون مساويا ل X يبقى ايش قال هنا is the greatest + +889 +01:28:27,880 --> 01:28:35,340 +integer اكبر رقم يكون مساويا او اقل منه فمثلا لما + +890 +01:28:35,340 --> 01:28:40,760 +قلتك اتنين وتسعة من عشرة ايش الرقم الصحيح اللي اقل + +891 +01:28:40,760 --> 01:28:48,300 +منه اتنين لما نقلتك اتنينإتنين لإنه قال لي أقل منه + +892 +01:28:48,300 --> 01:28:53,920 +أو مساويا له إذا بيساوي يبقى بنان عليه for example + +893 +01:28:53,920 --> 01:29:05,040 +بديها الرمز اللي هو F of X يساوي هيكو بقول X تمام + +894 +01:29:05,040 --> 01:29:09,340 +زي اللي قاعد على كرسي، يبقى هذه هي دالة اللي هو + +895 +01:29:09,340 --> 01:29:15,080 +الأرض، يبقى for example لو جيت قلتلك لإتنين، إيش + +896 +01:29:15,080 --> 01:29:23,020 +بدك تقول؟ لإتنين، لو قلتلك هنا دالة الأرض لإتنين + +897 +01:29:23,020 --> 01:29:30,050 +وتسعة وتسعين من مين؟إتنين برضه يبقى هذه اللي هو + +898 +01:29:30,050 --> 01:29:39,830 +الاتنين لو قلتلك جداش اتنين فاصلة زيرو واحد من + +899 +01:29:39,830 --> 01:29:44,790 +عاشر من مية برضه اتنين يعني هدول اتنين بيساوي بعض + +900 +01:29:44,790 --> 01:29:51,430 +و بيساوي هذا يساوي اتنين طيب بلاش دالة الأرض لزيرو + +901 +01:29:52,510 --> 01:30:01,910 +0 زي ما هي.طيب، دلت الأرض لمين؟ لسالب تلاتة وواحد + +902 +01:30:01,910 --> 01:30:07,870 +من العشرة.قول يا ابني.سالب أربعة.سالب أربعة، هي + +903 +01:30:07,870 --> 01:30:11,350 +الإجابة اللي بقول عليها.حد إيه اللي اعتراض على هذه + +904 +01:30:11,350 --> 01:30:17,230 +الإجابة؟سالب أربعة أقل من سالب تلاتة واحد من عشر، + +905 +01:30:17,230 --> 01:30:22,450 +وإحنا قلنا بأول رقم أقل منه، يبقى هذه إجابة سليمة + +906 +01:30:22,450 --> 01:30:29,290 +وما عداها فهي إجابة خاطية طيب، لو جيت قلتلك هذه يا + +907 +01:30:29,290 --> 01:30:34,030 +سيد العزيز سالب + +908 +01:30:34,030 --> 01:30:40,530 +تلاتة وتسعة وتسعين من الميةبرضه طيب ماشي الحالة + +909 +01:30:40,530 --> 01:30:48,310 +طيب بدي أقولك سالب زيرو و تلاتة من عشر سالب واحد + +910 +01:30:48,310 --> 01:30:53,990 +يعني كمان طيب سالب واحد ماشي سالب واحد و هكذا يبقى + +911 +01:30:53,990 --> 01:30:58,850 +هذه كلها إجابات صحيحة طيب هذه خلصنا إيه بدنا نروح + +912 +01:30:58,850 --> 01:31:03,230 +لنمرة V طبعا هرسملك إياها بعد قليل بس خلينا ناخد + +913 +01:31:03,230 --> 01:31:08,370 +نمرة Vيبقى بيننا بـ a the integer ceiling function + +914 +01:31:08,370 --> 01:31:14,230 +هي دالة السقف the integer ceiling + +915 +01:31:14,230 --> 01:31:18,110 +function + +916 +01:31:18,110 --> 01:31:27,230 +is the function whose value is the function whose + +917 +01:31:27,230 --> 01:31:36,290 +valueالقيمة بتابعة at any real number at any real + +918 +01:31:36,290 --> 01:31:51,750 +number x is the smallest is the smallest is + +919 +01:31:51,750 --> 01:31:58,070 +the smallest integer greater + +920 +01:31:58,070 --> 01:31:58,970 +than + +921 +01:32:03,570 --> 01:32:10,210 +Greater than or equal to + +922 +01:32:10,210 --> 01:32:11,270 +X + +923 +01:32:42,620 --> 01:32:49,700 +العدد الصحيح تبع السقف وليس تبع الأرض هو عبارة عن + +924 +01:32:49,700 --> 01:32:54,800 +الدالة whose value قيمتها number X عند أي عدد + +925 +01:32:54,800 --> 01:33:02,040 +حقيقي X هو أصغر + +926 +01:33:02,040 --> 01:33:08,150 +رقميكون greater than or equal to X يعني بدل ما كنت + +927 +01:33:08,150 --> 01:33:13,430 +بتنزل للأرض، هتطلع لوين؟ للسقف، تمام؟ طيب، بدي + +928 +01:33:13,430 --> 01:33:18,650 +أمسك الإعداد هذه و أشوف إذا لو أنا بدي دلة السقف + +929 +01:33:18,650 --> 01:33:23,630 +للإتنين، قداش بتساوي اتنين؟ طيب، يعني لاحظ السقف + +930 +01:33:23,630 --> 01:33:28,330 +والأرض للعدد الصحيح اتنين are equal طب لو جيت، + +931 +01:33:28,330 --> 01:33:36,970 +قلتلك دلة السقف للإتنينو Zero واحد يبقى تلاتة بدي + +932 +01:33:36,970 --> 01:33:42,650 +دالة السقف لتنين تسعة وتسعين من المية يبقى تلاتة + +933 +01:33:42,650 --> 01:33:48,030 +برضه كله بطل للعدد الصحيح من اللي بيجي بعدههذه + +934 +01:33:48,030 --> 01:33:54,150 +قولناها لو جيت قولتلك دلت السقف لمن؟ لزيرو يبقى + +935 +01:33:54,150 --> 01:34:03,990 +zero بده دلت السقف لسالب تلاتة واحد من عشر كتلة + +936 +01:34:03,990 --> 01:34:07,130 +الروايات زي المرض اللي فاتت + +937 +01:34:09,750 --> 01:34:15,470 +سالب تلاتة سالب تلاتة أكبر من سالب تلاتة واحد من + +938 +01:34:15,470 --> 01:34:21,150 +عشرة يبقى هذه السالب ركزي كويس من جيبها هذه كرناها + +939 +01:34:21,150 --> 01:34:25,370 +بدل المرة مرات في الخيارات المتعددة هذه اللي + +940 +01:34:25,370 --> 01:34:30,710 +بتسببك أشكالية بنحط السؤال فيها في الغالبتمام؟ طيب + +941 +01:34:30,710 --> 01:34:38,210 +لو جيت قولتلك دالة الصفر الزالب Zero و تلاتة من + +942 +01:34:38,210 --> 01:34:46,730 +عشرة0 ممتاز جدا يبقى 0 خلاصنا هي يبقى كل الأرقام + +943 +01:34:46,730 --> 01:34:53,130 +اللي موجودة عندنا طيب بنحاول نرسم A شكل الدالة يا + +944 +01:34:53,130 --> 01:34:58,910 +شباب نكتب هيك Y أو F of X يسوى دالة السقف ل X + +945 +01:34:58,910 --> 01:35:04,550 +بالشكل هذاهنا هنا هي كرسي هنا بنعملها سقف بالشكل + +946 +01:35:04,550 --> 01:35:08,510 +اللي عندنا بدأ نرسم كل function من ال functions + +947 +01:35:08,510 --> 01:35:15,010 +هدول بدأيجي لرسمة الدالة الأولى يبقى هذا محور X + +948 +01:35:15,010 --> 01:35:22,450 +هذا محور Y خلي بالك هنا بدأ تخيل عند الخط وهمي هذا + +949 +01:35:22,450 --> 01:35:26,890 +مش من ضمن الرسمة مالوش دعوة بالرسمة هذا الخط + +950 +01:35:26,890 --> 01:35:28,730 +الوهمي اللي عندك اكتر + +951 +01:35:31,740 --> 01:35:40,060 +هذا الخط اللي هو Y تساوي X شوف يا سيدي نبدأ من عند + +952 +01:35:40,060 --> 01:35:46,380 +الـ Zero هذا Zero و هذا واحد و هذا اتنين و هذا + +953 +01:35:46,380 --> 01:35:53,660 +تلاتة و هنا واحد و هنا اتنين و هنا تلاتة و هنا + +954 +01:35:53,660 --> 01:36:00,750 +سالب واحد و هنا سالب اتنين و هنا سالب تلاتةوهنا + +955 +01:36:00,750 --> 01:36:06,810 +سالب واحد ثم سالب اتنين ثم سالب تلاتة ثم سالب اربع + +956 +01:36:06,810 --> 01:36:07,870 +ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب + +957 +01:36:07,870 --> 01:36:09,470 +خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم + +958 +01:36:09,470 --> 01:36:10,370 +سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة + +959 +01:36:10,370 --> 01:36:11,310 +ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب + +960 +01:36:11,310 --> 01:36:17,690 +خمسة ثم سالب خمسة ثم سالب خمسة ثم سالب خمسة ثم + +961 +01:36:17,690 --> 01:36:28,760 +سالب خمسة ثم سالب خمسة ثم سالب خمسة ثفوق اتنين + +962 +01:36:28,760 --> 01:36:33,980 +هبسموها الدالة الدرجية او الدالة السلمية يبقى هنا + +963 +01:36:33,980 --> 01:36:39,600 +بديجيلك اللي هو الاتنين مغلقة وهي تلاتة لفوق وهي + +964 +01:36:39,600 --> 01:36:47,060 +تلاتة تمام؟ يبقى مغلقة وبعد هيك تمشي لقبال التلاتة + +965 +01:36:47,360 --> 01:36:53,040 +و بتكون مفتوحة و هكذا تمام؟ من الناحية هذه برضه + +966 +01:36:53,040 --> 01:36:58,840 +بنفس الطريقة بتيجي لتحت السلب واحد مغلقة و بتيجي + +967 +01:36:58,840 --> 01:37:05,080 +عند السلب واحد مفتوحة الآن بتيجي عند اتنين تحت + +968 +01:37:05,080 --> 01:37:14,050 +السلب اتنين مغلقة و هيك بتيجي مفتوحةهنا تحت السلب + +969 +01:37:14,050 --> 01:37:24,270 +تلاتة دوري مغلقة وهنا مفتوحة يبقى هذا رسم تمين ال + +970 +01:37:24,270 --> 01:37:31,030 +function الاولى اللى هو Y تساوي دالة الأرض لمن؟ لل + +971 +01:37:31,030 --> 01:37:36,760 +X نجى للدالة التانية اللى هى دالة السقفيبقى دالة + +972 +01:37:36,760 --> 01:37:43,340 +السقف هذا محور X هذا محور Y هذه نقطة الأصل اللي هي + +973 +01:37:43,340 --> 01:37:50,100 +Zero بدا أتخيل الخط الوهمي نفسه اللي هو Y تساوي X + +974 +01:37:50,100 --> 01:37:55,780 +Y تساوي X اللي بنص في الرابع الأول والربع التالت + +975 +01:37:55,780 --> 01:38:02,020 +بنفس الطريقة بدا أقول عندي اي واحد اي اتنين اي + +976 +01:38:02,020 --> 01:38:09,750 +تلاتة اي واحدأي اتنين أي تلاتة وهكذا هنا سالب واحد + +977 +01:38:09,750 --> 01:38:16,110 +سالب اتنين سالب تلاتة هنا سالب واحد سالب اتنين + +978 +01:38:16,110 --> 01:38:22,810 +سالب تلاتة وهكذا تمام؟ بدك تتخيل تماما نفس الرسم + +979 +01:38:22,810 --> 01:38:28,730 +بس جلبها عبر الخط Y تساوي X يعني رسمة الدالة + +980 +01:38:28,730 --> 01:38:35,740 +الأولى تحت الخط Y تساوي Xأعلى الخط Y27X يبقى هذه + +981 +01:38:35,740 --> 01:38:42,700 +بدها نقلبها هنا وتجيلك هنا مفتوحة تمام هذه بدها + +982 +01:38:42,700 --> 01:38:52,140 +تجيلك هنا مفتوحة هذه بدها تجيلك هنا مغلقة وتجيلك + +983 +01:38:52,140 --> 01:39:00,090 +هنا مفتوحة أعلى هذا مباشرةهذه بدأت تجيلك هنا مغلقة + +984 +01:39:00,090 --> 01:39:06,250 +وهنا بدأت تجيلك مفتوحة تحتها مباشرة بدأت تجي مغلقة + +985 +01:39:06,250 --> 01:39:16,230 +وهنا تجي مفتوحة وهكذا تمام؟ يبقى هذه رسمة الدالة Y + +986 +01:39:16,230 --> 01:39:21,290 +تساوي دالة صحيح X بس إيش؟ السقف + +987 +01:39:23,930 --> 01:39:30,210 +طيب، واحد بده يسأل وبده يقول السؤال التالي، من أين + +988 +01:39:30,210 --> 01:39:36,930 +لك هذا؟ يعني أنت حافظهم حافظ، والله هذه بدها فاهم، + +989 +01:39:36,930 --> 01:39:41,850 +بيقولك لا، بدنا فاهم وبدنا نتقيد بالتعريف و نيجي + +990 +01:39:41,850 --> 01:39:48,250 +نرسم، كيف؟طلّالي رسمة الدالة الأولى مثلا عند ال + +991 +01:39:48,250 --> 01:39:54,150 +zero دالة الأرض ب zero متفقين طيب لو كانت واحد من + +992 +01:39:54,150 --> 01:39:59,450 +عشرة بتنزل لوين ل zero يبقى عندما أمشي لغاية + +993 +01:39:59,450 --> 01:40:03,850 +الواحدة كلها ب zero هاي الخط الغامق اللي هو هنا ان + +994 +01:40:03,850 --> 01:40:08,510 +شاء الله يكون تسعة من عشرة بدك تنزل لمين ل ال zero + +995 +01:40:08,510 --> 01:40:15,780 +طيب وصلت واحد صحيةتقفز لو هي حاجة صحية، مظلوم؟ طب + +996 +01:40:15,780 --> 01:40:22,450 +واحد و نصواحد صحيح واحد وتسعة من عشرة واحد صحيح + +997 +01:40:22,450 --> 01:40:26,650 +اتنين واحد من عشرة اتنين و هكذا يبقى فاهمنا كيف + +998 +01:40:26,650 --> 01:40:32,290 +هذه تعالى نمشي للجزء السالم يبقى انا هذا بدأتي + +999 +01:40:32,290 --> 01:40:36,830 +لسالب تسعة من عشرة او سالب واحد تنزل لسالب واحد + +1000 +01:40:36,830 --> 01:40:42,090 +لكن سالب تسعة من عشرة بدك تنزلها لقل منها لو سالب + +1001 +01:40:42,090 --> 01:40:48,570 +واحد هيو سالب واحد من عشرة سالب واحدفبسالب واحد + +1002 +01:40:48,570 --> 01:40:53,830 +واحد من عشرة نزلها للاتنين و هكذا تبقى عارفين كيف + +1003 +01:40:53,830 --> 01:40:58,930 +الرسمة؟ هذي تعالى هذي هذي تبقى تطلع على فوق تمام + +1004 +01:40:58,930 --> 01:41:04,110 +عند ال zero ب zero عند ال واحدة من العشرة تطلع + +1005 +01:41:04,110 --> 01:41:08,050 +للواحد عند تسعة من العشرة تطلع للواحد عند الواحد + +1006 +01:41:08,050 --> 01:41:12,190 +بواحد عند الواحد واحد من العشرة تطلع للاتنين و + +1007 +01:41:12,190 --> 01:41:16,210 +هكذاوبالتالي الجزء السليم زي ذلك عرفنا كيف الرأس + +1008 +01:41:16,210 --> 01:41:20,950 +مجد مش حيال الله يخبط ويمشي لأ لأ هذه جت بناء على + +1009 +01:41:20,950 --> 01:41:27,690 +فهمنا اللي موجود هناك بدي أسأل سؤال جداش ايه ال + +1010 +01:41:27,690 --> 01:41:34,650 +domain لدالة الأرض هذه؟ + +1011 +01:41:36,310 --> 01:41:41,490 +الأولى كداش ال domain لها؟ هل هناك نقطة دالة غير + +1012 +01:41:41,490 --> 01:41:48,090 +معرفة عندها؟ لأ يعني لكل ال real line طيب هل هذا + +1013 +01:41:48,090 --> 01:41:56,910 +هو domain الدالة التانية تبعت السقف؟ هو نفسه ولا + +1014 +01:41:56,910 --> 01:42:02,630 +لأ؟ يعني ويسوي كداش؟ من سالب infinity إلى infinity + +1015 +01:42:02,630 --> 01:42:10,630 +لكل real lineطب بد ال range لدالة + +1016 +01:42:10,630 --> 01:42:18,290 +الأرض بد ال range كل + +1017 +01:42:18,290 --> 01:42:23,530 +الأعداد معنى إيش؟ ال range يعني أستفيد الأعداد + +1018 +01:42:23,530 --> 01:42:24,250 +الصحيحة + +1019 +01:42:29,140 --> 01:42:34,920 +كل الأعداد، كل الريال، يعني هدول؟ طيب، في الإجابة، + +1020 +01:42:34,920 --> 01:42:38,260 +استنى شوية، في الصورة اللي عندك هذا اللي انت + +1021 +01:42:38,260 --> 01:42:44,300 +شايفها، في كسر موجود؟ يبقى الإجابة بس اللي عدده + +1022 +01:42:44,300 --> 01:42:48,100 +صحيح، مش هستفيد اللي عدده الصحيح، بس تبعد كل + +1023 +01:42:48,100 --> 01:42:55,970 +الكسور، يبقىهتلاقي ال range لهذه هو نفس ال range + +1024 +01:42:55,970 --> 01:43:06,080 +لدلة السقف اللي عندنا هذه هو منهو الـ zero زاد أو + +1025 +01:43:06,080 --> 01:43:12,720 +ناقص واحد، زاد أو ناقص اتنين، زاد أو ناقص تلاتة، + +1026 +01:43:12,720 --> 01:43:19,500 +وفاصلة، وتظلك ماشي إلى أي شاء الله، يبقى عارفين + +1027 +01:43:19,500 --> 01:43:20,980 +الست هذه جسمها؟ + +1028 +01:43:23,210 --> 01:43:28,550 +مجموعة الأعداد الصحيحة the set of integers يبقى + +1029 +01:43:28,550 --> 01:43:36,830 +هذه بدل سوى set Z عندنا اللي هي the set of + +1030 +01:43:36,830 --> 01:43:43,930 +integers يبقى هذه عبارة عن مجموعة الأعداد الصحيحة + +1031 +01:43:43,930 --> 01:43:48,770 +بلا استثناء تمام؟ + +1032 +01:43:50,990 --> 01:43:54,630 +ركزي عليه الشغل هذه يبقى domain الدالة الأولى هو + +1033 +01:43:54,630 --> 01:43:58,950 +domain الدالة التانية the set of all real numbers + +1034 +01:43:58,950 --> 01:44:03,390 +ضال مين عندنا؟ ضال ال range ال range هنا بيعطينيش + +1035 +01:44:03,390 --> 01:44:09,190 +إلا أعداد صحية هذا الخط كله يعتبر قداش اتنين، هنا + +1036 +01:44:09,190 --> 01:44:14,420 +اتنين، هنا اتنين، هنا اتنين، كله اتنينهنا واحد هنا + +1037 +01:44:14,420 --> 01:44:19,520 +صفر هنا سالب واحد يبقى عندي zero واحد اتنين تلاتة + +1038 +01:44:19,520 --> 01:44:22,400 +اربعة خمسة سالب واحد سالب اتنين يبقى مجموعة + +1039 +01:44:22,400 --> 01:44:26,600 +الاعداد الصحية وهكذا بالنسبة للرسم التاني ال + +1040 +01:44:26,600 --> 01:44:29,140 +domain الدالة الأولى هو domain الدالة التانية هو + +1041 +01:44:29,140 --> 01:44:32,400 +the set of all real numbers ال range تبع الدالة + +1042 +01:44:32,400 --> 01:44:35,020 +الأولى هو ال range تبع الدالة التانية هو مجموعة + +1043 +01:44:35,020 --> 01:44:41,180 +الاعداد الصحيةلا يزال عندنا كلام كتير يبقى بنكتفي + +1044 +01:44:41,180 --> 01:44:46,240 +هذا اليوم أو في هذه المحاضرة وسنعود الى ال + +1045 +01:44:46,240 --> 01:44:51,200 +piecewise function بمثال جديد المحاضرة القادمة ان + +1046 +01:44:51,200 --> 01:44:51,700 +شاء الله + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aMhkzOkTdWU_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aMhkzOkTdWU_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..5dc8fd5e1c07c619055914b849033a758d26fcdb --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aMhkzOkTdWU_postprocess.srt @@ -0,0 +1,3632 @@ +1 +00:00:21,510 --> 00:00:26,410 +بسم الله الرحمن الرحيم المرة اللى فاتت اخر حاجة + +2 +00:00:26,410 --> 00:00:30,770 +اتكلمنا فيها اللى هو نوعين اللى هو ال horizontal + +3 +00:00:30,770 --> 00:00:34,830 +asymptotes و ال oblique asymptotes بالنسبة لل + +4 +00:00:34,830 --> 00:00:37,410 +horizontal asymptotes بيقولنا ناخد limit لل + +5 +00:00:37,410 --> 00:00:42,030 +function لما ال X بده تروح الى infinity او لسالب + +6 +00:00:42,030 --> 00:00:46,650 +infinity انطلع النتج يساوي رقم يبقى فيه ان + +7 +00:00:46,650 --> 00:00:50,770 +horizontal asymptote Y تساوي هذا الرقميبقى بيكون + +8 +00:00:50,770 --> 00:00:54,710 +هو ال horizontal asymptote سواء كان هذا الرقم zero + +9 +00:00:54,710 --> 00:00:59,630 +أو كمية موجبة أو كمية سالبة لكن إن كان طلع الناتج + +10 +00:00:59,630 --> 00:01:03,710 +infinity أو سالب infinity يبقى بنقول هنا the + +11 +00:01:03,710 --> 00:01:06,910 +horizontal line أو the horizontal asymptote does + +12 +00:01:06,910 --> 00:01:11,310 +not exist يعني ماعنديش horizontal asymptote ثم + +13 +00:01:11,310 --> 00:01:15,010 +انتقلنا بعد ذلك إلى ال obligasymptote وقولنا إذا + +14 +00:01:15,010 --> 00:01:19,580 +كانت درجة دلة البسطأعلى من درجة دالة المقام بمقدار + +15 +00:01:19,580 --> 00:01:24,580 +واحد يبقى بيكون عندي oblique asymptote تمام؟ الآن + +16 +00:01:24,580 --> 00:01:27,500 +قبل أن نذهب إلى ال asymptote الأخرى اللي هو ال + +17 +00:01:27,500 --> 00:01:31,560 +vertical asymptote فيه أنحاجة عرضية لازمالي لل + +18 +00:01:31,560 --> 00:01:35,680 +vertical asymptote فبدنا نتعرض للآن اللي هو ال + +19 +00:01:35,680 --> 00:01:41,940 +infinite limits يعني ال limit إذا كانت النتيجة + +20 +00:01:41,940 --> 00:01:47,610 +infinite لمين لدالة مايقول السؤال find the + +21 +00:01:47,610 --> 00:01:50,970 +following limits if it exists يوجهها للنهايات + +22 +00:01:50,970 --> 00:01:56,650 +التالية إن وجدت ما وجدتش خلاص مسمحينك فبدي بقول + +23 +00:01:56,650 --> 00:02:00,830 +limit ال X بده تروح للاتنين لل function واحد على X + +24 +00:02:00,830 --> 00:02:06,400 +minus twoيبقى لو جيت الآن بالتعويض المباشر لو قلنا + +25 +00:02:06,400 --> 00:02:10,580 +limit البسط على limit المقام يبقى واحد على زيرو + +26 +00:02:10,580 --> 00:02:14,920 +وهذا الكلام ماله ممنوع لكن هل ال function هذه + +27 +00:02:14,920 --> 00:02:20,750 +معرفة عندك سواء تماملو رجعنا بالذاكرة الى الوراء + +28 +00:02:20,750 --> 00:02:25,210 +الى ال chapter الماضى الى section 2 أربعة اللى كان + +29 +00:02:25,210 --> 00:02:30,050 +one sided limit كتبت عندك بالعربي بناخد ال limit + +30 +00:02:30,050 --> 00:02:33,990 +من اليمين و ال limit من الشمال في الحالات الأربعة + +31 +00:02:33,990 --> 00:02:38,750 +تمام؟ و روحنا أخدنا ثلاث حالات و أخدنا عليهم أمثلة + +32 +00:02:38,750 --> 00:02:41,930 +و بقيت الحالة الرابعة و قدت اقولك ان شاء الله + +33 +00:02:47,810 --> 00:02:53,410 +الدالة غير معرفة عند النقطة المراد حساب النهاية + +34 +00:02:53,410 --> 00:02:58,530 +عندها يبقى الدالة غير معرفة عند X يساوي 2 إذن سنتر + +35 +00:02:58,530 --> 00:03:03,950 +إلى أخذ النهاية من اليمين والنهاية من الشمال يبقى + +36 +00:03:03,950 --> 00:03:05,590 +بدنا نروح ناخد limit + +37 +00:03:09,020 --> 00:03:14,480 +لمان؟ لأ ال function واحد على X ناقص اتنين لما ال + +38 +00:03:14,480 --> 00:03:19,880 +X بتروح للاتنين على سبيل المثال من جهة اليسار يبقى + +39 +00:03:19,880 --> 00:03:25,060 +واحد على لو روحت للاتنين من جهة اليسار يبقى اي + +40 +00:03:25,060 --> 00:03:30,300 +اتنين وانا رايح لها من جهة اليسار يعني اقل من + +41 +00:03:30,300 --> 00:03:35,440 +اتنين يبقى المقام قيمة سالب ولا موجبة يبقى very + +42 +00:03:35,440 --> 00:03:40,420 +small negative quantityالنتيجة هي negative + +43 +00:03:40,420 --> 00:03:47,340 +quantity يبقى النتيجة لن تصبح سالب infinity طيب لو + +44 +00:03:47,340 --> 00:03:53,360 +أخدت ال limit لما ال X بدها تروح إلى 2 من جهة + +45 +00:03:53,360 --> 00:04:01,140 +اليمين لل 1 على X ناقص 2 يساوي 1 احنا راحيين ل 2 + +46 +00:04:01,140 --> 00:04:06,410 +من جهة اليمين يبقى بناء عليهلما اذهب للاتنين من + +47 +00:04:06,410 --> 00:04:11,650 +جهة اليمين يكون اتنين وكسر بسيط جدا نقص اتنين + +48 +00:04:11,650 --> 00:04:18,470 +بيبقى عندي very small positive quantity يبقى + +49 +00:04:18,470 --> 00:04:24,950 +النتيجة انها infinity صار في ان اللي هو من جهة + +50 +00:04:24,950 --> 00:04:29,110 +اليمين تختلف عن جهة الشمال يبقى ال limit exist ولا + +51 +00:04:29,110 --> 00:04:34,420 +does not existيبقى does not exist يبقى باجي بقوله + +52 +00:04:34,420 --> 00:04:40,400 +سا ال limit لواحد على X ناقص اتنين لما ال X بده + +53 +00:04:40,400 --> 00:04:50,340 +تروح للاتنين does not exist مالهاش وجود طيب نيجي + +54 +00:04:50,340 --> 00:04:55,680 +ناخد كمال مثال ثاني و نشوف شو النتيجة يبقى ال + +55 +00:04:55,680 --> 00:05:02,680 +limitلما ال X بدها تروح لا Zero لا واحد على X + +56 +00:05:02,680 --> 00:05:10,440 +تربيعهل الدالة معرفة عند X يساوي Zero؟ طبعا لا + +57 +00:05:10,440 --> 00:05:13,880 +يبقى بيننا العالي اذا انا اضطر ان انا اخد النهاية + +58 +00:05:13,880 --> 00:05:18,800 +من اليمين والنهاية من اليسار يبقى بدى اخد limit + +59 +00:05:18,800 --> 00:05:24,200 +لما ال X بدها تروح لل Zero من جهة الشمال لواحد على + +60 +00:05:24,200 --> 00:05:29,560 +X تربية ويساوي واحد على إذا أنا رايح لل Zero من + +61 +00:05:29,560 --> 00:05:34,630 +جهة اليسار يبقى القيم موجة بو الله سالبةسنة بيبقى + +62 +00:05:34,630 --> 00:05:40,610 +very small negative quantity يبقى very small + +63 +00:05:40,610 --> 00:05:48,750 +negative quantity بس اه لكل تربية يبقى بيصير واحد + +64 +00:05:48,750 --> 00:05:55,590 +على very small positive quantity اللي يبقى درجة ب + +65 +00:05:55,590 --> 00:06:01,600 +infinityطيب نروح ناخد ال limit لما ال X بدها تروح + +66 +00:06:01,600 --> 00:06:08,920 +ل 0 من جهتي اليمين ل 1 على X تربيع يبقى 1 على very + +67 +00:06:08,920 --> 00:06:15,340 +small positive quantity الكل تربيعاللي هيبقى تبقى + +68 +00:06:15,340 --> 00:06:21,240 +كمان positive أيضا يبقى النتيجة سوى كم؟ سوى + +69 +00:06:21,240 --> 00:06:26,920 +infinity من الاتنين هدول مع بعض بروح بقول limit + +70 +00:06:26,920 --> 00:06:32,280 +لما ال X بده تروح ل 0 من جهة اليمين لمين؟ ل 1 على + +71 +00:06:32,280 --> 00:06:40,280 +X تربيع تسوى كم؟ infinity وكأنها exist لكن تسوى + +72 +00:06:40,280 --> 00:06:45,870 +كم؟ما لا نهاية infinity يبقى هذا بيخلف عن السؤال + +73 +00:06:45,870 --> 00:06:50,150 +الأول، السؤال الأول اليمين غير الشمال يبقى قولنا + +74 +00:06:50,150 --> 00:06:55,300 +does not exist، هنا اليمين ساوة الشماللكن النتيجة + +75 +00:06:55,300 --> 00:06:59,840 +كانت infinity يبقى بقول ال limit تسوى من infinity + +76 +00:06:59,840 --> 00:07:05,420 +لاحظوا بالنسبة لهذا السؤال رسمناه قبل ذلك وقلنا لو + +77 +00:07:05,420 --> 00:07:10,600 +كان هذا محور X وهذا محور Y يبقى هذا ال function + +78 +00:07:10,600 --> 00:07:15,300 +اللي انا رسمت من Y تسوى واحد ع الاكس اربعة وهي + +79 +00:07:15,300 --> 00:07:20,430 +Zeroلو أنا رايح لـ 0 من جهة اليمين بلاجي الدالة + +80 +00:07:20,430 --> 00:07:24,850 +طالعة لـ infinity و لو روحت لـ 0 من جهة الشمال + +81 +00:07:24,850 --> 00:07:30,050 +كمان الدالة طالعة لوين إلى infinity و من هنا ال + +82 +00:07:30,050 --> 00:07:34,230 +limit من اليمين زي ال limit من الشمال وتساوي مين؟ + +83 +00:07:34,230 --> 00:07:42,950 +وتساوي infinity ناخد كمان مثال اللي هو رقم 3 رقم 3 + +84 +00:07:42,950 --> 00:07:44,230 +بدنا ال limit + +85 +00:07:47,130 --> 00:07:55,450 +لما ال X بدها تروح إلى تلاتة لمين لسالي باتنين على + +86 +00:07:55,450 --> 00:07:59,130 +X ناقص تلاتة لكل ربيع + +87 +00:08:01,340 --> 00:08:04,840 +يبقى بروح اخد ال limit من اليمين وال limit من + +88 +00:08:04,840 --> 00:08:10,920 +الشمال واشوف شو بده تعطينا يبقى بدنا نروح ناخد ال + +89 +00:08:10,920 --> 00:08:17,580 +limit لما ال X بده تروح لتلاتة من جهة اليسار لسالب + +90 +00:08:17,580 --> 00:08:23,520 +اتنين X ناقص تلاتة لكل تربية يسوى ناقص اتنين على + +91 +00:08:24,020 --> 00:08:28,780 +أحنا راحيين لتلاتة من جهة اليسار يعني قبل التلاتة + +92 +00:08:28,780 --> 00:08:33,840 +يبقى المقدار بين القوسين قمموجة ولا سالبة؟ سالبة + +93 +00:08:33,840 --> 00:08:45,020 +يبقى very small negative quantity كل سلبية سالب + +94 +00:08:45,020 --> 00:08:48,360 +اتنين سالب اتنين على + +95 +00:08:53,750 --> 00:08:59,670 +لو أطلع نهر الصين سنجد المجمع يبقى النتيجة السائل + +96 +00:08:59,670 --> 00:09:05,410 +تنفيه لو روحنا الشاشة النهرية وما ال X يبقى طوحي + +97 +00:09:05,410 --> 00:09:11,570 +إمالة من جهة اليمين يسلق اتنين على X ماقص تلاتة في + +98 +00:09:11,570 --> 00:09:18,870 +كل تلبية يسلق اتنين على تلاتة من جهة اليمين يبقى + +99 +00:09:18,870 --> 00:09:23,520 +أكبر من تلاتة ماقص تلاتةبقى ال very small positive + +100 +00:09:23,520 --> 00:09:29,660 +in quantity. if you are very small positive in + +101 +00:09:29,660 --> 00:09:37,380 +quantity كل تاريخ يبقى + +102 +00:09:37,380 --> 00:09:43,700 +اتنين هدول مع بعض بروح تقول انه لمد يسيب + +103 +00:09:49,020 --> 00:09:56,200 +يجب أن تذهب إلى تلاتة يسوى جدير سالب infinity يبقى + +104 +00:09:56,200 --> 00:10:01,280 +بالعنوان عليه مرة limit does not exist مرة limit + +105 +00:10:01,280 --> 00:10:07,380 +infinity مرة limit سالب infinityوبالتالي ماعنديش + +106 +00:10:07,380 --> 00:10:13,100 +شغلة محددة بتختلف النتيجة من سؤال إلى آخر هذا + +107 +00:10:13,100 --> 00:10:18,300 +بالنسبة لل infinite limits طب شو دخله يد في النص؟ + +108 +00:10:18,300 --> 00:10:25,400 +هذا ما سنعرفه بعد قليل لما ننتقل الآنالى من؟ الى + +109 +00:10:25,400 --> 00:10:30,640 +اخر نقطة في هذا ال section وهو اخر نوع من انواع ال + +110 +00:10:30,640 --> 00:10:36,280 +asymptotes اللي هي ال vertical asymptotes وهي + +111 +00:10:36,280 --> 00:10:41,740 +النقطة الأخيرة في هذا ال section يبقى بنا نيجي + +112 +00:10:41,740 --> 00:10:46,060 +للنقطة الرابعة والاخيرة في هذا ال section اللي هي + +113 +00:10:46,060 --> 00:10:51,840 +رقم أربعة ال vertical asymptotes + +114 +00:10:56,550 --> 00:11:08,330 +definition a line x يساوي a is a vertical + +115 +00:11:08,330 --> 00:11:12,070 +asymptote + +116 +00:11:12,070 --> 00:11:20,870 +خط قارب رأسي of the graph of + +117 +00:11:21,820 --> 00:11:33,440 +the function لدالة y تساوي f of x if either اما + +118 +00:11:33,440 --> 00:11:44,580 +limit لل f of x لما ال x بدها تروح لل aمن جهة + +119 +00:11:44,580 --> 00:11:53,140 +اليمين تساوي زائد او ناقص infinity or limit لل F + +120 +00:11:53,140 --> 00:11:58,820 +of X لما ال X بدها تروح لل A من جهة الشمال بده + +121 +00:11:58,820 --> 00:12:06,380 +يساوي من زائد او ناقص infinity ناخد مثال توضيحي + +122 +00:12:06,380 --> 00:12:10,200 +example find + +123 +00:12:13,790 --> 00:12:22,630 +the asymptotes of + +124 +00:12:22,630 --> 00:12:34,870 +the function f of x يسوى x على x تربيع ناقص أربع + +125 +00:13:02,580 --> 00:13:06,640 +يوجد آخر نوع من أنواع الـ asymptotes اللي هو الـ + +126 +00:13:06,640 --> 00:13:12,030 +vertical asymptoteبنعطيه خطوط التقارب الرأسية + +127 +00:13:12,030 --> 00:13:16,690 +بنعطي تعريف لخط التقارب الرأسي ففاجب اقول ال line + +128 +00:13:16,690 --> 00:13:23,390 +X يساوي A is a vertical asymptote ل الرسم البياني + +129 +00:13:23,390 --> 00:13:29,290 +لمنحنة ده لو Y تساوي F of X if either اما limit ال + +130 +00:13:29,290 --> 00:13:33,170 +F of X لما ال X بده يروح لل A بده يساوي موجب او + +131 +00:13:33,170 --> 00:13:36,970 +سلب infinity او limit ال F of X لما ال X بده يروح + +132 +00:13:36,970 --> 00:13:38,390 +لل A من جهة الشمال + +133 +00:13:41,920 --> 00:13:45,460 +معنى هذا الكلام ان limit ال F of X لما ال X بتروح + +134 +00:13:45,460 --> 00:13:51,720 +لل A قد يكون infinity و قد يكون سالب infinity مش + +135 +00:13:51,720 --> 00:13:56,100 +اتنين فيها من واحد اما هذه او تلك ماعنا مشكلة + +136 +00:14:08,160 --> 00:14:13,380 +السؤال هو هل ضروري اخد ال limit من اليمين و من + +137 +00:14:13,380 --> 00:14:18,770 +الشمال؟بالكافة الواحدة لكن يمكن التاني يجيب ال + +138 +00:14:18,770 --> 00:14:24,750 +vertical تاني مثلا كويس اتنين ممكن هذه تعطيني + +139 +00:14:24,750 --> 00:14:29,010 +infinity وهذه تعطيني infinity ممكن هذه تعطيني سالب + +140 +00:14:29,010 --> 00:14:32,670 +infinity وهذه تعطيني سالب infinityممكن انها تعطيني + +141 +00:14:32,670 --> 00:14:36,510 +موجة بالإنفينيتي وهذه تعطيني سالب بالإنفينيتي على + +142 +00:14:36,510 --> 00:14:40,650 +كل الأمر يعني ماعنديش مشكلة زي مين زي Y تسوى واحد + +143 +00:14:40,650 --> 00:14:44,430 +على X اذا روحت من جهة اليمين عند ال zero بتلاقي + +144 +00:14:44,430 --> 00:14:47,430 +اللي راح اتماه لنهاية اذا روحت ل zero من جهة + +145 +00:14:47,430 --> 00:14:51,550 +الشمال بتنزل لوين لسالب infinity اللي كانت مرسومته + +146 +00:14:51,550 --> 00:14:54,330 +قبلها قليل لما روح ل zero من اليمين ومن الشمال + +147 +00:14:54,330 --> 00:14:58,630 +لجهته infinity على الشجتين وبالتالي ماعناه مشكلة + +148 +00:14:58,930 --> 00:15:03,570 +هذه والله هذه السيانة متفرجش عنها، إذا اللي خدناته + +149 +00:15:03,570 --> 00:15:07,390 +و أساها ال limit ان النتيجة بدأ تبقى infinity كان + +150 +00:15:07,390 --> 00:15:12,670 +ضروري جدا لأنه لازم نشغل عليه وين عند حساب ال + +151 +00:15:12,670 --> 00:15:16,960 +vertical ال simplestالمثال اللي بين إيدينا بيقول + +152 +00:15:16,960 --> 00:15:21,400 +ما ياتي، بيقول هات للـasymptotes للدالة هذه، ولم + +153 +00:15:21,400 --> 00:15:25,540 +يقول لا vertical ولا oblique ولا horizontal، يبقى + +154 +00:15:25,540 --> 00:15:30,580 +انت لحالك بدك ايه؟ بدك تعرف، بيقوله بسيطة جدا، بس + +155 +00:15:30,580 --> 00:15:37,750 +هل نفسي هل هذه فيها oblique، asymptote؟لأن ضرائط + +156 +00:15:37,750 --> 00:15:43,790 +الباص أقل من ضرائط المقام يبقى الحل نطالب كل ال + +157 +00:15:43,790 --> 00:15:48,870 +asymptotes إذا موجودة بديها يبقى باجي بقول له + +158 +00:15:48,870 --> 00:16:01,950 +there is no oblig asymptote شو + +159 +00:16:01,950 --> 00:16:11,810 +السبب؟ becauseإن ال degree لل X أقل من ال degree + +160 +00:16:11,810 --> 00:16:19,010 +لل X تربية ناقص أربعةدرجة البص أقل من درجة المقام + +161 +00:16:19,010 --> 00:16:24,010 +وبالتالي ماعنديش Obligue ال symptom طب نشوف هل في + +162 +00:16:24,010 --> 00:16:30,350 +horizontal ولا لا، إذا بدروح أخد ال limit لل F of + +163 +00:16:30,350 --> 00:16:36,480 +X لما ال X بدها تروح لموجة ب Infinityطبعا الكون ال + +164 +00:16:36,480 --> 00:16:40,420 +polynomial و ال polynomial يبقى موجب و الله سالب + +165 +00:16:40,420 --> 00:16:47,240 +حياطين ايه نفس النتيجة يبقى هنا limit لما ال X بده + +166 +00:16:47,240 --> 00:16:54,080 +يروح لموجب او سالب infinity لل X على X تربية ناقص + +167 +00:16:54,080 --> 00:17:02,050 +4بعد ذلك اقسم كل المقام على X المرفوعة لأكبر أُس + +168 +00:17:02,050 --> 00:17:08,670 +في المقام يبقى النتيجة 1 على X واحد ناقص أربع على + +169 +00:17:08,670 --> 00:17:14,470 +X ثربية هذا Zero هذا Zero النتيجة Zero على واحد + +170 +00:17:14,470 --> 00:17:20,470 +اللي هو الجداش Zero يبقى بناء عليه Y تساوي هذه + +171 +00:17:20,470 --> 00:17:31,030 +القيمة اللي هي Zerois a horizontal asymptote + +172 +00:17:31,030 --> 00:17:34,550 +خط + +173 +00:17:34,550 --> 00:17:40,550 +قارب أفقي خط قارب مائلي بعتلك الله مافيش لم يبقى + +174 +00:17:40,550 --> 00:17:45,330 +عندي إلا مينالـ Vertical Asymptote بدنا نشوف فيه + +175 +00:17:45,330 --> 00:17:50,730 +ولا مافيهش يبقى الـ F of X بقدر اكتبها على الشكل + +176 +00:17:50,730 --> 00:17:58,030 +التالي هذا X والمقام اللي عندي معله فارق بين + +177 +00:17:58,030 --> 00:18:04,610 +المربعين إذا بحلله X نقص اتنين في X زائد اتنين + +178 +00:18:04,610 --> 00:18:12,300 +السؤال هو هل الدالة معرفة عند اتنينولا حتى سلب + +179 +00:18:12,300 --> 00:18:16,900 +اتنين مظبوط اذا هي قيم تانية ده اللي غير معرفة + +180 +00:18:16,900 --> 00:18:22,500 +عندهم اذا سنتر ناخد النهاية من اليمين ونهاية من + +181 +00:18:22,500 --> 00:18:28,060 +اليسار ونشوف هل في عندي vertical asymptote ام لا + +182 +00:18:28,060 --> 00:18:31,520 +بالنسبالي ال vertical asymptote بيقول ال limit من + +183 +00:18:31,520 --> 00:18:34,820 +اليمين والlimit من الشمال اذا infinity او سلب + +184 +00:18:34,820 --> 00:18:39,500 +infinity يبقى في عندك vertical asymptote وإذا does + +185 +00:18:39,500 --> 00:18:45,720 +not existلا يوجد عندي Vertical Asymptote اذا انا + +186 +00:18:45,720 --> 00:18:52,160 +بدرح اخد limit لل F of X لما ال X بده يروح لل + +187 +00:18:52,160 --> 00:18:57,400 +اتنين ناخد من جهة الشمال اولا يبقى هذا ال limit + +188 +00:18:57,400 --> 00:19:02,660 +لما ال X بده يروح لل اتنين من جهة الشمال لل X على + +189 +00:19:02,660 --> 00:19:08,780 +X ناقص اتنين في X زائد اتنين ويساوي اتنين مافيش + +190 +00:19:08,780 --> 00:19:13,990 +فيها مشكلة نيجي هذهأنا رايح الأتنين من جهة الشمال + +191 +00:19:13,990 --> 00:19:20,230 +يبقى هذه very small negative يبقى هذه very small + +192 +00:19:20,230 --> 00:19:26,610 +negative quantity هذه مافيش فيها مشكلة اتنين زائد + +193 +00:19:26,610 --> 00:19:33,950 +اتنين يبقى أداشة بطلع بطلع عندي واحد على اتنين في + +194 +00:19:33,950 --> 00:19:41,230 +very smallNegative quantity يعني إيه؟ سالب + +195 +00:19:41,230 --> 00:19:48,800 +infinityبعد هيك بتروح اخد ال limit لل F of X لما + +196 +00:19:48,800 --> 00:19:53,560 +ال X بده يروح لل اتنين من جهة اليمين يبجى هذا ال + +197 +00:19:53,560 --> 00:19:58,920 +limit لما ال X بده تروح لل اتنين من جهة اليمين لل + +198 +00:19:58,920 --> 00:20:06,500 +X على X ناقص اتنين في X زائد اتنين يبجى هذا الكلام + +199 +00:20:06,500 --> 00:20:11,780 +بده يساوي اتنين علىنحل اتنين من جهات اليمين يعني + +200 +00:20:11,780 --> 00:20:19,520 +اتنين وكسر بسيط نقص اتنين يبقى very small positive + +201 +00:20:19,520 --> 00:20:27,040 +quantity ثمين في اتنين زائد اتنين يبقى النتيجة + +202 +00:20:27,040 --> 00:20:29,560 +كده؟ infinity + +203 +00:20:31,120 --> 00:20:38,520 +يبقى النهاية من الشمال بسالب Infinity ومن اليمين ب + +204 +00:20:38,520 --> 00:20:45,580 +Infinity يبقى هنا يقول هذه أو تلك يبقى أنا تحقق + +205 +00:20:45,580 --> 00:20:49,500 +عندي واحدة منهم هذه موجودة إذا أنا بقدر أقول هذه + +206 +00:20:49,500 --> 00:20:56,390 +الخطة الأبرانيةvertical asymptote يبقى باجي بقول + +207 +00:20:56,390 --> 00:21:08,210 +له so ال X يساوي اتنين is a vertical asymptote + +208 +00:21:08,210 --> 00:21:13,110 +طيب اللي عملنا له اتنين بدنا نروح نعمله لمين؟ + +209 +00:21:13,110 --> 00:21:21,710 +لسالي باتنين يبقى باجي اخد الان limitلل F of X لما + +210 +00:21:21,710 --> 00:21:27,470 +ال X بده يروح لسالي باتنين من جهة الشمال يبقى ال + +211 +00:21:27,470 --> 00:21:33,350 +limit لما ال X بده تروح لسالي باتنين من جهة الشمال + +212 +00:21:33,350 --> 00:21:42,290 +لدالة X X ناقص اتنين في X زائد اتنين ويسوى سالي + +213 +00:21:42,290 --> 00:21:48,110 +باتنين سالي باتنين من جهة الشمال مع هذه مش فيها اي + +214 +00:21:48,110 --> 00:21:53,950 +مشكلةيبقى هنا هاي سالي باتنين سالي باتنين المشكلة + +215 +00:21:53,950 --> 00:21:58,390 +بيصير وين؟ في الجوس الثاني انا رايح اللي سالي + +216 +00:21:58,390 --> 00:22:03,450 +باتنين من جهة الشمال يبقى سالي باتنين وكسر زائد + +217 +00:22:03,450 --> 00:22:09,330 +اتنين بيضل very small positive ولا negative احنا + +218 +00:22:09,330 --> 00:22:14,130 +رايح اللي سالي باتنين من جهة الشماليبقى هنا ال + +219 +00:22:14,130 --> 00:22:23,110 +very small negative quantity طيب طلّالي ليه هذه؟ + +220 +00:22:23,110 --> 00:22:27,250 +هذه سالب اتنين وهذه سالب اربعة بروح و بضل بس very + +221 +00:22:27,250 --> 00:22:33,230 +small negative يعني مين؟ يعني واحد على اتنين في + +222 +00:22:33,230 --> 00:22:40,070 +very small negative quantity يبقى بسلب infinity + +223 +00:22:41,220 --> 00:22:47,720 +بالمثل بدنا ناخد limit لما ال X بدها تروح ل-2 من + +224 +00:22:47,720 --> 00:22:54,800 +جهة اليمين لل F of X يبقى ال X بدها تروح ل-2 من + +225 +00:22:54,800 --> 00:23:02,760 +جهة اليمينللـ x على x نقص 2 في الـ x زائد 2 عند + +226 +00:23:02,760 --> 00:23:07,480 +السلب 2 الجثث الأول مافيش فيه أي إشكالية يبقى أي + +227 +00:23:07,480 --> 00:23:15,540 +سلب 2 سلب 2 سلب 2 فين؟ سلب 2 من جهة اليمين، يعني + +228 +00:23:15,540 --> 00:23:21,680 +السلب 1وحط ساعات زي ما بدك بضل very small positive + +229 +00:23:21,680 --> 00:23:30,570 +يبقى very small positive quantityهذا سيعطيك نص + +230 +00:23:30,570 --> 00:23:38,090 +يبقى هذا الكلام واحد على اتنين very small positive + +231 +00:23:38,090 --> 00:23:45,370 +quantity يبقى هذا سيعطيك main infinity يبقى تحقق + +232 +00:23:45,370 --> 00:23:51,130 +الأولى على حده وتحقق الثاني على حده لنفس الخط يبقى + +233 +00:23:51,130 --> 00:23:59,560 +باجي بقول لهالـ x يساوي سالب اتنين is a vertical + +234 +00:23:59,560 --> 00:24:01,600 +asymptote + +235 +00:24:04,680 --> 00:24:08,960 +يبقى طالع عندنا بدل الخط اتنين vertical asymptote + +236 +00:24:08,960 --> 00:24:13,820 +و horizontal asymptote واحد وماعنديش oblique + +237 +00:24:13,820 --> 00:24:18,220 +asymptote فانتوا ملاحظين اننا بنحسب ال asymptotes + +238 +00:24:18,220 --> 00:24:24,940 +هذه نظريا لكن عمليا على أرض الواقع ماشوفناش بالمرة + +239 +00:24:24,940 --> 00:24:32,210 +لذلك بنحاول نعطيكمثال عملي ونحاول نرسم ال function + +240 +00:24:32,210 --> 00:24:38,850 +و ال asymptotes تبعتها يبقى نيجي ناخد مثال أخير + +241 +00:24:38,850 --> 00:24:42,930 +يبقى + +242 +00:24:42,930 --> 00:24:49,010 +example يقول + +243 +00:24:49,010 --> 00:24:56,030 +sketch the graph of the function sketch the graph + +244 +00:24:56,030 --> 00:25:08,210 +ofThe function دالة Y تساوي X تربيع ناقص واحد على + +245 +00:25:08,210 --> 00:25:19,590 +اتنين X زائد أربعة and و الله كذلك بعد ما ترسم + +246 +00:25:19,590 --> 00:25:28,050 +find the asymptotes and + +247 +00:25:30,380 --> 00:25:43,180 +Demonated terms السؤال + +248 +00:25:43,180 --> 00:25:49,860 +بين أدينا ثلاثة مطالب بدنا نتعرف على هذه المطالب + +249 +00:25:49,860 --> 00:25:57,340 +الثلاثة ونشوف كيف بدنا نحل هذا السؤال + +250 +00:26:00,110 --> 00:26:06,010 +سؤال مرة تانية بيقول ارسملي منحنى الدالة x تربية + +251 +00:26:06,010 --> 00:26:12,450 +ناقص واحد على اتنين x زائد اربع اتنين هاتل ال + +252 +00:26:12,450 --> 00:26:16,950 +asymptotes تبعات هذه ال function تلاتة ال + +253 +00:26:16,950 --> 00:26:22,330 +demanding terms يعني أجزاء التحكم بالنسبة لهذه + +254 +00:26:22,330 --> 00:26:27,260 +الدالةDemonetic terms اللي هو أجزاء التحكم لهذه + +255 +00:26:27,260 --> 00:26:32,220 +الدلة طبعا كلمة جديدة لم نسمع بها من قبل لكن + +256 +00:26:32,220 --> 00:26:36,480 +سمعناها لك اليوم و هنسمعها لك تاني كمان في شبط + +257 +00:26:36,480 --> 00:26:44,080 +الأربعة ان شاء الله تعالى طيب solutionليس بالضرورة + +258 +00:26:44,080 --> 00:26:48,540 +أن نبدأ عملية الرسم لأن ماعنديش معلومات لكن بقدر + +259 +00:26:48,540 --> 00:26:53,500 +أجيب له ال asymptotes و بعد هيك الdominant terms + +260 +00:26:53,500 --> 00:26:57,380 +مثلا و بعد هيك نرسم او نرسم و بعد هيك ال dominant + +261 +00:26:57,380 --> 00:27:01,020 +terms مش مشكلة لكن أبسط حاجة أني أحسبله ال + +262 +00:27:01,020 --> 00:27:05,880 +asymptotes السؤال هو هل يوجد عندي horizontal + +263 +00:27:05,880 --> 00:27:09,640 +asymptote في + +264 +00:27:11,780 --> 00:27:14,860 +يعني مش هنجيب ال horizontal بدي أخد ال limit لما + +265 +00:27:14,860 --> 00:27:21,080 +ال X بدها تروح ل infinity أو لسالب infinity درجة + +266 +00:27:21,080 --> 00:27:26,520 +البسط أعلى من درجة المقام يبقى النتيجة يا infinity + +267 +00:27:26,520 --> 00:27:29,900 +يا سالب infinity يعني في عندي horizontal asymptote + +268 +00:27:29,900 --> 00:27:34,900 +مافي إمكانية بالمرة يبقى هنا بقوله there is no + +269 +00:27:34,900 --> 00:27:40,900 +horizontal asymptote there is no + +270 +00:27:48,160 --> 00:27:52,820 +Horizontal asymptote مافيش عندي horizontal + +271 +00:27:52,820 --> 00:27:55,920 +asymptote، بدك تقوله ليش؟ + +272 +00:27:59,620 --> 00:28:08,240 +درجة البسط درجة الاكس تربيه ناقص واحد اكبر من + +273 +00:28:08,240 --> 00:28:13,540 +الدرجة للاتنين اكس زائد اربع وبالتالي اذا كانت + +274 +00:28:13,540 --> 00:28:18,420 +درجة دالة البسط اعلى من درجة دالة المقام فال limit + +275 +00:28:18,420 --> 00:28:23,840 +تساوي قداش تساوي infinity وبالتالي ال horizontal + +276 +00:28:24,440 --> 00:28:30,220 +السيمتوت لا يوجد، يبقى استبعدنا اللي هو + +277 +00:28:30,220 --> 00:28:35,120 +الهورزونتال للسيمتوت، درجة الباص أعلى من درجة + +278 +00:28:35,120 --> 00:28:40,140 +المقام بمقدار واحد، إذا فيه عندنا main oblige + +279 +00:28:40,140 --> 00:28:44,700 +السيمتوتمش هنجيب له بليه قسمته، قول لها بتروحه + +280 +00:28:44,700 --> 00:28:49,340 +اضيف شغل للباصته وشغل مقامه، تقسم او تقسم جسمة + +281 +00:28:49,340 --> 00:28:55,700 +مطولة من البداية، اذا لو روحنا قسمنا جسمة مطولة X + +282 +00:28:55,700 --> 00:29:02,430 +تربية ناقص واحد على اتنين X زائد اربعةX تربيع على + +283 +00:29:02,430 --> 00:29:11,890 +2 X ب X على 2 X على 2 في 2 X ب X تربيع X على 2 ضرب + +284 +00:29:11,890 --> 00:29:22,940 +4 بجزائد 2 Xالان نغيّر الإشارات وبنجمع يبقى هذه + +285 +00:29:22,940 --> 00:29:28,920 +ناقص وهذه ناقص وهذه مع السلامة صار عندنا ناقص + +286 +00:29:28,920 --> 00:29:35,150 +اتنين اكس ناقص واحدلا يزال الآن المقام من الدرجة + +287 +00:29:35,150 --> 00:29:41,090 +الأولى والمقصوم عليه من الدرجة الأولى كذلك إذا + +288 +00:29:41,090 --> 00:29:48,330 +بنروح وعاصل عملية القسمة يبقى ناقص 2X على 2X بقداش + +289 +00:29:48,510 --> 00:29:56,750 +بنقص واحد بنقص اتنين X وهنا ناقص اربع بنغير + +290 +00:29:56,750 --> 00:30:03,830 +الإشارات وبنروح نجمة يبقى هاي هذه زاد وهذه زاد مع + +291 +00:30:03,830 --> 00:30:09,110 +السلامة بيظل عندي قداش تلاتة اذا ال function عندنا + +292 +00:30:09,110 --> 00:30:17,160 +Yاللي هي عبارة عن X تربية ناقص واحد على اتنين X + +293 +00:30:17,160 --> 00:30:22,780 +زائد اربعة يمكن كتابتها على الشكل التالي خارج + +294 +00:30:22,780 --> 00:30:29,840 +القسمة X على اتنين ناقص واحد تمام؟ الآن الباقي + +295 +00:30:29,840 --> 00:30:35,340 +اللي هو زائد تلاتة لسه بده اجسمها على مين؟ على + +296 +00:30:35,340 --> 00:30:43,740 +المقام اللي هو اتنين X زائد اتنينإذن كإني كتبت + +297 +00:30:43,740 --> 00:30:49,100 +المسألة بشكل جديد بدل ما كانت بالشكل هذا حاطينا + +298 +00:30:49,100 --> 00:30:53,220 +خارج القسمة زائد البقى اللي هو تلاتة بالداجس + +299 +00:30:53,220 --> 00:30:56,640 +معالمين على المقصوم عليه اللي هو اتنين X زائد + +300 +00:30:56,640 --> 00:31:01,880 +اربعة او اتنين في X زائد اتنين الterm اللي طالع + +301 +00:31:01,880 --> 00:31:07,140 +عندنا هذا هو عبارة عن مين ال obligive symptom + +302 +00:31:07,140 --> 00:31:09,080 +فبروح بقولهم لا + +303 +00:31:14,090 --> 00:31:22,650 +اسمتوت Y يساوي X على 2 ناقص واحد + +304 +00:31:31,710 --> 00:31:36,730 +وهي معادلة خط مستقيم لأنها من الدرجة الخاط + +305 +00:31:36,730 --> 00:31:42,510 +المستقيم هذا هو الابليج اسمتت طيب هل هي result + +306 +00:31:42,510 --> 00:31:48,530 +مافيش طلعنا ابليج اسمتت السؤال هو في عند vertical + +307 +00:31:48,530 --> 00:31:55,310 +اسمتت ولا لأ اقول تعالى نشوف الدالة غير معرفة عند + +308 +00:31:55,310 --> 00:31:56,330 +X يساوي + +309 +00:32:04,680 --> 00:32:09,760 +الدالة غير معرّفة إذا احتمال ان يكون عند هذه + +310 +00:32:09,760 --> 00:32:14,880 +النقطة اللي هو main vertical asymptote واحتمال + +311 +00:32:14,880 --> 00:32:19,180 +يكون ثقوب في المنحنة مظبوط او لا يبقى بتأكد انه ما + +312 +00:32:19,180 --> 00:32:23,120 +هو ثقوب بتأكد انه vertical asymptote يبقى بتروح + +313 +00:32:23,120 --> 00:32:30,630 +اخد ال limitلل F of X لما ال X بده يروح لسالي + +314 +00:32:30,630 --> 00:32:36,050 +باتنين من جهة الشمال يبقى هاي ال limit لما ال X + +315 +00:32:36,050 --> 00:32:41,490 +بده تروح لسالي باتنين من جهة الشمال لمن؟ لل X على + +316 +00:32:41,490 --> 00:32:49,510 +اتنين ناقص واحد زائد تلاتة اتنين في Xزائد اتنين و + +317 +00:32:49,510 --> 00:32:55,310 +يساوي سالب اتنين طبعا من جهة الشمال يبقى هذه سالب + +318 +00:32:55,310 --> 00:33:01,530 +اتنين على اتنين سالب واحد زائد تلاتة على اتنين في + +319 +00:33:01,530 --> 00:33:06,270 +احنا راح نحلي سالب اتنين من جهة الشمال يبقى سالب + +320 +00:33:06,270 --> 00:33:12,670 +اتنين وكسر زائد اتنين مضل very small negative يبقى + +321 +00:33:12,670 --> 00:33:17,490 +very small negative quantity + +322 +00:33:19,520 --> 00:33:25,880 +هذا سالب واحد و سالب واحد يبقى بجداش بسالب اتنين + +323 +00:33:25,880 --> 00:33:32,620 +وهذه عدد على كمية سالبة بسالب infinity يبقى + +324 +00:33:32,620 --> 00:33:37,120 +النتيجة سالب infinityسالب infinity تضربها في رقم + +325 +00:33:37,120 --> 00:33:43,220 +تجمع لها رقم تطرح منها رقم كله بيظل إيه سالب + +326 +00:33:43,220 --> 00:33:49,640 +infinity لو جربنا أخدنا limit لل F of X لما ال X + +327 +00:33:49,640 --> 00:33:56,700 +بيروح لسالب 2 من جهة اليمينيبقى limit لما ال X بده + +328 +00:33:56,700 --> 00:34:03,700 +يروح ل-2 من جهة اليمين لل X على 2 ناقص واحد تلاتة + +329 +00:34:03,700 --> 00:34:09,440 +على اتنين في X زائد اتنين ويساوي سالب اتنين على + +330 +00:34:09,440 --> 00:34:16,930 +اتنين زائد واحد زائد تلاتة على اتنين فينرحل سالب + +331 +00:34:16,930 --> 00:34:22,190 +اتنين من جهة اليمين يبقى سالب واحد ومجموعة تسعة + +332 +00:34:22,190 --> 00:34:28,570 +مثلا زائد اتنين بيبقى very small positive يبقى + +333 +00:34:28,570 --> 00:34:36,530 +very small positive quantity يبقى هذا الكلام بده + +334 +00:34:36,530 --> 00:34:44,010 +يساوي سالب اتنين زائد infinity اللي هو infinity + +335 +00:34:44,790 --> 00:34:54,190 +بناء ان عليه صورة ان ال X + +336 +00:34:54,190 --> 00:35:06,750 +يساوي سالب اتنين is a vertical asymptote + +337 +00:35:06,750 --> 00:35:14,410 +يبقى خلاصة من المطلوب الأولبنانيج لمان؟ للمطلوب + +338 +00:35:14,410 --> 00:35:19,950 +الثاني في المثلة المطلوب التاني قال لي ارسم وقال + +339 +00:35:19,950 --> 00:35:26,170 +لي هاتلي ال terms اجزاء التحكم في هذه الدلة تعالى + +340 +00:35:26,170 --> 00:35:32,010 +نشوف ايش قصة اجزاء التحكم احنا انا y يسوى x على 2 + +341 +00:35:32,010 --> 00:35:37,850 +ناقص واحد تلاتة على اتنين في x زائد اتنين هذه + +342 +00:35:37,850 --> 00:35:44,660 +الدلةيبقى هذه ال function مكوّنة من جزئين هذا هو + +343 +00:35:44,660 --> 00:35:52,540 +الجزء الأول وهذا هو الجزء الثانيطلّع عليه كويس، لو + +344 +00:35:52,540 --> 00:35:59,100 +خلّيت ال X تكبر، كويس؟ تكبر عشر، عشرين، مية، + +345 +00:35:59,100 --> 00:36:04,680 +مليون، مليار، إلا كم، تكبر ال X، يبقى هذا بيصير + +346 +00:36:04,680 --> 00:36:10,480 +رقم كبير ولا صغير؟ كبير جدا، طيب هذا شو بيصير؟ + +347 +00:36:10,480 --> 00:36:16,320 +بيصير Zero، ممتاز جدايقول إنه يتحكم في سلوك الدالة + +348 +00:36:16,320 --> 00:36:21,080 +اللي هو من الجزء الأول، إيش يعني بتحكم فيها؟يعني + +349 +00:36:21,080 --> 00:36:27,080 +الدالة بدها تصير هى وهذا جرايب وحبايب، هى، بدهم + +350 +00:36:27,080 --> 00:36:31,800 +يسيلوا يمشوا مع بعض، تمام؟ هى معناها، طيب هذا خط + +351 +00:36:31,800 --> 00:36:36,470 +قاربإذا المنحلة بيصيحين قريب منه اتنين ماشيين + +352 +00:36:36,470 --> 00:36:41,590 +معاك، كل ما تكبر X هم مابتفرجوش، يبقى الذي يتحكم + +353 +00:36:41,590 --> 00:36:46,730 +في سلوك الدالة في هذه الحالة عندما تكون X كبيرة + +354 +00:36:46,730 --> 00:36:54,330 +جدا، بيكون مين الterm الأول، ايه؟ لو جربت على مين؟ + +355 +00:36:54,330 --> 00:37:00,020 +على سالب اتنينسواء جربت من اليمين أو من الشمال هذه + +356 +00:37:00,020 --> 00:37:05,380 +و هذه كلها بقداش سالب اتنين صح ولا لأ؟ لما جربت من + +357 +00:37:05,380 --> 00:37:09,900 +السالب اتنين هذول اقصى ما يمكن ان يصلوا الي السالب + +358 +00:37:09,900 --> 00:37:15,380 +اتنين طب هذه لما جربت من السالب اتنين بصير لسالب + +359 +00:37:15,380 --> 00:37:20,980 +infinity مظبوط او موجة ب infinity زي ما شوفنا هي + +360 +00:37:20,980 --> 00:37:25,960 +أخدناها يمين و شوف مرة infinityيعني كل ما اجرب على + +361 +00:37:25,960 --> 00:37:31,040 +السالب اتنين ال term التاني بيصغر ولا بيكبر؟ term + +362 +00:37:31,040 --> 00:37:38,160 +التاني بيكبر خالص، طبعا؟ يعني رايح لوين؟ رايح لل + +363 +00:37:38,160 --> 00:37:43,340 +infinity، طبعا؟ يبقى هذا هو ال term الذي سيتحكم في + +364 +00:37:43,340 --> 00:37:49,280 +سلوك الدالة في هذه العالم يبقى إذا X كبرت بقيمة + +365 +00:37:49,280 --> 00:37:54,950 +موجبة سيتحكم ال term الأولإذا X جربت على سالب + +366 +00:37:54,950 --> 00:38:00,150 +اتنين بدى يتحكم في الدالة ال term تنقل لو X راحت + +367 +00:38:00,150 --> 00:38:06,530 +لسالب infinity يعنى صارت X سالبة بدرجة كبيرة جدا + +368 +00:38:06,530 --> 00:38:11,350 +يبقى هذا كده كده تصير ال term سالب infinity وهذا + +369 +00:38:11,350 --> 00:38:19,130 +كده؟ Zero يبقى عدديا عندما X تكبر أو X تصغر خالص + +370 +00:38:19,130 --> 00:38:24,900 +يبقى اللى بدى يتحكم مين؟الترم الأول يعني إيش بده + +371 +00:38:24,900 --> 00:38:29,840 +يتحكم يعني ده اللي بده تلزج في مين في الترم الأول + +372 +00:38:29,840 --> 00:38:33,360 +طب الترم الأول خط مستقيم إذا ميبقى اللي ماشية مع + +373 +00:38:33,360 --> 00:38:38,100 +مين مع هذا الخط المستقيم اللي هو الابليج السمتت + +374 +00:38:38,100 --> 00:38:43,900 +طيب وإذا كان ال X راحة ل-2 سواء من اليمين و الله + +375 +00:38:43,900 --> 00:38:48,350 +من الشمال يبقى بده يتحكم مينالـ Term الثاني وليس + +376 +00:38:48,350 --> 00:38:54,250 +الـ Term الأول الكلام اللي سمعته بدأ أكتبه لك حتى + +377 +00:38:54,250 --> 00:38:59,070 +تعرف معنى الـ Demonic Terms يبقى باجي بقوله The + +378 +00:38:59,070 --> 00:39:12,290 +Term الو X على 2 ناقص 1 Demonats يتحكم + +379 +00:39:12,290 --> 00:39:23,010 +whenالـ X is numerically عدديا + +380 +00:39:23,010 --> 00:39:32,110 +يعني لا لما أقول عدديا large يعني سالبة أو موجبة + +381 +00:39:32,110 --> 00:39:35,150 +طيب، + +382 +00:39:35,150 --> 00:39:42,400 +that termاللي هو تلاتة على اتنين في x زائد اتنين + +383 +00:39:42,400 --> 00:39:54,380 +دمانات when x is near سالب اتنينلما تكون قريبة جدا + +384 +00:39:54,380 --> 00:40:01,920 +من مين؟ من سالب اتنى يبقى دالة تكونت من جزئين جزهم + +385 +00:40:01,920 --> 00:40:07,420 +بدى يتحكم عندما X ما تكون عدديا كبيرة جدا سواء + +386 +00:40:07,420 --> 00:40:11,900 +كانت بالموجب او بالسالب و لما تكون قريبين من + +387 +00:40:11,900 --> 00:40:17,270 +السالب اتنى بدى يتحكم من ال term التانىيتحكم يعني + +388 +00:40:17,270 --> 00:40:23,190 +ان يصبح ال function ماشية مع هذا ال term او مع هذا + +389 +00:40:23,190 --> 00:40:29,090 +ال term نرسم رسمة المنحنة اللي عندنا يبقى لو جينا + +390 +00:40:29,090 --> 00:40:36,390 +تخيلنا ان هذا محور X هذا محور Y هذه نقطة الأصل + +391 +00:40:36,390 --> 00:40:42,150 +اللي هي Zero بدنا نروح نرسم ال asymptote في + +392 +00:40:42,150 --> 00:40:48,760 +البداية يبقى ال asymptote التانيهو ال homain ال X + +393 +00:40:48,760 --> 00:40:54,100 +يساوي سالب اتنين هو ال vertical ال symptom يبقى + +394 +00:40:54,100 --> 00:41:01,980 +هذا الخط اللي عندنا اللي هو ال X يساوي سالب اتنين + +395 +00:41:01,980 --> 00:41:10,800 +هذا ال vertical ال symptomالاسمتت التاني اللي هو Y + +396 +00:41:10,800 --> 00:41:17,250 +تساوي X على 2 ناقص واحد اللي هو الابلاج الاسمتتهذا + +397 +00:41:17,250 --> 00:41:21,610 +خط مستقيم بدي أجيب نقطتين تقعان على هذا الخط + +398 +00:41:21,610 --> 00:41:27,050 +المستقيم أوصل بينهم بحصل على الأبلغ السيمتون بقول + +399 +00:41:27,050 --> 00:41:33,290 +لو كان ال X بزيرو يبقى ال Y بسالب واحد عندما ال X + +400 +00:41:33,290 --> 00:41:38,230 +بزيرو يبقى ال Y بسالب واحد يبقى هذا زيرو وسالب + +401 +00:41:38,230 --> 00:41:44,710 +واحدعندما تبقى ال y ب0 يبقى ال x على 2 ب1 يبقى ال + +402 +00:41:44,710 --> 00:41:54,750 +x ب2 يبقى 2 و 0 بدأ يجينا النقطة هذه ل 2 و 0 هدول + +403 +00:41:54,750 --> 00:42:00,860 +النقطتين تقعان علمين على الخط المستقيمأو على الـ + +404 +00:42:00,860 --> 00:42:06,440 +oblique asymptote يبقى بوصل بينهم و بمد على + +405 +00:42:06,440 --> 00:42:14,920 +استقامته بيصير هذا هو الـ oblique asymptote اللي + +406 +00:42:14,920 --> 00:42:23,960 +هو من الخط Y يسوى X على 2 نقص واحد يبقى رسم للـ + +407 +00:42:23,960 --> 00:42:29,500 +asymptote الآن بدنا نيجي للرسمةالرسمة، لما بدى + +408 +00:42:29,500 --> 00:42:32,800 +الجزء الأول بدى يتحكم، بدى تكون ماشية مع الـ + +409 +00:42:32,800 --> 00:42:37,520 +oblique asymptoteتمام؟ ولمّا الجزء الثاني بدي + +410 +00:42:37,520 --> 00:42:42,400 +اتحكم بيكون الرسم ماشية مع ال vertical ال center + +411 +00:42:42,400 --> 00:42:48,600 +تمام؟ إذا الرسم ممكن تكون ع الشجة اليمين وع الشجة + +412 +00:42:48,600 --> 00:42:53,260 +الشمال تكون ماشية مع هذا و مع هذا وماشية مع التاني + +413 +00:42:53,260 --> 00:42:57,660 +ومع هذا أو ممكن تكون في الجزء اللي فوق و الجزء + +414 +00:42:57,660 --> 00:43:02,680 +الثاني اللي تحت تكون ماشية هنا وماشية هنا بدل ما + +415 +00:43:02,680 --> 00:43:08,630 +كانت ماشية هنا وماشية تحتإذا أنا بدي أروح أحط قيم + +416 +00:43:08,630 --> 00:43:12,510 +من عندي و أشوف هل بتطلع على اليمين و على الشمال + +417 +00:43:12,510 --> 00:43:18,490 +ولا فوق و تحت فبعدين بقوله لو كانت ال X ب Zero على + +418 +00:43:18,490 --> 00:43:23,150 +سبيل المثال هذه الدالة اللي عندنا الأساسية لو كانت + +419 +00:43:23,150 --> 00:43:29,080 +ال X ب Zero يبقى ال Y بقداشسالب ربع يبقى Zero و + +420 +00:43:29,080 --> 00:43:32,680 +سالب ربع اللي هي النقطة اللي عندنا لأن هذه سالب + +421 +00:43:32,680 --> 00:43:38,460 +واحد يبقى النقطة هذه Zero و سالب ربع تمام؟ لو كانت + +422 +00:43:38,460 --> 00:43:44,220 +ال Y ب Zero يبقى ال bus مستوى Zero ولا المقام؟ ال + +423 +00:43:44,220 --> 00:43:48,120 +bus يعني X ترمية ناقص واحد مستوى Zero يعني X سوى + +424 +00:43:48,120 --> 00:43:54,200 +واحد أو سالب واحد يعني بدأ تجيلك هدف النص هنا و + +425 +00:43:54,200 --> 00:44:00,080 +هدف النص هناإذا المنحنة بدى يكون فوق وتحت وليس على + +426 +00:44:00,080 --> 00:44:05,120 +اليمين وعلى الشمال إذا لو جينا رسمنا المنحنة بدى + +427 +00:44:05,120 --> 00:44:12,580 +يمشي هيك ويجي نازل ويجي طالع بهذا الشكل مع النقطة + +428 +00:44:12,580 --> 00:44:19,120 +اللى عندنا هذهبديه يمر فيها و يضل ماشي مع مين؟ مع + +429 +00:44:19,120 --> 00:44:24,460 +صاحبه مع ال asymptote هذا و من هنا ييجي مع ال + +430 +00:44:24,460 --> 00:44:29,640 +asymptote لغاية ما يوصل لحد معين و يجي نازل بهذا + +431 +00:44:29,640 --> 00:44:36,540 +الشكليبقى هذه الرسمة اللي قدامنا طبعا رسم + +432 +00:44:36,540 --> 00:44:41,000 +character مش دقيق مية لمية لكن الرسم يدل على مين + +433 +00:44:41,000 --> 00:44:47,460 +يدل على الشكل وسنرجع إلى هذه الرسومات في chapter 4 + +434 +00:44:47,460 --> 00:44:53,100 +ان شاء الله لما نشوف واجتاش الدلة تزايدية واجتاش + +435 +00:44:53,100 --> 00:44:58,900 +تناقصيةوانت تقاطع مع محاور الأحداثيات وين النقاط + +436 +00:44:58,900 --> 00:45:03,840 +الحريجة؟ مين منها عظمة محلية ومين منها صغرة محلية؟ + +437 +00:45:03,840 --> 00:45:08,120 +وانتش المنحنة concave up و concave down مفتوح إلى + +438 +00:45:08,120 --> 00:45:13,040 +أسفل و مفتوح إلى أعلى؟ وين نقاط الإنقلاب للمنحنة؟ + +439 +00:45:13,040 --> 00:45:18,300 +كل هذا سنجله في chapter 4 ان شاء الله تعالى. تمام؟ + +440 +00:45:18,750 --> 00:45:22,730 +بعد ما ناخد chapter ثلاثة و نروح على chapter أربع + +441 +00:45:22,730 --> 00:45:26,810 +chapter ثلاثة الاشتقاق chapter أربع تطبيقات على + +442 +00:45:26,810 --> 00:45:31,250 +مين على الاشتقاق حاجة فيكم؟ بتسأل أي سؤال هنا؟ + +443 +00:45:35,140 --> 00:45:39,240 +في الأول لما حكيت عن ال vertical والsimple حكينا + +444 +00:45:39,240 --> 00:45:42,660 +ان لو كانت ال limit does not exist كل الشراء رضوا + +445 +00:45:42,660 --> 00:45:45,680 +انه مافيش vertical والsimple كل الأمثلة اللي + +446 +00:45:45,680 --> 00:45:47,620 +أخدناها ال limit كانت does not exist بس كانت لا + +447 +00:45:47,620 --> 00:45:53,600 +اتننى اجرأت تعرفي كويس قلنا هادي or هاديوحدة منهم + +448 +00:45:53,600 --> 00:45:56,760 +تكفي، لكن احنا نبحث التانية هل بتجيب vertical + +449 +00:45:56,760 --> 00:46:00,520 +السيمتون تاني؟ والله نفسه، ايه كل الهدف، لكن كفيني + +450 +00:46:00,520 --> 00:46:03,540 +واحدة منهم للvertical السيمتون، مش التن، مش + +451 +00:46:03,540 --> 00:46:07,460 +التنتين، لو لمينه شمال جابه نفس النتيجة، برضه + +452 +00:46:07,460 --> 00:46:13,220 +ماعناه مشكلة، تمام؟مظبوط في المثال اللي أخدناه، مش + +453 +00:46:13,220 --> 00:46:15,880 +لما .. مش dust not exist، dust not exist عن جهتي، + +454 +00:46:15,880 --> 00:46:20,220 +لكن من اليمين موجودة، خلّا بيكفيني، أشمال مش + +455 +00:46:20,220 --> 00:46:25,140 +لازمالي، لكن أنا بسوي احتياطا باس، ليس ال .. هل + +456 +00:46:25,140 --> 00:46:27,800 +بيجيبلي نفس النتيجة ولا نتيجة تانية، لكن يبقى + +457 +00:46:27,800 --> 00:46:32,220 +كافية واحدة منهم، واضح؟ بس واحدة، الله أعطيك + +458 +00:46:32,220 --> 00:46:33,500 +العافية، أه + +459 +00:46:37,230 --> 00:46:42,050 +هكذا هلما تقولي إذا الوبلاجة سمتة X على اتنين ناقص + +460 +00:46:42,050 --> 00:46:42,470 +واحد + +461 +00:46:46,010 --> 00:46:50,150 +تقول اللي هو ال vertical asymptote اتنين، شو + +462 +00:46:50,150 --> 00:46:55,670 +الاتنين هذا؟ Y والله X، الله يعلم، تكتبش بخصوم لك، + +463 +00:46:55,670 --> 00:47:00,130 +لكي تحدد، احنا بقولك X يسوى A vertical asymptote، + +464 +00:47:00,130 --> 00:47:05,390 +Y تسوى B يبقى horizontal asymptote، Y تسوى X زي B + +465 +00:47:05,390 --> 00:47:09,950 +يبقى obligal asymptote، لكي تكتب كلام واضح وكلام + +466 +00:47:09,950 --> 00:47:16,870 +ذو معنىلأ عدنا ننتهي هذا ال section وإليكم أرقام + +467 +00:47:16,870 --> 00:47:19,870 +المسائل ال exercises اتنين ستة + +468 +00:47:59,270 --> 00:48:04,970 +ننتقل الان الى ال section اللى كلكم استعدلين عليه + +469 +00:48:04,970 --> 00:48:08,220 +اللى derivativeيقول لي بقى جيبلي ال derivative + +470 +00:48:08,220 --> 00:48:14,960 +دوري تمام يبقى بننتقل إلى هذا ال section اللي هو + +471 +00:48:14,960 --> 00:48:20,500 +ال differentiation شبطر تلاتة يبقى الشبطر تلاتة + +472 +00:48:20,500 --> 00:48:23,500 +كله بتكلم عن الاشتقاق + +473 +00:48:59,780 --> 00:49:02,920 +عشان يعملوا اصلا عشان يعملوا اصلا عشان يعملوا اصلا + +474 +00:49:02,920 --> 00:49:27,140 +عشان يعملوا اصلا عشان يعملوا اصلا عشان يعملوا اصلا + +475 +00:49:51,860 --> 00:49:57,660 +التعريف هذا أخدته قبل ذلك بس مجرد تذكير ليس إلا + +476 +00:49:57,660 --> 00:50:13,420 +The slope of the curveof the curve ميل المنحنة the + +477 +00:50:13,420 --> 00:50:24,260 +slope of the curve Y تساوي F of X at the point عند + +478 +00:50:24,260 --> 00:50:30,360 +النقطة X0 وF + +479 +00:50:30,360 --> 00:50:31,780 +of X0 + +480 +00:50:34,480 --> 00:50:40,880 +is the number M + +481 +00:50:40,880 --> 00:50:50,100 +اللي هو بده يساوي limit لما H بده تروح لل zero لل + +482 +00:50:50,100 --> 00:50:57,180 +F of X node زاد ال H ناقص F of X node على H + +483 +00:50:57,180 --> 00:50:59,580 +provided the + +484 +00:51:05,320 --> 00:51:17,380 +القاعدة توجد تجارب + +485 +00:51:17,380 --> 00:51:21,480 +تجارب + +486 +00:51:21,480 --> 00:51:26,680 +تجارب تجارب تجارب + +487 +00:51:34,640 --> 00:51:38,520 +يبقى الـ tangent line to the curve Y تسوية F of X + +488 +00:51:38,520 --> 00:51:54,760 +at the point عند النقطة P of X0 فF of X0 is the + +489 +00:51:54,760 --> 00:51:56,740 +line + +490 +00:51:58,230 --> 00:52:11,830 +أثرى P خلال النقطة P with this slope M its + +491 +00:52:11,830 --> 00:52:13,150 +equation is + +492 +00:52:19,580 --> 00:52:32,100 +Y تساوي M X نقص X node زائد Y node كمان + +493 +00:52:32,100 --> 00:52:39,040 +derivative او definition of + +494 +00:52:39,040 --> 00:52:46,440 +the + +495 +00:52:46,440 --> 00:53:00,130 +functionالدريفتب دي فانكشن f at a point x0 denoted + +496 +00:53:00,130 --> 00:53:03,630 +by + +497 +00:53:03,630 --> 00:53:10,050 +f prime of x0 is + +498 +00:53:11,620 --> 00:53:19,440 +f prime of x node دي سوى ال limit لما ال h بده + +499 +00:53:19,440 --> 00:53:28,380 +تروح لل zero لل f of x node زاد ال h ناقص f of x + +500 +00:53:28,380 --> 00:53:36,400 +node على h provided the + +501 +00:53:36,400 --> 00:53:40,940 +limit exist + +502 +00:54:03,530 --> 00:54:06,330 +مش عارف + +503 +00:54:22,940 --> 00:54:24,380 +السلام عليكم + +504 +00:54:52,490 --> 00:54:54,070 +السلام عليكم و رحمه الله + +505 +00:55:51,790 --> 00:55:53,190 +السلام عليكم + +506 +00:56:32,090 --> 00:56:38,430 +أبعاد الرسم هذه كتبت معاها قبل ذلك وكذلك التعريف + +507 +00:56:38,430 --> 00:56:43,150 +الأول ان كتبت معاه قبل ذلك احنا بنذكره مشان مهدبه + +508 +00:56:43,150 --> 00:56:47,990 +فقط للتعريف الثاني اللي هو موضوع دراستنا في هذا + +509 +00:56:47,990 --> 00:56:53,340 +الشبطةيبقى هذا chapter differentiation يعني عملية + +510 +00:56:53,340 --> 00:56:59,180 +الاشتقاق أو عملية إيجاد المشتقة الأولى لدالة ما + +511 +00:56:59,180 --> 00:57:06,160 +هنبدأ بأول section بتتكلم عن نقطتين tangents خطوط + +512 +00:57:06,160 --> 00:57:11,610 +التماسوالـ derivative at a point المشتقة عند نقطة + +513 +00:57:11,610 --> 00:57:16,850 +وخطوط التماس عند نقطة للمنحنة التعريف الأول يقول + +514 +00:57:16,850 --> 00:57:21,630 +the slope of the curve ميل المنحنة y تساوي f of x + +515 +00:57:21,630 --> 00:57:27,030 +عند نقطة x node وf of x nodeهو عبارة عن العدد + +516 +00:57:27,030 --> 00:57:31,790 +limit لما الـ H بدأ تذهب لـ 0 لفوكس نود زاد الـ H + +517 +00:57:31,790 --> 00:57:35,730 +نقص الـ F of X node على H لما الـ H بدأ تذهب لـ 0 + +518 +00:57:35,730 --> 00:57:40,470 +بشرط ان الـ limit هذه معناها exist يبقى قولنا قبل + +519 +00:57:40,470 --> 00:57:46,750 +ذلك ان ميل المنحنة عنده نقطة هوبنقل المماث عند تلك + +520 +00:57:46,750 --> 00:57:52,170 +النقطة اظن هذا section 2 1 و نفس الرسم اياها + +521 +00:57:52,170 --> 00:57:56,140 +رسمناها و قلنا الكلمتين هدول بالضبط تماماإذا لم + +522 +00:57:56,140 --> 00:58:00,240 +نغير شيئا اتنين The tangent line to the curve + +523 +00:58:00,240 --> 00:58:06,560 +المماس للمنحنة عند النقطة اللي عندنا هذه هو عبارة + +524 +00:58:06,560 --> 00:58:13,600 +عن الخط الذي يمر بهذه النقطة وله نفس لسلوب M يعني + +525 +00:58:13,600 --> 00:58:18,880 +يقولنا ميل المنحنة عند نقطة يسوى ميل المماسعند تلك + +526 +00:58:18,880 --> 00:58:23,840 +النقطة هو معادلة المماس هي Y تستوي M في X نقص X + +527 +00:58:23,840 --> 00:58:27,940 +node زائد Y node X Y node وY node هو النقطة التي + +528 +00:58:27,940 --> 00:58:33,440 +يمر بها المماس يعني النقطة التماس و ال M هذه هو + +529 +00:58:33,440 --> 00:58:38,560 +ميل المنحنة أو ميل المماس للمنحنة عند النقطة بجانب + +530 +00:58:38,560 --> 00:58:43,630 +هذه كلها معلومات قديمة لم نأتي بحرف جديدالجديد هو + +531 +00:58:43,630 --> 00:58:47,210 +من الـ Definition الثاني الـ Definition التاني + +532 +00:58:47,210 --> 00:58:51,550 +بيقول الـ derivative of the function f مشتقة + +533 +00:58:51,550 --> 00:58:57,170 +الدالة f عند النقطة x0 denoted by يعني سنرمز لها + +534 +00:58:57,170 --> 00:59:03,980 +بالرمز أو التي سيرمز لها بالرمزf prime of x0 او f + +535 +00:59:03,980 --> 00:59:09,680 +dash of x0 او f شرطة of x0 اللي بدك ايه بس الدرجة + +536 +00:59:09,680 --> 00:59:16,180 +في لفنها هيكون f prime of x0 مين هو هو ال f prime + +537 +00:59:16,180 --> 00:59:20,900 +of x0 بده يساوي نفس ال limit اللي فوق ال limit لما + +538 +00:59:20,900 --> 00:59:25,900 +ال h بده تروح لل zero لل f of x0 زادتش على f of x0 + +539 +00:59:25,900 --> 00:59:30,610 +زاد ال h نقص f of x0 على hبشرط ان ال limit هذه + +540 +00:59:30,610 --> 00:59:37,730 +exist شيل ال h هذه تعالى على الرسم الان باجي بقول + +541 +00:59:37,730 --> 00:59:42,950 +لو ان المنحنة اللي عندنا هذا y تساوي f of x + +542 +00:59:42,950 --> 00:59:50,160 +المنحنة هذا هاه اللي هو y تساوي f of xروحت أخدت + +543 +00:59:50,160 --> 00:59:54,960 +نقطتين عليه زي النقطة اللي عندنا هذه النقطة هذه ال + +544 +00:59:54,960 --> 01:00:00,300 +result كانت المسافة هذه كلها x0 يبجي يحدث النقطة + +545 +01:00:00,300 --> 01:00:05,260 +هذه x0 صورة x0 هي f of x0 اللي هي المسافة اللي + +546 +01:00:05,260 --> 01:00:12,140 +عندنا هذه يعني هذه من هنا لهنا كمان جديش ل F of x0 + +547 +01:00:12,140 --> 01:00:17,920 +جد هذه بالضبط تماماطيب لو ال X node حصل فيها تغير + +548 +01:00:17,920 --> 01:00:24,080 +ما هذا التغير مقدره H وصلت إلى هذه النقطة يبقى + +549 +01:00:24,080 --> 01:00:28,440 +النقطة هذه اللي حدثت تبقى ال X node زائد ال H قلنا + +550 +01:00:28,440 --> 01:00:33,940 +ال X node زاد الشي بقى ال X حصل فيها تغير مقدر من + +551 +01:00:33,940 --> 01:00:40,360 +Hنتيجة لذلك ستكون القيمة التي عندنا هي F of X0 زي + +552 +01:00:40,360 --> 01:00:46,280 +H إذا إحداث النقطة اللي فوق هذه هه هي X0 زي الـH و + +553 +01:00:46,280 --> 01:00:53,490 +F of X0 زي الـH و سأسميها Qلو وصلت من ال P للي Q + +554 +01:00:53,490 --> 01:01:00,110 +مديت الخط هذا هذا مسمي قاطع للمنحنة يبقى هذا سمينا + +555 +01:01:00,110 --> 01:01:06,630 +قبل ذلك second تمام ابتدوا تذكروا قولنا متوسط + +556 +01:01:06,630 --> 01:01:12,190 +معدلي التغير لده اللي هو F of X node زي دلتش نقص + +557 +01:01:12,190 --> 01:01:15,510 +ال F of X node على اتش اللي كنا نقول هو عبارة عن + +558 +01:01:15,510 --> 01:01:20,960 +Delta Y على Delta Xلكن قلنا إذا Delta X قالت إلى + +559 +01:01:20,960 --> 01:01:26,780 +Zero بصير ال second هو مماس وقلنا لكوا يومها إذا + +560 +01:01:26,780 --> 01:01:32,080 +أجت لكيوب ده تسلم على P بنسبة العيد أجت نازلة ورا + +561 +01:01:32,080 --> 01:01:37,580 +مع المنحنةلما تجي الناس لكي ورايحة مع المنحنى على + +562 +01:01:37,580 --> 01:01:43,300 +النقطة P يبقى القاطع بيصير بالشكل اللي عندنا هذا + +563 +01:01:43,300 --> 01:01:53,100 +مماس للمنحنى عند هذه النقطة يبقى بيصير tangent عند + +564 +01:01:53,100 --> 01:01:58,420 +هذه النقطة يبقى الخط الأحمر هذا هو ال tangent + +565 +01:01:58,420 --> 01:02:04,740 +بيصبح للمنحنى عند هذه النقطةبينحصل عليه واجتاش لو + +566 +01:02:04,740 --> 01:02:10,180 +الـH هذه قالت إلى الـ0 يعني هذه الـQ لو وصلت لهنا + +567 +01:02:10,180 --> 01:02:16,200 +الـH زغرت جربت الـH تصغر جربت أكتر يبقى لما تكاد + +568 +01:02:16,200 --> 01:02:21,640 +الـQ تنطبق على الـP تكاد الـH تصبح كمبالـ zero او + +569 +01:02:21,640 --> 01:02:25,760 +تروح للـ zero ومن هنا روحنا قولنا ان ال limit ل ال + +570 +01:02:25,760 --> 01:02:29,360 +prefix node زاد ال H نقص ال prefix node على H لما + +571 +01:02:29,360 --> 01:02:34,460 +ال H بده يروح ل zero هو معناه المشتقة الأولى لدالك + +572 +01:02:34,460 --> 01:02:42,620 +طيب من هذا الكلام نخلص إلى ما يأتي حالة الأولىميل + +573 +01:02:42,620 --> 01:02:48,960 +المنحنى عند نقطة X node جداش يساوي يساوي ال limit + +574 +01:02:48,960 --> 01:02:55,560 +صح ولا لأ ثانى ميل المماس للمنحنى عند نقطة X node + +575 +01:02:55,560 --> 01:02:59,800 +جداش يساوي ميل المنحنى هو نفس القيمة اللي عندنا + +576 +01:02:59,800 --> 01:03:06,900 +تلاتة مش متوسط معدلة لأ معدلة تغير للدالة عند X + +577 +01:03:06,900 --> 01:03:14,430 +يساوي X node هو هذا مظبوطأربعة، ميل المماس لمنحنى + +578 +01:03:14,430 --> 01:03:19,610 +الظل الزاوية اللى بيعملها المماس مع الاتجاه الموجب + +579 +01:03:19,610 --> 01:03:26,070 +لمين؟ لمحور X خمسة، هذا معناه مين؟ المشتقة الأولى + +580 +01:03:26,070 --> 01:03:31,330 +لدالة لما أقول ميل المماس المحدد مقصوده ظل الزاوية + +581 +01:03:31,330 --> 01:03:35,310 +اللى يصنعها مع الاتجاه الموجب لمحور X أو حسب ما + +582 +01:03:35,310 --> 01:03:40,800 +كان عندنا هذا هو المشتقة الأولى، إذا بلخصكل ما يهم + +583 +01:03:40,800 --> 01:03:46,120 +هذه ال limit في ال remark التالية بنحطها في الأربع + +584 +01:03:46,120 --> 01:03:54,320 +نقاط التالية يبقى remark the + +585 +01:03:54,320 --> 01:03:54,880 +limit + +586 +01:03:58,710 --> 01:04:05,090 +اللي هي limit لما ال H بده تروح لل zero لل F of X + +587 +01:04:05,090 --> 01:04:12,310 +naught زائد ال H ناقص F of X naught على H means + +588 +01:04:12,310 --> 01:04:22,250 +ماذا تعني؟ تعني الشغل الأولى اللي هو the slope of + +589 +01:04:22,250 --> 01:04:34,280 +the curveميل المنحنى Y تساوي F of X at X يساوي X + +590 +01:04:34,280 --> 01:04:43,540 +non او المعنى الثاني The slope of the tangent to + +591 +01:04:43,540 --> 01:04:53,240 +the curveمن المماثل الملحنة y تساوي f of x at ال x + +592 +01:04:53,240 --> 01:05:02,540 +يساوي ال x naught او المعنى الثالث the rate of + +593 +01:05:02,540 --> 01:05:12,360 +exchange معدل التغير the rate of exchange of ال f + +594 +01:05:12,360 --> 01:05:14,780 +of x with + +595 +01:05:19,500 --> 01:05:29,840 +respect with respect to x at ال x يساوي ال x + +596 +01:05:29,840 --> 01:05:39,800 +naught او النقطة الرابعة ال derivative ال + +597 +01:05:39,800 --> 01:05:45,000 +derivative of ال f of x + +598 +01:05:58,010 --> 01:06:03,230 +يبقى هذول الأربعة شغلات كله نفس الشيء + +599 +01:06:25,230 --> 01:06:35,490 +أول مثال على هذا الموضوع example find + +600 +01:06:35,490 --> 01:06:44,890 +the slope of the function find نمرة a find the + +601 +01:06:44,890 --> 01:06:55,340 +slope of the functionf of x يساوي الجذر التربيع + +602 +01:06:55,340 --> 01:07:05,680 +إلى x زائد واحد at the point عند النقطة في تمانية + +603 +01:07:05,680 --> 01:07:13,240 +و تلاتة نمر أبيه find the equation of the tangent + +604 +01:07:13,240 --> 01:07:23,780 +find the equation ofthe tangent مواد المماثل + +605 +01:07:23,780 --> 01:07:31,820 +المنحنة line at T ثمانية و تلاتة + +606 +01:08:02,370 --> 01:08:08,890 +مرة تانية بقول نرجع ال remark تبعتنا ال limit اللي + +607 +01:08:08,890 --> 01:08:14,560 +عندنا هذا بتعطيني أربع شغلاتالشغل الأولى ال limit + +608 +01:08:14,560 --> 01:08:19,580 +هديشو معناها معناها ميل المنحنى عند النقطة x0 + +609 +01:08:19,580 --> 01:08:24,560 +المعنى الثاني ميل المماثل المنحنى عند النقطة x0 + +610 +01:08:24,560 --> 01:08:29,720 +المعنى الثالث معدل التغير للدالة f of x بالنسبة + +611 +01:08:29,720 --> 01:08:36,660 +للمتغير x عند ال x0 المعنى الرابع مشتقة الدالة f + +612 +01:08:36,660 --> 01:08:39,700 +of x عند ال x0 + +613 +01:08:48,250 --> 01:08:53,690 +الان نبدأ ناخد أمثلة تطبيقية عالميا على إيجاد + +614 +01:08:53,690 --> 01:08:59,440 +المشتقة لدالة عند نقطةبقول المثال هات لـ slope تبع + +615 +01:08:59,440 --> 01:09:06,420 +الدالة عند النقطة لـP8 و3 اتنين هات لمعادلة المماس + +616 +01:09:06,420 --> 01:09:12,340 +عند النقطة 8 و3 بنجي للنقطة الأولى بده اجيب ال + +617 +01:09:12,340 --> 01:09:15,200 +slope يبقى ال slope تبع ال curve + +618 +01:09:21,510 --> 01:09:27,850 +الـ male بده يساوي ال limit لما ال H بدها تروح لل + +619 +01:09:27,850 --> 01:09:34,550 +zero لمن؟ لل F of X0 زي .. كدهش ال X0 عندي هنا؟ + +620 +01:09:34,550 --> 01:09:38,670 +تمانية، بدل من أقول X0 بده أقول تمانية زي ال H + +621 +01:09:38,670 --> 01:09:44,850 +ناقص F of تمانية كله عالميا على H + +622 +01:09:47,450 --> 01:09:52,830 +هذا هو المطلوب الأول من المثلة يبقى يصير الميال + +623 +01:09:52,830 --> 01:09:58,570 +الـ Limit لما الـ H بده تروح لـ Zero إذا بدي أشيل + +624 +01:09:58,570 --> 01:10:05,470 +كل X و أحط مكانها تمانية زائد H هي الدالة فوق يبقى + +625 +01:10:05,470 --> 01:10:12,360 +هي الجدر التربية تمانية زائد Hزائد واحد ناقص F of + +626 +01:10:12,360 --> 01:10:17,840 +تمانية الجدرى التربية الى تمانية زائد واحد كله على + +627 +01:10:17,840 --> 01:10:23,480 +H يبقى هذا الكلام بده يساوي ال limit لما ال H بدها + +628 +01:10:23,480 --> 01:10:29,660 +تروح لمين؟ لل zero للجدرى التربية الى تسعة زائد ال + +629 +01:10:29,660 --> 01:10:36,220 +H ناقص تلاتة كله على مين؟ على H لو جاء تعوض تعويد + +630 +01:10:36,220 --> 01:10:43,130 +مباشر بطلع الناتجزيرو على زيرو شو نعمل في جدر نضرب + +631 +01:10:43,130 --> 01:10:48,970 +في مرافق البصد يبقى لو ضربنا في مرافق البصد بصير + +632 +01:10:48,970 --> 01:10:55,510 +تسعة زائد ال H زائد تلاتة كله مقسوما على تسعة زائد + +633 +01:10:55,510 --> 01:11:01,150 +ال H تحت الجدر زائد تلاتةيبقى النتيجة تساوي ال + +634 +01:11:01,150 --> 01:11:06,010 +limit لما ال H بدها تروح على zero ال bust هو الفرق + +635 +01:11:06,010 --> 01:11:11,950 +بين المربعين يبقى مربع القيمة الأولى ناقص مربع + +636 +01:11:11,950 --> 01:11:19,330 +القيمة التانية على H تسعة زائد ال H زائد التلاتة + +637 +01:11:19,330 --> 01:11:25,410 +بالشكل اللي عنهاتسعة مع تسعة بتروح بيظهر limit لما + +638 +01:11:25,410 --> 01:11:31,350 +ال H بده تروح لل zero لل H على H الجدر التربية + +639 +01:11:31,350 --> 01:11:37,270 +تسعة زائد ال H زائد تلاتة ال H مع ال H كذلك يبقى + +640 +01:11:37,270 --> 01:11:43,590 +بتصير limit لما ال H بده تروح لل zero لواحد تسعة + +641 +01:11:43,590 --> 01:11:50,630 +زائد H زائد تلاتةلما الـH بدأ تروح للـ0 بيظهر لنا + +642 +01:11:50,630 --> 01:11:59,750 +كدهش؟ واحد على جدر تسعة زائد تلاتة كدهش؟ سُدس يبقى + +643 +01:11:59,750 --> 01:12:09,630 +النتيجة بدأ تعطينا سُدس في هذه الحالة طيب يبقى + +644 +01:12:09,630 --> 01:12:14,130 +أصبح ال slope تبع ال curve يساوي السُدس طب هذا بده + +645 +01:12:14,130 --> 01:12:19,010 +يساوي ال slope تبع مين؟بالتانجين يبقى احنا خلصنا + +646 +01:12:19,010 --> 01:12:36,350 +المطلوب الأول وفي نفس الوقت هذا بده يساوي خلاصنا + +647 +01:12:36,350 --> 01:12:40,860 +المطلوب الأول بنجي لمطلوب التاني نمر بينمرة بي + +648 +01:12:40,860 --> 01:12:45,520 +قالتلي معادلة المماثل المنحنة مشان اجيب معادلة + +649 +01:12:45,520 --> 01:12:49,860 +المماثل يعني معادلة خط المستقيم بدي ميلو و نقطة + +650 +01:12:49,860 --> 01:12:54,780 +واقع عليه ميلو هي موجود و النقطة موجودة تهينة منه + +651 +01:12:54,780 --> 01:13:02,690 +يبقى باجي بقوله هنا the question ofthe tangent + +652 +01:13:02,690 --> 01:13:13,450 +يبقى معادلة المماس at P تمانية و تلاتة is Y يسوى + +653 +01:13:13,450 --> 01:13:20,250 +الميال في ال X ناقص ال X node زائد ال Y node يبقى + +654 +01:13:20,250 --> 01:13:28,350 +Y يسوى الميال هو سُدس في ال X ناقص تمانية زائد + +655 +01:13:28,350 --> 01:13:37,260 +تلاتةلو ضربنا كله في ستة بصير ستة Y يساوي X ناقص + +656 +01:13:37,260 --> 01:13:46,380 +تمانية زائد ثمانية عشر يبقى المعادلة ستة Y يساوي X + +657 +01:13:46,380 --> 01:13:53,120 +زائد عشرة ناقص تمانية زائد تمانتاش بصير زائد عشرة + +658 +01:13:53,120 --> 01:13:58,280 +يبقى هذه معادلة المماثل المنحنة المطلوبة + +659 +01:14:04,990 --> 01:14:14,890 +بنعطي كمان مثال example + +660 +01:14:14,890 --> 01:14:20,810 +2 بقول + +661 +01:14:20,810 --> 01:14:22,610 +find equations + +662 +01:14:27,050 --> 01:14:38,550 +of all lines معادل الخطوط المستقيمة having slope + +663 +01:14:38,550 --> 01:14:50,430 +الويل تبعها سالب واحد that are tangent that are + +664 +01:14:50,430 --> 01:14:54,970 +tangent to the curve + +665 +01:15:11,320 --> 01:15:19,240 +سؤال مرة تانيةهذا مقدار الميل ونشوف ايش اللي مش + +666 +01:15:19,240 --> 01:15:23,320 +موجود و ايش اللي مش موجود عشان نقدر نوجه و نجاوب + +667 +01:15:23,320 --> 01:15:27,640 +على السؤال سؤال مرة تانية بيقول لهذه معادلات + +668 +01:15:27,640 --> 01:15:32,680 +الخطوط المستقيمة اللي ميلها يساوي سالب واحدواللي + +669 +01:15:32,680 --> 01:15:37,840 +بتكون مماس للمنحنة يبقى أنا عندي منحنة وعندي مماس + +670 +01:15:37,840 --> 01:15:43,580 +لهذا المنحنة وعندي ميل المنحنة وقال لي بدي معادلة + +671 +01:15:43,580 --> 01:15:50,580 +المماس لهذا المنحنة المماس خط مستقيم بلزمني شغلتين + +672 +01:15:50,580 --> 01:15:56,020 +الميل ونقطة التماس ميعطينا نقطة التماس يبقى اتلك + +673 +01:15:56,020 --> 01:16:00,890 +الله يبقى دورك توجد نقطة التماسإن أوجدنا نقطة + +674 +01:16:00,890 --> 01:16:05,650 +التماس يبقى وربما يكون هناك أكتر من نقطة التماس + +675 +01:16:05,650 --> 01:16:10,430 +لأنه قال لي هاتلي كل المعادلات يعني احتمال يطلع + +676 +01:16:10,430 --> 01:16:14,670 +نقطتين، تلاتة، أربعة، الله أعلم، قد ما يطلع ما + +677 +01:16:14,670 --> 01:16:18,610 +يطلع ماعنديش مشكلةيبقى اول شغلة بدنا نروح نجيب + +678 +01:16:18,610 --> 01:16:24,210 +احداثيات هذه النقاط ماعنديش الا التعريف يبقى انا + +679 +01:16:24,210 --> 01:16:30,250 +عندي ال mail بده يساوي ال limit لما ال H بده تروح + +680 +01:16:30,250 --> 01:16:36,150 +لل zero F of X node زائد ال H ناقص F of X node على + +681 +01:16:36,150 --> 01:16:42,200 +Hالـ mail مُعطَى اللي هو جداش سالب واحد يبقى ال X + +682 +01:16:42,200 --> 01:16:46,840 +note ماعرفهاش يبقى بدي أشيل كل X و أحط مكانها X + +683 +01:16:46,840 --> 01:16:51,260 +note زايدة شوية بدي أخد ال limit بس يبقى بدي أكتب + +684 +01:16:51,260 --> 01:16:57,220 +ال limit في الأوليبقى هذه ال limit لما ال H بدها + +685 +01:16:57,220 --> 01:17:04,760 +تروح لل zero لواحد على X node زيد ال H ناقص واحد + +686 +01:17:04,760 --> 01:17:11,780 +ناقص صفر X node يبقى X node ناقص واحد كله على H + +687 +01:17:12,290 --> 01:17:17,610 +حطيت ال limit و عوضت فيها تعويضا مباشرة يبقى هذا + +688 +01:17:17,610 --> 01:17:23,090 +الكلام بده يساوي او سالب واحد بده يساوي limit لما + +689 +01:17:23,090 --> 01:17:27,390 +ال H بدها تروح ل zero هذا ال H اللي تحت مالهاش + +690 +01:17:27,390 --> 01:17:33,290 +دعوةبدا اوحد المقامات للباصلة يبقى بصير اندينامين + +691 +01:17:33,290 --> 01:17:40,950 +X node زي ال H ناقص واحد في X node ناقص واحد يبقى + +692 +01:17:40,950 --> 01:17:49,130 +X node ناقص واحد ناقص X node ناقص H زي واحد و ال + +693 +01:17:49,130 --> 01:17:54,720 +limit لهنقص X node وزايد X node ناقص واحد وزايد + +694 +01:17:54,720 --> 01:18:00,780 +واحد مع السلامة يبقى قالة النتيجة الى ال limit لما + +695 +01:18:00,780 --> 01:18:08,020 +ال H بده تروح ل zero لناقص H على H X node زايد ال + +696 +01:18:08,020 --> 01:18:14,120 +H ناقص واحد X node ناقص الواحد نختصر ال H مع ال H + +697 +01:18:14,120 --> 01:18:19,580 +كذلك لان المضربات في بعض ضرم يبقى هذا بده يسوي ال + +698 +01:18:19,580 --> 01:18:26,510 +limitلما ال H بدها تروح لل zero لسالب واحد على X + +699 +01:18:26,510 --> 01:18:35,380 +node زيدي ال H ناقص واحد في X node ناقص واحدهذا + +700 +01:18:35,380 --> 01:18:39,800 +بدي أعطيك مياتي الطرف الشمال سالب واحد الطرف اليمن + +701 +01:18:39,800 --> 01:18:46,680 +نحط HB0 يبقى لو حطين HB0 بيظل سالب واحد X node + +702 +01:18:46,680 --> 01:18:53,620 +ناقص واحد في ال X node ناقص واحد يعني مين؟ يعني + +703 +01:18:53,620 --> 01:19:01,720 +سالب واحد X node ناقص واحد الكل تربية يبقى معادلة + +704 +01:19:01,720 --> 01:19:07,340 +فيها مجهول واحد هو مين؟X0 يعني الاحداث الصيني + +705 +01:19:07,340 --> 01:19:12,540 +لنقطة التماسك بده حل المعادلة ده لو ضربنا في سالب + +706 +01:19:12,540 --> 01:19:19,120 +واحد بصير كلها مجمة شجلبنا بصير عند X0 ناقص واحد + +707 +01:19:19,120 --> 01:19:25,460 +لكل تربية يسوى كده؟ واحدبدي أخد الجذر التربيع إلى + +708 +01:19:25,460 --> 01:19:31,060 +الطرفين يبقى بيصير absolute value لل X node ناقص + +709 +01:19:31,060 --> 01:19:36,260 +واحد يساوي absolute value للواحد اللي هو بواحد، + +710 +01:19:36,260 --> 01:19:42,050 +بدي أتخلص من ال absolute valueيبقى ال X node ناقص + +711 +01:19:42,050 --> 01:19:47,890 +واحد يساوي زائد او ناقص واحد اذا هذه هتعطيني + +712 +01:19:47,890 --> 01:19:53,550 +معادلتين المعادلة الاولى X node ناقص واحد يساوي + +713 +01:19:53,550 --> 01:19:59,110 +واحد والمعادلة التانية X node ناقص واحد يساوي ناقص + +714 +01:19:59,110 --> 01:20:05,600 +واحد اذا هذول بدهم يعطوني ما يأتي ان ال X nodeيبدو + +715 +01:20:05,600 --> 01:20:13,720 +يساوي 2 والـ X0 يبدو يساوي كده؟ Zero طبعا يبدو ان + +716 +01:20:13,720 --> 01:20:19,720 +انا جبت الاحداث الصيني لنقطتي التماسك بناروح نجيب + +717 +01:20:19,720 --> 01:20:28,300 +الاحداث الصادم هذه لو كانت X0 ب2 يبقى ال Y تساوي + +718 +01:20:28,300 --> 01:20:36,970 +برجع لوين؟ لراس المثل اللي فوق او سميها Y0يبقى y + +719 +01:20:36,970 --> 01:20:43,630 +node تساوي يبقى واحد على x node اللي هو باتنين + +720 +01:20:43,630 --> 01:20:48,970 +ناقص واحد عوضنا في اللي فوق يبقى بتطلع جداش واحد + +721 +01:20:48,970 --> 01:20:56,430 +هذه بدأت يعطيلك ان y node بده يساوي واحد على zero + +722 +01:20:56,430 --> 01:21:03,620 +ناقص واحد ليه بيساوي جداش ناقص واحدبناء عليه جبنا + +723 +01:21:03,620 --> 01:21:21,260 +نقطتي التماس للمنحنة يبقى + +724 +01:21:21,260 --> 01:21:28,540 +باجي بقوله the points of tangency + +725 +01:21:31,770 --> 01:21:38,890 +نقاط التماس are النقطة الأولى اللى اتنين و واحد + +726 +01:21:38,890 --> 01:21:48,110 +and النقطة الثانية اللى هو zero سالف واحد zero و + +727 +01:21:48,110 --> 01:21:54,890 +سالف واحد تمام إذا بقدر أجيب معادلة كل مماس من هذه + +728 +01:21:54,890 --> 01:21:59,430 +المماسات the first tangent + +729 +01:22:01,040 --> 01:22:10,360 +is Y تساوي المقل اللي هو السالب واحد X ناقص اتنين + +730 +01:22:10,360 --> 01:22:17,940 +زائد واحد يعني هذا بدي اعطيك ان Y يساوي ناقص X + +731 +01:22:17,940 --> 01:22:23,680 +زائد تلاتة زائد اتنين وزائد واحد زائد تلاتة يبقى + +732 +01:22:23,680 --> 01:22:29,640 +هذا هو المماثل الأول ابنجي the second + +733 +01:22:31,190 --> 01:22:41,190 +Tangent is Y يساوي نفسي الميل ال X ناقص X ناقص + +734 +01:22:41,190 --> 01:22:48,690 +واحد يعني Y يساوي ناقص X ناقص واحد هذا هو المماث + +735 +01:22:48,690 --> 01:22:53,910 +الثاني قال لي هاتلك كل المماثات هي جبتله المماثات + +736 +01:22:53,910 --> 01:22:58,750 +طب السؤال اليكوا هل الخطين الأثنين هذول بيكونوا + +737 +01:22:58,750 --> 01:23:03,890 +متوازينبالتأكيد من نفس المكان تعالى نشوفه مع + +738 +01:23:03,890 --> 01:23:08,130 +الطبيعة ماقال ليش ارسم لكن انا بدأ ارسم حتى اتيقن + +739 +01:23:08,130 --> 01:23:14,070 +من شغل هذا صح ولا خطأ بقوله بسيطة هذا المنحدر اللي + +740 +01:23:14,070 --> 01:23:20,150 +عندك هذا محور X هذا محور Y وهذا الـ Zero هذه + +741 +01:23:20,150 --> 01:23:26,990 +الدالة هي رسمة واحد على X بس معمولة لـ Shift وين؟ + +742 +01:23:26,990 --> 01:23:35,250 +شمال، يمين، فوق، تحتيمين بمقدار نطرح للواحد من + +743 +01:23:35,250 --> 01:23:40,630 +المتغير وليس من الدالة يبقى بدي أعمل ال shift هذا + +744 +01:23:40,630 --> 01:23:46,550 +له بمقدار واحد على اليمين يبقى هذا من هذا له من + +745 +01:23:46,550 --> 01:23:54,070 +واحد إذا الدالة هي هيكهو هذا الدالة التالية بالشكل + +746 +01:23:54,070 --> 01:24:01,510 +اللي عندنا رسمة المنحنى Y تسوى واحد على X تمام عند + +747 +01:24:01,510 --> 01:24:06,950 +ال zero عند ال zero قيمة الدالة اللي هو بسالب واحد + +748 +01:24:06,950 --> 01:24:13,990 +اليمين النقطة اللي عندنا هذه وعند اتنين يبقى اتنين + +749 +01:24:14,310 --> 01:24:20,010 +الدالة في قد ياشقليب واحد يبقى هذه اتنين واحد وهذه + +750 +01:24:20,010 --> 01:24:25,670 +عبارة عن زيرو وسالب واحد إذا لو رسمت المماثات + +751 +01:24:25,670 --> 01:24:31,110 +لاتنين هيصير المماث الأول الشكل اللي عنها داج + +752 +01:24:32,070 --> 01:24:37,130 +والمماث الثاني بنفس النتيجة بالشكل اللي عندنا هذا + +753 +01:24:37,130 --> 01:24:42,790 +يبقى ايه المماثات الاتنين اللي هو الاولاني تبع + +754 +01:24:42,790 --> 01:24:51,070 +النقطة 2 1 هذا Y تساوي ناقص X زائد 3 وهذا Y يساوي + +755 +01:24:51,070 --> 01:24:58,460 +ناقص X ناقص 1يعني هذا اللي هو Y تساوي سالب X + +756 +01:24:58,460 --> 01:25:03,940 +رفعناه مقدار تلاتة هذا نزلناه مقدار واحد وزم انت + +757 +01:25:03,940 --> 01:25:10,000 +شايف الممثلة اتنين ارتبالت مجرد معلومة زيادة ليس + +758 +01:25:10,000 --> 01:25:17,740 +الالحد هنا انت هنا من الجزء النظري تبع هذا ال + +759 +01:25:17,740 --> 01:25:24,560 +section لكراه حطلنا معلومة في التمرين وحط عليها + +760 +01:25:24,560 --> 01:25:31,560 +أسئلة بدنا نشوف ما هي هذه المعلومة وما نوعية هذه + +761 +01:25:31,560 --> 01:25:38,580 +المثلة المعلومة هذه بقولي قد يكون المماس رأسيا + +762 +01:25:38,580 --> 01:25:44,680 +vertical tangentيبقى بإني أعطيله تعريف ونشوف كيف + +763 +01:25:44,680 --> 01:25:53,360 +بإني أحسب الشغلة هذه يبقى definition the + +764 +01:25:53,360 --> 01:25:58,280 +curve المنحنة + +765 +01:25:58,280 --> 01:26:09,540 +y تساوي f of x has a vertical tangent + +766 +01:26:13,640 --> 01:26:28,380 +مماس رأسي X يساوي X node at the point X + +767 +01:26:28,380 --> 01:26:36,260 +node F إذا كان Limit لما الـ H بدأ تروح للـ Zero + +768 +01:26:36,260 --> 01:26:42,120 +للـ F of X node زائد الـ Hنقص نقص نقص نقص نقص نقص + +769 +01:26:42,120 --> 01:26:42,520 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +770 +01:26:42,520 --> 01:26:48,980 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +771 +01:26:48,980 --> 01:26:50,120 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +772 +01:26:50,120 --> 01:26:51,440 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +773 +01:26:51,440 --> 01:26:56,480 +نقص نقص نقص + +774 +01:26:56,480 --> 01:27:03,200 +نقص نقص نقص نقص نقص + +775 +01:27:03,200 --> 01:27:09,620 +نق + +776 +01:27:09,830 --> 01:27:20,730 +f of x يسوى الـ x ناقص واحد قص تلت وبسأل is the + +777 +01:27:20,730 --> 01:27:32,490 +function has a vertical tangent + +778 +01:27:32,490 --> 01:27:42,150 +هل لها vertical tangent atX يساوي واحد ام لا + +779 +01:28:10,920 --> 01:28:14,000 +المعلومة هذه راح حطها في التمرين و ليس في الجزء + +780 +01:28:14,000 --> 01:28:17,580 +النظري تبع ال section حطها في التمرين و حط عليها + +781 +01:28:17,580 --> 01:28:24,020 +مجموعة من الأسلة بيقول المنحنى y تساوي f of x has + +782 +01:28:24,020 --> 01:28:29,800 +a vertical tangent مش vertical asymptote تتفرج بين + +783 +01:28:29,800 --> 01:28:33,170 +ال asymptote و من ال tangentللـ asymptote بيجي + +784 +01:28:33,170 --> 01:28:35,770 +ناخد ال limit، من اليمين هو ال limit، من الشمال + +785 +01:28:35,770 --> 01:28:41,730 +بيطلع اليمين infinity أو سالب infinity، مظبوط، + +786 +01:28:41,730 --> 01:28:46,970 +بقول يبقى في عندي vertical asymptoteهنا vertical + +787 +01:28:46,970 --> 01:28:50,170 +tangent بيقول اللي بتروح تاخد ال limit لل focus + +788 +01:28:50,170 --> 01:28:54,270 +node بداية ال H نقص ال focus node على H لما ال H + +789 +01:28:54,270 --> 01:29:00,570 +بتروح ل 0 بد النتج يطلع infinity او سالب infinity + +790 +01:29:00,570 --> 01:29:04,700 +ان حد هدى او هدى مش الاتنين في انواع Rبتعني + +791 +01:29:04,700 --> 01:29:09,880 +النتيجة infinity او سالب infinity ان حدث ذلك يبقى + +792 +01:29:09,880 --> 01:29:14,480 +النقطة x0 اللي عندك x يساوي x0 تبقى vertical + +793 +01:29:14,480 --> 01:29:20,900 +tangent يبقى مماس للمنحنة عند x0 مثال جالي ارسملي + +794 +01:29:20,900 --> 01:29:26,420 +منحنة ده لهذه وبيسأل هل هذه لها vertical tangent + +795 +01:29:26,420 --> 01:29:31,660 +ام لابقوله بسيطة جدا، احنا هذه لو جينا رسمناها، + +796 +01:29:31,660 --> 01:29:37,640 +هذا المنحنة اللي عندنا، هذا المنحنة X وهذا Y وهذا + +797 +01:29:37,640 --> 01:29:48,110 +Zero، أصلا المنحنة X بيجيني في هذا الشكلY يساوي X + +798 +01:29:48,110 --> 01:29:54,310 +أس تلت ناقص واحد روح نعمله shift جهة اليمين بمقدار + +799 +01:29:54,310 --> 01:30:00,370 +كده؟ بمقدار واحد يبقى لو جينا هنا قولنا أي واحد + +800 +01:30:00,370 --> 01:30:06,650 +وتخيلنا هذا الخط الموازي لمحور Y و جينا رسمنا + +801 +01:30:06,650 --> 01:30:11,770 +المنحنة يبقى المنحنة هيجين هيك بالشكل اللي عندنا + +802 +01:30:11,770 --> 01:30:12,130 +هذا + +803 +01:30:15,830 --> 01:30:23,070 +يبقى هذا المنحنى y يساوي x ناقص واحد أسطول رسمنا + +804 +01:30:23,070 --> 01:30:28,150 +رسمنا قال لي بعدك هل هذا المنحنى له vertical + +805 +01:30:28,150 --> 01:30:33,550 +tangent عند x يساوي واحد يعني x node عندى بقدرش + +806 +01:30:33,550 --> 01:30:41,200 +اللي هو تساوي واحدأذا بدأ احسب لهذا الـ Limit لما + +807 +01:30:41,200 --> 01:30:48,640 +الـ H بدأ تذهب لـ 0 للـ F of 1 زائد الـ H نقص الـ + +808 +01:30:48,640 --> 01:30:54,230 +F of 1 على Hونشوف شو اللي بدى يحصل هذا الكلام + +809 +01:30:54,230 --> 01:31:00,090 +يساوي الدلال يبقى اشيل كل X وحط مكانها واحد زيد H + +810 +01:31:00,090 --> 01:31:06,430 +يبقى هاي limit لما ال H بدها تروح لل zero لمن؟ + +811 +01:31:06,430 --> 01:31:12,750 +للواحد زيد ال H ناقص واحد أس تلت ناقص واحد ناقص + +812 +01:31:12,750 --> 01:31:19,660 +واحد أس تلت كله على H طبعا هذا بقدرشبزيرو هذا بده + +813 +01:31:19,660 --> 01:31:25,200 +يصير اللي هو ال limit لما ال H بده تروح لوين لزيرو + +814 +01:31:25,200 --> 01:31:34,200 +هذا كمان سالب واحد مع واحد بيضل H أس تلت على H + +815 +01:31:34,200 --> 01:31:42,680 +كمان يعني قداش limit لما ال H بده تروح لزيرو لواحد + +816 +01:31:42,680 --> 01:31:45,520 +على H أس تلتين + +817 +01:31:47,590 --> 01:31:52,710 +هل هي دالة معرفة عند H يساوي Zero لأ يبقى يضطر + +818 +01:31:52,710 --> 01:31:57,130 +ياخد ال limit من اليمين و من الشمال يبقى هاي ال + +819 +01:31:57,130 --> 01:32:02,710 +limit لما ال H بده تروح ل Zero من جهة الشمال لواحد + +820 +01:32:02,710 --> 01:32:09,670 +على H تربيه أس تلت مش هيكوا أس تلتينطيب يبقى هذا + +821 +01:32:09,670 --> 01:32:15,350 +الكلام بده يصير واحد على zero من جهة الشمال يبقى H + +822 +01:32:15,350 --> 01:32:21,390 +سالي بقى يبقى very small negative لكل تربيع يبقى + +823 +01:32:21,390 --> 01:32:30,320 +very small negative quantityتربيع كل أسطل يعني + +824 +01:32:30,320 --> 01:32:39,040 +بيصير واحد very small positive quantity أسطل يعني + +825 +01:32:39,040 --> 01:32:47,050 +قداش infinityبالمثل بتروح اخد limit لما ال H بده + +826 +01:32:47,050 --> 01:32:55,590 +تروح ل 0 من جهة اليمين ل 1 على H أس تلتين يعني + +827 +01:32:55,590 --> 01:33:02,110 +limit لما ال H بده تروح ل 0 من جهة اليمين ل 1 very + +828 +01:33:02,110 --> 01:33:04,590 +small positive + +829 +01:33:07,900 --> 01:33:15,060 +هذه موجة دائما و أبدا يبقى dash infinity يبقى ساق + +830 +01:33:15,060 --> 01:33:20,760 +limit لما ال H بدأ تروح ل zero من جهات اليمين واحد + +831 +01:33:20,760 --> 01:33:28,550 +على H أس تلتين يسوى كده؟أظن حسب التعريف يكون X + +832 +01:33:28,550 --> 01:33:33,770 +يساوي واحد هو عبارة عن mean vertical tangent + +833 +01:33:48,000 --> 01:34:03,980 +للمنحنة y يساوي x ناقص واحد كله أس تلت تمام + +834 +01:34:05,550 --> 01:34:09,290 +يبقى طلعلي في الخط على دي اللي احنا رسمينه يعني + +835 +01:34:09,290 --> 01:34:15,110 +الخط المنقط هداشي اعتبر مماس و قاطع في نفس الوقت + +836 +01:34:15,110 --> 01:34:21,170 +من فوق هنا يمسي الجزء العلوي من المنحنة و من تحت + +837 +01:34:21,170 --> 01:34:26,590 +يمسي السفلي منحنة يبقى هو المماس لمين؟ للمنحنة + +838 +01:34:26,590 --> 01:34:33,530 +اللي عندنا آخر مثال في محاضرة اليوم بيقول ما يأتي + +839 +01:34:33,530 --> 01:34:34,850 +example + +840 +01:34:41,170 --> 01:34:51,990 +لت ال f of x يسوى أحد أمرين x sine واحد على x لما + +841 +01:34:51,990 --> 01:34:57,410 +ال x لا تساوي ال zero هو ال zero لما ال x بده + +842 +01:34:57,410 --> 01:35:03,770 +يساوي ال zero السؤال هو النقطة الأولى show that + +843 +01:35:05,490 --> 01:35:19,510 +بايل لي ان ال F is continuous at X يساوي Zero نقطة + +844 +01:35:19,510 --> 01:35:20,390 +ثانية + +845 +01:35:23,060 --> 01:35:33,800 +Does the graph of F have + +846 +01:35:33,800 --> 01:35:42,340 +a vertical tangent + +847 +01:35:42,340 --> 01:35:55,650 +at X يساوي Zero أم لا؟سمعت كإنه حد بدى يسأل هنا شو + +848 +01:35:55,650 --> 01:36:06,710 +تاريف التاني؟ وإيش + +849 +01:36:06,710 --> 01:36:12,410 +افرجت يعني؟ هو لأبسط و لا هاي اتنين نفس الشيء هتجي + +850 +01:36:12,410 --> 01:36:18,780 +معه تطرح نفس المعلومةعلى اي حال بيعطيني كمان سؤال + +851 +01:36:18,780 --> 01:36:24,040 +بيقول افترض ان f of x مجزة الى جزئين الجزء الاول x + +852 +01:36:24,040 --> 01:36:27,800 +صين واحد على x الجزء التاني zero لما x يساوي zero + +853 +01:36:27,800 --> 01:36:32,520 +لما x يساوي zero لا يساوي zero طلب مطلوبين هل + +854 +01:36:32,520 --> 01:36:37,060 +الدالة متصلة عند ال zero ولا لا اتنين هل الها + +855 +01:36:37,060 --> 01:36:42,580 +vertical tangent ولا لا طبعا شباب لو ماكنتش متصلة + +856 +01:36:42,580 --> 01:36:48,180 +عند ال zeroبروح بدور على ال vertical tangent لأ + +857 +01:36:48,180 --> 01:36:52,380 +لإن خلاص الدالة مش معرفة عنده كي بده يحصل تماث + +858 +01:36:52,380 --> 01:36:58,120 +يعني لا توجد نقطة على المنحنة إذا السؤال الأول أو + +859 +01:36:58,120 --> 01:37:04,930 +المطلوب الأول كتبه متعمديعني مشان تعرف ان الدالة + +860 +01:37:04,930 --> 01:37:11,350 +عند X يساوي Zero هي دالة متاصلة و ده متاصلة يمكن + +861 +01:37:11,350 --> 01:37:16,870 +يكون في مماس عندها و يمكن يكون مافيش مماس تعالى + +862 +01:37:16,870 --> 01:37:24,710 +نشوف المطلوب الأول ابقى solution ايش + +863 +01:37:24,710 --> 01:37:26,830 +تعريف ال continuity عند نقطة + +864 +01:37:31,910 --> 01:37:37,810 +بدي يكون نهاية الدالة عند تلك النقطة يساوي قيمة + +865 +01:37:37,810 --> 01:37:42,910 +الدالة مش هيك الاتصال تمام اذا بدنا نروح نشوف ال F + +866 +01:37:42,910 --> 01:37:48,870 +of Zero عندنا ال F of Zero بدي يساوي Zero معطاها + +867 +01:37:48,870 --> 01:37:57,830 +هيا جاهزة طب ال limitلل F of X لما ال X بدي روح لل + +868 +01:37:57,830 --> 01:38:03,830 +Zero يبقى limit لما ال X بدي روح لل Zero لل X Sine + +869 +01:38:03,830 --> 01:38:11,250 +واحد على X كام مرة حلينا السؤال هذا؟مرة مرة مرة + +870 +01:38:11,250 --> 01:38:17,470 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +871 +01:38:17,470 --> 01:38:18,410 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +872 +01:38:18,410 --> 01:38:18,630 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +873 +01:38:18,630 --> 01:38:18,910 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +874 +01:38:18,910 --> 01:38:19,050 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +875 +01:38:19,050 --> 01:38:19,090 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +876 +01:38:19,090 --> 01:38:24,530 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +877 +01:38:24,530 --> 01:38:31,850 +مرةExample مثال سبع يبقى حل هنا بدل المرة مرتين + +878 +01:38:31,850 --> 01:38:39,130 +مدام ال limit ساوة قيمة الدالة يبقى ساعة ال F of + +879 +01:38:39,130 --> 01:38:51,490 +Zero يساوي limit لصين X في صين X limitلما ال X بده + +880 +01:38:51,490 --> 01:38:59,270 +تروح لل Zero لل X في Sin واحد على X هذا بده يعطينا + +881 +01:38:59,270 --> 01:39:08,650 +ان ال F is continuous at X يساوي Zero هذا كل الشغل + +882 +01:39:08,650 --> 01:39:15,430 +اشتغلناه اللي هو المطلوب الأول من المسألة نجي + +883 +01:39:15,430 --> 01:39:16,850 +للمطلوب الثاني + +884 +01:39:19,660 --> 01:39:24,280 +المطموب التاني بيقول لي هل هذه لها vertical + +885 +01:39:24,280 --> 01:39:30,640 +tangent عند ال zero ولا لا بنقول له الله أعلم يبقى + +886 +01:39:30,640 --> 01:39:36,380 +احنا بدنا نروح ناخد main limit لما ال H بدها تروح + +887 +01:39:36,380 --> 01:39:43,700 +لل zero لل F of zero زائد ال H ناقص ال F of zero + +888 +01:39:43,700 --> 01:39:50,830 +على Hمظهر ونشوف هل هذه ال limit تساوي infinity و + +889 +01:39:50,830 --> 01:39:56,070 +الله سالب infinity و الله غير ذلك يبقى هذا limit + +890 +01:39:56,070 --> 01:40:01,790 +لما ال H بدها تروح ل zero برجع لمين؟للـ function + +891 +01:40:01,790 --> 01:40:06,850 +اللي عندنا ال F of Zero زائد H يبقى بده أشيل كل X + +892 +01:40:06,850 --> 01:40:15,010 +و أحط مكانها Zero زائد H يبقى هنا Zero زائد ال H + +893 +01:40:15,010 --> 01:40:22,850 +Sin واحد على Zero زائد ال H ناقص F of Zero اللي هو + +894 +01:40:22,850 --> 01:40:30,600 +بده أشبـ 0 كله على H يبقى النتيجة صارت limit لما + +895 +01:40:30,600 --> 01:40:37,780 +الـ H بده تروح للـ 0 للـ H sin 1 على H كله على H + +896 +01:40:37,780 --> 01:40:45,340 +يبقى limit لما الـ H بده تروح للـ 0 لـ sin 1 على H + +897 +01:40:45,340 --> 01:40:50,640 +فقط لغاية الـ H هذه ستختصر مع ميهم مع الـ H اللي + +898 +01:40:50,640 --> 01:40:58,120 +عندنا هذه 1 على 0infinity مظبوط sign ال infinity + +899 +01:40:58,120 --> 01:41:05,560 +الله أعلم ماعرفهاش يبقى does not exist يبقى هذه + +900 +01:41:05,560 --> 01:41:16,160 +does not exist ماعرفهاش مش موجودة بناء عليه هل في + +901 +01:41:16,160 --> 01:41:20,800 +عندي vertical tangent لأ اشتراطنا لازم يعطيني اما + +902 +01:41:20,800 --> 01:41:24,460 +infinityهذا لا يمكنني أن أقول infinity ولا يمكنني + +903 +01:41:24,460 --> 01:41:31,520 +أن أقول سالب infinity يبقى باجي بقول له ف ال F has + +904 +01:41:31,520 --> 01:41:46,410 +no vertical tangent at X يساوي Zالان وصلنا الى + +905 +01:41:46,410 --> 01:41:52,950 +أرقام المسائل ل section تلاتة واحد يبقى exercises + +906 +01:41:52,950 --> 01:42:02,950 +تلاتة واحد المسائل التالية من واحد لخمسة وعشرين + +907 +01:42:02,950 --> 01:42:06,070 +القدر + +908 +01:42:06,070 --> 01:42:12,170 +وخمسة وتلاتين وستة وتلاتين + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aMhkzOkTdWU_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aMhkzOkTdWU_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..74aeeecd6edefea4e2388da5d4450c2abb3c2e5e --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aMhkzOkTdWU_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 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46.19, "word": " يبقى", "probability": 0.915283203125}, {"start": 46.19, "end": 46.41, "word": " فيه", "probability": 0.855224609375}, {"start": 46.41, "end": 46.65, "word": " ان", "probability": 0.64501953125}, {"start": 46.65, "end": 47.67, "word": " horizontal", "probability": 0.63720703125}, {"start": 47.67, "end": 48.29, "word": " asymptote", "probability": 0.844482421875}, {"start": 48.29, "end": 48.55, "word": " Y", "probability": 0.61669921875}, {"start": 48.55, "end": 49.05, "word": " تساوي", "probability": 0.9627685546875}, {"start": 49.05, "end": 49.31, "word": " هذا", "probability": 0.9697265625}, {"start": 49.31, "end": 49.83, "word": " الرقم", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 2, "seek": 7683, "start": 50.03, "end": 76.83, "text": "يبقى بيكون هو ال horizontal asymptote سواء كان هذا الرقم zero أو كمية موجبة أو كمية سالبة لكن إن كان طلع الناتج infinity أو سالب infinity يبقى بنقول هنا the horizontal line أو the horizontal asymptote does not exist 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"probability": 0.88037109375}, {"start": 90.5, "end": 91.38, "word": " لازمالي", "probability": 0.8767578125}, {"start": 91.38, "end": 91.56, "word": " لل", "probability": 0.96142578125}, {"start": 91.56, "end": 92.04, "word": " vertical", "probability": 0.68017578125}, {"start": 92.04, "end": 92.8, "word": " asymptote", "probability": 0.81884765625}, {"start": 92.8, "end": 93.54, "word": " فبدنا", "probability": 0.89306640625}, {"start": 93.54, "end": 94.1, "word": " نتعرض", "probability": 0.9881591796875}, {"start": 94.1, "end": 94.78, "word": " للآن", "probability": 0.51416015625}, {"start": 94.78, "end": 95.32, "word": " اللي", "probability": 0.97998046875}, {"start": 95.32, "end": 95.48, "word": " هو", "probability": 0.98291015625}, {"start": 95.48, "end": 95.68, "word": " ال", "probability": 0.74755859375}, {"start": 95.68, "end": 96.28, "word": " infinite", "probability": 0.79052734375}, {"start": 96.28, "end": 97.46, "word": " limits", "probability": 0.8212890625}, {"start": 97.46, "end": 98.38, "word": " يعني", "probability": 0.919189453125}, {"start": 98.38, "end": 99.88, "word": " ال", "probability": 0.86279296875}, {"start": 99.88, "end": 100.3, "word": " limit", "probability": 0.91162109375}, {"start": 100.3, "end": 100.72, "word": " إذا", "probability": 0.965087890625}, {"start": 100.72, "end": 101.2, "word": " كانت", "probability": 0.990234375}, {"start": 101.2, "end": 101.94, "word": " النتيجة", "probability": 0.9625244140625}, {"start": 101.94, "end": 102.8, "word": " infinite", "probability": 0.90283203125}, {"start": 102.8, "end": 104.04, "word": " لمين", "probability": 0.6829833984375}, {"start": 104.04, "end": 105.16, "word": " لدالة", "probability": 0.9569091796875}, {"start": 105.16, "end": 105.72, "word": " ما", "probability": 0.89013671875}], "temperature": 1.0}, {"id": 4, "seek": 12189, "start": 106.29, "end": 121.89, "text": "يقول السؤال find the following limits if it exists يوجهها للنهايات التالية إن وجدت ما وجدتش خلاص مسمحينك فبدي بقول limit ال X بده تروح للاتنين لل function واحد على X minus two", "tokens": [1829, 39648, 21136, 33604, 6027, 915, 264, 3480, 10406, 498, 309, 8198, 7251, 29245, 3224, 11296, 24976, 1863, 11296, 1829, 9307, 16712, 6027, 10632, 36145, 49610, 3215, 2655, 19446, 49610, 3215, 2655, 8592, 16490, 1211, 33546, 3714, 38251, 5016, 9957, 4117, 6156, 3555, 16254, 4724, 39648, 4948, 2423, 1783, 47525, 3224, 6055, 32887, 5016, 24976, 9307, 1863, 9957, 24976, 2445, 36764, 24401, 15844, 1783, 3175, 732], "avg_logprob": -0.3365205170503303, "compression_ratio": 1.398936170212766, "no_speech_prob": 0.0, "words": [{"start": 106.29, "end": 106.69, "word": "يقول", "probability": 0.272064208984375}, {"start": 106.69, "end": 107.15, "word": " السؤال", "probability": 0.7311604817708334}, {"start": 107.15, "end": 107.43, "word": " find", "probability": 0.2374267578125}, {"start": 107.43, "end": 107.61, "word": " the", "probability": 0.8828125}, {"start": 107.61, "end": 107.91, "word": " following", 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409.17, "end": 409.77, "word": " يبقى", "probability": 0.93994140625}, {"start": 409.77, "end": 410.15, "word": " قولنا", "probability": 0.6417236328125}, {"start": 410.15, "end": 410.49, "word": " does", "probability": 0.48046875}, {"start": 410.49, "end": 411.01, "word": " not", "probability": 0.97314453125}, {"start": 411.01, "end": 412.13, "word": " exist،", "probability": 0.76123046875}, {"start": 412.13, "end": 412.37, "word": " هنا", "probability": 0.230224609375}, {"start": 412.37, "end": 412.85, "word": " اليمين", "probability": 0.8248697916666666}, {"start": 412.85, "end": 413.31, "word": " ساوة", "probability": 0.7264404296875}, {"start": 413.31, "end": 413.87, "word": " الشمال", "probability": 0.9890950520833334}], "temperature": 1.0}, {"id": 18, "seek": 43572, "start": 414.06, "end": 435.72, "text": "لكن النتيجة كانت infinity يبقى بقول ال limit تسوى من infinity لاحظوا بالنسبة لهذا السؤال رسمناه قبل ذلك وقلنا لو كان هذا محور X وهذا محور Y يبقى هذا ال function اللي انا رسمت من Y تسوى واحد ع الاكس اربعة وهي Zero", "tokens": [1211, 19452, 28239, 31371, 7435, 3660, 25961, 2655, 13202, 7251, 3555, 4587, 7578, 4724, 39648, 2423, 4948, 6055, 3794, 2407, 7578, 9154, 13202, 20193, 5016, 19913, 14407, 20666, 1863, 35457, 3660, 46740, 15730, 21136, 33604, 6027, 12602, 38251, 8315, 3224, 12174, 36150, 29910, 23275, 4032, 4587, 1211, 8315, 45164, 25961, 23758, 3714, 5016, 13063, 1783, 37037, 15730, 3714, 5016, 13063, 398, 7251, 3555, 4587, 7578, 23758, 2423, 2445, 13672, 1829, 1975, 8315, 12602, 38251, 2655, 9154, 398, 6055, 3794, 2407, 7578, 36764, 24401, 6225, 42963, 4117, 3794, 1975, 25513, 27884, 37037, 1829, 17182], "avg_logprob": -0.2779255322319396, "compression_ratio": 1.73, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 414.06, "end": 414.64, "word": "لكن", "probability": 0.65087890625}, {"start": 414.64, "end": 415.3, "word": " النتيجة", "probability": 0.9591064453125}, {"start": 415.3, "end": 415.78, "word": " كانت", "probability": 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479.13, "text": "لما ال X بدها تروح إلى تلاتة لمين لسالي باتنين على X ناقص تلاتة لكل ربيع", "tokens": [1211, 15042, 2423, 1783, 47525, 11296, 6055, 32887, 5016, 30731, 6055, 1211, 9307, 3660, 32767, 9957, 5296, 3794, 6027, 1829, 4724, 9307, 1863, 9957, 15844, 1783, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 5296, 28820, 12602, 3555, 40228], "avg_logprob": -0.25703126192092896, "compression_ratio": 1.3655913978494623, "no_speech_prob": 0.0, "words": [{"start": 467.13, "end": 467.71, "word": "لما", "probability": 0.52203369140625}, {"start": 467.71, "end": 467.91, "word": " ال", "probability": 0.603515625}, {"start": 467.91, "end": 468.41, "word": " X", "probability": 0.400634765625}, {"start": 468.41, "end": 469.39, "word": " بدها", "probability": 0.94580078125}, {"start": 469.39, "end": 470.09, "word": " تروح", "probability": 0.9122721354166666}, {"start": 470.09, "end": 470.55, "word": " إلى", "probability": 0.7109375}, {"start": 470.55, "end": 471.63, "word": " تلاتة", 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{"start": 643.5, "end": 643.78, "word": " في", "probability": 0.97216796875}, {"start": 643.78, "end": 644.12, "word": " هذا", "probability": 0.97802734375}, {"start": 644.12, "end": 644.3, "word": " ال", "probability": 0.94921875}, {"start": 644.3, "end": 644.74, "word": " section", "probability": 0.85888671875}, {"start": 644.74, "end": 645.88, "word": " اللي", "probability": 0.92529296875}, {"start": 645.88, "end": 646.06, "word": " هي", "probability": 0.9130859375}, {"start": 646.06, "end": 646.62, "word": " رقم", "probability": 0.8898111979166666}, {"start": 646.62, "end": 647.36, "word": " أربعة", "probability": 0.74951171875}, {"start": 647.36, "end": 648.16, "word": " ال", "probability": 0.94970703125}, {"start": 648.16, "end": 649.16, "word": " vertical", "probability": 0.85205078125}, {"start": 649.16, "end": 651.84, "word": " asymptotes", "probability": 0.913330078125}], "temperature": 1.0}, {"id": 28, "seek": 68087, "start": 656.55, "end": 680.87, "text": "definition a line x يساوي a is a vertical asymptote خط قارب رأسي of the graph of", "tokens": [1479, 5194, 849, 257, 1622, 2031, 7251, 3794, 995, 45865, 257, 307, 257, 9429, 35114, 1370, 16490, 9566, 12174, 9640, 3555, 12602, 10721, 3794, 1829, 295, 264, 4295, 295], "avg_logprob": -0.19726562301317851, "compression_ratio": 0.9895833333333334, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 656.5500000000001, "end": 657.95, "word": "definition", "probability": 0.7006022135416666}, {"start": 657.95, "end": 659.35, "word": " a", "probability": 0.53125}, {"start": 659.35, "end": 660.09, "word": " line", "probability": 0.96240234375}, {"start": 660.09, "end": 661.71, "word": " x", "probability": 0.6484375}, {"start": 661.71, "end": 662.65, "word": " يساوي", "probability": 0.8216552734375}, {"start": 662.65, "end": 663.35, "word": " a", "probability": 0.849609375}, {"start": 663.35, "end": 665.07, "word": " is", "probability": 0.86376953125}, {"start": 665.07, "end": 666.79, "word": " a", "probability": 0.974609375}, {"start": 666.79, "end": 668.33, "word": " vertical", "probability": 0.90576171875}, {"start": 668.33, "end": 672.07, "word": " asymptote", "probability": 0.9453125}, {"start": 672.07, "end": 673.03, "word": " خط", "probability": 0.6414794921875}, {"start": 673.03, "end": 673.71, "word": " قارب", "probability": 0.88330078125}, {"start": 673.71, "end": 675.45, "word": " رأسي", "probability": 0.988525390625}, {"start": 675.45, "end": 676.17, "word": " of", "probability": 0.96923828125}, {"start": 676.17, "end": 677.73, "word": " the", "probability": 0.8935546875}, {"start": 677.73, "end": 678.59, "word": " graph", "probability": 0.9638671875}, {"start": 678.59, "end": 680.87, "word": " of", "probability": 0.98193359375}], "temperature": 1.0}, {"id": 29, "seek": 70312, "start": 681.82, "end": 703.12, "text": "the function لدالة y تساوي f of x if either اما limit لل f of x لما ال x بدها تروح لل a", "tokens": [3322, 2445, 5296, 3215, 6027, 3660, 288, 6055, 3794, 995, 45865, 283, 295, 2031, 498, 2139, 1975, 15042, 4948, 24976, 283, 295, 2031, 5296, 15042, 2423, 2031, 47525, 11296, 6055, 32887, 5016, 24976, 257], "avg_logprob": -0.2526785663196019, "compression_ratio": 1.1584158415841583, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 681.82, "end": 682.24, "word": "the", "probability": 0.04888916015625}, {"start": 682.24, "end": 683.3, "word": " function", "probability": 0.96923828125}, {"start": 683.3, "end": 685.68, "word": " لدالة", "probability": 0.77325439453125}, {"start": 685.68, "end": 686.8, "word": " y", "probability": 0.55224609375}, {"start": 686.8, "end": 687.82, "word": " تساوي", "probability": 0.76739501953125}, {"start": 687.82, "end": 688.5, "word": " f", "probability": 0.83056640625}, {"start": 688.5, "end": 688.94, "word": " of", "probability": 0.716796875}, {"start": 688.94, "end": 689.46, "word": " x", "probability": 0.9658203125}, {"start": 689.46, "end": 690.68, "word": " if", "probability": 0.736328125}, {"start": 690.68, "end": 691.84, "word": " either", "probability": 0.94140625}, {"start": 691.84, "end": 693.44, "word": " اما", "probability": 0.62939453125}, {"start": 693.44, "end": 695.3, "word": " limit", "probability": 0.98046875}, {"start": 695.3, "end": 696.6, "word": " لل", "probability": 0.77197265625}, {"start": 696.6, "end": 697.1, "word": " f", "probability": 0.52392578125}, {"start": 697.1, "end": 697.54, "word": " of", "probability": 0.96923828125}, {"start": 697.54, "end": 698.12, "word": " x", "probability": 0.994140625}, {"start": 698.12, "end": 699.06, "word": " لما", "probability": 0.90869140625}, {"start": 699.06, "end": 699.28, "word": " ال", "probability": 0.9169921875}, {"start": 699.28, "end": 699.66, "word": " x", "probability": 0.80126953125}, {"start": 699.66, "end": 700.62, "word": " بدها", "probability": 0.9609375}, {"start": 700.62, "end": 701.42, "word": " تروح", "probability": 0.9957682291666666}, {"start": 701.42, "end": 702.52, "word": " لل", 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"word": "من", "probability": 0.329345703125}, {"start": 703.88, "end": 704.58, "word": " جهة", "probability": 0.8837890625}, {"start": 704.58, "end": 705.58, "word": " اليمين", "probability": 0.8505859375}, {"start": 705.58, "end": 706.9, "word": " تساوي", "probability": 0.9075927734375}, {"start": 706.9, "end": 707.6, "word": " زائد", "probability": 0.7430826822916666}, {"start": 707.6, "end": 707.92, "word": " او", "probability": 0.7939453125}, {"start": 707.92, "end": 708.48, "word": " ناقص", "probability": 0.97998046875}, {"start": 708.48, "end": 709.38, "word": " infinity", "probability": 0.73193359375}, {"start": 709.38, "end": 710.7, "word": " or", "probability": 0.7021484375}, {"start": 710.7, "end": 712.0, "word": " limit", "probability": 0.9716796875}, {"start": 712.0, "end": 712.74, "word": " لل", "probability": 0.83154296875}, {"start": 712.74, "end": 713.14, "word": " F", "probability": 0.473876953125}, {"start": 713.14, "end": 713.48, "word": " of", "probability": 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تربيع ناقص أربع", "tokens": [3322, 35114, 17251, 295, 264, 2445, 283, 295, 2031, 7251, 3794, 2407, 7578, 2031, 15844, 2031, 6055, 2288, 21292, 3615, 8717, 995, 4587, 9381, 5551, 25513, 3615], "avg_logprob": -0.2795758896640369, "compression_ratio": 1.011764705882353, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 733.7900000000001, "end": 735.19, "word": "the", "probability": 0.1104736328125}, {"start": 735.19, "end": 736.59, "word": " asymptotes", "probability": 0.91162109375}, {"start": 736.59, "end": 742.63, "word": " of", "probability": 0.63134765625}, {"start": 742.63, "end": 744.57, "word": " the", "probability": 0.93212890625}, {"start": 744.57, "end": 746.45, "word": " function", "probability": 0.97412109375}, {"start": 746.45, "end": 747.77, "word": " f", "probability": 0.75146484375}, {"start": 747.77, "end": 748.21, "word": " of", "probability": 0.406982421875}, {"start": 748.21, "end": 748.79, "word": " x", "probability": 0.95361328125}, {"start": 748.79, 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{"start": 1592.22, "end": 1592.96, "word": " سمعناها", "probability": 0.95048828125}, {"start": 1592.96, "end": 1593.14, "word": " لك", "probability": 0.840087890625}, {"start": 1593.14, "end": 1593.58, "word": " اليوم", "probability": 0.98095703125}, {"start": 1593.58, "end": 1593.98, "word": " و", "probability": 0.9296875}, {"start": 1593.98, "end": 1594.64, "word": " هنسمعها", "probability": 0.87509765625}, {"start": 1594.64, "end": 1594.86, "word": " لك", "probability": 0.99072265625}, {"start": 1594.86, "end": 1595.14, "word": " تاني", "probability": 0.9729817708333334}, {"start": 1595.14, "end": 1595.6, "word": " كمان", "probability": 0.9767252604166666}, {"start": 1595.6, "end": 1596.08, "word": " في", "probability": 0.9072265625}, {"start": 1596.08, "end": 1596.48, "word": " شبط", "probability": 0.7699381510416666}, {"start": 1596.48, "end": 1597.22, "word": " الأربعة", "probability": 0.6767578125}, {"start": 1597.22, "end": 1597.56, "word": " ان", "probability": 0.5751953125}, {"start": 1597.56, "end": 1597.9, "word": " شاء", "probability": 0.97216796875}, {"start": 1597.9, "end": 1598.2, "word": " الله", "probability": 0.9306640625}, {"start": 1598.2, "end": 1598.96, "word": " تعالى", "probability": 0.9656575520833334}, {"start": 1598.96, "end": 1600.04, "word": " طيب", "probability": 0.8995768229166666}, {"start": 1600.04, "end": 1600.84, "word": " solution", "probability": 0.61083984375}], "temperature": 1.0}, {"id": 69, "seek": 162964, "start": 1602.3, "end": 1629.64, "text": "ليس بالضرورة أن نبدأ عملية الرسم لأن ماعنديش معلومات لكن بقدر أجيب له ال asymptotes و بعد هيك الdominant terms مثلا و بعد هيك نرسم او نرسم و بعد هيك ال dominant terms مش مشكلة لكن أبسط حاجة أني أحسبله ال asymptotes السؤال هو هل يوجد عندي horizontal asymptote في", "tokens": [20292, 3794, 20666, 11242, 2288, 13063, 3660, 14739, 8717, 44510, 10721, 6225, 42213, 10632, 34892, 38251, 5296, 33456, 19446, 3615, 1863, 16254, 8592, 20449, 1211, 20498, 9307, 44381, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 46740, 2423, 35114, 17251, 4032, 39182, 39896, 4117, 2423, 4121, 259, 394, 2115, 50113, 15040, 4032, 39182, 39896, 4117, 8717, 2288, 38251, 1975, 2407, 8717, 2288, 38251, 4032, 39182, 39896, 4117, 2423, 15657, 2115, 37893, 37893, 28820, 3660, 44381, 5551, 3555, 3794, 9566, 11331, 26108, 3660, 14739, 1829, 5551, 5016, 35457, 43761, 2423, 35114, 17251, 21136, 33604, 6027, 31439, 8032, 1211, 7251, 29245, 3215, 18871, 16254, 12750, 35114, 1370, 8978], "avg_logprob": -0.18661557152023855, "compression_ratio": 1.8053097345132743, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1602.3, "end": 1603.12, "word": "ليس", "probability": 0.743408203125}, {"start": 1603.12, "end": 1604.08, "word": " بالضرورة", "probability": 0.9728515625}, {"start": 1604.08, "end": 1604.36, "word": " أن", "probability": 0.52978515625}, {"start": 1604.36, "end": 1604.74, "word": " نبدأ", "probability": 0.736572265625}, {"start": 1604.74, "end": 1605.28, "word": " عملية", "probability": 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"probability": 0.9716796875}, {"start": 1621.02, "end": 1621.76, "word": " asymptotes", "probability": 0.971435546875}, {"start": 1621.76, "end": 1622.34, "word": " السؤال", "probability": 0.9833984375}, {"start": 1622.34, "end": 1622.64, "word": " هو", "probability": 0.99365234375}, {"start": 1622.64, "end": 1623.7, "word": " هل", "probability": 0.91064453125}, {"start": 1623.7, "end": 1624.32, "word": " يوجد", "probability": 0.9833984375}, {"start": 1624.32, "end": 1624.94, "word": " عندي", "probability": 0.6966552734375}, {"start": 1624.94, "end": 1625.88, "word": " horizontal", "probability": 0.85791015625}, {"start": 1625.88, "end": 1628.62, "word": " asymptote", "probability": 0.912841796875}, {"start": 1628.62, "end": 1629.64, "word": " في", "probability": 0.59716796875}], "temperature": 1.0}, {"id": 70, "seek": 166090, "start": 1631.78, "end": 1660.9, "text": "يعني مش هنجيب ال horizontal بدي أخد ال limit لما ال X بدها تروح ل infinity أو لسالب infinity درجة البسط أعلى من درجة المقام يبقى النتيجة يا infinity يا سالب infinity يعني في عندي horizontal asymptote مافي إمكانية بالمرة يبقى هنا بقوله there is no horizontal asymptote there is no", "tokens": [40228, 22653, 37893, 8032, 1863, 7435, 1829, 3555, 2423, 12750, 4724, 16254, 5551, 9778, 3215, 2423, 4948, 5296, 15042, 2423, 1783, 47525, 11296, 6055, 32887, 5016, 5296, 13202, 34051, 5296, 3794, 6027, 3555, 13202, 11778, 47341, 3660, 29739, 3794, 9566, 5551, 3615, 23942, 9154, 11778, 47341, 3660, 9673, 4587, 10943, 7251, 3555, 4587, 7578, 28239, 31371, 7435, 3660, 35186, 13202, 35186, 8608, 6027, 3555, 13202, 37495, 22653, 8978, 18871, 16254, 12750, 35114, 1370, 19446, 41185, 11933, 2304, 41361, 10632, 20666, 2304, 25720, 7251, 3555, 4587, 7578, 34105, 4724, 39648, 3224, 456, 307, 572, 12750, 35114, 1370, 456, 307, 572], "avg_logprob": -0.2631250047683716, "compression_ratio": 1.853211009174312, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1631.78, "end": 1632.28, "word": "يعني", "probability": 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0.9404296875}], "temperature": 1.0}, {"id": 165, "seek": 394500, "start": 3919.5, "end": 3945.0, "text": "respect with respect to x at ال x يساوي ال x naught او النقطة الرابعة ال derivative ال derivative of ال f of x", "tokens": [19575, 365, 3104, 281, 2031, 412, 2423, 2031, 7251, 3794, 995, 45865, 2423, 2031, 13138, 1975, 2407, 28239, 47432, 3660, 34892, 16758, 27884, 2423, 13760, 2423, 13760, 295, 2423, 283, 295, 2031], "avg_logprob": -0.3340435606060606, "compression_ratio": 1.4141414141414141, "no_speech_prob": 0.0, "words": [{"start": 3919.5, "end": 3920.9, "word": "respect", "probability": 0.1964111328125}, {"start": 3920.9, "end": 3922.3, "word": " with", "probability": 0.81396484375}, {"start": 3922.3, "end": 3923.18, "word": " respect", "probability": 0.96826171875}, {"start": 3923.18, "end": 3924.24, "word": " to", "probability": 0.9423828125}, {"start": 3924.24, "end": 3926.3, "word": " x", "probability": 0.66552734375}, {"start": 3926.3, "end": 3927.4, "word": " at", "probability": 0.81201171875}, {"start": 3927.4, "end": 3928.14, "word": " ال", "probability": 0.279541015625}, {"start": 3928.14, "end": 3928.64, "word": " x", "probability": 0.4580078125}, {"start": 3928.64, "end": 3929.38, "word": " يساوي", "probability": 0.8062744140625}, {"start": 3929.38, "end": 3929.58, "word": " ال", "probability": 0.841796875}, {"start": 3929.58, "end": 3929.84, "word": " x", "probability": 0.8798828125}, {"start": 3929.84, "end": 3930.24, "word": " naught", "probability": 0.1695556640625}, {"start": 3930.24, "end": 3931.36, "word": " او", "probability": 0.66357421875}, {"start": 3931.36, "end": 3931.96, "word": " النقطة", "probability": 0.97412109375}, {"start": 3931.96, "end": 3932.72, "word": " الرابعة", "probability": 0.97802734375}, {"start": 3932.72, "end": 3933.72, "word": " ال", "probability": 0.3740234375}, {"start": 3933.72, "end": 3934.42, "word": " derivative", "probability": 0.859375}, {"start": 3934.42, "end": 3939.8, "word": " ال", "probability": 0.509765625}, {"start": 3939.8, "end": 3940.44, "word": " derivative", "probability": 0.953125}, {"start": 3940.44, "end": 3942.0, "word": " of", "probability": 0.947265625}, {"start": 3942.0, "end": 3943.46, "word": " ال", "probability": 0.6875}, {"start": 3943.46, "end": 3943.92, "word": " f", "probability": 0.62548828125}, {"start": 3943.92, "end": 3944.36, "word": " of", "probability": 0.84033203125}, {"start": 3944.36, "end": 3945.0, "word": " x", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 166, "seek": 396323, "start": 3958.01, "end": 3963.23, "text": "يبقى هذول الأربعة شغلات كله نفس الشيء", "tokens": [1829, 3555, 4587, 7578, 8032, 8848, 12610, 16247, 25513, 27884, 13412, 17082, 1211, 9307, 28242, 3224, 8717, 36178, 25124, 1829, 38207], "avg_logprob": -0.328125, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 3958.0099999999998, "end": 3959.41, "word": "يبقى", "probability": 0.705963134765625}, {"start": 3959.41, "end": 3959.73, "word": " هذول", "probability": 0.61474609375}, {"start": 3959.73, "end": 3960.29, "word": " الأربعة", "probability": 0.7355143229166666}, {"start": 3960.29, "end": 3960.99, "word": " شغلات", "probability": 0.927734375}, {"start": 3960.99, "end": 3962.03, "word": " كله", "probability": 0.6500244140625}, {"start": 3962.03, "end": 3962.47, "word": " نفس", "probability": 0.994384765625}, {"start": 3962.47, "end": 3963.23, "word": " الشيء", "probability": 0.8570963541666666}], "temperature": 1.0}, {"id": 167, "seek": 401039, "start": 3985.23, "end": 4010.39, "text": "أول مثال على هذا الموضوع example find the slope of the function find نمرة a find the slope of the function", "tokens": [10721, 12610, 50113, 6027, 15844, 23758, 9673, 2407, 11242, 45367, 1365, 915, 264, 13525, 295, 264, 2445, 915, 8717, 2304, 25720, 257, 915, 264, 13525, 295, 264, 2445], "avg_logprob": -0.2578124876680045, "compression_ratio": 1.3131313131313131, "no_speech_prob": 0.0, "words": [{"start": 3985.23, "end": 3985.63, "word": "أول", "probability": 0.893798828125}, {"start": 3985.63, "end": 3986.09, "word": " مثال", "probability": 0.962158203125}, {"start": 3986.09, "end": 3986.29, "word": " على", "probability": 0.76025390625}, {"start": 3986.29, "end": 3986.61, "word": " هذا", "probability": 0.9619140625}, {"start": 3986.61, "end": 3987.39, "word": " الموضوع", "probability": 0.9984130859375}, {"start": 3987.39, "end": 3989.55, "word": " example", "probability": 0.156982421875}, {"start": 3989.55, "end": 3995.49, "word": " find", "probability": 0.49560546875}, {"start": 3995.49, "end": 3995.71, "word": " the", "probability": 0.7763671875}, {"start": 3995.71, "end": 3996.05, "word": " slope", "probability": 0.96728515625}, {"start": 3996.05, "end": 3996.23, "word": " of", "probability": 0.98388671875}, {"start": 3996.23, "end": 3996.39, "word": " the", "probability": 0.87646484375}, {"start": 3996.39, "end": 3997.07, "word": " function", "probability": 0.98095703125}, {"start": 3997.07, "end": 3998.49, "word": " find", "probability": 0.37890625}, {"start": 3998.49, "end": 4000.49, "word": " نمرة", "probability": 0.6997884114583334}, {"start": 4000.49, "end": 4001.01, "word": " a", "probability": 0.43310546875}, {"start": 4001.01, "end": 4003.39, "word": " find", "probability": 0.8271484375}, {"start": 4003.39, "end": 4004.89, "word": " the", "probability": 0.771484375}, {"start": 4004.89, "end": 4006.23, "word": " slope", "probability": 0.95263671875}, {"start": 4006.23, "end": 4008.19, "word": " of", "probability": 0.97900390625}, {"start": 4008.19, "end": 4009.49, "word": " the", "probability": 0.8994140625}, {"start": 4009.49, "end": 4010.39, "word": " function", "probability": 0.97998046875}], "temperature": 1.0}, {"id": 168, "seek": 403888, "start": 4011.46, "end": 4038.88, "text": "f of x يساوي الجذر التربيع إلى x زائد واحد at the point عند النقطة في تمانية و تلاتة نمر أبيه find the equation of the tangent find the equation of", "tokens": [69, 295, 2031, 7251, 3794, 995, 45865, 25724, 8848, 2288, 16712, 2288, 21292, 3615, 30731, 2031, 30767, 16373, 3215, 36764, 24401, 412, 264, 935, 43242, 28239, 47432, 3660, 8978, 46811, 7649, 10632, 4032, 6055, 1211, 9307, 3660, 8717, 29973, 5551, 21292, 3224, 915, 264, 5367, 295, 264, 27747, 915, 264, 5367, 295], "avg_logprob": -0.2880306626265904, "compression_ratio": 1.385135135135135, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4011.46, "end": 4011.94, "word": "f", "probability": 0.21728515625}, {"start": 4011.94, "end": 4012.4, "word": " of", "probability": 0.5048828125}, {"start": 4012.4, "end": 4012.94, "word": " x", "probability": 0.9267578125}, {"start": 4012.94, "end": 4014.2, "word": " يساوي", "probability": 0.78515625}, {"start": 4014.2, "end": 4014.66, "word": " الجذر", "probability": 0.6923014322916666}, {"start": 4014.66, "end": 4015.34, "word": " التربيع", "probability": 0.84228515625}, {"start": 4015.34, "end": 4015.54, "word": " إلى", "probability": 0.5634765625}, {"start": 4015.54, "end": 4015.82, "word": " x", "probability": 0.78076171875}, {"start": 4015.82, "end": 4016.18, "word": " زائد", "probability": 0.84765625}, {"start": 4016.18, "end": 4016.74, "word": " واحد", "probability": 0.94921875}, {"start": 4016.74, "end": 4018.0, "word": " at", "probability": 0.7236328125}, {"start": 4018.0, "end": 4019.34, "word": " the", "probability": 0.66357421875}, {"start": 4019.34, "end": 4021.0, "word": " point", "probability": 0.9853515625}, {"start": 4021.0, "end": 4022.02, "word": " عند", "probability": 0.84521484375}, {"start": 4022.02, "end": 4023.5, "word": " النقطة", "probability": 0.98095703125}, {"start": 4023.5, "end": 4024.02, "word": " في", "probability": 0.69091796875}, {"start": 4024.02, "end": 4025.68, "word": " تمانية", "probability": 0.9347330729166666}, {"start": 4025.68, "end": 4026.18, "word": " و", "probability": 0.61767578125}, {"start": 4026.18, "end": 4027.32, "word": " تلاتة", "probability": 0.836669921875}, {"start": 4027.32, "end": 4028.68, "word": " نمر", "probability": 0.54345703125}, {"start": 4028.68, "end": 4030.06, "word": " أبيه", "probability": 0.483154296875}, {"start": 4030.06, "end": 4031.62, "word": " find", "probability": 0.54248046875}, {"start": 4031.62, "end": 4031.84, "word": " the", "probability": 0.80126953125}, {"start": 4031.84, "end": 4032.1, "word": " equation", "probability": 0.488525390625}, {"start": 4032.1, "end": 4032.32, "word": " of", "probability": 0.9541015625}, {"start": 4032.32, "end": 4032.5, "word": " the", "probability": 0.8251953125}, {"start": 4032.5, "end": 4033.24, "word": " tangent", "probability": 0.90283203125}, {"start": 4033.24, "end": 4034.62, "word": " find", "probability": 0.6904296875}, {"start": 4034.62, "end": 4035.86, "word": " the", "probability": 0.8759765625}, {"start": 4035.86, "end": 4037.56, "word": " equation", "probability": 0.9638671875}, {"start": 4037.56, "end": 4038.88, "word": " of", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 169, "seek": 405182, "start": 4039.92, "end": 4051.82, "text": "the tangent مواد المماثل المنحنة line at T ثمانية و تلاتة", "tokens": [3322, 27747, 3714, 14407, 3215, 9673, 2304, 5718, 104, 1211, 9673, 1863, 5016, 1863, 3660, 1622, 412, 314, 38637, 2304, 7649, 10632, 4032, 6055, 1211, 9307, 3660], "avg_logprob": -0.3529575935431889, "compression_ratio": 1.0481927710843373, "no_speech_prob": 0.0, "words": [{"start": 4039.92, "end": 4040.34, "word": "the", "probability": 0.148681640625}, {"start": 4040.34, "end": 4041.66, "word": " tangent", "probability": 0.88232421875}, {"start": 4041.66, "end": 4043.14, "word": " مواد", "probability": 0.516845703125}, {"start": 4043.14, "end": 4043.78, "word": " المماثل", "probability": 0.9001953125}, {"start": 4043.78, "end": 4045.2, "word": " المنحنة", "probability": 0.9291015625}, {"start": 4045.2, "end": 4046.46, "word": " line", "probability": 0.76806640625}, {"start": 4046.46, "end": 4048.08, "word": " at", "probability": 0.489501953125}, {"start": 4048.08, "end": 4049.22, "word": " T", "probability": 0.291015625}, {"start": 4049.22, "end": 4050.88, "word": " ثمانية", "probability": 0.8311767578125}, {"start": 4050.88, "end": 4051.34, "word": " و", "probability": 0.515625}, {"start": 4051.34, "end": 4051.82, "word": " تلاتة", "probability": 0.8572998046875}], "temperature": 1.0}, {"id": 170, "seek": 409147, "start": 4082.37, "end": 4091.47, "text": "مرة تانية بقول نرجع ال remark تبعتنا ال limit اللي عندنا هذا بتعطيني أربع شغلات", "tokens": [2304, 25720, 6055, 7649, 10632, 4724, 39648, 8717, 47341, 3615, 2423, 7942, 6055, 3555, 34268, 8315, 2423, 4948, 13672, 1829, 43242, 8315, 23758, 39894, 3615, 9566, 9957, 1829, 5551, 25513, 3615, 13412, 17082, 1211, 9307], "avg_logprob": -0.3604600619938638, "compression_ratio": 1.1875, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4082.37, "end": 4083.41, "word": "مرة", "probability": 0.724365234375}, {"start": 4083.41, "end": 4083.75, "word": " تانية", "probability": 0.9134114583333334}, {"start": 4083.75, "end": 4084.27, "word": " بقول", "probability": 0.580810546875}, {"start": 4084.27, "end": 4085.85, "word": " نرجع", "probability": 0.6797688802083334}, {"start": 4085.85, "end": 4085.99, "word": " ال", "probability": 0.1026611328125}, {"start": 4085.99, "end": 4086.31, "word": " remark", "probability": 0.431396484375}, {"start": 4086.31, "end": 4087.27, "word": " تبعتنا", "probability": 0.8907470703125}, {"start": 4087.27, "end": 4088.31, "word": " ال", "probability": 0.76611328125}, {"start": 4088.31, "end": 4088.65, "word": " limit", "probability": 0.95654296875}, {"start": 4088.65, "end": 4088.89, "word": " اللي", "probability": 0.76953125}, {"start": 4088.89, "end": 4089.25, "word": " عندنا", "probability": 0.641845703125}, {"start": 4089.25, "end": 4089.49, "word": " هذا", "probability": 0.304931640625}, {"start": 4089.49, "end": 4090.29, "word": " بتعطيني", "probability": 0.84775390625}, {"start": 4090.29, "end": 4090.81, "word": " أربع", "probability": 0.69677734375}, {"start": 4090.81, "end": 4091.47, "word": " شغلات", "probability": 0.976806640625}], "temperature": 1.0}, {"id": 171, "seek": 411970, "start": 4092.12, "end": 4119.7, "text": "الشغل الأولى ال limit هديشو معناها معناها ميل المنحنى عند النقطة x0 المعنى الثاني ميل المماثل المنحنى عند النقطة x0 المعنى الثالث معدل التغير للدالة f of x بالنسبة للمتغير x عند ال x0 المعنى الرابع مشتقة الدالة f of x عند ال x0", "tokens": [6027, 8592, 17082, 1211, 16247, 12610, 7578, 2423, 4948, 8032, 16254, 8592, 2407, 20449, 8315, 11296, 20449, 8315, 11296, 3714, 26895, 9673, 1863, 5016, 1863, 7578, 43242, 28239, 47432, 3660, 2031, 15, 9673, 3615, 1863, 7578, 6024, 104, 7649, 1829, 3714, 26895, 9673, 2304, 5718, 104, 1211, 9673, 1863, 5016, 1863, 7578, 43242, 28239, 47432, 3660, 2031, 15, 9673, 3615, 1863, 7578, 6024, 104, 6027, 12984, 20449, 3215, 1211, 16712, 17082, 13546, 24976, 3215, 6027, 3660, 283, 295, 2031, 20666, 1863, 35457, 3660, 5296, 19528, 2655, 17082, 13546, 2031, 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negative quantity", "tokens": [9566, 1829, 3555, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 9381, 13546, 36764, 24401, 15844, 4018, 9154, 10874, 3224, 3660, 25124, 2304, 6027, 7251, 3555, 4587, 7578, 389, 8608, 6027, 1829, 4724, 4587, 7578, 7251, 3555, 4587, 7578, 588, 1359, 3671, 5296, 28820, 6055, 2288, 21292, 3615, 7251, 3555, 4587, 7578, 588, 1359, 3671, 11275], "avg_logprob": -0.22109375124176342, "compression_ratio": 1.4513888888888888, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 5527.93, "end": 5528.61, "word": "طيب", "probability": 0.646728515625}, {"start": 5528.61, "end": 5529.37, "word": " يبقى", "probability": 0.9183349609375}, {"start": 5529.37, "end": 5529.67, "word": " هذا", "probability": 0.90673828125}, {"start": 5529.67, "end": 5530.33, "word": " الكلام", "probability": 0.9513346354166666}, {"start": 5530.33, "end": 5530.87, "word": " بده", "probability": 0.3184814453125}, {"start": 5530.87, "end": 5531.39, "word": " يصير", 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"word": " very", "probability": 0.7978515625}, {"start": 5537.37, "end": 5537.83, "word": " small", "probability": 0.93115234375}, {"start": 5537.83, "end": 5538.53, "word": " negative", "probability": 0.94580078125}, {"start": 5538.53, "end": 5539.33, "word": " لكل", "probability": 0.820556640625}, {"start": 5539.33, "end": 5540.31, "word": " تربيع", "probability": 0.8533935546875}, {"start": 5540.31, "end": 5541.39, "word": " يبقى", "probability": 0.96240234375}, {"start": 5541.39, "end": 5541.89, "word": " very", "probability": 0.83984375}, {"start": 5541.89, "end": 5543.37, "word": " small", "probability": 0.89697265625}, {"start": 5543.37, "end": 5544.73, "word": " negative", "probability": 0.9619140625}, {"start": 5544.73, "end": 5546.21, "word": " quantity", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 232, "seek": 556032, "start": 5546.68, "end": 5560.32, "text": "تربيع كل أسطل يعني بيصير واحد very small positive quantity أسطل يعني قداش infinity", "tokens": 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تروح", "probability": 0.9654947916666666}, {"start": 5567.45, "end": 5567.63, "word": " ل", "probability": 0.69091796875}, {"start": 5567.63, "end": 5567.97, "word": " 0", "probability": 0.2181396484375}, {"start": 5567.97, "end": 5568.23, "word": " من", "probability": 0.9912109375}, {"start": 5568.23, "end": 5568.67, "word": " جهة", "probability": 0.9638671875}, {"start": 5568.67, "end": 5569.37, "word": " اليمين", "probability": 0.8583984375}, {"start": 5569.37, "end": 5570.19, "word": " ل", "probability": 0.82373046875}, {"start": 5570.19, "end": 5571.45, "word": " 1", "probability": 0.71728515625}, {"start": 5571.45, "end": 5572.61, "word": " على", "probability": 0.50634765625}, {"start": 5572.61, "end": 5573.23, "word": " H", "probability": 0.90283203125}, {"start": 5573.23, "end": 5573.77, "word": " أس", "probability": 0.76513671875}, {"start": 5573.77, "end": 5574.73, "word": " تلتين", "probability": 0.85760498046875}, {"start": 5574.73, "end": 5575.59, "word": " يعني", "probability": 0.80322265625}, {"start": 5575.59, "end": 5576.25, "word": " limit", "probability": 0.7490234375}, {"start": 5576.25, "end": 5576.89, "word": " لما", "probability": 0.975830078125}, {"start": 5576.89, "end": 5577.09, "word": " ال", "probability": 0.98046875}, {"start": 5577.09, "end": 5577.39, "word": " H", "probability": 0.95458984375}, {"start": 5577.39, "end": 5577.73, "word": " بده", "probability": 0.939697265625}, {"start": 5577.73, "end": 5578.07, "word": " تروح", "probability": 0.99462890625}, {"start": 5578.07, "end": 5578.25, "word": " ل", "probability": 0.9482421875}, {"start": 5578.25, "end": 5578.61, "word": " 0", "probability": 0.8154296875}, {"start": 5578.61, "end": 5578.85, "word": " من", "probability": 0.9921875}, {"start": 5578.85, "end": 5579.29, "word": " جهة", "probability": 0.990234375}, {"start": 5579.29, "end": 5579.95, "word": " اليمين", "probability": 0.8766276041666666}, {"start": 5579.95, "end": 5580.49, "word": " ل", "probability": 0.92626953125}, {"start": 5580.49, "end": 5581.07, "word": " 1", "probability": 0.802734375}, {"start": 5581.07, "end": 5582.11, "word": " very", "probability": 0.6962890625}, {"start": 5582.11, "end": 5583.51, "word": " small", "probability": 0.900390625}, {"start": 5583.51, "end": 5584.59, "word": " positive", "probability": 0.94970703125}], "temperature": 1.0}, {"id": 234, "seek": 560336, "start": 5587.9, "end": 5603.36, "text": "هذه موجة دائما و أبدا يبقى dash infinity يبقى ساق limit لما ال H بدأ تروح ل zero من جهات اليمين واحد على H أس تلتين يسوى كده؟", "tokens": [3224, 24192, 3714, 29245, 3660, 11778, 16373, 15042, 4032, 5551, 3555, 28259, 7251, 3555, 4587, 7578, 8240, 13202, 7251, 3555, 4587, 7578, 8608, 995, 4587, 4948, 5296, 15042, 2423, 389, 47525, 10721, 6055, 32887, 5016, 5296, 4018, 9154, 10874, 3224, 9307, 2423, 32640, 9957, 36764, 24401, 15844, 389, 5551, 3794, 6055, 1211, 2655, 9957, 7251, 3794, 2407, 7578, 9122, 3215, 3224, 22807], "avg_logprob": -0.4372519850730896, "compression_ratio": 1.3157894736842106, "no_speech_prob": 2.86102294921875e-06, "words": [{"start": 5587.9, "end": 5588.9, "word": "هذه", "probability": 0.21484375}, {"start": 5588.9, "end": 5589.42, "word": " موجة", "probability": 0.7176920572916666}, {"start": 5589.42, "end": 5590.0, "word": " دائما", "probability": 0.7373046875}, {"start": 5590.0, "end": 5590.18, "word": " و", "probability": 0.73486328125}, {"start": 5590.18, "end": 5590.76, "word": " أبدا", "probability": 0.74072265625}, {"start": 5590.76, "end": 5591.42, "word": " يبقى", "probability": 0.851318359375}, {"start": 5591.42, "end": 5592.02, "word": " dash", "probability": 0.1517333984375}, {"start": 5592.02, "end": 5593.04, "word": " infinity", "probability": 0.4453125}, {"start": 5593.04, "end": 5594.48, "word": " يبقى", "probability": 0.935302734375}, {"start": 5594.48, "end": 5595.06, "word": " ساق", "probability": 0.5992024739583334}, {"start": 5595.06, "end": 5596.1, "word": " limit", "probability": 0.38232421875}, {"start": 5596.1, "end": 5596.82, "word": " لما", "probability": 0.769775390625}, {"start": 5596.82, "end": 5597.02, "word": " ال", "probability": 0.78759765625}, {"start": 5597.02, "end": 5597.28, "word": " H", "probability": 0.447998046875}, {"start": 5597.28, "end": 5597.68, "word": " بدأ", "probability": 0.5078125}, {"start": 5597.68, "end": 5598.0, "word": " تروح", "probability": 0.8006184895833334}, {"start": 5598.0, "end": 5598.14, "word": " ل", "probability": 0.56396484375}, {"start": 5598.14, "end": 5598.5, "word": " zero", "probability": 0.26171875}, {"start": 5598.5, "end": 5598.72, "word": " من", "probability": 0.97607421875}, {"start": 5598.72, "end": 5599.16, "word": " جهات", "probability": 0.8551432291666666}, {"start": 5599.16, "end": 5599.76, "word": " اليمين", "probability": 0.8662109375}, {"start": 5599.76, "end": 5600.76, "word": " واحد", "probability": 0.819091796875}, {"start": 5600.76, "end": 5601.04, "word": " على", "probability": 0.6689453125}, {"start": 5601.04, "end": 5601.36, "word": " H", "probability": 0.7177734375}, {"start": 5601.36, "end": 5601.68, "word": " أس", "probability": 0.80419921875}, {"start": 5601.68, "end": 5602.16, "word": " تلتين", "probability": 0.834228515625}, {"start": 5602.16, "end": 5602.56, "word": " يسوى", "probability": 0.746826171875}, {"start": 5602.56, "end": 5603.36, "word": " كده؟", "probability": 0.61566162109375}], "temperature": 1.0}, {"id": 235, "seek": 561377, "start": 5604.61, "end": 5613.77, "text": "أظن حسب التعريف يكون X يساوي واحد هو عبارة عن mean vertical tangent", "tokens": [10721, 19913, 1863, 11331, 35457, 16712, 3615, 16572, 5172, 7251, 30544, 1783, 7251, 3794, 995, 45865, 36764, 24401, 31439, 6225, 3555, 9640, 3660, 18871, 914, 9429, 27747], "avg_logprob": -0.36328124361378805, "compression_ratio": 1.0515463917525774, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 5604.61, "end": 5605.73, "word": "أظن", "probability": 0.6172078450520834}, {"start": 5605.73, "end": 5606.21, "word": " حسب", "probability": 0.903076171875}, {"start": 5606.21, "end": 5607.19, "word": " التعريف", "probability": 0.97998046875}, {"start": 5607.19, "end": 5608.09, "word": " يكون", "probability": 0.54150390625}, {"start": 5608.09, "end": 5608.55, "word": " X", "probability": 0.476806640625}, {"start": 5608.55, "end": 5609.29, "word": " يساوي", "probability": 0.7190704345703125}, {"start": 5609.29, "end": 5609.85, "word": " واحد", "probability": 0.930908203125}, {"start": 5609.85, "end": 5610.39, "word": " هو", "probability": 0.61962890625}, {"start": 5610.39, "end": 5610.77, "word": " عبارة", "probability": 0.9451904296875}, {"start": 5610.77, "end": 5611.01, "word": " عن", "probability": 0.958984375}, {"start": 5611.01, "end": 5611.33, "word": " mean", "probability": 0.262939453125}, {"start": 5611.33, "end": 5612.75, "word": " vertical", "probability": 0.75244140625}, {"start": 5612.75, "end": 5613.77, "word": " tangent", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 236, "seek": 564398, "start": 5628.0, "end": 5643.98, "text": "للمنحنة y يساوي x ناقص واحد كله أس تلت تمام", "tokens": [1211, 19528, 1863, 5016, 1863, 3660, 288, 7251, 3794, 995, 45865, 2031, 8717, 995, 4587, 9381, 36764, 24401, 28242, 3224, 5551, 3794, 6055, 1211, 2655, 46811, 10943], "avg_logprob": -0.1856863796710968, "compression_ratio": 1.0273972602739727, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 5628.0, "end": 5629.4, "word": "للمنحنة", "probability": 0.8498942057291666}, {"start": 5629.4, "end": 5629.98, "word": " y", "probability": 0.426025390625}, {"start": 5629.98, "end": 5631.08, "word": " يساوي", "probability": 0.7377471923828125}, {"start": 5631.08, "end": 5632.22, "word": " x", "probability": 0.93505859375}, {"start": 5632.22, "end": 5633.38, "word": " ناقص", "probability": 0.912841796875}, {"start": 5633.38, "end": 5634.24, "word": " واحد", "probability": 0.982666015625}, {"start": 5634.24, "end": 5635.28, "word": " كله", "probability": 0.935791015625}, {"start": 5635.28, "end": 5635.72, "word": " أس", "probability": 0.703857421875}, {"start": 5635.72, "end": 5636.58, "word": " تلت", "probability": 0.9153645833333334}, {"start": 5636.58, "end": 5643.98, "word": " تمام", "probability": 0.87353515625}], "temperature": 1.0}, {"id": 237, "seek": 567485, "start": 5645.55, "end": 5674.85, "text": "يبقى طلعلي في الخط على دي اللي احنا رسمينه يعني الخط المنقط هداشي اعتبر مماس و قاطع في نفس الوقت من فوق هنا يمسي الجزء العلوي من المنحنة و من تحت يمسي السفلي منحنة يبقى هو المماس لمين؟ للمنحنة اللي عندنا آخر مثال في محاضرة اليوم بيقول ما يأتي example", "tokens": [1829, 3555, 4587, 7578, 23032, 1211, 3615, 20292, 8978, 33962, 9566, 15844, 11778, 1829, 13672, 1829, 1975, 5016, 8315, 12602, 38251, 9957, 3224, 37495, 22653, 33962, 9566, 9673, 1863, 47432, 8032, 3215, 33599, 1829, 1975, 34268, 26890, 3714, 15042, 3794, 4032, 12174, 41193, 3615, 8978, 8717, 36178, 2423, 30543, 2655, 9154, 6156, 30543, 34105, 7251, 2304, 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"probability": 0.93994140625}, {"start": 5908.33, "end": 5908.99, "word": " سبع", "probability": 0.6446940104166666}, {"start": 5908.99, "end": 5909.95, "word": " يبقى", "probability": 0.887939453125}, {"start": 5909.95, "end": 5910.25, "word": " حل", "probability": 0.8173828125}, {"start": 5910.25, "end": 5910.45, "word": " هنا", "probability": 0.93798828125}, {"start": 5910.45, "end": 5910.83, "word": " بدل", "probability": 0.9765625}, {"start": 5910.83, "end": 5911.27, "word": " المرة", "probability": 0.9677734375}, {"start": 5911.27, "end": 5911.85, "word": " مرتين", "probability": 0.95556640625}, {"start": 5911.85, "end": 5912.69, "word": " مدام", "probability": 0.68505859375}, {"start": 5912.69, "end": 5912.91, "word": " ال", "probability": 0.8291015625}, {"start": 5912.91, "end": 5913.27, "word": " limit", "probability": 0.5751953125}, {"start": 5913.27, "end": 5913.79, "word": " ساوة", "probability": 0.702392578125}, {"start": 5913.79, "end": 5914.27, "word": " قيمة", "probability": 0.9933268229166666}, {"start": 5914.27, "end": 5915.41, "word": " الدالة", "probability": 0.9602864583333334}, {"start": 5915.41, "end": 5916.67, "word": " يبقى", "probability": 0.9739990234375}, {"start": 5916.67, "end": 5917.49, "word": " ساعة", "probability": 0.8518880208333334}, {"start": 5917.49, "end": 5918.21, "word": " ال", "probability": 0.791015625}, {"start": 5918.21, "end": 5918.69, "word": " F", "probability": 0.6181640625}, {"start": 5918.69, "end": 5919.13, "word": " of", "probability": 0.7783203125}, {"start": 5919.13, "end": 5919.75, "word": " Zero", "probability": 0.4833984375}, {"start": 5919.75, "end": 5921.01, "word": " يساوي", "probability": 0.57147216796875}, {"start": 5921.01, "end": 5921.65, "word": " limit", "probability": 0.71728515625}, {"start": 5921.65, "end": 5922.97, "word": " لصين", "probability": 0.5230916341145834}, {"start": 5922.97, "end": 5924.09, "word": " X", "probability": 0.40478515625}, {"start": 5924.09, "end": 5925.13, "word": " في", "probability": 0.87841796875}, {"start": 5925.13, "end": 5925.87, "word": " صين", "probability": 0.92919921875}, {"start": 5925.87, "end": 5926.65, "word": " X", "probability": 0.90283203125}, {"start": 5926.65, "end": 5927.83, "word": " limit", "probability": 0.68896484375}], "temperature": 1.0}, {"id": 249, "seek": 595685, "start": 5929.25, "end": 5956.85, "text": "لما ال X بده تروح لل Zero لل X في Sin واحد على X هذا بده يعطينا ان ال F is continuous at X يساوي Zero هذا كل الشغل اشتغلناه اللي هو المطلوب الأول من المسألة نجي للمطلوب الثاني", "tokens": [1211, 15042, 2423, 1783, 47525, 3224, 6055, 32887, 5016, 24976, 17182, 24976, 1783, 8978, 11187, 36764, 24401, 15844, 1783, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 2423, 479, 307, 10957, 412, 1783, 7251, 3794, 995, 45865, 17182, 23758, 28242, 25124, 17082, 1211, 1975, 8592, 2655, 17082, 1211, 8315, 3224, 13672, 1829, 31439, 9673, 9566, 1211, 37746, 16247, 12610, 9154, 9673, 3794, 10721, 37977, 8717, 7435, 1829, 5296, 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5935.31, "word": " Sin", "probability": 0.164306640625}, {"start": 5935.31, "end": 5936.45, "word": " واحد", "probability": 0.788330078125}, {"start": 5936.45, "end": 5936.99, "word": " على", "probability": 0.6240234375}, {"start": 5936.99, "end": 5937.55, "word": " X", "probability": 0.97119140625}, {"start": 5937.55, "end": 5938.17, "word": " هذا", "probability": 0.73876953125}, {"start": 5938.17, "end": 5938.61, "word": " بده", "probability": 0.781005859375}, {"start": 5938.61, "end": 5939.27, "word": " يعطينا", "probability": 0.9320068359375}, {"start": 5939.27, "end": 5939.87, "word": " ان", "probability": 0.7626953125}, {"start": 5939.87, "end": 5940.13, "word": " ال", "probability": 0.80126953125}, {"start": 5940.13, "end": 5940.55, "word": " F", "probability": 0.865234375}, {"start": 5940.55, "end": 5941.25, "word": " is", "probability": 0.9208984375}, {"start": 5941.25, "end": 5943.43, "word": " continuous", "probability": 0.90087890625}, {"start": 5943.43, "end": 5944.73, "word": " at", "probability": 0.92626953125}, {"start": 5944.73, "end": 5945.81, "word": " X", "probability": 0.9677734375}, {"start": 5945.81, "end": 5946.81, "word": " يساوي", "probability": 0.76904296875}, {"start": 5946.81, "end": 5947.11, "word": " Zero", "probability": 0.82763671875}, {"start": 5947.11, "end": 5947.93, "word": " هذا", "probability": 0.8037109375}, {"start": 5947.93, "end": 5948.27, "word": " كل", "probability": 0.9765625}, {"start": 5948.27, "end": 5948.65, "word": " الشغل", "probability": 0.9069010416666666}, {"start": 5948.65, "end": 5949.81, "word": " اشتغلناه", "probability": 0.9357561383928571}, {"start": 5949.81, "end": 5950.09, "word": " اللي", "probability": 0.929931640625}, {"start": 5950.09, "end": 5950.23, "word": " هو", "probability": 0.9912109375}, {"start": 5950.23, "end": 5951.07, "word": " المطلوب", "probability": 0.968994140625}, {"start": 5951.07, "end": 5951.99, "word": " الأول", "probability": 0.8662109375}, {"start": 5951.99, "end": 5952.77, "word": " من", "probability": 0.9873046875}, {"start": 5952.77, "end": 5954.31, "word": " المسألة", "probability": 0.9638671875}, {"start": 5954.31, "end": 5955.43, "word": " نجي", "probability": 0.90283203125}, {"start": 5955.43, "end": 5956.09, "word": " للمطلوب", "probability": 0.9244140625}, {"start": 5956.09, "end": 5956.85, "word": " الثاني", "probability": 0.9500732421875}], "temperature": 1.0}, {"id": 250, "seek": 598446, "start": 5959.66, "end": 5984.46, "text": "المطموب التاني بيقول لي هل هذه لها vertical tangent عند ال zero ولا لا بنقول له الله أعلم يبقى احنا بدنا نروح ناخد main limit لما ال H بدها تروح لل zero لل F of zero زائد ال H ناقص ال F of zero على H", "tokens": [45340, 9566, 2304, 2407, 3555, 16712, 7649, 1829, 4724, 1829, 39648, 32239, 8032, 1211, 29538, 5296, 11296, 9429, 27747, 43242, 2423, 4018, 49429, 20193, 44945, 39648, 46740, 21984, 5551, 3615, 19528, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 47525, 8315, 8717, 32887, 5016, 8717, 47283, 3215, 2135, 4948, 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"word": " tangent", "probability": 0.93994140625}, {"start": 5965.24, "end": 5966.04, "word": " عند", "probability": 0.9267578125}, {"start": 5966.04, "end": 5966.24, "word": " ال", "probability": 0.84716796875}, {"start": 5966.24, "end": 5966.58, "word": " zero", "probability": 0.46044921875}, {"start": 5966.58, "end": 5966.84, "word": " ولا", "probability": 0.87744140625}, {"start": 5966.84, "end": 5967.2, "word": " لا", "probability": 0.6064453125}, {"start": 5967.2, "end": 5967.98, "word": " بنقول", "probability": 0.530853271484375}, {"start": 5967.98, "end": 5968.18, "word": " له", "probability": 0.4345703125}, {"start": 5968.18, "end": 5968.88, "word": " الله", "probability": 0.83251953125}, {"start": 5968.88, "end": 5969.66, "word": " أعلم", "probability": 0.97265625}, {"start": 5969.66, "end": 5970.64, "word": " يبقى", "probability": 0.9339599609375}, {"start": 5970.64, "end": 5971.04, "word": " احنا", "probability": 0.91015625}, {"start": 5971.04, "end": 5971.42, "word": " بدنا", "probability": 0.793212890625}, {"start": 5971.42, "end": 5971.74, "word": " نروح", "probability": 0.9580078125}, {"start": 5971.74, "end": 5972.18, "word": " ناخد", "probability": 0.95556640625}, {"start": 5972.18, "end": 5972.62, "word": " main", "probability": 0.54541015625}, {"start": 5972.62, "end": 5973.94, "word": " limit", "probability": 0.984375}, {"start": 5973.94, "end": 5974.74, "word": " لما", "probability": 0.842529296875}, {"start": 5974.74, "end": 5974.96, "word": " ال", "probability": 0.9384765625}, {"start": 5974.96, "end": 5975.28, "word": " H", "probability": 0.4052734375}, {"start": 5975.28, "end": 5975.82, "word": " بدها", "probability": 0.930419921875}, {"start": 5975.82, "end": 5976.38, "word": " تروح", "probability": 0.9921875}, {"start": 5976.38, "end": 5976.74, "word": " لل", "probability": 0.45703125}, {"start": 5976.74, "end": 5977.36, "word": " zero", "probability": 0.73193359375}, {"start": 5977.36, "end": 5978.22, "word": " لل", "probability": 0.89501953125}, {"start": 5978.22, "end": 5978.74, "word": " F", "probability": 0.83447265625}, {"start": 5978.74, "end": 5979.2, "word": " of", "probability": 0.779296875}, {"start": 5979.2, "end": 5979.7, "word": " zero", "probability": 0.6533203125}, {"start": 5979.7, "end": 5980.46, "word": " زائد", "probability": 0.90185546875}, {"start": 5980.46, "end": 5980.72, "word": " ال", "probability": 0.89111328125}, {"start": 5980.72, "end": 5981.1, "word": " H", "probability": 0.94775390625}, {"start": 5981.1, "end": 5982.26, "word": " ناقص", "probability": 0.907958984375}, {"start": 5982.26, "end": 5982.46, "word": " ال", "probability": 0.73193359375}, {"start": 5982.46, "end": 5982.84, "word": " F", "probability": 0.96142578125}, {"start": 5982.84, "end": 5983.26, "word": " of", "probability": 0.96337890625}, {"start": 5983.26, "end": 5983.7, "word": " zero", "probability": 0.8447265625}, {"start": 5983.7, "end": 5984.02, "word": " على", "probability": 0.697265625}, {"start": 5984.02, "end": 5984.46, "word": " H", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 251, "seek": 600079, "start": 5985.71, "end": 6000.79, "text": "مظهر ونشوف هل هذه ال limit تساوي infinity و الله سالب infinity و الله غير ذلك يبقى هذا limit لما ال H بدها تروح ل zero برجع لمين؟", "tokens": [2304, 19913, 3224, 2288, 4032, 1863, 8592, 38688, 8032, 1211, 29538, 2423, 4948, 6055, 3794, 995, 45865, 13202, 4032, 21984, 8608, 6027, 3555, 13202, 4032, 21984, 32771, 13546, 29910, 23275, 7251, 3555, 4587, 7578, 23758, 4948, 5296, 15042, 2423, 389, 47525, 11296, 6055, 32887, 5016, 5296, 4018, 4724, 47341, 3615, 32767, 9957, 22807], "avg_logprob": -0.33506943892549584, "compression_ratio": 1.4285714285714286, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 5985.71, "end": 5986.43, "word": "مظهر", "probability": 0.4998931884765625}, {"start": 5986.43, "end": 5987.29, "word": " ونشوف", "probability": 0.5216064453125}, {"start": 5987.29, "end": 5987.59, "word": " هل", "probability": 0.902099609375}, {"start": 5987.59, "end": 5987.97, "word": " هذه", "probability": 0.60498046875}, {"start": 5987.97, "end": 5988.17, "word": " ال", "probability": 0.50927734375}, {"start": 5988.17, "end": 5988.55, "word": " limit", "probability": 0.64990234375}, {"start": 5988.55, "end": 5989.47, "word": " تساوي", "probability": 0.880859375}, {"start": 5989.47, "end": 5990.25, "word": " infinity", "probability": 0.7763671875}, {"start": 5990.25, "end": 5990.83, "word": " و", "probability": 0.439453125}, {"start": 5990.83, "end": 5991.03, "word": " الله", "probability": 0.888671875}, {"start": 5991.03, "end": 5991.53, "word": " سالب", "probability": 0.8458658854166666}, {"start": 5991.53, "end": 5992.17, "word": " infinity", "probability": 0.8662109375}, {"start": 5992.17, "end": 5992.83, "word": " و", "probability": 0.91845703125}, {"start": 5992.83, "end": 5993.11, "word": " الله", "probability": 0.96240234375}, {"start": 5993.11, "end": 5993.51, "word": " غير", "probability": 0.98486328125}, {"start": 5993.51, "end": 5994.27, "word": " ذلك", "probability": 0.982177734375}, {"start": 5994.27, "end": 5995.31, "word": " يبقى", "probability": 0.931640625}, {"start": 5995.31, "end": 5995.57, "word": " هذا", "probability": 0.72802734375}, {"start": 5995.57, "end": 5996.07, "word": " limit", "probability": 0.88623046875}, {"start": 5996.07, "end": 5996.89, "word": " لما", "probability": 0.8525390625}, {"start": 5996.89, "end": 5997.07, "word": " ال", "probability": 0.91552734375}, {"start": 5997.07, "end": 5997.43, "word": " H", "probability": 0.456787109375}, {"start": 5997.43, "end": 5997.87, "word": " بدها", "probability": 0.756103515625}, {"start": 5997.87, "end": 5998.59, "word": " تروح", "probability": 0.962890625}, {"start": 5998.59, "end": 5998.75, "word": " ل", "probability": 0.5830078125}, {"start": 5998.75, "end": 5999.17, "word": " zero", "probability": 0.37255859375}, {"start": 5999.17, "end": 6000.17, "word": " برجع", "probability": 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+1,3644 @@ +1 +00:00:21,510 --> 00:00:26,410 +بسم الله الرحمن الرحيم المرة اللى فاتت اخر حاجة + +2 +00:00:26,410 --> 00:00:30,770 +اتكلمنا فيها اللى هو نوعين اللى هو ال horizontal + +3 +00:00:30,770 --> 00:00:34,830 +asymptotes و ال oblique asymptotes بالنسبة لل + +4 +00:00:34,830 --> 00:00:37,410 +horizontal asymptotes بيقولنا ناخد limit لل + +5 +00:00:37,410 --> 00:00:42,030 +function لما ال X بده تروح الى infinity او لسالب + +6 +00:00:42,030 --> 00:00:46,650 +infinity انطلع النتج يساوي رقم يبقى فيه ان + +7 +00:00:46,650 --> 00:00:50,770 +horizontal asymptote Y تساوي هذا الرقميبقى بيكون + +8 +00:00:50,770 --> 00:00:54,710 +هو ال horizontal asymptote سواء كان هذا الرقم zero + +9 +00:00:54,710 --> 00:00:59,630 +أو كمية موجبة أو كمية سالبة لكن إن كان طلع الناتج + +10 +00:00:59,630 --> 00:01:03,710 +infinity أو سالب infinity يبقى بنقول هنا the + +11 +00:01:03,710 --> 00:01:06,910 +horizontal line أو the horizontal asymptote does + +12 +00:01:06,910 --> 00:01:11,310 +not exist يعني ماعنديش horizontal asymptote ثم + +13 +00:01:11,310 --> 00:01:15,010 +انتقلنا بعد ذلك إلى ال obligasymptote وقولنا إذا + +14 +00:01:15,010 --> 00:01:19,580 +كانت درجة دلة البسطأعلى من درجة دالة المقام بمقدار + +15 +00:01:19,580 --> 00:01:24,580 +واحد يبقى بيكون عندي oblique asymptote تمام؟ الآن + +16 +00:01:24,580 --> 00:01:27,500 +قبل أن نذهب إلى ال asymptote الأخرى اللي هو ال + +17 +00:01:27,500 --> 00:01:31,560 +vertical asymptote فيه أنحاجة عرضية لازمالي لل + +18 +00:01:31,560 --> 00:01:35,680 +vertical asymptote فبدنا نتعرض للآن اللي هو ال + +19 +00:01:35,680 --> 00:01:41,940 +infinite limits يعني ال limit إذا كانت النتيجة + +20 +00:01:41,940 --> 00:01:47,610 +infinite لمين لدالة مايقول السؤال find the + +21 +00:01:47,610 --> 00:01:50,970 +following limits if it exists يوجهها للنهايات + +22 +00:01:50,970 --> 00:01:56,650 +التالية إن وجدت ما وجدتش خلاص مسمحينك فبدي بقول + +23 +00:01:56,650 --> 00:02:00,830 +limit ال X بده تروح للاتنين لل function واحد على X + +24 +00:02:00,830 --> 00:02:06,400 +minus twoيبقى لو جيت الآن بالتعويض المباشر لو قلنا + +25 +00:02:06,400 --> 00:02:10,580 +limit البسط على limit المقام يبقى واحد على زيرو + +26 +00:02:10,580 --> 00:02:14,920 +وهذا الكلام ماله ممنوع لكن هل ال function هذه + +27 +00:02:14,920 --> 00:02:20,750 +معرفة عندك سواء تماملو رجعنا بالذاكرة الى الوراء + +28 +00:02:20,750 --> 00:02:25,210 +الى ال chapter الماضى الى section 2 أربعة اللى كان + +29 +00:02:25,210 --> 00:02:30,050 +one sided limit كتبت عندك بالعربي بناخد ال limit + +30 +00:02:30,050 --> 00:02:33,990 +من اليمين و ال limit من الشمال في الحالات الأربعة + +31 +00:02:33,990 --> 00:02:38,750 +تمام؟ و روحنا أخدنا ثلاث حالات و أخدنا عليهم أمثلة + +32 +00:02:38,750 --> 00:02:41,930 +و بقيت الحالة الرابعة و قدت اقولك ان شاء الله + +33 +00:02:47,810 --> 00:02:53,410 +الدالة غير معرفة عند النقطة المراد حساب النهاية + +34 +00:02:53,410 --> 00:02:58,530 +عندها يبقى الدالة غير معرفة عند X يساوي 2 إذن سنتر + +35 +00:02:58,530 --> 00:03:03,950 +إلى أخذ النهاية من اليمين والنهاية من الشمال يبقى + +36 +00:03:03,950 --> 00:03:05,590 +بدنا نروح ناخد limit + +37 +00:03:09,020 --> 00:03:14,480 +لمان؟ لأ ال function واحد على X ناقص اتنين لما ال + +38 +00:03:14,480 --> 00:03:19,880 +X بتروح للاتنين على سبيل المثال من جهة اليسار يبقى + +39 +00:03:19,880 --> 00:03:25,060 +واحد على لو روحت للاتنين من جهة اليسار يبقى اي + +40 +00:03:25,060 --> 00:03:30,300 +اتنين وانا رايح لها من جهة اليسار يعني اقل من + +41 +00:03:30,300 --> 00:03:35,440 +اتنين يبقى المقام قيمة سالب ولا موجبة يبقى very + +42 +00:03:35,440 --> 00:03:40,420 +small negative quantityالنتيجة هي negative + +43 +00:03:40,420 --> 00:03:47,340 +quantity يبقى النتيجة لن تصبح سالب infinity طيب لو + +44 +00:03:47,340 --> 00:03:53,360 +أخدت ال limit لما ال X بدها تروح إلى 2 من جهة + +45 +00:03:53,360 --> 00:04:01,140 +اليمين لل 1 على X ناقص 2 يساوي 1 احنا راحيين ل 2 + +46 +00:04:01,140 --> 00:04:06,410 +من جهة اليمين يبقى بناء عليهلما اذهب للاتنين من + +47 +00:04:06,410 --> 00:04:11,650 +جهة اليمين يكون اتنين وكسر بسيط جدا نقص اتنين + +48 +00:04:11,650 --> 00:04:18,470 +بيبقى عندي very small positive quantity يبقى + +49 +00:04:18,470 --> 00:04:24,950 +النتيجة انها infinity صار في ان اللي هو من جهة + +50 +00:04:24,950 --> 00:04:29,110 +اليمين تختلف عن جهة الشمال يبقى ال limit exist ولا + +51 +00:04:29,110 --> 00:04:34,420 +does not existيبقى does not exist يبقى باجي بقوله + +52 +00:04:34,420 --> 00:04:40,400 +سا ال limit لواحد على X ناقص اتنين لما ال X بده + +53 +00:04:40,400 --> 00:04:50,340 +تروح للاتنين does not exist مالهاش وجود طيب نيجي + +54 +00:04:50,340 --> 00:04:55,680 +ناخد كمال مثال ثاني و نشوف شو النتيجة يبقى ال + +55 +00:04:55,680 --> 00:05:02,680 +limitلما ال X بدها تروح لا Zero لا واحد على X + +56 +00:05:02,680 --> 00:05:10,440 +تربيعهل الدالة معرفة عند X يساوي Zero؟ طبعا لا + +57 +00:05:10,440 --> 00:05:13,880 +يبقى بيننا العالي اذا انا اضطر ان انا اخد النهاية + +58 +00:05:13,880 --> 00:05:18,800 +من اليمين والنهاية من اليسار يبقى بدى اخد limit + +59 +00:05:18,800 --> 00:05:24,200 +لما ال X بدها تروح لل Zero من جهة الشمال لواحد على + +60 +00:05:24,200 --> 00:05:29,560 +X تربية ويساوي واحد على إذا أنا رايح لل Zero من + +61 +00:05:29,560 --> 00:05:34,630 +جهة اليسار يبقى القيم موجة بو الله سالبةسنة بيبقى + +62 +00:05:34,630 --> 00:05:40,610 +very small negative quantity يبقى very small + +63 +00:05:40,610 --> 00:05:48,750 +negative quantity بس اه لكل تربية يبقى بيصير واحد + +64 +00:05:48,750 --> 00:05:55,590 +على very small positive quantity اللي يبقى درجة ب + +65 +00:05:55,590 --> 00:06:01,600 +infinityطيب نروح ناخد ال limit لما ال X بدها تروح + +66 +00:06:01,600 --> 00:06:08,920 +ل 0 من جهتي اليمين ل 1 على X تربيع يبقى 1 على very + +67 +00:06:08,920 --> 00:06:15,340 +small positive quantity الكل تربيعاللي هيبقى تبقى + +68 +00:06:15,340 --> 00:06:21,240 +كمان positive أيضا يبقى النتيجة سوى كم؟ سوى + +69 +00:06:21,240 --> 00:06:26,920 +infinity من الاتنين هدول مع بعض بروح بقول limit + +70 +00:06:26,920 --> 00:06:32,280 +لما ال X بده تروح ل 0 من جهة اليمين لمين؟ ل 1 على + +71 +00:06:32,280 --> 00:06:40,280 +X تربيع تسوى كم؟ infinity وكأنها exist لكن تسوى + +72 +00:06:40,280 --> 00:06:45,870 +كم؟ما لا نهاية infinity يبقى هذا بيخلف عن السؤال + +73 +00:06:45,870 --> 00:06:50,150 +الأول، السؤال الأول اليمين غير الشمال يبقى قولنا + +74 +00:06:50,150 --> 00:06:55,300 +does not exist، هنا اليمين ساوة الشماللكن النتيجة + +75 +00:06:55,300 --> 00:06:59,840 +كانت infinity يبقى بقول ال limit تسوى من infinity + +76 +00:06:59,840 --> 00:07:05,420 +لاحظوا بالنسبة لهذا السؤال رسمناه قبل ذلك وقلنا لو + +77 +00:07:05,420 --> 00:07:10,600 +كان هذا محور X وهذا محور Y يبقى هذا ال function + +78 +00:07:10,600 --> 00:07:15,300 +اللي انا رسمت من Y تسوى واحد ع الاكس اربعة وهي + +79 +00:07:15,300 --> 00:07:20,430 +Zeroلو أنا رايح لـ 0 من جهة اليمين بلاجي الدالة + +80 +00:07:20,430 --> 00:07:24,850 +طالعة لـ infinity و لو روحت لـ 0 من جهة الشمال + +81 +00:07:24,850 --> 00:07:30,050 +كمان الدالة طالعة لوين إلى infinity و من هنا ال + +82 +00:07:30,050 --> 00:07:34,230 +limit من اليمين زي ال limit من الشمال وتساوي مين؟ + +83 +00:07:34,230 --> 00:07:42,950 +وتساوي infinity ناخد كمان مثال اللي هو رقم 3 رقم 3 + +84 +00:07:42,950 --> 00:07:44,230 +بدنا ال limit + +85 +00:07:47,130 --> 00:07:55,450 +لما ال X بدها تروح إلى تلاتة لمين لسالي باتنين على + +86 +00:07:55,450 --> 00:07:59,130 +X ناقص تلاتة لكل ربيع + +87 +00:08:01,340 --> 00:08:04,840 +يبقى بروح اخد ال limit من اليمين وال limit من + +88 +00:08:04,840 --> 00:08:10,920 +الشمال واشوف شو بده تعطينا يبقى بدنا نروح ناخد ال + +89 +00:08:10,920 --> 00:08:17,580 +limit لما ال X بده تروح لتلاتة من جهة اليسار لسالب + +90 +00:08:17,580 --> 00:08:23,520 +اتنين X ناقص تلاتة لكل تربية يسوى ناقص اتنين على + +91 +00:08:24,020 --> 00:08:28,780 +أحنا راحيين لتلاتة من جهة اليسار يعني قبل التلاتة + +92 +00:08:28,780 --> 00:08:33,840 +يبقى المقدار بين القوسين قمموجة ولا سالبة؟ سالبة + +93 +00:08:33,840 --> 00:08:45,020 +يبقى very small negative quantity كل سلبية سالب + +94 +00:08:45,020 --> 00:08:48,360 +اتنين سالب اتنين على + +95 +00:08:53,750 --> 00:08:59,670 +لو أطلع نهر الصين سنجد المجمع يبقى النتيجة السائل + +96 +00:08:59,670 --> 00:09:05,410 +تنفيه لو روحنا الشاشة النهرية وما ال X يبقى طوحي + +97 +00:09:05,410 --> 00:09:11,570 +إمالة من جهة اليمين يسلق اتنين على X ماقص تلاتة في + +98 +00:09:11,570 --> 00:09:18,870 +كل تلبية يسلق اتنين على تلاتة من جهة اليمين يبقى + +99 +00:09:18,870 --> 00:09:23,520 +أكبر من تلاتة ماقص تلاتةبقى ال very small positive + +100 +00:09:23,520 --> 00:09:29,660 +in quantity. if you are very small positive in + +101 +00:09:29,660 --> 00:09:37,380 +quantity كل تاريخ يبقى + +102 +00:09:37,380 --> 00:09:43,700 +اتنين هدول مع بعض بروح تقول انه لمد يسيب + +103 +00:09:49,020 --> 00:09:56,200 +يجب أن تذهب إلى تلاتة يسوى جدير سالب infinity يبقى + +104 +00:09:56,200 --> 00:10:01,280 +بالعنوان عليه مرة limit does not exist مرة limit + +105 +00:10:01,280 --> 00:10:07,380 +infinity مرة limit سالب infinityوبالتالي ماعنديش + +106 +00:10:07,380 --> 00:10:13,100 +شغلة محددة بتختلف النتيجة من سؤال إلى آخر هذا + +107 +00:10:13,100 --> 00:10:18,300 +بالنسبة لل infinite limits طب شو دخله يد في النص؟ + +108 +00:10:18,300 --> 00:10:25,400 +هذا ما سنعرفه بعد قليل لما ننتقل الآنالى من؟ الى + +109 +00:10:25,400 --> 00:10:30,640 +اخر نقطة في هذا ال section وهو اخر نوع من انواع ال + +110 +00:10:30,640 --> 00:10:36,280 +asymptotes اللي هي ال vertical asymptotes وهي + +111 +00:10:36,280 --> 00:10:41,740 +النقطة الأخيرة في هذا ال section يبقى بنا نيجي + +112 +00:10:41,740 --> 00:10:46,060 +للنقطة الرابعة والاخيرة في هذا ال section اللي هي + +113 +00:10:46,060 --> 00:10:51,840 +رقم أربعة ال vertical asymptotes + +114 +00:10:56,550 --> 00:11:08,330 +definition a line x يساوي a is a vertical + +115 +00:11:08,330 --> 00:11:12,070 +asymptote + +116 +00:11:12,070 --> 00:11:20,870 +خط قارب رأسي of the graph of + +117 +00:11:21,820 --> 00:11:33,440 +the function لدالة y تساوي f of x if either اما + +118 +00:11:33,440 --> 00:11:44,580 +limit لل f of x لما ال x بدها تروح لل aمن جهة + +119 +00:11:44,580 --> 00:11:53,140 +اليمين تساوي زائد او ناقص infinity or limit لل F + +120 +00:11:53,140 --> 00:11:58,820 +of X لما ال X بدها تروح لل A من جهة الشمال بده + +121 +00:11:58,820 --> 00:12:06,380 +يساوي من زائد او ناقص infinity ناخد مثال توضيحي + +122 +00:12:06,380 --> 00:12:10,200 +example find + +123 +00:12:13,790 --> 00:12:22,630 +the asymptotes of + +124 +00:12:22,630 --> 00:12:34,870 +the function f of x يسوى x على x تربيع ناقص أربع + +125 +00:13:02,580 --> 00:13:06,640 +يوجد آخر نوع من أنواع الـ asymptotes اللي هو الـ + +126 +00:13:06,640 --> 00:13:12,030 +vertical asymptoteبنعطيه خطوط التقارب الرأسية + +127 +00:13:12,030 --> 00:13:16,690 +بنعطي تعريف لخط التقارب الرأسي ففاجب اقول ال line + +128 +00:13:16,690 --> 00:13:23,390 +X يساوي A is a vertical asymptote ل الرسم البياني + +129 +00:13:23,390 --> 00:13:29,290 +لمنحنة ده لو Y تساوي F of X if either اما limit ال + +130 +00:13:29,290 --> 00:13:33,170 +F of X لما ال X بده يروح لل A بده يساوي موجب او + +131 +00:13:33,170 --> 00:13:36,970 +سلب infinity او limit ال F of X لما ال X بده يروح + +132 +00:13:36,970 --> 00:13:38,390 +لل A من جهة الشمال + +133 +00:13:41,920 --> 00:13:45,460 +معنى هذا الكلام ان limit ال F of X لما ال X بتروح + +134 +00:13:45,460 --> 00:13:51,720 +لل A قد يكون infinity و قد يكون سالب infinity مش + +135 +00:13:51,720 --> 00:13:56,100 +اتنين فيها من واحد اما هذه او تلك ماعنا مشكلة + +136 +00:14:08,160 --> 00:14:13,380 +السؤال هو هل ضروري اخد ال limit من اليمين و من + +137 +00:14:13,380 --> 00:14:18,770 +الشمال؟بالكافة الواحدة لكن يمكن التاني يجيب ال + +138 +00:14:18,770 --> 00:14:24,750 +vertical تاني مثلا كويس اتنين ممكن هذه تعطيني + +139 +00:14:24,750 --> 00:14:29,010 +infinity وهذه تعطيني infinity ممكن هذه تعطيني سالب + +140 +00:14:29,010 --> 00:14:32,670 +infinity وهذه تعطيني سالب infinityممكن انها تعطيني + +141 +00:14:32,670 --> 00:14:36,510 +موجة بالإنفينيتي وهذه تعطيني سالب بالإنفينيتي على + +142 +00:14:36,510 --> 00:14:40,650 +كل الأمر يعني ماعنديش مشكلة زي مين زي Y تسوى واحد + +143 +00:14:40,650 --> 00:14:44,430 +على X اذا روحت من جهة اليمين عند ال zero بتلاقي + +144 +00:14:44,430 --> 00:14:47,430 +اللي راح اتماه لنهاية اذا روحت ل zero من جهة + +145 +00:14:47,430 --> 00:14:51,550 +الشمال بتنزل لوين لسالب infinity اللي كانت مرسومته + +146 +00:14:51,550 --> 00:14:54,330 +قبلها قليل لما روح ل zero من اليمين ومن الشمال + +147 +00:14:54,330 --> 00:14:58,630 +لجهته infinity على الشجتين وبالتالي ماعناه مشكلة + +148 +00:14:58,930 --> 00:15:03,570 +هذه والله هذه السيانة متفرجش عنها، إذا اللي خدناته + +149 +00:15:03,570 --> 00:15:07,390 +و أساها ال limit ان النتيجة بدأ تبقى infinity كان + +150 +00:15:07,390 --> 00:15:12,670 +ضروري جدا لأنه لازم نشغل عليه وين عند حساب ال + +151 +00:15:12,670 --> 00:15:16,960 +vertical ال simplestالمثال اللي بين إيدينا بيقول + +152 +00:15:16,960 --> 00:15:21,400 +ما ياتي، بيقول هات للـasymptotes للدالة هذه، ولم + +153 +00:15:21,400 --> 00:15:25,540 +يقول لا vertical ولا oblique ولا horizontal، يبقى + +154 +00:15:25,540 --> 00:15:30,580 +انت لحالك بدك ايه؟ بدك تعرف، بيقوله بسيطة جدا، بس + +155 +00:15:30,580 --> 00:15:37,750 +هل نفسي هل هذه فيها oblique، asymptote؟لأن ضرائط + +156 +00:15:37,750 --> 00:15:43,790 +الباص أقل من ضرائط المقام يبقى الحل نطالب كل ال + +157 +00:15:43,790 --> 00:15:48,870 +asymptotes إذا موجودة بديها يبقى باجي بقول له + +158 +00:15:48,870 --> 00:16:01,950 +there is no oblig asymptote شو + +159 +00:16:01,950 --> 00:16:11,810 +السبب؟ becauseإن ال degree لل X أقل من ال degree + +160 +00:16:11,810 --> 00:16:19,010 +لل X تربية ناقص أربعةدرجة البص أقل من درجة المقام + +161 +00:16:19,010 --> 00:16:24,010 +وبالتالي ماعنديش Obligue ال symptom طب نشوف هل في + +162 +00:16:24,010 --> 00:16:30,350 +horizontal ولا لا، إذا بدروح أخد ال limit لل F of + +163 +00:16:30,350 --> 00:16:36,480 +X لما ال X بدها تروح لموجة ب Infinityطبعا الكون ال + +164 +00:16:36,480 --> 00:16:40,420 +polynomial و ال polynomial يبقى موجب و الله سالب + +165 +00:16:40,420 --> 00:16:47,240 +حياطين ايه نفس النتيجة يبقى هنا limit لما ال X بده + +166 +00:16:47,240 --> 00:16:54,080 +يروح لموجب او سالب infinity لل X على X تربية ناقص + +167 +00:16:54,080 --> 00:17:02,050 +4بعد ذلك اقسم كل المقام على X المرفوعة لأكبر أُس + +168 +00:17:02,050 --> 00:17:08,670 +في المقام يبقى النتيجة 1 على X واحد ناقص أربع على + +169 +00:17:08,670 --> 00:17:14,470 +X ثربية هذا Zero هذا Zero النتيجة Zero على واحد + +170 +00:17:14,470 --> 00:17:20,470 +اللي هو الجداش Zero يبقى بناء عليه Y تساوي هذه + +171 +00:17:20,470 --> 00:17:31,030 +القيمة اللي هي Zerois a horizontal asymptote + +172 +00:17:31,030 --> 00:17:34,550 +خط + +173 +00:17:34,550 --> 00:17:40,550 +قارب أفقي خط قارب مائلي بعتلك الله مافيش لم يبقى + +174 +00:17:40,550 --> 00:17:45,330 +عندي إلا مينالـ Vertical Asymptote بدنا نشوف فيه + +175 +00:17:45,330 --> 00:17:50,730 +ولا مافيهش يبقى الـ F of X بقدر اكتبها على الشكل + +176 +00:17:50,730 --> 00:17:58,030 +التالي هذا X والمقام اللي عندي معله فارق بين + +177 +00:17:58,030 --> 00:18:04,610 +المربعين إذا بحلله X نقص اتنين في X زائد اتنين + +178 +00:18:04,610 --> 00:18:12,300 +السؤال هو هل الدالة معرفة عند اتنينولا حتى سلب + +179 +00:18:12,300 --> 00:18:16,900 +اتنين مظبوط اذا هي قيم تانية ده اللي غير معرفة + +180 +00:18:16,900 --> 00:18:22,500 +عندهم اذا سنتر ناخد النهاية من اليمين ونهاية من + +181 +00:18:22,500 --> 00:18:28,060 +اليسار ونشوف هل في عندي vertical asymptote ام لا + +182 +00:18:28,060 --> 00:18:31,520 +بالنسبالي ال vertical asymptote بيقول ال limit من + +183 +00:18:31,520 --> 00:18:34,820 +اليمين والlimit من الشمال اذا infinity او سلب + +184 +00:18:34,820 --> 00:18:39,500 +infinity يبقى في عندك vertical asymptote وإذا does + +185 +00:18:39,500 --> 00:18:45,720 +not existلا يوجد عندي Vertical Asymptote اذا انا + +186 +00:18:45,720 --> 00:18:52,160 +بدرح اخد limit لل F of X لما ال X بده يروح لل + +187 +00:18:52,160 --> 00:18:57,400 +اتنين ناخد من جهة الشمال اولا يبقى هذا ال limit + +188 +00:18:57,400 --> 00:19:02,660 +لما ال X بده يروح لل اتنين من جهة الشمال لل X على + +189 +00:19:02,660 --> 00:19:08,780 +X ناقص اتنين في X زائد اتنين ويساوي اتنين مافيش + +190 +00:19:08,780 --> 00:19:13,990 +فيها مشكلة نيجي هذهأنا رايح الأتنين من جهة الشمال + +191 +00:19:13,990 --> 00:19:20,230 +يبقى هذه very small negative يبقى هذه very small + +192 +00:19:20,230 --> 00:19:26,610 +negative quantity هذه مافيش فيها مشكلة اتنين زائد + +193 +00:19:26,610 --> 00:19:33,950 +اتنين يبقى أداشة بطلع بطلع عندي واحد على اتنين في + +194 +00:19:33,950 --> 00:19:41,230 +very smallNegative quantity يعني إيه؟ سالب + +195 +00:19:41,230 --> 00:19:48,800 +infinityبعد هيك بتروح اخد ال limit لل F of X لما + +196 +00:19:48,800 --> 00:19:53,560 +ال X بده يروح لل اتنين من جهة اليمين يبجى هذا ال + +197 +00:19:53,560 --> 00:19:58,920 +limit لما ال X بده تروح لل اتنين من جهة اليمين لل + +198 +00:19:58,920 --> 00:20:06,500 +X على X ناقص اتنين في X زائد اتنين يبجى هذا الكلام + +199 +00:20:06,500 --> 00:20:11,780 +بده يساوي اتنين علىنحل اتنين من جهات اليمين يعني + +200 +00:20:11,780 --> 00:20:19,520 +اتنين وكسر بسيط نقص اتنين يبقى very small positive + +201 +00:20:19,520 --> 00:20:27,040 +quantity ثمين في اتنين زائد اتنين يبقى النتيجة + +202 +00:20:27,040 --> 00:20:29,560 +كده؟ infinity + +203 +00:20:31,120 --> 00:20:38,520 +يبقى النهاية من الشمال بسالب Infinity ومن اليمين ب + +204 +00:20:38,520 --> 00:20:45,580 +Infinity يبقى هنا يقول هذه أو تلك يبقى أنا تحقق + +205 +00:20:45,580 --> 00:20:49,500 +عندي واحدة منهم هذه موجودة إذا أنا بقدر أقول هذه + +206 +00:20:49,500 --> 00:20:56,390 +الخطة الأبرانيةvertical asymptote يبقى باجي بقول + +207 +00:20:56,390 --> 00:21:08,210 +له so ال X يساوي اتنين is a vertical asymptote + +208 +00:21:08,210 --> 00:21:13,110 +طيب اللي عملنا له اتنين بدنا نروح نعمله لمين؟ + +209 +00:21:13,110 --> 00:21:21,710 +لسالي باتنين يبقى باجي اخد الان limitلل F of X لما + +210 +00:21:21,710 --> 00:21:27,470 +ال X بده يروح لسالي باتنين من جهة الشمال يبقى ال + +211 +00:21:27,470 --> 00:21:33,350 +limit لما ال X بده تروح لسالي باتنين من جهة الشمال + +212 +00:21:33,350 --> 00:21:42,290 +لدالة X X ناقص اتنين في X زائد اتنين ويسوى سالي + +213 +00:21:42,290 --> 00:21:48,110 +باتنين سالي باتنين من جهة الشمال مع هذه مش فيها اي + +214 +00:21:48,110 --> 00:21:53,950 +مشكلةيبقى هنا هاي سالي باتنين سالي باتنين المشكلة + +215 +00:21:53,950 --> 00:21:58,390 +بيصير وين؟ في الجوس الثاني انا رايح اللي سالي + +216 +00:21:58,390 --> 00:22:03,450 +باتنين من جهة الشمال يبقى سالي باتنين وكسر زائد + +217 +00:22:03,450 --> 00:22:09,330 +اتنين بيضل very small positive ولا negative احنا + +218 +00:22:09,330 --> 00:22:14,130 +رايح اللي سالي باتنين من جهة الشماليبقى هنا ال + +219 +00:22:14,130 --> 00:22:23,110 +very small negative quantity طيب طلّالي ليه هذه؟ + +220 +00:22:23,110 --> 00:22:27,250 +هذه سالب اتنين وهذه سالب اربعة بروح و بضل بس very + +221 +00:22:27,250 --> 00:22:33,230 +small negative يعني مين؟ يعني واحد على اتنين في + +222 +00:22:33,230 --> 00:22:40,070 +very small negative quantity يبقى بسلب infinity + +223 +00:22:41,220 --> 00:22:47,720 +بالمثل بدنا ناخد limit لما ال X بدها تروح ل-2 من + +224 +00:22:47,720 --> 00:22:54,800 +جهة اليمين لل F of X يبقى ال X بدها تروح ل-2 من + +225 +00:22:54,800 --> 00:23:02,760 +جهة اليمينللـ x على x نقص 2 في الـ x زائد 2 عند + +226 +00:23:02,760 --> 00:23:07,480 +السلب 2 الجثث الأول مافيش فيه أي إشكالية يبقى أي + +227 +00:23:07,480 --> 00:23:15,540 +سلب 2 سلب 2 سلب 2 فين؟ سلب 2 من جهة اليمين، يعني + +228 +00:23:15,540 --> 00:23:21,680 +السلب 1وحط ساعات زي ما بدك بضل very small positive + +229 +00:23:21,680 --> 00:23:30,570 +يبقى very small positive quantityهذا سيعطيك نص + +230 +00:23:30,570 --> 00:23:38,090 +يبقى هذا الكلام واحد على اتنين very small positive + +231 +00:23:38,090 --> 00:23:45,370 +quantity يبقى هذا سيعطيك main infinity يبقى تحقق + +232 +00:23:45,370 --> 00:23:51,130 +الأولى على حده وتحقق الثاني على حده لنفس الخط يبقى + +233 +00:23:51,130 --> 00:23:59,560 +باجي بقول لهالـ x يساوي سالب اتنين is a vertical + +234 +00:23:59,560 --> 00:24:01,600 +asymptote + +235 +00:24:04,680 --> 00:24:08,960 +يبقى طالع عندنا بدل الخط اتنين vertical asymptote + +236 +00:24:08,960 --> 00:24:13,820 +و horizontal asymptote واحد وماعنديش oblique + +237 +00:24:13,820 --> 00:24:18,220 +asymptote فانتوا ملاحظين اننا بنحسب ال asymptotes + +238 +00:24:18,220 --> 00:24:24,940 +هذه نظريا لكن عمليا على أرض الواقع ماشوفناش بالمرة + +239 +00:24:24,940 --> 00:24:32,210 +لذلك بنحاول نعطيكمثال عملي ونحاول نرسم ال function + +240 +00:24:32,210 --> 00:24:38,850 +و ال asymptotes تبعتها يبقى نيجي ناخد مثال أخير + +241 +00:24:38,850 --> 00:24:42,930 +يبقى + +242 +00:24:42,930 --> 00:24:49,010 +example يقول + +243 +00:24:49,010 --> 00:24:56,030 +sketch the graph of the function sketch the graph + +244 +00:24:56,030 --> 00:25:08,210 +ofThe function دالة Y تساوي X تربيع ناقص واحد على + +245 +00:25:08,210 --> 00:25:19,590 +اتنين X زائد أربعة and و الله كذلك بعد ما ترسم + +246 +00:25:19,590 --> 00:25:28,050 +find the asymptotes and + +247 +00:25:30,380 --> 00:25:43,180 +Demonated terms السؤال + +248 +00:25:43,180 --> 00:25:49,860 +بين أدينا ثلاثة مطالب بدنا نتعرف على هذه المطالب + +249 +00:25:49,860 --> 00:25:57,340 +الثلاثة ونشوف كيف بدنا نحل هذا السؤال + +250 +00:26:00,110 --> 00:26:06,010 +سؤال مرة تانية بيقول ارسملي منحنى الدالة x تربية + +251 +00:26:06,010 --> 00:26:12,450 +ناقص واحد على اتنين x زائد اربع اتنين هاتل ال + +252 +00:26:12,450 --> 00:26:16,950 +asymptotes تبعات هذه ال function تلاتة ال + +253 +00:26:16,950 --> 00:26:22,330 +demanding terms يعني أجزاء التحكم بالنسبة لهذه + +254 +00:26:22,330 --> 00:26:27,260 +الدالةDemonetic terms اللي هو أجزاء التحكم لهذه + +255 +00:26:27,260 --> 00:26:32,220 +الدلة طبعا كلمة جديدة لم نسمع بها من قبل لكن + +256 +00:26:32,220 --> 00:26:36,480 +سمعناها لك اليوم و هنسمعها لك تاني كمان في شبط + +257 +00:26:36,480 --> 00:26:44,080 +الأربعة ان شاء الله تعالى طيب solutionليس بالضرورة + +258 +00:26:44,080 --> 00:26:48,540 +أن نبدأ عملية الرسم لأن ماعنديش معلومات لكن بقدر + +259 +00:26:48,540 --> 00:26:53,500 +أجيب له ال asymptotes و بعد هيك الdominant terms + +260 +00:26:53,500 --> 00:26:57,380 +مثلا و بعد هيك نرسم او نرسم و بعد هيك ال dominant + +261 +00:26:57,380 --> 00:27:01,020 +terms مش مشكلة لكن أبسط حاجة أني أحسبله ال + +262 +00:27:01,020 --> 00:27:05,880 +asymptotes السؤال هو هل يوجد عندي horizontal + +263 +00:27:05,880 --> 00:27:09,640 +asymptote في + +264 +00:27:11,780 --> 00:27:14,860 +يعني مش هنجيب ال horizontal بدي أخد ال limit لما + +265 +00:27:14,860 --> 00:27:21,080 +ال X بدها تروح ل infinity أو لسالب infinity درجة + +266 +00:27:21,080 --> 00:27:26,520 +البسط أعلى من درجة المقام يبقى النتيجة يا infinity + +267 +00:27:26,520 --> 00:27:29,900 +يا سالب infinity يعني في عندي horizontal asymptote + +268 +00:27:29,900 --> 00:27:34,900 +مافي إمكانية بالمرة يبقى هنا بقوله there is no + +269 +00:27:34,900 --> 00:27:40,900 +horizontal asymptote there is no + +270 +00:27:48,160 --> 00:27:52,820 +Horizontal asymptote مافيش عندي horizontal + +271 +00:27:52,820 --> 00:27:55,920 +asymptote، بدك تقوله ليش؟ + +272 +00:27:59,620 --> 00:28:08,240 +درجة البسط درجة الاكس تربيه ناقص واحد اكبر من + +273 +00:28:08,240 --> 00:28:13,540 +الدرجة للاتنين اكس زائد اربع وبالتالي اذا كانت + +274 +00:28:13,540 --> 00:28:18,420 +درجة دالة البسط اعلى من درجة دالة المقام فال limit + +275 +00:28:18,420 --> 00:28:23,840 +تساوي قداش تساوي infinity وبالتالي ال horizontal + +276 +00:28:24,440 --> 00:28:30,220 +السيمتوت لا يوجد، يبقى استبعدنا اللي هو + +277 +00:28:30,220 --> 00:28:35,120 +الهورزونتال للسيمتوت، درجة الباص أعلى من درجة + +278 +00:28:35,120 --> 00:28:40,140 +المقام بمقدار واحد، إذا فيه عندنا main oblige + +279 +00:28:40,140 --> 00:28:44,700 +السيمتوتمش هنجيب له بليه قسمته، قول لها بتروحه + +280 +00:28:44,700 --> 00:28:49,340 +اضيف شغل للباصته وشغل مقامه، تقسم او تقسم جسمة + +281 +00:28:49,340 --> 00:28:55,700 +مطولة من البداية، اذا لو روحنا قسمنا جسمة مطولة X + +282 +00:28:55,700 --> 00:29:02,430 +تربية ناقص واحد على اتنين X زائد اربعةX تربيع على + +283 +00:29:02,430 --> 00:29:11,890 +2 X ب X على 2 X على 2 في 2 X ب X تربيع X على 2 ضرب + +284 +00:29:11,890 --> 00:29:22,940 +4 بجزائد 2 Xالان نغيّر الإشارات وبنجمع يبقى هذه + +285 +00:29:22,940 --> 00:29:28,920 +ناقص وهذه ناقص وهذه مع السلامة صار عندنا ناقص + +286 +00:29:28,920 --> 00:29:35,150 +اتنين اكس ناقص واحدلا يزال الآن المقام من الدرجة + +287 +00:29:35,150 --> 00:29:41,090 +الأولى والمقصوم عليه من الدرجة الأولى كذلك إذا + +288 +00:29:41,090 --> 00:29:48,330 +بنروح وعاصل عملية القسمة يبقى ناقص 2X على 2X بقداش + +289 +00:29:48,510 --> 00:29:56,750 +بنقص واحد بنقص اتنين X وهنا ناقص اربع بنغير + +290 +00:29:56,750 --> 00:30:03,830 +الإشارات وبنروح نجمة يبقى هاي هذه زاد وهذه زاد مع + +291 +00:30:03,830 --> 00:30:09,110 +السلامة بيظل عندي قداش تلاتة اذا ال function عندنا + +292 +00:30:09,110 --> 00:30:17,160 +Yاللي هي عبارة عن X تربية ناقص واحد على اتنين X + +293 +00:30:17,160 --> 00:30:22,780 +زائد اربعة يمكن كتابتها على الشكل التالي خارج + +294 +00:30:22,780 --> 00:30:29,840 +القسمة X على اتنين ناقص واحد تمام؟ الآن الباقي + +295 +00:30:29,840 --> 00:30:35,340 +اللي هو زائد تلاتة لسه بده اجسمها على مين؟ على + +296 +00:30:35,340 --> 00:30:43,740 +المقام اللي هو اتنين X زائد اتنينإذن كإني كتبت + +297 +00:30:43,740 --> 00:30:49,100 +المسألة بشكل جديد بدل ما كانت بالشكل هذا حاطينا + +298 +00:30:49,100 --> 00:30:53,220 +خارج القسمة زائد البقى اللي هو تلاتة بالداجس + +299 +00:30:53,220 --> 00:30:56,640 +معالمين على المقصوم عليه اللي هو اتنين X زائد + +300 +00:30:56,640 --> 00:31:01,880 +اربعة او اتنين في X زائد اتنين الterm اللي طالع + +301 +00:31:01,880 --> 00:31:07,140 +عندنا هذا هو عبارة عن مين ال obligive symptom + +302 +00:31:07,140 --> 00:31:09,080 +فبروح بقولهم لا + +303 +00:31:14,090 --> 00:31:22,650 +اسمتوت Y يساوي X على 2 ناقص واحد + +304 +00:31:31,710 --> 00:31:36,730 +وهي معادلة خط مستقيم لأنها من الدرجة الخاط + +305 +00:31:36,730 --> 00:31:42,510 +المستقيم هذا هو الابليج اسمتت طيب هل هي result + +306 +00:31:42,510 --> 00:31:48,530 +مافيش طلعنا ابليج اسمتت السؤال هو في عند vertical + +307 +00:31:48,530 --> 00:31:55,310 +اسمتت ولا لأ اقول تعالى نشوف الدالة غير معرفة عند + +308 +00:31:55,310 --> 00:31:56,330 +X يساوي + +309 +00:32:04,680 --> 00:32:09,760 +الدالة غير معرّفة إذا احتمال ان يكون عند هذه + +310 +00:32:09,760 --> 00:32:14,880 +النقطة اللي هو main vertical asymptote واحتمال + +311 +00:32:14,880 --> 00:32:19,180 +يكون ثقوب في المنحنة مظبوط او لا يبقى بتأكد انه ما + +312 +00:32:19,180 --> 00:32:23,120 +هو ثقوب بتأكد انه vertical asymptote يبقى بتروح + +313 +00:32:23,120 --> 00:32:30,630 +اخد ال limitلل F of X لما ال X بده يروح لسالي + +314 +00:32:30,630 --> 00:32:36,050 +باتنين من جهة الشمال يبقى هاي ال limit لما ال X + +315 +00:32:36,050 --> 00:32:41,490 +بده تروح لسالي باتنين من جهة الشمال لمن؟ لل X على + +316 +00:32:41,490 --> 00:32:49,510 +اتنين ناقص واحد زائد تلاتة اتنين في Xزائد اتنين و + +317 +00:32:49,510 --> 00:32:55,310 +يساوي سالب اتنين طبعا من جهة الشمال يبقى هذه سالب + +318 +00:32:55,310 --> 00:33:01,530 +اتنين على اتنين سالب واحد زائد تلاتة على اتنين في + +319 +00:33:01,530 --> 00:33:06,270 +احنا راح نحلي سالب اتنين من جهة الشمال يبقى سالب + +320 +00:33:06,270 --> 00:33:12,670 +اتنين وكسر زائد اتنين مضل very small negative يبقى + +321 +00:33:12,670 --> 00:33:17,490 +very small negative quantity + +322 +00:33:19,520 --> 00:33:25,880 +هذا سالب واحد و سالب واحد يبقى بجداش بسالب اتنين + +323 +00:33:25,880 --> 00:33:32,620 +وهذه عدد على كمية سالبة بسالب infinity يبقى + +324 +00:33:32,620 --> 00:33:37,120 +النتيجة سالب infinityسالب infinity تضربها في رقم + +325 +00:33:37,120 --> 00:33:43,220 +تجمع لها رقم تطرح منها رقم كله بيظل إيه سالب + +326 +00:33:43,220 --> 00:33:49,640 +infinity لو جربنا أخدنا limit لل F of X لما ال X + +327 +00:33:49,640 --> 00:33:56,700 +بيروح لسالب 2 من جهة اليمينيبقى limit لما ال X بده + +328 +00:33:56,700 --> 00:34:03,700 +يروح ل-2 من جهة اليمين لل X على 2 ناقص واحد تلاتة + +329 +00:34:03,700 --> 00:34:09,440 +على اتنين في X زائد اتنين ويساوي سالب اتنين على + +330 +00:34:09,440 --> 00:34:16,930 +اتنين زائد واحد زائد تلاتة على اتنين فينرحل سالب + +331 +00:34:16,930 --> 00:34:22,190 +اتنين من جهة اليمين يبقى سالب واحد ومجموعة تسعة + +332 +00:34:22,190 --> 00:34:28,570 +مثلا زائد اتنين بيبقى very small positive يبقى + +333 +00:34:28,570 --> 00:34:36,530 +very small positive quantity يبقى هذا الكلام بده + +334 +00:34:36,530 --> 00:34:44,010 +يساوي سالب اتنين زائد infinity اللي هو infinity + +335 +00:34:44,790 --> 00:34:54,190 +بناء ان عليه صورة ان ال X + +336 +00:34:54,190 --> 00:35:06,750 +يساوي سالب اتنين is a vertical asymptote + +337 +00:35:06,750 --> 00:35:14,410 +يبقى خلاصة من المطلوب الأولبنانيج لمان؟ للمطلوب + +338 +00:35:14,410 --> 00:35:19,950 +الثاني في المثلة المطلوب التاني قال لي ارسم وقال + +339 +00:35:19,950 --> 00:35:26,170 +لي هاتلي ال terms اجزاء التحكم في هذه الدلة تعالى + +340 +00:35:26,170 --> 00:35:32,010 +نشوف ايش قصة اجزاء التحكم احنا انا y يسوى x على 2 + +341 +00:35:32,010 --> 00:35:37,850 +ناقص واحد تلاتة على اتنين في x زائد اتنين هذه + +342 +00:35:37,850 --> 00:35:44,660 +الدلةيبقى هذه ال function مكوّنة من جزئين هذا هو + +343 +00:35:44,660 --> 00:35:52,540 +الجزء الأول وهذا هو الجزء الثانيطلّع عليه كويس، لو + +344 +00:35:52,540 --> 00:35:59,100 +خلّيت ال X تكبر، كويس؟ تكبر عشر، عشرين، مية، + +345 +00:35:59,100 --> 00:36:04,680 +مليون، مليار، إلا كم، تكبر ال X، يبقى هذا بيصير + +346 +00:36:04,680 --> 00:36:10,480 +رقم كبير ولا صغير؟ كبير جدا، طيب هذا شو بيصير؟ + +347 +00:36:10,480 --> 00:36:16,320 +بيصير Zero، ممتاز جدايقول إنه يتحكم في سلوك الدالة + +348 +00:36:16,320 --> 00:36:21,080 +اللي هو من الجزء الأول، إيش يعني بتحكم فيها؟يعني + +349 +00:36:21,080 --> 00:36:27,080 +الدالة بدها تصير هى وهذا جرايب وحبايب، هى، بدهم + +350 +00:36:27,080 --> 00:36:31,800 +يسيلوا يمشوا مع بعض، تمام؟ هى معناها، طيب هذا خط + +351 +00:36:31,800 --> 00:36:36,470 +قاربإذا المنحلة بيصيحين قريب منه اتنين ماشيين + +352 +00:36:36,470 --> 00:36:41,590 +معاك، كل ما تكبر X هم مابتفرجوش، يبقى الذي يتحكم + +353 +00:36:41,590 --> 00:36:46,730 +في سلوك الدالة في هذه الحالة عندما تكون X كبيرة + +354 +00:36:46,730 --> 00:36:54,330 +جدا، بيكون مين الterm الأول، ايه؟ لو جربت على مين؟ + +355 +00:36:54,330 --> 00:37:00,020 +على سالب اتنينسواء جربت من اليمين أو من الشمال هذه + +356 +00:37:00,020 --> 00:37:05,380 +و هذه كلها بقداش سالب اتنين صح ولا لأ؟ لما جربت من + +357 +00:37:05,380 --> 00:37:09,900 +السالب اتنين هذول اقصى ما يمكن ان يصلوا الي السالب + +358 +00:37:09,900 --> 00:37:15,380 +اتنين طب هذه لما جربت من السالب اتنين بصير لسالب + +359 +00:37:15,380 --> 00:37:20,980 +infinity مظبوط او موجة ب infinity زي ما شوفنا هي + +360 +00:37:20,980 --> 00:37:25,960 +أخدناها يمين و شوف مرة infinityيعني كل ما اجرب على + +361 +00:37:25,960 --> 00:37:31,040 +السالب اتنين ال term التاني بيصغر ولا بيكبر؟ term + +362 +00:37:31,040 --> 00:37:38,160 +التاني بيكبر خالص، طبعا؟ يعني رايح لوين؟ رايح لل + +363 +00:37:38,160 --> 00:37:43,340 +infinity، طبعا؟ يبقى هذا هو ال term الذي سيتحكم في + +364 +00:37:43,340 --> 00:37:49,280 +سلوك الدالة في هذه العالم يبقى إذا X كبرت بقيمة + +365 +00:37:49,280 --> 00:37:54,950 +موجبة سيتحكم ال term الأولإذا X جربت على سالب + +366 +00:37:54,950 --> 00:38:00,150 +اتنين بدى يتحكم في الدالة ال term تنقل لو X راحت + +367 +00:38:00,150 --> 00:38:06,530 +لسالب infinity يعنى صارت X سالبة بدرجة كبيرة جدا + +368 +00:38:06,530 --> 00:38:11,350 +يبقى هذا كده كده تصير ال term سالب infinity وهذا + +369 +00:38:11,350 --> 00:38:19,130 +كده؟ Zero يبقى عدديا عندما X تكبر أو X تصغر خالص + +370 +00:38:19,130 --> 00:38:24,900 +يبقى اللى بدى يتحكم مين؟الترم الأول يعني إيش بده + +371 +00:38:24,900 --> 00:38:29,840 +يتحكم يعني ده اللي بده تلزج في مين في الترم الأول + +372 +00:38:29,840 --> 00:38:33,360 +طب الترم الأول خط مستقيم إذا ميبقى اللي ماشية مع + +373 +00:38:33,360 --> 00:38:38,100 +مين مع هذا الخط المستقيم اللي هو الابليج السمتت + +374 +00:38:38,100 --> 00:38:43,900 +طيب وإذا كان ال X راحة ل-2 سواء من اليمين و الله + +375 +00:38:43,900 --> 00:38:48,350 +من الشمال يبقى بده يتحكم مينالـ Term الثاني وليس + +376 +00:38:48,350 --> 00:38:54,250 +الـ Term الأول الكلام اللي سمعته بدأ أكتبه لك حتى + +377 +00:38:54,250 --> 00:38:59,070 +تعرف معنى الـ Demonic Terms يبقى باجي بقوله The + +378 +00:38:59,070 --> 00:39:12,290 +Term الو X على 2 ناقص 1 Demonats يتحكم + +379 +00:39:12,290 --> 00:39:23,010 +whenالـ X is numerically عدديا + +380 +00:39:23,010 --> 00:39:32,110 +يعني لا لما أقول عدديا large يعني سالبة أو موجبة + +381 +00:39:32,110 --> 00:39:35,150 +طيب، + +382 +00:39:35,150 --> 00:39:42,400 +that termاللي هو تلاتة على اتنين في x زائد اتنين + +383 +00:39:42,400 --> 00:39:54,380 +دمانات when x is near سالب اتنينلما تكون قريبة جدا + +384 +00:39:54,380 --> 00:40:01,920 +من مين؟ من سالب اتنى يبقى دالة تكونت من جزئين جزهم + +385 +00:40:01,920 --> 00:40:07,420 +بدى يتحكم عندما X ما تكون عدديا كبيرة جدا سواء + +386 +00:40:07,420 --> 00:40:11,900 +كانت بالموجب او بالسالب و لما تكون قريبين من + +387 +00:40:11,900 --> 00:40:17,270 +السالب اتنى بدى يتحكم من ال term التانىيتحكم يعني + +388 +00:40:17,270 --> 00:40:23,190 +ان يصبح ال function ماشية مع هذا ال term او مع هذا + +389 +00:40:23,190 --> 00:40:29,090 +ال term نرسم رسمة المنحنة اللي عندنا يبقى لو جينا + +390 +00:40:29,090 --> 00:40:36,390 +تخيلنا ان هذا محور X هذا محور Y هذه نقطة الأصل + +391 +00:40:36,390 --> 00:40:42,150 +اللي هي Zero بدنا نروح نرسم ال asymptote في + +392 +00:40:42,150 --> 00:40:48,760 +البداية يبقى ال asymptote التانيهو ال homain ال X + +393 +00:40:48,760 --> 00:40:54,100 +يساوي سالب اتنين هو ال vertical ال symptom يبقى + +394 +00:40:54,100 --> 00:41:01,980 +هذا الخط اللي عندنا اللي هو ال X يساوي سالب اتنين + +395 +00:41:01,980 --> 00:41:10,800 +هذا ال vertical ال symptomالاسمتت التاني اللي هو Y + +396 +00:41:10,800 --> 00:41:17,250 +تساوي X على 2 ناقص واحد اللي هو الابلاج الاسمتتهذا + +397 +00:41:17,250 --> 00:41:21,610 +خط مستقيم بدي أجيب نقطتين تقعان على هذا الخط + +398 +00:41:21,610 --> 00:41:27,050 +المستقيم أوصل بينهم بحصل على الأبلغ السيمتون بقول + +399 +00:41:27,050 --> 00:41:33,290 +لو كان ال X بزيرو يبقى ال Y بسالب واحد عندما ال X + +400 +00:41:33,290 --> 00:41:38,230 +بزيرو يبقى ال Y بسالب واحد يبقى هذا زيرو وسالب + +401 +00:41:38,230 --> 00:41:44,710 +واحدعندما تبقى ال y ب0 يبقى ال x على 2 ب1 يبقى ال + +402 +00:41:44,710 --> 00:41:54,750 +x ب2 يبقى 2 و 0 بدأ يجينا النقطة هذه ل 2 و 0 هدول + +403 +00:41:54,750 --> 00:42:00,860 +النقطتين تقعان علمين على الخط المستقيمأو على الـ + +404 +00:42:00,860 --> 00:42:06,440 +oblique asymptote يبقى بوصل بينهم و بمد على + +405 +00:42:06,440 --> 00:42:14,920 +استقامته بيصير هذا هو الـ oblique asymptote اللي + +406 +00:42:14,920 --> 00:42:23,960 +هو من الخط Y يسوى X على 2 نقص واحد يبقى رسم للـ + +407 +00:42:23,960 --> 00:42:29,500 +asymptote الآن بدنا نيجي للرسمةالرسمة، لما بدى + +408 +00:42:29,500 --> 00:42:32,800 +الجزء الأول بدى يتحكم، بدى تكون ماشية مع الـ + +409 +00:42:32,800 --> 00:42:37,520 +oblique asymptoteتمام؟ ولمّا الجزء الثاني بدي + +410 +00:42:37,520 --> 00:42:42,400 +اتحكم بيكون الرسم ماشية مع ال vertical ال center + +411 +00:42:42,400 --> 00:42:48,600 +تمام؟ إذا الرسم ممكن تكون ع الشجة اليمين وع الشجة + +412 +00:42:48,600 --> 00:42:53,260 +الشمال تكون ماشية مع هذا و مع هذا وماشية مع التاني + +413 +00:42:53,260 --> 00:42:57,660 +ومع هذا أو ممكن تكون في الجزء اللي فوق و الجزء + +414 +00:42:57,660 --> 00:43:02,680 +الثاني اللي تحت تكون ماشية هنا وماشية هنا بدل ما + +415 +00:43:02,680 --> 00:43:08,630 +كانت ماشية هنا وماشية تحتإذا أنا بدي أروح أحط قيم + +416 +00:43:08,630 --> 00:43:12,510 +من عندي و أشوف هل بتطلع على اليمين و على الشمال + +417 +00:43:12,510 --> 00:43:18,490 +ولا فوق و تحت فبعدين بقوله لو كانت ال X ب Zero على + +418 +00:43:18,490 --> 00:43:23,150 +سبيل المثال هذه الدالة اللي عندنا الأساسية لو كانت + +419 +00:43:23,150 --> 00:43:29,080 +ال X ب Zero يبقى ال Y بقداشسالب ربع يبقى Zero و + +420 +00:43:29,080 --> 00:43:32,680 +سالب ربع اللي هي النقطة اللي عندنا لأن هذه سالب + +421 +00:43:32,680 --> 00:43:38,460 +واحد يبقى النقطة هذه Zero و سالب ربع تمام؟ لو كانت + +422 +00:43:38,460 --> 00:43:44,220 +ال Y ب Zero يبقى ال bus مستوى Zero ولا المقام؟ ال + +423 +00:43:44,220 --> 00:43:48,120 +bus يعني X ترمية ناقص واحد مستوى Zero يعني X سوى + +424 +00:43:48,120 --> 00:43:54,200 +واحد أو سالب واحد يعني بدأ تجيلك هدف النص هنا و + +425 +00:43:54,200 --> 00:44:00,080 +هدف النص هناإذا المنحنة بدى يكون فوق وتحت وليس على + +426 +00:44:00,080 --> 00:44:05,120 +اليمين وعلى الشمال إذا لو جينا رسمنا المنحنة بدى + +427 +00:44:05,120 --> 00:44:12,580 +يمشي هيك ويجي نازل ويجي طالع بهذا الشكل مع النقطة + +428 +00:44:12,580 --> 00:44:19,120 +اللى عندنا هذهبديه يمر فيها و يضل ماشي مع مين؟ مع + +429 +00:44:19,120 --> 00:44:24,460 +صاحبه مع ال asymptote هذا و من هنا ييجي مع ال + +430 +00:44:24,460 --> 00:44:29,640 +asymptote لغاية ما يوصل لحد معين و يجي نازل بهذا + +431 +00:44:29,640 --> 00:44:36,540 +الشكليبقى هذه الرسمة اللي قدامنا طبعا رسم + +432 +00:44:36,540 --> 00:44:41,000 +character مش دقيق مية لمية لكن الرسم يدل على مين + +433 +00:44:41,000 --> 00:44:47,460 +يدل على الشكل وسنرجع إلى هذه الرسومات في chapter 4 + +434 +00:44:47,460 --> 00:44:53,100 +ان شاء الله لما نشوف واجتاش الدلة تزايدية واجتاش + +435 +00:44:53,100 --> 00:44:58,900 +تناقصيةوانت تقاطع مع محاور الأحداثيات وين النقاط + +436 +00:44:58,900 --> 00:45:03,840 +الحريجة؟ مين منها عظمة محلية ومين منها صغرة محلية؟ + +437 +00:45:03,840 --> 00:45:08,120 +وانتش المنحنة concave up و concave down مفتوح إلى + +438 +00:45:08,120 --> 00:45:13,040 +أسفل و مفتوح إلى أعلى؟ وين نقاط الإنقلاب للمنحنة؟ + +439 +00:45:13,040 --> 00:45:18,300 +كل هذا سنجله في chapter 4 ان شاء الله تعالى. تمام؟ + +440 +00:45:18,750 --> 00:45:22,730 +بعد ما ناخد chapter ثلاثة و نروح على chapter أربع + +441 +00:45:22,730 --> 00:45:26,810 +chapter ثلاثة الاشتقاق chapter أربع تطبيقات على + +442 +00:45:26,810 --> 00:45:31,250 +مين على الاشتقاق حاجة فيكم؟ بتسأل أي سؤال هنا؟ + +443 +00:45:35,140 --> 00:45:39,240 +في الأول لما حكيت عن ال vertical والsimple حكينا + +444 +00:45:39,240 --> 00:45:42,660 +ان لو كانت ال limit does not exist كل الشراء رضوا + +445 +00:45:42,660 --> 00:45:45,680 +انه مافيش vertical والsimple كل الأمثلة اللي + +446 +00:45:45,680 --> 00:45:47,620 +أخدناها ال limit كانت does not exist بس كانت لا + +447 +00:45:47,620 --> 00:45:53,600 +اتننى اجرأت تعرفي كويس قلنا هادي or هاديوحدة منهم + +448 +00:45:53,600 --> 00:45:56,760 +تكفي، لكن احنا نبحث التانية هل بتجيب vertical + +449 +00:45:56,760 --> 00:46:00,520 +السيمتون تاني؟ والله نفسه، ايه كل الهدف، لكن كفيني + +450 +00:46:00,520 --> 00:46:03,540 +واحدة منهم للvertical السيمتون، مش التن، مش + +451 +00:46:03,540 --> 00:46:07,460 +التنتين، لو لمينه شمال جابه نفس النتيجة، برضه + +452 +00:46:07,460 --> 00:46:13,220 +ماعناه مشكلة، تمام؟مظبوط في المثال اللي أخدناه، مش + +453 +00:46:13,220 --> 00:46:15,880 +لما .. مش dust not exist، dust not exist عن جهتي، + +454 +00:46:15,880 --> 00:46:20,220 +لكن من اليمين موجودة، خلّا بيكفيني، أشمال مش + +455 +00:46:20,220 --> 00:46:25,140 +لازمالي، لكن أنا بسوي احتياطا باس، ليس ال .. هل + +456 +00:46:25,140 --> 00:46:27,800 +بيجيبلي نفس النتيجة ولا نتيجة تانية، لكن يبقى + +457 +00:46:27,800 --> 00:46:32,220 +كافية واحدة منهم، واضح؟ بس واحدة، الله أعطيك + +458 +00:46:32,220 --> 00:46:33,500 +العافية، أه + +459 +00:46:37,230 --> 00:46:42,050 +هكذا هلما تقولي إذا الوبلاجة سمتة X على اتنين ناقص + +460 +00:46:42,050 --> 00:46:42,470 +واحد + +461 +00:46:46,010 --> 00:46:50,150 +تقول اللي هو ال vertical asymptote اتنين، شو + +462 +00:46:50,150 --> 00:46:55,670 +الاتنين هذا؟ Y والله X، الله يعلم، تكتبش بخصوم لك، + +463 +00:46:55,670 --> 00:47:00,130 +لكي تحدد، احنا بقولك X يسوى A vertical asymptote، + +464 +00:47:00,130 --> 00:47:05,390 +Y تسوى B يبقى horizontal asymptote، Y تسوى X زي B + +465 +00:47:05,390 --> 00:47:09,950 +يبقى obligal asymptote، لكي تكتب كلام واضح وكلام + +466 +00:47:09,950 --> 00:47:16,870 +ذو معنىلأ عدنا ننتهي هذا ال section وإليكم أرقام + +467 +00:47:16,870 --> 00:47:19,870 +المسائل ال exercises اتنين ستة + +468 +00:47:59,270 --> 00:48:04,970 +ننتقل الان الى ال section اللى كلكم استعدلين عليه + +469 +00:48:04,970 --> 00:48:08,220 +اللى derivativeيقول لي بقى جيبلي ال derivative + +470 +00:48:08,220 --> 00:48:14,960 +دوري تمام يبقى بننتقل إلى هذا ال section اللي هو + +471 +00:48:14,960 --> 00:48:20,500 +ال differentiation شبطر تلاتة يبقى الشبطر تلاتة + +472 +00:48:20,500 --> 00:48:23,500 +كله بتكلم عن الاشتقاق + +473 +00:48:59,780 --> 00:49:02,920 +عشان يعملوا اصلا عشان يعملوا اصلا عشان يعملوا اصلا + +474 +00:49:02,920 --> 00:49:27,140 +عشان يعملوا اصلا عشان يعملوا اصلا عشان يعملوا اصلا + +475 +00:49:51,860 --> 00:49:57,660 +التعريف هذا أخدته قبل ذلك بس مجرد تذكير ليس إلا + +476 +00:49:57,660 --> 00:50:13,420 +The slope of the curveof the curve ميل المنحنة the + +477 +00:50:13,420 --> 00:50:24,260 +slope of the curve Y تساوي F of X at the point عند + +478 +00:50:24,260 --> 00:50:30,360 +النقطة X0 وF + +479 +00:50:30,360 --> 00:50:31,780 +of X0 + +480 +00:50:34,480 --> 00:50:40,880 +is the number M + +481 +00:50:40,880 --> 00:50:50,100 +اللي هو بده يساوي limit لما H بده تروح لل zero لل + +482 +00:50:50,100 --> 00:50:57,180 +F of X node زاد ال H ناقص F of X node على H + +483 +00:50:57,180 --> 00:50:59,580 +provided the + +484 +00:51:05,320 --> 00:51:17,380 +القاعدة توجد تجارب + +485 +00:51:17,380 --> 00:51:21,480 +تجارب + +486 +00:51:21,480 --> 00:51:26,680 +تجارب تجارب تجارب + +487 +00:51:34,640 --> 00:51:38,520 +يبقى الـ tangent line to the curve Y تسوية F of X + +488 +00:51:38,520 --> 00:51:54,760 +at the point عند النقطة P of X0 فF of X0 is the + +489 +00:51:54,760 --> 00:51:56,740 +line + +490 +00:51:58,230 --> 00:52:11,830 +أثرى P خلال النقطة P with this slope M its + +491 +00:52:11,830 --> 00:52:13,150 +equation is + +492 +00:52:19,580 --> 00:52:32,100 +Y تساوي M X نقص X node زائد Y node كمان + +493 +00:52:32,100 --> 00:52:39,040 +derivative او definition of + +494 +00:52:39,040 --> 00:52:46,440 +the + +495 +00:52:46,440 --> 00:53:00,130 +functionالدريفتب دي فانكشن f at a point x0 denoted + +496 +00:53:00,130 --> 00:53:03,630 +by + +497 +00:53:03,630 --> 00:53:10,050 +f prime of x0 is + +498 +00:53:11,620 --> 00:53:19,440 +f prime of x node دي سوى ال limit لما ال h بده + +499 +00:53:19,440 --> 00:53:28,380 +تروح لل zero لل f of x node زاد ال h ناقص f of x + +500 +00:53:28,380 --> 00:53:36,400 +node على h provided the + +501 +00:53:36,400 --> 00:53:40,940 +limit exist + +502 +00:54:03,530 --> 00:54:06,330 +مش عارف + +503 +00:54:22,940 --> 00:54:24,380 +السلام عليكم + +504 +00:54:52,490 --> 00:54:54,070 +السلام عليكم و رحمه الله + +505 +00:55:51,790 --> 00:55:53,190 +السلام عليكم + +506 +00:56:32,090 --> 00:56:38,430 +أبعاد الرسم هذه كتبت معاها قبل ذلك وكذلك التعريف + +507 +00:56:38,430 --> 00:56:43,150 +الأول ان كتبت معاه قبل ذلك احنا بنذكره مشان مهدبه + +508 +00:56:43,150 --> 00:56:47,990 +فقط للتعريف الثاني اللي هو موضوع دراستنا في هذا + +509 +00:56:47,990 --> 00:56:53,340 +الشبطةيبقى هذا chapter differentiation يعني عملية + +510 +00:56:53,340 --> 00:56:59,180 +الاشتقاق أو عملية إيجاد المشتقة الأولى لدالة ما + +511 +00:56:59,180 --> 00:57:06,160 +هنبدأ بأول section بتتكلم عن نقطتين tangents خطوط + +512 +00:57:06,160 --> 00:57:11,610 +التماسوالـ derivative at a point المشتقة عند نقطة + +513 +00:57:11,610 --> 00:57:16,850 +وخطوط التماس عند نقطة للمنحنة التعريف الأول يقول + +514 +00:57:16,850 --> 00:57:21,630 +the slope of the curve ميل المنحنة y تساوي f of x + +515 +00:57:21,630 --> 00:57:27,030 +عند نقطة x node وf of x nodeهو عبارة عن العدد + +516 +00:57:27,030 --> 00:57:31,790 +limit لما الـ H بدأ تذهب لـ 0 لفوكس نود زاد الـ H + +517 +00:57:31,790 --> 00:57:35,730 +نقص الـ F of X node على H لما الـ H بدأ تذهب لـ 0 + +518 +00:57:35,730 --> 00:57:40,470 +بشرط ان الـ limit هذه معناها exist يبقى قولنا قبل + +519 +00:57:40,470 --> 00:57:46,750 +ذلك ان ميل المنحنة عنده نقطة هوبنقل المماث عند تلك + +520 +00:57:46,750 --> 00:57:52,170 +النقطة اظن هذا section 2 1 و نفس الرسم اياها + +521 +00:57:52,170 --> 00:57:56,140 +رسمناها و قلنا الكلمتين هدول بالضبط تماماإذا لم + +522 +00:57:56,140 --> 00:58:00,240 +نغير شيئا اتنين The tangent line to the curve + +523 +00:58:00,240 --> 00:58:06,560 +المماس للمنحنة عند النقطة اللي عندنا هذه هو عبارة + +524 +00:58:06,560 --> 00:58:13,600 +عن الخط الذي يمر بهذه النقطة وله نفس لسلوب M يعني + +525 +00:58:13,600 --> 00:58:18,880 +يقولنا ميل المنحنة عند نقطة يسوى ميل المماسعند تلك + +526 +00:58:18,880 --> 00:58:23,840 +النقطة هو معادلة المماس هي Y تستوي M في X نقص X + +527 +00:58:23,840 --> 00:58:27,940 +node زائد Y node X Y node وY node هو النقطة التي + +528 +00:58:27,940 --> 00:58:33,440 +يمر بها المماس يعني النقطة التماس و ال M هذه هو + +529 +00:58:33,440 --> 00:58:38,560 +ميل المنحنة أو ميل المماس للمنحنة عند النقطة بجانب + +530 +00:58:38,560 --> 00:58:43,630 +هذه كلها معلومات قديمة لم نأتي بحرف جديدالجديد هو + +531 +00:58:43,630 --> 00:58:47,210 +من الـ Definition الثاني الـ Definition التاني + +532 +00:58:47,210 --> 00:58:51,550 +بيقول الـ derivative of the function f مشتقة + +533 +00:58:51,550 --> 00:58:57,170 +الدالة f عند النقطة x0 denoted by يعني سنرمز لها + +534 +00:58:57,170 --> 00:59:03,980 +بالرمز أو التي سيرمز لها بالرمزf prime of x0 او f + +535 +00:59:03,980 --> 00:59:09,680 +dash of x0 او f شرطة of x0 اللي بدك ايه بس الدرجة + +536 +00:59:09,680 --> 00:59:16,180 +في لفنها هيكون f prime of x0 مين هو هو ال f prime + +537 +00:59:16,180 --> 00:59:20,900 +of x0 بده يساوي نفس ال limit اللي فوق ال limit لما + +538 +00:59:20,900 --> 00:59:25,900 +ال h بده تروح لل zero لل f of x0 زادتش على f of x0 + +539 +00:59:25,900 --> 00:59:30,610 +زاد ال h نقص f of x0 على hبشرط ان ال limit هذه + +540 +00:59:30,610 --> 00:59:37,730 +exist شيل ال h هذه تعالى على الرسم الان باجي بقول + +541 +00:59:37,730 --> 00:59:42,950 +لو ان المنحنة اللي عندنا هذا y تساوي f of x + +542 +00:59:42,950 --> 00:59:50,160 +المنحنة هذا هاه اللي هو y تساوي f of xروحت أخدت + +543 +00:59:50,160 --> 00:59:54,960 +نقطتين عليه زي النقطة اللي عندنا هذه النقطة هذه ال + +544 +00:59:54,960 --> 01:00:00,300 +result كانت المسافة هذه كلها x0 يبجي يحدث النقطة + +545 +01:00:00,300 --> 01:00:05,260 +هذه x0 صورة x0 هي f of x0 اللي هي المسافة اللي + +546 +01:00:05,260 --> 01:00:12,140 +عندنا هذه يعني هذه من هنا لهنا كمان جديش ل F of x0 + +547 +01:00:12,140 --> 01:00:17,920 +جد هذه بالضبط تماماطيب لو ال X node حصل فيها تغير + +548 +01:00:17,920 --> 01:00:24,080 +ما هذا التغير مقدره H وصلت إلى هذه النقطة يبقى + +549 +01:00:24,080 --> 01:00:28,440 +النقطة هذه اللي حدثت تبقى ال X node زائد ال H قلنا + +550 +01:00:28,440 --> 01:00:33,940 +ال X node زاد الشي بقى ال X حصل فيها تغير مقدر من + +551 +01:00:33,940 --> 01:00:40,360 +Hنتيجة لذلك ستكون القيمة التي عندنا هي F of X0 زي + +552 +01:00:40,360 --> 01:00:46,280 +H إذا إحداث النقطة اللي فوق هذه هه هي X0 زي الـH و + +553 +01:00:46,280 --> 01:00:53,490 +F of X0 زي الـH و سأسميها Qلو وصلت من ال P للي Q + +554 +01:00:53,490 --> 01:01:00,110 +مديت الخط هذا هذا مسمي قاطع للمنحنة يبقى هذا سمينا + +555 +01:01:00,110 --> 01:01:06,630 +قبل ذلك second تمام ابتدوا تذكروا قولنا متوسط + +556 +01:01:06,630 --> 01:01:12,190 +معدلي التغير لده اللي هو F of X node زي دلتش نقص + +557 +01:01:12,190 --> 01:01:15,510 +ال F of X node على اتش اللي كنا نقول هو عبارة عن + +558 +01:01:15,510 --> 01:01:20,960 +Delta Y على Delta Xلكن قلنا إذا Delta X قالت إلى + +559 +01:01:20,960 --> 01:01:26,780 +Zero بصير ال second هو مماس وقلنا لكوا يومها إذا + +560 +01:01:26,780 --> 01:01:32,080 +أجت لكيوب ده تسلم على P بنسبة العيد أجت نازلة ورا + +561 +01:01:32,080 --> 01:01:37,580 +مع المنحنةلما تجي الناس لكي ورايحة مع المنحنى على + +562 +01:01:37,580 --> 01:01:43,300 +النقطة P يبقى القاطع بيصير بالشكل اللي عندنا هذا + +563 +01:01:43,300 --> 01:01:53,100 +مماس للمنحنى عند هذه النقطة يبقى بيصير tangent عند + +564 +01:01:53,100 --> 01:01:58,420 +هذه النقطة يبقى الخط الأحمر هذا هو ال tangent + +565 +01:01:58,420 --> 01:02:04,740 +بيصبح للمنحنى عند هذه النقطةبينحصل عليه واجتاش لو + +566 +01:02:04,740 --> 01:02:10,180 +الـH هذه قالت إلى الـ0 يعني هذه الـQ لو وصلت لهنا + +567 +01:02:10,180 --> 01:02:16,200 +الـH زغرت جربت الـH تصغر جربت أكتر يبقى لما تكاد + +568 +01:02:16,200 --> 01:02:21,640 +الـQ تنطبق على الـP تكاد الـH تصبح كمبالـ zero او + +569 +01:02:21,640 --> 01:02:25,760 +تروح للـ zero ومن هنا روحنا قولنا ان ال limit ل ال + +570 +01:02:25,760 --> 01:02:29,360 +prefix node زاد ال H نقص ال prefix node على H لما + +571 +01:02:29,360 --> 01:02:34,460 +ال H بده يروح ل zero هو معناه المشتقة الأولى لدالك + +572 +01:02:34,460 --> 01:02:42,620 +طيب من هذا الكلام نخلص إلى ما يأتي حالة الأولىميل + +573 +01:02:42,620 --> 01:02:48,960 +المنحنى عند نقطة X node جداش يساوي يساوي ال limit + +574 +01:02:48,960 --> 01:02:55,560 +صح ولا لأ ثانى ميل المماس للمنحنى عند نقطة X node + +575 +01:02:55,560 --> 01:02:59,800 +جداش يساوي ميل المنحنى هو نفس القيمة اللي عندنا + +576 +01:02:59,800 --> 01:03:06,900 +تلاتة مش متوسط معدلة لأ معدلة تغير للدالة عند X + +577 +01:03:06,900 --> 01:03:14,430 +يساوي X node هو هذا مظبوطأربعة، ميل المماس لمنحنى + +578 +01:03:14,430 --> 01:03:19,610 +الظل الزاوية اللى بيعملها المماس مع الاتجاه الموجب + +579 +01:03:19,610 --> 01:03:26,070 +لمين؟ لمحور X خمسة، هذا معناه مين؟ المشتقة الأولى + +580 +01:03:26,070 --> 01:03:31,330 +لدالة لما أقول ميل المماس المحدد مقصوده ظل الزاوية + +581 +01:03:31,330 --> 01:03:35,310 +اللى يصنعها مع الاتجاه الموجب لمحور X أو حسب ما + +582 +01:03:35,310 --> 01:03:40,800 +كان عندنا هذا هو المشتقة الأولى، إذا بلخصكل ما يهم + +583 +01:03:40,800 --> 01:03:46,120 +هذه ال limit في ال remark التالية بنحطها في الأربع + +584 +01:03:46,120 --> 01:03:54,320 +نقاط التالية يبقى remark the + +585 +01:03:54,320 --> 01:03:54,880 +limit + +586 +01:03:58,710 --> 01:04:05,090 +اللي هي limit لما ال H بده تروح لل zero لل F of X + +587 +01:04:05,090 --> 01:04:12,310 +naught زائد ال H ناقص F of X naught على H means + +588 +01:04:12,310 --> 01:04:22,250 +ماذا تعني؟ تعني الشغل الأولى اللي هو the slope of + +589 +01:04:22,250 --> 01:04:34,280 +the curveميل المنحنى Y تساوي F of X at X يساوي X + +590 +01:04:34,280 --> 01:04:43,540 +non او المعنى الثاني The slope of the tangent to + +591 +01:04:43,540 --> 01:04:53,240 +the curveمن المماثل الملحنة y تساوي f of x at ال x + +592 +01:04:53,240 --> 01:05:02,540 +يساوي ال x naught او المعنى الثالث the rate of + +593 +01:05:02,540 --> 01:05:12,360 +exchange معدل التغير the rate of exchange of ال f + +594 +01:05:12,360 --> 01:05:14,780 +of x with + +595 +01:05:19,500 --> 01:05:29,840 +respect with respect to x at ال x يساوي ال x + +596 +01:05:29,840 --> 01:05:39,800 +naught او النقطة الرابعة ال derivative ال + +597 +01:05:39,800 --> 01:05:45,000 +derivative of ال f of x + +598 +01:05:58,010 --> 01:06:03,230 +يبقى هذول الأربعة شغلات كله نفس الشيء + +599 +01:06:25,230 --> 01:06:35,490 +أول مثال على هذا الموضوع example find + +600 +01:06:35,490 --> 01:06:44,890 +the slope of the function find نمرة a find the + +601 +01:06:44,890 --> 01:06:55,340 +slope of the functionf of x يساوي الجذر التربيع + +602 +01:06:55,340 --> 01:07:05,680 +إلى x زائد واحد at the point عند النقطة في تمانية + +603 +01:07:05,680 --> 01:07:13,240 +و تلاتة نمر أبيه find the equation of the tangent + +604 +01:07:13,240 --> 01:07:23,780 +find the equation ofthe tangent مواد المماثل + +605 +01:07:23,780 --> 01:07:31,820 +المنحنة line at T ثمانية و تلاتة + +606 +01:08:02,370 --> 01:08:08,890 +مرة تانية بقول نرجع ال remark تبعتنا ال limit اللي + +607 +01:08:08,890 --> 01:08:14,560 +عندنا هذا بتعطيني أربع شغلاتالشغل الأولى ال limit + +608 +01:08:14,560 --> 01:08:19,580 +هديشو معناها معناها ميل المنحنى عند النقطة x0 + +609 +01:08:19,580 --> 01:08:24,560 +المعنى الثاني ميل المماثل المنحنى عند النقطة x0 + +610 +01:08:24,560 --> 01:08:29,720 +المعنى الثالث معدل التغير للدالة f of x بالنسبة + +611 +01:08:29,720 --> 01:08:36,660 +للمتغير x عند ال x0 المعنى الرابع مشتقة الدالة f + +612 +01:08:36,660 --> 01:08:39,700 +of x عند ال x0 + +613 +01:08:48,250 --> 01:08:53,690 +الان نبدأ ناخد أمثلة تطبيقية عالميا على إيجاد + +614 +01:08:53,690 --> 01:08:59,440 +المشتقة لدالة عند نقطةبقول المثال هات لـ slope تبع + +615 +01:08:59,440 --> 01:09:06,420 +الدالة عند النقطة لـP8 و3 اتنين هات لمعادلة المماس + +616 +01:09:06,420 --> 01:09:12,340 +عند النقطة 8 و3 بنجي للنقطة الأولى بده اجيب ال + +617 +01:09:12,340 --> 01:09:15,200 +slope يبقى ال slope تبع ال curve + +618 +01:09:21,510 --> 01:09:27,850 +الـ male بده يساوي ال limit لما ال H بدها تروح لل + +619 +01:09:27,850 --> 01:09:34,550 +zero لمن؟ لل F of X0 زي .. كدهش ال X0 عندي هنا؟ + +620 +01:09:34,550 --> 01:09:38,670 +تمانية، بدل من أقول X0 بده أقول تمانية زي ال H + +621 +01:09:38,670 --> 01:09:44,850 +ناقص F of تمانية كله عالميا على H + +622 +01:09:47,450 --> 01:09:52,830 +هذا هو المطلوب الأول من المثلة يبقى يصير الميال + +623 +01:09:52,830 --> 01:09:58,570 +الـ Limit لما الـ H بده تروح لـ Zero إذا بدي أشيل + +624 +01:09:58,570 --> 01:10:05,470 +كل X و أحط مكانها تمانية زائد H هي الدالة فوق يبقى + +625 +01:10:05,470 --> 01:10:12,360 +هي الجدر التربية تمانية زائد Hزائد واحد ناقص F of + +626 +01:10:12,360 --> 01:10:17,840 +تمانية الجدرى التربية الى تمانية زائد واحد كله على + +627 +01:10:17,840 --> 01:10:23,480 +H يبقى هذا الكلام بده يساوي ال limit لما ال H بدها + +628 +01:10:23,480 --> 01:10:29,660 +تروح لمين؟ لل zero للجدرى التربية الى تسعة زائد ال + +629 +01:10:29,660 --> 01:10:36,220 +H ناقص تلاتة كله على مين؟ على H لو جاء تعوض تعويد + +630 +01:10:36,220 --> 01:10:43,130 +مباشر بطلع الناتجزيرو على زيرو شو نعمل في جدر نضرب + +631 +01:10:43,130 --> 01:10:48,970 +في مرافق البصد يبقى لو ضربنا في مرافق البصد بصير + +632 +01:10:48,970 --> 01:10:55,510 +تسعة زائد ال H زائد تلاتة كله مقسوما على تسعة زائد + +633 +01:10:55,510 --> 01:11:01,150 +ال H تحت الجدر زائد تلاتةيبقى النتيجة تساوي ال + +634 +01:11:01,150 --> 01:11:06,010 +limit لما ال H بدها تروح على zero ال bust هو الفرق + +635 +01:11:06,010 --> 01:11:11,950 +بين المربعين يبقى مربع القيمة الأولى ناقص مربع + +636 +01:11:11,950 --> 01:11:19,330 +القيمة التانية على H تسعة زائد ال H زائد التلاتة + +637 +01:11:19,330 --> 01:11:25,410 +بالشكل اللي عنهاتسعة مع تسعة بتروح بيظهر limit لما + +638 +01:11:25,410 --> 01:11:31,350 +ال H بده تروح لل zero لل H على H الجدر التربية + +639 +01:11:31,350 --> 01:11:37,270 +تسعة زائد ال H زائد تلاتة ال H مع ال H كذلك يبقى + +640 +01:11:37,270 --> 01:11:43,590 +بتصير limit لما ال H بده تروح لل zero لواحد تسعة + +641 +01:11:43,590 --> 01:11:50,630 +زائد H زائد تلاتةلما الـH بدأ تروح للـ0 بيظهر لنا + +642 +01:11:50,630 --> 01:11:59,750 +كدهش؟ واحد على جدر تسعة زائد تلاتة كدهش؟ سُدس يبقى + +643 +01:11:59,750 --> 01:12:09,630 +النتيجة بدأ تعطينا سُدس في هذه الحالة طيب يبقى + +644 +01:12:09,630 --> 01:12:14,130 +أصبح ال slope تبع ال curve يساوي السُدس طب هذا بده + +645 +01:12:14,130 --> 01:12:19,010 +يساوي ال slope تبع مين؟بالتانجين يبقى احنا خلصنا + +646 +01:12:19,010 --> 01:12:36,350 +المطلوب الأول وفي نفس الوقت هذا بده يساوي خلاصنا + +647 +01:12:36,350 --> 01:12:40,860 +المطلوب الأول بنجي لمطلوب التاني نمر بينمرة بي + +648 +01:12:40,860 --> 01:12:45,520 +قالتلي معادلة المماثل المنحنة مشان اجيب معادلة + +649 +01:12:45,520 --> 01:12:49,860 +المماثل يعني معادلة خط المستقيم بدي ميلو و نقطة + +650 +01:12:49,860 --> 01:12:54,780 +واقع عليه ميلو هي موجود و النقطة موجودة تهينة منه + +651 +01:12:54,780 --> 01:13:02,690 +يبقى باجي بقوله هنا the question ofthe tangent + +652 +01:13:02,690 --> 01:13:13,450 +يبقى معادلة المماس at P تمانية و تلاتة is Y يسوى + +653 +01:13:13,450 --> 01:13:20,250 +الميال في ال X ناقص ال X node زائد ال Y node يبقى + +654 +01:13:20,250 --> 01:13:28,350 +Y يسوى الميال هو سُدس في ال X ناقص تمانية زائد + +655 +01:13:28,350 --> 01:13:37,260 +تلاتةلو ضربنا كله في ستة بصير ستة Y يساوي X ناقص + +656 +01:13:37,260 --> 01:13:46,380 +تمانية زائد ثمانية عشر يبقى المعادلة ستة Y يساوي X + +657 +01:13:46,380 --> 01:13:53,120 +زائد عشرة ناقص تمانية زائد تمانتاش بصير زائد عشرة + +658 +01:13:53,120 --> 01:13:58,280 +يبقى هذه معادلة المماثل المنحنة المطلوبة + +659 +01:14:04,990 --> 01:14:14,890 +بنعطي كمان مثال example + +660 +01:14:14,890 --> 01:14:20,810 +2 بقول + +661 +01:14:20,810 --> 01:14:22,610 +find equations + +662 +01:14:27,050 --> 01:14:38,550 +of all lines معادل الخطوط المستقيمة having slope + +663 +01:14:38,550 --> 01:14:50,430 +الويل تبعها سالب واحد that are tangent that are + +664 +01:14:50,430 --> 01:14:54,970 +tangent to the curve + +665 +01:15:11,320 --> 01:15:19,240 +سؤال مرة تانيةهذا مقدار الميل ونشوف ايش اللي مش + +666 +01:15:19,240 --> 01:15:23,320 +موجود و ايش اللي مش موجود عشان نقدر نوجه و نجاوب + +667 +01:15:23,320 --> 01:15:27,640 +على السؤال سؤال مرة تانية بيقول لهذه معادلات + +668 +01:15:27,640 --> 01:15:32,680 +الخطوط المستقيمة اللي ميلها يساوي سالب واحدواللي + +669 +01:15:32,680 --> 01:15:37,840 +بتكون مماس للمنحنة يبقى أنا عندي منحنة وعندي مماس + +670 +01:15:37,840 --> 01:15:43,580 +لهذا المنحنة وعندي ميل المنحنة وقال لي بدي معادلة + +671 +01:15:43,580 --> 01:15:50,580 +المماس لهذا المنحنة المماس خط مستقيم بلزمني شغلتين + +672 +01:15:50,580 --> 01:15:56,020 +الميل ونقطة التماس ميعطينا نقطة التماس يبقى اتلك + +673 +01:15:56,020 --> 01:16:00,890 +الله يبقى دورك توجد نقطة التماسإن أوجدنا نقطة + +674 +01:16:00,890 --> 01:16:05,650 +التماس يبقى وربما يكون هناك أكتر من نقطة التماس + +675 +01:16:05,650 --> 01:16:10,430 +لأنه قال لي هاتلي كل المعادلات يعني احتمال يطلع + +676 +01:16:10,430 --> 01:16:14,670 +نقطتين، تلاتة، أربعة، الله أعلم، قد ما يطلع ما + +677 +01:16:14,670 --> 01:16:18,610 +يطلع ماعنديش مشكلةيبقى اول شغلة بدنا نروح نجيب + +678 +01:16:18,610 --> 01:16:24,210 +احداثيات هذه النقاط ماعنديش الا التعريف يبقى انا + +679 +01:16:24,210 --> 01:16:30,250 +عندي ال mail بده يساوي ال limit لما ال H بده تروح + +680 +01:16:30,250 --> 01:16:36,150 +لل zero F of X node زائد ال H ناقص F of X node على + +681 +01:16:36,150 --> 01:16:42,200 +Hالـ mail مُعطَى اللي هو جداش سالب واحد يبقى ال X + +682 +01:16:42,200 --> 01:16:46,840 +note ماعرفهاش يبقى بدي أشيل كل X و أحط مكانها X + +683 +01:16:46,840 --> 01:16:51,260 +note زايدة شوية بدي أخد ال limit بس يبقى بدي أكتب + +684 +01:16:51,260 --> 01:16:57,220 +ال limit في الأوليبقى هذه ال limit لما ال H بدها + +685 +01:16:57,220 --> 01:17:04,760 +تروح لل zero لواحد على X node زيد ال H ناقص واحد + +686 +01:17:04,760 --> 01:17:11,780 +ناقص صفر X node يبقى X node ناقص واحد كله على H + +687 +01:17:12,290 --> 01:17:17,610 +حطيت ال limit و عوضت فيها تعويضا مباشرة يبقى هذا + +688 +01:17:17,610 --> 01:17:23,090 +الكلام بده يساوي او سالب واحد بده يساوي limit لما + +689 +01:17:23,090 --> 01:17:27,390 +ال H بدها تروح ل zero هذا ال H اللي تحت مالهاش + +690 +01:17:27,390 --> 01:17:33,290 +دعوةبدا اوحد المقامات للباصلة يبقى بصير اندينامين + +691 +01:17:33,290 --> 01:17:40,950 +X node زي ال H ناقص واحد في X node ناقص واحد يبقى + +692 +01:17:40,950 --> 01:17:49,130 +X node ناقص واحد ناقص X node ناقص H زي واحد و ال + +693 +01:17:49,130 --> 01:17:54,720 +limit لهنقص X node وزايد X node ناقص واحد وزايد + +694 +01:17:54,720 --> 01:18:00,780 +واحد مع السلامة يبقى قالة النتيجة الى ال limit لما + +695 +01:18:00,780 --> 01:18:08,020 +ال H بده تروح ل zero لناقص H على H X node زايد ال + +696 +01:18:08,020 --> 01:18:14,120 +H ناقص واحد X node ناقص الواحد نختصر ال H مع ال H + +697 +01:18:14,120 --> 01:18:19,580 +كذلك لان المضربات في بعض ضرم يبقى هذا بده يسوي ال + +698 +01:18:19,580 --> 01:18:26,510 +limitلما ال H بدها تروح لل zero لسالب واحد على X + +699 +01:18:26,510 --> 01:18:35,380 +node زيدي ال H ناقص واحد في X node ناقص واحدهذا + +700 +01:18:35,380 --> 01:18:39,800 +بدي أعطيك مياتي الطرف الشمال سالب واحد الطرف اليمن + +701 +01:18:39,800 --> 01:18:46,680 +نحط HB0 يبقى لو حطين HB0 بيظل سالب واحد X node + +702 +01:18:46,680 --> 01:18:53,620 +ناقص واحد في ال X node ناقص واحد يعني مين؟ يعني + +703 +01:18:53,620 --> 01:19:01,720 +سالب واحد X node ناقص واحد الكل تربية يبقى معادلة + +704 +01:19:01,720 --> 01:19:07,340 +فيها مجهول واحد هو مين؟X0 يعني الاحداث الصيني + +705 +01:19:07,340 --> 01:19:12,540 +لنقطة التماسك بده حل المعادلة ده لو ضربنا في سالب + +706 +01:19:12,540 --> 01:19:19,120 +واحد بصير كلها مجمة شجلبنا بصير عند X0 ناقص واحد + +707 +01:19:19,120 --> 01:19:25,460 +لكل تربية يسوى كده؟ واحدبدي أخد الجذر التربيع إلى + +708 +01:19:25,460 --> 01:19:31,060 +الطرفين يبقى بيصير absolute value لل X node ناقص + +709 +01:19:31,060 --> 01:19:36,260 +واحد يساوي absolute value للواحد اللي هو بواحد، + +710 +01:19:36,260 --> 01:19:42,050 +بدي أتخلص من ال absolute valueيبقى ال X node ناقص + +711 +01:19:42,050 --> 01:19:47,890 +واحد يساوي زائد او ناقص واحد اذا هذه هتعطيني + +712 +01:19:47,890 --> 01:19:53,550 +معادلتين المعادلة الاولى X node ناقص واحد يساوي + +713 +01:19:53,550 --> 01:19:59,110 +واحد والمعادلة التانية X node ناقص واحد يساوي ناقص + +714 +01:19:59,110 --> 01:20:05,600 +واحد اذا هذول بدهم يعطوني ما يأتي ان ال X nodeيبدو + +715 +01:20:05,600 --> 01:20:13,720 +يساوي 2 والـ X0 يبدو يساوي كده؟ Zero طبعا يبدو ان + +716 +01:20:13,720 --> 01:20:19,720 +انا جبت الاحداث الصيني لنقطتي التماسك بناروح نجيب + +717 +01:20:19,720 --> 01:20:28,300 +الاحداث الصادم هذه لو كانت X0 ب2 يبقى ال Y تساوي + +718 +01:20:28,300 --> 01:20:36,970 +برجع لوين؟ لراس المثل اللي فوق او سميها Y0يبقى y + +719 +01:20:36,970 --> 01:20:43,630 +node تساوي يبقى واحد على x node اللي هو باتنين + +720 +01:20:43,630 --> 01:20:48,970 +ناقص واحد عوضنا في اللي فوق يبقى بتطلع جداش واحد + +721 +01:20:48,970 --> 01:20:56,430 +هذه بدأت يعطيلك ان y node بده يساوي واحد على zero + +722 +01:20:56,430 --> 01:21:03,620 +ناقص واحد ليه بيساوي جداش ناقص واحدبناء عليه جبنا + +723 +01:21:03,620 --> 01:21:21,260 +نقطتي التماس للمنحنة يبقى + +724 +01:21:21,260 --> 01:21:28,540 +باجي بقوله the points of tangency + +725 +01:21:31,770 --> 01:21:38,890 +نقاط التماس are النقطة الأولى اللى اتنين و واحد + +726 +01:21:38,890 --> 01:21:48,110 +and النقطة الثانية اللى هو zero سالف واحد zero و + +727 +01:21:48,110 --> 01:21:54,890 +سالف واحد تمام إذا بقدر أجيب معادلة كل مماس من هذه + +728 +01:21:54,890 --> 01:21:59,430 +المماسات the first tangent + +729 +01:22:01,040 --> 01:22:10,360 +is Y تساوي المقل اللي هو السالب واحد X ناقص اتنين + +730 +01:22:10,360 --> 01:22:17,940 +زائد واحد يعني هذا بدي اعطيك ان Y يساوي ناقص X + +731 +01:22:17,940 --> 01:22:23,680 +زائد تلاتة زائد اتنين وزائد واحد زائد تلاتة يبقى + +732 +01:22:23,680 --> 01:22:29,640 +هذا هو المماثل الأول ابنجي the second + +733 +01:22:31,190 --> 01:22:41,190 +Tangent is Y يساوي نفسي الميل ال X ناقص X ناقص + +734 +01:22:41,190 --> 01:22:48,690 +واحد يعني Y يساوي ناقص X ناقص واحد هذا هو المماث + +735 +01:22:48,690 --> 01:22:53,910 +الثاني قال لي هاتلك كل المماثات هي جبتله المماثات + +736 +01:22:53,910 --> 01:22:58,750 +طب السؤال اليكوا هل الخطين الأثنين هذول بيكونوا + +737 +01:22:58,750 --> 01:23:03,890 +متوازينبالتأكيد من نفس المكان تعالى نشوفه مع + +738 +01:23:03,890 --> 01:23:08,130 +الطبيعة ماقال ليش ارسم لكن انا بدأ ارسم حتى اتيقن + +739 +01:23:08,130 --> 01:23:14,070 +من شغل هذا صح ولا خطأ بقوله بسيطة هذا المنحدر اللي + +740 +01:23:14,070 --> 01:23:20,150 +عندك هذا محور X هذا محور Y وهذا الـ Zero هذه + +741 +01:23:20,150 --> 01:23:26,990 +الدالة هي رسمة واحد على X بس معمولة لـ Shift وين؟ + +742 +01:23:26,990 --> 01:23:35,250 +شمال، يمين، فوق، تحتيمين بمقدار نطرح للواحد من + +743 +01:23:35,250 --> 01:23:40,630 +المتغير وليس من الدالة يبقى بدي أعمل ال shift هذا + +744 +01:23:40,630 --> 01:23:46,550 +له بمقدار واحد على اليمين يبقى هذا من هذا له من + +745 +01:23:46,550 --> 01:23:54,070 +واحد إذا الدالة هي هيكهو هذا الدالة التالية بالشكل + +746 +01:23:54,070 --> 01:24:01,510 +اللي عندنا رسمة المنحنى Y تسوى واحد على X تمام عند + +747 +01:24:01,510 --> 01:24:06,950 +ال zero عند ال zero قيمة الدالة اللي هو بسالب واحد + +748 +01:24:06,950 --> 01:24:13,990 +اليمين النقطة اللي عندنا هذه وعند اتنين يبقى اتنين + +749 +01:24:14,310 --> 01:24:20,010 +الدالة في قد ياشقليب واحد يبقى هذه اتنين واحد وهذه + +750 +01:24:20,010 --> 01:24:25,670 +عبارة عن زيرو وسالب واحد إذا لو رسمت المماثات + +751 +01:24:25,670 --> 01:24:31,110 +لاتنين هيصير المماث الأول الشكل اللي عنها داج + +752 +01:24:32,070 --> 01:24:37,130 +والمماث الثاني بنفس النتيجة بالشكل اللي عندنا هذا + +753 +01:24:37,130 --> 01:24:42,790 +يبقى ايه المماثات الاتنين اللي هو الاولاني تبع + +754 +01:24:42,790 --> 01:24:51,070 +النقطة 2 1 هذا Y تساوي ناقص X زائد 3 وهذا Y يساوي + +755 +01:24:51,070 --> 01:24:58,460 +ناقص X ناقص 1يعني هذا اللي هو Y تساوي سالب X + +756 +01:24:58,460 --> 01:25:03,940 +رفعناه مقدار تلاتة هذا نزلناه مقدار واحد وزم انت + +757 +01:25:03,940 --> 01:25:10,000 +شايف الممثلة اتنين ارتبالت مجرد معلومة زيادة ليس + +758 +01:25:10,000 --> 01:25:17,740 +الالحد هنا انت هنا من الجزء النظري تبع هذا ال + +759 +01:25:17,740 --> 01:25:24,560 +section لكراه حطلنا معلومة في التمرين وحط عليها + +760 +01:25:24,560 --> 01:25:31,560 +أسئلة بدنا نشوف ما هي هذه المعلومة وما نوعية هذه + +761 +01:25:31,560 --> 01:25:38,580 +المثلة المعلومة هذه بقولي قد يكون المماس رأسيا + +762 +01:25:38,580 --> 01:25:44,680 +vertical tangentيبقى بإني أعطيله تعريف ونشوف كيف + +763 +01:25:44,680 --> 01:25:53,360 +بإني أحسب الشغلة هذه يبقى definition the + +764 +01:25:53,360 --> 01:25:58,280 +curve المنحنة + +765 +01:25:58,280 --> 01:26:09,540 +y تساوي f of x has a vertical tangent + +766 +01:26:13,640 --> 01:26:28,380 +مماس رأسي X يساوي X node at the point X + +767 +01:26:28,380 --> 01:26:36,260 +node F إذا كان Limit لما الـ H بدأ تروح للـ Zero + +768 +01:26:36,260 --> 01:26:42,120 +للـ F of X node زائد الـ Hنقص نقص نقص نقص نقص نقص + +769 +01:26:42,120 --> 01:26:42,520 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +770 +01:26:42,520 --> 01:26:48,980 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +771 +01:26:48,980 --> 01:26:50,120 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +772 +01:26:50,120 --> 01:26:50,120 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +773 +01:26:50,120 --> 01:26:51,440 +نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص نقص + +774 +01:26:51,440 --> 01:26:56,480 +نقص نقص نقص + +775 +01:26:56,480 --> 01:27:03,200 +نقص نقص نقص نقص نقص + +776 +01:27:03,200 --> 01:27:09,620 +نق + +777 +01:27:09,830 --> 01:27:20,730 +f of x يسوى الـ x ناقص واحد قص تلت وبسأل is the + +778 +01:27:20,730 --> 01:27:32,490 +function has a vertical tangent + +779 +01:27:32,490 --> 01:27:42,150 +هل لها vertical tangent atX يساوي واحد ام لا + +780 +01:28:10,920 --> 01:28:14,000 +المعلومة هذه راح حطها في التمرين و ليس في الجزء + +781 +01:28:14,000 --> 01:28:17,580 +النظري تبع ال section حطها في التمرين و حط عليها + +782 +01:28:17,580 --> 01:28:24,020 +مجموعة من الأسلة بيقول المنحنى y تساوي f of x has + +783 +01:28:24,020 --> 01:28:29,800 +a vertical tangent مش vertical asymptote تتفرج بين + +784 +01:28:29,800 --> 01:28:33,170 +ال asymptote و من ال tangentللـ asymptote بيجي + +785 +01:28:33,170 --> 01:28:35,770 +ناخد ال limit، من اليمين هو ال limit، من الشمال + +786 +01:28:35,770 --> 01:28:41,730 +بيطلع اليمين infinity أو سالب infinity، مظبوط، + +787 +01:28:41,730 --> 01:28:46,970 +بقول يبقى في عندي vertical asymptoteهنا vertical + +788 +01:28:46,970 --> 01:28:50,170 +tangent بيقول اللي بتروح تاخد ال limit لل focus + +789 +01:28:50,170 --> 01:28:54,270 +node بداية ال H نقص ال focus node على H لما ال H + +790 +01:28:54,270 --> 01:29:00,570 +بتروح ل 0 بد النتج يطلع infinity او سالب infinity + +791 +01:29:00,570 --> 01:29:04,700 +ان حد هدى او هدى مش الاتنين في انواع Rبتعني + +792 +01:29:04,700 --> 01:29:09,880 +النتيجة infinity او سالب infinity ان حدث ذلك يبقى + +793 +01:29:09,880 --> 01:29:14,480 +النقطة x0 اللي عندك x يساوي x0 تبقى vertical + +794 +01:29:14,480 --> 01:29:20,900 +tangent يبقى مماس للمنحنة عند x0 مثال جالي ارسملي + +795 +01:29:20,900 --> 01:29:26,420 +منحنة ده لهذه وبيسأل هل هذه لها vertical tangent + +796 +01:29:26,420 --> 01:29:31,660 +ام لابقوله بسيطة جدا، احنا هذه لو جينا رسمناها، + +797 +01:29:31,660 --> 01:29:37,640 +هذا المنحنة اللي عندنا، هذا المنحنة X وهذا Y وهذا + +798 +01:29:37,640 --> 01:29:48,110 +Zero، أصلا المنحنة X بيجيني في هذا الشكلY يساوي X + +799 +01:29:48,110 --> 01:29:54,310 +أس تلت ناقص واحد روح نعمله shift جهة اليمين بمقدار + +800 +01:29:54,310 --> 01:30:00,370 +كده؟ بمقدار واحد يبقى لو جينا هنا قولنا أي واحد + +801 +01:30:00,370 --> 01:30:06,650 +وتخيلنا هذا الخط الموازي لمحور Y و جينا رسمنا + +802 +01:30:06,650 --> 01:30:11,770 +المنحنة يبقى المنحنة هيجين هيك بالشكل اللي عندنا + +803 +01:30:11,770 --> 01:30:12,130 +هذا + +804 +01:30:15,830 --> 01:30:23,070 +يبقى هذا المنحنى y يساوي x ناقص واحد أسطول رسمنا + +805 +01:30:23,070 --> 01:30:28,150 +رسمنا قال لي بعدك هل هذا المنحنى له vertical + +806 +01:30:28,150 --> 01:30:33,550 +tangent عند x يساوي واحد يعني x node عندى بقدرش + +807 +01:30:33,550 --> 01:30:41,200 +اللي هو تساوي واحدأذا بدأ احسب لهذا الـ Limit لما + +808 +01:30:41,200 --> 01:30:48,640 +الـ H بدأ تذهب لـ 0 للـ F of 1 زائد الـ H نقص الـ + +809 +01:30:48,640 --> 01:30:54,230 +F of 1 على Hونشوف شو اللي بدى يحصل هذا الكلام + +810 +01:30:54,230 --> 01:31:00,090 +يساوي الدلال يبقى اشيل كل X وحط مكانها واحد زيد H + +811 +01:31:00,090 --> 01:31:06,430 +يبقى هاي limit لما ال H بدها تروح لل zero لمن؟ + +812 +01:31:06,430 --> 01:31:12,750 +للواحد زيد ال H ناقص واحد أس تلت ناقص واحد ناقص + +813 +01:31:12,750 --> 01:31:19,660 +واحد أس تلت كله على H طبعا هذا بقدرشبزيرو هذا بده + +814 +01:31:19,660 --> 01:31:25,200 +يصير اللي هو ال limit لما ال H بده تروح لوين لزيرو + +815 +01:31:25,200 --> 01:31:34,200 +هذا كمان سالب واحد مع واحد بيضل H أس تلت على H + +816 +01:31:34,200 --> 01:31:42,680 +كمان يعني قداش limit لما ال H بده تروح لزيرو لواحد + +817 +01:31:42,680 --> 01:31:45,520 +على H أس تلتين + +818 +01:31:47,590 --> 01:31:52,710 +هل هي دالة معرفة عند H يساوي Zero لأ يبقى يضطر + +819 +01:31:52,710 --> 01:31:57,130 +ياخد ال limit من اليمين و من الشمال يبقى هاي ال + +820 +01:31:57,130 --> 01:32:02,710 +limit لما ال H بده تروح ل Zero من جهة الشمال لواحد + +821 +01:32:02,710 --> 01:32:09,670 +على H تربيه أس تلت مش هيكوا أس تلتينطيب يبقى هذا + +822 +01:32:09,670 --> 01:32:15,350 +الكلام بده يصير واحد على zero من جهة الشمال يبقى H + +823 +01:32:15,350 --> 01:32:21,390 +سالي بقى يبقى very small negative لكل تربيع يبقى + +824 +01:32:21,390 --> 01:32:30,320 +very small negative quantityتربيع كل أسطل يعني + +825 +01:32:30,320 --> 01:32:39,040 +بيصير واحد very small positive quantity أسطل يعني + +826 +01:32:39,040 --> 01:32:47,050 +قداش infinityبالمثل بتروح اخد limit لما ال H بده + +827 +01:32:47,050 --> 01:32:55,590 +تروح ل 0 من جهة اليمين ل 1 على H أس تلتين يعني + +828 +01:32:55,590 --> 01:33:02,110 +limit لما ال H بده تروح ل 0 من جهة اليمين ل 1 very + +829 +01:33:02,110 --> 01:33:04,590 +small positive + +830 +01:33:07,900 --> 01:33:15,060 +هذه موجة دائما و أبدا يبقى dash infinity يبقى ساق + +831 +01:33:15,060 --> 01:33:20,760 +limit لما ال H بدأ تروح ل zero من جهات اليمين واحد + +832 +01:33:20,760 --> 01:33:28,550 +على H أس تلتين يسوى كده؟أظن حسب التعريف يكون X + +833 +01:33:28,550 --> 01:33:33,770 +يساوي واحد هو عبارة عن mean vertical tangent + +834 +01:33:48,000 --> 01:34:03,980 +للمنحنة y يساوي x ناقص واحد كله أس تلت تمام + +835 +01:34:05,550 --> 01:34:09,290 +يبقى طلعلي في الخط على دي اللي احنا رسمينه يعني + +836 +01:34:09,290 --> 01:34:15,110 +الخط المنقط هداشي اعتبر مماس و قاطع في نفس الوقت + +837 +01:34:15,110 --> 01:34:21,170 +من فوق هنا يمسي الجزء العلوي من المنحنة و من تحت + +838 +01:34:21,170 --> 01:34:26,590 +يمسي السفلي منحنة يبقى هو المماس لمين؟ للمنحنة + +839 +01:34:26,590 --> 01:34:33,530 +اللي عندنا آخر مثال في محاضرة اليوم بيقول ما يأتي + +840 +01:34:33,530 --> 01:34:34,850 +example + +841 +01:34:41,170 --> 01:34:51,990 +لت ال f of x يسوى أحد أمرين x sine واحد على x لما + +842 +01:34:51,990 --> 01:34:57,410 +ال x لا تساوي ال zero هو ال zero لما ال x بده + +843 +01:34:57,410 --> 01:35:03,770 +يساوي ال zero السؤال هو النقطة الأولى show that + +844 +01:35:05,490 --> 01:35:19,510 +بايل لي ان ال F is continuous at X يساوي Zero نقطة + +845 +01:35:19,510 --> 01:35:20,390 +ثانية + +846 +01:35:23,060 --> 01:35:33,800 +Does the graph of F have + +847 +01:35:33,800 --> 01:35:42,340 +a vertical tangent + +848 +01:35:42,340 --> 01:35:55,650 +at X يساوي Zero أم لا؟سمعت كإنه حد بدى يسأل هنا شو + +849 +01:35:55,650 --> 01:36:06,710 +تاريف التاني؟ وإيش + +850 +01:36:06,710 --> 01:36:12,410 +افرجت يعني؟ هو لأبسط و لا هاي اتنين نفس الشيء هتجي + +851 +01:36:12,410 --> 01:36:18,780 +معه تطرح نفس المعلومةعلى اي حال بيعطيني كمان سؤال + +852 +01:36:18,780 --> 01:36:24,040 +بيقول افترض ان f of x مجزة الى جزئين الجزء الاول x + +853 +01:36:24,040 --> 01:36:27,800 +صين واحد على x الجزء التاني zero لما x يساوي zero + +854 +01:36:27,800 --> 01:36:32,520 +لما x يساوي zero لا يساوي zero طلب مطلوبين هل + +855 +01:36:32,520 --> 01:36:37,060 +الدالة متصلة عند ال zero ولا لا اتنين هل الها + +856 +01:36:37,060 --> 01:36:42,580 +vertical tangent ولا لا طبعا شباب لو ماكنتش متصلة + +857 +01:36:42,580 --> 01:36:48,180 +عند ال zeroبروح بدور على ال vertical tangent لأ + +858 +01:36:48,180 --> 01:36:52,380 +لإن خلاص الدالة مش معرفة عنده كي بده يحصل تماث + +859 +01:36:52,380 --> 01:36:58,120 +يعني لا توجد نقطة على المنحنة إذا السؤال الأول أو + +860 +01:36:58,120 --> 01:37:04,930 +المطلوب الأول كتبه متعمديعني مشان تعرف ان الدالة + +861 +01:37:04,930 --> 01:37:11,350 +عند X يساوي Zero هي دالة متاصلة و ده متاصلة يمكن + +862 +01:37:11,350 --> 01:37:16,870 +يكون في مماس عندها و يمكن يكون مافيش مماس تعالى + +863 +01:37:16,870 --> 01:37:24,710 +نشوف المطلوب الأول ابقى solution ايش + +864 +01:37:24,710 --> 01:37:26,830 +تعريف ال continuity عند نقطة + +865 +01:37:31,910 --> 01:37:37,810 +بدي يكون نهاية الدالة عند تلك النقطة يساوي قيمة + +866 +01:37:37,810 --> 01:37:42,910 +الدالة مش هيك الاتصال تمام اذا بدنا نروح نشوف ال F + +867 +01:37:42,910 --> 01:37:48,870 +of Zero عندنا ال F of Zero بدي يساوي Zero معطاها + +868 +01:37:48,870 --> 01:37:57,830 +هيا جاهزة طب ال limitلل F of X لما ال X بدي روح لل + +869 +01:37:57,830 --> 01:38:03,830 +Zero يبقى limit لما ال X بدي روح لل Zero لل X Sine + +870 +01:38:03,830 --> 01:38:11,250 +واحد على X كام مرة حلينا السؤال هذا؟مرة مرة مرة + +871 +01:38:11,250 --> 01:38:17,470 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +872 +01:38:17,470 --> 01:38:18,410 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +873 +01:38:18,410 --> 01:38:18,630 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +874 +01:38:18,630 --> 01:38:18,910 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +875 +01:38:18,910 --> 01:38:18,910 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +876 +01:38:18,910 --> 01:38:19,050 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +877 +01:38:19,050 --> 01:38:19,090 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +878 +01:38:19,090 --> 01:38:19,090 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +879 +01:38:19,090 --> 01:38:24,530 +مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة مرة + +880 +01:38:24,530 --> 01:38:31,850 +مرةExample مثال سبع يبقى حل هنا بدل المرة مرتين + +881 +01:38:31,850 --> 01:38:39,130 +مدام ال limit ساوة قيمة الدالة يبقى ساعة ال F of + +882 +01:38:39,130 --> 01:38:51,490 +Zero يساوي limit لصين X في صين X limitلما ال X بده + +883 +01:38:51,490 --> 01:38:59,270 +تروح لل Zero لل X في Sin واحد على X هذا بده يعطينا + +884 +01:38:59,270 --> 01:39:08,650 +ان ال F is continuous at X يساوي Zero هذا كل الشغل + +885 +01:39:08,650 --> 01:39:15,430 +اشتغلناه اللي هو المطلوب الأول من المسألة نجي + +886 +01:39:15,430 --> 01:39:16,850 +للمطلوب الثاني + +887 +01:39:19,660 --> 01:39:24,280 +المطموب التاني بيقول لي هل هذه لها vertical + +888 +01:39:24,280 --> 01:39:30,640 +tangent عند ال zero ولا لا بنقول له الله أعلم يبقى + +889 +01:39:30,640 --> 01:39:36,380 +احنا بدنا نروح ناخد main limit لما ال H بدها تروح + +890 +01:39:36,380 --> 01:39:43,700 +لل zero لل F of zero زائد ال H ناقص ال F of zero + +891 +01:39:43,700 --> 01:39:50,830 +على Hمظهر ونشوف هل هذه ال limit تساوي infinity و + +892 +01:39:50,830 --> 01:39:56,070 +الله سالب infinity و الله غير ذلك يبقى هذا limit + +893 +01:39:56,070 --> 01:40:01,790 +لما ال H بدها تروح ل zero برجع لمين؟للـ function + +894 +01:40:01,790 --> 01:40:06,850 +اللي عندنا ال F of Zero زائد H يبقى بده أشيل كل X + +895 +01:40:06,850 --> 01:40:15,010 +و أحط مكانها Zero زائد H يبقى هنا Zero زائد ال H + +896 +01:40:15,010 --> 01:40:22,850 +Sin واحد على Zero زائد ال H ناقص F of Zero اللي هو + +897 +01:40:22,850 --> 01:40:30,600 +بده أشبـ 0 كله على H يبقى النتيجة صارت limit لما + +898 +01:40:30,600 --> 01:40:37,780 +الـ H بده تروح للـ 0 للـ H sin 1 على H كله على H + +899 +01:40:37,780 --> 01:40:45,340 +يبقى limit لما الـ H بده تروح للـ 0 لـ sin 1 على H + +900 +01:40:45,340 --> 01:40:50,640 +فقط لغاية الـ H هذه ستختصر مع ميهم مع الـ H اللي + +901 +01:40:50,640 --> 01:40:58,120 +عندنا هذه 1 على 0infinity مظبوط sign ال infinity + +902 +01:40:58,120 --> 01:41:05,560 +الله أعلم ماعرفهاش يبقى does not exist يبقى هذه + +903 +01:41:05,560 --> 01:41:16,160 +does not exist ماعرفهاش مش موجودة بناء عليه هل في + +904 +01:41:16,160 --> 01:41:20,800 +عندي vertical tangent لأ اشتراطنا لازم يعطيني اما + +905 +01:41:20,800 --> 01:41:24,460 +infinityهذا لا يمكنني أن أقول infinity ولا يمكنني + +906 +01:41:24,460 --> 01:41:31,520 +أن أقول سالب infinity يبقى باجي بقول له ف ال F has + +907 +01:41:31,520 --> 01:41:46,410 +no vertical tangent at X يساوي Zالان وصلنا الى + +908 +01:41:46,410 --> 01:41:52,950 +أرقام المسائل ل section تلاتة واحد يبقى exercises + +909 +01:41:52,950 --> 01:42:02,950 +تلاتة واحد المسائل التالية من واحد لخمسة وعشرين + +910 +01:42:02,950 --> 01:42:06,070 +القدر + +911 +01:42:06,070 --> 01:42:12,170 +وخمسة وتلاتين وستة وتلاتين + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aWC3bUHpxP8_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aWC3bUHpxP8_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..9f31d8cdae31c34d1e729865b354113f714b06c2 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/aWC3bUHpxP8_raw.srt @@ -0,0 +1,3204 @@ +1 +00:00:21,460 --> 00:00:26,480 +بسم الله الرحمن الرحيم انتهينا المرة الماضية من + +2 +00:00:26,480 --> 00:00:32,420 +chapter 4 اللي كان تطبيقات على التفاضل يعني أخدنا + +3 +00:00:32,420 --> 00:00:38,500 +chapter 3 تفاضل chapter 4 تطبيقات على التفاضل الآن + +4 +00:00:38,500 --> 00:00:43,640 +chapter 5 هو تكامل و chapter 6 تطبيقات على التكامل + +5 +00:00:44,260 --> 00:00:50,200 +يبقى شبتر خمسة كله integration يبقى نشتغل كله + +6 +00:00:50,200 --> 00:00:56,200 +تكامل عن مهد لهذا التكامل ببعض المعلومات البسيطة + +7 +00:00:56,200 --> 00:01:00,780 +أول section هو ال arian cementing with finite sum + +8 +00:01:01,390 --> 00:01:08,030 +يبقى area معناته المساحة و estimating تقدير with + +9 +00:01:08,030 --> 00:01:12,470 +finite sum يعني احنا بنحاول نقدر جداش المساحة اللي + +10 +00:01:12,470 --> 00:01:18,510 +محصورة من المنحنة ومحور X عن طريق مجموع محدود + +11 +00:01:18,510 --> 00:01:24,660 +لشغلات شو الشغلات هذه هذا ما سنعرفه بعد قليلبنعطي + +12 +00:01:24,660 --> 00:01:27,700 +مثال فوضيح لهذا الكلام بيقول use finite + +13 +00:01:27,700 --> 00:01:32,240 +approximation استخدم التقريب المحدود to estimate + +14 +00:01:32,240 --> 00:01:36,720 +تقدر the area under the graph of the function بشأن + +15 +00:01:36,720 --> 00:01:40,760 +القدر اللي يقدش المساحة اللي محصورة بين المنحنة y + +16 +00:01:40,760 --> 00:01:46,010 +تساوي x تربية ومحور x من عند x تساوي zeroلغاية X + +17 +00:01:46,010 --> 00:01:53,150 +يساوي اتمام بدنا نقدر قداش المساحة هذه بمين بثلاثة + +18 +00:01:53,150 --> 00:01:58,570 +أمور الأمر الأول بوسطة ال lower sum يعني بدي أعرف + +19 +00:01:58,570 --> 00:02:03,010 +المساحة محصولة بين مين ومين يبقى في عندي lower sum + +20 +00:02:03,010 --> 00:02:05,610 +يعني مجموعة منخفض + +21 +00:02:08,240 --> 00:02:14,760 +أربع مستطيلات of equal width للتساع تبعهم هو نفسه + +22 +00:02:26,150 --> 00:02:31,810 +الأمر الثاني upper sum يبقى مجموع علوي أو أعلى + +23 +00:02:31,810 --> 00:02:37,350 +مجموع of four rectangles لأربع مستطيلات of equal + +24 +00:02:37,350 --> 00:02:43,650 +width كذلك الأمر الثالث midpoint rule قاعدة نقطة + +25 +00:02:43,650 --> 00:02:48,910 +المنتصف لأربع مستطيلات with four widthsطلبنا ان + +26 +00:02:48,910 --> 00:02:55,730 +نوضح هذا الكلام لانه يجب ان نرسم الرسمة فلو رسمنا + +27 +00:02:55,730 --> 00:03:00,790 +الرسمة و قلنا هذا محور X وهذا محور Y وهذا نقطة + +28 +00:03:00,790 --> 00:03:06,310 +الأصل التي هي Zero المنحنة اللي بين إيدينا اللي هو + +29 +00:03:06,310 --> 00:03:11,480 +أصله F of X يساوي X تربيعبارابولا مفتوحة لأعلى + +30 +00:03:11,480 --> 00:03:15,580 +سبقت من شرط سليف يبقى تصير مقلوب إلى أين؟ إلى أسفل + +31 +00:03:15,580 --> 00:03:20,480 +زائد أربع إذا شفت إلى فوق بمقدار أربع لكن أنا ما + +32 +00:03:20,480 --> 00:03:24,000 +بديش البرابولة كمان بدي بقى X سواء Zero لغاية X + +33 +00:03:24,000 --> 00:03:28,980 +سواء قداش اتنين يبقى لو جيتلي هذه البرابولة هتاخد + +34 +00:03:28,980 --> 00:03:33,940 +الشكل التالي لو قلت هذا الرقم اتنين وهنا هتكون + +35 +00:03:33,940 --> 00:03:39,460 +قداش اللي هي الأربع وهذا ال Zeroيبقى هذه المنطقة + +36 +00:03:39,460 --> 00:03:44,920 +اللي احنا بنحاول انقدر قداش مساعتها جلبلك انقدر + +37 +00:03:44,920 --> 00:03:50,900 +مساعتها جسمليها الى اربعة اقسام او اربع مستطيلات + +38 +00:03:50,900 --> 00:03:57,790 +بقول كويس هنا ها هذا واحد هنا بديكون مين؟بدي يكون + +39 +00:03:57,790 --> 00:04:01,930 +نص هنا بدي يكون واحدة و نص اللي هو تلاتة على اتنين + +40 +00:04:01,930 --> 00:04:08,030 +ليش جسمت بين اضافة وانجلي equal width البعض هذا جد + +41 +00:04:08,030 --> 00:04:11,270 +البعض هذا جد البعض هذا جد يبقى كل واحد فيهم يقول + +42 +00:04:11,270 --> 00:04:16,550 +يساوي جد ياشيالان بدى اجي أسوي المستطيلات فبجي + +43 +00:04:16,550 --> 00:04:21,090 +طالع بالشكل عن هذا لغاية مقابل المنحنة و من هنا + +44 +00:04:21,090 --> 00:04:25,410 +باجي طالع لغاية مقابل المنحنة و من هنا باجي طالع + +45 +00:04:25,410 --> 00:04:31,170 +لغاية مقابل المنحنةماذا قال لي؟ قال لي المطلوب + +46 +00:04:31,170 --> 00:04:38,070 +الأول بدي قداش المساحة دي باستخدام lower sum ل + +47 +00:04:38,070 --> 00:04:43,350 +four rectangles يبقى احنا هنا بنحاول نعمل أربع + +48 +00:04:43,350 --> 00:04:51,610 +مستطيلات بها تكون المساحة دي أقل من المساحة + +49 +00:04:51,610 --> 00:04:57,420 +الحقيقية لأنه قال لي lower sumتمام؟ يبقى بدي أكون + +50 +00:04:57,420 --> 00:05:01,380 +الأربع مستطيلات، هل الأشكال الأربع هذه مستطيلات؟ + +51 +00:05:01,380 --> 00:05:07,440 +طبعا لأ، لذلك بروح أخلق أربع مستطيلات، إذا لو جيت + +52 +00:05:07,440 --> 00:05:13,520 +من هنا رسمت خط أفقي و من هنا جيت رسمت خط أفقي و من + +53 +00:05:13,520 --> 00:05:18,700 +هنا جيت رسمت خط أفقي و من هنا ماعنديش فصار الخط + +54 +00:05:18,700 --> 00:05:23,800 +منطبق عالمياعلى محور الصينات يبقى هي الأشكال + +55 +00:05:23,800 --> 00:05:27,820 +الأربعة اللي عاملة إذا لو جبت المساحة هذه و + +56 +00:05:27,820 --> 00:05:32,440 +المساحة هذه و المساحة هذه و المساحة هذه يعني ها + +57 +00:05:32,440 --> 00:05:36,060 +بتكون جد المساحة بس أقل شوية أقل شوية لإنه في + +58 +00:05:36,060 --> 00:05:40,960 +فراغات هنا ضالت هذه مانحسبتش طيب تعالى نحسب + +59 +00:05:40,960 --> 00:05:44,660 +المساحات اللي عندنا هنا مش هنحسب المساحات اللي + +60 +00:05:44,660 --> 00:05:48,020 +عندنا بتعرف جدش الطول هذا و الطول هذا و الطول هذا + +61 +00:05:48,500 --> 00:05:55,240 +هذا هو F of نص وهذا هو F of واحد وهذا F of تلاتة + +62 +00:05:55,240 --> 00:05:59,560 +على اتنين يبقى بالداجي اقول له هذا النقطة الاولى + +63 +00:05:59,560 --> 00:06:06,360 +بدي احسبله F of نص ايه بدي اساوي منه اربع ناقص نص + +64 +00:06:06,360 --> 00:06:12,080 +لكل تربية يعني اربع ناقص رابعماذا يعني؟ يعني + +65 +00:06:12,080 --> 00:06:16,500 +خمستاشر على أربعة أربعة في أربعة في ستاشر يعني + +66 +00:06:16,500 --> 00:06:21,440 +خمستاشر على مين على أربعة إذا الارتفاع هذا هو + +67 +00:06:21,440 --> 00:06:28,100 +عبارة عن خمستاشر على أربعة والعرض تبع هذا كم؟ نص + +68 +00:06:28,100 --> 00:06:31,560 +تمام يبقى بقدر أجيب مساحة الموساطية اللي عن هنا + +69 +00:06:31,560 --> 00:06:38,140 +بالمرة خليني أجيب F of oneيبقى F of one بدى يسوى + +70 +00:06:38,140 --> 00:06:42,880 +أربعة ناقص واحد لكل تربيع يسوى قداش تلاتة زى ماذا + +71 +00:06:42,880 --> 00:06:48,280 +خمستاشر على أربعة بعد هيك بدى أجيب F of تلاتة على + +72 +00:06:48,280 --> 00:06:55,420 +اتنين اللى هو أربعة ناقص تلاتة على اتنين لكل تربيع + +73 +00:06:55,420 --> 00:07:02,380 +يعني أربعة ناقص تسعة على أربعة اللى هو قداش خمسة و + +74 +00:07:02,380 --> 00:07:03,020 +لا سبعة + +75 +00:07:08,240 --> 00:07:16,900 +يبقى هذا طوله تلاتة و هذا طوله سبعة عالميا على + +76 +00:07:16,900 --> 00:07:22,880 +أربعة يبقى بداجي اشوف ال area اللي عندي هذه اللي + +77 +00:07:22,880 --> 00:07:28,640 +هي المساحات اللي كلها هذه المساحات هذه باجي بقول + +78 +00:07:28,640 --> 00:07:41,400 +هنا the totalarea of the rectangles + +79 +00:07:41,400 --> 00:07:44,760 +بتساوي + +80 +00:07:44,760 --> 00:07:50,920 +تقريبا لاتساوي المساحة الحقيقية وانما تساوي تقريبا + +81 +00:07:50,920 --> 00:07:55,760 +ليش لان لو يزال عندي فراغات هذه ماتخرجش في الحساب + +82 +00:07:55,760 --> 00:08:00,040 +انا بدأ اخد مساحة من المساطلات كده هو مساحة + +83 +00:08:00,040 --> 00:08:05,750 +المساطلطول في العرض يبقى طولا لخمستاشر على أربعة و + +84 +00:08:05,750 --> 00:08:12,630 +العرض نص يبقى هي خمستاشر على أربعة مضروب في نص + +85 +00:08:12,630 --> 00:08:19,710 +زائد التاني تلاتة مضروب في جداش في نص برضه العرض + +86 +00:08:19,710 --> 00:08:25,590 +تبقى نص لأن كله equal width زائد سبعة على أربعة + +87 +00:08:25,590 --> 00:08:32,460 +مضروب في نص زائد جداش ارتفاعه هنا0 مضروب في كمان + +88 +00:08:32,460 --> 00:08:33,780 +قداش فيه نص + +89 +00:08:43,830 --> 00:08:48,630 +بتقول اني كدهش؟ خمستاشر على على أربعة زائد تلاتة + +90 +00:08:48,630 --> 00:08:54,290 +زائد سبعة على أربعة مافيش غيرهم طيب هذا الكلام بده + +91 +00:08:54,290 --> 00:09:00,670 +يساوي نص في تلاتة زائد هذا و هذا نفس المقامات يبقى + +92 +00:09:00,670 --> 00:09:07,710 +سبعة على خمستاشر باتنين و عشرين على أربعة يعني نص + +93 +00:09:07,710 --> 00:09:10,790 +في اتنين و عشرين على أربعة يعني احداشر على اتنين + +94 +00:09:11,290 --> 00:09:20,190 +يبقى تلاتة زائد أحداشر على اتنين يبقى نص فيه هذا + +95 +00:09:20,190 --> 00:09:25,650 +باعتبار اتنين في تلاتة بستة ستة و أحداشر سبعتاشر + +96 +00:09:25,650 --> 00:09:32,090 +على اتنين يبقى سبعتاشر على اتنين يعني السبعتاشر + +97 +00:09:32,090 --> 00:09:36,590 +على أربعة مقدار هذه المساعة يعني أربعة و ربعة + +98 +00:09:36,590 --> 00:09:42,440 +أربعة و ربعة يعني أربعةو خمسة و عشرين بالمية + +99 +00:09:42,440 --> 00:09:49,360 +تقريبا تمام؟ بدنا نروح و نخلص من نمرة A بدنا نجي + +100 +00:09:49,360 --> 00:09:56,230 +لنمرة B يبقى بدنا نجي لنمرة Bقال لي يبقى هذا اللي + +101 +00:09:56,230 --> 00:10:02,690 +هو أقل مساحة للمستطيلات لما نجسم إلى أربع أقسام + +102 +00:10:02,690 --> 00:10:08,290 +طيب سؤالي هو لو جسمت هذه مش أربع أقسام تمان أقسام + +103 +00:10:08,290 --> 00:10:14,270 +يا ترى هذه المساحة بدها تزيد ولا تقل؟بزيد بس بصير + +104 +00:10:14,270 --> 00:10:19,450 +جريبة من المساحة الحقيقية كل ما يزيد عدد التقسيمات + +105 +00:10:19,450 --> 00:10:24,650 +كل من عدم اتمين المساحات اللي هنا وبالتالي بنجرب + +106 +00:10:24,650 --> 00:10:30,230 +لمين؟ للمساحة الحقيقية طب هذا لو أخدت المستطيلات + +107 +00:10:30,230 --> 00:10:36,290 +داخل المنطقة اللي أنا بديها هذه KRالـ Region هذه R + +108 +00:10:36,290 --> 00:10:40,630 +كلها، تمام؟ أنا أخد مستطيلات داخلها، لو أخد + +109 +00:10:40,630 --> 00:10:47,330 +مستطيلات خارجها بنفس الأربع تقسيمات، بحصل على من؟ + +110 +00:10:47,330 --> 00:10:52,880 +على الـ Upper Sum في هذه الحالةيبقى بالداجي اخد له + +111 +00:10:52,880 --> 00:10:57,440 +هذا الرسم اللي عندنا بالشكل اللي عندنا هذا هذا + +112 +00:10:57,440 --> 00:11:04,120 +محور X وهذا محور Y وهذا Zero وهذا المنحنة هاي اللي + +113 +00:11:04,120 --> 00:11:11,580 +اتنين وهنا واحد وهنا نصف وهنا تلاتة على اتنين + +114 +00:11:11,580 --> 00:11:16,400 +وهيجينا طالعين رأسي بالشكل اللي عندنا هذا وهنا + +115 +00:11:16,400 --> 00:11:19,840 +جينا طالعين بالشكل اللي عندنا هذا وهنا بالشكل اللي + +116 +00:11:19,840 --> 00:11:27,470 +عندنا هذاطيب هذه اللي هي أربعةتمام؟ طيب الان بدي + +117 +00:11:27,470 --> 00:11:33,030 +اعمل مستطيلات بدي اجتمل عالمين على كل الاروا زيادة + +118 +00:11:33,030 --> 00:11:38,550 +شوية كيف؟ بدي اقول له هذا انت امشي هيك الى اعلى + +119 +00:11:38,550 --> 00:11:45,270 +لغاية مصير افقي وانت امشي هيك لغاية مصير افقي وانت + +120 +00:11:45,270 --> 00:11:51,830 +امشي هيك لغاية مصير افقي وانت ضلك طالع هيك لغاية + +121 +00:11:51,830 --> 00:11:56,700 +مصير افقي بالشكل هذايبقى المرة هذه صار فعلا عندي + +122 +00:11:56,700 --> 00:12:02,640 +أربعة و مصطلعة جابت كل المساحة اللي هي ا و زيادة + +123 +00:12:02,640 --> 00:12:08,150 +شويةهذه كان فيها نقص شوية يبقى هذا يبقى هذا ال + +124 +00:12:08,150 --> 00:12:14,210 +upper sum والأولاني هو مين ال lower sum تمام يبقى + +125 +00:12:14,210 --> 00:12:19,690 +بالداخل ال upper sum ال F نصف هيها مش هتتغير اللي + +126 +00:12:19,690 --> 00:12:25,350 +قداش خمستاشر على أربعة إذا هذا هو خمستاشر على + +127 +00:12:25,350 --> 00:12:32,840 +أربعةاللي بعده بدي F of واحد، لأ لأ لأ لأ لأ هذا + +128 +00:12:32,840 --> 00:12:37,340 +الطول اللي هو أربعة، يبقى هذا مش خمساشر على أربعة، + +129 +00:12:37,340 --> 00:12:43,880 +هذا اللي هو أربعة، تمام؟ وهذا الطول كمان جد الطول، + +130 +00:12:43,880 --> 00:12:51,320 +لأن هذا يبقى هذا الطول، هذا الآنسنة و سنة شوية هذا + +131 +00:12:51,320 --> 00:12:55,980 +الطول اللي هو أربعة لإنه أخدنا ال F of Zero يبقى + +132 +00:12:55,980 --> 00:13:01,520 +ال F of Zero بدي ساوي قداش اللي هو أربعة التاني + +133 +00:13:01,520 --> 00:13:10,850 +هذا اللي هو ال F of نصف من نص هو خمستاشر على أربعة + +134 +00:13:10,850 --> 00:13:16,630 +يبقى هذا فعلا هو خمستاشر على أربعة نجي للي بعده + +135 +00:13:16,630 --> 00:13:22,390 +هذا اللي هو قداش قلنا تلاتة والف من واحد اللي هو + +136 +00:13:22,390 --> 00:13:24,610 +يساوي قداش تلاتة + +137 +00:13:29,830 --> 00:13:34,250 +هذا ما احنا قلناه من هنا، ولا همك، مشان ما يصيرش + +138 +00:13:34,250 --> 00:13:40,010 +إشكال عندك، بده رايحك خالص، هه بده أغيرلك كتابة + +139 +00:13:40,010 --> 00:13:47,240 +مرة تانيةهذا الطول كله اللي هو أربعة لغاية هنا + +140 +00:13:47,240 --> 00:13:53,180 +تمام جد هذا بالضبط أربعة و هذا اللي هو خمستاشر على + +141 +00:13:53,180 --> 00:13:59,740 +أربعة لغاية هنا هذا الآن تلاتة و بنجي ال F of + +142 +00:13:59,740 --> 00:14:05,000 +اتنين ال F of تلاتة على اتنين و ال F of تلاتة على + +143 +00:14:05,000 --> 00:14:08,740 +اتنين سبعة على أربعة و هذا الطول تبقى اللي هو جداش + +144 +00:14:08,740 --> 00:14:17,360 +سبعة على أربعةوالـ F of تلاتة على اتنين يسوى سبعة + +145 +00:14:17,360 --> 00:14:22,420 +على اربعة.الان بدي احسب المساحات اللي عندنا هذه + +146 +00:14:22,420 --> 00:14:27,940 +يبقى هذا كان the total area او يا بتقول ال total + +147 +00:14:27,940 --> 00:14:34,830 +area يا بتقول ال lower sumيبقى هنا بالداخل ال + +148 +00:14:34,830 --> 00:14:47,590 +upper sum يبقى the upper sum is ال A تساوي تقريبا + +149 +00:14:48,200 --> 00:14:54,480 +مين؟ الأولاني اللي هو أربعة مضروب في نص التاني + +150 +00:14:54,480 --> 00:15:03,920 +خمستاشر على أربعة مضروب في نص التالت تلاتة مضروب + +151 +00:15:03,920 --> 00:15:12,060 +في نصاللي بعده سبعة على أربعة مضروب كذلك في نص هي + +152 +00:15:12,060 --> 00:15:17,380 +مساحة المص طيلة بقدر أخد نص عامل مشارك بيبقى أربعة + +153 +00:15:17,380 --> 00:15:24,480 +خمستاشر على أربعة زائد تلاتة زائد سبعة عالمين على + +154 +00:15:24,480 --> 00:15:31,020 +أربعةهذا بده يعطيك نص برا وهنا سبعة زائد اتنين + +155 +00:15:31,020 --> 00:15:40,060 +وعشرين على اربعة يبقى نص في سبعة زائد احد عشر على + +156 +00:15:40,060 --> 00:15:49,050 +اتنين ويساويمصفي هذي أربعتاش و أحداش خمسة و عشرين + +157 +00:15:49,050 --> 00:15:56,950 +على اتنين يبقى خمسة و عشرين على أربعة له ستة و ربع + +158 +00:15:56,950 --> 00:16:06,510 +يعني ستة و خمسة و عشرين من المية يبقى هنا the area + +159 +00:16:06,510 --> 00:16:10,570 +of the region + +160 +00:16:14,790 --> 00:16:24,290 +is a where حيث ال a هذه أكبر من مين من القيمة اللي + +161 +00:16:24,290 --> 00:16:28,850 +طلعناها في الأول اللي هو أربعة و خمسة و عشرين من + +162 +00:16:28,850 --> 00:16:35,650 +مية و أقل من اللي طلعناته لستة و خمسة و عشرين من + +163 +00:16:35,650 --> 00:16:41,850 +مية طيب نمرأ ال c نمرأ ال c ايش بيقولبقى اللى بدى + +164 +00:16:41,850 --> 00:16:47,470 +أخد اللى بدى أخد اللى بدى أخد اللى بدى أخد اللى + +165 +00:16:47,470 --> 00:16:49,230 +بدى أخد اللى بدى أخد اللى بدى أخد اللى بدى أخد + +166 +00:16:49,230 --> 00:16:49,290 +اللى بدى أخد اللى بدى أخد اللى بدى أخد اللى بدى + +167 +00:16:49,290 --> 00:16:50,010 +أخد اللى بدى أخد اللى بدى أخد اللى بدى أخد اللى + +168 +00:16:50,010 --> 00:16:51,850 +بدى أخد اللى بدى أخد اللى بدى أخد اللى بدى أخد + +169 +00:16:51,850 --> 00:16:55,650 +اللى بدى أخد اللى بدى أخد اللى بدى أخد اللى بدى + +170 +00:16:55,650 --> 00:16:59,530 +أخد اللى بدى أخد اللى بدى أخد اللى بدى أخد اللى + +171 +00:16:59,530 --> 00:17:01,270 +بدى أخد اللى بدى أخد اللى بدى أخد اللى بدى أخد + +172 +00:17:01,270 --> 00:17:08,470 +اللى بدى أخد اللى بدى + +173 +00:17:08,510 --> 00:17:13,710 +وبدأ أجسم التقسيمات الأربعة تبعت إيه هي هي يبقى + +174 +00:17:13,710 --> 00:17:21,910 +هذا هنا واحد وهنا نص وهنا تلاتة على اتنين وبدأ + +175 +00:17:21,910 --> 00:17:26,690 +يطالع هوك بالشكل اللي عندنا هذا وهنا بالشكل اللي + +176 +00:17:26,690 --> 00:17:32,150 +عندنا هذا وهنا بالشكل اللي عندنا هذا قريباً كويس + +177 +00:17:32,780 --> 00:17:39,640 +كيف بده يسوي هنا هنا قال لي بدي اخد نقطة في نص ال + +178 +00:17:39,640 --> 00:17:44,940 +interval ال mid point النقطة هذه يبقى هذه الأحداث + +179 +00:17:44,940 --> 00:17:51,680 +تبعها قداش ربع و بدك تيجي تطالع فوق لغاية ما تقابل + +180 +00:17:51,680 --> 00:17:58,900 +المنحنة و تعملي مص طاطيل بالشكل اللي عندنايعني + +181 +00:17:58,900 --> 00:18:03,580 +اهملنا جزء جوا و جيبنا جزء من برا اللي اقرب ما + +182 +00:18:03,580 --> 00:18:08,940 +يكون من الصحية لكن احنا مش متأكدين هذه بتبقى كده؟ + +183 +00:18:08,940 --> 00:18:14,280 +تلات اربع لانها جاية في النص وبتدهش يطالع فوق هيك + +184 +00:18:14,280 --> 00:18:21,560 +بدي امشي وفقه وامشي وفقه بالشكل اللي عندنا هذابعد + +185 +00:18:21,560 --> 00:18:30,100 +هيك هذه واحد وربع يعني كده؟ واحد وربع يعني واحد + +186 +00:18:30,100 --> 00:18:38,630 +وربع خمسة على أربعةخمسة على أربعة و نجي طالعين فوق + +187 +00:18:38,630 --> 00:18:45,730 +بشكل أنهان و نروح نرسم بشكل أنهان هنا هذه اللي هو + +188 +00:18:45,730 --> 00:18:52,030 +قداش سبعة على أربعة لواحد و تلت تربع نجي طالعين + +189 +00:18:52,030 --> 00:18:59,150 +فوقك و نجي نعمل المستطيل تبعنا بهذا الشكلهذا + +190 +00:18:59,150 --> 00:19:05,670 +احتمال يكون قريب جدا او ادق من مين من الكميات اللى + +191 +00:19:05,670 --> 00:19:09,950 +فاتت الحين يبقى بنا نحسب F of ربع F of تلاتة اربع + +192 +00:19:09,950 --> 00:19:15,170 +F of خمس اربع F of سبعة اربع ونشوف كده يستوي اذا + +193 +00:19:15,170 --> 00:19:21,340 +احنا هنا بدى ناخد ال F of رابعاللي هو قداش؟ أربع + +194 +00:19:21,340 --> 00:19:27,420 +ناقص ربع لكل تربية، يعني أربع ناقص واحد على ستة + +195 +00:19:27,420 --> 00:19:35,050 +عشر، يبقى تلاتة وستين على ستة عشرنمسك اللي بعدها + +196 +00:19:35,050 --> 00:19:42,470 +بدي F of تلات تربع و يساوي اللي هو أربع ناقص تلات + +197 +00:19:42,470 --> 00:19:51,030 +تربع لكل تربيع يبقى أربع ناقص تسعة على ستاشر أربع + +198 +00:19:51,030 --> 00:19:55,830 +أو ستين بدي أشيل منها تسعة بصير خمسة و خمسين يبقى + +199 +00:19:55,830 --> 00:20:03,940 +خمسة و خمسين على ستاشر بدنا ال F ofاللي هو خمس + +200 +00:20:03,940 --> 00:20:10,580 +أربعة خمس أربعة و يسوى أربعة ناقص خمسة على أربعة + +201 +00:20:10,580 --> 00:20:17,360 +لكل تربية و يسوى أربعة ناقص خمسة و عشرين على ستة + +202 +00:20:17,360 --> 00:20:24,620 +عشر أربعة و ستين، بدي أشيل منهم كم؟ خمسة و عشرين و + +203 +00:20:24,620 --> 00:20:30,320 +يسوىالاربعة و ستين لو شلت منهم خمسة و عشرين بيظل + +204 +00:20:30,320 --> 00:20:37,380 +تلاتة و اربعين، مظبوط هيك؟ صح ولا لا؟ تلاتة و + +205 +00:20:37,380 --> 00:20:43,540 +اربعين على ستاش لو جمعت هدول، بده يعطيني قداش؟ بده + +206 +00:20:43,540 --> 00:20:48,340 +يعطيني اربعة و ستين طبعا تجيش هيك ده اربعة و ستين + +207 +00:20:48,340 --> 00:20:57,670 +تسعة و تلاتينتسعة وتلاتين هك مظبوط يبقى تلاتين + +208 +00:20:57,670 --> 00:21:01,710 +تسعة وتلاتين لو جمعت طول بيطلع اربعة وستين تسعة + +209 +00:21:01,710 --> 00:21:05,790 +وخمسة اربعة اتاش تلاتة تلاتة ستة مظبوط يبقى تسعة + +210 +00:21:05,790 --> 00:21:13,650 +وتلاتين على ستاش بدنا نروح نحسب كذلك F of اخر واحد + +211 +00:21:13,650 --> 00:21:22,170 +سبعة على اربعة7 على 4 و يسوي 4 ناقص 7 على 4 لكل + +212 +00:21:22,170 --> 00:21:34,470 +تربية اللي هو 4 ناقص 49 على 16 15 على 16 اللي هو + +213 +00:21:34,470 --> 00:21:42,550 +بيعطينا 15 على 16الان بقدر احسب المساحات هذه كلها + +214 +00:21:42,550 --> 00:21:48,670 +يبقى بدي امسح السؤال نفسه واروح اكتب هذه المساحات + +215 +00:21:48,670 --> 00:22:02,310 +هذه + +216 +00:22:02,310 --> 00:22:08,620 +area مش اعلى يا شباب the area of the regionيبقى + +217 +00:22:08,620 --> 00:22:19,120 +باجي بقول هنا the area of the region the area of + +218 +00:22:19,120 --> 00:22:25,560 +the region لأ مش ال area of the region يعني يبقى + +219 +00:22:25,560 --> 00:22:31,440 +هذه لا upper sum ولا lower sum يبقى باجي بقول the + +220 +00:22:31,440 --> 00:22:34,360 +estimating + +221 +00:22:36,340 --> 00:22:46,100 +some تقضيه لمجموعة of the area is ال a تساوي + +222 +00:22:46,100 --> 00:22:53,460 +تقريبا الطول الأولان يقولها كم؟ تلاتة و ستين تلاتة + +223 +00:22:53,460 --> 00:22:58,580 +و ستين على ستة عشر طبعا ال width الاتساع اللي هو + +224 +00:22:58,580 --> 00:23:03,600 +هذا شبه كم؟ نص كله في نص + +225 +00:23:11,460 --> 00:23:18,560 +خمسة و خمسين على ستاش كذلك في نص اللي بعده تسعة و + +226 +00:23:18,560 --> 00:23:27,460 +تلاتين على ستاش كذلك في نص اللي بعده خمستاشر على + +227 +00:23:27,460 --> 00:23:33,910 +ستاشر مضروب في نصهذا الكلام بده يساوي كله لو أخدت + +228 +00:23:33,910 --> 00:23:39,450 +النص عامل مشترك، وإيش رايك؟ اتنين في ستاش كذلك + +229 +00:23:39,450 --> 00:23:45,930 +عامل مشترك ربرا؟ ربرا؟ ربرا؟ ربرا؟ ربرا؟ ربرا؟ + +230 +00:23:48,460 --> 00:23:55,560 +طيب، هذا ربع بس هذا، أيه المستطيل كله؟ باخد + +231 +00:23:55,560 --> 00:23:59,780 +مستطيلات العرض تبعه يساوي نص، الخلاف بصار في + +232 +00:23:59,780 --> 00:24:05,660 +الارتفاع، تمام؟ يبقى بدا أخد واحد على اتنينه في + +233 +00:24:05,660 --> 00:24:11,010 +ستاشر عام المشترك، بظل عند مين؟بظل عندي تلاتة + +234 +00:24:11,010 --> 00:24:17,890 +وستين زائد خمسة وخمسين زائد تسعة وتلاتين زائد + +235 +00:24:17,890 --> 00:24:24,230 +خمستاشر هذا الكلام بده يساوي خمسة وخمسة عشرة وتسعة + +236 +00:24:24,230 --> 00:24:31,270 +تسعة عشر تسعة عشر وتلاتة اتنين وعشرين تلاتة وتلاتة + +237 +00:24:31,270 --> 00:24:38,610 +ستة وخمسة احداشر احداشر وستة سبعتاشركله على اتنين + +238 +00:24:38,610 --> 00:24:45,090 +في ستة عشر بتجي على الأربعة يبقى على الأربعة فيها + +239 +00:24:45,090 --> 00:24:50,850 +الأربعة بيظل اتناشر على أربعة فيها التلاتة وهادي + +240 +00:24:50,850 --> 00:24:56,890 +على أربعة على أربعة بيظل أربعة في اتنين في تمانية + +241 +00:24:57,520 --> 00:25:05,360 +يبقى هذه ويساوي خمسة و تلت أتمان، تلت أتمان اللي + +242 +00:25:05,360 --> 00:25:13,300 +هو خمسة وفاصلة و تلت أتمان عندنا اللي هو تلت + +243 +00:25:13,300 --> 00:25:20,120 +مية وخمسة وسبعين من الفطلع المساحة اللى حصلنا + +244 +00:25:20,120 --> 00:25:24,960 +عليها هذه ايه؟ واضح انها محصورة بين مين؟ بين + +245 +00:25:24,960 --> 00:25:30,680 +المساحتين أربعة وربعة وستة وربعة، هي موجودة، لو ما + +246 +00:25:30,680 --> 00:25:34,410 +طلعتش موجودة بينهم، معناهش شغلك كده مألوفغلط، + +247 +00:25:34,410 --> 00:25:38,930 +الراديو يجب أن يقع بين المساحاتين، وهي أقرب ما + +248 +00:25:38,930 --> 00:25:45,150 +يكون إلى المساحة الحقيقية، لكن مش تقريبا، مقدرش + +249 +00:25:45,150 --> 00:25:48,670 +أقول مية لمية، لكن أقرب ما يكون إلى المساحة + +250 +00:25:48,670 --> 00:25:52,040 +الحقيقيةيبقى يا شباب احنا بالنسبة للمساعة فيها + +251 +00:25:52,040 --> 00:25:56,560 +اننا يبقى هذه كلها اللي هي R هذه اللي هي المساعة + +252 +00:25:56,560 --> 00:26:01,620 +كلها اللي هي R فيها اننا upper sum لل area وفيها + +253 +00:26:01,620 --> 00:26:06,220 +اننا lower sum لل area وفيه ال middle اللي هو + +254 +00:26:06,220 --> 00:26:10,480 +المنتصف خلّي هذه المعلومات عندك يمكن يلزموننا في + +255 +00:26:10,480 --> 00:26:14,700 +يوم من الأياملحد هنا stop الله يعطيك العافية + +256 +00:26:14,700 --> 00:26:19,400 +نكفينا المعلومات هذه من هذا ال section ويليك أرقام + +257 +00:26:19,400 --> 00:26:28,780 +المسائل يبقى exercises exercises + +258 +00:26:28,780 --> 00:26:38,140 +خمسة واحد المسائل من واحد لغاية سبعة القدر نكفي + +259 +00:26:47,280 --> 00:26:51,400 +المطلوب ان هذا ال section خلّي بلا كده تعرف بس ال + +260 +00:26:51,400 --> 00:26:55,380 +upper some و ال lower some و ما بينهما اكتر ما هيك + +261 +00:26:55,380 --> 00:26:59,360 +بدناش طبعا؟ لأ هايجيك في ال section اللي بعد و + +262 +00:26:59,360 --> 00:27:05,560 +اتوكل على الله هو يعني مش البلاش هو تمهيد لما يلي + +263 +00:27:05,560 --> 00:27:06,640 +بعد ذلك + +264 +00:27:44,920 --> 00:27:52,140 +خلاص يا ابني هي السطر هذا كله عندك والنتيجة هيخلاص + +265 +00:27:52,140 --> 00:27:55,380 +بالكالكوليوتر تجيب هذه خمس ساعات المجموعة ده كله + +266 +00:27:55,380 --> 00:28:10,380 +والمساهم من واحد لسبع section + +267 +00:28:10,380 --> 00:28:17,020 +الجديد اللي هو خمس اتنين sigma + +268 +00:28:17,020 --> 00:28:17,840 +notation + +269 +00:28:23,190 --> 00:28:32,390 +Sigma notation and limits and limits of finite + +270 +00:28:32,390 --> 00:28:43,850 +sums Definition + +271 +00:28:43,850 --> 00:28:48,170 +The + +272 +00:28:48,170 --> 00:28:50,670 +Sigma + +273 +00:28:55,470 --> 00:29:03,950 +الصيغمه نوتشن لصمه + +274 +00:29:03,950 --> 00:29:04,510 +الفينيه + +275 +00:29:11,690 --> 00:29:25,650 +الرمز A1 زائد A2 زائد AN is denoted by + +276 +00:29:32,140 --> 00:29:40,460 +لغاية ال N لل A K يبقى ال sigma notation اللي هو + +277 +00:29:40,460 --> 00:29:46,010 +الجامعة يعني إشارة جامعةكنت بتقولها في التوجيه + +278 +00:29:46,010 --> 00:29:50,710 +بتحط نفس الإشارة بس بتكون بتعطيها مجموعة يعني + +279 +00:29:50,710 --> 00:29:55,310 +اختصار لكلمة مجموعة فبعدين بقول sigma notation + +280 +00:29:55,310 --> 00:29:59,770 +الإشارة أو الرمز تبع ال sigma اللي قدامنا هذا ل + +281 +00:29:59,770 --> 00:30:07,770 +finite sum لعدد محدود من الجمع لترماتزي a1 زي a2 + +282 +00:30:07,770 --> 00:30:17,290 +زي a3 زي a2 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي + +283 +00:30:17,290 --> 00:30:18,250 +a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 + +284 +00:30:18,250 --> 00:30:18,310 +زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي + +285 +00:30:18,310 --> 00:30:18,870 +a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 + +286 +00:30:18,870 --> 00:30:18,870 +زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي + +287 +00:30:18,870 --> 00:30:21,470 +a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 زي a3 + +288 +00:30:21,470 --> 00:30:27,810 +زي a3 زي + +289 +00:30:27,810 --> 00:30:39,960 +a3 زي a3يبقى هنا بقول ال a1 is the first term و a2 + +290 +00:30:39,960 --> 00:30:51,300 +is the second term و لو ضليت ماشي هوصل لak اللي هو + +291 +00:30:51,300 --> 00:30:54,620 +the keth term + +292 +00:30:56,160 --> 00:31:02,160 +يبقى الحد رقم K لما نوصل لآخر حد له A N يبقى هو + +293 +00:31:02,160 --> 00:31:08,420 +الحد النوني the end term طبعا طيب الأن بدنا نشتغل + +294 +00:31:08,420 --> 00:31:12,660 +هذا الكلام شغل عمل يعني بدنا أمثلة توضيحية يبقى + +295 +00:31:12,660 --> 00:31:16,620 +كلمة sum تعني مجموعة لمن بدي أجيب هذا ال K + +296 +00:31:20,620 --> 00:31:25,940 +عندما أقول كتو ساوي واحد فأبدا من عند كتو ساوي + +297 +00:31:25,940 --> 00:31:30,280 +واحد لغاية الان اللي فوقي بقى أخر حاجة بدي اكتبها + +298 +00:31:30,280 --> 00:31:35,060 +هو الحد النوني تمام فبعدين بقول لو كانت كب واحد + +299 +00:31:35,060 --> 00:31:41,490 +ايه بدي اشيل كب واحد مكانه؟Summation يبقى زائد بعد + +300 +00:31:41,490 --> 00:31:48,390 +و جمع بدي أضع K باتنين بيصير A2 زائد A3 زائد A4 + +301 +00:31:48,390 --> 00:31:53,030 +زائد AK زائد AK زائد 1 لغاية ما أوصل لغاية مين + +302 +00:31:53,030 --> 00:31:59,070 +لغاية AN يبقى هذا المقصود نعطي مثال عملي على ذلك + +303 +00:31:59,070 --> 00:32:02,550 +يبقى example one والله examples + +304 +00:32:15,000 --> 00:32:29,960 +evaluate تحسبلي the value of the following the + +305 +00:32:29,960 --> 00:32:40,820 +value of the following summations برأي + +306 +00:32:42,440 --> 00:32:51,120 +Summation على K تربيع من K تساوي واحد لغاية الخمسة + +307 +00:32:51,120 --> 00:33:00,920 +نمر بي Summation من K تساوي اتنين لغاية ستة لكي + +308 +00:33:00,920 --> 00:33:08,140 +minus ال one نمر سي Summation من K تساوي واحد + +309 +00:33:08,140 --> 00:33:11,740 +لغاية اربعة + +310 +00:33:13,170 --> 00:33:20,970 +لغاية الأربعة لناقص واحد to the power K cosine K + +311 +00:33:20,970 --> 00:33:21,610 +في ال + +312 +00:33:31,780 --> 00:33:37,620 +نحسب كل sum من هذه الاسمينة ثلاثا سمينة سمينة + +313 +00:33:37,620 --> 00:33:44,280 +سمينة من ك يبدأ يساوي واحد لغاية خمسة لكي تربيع + +314 +00:33:44,280 --> 00:33:48,220 +معناته يبدأ يشيل كل ك ويحط مرة واحد ومرة اتنين + +315 +00:33:48,220 --> 00:33:52,640 +ومرة تلاتة ومرة اربعة لغاية ما يوصل لين لخمسة يبقى + +316 +00:33:52,640 --> 00:33:57,370 +stop بعد ما تقدر تمشي ولا خطوةيبقى هذا الكلام بده + +317 +00:33:57,370 --> 00:34:01,410 +يساوي واحد تربية، بعد واحد بيجينا اتنين، يبقى + +318 +00:34:01,410 --> 00:34:07,290 +اتنين تربية، تلاتة تربية، اربعة تربية، خمسة تربية، + +319 +00:34:07,290 --> 00:34:13,100 +لغاية خمسة ممنوعة تفوت الخمسةيبقى انا وصلت لغاية K + +320 +00:34:13,100 --> 00:34:18,380 +تساوي خمسة وقفت طب بدي اعرف قداش المجموع يبقى ده + +321 +00:34:18,380 --> 00:34:26,080 +واحد زائد اربعة زائد تسعة زائد ستاشر زائد خمسة + +322 +00:34:26,080 --> 00:34:31,590 +وعشرينخمسة وعشرين واستتاشر واحد واربعين خمسين خمسة + +323 +00:34:31,590 --> 00:34:38,170 +وخمسين يبقى قيمة هذا هي قداش خمسة وخمسين هذا نمر + +324 +00:34:38,170 --> 00:34:43,490 +ايه من المثال نجي لنمر بي نمر بي بدي ال summation + +325 +00:34:43,490 --> 00:34:50,970 +من k تساوي اتنين لغاية ستة لكي minus ال oneليس + +326 +00:34:50,970 --> 00:34:54,910 +بالضرورة أني أبدأ دائما و أبدا من عند الواحد، من + +327 +00:34:54,910 --> 00:34:57,250 +أين أريد أن أقول لك ابدأ، بداك تبدأ، ان شاء الله + +328 +00:34:57,250 --> 00:34:59,910 +يقول لي من عندك إتس أو مية، بدا أبدأ المية و مليش، + +329 +00:34:59,910 --> 00:35:03,850 +دعوة في اللي جابلي، يبقى أنا بتقيت بالرقم أو ال + +330 +00:35:03,850 --> 00:35:07,250 +index، الدليل اللي بحطه ليه تحت ال summation + +331 +00:35:07,250 --> 00:35:13,510 +والدليل اللي بحطه ليه أعلى ال summationيبقى باجي + +332 +00:35:13,510 --> 00:35:18,550 +بقول له او هذا بسمي ال lower limit of summation و + +333 +00:35:18,550 --> 00:35:22,970 +هذا ال upper limit of summation النهاية العلوى لل + +334 +00:35:22,970 --> 00:35:26,290 +summation و النهاية السفلى لل summation يبقى هذا + +335 +00:35:26,290 --> 00:35:30,550 +الكلام بدي يساوي بدي اشيل ك مرة احط اتنين مرة + +336 +00:35:30,550 --> 00:35:36,690 +تلاتة مرة اربعة مرة خمسة مرة ستة يبقى هنا اتنين + +337 +00:35:36,690 --> 00:35:41,700 +ناقص واحد زادخلصنا من عنده اتنين بيجينا بعد ايش + +338 +00:35:41,700 --> 00:35:51,360 +تلاتة يبقى تلاتة ناقص واحد اربع ناقص واحد خمسة + +339 +00:35:51,360 --> 00:36:00,200 +ناقص واحد ستة ناقص واحد استطبع ال Autographyيبقى + +340 +00:36:00,200 --> 00:36:06,100 +هذه عبارة عن مين؟ واحد زيدي اتنين زيدي تلاتة زيدي + +341 +00:36:06,100 --> 00:36:11,500 +اربعة زيدي خمسة خمسة واربعة تسعة وتلاتة اتناش + +342 +00:36:11,500 --> 00:36:17,120 +اتناش وتلاتة خمستاش يبقى النتيجة هذه خمستاش + +343 +00:36:17,120 --> 00:36:22,690 +والنتيجة الأولى كانت خمسة وخمسينبعدها نجي لنمرة C + +344 +00:36:22,690 --> 00:36:30,270 +نمرة C summation من K تسوى واحد لغاية الأربع لنقص + +345 +00:36:30,270 --> 00:36:38,980 +واحد to the power K لكو صين K بي ويالان بدي اشيل ك + +346 +00:36:38,980 --> 00:36:43,340 +و احط مكانها واحد اشيل ك و احط مكانها اتنين اشيل ك + +347 +00:36:43,340 --> 00:36:48,420 +و احط مكانها تلاتة و هكذا طيب يبقى بدي ابدأ بناقص + +348 +00:36:48,420 --> 00:36:55,060 +واحد to the power one lacosine byزاد ناقص واحد to + +349 +00:36:55,060 --> 00:37:01,580 +the power اتنين cosine اتنين by ناقص واحد لكل + +350 +00:37:01,580 --> 00:37:08,680 +تكييب cosine تلاتة by زاد ناقص واحد أس اربعة + +351 +00:37:08,680 --> 00:37:17,490 +cosine اربعة byكمان خلصنا بدي أحسب قدش القيم + +352 +00:37:17,490 --> 00:37:23,150 +العددية إليها يبقى هذا الكلام بده يساوي هذي سالب + +353 +00:37:23,150 --> 00:37:28,070 +واحد طب وقصان مية و تمانين سالب واحد هذي واحد + +354 +00:37:28,070 --> 00:37:33,880 +تربية اللي هو واحد راحت قصين اتنين بايدورة كاملة + +355 +00:37:33,880 --> 00:37:38,600 +زي cosine الصفر cosine الصفر بيبقى اداش بواحد اللي + +356 +00:37:38,600 --> 00:37:44,740 +بعدها زائد ناقص واحد ناقص واحد اكيلو بناقص واحد + +357 +00:37:44,740 --> 00:37:49,560 +cosine تلاتة باي بقول ال period اتنين باي اهملها + +358 +00:37:49,560 --> 00:37:54,460 +بيبقى ال جداش باي واحدة cosine ال باي سالب واحد + +359 +00:37:54,460 --> 00:38:04,130 +يبقى فيه سالب واحد اش فيههي التاني يا ابني زي + +360 +00:38:04,130 --> 00:38:08,890 +cosine الصفر cosine اتنين by دورة كاملة يبقى رجال + +361 +00:38:08,890 --> 00:38:14,410 +زي cosine الصفر مش بصفر تمام طيب دينا لان اخر نقطة + +362 +00:38:14,410 --> 00:38:18,330 +ناقص واحد قصة اربعة اللي هو بواحد cosine اربعة by + +363 +00:38:18,330 --> 00:38:23,620 +معناته two periodيبقى دورتين يبقى دورتين كذا كوصين + +364 +00:38:23,620 --> 00:38:28,380 +الصفر كوصين الصفر كده ايه بواحد يبقى الجواب يساوي + +365 +00:38:28,380 --> 00:38:36,240 +كده اربع فقط لا غير طيب هذا ال summation فكته و + +366 +00:38:36,240 --> 00:38:40,200 +طلعت المجموعة طب لو انا عند المجموعة بدي احطه على + +367 +00:38:40,200 --> 00:38:45,790 +شكل summationعملية عكسية مظبوط يبقى انا عندي + +368 +00:38:45,790 --> 00:38:50,830 +summation كتبته على شكل المجموع و روحت حسبته بتبقى + +369 +00:38:50,830 --> 00:38:58,710 +دي example تاني يبقى example two example + +370 +00:38:58,710 --> 00:39:07,810 +two بقول express the following sums express the + +371 +00:39:07,810 --> 00:39:12,110 +following sums + +372 +00:39:15,070 --> 00:39:23,270 +السماوات في الـ Sigma Notation + +373 +00:39:23,270 --> 00:39:29,790 +نمرأة + +374 +00:39:32,070 --> 00:39:42,150 +واحد زائد تلاتة زائد خمسة زائد سبعة زائد تسعة زائد + +375 +00:39:42,150 --> 00:39:54,010 +أحداش زائد تلاتاش نمرأ ب سالب خمس زائد خمسين سالب + +376 +00:39:54,010 --> 00:40:00,930 +تلت أخمس زائد أربع أخمس ناقص خمس أخمس + +377 +00:40:03,980 --> 00:40:09,560 +سؤال مرة تانية بيقول express عبرلي عن المجاميع + +378 +00:40:09,560 --> 00:40:13,640 +التالية بدلالة ال sigma notation يعني بدل ما هو + +379 +00:40:13,640 --> 00:40:17,720 +مكتوب بالشكل بقول بده كتبه على شكل مين على شكل + +380 +00:40:17,720 --> 00:40:22,300 +summation زي ما هو موجود عندنا بقوله بسيطة تعالى + +381 +00:40:22,300 --> 00:40:33,390 +نمسك مين الأولانيSummation 1 2 3 4 5 6 7 يبقى سبعة + +382 +00:40:33,390 --> 00:40:40,910 +كلمات لو بدى ابدأ من عند كيتو سواء هنتهي وين لغاية + +383 +00:40:40,910 --> 00:40:46,670 +سبعة طبعا ضال بدى ما هو شكل الحد النوني اللى هنا + +384 +00:40:47,160 --> 00:40:52,280 +طبعا لإن هذا .. لما أقول summation هذا يعتبر الحد + +385 +00:40:52,280 --> 00:40:57,580 +النوني في من؟ في المجموعة، ليه بقى إيش بده أقول؟ + +386 +00:40:57,580 --> 00:41:02,550 +بجيب أطلع في الأدادة كلها أعداد فرديةلما اقول + +387 +00:41:02,550 --> 00:41:05,130 +اتنين كي اتنين كي اتنين كي اتنين كي اتنين كي اتنين + +388 +00:41:05,130 --> 00:41:07,330 +كي اتنين كي اتنين كي اتنين كي اتنين كي اتنين كي + +389 +00:41:07,330 --> 00:41:10,890 +اتنين كي اتنين كي اتنين كي اتنين كي اتنين كي اتنين + +390 +00:41:10,890 --> 00:41:10,890 +كي اتنين كي اتنين كي اتنين كي اتنين كي اتنين كي + +391 +00:41:10,890 --> 00:41:11,670 +اتنين كي اتنين كي اتنين كي اتنين كي اتنين كي اتنين + +392 +00:41:11,670 --> 00:41:14,330 +كي اتنين كي اتنين كي اتنين كي اتنين كي اتنين كي + +393 +00:41:14,330 --> 00:41:18,110 +اتنين + +394 +00:41:18,110 --> 00:41:22,070 +كي اتنين + +395 +00:41:22,070 --> 00:41:30,590 +كي اتنين كي اتنين + +396 +00:41:32,120 --> 00:41:37,840 +حط كيب اتنين بصير اربعة ناقص واحد تلاتة حط كيب + +397 +00:41:37,840 --> 00:41:42,820 +تلاتة بصير ستة ناقص واحد خمسة يبقى كلام سليم مائة + +398 +00:41:42,820 --> 00:41:50,680 +بالمائة تمام كيب ماعنديش مشكلة حط زي ما بدك من وين + +399 +00:41:50,680 --> 00:41:53,520 +بتبدأ ال index ان شاء الله تبدأ عندك اتزاوية عشرة + +400 +00:41:54,320 --> 00:42:00,660 +ماعنديش مشكلة يبقى انت بدك تكتبها بطريقة فعلا يصير + +401 +00:42:00,660 --> 00:42:04,460 +عندك يعني انا لو بدي ابدأ من عند العشرة من عند كتر + +402 +00:42:04,460 --> 00:42:10,000 +تسوية عشرة كويس؟ بقوله ماشاء الله اتنين كتر ناقص + +403 +00:42:10,000 --> 00:42:17,000 +تسعة مثلا لأ ناقص تسعة وطعش نصبوه؟ يبقى بتبدأ من + +404 +00:42:17,000 --> 00:42:19,440 +عندك كتر تسعة وعشر وصير اتنين وعشرة وعبر عشرين + +405 +00:42:19,440 --> 00:42:25,560 +ناقص تسعة وطعش وصير واحديبقى بدى اكتبها هدى ال + +406 +00:42:25,560 --> 00:42:30,940 +summation من عند كت والساوية عشرة لغاية السبعة + +407 +00:42:30,940 --> 00:42:37,460 +لغاية السبعتاش طبعا لغاية السبعتاش لمن؟ للي اتنين + +408 +00:42:37,460 --> 00:42:43,310 +كناقص تسعتاشحط عشرة بصير عشرين نقص ساعة و عشرة + +409 +00:42:43,310 --> 00:42:45,310 +بواحد بعد عشرة بصير عشرة وحد عشرة وحد عشرة وحد + +410 +00:42:45,310 --> 00:42:46,930 +عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة + +411 +00:42:46,930 --> 00:42:50,990 +وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد + +412 +00:42:50,990 --> 00:42:54,990 +عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة + +413 +00:42:54,990 --> 00:42:58,790 +وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد + +414 +00:42:58,790 --> 00:42:58,810 +عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة + +415 +00:42:58,810 --> 00:43:01,450 +وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد عشرة وحد + +416 +00:43:01,450 --> 00:43:06,530 +عشرة وحد عشرة وحد عشرة + +417 +00:43:26,230 --> 00:43:33,290 +طب نجي لنمرا فيهنبرى بي اي summation اكم حد دول؟ + +418 +00:43:33,290 --> 00:43:37,250 +نين اربع خمسة بدك تبدأ من عند الواحد اللي هو + +419 +00:43:37,250 --> 00:43:40,730 +بالفضل احنا نبدأ من عنده دائما وابدأ نبدأ من عندك + +420 +00:43:40,730 --> 00:43:45,930 +K تساوي واحد الى infinity انسى السالب نتفهم عليها + +421 +00:43:45,930 --> 00:43:52,750 +تصبر علينا شوية فيهشوف يا سيدي باجي بتطلع الى غاية + +422 +00:43:52,750 --> 00:43:57,170 +خمسة قولنا كتبنا خمسة اصلا داري على ال series تبع + +423 +00:43:57,170 --> 00:44:00,990 +ال calculus بيها دماغي كلها ل infinityيبقى من كتر + +424 +00:44:00,990 --> 00:44:05,550 +تسوى واحد لغاية من؟ لغاية خمسة لأن أنا ماعنديش إلا + +425 +00:44:05,550 --> 00:44:14,090 +خمسة حدود تمام فبشرأك حطل عليها زائد ستة على خمسة + +426 +00:44:14,090 --> 00:44:17,710 +لا حسيني قولي واحد ما هي كله لشان الخمسات تحت روحت + +427 +00:44:17,710 --> 00:44:22,210 +حطيت خمسة لا حطل كمان ستة على خمسة إذا هذا بيصير + +428 +00:44:22,210 --> 00:44:28,880 +لوين؟ لغاية ستة تمامطيب بقوله كويس يبقى أنا بدي + +429 +00:44:28,880 --> 00:44:32,120 +أتي أشوف ما هو الشكل الحد النولي في هذه الحالة + +430 +00:44:32,120 --> 00:44:36,980 +بقول سيبقى الإشارة متهم عليها البصر واحد، اتنين، + +431 +00:44:36,980 --> 00:44:42,260 +تلاتة، أربعة، خمسة، يبقى بقوله K مظبوط ولا زيد ولا + +432 +00:44:42,260 --> 00:44:49,980 +أحد، K زي ما هي يبقى هذه K على باجي في المقام ثابت + +433 +00:44:49,980 --> 00:44:55,960 +لم يتغير يبقى هذا بتغيرش بحط الرقم ثابت زي ما هو + +434 +00:44:57,200 --> 00:45:03,540 +صحيح؟ ضلت مشكلتنا وين؟ عندي السالب غمّب و اكتب ما + +435 +00:45:03,540 --> 00:45:11,320 +يأتي سالب واحد اسكيإذا و الله طلع كلامنا صح خلاص + +436 +00:45:11,320 --> 00:45:16,840 +ماعش الحال، طلع غلط في الإشارة، بحط هذه بس ك زائد + +437 +00:45:16,840 --> 00:45:19,640 +واحد، و هذه بتبقى لها زائد واحد، مالعيش علاقة، + +438 +00:45:19,640 --> 00:45:25,400 +كويس؟ لكي نجيب الإشارة، بحط سالب واحد أس ك، زبطت + +439 +00:45:25,400 --> 00:45:28,760 +كان بها، ما زبطت بحط بس زايد واحد، تجيها جات معاك + +440 +00:45:28,760 --> 00:45:34,860 +دوريفتعالى نشوف كلنا صح ولا لأ حط كب واحد يبقى + +441 +00:45:34,860 --> 00:45:42,720 +بصير سالب خمس حد الاول اه والله سالب خمس تمام يبقى + +442 +00:45:42,720 --> 00:45:47,320 +حط كب اتنين بصير هادي موجب بصير اتنين على خمسة + +443 +00:45:47,320 --> 00:45:52,180 +فعلا اتنين على خمسة و هكذا يبقى كله كلام سليم مائة + +444 +00:45:52,180 --> 00:45:55,460 +بالمائة مافيش عندنا اي مشكلة فيه + +445 +00:46:07,460 --> 00:46:13,400 +القواعد الجابرية for finite + +446 +00:46:13,400 --> 00:46:16,660 +sums + +447 +00:46:20,540 --> 00:46:24,180 +القاعدة الأولى بتقول لي ما يأتي لو عندك summation + +448 +00:46:24,180 --> 00:46:34,440 +من K تستوي واحد لغاية ال N لمن لل A K زائد او ناقص + +449 +00:46:34,440 --> 00:46:41,450 +BK تقدر توزع summation للي اتنينمن K تساوي واحد + +450 +00:46:41,450 --> 00:46:48,830 +لغاية ال N لل A K زاد أو ناقص summation من K تساوي + +451 +00:46:48,830 --> 00:46:57,200 +واحد لغاية ال N لل BKالقاعدة الثانية لو كان عندك + +452 +00:46:57,200 --> 00:47:05,860 +summation من K تساوي واحد لغاية ال N ل C في ال AK + +453 +00:47:05,860 --> 00:47:10,180 +ال C مقدر ثابت بس هنا مالوش لعب في ال summation + +454 +00:47:10,180 --> 00:47:15,120 +بتقدر تطلع برا ال summation وبالتالي هتقول لي C في + +455 +00:47:15,120 --> 00:47:21,620 +summation من K تساوي واحد لغاية ال N لل AK فقط + +456 +00:47:23,880 --> 00:47:30,840 +القاعدة الثالثة يبقى القاعدة الثالثة summation من + +457 +00:47:30,840 --> 00:47:38,700 +K تساوي واحد لغاية ال N لل constant C بدي يساوي N + +458 +00:47:38,700 --> 00:47:44,700 +في C where C is constant + +459 +00:48:12,930 --> 00:48:17,190 +طيب يبقى هدول القواعد الثلاثة اللي عندنا القواعد + +460 +00:48:17,190 --> 00:48:22,590 +الأولى summation للمجموع الجابري لحدين نونيين + +461 +00:48:22,590 --> 00:48:26,830 +يساوي summation للحد الأول زاد أو نقص summation + +462 +00:48:26,830 --> 00:48:31,190 +للحد الثاني اللي بعد اللي كان summation ل constant + +463 +00:48:31,190 --> 00:48:35,110 +في حد نوني بقول ال constant مالكش دعوة إيش ما + +464 +00:48:35,110 --> 00:48:38,590 +تتغير الكيملكش لأن ده مقدار ثابتيبقى خلّيك برا ال + +465 +00:48:38,590 --> 00:48:42,770 +summation في summation من K تساوي واحد ل N لل A K + +466 +00:48:42,770 --> 00:48:49,170 +itself بعد هيك لو كان summation على C يعني ماعنديش + +467 +00:48:49,170 --> 00:48:55,090 +K زي summation من K تساوي واحد لغاية N على خمسة + +468 +00:48:56,160 --> 00:49:00,260 +بقول لما تبقى k واحد تبقى خمسة و لما تبقى k اتنين + +469 +00:49:00,260 --> 00:49:05,240 +خمسة و لما تبقى k تلاتة خمسة و لما تبقى k أربعة + +470 +00:49:05,240 --> 00:49:09,160 +خمسة و لما تبقى k خمسة و لما تبقى k أربعة خمسة و + +471 +00:49:09,160 --> 00:49:09,740 +لما تبقى k أربعة خمسة و لما تبقى k أربعة خمسة و + +472 +00:49:09,740 --> 00:49:11,000 +لما تبقى k أربعة خمسة و لما تبقى k أربعة خمسة و + +473 +00:49:11,000 --> 00:49:11,840 +لما تبقى k أربعة خمسة و لما تبقى k أربعة خمسة و + +474 +00:49:11,840 --> 00:49:14,220 +لما تبقى k أربعة خمسة و لما تبقى k أربعة خمسة و + +475 +00:49:14,220 --> 00:49:20,630 +لما تبقى k أربعةومن هنا قلنا مين N في C لأن C لا + +476 +00:49:20,630 --> 00:49:28,970 +تتغير لكن نجمعها إلى نفس عدد يساوي N يبقى معناته N + +477 +00:49:28,970 --> 00:49:33,230 +في C وانتهينا من الشيء الوحيد طيب نعطي أمثلة + +478 +00:49:33,230 --> 00:49:36,990 +توضحية على ذلك example + +479 +00:49:46,710 --> 00:49:58,890 +Find the value of summation من K تسوى واحد لغاية + +480 +00:49:58,890 --> 00:50:06,590 +سبعة لمين للبعيد Solutions + +481 +00:50:09,010 --> 00:50:15,230 +Summation من K تساوي واحد لغاية سبعة لبي يساوي لأن + +482 +00:50:15,230 --> 00:50:20,450 +البي مقدار ثابت كونصان مالوش دعوة ال N عندي قداش + +483 +00:50:20,450 --> 00:50:25,850 +سبعة تبقى للخاصية الأخيرة يبقى هذا يساوي قداش سبعة + +484 +00:50:25,850 --> 00:50:30,950 +باي وانتهينا منها بس بداش نشتغل لكن لو ماكنتش عارف + +485 +00:50:30,950 --> 00:50:35,390 +القاعدة هذه بدي اقول باي زاد باي زاد باي سبعة مرات + +486 +00:50:35,390 --> 00:50:49,570 +يبقى سبعة بايطيب هذا بصير example two suppose + +487 +00:50:49,570 --> 00:50:53,610 +that افترض + +488 +00:50:53,610 --> 00:51:03,800 +انه summationمن K تساوي واحد لغاية ال N لل A كي + +489 +00:51:03,800 --> 00:51:16,020 +يساوي سالب خمسة and and summation and + +490 +00:51:16,020 --> 00:51:24,380 +summation من K تساوي واحد لغاية ال N لل B كي يساوي + +491 +00:51:24,380 --> 00:51:25,160 +ستة + +492 +00:51:28,920 --> 00:51:38,940 +The value of summation من K تساوي واحد لغاية ال N + +493 +00:51:38,940 --> 00:51:56,080 +لل BK ناقص اتنين AK خلّي + +494 +00:51:56,080 --> 00:52:01,710 +بركةأحنا عندنا هذا الـ summation بقدر اوزعه إلى + +495 +00:52:01,710 --> 00:52:07,370 +two summations تبقى لمين للقاعدة الأولى يبقى هذا + +496 +00:52:07,370 --> 00:52:13,010 +بيصير ال summation من K تسوى واحد لغاية ال N لل BK + +497 +00:52:13,010 --> 00:52:18,630 +ناقص summation من K تسوى واحد لغاية ال N لليتنين + +498 +00:52:18,630 --> 00:52:24,980 +AKيبقى هذا طبقال للقاعدة الأولى، بدأجي للقاعدة + +499 +00:52:24,980 --> 00:52:28,720 +الثانية، إذا عندك مقدار ثابت بتقدر تطلع وين؟ برا + +500 +00:52:28,720 --> 00:52:34,280 +ال summation، إذا هذا بدي يسوى summation على bk من + +501 +00:52:34,280 --> 00:52:40,040 +k تسوى واحد لغاية ال N ناقصي اتنين summation من k + +502 +00:52:40,040 --> 00:52:46,530 +تسوى واحد لغاية ال N لمن؟ لل a kهذا الكلام دي + +503 +00:52:46,530 --> 00:52:50,710 +يساوي summation على بك مُعطَى اللي هو بقداش ستة + +504 +00:52:50,710 --> 00:52:55,930 +يبقى هاي ستة ناقص اتنين فيه summation على بك + +505 +00:52:55,930 --> 00:53:01,630 +مُعطَى بقداش بناقص خمسة يبقى ناقص خمسة ويساوي ستة + +506 +00:53:01,630 --> 00:53:06,950 +زي عشر يبقى قيمة ال summation هذا يساوي كداش يساوي + +507 +00:53:06,950 --> 00:53:08,610 +ستة عشر + +508 +00:53:13,520 --> 00:53:20,920 +نجي بعض المجاميع الأساسية هذه اللي هي لا يستغنى + +509 +00:53:20,920 --> 00:53:22,580 +عنها بعد ذلك + +510 +00:53:47,550 --> 00:53:53,950 +some formulas some + +511 +00:53:53,950 --> 00:54:10,250 +formulas for positive integers if + +512 +00:54:10,250 --> 00:54:15,870 +ال N is a positive + +513 +00:54:24,230 --> 00:54:32,150 +نقطة الأولى summation + +514 +00:54:32,150 --> 00:54:42,030 +من كي تساوي واحد لغاية الان للكي يساوي ان في ان + +515 +00:54:42,030 --> 00:54:51,000 +زائد واحد على مين على اتنيننمرة اتنين summation من + +516 +00:54:51,000 --> 00:55:00,960 +K تسوى واحد لل N لل K تربيع يسوى N في N زائد واحد + +517 +00:55:00,960 --> 00:55:07,840 +في اتنين N زائد واحد كله على ستة نمرة تلاتة + +518 +00:55:07,840 --> 00:55:16,360 +summation من K تسوى واحد لغاية ال N لل K تكيب يسوى + +519 +00:55:16,360 --> 00:55:16,820 +N + +520 +00:55:19,550 --> 00:55:30,890 +ن بن زائد واحد على اتنين الكل تربيع example + +521 +00:55:30,890 --> 00:55:36,410 +evaluate + +522 +00:55:36,410 --> 00:55:37,690 +the following sums + +523 +00:56:43,330 --> 00:56:47,910 +بنرجع مرة تانية بقول some formulas for positive + +524 +00:56:47,910 --> 00:56:53,850 +integers بعض القواعد الأساسية للأعداد الصحيحة + +525 +00:56:53,850 --> 00:56:58,630 +الموجبة بقول لو كانت أن أدد صحيح موجب فإن + +526 +00:56:58,630 --> 00:57:04,900 +summation على k من أن k تساوي واحدلغاية الان هو + +527 +00:57:04,900 --> 00:57:10,600 +عبارة عن ان في ان زائد واحد على اتنين طبعا هذه + +528 +00:57:10,600 --> 00:57:15,360 +برهانة سهلة عن طريق المتواليات العددية ان هذه اصلا + +529 +00:57:15,360 --> 00:57:20,000 +واحد زائد اتنين زائد تلتة زائد اربعة زائد ان وانت + +530 +00:57:20,000 --> 00:57:25,070 +بتعرفواان المجموعة تبع المتوالي العددية بذات الحد + +531 +00:57:25,070 --> 00:57:31,210 +الأول والاخير اللي هو N على 2 في ألف زائد لم ألف + +532 +00:57:31,210 --> 00:57:37,000 +واحد ولم N يبقى N على 2 في واحد زائد N مية الميةبس + +533 +00:57:37,000 --> 00:57:40,600 +احنا المطلوب ان بارهنا بال induction بالاستنتاج + +534 +00:57:40,600 --> 00:57:43,900 +الرياضي وكونكوا مااخدتوش استنتاج رياضي يبقى + +535 +00:57:43,900 --> 00:57:48,460 +مسامحينكوا في البراهين بس تعرفلي ايها فقط ان + +536 +00:57:48,460 --> 00:57:53,100 +summation على k يسوى n في n زي 1 على 2 طب لو كان + +537 +00:57:53,100 --> 00:57:57,740 +summation على k تربيع يعني 1 تربية زي 2 تربية زي 3 + +538 +00:57:57,740 --> 00:58:01,300 +تربية زي 4 تربيةقبل قليل بقينا نربع و نروح نجمع + +539 +00:58:01,300 --> 00:58:05,320 +انا بدى أبطل اربع بدى احسب النتيجة المباشرة الآن + +540 +00:58:05,320 --> 00:58:10,120 +من خلال هذه القاعدة يبقى بقول ان في ان زاد واحد في + +541 +00:58:10,120 --> 00:58:14,320 +اتنين ان زاد واحد كله مجسوم على ستة حاصل ضرب تلت + +542 +00:58:14,320 --> 00:58:18,740 +كميات في بعضها و كله مجسوم على ستة الان summation + +543 +00:58:18,740 --> 00:58:22,680 +كتس واحدة لإن لكي تكعيب هو نتيجة ال summation + +544 +00:58:22,680 --> 00:58:28,460 +الأولاني بقص مروح اياه بربهيبقى N في N زي 1 على 2 + +545 +00:58:28,460 --> 00:58:33,400 +لكل تربيع يبقى هذا summation على مين على كتا كيم + +546 +00:58:33,400 --> 00:58:39,020 +هذه تعتبر تلت قواعد بدي استخدم هذه القواعد الثلاث + +547 +00:58:39,020 --> 00:58:44,500 +متى لازمةالامر فبنعطي مثال توضيح على ذلك بيقول + +548 +00:58:44,500 --> 00:58:50,260 +الصماشن من كتس واحد إلى سبعة لكف اتنين ك زائد واحد + +549 +00:58:50,260 --> 00:58:55,120 +يبقى اتك الجثة اللى فكتها بيصير اتنين ك تربية زائد + +550 +00:58:55,120 --> 00:58:59,160 +ك بدى اطبق الصماشن اللى استخدمناه قبلها اللى هو + +551 +00:58:59,160 --> 00:59:03,580 +توزيع الصماشن على الكميتين الأتنين وهذا كونص ان + +552 +00:59:03,580 --> 00:59:08,180 +بقدر اخده برا اذا هذا الكلام بدى يساويإتنين + +553 +00:59:08,180 --> 00:59:14,040 +summation من K تسوى واحد لغاية سبعة لل K تربية + +554 +00:59:14,040 --> 00:59:21,440 +زائد summation من K تسوى واحد لغاية سبعة لمين لل K + +555 +00:59:21,440 --> 00:59:27,710 +itselfطيب هذا الكلام ماذا يساوي؟ نين مالهاش دوة، + +556 +00:59:27,710 --> 00:59:32,610 +تمام؟ ندي summation على كتر بيها هيه، يعني بدي + +557 +00:59:32,610 --> 00:59:38,210 +أشيل كل إن عندي و أحط مكان أجبهاش، سبعة، تمام؟ + +558 +00:59:38,210 --> 00:59:42,980 +يبقى هذا جوزوبدأ يطبق القاعدة اللي عندى انه كتر + +559 +00:59:42,980 --> 00:59:48,160 +بيها هى اللى موجودة عندى يبقى سبعة في سبعة زائد + +560 +00:59:48,160 --> 00:59:55,080 +واحد اتنين في سبعة اربعتاشر زائد واحد كل هذا + +561 +00:59:55,080 --> 01:00:03,000 +الكلام على ستة هذا الجزء الاول الجزء التانى زائد + +562 +01:00:07,880 --> 01:00:16,260 +يبقى سبعة في سبعة زائد واحد كله على اتنين تعالى + +563 +01:00:16,260 --> 01:00:21,990 +نحسب هذا الكلام ويساوياتنين مع ستة بيظل تلاتة في + +564 +01:00:21,990 --> 01:00:27,570 +المقام يبقى ضال عندنا هنا جداش تلاتة وهنا بيظل + +565 +01:00:27,570 --> 01:00:34,090 +عندنا سبعة في تمانية واربعتاش زي واحد جداش اللي هو + +566 +01:00:34,090 --> 01:00:42,470 +خمستاشرتمام؟ هذا ال term الأول زائد سبعة في تمانية + +567 +01:00:42,470 --> 01:00:47,490 +كله على اتنين هذه التلاتة مع هذه بيبقى الجداش + +568 +01:00:47,490 --> 01:00:54,210 +بيبقى الخمسة يبقى هذه بتتساوي سبعة في تمانية في + +569 +01:00:54,210 --> 01:01:04,380 +خمسة زائد سبعة في أربعة ويساويخمسة في تمانية يبقى + +570 +01:01:04,380 --> 01:01:11,220 +أربعين أربعين في سبعة متين و تمانين يبقى هذه متين + +571 +01:01:11,220 --> 01:01:17,980 +و تمانين و أربع في سبعة تمانية و عشرين و الجواب + +572 +01:01:17,980 --> 01:01:24,740 +تلتمية و تمانية نجي ناخد النقطة التانية اللي هي + +573 +01:01:24,740 --> 01:01:30,580 +نمرة B نمرة B بيقول ال summation + +574 +01:01:33,800 --> 01:01:42,840 +من ك تسوى واحد لغاية سبعة لمن؟ للك هذا كله تربيع + +575 +01:01:42,840 --> 01:01:49,120 +مضافا إليه summation من ك تسوى واحد لغاية سبعة + +576 +01:01:49,120 --> 01:01:57,220 +لمن؟ للك تكيب على أربعة ك تكيب على أربعة ويسوىنجي + +577 +01:01:57,220 --> 01:02:03,480 +لل term الأول اللي بين جثين يبقى summation على K N + +578 +01:02:03,480 --> 01:02:10,540 +في N زياد واحد يبقى سبعة في سبعة زياد واحد على + +579 +01:02:10,540 --> 01:02:17,960 +اتنين سبعة في سبعة زياد واحد على اتنين هذا بيصير + +580 +01:02:17,960 --> 01:02:23,280 +كل تربيع اللي هو ال term الأولاللي بعده ناقص ربع + +581 +01:02:23,280 --> 01:02:28,860 +مالوش دارة وبظل انه قداش summation من كتس واحد + +582 +01:02:28,860 --> 01:02:35,410 +لغاية سبعة لمين لكت كتيبقى هذا الكلام بديه ساوي + +583 +01:02:35,410 --> 01:02:42,290 +سبعة في سبعة تسعة واربعين وسبعة واحد تمانية في + +584 +01:02:42,290 --> 01:02:48,510 +تمانية اربعة وستين اربعة وستين تسعة واربعين في + +585 +01:02:48,510 --> 01:02:55,750 +اربعة وستين وكل هذا مقسما عالميا على اربعة ناقص + +586 +01:02:55,750 --> 01:03:00,190 +ربعنجي للكتة كايب، بدي أشيلها و أحط مكانها كل + +587 +01:03:00,190 --> 01:03:06,870 +واحدة سبعة يبقى سبعة في تمانية و سبعة في اتنينة + +588 +01:03:06,870 --> 01:03:13,390 +بقى اربع طاشر و واحد خمس طاشر كله على قداش على ستة + +589 +01:03:16,430 --> 01:03:22,710 +خيص؟ طيب، هذا الكلام بده يساوي، هذه بصير تسعة و + +590 +01:03:22,710 --> 01:03:28,730 +أربعين في ستة عشر، هذه فيها ستة عشر و نيجي لهذه + +591 +01:03:28,730 --> 01:03:34,690 +تمام؟ التمانية هذه بتروح مع الأربعة و مع اتنين + +592 +01:03:34,690 --> 01:03:39,370 +بيبقى تلاتة و تلاتة بيبقى خمسة في سبعة خمسة و + +593 +01:03:39,370 --> 01:03:40,010 +تلاتين + +594 +01:03:43,640 --> 01:03:52,100 +اه تكيب استنا شوية استنا شوية هذه الأولى مشكلة بس + +595 +01:03:52,100 --> 01:04:00,560 +في الأخيرة هذه تمام؟ الأخيرةيبقى ناقص ربع كتا كايب + +596 +01:04:00,560 --> 01:04:06,480 +اللي هي القمة اللي تحت اليمين اللي هو سبعة تربيع + +597 +01:04:06,480 --> 01:04:13,540 +في سبعة زائد واحد لكل تربيع على مين؟ على أربع + +598 +01:04:16,230 --> 01:04:20,830 +تمام؟ طيب، هذه نفس الأولى ليها، بس بتفرج، لا فيها + +599 +01:04:20,830 --> 01:04:27,290 +ربع عادي، يبقى هنا لو قلنا هذا الربع برا، تمام؟ + +600 +01:04:27,290 --> 01:04:32,490 +هذا الربع برا، والله أنا اختصر بيهم الشريعة + +601 +01:04:35,390 --> 01:04:42,950 +هذه بدأت تساوي هي تسعة وأربعين في ستة عشر خلي بالك + +602 +01:04:42,950 --> 01:04:51,810 +هنا وهذه يا سيدي ناقص اللي هو هي تسعة وأربعين وهذه + +603 +01:04:51,810 --> 01:04:58,510 +تمانية في تمانية في أربعة وستين وهذه عليها على ستة + +604 +01:04:58,510 --> 01:05:03,390 +عشر يبقى على ستة عشر وعلى ستة عشر كده؟ أربعة + +605 +01:05:25,000 --> 01:05:32,440 +هو مجرد مجرد مجرد مجرد مجرد + +606 +01:06:19,110 --> 01:06:20,870 +هو ايه + +607 +01:07:14,020 --> 01:07:16,700 +السلام عليكم ورحمة الله وبركاته + +608 +01:08:02,510 --> 01:08:03,910 +العزيزي + +609 +01:08:29,460 --> 01:08:34,040 +DELTA XK-XK-1 + +610 +01:09:08,940 --> 01:09:13,900 +بنعرف أن هنا شغلتين الشغل الأولى partition ل + +611 +01:09:13,900 --> 01:09:19,820 +interval يعني تجزيء ل interval ما والأمر الثاني + +612 +01:09:19,820 --> 01:09:25,920 +بأن ال sub interval الرقم k اللي هو the length of + +613 +01:09:25,920 --> 01:09:30,740 +the kth sub interval يبقى طول كل فترة جزئية من + +614 +01:09:30,740 --> 01:09:36,220 +الفترة الأساسية نجل ال partition لو أندي real line + +615 +01:09:36,220 --> 01:09:42,420 +مثل هذا ال real lineبدأت بالنقطة A الانترفال + +616 +01:09:42,420 --> 01:09:50,320 +وانتهيت بالنقطة B ال A هذه لو سميتها X node يبقى + +617 +01:09:50,320 --> 01:09:57,660 +جهاز سميت هذه X1 سميت هذه X2 طبعا مش بضرورة + +618 +01:09:57,660 --> 01:10:02,220 +المسافة جت بعضها ماقولتش اتنين كل مسافات متساوية + +619 +01:10:02,650 --> 01:10:11,170 +أذا هوصل بعد قليل الى مين الى النقطة xk-1 و الى + +620 +01:10:11,170 --> 01:10:18,690 +مين النقطة xk وظل مستمر هوصل الى بيه اللى عبارة عن + +621 +01:10:18,690 --> 01:10:30,290 +مين عن ال xn اللى قبلها هنا هتبقى xn-1 وهكذايبقى + +622 +01:10:30,290 --> 01:10:36,830 +اش بيقول افترض ان X1 و X2 و Xn ناقص واحد هذا X1 X2 + +623 +01:10:36,830 --> 01:10:42,470 +X3 X4 Xk ناقص واحد Xk Xk زاد واحد ضالية لغاية Xn + +624 +01:10:42,470 --> 01:10:47,030 +ناقص واحد و Xn اللي عبارة عن مين عن بيه Xn يساوي + +625 +01:10:47,030 --> 01:10:53,010 +بيه اللاحق ان ال A أقل من X1 و X1 أقل من X2 يعني + +626 +01:10:53,010 --> 01:10:58,120 +مرتبة ترتيب دقيقةو X2 اقل من X3 و X3 اقل من X3 و + +627 +01:10:58,120 --> 01:10:59,760 +X3 اقل من X3 و X3 اقل من X3 و X3 اقل من X3 و X3 + +628 +01:10:59,760 --> 01:10:59,960 +اقل من X3 و X3 اقل من X3 اقل من X3 اقل من X3 اقل + +629 +01:10:59,960 --> 01:10:59,960 +من X3 اقل من X3 اقل من X3 اقل من X3 اقل من X3 اقل + +630 +01:10:59,960 --> 01:11:00,680 +من X3 اقل من X3 اقل من X3 اقل من X3 اقل من X3 اقل + +631 +01:11:00,680 --> 01:11:01,240 +من X3 اقل من X3 اقل من X3 اقل من X3 اقل من X3 اقل + +632 +01:11:01,240 --> 01:11:02,680 +من X3 اقل من X3 اقل من X3 اقل من X3 اقل من X3 اقل + +633 +01:11:02,680 --> 01:11:07,540 +من X3 + +634 +01:11:07,540 --> 01:11:14,620 +اقل من X3 اقل من X3 اقل + +635 +01:11:14,620 --> 01:11:21,020 +من X3 اقل من Xهذه الفترة الأولى وهذه الفترة + +636 +01:11:21,020 --> 01:11:26,020 +التانية الفترة التالتة الرابعة الخامسة الأخيرة + +637 +01:11:26,020 --> 01:11:32,020 +يبقى بداخل رمز يدل على أي فترة من هذه الفترات + +638 +01:11:32,020 --> 01:11:37,660 +وليكن xk minus one وxk تدل على أي فترة من هذه + +639 +01:11:37,660 --> 01:11:42,500 +الفترات فبعدين بيقول the length of the kth sub + +640 +01:11:42,500 --> 01:11:49,300 +interval طول ال sub interval رقم kالتي عبارة عن + +641 +01:11:49,300 --> 01:11:55,240 +ما؟ XK-1 و XK اللي هو الطول تبعها بدي أسميه Delta + +642 +01:11:55,240 --> 01:12:02,180 +XK و اللي هو بدي أسميه XK-XK-1 يبقى طول المسافة + +643 +01:12:02,180 --> 01:12:07,580 +اللي عندنا هذه دلتا + +644 +01:12:07,580 --> 01:12:17,040 +XK طب لو حطيت X بواحد مش بتعطيني هذهدلتا اكس واحد + +645 +01:12:17,040 --> 01:12:23,940 +يبقى هذه هتعطيني دلتا اكس اتنين وهكذا هذه دلتا اكس + +646 +01:12:23,940 --> 01:12:30,760 +كي يبقى هذه هتعطيني دلتا اكس ان وهكذا يبقى هذا + +647 +01:12:30,760 --> 01:12:34,960 +بيقول the length of the sub interval + +648 +01:12:37,430 --> 01:12:43,430 +هو عبارة عن xk-1 لغاية الـ xk الطول التابعة اللي + +649 +01:12:43,430 --> 01:12:49,250 +هو delta xk بده يسوى xk-xk-1 نعطي مثال عدد بسيط + +650 +01:12:49,250 --> 01:12:53,170 +توضيحي قال لي consider the interval إتنين و سبعة + +651 +01:12:53,170 --> 01:12:58,010 +إتنين و سبعة عملت لها partition تجزي كيف بدأت من + +652 +01:12:58,010 --> 01:13:05,100 +عند إتنين ثلاثة أربعة و نص خمسة من خمسة لسبعةزي ما + +653 +01:13:05,100 --> 01:13:11,280 +بدي اضافة اي ارقام من خمسة الى سبعة ثم بدي اضافة + +654 +01:13:11,280 --> 01:13:25,080 +Delta X واحد يبقى دلتا X واحد يبقى X واحد ناقص X + +655 +01:13:25,080 --> 01:13:30,670 +نوتيبقى اليمين المسافة اللى عندنا هذه طيب x واحد + +656 +01:13:30,670 --> 01:13:37,730 +عندى هنا بقداش ناقص x node يبقى تلاتة ناقص اتنين و + +657 +01:13:37,730 --> 01:13:47,110 +يسوى قداش واحد لو بدى اجيب له delta x اتنين4.5-3 + +658 +01:13:47,110 --> 01:13:58,850 +يبقى 4.5-3 يبقى 1.5 يبقى 5 + +659 +01:13:58,850 --> 01:14:12,200 +-4.5 يبقى 5-4.5 يبقى 5-4.5 يبقى 5-4.5يبقى delta X + +660 +01:14:12,200 --> 01:14:18,500 +أربعة Y ساوي اللي هو السابعة ناقص خمسة Y ساوية كده + +661 +01:14:18,500 --> 01:14:22,420 +اش اتنين لاحظ ولا واحدة زي التانية ممكن تيجي واحدة + +662 +01:14:22,420 --> 01:14:25,940 +جد تانية يعني ماعندناش مشكلة وممكن يطلعوا كلهم جد + +663 +01:14:25,940 --> 01:14:29,780 +بعض حسب التجزيه بتبعهم في السؤال اللي أخدناه في ال + +664 +01:14:29,780 --> 01:14:34,080 +section الماضي قلنا جسم إلى أربعة انتشر وكلهم جد + +665 +01:14:34,080 --> 01:14:38,360 +بعض يبقى كل واحدة كم ولا يسوى نصف هنا ليس بالضرورة + +666 +01:14:38,540 --> 01:14:42,580 +ما قلتش كلهم of equal length لأ كل واحدة إلى طول + +667 +01:14:42,580 --> 01:14:47,680 +مختلفة عن الثانية يبقى هذا اللي هو delta X وهذا + +668 +01:14:47,680 --> 01:14:52,660 +ترتشه لمن؟ للمسألة اللي عندنا طيب هذا الكلام الآن + +669 +01:14:52,660 --> 01:15:00,220 +سنستخدمه في أشياء بعد قليل نعطي تعريف اللي أخدته + +670 +01:15:00,220 --> 01:15:05,440 +أنت في الثانوية العامة ريمان صام مجميع ريمان + +671 +01:15:07,770 --> 01:15:12,190 +يبقى ريمان sum + +672 +01:15:12,190 --> 01:15:24,870 +مجموعة ريمان let ال F let + +673 +01:15:24,870 --> 01:15:28,870 +ال F بيه + +674 +01:15:28,870 --> 01:15:33,050 +continuous function + +675 +01:15:34,110 --> 01:15:41,550 +على الفترة المغلقة a و b let + +676 +01:15:41,550 --> 01:15:47,510 +P تساوي + +677 +01:15:47,510 --> 01:16:00,510 +x naught x one x two x n minus one x n ب a + +678 +01:16:00,510 --> 01:16:01,550 +partition + +679 +01:16:06,530 --> 01:16:17,750 +be a partition of ال interval a و b and + +680 +01:16:17,750 --> 01:16:30,550 +let ck موجودة xk و ال xk minus ال one او ال xk + +681 +01:16:30,550 --> 01:16:35,230 +minus ال one و ال xk + +682 +01:16:42,670 --> 01:16:49,250 +ثم اريمان صم + +683 +01:16:49,250 --> 01:16:57,410 +اريمان صم فور الوضع + +684 +01:16:57,410 --> 01:17:05,010 +فور + +685 +01:17:09,810 --> 01:17:15,270 +the area for + +686 +01:17:15,270 --> 01:17:22,470 +the area enclosed + +687 +01:17:22,470 --> 01:17:36,590 +by the function f on the closed interval a,b as + +688 +01:17:41,530 --> 01:17:52,390 +define as SP summation من K وساوية واحد لغاية ال N + +689 +01:17:52,390 --> 01:18:06,640 +لل F of CK Delta XK يعني F of C1 Delta X1F of C2 + +690 +01:18:06,640 --> 01:18:15,920 +Delta X2 زائد F of CN Delta XN + +691 +01:19:32,000 --> 01:19:33,920 +أفضل عشان أفضل أفضل + +692 +01:20:20,710 --> 01:20:26,630 +نرجع الكلام اللي احنا جايله هذا تاني قصد بلكنه + +693 +01:20:26,630 --> 01:20:32,810 +اللهبقول ايه ان انا اتعرف على ريمان صمع او على + +694 +01:20:32,810 --> 01:20:37,330 +مجموع ريمان بقول افترض ان انا عندي دالة متصلة على + +695 +01:20:37,330 --> 01:20:42,430 +الفترة المغلقة a وb وافترضنا انه عندي partition + +696 +01:20:42,430 --> 01:20:50,790 +لهذه ال interval p x0 وx1 وx2 وx3 وxk- وxk وضلنا + +697 +01:20:50,790 --> 01:20:57,720 +مشيه لغاية xn اللي هي تساوي bيبقى a هذه هي عبارة + +698 +01:20:57,720 --> 01:21:07,080 +عن x node وb هذه عبارة عن xm تمام بعد كده ايش هذا + +699 +01:21:07,080 --> 01:21:11,380 +partition للفترة هناك جليلة ck موجودة في ال + +700 +01:21:11,380 --> 01:21:17,440 +interval اللي هو main xk minus one وxk يبقى انا + +701 +01:21:17,440 --> 01:21:24,090 +بدي افترض انه عندي هنا نقطة والتكناللي همين C1 + +702 +01:21:24,090 --> 01:21:33,330 +نقطة هنا والتكن C2 لأ لأ هنا لأ هذه ملاش داعو لإن + +703 +01:21:33,330 --> 01:21:40,190 +الدالة بتوقف لحد هنا يبقى هذه C1 هنا C2 هنا بدأ + +704 +01:21:40,190 --> 01:21:49,340 +تجيلك مثلا CK وهكذا طيب الآن بقول ايه؟حط هنا + +705 +01:21:49,340 --> 01:21:54,080 +النقفة هذه موجودة هنا ولم يحدد مجليش في النص في + +706 +01:21:54,080 --> 01:21:58,260 +الطرف الشمال ولا في الطرف اليمين لأن في الطرف + +707 +01:21:58,260 --> 01:22:02,480 +الشمال ممكن يكون اللي هو upper sum في الطرف اليمين + +708 +01:22:02,480 --> 01:22:06,600 +ممكن يكون lower sum او العكس لو حطيتها في النص + +709 +01:22:06,600 --> 01:22:10,080 +بيكون ال midpoint rule هذا اللي حطيته في النص لكن + +710 +01:22:10,080 --> 01:22:14,740 +مجليش ده اللي حطها داخل الفترة و اللي مابدك حطها + +711 +01:22:14,740 --> 01:22:17,920 +يبقى انا أخدت عشوائيا بالشكل اللي عندنا هذا + +712 +01:22:20,990 --> 01:22:26,830 +لغاية ما قابلت المنحنى اللى عندنا و رحت رسمت خط + +713 +01:22:26,830 --> 01:22:32,950 +أفقي بالشكل اللى عندنا صار عندنا مستطيل هذا الخط + +714 +01:22:32,950 --> 01:22:40,740 +الأحمر هو F of C1هذه المسافة من هنا إلى هنا هي مين + +715 +01:22:40,740 --> 01:22:52,420 +Delta X1 هذه المسافة هي Delta X1 يبقى هنا Delta X1 + +716 +01:22:52,420 --> 01:23:01,920 +وهذه النقطة اللي عندنا هذه كذلك Delta X2وهذا لو + +717 +01:23:01,920 --> 01:23:08,740 +جاءت طالع هيك رأسي وقابلت المنحنى وروحت رسمت الخط + +718 +01:23:08,740 --> 01:23:13,920 +الأفقي يبقى صار عندنا المستطيل هذا وهذا صار عندنا + +719 +01:23:13,920 --> 01:23:21,270 +F of C2بارضه هنا لو جيت مشيت لهذه اكتشافات و روحت + +720 +01:23:21,270 --> 01:23:27,230 +رسمت الخط الأفقي بالشكل اللي لان هذا وكملناه بيكون + +721 +01:23:27,230 --> 01:23:36,030 +هذا F of C K و هذه كلها المسافة بتبقى Delta X K + +722 +01:23:36,950 --> 01:23:42,710 +الان لو بدى اجمع المستطيلات دى مساحتها هذا بيكون + +723 +01:23:42,710 --> 01:23:48,830 +هو مين هو عبارة عن الريمان صم لمام للمساحة اللى + +724 +01:23:48,830 --> 01:23:53,830 +عندنا يبقى الريمان صم يبقى then الريمان صم for the + +725 +01:23:53,830 --> 01:23:59,550 +area enclosed للمساحة المغلقة بي اضالة if على + +726 +01:23:59,550 --> 01:24:06,040 +الفترة a و b is defined as بعرفك التالييبقى بتقول + +727 +01:24:06,040 --> 01:24:11,360 +SP رمز لريمان sum بتسوى summation من K تسوى واحد + +728 +01:24:11,360 --> 01:24:16,660 +إلى N حسب عدد التقسيمات اللي عن هنا احنا جسمناها + +729 +01:24:16,660 --> 01:24:21,890 +إلى إيه؟ إلى N من الأقسام يبقى بادي بقوليبقى + +730 +01:24:21,890 --> 01:24:27,370 +الريمان صم للمساحة لأن مساحة المستطيلات هذه بدا + +731 +01:24:27,370 --> 01:24:32,970 +دليل رمز SP صم ميشن من K تسعة واحد لغاية N لل F of + +732 +01:24:32,970 --> 01:24:38,490 +C K Delta X K هذا صم ميشن بدا اكتبه طريقة طويلة + +733 +01:24:38,490 --> 01:24:43,990 +بدا جي لمساحة المستطيل الأول عندنا هذا العرض تبعه + +734 +01:24:43,990 --> 01:24:49,710 +Delta X واحدوالطول F of C1 يبقى مساحة المساية + +735 +01:24:49,710 --> 01:24:54,830 +الطول في العضل F of C1 Delta X1 يعني حطينا K هنا + +736 +01:24:54,830 --> 01:25:01,670 +بجداش واحد وحطها باتنين بصير F of C2 Delta X2 يبقى + +737 +01:25:01,670 --> 01:25:07,050 +هاي Delta X2 هوي في F of C2 لبعدها F of C3 Delta + +738 +01:25:07,050 --> 01:25:15,900 +X3 لغاية ما نوصل لغاية ما F of CKفى delta xk يبقى + +739 +01:25:15,900 --> 01:25:21,620 +f of ck delta xk وابقى الماشي لغاية اخر واحدة اللى + +740 +01:25:21,620 --> 01:25:27,940 +هو f of cn delta xn يبقى هذا شكل ال summation اللى + +741 +01:25:27,940 --> 01:25:33,540 +عندنا في هذه الحالة طبعا لو بدى احسب حسابات دقيقة + +742 +01:25:33,540 --> 01:25:37,940 +هتطلع روحى إذا كانوا مسافات مش جات بعض بس إذا + +743 +01:25:37,940 --> 01:25:43,460 +كانوا مسافات جات بعض سيصبح العملية سهلة جداعلى اي + +744 +01:25:43,460 --> 01:25:47,920 +حال احنا نتكلم في هذا الكلام in general، المسافات + +745 +01:25:47,920 --> 01:25:53,220 +اللي جسمناها هذه ما هيش تجزيء الفرطش اللي عملته، + +746 +01:25:53,220 --> 01:25:57,360 +الفترات اللي عندي ليس بالضرورة ان تكون جد بعض اش + +747 +01:25:57,360 --> 01:26:01,360 +كبير و اش صغير و ما إلى ذلكطيب بدنا نعطي الان + +748 +01:26:01,360 --> 01:26:07,620 +تعريف جديد بسيط اللي هو بنسميه ال norm يبقى بتاعي + +749 +01:26:07,620 --> 01:26:11,660 +ل definition برضه متعلق بمين والكلام اللي احنا + +750 +01:26:11,660 --> 01:26:16,500 +راسمينه هذا بيقول لي the norm of a partition the + +751 +01:26:16,500 --> 01:26:25,540 +norm of a partition of + +752 +01:26:25,540 --> 01:26:27,840 +a partition + +753 +01:26:30,280 --> 01:26:40,640 +يبقى the norm of a partition P يساوي اللي هو ال X0 + +754 +01:26:40,640 --> 01:26:59,440 +و X1 و X2 و Xn-1والـ Xm هو رمز نارم لـ P ويساوي + +755 +01:26:59,440 --> 01:27:12,820 +maximum ل Delta X0 Delta X1 Delta X2 ونظل ماشيين + +756 +01:27:12,820 --> 01:27:15,760 +لغاية Delta Xn + +757 +01:27:24,900 --> 01:27:32,900 +أو بدل ما يصير خطأ يقول دلتا X1 ودلتا X2 ودلتا X3 + +758 +01:27:32,900 --> 01:27:40,640 +ودلتا XN يبقى دول عددهم بصير M ايش يعني بيقول لو + +759 +01:27:40,640 --> 01:27:45,380 +احنا عملنا partition اللي عندنا هذا يبقى جزقنا ال + +760 +01:27:45,380 --> 01:27:50,020 +interval اللي عندنا A وB إلى interval أولى + +761 +01:27:50,020 --> 01:27:55,100 +interval تانية تالتة رابعة خمسة سادسة نونيةبالدالي + +762 +01:27:55,100 --> 01:27:59,500 +هذول الانترنت مش جات بعض، يبقى أكبر واحدة فيهم + +763 +01:27:59,500 --> 01:28:05,120 +بتكون هي اللي بنسميها ال norm تبع ال P يبقى ال + +764 +01:28:05,120 --> 01:28:10,340 +norm تبع ال partition هو أطول فترة جسمناها من + +765 +01:28:10,340 --> 01:28:14,980 +الفترة الأساسية، قولنا maximum الدلتات هذول، أكبر + +766 +01:28:14,980 --> 01:28:20,000 +واحدة فيهم بتكون هي ال norm تبع من؟ تبع ال P + +767 +01:28:27,170 --> 01:28:37,070 +او ايه نورم؟ نورم تبع + +768 +01:28:37,070 --> 01:28:41,210 +التجزيه هو ال maximum هذا نعطي مثال توضيح بسيط + +769 +01:28:41,210 --> 01:28:46,690 +واحدة منهم الكبيرة فيهم مين زي ما اقولك ماكننا + +770 +01:28:46,690 --> 01:28:51,710 +نجيب delta مش كنا نقول delta minimum التنتين يبقى + +771 +01:28:51,710 --> 01:28:56,870 +الصغراء فيهم وهنا نقول الكبرة فيهم كلهمطب نعطيك + +772 +01:28:56,870 --> 01:29:04,390 +مثال فوضيحي example find + +773 +01:29:04,390 --> 01:29:12,450 +the norm of + +774 +01:29:12,450 --> 01:29:15,570 +the partition + +775 +01:29:21,240 --> 01:29:29,560 +P يبدو يساوي سالب اتنين سالب واحد وستة من عشرة + +776 +01:29:29,560 --> 01:29:43,560 +سالب نص سالب نص Zero تمانية من عشرة تمانية + +777 +01:29:43,560 --> 01:29:46,000 +من عشرة واحد + +778 +01:29:58,190 --> 01:30:02,970 +نور طول، مسافة، زي absolute value، تمام، هذا اللي + +779 +01:30:02,970 --> 01:30:06,290 +هو المعنى، لكن أنا بديش اللي هو المعنى الرياضي، + +780 +01:30:06,290 --> 01:30:10,760 +هذا هو هي اللي بدنا يعنييبقى هنا بروح أجيب كل + +781 +01:30:10,760 --> 01:30:15,340 +الـDelta's اللي هنا وروح أخد أكبر واحدة فيهم بتكون + +782 +01:30:15,340 --> 01:30:21,160 +هي الـNormal المطلوبة إذا أنا بدأجي أخد Delta X1 + +783 +01:30:21,160 --> 01:30:27,040 +يبقى هذه بدأت ساوي سالب واحد وستة من عشرة سالب + +784 +01:30:27,040 --> 01:30:32,140 +لسالب اتنين ايه المسافة اللي عندنا هنا يبقى هذه + +785 +01:30:32,140 --> 01:30:35,560 +بدل القداش اربعة من عشرة + +786 +01:30:38,980 --> 01:30:46,960 +دلتا اكس تو يبقى بده ساوي سالب زير وخمسة من عشرة + +787 +01:30:46,960 --> 01:30:55,130 +سالب سالب واحد وستة من عشرةطبعا هنا موجة بواحد و + +788 +01:30:55,130 --> 01:31:01,730 +ستة من عشرة بده يصير واحد واحد من عشرة واحد واحد + +789 +01:31:01,730 --> 01:31:09,630 +من عشرة بعد هيك بداجي Delta X3 يبقى بده يساوي + +790 +01:31:09,630 --> 01:31:16,570 +أخدنا الخمسة يبقى Zero ناقص ناقص Zero خمسة اللي هو + +791 +01:31:16,570 --> 01:31:27,090 +داجي نص Zero خمسةاللي بعده دلتا اكس ثري دلتا اكس + +792 +01:31:27,090 --> 01:31:34,270 +فار ويساوي زيرو و تمانية ناقص زيرو بزيرو و تمانية + +793 +01:31:34,270 --> 01:31:42,590 +اخر واحدة دلتا اكس فايف اللي هو عبارة عن واحد ناقص + +794 +01:31:42,590 --> 01:31:49,900 +زيرو تمانية من عشرة ببقى زيرو اتنين من عشرةيبقى + +795 +01:31:49,900 --> 01:31:57,560 +بدنا نرم تبع ال P يبقى سة النرم بتبع ال P بدي ساوي + +796 +01:31:57,560 --> 01:32:04,560 +maximum لمن؟ للقيم اللي طلعت Zero أربعة من عشرة + +797 +01:32:04,560 --> 01:32:12,680 +واللي بعدها واحد واحد من عشرة واللي بعدها نصواللي + +798 +01:32:12,680 --> 01:32:17,780 +بعدها Zero تمانية من عشرة واللي بعدها Zero اتنين + +799 +01:32:17,780 --> 01:32:22,320 +من عشرة، مين اكبر احدة فيهم؟ يبقى واحد واحد من + +800 +01:32:22,320 --> 01:32:27,240 +عشرة هذا ال norm بتباع ال P طب خلينا المرة القادمة + +801 +01:32:27,240 --> 01:32:28,160 +ان شاء الله + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/gPP3rP0CXnk.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/gPP3rP0CXnk.srt new file mode 100644 index 0000000000000000000000000000000000000000..15f490eacd1daa7daf4041bee0728b827a76815d --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/gPP3rP0CXnk.srt @@ -0,0 +1,3276 @@ +1 +00:00:20,920 --> 00:00:25,520 +بسم الله الرحمن الرحيم عودة على بداية المرة اللي + +2 +00:00:25,520 --> 00:00:30,660 +فاتت بدأنا في التكاملات المحدودة كيف بدنا نكامل + +3 +00:00:30,660 --> 00:00:36,780 +تكاملات محدودة باستخدام التعويض وبتغيير حدود + +4 +00:00:36,780 --> 00:00:41,600 +التكامل طبقا للتعويض اللي بيعطيها وعطينا على ذلك + +5 +00:00:41,600 --> 00:00:46,920 +مجموعة من الأمثلة ونحن نكمل هذه الأمثلة أخذنا ستة + +6 +00:00:46,920 --> 00:00:51,700 +أمثلة وهذا هو المثال رقم سبعة بقول يتكامل من الصفر + +7 +00:00:51,700 --> 00:00:56,480 +اللي هيتبعي على أربع لتان تكعيب سكتر بيه ال X DX + +8 +00:00:56,480 --> 00:01:02,100 +طبعا مباشرة هيك بقدرش لكن بقدر أعمل تعويضة محددة + +9 +00:01:02,100 --> 00:01:06,900 +باجي بطلع في المثل اللي عندي والتان كده تفاضلها؟ + +10 +00:01:07,400 --> 00:01:12,500 +سكتر بيع موجودة إذا اللي بدي أشيله وأغيره بدي + +11 +00:01:12,500 --> 00:01:18,300 +أشيل التان وأحط بدلها دل جديدة إذا لو حطيت ال T + +12 +00:01:18,300 --> 00:01:25,400 +تساوي تان ال X يبقى ال DT بدي أساوي سكتر بيع ال X + +13 +00:01:25,400 --> 00:01:31,500 +DX إذا ممكن أشيل سكتر بيع ال X DX هذه وقت بدلها DT + +14 +00:01:31,880 --> 00:01:40,260 +يبقى آلة المسألة إلى تكامل ل T تكعيب DT بقيت حدود + +15 +00:01:40,260 --> 00:01:44,460 +التكامل بدي أغير حدود التكامل صفقة لهذه التعويضة + +16 +00:01:44,460 --> 00:01:49,110 +الجديدة فبجي بقول لما تبقى ال X باي على أربعة + +17 +00:01:49,110 --> 00:01:55,590 +يبقى ال T هنا تساوي واحد يبقى ال X ب zero + +18 +00:01:55,590 --> 00:02:02,510 +يبقى T تساوي zero إذا غيرنا حدود التكامل طبق + +19 +00:02:02,510 --> 00:02:07,750 +لمين؟ طبق التعويضة الجديدة اللي حطيناها يبقى هذا + +20 +00:02:07,750 --> 00:02:13,150 +النتيجة تساوي T أس أربعة على أربعة والكلام من zero + +21 +00:02:13,150 --> 00:02:19,080 +لغاية واحد يبقى هذا الكلام يساوي ربع في + +22 +00:02:19,080 --> 00:02:24,580 +واحد أس أربعة ناقص Zero أس أربعة اللي هو Zero واحد + +23 +00:02:24,580 --> 00:02:32,200 +أس أربعة باربع يبقى النتيجة تساوي ربع التكامل اللي + +24 +00:02:32,200 --> 00:02:40,490 +بعده تكامل رقم ثمانية يبقى integration من سالب واحد + +25 +00:02:40,490 --> 00:02:42,370 +لغاية سالب نص + +26 +00:03:00,500 --> 00:03:04,700 +طيب، بعدي بتطلع في المثل اللي عندي، شو اللي وضعه + +27 +00:03:04,700 --> 00:03:09,260 +غير طبيعي في المثل أو اللي مصعب شكلها؟ الزاوية + +28 +00:03:09,260 --> 00:03:13,840 +تبع الصين، يبقى الزاوية هي اللي مصعبة المثل، نهيك + +29 +00:03:13,840 --> 00:03:18,340 +على أنه مشتقة الزاوية بتعطينا مين؟ ال term اللي + +30 +00:03:18,340 --> 00:03:24,750 +بره يبقى بدي اكتب المثلة بشكل لطيف أو سهل جدا يبقى + +31 +00:03:24,750 --> 00:03:31,230 +بدي أشيل كل هذا وبدي احط ال X يساوي واحد زائد واحد + +32 +00:03:31,230 --> 00:03:38,810 +على T لو جينا اشتقيناها يبقى DX بدي أساوي سالب واحد + +33 +00:03:38,810 --> 00:03:47,180 +على T تربيع DT أو بقدر أقول سالب DX بدي أساوي T + +34 +00:03:47,180 --> 00:03:54,280 +السالب اثنين DT إذا بقدر T السالب اثنين هذه مع DT + +35 +00:03:54,280 --> 00:04:00,400 +أشيلها وأكتف بدل جديد سالب DX يبقى هاي السالب بدي + +36 +00:04:00,400 --> 00:04:07,120 +أخده برا وهاي تكامل وهادي ال sign تربيع ال X كله + +37 +00:04:07,120 --> 00:04:13,580 +في DX بقيت حدود التكامل لما تبقى ال X يساوي سالب T + +38 +00:04:13,580 --> 00:04:19,260 +تساوي سالب نص يبقى سالب نص بصير هذي فوق باتنين + +39 +00:04:19,260 --> 00:04:24,360 +اثنين بالسالب يبقى واحد سالب اثنين مضل قداش سالب + +40 +00:04:24,360 --> 00:04:29,300 +واحد يبقى هذي بيصير سالب واحد ولما تبقى T بسالب + +41 +00:04:29,300 --> 00:04:34,100 +واحد بصير ال term هذا كله بسالب واحد يبقى كله بصير + +42 +00:04:34,100 --> 00:04:40,130 +Zero يبقى من Zero ل سالب واحد ل main لل sign تربيع + +43 +00:04:40,130 --> 00:04:44,630 +ال X DX واضح أن ال index الكبير هو اللي تحته + +44 +00:04:44,630 --> 00:04:49,170 +والصغير هو ال fourth يبقى بنجلب حدود التكامل وبنضيع + +45 +00:04:49,170 --> 00:04:53,510 +الإشارة اللي عندنا طبقا لأول خاصية من خاصة + +46 +00:04:53,510 --> 00:04:59,250 +تكامل المحدود يبقى هذا الكلام بده يساوي تكامل من + +47 +00:04:59,250 --> 00:05:04,630 +سالب واحد لغاية Zero ل sign تربيع ال X DX + +48 +00:05:11,900 --> 00:05:17,720 +يبقى هذا الكلام بده يساوي تكامل من سالب واحد لغاية + +49 +00:05:17,720 --> 00:05:24,590 +Zero لنص في واحد ناقص cosine اثنين ال X DX من + +50 +00:05:24,590 --> 00:05:28,410 +المستطابقات تبعات حساب المثلثات sin تربيع ال X هو + +51 +00:05:28,410 --> 00:05:34,390 +نص في واحد ناقص cosine اثنين X يبقى النص هذا بدي + +52 +00:05:34,390 --> 00:05:40,870 +يظل برا وعندك هذا جزء تكامل الواحد ب X وتكامل ال + +53 +00:05:40,870 --> 00:05:46,690 +cosine ب sin اثنين X على اثنين والكلام من سالب واحد + +54 +00:05:46,690 --> 00:05:53,240 +لغاية ال Zero يبقى يا نص خليك برا وبدنا نبدأ نعوض + +55 +00:05:53,240 --> 00:06:00,140 +بحدود التكامل يبقى Zero و Sin Zero Zero كذلك يبقى + +56 +00:06:00,140 --> 00:06:06,210 +هاي Zero ناقص Zero ناقص بدا ابدأ اعوض بالقيمة اللي + +57 +00:06:06,210 --> 00:06:11,670 +تحت يبقى ال X بدي أشيله أو اكتبه لجداش ناقص واحد + +58 +00:06:11,670 --> 00:06:16,430 +وهي الناقص اللي عندنا بدي أشيل ال X واحطه مكان + +59 +00:06:16,430 --> 00:06:23,750 +جداش سالب واحد يبقى بصير سالب اثنين يبقى ال sign + +60 +00:06:23,750 --> 00:06:30,610 +لسالب اثنين على اثنين بالشكل اللي عندنا هذا تمام + +61 +00:06:31,240 --> 00:06:36,140 +يبقى هذا الكلام بده يساوي هذا النص اللي برا وده + +62 +00:06:36,140 --> 00:06:41,720 +دخل السلب اللي عندها ده يوم بصير عندي واحد ناقص + +63 +00:06:41,720 --> 00:06:47,540 +sign اثنين على اثنين بالشكل اللي عندنا طبعا ال + +64 +00:06:47,540 --> 00:06:53,480 +sign odd السلب بطلع برا بصير موجب في سلب مضروب برا + +65 +00:06:53,480 --> 00:06:59,100 +يبقى بصير سالب يبقى واحد ناقص sign اثنين على اثنين + +66 +00:06:59,270 --> 00:07:03,270 +انت هنا مثلا بدك تكتب لي نص ناقص ربع sign اثنين + +67 +00:07:03,270 --> 00:07:09,750 +سيانة بتفرجش يبقى هذه لو قلت نص ناقص ربع sign + +68 +00:07:09,750 --> 00:07:18,000 +اثنين هذه هي نتيجة من التكامل طيب، الآن في عندنا + +69 +00:07:18,000 --> 00:07:24,100 +كمان مثال آخر غير هذه الأنواع من الأمثلة وهذا + +70 +00:07:24,100 --> 00:07:29,200 +المثال جئنا به في إحدى الامتحانات السابقة يبقى + +71 +00:07:29,200 --> 00:07:35,000 +كمان example بيقول + +72 +00:07:35,000 --> 00:07:39,580 +use the integral استخدم التكامل + +73 +00:07:42,290 --> 00:07:50,670 +تكامل من واحد لغاية اثنين للـ F of Z DZ بده يساوي + +74 +00:07:50,670 --> 00:07:56,650 +ثلاثة to find + +75 +00:07:56,650 --> 00:08:05,110 +the value of مشان تحسبلي قداش قيمة تكامل من نص + +76 +00:08:05,110 --> 00:08:12,750 +لغاية واحد لواحد على X تربيع F of واحد على X نفس + +77 +00:08:20,110 --> 00:08:26,750 +يبقى شكل هذا المثال يختلف عن شكل سابقاته من الأمثلة + +78 +00:08:26,750 --> 00:08:31,530 +قبل أن نتكامل ونتكامل على طول الخط هذا بيقول + +79 +00:08:31,530 --> 00:08:37,250 +استخدم هذا التكامل يبقى هذا معطى للحصول على قيمة + +80 +00:08:37,250 --> 00:08:41,450 +التكامل هذا باجي بطلع في التكامل اللي عندي وهذا + +81 +00:08:41,450 --> 00:08:47,090 +بيختلف كليا عن بعض لكن هذا مقطع إذا ما لي علاقة + +82 +00:08:47,090 --> 00:08:51,550 +فيه لما بلزمني بستخدمه بلزمنيش ما بستخدموش إذا + +83 +00:08:51,550 --> 00:08:56,590 +مشكلتنا مع مين؟ مع هذا التكامل مشان اشتغل هذا + +84 +00:08:56,590 --> 00:09:01,290 +التكامل في شغل غير طبيعي الغير طبيعي واحد على X + +85 +00:09:01,290 --> 00:09:04,150 +طبيعي ولا واحد على X؟ واحد على X، واحد على + +86 +00:09:04,150 --> 00:09:04,850 +X، واحد على X، واحد على X، واحد على X، + +87 +00:09:04,850 --> 00:09:04,870 +واحد على X، واحد على X، واحد على X، واحد على + +88 +00:09:04,870 --> 00:09:05,230 +X، واحد على X، واحد على X، واحد على X، + +89 +00:09:05,230 --> 00:09:08,210 +واحد على X، واحد على X، واحد على X، واحد على + +90 +00:09:08,210 --> 00:09:08,670 +X، واحد على X، واحد على X، واحد على X، + +91 +00:09:08,670 --> 00:09:12,390 +واحد على X، واحد على X، واحد على X، واحد على + +92 +00:09:12,390 --> 00:09:21,100 +X، واحد على X، واحد على X، لو مثلا حطيت هنا Z + +93 +00:09:21,100 --> 00:09:28,700 +تساوي واحد على X أو T أو W أو اللي بدك إياه يبقى + +94 +00:09:28,700 --> 00:09:34,000 +بدنا نيجي نشتقه يبقى DZ يساوي سالب واحد على X + +95 +00:09:34,000 --> 00:09:40,270 +تربيع دي واحد على X تربيع موجودة عندي بس سالب ما عنديش + +96 +00:09:40,270 --> 00:09:46,430 +يبقى بضرب الطرفين بإشارة سالب يبقى بصير عندي سالب DZ + +97 +00:09:46,430 --> 00:09:53,230 +يساوي واحد على X تربيع DX إذا الواحد على X تربيع هذه + +98 +00:09:53,230 --> 00:09:58,250 +كلها مع ال DX كلها تبع المسألة بقدر أشيلها وأكتب + +99 +00:09:58,250 --> 00:10:04,950 +بدالها سالب DZ يبقى صارت مسألة تكامل من نص لغاية + +100 +00:10:04,950 --> 00:10:11,050 +واحد لواحد على X تربيع لل F of واحد على X DX + +101 +00:10:11,050 --> 00:10:20,030 +يساوي تكامل F of Z تمام واحد على X تربيع DX بدأت + +102 +00:10:20,030 --> 00:10:26,550 +بهذه السالب برا وهذه يمين DX يبقى صار شكل المثل + +103 +00:10:26,550 --> 00:10:30,110 +اللي عنده هناك اللي هو الشكل هذا بالشكل الجديد إلا + +104 +00:10:30,110 --> 00:10:35,570 +أنه لكن بنروح نغير حدود التكامل طبقا للتعويض اللي + +105 +00:10:35,570 --> 00:10:42,450 +احنا حاطينا فباجي بقول لو كانت ال X بواحد يبقى Z + +106 +00:10:42,450 --> 00:10:50,090 +بواحد طب لو كانت ال X باثنين بصير واحد على نص + +107 +00:10:50,090 --> 00:10:56,950 +بتنجلبه بصير جداش باثنين بالشكل اللي عنها ده طيب + +108 +00:10:56,950 --> 00:11:02,270 +الآن صار الرقم الكبير تحت والرقم الصغير فوق في + +109 +00:11:02,270 --> 00:11:06,570 +حدود التكامل من شكل بهذه المواد على limits of + +110 +00:11:06,570 --> 00:11:11,250 +integration وبالتالي طبقا للخاصية الأولى من خاصة + +111 +00:11:11,250 --> 00:11:16,710 +تكامل المحدود بيطير إشارة السالب يبقى هذا بيصير + +112 +00:11:16,710 --> 00:11:27,120 +تكامل من 1 ل 2 لل F of Z DZ أظن هذا موضوع خلصنا يبقى + +113 +00:11:27,120 --> 00:11:35,620 +هذا الكلام بده يساوي ثلاثة بدون ما تكمل طيب فيه + +114 +00:11:35,620 --> 00:11:41,640 +قاعدة بتسهل لي عملية حساب بعض التكاملات الصعبة + +115 +00:11:41,640 --> 00:11:48,620 +شوية هذه النظرية بتقول لي ما يأتي بتقول + +116 +00:11:48,620 --> 00:11:53,980 +الـ F بـ continuous + +117 +00:11:56,460 --> 00:12:08,760 +function اللي متصلة on the symmetric interval + +118 +00:12:08,760 --> 00:12:12,740 +اللي + +119 +00:12:12,740 --> 00:12:18,900 +هو سالب a و a النقطة + +120 +00:12:18,900 --> 00:12:22,560 +الأولى if + +121 +00:12:24,020 --> 00:12:36,520 +الـ F is even دالة زوجية then تكامل من سالب A إلى A + +122 +00:12:36,520 --> 00:12:46,520 +لل F of X DX يساوي اثنين تكامل من Zero إلى A لل F + +123 +00:12:46,520 --> 00:13:00,370 +of X DX النقطة الثانية الـ F is odd then تكامل من + +124 +00:13:00,370 --> 00:13:07,930 +سالب A إلى A لل F of X DX بدي أساوي كده؟ بدي أساوي + +125 +00:13:07,930 --> 00:13:15,630 +Zero Example Find + +126 +00:13:15,630 --> 00:13:22,440 +the value of the following integrals Find the value + +127 +00:13:22,440 --> 00:13:30,780 +of the following integrals + +128 +00:13:30,780 --> 00:13:36,360 +التكاملات + +129 +00:13:36,360 --> 00:13:37,300 +التالية + +130 +00:13:55,670 --> 00:14:04,990 +تكامل الأول بدنا تكامل من سالب اثنين إلى اثنين + +131 +00:14:04,990 --> 00:14:22,090 +لثلاثة X على تسعة زائد X تربيع الكل تربيع DX نرجع + +132 +00:14:22,090 --> 00:14:27,100 +لهذه النظرية مرة ثانية ونحاول نفهم هذه النظرية + +133 +00:14:27,100 --> 00:14:33,050 +مشان نشوف كيف بدنا نطبقها بقول افترض الدالة F دالة + +134 +00:14:33,050 --> 00:14:39,490 +متصلة على الفترة المتماثلة ناقص a و a لما أقول + +135 +00:14:39,490 --> 00:14:44,310 +symmetric interval يعني من عند Zero على اليمين جد + +136 +00:14:44,310 --> 00:14:48,510 +اللي من عند Zero على الشمال بالضبط تماما فلما أقول + +137 +00:14:48,510 --> 00:14:54,490 +من ناقص a إلى a يبقى الصفر يجي وين في منتصف الفترة + +138 +00:14:54,490 --> 00:15:00,550 +يعني الفترة المتماثلة على طرفي Zero أو على طرفي + +139 +00:15:00,550 --> 00:15:05,490 +محور Y يبقى هاي المقصود في هذه الكتابة تالك ما قص A + +140 +00:15:05,490 --> 00:15:10,250 +و A يعني الرقم اللي عندنا هنا هو نفس الرقم هذا بس + +141 +00:15:10,250 --> 00:15:14,290 +بإشارة مخالفة يبقى هذه بسميها الـ Symmetric + +142 +00:15:14,290 --> 00:15:20,750 +Interval بقول والله إذا دالة كانت even يبقى تكامل + +143 +00:15:20,750 --> 00:15:26,830 +من ناقص A إلى A لل F of X DX يساوي اثنين التكامل من + +144 +00:15:26,830 --> 00:15:34,150 +Zero إلى A لل F of X DX السؤال لماذا؟ وماذا نستفيد + +145 +00:15:34,150 --> 00:15:40,350 +من ذلك؟ خلي بالك معاك يبقى ليش تكامل من سالب A إلى + +146 +00:15:40,350 --> 00:15:45,750 +A لل F of X DX يساوي 2 تكامل من 0 إلى A لل F of X + +147 +00:15:45,750 --> 00:15:50,190 +DX نرجع بالذاكرة إلى أول chapter درسنا فيه + +148 +00:15:50,190 --> 00:15:55,910 +Calculus A لما أقول even function يعني المنحنى + +149 +00:15:55,910 --> 00:16:02,120 +مالهم متماثل + +150 +00:16:02,120 --> 00:16:06,160 +بالنسبة لمين؟ لمحور ويمجد النص الرسمى اللى على + +151 +00:16:06,160 --> 00:16:10,240 +اليمين زى نص الرسمى اللى وين يعنى المساحة اللى + +152 +00:16:10,240 --> 00:16:15,500 +حصرها المنحنى على يمين المحور Y بينه وبين محور X جد + +153 +00:16:15,500 --> 00:16:19,640 +المساحة اللي حصرها المنحنة على الشمال محور Y بينه + +154 +00:16:19,640 --> 00:16:24,300 +وبين محور X تمام؟ إذا مدام المساحتين كانوا بعضيا + +155 +00:16:24,300 --> 00:16:29,280 +يكفيني حساب مساحة واحدة بضرب منين في اثنين من هنا + +156 +00:16:29,280 --> 00:16:34,660 +قولنا هذا بدي يساوي اثنين التكامل على نص في الفترة + +157 +00:16:34,660 --> 00:16:38,100 +مدام في تمثل اللي على اليمين زي اللي على الشمال + +158 +00:16:38,100 --> 00:16:43,570 +يبقى المساحة الأولى جد المساحة الثانية يبقى يكفيني + +159 +00:16:43,570 --> 00:16:47,950 +حساب واحدة فيهم بروح مضروبة في مهم في اثنين يبقى + +160 +00:16:47,950 --> 00:16:52,930 +هذا يساوي اثنين تكامل من Zero إلى A لل F of X DX + +161 +00:16:52,930 --> 00:16:57,050 +يبقى هاي أجابنا على السؤال الأول ليش هذا التكامل + +162 +00:16:57,050 --> 00:17:02,730 +يساوي التكامل الثاني سؤال الثاني قلنا ماذا نستفيد + +163 +00:17:02,730 --> 00:17:07,270 +من ذلك؟ أيهم السهل؟ اللي لما تكمل الدالة لو تروح + +164 +00:17:07,270 --> 00:17:10,210 +تعوض بالقيمة اللي فوق والقيمة اللي تحت والله لما + +165 +00:17:10,210 --> 00:17:14,090 +تبقى اللي تحت زيرو السهل ليه؟ لما تبقى زيرو السهل + +166 +00:17:14,090 --> 00:17:20,530 +يبقى المقصود هو من ذلك تبسيط عملية إجراء التكامل + +167 +00:17:20,530 --> 00:17:24,670 +تمام؟ يبقى هاي المقصود فيه طيب هذا بالنسبة + +168 +00:17:24,670 --> 00:17:28,770 +للنقطة الأولى النقطة الثانية قال لو كانت الدالة + +169 +00:17:28,770 --> 00:17:35,350 +odd يبقى قيمة التكامل تساوي صفر شو المعنى الهندسي لل + +170 +00:17:35,350 --> 00:17:41,750 +odd function يعني المنحنى متماثل حول ال origin يبقى + +171 +00:17:41,750 --> 00:17:47,050 +أي نقطة إحداثيتها a و b بديكون لها نقطة سالب a و + +172 +00:17:47,050 --> 00:17:51,410 +سالب b يعني الجزء اللي فوق اللي أعلى محور X بديكون + +173 +00:17:51,410 --> 00:17:56,570 +فيه جزء مقابله أسفل محور X يعني لو المنحنى في + +174 +00:17:56,570 --> 00:17:59,850 +الربع الأول بديكون المنحنى الثاني في الربع الثالث + +175 +00:18:00,050 --> 00: + +201 +00:20:15,430 --> 00:20:21,030 +تربية تربية تمام السالب هذا بقدر أقوله شرفني برا + +202 +00:20:21,030 --> 00:20:27,390 +وبصير عندي هاي تلاتة X وهذه تسعة زي X تربيع لكل + +203 +00:20:27,390 --> 00:20:32,510 +تربيع يبقى odd والله even odd function لإن F of + +204 +00:20:32,510 --> 00:20:39,390 +سالب X سوى سالب F of X يبقى هذه odd يبقى هذه + +205 +00:20:39,390 --> 00:20:47,820 +النتيجة كده؟يساوي زيرو لان + +206 +00:20:47,820 --> 00:20:55,240 +التلاتة اكس على تسعة زائد اكس تربيع تربيع is an + +207 +00:20:55,240 --> 00:21:00,510 +odd function يبقى نظرا لإنها دالة فردية فقيمة + +208 +00:21:00,510 --> 00:21:05,730 +التكامل يتساوي صفر بدون إجراء عملية التكامل يبقى + +209 +00:21:05,730 --> 00:21:13,170 +أعوض مباشرة بدون ما أقوم بعملية التكامل نمر اتنين + +210 +00:21:13,170 --> 00:21:19,910 +بدنا تكامل من سالب باي على أربعة إلى باي على أربعة + +211 +00:21:19,910 --> 00:21:25,770 +للـ X تربيه زائد سك تربيه الـ X كله في DX + +212 +00:21:28,590 --> 00:21:33,510 +باجي بتطلع برضه بنفس الطريقة الرقم اللي فوق هو نفس + +213 +00:21:33,510 --> 00:21:37,270 +الرقم اللي تحت بس بإشارة هي بإشارة مخالفة + +214 +00:21:49,870 --> 00:21:58,330 +ماعنديش إلا تنتين even والاربعة odd يبقى اللي قلنا + +215 +00:21:58,330 --> 00:22:03,710 +الـ sec والـ cos هي الـ even فقط يبقى ليس تحكيش غير + +216 +00:22:03,710 --> 00:22:09,110 +تعرف يبقى الـ sec وعكس اللي هو الـ cos هم التنتين even + +217 +00:22:09,110 --> 00:22:14,070 +وباقي الأربعة odd يبقى هذا even تمام؟ والـ X + +218 +00:22:14,070 --> 00:22:20,330 +تربيع؟يبقى معناته هذا الكلام يساوي 2 تكامل من 0 ل + +219 +00:22:20,330 --> 00:22:26,570 +5 على 4 يبقى هذا الكلام يساوي 2 تكامل من 0 ل 5 على + +220 +00:22:26,570 --> 00:22:31,770 +4 ل X تربيع زائد سك تربيع X DX + +221 +00:22:45,270 --> 00:22:49,490 +اللي مايعرفش بشيل كل X و بحط مكانها سالب X تربية + +222 +00:22:49,490 --> 00:22:53,610 +بتبقى كما هي هذي ال cycle ناقص X لكل تربية هي + +223 +00:22:53,610 --> 00:22:58,330 +بcycle X تربية بتبقى تربية كما هي بنال عليها صارت + +224 +00:22:58,330 --> 00:23:04,040 +هذه even function يبقى و هذا الكلام بده يسوى اتنين + +225 +00:23:04,040 --> 00:23:11,240 +فيه بدك تعمل هذه الدالة يبقى X تكيب على تلاتة زائد + +226 +00:23:11,240 --> 00:23:16,980 +تان الـ X من و لا وين من Zero لغاية Pi على أربع + +227 +00:23:17,420 --> 00:23:22,820 +تمام؟ يبقى هذا اتنين برا مالوش دعوة وهذه بدي أشيل + +228 +00:23:22,820 --> 00:23:28,360 +الـ X و أحط مكانها باي على اربعة فهيصير باي تكعيب على + +229 +00:23:28,360 --> 00:23:35,440 +اربعة وستين مظبوط؟ يبقى هذه باي تكعيب على اربعة + +230 +00:23:35,440 --> 00:23:44,400 +وستين في تلاتة والخمسه واربعين بواحد ناقص عوضنا من + +231 +00:23:44,400 --> 00:23:49,140 +القيم اللي فوق ناقص اللي تحت Zero و تاني Zero ب + +232 +00:23:49,140 --> 00:23:55,700 +Zero يبقى ناقص ال Zero يبقى النتيجة تساوي باي + +233 +00:23:55,700 --> 00:24:03,070 +تكعيب على عندك هنا اربعة و ستين اربعة و ستين في + +234 +00:24:03,070 --> 00:24:07,610 +تلاتة اللي هو قداش تلاتة في اربعة باطناش و تلاتة + +235 +00:24:07,610 --> 00:24:13,470 +بازمية و اتنين و تسعين يبقى هذا لأ هو بقى اتنين و + +236 +00:24:13,470 --> 00:24:16,910 +تلاتين هذه اتنين و تلاتين في تلاتة ليه بستة و + +237 +00:24:16,910 --> 00:24:24,830 +تسعين مظلوم يبقى هذه ستة و تسعين و هنا زائد اتنين + +238 +00:24:24,830 --> 00:24:30,340 +يبقى هذا قيمة التكامل اللي عندنا طب احنا حتى الآن + +239 +00:24:30,340 --> 00:24:36,220 +يا شباب لو رجعت للعنوان تبع section 5-6 لحتى الآن + +240 +00:24:36,220 --> 00:24:42,200 +احنا كل اللي اشتغلناه على النقطة الأولى من العنوان + +241 +00:24:42,200 --> 00:24:47,240 +وهو الـ substitution لكن الـ area between two curves + +242 +00:24:47,240 --> 00:24:53,780 +لم نتعرض لها بأي مثال حتى هذه اللحظة لذن قبل ان تضع + +243 +00:24:53,780 --> 00:24:58,400 +أي مثال يجب ان تضع قاعدة المساحة المحصورة بين + +244 +00:24:58,400 --> 00:25:03,580 +المنحنيات ومن ثم نذهب ناخد امثلة عليها يجب ان + +245 +00:25:03,580 --> 00:25:10,600 +اعطيها definition أكثر definition if + +246 +00:25:10,600 --> 00:25:18,200 +الـ f والـ g are continuous functions + +247 +00:25:27,480 --> 00:25:38,960 +F of X أكبر من أو يساوي الـ G of X أثره خلال الفترة + +248 +00:25:38,960 --> 00:25:41,860 +المغلقة A وB + +249 +00:25:58,080 --> 00:26:04,380 +النطاق بين الثقافات + +250 +00:26:04,380 --> 00:26:17,840 +بين الثقافات y تساوي f of x و y تساوي g of x from + +251 +00:26:17,840 --> 00:26:20,560 +a + +252 +00:26:21,840 --> 00:26:27,160 +to be is defined + +253 +00:26:27,160 --> 00:26:32,260 +as + +254 +00:26:32,260 --> 00:26:41,280 +من عرفة كتالي الـ area a يسوى تكامل من a إلى b للـ f + +255 +00:26:41,280 --> 00:26:45,600 +of x منعقص الـ g of x dx + +256 +00:27:05,430 --> 00:27:10,190 +بنرجع للتعريف مرة تانية قال إذا عندك ذالة f و g و + +257 +00:27:10,190 --> 00:27:16,330 +اتين اتين دوال متصلة دوال متصلة يعني قابلة للتكامل + +258 +00:27:16,330 --> 00:27:22,890 +طيب في اندي كونديشن حطوا ان الـ f of x أكبر من الـ g + +259 +00:27:22,890 --> 00:27:28,350 +of x على كل الفترة من a إلى b يعني دائما و أبدا الـ + +260 +00:27:28,350 --> 00:27:32,880 +f of x بتاخد قيم أكبر من القيم اللي تاخدها g of x + +261 +00:27:32,880 --> 00:27:37,340 +على الفترة بعد الـ a والـ b مالاش علاقة فيها او قبلها + +262 +00:27:37,340 --> 00:27:42,560 +انا ماخد فترة من a إلى b فلو جيت قلت افترض على + +263 +00:27:42,560 --> 00:27:51,160 +سبيل المثال ان هذه الدالة y تساوي f of x أجدت دالة + +264 +00:27:51,160 --> 00:27:57,980 +g of x بالشكل اللي عندنا هذا يبقى هذه y تساوي g of + +265 +00:27:57,980 --> 00:28:03,640 +x روحت أنا أخدت الفترة على سبيل المثال من عند + +266 +00:28:03,640 --> 00:28:10,580 +النقطة a لعند النقطة b بالشكل اللي عندنا هذا جهة + +267 +00:28:10,580 --> 00:28:18,570 +طالع هيك جهة طالع هيك يبقى انحصرت المسافة ما بين + +268 +00:28:18,570 --> 00:28:25,910 +الاتنين اللي هي المسافة اللي عندنا هذه يبقى هذه هي + +269 +00:28:25,910 --> 00:28:31,940 +الـ area a الآن انا لو كاملت على الـ F of X بيعطيني + +270 +00:28:31,940 --> 00:28:38,120 +المساحة هذه كلها أسفل المنحنة ومحور X المظلة زائد + +271 +00:28:38,120 --> 00:28:44,100 +المنطقة البيضة هذه تمام؟ لو كاملت على الـ G of X + +272 +00:28:44,100 --> 00:28:47,920 +بيعطيني المساحة اللى تحت المنحنة اللى المنطقة + +273 +00:28:47,920 --> 00:28:52,260 +البيضة لو طرحت الـ two two من بعض بتظلها المنطقة + +274 +00:28:52,260 --> 00:28:56,460 +المظللة يبقى الشدد area يبقى المنطقة اللي حاطط + +275 +00:28:56,460 --> 00:29:01,500 +عليها خطورة إذا مساحة هذه المنطقة هو تكامل الدالة + +276 +00:29:01,500 --> 00:29:05,780 +الأولى ناقص تكامل الدالة الثانية يبقى التكامل نفسه + +277 +00:29:05,780 --> 00:29:10,820 +على الفترة من a إلى b يبقى على الفترة من عند الـ a + +278 +00:29:10,820 --> 00:29:17,300 +لغاية من لغاية الـ b إذا بقول له لأ يبقى من البداية + +279 +00:29:17,300 --> 00:29:21,720 +تكامل الـ F of X ناقص الـ G of X و بروح بكامل على + +280 +00:29:21,720 --> 00:29:26,420 +فترة من A إلى B بيعطيني قداش المساحة اللي موجودة + +281 +00:29:26,420 --> 00:29:33,100 +عندنا طيب هذا لو كانت الدالة F of X فوق و G of X + +282 +00:29:33,100 --> 00:29:37,020 +تحت طب افترض واحدة على اليمين و واحدة على الشمال + +283 +00:29:37,020 --> 00:29:42,270 +لاحظ التكامل هنا بالنسبة لمين؟ لو كانت واحدة على + +284 +00:29:42,270 --> 00:29:47,310 +اليمين و واحدة على الشمال كيف نعمل تكامل بالنسبة + +285 +00:29:47,310 --> 00:29:54,090 +لماين إلى واي يبقى باجي بقوله similarly يعني بنفس + +286 +00:29:54,090 --> 00:30:00,310 +الطريقة الـ area ايه بقدر اقول تكامل من C إلى D للـ + +287 +00:30:00,310 --> 00:30:09,910 +F of Y ناقص الـ G of Y كل هذا في DY كيف كتالة افترض + +288 +00:30:09,910 --> 00:30:17,070 +ان هذا منحنى محور X وهذا Y وهذا نقطة الاصل الهيمين + +289 +00:30:17,070 --> 00:30:24,350 +Zero افترض كانت عند الدالة بهذا الشكل هذا المنحنى + +290 +00:30:24,350 --> 00:30:34,090 +Y تساوي F او X مقطع على صيغة X تساوي F of Y جيت على + +291 +00:30:34,090 --> 00:30:39,550 +منحنى ثانى نفترض ان هذا المنحنى كان بالشكل اللى + +292 +00:30:39,550 --> 00:30:49,470 +عندنا هذا يبقى هذا X يساوي G of Y تمام وانا روحت + +293 +00:30:49,470 --> 00:30:56,830 +اخدت المنطقة من نقطة التقاطة مثلا ها لغاية النقطة + +294 +00:30:56,830 --> 00:31:02,610 +اللي عندها دي و قلت هذه C وهذه D و جيت رسمت خط + +295 +00:31:02,610 --> 00:31:06,970 +أفقي بالشكل اللي عندها ده يبقى المساحة اللي محصورة + +296 +00:31:06,970 --> 00:31:12,030 +بين المنحنيين هي المنطقة المظللة اللي عندها دي + +297 +00:31:12,030 --> 00:31:20,050 +تمام يبقى بدى اعرف قدش المنطقة المظلة لأ يبقى صارت + +298 +00:31:20,050 --> 00:31:24,830 +كأنه هذه هي الدالة الكبيرة وهذه هي مين الدالة + +299 +00:31:24,830 --> 00:31:29,790 +الصغيرة على الفترة من وين لوين من C إلى D يعني + +300 +00:31:29,790 --> 00:31:36,590 +صارت F of Y أكبر من مين من G of Y أو بالبلد هيك + +301 +00:31:36,590 --> 00:31:41,270 +اللي على إيدك اليمين ناقص اللي على إيدك الشمال + +302 +00:31:41,270 --> 00:31:46,750 +بتجيبها بالضبط تماما يبقى من المثل الـ area يبدو + +303 +00:31:46,750 --> 00:31:52,510 +سوية كامل من C إلى D للـ F of Y ناقص G of Y السؤال + +304 +00:31:52,510 --> 00:31:56,810 +هو لو جاني السؤال بيقولي كامل بالنسبة لـ X والله + +305 +00:31:56,810 --> 00:32:02,580 +كامل بالنسبة لـ Y بيقولي في المثلة لا بحكيش أبدا، + +306 +00:32:02,580 --> 00:32:05,680 +بيعطيك السؤال وانت حار كامل بالنسبة لـ X كامل + +307 +00:32:05,680 --> 00:32:10,700 +بالنسبة لـ Y، هذا شأنك، مالو يشتغل فيك، خلاص؟ حد + +308 +00:32:10,700 --> 00:32:16,630 +يلعب يتساول هنا؟ طيب، الأن لم يبقى إلا مجموعة من + +309 +00:32:16,630 --> 00:32:23,090 +الأمثلة على هذا الـ definition وحنعطي أمثلة بحيث + +310 +00:32:23,090 --> 00:32:28,370 +مرة نكمل بالنسبة إلى Y و أحيانا نكمل بالنسبة إلى X + +311 +00:32:28,370 --> 00:32:34,450 +كله بيرجع لطبيعة المسألة اللي موجودة نبدأ ناخد + +312 +00:32:34,450 --> 00:32:39,810 +أمثلة و بنيجي للمثال الأول يبقى example one + +313 +00:33:04,880 --> 00:33:12,780 +والمغلقة بيه او المحدودة بيه By the following + +314 +00:33:26,250 --> 00:33:37,650 +Y تساوي X ترابيع ناقص اتنين Y يساوي اتنين + +315 +00:33:38,700 --> 00:33:45,300 +المساحة المحصورة بين كل من المنحنيات والمستقيمات + +316 +00:33:45,300 --> 00:33:50,860 +الاتية نمر ايام اعطيني منحنى والتاني خط مستقيم اذا + +317 +00:33:50,860 --> 00:33:55,020 +اول خطة بنعملها بنحاول نرسم الرسم اللي عندنا هذه + +318 +00:33:55,020 --> 00:33:58,420 +ومن خلالها نحدد حدود التكامل طبعا هو بطنيش حدود + +319 +00:33:58,420 --> 00:34:02,580 +التكامل لحالك انت بدك تستنتج حدود التكامل من خلال + +320 +00:34:02,580 --> 00:34:06,860 +الرسم وبدك تعرف تتكامل بالنسبة ليكسب بالنسبة أو + +321 +00:34:06,860 --> 00:34:10,520 +بالنسبة إلى Y يبقى لو جينا للرسمة اللي عندنا هذه + +322 +00:34:10,520 --> 00:34:16,760 +وروح نقول هذا محور X وهذا محور Y وهذا نقطة الأصل + +323 +00:34:16,760 --> 00:34:21,840 +اللي هي Zero لو جيت للمنحنة Y تساوي X تربية ناقص + +324 +00:34:21,840 --> 00:34:26,880 +اتنين و Y تساوي X تربيع تربيع مفتوحة إلى أعلى وتمر + +325 +00:34:26,880 --> 00:34:32,340 +بنقطة الأصل سالب اتنين يبقى Shift إلى أسفل بمقدار + +326 +00:34:32,340 --> 00:34:37,760 +اتنين يبقى هنا المنحنة بدى ينزل الى أسفل بمقدار + +327 +00:34:37,760 --> 00:34:44,920 +اتنين والبرابله بدى تصير بالشكل اللى قلناه هنا طيب + +328 +00:34:44,920 --> 00:34:51,330 +هذا اللي هو Y يساوي X ربيع ناقص اتنين المنحنى + +329 +00:34:51,330 --> 00:34:56,830 +التاني هو خط مستقيم Y تساوي اتنين خط يوازي محور X + +330 +00:34:56,830 --> 00:35:02,190 +ويبعد عنه مسافة مقدارها اتنين يبقى هذا الخط Y + +331 +00:35:02,190 --> 00:35:06,630 +تساوي مين؟ Y تساوي اتنين اذا المنطقة اللي بدنا + +332 +00:35:06,630 --> 00:35:11,830 +ياها هي المحصورة بين المنحنيين الاتنين هدول اللي + +333 +00:35:11,830 --> 00:35:18,040 +هي المنطقة المظللة واضح انه في منحنى فوق كبير و + +334 +00:35:18,040 --> 00:35:23,660 +اللي تحت يعتبر مان صغير يعني منحنى هي فوق و منحنى + +335 +00:35:23,660 --> 00:35:29,320 +تاني تحت اذا انا بدي اطبق من القاعدة الأولى يعني + +336 +00:35:29,320 --> 00:35:34,260 +التكامل بتكون من نسبة لمن؟ من نسبة لمحور X بس مش + +337 +00:35:34,260 --> 00:35:38,240 +هان اطبق هذه بدي اعرف الـ X بده تتغير من ويلة وين + +338 +00:35:38,240 --> 00:35:45,220 +باجي على أول نقطة هناها و بدي اعرف قداش قيمة X هنا + +339 +00:35:45,220 --> 00:35:49,460 +و بدي اجي على اخر نقطة في المساحة اللي عنده و بدي + +340 +00:35:49,460 --> 00:35:55,390 +اعرف قداش X بدها تكون عند هذه النقطة هذه النقطة + +341 +00:35:55,390 --> 00:36:00,150 +وهذه النقطة هي نقاط تقاطع المنحنة مع من؟ مع الخط + +342 +00:36:00,150 --> 00:36:04,150 +المستقيم اذا مش هنجيب الأحداثيات، بدتي أحلي + +343 +00:36:04,150 --> 00:36:09,070 +المعادلتين هدول مع بعض، هنا عندي Y وهنا Y، يبقى + +344 +00:36:09,070 --> 00:36:13,850 +بدي أساوي التنتين بمن؟ بعضهم، يبقى بدي أروح أحط + +345 +00:36:13,850 --> 00:36:15,390 +solution + +346 +00:36:17,940 --> 00:36:24,760 +يبقى بضع X تربيع ناقص اتنين يساوي كم؟ اتنين يبقى X + +347 +00:36:24,760 --> 00:36:29,900 +تربيع تساوي اربعة معناته ان الـ X يساوي زائد او + +348 +00:36:29,900 --> 00:36:34,100 +ناقص اتنين اذا النقف اللي على شمال الـ zero هذا + +349 +00:36:34,100 --> 00:36:38,480 +سالب اتنين واللي على يمين الـ zero هذا كم؟ اتنين + +350 +00:36:38,760 --> 00:36:45,520 +يبقى أقل قيمة للمنطق المضلل لـ X هي سالب اتنين و + +351 +00:36:45,520 --> 00:36:49,580 +أكبر قيمة تاخدها X على المنطق المضلل هو عبارة من + +352 +00:36:49,580 --> 00:36:56,220 +اتنين إذا بناء عليه بقول الـ area A يستوي تكامل من + +353 +00:36:56,220 --> 00:37:01,150 +سالب اتنين إلى اتنين الدالة الكبيرة هي الدالة اللي + +354 +00:37:01,150 --> 00:37:06,110 +فوق الـ y تساوي كداش؟ اتنين الدالة الصغيرة اللي + +355 +00:37:06,110 --> 00:37:12,490 +تحتها الـ X تربيع ناقص اتنين كل اللي عندها ده هنجيبها + +356 +00:37:12,490 --> 00:37:18,790 +بالنسبة لمن؟ بالنسبة إلى DX اللي بكتب هذا الكلام + +357 +00:37:18,790 --> 00:37:22,870 +صحيح بظل الكلام اللي باقي كله كلام فارغ، شغل + +358 +00:37:22,870 --> 00:37:28,590 +روتيني عادي جدا، تمام؟ يبقى احنا بدنا نروح نكامل + +359 +00:37:28,590 --> 00:37:33,290 +هذه ونجي نقول هذه من سالب اتنين إلى اتنين، لو + +360 +00:37:33,290 --> 00:37:40,290 +فكتها بصير اربعة ناقص extra بدي، تمام؟ قبل ما + +361 +00:37:40,290 --> 00:37:46,860 +كامل، هذه الدالة even والله odd خلص يبقى 2 تكامل + +362 +00:37:46,860 --> 00:37:55,380 +على نصف الفترة يبقى هذا 2 تكامل من 0 إلى 2 للـ 4 + +363 +00:37:55,380 --> 00:38:00,840 +ناقص X تربيع دي ستطلع هنا هاي الخط بجسمها إلى نصين + +364 +00:38:00,840 --> 00:38:08,020 +ما لهم زي بعض يبقى روحان كامل 2 هيها برا هذه 4X + +365 +00:38:08,020 --> 00:38:15,680 +ناقص X تكعيب على 3 كله من صفر لغاية اتنين يبقى هذه + +366 +00:38:15,680 --> 00:38:22,020 +اتنين و بتعوض اتنين في اربعة بتمانية ناقص تمانية + +367 +00:38:22,020 --> 00:38:29,270 +على تلاتة ناقص Zero كل هذا ب Zero على أي حال تلاتة + +368 +00:38:29,270 --> 00:38:35,170 +في تمانية باربع وعشرين ناقص تمانية بدل قدر 16 على + +369 +00:38:35,170 --> 00:38:40,5 + +401 +00:42:05,350 --> 00:42:11,350 +مستقيمين X يساوي سالب اثنين و X يساوي اثنين X + +402 +00:42:11,350 --> 00:42:16,170 +يساوي سالب اثنين يبقى هذا الخط الطالع رأسي هكذا + +403 +00:42:18,200 --> 00:42:23,160 +والخط الثاني X يساوي اثنين وهو الخط اللي عندنا هذا + +404 +00:42:23,160 --> 00:42:30,100 +تمام يبقى هذا X يساوي اثنين وهذا X يساوي سالب + +405 +00:42:30,100 --> 00:42:36,800 +اثنين يبقى صار هل هناك ما بين X يساوي 2 ومساحة + +406 +00:42:36,800 --> 00:42:40,940 +ثانية فيه محصورة بينه وبين المنحنيات؟ لا ثلاثة + +407 +00:42:40,940 --> 00:42:45,020 +اتقطعوا في نفس مين؟ في نفس النقطة إذا ما عنديش + +408 +00:42:45,020 --> 00:42:49,200 +مساحة محددة مع الخط الرأسي الأول لكن مع الخط + +409 +00:42:49,200 --> 00:42:53,580 +الرأسي الثاني صار عندي مساحة محددة يبقى أنا في + +410 +00:42:53,580 --> 00:42:59,220 +عندي المساحة دي محصورة ما بين خطين من الخطوط + +411 +00:42:59,220 --> 00:43:00,800 +المستقيمة + +412 +00:43:04,700 --> 00:43:13,180 +المساحة المحصورة بين خطين مستقيمين ومنحنى المساحة + +413 +00:43:13,180 --> 00:43:20,560 +المحصورة بين الخطين + +414 +00:43:20,560 --> 00:43:31,160 +المستقيمين ومنحنى المستقيمين + +415 +00:43:31,180 --> 00:43:34,000 +الخط رأسي يتخيل خط رأسي يتخيل خط رأسي يتخيل خط + +416 +00:43:34,000 --> 00:43:35,220 +رأسي يتخيل خط رأسي يتخيل خط رأسي يتخيل خط رأسي + +417 +00:43:35,220 --> 00:43:37,800 +يتخيل خط رأسي يتخيل خط رأسي يتخيل خط رأسي يتخيل خط + +418 +00:43:37,800 --> 00:43:38,160 +رأسي يتخيل خط رأسي يتخيل خط رأسي يتخيل خط رأسي + +419 +00:43:38,160 --> 00:43:39,800 +يتخيل خط رأسي يتخيل خط رأسي يتخيل خط رأسي يتخيل خط + +420 +00:43:39,800 --> 00:43:44,700 +رأسي يتخيل خط رأسي يتخيل خط رأسي يتخيل خط رأسي + +421 +00:43:44,700 --> 00:43:52,800 +يتخيل خط رأسي يتخيل خط رأسي يتخيل خط رأسي يتخيل خط + +422 +00:43:52,800 --> 00:43:58,640 +رأسي يتبقى هذا كل منحنى كل واحد كتب عليه معادلة + +423 +00:43:58,640 --> 00:44:06,010 +إذا ما عندناش مساحة واحدة وإنما عندنا مجموع مساحتين صح + +424 +00:44:06,010 --> 00:44:10,470 +ولا لا؟ أيوة طب اثنين بدنا نكمل بالنسبة لـ X ولا + +425 +00:44:10,470 --> 00:44:16,170 +بالنسبة لـ Y تعال نشوف كل مساحة من هذه المساحات لو + +426 +00:44:16,170 --> 00:44:20,150 +جيت للمساحة اللي عندنا هذه يبقى في منحنى فوق وفي + +427 +00:44:20,150 --> 00:44:26,430 +منحنى تحت هنا في منحنى فوق وفي منحنى تحت لكن لو + +428 +00:44:26,430 --> 00:44:31,120 +جيتي يمين وشمال اه ممكن ممكن يا مشوال بياخد تروح + +429 +00:44:31,120 --> 00:44:34,260 +ترسم خط أفقي بيصير هذا على اليمين وهذا على الشمال + +430 +00:44:34,260 --> 00:44:38,440 +وهذا على اليمين وهذا على الشمال يبدو يتكاملينو + +431 +00:44:38,440 --> 00:44:44,560 +بعد هيك هذه يمين وشمال ما عنديش مش هتظبط هذه لذلك + +432 +00:44:44,560 --> 00:44:49,400 +أفضل حاجة خلص بالنسبة لـ X وانسى الموضوع تمام يبقى + +433 +00:44:49,400 --> 00:44:54,780 +بروح بكمل إس الـ X بس بدي اروح احدد حدود التكوين + +434 +00:44:54,780 --> 00:44:59,720 +بدي اعرف قد ايش الإحداثيات تبع نقطة التقاطع هنا يعني + +435 +00:44:59,720 --> 00:45:04,160 +قد ايش قيم هذه معروفة هذه المعروفة أو هذه + +436 +00:45:04,160 --> 00:45:12,060 +المعروفة أو هذه المعروفة + +437 +00:45:12,060 --> 00:45:13,400 +أو هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +438 +00:45:13,400 --> 00:45:14,420 +هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +439 +00:45:14,420 --> 00:45:14,720 +هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +440 +00:45:14,720 --> 00:45:16,340 +هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +441 +00:45:16,340 --> 00:45:17,220 +هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +442 +00:45:17,220 --> 00:45:19,100 +هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +443 +00:45:19,100 --> 00:45:22,880 +هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +444 +00:45:22,880 --> 00:45:25,880 +هذه المعروفة أو هذه المعروفة أو هذه المعروفة أو + +445 +00:45:25,880 --> 00:45:25,980 +هذه المعروفة ا + +446 +00:45:30,240 --> 00:45:37,260 +بدي آخذ أربعة ناقص X تربيع يساوي اثنين ناقص X بدي + +447 +00:45:37,260 --> 00:45:41,460 +أعملها معادلة صفرية لهذه الشغلة الثانية بيصير X + +448 +00:45:41,460 --> 00:45:49,240 +تربيع بالموجب ناقص X زي ما هي ما تغيرتي أربعة + +449 +00:45:49,240 --> 00:45:55,160 +بتجيلك بالسالب وعندك اثنين بيظل سالب اثنين يساوي + +450 +00:45:55,160 --> 00:45:55,720 +زيرو + +451 +00:46:02,100 --> 00:46:10,840 +هنا X وهنا X وهنا اثنين وهنا واحد وهنا سالب + +452 +00:46:10,840 --> 00:46:17,820 +وهنا موجب يبقى ناقص اثنين X وزاد X يبقى ناقص + +453 +00:46:17,820 --> 00:46:22,720 +X يبقى بناء عليه الـ X الأولى ساوي سالب واحد + +454 +00:46:22,720 --> 00:46:29,630 +والـ X الثانية ساوي قد ايش؟ اثنين فعلاً نقطة التقاطع + +455 +00:46:29,630 --> 00:46:34,670 +الأولى سالب واحد ونقطة التقاطع الثانية قد ايش؟ اثنين + +456 +00:46:34,670 --> 00:46:39,790 +هي مع الخط والمنحنى يبقى عند اثنين يبقى معناته + +457 +00:46:39,790 --> 00:46:50,200 +عندي تكاملين يبقى الـ area المطلوبة الـ area من سالب اثنين + +458 +00:46:50,200 --> 00:46:55,040 +لغاية سالب واحد + +459 +00:46:55,040 --> 00:47:00,060 +يبقى الخط المستقيم هذا اللي فوق اللي هو 2 ناقص X + +460 +00:47:00,600 --> 00:47:06,660 +اثنين ناقص X ناقص المنحنى اللي تحت هذا اللي هو + +461 +00:47:06,660 --> 00:47:13,380 +أربعة ناقص X تربيع يبقى أربعة ناقص X تربيع وهي + +462 +00:47:13,380 --> 00:47:17,840 +الجزء ودي بالك وانت بتشتغل مش هحط السالب للأربعة و + +463 +00:47:17,840 --> 00:47:21,740 +تسيب الثانية يبقى السالب وبتحط الدالة بالكامل اللي + +464 +00:47:21,740 --> 00:47:25,060 +بين الجزئين مشان شرط السالب تدخل على term من هذه + +465 +00:47:25,060 --> 00:47:28,780 +ترميزة اللي بيساووا بعضكم أو بروح بغلّط الإشارة وبيظل + +466 +00:47:28,780 --> 00:47:32,920 +يخبص وهدّاك وبتطلع اليوم ما عمّشت بصواب هدا ايه نطلع + +467 +00:47:32,920 --> 00:47:38,260 +جواب طيب يبقى هذا الكلام بدو يساوي تكامل من سالب + +468 +00:47:38,260 --> 00:47:44,600 +اثنين إلى سالب واحد لمين؟ لل اثنين ناقص X ناقص أربعة + +469 +00:47:44,600 --> 00:47:50,000 +زائد X تربيع كله بالنسبة لـ DX من ناقص اثنين + +470 +00:47:50,000 --> 00:47:55,500 +لناقص واحد X تربيع موجبة وهي ناقص X ناقص أربعة + +471 +00:47:55,500 --> 00:48:00,680 +زي دي اثنين بيظل قد ايش؟ ناقص اثنين كله بالنسبة لـ + +472 +00:48:00,680 --> 00:48:05,480 +DX بدنا نيجي اه لسه عملنا هيك لسه في تكامل ثاني + +473 +00:48:05,480 --> 00:48:10,000 +خليها واحد طيب خليها واحد ولا يهمك هذه واحد + +474 +00:48:10,000 --> 00:48:17,640 +خلينا ماشيين يبقى هذه A واحد وهذه A اثنين يبقى بدنا + +475 +00:48:17,640 --> 00:48:26,060 +نحسب هذه يبقى بيصير X تكعيب على 3 ناقص X تربيع على 2 + +476 +00:48:26,060 --> 00:48:36,080 +ناقص 2X كله من سالب 2 لغاية سالب 1 عوض بالقيمة اللي + +477 +00:48:36,080 --> 00:48:40,380 +فوق يا شباب يبقى ناقص واحد تكعيب اللي هو ناقص واحد + +478 +00:48:40,380 --> 00:48:45,820 +يبقى ناقص طول اللي بعدها ناقص واحد تربيع اللي هو + +479 +00:48:45,820 --> 00:48:50,780 +واحد على اثنين والناقص هذه بتظلها زي ما هي النص + +480 +00:48:50,780 --> 00:48:57,980 +هذه زائد اثنين خلصنا القيمة اللي فوق ناقص افتح قوس + +481 +00:48:58,610 --> 00:49:04,630 +هنا هذا بتعطيك ناقص ثمانية على ثلاثة يبقى ناقص + +482 +00:49:04,630 --> 00:49:09,510 +ثمانية على ثلاثة هذي بيصير أربعة على اثنين اللي هو + +483 +00:49:09,510 --> 00:49:15,570 +بيقدرش باثنين بالسالب وهي سالب اثنين هذي بيبقى + +484 +00:49:15,570 --> 00:49:22,450 +زائد أربعة يبقى زائد أربعة يبقى النتيجة كالتالي وهي + +485 +00:49:22,450 --> 00:49:29,030 +سالب طول وهي سالب نصف وهي زائد اثنين وهي زائد + +486 +00:49:29,030 --> 00:49:35,870 +ثمانية ثلاثة وهي زائد اثنين وانا ناقص أربعة طلّعلي + +487 +00:49:35,870 --> 00:49:43,610 +هذه وهذه بطل قد ايش؟ سبعة على ثلاثة يبقى هذه يساوي + +488 +00:49:43,610 --> 00:49:49,790 +سبعة على ثلاثة وناقص نصف ما فيش غيره وهذه ناقص نصف + +489 +00:49:49,790 --> 00:49:56,370 +بطل عندي اثنين واثنين أربعة مع الأربعة مع السلامة + +490 +00:49:56,790 --> 00:50:03,590 +يبقى هذه سالب أربعة مع اثنين ومع اثنين يبقى كله + +491 +00:50:03,590 --> 00:50:09,850 +على قد ايش؟ على ستة ستة على ثلاثة في اثنين في سبعة + +492 +00:50:09,850 --> 00:50:17,510 +بـ 14 ناقص ستة على اثنين فيها الثلاثة في واحد + +493 +00:50:17,510 --> 00:50:26,220 +بثلاثة يبقى النتيجة يساوي 11 على 6 بنروح نجيب + +494 +00:50:26,220 --> 00:50:32,580 +اثنين للمساحة الثانية يبقى تكامل من سالب واحد + +495 +00:50:32,580 --> 00:50:37,860 +لغاية اثنين الدالة اللي فوق ناقص الدالة اللي تحت + +496 +00:50:37,860 --> 00:50:43,100 +يبقى أربعة ناقص X تربيع ناقص الدالة اللي تحت لها + +497 +00:50:43,100 --> 00:50:50,460 +اثنين ناقص X كله بالنسبة لـ DX يبقى تكامل من + +498 +00:50:50,460 --> 00:50:58,150 +سالب واحد لغاية اثنين لمين؟ لل أربعة ناقص X تربيع + +499 +00:50:58,150 --> 00:51:06,070 +ناقص اثنين زائد الـ X كل هذا الكلام بالنسبة لـ DX + +500 +00:51:06,070 --> 00:51:13,410 +ويساوي ناقص اثنين وزائد أربعة بيقول قد ايش؟ اثنين تكامل + +501 +00:51:13,410 --> 00:51:20,890 +من سالب واحد لاثنين ل اثنين زائد X ناقص X تربيع كله + +502 +00:51:20,890 --> 00:51:28,190 +بالنسبة لـ DX يبقى النتيجة 2X X تربيع على 2 ناقص + +503 +00:51:28,190 --> 00:51:33,950 +X تكعيب على 3 كله من ناقص 1 لغاية 2 + +504 +00:51:37,780 --> 00:51:43,620 +يبقى هذه النتيجة تساوي اثنين في اثنين بأربعة زائد + +505 +00:51:43,620 --> 00:51:50,000 +أربعة على اثنين باثنين ناقص ثمانية على ثلاثة ثمانية + +506 +00:51:50,000 --> 00:51:54,460 +على ثلاثة ناقص يفتح قوس نعوض بالقيمة هذه اللي هي + +507 +00:51:54,460 --> 00:52:03,680 +ناقص اثنين وهنا زائد نصف وعندك هنا ناقص وناقص + +508 +00:52:03,680 --> 00:52:12,420 +بيصير زائد ثلاثة هذي بيصير ستة ناقص ثمانية على ثلاثة + +509 +00:52:12,420 --> 00:52:21,060 +وهنا زائد اثنين وناقص نصف ناقص ثلث ويساوي اثنين + +510 +00:52:21,060 --> 00:52:26,400 +وستة ثمانية عندك ناقص ثمانية على ثلاثة وناقص ثلث + +511 +00:52:26,400 --> 00:52:33,740 +بناقص تسعة على ثلاثة يعني قد ايش؟ ناقص ثلاثة وبيظل + +512 +00:52:33,740 --> 00:52:41,040 +عندك هنا ناقص نصف يبقى هاي اثنين وستة ثمانية ثمانية + +513 +00:52:41,040 --> 00:52:47,500 +بدي أشيل منهم ثلاثة بضل قد ايش؟ بضل اللي هو خمسة + +514 +00:52:47,500 --> 00:52:54,670 +يساوي خمسة ناقص نصف الآن بدي المساحة الكلية يبقى الـ + +515 +00:52:54,670 --> 00:53:01,630 +area اللي بدو اياها A يساوي A1 زائد A2 A1 طلعناها + +516 +00:53:01,630 --> 00:53:11,850 +قد ايش؟ بـ 11 على 6 زائد 9 على 2 كله على 6 بضل 11 + +517 +00:53:11,850 --> 00:53:21,790 +زائد 6 على 2 ديال 3 في 9 بـ 27 يبقى ثمانية + +518 +00:53:21,790 --> 00:53:28,970 +وثلاثين على ستة أو 29 على 3 هذه + +519 +00:53:28,970 --> 00:53:32,130 +المساحة الكلية المطلوبة + +520 +00:53:51,040 --> 00:53:51,600 +أيوة + +521 +00:53:55,410 --> 00:54:02,850 +وين واي تساوي سالب واحد؟ واي تساوي + +522 +00:54:02,850 --> 00:54:04,830 +سالب واحد بده يجيلك هنا. + +523 +00:54:08,370 --> 00:54:15,810 +كيف العملية + +524 +00:54:15,810 --> 00:54:20,230 +ليست سهلة بدو يصير عندك واي تساوي سالب أدتك كمان + +525 +00:54:20,230 --> 00:54:25,400 +مساحة هيك هيك هيك تمام؟ وبعدين تمدوا على + +526 +00:54:25,400 --> 00:54:29,140 +استقامته في كمان هذه مساحة وبعدين تمدوا على هذه + +527 +00:54:29,140 --> 00:54:34,320 +وهنا كمان مساحة وتمدوا هنا وهنا كمان مساحة إن شاء + +528 +00:54:34,320 --> 00:54:35,780 +الله للعصر بنخلص اليوم + +529 +00:54:40,360 --> 00:54:44,760 +بيصير ما له قيمة ما له أي اعتبار إن احنا بندور + +530 +00:54:44,760 --> 00:54:48,200 +المساحة المحصورة بين المنحنيات بتطلعش منها إلا إذا + +531 +00:54:48,200 --> 00:54:51,760 +قال لي بين X يساوي Zero وY يساوي Zero اه تدخل + +532 +00:54:51,760 --> 00:54:56,080 +المحاور معاه ما جاليش يبقى أنا مقيد بس بالمنحنيات + +533 +00:54:56,080 --> 00:55:00,460 +اللي بنوصل عليها غير هيك ما لك علاقة فيه طبعا طيب + +534 +00:55:00,460 --> 00:55:07,710 +هذا نمرة B من المثلة نمرة C نمرة الـ C بيقول يا سيدي + +535 +00:55:07,710 --> 00:55:16,650 +X يساوي Y تربيع and X يساوي Y زائد اثنين + +536 +00:55:19,450 --> 00:55:25,350 +يبقى بنروح نرسم المثلة مشان نعرف شو شكلها بالضبط + +537 +00:55:25,350 --> 00:55:31,730 +يبقى باجي بقول هاي المحاور هذا محور X هذا محور Y + +538 +00:55:31,730 --> 00:55:36,990 +هذه نقطة الأصل اللي هي Zero X يساوي Y تربيع هو + +539 +00:55:36,990 --> 00:55:44,260 +قنابلة مفتوح جهة اليمين يبقى هذا ال parabola لأن X + +540 +00:55:44,260 --> 00:55:51,020 +بدو يساوي 100Y تربيع يبقى هذا ال X بدو يساوي Y تربيع + +541 +00:55:51,020 --> 00:55:58,000 +بداية للخط المستقيم لأن لو كانت Y بـ 0 X بـ 2 يبقى لو + +542 +00:55:58,000 --> 00:56:04,830 +جيت قلت هاي اثنين لو كانت X بـ 0 وY بسالب اثنين X + +543 +00:56:04,830 --> 00:56:07,830 +بـ 0 وY بسالب اثنين X بـ 0 وY بسالب اثنين X بـ 0 + +544 +00:56:07,830 --> 00:56:07,850 +وY بسالب اثنين X بـ 0 وY بسالب اثنين X بـ 0 وY + +545 +00:56:07,850 --> 00:56:08,050 +بسال اثنين X بـ 0 وY بسالب اثنين X بـ 0 وY + +546 +00:56:08,050 --> 00:56:08,790 +بسال اثنين X بـ 0 وY بسالب اثنين X بـ 0 وY + +547 +00:56:08,790 --> 00:56:08,930 +بسال اثنين X بـ 0 وY بسالب اثنين X بـ 0 وY + +548 +00:56:08,930 --> 00:56:12,830 +بسال اثنين X بـ 0 وY بسالب اثنين X بـ 0 وY + +549 +00:56:12,830 --> 00:56:20,910 +بسال اثنين X بـ 0 وY بسالب اثنين X بـ 0 وY + +550 +00:56:20,910 --> 00:56:28,950 +بسالبو بمد الخط على استقامته يبقى هذا اللي هو + +551 +00:56:28,950 --> 00:56:34,210 +تقاطع مع المنحنى يبقى المنطقة المظللة هذه هي + +552 +00:56:34,210 --> 00:56:40,770 +المنطقة المحصورة ما بين المنحنى اللي عندنا والخط + +553 +00:56:40,770 --> 00:56:49,940 +المستقيم يبقى الخط المستقيم هذا X يساوي Y زائد 2 Y + +554 +00:56:49,940 --> 00:56:56,620 +المنحنى اللي يفوت هو X يساوي Y تربيع بالشكل اللي + +555 +00:56:56,620 --> 00:56:56,980 +عندنا + +556 +00:57:01,010 --> 00:57:07,330 +تمام طيب واضح انه لو تيجي تقوله هذه فوق هذه تحت + +557 +00:57:07,330 --> 00:57:11,390 +هنا تنتل بيصيروا فوق بعض بيصير واحد على يمين واحد + +558 +00:57:11,390 --> 00:57:15,870 +على شمال مش هتظبط معاه لكن واضح انه الخط هذا على + +559 +00:57:15,870 --> 00:57:19,470 +اليمين وهذا الجزء منه منحنى وين عليه شمال يعني + +560 +00:57:19,470 --> 00:57:23,360 +واحد جهة ايدي شمال وواحد جهة ايدي اليمين إذا هنا + +561 +00:57:23,360 --> 00:57:27,840 +التكامل بيشير بالنسبة لـ Y يبقى بروح بقول لو بدي + +562 +00:57:27,840 --> 00:57:34,600 +أعرف قد ايش أقل قيمة بتاخذها Y وقد ايش أكبر قيمة هنا + +563 +00:57:34,600 --> 00:57:39,900 +بتاخذها من Y يبقى معناته بدي أحل المعادلتين هدول + +564 +00:57:39,900 --> 00:57:46,120 +مع بعض يبقى عندي Y تربيع بدها تساوي الـ Y زائد + +565 +00:57:46,120 --> 00:57:51,300 +اثنين او الـ Y تربيع ناقص Y ناقص اثنين بدها تساوي + +566 +00:5 + +601 +01:02:38,640 --> 01:02:47,740 +لو جئت للمنحنى الأول هذا محور X وهذا محور Y وهذا + +602 +01:02:47,740 --> 01:02:55,080 +نقطة الأصل، المنحدر هو X يساوي Y تربيع، رسمناه قبل + +603 +01:02:55,080 --> 01:03:01,160 +قليل بالشكل اللي عندنا هذا، يبقى هذا الـ X يساوي Y + +604 +01:03:01,160 --> 01:03:06,910 +تربيع، المنحنى الثاني هذا عبارة عن إيش؟ عبارة عن x + +605 +01:03:06,910 --> 01:03:13,790 +بده يساوي سالب اثنين Y تربيع زائد ثلاثة، يعني هذا + +606 +01:03:13,790 --> 01:03:20,370 +لو رحت قعدت أكتبه مرة ثانية بمين؟ بـ X يساوي سالب + +607 +01:03:20,370 --> 01:03:25,470 +اثنين Y تربيع زائد ثلاثة، بقول: واسة اثنين والثلاثة + +608 +01:03:26,210 --> 01:03:31,430 +يبقى Y تساوي، X يساوي سالب Y تربيع، يبقى هذا بس + +609 +01:03:31,430 --> 01:03:36,750 +بعدين أقلبه وين؟ على الشجة الثانية، طيب اثنين هذه + +610 +01:03:36,750 --> 01:03:40,510 +بتخليه يقرب على المنحنى أو يبعد، الرقم اللي عندي + +611 +01:03:40,510 --> 01:03:46,430 +تمام، الثلاثة هي Shift بس، إن من الـ Shift إلى أعلى + +612 +01:03:46,430 --> 01:03:50,850 +الرسم يمين وشمال، إذا الـ Shift جهة اليمين بمقدار + +613 +01:03:50,850 --> 01:03:56,050 +ثلاثة، يبقى المنحنى على اليسار هكذا، وسأعمل Shift + +614 +01:03:56,050 --> 01:04:04,930 +للخلف بمقدار 3، لماذا؟ لأن لو كانت Y بـ 0 يبقى X بـ 3 + +615 +01:04:04,930 --> 01:04:10,810 +يبقى هذا X بـ 3 وY بـ 0، والـ parabola ستصبح بالشكل + +616 +01:04:10,810 --> 01:04:16,760 +اللي عندنا هذا، هكذا، طبعًا يبقى هذا المنحنى اللي هو X + +617 +01:04:16,760 --> 01:04:23,700 +يساوي سالب اثنين Y تربيع زائد ثلاثة، إذا المنطقة + +618 +01:04:23,700 --> 01:04:29,320 +اللي بينهم هي المنطقة المظللة اللي عندنا، أيوة، + +619 +01:04:29,320 --> 01:04:32,720 +وشايف + +620 +01:04:32,720 --> 01:04:36,280 +المنحنى اللي عندك ولا لا، حق واي بزيرو قداش تكون + +621 +01:04:37,860 --> 01:04:42,940 +سمعت بالـ Shift تبع الدالة لما كانت Y تساوي مثلًا X + +622 +01:04:42,940 --> 01:04:47,880 +تربيع أو X كام، يبقى Shift إلى أعلى، إذا الرقم لـ Y + +623 +01:04:47,880 --> 01:04:51,260 +بيصير Shift جهة اليمين أو جهة اليسار حسب القيمة + +624 +01:04:51,260 --> 01:04:55,080 +تبعته، طيب إذا ما أنت مش عارف الـ Shift ولا حاجة + +625 +01:04:55,080 --> 01:04:59,320 +بقول له: حط الـ Y بـ 0 وشوف X وين بتروح، يبقى بنحدد + +626 +01:04:59,320 --> 01:05:01,100 +القيمة في هذه الحالة + +627 +01:05:05,430 --> 01:05:13,290 +كيف؟ المثل معطلك X يساوي Y كيف + +628 +01:05:13,290 --> 01:05:19,410 +مش مفروض؟ ثلاث معروفات هي X يساوي Y، ثلاث بدكش حط + +629 +01:05:19,410 --> 01:05:27,210 +لـ Y تساوي جذر X، جذر X معروف هي جذر X الموجب وجذر X + +630 +01:05:27,210 --> 01:05:33,820 +الثاني، صحيح ولا لأ؟ ما عندكش خبر، مش مشكلة، طيب خليك + +631 +01:05:33,820 --> 01:05:39,180 +معنا يا شباب، يبقى هاي رسمنا الـ X يساوي Y تربيع، و + +632 +01:05:39,180 --> 01:05:44,080 +المنحنى الثاني X زائد 2Y تربيع يساوي 3، رسمناها يبقى + +633 +01:05:44,080 --> 01:05:49,080 +المنطقة المظللة هي المنطقة بين المنحنيين، واضح أن في + +634 +01:05:49,080 --> 01:05:53,820 +منحنى عندي على اليمين، ومنحنى ثاني وين؟ على اليسار + +635 +01:05:53,820 --> 01:05:58,960 +يبقى أنا بدي أقل قيمة بتاخدها Y، أكبر قيمة هنا + +636 +01:05:58,960 --> 01:05:59,860 +بتاخدها مين؟ + +637 +01:06:03,430 --> 01:06:09,990 +يبقى أنا عند X يساوي Y تربيع وعندي X الثانية ناقص + +638 +01:06:09,990 --> 01:06:18,570 +اثنين Y تربيع زائد ثلاثة، يبقى Y تربيع + +639 +01:06:18,570 --> 01:06:23,910 +يساوي اثنين Y تربيع زائد ثلاثة، يبقى Y تساوي زائد + +640 +01:06:23,910 --> 01:06:30,360 +أو ناقص، إذا هذه سالب واحد وهذه مين؟ وهذه واحد يبقى + +641 +01:06:30,360 --> 01:06:35,400 +النقطة إن هذه سالب واحد والنقطة هذه واحد يبقى الـ + +642 +01:06:35,400 --> 01:06:39,900 +area اللي عندنا بدأت تساوي تكامل من سالب واحد إلى + +643 +01:06:39,900 --> 01:06:44,180 +واحد، الدالة اللي على اليمين اللي هي اثنين Y تربيع + +644 +01:06:44,180 --> 01:06:48,180 +زائد ثلاثة ناقص الدالة اللي على اليسار اللي هي مين؟ + +645 +01:06:48,480 --> 01:06:58,220 +X يساوي Y تربيع، كل هذا بالنسبة لمين؟ إلى dY، سالب + +646 +01:06:58,220 --> 01:07:05,260 +اثنين Y تربيع زي الثلاث سالب Y تربيع، يبقى كأن + +647 +01:07:05,260 --> 01:07:13,190 +المسألة تكامل من سالب واحد إلى واحد لمين؟ لثلاثة ناقص + +648 +01:07:13,190 --> 01:07:27,610 +ثلاثة Y تربيع، كلّه بالنسبة إلى dY، يبقى + +649 +01:07:27,610 --> 01:07:32,850 +even function، ممكن أقول من الصفر لغاية كده؟ لغاية + +650 +01:07:32,850 --> 01:07:36,330 +واحدة، أنسى مش مشكلة، فالمساحة اللي فوق واضحة إنها + +651 +01:07:36,330 --> 01:07:40,150 +جد المساحة اللي تحت، يعني لو أخذت واحدة وضربتها في + +652 +01:07:40,150 --> 01:07:43,650 +اثنين بيمشي الحال، إيجى في بلد كان فيها مجاش، ما عندناش + +653 +01:07:43,650 --> 01:07:48,490 +مشكلة، يبقى لو خليتها زي ما هي، مجاش في باقي، بقول له: + +654 +01:07:48,490 --> 01:07:53,730 +هذه ثلاثة Y ناقص Y تكعيبها على ثلاثة، بتروح وبظل + +655 +01:07:53,730 --> 01:07:58,890 +المساحة من سالب واحد لغاية قداش؟ واحد، يبقى بدّه + +656 +01:07:58,890 --> 01:08:06,830 +يساوي ثلاثة ناقص ثلاثة، هذه Y تكعيبها على ثلاثة، بتروح مع + +657 +01:08:06,830 --> 01:08:14,120 +ثلاثة، يبقى عند الواحد ثلاثة ناقص واحد، ناقص هنا بصير + +658 +01:08:14,120 --> 01:08:21,540 +ناقص ثلاثة وهنا يا سيد العزيز ناقص واحد بصير زائد + +659 +01:08:21,540 --> 01:08:28,460 +واحد، يبقى الجواب بيصير ثلاثة ناقص واحد زائد ثلاثة + +660 +01:08:28,460 --> 01:08:33,300 +كمان ناقص واحد، يبقى النتيجة كم؟ أربعة، يبقى قيمة + +661 +01:08:33,300 --> 01:08:39,380 +المساحة تساوي أربعة، هذا نمر إيه من المثلة؟ نمر ب + +662 +01:08:40,960 --> 01:08:51,820 +نمر ب، يبقى Y تساوي X تربيع، and يبقى Y ناقص X + +663 +01:08:51,820 --> 01:08:55,720 +تربيع زائد 4X + +664 +01:09:04,920 --> 01:09:09,140 +هذه برضه معادلة من الدرجة الثانية في X يبقى هذه + +665 +01:09:09,140 --> 01:09:14,120 +Parabola، وهذه كذلك Parabola بس هذه الـ vertex تبعها + +666 +01:09:14,120 --> 01:09:19,700 +نقطة، هذه معمولة لها إيه؟ شوف، بدي أحدد وين الـ + +667 +01:09:19,700 --> 01:09:25,500 +vertex تبع هذه الـ Parabola، فأروح بعمل إكمال المربع + +668 +01:09:25,500 --> 01:09:29,120 +هذه قد إيش بدها مشان يصير إكمال المربع؟ + +669 +01:09:37,320 --> 01:09:45,580 +يبقى هذا الكلام يصبح على الشكل التالي: عندك الـ Y + +670 +01:09:45,580 --> 01:09:54,660 +يساوي ناقص X تربيع زائد 4X ناقص 4 زائد 4، أو بمعنى + +671 +01:09:54,660 --> 01:10:01,440 +آخر هذه ها ها بدّه يصير Y ناقص أربعة بده يساوي هاي + +672 +01:10:01,440 --> 01:10:07,020 +ناقص أخذناه عامل مشترك، بظل X تربيع ناقص أربعة X + +673 +01:10:07,020 --> 01:10:12,660 +زائد أربعة، هذه الأربعة نعشج هذه، هدول الثلاثة أخذنا + +674 +01:10:12,660 --> 01:10:18,440 +منهم سالب عامل مشترك، يبقى بصير الـ Y ناقص أربعة + +675 +01:10:18,440 --> 01:10:25,790 +يساوي الـ X ناقص اثنين لكل تربيع، يبقى هذه البارابولا + +676 +01:10:25,790 --> 01:10:31,490 +والـ vertex تبعها هي بين 2 و4، يبقى أنا لو رحت + +677 +01:10:31,490 --> 01:10:37,050 +رسمت الرسمة اللي عندنا هذه فبدي بقوله: هذا محور X + +678 +01:10:37,050 --> 01:10:43,350 +وهذا محور Y، وهذه نقطة الأصل اللي هي Zero، البارابولا + +679 +01:10:43,350 --> 01:10:48,670 +الأولى Y تساوي X تربيع، يبقى Y تساوي X تربيع، + +680 +01:10:48,670 --> 01:10:56,690 +البارابولا اللي عندنا هذه هيك، يبقى هذه اللي هي هذه + +681 +01:10:56,690 --> 01:11:03,650 +فوق X يساوي Y تربيع، هذه Y تساوي X تربيع، بتدخل الـ + +682 +01:11:03,650 --> 01:11:08,490 +parabola الثانية، الـ vertex تبعها اللي هو اثنين + +683 +01:11:08,490 --> 01:11:14,750 +وأربعة، يبقى اتحرك اثنين هنا على اليمين، وده يطلع + +684 +01:11:14,750 --> 01:11:20,710 +فوق قداش؟ أربعة، يبقى هذه النقطة اثنين وأربعة، طب ليش + +685 +01:11:20,710 --> 01:11:25,530 +أجت على المنحنى ولم أجت فوق أو أجت تحت، لأن Y تساوي + +686 +01:11:25,530 --> 01:11:28,770 +X تساوي اثنين، لما الـ X تساوي اثنين بتبقى أربعة، إذا + +687 +01:11:28,770 --> 01:11:33,870 +انتقى على مين؟ على المنحنى بالضبط، تمام، طيب هذا الـ + +688 +01:11:33,870 --> 01:11:38,070 +vertex تبع اثنين وأربعة، open up ولا open down؟ + +689 +01:11:38,070 --> 01:11:43,730 +open down بسبب الإشارة السلبية، اثنين يا مربى نقطة + +690 +01:11:43,730 --> 01:11:49,390 +الأصل والله، ليه يا مربى نقطة الأصل؟ طلع المعادلة لو + +691 +01:11:49,390 --> 01:11:55,910 +حطيت X بـ Zero، Y بقدّيش؟ يبقى دي مربى نقطة الأصل غصب + +692 +01:11:55,910 --> 01:12:00,270 +من علمه يرضى، يبقى الـ parabola هذه بدها تيجي بالشكل + +693 +01:12:00,270 --> 01:12:07,100 +اللي عندنا هذا، ومن هنا parabola بالشكل هذا، ومن هنا + +694 +01:12:07,100 --> 01:12:13,660 +parabola بالشكل هذا، يبقى البارابولا إلى أسفل، + +695 +01:12:13,660 --> 01:12:27,760 +البارابولا + +696 +01:12:27,760 --> 01:12:30,160 +إذا المنطقة اللي بينهم هي + +697 +01:12:39,220 --> 01:12:47,280 +هذا المنطقة المظللة بين الاثنين هي المنطقة المطلوبة + +698 +01:12:53,660 --> 01:12:58,640 +الـ X هتتغير من أين لأين؟ وإذا أنا أريد نسبة Y من + +699 +01:12:58,640 --> 01:13:05,660 +صفر لغاية أربعة، أيام، طيب أيهم أفضل: كامل بالنسبة لـ + +700 +01:13:05,660 --> 01:13:12,980 +X ولا بالنسبة لـ Y؟ أنفع الشجتين، بس الـ X أسهل كثير + +701 +01:13:12,980 --> 01:13:18,340 +لأن الـ X لسه بيتحول، وتاخد جذر وجثة طويلة، يبقى + +702 +01:13:18,340 --> 01:13:24,790 +أنا لو جئت وقلت الـ area A بدّه يساوي تكامل الـ X + +703 +01:13:24,790 --> 01:13:30,290 +هتتغير من صفر لين؟ لغاية الاثنين، بدي الدالة اللي + +704 +01:13:30,290 --> 01:13:33,970 +فوق، الدالة اللي فوق اللي هو المنحنى اللي عندها ده + +705 +01:13:33,970 --> 01:13:38,850 +Y يساوي ناقص X تربيع زي تربيع، هذه الدالة اللي فوق + +706 +01:13:38,850 --> 01:13:45,430 +والـ X تربيع هي من الدالة اللي تحت، يبقى لناقص X + +707 +01:13:45,430 --> 01:13:53,640 +تربيع زائد أربعة X، هذه كلها ناقص الـ X تربيع اللي هي + +708 +01:13:53,640 --> 01:13:58,300 +الدالة الثانية، كلها بالنسبة لمين؟ بالنسبة إلى dX + +709 +01:13:58,300 --> 01:14:04,560 +يبقى هذا الكلام بيساوي تكامل من صفر لـ اثنين للـ أربعة + +710 +01:14:04,560 --> 01:14:12,260 +X ناقص اثنين X تربيع، كل هذا الكلام بالنسبة لمين؟ + +711 +01:14:12,260 --> 01:14:19,680 +إلى dX، يبقى هذا بدّه يساوي اللي هو اثنين X تربيع + +712 +01:14:19,680 --> 01:14:27,920 +ناقص اثنينين X تكعيب من صفر لغاية اثنين، يبقى هنا + +713 +01:14:27,920 --> 01:14:36,500 +ثمانية ناقص هنا ثمانية، 16 على ثلاثة ناقص الـ + +714 +01:14:36,500 --> 01:14:41,960 +Zero، يبقى هذا كله على ثلاثة في ثمانية، 24 + +715 +01:14:41,960 --> 01:14:50,600 +من 16 بيظل ثمانية على ثلاثة فقط لا غير، يبقى لما + +716 +01:14:50,600 --> 01:14:55,740 +ترسم صح أو تحدد حدود التكامل صح، باقي الشغل كله + +717 +01:14:55,740 --> 01:14:57,820 +بيصير شغل روتيني أيضًا + +718 +01:15:01,970 --> 01:15:06,430 +أنا بقول لك: الامتحانات اللي بخليها لك بقسمها لك، لكن + +719 +01:15:06,430 --> 01:15:10,970 +الامتحانات اللي بقسمها لك بقسمها لك، إيه نعم؟ لو + +720 +01:15:10,970 --> 01:15:14,850 +طلعت على الامتحانات السابقة، هتلاقي بعض المسائل + +721 +01:15:14,850 --> 01:15:17,970 +اللي على الموضوع هذا، ما رسمينها، ومظللينها مش + +722 +01:15:17,970 --> 01:15:24,230 +هأقول لك هي المساحة اللي بدنا يعني، أيوة، كده؟ الرسم + +723 +01:15:24,230 --> 01:15:26,130 +الثاني، كده؟ + +724 +01:15:31,170 --> 01:15:36,970 +هي رسمة قدامك + +725 +01:15:36,970 --> 01:15:41,490 +رسمة المنحنى الثانية ما أنتشرش اللي سوناه مش هي + +726 +01:15:41,490 --> 01:15:46,630 +المنحنى، روحت أملت وأكمل المربع لغاية ما وصلت لهنا + +727 +01:15:47,440 --> 01:15:51,540 +هذه parabola، بسمعولي لو شيلت الأربعة واثنين بصير Y + +728 +01:15:51,540 --> 01:15:55,880 +تساوي سالب X تربيع، parabola إلى أسفل، بس ممكن + +729 +01:15:55,880 --> 01:15:59,120 +تسمعوليها زاحة لليمين وزاحة لأعلى مشان الـ vertex + +730 +01:15:59,120 --> 01:16:04,060 +اثنين وأربعة، وبالتالي صلة بسيطة جدًا، طيب الـ هذا + +731 +01:16:04,060 --> 01:16:11,120 +نمر ب من السؤال، كان بدنا نروح لنمر C، نمر C + +732 +01:16:11,120 --> 01:16:16,240 +بقول لي: Y تساوي X تكعيب، and + +733 +01:16:18,190 --> 01:16:24,870 +ثلاثة X تربيعها ناقص Y يساوي أربعة + +734 +01:16:32,700 --> 01:16:37,540 +يبقى بنروح نرسم الرسم اللي عندنا بس قبل أنا أرسمها + +735 +01:16:37,540 --> 01:16:43,240 +ها دي ها ها، بقدر أحطها في الشكل الطبيعي تبعها يبقى + +736 +01:16:43,240 --> 01:16:47,240 +لو جبت الـ Y على اليمين والأربعة شمال بصير Y + +737 +01:16:47,240 --> 01:16:52,920 +يساوي ثلاثة X تربيع وناقص أربعة، أبدأ برضه هذه الـ + +738 +01:16:52,920 --> 01:16:56,400 +parabola، شيل الأربعة وشيل الثلاثة، بصير Y تساوي X + +739 +01:16:56,400 --> 01:17:01,850 +تربيع، ثلاثة بتتجرّب على محور Y، سالب أربعة، شفت الأصل + +740 +01:17:01,850 --> 01:17:06,530 +بمقدار أربعة، إذا لو جئت رسمت الرسم اللي عندنا + +741 +01:17:06,530 --> 01:17:13,510 +الرسم بالشكل هذا، هذا محور X، هذا محور Y، هذه نقطة + +742 +01:17:13,510 --> 01:17:18,870 +الأصل اللي هي Zero، طلع لي كويسة، النقطة الأولى Y + +743 +01:17:18,870 --> 01:17:23,690 +تساوي X تكعيب، مشهور عند المنحنى ومعروف، يبقى المنحنى + +744 +01:17:23,690 --> 01:17:25,590 +بدّه يجيك X + +745 +01:17:28,980 --> 01:17:38,190 +يبقى هذا المنحنى Y تساوي X تكعيب، بتجي للمنحنى لأن Y + +746 +01:17:38,190 --> 01:17:42,750 +تساوي X تربيع، الـ parabola إلى أعلى ثلاثة يبقى + +747 +01:17:42,750 --> 01:17:47,690 +بتجرب على محور Y سالب أربعة، يبقى Shift إلى أسفل + +748 +01:17:47,690 --> 01:17:52,410 +بمقدار سالب أربعة، إذا لو رحت قلت: هذه اللي هي + +749 +01:17:52,410 --> 01:17:57,630 +main سالب أربعة، والـ parabola بتجي أرسمها يبقى الـ + +750 +01:17:57,630 --> 01:18:01,830 +parabola بتاخذ الشكل التالي اللي عندنا هيك، وبتجي + +751 +01:18:01,830 --> 01:18:03,110 +تاخذ الشكل هذا + +752 +01:18:06,190 --> 01:18:11,150 +المساحة الموجودة بين المنحنيين هي المساحة اللي + +753 +01:18:11,150 --> 01:18:11,790 +عندنا هنا + +754 +01:18:19,960 --> 01:18:27,140 +واضح أن هناك منحنى أعلى ومنحنى أسفل، هذا المنحنى + +755 +01:18:27,140 --> 01:18:34,200 +الأسفل يساوي ثلاثة X تربيع ناقص أربعة، ومنحنى + +756 +01:18:34,200 --> 01:18:39,620 +الأعلى Y تساوي X تكعيب، إذا هذا تكامل بالنسبة لـ X + +757 +01:18:39,620 --> 01:18:46,560 +إذا بيلزمني أعرف قدر أقل قيمة لـ X هنا وقدر أكبر + +758 +01:18:46,560 --> 01:18:54,060 +قيمة لـ X هنا، بتروح أحل المعادلتين مع بعض بالنسبة + +759 +01:18:54,060 --> 01:19:00,200 +لمين؟ إلى X، يبقى بالدرجة أقول X تكعيب يساوي ثلاثة X + +760 +01:19:00,200 --> 01:19:08,760 +تربيع ناقص أربعة، أو X تكعيب ناقص ثلاثة X، اص أربعة + +761 +01:19:08,760 --> 01:19:17,160 +زائد أربعة يساوي Zero، X تربيع زائد أربعة يساوي + +762 +01:19:17,160 --> 01:19:24,370 +Zero، نقدر نحللها هيك؟ نسأل الموضوع، اه، يبقى هذه + +763 +01:19:24,370 --> 01:19:32,870 +معادلة من الدرجة الثالثة، يبقى شغل مخك مين + +764 +01:19:32,870 --> 01:19:39,310 +قال لك: not exist يا شاطر أنت؟ هو اللي وجهك + +801 +01:23:22,280 --> 01:23:30,180 +ترابيع ناقص x ناقص اثنين كله بده يساوي قداش بده + +802 +01:23:30,180 --> 01:23:36,120 +يساوي زيرو الحين هذه بقدر أحللها يبقى هذه x ناقص + +803 +01:23:36,120 --> 01:23:46,240 +اثنين وهذا قوس وهذا قوس ويساوي زيرو x1 2 ناقص زائد + +804 +01:23:46,240 --> 01:23:52,480 +صار القوس هذا هو نفس القوس هذا يبقى صار عندي x ناقص + +805 +01:23:52,480 --> 01:23:58,500 +2 لكل تربيع في x زائد واحد بده يساوي zero هذا + +806 +01:23:58,500 --> 01:24:03,500 +معناه أن x بده يساوي 2 والـx بده يساوي سالب واحد + +807 +01:24:03,500 --> 01:24:08,660 +إذا النقطة هذه سالب واحد والنقطة هذه 2 يعني + +808 +01:24:08,660 --> 01:24:13,140 +النقطة دي لما أقول X ناقص اثنين لكل تربيع يعني طلعت + +809 +01:24:13,140 --> 01:24:19,740 +نفس النقطة بس إيه مكررة مرتين تمام يبقى معنا هذا + +810 +01:24:19,740 --> 01:24:24,960 +الكلام بدي أقوله الـarea إيه بده يساوي تكامل من عند + +811 +01:24:24,960 --> 01:24:30,640 +السالب واحد لغاية الاثنين الدالة اللي فوق هي من X + +812 +01:24:30,640 --> 01:24:39,070 +تكعيب ناقص الدالة التي تحتها ثلاثه X تربيع ناقص أربعة Y + +813 +01:24:39,070 --> 01:24:45,650 +تساوي ثلاثة X تربيع ناقص أربعة ثلاثة X تربيع ناقص + +814 +01:24:45,650 --> 01:24:51,370 +أربعة كله بالنسبة لمين إلى DX يبقى هذا الكلام + +815 +01:24:51,370 --> 01:24:56,630 +يساوي تكامل من سالب واحد لاثنين للـ X تكعيب ناقص + +816 +01:24:56,630 --> 01:25:03,510 +ثلاثة X تربيع زائد أربعة كله بالنسبة إلى DX + +817 +01:25:03,510 --> 01:25:10,170 +كامل يبقى X أس أربعة على أربعة ناقص x تكعيب على 3 + +818 +01:25:10,170 --> 01:25:19,560 +مع 3 زائد 4x كله من ناقص 1 لغاية 2 نعوض بالقيمة + +819 +01:25:19,560 --> 01:25:27,100 +اللي فوق ناقص القيمة اللي تحت يبقى يساوي 16 على 4 + +820 +01:25:27,100 --> 01:25:37,240 +ناقص ثمانية زائد ثمانية ناقص قوس هنا بصير ربع وهنا + +821 +01:25:37,240 --> 01:25:45,200 +زائد واحد وهنا ناقص أربعة هذه ستصبح ثمانية وثمانية + +822 +01:25:45,200 --> 01:25:52,320 +مع السلامة هذه ستصبح أربعة ناقص ربع ناقص واحد زائد + +823 +01:25:52,320 --> 01:25:57,780 +أربعة أربعة وأربعة ثمانية ثمانية بدنا نشيل منها + +824 +01:25:57,780 --> 01:26:06,880 +واحد بضل سبعه ناقص ربع يعني ستة وثلاثة أرباع يعني + +825 +01:26:06,880 --> 01:26:11,460 +سبعة وعشرين على قداش على أربعة + +826 +01:26:13,950 --> 01:26:20,170 +المثال الأخير بيقول + +827 +01:26:20,170 --> 01:26:29,970 +example 3 find the area + +828 +01:26:29,970 --> 01:26:33,130 +enclosed + +829 +01:26:33,130 --> 01:26:38,010 +by + +830 +01:26:38,010 --> 01:26:41,150 +the + +831 +01:26:41,150 --> 01:26:42,810 +y-axis + +832 +01:26:46,800 --> 01:26:56,180 +والـcurve هو المنحنى x يساوي y ناقص واحد لكل + +833 +01:26:56,180 --> 01:27:07,580 +تربيع و الـx يساوي ثلاثة ناقص الـy and الـx يساوي + +834 +01:27:07,580 --> 01:27:20,300 +اثنين جذر الـy as shown in the figure كما هو مبين + +835 +01:27:20,300 --> 01:27:25,600 +بالشكل وراح يرسم لي طبعا هذا سؤال في الكتاب راح + +836 +01:27:25,600 --> 01:27:33,340 +يرسم لي هذا الشكل اللي محصور بين هذه المنحنيات وطلب + +837 +01:27:33,340 --> 01:27:35,600 +مساحة هذا الشكل + +838 +01:28:03,030 --> 01:28:05,110 +السلام عليكم ورحمة الله + +839 +01:28:19,970 --> 01:28:24,190 +الله أكبر الله أكبر الله أكبر + +840 +01:28:44,230 --> 01:28:49,510 +قال لي أوجد لي مساحة المنطقة المغلقة بمحور Y يبقى + +841 +01:28:49,510 --> 01:28:56,030 +محور Y أحد المنحنيات X يساوي Y ناقص واحد لكل تربيع + +842 +01:28:56,030 --> 01:29:01,930 +و X يساوي ثلاثة ناقص Y و X يساوي اثنين جذر الـY + +843 +01:29:01,930 --> 01:29:06,990 +يبقى المساحة اللي بينهم هي المساحة المظللة اللي + +844 +01:29:06,990 --> 01:29:12,150 +عندنا هذه وقال لي هنا النقطة بقى لدي الواحد تمام + +845 +01:29:13,460 --> 01:29:17,920 +طبعا الكتاب حط السؤال ورسم لك الرسمة وقال لك هات لي + +846 +01:29:17,920 --> 01:29:23,580 +المساحة اللي عندنا بقول لك بسيطة منحنى لو جيت قلت + +847 +01:29:23,580 --> 01:29:27,380 +اللي تحت واللي فوق صار اللي فوق منحنيين واللي + +848 +01:29:27,380 --> 01:29:31,620 +تحت منحنى واحد صحيح إذا ما ظبطتش لو جيت اللي + +849 +01:29:31,620 --> 01:29:36,280 +على اليمين واللي على اليسار بيصيروا اثنين على + +850 +01:29:36,280 --> 01:29:39,960 +اليمين وخط على اليسار وبعدين واحد فباجي من + +851 +01:29:39,960 --> 01:29:46,520 +الخربطة هذه لكن لو جيت قلت بتهيئ الجسم هذا المنحنى + +852 +01:29:46,520 --> 01:29:52,460 +إلى منطقتين بالشكل اللي عندنا هذا يبقى هاي المنطقة + +853 +01:29:52,460 --> 01:29:56,380 +و + +854 +01:29:56,380 --> 01:30:01,340 +المنطقة الثانية عندما أخذ هذه المنطقة وأخذ هذه + +855 +01:30:01,340 --> 01:30:04,220 +المنطقة وأخذ هذه المنطقة وأخذ هذه المنطقة وأخذ + +856 +01:30:04,220 --> 01:30:05,400 +هذه المنطقة وأخذ هذه المنطقة وأخذ هذه المنطقة و + +857 +01:30:05,400 --> 01:30:07,160 +أخذ هذه المنطقة وأخذ هذه المنطقة وأخذ هذه + +858 +01:30:07,160 --> 01:30:12,280 +المنطقة وأخذ هذه المنطقة وأخذ هذه المنطقة وأخذ + +859 +01:30:12,280 --> 01:30:18,900 +هذه المنطقة وأخذ هذه المنطقة وأخذ هذه المنطقة + +860 +01:30:18,950 --> 01:30:24,010 +يبقى أنا عندي هنا x يساوي y ناقص واحد لكل تربيع + +861 +01:30:24,010 --> 01:30:30,150 +وعندي x يساوي ثلاثة ناقص y يبقى بقدر أجيب قيمة y + +862 +01:30:30,150 --> 01:30:36,530 +بس أنا لازم لي قيمة x وليس قيمة y إذا + +863 +01:30:36,530 --> 01:30:43,810 +أنا هنا بقدر أقول المنحنى الأول X يساوي Y ناقص + +864 +01:30:43,810 --> 01:30:49,930 +واحد لكل تربيع والمنحنى الثاني X يساوي ثلاثة ناقص + +865 +01:30:49,930 --> 01:30:54,250 +Y حليت بالنسبة لـX في الأول وحليت بالنسبة لـY في + +866 +01:30:54,250 --> 01:30:58,990 +الأول لا تفرق عندنا هذه والله هذه السيان يبقى احنا + +867 +01:30:58,990 --> 01:31:02,870 +لو جينا قلنا بدي أخليها زي ما هي مثلا يبقى الـY + +868 +01:31:02,870 --> 01:31:10,050 +ناقص واحد لكل تربيع تساوي ثلاثة ناقص Y أو بمعنى آخر + +869 +01:31:10,050 --> 01:31:17,130 +Y تربيع ناقص اثنين Y زائد واحد يساوي ثلاثة ناقص Y + +870 +01:31:17,130 --> 01:31:23,630 +ممكن نعملها معادلة صفرية بصير Y تربيع هات Y هنا + +871 +01:31:23,630 --> 01:31:30,270 +بصير موجبة بصير ناقص Y هات هات هنا بصير سالب ثلاثة + +872 +01:31:30,270 --> 01:31:34,810 +مع واحد بيبقى سالب اثنين يساوي زيرو هذه لو راحت + +873 +01:31:34,810 --> 01:31:41,950 +حليتها كقوسين يساوي زيرو يبقى هنا Y هنا Y واحد + +874 +01:31:41,950 --> 01:31:47,610 +اثنين سالب اللي هو اثنين Y وموجبة بيبقى سالب Y + +875 +01:31:47,610 --> 01:31:54,140 +مظبوط إذا أنا عندي Y سالب واحد و Y اثنين يبقى هنا y + +876 +01:31:54,140 --> 01:32:01,240 +يساوي سالب واحد و y تساوي اثنين يبقى أنا أنا حليت + +877 +01:32:01,240 --> 01:32:08,020 +الاثنين هدول مع بعض مرة بدهم يتقاطع عند y تساوي + +878 +01:32:08,020 --> 01:32:13,900 +سالب واحد ومرة عند y تساوي من الاثنين إذا للإحداث + +879 +01:32:13,900 --> 01:32:19,300 +النقطة هذه بيكون قداش لاثنين هذا المنحنى لو كملته + +880 +01:32:19,300 --> 01:32:24,380 +أجه هيتقاطع مع مين؟ مع الخط عند نقطة Y تساوي سالب + +881 +01:32:24,380 --> 01:32:27,800 +واحد إذا ما لي علاقة فيه يبقى أنا إلي علاقة في الـ + +882 +01:32:27,800 --> 01:32:34,270 +Y تساوي مين؟ اثنين لو جيت أخذت Y تساوي 2 وعوضت بها + +883 +01:32:34,270 --> 01:32:41,110 +في أي من المعادلتين يبقى هذا بيعطيك أن X بيساوي + +884 +01:32:41,110 --> 01:32:46,210 +ثلاثة ناقص اثنين اللي هو قداش واحد إذا إحداث النقطة + +885 +01:32:46,210 --> 01:32:52,510 +هذه هو واحد واثنين يبقى X عند هنا بقداش تساوي + +886 +01:32:52,510 --> 01:32:56,990 +واحد بالدالي النقطة اللي عندنا هذه كمان بدي أعرف + +887 +01:32:56,990 --> 01:32:59,390 +قداش القيمة بتاعتها + +888 +01:33:02,590 --> 01:33:06,690 +يبقى بدي أعرف قداش لحظاتي معناته بدي أحل معادلة + +889 +01:33:06,690 --> 01:33:11,290 +المنحنى هذا مع مين مع معادلة المنحنى اللي عندنا + +890 +01:33:11,290 --> 01:33:21,490 +هذا هذا المنحنى اللي همين X بده يساوي ثلاثة ناقص Y + +891 +01:33:21,490 --> 01:33:31,470 +and الـX بده يساوي اثنين جذر الـY بقدر أقول هذه why + +892 +01:33:31,470 --> 01:33:39,720 +تساوي؟ ثلاثة ناقص X ثلاثة ناقص X and هذه لو جيت + +893 +01:33:39,720 --> 01:33:47,820 +ربعت الطرفين بصير Y يساوي ربع الـX يبقى Y تساوي + +894 +01:33:47,820 --> 01:33:55,800 +ربع الـX تربيع يبقى لو حليت الاثنين مع بعض ربع X + +895 +01:33:55,800 --> 01:34:02,930 +تربيع بدها تساوي ثلاثة ناقص X أضرب كله في أربعة + +896 +01:34:02,930 --> 01:34:10,670 +بيصير عندك مين X تربيع يساوي اثنا عشر ناقص أربعة X + +897 +01:34:10,670 --> 01:34:19,070 +يبقى هذا الكلام بيصير X تربيع زائد أربعة X ناقص + +898 +01:34:19,070 --> 01:34:25,440 +اثنا عشر يساوي كده؟ يساوي Zero نحلل هذا الكلام كقوسين + +899 +01:34:25,440 --> 01:34:32,680 +يساوي Zero يبقى هنا X هنا X هذه ستة في اثنين ستة + +900 +01:34:32,680 --> 01:34:38,020 +في اثنين هذه زائد وهذه ناقص زائد ستة X وناقص اثنين + +901 +01:34:38,020 --> 01:34:42,900 +X يبقى زائد أربعة X يبقى بناء عليه الـX بده + +902 +01:34:42,900 --> 01:34:50,900 +يساوي اثنين والـX بده يساوي سالب ستة يبقى هذا + +903 +01:34:50,900 --> 01:34:55,380 +الكلام لو كملنا المنحنى لو أجي معه هذا هيتقطع + +904 +01:34:55,380 --> 01:34:58,900 +عند السالب ستة ما لي علاقة فيها إيه اللي علاقة في + +905 +01:34:58,900 --> 01:35:05,180 +قداش؟ فيه للاثنين يبقى بصير التكامل عندنا بهذا + +906 +01:35:05,180 --> 01:35:12,070 +الشكل يبقى الآن حددت حدود التكامل قسمت المنطقة إلى + +907 +01:35:12,070 --> 01:35:18,850 +منطقتين إذا بقدر أحسب قداش قيمة هذه المساحة + +908 +01:35:18,850 --> 01:35:25,110 +المحصورة بين المنحنيين فبروح بقول له الـA to Z + +909 +01:35:26,800 --> 01:35:31,780 +تكامل من عند الـzero لغاية الواحد من الـzero + +910 +01:35:31,780 --> 01:35:39,200 +لغاية الواحد الدالة اللي فوق آه هذه مرتبناش هذه + +911 +01:35:39,200 --> 01:35:48,580 +بدها تصير جذر الـX بده يساوي Y ناقص واحد طبعا هأحمل + +912 +01:35:48,580 --> 01:35:49,880 +الـY السالبة + +913 +01:35:54,960 --> 01:36:04,070 +يبقى هذا معناه أن Y تساوي جذر الـX زائد واحديبقى + +914 +01:36:04,070 --> 01:36:10,530 +الدالة اللي فوق هذه Y تساوي جذر الـX زائد واحد هي + +915 +01:36:10,530 --> 01:36:17,410 +الدالة اللي فوق يبقى جذر الـX زائد واحد ناقص + +916 +01:36:17,410 --> 01:36:24,410 +الدالة اللي تحت هذه طلعناها كده؟ ربع X تربيع يبقى + +917 +01:36:24,410 --> 01:36:32,130 +ناقص ربع X تربيع كله بالنسبة إلى DX زائد تكامل + +918 +01:36:32,130 --> 01:36:37,440 +المنطقة الثانية من واحد لاثنين الدالة اللي فوق + +919 +01:36:37,440 --> 01:36:45,180 +هذه يقول أنه يساوي ثلاثة ناقص X ثلاثة ناقص X ناقص + +920 +01:36:45,180 --> 01:36:52,180 +اللي هو ربع X تربيع يبقى ناقص ربع X تربيع كله + +921 +01:36:52,180 --> 01:36:58,300 +بالنسبة إلى DX يبقى + +922 +01:36:58,300 --> 01:37:03,660 +هذه الـarea إيه تساوي من درجة التكامل الأول يبقى + +923 +01:37:03,660 --> 01:37:05,420 +هذا طول تان + +924 +01:37:08,270 --> 01:37:16,990 +زي الاكس ناقص x تكعيب على قداش على الاثنا عشر + +925 +01:37:16,990 --> 01:37:22,550 +الحكاية دي من عند الـzero لغاية الواحد نجي للتكامل + +926 +01:37:22,550 --> 01:37:30,680 +اللي بعده ثلاثة x ناقص x تربيع على اثنين ناقص x + +927 +01:37:30,680 --> 01:37:37,740 +تكعيب على الاثنا عشر كل هذا الكلام من الواحد لغاية + +928 +01:37:37,740 --> 01:37:45,220 +اثنين يبقى هذا بده يساوي ثلاثة على اثنين زائد واحد ناقص واحد + +929 +01:37:45,220 --> 01:37:49,800 +على الاثنا عشر والـzero الباقي كله بيطير بـzero نجي + +930 +01:37:49,800 --> 01:37:56,940 +لبعدها زائد اثنين في ثلاثة بستة وهنا ناقص اثنين وهنا + +931 +01:37:56,940 --> 01:38:05,340 +هنا ناقص ثمانية على الاثنا عشر فيها اثنين على ثلاثة + +932 +01:38:13,030 --> 01:38:18,050 +خلصنا الـterm اللي فوق ناقص الـterm اللي تحت + +933 +01:38:18,050 --> 01:38:27,050 +ثلاثة ناقص نصف ناقص واحد على الاثنا عشر هذا الكلام + +934 +01:38:27,050 --> 01:38:28,930 +يساوي كل term + +935 +01:38:34,510 --> 01:38:41,450 +هذه اثنين على ثلاثة مع سالب اثنين على ثلاثة وعندك هنا + +936 +01:38:41,450 --> 01:38:50,690 +سبعة وسالب اثنين بضل خمسة خمسة ناقص واحد على + +937 +01:38:50,690 --> 01:38:59,310 +الاثنا عشر مع يا راجل ناقص ثلاثة زائد نصف زائد واحد + +938 +01:38:59,310 --> 01:39:02,950 +على الاثنا عشر ناقص واحد على اثنا عشر وزائد واحد على + +939 +01:39:02,950 --> 01:39:09,490 +اثنا عشر بيروح بيضل عندنا قداش اثنين ونصف يبقى خمسة + +940 +01:39:09,490 --> 01:39:17,460 +على اثنين مقدار هذه المساحة تمام؟ طيب لحد هنا + +941 +01:39:17,460 --> 01:39:22,040 +انتهى الـsection اللي هو خمسة ستة يليكم أرقام + +942 +01:39:22,040 --> 01:39:31,000 +المسائل يبقى exercises خمسة ستة المسائل التالية + +943 +01:39:31,000 --> 01:39:35,780 +واحد لتسعة + +944 +01:39:35,780 --> 01:39:44,380 +وستين يعني واحد لتسعة وستين والأخرى من ثلاثة وسبعين + +945 +01:39:44,380 --> 01:39:50,560 +لغاية ثمانية وسبعين وكذلك + +946 +01:39:50,560 --> 01:39:53,320 +من ثمانين لتسعين diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/gPP3rP0CXnk_postprocess.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/gPP3rP0CXnk_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..06f6c4205e1eb5cf9af16e1ee14bf2c645ca756a --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/gPP3rP0CXnk_postprocess.srt @@ -0,0 +1,3784 @@ +1 +00:00:20,920 --> 00:00:25,520 +بسم الله الرحمن الرحيم عودة على بدء المرة اللي + +2 +00:00:25,520 --> 00:00:30,660 +فاتت بدأنا في التكاملات المحدودة كيف بدنا نكامل + +3 +00:00:30,660 --> 00:00:36,780 +تكاملات محدودة باستخدام التعويض وبتغيير حدود + +4 +00:00:36,780 --> 00:00:41,600 +التكامل طبقا للتعويض اللي بيعطيها وعطينا على ذلك + +5 +00:00:41,600 --> 00:00:46,920 +مجموعة من الأمثلة وانان بنكمل هذه الأمثلةأخدنا ستة + +6 +00:00:46,920 --> 00:00:51,700 +أمثلة وهذا هو المثال رقم سبعة بقول يتكامل من الصفر + +7 +00:00:51,700 --> 00:00:56,480 +اللي هيتبعي على أربع لتان تكيب سكتر بيه ال X DX + +8 +00:00:56,480 --> 00:01:02,100 +طبعا مباشرة هيك بقدرش لكن بقدر أعمل تعويضة محددة + +9 +00:01:02,100 --> 00:01:06,900 +باجي بطلع في المثل اللي عندى و التان كده تفاضلها؟ + +10 +00:01:07,400 --> 00:01:12,500 +سكتر بيع موجودة إذا اللي بدي أشيله و أغيره بدي + +11 +00:01:12,500 --> 00:01:18,300 +أشيل التان و أحط بدلها دل جديدة إذا لو حطيت ال T + +12 +00:01:18,300 --> 00:01:25,400 +تساوي تان ال X يبقى ال DT بدي أساوي سكتر بيع ال X + +13 +00:01:25,400 --> 00:01:31,500 +DX إذا ممكن أشيل سكتر بيع ال X DX هذه وقت بدلها DT + +14 +00:01:31,880 --> 00:01:40,260 +يبقى آلة المسألة الى تكامل ل T تكعيب DT بقيت حدود + +15 +00:01:40,260 --> 00:01:44,460 +التكامل بدي أغير حدود التكامل صفقة لهذه التعويضة + +16 +00:01:44,460 --> 00:01:49,110 +الجديدةفبجي بقول لما تبقى ال X باي على أربعة ضل + +17 +00:01:49,110 --> 00:01:55,590 +الخمسة واربعين يبقى ال T هنا تساوي واحد ضل ال zero + +18 +00:01:55,590 --> 00:02:02,510 +ب zero يبقى T تساوي zero إذا غيرنا حدود التكمل طبق + +19 +00:02:02,510 --> 00:02:07,750 +لمين؟ طبق التعويضة الجديدة اللي حاطناها يبقى هذا + +20 +00:02:07,750 --> 00:02:13,150 +النتيجة تساوي T أس أربعة على أربعة والكلام من zero + +21 +00:02:13,150 --> 00:02:19,080 +لغاية 13لغاية واحد يبقى هذا الكلام يساوي ربع في + +22 +00:02:19,080 --> 00:02:24,580 +واحد أس أربع ناقص Zero أس أربع اللي هو Zero واحد + +23 +00:02:24,580 --> 00:02:32,200 +أس أربع باربع يبقى النتيجة تساوي ربع التكامل اللي + +24 +00:02:32,200 --> 00:02:40,490 +بعده تكامل رقم تمانيةيبقى integration من سالب واحد + +25 +00:02:40,490 --> 00:02:42,370 +لغاية سالب نص + +26 +00:03:00,500 --> 00:03:04,700 +طيب، بعدي بتطلع في المثل اللي عندي، شو اللي وضعه + +27 +00:03:04,700 --> 00:03:09,260 +غير طبيعي في المثل أو اللي مصعب شكلها؟ الزاوية + +28 +00:03:09,260 --> 00:03:13,840 +تبعت الصين، يبقى الزاوية هي اللي مصعبة المثل، نهيك + +29 +00:03:13,840 --> 00:03:18,340 +على انه مشتقت الزاوية بتعطينا مين؟ ال term اللي + +30 +00:03:18,340 --> 00:03:24,750 +برايبقى بدي اكتب المثلة بشكل لطيف أو سهل جدا يبقى + +31 +00:03:24,750 --> 00:03:31,230 +بدي اشيل كل هذا و بدي احط ال X يسوى واحد زائد واحد + +32 +00:03:31,230 --> 00:03:38,810 +على T لو جينا اشتقناها يبقى DX بدي اساوي سالب واحد + +33 +00:03:38,810 --> 00:03:47,180 +على T تربية DTأو بقدر أقول سالب DX بدي أساوي T + +34 +00:03:47,180 --> 00:03:54,280 +السالب اتنين DT إذا بقدر T السالب اتنين هذه مع DT + +35 +00:03:54,280 --> 00:04:00,400 +أشيلها و أكتف بدل جديد سالب DX يبقى هاي السالب بدي + +36 +00:04:00,400 --> 00:04:07,120 +أخده برا و هاي تكامل و هادي ال sign تربيع ال X كله + +37 +00:04:07,120 --> 00:04:13,580 +في DXبقيت حدود التكامل لما تبقى ال X يساوي سالب T + +38 +00:04:13,580 --> 00:04:19,260 +تساوي سالب نص يبقى سالب نص بصير هذي فوق باتنين + +39 +00:04:19,260 --> 00:04:24,360 +اتنين بالسالب يبقى واحد سالب اتنين مضل قداش سالب + +40 +00:04:24,360 --> 00:04:29,300 +واحد يبقى هذي بيصير سالب واحد و لما تبقى T بسالب + +41 +00:04:29,300 --> 00:04:34,100 +واحد بصير ال term هذا كله بسالب واحد يبقى كله بصير + +42 +00:04:34,100 --> 00:04:40,130 +Zeroيبقى من zero ل سالب واحد ل main لل sign تربيع + +43 +00:04:40,130 --> 00:04:44,630 +ال X DX واضح ان ال index الكبير هو اللي تحته + +44 +00:04:44,630 --> 00:04:49,170 +والصغير هو ال fourth يبقى بنجلب حدود التكامل و + +45 +00:04:49,170 --> 00:04:53,510 +بنضيع الإشارة اللي عندنا طبقا لأول خاصية من خاصة + +46 +00:04:53,510 --> 00:04:59,250 +تكامل المحدود يبقى هذا الكلام بده يساوي تكامل من + +47 +00:04:59,250 --> 00:05:04,630 +سالب واحد لغاية zero ل sign تربيع ال X DX + +48 +00:05:11,900 --> 00:05:17,720 +يبقى هذا الكلام بده يساوي تكامل من سالب واحد لغاية + +49 +00:05:17,720 --> 00:05:24,590 +Zero لنص في واحد ناقص cosine اتنين ال X DXمن + +50 +00:05:24,590 --> 00:05:28,410 +المستطابقات تبعات حساب المثلثات sin تربيه ال X هو + +51 +00:05:28,410 --> 00:05:34,390 +نص في واحد ناقص cosine اتنين X يبقى النص هذا بدي + +52 +00:05:34,390 --> 00:05:40,870 +يظل برا و عندك هذا جزء تكامل الواحد ب X وتكامل ال + +53 +00:05:40,870 --> 00:05:46,690 +cosine بsin اتنين X على اتنين والكلام من سالب واحد + +54 +00:05:46,690 --> 00:05:53,240 +لغاية ال zeroيبقى يا نص خلّيك برا و بدنا نبدأ نعوض + +55 +00:05:53,240 --> 00:06:00,140 +بحدود التكامل يبقى Zero و Sin Zero Zero كذلك يبقى + +56 +00:06:00,140 --> 00:06:06,210 +هاي Zero ناقص Zero ناقصبدا ابدأ اعوض بالقيمة اللى + +57 +00:06:06,210 --> 00:06:11,670 +تحتى يبقى ال X بدي اشيله لأو اكتبه لجداش ناقص واحد + +58 +00:06:11,670 --> 00:06:16,430 +وهي الناقص اللى عندنا بدي اشيل ال X و احطه مكان + +59 +00:06:16,430 --> 00:06:23,750 +جداش سالب واحد يبقى بصير سالي باتنين يبقى ال sign + +60 +00:06:23,750 --> 00:06:30,610 +لسالي باتنين على اتنين بالشكل اللى عندنا هذا تمام + +61 +00:06:31,240 --> 00:06:36,140 +يبقى هذا الكلام بده يساوي هذا النص اللي برا وده + +62 +00:06:36,140 --> 00:06:41,720 +دخل السلب اللي عندها ده يوم بصير عندي واحد ناقص + +63 +00:06:41,720 --> 00:06:47,540 +sign اتنين على اتنين بالشكل اللي عندنا طبعا ال + +64 +00:06:47,540 --> 00:06:53,480 +sign odd السلب بطلع برا بصير موجب في سلب مضروب برا + +65 +00:06:53,480 --> 00:06:59,100 +يبقى بصير سلب يبقى واحد ناقص sign اتنين على اتنين + +66 +00:06:59,270 --> 00:07:03,270 +انت هنا مثلا بدك تكتب لي نص ناقص ربع sign اتنين + +67 +00:07:03,270 --> 00:07:09,750 +سيانة بتفرجش يبقى هذه لو قلت نص ناقص ربع sign + +68 +00:07:09,750 --> 00:07:18,000 +اتنين هذه هي نتيجة من التكاملطيب، الآن في عندنا + +69 +00:07:18,000 --> 00:07:24,100 +كمان مثال آخر غير هذه الأنواع من الأمثلة و هذا + +70 +00:07:24,100 --> 00:07:29,200 +المثال جئنا به في إحدى الامتحانات السابقة يبقى + +71 +00:07:29,200 --> 00:07:35,000 +كمان example بيقول + +72 +00:07:35,000 --> 00:07:39,580 +use the integral استخدم التكامل + +73 +00:07:42,290 --> 00:07:50,670 +تكامل من واحد لغاية اتنينللـ F of Z DZ بده يساوي + +74 +00:07:50,670 --> 00:07:56,650 +تلاتة to find + +75 +00:07:56,650 --> 00:08:05,110 +the value of مشان تحسبلي قداش قيمة تكامل من نص + +76 +00:08:05,110 --> 00:08:12,750 +لغاية واحد لواحد على X تربية F of واحد على X نقس + +77 +00:08:20,110 --> 00:08:26,750 +يبقى شكل هذا المثال يختلف عن شكل سابقاته من الأمثل + +78 +00:08:26,750 --> 00:08:31,530 +قبل أن نتكامل و نتكامل على طول الخط هذا بيقول + +79 +00:08:31,530 --> 00:08:37,250 +استخدم هذا التكامل يبقى هذا معطيان للحصول على قيمة + +80 +00:08:37,250 --> 00:08:41,450 +التكامل هذاباجي باطلع في التكامل اللي عندي وهذا + +81 +00:08:41,450 --> 00:08:47,090 +بختلفه كليا عن بعض، لكن هذا مقطع إذا ماليش علاقة + +82 +00:08:47,090 --> 00:08:51,550 +فيه لما بلزمني بستخدمه، بلزمنيش بستخدموش، إذا + +83 +00:08:51,550 --> 00:08:56,590 +مشكلتنا مع مين؟ مع هذا التكاملمشان اشتغل هذا + +84 +00:08:56,590 --> 00:09:01,290 +التكامل في شغل غير طبيعى، الغير طبيعى واحد على اكس + +85 +00:09:01,290 --> 00:09:04,150 +طبيعى ولا واحد على اكس؟ واحد على اكس، واحد على + +86 +00:09:04,150 --> 00:09:04,850 +اكس، واحد على اكس، واحد على اكس، واحد على اكس، + +87 +00:09:04,850 --> 00:09:04,870 +واحد على اكس، واحد على اكس، واحد على اكس، واحد على + +88 +00:09:04,870 --> 00:09:05,230 +اكس، واحد على اكس، واحد على اكس، واحد على اكس، + +89 +00:09:05,230 --> 00:09:08,210 +واحد على اكس، واحد على اكس، واحد على اكس، واحد على + +90 +00:09:08,210 --> 00:09:08,670 +اكس، واحد على اكس، واحد على اكس، واحد على اكس، + +91 +00:09:08,670 --> 00:09:12,390 +واحد على اكس، واحد على اكس، واحد على اكس، واحد على + +92 +00:09:12,390 --> 00:09:21,100 +اكس، واحد على اكس، واحد على اكس،لو مثلا حطيت هنا Z + +93 +00:09:21,100 --> 00:09:28,700 +تساوي واحد على X أو T أو W أو اللي بدك هيه يبقى + +94 +00:09:28,700 --> 00:09:34,000 +بدنا نيجي نشتقه يبقى DZ يساوي سالب واحد على X + +95 +00:09:34,000 --> 00:09:40,270 +تربيه دي1 على X تربية موجودة عندى بس سلب ماعنديش + +96 +00:09:40,270 --> 00:09:46,430 +يبقى بضرب الطرفين بإشارة سلب يبقى بصير عندى سلب DZ + +97 +00:09:46,430 --> 00:09:53,230 +يسوى 1 على X تربية DX إذا ال 1 على X تربية هذه + +98 +00:09:53,230 --> 00:09:58,250 +كلها مع ال DX كلها تبعت المسألة بقدر أشيلها و أكتب + +99 +00:09:58,250 --> 00:10:04,950 +بدالها سلب DZيبقى صارت مسألة تكامل من نص لغاية + +100 +00:10:04,950 --> 00:10:11,050 +واحد للواحد على اكس تربيع لل F of واحد على اكس DX + +101 +00:10:11,050 --> 00:10:20,030 +يسوى تكامل F of Z تمام واحد على اكس تربيع DX بدأت + +102 +00:10:20,030 --> 00:10:26,550 +بهذه السانب برا وهذه يمين DX يبقى صار شكل المثل + +103 +00:10:26,550 --> 00:10:30,110 +اللي عنده هناك اللي هو الشكل هذا بالشكل الجديد الا + +104 +00:10:30,110 --> 00:10:35,570 +انهلكن بناروح نغير حدود التكامل طبقا للتعويض اللي + +105 +00:10:35,570 --> 00:10:42,450 +احنا حاطينا فباجي بقول لو كانت ال X بواحد يبقى Z + +106 +00:10:42,450 --> 00:10:50,090 +بواحد طب لو كانت ال X باتنين بصير واحد على نص + +107 +00:10:50,090 --> 00:10:56,950 +بتنجلبه بصير جداش بالاتنين بالشكل اللي عنها دهطيب + +108 +00:10:56,950 --> 00:11:02,270 +الان صار الرقم الكبير تحت والرقم الصغير فوق في + +109 +00:11:02,270 --> 00:11:06,570 +حدود التكامل من شكل بهذه المواد على limits of + +110 +00:11:06,570 --> 00:11:11,250 +integration وبالتالي طبقا للخاصية الأولى من خاصة + +111 +00:11:11,250 --> 00:11:16,710 +تكامل المحدود بيطير إشارة السالب يبقى هذا بيصير + +112 +00:11:16,710 --> 00:11:27,120 +تكامل من 1 ل2 لل F of Z DZ أظن هذا موضوعخلصنا يبقى + +113 +00:11:27,120 --> 00:11:35,620 +هذا الكلام بده يساوي تلاتة بدون ماتكمل طيب فيه + +114 +00:11:35,620 --> 00:11:41,640 +قاعدة بتسهل لي عملية حساب بعض التكاملات الصعبة + +115 +00:11:41,640 --> 00:11:48,620 +شوية هذه النظرية بتقول لي ما يأتي بتقولت + +116 +00:11:48,620 --> 00:11:53,980 +ال F ب continuous + +117 +00:11:56,460 --> 00:12:08,760 +function دا اللي متصلة on the symmetric interval + +118 +00:12:08,760 --> 00:12:12,740 +اللي + +119 +00:12:12,740 --> 00:12:18,900 +هو سالب a و a النقطة + +120 +00:12:18,900 --> 00:12:22,560 +الأولى if + +121 +00:12:24,020 --> 00:12:36,520 +الـ F is even دالة زوجية then تكامل من سلب A إلى A + +122 +00:12:36,520 --> 00:12:46,520 +لل F of X DX يساوي اتنين تكامل من Zero إلى A لل F + +123 +00:12:46,520 --> 00:13:00,370 +of X DX النقطة الثانيةالـ F is odd then تكامل من + +124 +00:13:00,370 --> 00:13:07,930 +سلب A إلى A لل F of X DX بدي ساوي كده؟ بدي ساوي + +125 +00:13:07,930 --> 00:13:15,630 +Zero Example Find + +126 +00:13:15,630 --> 00:13:22,440 +the value of the following integrals Find thevalue + +127 +00:13:22,440 --> 00:13:30,780 +of the following integrals + +128 +00:13:30,780 --> 00:13:36,360 +التكاملات + +129 +00:13:36,360 --> 00:13:37,300 +التالية + +130 +00:13:55,670 --> 00:14:04,990 +تكامل الأول بدنا تكامل من سالب اتنين إلى اتنين + +131 +00:14:04,990 --> 00:14:22,090 +لتلاتة X على تسعة زائد X ترابيع لكل ترابيع DX نرجع + +132 +00:14:22,090 --> 00:14:27,100 +لهذه النظرية مرة ثانيةو نحاول نفهم هذه النظرية + +133 +00:14:27,100 --> 00:14:33,050 +مشان نشوف كيف بدنا نطبقهابقول افترض الدالة F دالة + +134 +00:14:33,050 --> 00:14:39,490 +متصلة على الفترة المتماثلة ناقص a و a لما اقول + +135 +00:14:39,490 --> 00:14:44,310 +symmetric interval يعني من عند zero على اليمين جد + +136 +00:14:44,310 --> 00:14:48,510 +اللي من عند zero على الشمال بالضبط تماما فلما اقول + +137 +00:14:48,510 --> 00:14:54,490 +من ناقص a إلى a يبقى الصفر يجي وين في منتصف الفترة + +138 +00:14:54,490 --> 00:15:00,550 +يعني الفترة المتماثلةعلى طرفي Zero أو على طرفي + +139 +00:15:00,550 --> 00:15:05,490 +محور Y يبقى هاي المقصود في هذه الكتابة تالك ماقص A + +140 +00:15:05,490 --> 00:15:10,250 +وA يعني الرقم اللي عندنا هنا هو نفس الرقم هذا بس + +141 +00:15:10,250 --> 00:15:14,290 +بإشارة مخالفةيبقى هذه بسميها الـ Symmetric + +142 +00:15:14,290 --> 00:15:20,750 +Interval بقول والله إذا دالة كانت even يبقى تكامل + +143 +00:15:20,750 --> 00:15:26,830 +من ناقص A إلى A لل F of X DX يسوى اتنين التكامل من + +144 +00:15:26,830 --> 00:15:34,150 +Zero إلى A لل F of X DX السؤال لماذا؟ وماذا نستفيد + +145 +00:15:34,150 --> 00:15:40,350 +من ذلك؟ خلي بالك معاكيبقى ليش تكامل من سالب A إلى + +146 +00:15:40,350 --> 00:15:45,750 +A لل F of X DX يسوي 2 تكامل من 0 إلى A لل F of X + +147 +00:15:45,750 --> 00:15:50,190 +DX نرجع بالذاكرة إلى أول chapter درسنا فيه + +148 +00:15:50,190 --> 00:15:55,910 +Calculus A لما أقول even function يعني المنحنى + +149 +00:15:55,910 --> 00:16:02,120 +مالهمو تماثل + +150 +00:16:02,120 --> 00:16:06,160 +بالنسبة لمين؟ لمحور ويمجد النص الرسمى اللى على + +151 +00:16:06,160 --> 00:16:10,240 +اليمين زى نص الرسمى اللى وين يعنى المساحة اللى + +152 +00:16:10,240 --> 00:16:15,500 +حصرها المنحنى على يمين المحورY بينه بين محور X جد + +153 +00:16:15,500 --> 00:16:19,640 +المساحة اللي حصرها المنحنة على الشمال محور Y بينه + +154 +00:16:19,640 --> 00:16:24,300 +بين محور X تمام؟ إذا مدام المساحتين كانوا بعضيا + +155 +00:16:24,300 --> 00:16:29,280 +يكفيني حساب مساحة واحدة بضرب منين في اتنين من هنا + +156 +00:16:29,280 --> 00:16:34,660 +قولنا هذا بدي يسوى اتنين التكامل على نص في الفترة + +157 +00:16:34,660 --> 00:16:38,100 +مدام في تمثل اللي على اليمين زي اللي على الشمال + +158 +00:16:38,100 --> 00:16:43,570 +يبقى المساحة الأولى جد المساحةالثانية يبقى يكفيني + +159 +00:16:43,570 --> 00:16:47,950 +حساب واحدة فيهم بروح مضروبة في مهم في اتنين يبقى + +160 +00:16:47,950 --> 00:16:52,930 +هذا يسوى اتنين تكامل من Zero إلى A لل F of X DX + +161 +00:16:52,930 --> 00:16:57,050 +يبقى هاي أجابنا على السؤال الأول ليش هذا التكامل + +162 +00:16:57,050 --> 00:17:02,730 +يسوى التكامل الثانيسؤال الثاني، قلنا ماذا نستفيد + +163 +00:17:02,730 --> 00:17:07,270 +من ذلك؟ أيهما السل؟ اللي لما تكمل الدل لو تروح + +164 +00:17:07,270 --> 00:17:10,210 +تعوض بالقمة اللي فوق والقمة اللي تحت، والله لما + +165 +00:17:10,210 --> 00:17:14,090 +تبقى اللي تحت زيرو السل ليه؟ لما تبقى زيرو السل + +166 +00:17:14,090 --> 00:17:20,530 +يبقى المقصود هو من ذلك تبسيط عملية إجراء التكامل، + +167 +00:17:20,530 --> 00:17:24,670 +تمام؟ يبقى هاي المقصود فيه، طيب، هذا بالنسبة + +168 +00:17:24,670 --> 00:17:28,770 +للنقطة الأولى، النقطة الثانيةقال لو كانت الدالة + +169 +00:17:28,770 --> 00:17:35,350 +odd يبقى قيمة التكمل تساوي صفرشو المعنى الهندسي لل + +170 +00:17:35,350 --> 00:17:41,750 +odd function يعني المنحنى متمثل حول ال origin يبقى + +171 +00:17:41,750 --> 00:17:47,050 +أى نقطة إحدثيتها a و b بديكون إلها نقطة سالب a و + +172 +00:17:47,050 --> 00:17:51,410 +سالب b يعني الجزء اللى فوق اللى أعلى محور X بديكون + +173 +00:17:51,410 --> 00:17:56,570 +فيه جزء أقباله أسفل محور X يعني لو المنحنى في + +174 +00:17:56,570 --> 00:17:59,850 +الربع الأول بديكون المنحنى التاني في الربع التالت + +175 +00:18:00,050 --> 00:18:03,130 +لو كان منحنى في الرابع الثاني، فهو يكون في الرابع + +176 +00:18:03,130 --> 00:18:08,310 +الرابع للجبال وهكذا، يعني في جزء محصور بين منحنى + +177 +00:18:08,310 --> 00:18:14,210 +ومحور X positive area وفي جزء تاني negative area، + +178 +00:18:14,210 --> 00:18:19,010 +يبقى لو جمعت التنتينبطلع صفر انا مش طالب ال total + +179 +00:18:19,010 --> 00:18:23,270 +area total area يسوى اتنين مساحة واحدة فيهم مظبوط + +180 +00:18:23,270 --> 00:18:26,090 +بس انا مش طالب ال total area بدي اكمل و بدي اعرف + +181 +00:18:26,090 --> 00:18:31,470 +كدهش نتيجة التكمل و ليس حساب ال total area يبقى + +182 +00:18:31,470 --> 00:18:35,210 +التكمل في هذا الحالة بدي سوى مين بدي سوى 0 يبقى + +183 +00:18:35,210 --> 00:18:40,270 +هذا ببسط لعملية الحسابة الطلة فالضالة اذا الرقم + +184 +00:18:40,270 --> 00:18:43,550 +اللي تحت التكمل هو نفس الرقم اللي فوق بإشارة + +185 +00:18:43,550 --> 00:18:48,360 +مخالفةيبقى ماجي بطلع والله إذا اتدالى even يبقى + +186 +00:18:48,360 --> 00:18:52,860 +اتنين في التكامل على نصف الفترة وإذا اتدالى يبقى + +187 +00:18:52,860 --> 00:18:56,940 +قيمة التكامل يساوي صفر بدون ما أروح أحسب و أخبص و + +188 +00:18:56,940 --> 00:18:58,760 +أجيب أما أجيب الاخرين فضل + +189 +00:19:07,340 --> 00:19:10,940 +وهذا موجب بناخد الـ Absolute Value زي ما قلنا في + +190 +00:19:10,940 --> 00:19:16,600 +المحاضرة الماضية بدي الـ Total Area بحسب أو بجسم + +191 +00:19:16,600 --> 00:19:20,820 +اللي الفترة طبقا لأسفار الدالة وبكمل على كل منطقة + +192 +00:19:20,820 --> 00:19:24,200 +وبعدين باخد الـ Absolute Value بكون جبت المساحة + +193 +00:19:24,200 --> 00:19:30,940 +الحقيقية طيب نرجع لتطبيق مباشر على هذه النظرية + +194 +00:19:31,190 --> 00:19:36,130 +جالهات لقيمة كل من التكاملات التالية وعطاني دالة + +195 +00:19:36,130 --> 00:19:42,210 +بهذا الشكل بدأ اكمل هذه الدالة بقول بسيطة بطلع في + +196 +00:19:42,210 --> 00:19:46,110 +حدود التكامل اللي فوق زي اللي تحت بالضبط تماما + +197 +00:19:46,110 --> 00:19:52,570 +الدالة هذه odd ولا even واضحة + +198 +00:19:52,570 --> 00:20:02,770 +مثل الشمس even هذاعندك ال F of X بده يساوي تلاتة X + +199 +00:20:02,770 --> 00:20:08,790 +على تسعة زائد X تربية لكل تربية بدك F of سالب X + +200 +00:20:08,790 --> 00:20:15,430 +يبقى تلاتة في سالب X على تسعة زائد سالب X لكل + +201 +00:20:15,430 --> 00:20:21,030 +تربية تربيةتمام السالب هذا بقدر أقوله شرفني برا + +202 +00:20:21,030 --> 00:20:27,390 +وبصير عندي هاي تلاتة X وهذه تسعة زي X تربيع لكل + +203 +00:20:27,390 --> 00:20:32,510 +تربيع يبقى odd والله even odd function لإن F of + +204 +00:20:32,510 --> 00:20:39,390 +سالب X سوى سالب F of X يبقى هذه odd يبقى هذه + +205 +00:20:39,390 --> 00:20:47,820 +النتيجة كده؟يساوي زيرو لان + +206 +00:20:47,820 --> 00:20:55,240 +التلاتة اكس على تسعة زائد اكس تربيع تربيع is an + +207 +00:20:55,240 --> 00:21:00,510 +odd functionيبقى نظرا لإنها دالة فردية فقيمة + +208 +00:21:00,510 --> 00:21:05,730 +التكامل يتساوي صفر بدون إجراء عملية التكامل يبقى + +209 +00:21:05,730 --> 00:21:13,170 +أعوض مباشرة بدون ما أقوم بعملية التكامل نمر اتنين + +210 +00:21:13,170 --> 00:21:19,910 +بدنا تكامل من سالب باي على أربعة إلى باي على أربعة + +211 +00:21:19,910 --> 00:21:25,770 +لل X تربيه زائد سك تربيه ال X كله في DX + +212 +00:21:28,590 --> 00:21:33,510 +باجي بتطلع برضه بنفس الطريقة الرقم اللي فوق هو نفس + +213 +00:21:33,510 --> 00:21:37,270 +الرقم اللي تحت بس بإشارة هي بإشارة مخالفة + +214 +00:21:49,870 --> 00:21:58,330 +ماعنديش إلا تنتين even والاربعة odd يبقى اللي قلنا + +215 +00:21:58,330 --> 00:22:03,710 +السك والكسين هي ال even فقط يبقى ليس تحكيش غير + +216 +00:22:03,710 --> 00:22:09,110 +تعرف يبقى السك وعكس اللي هو الكسين هم التنتين even + +217 +00:22:09,110 --> 00:22:14,070 +وباقي الأربعة odd يبقى هذا even تمام؟ والاكس + +218 +00:22:14,070 --> 00:22:20,330 +تربيع؟يبقى معناته هذا الكلام يساوي 2 تكامل من 0 ل + +219 +00:22:20,330 --> 00:22:26,570 +5 على 4 يبقى هذا الكلام يساوي 2 تكامل من 0 ل 5 على + +220 +00:22:26,570 --> 00:22:31,770 +4 ل X تربيع زائد سك تربيع X DX + +221 +00:22:45,270 --> 00:22:49,490 +اللي مايعرفش بشيل كل X و بحط مكانها سالب X تربية + +222 +00:22:49,490 --> 00:22:53,610 +بتبقى كما هي هذي ال cycle ناقص X لكل تربية هي + +223 +00:22:53,610 --> 00:22:58,330 +بcycle X تربية بتبقى تربية كما هي بنال عليها صارت + +224 +00:22:58,330 --> 00:23:04,040 +هذه even functionيبقى و هذا الكلام بده يسوى اتنين + +225 +00:23:04,040 --> 00:23:11,240 +فيه بدك تعمل هذه الدالة يبقى X تكيب على تلاتة زائد + +226 +00:23:11,240 --> 00:23:16,980 +تاني ال X من و لا وين من Zero لغاية Pi على أربع + +227 +00:23:17,420 --> 00:23:22,820 +تمام؟ يبقى هذا اتنين برا مالوش دعوة وهذه بدي أشيل + +228 +00:23:22,820 --> 00:23:28,360 +ال X و أحط مكانها باي على اربعة فهيصير بايتكيب على + +229 +00:23:28,360 --> 00:23:35,440 +اربعة وستين مظبوط؟ يبقى هذه بايتكيب على اربعة + +230 +00:23:35,440 --> 00:23:44,400 +وستين في تلاتةوالخمسة واربعين بواحد ناقص عوضنا من + +231 +00:23:44,400 --> 00:23:49,140 +القيم اللي فوق ناقص اللي تحت Zero و تاني Zero ب + +232 +00:23:49,140 --> 00:23:55,700 +Zero يبقى ناقص ال Zero يبقى النتيجة تساوي باي + +233 +00:23:55,700 --> 00:24:03,070 +تكعيب علىعندك هنا اربعة و ستين اربعة و ستين في + +234 +00:24:03,070 --> 00:24:07,610 +تلاتة اللي هو قداش تلاتة في اربعة باطناش و تلاتة + +235 +00:24:07,610 --> 00:24:13,470 +بازمية و اتنين و تسعين يبقى هذا لأ هو بقى اتنين و + +236 +00:24:13,470 --> 00:24:16,910 +تلاتين هذه اتنين و تلاتين في تلاتة ليه بستة و + +237 +00:24:16,910 --> 00:24:24,830 +تسعين مظلوم يبقى هذه ستة و تسعين و هنا زائد اتنين + +238 +00:24:24,830 --> 00:24:30,340 +يبقى هذا قيمة التكامل اللي عندناطب احنا حتى الآن + +239 +00:24:30,340 --> 00:24:36,220 +يا شباب لو رجعت للعنوان تبع section 5-6 لحتى الآن + +240 +00:24:36,220 --> 00:24:42,200 +احنا كل اللي اشتغلناه على النقطة الأولى من العنوان + +241 +00:24:42,200 --> 00:24:47,240 +وهو ال substitution لكن ال area between two curves + +242 +00:24:47,240 --> 00:24:53,780 +لم نتعرض لها بأي مثال حتى هذه اللحظةلذن قبل ان تضع + +243 +00:24:53,780 --> 00:24:58,400 +اي مثال يجب ان تضع قاعدة المساحة المحصورة بين + +244 +00:24:58,400 --> 00:25:03,580 +المنحنيات ومن ثم نذهب ناخد امثلة عليها يجب ان + +245 +00:25:03,580 --> 00:25:10,600 +اعطيها definition اكتري definition if + +246 +00:25:10,600 --> 00:25:18,200 +ال if and ال g are continuous functions + +247 +00:25:27,480 --> 00:25:38,960 +F of X أكبر من أو يساوي الـG of X أثره خلال الفترة + +248 +00:25:38,960 --> 00:25:41,860 +المغلقة A وB + +249 +00:25:58,080 --> 00:26:04,380 +النطاق بين الثقافات + +250 +00:26:04,380 --> 00:26:17,840 +بين الثقافات y تساوي f of x و y تساوي g of x from + +251 +00:26:17,840 --> 00:26:20,560 +a + +252 +00:26:21,840 --> 00:26:27,160 +to be is defined + +253 +00:26:27,160 --> 00:26:32,260 +as + +254 +00:26:32,260 --> 00:26:41,280 +من عرفة كتالي ال area a يسوى تكامل من a إلى b لل f + +255 +00:26:41,280 --> 00:26:45,600 +of x منعقص ال g of x dx + +256 +00:27:05,430 --> 00:27:10,190 +بنرجع للتعريف مرة تانية قال إذا عندك ذالة f و g و + +257 +00:27:10,190 --> 00:27:16,330 +اتين اتين دوال متصلة دوال متصلة يعني قابلة للتكامل + +258 +00:27:16,330 --> 00:27:22,890 +طيب في اندي كونديشن حطوا ان ال f of x أكبر من ال g + +259 +00:27:22,890 --> 00:27:28,350 +of x على كل الفترة من a إلى b يعني دائما و أبدا ال + +260 +00:27:28,350 --> 00:27:32,880 +f of x بتاخد قيمأكبر من القيم اللي تاخدها g of x + +261 +00:27:32,880 --> 00:27:37,340 +على الفترة بعد ال a والb مالاش علاقة فيها او قبلها + +262 +00:27:37,340 --> 00:27:42,560 +انا ماخد فترة من a إلى b فلو جيت قلت افترض على + +263 +00:27:42,560 --> 00:27:51,160 +سبيل المثال ان هذه الدالة y تساوي f of xأجدت دالة + +264 +00:27:51,160 --> 00:27:57,980 +g of x بالشكل اللي عندنا هذا يبقى هذه y تساوي g of + +265 +00:27:57,980 --> 00:28:03,640 +x روحت أنا أخدت الفترة على سبيل المثال من عند + +266 +00:28:03,640 --> 00:28:10,580 +النقطة a لعند النقطة b بالشكل اللي عندنا هذا جهة + +267 +00:28:10,580 --> 00:28:18,570 +طالع هيك جهة طالع هيكيبقى انحصرت المسافة ما بين + +268 +00:28:18,570 --> 00:28:25,910 +الاتنين اللي هي المسافة اللي عندنا هذه يبقى هذه هي + +269 +00:28:25,910 --> 00:28:31,940 +ال area aالان انا لو كاملت على ال F of X بيعطيني + +270 +00:28:31,940 --> 00:28:38,120 +المساحة هذه كلها أسفل المنحنة ومحور X المظلة زائد + +271 +00:28:38,120 --> 00:28:44,100 +المنطقة البيضة هذه تمام؟ لو كاملت على ال G of X + +272 +00:28:44,100 --> 00:28:47,920 +بيعطيني المساحة اللى تحت المنحنة اللى المنطقة + +273 +00:28:47,920 --> 00:28:52,260 +البيضة لو طرحت ال two two من بعضبتظلها المنطقة + +274 +00:28:52,260 --> 00:28:56,460 +المظللة يبقى الشدد area يبقى المنطقة اللي حاطط + +275 +00:28:56,460 --> 00:29:01,500 +عليها خطورة إذا مساحة هذه المنطقة هو تكامل الدالة + +276 +00:29:01,500 --> 00:29:05,780 +الأولى ناقص تكامل الدالة الثانية يبقى التكامل نفسه + +277 +00:29:05,780 --> 00:29:10,820 +على الفترة من a إلى b يبقى على الفترة من عند ال a + +278 +00:29:10,820 --> 00:29:17,300 +لغاية من لغاية ال bأذا بقول له لأ يبقى من البداية + +279 +00:29:17,300 --> 00:29:21,720 +تكامل ال F of X ناقص ال G of X و بروح بكامل على + +280 +00:29:21,720 --> 00:29:26,420 +فترة من A إلى B بيعطيني قداش المساحة اللي موجودة + +281 +00:29:26,420 --> 00:29:33,100 +عندنا طيب هذا لو كانت الدالة F of X فوق و G of X + +282 +00:29:33,100 --> 00:29:37,020 +تحت طب افترض واحدة على اليمين و واحدة على الشمال + +283 +00:29:37,020 --> 00:29:42,270 +لاحظ التكامل هنا بالنسبة لمين؟لو كانت واحدة على + +284 +00:29:42,270 --> 00:29:47,310 +اليمين و واحدة على الشمال كيف نعمل تكامل بالنسبة + +285 +00:29:47,310 --> 00:29:54,090 +لماين إلى واي يبقى باجي بقوله similarly يعني بنفس + +286 +00:29:54,090 --> 00:30:00,310 +الطريقة ال area ايه بقدر اقول تكامل من C إلى D لل + +287 +00:30:00,310 --> 00:30:09,910 +F of Y ناقص ال G of Y كل هذا في DY كيف كتالةافترض + +288 +00:30:09,910 --> 00:30:17,070 +ان هذا منحنى محور X وهذا Y وهذا نقطة الاصل الهيمين + +289 +00:30:17,070 --> 00:30:24,350 +Zero افترض كانت عند الدالة بهذا الشكل هذا المنحنى + +290 +00:30:24,350 --> 00:30:34,090 +Y تساوي F او X مقطع على صيغة X تساوي F of Yجيت على + +291 +00:30:34,090 --> 00:30:39,550 +منحنى ثانى نفترض ان هذا المنحنى كان بالشكل اللى + +292 +00:30:39,550 --> 00:30:49,470 +عندنا هذا يبقى هذا X يساوي G of Y تمام وانا روحت + +293 +00:30:49,470 --> 00:30:56,830 +اخدت المنطقةمن نقطة التقاطة مثلا ها لغاية النقطة + +294 +00:30:56,830 --> 00:31:02,610 +اللي عندها دي و قلت هذه C وهذه D و جيت رسمت خط + +295 +00:31:02,610 --> 00:31:06,970 +أفقي بالشكل اللي عندها ده يبقى المساحة اللي محصورة + +296 +00:31:06,970 --> 00:31:12,030 +بين المنحنيين هي المنطقة المظللة اللي عندها دي + +297 +00:31:12,030 --> 00:31:20,050 +تماميبقى بدى اعرف قدش المنطقة المظلة لأ يبقى صارت + +298 +00:31:20,050 --> 00:31:24,830 +كأنه هذه هي الدالة الكبيرة وهذه هي مين الدالة + +299 +00:31:24,830 --> 00:31:29,790 +الصغيرة على الفترة من وين لوين من C إلى D يعني + +300 +00:31:29,790 --> 00:31:36,590 +صارت F of Y أكبر من مينمن G of Y أو بالبلد هيك + +301 +00:31:36,590 --> 00:31:41,270 +اللي على إيدك اليمين ناقص اللي على إيدك الشمال + +302 +00:31:41,270 --> 00:31:46,750 +بتجيبها بالضبط تماما يبقى من المثل ال area يبدو + +303 +00:31:46,750 --> 00:31:52,510 +سوية كامل من C إلى D لل F of Y ناقص G of Y السؤال + +304 +00:31:52,510 --> 00:31:56,810 +هو لو جاني السؤال بيقولي كامل بالنسبة ل X والله + +305 +00:31:56,810 --> 00:32:02,580 +كامل بالنسبة ل Y بيقولي في المثلةلا بحكيش أبدا، + +306 +00:32:02,580 --> 00:32:05,680 +بيعطيك السؤال وانت حار كامل بالنسبة ل X كامل + +307 +00:32:05,680 --> 00:32:10,700 +بالنسبة ل Y، هذا شأنك، مالو يشتغل فيك، خلاص؟ حد + +308 +00:32:10,700 --> 00:32:16,630 +يلعب يتساول هنا؟طيب، الأن لم يبقى إلا مجموعة من + +309 +00:32:16,630 --> 00:32:23,090 +الأمثلة على هذا ال definition وحنعطي أمثلة بحيث + +310 +00:32:23,090 --> 00:32:28,370 +مرة نكمل بالنسبة إلى Y و أحيانا نكمل بالنسبة إلى X + +311 +00:32:28,370 --> 00:32:34,450 +كله بيرجع لطبيعة المسألة اللي موجودة نبدأ ناخد + +312 +00:32:34,450 --> 00:32:39,810 +أمثلة و بنيجي للمثال الأول يبقى example one + +313 +00:33:04,880 --> 00:33:12,780 +والمغلقة بيه او المحدودة بيه By the following + +314 +00:33:26,250 --> 00:33:37,650 +Y تساوي X ترابيع ناقص اتنين Y يساوي اتنين + +315 +00:33:38,700 --> 00:33:45,300 +المساحة المحصورة بين كل من المنحنيات والمستقيمات + +316 +00:33:45,300 --> 00:33:50,860 +الاتية نمر ايام اعطيني منحنى والتاني خط مستقيم اذا + +317 +00:33:50,860 --> 00:33:55,020 +اول خطة بنعملها بنحاول نرسم الرسم اللي عندنا هذه + +318 +00:33:55,020 --> 00:33:58,420 +ومن خلالها نحدد حدود التكامل طبعا هو بطنيش حدود + +319 +00:33:58,420 --> 00:34:02,580 +التكامل لحالك انت بدك تستنتج حدود التكامل من خلال + +320 +00:34:02,580 --> 00:34:06,860 +الرسم وبدك تعرف تتكامل بالنسبة ليكسب بالنسبةأو + +321 +00:34:06,860 --> 00:34:10,520 +بالنسبة إلى Y يبقى لو جينا للرسمة اللي عندنا هذه + +322 +00:34:10,520 --> 00:34:16,760 +وروح نقول هذا محور X وهذا محور Y وهذا نقطة الأصل + +323 +00:34:16,760 --> 00:34:21,840 +اللي هي Zero لو جيت للمنحنة Y تساوي X تربية ناقص + +324 +00:34:21,840 --> 00:34:26,880 +اتنين وY تساوي X تربية ترابه لمفتوحة إلى أعلى وتمر + +325 +00:34:26,880 --> 00:34:32,340 +بنقطة الأصل سالي باتنين يبقى Shift إلى أسفل بمقدار + +326 +00:34:32,340 --> 00:34:37,760 +اتنينيبقى هنا المنحنة بدى ينزل الى أسفل بمقدار + +327 +00:34:37,760 --> 00:34:44,920 +اتنين والبرابله بدى تصير بالشكل اللى قلناه هنا طيب + +328 +00:34:44,920 --> 00:34:51,330 +هذا اللى هو Y يساوي X ربيع ناقص اتنينالمنحنى + +329 +00:34:51,330 --> 00:34:56,830 +التانى هو خط مستقيم Y تساوي اتنين خط يوازي محور X + +330 +00:34:56,830 --> 00:35:02,190 +ويبعد عنه مسافة مقدارها اتنين يبقى هذا الخط Y + +331 +00:35:02,190 --> 00:35:06,630 +تساوي مين؟ Y تساوي اتنين اذا المنطقة اللى بدنا + +332 +00:35:06,630 --> 00:35:11,830 +ياها هي المحصورة بين المنحنيين الاتنين هدول اللى + +333 +00:35:11,830 --> 00:35:18,040 +هي المنطقة المظللةواضح انه في منحنى فوق كبير و + +334 +00:35:18,040 --> 00:35:23,660 +اللي تحت يعتبر مان صغير يعني منحنى هي فوق و منحنى + +335 +00:35:23,660 --> 00:35:29,320 +تاني تحتإذا انا بدى اطبق من القاعدة الأولى يعني + +336 +00:35:29,320 --> 00:35:34,260 +التكمل بتكون من نسبة لمن؟ من نسبة لمحور X بس مش + +337 +00:35:34,260 --> 00:35:38,240 +هان اطبق هذه بدي اعرف ال X بده تتغير من ويلة وين + +338 +00:35:38,240 --> 00:35:45,220 +باجي على أول نقطة هناها و بدي اعرف قداش قيمة X هنا + +339 +00:35:45,220 --> 00:35:49,460 +و بدي اجي على اخر نقطة في المساحة اللي عنده و بدي + +340 +00:35:49,460 --> 00:35:55,390 +اعرف قداش X بدها تكون عند هذه النقطةهذه النقطة + +341 +00:35:55,390 --> 00:36:00,150 +وهذه النقطة هي نقاط تقاطع المنحنة مع من؟ مع الخط + +342 +00:36:00,150 --> 00:36:04,150 +المستقيم إذا مش هنجيب الأحداثيات، بدتي أحلي + +343 +00:36:04,150 --> 00:36:09,070 +المعادلتين هدول مع بعض، هنا عندي Y وهنا Y، يبقى + +344 +00:36:09,070 --> 00:36:13,850 +بدي أساوي التنتين بمن؟ بعضهم، يبقى بدي أروح أحط + +345 +00:36:13,850 --> 00:36:15,390 +solution + +346 +00:36:17,940 --> 00:36:24,760 +يبقى بضع X تربيع ناقص اتنين يساوي كم؟ اتنين يبقى X + +347 +00:36:24,760 --> 00:36:29,900 +تربيع تساوي اربعة معناته ان ال X يساوي زائد او + +348 +00:36:29,900 --> 00:36:34,100 +ناقص اتنين اذا النقف اللي على شمال ال zero هذا + +349 +00:36:34,100 --> 00:36:38,480 +سالب اتنين واللي على يمين ال zero هذا كم؟ اتنين + +350 +00:36:38,760 --> 00:36:45,520 +يبقى أقل قيمة للمنطق المضلل لـ X هي سالب اتنين و + +351 +00:36:45,520 --> 00:36:49,580 +أكبر قيمة تاخدها X على المنطق المضلل هو عبارة من + +352 +00:36:49,580 --> 00:36:56,220 +اتنين إذا بناء عليه بقول ال area A يستوي تكامل من + +353 +00:36:56,220 --> 00:37:01,150 +سالب اتنين إلى اتنينالدالة الكبيرة هي الدالة اللى + +354 +00:37:01,150 --> 00:37:06,110 +فوق الـ UY تساوي كداش؟ اتنين الدالة الصغيرة اللى + +355 +00:37:06,110 --> 00:37:12,490 +تحتها الـ X تربيع ناقص اتنين كل اللى عندها دهاج + +356 +00:37:12,490 --> 00:37:18,790 +بالنسبة لمن؟ بالنسبة إلى DXاللي بكتب هذا الكلام + +357 +00:37:18,790 --> 00:37:22,870 +صحيح بظل الكلام اللي باقي كله كلام فارغ، شغل + +358 +00:37:22,870 --> 00:37:28,590 +روتيني عادي جدا، تمام؟ يبقى احنا بدنا نروح نكامل + +359 +00:37:28,590 --> 00:37:33,290 +هذه ونجي نقول هذه من سالي باتنين إلى اتنين، لو + +360 +00:37:33,290 --> 00:37:40,290 +فكتها بصير اربعة ناقص extra بادي، تمام؟ قبل ما + +361 +00:37:40,290 --> 00:37:46,860 +كامل، هذه الدالة even والله oddخلص يبقى 2 تكامل + +362 +00:37:46,860 --> 00:37:55,380 +على نصف الفترة يبقى هذا 2 تكامل من 0 إلى 2 لل 4 + +363 +00:37:55,380 --> 00:38:00,840 +ناقص X تربية دي ستطلع هنا هاي الخط بجسمها إلى نصين + +364 +00:38:00,840 --> 00:38:08,020 +ما لهم زي بعض يبقى روحان كامل 2 هيها برا هذه 4X + +365 +00:38:08,020 --> 00:38:15,680 +ناقص X تكيب على 3كله من صفر لغاية اتنين يبقى هذه + +366 +00:38:15,680 --> 00:38:22,020 +اتنين وبتعوب اتنين في اربعة بتمانية ناقص تمانية + +367 +00:38:22,020 --> 00:38:29,270 +على تلاتة ناقص Zero كل هذا ب Zeroعلى أي حال تلاتة + +368 +00:38:29,270 --> 00:38:35,170 +في تمانية باربع وعشرين ناقص تمانية بدل قدر 16 على + +369 +00:38:35,170 --> 00:38:40,590 +تلاتة يبقى اتنين في ستاشر على تلاتة يبقى اتنين + +370 +00:38:40,590 --> 00:38:48,790 +وتلاتين على تلاتة ال area المطلوبة نجي لنمرى بيه + +371 +00:38:51,360 --> 00:39:00,140 +نمر بيه؟ بيقول لي Y تساوي أربعة ناقص X تربيع وال Y + +372 +00:39:00,140 --> 00:39:11,360 +تساوي اتنين ناقص X وال X يساوي سالب اتنين و X + +373 +00:39:11,360 --> 00:39:14,520 +يساوي اتنين + +374 +00:39:17,180 --> 00:39:22,040 +هذا السؤال جئنا به في احدى الامتحانات قبل يمكن + +375 +00:39:22,040 --> 00:39:26,920 +اربع سنين تقريبا + +376 +00:39:30,310 --> 00:39:32,790 +المثال الأول ماحش الكامل بالنسبة للأصحاب اللي + +377 +00:39:32,790 --> 00:39:37,970 +قاعدين فيه انك واقف استخدامهم صحيح؟ ميشان الكامل + +378 +00:39:37,970 --> 00:39:43,450 +بالنسبة لو بدك معادلة او بدك تجيب منحنى على اليمين + +379 +00:39:43,450 --> 00:39:47,410 +ومنحنى على الشمال وين المنحنى اللي على اليمين وين + +380 +00:39:47,410 --> 00:39:48,690 +على الشمال؟ فيه؟ + +381 +00:39:51,790 --> 00:39:54,910 +ما هو بالنسبة للأول، معناته منحنى بدي يكون على + +382 +00:39:54,910 --> 00:39:59,370 +اليمين ومنحنى على الشمال، فيه عندنا؟ عندنا، + +383 +00:39:59,370 --> 00:40:04,310 +وبالتالي مستخدم كلامي مش صحيح، خلاص ما؟ طيب، ندي + +384 +00:40:04,310 --> 00:40:08,890 +له المثل اللي عندنا هذا، يبقى هذا مش خط مستخدم + +385 +00:40:08,890 --> 00:40:13,730 +منحنى، هذا تلت خطوط مستخدمه منحنى، يبقى ربنا يرسله + +386 +00:40:14,290 --> 00:40:18,130 +الله أعلم كيف تكون هذا مش هيك باجي بقوله كويس + +387 +00:40:18,130 --> 00:40:22,630 +بالضبط على الرسم اللي عندنا باجي بقوله هذا المحور + +388 +00:40:22,630 --> 00:40:29,870 +هذا محور X وهذا اللي عندنا اللي هو main وهذا اللي + +389 +00:40:29,870 --> 00:40:39,870 +هو محور Yطيب بيجي على المنحنة الأول أربعة ناقص X + +390 +00:40:39,870 --> 00:40:44,670 +تربيع يبقى X تربيع إلى أسفل وشفر إلى أعلى بمقدار + +391 +00:40:44,670 --> 00:40:52,470 +أربعة يبقى لو جيت للمنحنة هذا يبقى المنحنة + +392 +00:40:52,470 --> 00:40:57,410 +بالشكل هذا يبقى + +393 +00:40:57,410 --> 00:41:03,590 +هذا المنحنة Y يساوي أربعة ناقص X تربيعبعد ذلك اذا + +394 +00:41:03,590 --> 00:41:10,330 +كان عندك خط مستقيم y تساوي اتنين ناقص ال x بقول لو + +395 +00:41:10,330 --> 00:41:18,070 +كانت x بيزيرو يبقى y باتنين لو كانت x بيزيرو y + +396 +00:41:18,070 --> 00:41:23,270 +باتنين يعني في نص المسافة فوق اربعة يبقى هات اتنين + +397 +00:41:23,270 --> 00:41:29,880 +واللي بعدهلو كانت Y ب0 يبقى X ب2 + +398 +00:41:46,910 --> 00:41:52,930 +يبقى النقطتين الاتنين يقعني على الخط المستقيم إذا + +399 +00:41:52,930 --> 00:41:59,110 +بجيب المصدر هك و بوصل ما بين النقطتين هدول و بمد + +400 +00:41:59,110 --> 00:42:05,350 +هذا على استقالة ماخلصناش جال بعد هيك في عندك خطين + +401 +00:42:05,350 --> 00:42:11,350 +مستقيمين X يساوي سالب اتنين و X يساوي اتنين X + +402 +00:42:11,350 --> 00:42:16,170 +يساوي سالب اتنين يبقى هذا الخط الطالع رأسي دوري هك + +403 +00:42:18,200 --> 00:42:23,160 +والخط التاني X يساوي اتنين وهو الخط اللي عندنا هذا + +404 +00:42:23,160 --> 00:42:30,100 +تمام يبقى هذا X يساوي اتنين وهذا X يساوي سالب + +405 +00:42:30,100 --> 00:42:36,800 +اتنين يبقى صارتهل هناك ما بين X يساوي 2 ومساحة + +406 +00:42:36,800 --> 00:42:40,940 +تانية فيه محصورة بينه بين المنحنيات؟ لأ التلاتة + +407 +00:42:40,940 --> 00:42:45,020 +اتقطعوا في نفس مين؟ في نفس النقطة إذا ماعنديش + +408 +00:42:45,020 --> 00:42:49,200 +مساحة محددة مع الخط الرأسي الأول لكن مع الخط + +409 +00:42:49,200 --> 00:42:53,580 +الرأسي التاني صار عندي مساحة محددة يبقى أنا في + +410 +00:42:53,580 --> 00:42:59,220 +عندي المساحة دي محصورة ما بين خطين من الخطوط + +411 +00:42:59,220 --> 00:43:00,800 +المستقيمة + +412 +00:43:04,700 --> 00:43:13,180 +المساحة المحصورة بين خطين مستقيمين ومنحنة المساحة + +413 +00:43:13,180 --> 00:43:20,560 +المحصورة بين الخطين + +414 +00:43:20,560 --> 00:43:31,160 +المستقيمين ومنحنة المستقيمين + +415 +00:43:31,180 --> 00:43:34,000 +الخط المالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +416 +00:43:34,000 --> 00:43:35,220 +مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي + +417 +00:43:35,220 --> 00:43:37,800 +يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +418 +00:43:37,800 --> 00:43:38,160 +مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي + +419 +00:43:38,160 --> 00:43:39,800 +يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +420 +00:43:39,800 --> 00:43:44,700 +مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي + +421 +00:43:44,700 --> 00:43:52,800 +يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +422 +00:43:52,800 --> 00:43:58,640 +مالي يتيبقى هذا كل منحنط كل واحد كتب عليه معادلة + +423 +00:43:58,640 --> 00:44:06,010 +إذا ماعناش مساحة واحدة وانما عندنا مجموعمساحتين صح + +424 +00:44:06,010 --> 00:44:10,470 +ولا لا؟ ايوة طب اتنين بدنا نكمل بالنسبة ل X ولا + +425 +00:44:10,470 --> 00:44:16,170 +بالنسبة ل Y تعالى نشوف كل مساحة من هذه المساحات لو + +426 +00:44:16,170 --> 00:44:20,150 +جيت للمساحة اللى عندنا هذه يبقى فى منحنى فوق وفى + +427 +00:44:20,150 --> 00:44:26,430 +منحنى تحت هنا فى منحنى فوق وفى منحنى تحت لكن لو + +428 +00:44:26,430 --> 00:44:31,120 +جيتى يمين وشمال اه ممكنممكن يا مشوال بياخد تروح + +429 +00:44:31,120 --> 00:44:34,260 +ترسم خط أفق بيصير هذا على اليمين و هذا على الشمال + +430 +00:44:34,260 --> 00:44:38,440 +و هذا على اليمين و هذا على الشمال يبدو يتكاملينو + +431 +00:44:38,440 --> 00:44:44,560 +بعد هيك هذه يمين و شمال ماعنديش مش هتظبط هذه لذلك + +432 +00:44:44,560 --> 00:44:49,400 +افضل حاجة خلص بالنسبة ل X و انسى الموضوع تمام يبقى + +433 +00:44:49,400 --> 00:44:54,780 +بروح بكمل اس ال X بس بدي اروح احدد حدود التكوين + +434 +00:44:54,780 --> 00:44:59,720 +بدي اعرف قداش الاحداث تبع نقطة التقاطع هنا يعني + +435 +00:44:59,720 --> 00:45:04,160 +قداش قيم دسك هذه معروفةهذه المعروفة او هذه + +436 +00:45:04,160 --> 00:45:12,060 +المعروفة او هذه المعروفة + +437 +00:45:12,060 --> 00:45:13,400 +او هذه المعروفة او هذه المعروفة او هذه المعروفة او + +438 +00:45:13,400 --> 00:45:14,420 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +439 +00:45:14,420 --> 00:45:14,720 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +440 +00:45:14,720 --> 00:45:16,340 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +441 +00:45:16,340 --> 00:45:17,220 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +442 +00:45:17,220 --> 00:45:19,100 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +443 +00:45:19,100 --> 00:45:22,880 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +444 +00:45:22,880 --> 00:45:25,880 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +445 +00:45:25,880 --> 00:45:25,980 +هذه المعروفة ا + +446 +00:45:30,240 --> 00:45:37,260 +بدي اخد اربعة ناقص X تربيع يساوي اتنين ناقص X بدي + +447 +00:45:37,260 --> 00:45:41,460 +اعملها معادلة صفريهات لهذه الشجة التانية بيصير X + +448 +00:45:41,460 --> 00:45:49,240 +تربيع بالموجة ناقص X زي ما هي ماتغيراتي اربعة + +449 +00:45:49,240 --> 00:45:55,160 +بتجيلك بالسالب و عندك اتنين بيظل سالب اتنين يساوي + +450 +00:45:55,160 --> 00:45:55,720 +زيرو + +451 +00:46:02,100 --> 00:46:10,840 +هنا اكس وهنا اكس وهنا اتنين وهنا واحد وهنا سالب + +452 +00:46:10,840 --> 00:46:17,820 +وهنا مجد يبقى ناقص اتنين اكس وزاد اكس يبقى ناقص + +453 +00:46:17,820 --> 00:46:22,720 +اكس يبقى بناء عليه الاكس الاولى ساوي سالب واحد + +454 +00:46:22,720 --> 00:46:29,630 +والاكس التانى ساوي قداشرإتنين فعلا نقطة التقاطع + +455 +00:46:29,630 --> 00:46:34,670 +الأولى سالب واحد ونقطة التقاطع التانية جداش اتنين + +456 +00:46:34,670 --> 00:46:39,790 +هي مع الخط والمنحنى يبقى عند اتنين يبقى معناته + +457 +00:46:39,790 --> 00:46:50,200 +عندي تكاملين يبقى ال area المطلوبة ال areaمن سلب 2 + +458 +00:46:50,200 --> 00:46:55,040 +لغاية سلب 1 + +459 +00:46:55,040 --> 00:47:00,060 +يبقى الخط المستقيم هذا اللي فوق اللي هو 2 ناقص X + +460 +00:47:00,600 --> 00:47:06,660 +أتنين ناقص X ناقص المنحنى اللى تحت هذا اللى همين + +461 +00:47:06,660 --> 00:47:13,380 +أربعة ناقص X تربية يبقى أربعة ناقص X تربية وهي + +462 +00:47:13,380 --> 00:47:17,840 +الجزء ودير بالك وانت بتشتغل مش هحط السلب للأربعة و + +463 +00:47:17,840 --> 00:47:21,740 +تسيب التانية يبقى السلب و بتحط الدالة بالكام اللى + +464 +00:47:21,740 --> 00:47:25,060 +بين الجزين مشان شرط السلب تدخل على term من هذه + +465 +00:47:25,060 --> 00:47:28,780 +ترميزة اللى بيسووا بعضكواو بروح بغلط الاشارة و بظل + +466 +00:47:28,780 --> 00:47:32,920 +يخبص و هداك و بتطلع اليوم ماعمش بصبوط هدا إيه نطلع + +467 +00:47:32,920 --> 00:47:38,260 +جواب طيب يبقى هذا الكلام بد يساوي تكامل من سالب + +468 +00:47:38,260 --> 00:47:44,600 +اتنين إلى سالب واحد لمن؟ للاتنين ناقص X ناقص أربعة + +469 +00:47:44,600 --> 00:47:50,000 +زائد X تربيع كله بالنسبة إلى DX من ناقص اتنين + +470 +00:47:50,000 --> 00:47:55,500 +لناقص واحداكس تربية موجبة وهي ناقص اكس ناقص اربعة + +471 +00:47:55,500 --> 00:48:00,680 +زي دي اتنين بيظل جداش ناقص اتنين كله بالنسبة الى + +472 +00:48:00,680 --> 00:48:05,480 +DX بدنا نيجي اه لسه عملنا هيك لسه في تكامل تاني + +473 +00:48:05,480 --> 00:48:10,000 +خلي ا واحد طيب خلي ا واحد ولا يهمك هذه ا واحد + +474 +00:48:10,000 --> 00:48:17,640 +خلينا ماشيين يبقى هذه ا واحد وهذه ا اتنينيبقى بدنا + +475 +00:48:17,640 --> 00:48:26,060 +نحسب هذه يبقى بصير x تكيب على 3 ناقص x تربيع على 2 + +476 +00:48:26,060 --> 00:48:36,080 +ناقص 2x كله من سلب 2 لراية سلب 1عوض بالقيمة اللي + +477 +00:48:36,080 --> 00:48:40,380 +فوق يا شباب يبقى ناقص واحد تكييب اللي هو ناقص واحد + +478 +00:48:40,380 --> 00:48:45,820 +يبقى ناقص طول اللي بعدها ناقص واحد تربيع اللي هو + +479 +00:48:45,820 --> 00:48:50,780 +واحد على اتنين والناقص هذه بتظلها زي ما هي النص + +480 +00:48:50,780 --> 00:48:57,980 +هذه زائد اتنين خلصنا القيمة اللي فوق ناقص افتح قوس + +481 +00:48:58,610 --> 00:49:04,630 +هنا هذا بتعطيك ناقص تمانية على تلاتة يبقى ناقص + +482 +00:49:04,630 --> 00:49:09,510 +تمانية على تلاتة هذي بيصير اربعة على اتنين اللي هو + +483 +00:49:09,510 --> 00:49:15,570 +بيقدرش باتنين بالسالب وهي سالب اتنين هذي بيبقى + +484 +00:49:15,570 --> 00:49:22,450 +زائد اربعة يبقى زائد اربعةيبقى النتيجة كالتالت وهي + +485 +00:49:22,450 --> 00:49:29,030 +سالب طول وهي سالب نص وهي زائد اتنين وهي زائد + +486 +00:49:29,030 --> 00:49:35,870 +تمانية تلاتة وهي زائد اتنين وانا ناقص اربعطلّعلي + +487 +00:49:35,870 --> 00:49:43,610 +هذه وهذه بطل قداش سبعة على تلاتة يبقى هذه يساوي + +488 +00:49:43,610 --> 00:49:49,790 +سبعة على تلاتة وناقص نص مافيش غيره وهذه ناقص نص + +489 +00:49:49,790 --> 00:49:56,370 +بطل عندى اتنين واتنين اربعة مع الأربعة مع السلامة + +490 +00:49:56,790 --> 00:50:03,590 +يبقى هذه سالب أربع مع اتنين و مع اتنين يبقى كله + +491 +00:50:03,590 --> 00:50:09,850 +على قداش على ستة ستة على تلاتة في اتنين في سبعة + +492 +00:50:09,850 --> 00:50:17,510 +باربعتاش نقص ستة على اتنين فيها التلاتة في واحد + +493 +00:50:17,510 --> 00:50:26,220 +بتلاتة يبقى النتيجة يسوى احداشر على ستةبنروح نجيب + +494 +00:50:26,220 --> 00:50:32,580 +اتنين للمساحة الثانية يبقى تكامل من سالب واحد + +495 +00:50:32,580 --> 00:50:37,860 +لغاية اتنين الدالة اللى فوق ناقص الدالة اللى تحت + +496 +00:50:37,860 --> 00:50:43,100 +يبقى اربعة ناقص X تربية ناقص الدالة اللى تحت له + +497 +00:50:43,100 --> 00:50:50,460 +لاتنين ناقص X كله بالنسبة الى DX يبقى تكامل من + +498 +00:50:50,460 --> 00:50:58,150 +سالب واحد لغاية اتنينللمين للاربع ناقص X تربية + +499 +00:50:58,150 --> 00:51:06,070 +ناقص اتنين زائد ال X كل هذا الكلام بالنسبة إلى DX + +500 +00:51:06,070 --> 00:51:13,410 +ويساوينقص اتنين وزايد اربع بيقول قداش اتنين تكامل + +501 +00:51:13,410 --> 00:51:20,890 +من سلب واحد لاتنين لاتنين زايد X ناقص X تربيع كله + +502 +00:51:20,890 --> 00:51:28,190 +بالنسبة الى DX يبقى النتيجة 2X X تربيع على 2 ناقص + +503 +00:51:28,190 --> 00:51:33,950 +X تكيب على 3 كله من ناقص 1 لغاية 2 + +504 +00:51:37,780 --> 00:51:43,620 +يبقى هذه النتيجة تساوي اتنين في اتنين باربع زائد + +505 +00:51:43,620 --> 00:51:50,000 +اربع على اتنين باتنين ناقص تمانية على تلاتة تمانية + +506 +00:51:50,000 --> 00:51:54,460 +على تلاتة ناقص يفتح جوز نعود بالقيمة هذه اللي هي + +507 +00:51:54,460 --> 00:52:03,680 +ناقص اتنين و هنا زائد نص و عندك هنا ناقص و ناقص + +508 +00:52:03,680 --> 00:52:12,420 +بيصير زائد تلتهذا بيصير ستة ناقص تمانية على تلاتة + +509 +00:52:12,420 --> 00:52:21,060 +و هنا زائد اتنين و ناقص نص ناقص تلت و يساوي اتنين + +510 +00:52:21,060 --> 00:52:26,400 +و ستة تمانية عندك ناقص تمانية على تلاتة و ناقص تلت + +511 +00:52:26,400 --> 00:52:33,740 +بناقص تسع على تلاتة يعني قداش ناقص تلاتة و بيظل + +512 +00:52:33,740 --> 00:52:41,040 +عندك هنا ناقص نصيبقى هاي اتنين وستة تمانية تمانية + +513 +00:52:41,040 --> 00:52:47,500 +بدي اشيل منهم تلاتة بضل قداش بضل اللي هو خمسة + +514 +00:52:47,500 --> 00:52:54,670 +يساوي خمسة ناطص نصف الان بدي المساحة الكليةيبقى ال + +515 +00:52:54,670 --> 00:53:01,630 +area اللي بدوا إياها A يسوى A1 زائد A2 A1 طلعناها + +516 +00:53:01,630 --> 00:53:11,850 +مداشر ب 11 عالى 6 زائد 9 عالى 2 كله عالى 6 بضل 11 + +517 +00:53:11,850 --> 00:53:21,790 +زائد 6 عالى 2 ديال 3 في 9بسبعة و عشرين يبقى تمانية + +518 +00:53:21,790 --> 00:53:28,970 +و تلاتين على ستة أو تسعة و عشر على تلاتة هذه + +519 +00:53:28,970 --> 00:53:32,130 +المساحة الكلية المطلوبة + +520 +00:53:51,040 --> 00:53:51,600 +أيوة + +521 +00:53:55,410 --> 00:54:02,850 +وين وي تسوي سالب واحد؟ وي تسوي + +522 +00:54:02,850 --> 00:54:04,830 +سالب واحد، بده يجيلك هنا. + +523 +00:54:08,370 --> 00:54:15,810 +كيف؟ العملية + +524 +00:54:15,810 --> 00:54:20,230 +ليست سهلة، بده يصير عندك وي تسوي سالب أدتك، كمان + +525 +00:54:20,230 --> 00:54:25,400 +مساحة، هيك، هيك، هيكتمام؟ وبعدين تمدوا على + +526 +00:54:25,400 --> 00:54:29,140 +استقانته، فيه كمان هذه مساحة وبعدين تمدوا على هذه + +527 +00:54:29,140 --> 00:54:34,320 +وهنا كمان مساحة وتمدوا هنا وهنا كمان مساحة ان شاء + +528 +00:54:34,320 --> 00:54:35,780 +الله للعصر بنخلص اليوم + +529 +00:54:40,360 --> 00:54:44,760 +بصير ملوش قيمة، ملوش اي اعتبار، ان احنا بندور + +530 +00:54:44,760 --> 00:54:48,200 +المساحة المحصورة بين المنحنات، بتطلعش منها إلا إذا + +531 +00:54:48,200 --> 00:54:51,760 +قال لي بين X يساوي Zero و Y يساوي Zero، اه تدخل + +532 +00:54:51,760 --> 00:54:56,080 +المحاور معاه، مجاليش يبقى أنا مقيد بس بالمنحنات + +533 +00:54:56,080 --> 00:55:00,460 +اللي بنوصل عليها، غيريك مليش علاقة فيه، طبعا، طيب + +534 +00:55:00,460 --> 00:55:07,710 +هذا نمرة B من المثلة نمرة Cنمر ال C بيقول يا سيدي + +535 +00:55:07,710 --> 00:55:16,650 +X يساوي Y تربية and ال X يساوي Y زائد اتنين + +536 +00:55:19,450 --> 00:55:25,350 +يبقى بناروح نرسم المثلة مشان نعرف شو شكلها بالضبط + +537 +00:55:25,350 --> 00:55:31,730 +يبقى باجي بقول هاي المحاور هذا محور X هذا محور Y + +538 +00:55:31,730 --> 00:55:36,990 +هذا نقطة الأصل اللي هي Zero X يسوى Y تربية هو + +539 +00:55:36,990 --> 00:55:44,260 +قنابلة مفتوح جهتي اليمينيبقى هذا ال parabola لأن x + +540 +00:55:44,260 --> 00:55:51,020 +بدي يسوى 100y تربيع يبقى هذا ال x بدي يسوى y تربيع + +541 +00:55:51,020 --> 00:55:58,000 +بداية للخط المستقيم لأن لو كانت y ب0x ب2 يبقى لو + +542 +00:55:58,000 --> 00:56:04,830 +جيت قلت هاي اتنينلو كانت X بزير و Y بسالب اتنين X + +543 +00:56:04,830 --> 00:56:07,830 +بزير و Y بسالب اتنين X بزير و Y بسالب اتنين X بزير + +544 +00:56:07,830 --> 00:56:07,850 +و Y بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +545 +00:56:07,850 --> 00:56:08,050 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +546 +00:56:08,050 --> 00:56:08,790 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +547 +00:56:08,790 --> 00:56:08,930 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +548 +00:56:08,930 --> 00:56:12,830 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +549 +00:56:12,830 --> 00:56:20,910 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +550 +00:56:20,910 --> 00:56:28,950 +بسالبو بمد الخط على استقامته يبقى هذا اللي هو + +551 +00:56:28,950 --> 00:56:34,210 +تقاطع مع المنحنة يبقى المنطقة المظلة لهذه هي + +552 +00:56:34,210 --> 00:56:40,770 +المنطقة المحصورة ما بين المنحنة اللي عندنا و الخط + +553 +00:56:40,770 --> 00:56:49,940 +المستقيم يبقى الخط المستقيم هذا X يساوي Y زائد 2Y + +554 +00:56:49,940 --> 00:56:56,620 +المنحنى اللي يفوت هو X يساوي Y تربيه بالشكل اللي + +555 +00:56:56,620 --> 00:56:56,980 +عندنا + +556 +00:57:01,010 --> 00:57:07,330 +تمام طيب واضح انه لو تيجي تقوله هذه فوق هذه تحت + +557 +00:57:07,330 --> 00:57:11,390 +هنا تنتل بيصيروا جبال بعض بيصير واحد على يمين واحد + +558 +00:57:11,390 --> 00:57:15,870 +على شمال مش هتظبط معاه لكن واضح انه الخط هذا على + +559 +00:57:15,870 --> 00:57:19,470 +اليمين وهذا الجزء منه منحنى وين عليه شمال يعني + +560 +00:57:19,470 --> 00:57:23,360 +واحد جهة إيدي شمال وواحد جهة إيدياليمين إذا هنا + +561 +00:57:23,360 --> 00:57:27,840 +التكامل بيشير بالنسبة ل Y يبقى بروح بقول لو بدي + +562 +00:57:27,840 --> 00:57:34,600 +أعرف قداش أقل قيمة بتاخدها Y و قداش أكبر قيمة هنا + +563 +00:57:34,600 --> 00:57:39,900 +بتاخدها من Y يبقى معناته بدي أحل المعادلاتين هدول + +564 +00:57:39,900 --> 00:57:46,120 +مع بعضيبقى عندي y تربية بدها تساوي ال y زائدي + +565 +00:57:46,120 --> 00:57:51,300 +اتنين او ال y تربية ناقص y ناقص اتنين بده يساوي + +566 +00:57:51,300 --> 00:57:57,860 +zero وهي قوسين بده يساوي zero يبقى هنا y هنا y هنا + +567 +00:57:57,860 --> 00:58:02,630 +واحد هنا اتنين سالف موجةيبقى موجة بواي و سالب + +568 +00:58:02,630 --> 00:58:07,210 +اتنين واي بيظل سالب واي مظبوط إذا واي تسوى سالب + +569 +00:58:07,210 --> 00:58:12,190 +واحد و واي تسوى قداش اتنين يبقى النقطة هذه سالب + +570 +00:58:12,190 --> 00:58:18,170 +واحد و النقطة هذه قداش اتنينيبقى ال area اللي بدنا + +571 +00:58:18,170 --> 00:58:23,030 +ياها هي تكامل من سالب واحد لغاية مين دالية اتنين + +572 +00:58:23,030 --> 00:58:28,290 +الدالة اللي على اليمين واضح انها Y زي D2 الدالة + +573 +00:58:28,290 --> 00:58:33,150 +اللي على الشمال الييمين Y تربيع كله بالنسبة إلى + +574 +00:58:33,150 --> 00:58:39,860 +مين إلى DYالان التكامل هذا حددت حدود التكامل صح + +575 +00:58:39,860 --> 00:58:46,300 +يبقى الباقي كله بيصير شغل روتيني فقط لغاية يبقى + +576 +00:58:46,300 --> 00:58:53,880 +هذا الكلام بيصير Y تربيه على 2 زي 2Y ناقص Y تكعيب + +577 +00:58:53,880 --> 00:59:00,770 +على 3 كله من سالب 1 لغاية 2نعوض بالقيمة اللى فوق + +578 +00:59:00,770 --> 00:59:05,050 +ناقص القيمة اللى تحت يبقى بيصير اربع على اتنين + +579 +00:59:05,050 --> 00:59:14,110 +باتنين زائد اربع ناقص تمانية على تلاتة ناقص + +580 +00:59:14,110 --> 00:59:19,830 +افتحانوز هنا ناقص واحد تربية لو واحد بيبقى عندي نص + +581 +00:59:21,620 --> 00:59:28,880 +وهنا ناقص اتنين تمام وهنا ناقص واحد بيصير ناقص مع + +582 +00:59:28,880 --> 00:59:36,620 +ناقص بيصير زائد طلت بالشكل اللي عنها يبقى النتيجة + +583 +00:59:36,620 --> 00:59:43,240 +اتنين واربعة ستة ناقص تمانية على تلاتة ناقص نص + +584 +00:59:43,240 --> 00:59:57,190 +زائد اتنين ناقص طلت ويساويتمنية تمنية تمنية + +585 +00:59:57,190 --> 01:00:05,590 +تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية + +586 +01:00:05,590 --> 01:00:14,950 +تمنية تمنية تمنية تمنية تمنية تمنية + +587 +01:00:24,970 --> 01:00:28,490 +هذا النوع الأول من المسائل اللي هو المساحة + +588 +01:00:28,490 --> 01:00:33,910 +المحصورة بين منحنى وخط مستقيم ممكن أن تكون المساحة + +589 +01:00:33,910 --> 01:00:41,470 +موجودة بين منحنيين وليس بين منحنى وخط مستقيم إذا + +590 +01:00:41,470 --> 01:00:44,530 +نذهب إلى المثال رقم 2 + +591 +01:00:52,580 --> 01:00:57,320 +بقول find the + +592 +01:00:57,320 --> 01:01:12,380 +area of the region enclosed by + +593 +01:01:12,380 --> 01:01:13,780 +the following curves + +594 +01:01:23,150 --> 01:01:30,030 +بندى المساحة المحصورة ما بين المنحنيات القاتلة نمر + +595 +01:01:30,030 --> 01:01:42,490 +A X يساوي Y تربيع and X زائد 2Y تربيع بده يساوي + +596 +01:01:42,490 --> 01:01:44,290 +كده؟ بده يساوي 3 + +597 +01:02:13,930 --> 01:02:19,810 +هذه المساحة الموجودة بين المنحنات X يساوي Y تربيع + +598 +01:02:19,810 --> 01:02:26,880 +و X زائد 2Y تربيع يساوي 3بنروح نرسم كل منحنى من + +599 +01:02:26,880 --> 01:02:30,880 +هذه المنحنيات مشان نعرف انها مكمل بالنسبة ل X و + +600 +01:02:30,880 --> 01:02:38,640 +بالنسبة ل Y و نحدد النقاط اللي هي حدود التكامل اذا + +601 +01:02:38,640 --> 01:02:47,740 +لو جيت للمنحنى الأول هذا محور X وهذا محور Y وهذا + +602 +01:02:47,740 --> 01:02:55,080 +نقطة الأصل Zالمنحدر هو X يسوى Y تربيع رسمناه قبل + +603 +01:02:55,080 --> 01:03:01,160 +قليل بالشكل اللي عندنا هذا يبقى هذا ال X يسوى Y + +604 +01:03:01,160 --> 01:03:06,910 +تربيعالمنحنى الثانى هذا عبارة عن ايش؟ عبارة عن x + +605 +01:03:06,910 --> 01:03:13,790 +بده يساوي سالب اتنين y تربية زائد تلاتة يعني هذا + +606 +01:03:13,790 --> 01:03:20,370 +لو روحت قعدت كتابته مرة تانية بمين؟ ب x يساوي سالب + +607 +01:03:20,370 --> 01:03:25,470 +اتنين y تربية زائد تلاتة بقول واسة اتنين والتلاتة + +608 +01:03:26,210 --> 01:03:31,430 +يبقى Y تساوي X يساوي سالب Y تربيع يبقى هذا بس + +609 +01:03:31,430 --> 01:03:36,750 +بعدين اقلبه وين؟ ع الشجة التانية طيب اتنين هذه + +610 +01:03:36,750 --> 01:03:40,510 +بتخليه يقرب على المنحنى او يبعد الرقم اللي عندي + +611 +01:03:40,510 --> 01:03:46,430 +تمام التلاتة هي shift بس ان من ال shift الى اعلى + +612 +01:03:46,430 --> 01:03:50,850 +الرسم يمين وشمال اذا ال shift جهة اليمين بمقدار + +613 +01:03:50,850 --> 01:03:56,050 +تلاتةيبقى المنحنة على الإشمال هكذا و سأعمل shift + +614 +01:03:56,050 --> 01:04:04,930 +للخلف بمقدار 3 لماذا؟ لأن لو كانت Y ب0 يبقى X ب3 + +615 +01:04:04,930 --> 01:04:10,810 +يبقى هذا X ب3 و Y ب0 و الparabola ستصبح بالشكل + +616 +01:04:10,810 --> 01:04:16,760 +اللي عندنا هذا هكذاطبعا يبقى هذا المنحنى اللي هو X + +617 +01:04:16,760 --> 01:04:23,700 +يساوي سالب اتنين Y تربيع زائد تلاتة اذا المنطقة + +618 +01:04:23,700 --> 01:04:29,320 +اللي بينهم هي المنطقة المضللة اللي عندنا ايوة + +619 +01:04:29,320 --> 01:04:32,720 +وشايف + +620 +01:04:32,720 --> 01:04:36,280 +المنحنى اللي عندك ولا لا حق واي بزير قداشك تكون + +621 +01:04:37,860 --> 01:04:42,940 +سمعت بالـ shift تبع الدالة لما كانت y تساوي مثلا x + +622 +01:04:42,940 --> 01:04:47,880 +سربيع او x كام يبقى shift الى اعلى اذا الرقم ل y + +623 +01:04:47,880 --> 01:04:51,260 +بصير shift جهة اليمين او جهة الشمال حسب القيمة + +624 +01:04:51,260 --> 01:04:55,080 +تبعته طيب اذا ماانت مش عارف ال shift ولا حاجة + +625 +01:04:55,080 --> 01:04:59,320 +بقوله حط ال y ب 0 وشوف x وين بتروح يبقى بنحدد + +626 +01:04:59,320 --> 01:05:01,100 +القيمة في هذه الحالة + +627 +01:05:05,430 --> 01:05:13,290 +كيف؟ المثل معطلك X يساوي Y كيف + +628 +01:05:13,290 --> 01:05:19,410 +مش مفروض؟ تلتان معروفات هي X يساوي Y تلتان بدكش حط + +629 +01:05:19,410 --> 01:05:27,210 +ل Y تساوي جدر X جدر X معروف هي جدر X الموجب وجدر X + +630 +01:05:27,210 --> 01:05:33,820 +الثاني صحيح ولا لأ؟ ماعكش خبر مش مشكلةطيب خليكم + +631 +01:05:33,820 --> 01:05:39,180 +معنا يا شباب يبقى هاي رسمنا ال X يساوي Y تربية و + +632 +01:05:39,180 --> 01:05:44,080 +المنحنة تاني X زائد 2Y تربية يساوي 3 رسمناها يبقى + +633 +01:05:44,080 --> 01:05:49,080 +المنطقة المظلة هي المنطقة بين المنحنيين واضح ان في + +634 +01:05:49,080 --> 01:05:53,820 +منحنة عندي على اليمين ومنحنة تاني وين على الشمال + +635 +01:05:53,820 --> 01:05:58,960 +يبقى انا بدي اقل قيمة بتاخدها Y اكبر قيمة هنا + +636 +01:05:58,960 --> 01:05:59,860 +بتاخدها مين + +637 +01:06:03,430 --> 01:06:09,990 +يبقى انا عند X يساوي Y تربية وعندي X التانية ناقص + +638 +01:06:09,990 --> 01:06:18,570 +اتنين Y تربية زائد تلاتة يبقى Y تربية + +639 +01:06:18,570 --> 01:06:23,910 +يساوي اتنين Y تربية زائد تلاتة يبقى Y تساوي زائد + +640 +01:06:23,910 --> 01:06:30,360 +او ناقصإذا هذه سالب واحد وهذه مين وهذه واحد يبقى + +641 +01:06:30,360 --> 01:06:35,400 +النقطة ان هذه سالب واحد والنقطة هذه واحد يبقى ال + +642 +01:06:35,400 --> 01:06:39,900 +area اللي عندنا بدأ تساوي تكمل من سالب واحد إلى + +643 +01:06:39,900 --> 01:06:44,180 +واحد الدالة اللي على اليمين اللي هي اتنين Y تربية + +644 +01:06:44,180 --> 01:06:48,180 +زائد تلاتة ناقص الدالة اللي على الشمال اللي هي مين + +645 +01:06:48,480 --> 01:06:58,220 +x يساوي y تربيع كل هذا بالنسبة لمين الى dy سالب + +646 +01:06:58,220 --> 01:07:05,260 +اتنين y تربيع زي التلاتة سالب y تربيع يبقى كأن + +647 +01:07:05,260 --> 01:07:13,190 +المسألة تكامل من سالب واحد الى واحد لمين لتلاتةنقص + +648 +01:07:13,190 --> 01:07:27,610 +ثلاثة Y تربيع كله بالنسبة الى D1 يبقى + +649 +01:07:27,610 --> 01:07:32,850 +even function ممكن اقول من الصفرلغاية كده؟ لغاية + +650 +01:07:32,850 --> 01:07:36,330 +واحدة انسى مش مشكلة فالمساحة اللى فوق واضحة انها + +651 +01:07:36,330 --> 01:07:40,150 +جد المساحة اللى تحت يعني لو خدت واحدة وضربتها في + +652 +01:07:40,150 --> 01:07:43,650 +اتنين بمشي الحال اجى فى بلد كان فيها مجاش ماعناش + +653 +01:07:43,650 --> 01:07:48,490 +مشكلة يبقى لو خلتها زى ما هو مجاش فى باقيبقول له + +654 +01:07:48,490 --> 01:07:53,730 +هذه تلاتة Y ناقص Y تكيبها تلاتة بتروح و بظل + +655 +01:07:53,730 --> 01:07:58,890 +المساحة من سالب واحد لغاية قداش واحد يبقى بده + +656 +01:07:58,890 --> 01:08:06,830 +يساوي تلاتة ناقص تلاتة هذه Y تكيبها تلاتة بتروح مع + +657 +01:08:06,830 --> 01:08:14,120 +تلاتة يبقى عند الواحد تلاتة ناقص واحد ناقصهنا بصير + +658 +01:08:14,120 --> 01:08:21,540 +ناقص تلاتة وهنا يا سيد العزيز ناقص واحد بصير زائد + +659 +01:08:21,540 --> 01:08:28,460 +واحد يبقى الجواب بيصير تلاتة ناقص واحد زائد تلاتة + +660 +01:08:28,460 --> 01:08:33,300 +كمان ناقص واحد يبقى النتيجة كم؟ أربع يبقى قيمة + +661 +01:08:33,300 --> 01:08:39,380 +المساحة تساوي أربع هذا نمر ايه من المثلة؟ نمر بيه + +662 +01:08:40,960 --> 01:08:51,820 +نمر بيبقى يبقى y تساوي x تربيع and يبقى y ناقص x + +663 +01:08:51,820 --> 01:08:55,720 +تربيع زائد 4x + +664 +01:09:04,920 --> 01:09:09,140 +هذه برضه معادلة من درجة ثانية في X يبقى هذه + +665 +01:09:09,140 --> 01:09:14,120 +Parabola وهذه كذلك Parabola بس هذه ال vertex تبعها + +666 +01:09:14,120 --> 01:09:19,700 +نقطة هذه معمولة لها إيه؟ شوف، بدي أحدد وين ال + +667 +01:09:19,700 --> 01:09:25,500 +vertex تبع هذه ال Parabola فاروح بعمل إكمال المربع + +668 +01:09:25,500 --> 01:09:29,120 +هذه قد إيش بدها مشان يصير إكمال المربع؟ + +669 +01:09:37,320 --> 01:09:45,580 +يبقى هذا الكلام يصبح على الشكل التالي عندك ال Y + +670 +01:09:45,580 --> 01:09:54,660 +يسوى ناقص X تربيع زائد 4 X ناقص 4 زائد 4أو بمعنى + +671 +01:09:54,660 --> 01:10:01,440 +آخر هذه ها ها بد يصير y ناقص أربعة بد يساوي هاي + +672 +01:10:01,440 --> 01:10:07,020 +ناقص أخدناه عام المشترك بظال x تربيه ناقص أربعة x + +673 +01:10:07,020 --> 01:10:12,660 +زائد أربعة هذه الأربعة نعشج هذه هدول التلاتة أخدنا + +674 +01:10:12,660 --> 01:10:18,440 +منهم سالب عام المشترك يبقى بصير ال y ناقص أربعة + +675 +01:10:18,440 --> 01:10:25,790 +يساوي ال x ناقص اتنين لكل تربيهيبقى هذه البرابولة + +676 +01:10:25,790 --> 01:10:31,490 +و ال vertex تبعها هي بين 2 و 4 يبقى انا لو روحت + +677 +01:10:31,490 --> 01:10:37,050 +رسمت الرسمة اللي عندنا هذه فبدي بقوله هذا محور X + +678 +01:10:37,050 --> 01:10:43,350 +وهذا محور Y وهذه نقطة الأصل اللي هي Zero البرابولة + +679 +01:10:43,350 --> 01:10:48,670 +الأولى Y تساوي X تربيع يبقى Y تساوي X تربيع + +680 +01:10:48,670 --> 01:10:56,690 +البرابولة اللي عندنا هذه هيكيبقى هذه اللي هي هذه + +681 +01:10:56,690 --> 01:11:03,650 +فوق X يساوي Y تربيع هذه Y تساوي X تربيعبتدخل ال + +682 +01:11:03,650 --> 01:11:08,490 +parabola التانية ال vertex تبعها اللي هو اتنين + +683 +01:11:08,490 --> 01:11:14,750 +واربعة يبقى اتحرك اتنين هنا على اليمين وده يطالع + +684 +01:11:14,750 --> 01:11:20,710 +فوق اداش اربعة يبقى هذه النقطة اتنين واربعة طب ليش + +685 +01:11:20,710 --> 01:11:25,530 +اجت على المنحنة ولم تجت فوق او جت تحت لأن y تساوي + +686 +01:11:25,530 --> 01:11:28,770 +x تساوي اتنين لما ال x تساوي اتنين تبقى اربعة إذا + +687 +01:11:28,770 --> 01:11:33,870 +انتقى على مين على المنحنة بالضبط تماماطيب هذا ال + +688 +01:11:33,870 --> 01:11:38,070 +vertex تبع اتنين و اربعة open up ولا open down + +689 +01:11:38,070 --> 01:11:43,730 +open down بسبب الإشارة السلبية اتنين يا مربى نقطة + +690 +01:11:43,730 --> 01:11:49,390 +الاصل والله ليه يا مربى نقطة الاصل طلع المعادلة لو + +691 +01:11:49,390 --> 01:11:55,910 +حطيت x ب zero y بقدرش يبقى دي مربى نقطة الاصل غصب + +692 +01:11:55,910 --> 01:12:00,270 +من علمه يرضى يبقى ال parabola هذه بدها تيجي بالشكل + +693 +01:12:00,270 --> 01:12:07,100 +اللي عندنا هذاو من هنا فرابولة بالشكل هذا و من هنا + +694 +01:12:07,100 --> 01:12:13,660 +فرابولة بالشكل هذا يبقى الفرابولة إلى أسفل + +695 +01:12:13,660 --> 01:12:27,760 +الفرابولة + +696 +01:12:27,760 --> 01:12:30,160 +إذا المنطقة اللي بينهم هي + +697 +01:12:39,220 --> 01:12:47,280 +هذا المنطقة المظلة بين الاتنين هي المنطقة المطلوبة + +698 +01:12:53,660 --> 01:12:58,640 +ال X هتتغير من اين لين و اذا انا اريد نسبة Y من + +699 +01:12:58,640 --> 01:13:05,660 +صفر لغاية اربعة ايام طيب ايهم افضل كامل بالنسبة ل + +700 +01:13:05,660 --> 01:13:12,980 +X ولا بالنسبة ل Y انفع الشجتين بس ال X أسهل كتير + +701 +01:13:12,980 --> 01:13:18,340 +لان ال X لسه بيتحول و تاخد جذر و جثة طويلة يبقى + +702 +01:13:18,340 --> 01:13:24,790 +انا لو جيت و قلت ال area Aبدي يساوي تكامل ال X + +703 +01:13:24,790 --> 01:13:30,290 +هتتغير من صفر لين لغاية الاتنين بدي الدالة اللي + +704 +01:13:30,290 --> 01:13:33,970 +فوق الدالة اللي فوق اللي هو المنحنة اللي عندها ده + +705 +01:13:33,970 --> 01:13:38,850 +Y يساوي ناقص X تربيع زي دربيع هذه الدالة اللي فوق + +706 +01:13:38,850 --> 01:13:45,430 +وال X تربيع هي من الدالة اللي تحت يبقى لناقص X + +707 +01:13:45,430 --> 01:13:53,640 +تربيعزائد أربعة X هذه كلها ناقص ال X تربية اللي هي + +708 +01:13:53,640 --> 01:13:58,300 +الدالة التانية كلها بالنسبة إلى مين بالنسبة إلى DX + +709 +01:13:58,300 --> 01:14:04,560 +يبقى هذا الكلام بيساوي تكامل من صفر لإتنين للاربعة + +710 +01:14:04,560 --> 01:14:12,260 +X ناقص اتنين X تربية كل هذا الكلام بالنسبة إلى مين + +711 +01:14:12,260 --> 01:14:19,680 +إلى DXيبقى هذا بده يساوي اللي هو اتنين X تربية + +712 +01:14:19,680 --> 01:14:27,920 +ناقص طولتين X تكيب من صفر لغاية اتنين يبقى هنا + +713 +01:14:27,920 --> 01:14:36,500 +تمانية ناقص هنا تمانية ستاشر على تلاتة ناقص ال + +714 +01:14:36,500 --> 01:14:41,960 +zeroيبقى هذا كله على تلاتة في تمانية باربعة وإشرين + +715 +01:14:41,960 --> 01:14:50,600 +من ستاشر بيظل تمانية على تلاتة فقط لا غير يبقى لما + +716 +01:14:50,600 --> 01:14:55,740 +ترسم صح أو تحدد حدود التكمل صح، باقي الشغل كله + +717 +01:14:55,740 --> 01:14:57,820 +بيصير شغل روتيني أيضا + +718 +01:15:01,970 --> 01:15:06,430 +أنا بقولك الامتحانات اللي بخليها لك بقسمها لك، لكن + +719 +01:15:06,430 --> 01:15:10,970 +الامتحانات اللي بقسمها لك بقسمها لك، ايه نعم؟ لو + +720 +01:15:10,970 --> 01:15:14,850 +طلعت على الامتحانات السابقة، هتلاقي بعض المسائل + +721 +01:15:14,850 --> 01:15:17,970 +اللي على الموضوع هذا ما الرسمينها، ومظللينها مش + +722 +01:15:17,970 --> 01:15:24,230 +هقولك هي المساحة اللي بدنا يعني، ايوة، كده؟ الرسم + +723 +01:15:24,230 --> 01:15:26,130 +التاني، كده؟ + +724 +01:15:31,170 --> 01:15:36,970 +هي رسمة قدامك + +725 +01:15:36,970 --> 01:15:41,490 +رسمة المنحنة التانية ما انتشرفش اللي سوناه مش هي + +726 +01:15:41,490 --> 01:15:46,630 +المنحنة روحت املت و اكمل المربع لغاية ما وصلت لهنا + +727 +01:15:47,440 --> 01:15:51,540 +هذه برابولة بسمعولي لو شيلت الاربعة و اتنين بصير Y + +728 +01:15:51,540 --> 01:15:55,880 +تساوي سالب X تربيع برابولة الى أسفل بس ممكن + +729 +01:15:55,880 --> 01:15:59,120 +تسمعليها زاحة لليمين و زاحة لأعلى مشان الverse X + +730 +01:15:59,120 --> 01:16:04,060 +اتنين و اربعة وبالتالي صلة بسيطة جدا طيب ال هذا + +731 +01:16:04,060 --> 01:16:11,120 +نمر بي من السؤال كان بدنا نروح لنمره C نمره C + +732 +01:16:11,120 --> 01:16:16,240 +بقولي Y تساوي X كيب and + +733 +01:16:18,190 --> 01:16:24,870 +تلاتة X تربيها ناقص Y يساوي اربعة + +734 +01:16:32,700 --> 01:16:37,540 +يبقى بنروح نرسم الرسم اللى عندنا بس قبل انا ارسمها + +735 +01:16:37,540 --> 01:16:43,240 +ها دي ها ها بقدر احطها فى الشكل الطبيعى تبعها يبقى + +736 +01:16:43,240 --> 01:16:47,240 +لو جبت ال Y على اليمين والاربعة الشمال بصير Y + +737 +01:16:47,240 --> 01:16:52,920 +يساوي تلاتة X تربية وناقص اربعة أبدا برضه هذه ال + +738 +01:16:52,920 --> 01:16:56,400 +parabola شيل الاربعة وشيل التلاتة بصير Y تساوي X + +739 +01:16:56,400 --> 01:17:01,850 +تربيةتلاتة تتجرب على محور Y سالب اربعة شفت الاصل + +740 +01:17:01,850 --> 01:17:06,530 +بمقدار اربعة اذا لو جيت رسمت الرسم اللي عندنا + +741 +01:17:06,530 --> 01:17:13,510 +الرسم بالشكل هذا هذا محور X هذا محور Y هذا نقطة + +742 +01:17:13,510 --> 01:17:18,870 +الاصل اللي هي Zero طلعلي كويسة النقطة الأولى Y + +743 +01:17:18,870 --> 01:17:23,690 +تساوي X تكيب مشهور عند المنحنة ومعروف يبقى المنحنة + +744 +01:17:23,690 --> 01:17:25,590 +بده يجيلك X + +745 +01:17:28,980 --> 01:17:38,190 +يبقى هذا المنحنى Y تساوي X تكيببتجي للمنحنة لأن Y + +746 +01:17:38,190 --> 01:17:42,750 +تساوي X تربيه ال Parabola إلى أعلى تلاتة يبقى + +747 +01:17:42,750 --> 01:17:47,690 +بتجرب على محور Y سالب أربعة يبقى shift إلى أسفل + +748 +01:17:47,690 --> 01:17:52,410 +بمقدار سالب أربعة إذا لو روحت قولت هذه اللي هي + +749 +01:17:52,410 --> 01:17:57,630 +main سالب أربعة و ال parabola بتجي أرسمها يبقى ال + +750 +01:17:57,630 --> 01:18:01,830 +parabola بتاخد الشكل التالي اللي عندنا هيك و بتجي + +751 +01:18:01,830 --> 01:18:03,110 +تاخد الشكل هذا + +752 +01:18:06,190 --> 01:18:11,150 +المساحة الموجودة بين المنحنيين هي المساحة اللي + +753 +01:18:11,150 --> 01:18:11,790 +عندنا هنا + +754 +01:18:19,960 --> 01:18:27,140 +واضح أن هناك منحنى أعلى ومنحنى أسفل هذا المنحنى + +755 +01:18:27,140 --> 01:18:34,200 +الأسفل يساوي تلاتة X تربية ناقص أربعة ومنحنى + +756 +01:18:34,200 --> 01:18:39,620 +الأعلى Y تساوي X تتانية إذا هذا تكمل بالنسبة ل X + +757 +01:18:39,620 --> 01:18:46,560 +إذا بلزمني أعرف قدر أقل قيمة ل X هنا وقدر أكبر + +758 +01:18:46,560 --> 01:18:54,060 +قيمة ل X هنابتروح احل المعادلاتين مع بعض بالنسبة + +759 +01:18:54,060 --> 01:19:00,200 +لمين الى X يبقى بالدرجة اقول X تكيب يساوي تلاتة X + +760 +01:19:00,200 --> 01:19:08,760 +تربيع ناقص أربعة او X تكيب ناقص تلاتة X أُص أربعة + +761 +01:19:08,760 --> 01:19:17,160 +زائد أربعة يساوي Zero X تربيع زائد أربعة يساوي + +762 +01:19:17,160 --> 01:19:24,370 +Zeroنقدر نحللها هيك؟ نسأل الموضوع، اه يبقى هذه + +763 +01:19:24,370 --> 01:19:32,870 +معادلة من الدرجة التالتة يبقى شغل مخك مين + +764 +01:19:32,870 --> 01:19:39,310 +قالك not exist يا شاطر انت؟ هو اللي وجهك الامتعان + +765 +01:19:39,310 --> 01:19:43,110 +وقلتلنا does not exist هو اللي بقولك العلامة does + +766 +01:19:43,110 --> 01:19:46,790 +not exist نفس الإجابة + +767 +01:19:52,010 --> 01:20:00,210 +طبعا شو بيزددى؟ بدي أنزل الدرجة بتاعتها من الدرجة + +768 +01:20:00,210 --> 01:20:06,650 +التالتة للدرجة التانية اتفكرا اولا كي بتروح على ال + +769 +01:20:06,650 --> 01:20:12,190 +constant و بتشوف قواسم ال constant واحد سالب واحد + +770 +01:20:12,190 --> 01:20:17,150 +اتنين سالب اتنين اربعة سالب اربعة يبقى ان عندي ستة + +771 +01:20:17,150 --> 01:20:23,410 +قواسم واحد منهم لازم يحقق المعادلةبقول جرب الواحد + +772 +01:20:23,410 --> 01:20:27,990 +والسالب واحد انسى الموضوع تمام والله يمكن يجيبوها + +773 +01:20:27,990 --> 01:20:34,970 +لو قلت هنا واحد واربع خمس سالب تسبطش لو قلت سالب + +774 +01:20:34,970 --> 01:20:40,050 +واحد بصير سالب واحد و هدى السالب تلاته بصير سالب + +775 +01:20:40,050 --> 01:20:41,890 +اه والله سالب واحد تيجي بنفع + +776 +01:20:46,000 --> 01:21:04,500 +ماذا لو انا + +777 +01:21:04,500 --> 01:21:08,200 +انا انا انا انا انا انا انا انا انا انا انا انا + +778 +01:21:08,200 --> 01:21:08,300 +انا انا انا انا انا انا انا انا انا انا انا انا + +779 +01:21:08,300 --> 01:21:08,340 +انا انا انا انا انا انا انا انا انا انا انا انا + +780 +01:21:08,340 --> 01:21:09,240 +انا انا انا انا انا انا انا انا انا انا انا انا + +781 +01:21:09,240 --> 01:21:14,600 +اناequation one سميه لهذا ال equation one يعني + +782 +01:21:14,600 --> 01:21:19,600 +معنى هذا الكلام ان ال X نقص اتنين هو احد العوامل + +783 +01:21:19,600 --> 01:21:28,580 +للمعادلة يبقى هنا ال X نقص اتنين is a factor of + +784 +01:21:28,580 --> 01:21:33,400 +equation oneماذا يعني factor of equation one؟ يعني + +785 +01:21:33,400 --> 01:21:39,000 +لو جسمت المعادلة هذه على x نقص اتنين تقبل القسمة + +786 +01:21:39,000 --> 01:21:44,060 +بدون باقيطيب تعالى اتأكد كلامنا صحيح و الله كله + +787 +01:21:44,060 --> 01:21:50,080 +كلام اذا بتروح اقسم اللى عندنا اللى هو main x تكيب + +788 +01:21:50,080 --> 01:21:57,900 +ناقص قداش اتنين ناقص تلاتة x تربية ناقص تلاتة زائد + +789 +01:21:57,900 --> 01:22:05,120 +اربعة كله على x ناقص اتنينبعدين بقولوا x تكييب على + +790 +01:22:05,120 --> 01:22:12,580 +x فيها كده؟ x تربيه طيب x تربيه في x بx تكييب نقص + +791 +01:22:12,580 --> 01:22:18,740 +اتنين x تربيه زائد بصير نقص وهذه زائد مع سلامة + +792 +01:22:18,740 --> 01:22:27,120 +زائد اتنين x تربيه بظل سالب x تربيه زائد اربعةسالب + +793 +01:22:27,120 --> 01:22:34,820 +X تربيع على X بظال جديش سالب X سالب X تربيع زائد + +794 +01:22:34,820 --> 01:22:43,140 +2X زائد ناقص مع السلامة بظال ناقص 2X زائد جديش + +795 +01:22:43,630 --> 01:22:48,490 +أربعة الباقي من الدرجة الأولى والمقصوم عليه من + +796 +01:22:48,490 --> 01:22:54,610 +الدرجة الأولى يبقى بنواصل عملية القسمة يبقى ناقص + +797 +01:22:54,610 --> 01:23:02,450 +اتنين X على X بثالث اتنين بثالث اتنين X زائد أربعة + +798 +01:23:02,450 --> 01:23:09,900 +زائد ناقص بصير Zero فعلا هي قسمت بدون باقييبقى + +799 +01:23:09,900 --> 01:23:15,880 +مسألتي هذه هاها بصير على الشكل التالي هذا المثل + +800 +01:23:15,880 --> 01:23:22,280 +بصير أخدت x ناقص اتنين طالع النتج عندي قداش x + +801 +01:23:22,280 --> 01:23:30,180 +ترابيع ناقص xنقص اتنين كله بده يساوي قداش بده + +802 +01:23:30,180 --> 01:23:36,120 +يساوي زيرو الحين هذه بقدر احللها يبقى هذه x نقص + +803 +01:23:36,120 --> 01:23:46,240 +اتنين وهذا قص وهذا قص ويساوي زيرو x1 2 ناقص زاد + +804 +01:23:46,240 --> 01:23:52,480 +صار الجث هذا هو نفس الجث هذا يبقى صار عندي x ناقص + +805 +01:23:52,480 --> 01:23:58,500 +2 لكل تربية في x زائد واحد بده يساوي zero هذا + +806 +01:23:58,500 --> 01:24:03,500 +معناه ان x بده يساوي 2 والx بده يساوي جدال سالب + +807 +01:24:03,500 --> 01:24:08,660 +واحد إذا النقطة هذه سالب واحد والنقطة هذه 8يعني + +808 +01:24:08,660 --> 01:24:13,140 +النقطة دي لما أقول X نقص اتنين لكل تربية يعني طلعت + +809 +01:24:13,140 --> 01:24:19,740 +نفس النقطة بس إيه مكررة مرتم تمام يبقى معنا هذا + +810 +01:24:19,740 --> 01:24:24,960 +الكلام بدي أقوله ال area إيه بده سوى تكامل من عند + +811 +01:24:24,960 --> 01:24:30,640 +السلب واحد لغاية الإتنين الدالة اللي فوق هي من X + +812 +01:24:30,640 --> 01:24:39,070 +تكيمنقص الدلة التي تحتلت تلاتة X تربية ناقص أربعةY + +813 +01:24:39,070 --> 01:24:45,650 +تساوي تلاتة X تربية ناقص أربعة تلاتة X تربية ناقص + +814 +01:24:45,650 --> 01:24:51,370 +أربعة كله بالنسبة لمين إلى DX يبقى هذا الكلام + +815 +01:24:51,370 --> 01:24:56,630 +يساوي تكامل من سلب واحد لاتنين لل X تكيب ناقص + +816 +01:24:56,630 --> 01:25:03,510 +تلاتة X تربية زائد أربعة كله بالنسبة إلى DX ان + +817 +01:25:03,510 --> 01:25:10,170 +كامل يبقى X أقصى أربعة على أربعةنقص x تكيب على 3 + +818 +01:25:10,170 --> 01:25:19,560 +مع 3 زائد 4x كله من ناقص 1 لغاية 2نعود بالقيمة + +819 +01:25:19,560 --> 01:25:27,100 +اللى فوق ناقص القيمة اللى تحت يبقى يساوي 16 على 4 + +820 +01:25:27,100 --> 01:25:37,240 +ناقص تمانية زائد تمانية ناقص قوس هنا بصير ربع وهنا + +821 +01:25:37,240 --> 01:25:45,200 +زائد واحد وهنا ناقص أربعةهذه ستصبح تمانية و تمانية + +822 +01:25:45,200 --> 01:25:52,320 +مع السلامة هذه ستصبح أربعة ناقص ربع ناقص واحد زائد + +823 +01:25:52,320 --> 01:25:57,780 +أربعة أربعة و أربعة تمانية تمانية بدنا نشيل منها + +824 +01:25:57,780 --> 01:26:06,880 +واحد ثبال سبعة ناقص ربع يعني ستة و تلت أربع يعني + +825 +01:26:06,880 --> 01:26:11,460 +سبعة و عشرين على قداش على أربعة + +826 +01:26:13,950 --> 01:26:20,170 +المثال الأخير بيقول + +827 +01:26:20,170 --> 01:26:29,970 +example 3 find the area + +828 +01:26:29,970 --> 01:26:33,130 +enclosed + +829 +01:26:33,130 --> 01:26:38,010 +by + +830 +01:26:38,010 --> 01:26:41,150 +the + +831 +01:26:41,150 --> 01:26:42,810 +y-axis + +832 +01:26:46,800 --> 01:26:56,180 +والـ curve هو المنحنة x يساوي y ناقص واحد لكل + +833 +01:26:56,180 --> 01:27:07,580 +تربيع و ال x يساوي تلاتة ناقص ال y and ال x يساوي + +834 +01:27:07,580 --> 01:27:20,300 +اتنين جذر ال yas shown in the figure كما هو مبين + +835 +01:27:20,300 --> 01:27:25,600 +بالشكل وراح رسملي طبعا هذا سؤال في الكتاب راح + +836 +01:27:25,600 --> 01:27:33,340 +رسملي هذا الشكل اللي محصور بين هذه المنحنيات وطلب + +837 +01:27:33,340 --> 01:27:35,600 +مساحة هذا الشكل + +838 +01:28:03,030 --> 01:28:05,110 +السلام عليكم و رحمه الله + +839 +01:28:19,970 --> 01:28:24,190 +الله أكبر الله أكبر الله أكبر + +840 +01:28:44,230 --> 01:28:49,510 +قال لي اتلي مساحة المنطقة المغلقة بمحور Y يبقى + +841 +01:28:49,510 --> 01:28:56,030 +محور Y احد المنحنيات X يساوي Y ناقص واحد لكل تربيع + +842 +01:28:56,030 --> 01:29:01,930 +و X يساوي تلاتة ناقص Y و X يساوي اتنين جذر ال Y + +843 +01:29:01,930 --> 01:29:06,990 +يبقى المساحة اللي بينهم هي المساحة المظللة اللي + +844 +01:29:06,990 --> 01:29:12,150 +عندنا هذه و قال لي هنا النقطة بقى لدي الواحد تمام + +845 +01:29:13,460 --> 01:29:17,920 +طبعا الكتاب حط السؤال و رسمك الرسمة و قولك هات ليه + +846 +01:29:17,920 --> 01:29:23,580 +المساحة اللى عندنا بقوله بسيطة منحنى لو جيت قولت + +847 +01:29:23,580 --> 01:29:27,380 +اللى تحت و اللى فوق صار اللى فوق منحنيات اتنين و + +848 +01:29:27,380 --> 01:29:31,620 +اللى تحت منحنى واحد صحيح إذا ماتظبطشلو جيت اللى + +849 +01:29:31,620 --> 01:29:36,280 +علي اليمين و اللى علي الإشمال بيصيروا اتنين علي + +850 +01:29:36,280 --> 01:29:39,960 +اليمين و خط علي الإشمال و بعدين واحد فاجهي من + +851 +01:29:39,960 --> 01:29:46,520 +الخربطة هذه لكن لو جيت قلت بتهيأجسم هذا المنحنى + +852 +01:29:46,520 --> 01:29:52,460 +إلى منطقتين بالشكل اللى عندنا هذا يبقى هاي المنطقة + +853 +01:29:52,460 --> 01:29:56,380 +و + +854 +01:29:56,380 --> 01:30:01,340 +المنطقة التانيةعندما أخذ هذه المنطقة و أخذ هذه + +855 +01:30:01,340 --> 01:30:04,220 +المنطقة و أخد هذه المنطقة و أخد هذه المنطقة و أخد + +856 +01:30:04,220 --> 01:30:05,400 +هذه المنطقة و أخد هذه المنطقة و أخد هذه المنطقة و + +857 +01:30:05,400 --> 01:30:07,160 +أخد هذه المنطقة و أخد هذه المنطقة و أخد هذه + +858 +01:30:07,160 --> 01:30:12,280 +المنطقة و أخد هذه المنطقة و أخد هذه المنطقة و أخد + +859 +01:30:12,280 --> 01:30:18,900 +هذه المنطقة و أخد هذه المنطقة و أخد هذه المنطقة + +860 +01:30:18,950 --> 01:30:24,010 +يبقى انا عند هنا x يساوي y ناقص واحد لكل تربية + +861 +01:30:24,010 --> 01:30:30,150 +وعندي x يساوي تلاتة ناقص y يبقى بقدر اجيب قيمة y + +862 +01:30:30,150 --> 01:30:36,530 +بس انا لازمالي mainلازمالى قيمة X وليس قيمة Y اذا + +863 +01:30:36,530 --> 01:30:43,810 +انا هنا بقدر اقول المنحنى الاول X يساوي Y ناقص + +864 +01:30:43,810 --> 01:30:49,930 +واحد لكل تربية والمنحنى التانى X يساوي تلاتة ناقص + +865 +01:30:49,930 --> 01:30:54,250 +Yحلّيت بالنسبة ل X في الأول وحلّيت بالنسبة ل Y في + +866 +01:30:54,250 --> 01:30:58,990 +الأول، لا تفرق عننا هذي والله هذي السيان يبقى احنا + +867 +01:30:58,990 --> 01:31:02,870 +لو جينا قولنا بدي أخليها زي ما هي مثلا يبقى ال Y + +868 +01:31:02,870 --> 01:31:10,050 +ناقص واحد لكل تربية تسوى تلاتة ناقص Yأو بمعنى آخر + +869 +01:31:10,050 --> 01:31:17,130 +Y تربية ناقص اتنين Y زائد واحد يساوي تلاتة ناقص Y + +870 +01:31:17,130 --> 01:31:23,630 +ممكن نعملها معادلة صفرية بصير Y تربية هات Y هنا + +871 +01:31:23,630 --> 01:31:30,270 +بصير موجة بصير ناقص Y هات هات هنا بصير سالبتلاتة + +872 +01:31:30,270 --> 01:31:34,810 +مع واحد بيبقى سالب اتنين يساوي زيرو هذه لو روحت + +873 +01:31:34,810 --> 01:31:41,950 +حللتها كقوسين يساوي زيرو يبقى هنا Y هنا Y واحد + +874 +01:31:41,950 --> 01:31:47,610 +اتنين سالب اللي هو اتنين Y وموجة بيبقى سالب Y + +875 +01:31:47,610 --> 01:31:54,140 +مظبوط اذا انا عندي Y سالب واحد وY اتنينيبقى هنا y + +876 +01:31:54,140 --> 01:32:01,240 +يساوي سالب واحد و y تساوي اتنين يبقى انا انا حلت + +877 +01:32:01,240 --> 01:32:08,020 +الاتنين هدول مع بعض مرة بدهم يتقفع عند y تساوي + +878 +01:32:08,020 --> 01:32:13,900 +سالب واحد و مرة عند y تساوي من الاتنينإذا للإحداث + +879 +01:32:13,900 --> 01:32:19,300 +النقطة هذه بيكون جداش لإتنين هذا المنحنى لو كملته + +880 +01:32:19,300 --> 01:32:24,380 +أجه هيتقاطع مع مين؟ مع الخط عنده نقطة Y تساوي سالب + +881 +01:32:24,380 --> 01:32:27,800 +واحد إذا ماليش علاقة فيه يبقى أنا إليه علاقة في ال + +882 +01:32:27,800 --> 01:32:34,270 +Y تساوي مين؟ إتنينلو جيت أخدت Y تساوي 2 و عوضت بها + +883 +01:32:34,270 --> 01:32:41,110 +في أي من المعادلتين يبقى هذا بيعطيك ان X بيساوي + +884 +01:32:41,110 --> 01:32:46,210 +تلاتة نقص اتنين اللي هو قداش واحد إذا إحداث النقطة + +885 +01:32:46,210 --> 01:32:52,510 +هذه هو واحد و اتنين يبقى X عند هنا بقداش تساوي + +886 +01:32:52,510 --> 01:32:56,990 +واحد بالدالي النقطة اللي عندنا هذه كمان بدي أعرف + +887 +01:32:56,990 --> 01:32:59,390 +قداش القيمة بتبعتها + +888 +01:33:02,590 --> 01:33:06,690 +يبقى بدى اعرف جداش لحظاتى معناته بدى احل معادلة + +889 +01:33:06,690 --> 01:33:11,290 +المنحنى هذا مع مين مع معادلة المنحنى اللى عندنا + +890 +01:33:11,290 --> 01:33:21,490 +هذا هذا المنحنى اللى همين X بده يساوي تلاتة ناقص Y + +891 +01:33:21,490 --> 01:33:31,470 +and ال X بده يساوي اتنين جذر ال Yبقدر اقول هذه why + +892 +01:33:31,470 --> 01:33:39,720 +تساوي؟تلاتة ناقص X تلاتة ناقص X and هذه لو جيت + +893 +01:33:39,720 --> 01:33:47,820 +ربعت الطرفين بصير Y يساوي ربع ال X يبقى Y تساوي + +894 +01:33:47,820 --> 01:33:55,800 +ربع ال X تربية يبقى لو حلت الاتنين مع بعض ربع X + +895 +01:33:55,800 --> 01:34:02,930 +تربية بدها تساوي تلاتة ناقص Xأضرب كله في أربعة + +896 +01:34:02,930 --> 01:34:10,670 +بيصير عندك مين X تربية يساوي اتناشر ناقص أربعة X + +897 +01:34:10,670 --> 01:34:19,070 +يبقى هذا الكلام بيصير X تربية زائد أربعة X ناقص + +898 +01:34:19,070 --> 01:34:25,440 +اتناشر يساوي كده؟ يساوي Zeroنحلل هذا الكلام كقوسين + +899 +01:34:25,440 --> 01:34:32,680 +يساوي Zero يبقى هنا X هنا X هذي ستة في اتنين ستة + +900 +01:34:32,680 --> 01:34:38,020 +في اتنين هذي زائد و هذي نقص زائد ستة X و نقص اتنين + +901 +01:34:38,020 --> 01:34:42,900 +X يبقى زائد اربع X يبقى بناء ان عليه ال X بده + +902 +01:34:42,900 --> 01:34:50,900 +يساوي اتنين و ال X بده يساوي سالب ستةيبقى هذا + +903 +01:34:50,900 --> 01:34:55,380 +الكلام، لو كملنا المنحة، لو أجى معاه، هذا هيتقطع + +904 +01:34:55,380 --> 01:34:58,900 +عند السلف ستة، ماليش علاقة فيها، إيه اللي علاقة في + +905 +01:34:58,900 --> 01:35:05,180 +جداش؟ فيه ليتنين، يبقى بصير التكامل عندنا بهذا + +906 +01:35:05,180 --> 01:35:12,070 +الشكليبقى الآن حددت حدود التكامل، قسمت المنطقة إلى + +907 +01:35:12,070 --> 01:35:18,850 +منطقتين، إذا بقدر أحسب قداش قيمة هذه المساحة + +908 +01:35:18,850 --> 01:35:25,110 +المحصورة بين المنحنيين، فبروح بقوله الـ A to Z + +909 +01:35:26,800 --> 01:35:31,780 +تكامل من عند ال zero لغاية ال واحد من ال zero + +910 +01:35:31,780 --> 01:35:39,200 +لغاية ال واحد الدالة اللى فوق اه هذه مرتبناش هذه + +911 +01:35:39,200 --> 01:35:48,580 +بدها تصير جذر ال X بده ساوي Y ناقص واحد طبعا هحمل + +912 +01:35:48,580 --> 01:35:49,880 +ال Y السالبة + +913 +01:35:54,960 --> 01:36:04,070 +يبقى هذا معناه ان Y تساوي جذر ال X زائد واحديبقى + +914 +01:36:04,070 --> 01:36:10,530 +الدالة اللي فوق هذه Y تساوي جدر ال X زائد واحد هي + +915 +01:36:10,530 --> 01:36:17,410 +الدالة اللي فوق، يبقى جدر ال X زائد واحد ناقص + +916 +01:36:17,410 --> 01:36:24,410 +الدالة اللي تحت، هذه طلعناها كده؟رابع X تربيع يبقى + +917 +01:36:24,410 --> 01:36:32,130 +ناقص رابع X تربيع كله بالنسبة إلى DX زائد تكمل + +918 +01:36:32,130 --> 01:36:37,440 +المنطقة الثانية من واحد لغاية اتنينالدالة اللى فوق + +919 +01:36:37,440 --> 01:36:45,180 +هذى يقول انه يسوى تلاتة ناقص X تلاتة ناقص X ناقص + +920 +01:36:45,180 --> 01:36:52,180 +اللى هو ربع X تربيع يبقى ناقص ربع X تربيع كله + +921 +01:36:52,180 --> 01:36:58,300 +بالنسبة إلى DX يبقى + +922 +01:36:58,300 --> 01:37:03,660 +هذه ال area ايه تساوي من درجة التكمل الأول يبقى + +923 +01:37:03,660 --> 01:37:05,420 +هذا طول تان + +924 +01:37:08,270 --> 01:37:16,990 +زي الاكس ناقص اكس تكييب على جداش على الاطناع + +925 +01:37:16,990 --> 01:37:22,550 +الحكاية ده من عند ال zero لغاية الواحد نجي للتكامل + +926 +01:37:22,550 --> 01:37:30,680 +اللي بعده ثلاثة اكسنقص x تربيه على اتنين نقص x + +927 +01:37:30,680 --> 01:37:37,740 +تكيب على الاطمعاش كل هذا الكلام من الواحد لغاية + +928 +01:37:37,740 --> 01:37:45,220 +اتنين يبقى هذا بده يساوي تلتين زائد واحد ناقص واحد + +929 +01:37:45,220 --> 01:37:49,800 +على الاطمعاش و ال zero ال باقي كله بطير ب zeroنجي + +930 +01:37:49,800 --> 01:37:56,940 +لبعدها زائد اتنين في تلاتة بستة و هنا ناقص اتنين و + +931 +01:37:56,940 --> 01:38:05,340 +هنا ناقص تمانية على الاتماشر فيها اتنين على تلاتة + +932 +01:38:13,030 --> 01:38:18,050 +خلّصنا ال term اللي فوق ناقص ال term اللي تحت + +933 +01:38:18,050 --> 01:38:27,050 +تلاتة ناقص نص ناقص واحد على الاطمعاش هذا الكلام + +934 +01:38:27,050 --> 01:38:28,930 +يساوي كل term + +935 +01:38:34,510 --> 01:38:41,450 +هذه اتنين ع تلاتة مع سالب اتنين ع تلاتة و عندك هنا + +936 +01:38:41,450 --> 01:38:50,690 +سبعة و سالب اتنين بيضال خمسة خمسة نقص واحد ع + +937 +01:38:50,690 --> 01:38:59,310 +الاطماناسمع يا راجل ناقص ثلاثة زائد نص زائد واحد + +938 +01:38:59,310 --> 01:39:02,950 +على الاطناش ناقص واحد على اطناش وزائد واحد على + +939 +01:39:02,950 --> 01:39:09,490 +اطناش بيروح بيضل عندنا جداش اتنين و نص يبقى خمسة + +940 +01:39:09,490 --> 01:39:17,460 +على اتنين مقدار هذه المساحة، تمام؟طيب لحد هنا + +941 +01:39:17,460 --> 01:39:22,040 +انتهى ال section اللي هو خمسة ستة ويليكم أرقام + +942 +01:39:22,040 --> 01:39:31,000 +المسائل يبقى exercises خمسة ستة المسائل التالية + +943 +01:39:31,000 --> 01:39:35,780 +واحد لتسعة + +944 +01:39:35,780 --> 01:39:44,380 +وستين يعني واحد لتسعة وستين الأدومن تلاتة وسبعين + +945 +01:39:44,380 --> 01:39:50,560 +لغاية تمانية وسبعين وكذلك + +946 +01:39:50,560 --> 01:39:53,320 +من تمانية لتسعين + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/gPP3rP0CXnk_raw.json 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مباشرة هيك بقدرش لكن بقدر أعمل تعويضة محددة + +9 +00:01:02,100 --> 00:01:06,900 +باجي بطلع في المثل اللي عندى و التان كده تفاضلها؟ + +10 +00:01:07,400 --> 00:01:12,500 +سكتر بيع موجودة إذا اللي بدي أشيله و أغيره بدي + +11 +00:01:12,500 --> 00:01:18,300 +أشيل التان و أحط بدلها دل جديدة إذا لو حطيت ال T + +12 +00:01:18,300 --> 00:01:25,400 +تساوي تان ال X يبقى ال DT بدي أساوي سكتر بيع ال X + +13 +00:01:25,400 --> 00:01:31,500 +DX إذا ممكن أشيل سكتر بيع ال X DX هذه وقت بدلها DT + +14 +00:01:31,880 --> 00:01:40,260 +يبقى آلة المسألة الى تكامل ل T تكعيب DT بقيت حدود + +15 +00:01:40,260 --> 00:01:44,460 +التكامل بدي أغير حدود التكامل صفقة لهذه التعويضة + +16 +00:01:44,460 --> 00:01:49,110 +الجديدةفبجي بقول لما تبقى ال X باي على أربعة ضل + +17 +00:01:49,110 --> 00:01:55,590 +الخمسة واربعين يبقى ال T هنا تساوي واحد ضل ال zero + +18 +00:01:55,590 --> 00:02:02,510 +ب zero يبقى T تساوي zero إذا غيرنا حدود التكمل طبق + +19 +00:02:02,510 --> 00:02:07,750 +لمين؟ طبق التعويضة الجديدة اللي حاطناها يبقى هذا + +20 +00:02:07,750 --> 00:02:13,150 +النتيجة تساوي T أس أربعة على أربعة والكلام من zero + +21 +00:02:13,150 --> 00:02:19,080 +لغاية 13لغاية واحد يبقى هذا الكلام يساوي ربع في + +22 +00:02:19,080 --> 00:02:24,580 +واحد أس أربع ناقص Zero أس أربع اللي هو Zero واحد + +23 +00:02:24,580 --> 00:02:32,200 +أس أربع باربع يبقى النتيجة تساوي ربع التكامل اللي + +24 +00:02:32,200 --> 00:02:40,490 +بعده تكامل رقم تمانيةيبقى integration من سالب واحد + +25 +00:02:40,490 --> 00:02:42,370 +لغاية سالب نص + +26 +00:03:00,500 --> 00:03:04,700 +طيب، بعدي بتطلع في المثل اللي عندي، شو اللي وضعه + +27 +00:03:04,700 --> 00:03:09,260 +غير طبيعي في المثل أو اللي مصعب شكلها؟ الزاوية + +28 +00:03:09,260 --> 00:03:13,840 +تبعت الصين، يبقى الزاوية هي اللي مصعبة المثل، نهيك + +29 +00:03:13,840 --> 00:03:18,340 +على انه مشتقت الزاوية بتعطينا مين؟ ال term اللي + +30 +00:03:18,340 --> 00:03:24,750 +برايبقى بدي اكتب المثلة بشكل لطيف أو سهل جدا يبقى + +31 +00:03:24,750 --> 00:03:31,230 +بدي اشيل كل هذا و بدي احط ال X يسوى واحد زائد واحد + +32 +00:03:31,230 --> 00:03:38,810 +على T لو جينا اشتقناها يبقى DX بدي اساوي سالب واحد + +33 +00:03:38,810 --> 00:03:47,180 +على T تربية DTأو بقدر أقول سالب DX بدي أساوي T + +34 +00:03:47,180 --> 00:03:54,280 +السالب اتنين DT إذا بقدر T السالب اتنين هذه مع DT + +35 +00:03:54,280 --> 00:04:00,400 +أشيلها و أكتف بدل جديد سالب DX يبقى هاي السالب بدي + +36 +00:04:00,400 --> 00:04:07,120 +أخده برا و هاي تكامل و هادي ال sign تربيع ال X كله + +37 +00:04:07,120 --> 00:04:13,580 +في DXبقيت حدود التكامل لما تبقى ال X يساوي سالب T + +38 +00:04:13,580 --> 00:04:19,260 +تساوي سالب نص يبقى سالب نص بصير هذي فوق باتنين + +39 +00:04:19,260 --> 00:04:24,360 +اتنين بالسالب يبقى واحد سالب اتنين مضل قداش سالب + +40 +00:04:24,360 --> 00:04:29,300 +واحد يبقى هذي بيصير سالب واحد و لما تبقى T بسالب + +41 +00:04:29,300 --> 00:04:34,100 +واحد بصير ال term هذا كله بسالب واحد يبقى كله بصير + +42 +00:04:34,100 --> 00:04:40,130 +Zeroيبقى من zero ل سالب واحد ل main لل sign تربيع + +43 +00:04:40,130 --> 00:04:44,630 +ال X DX واضح ان ال index الكبير هو اللي تحته + +44 +00:04:44,630 --> 00:04:49,170 +والصغير هو ال fourth يبقى بنجلب حدود التكامل و + +45 +00:04:49,170 --> 00:04:53,510 +بنضيع الإشارة اللي عندنا طبقا لأول خاصية من خاصة + +46 +00:04:53,510 --> 00:04:59,250 +تكامل المحدود يبقى هذا الكلام بده يساوي تكامل من + +47 +00:04:59,250 --> 00:05:04,630 +سالب واحد لغاية zero ل sign تربيع ال X DX + +48 +00:05:11,900 --> 00:05:17,720 +يبقى هذا الكلام بده يساوي تكامل من سالب واحد لغاية + +49 +00:05:17,720 --> 00:05:24,590 +Zero لنص في واحد ناقص cosine اتنين ال X DXمن + +50 +00:05:24,590 --> 00:05:28,410 +المستطابقات تبعات حساب المثلثات sin تربيه ال X هو + +51 +00:05:28,410 --> 00:05:34,390 +نص في واحد ناقص cosine اتنين X يبقى النص هذا بدي + +52 +00:05:34,390 --> 00:05:40,870 +يظل برا و عندك هذا جزء تكامل الواحد ب X وتكامل ال + +53 +00:05:40,870 --> 00:05:46,690 +cosine بsin اتنين X على اتنين والكلام من سالب واحد + +54 +00:05:46,690 --> 00:05:53,240 +لغاية ال zeroيبقى يا نص خلّيك برا و بدنا نبدأ نعوض + +55 +00:05:53,240 --> 00:06:00,140 +بحدود التكامل يبقى Zero و Sin Zero Zero كذلك يبقى + +56 +00:06:00,140 --> 00:06:06,210 +هاي Zero ناقص Zero ناقصبدا ابدأ اعوض بالقيمة اللى + +57 +00:06:06,210 --> 00:06:11,670 +تحتى يبقى ال X بدي اشيله لأو اكتبه لجداش ناقص واحد + +58 +00:06:11,670 --> 00:06:16,430 +وهي الناقص اللى عندنا بدي اشيل ال X و احطه مكان + +59 +00:06:16,430 --> 00:06:23,750 +جداش سالب واحد يبقى بصير سالي باتنين يبقى ال sign + +60 +00:06:23,750 --> 00:06:30,610 +لسالي باتنين على اتنين بالشكل اللى عندنا هذا تمام + +61 +00:06:31,240 --> 00:06:36,140 +يبقى هذا الكلام بده يساوي هذا النص اللي برا وده + +62 +00:06:36,140 --> 00:06:41,720 +دخل السلب اللي عندها ده يوم بصير عندي واحد ناقص + +63 +00:06:41,720 --> 00:06:47,540 +sign اتنين على اتنين بالشكل اللي عندنا طبعا ال + +64 +00:06:47,540 --> 00:06:53,480 +sign odd السلب بطلع برا بصير موجب في سلب مضروب برا + +65 +00:06:53,480 --> 00:06:59,100 +يبقى بصير سلب يبقى واحد ناقص sign اتنين على اتنين + +66 +00:06:59,270 --> 00:07:03,270 +انت هنا مثلا بدك تكتب لي نص ناقص ربع sign اتنين + +67 +00:07:03,270 --> 00:07:09,750 +سيانة بتفرجش يبقى هذه لو قلت نص ناقص ربع sign + +68 +00:07:09,750 --> 00:07:18,000 +اتنين هذه هي نتيجة من التكاملطيب، الآن في عندنا + +69 +00:07:18,000 --> 00:07:24,100 +كمان مثال آخر غير هذه الأنواع من الأمثلة و هذا + +70 +00:07:24,100 --> 00:07:29,200 +المثال جئنا به في إحدى الامتحانات السابقة يبقى + +71 +00:07:29,200 --> 00:07:35,000 +كمان example بيقول + +72 +00:07:35,000 --> 00:07:39,580 +use the integral استخدم التكامل + +73 +00:07:42,290 --> 00:07:50,670 +تكامل من واحد لغاية اتنينللـ F of Z DZ بده يساوي + +74 +00:07:50,670 --> 00:07:56,650 +تلاتة to find + +75 +00:07:56,650 --> 00:08:05,110 +the value of مشان تحسبلي قداش قيمة تكامل من نص + +76 +00:08:05,110 --> 00:08:12,750 +لغاية واحد لواحد على X تربية F of واحد على X نقس + +77 +00:08:20,110 --> 00:08:26,750 +يبقى شكل هذا المثال يختلف عن شكل سابقاته من الأمثل + +78 +00:08:26,750 --> 00:08:31,530 +قبل أن نتكامل و نتكامل على طول الخط هذا بيقول + +79 +00:08:31,530 --> 00:08:37,250 +استخدم هذا التكامل يبقى هذا معطيان للحصول على قيمة + +80 +00:08:37,250 --> 00:08:41,450 +التكامل هذاباجي باطلع في التكامل اللي عندي وهذا + +81 +00:08:41,450 --> 00:08:47,090 +بختلفه كليا عن بعض، لكن هذا مقطع إذا ماليش علاقة + +82 +00:08:47,090 --> 00:08:51,550 +فيه لما بلزمني بستخدمه، بلزمنيش بستخدموش، إذا + +83 +00:08:51,550 --> 00:08:56,590 +مشكلتنا مع مين؟ مع هذا التكاملمشان اشتغل هذا + +84 +00:08:56,590 --> 00:09:01,290 +التكامل في شغل غير طبيعى، الغير طبيعى واحد على اكس + +85 +00:09:01,290 --> 00:09:04,150 +طبيعى ولا واحد على اكس؟ واحد على اكس، واحد على + +86 +00:09:04,150 --> 00:09:04,850 +اكس، واحد على اكس، واحد على اكس، واحد على اكس، + +87 +00:09:04,850 --> 00:09:04,870 +واحد على اكس، واحد على اكس، واحد على اكس، واحد على + +88 +00:09:04,870 --> 00:09:05,230 +اكس، واحد على اكس، واحد على اكس، واحد على اكس، + +89 +00:09:05,230 --> 00:09:08,210 +واحد على اكس، واحد على اكس، واحد على اكس، واحد على + +90 +00:09:08,210 --> 00:09:08,670 +اكس، واحد على اكس، واحد على اكس، واحد على اكس، + +91 +00:09:08,670 --> 00:09:12,390 +واحد على اكس، واحد على اكس، واحد على اكس، واحد على + +92 +00:09:12,390 --> 00:09:21,100 +اكس، واحد على اكس، واحد على اكس،لو مثلا حطيت هنا Z + +93 +00:09:21,100 --> 00:09:28,700 +تساوي واحد على X أو T أو W أو اللي بدك هيه يبقى + +94 +00:09:28,700 --> 00:09:34,000 +بدنا نيجي نشتقه يبقى DZ يساوي سالب واحد على X + +95 +00:09:34,000 --> 00:09:40,270 +تربيه دي1 على X تربية موجودة عندى بس سلب ماعنديش + +96 +00:09:40,270 --> 00:09:46,430 +يبقى بضرب الطرفين بإشارة سلب يبقى بصير عندى سلب DZ + +97 +00:09:46,430 --> 00:09:53,230 +يسوى 1 على X تربية DX إذا ال 1 على X تربية هذه + +98 +00:09:53,230 --> 00:09:58,250 +كلها مع ال DX كلها تبعت المسألة بقدر أشيلها و أكتب + +99 +00:09:58,250 --> 00:10:04,950 +بدالها سلب DZيبقى صارت مسألة تكامل من نص لغاية + +100 +00:10:04,950 --> 00:10:11,050 +واحد للواحد على اكس تربيع لل F of واحد على اكس DX + +101 +00:10:11,050 --> 00:10:20,030 +يسوى تكامل F of Z تمام واحد على اكس تربيع DX بدأت + +102 +00:10:20,030 --> 00:10:26,550 +بهذه السانب برا وهذه يمين DX يبقى صار شكل المثل + +103 +00:10:26,550 --> 00:10:30,110 +اللي عنده هناك اللي هو الشكل هذا بالشكل الجديد الا + +104 +00:10:30,110 --> 00:10:35,570 +انهلكن بناروح نغير حدود التكامل طبقا للتعويض اللي + +105 +00:10:35,570 --> 00:10:42,450 +احنا حاطينا فباجي بقول لو كانت ال X بواحد يبقى Z + +106 +00:10:42,450 --> 00:10:50,090 +بواحد طب لو كانت ال X باتنين بصير واحد على نص + +107 +00:10:50,090 --> 00:10:56,950 +بتنجلبه بصير جداش بالاتنين بالشكل اللي عنها دهطيب + +108 +00:10:56,950 --> 00:11:02,270 +الان صار الرقم الكبير تحت والرقم الصغير فوق في + +109 +00:11:02,270 --> 00:11:06,570 +حدود التكامل من شكل بهذه المواد على limits of + +110 +00:11:06,570 --> 00:11:11,250 +integration وبالتالي طبقا للخاصية الأولى من خاصة + +111 +00:11:11,250 --> 00:11:16,710 +تكامل المحدود بيطير إشارة السالب يبقى هذا بيصير + +112 +00:11:16,710 --> 00:11:27,120 +تكامل من 1 ل2 لل F of Z DZ أظن هذا موضوعخلصنا يبقى + +113 +00:11:27,120 --> 00:11:35,620 +هذا الكلام بده يساوي تلاتة بدون ماتكمل طيب فيه + +114 +00:11:35,620 --> 00:11:41,640 +قاعدة بتسهل لي عملية حساب بعض التكاملات الصعبة + +115 +00:11:41,640 --> 00:11:48,620 +شوية هذه النظرية بتقول لي ما يأتي بتقولت + +116 +00:11:48,620 --> 00:11:53,980 +ال F ب continuous + +117 +00:11:56,460 --> 00:12:08,760 +function دا اللي متصلة on the symmetric interval + +118 +00:12:08,760 --> 00:12:12,740 +اللي + +119 +00:12:12,740 --> 00:12:18,900 +هو سالب a و a النقطة + +120 +00:12:18,900 --> 00:12:22,560 +الأولى if + +121 +00:12:24,020 --> 00:12:36,520 +الـ F is even دالة زوجية then تكامل من سلب A إلى A + +122 +00:12:36,520 --> 00:12:46,520 +لل F of X DX يساوي اتنين تكامل من Zero إلى A لل F + +123 +00:12:46,520 --> 00:13:00,370 +of X DX النقطة الثانيةالـ F is odd then تكامل من + +124 +00:13:00,370 --> 00:13:07,930 +سلب A إلى A لل F of X DX بدي ساوي كده؟ بدي ساوي + +125 +00:13:07,930 --> 00:13:15,630 +Zero Example Find + +126 +00:13:15,630 --> 00:13:22,440 +the value of the following integrals Find thevalue + +127 +00:13:22,440 --> 00:13:30,780 +of the following integrals + +128 +00:13:30,780 --> 00:13:36,360 +التكاملات + +129 +00:13:36,360 --> 00:13:37,300 +التالية + +130 +00:13:55,670 --> 00:14:04,990 +تكامل الأول بدنا تكامل من سالب اتنين إلى اتنين + +131 +00:14:04,990 --> 00:14:22,090 +لتلاتة X على تسعة زائد X ترابيع لكل ترابيع DX نرجع + +132 +00:14:22,090 --> 00:14:27,100 +لهذه النظرية مرة ثانيةو نحاول نفهم هذه النظرية + +133 +00:14:27,100 --> 00:14:33,050 +مشان نشوف كيف بدنا نطبقهابقول افترض الدالة F دالة + +134 +00:14:33,050 --> 00:14:39,490 +متصلة على الفترة المتماثلة ناقص a و a لما اقول + +135 +00:14:39,490 --> 00:14:44,310 +symmetric interval يعني من عند zero على اليمين جد + +136 +00:14:44,310 --> 00:14:48,510 +اللي من عند zero على الشمال بالضبط تماما فلما اقول + +137 +00:14:48,510 --> 00:14:54,490 +من ناقص a إلى a يبقى الصفر يجي وين في منتصف الفترة + +138 +00:14:54,490 --> 00:15:00,550 +يعني الفترة المتماثلةعلى طرفي Zero أو على طرفي + +139 +00:15:00,550 --> 00:15:05,490 +محور Y يبقى هاي المقصود في هذه الكتابة تالك ماقص A + +140 +00:15:05,490 --> 00:15:10,250 +وA يعني الرقم اللي عندنا هنا هو نفس الرقم هذا بس + +141 +00:15:10,250 --> 00:15:14,290 +بإشارة مخالفةيبقى هذه بسميها الـ Symmetric + +142 +00:15:14,290 --> 00:15:20,750 +Interval بقول والله إذا دالة كانت even يبقى تكامل + +143 +00:15:20,750 --> 00:15:26,830 +من ناقص A إلى A لل F of X DX يسوى اتنين التكامل من + +144 +00:15:26,830 --> 00:15:34,150 +Zero إلى A لل F of X DX السؤال لماذا؟ وماذا نستفيد + +145 +00:15:34,150 --> 00:15:40,350 +من ذلك؟ خلي بالك معاكيبقى ليش تكامل من سالب A إلى + +146 +00:15:40,350 --> 00:15:45,750 +A لل F of X DX يسوي 2 تكامل من 0 إلى A لل F of X + +147 +00:15:45,750 --> 00:15:50,190 +DX نرجع بالذاكرة إلى أول chapter درسنا فيه + +148 +00:15:50,190 --> 00:15:55,910 +Calculus A لما أقول even function يعني المنحنى + +149 +00:15:55,910 --> 00:16:02,120 +مالهمو تماثل + +150 +00:16:02,120 --> 00:16:06,160 +بالنسبة لمين؟ لمحور ويمجد النص الرسمى اللى على + +151 +00:16:06,160 --> 00:16:10,240 +اليمين زى نص الرسمى اللى وين يعنى المساحة اللى + +152 +00:16:10,240 --> 00:16:15,500 +حصرها المنحنى على يمين المحورY بينه بين محور X جد + +153 +00:16:15,500 --> 00:16:19,640 +المساحة اللي حصرها المنحنة على الشمال محور Y بينه + +154 +00:16:19,640 --> 00:16:24,300 +بين محور X تمام؟ إذا مدام المساحتين كانوا بعضيا + +155 +00:16:24,300 --> 00:16:29,280 +يكفيني حساب مساحة واحدة بضرب منين في اتنين من هنا + +156 +00:16:29,280 --> 00:16:34,660 +قولنا هذا بدي يسوى اتنين التكامل على نص في الفترة + +157 +00:16:34,660 --> 00:16:38,100 +مدام في تمثل اللي على اليمين زي اللي على الشمال + +158 +00:16:38,100 --> 00:16:43,570 +يبقى المساحة الأولى جد المساحةالثانية يبقى يكفيني + +159 +00:16:43,570 --> 00:16:47,950 +حساب واحدة فيهم بروح مضروبة في مهم في اتنين يبقى + +160 +00:16:47,950 --> 00:16:52,930 +هذا يسوى اتنين تكامل من Zero إلى A لل F of X DX + +161 +00:16:52,930 --> 00:16:57,050 +يبقى هاي أجابنا على السؤال الأول ليش هذا التكامل + +162 +00:16:57,050 --> 00:17:02,730 +يسوى التكامل الثانيسؤال الثاني، قلنا ماذا نستفيد + +163 +00:17:02,730 --> 00:17:07,270 +من ذلك؟ أيهما السل؟ اللي لما تكمل الدل لو تروح + +164 +00:17:07,270 --> 00:17:10,210 +تعوض بالقمة اللي فوق والقمة اللي تحت، والله لما + +165 +00:17:10,210 --> 00:17:14,090 +تبقى اللي تحت زيرو السل ليه؟ لما تبقى زيرو السل + +166 +00:17:14,090 --> 00:17:20,530 +يبقى المقصود هو من ذلك تبسيط عملية إجراء التكامل، + +167 +00:17:20,530 --> 00:17:24,670 +تمام؟ يبقى هاي المقصود فيه، طيب، هذا بالنسبة + +168 +00:17:24,670 --> 00:17:28,770 +للنقطة الأولى، النقطة الثانيةقال لو كانت الدالة + +169 +00:17:28,770 --> 00:17:35,350 +odd يبقى قيمة التكمل تساوي صفرشو المعنى الهندسي لل + +170 +00:17:35,350 --> 00:17:41,750 +odd function يعني المنحنى متمثل حول ال origin يبقى + +171 +00:17:41,750 --> 00:17:47,050 +أى نقطة إحدثيتها a و b بديكون إلها نقطة سالب a و + +172 +00:17:47,050 --> 00:17:51,410 +سالب b يعني الجزء اللى فوق اللى أعلى محور X بديكون + +173 +00:17:51,410 --> 00:17:56,570 +فيه جزء أقباله أسفل محور X يعني لو المنحنى في + +174 +00:17:56,570 --> 00:17:59,850 +الربع الأول بديكون المنحنى التاني في الربع التالت + +175 +00:18:00,050 --> 00:18:03,130 +لو كان منحنى في الرابع الثاني، فهو يكون في الرابع + +176 +00:18:03,130 --> 00:18:08,310 +الرابع للجبال وهكذا، يعني في جزء محصور بين منحنى + +177 +00:18:08,310 --> 00:18:14,210 +ومحور X positive area وفي جزء تاني negative area، + +178 +00:18:14,210 --> 00:18:19,010 +يبقى لو جمعت التنتينبطلع صفر انا مش طالب ال total + +179 +00:18:19,010 --> 00:18:23,270 +area total area يسوى اتنين مساحة واحدة فيهم مظبوط + +180 +00:18:23,270 --> 00:18:26,090 +بس انا مش طالب ال total area بدي اكمل و بدي اعرف + +181 +00:18:26,090 --> 00:18:31,470 +كدهش نتيجة التكمل و ليس حساب ال total area يبقى + +182 +00:18:31,470 --> 00:18:35,210 +التكمل في هذا الحالة بدي سوى مين بدي سوى 0 يبقى + +183 +00:18:35,210 --> 00:18:40,270 +هذا ببسط لعملية الحسابة الطلة فالضالة اذا الرقم + +184 +00:18:40,270 --> 00:18:43,550 +اللي تحت التكمل هو نفس الرقم اللي فوق بإشارة + +185 +00:18:43,550 --> 00:18:48,360 +مخالفةيبقى ماجي بطلع والله إذا اتدالى even يبقى + +186 +00:18:48,360 --> 00:18:52,860 +اتنين في التكامل على نصف الفترة وإذا اتدالى يبقى + +187 +00:18:52,860 --> 00:18:56,940 +قيمة التكامل يساوي صفر بدون ما أروح أحسب و أخبص و + +188 +00:18:56,940 --> 00:18:58,760 +أجيب أما أجيب الاخرين فضل + +189 +00:19:07,340 --> 00:19:10,940 +وهذا موجب بناخد الـ Absolute Value زي ما قلنا في + +190 +00:19:10,940 --> 00:19:16,600 +المحاضرة الماضية بدي الـ Total Area بحسب أو بجسم + +191 +00:19:16,600 --> 00:19:20,820 +اللي الفترة طبقا لأسفار الدالة وبكمل على كل منطقة + +192 +00:19:20,820 --> 00:19:24,200 +وبعدين باخد الـ Absolute Value بكون جبت المساحة + +193 +00:19:24,200 --> 00:19:30,940 +الحقيقية طيب نرجع لتطبيق مباشر على هذه النظرية + +194 +00:19:31,190 --> 00:19:36,130 +جالهات لقيمة كل من التكاملات التالية وعطاني دالة + +195 +00:19:36,130 --> 00:19:42,210 +بهذا الشكل بدأ اكمل هذه الدالة بقول بسيطة بطلع في + +196 +00:19:42,210 --> 00:19:46,110 +حدود التكامل اللي فوق زي اللي تحت بالضبط تماما + +197 +00:19:46,110 --> 00:19:52,570 +الدالة هذه odd ولا even واضحة + +198 +00:19:52,570 --> 00:20:02,770 +مثل الشمس even هذاعندك ال F of X بده يساوي تلاتة X + +199 +00:20:02,770 --> 00:20:08,790 +على تسعة زائد X تربية لكل تربية بدك F of سالب X + +200 +00:20:08,790 --> 00:20:15,430 +يبقى تلاتة في سالب X على تسعة زائد سالب X لكل + +201 +00:20:15,430 --> 00:20:21,030 +تربية تربيةتمام السالب هذا بقدر أقوله شرفني برا + +202 +00:20:21,030 --> 00:20:27,390 +وبصير عندي هاي تلاتة X وهذه تسعة زي X تربيع لكل + +203 +00:20:27,390 --> 00:20:32,510 +تربيع يبقى odd والله even odd function لإن F of + +204 +00:20:32,510 --> 00:20:39,390 +سالب X سوى سالب F of X يبقى هذه odd يبقى هذه + +205 +00:20:39,390 --> 00:20:47,820 +النتيجة كده؟يساوي زيرو لان + +206 +00:20:47,820 --> 00:20:55,240 +التلاتة اكس على تسعة زائد اكس تربيع تربيع is an + +207 +00:20:55,240 --> 00:21:00,510 +odd functionيبقى نظرا لإنها دالة فردية فقيمة + +208 +00:21:00,510 --> 00:21:05,730 +التكامل يتساوي صفر بدون إجراء عملية التكامل يبقى + +209 +00:21:05,730 --> 00:21:13,170 +أعوض مباشرة بدون ما أقوم بعملية التكامل نمر اتنين + +210 +00:21:13,170 --> 00:21:19,910 +بدنا تكامل من سالب باي على أربعة إلى باي على أربعة + +211 +00:21:19,910 --> 00:21:25,770 +لل X تربيه زائد سك تربيه ال X كله في DX + +212 +00:21:28,590 --> 00:21:33,510 +باجي بتطلع برضه بنفس الطريقة الرقم اللي فوق هو نفس + +213 +00:21:33,510 --> 00:21:37,270 +الرقم اللي تحت بس بإشارة هي بإشارة مخالفة + +214 +00:21:49,870 --> 00:21:58,330 +ماعنديش إلا تنتين even والاربعة odd يبقى اللي قلنا + +215 +00:21:58,330 --> 00:22:03,710 +السك والكسين هي ال even فقط يبقى ليس تحكيش غير + +216 +00:22:03,710 --> 00:22:09,110 +تعرف يبقى السك وعكس اللي هو الكسين هم التنتين even + +217 +00:22:09,110 --> 00:22:14,070 +وباقي الأربعة odd يبقى هذا even تمام؟ والاكس + +218 +00:22:14,070 --> 00:22:20,330 +تربيع؟يبقى معناته هذا الكلام يساوي 2 تكامل من 0 ل + +219 +00:22:20,330 --> 00:22:26,570 +5 على 4 يبقى هذا الكلام يساوي 2 تكامل من 0 ل 5 على + +220 +00:22:26,570 --> 00:22:31,770 +4 ل X تربيع زائد سك تربيع X DX + +221 +00:22:45,270 --> 00:22:49,490 +اللي مايعرفش بشيل كل X و بحط مكانها سالب X تربية + +222 +00:22:49,490 --> 00:22:53,610 +بتبقى كما هي هذي ال cycle ناقص X لكل تربية هي + +223 +00:22:53,610 --> 00:22:58,330 +بcycle X تربية بتبقى تربية كما هي بنال عليها صارت + +224 +00:22:58,330 --> 00:23:04,040 +هذه even functionيبقى و هذا الكلام بده يسوى اتنين + +225 +00:23:04,040 --> 00:23:11,240 +فيه بدك تعمل هذه الدالة يبقى X تكيب على تلاتة زائد + +226 +00:23:11,240 --> 00:23:16,980 +تاني ال X من و لا وين من Zero لغاية Pi على أربع + +227 +00:23:17,420 --> 00:23:22,820 +تمام؟ يبقى هذا اتنين برا مالوش دعوة وهذه بدي أشيل + +228 +00:23:22,820 --> 00:23:28,360 +ال X و أحط مكانها باي على اربعة فهيصير بايتكيب على + +229 +00:23:28,360 --> 00:23:35,440 +اربعة وستين مظبوط؟ يبقى هذه بايتكيب على اربعة + +230 +00:23:35,440 --> 00:23:44,400 +وستين في تلاتةوالخمسة واربعين بواحد ناقص عوضنا من + +231 +00:23:44,400 --> 00:23:49,140 +القيم اللي فوق ناقص اللي تحت Zero و تاني Zero ب + +232 +00:23:49,140 --> 00:23:55,700 +Zero يبقى ناقص ال Zero يبقى النتيجة تساوي باي + +233 +00:23:55,700 --> 00:24:03,070 +تكعيب علىعندك هنا اربعة و ستين اربعة و ستين في + +234 +00:24:03,070 --> 00:24:07,610 +تلاتة اللي هو قداش تلاتة في اربعة باطناش و تلاتة + +235 +00:24:07,610 --> 00:24:13,470 +بازمية و اتنين و تسعين يبقى هذا لأ هو بقى اتنين و + +236 +00:24:13,470 --> 00:24:16,910 +تلاتين هذه اتنين و تلاتين في تلاتة ليه بستة و + +237 +00:24:16,910 --> 00:24:24,830 +تسعين مظلوم يبقى هذه ستة و تسعين و هنا زائد اتنين + +238 +00:24:24,830 --> 00:24:30,340 +يبقى هذا قيمة التكامل اللي عندناطب احنا حتى الآن + +239 +00:24:30,340 --> 00:24:36,220 +يا شباب لو رجعت للعنوان تبع section 5-6 لحتى الآن + +240 +00:24:36,220 --> 00:24:42,200 +احنا كل اللي اشتغلناه على النقطة الأولى من العنوان + +241 +00:24:42,200 --> 00:24:47,240 +وهو ال substitution لكن ال area between two curves + +242 +00:24:47,240 --> 00:24:53,780 +لم نتعرض لها بأي مثال حتى هذه اللحظةلذن قبل ان تضع + +243 +00:24:53,780 --> 00:24:58,400 +اي مثال يجب ان تضع قاعدة المساحة المحصورة بين + +244 +00:24:58,400 --> 00:25:03,580 +المنحنيات ومن ثم نذهب ناخد امثلة عليها يجب ان + +245 +00:25:03,580 --> 00:25:10,600 +اعطيها definition اكتري definition if + +246 +00:25:10,600 --> 00:25:18,200 +ال if and ال g are continuous functions + +247 +00:25:27,480 --> 00:25:38,960 +F of X أكبر من أو يساوي الـG of X أثره خلال الفترة + +248 +00:25:38,960 --> 00:25:41,860 +المغلقة A وB + +249 +00:25:58,080 --> 00:26:04,380 +النطاق بين الثقافات + +250 +00:26:04,380 --> 00:26:17,840 +بين الثقافات y تساوي f of x و y تساوي g of x from + +251 +00:26:17,840 --> 00:26:20,560 +a + +252 +00:26:21,840 --> 00:26:27,160 +to be is defined + +253 +00:26:27,160 --> 00:26:32,260 +as + +254 +00:26:32,260 --> 00:26:41,280 +من عرفة كتالي ال area a يسوى تكامل من a إلى b لل f + +255 +00:26:41,280 --> 00:26:45,600 +of x منعقص ال g of x dx + +256 +00:27:05,430 --> 00:27:10,190 +بنرجع للتعريف مرة تانية قال إذا عندك ذالة f و g و + +257 +00:27:10,190 --> 00:27:16,330 +اتين اتين دوال متصلة دوال متصلة يعني قابلة للتكامل + +258 +00:27:16,330 --> 00:27:22,890 +طيب في اندي كونديشن حطوا ان ال f of x أكبر من ال g + +259 +00:27:22,890 --> 00:27:28,350 +of x على كل الفترة من a إلى b يعني دائما و أبدا ال + +260 +00:27:28,350 --> 00:27:32,880 +f of x بتاخد قيمأكبر من القيم اللي تاخدها g of x + +261 +00:27:32,880 --> 00:27:37,340 +على الفترة بعد ال a والb مالاش علاقة فيها او قبلها + +262 +00:27:37,340 --> 00:27:42,560 +انا ماخد فترة من a إلى b فلو جيت قلت افترض على + +263 +00:27:42,560 --> 00:27:51,160 +سبيل المثال ان هذه الدالة y تساوي f of xأجدت دالة + +264 +00:27:51,160 --> 00:27:57,980 +g of x بالشكل اللي عندنا هذا يبقى هذه y تساوي g of + +265 +00:27:57,980 --> 00:28:03,640 +x روحت أنا أخدت الفترة على سبيل المثال من عند + +266 +00:28:03,640 --> 00:28:10,580 +النقطة a لعند النقطة b بالشكل اللي عندنا هذا جهة + +267 +00:28:10,580 --> 00:28:18,570 +طالع هيك جهة طالع هيكيبقى انحصرت المسافة ما بين + +268 +00:28:18,570 --> 00:28:25,910 +الاتنين اللي هي المسافة اللي عندنا هذه يبقى هذه هي + +269 +00:28:25,910 --> 00:28:31,940 +ال area aالان انا لو كاملت على ال F of X بيعطيني + +270 +00:28:31,940 --> 00:28:38,120 +المساحة هذه كلها أسفل المنحنة ومحور X المظلة زائد + +271 +00:28:38,120 --> 00:28:44,100 +المنطقة البيضة هذه تمام؟ لو كاملت على ال G of X + +272 +00:28:44,100 --> 00:28:47,920 +بيعطيني المساحة اللى تحت المنحنة اللى المنطقة + +273 +00:28:47,920 --> 00:28:52,260 +البيضة لو طرحت ال two two من بعضبتظلها المنطقة + +274 +00:28:52,260 --> 00:28:56,460 +المظللة يبقى الشدد area يبقى المنطقة اللي حاطط + +275 +00:28:56,460 --> 00:29:01,500 +عليها خطورة إذا مساحة هذه المنطقة هو تكامل الدالة + +276 +00:29:01,500 --> 00:29:05,780 +الأولى ناقص تكامل الدالة الثانية يبقى التكامل نفسه + +277 +00:29:05,780 --> 00:29:10,820 +على الفترة من a إلى b يبقى على الفترة من عند ال a + +278 +00:29:10,820 --> 00:29:17,300 +لغاية من لغاية ال bأذا بقول له لأ يبقى من البداية + +279 +00:29:17,300 --> 00:29:21,720 +تكامل ال F of X ناقص ال G of X و بروح بكامل على + +280 +00:29:21,720 --> 00:29:26,420 +فترة من A إلى B بيعطيني قداش المساحة اللي موجودة + +281 +00:29:26,420 --> 00:29:33,100 +عندنا طيب هذا لو كانت الدالة F of X فوق و G of X + +282 +00:29:33,100 --> 00:29:37,020 +تحت طب افترض واحدة على اليمين و واحدة على الشمال + +283 +00:29:37,020 --> 00:29:42,270 +لاحظ التكامل هنا بالنسبة لمين؟لو كانت واحدة على + +284 +00:29:42,270 --> 00:29:47,310 +اليمين و واحدة على الشمال كيف نعمل تكامل بالنسبة + +285 +00:29:47,310 --> 00:29:54,090 +لماين إلى واي يبقى باجي بقوله similarly يعني بنفس + +286 +00:29:54,090 --> 00:30:00,310 +الطريقة ال area ايه بقدر اقول تكامل من C إلى D لل + +287 +00:30:00,310 --> 00:30:09,910 +F of Y ناقص ال G of Y كل هذا في DY كيف كتالةافترض + +288 +00:30:09,910 --> 00:30:17,070 +ان هذا منحنى محور X وهذا Y وهذا نقطة الاصل الهيمين + +289 +00:30:17,070 --> 00:30:24,350 +Zero افترض كانت عند الدالة بهذا الشكل هذا المنحنى + +290 +00:30:24,350 --> 00:30:34,090 +Y تساوي F او X مقطع على صيغة X تساوي F of Yجيت على + +291 +00:30:34,090 --> 00:30:39,550 +منحنى ثانى نفترض ان هذا المنحنى كان بالشكل اللى + +292 +00:30:39,550 --> 00:30:49,470 +عندنا هذا يبقى هذا X يساوي G of Y تمام وانا روحت + +293 +00:30:49,470 --> 00:30:56,830 +اخدت المنطقةمن نقطة التقاطة مثلا ها لغاية النقطة + +294 +00:30:56,830 --> 00:31:02,610 +اللي عندها دي و قلت هذه C وهذه D و جيت رسمت خط + +295 +00:31:02,610 --> 00:31:06,970 +أفقي بالشكل اللي عندها ده يبقى المساحة اللي محصورة + +296 +00:31:06,970 --> 00:31:12,030 +بين المنحنيين هي المنطقة المظللة اللي عندها دي + +297 +00:31:12,030 --> 00:31:20,050 +تماميبقى بدى اعرف قدش المنطقة المظلة لأ يبقى صارت + +298 +00:31:20,050 --> 00:31:24,830 +كأنه هذه هي الدالة الكبيرة وهذه هي مين الدالة + +299 +00:31:24,830 --> 00:31:29,790 +الصغيرة على الفترة من وين لوين من C إلى D يعني + +300 +00:31:29,790 --> 00:31:36,590 +صارت F of Y أكبر من مينمن G of Y أو بالبلد هيك + +301 +00:31:36,590 --> 00:31:41,270 +اللي على إيدك اليمين ناقص اللي على إيدك الشمال + +302 +00:31:41,270 --> 00:31:46,750 +بتجيبها بالضبط تماما يبقى من المثل ال area يبدو + +303 +00:31:46,750 --> 00:31:52,510 +سوية كامل من C إلى D لل F of Y ناقص G of Y السؤال + +304 +00:31:52,510 --> 00:31:56,810 +هو لو جاني السؤال بيقولي كامل بالنسبة ل X والله + +305 +00:31:56,810 --> 00:32:02,580 +كامل بالنسبة ل Y بيقولي في المثلةلا بحكيش أبدا، + +306 +00:32:02,580 --> 00:32:05,680 +بيعطيك السؤال وانت حار كامل بالنسبة ل X كامل + +307 +00:32:05,680 --> 00:32:10,700 +بالنسبة ل Y، هذا شأنك، مالو يشتغل فيك، خلاص؟ حد + +308 +00:32:10,700 --> 00:32:16,630 +يلعب يتساول هنا؟طيب، الأن لم يبقى إلا مجموعة من + +309 +00:32:16,630 --> 00:32:23,090 +الأمثلة على هذا ال definition وحنعطي أمثلة بحيث + +310 +00:32:23,090 --> 00:32:28,370 +مرة نكمل بالنسبة إلى Y و أحيانا نكمل بالنسبة إلى X + +311 +00:32:28,370 --> 00:32:34,450 +كله بيرجع لطبيعة المسألة اللي موجودة نبدأ ناخد + +312 +00:32:34,450 --> 00:32:39,810 +أمثلة و بنيجي للمثال الأول يبقى example one + +313 +00:33:04,880 --> 00:33:12,780 +والمغلقة بيه او المحدودة بيه By the following + +314 +00:33:26,250 --> 00:33:37,650 +Y تساوي X ترابيع ناقص اتنين Y يساوي اتنين + +315 +00:33:38,700 --> 00:33:45,300 +المساحة المحصورة بين كل من المنحنيات والمستقيمات + +316 +00:33:45,300 --> 00:33:50,860 +الاتية نمر ايام اعطيني منحنى والتاني خط مستقيم اذا + +317 +00:33:50,860 --> 00:33:55,020 +اول خطة بنعملها بنحاول نرسم الرسم اللي عندنا هذه + +318 +00:33:55,020 --> 00:33:58,420 +ومن خلالها نحدد حدود التكامل طبعا هو بطنيش حدود + +319 +00:33:58,420 --> 00:34:02,580 +التكامل لحالك انت بدك تستنتج حدود التكامل من خلال + +320 +00:34:02,580 --> 00:34:06,860 +الرسم وبدك تعرف تتكامل بالنسبة ليكسب بالنسبةأو + +321 +00:34:06,860 --> 00:34:10,520 +بالنسبة إلى Y يبقى لو جينا للرسمة اللي عندنا هذه + +322 +00:34:10,520 --> 00:34:16,760 +وروح نقول هذا محور X وهذا محور Y وهذا نقطة الأصل + +323 +00:34:16,760 --> 00:34:21,840 +اللي هي Zero لو جيت للمنحنة Y تساوي X تربية ناقص + +324 +00:34:21,840 --> 00:34:26,880 +اتنين وY تساوي X تربية ترابه لمفتوحة إلى أعلى وتمر + +325 +00:34:26,880 --> 00:34:32,340 +بنقطة الأصل سالي باتنين يبقى Shift إلى أسفل بمقدار + +326 +00:34:32,340 --> 00:34:37,760 +اتنينيبقى هنا المنحنة بدى ينزل الى أسفل بمقدار + +327 +00:34:37,760 --> 00:34:44,920 +اتنين والبرابله بدى تصير بالشكل اللى قلناه هنا طيب + +328 +00:34:44,920 --> 00:34:51,330 +هذا اللى هو Y يساوي X ربيع ناقص اتنينالمنحنى + +329 +00:34:51,330 --> 00:34:56,830 +التانى هو خط مستقيم Y تساوي اتنين خط يوازي محور X + +330 +00:34:56,830 --> 00:35:02,190 +ويبعد عنه مسافة مقدارها اتنين يبقى هذا الخط Y + +331 +00:35:02,190 --> 00:35:06,630 +تساوي مين؟ Y تساوي اتنين اذا المنطقة اللى بدنا + +332 +00:35:06,630 --> 00:35:11,830 +ياها هي المحصورة بين المنحنيين الاتنين هدول اللى + +333 +00:35:11,830 --> 00:35:18,040 +هي المنطقة المظللةواضح انه في منحنى فوق كبير و + +334 +00:35:18,040 --> 00:35:23,660 +اللي تحت يعتبر مان صغير يعني منحنى هي فوق و منحنى + +335 +00:35:23,660 --> 00:35:29,320 +تاني تحتإذا انا بدى اطبق من القاعدة الأولى يعني + +336 +00:35:29,320 --> 00:35:34,260 +التكمل بتكون من نسبة لمن؟ من نسبة لمحور X بس مش + +337 +00:35:34,260 --> 00:35:38,240 +هان اطبق هذه بدي اعرف ال X بده تتغير من ويلة وين + +338 +00:35:38,240 --> 00:35:45,220 +باجي على أول نقطة هناها و بدي اعرف قداش قيمة X هنا + +339 +00:35:45,220 --> 00:35:49,460 +و بدي اجي على اخر نقطة في المساحة اللي عنده و بدي + +340 +00:35:49,460 --> 00:35:55,390 +اعرف قداش X بدها تكون عند هذه النقطةهذه النقطة + +341 +00:35:55,390 --> 00:36:00,150 +وهذه النقطة هي نقاط تقاطع المنحنة مع من؟ مع الخط + +342 +00:36:00,150 --> 00:36:04,150 +المستقيم إذا مش هنجيب الأحداثيات، بدتي أحلي + +343 +00:36:04,150 --> 00:36:09,070 +المعادلتين هدول مع بعض، هنا عندي Y وهنا Y، يبقى + +344 +00:36:09,070 --> 00:36:13,850 +بدي أساوي التنتين بمن؟ بعضهم، يبقى بدي أروح أحط + +345 +00:36:13,850 --> 00:36:15,390 +solution + +346 +00:36:17,940 --> 00:36:24,760 +يبقى بضع X تربيع ناقص اتنين يساوي كم؟ اتنين يبقى X + +347 +00:36:24,760 --> 00:36:29,900 +تربيع تساوي اربعة معناته ان ال X يساوي زائد او + +348 +00:36:29,900 --> 00:36:34,100 +ناقص اتنين اذا النقف اللي على شمال ال zero هذا + +349 +00:36:34,100 --> 00:36:38,480 +سالب اتنين واللي على يمين ال zero هذا كم؟ اتنين + +350 +00:36:38,760 --> 00:36:45,520 +يبقى أقل قيمة للمنطق المضلل لـ X هي سالب اتنين و + +351 +00:36:45,520 --> 00:36:49,580 +أكبر قيمة تاخدها X على المنطق المضلل هو عبارة من + +352 +00:36:49,580 --> 00:36:56,220 +اتنين إذا بناء عليه بقول ال area A يستوي تكامل من + +353 +00:36:56,220 --> 00:37:01,150 +سالب اتنين إلى اتنينالدالة الكبيرة هي الدالة اللى + +354 +00:37:01,150 --> 00:37:06,110 +فوق الـ UY تساوي كداش؟ اتنين الدالة الصغيرة اللى + +355 +00:37:06,110 --> 00:37:12,490 +تحتها الـ X تربيع ناقص اتنين كل اللى عندها دهاج + +356 +00:37:12,490 --> 00:37:18,790 +بالنسبة لمن؟ بالنسبة إلى DXاللي بكتب هذا الكلام + +357 +00:37:18,790 --> 00:37:22,870 +صحيح بظل الكلام اللي باقي كله كلام فارغ، شغل + +358 +00:37:22,870 --> 00:37:28,590 +روتيني عادي جدا، تمام؟ يبقى احنا بدنا نروح نكامل + +359 +00:37:28,590 --> 00:37:33,290 +هذه ونجي نقول هذه من سالي باتنين إلى اتنين، لو + +360 +00:37:33,290 --> 00:37:40,290 +فكتها بصير اربعة ناقص extra بادي، تمام؟ قبل ما + +361 +00:37:40,290 --> 00:37:46,860 +كامل، هذه الدالة even والله oddخلص يبقى 2 تكامل + +362 +00:37:46,860 --> 00:37:55,380 +على نصف الفترة يبقى هذا 2 تكامل من 0 إلى 2 لل 4 + +363 +00:37:55,380 --> 00:38:00,840 +ناقص X تربية دي ستطلع هنا هاي الخط بجسمها إلى نصين + +364 +00:38:00,840 --> 00:38:08,020 +ما لهم زي بعض يبقى روحان كامل 2 هيها برا هذه 4X + +365 +00:38:08,020 --> 00:38:15,680 +ناقص X تكيب على 3كله من صفر لغاية اتنين يبقى هذه + +366 +00:38:15,680 --> 00:38:22,020 +اتنين وبتعوب اتنين في اربعة بتمانية ناقص تمانية + +367 +00:38:22,020 --> 00:38:29,270 +على تلاتة ناقص Zero كل هذا ب Zeroعلى أي حال تلاتة + +368 +00:38:29,270 --> 00:38:35,170 +في تمانية باربع وعشرين ناقص تمانية بدل قدر 16 على + +369 +00:38:35,170 --> 00:38:40,590 +تلاتة يبقى اتنين في ستاشر على تلاتة يبقى اتنين + +370 +00:38:40,590 --> 00:38:48,790 +وتلاتين على تلاتة ال area المطلوبة نجي لنمرى بيه + +371 +00:38:51,360 --> 00:39:00,140 +نمر بيه؟ بيقول لي Y تساوي أربعة ناقص X تربيع وال Y + +372 +00:39:00,140 --> 00:39:11,360 +تساوي اتنين ناقص X وال X يساوي سالب اتنين و X + +373 +00:39:11,360 --> 00:39:14,520 +يساوي اتنين + +374 +00:39:17,180 --> 00:39:22,040 +هذا السؤال جئنا به في احدى الامتحانات قبل يمكن + +375 +00:39:22,040 --> 00:39:26,920 +اربع سنين تقريبا + +376 +00:39:30,310 --> 00:39:32,790 +المثال الأول ماحش الكامل بالنسبة للأصحاب اللي + +377 +00:39:32,790 --> 00:39:37,970 +قاعدين فيه انك واقف استخدامهم صحيح؟ ميشان الكامل + +378 +00:39:37,970 --> 00:39:43,450 +بالنسبة لو بدك معادلة او بدك تجيب منحنى على اليمين + +379 +00:39:43,450 --> 00:39:47,410 +ومنحنى على الشمال وين المنحنى اللي على اليمين وين + +380 +00:39:47,410 --> 00:39:48,690 +على الشمال؟ فيه؟ + +381 +00:39:51,790 --> 00:39:54,910 +ما هو بالنسبة للأول، معناته منحنى بدي يكون على + +382 +00:39:54,910 --> 00:39:59,370 +اليمين ومنحنى على الشمال، فيه عندنا؟ عندنا، + +383 +00:39:59,370 --> 00:40:04,310 +وبالتالي مستخدم كلامي مش صحيح، خلاص ما؟ طيب، ندي + +384 +00:40:04,310 --> 00:40:08,890 +له المثل اللي عندنا هذا، يبقى هذا مش خط مستخدم + +385 +00:40:08,890 --> 00:40:13,730 +منحنى، هذا تلت خطوط مستخدمه منحنى، يبقى ربنا يرسله + +386 +00:40:14,290 --> 00:40:18,130 +الله أعلم كيف تكون هذا مش هيك باجي بقوله كويس + +387 +00:40:18,130 --> 00:40:22,630 +بالضبط على الرسم اللي عندنا باجي بقوله هذا المحور + +388 +00:40:22,630 --> 00:40:29,870 +هذا محور X وهذا اللي عندنا اللي هو main وهذا اللي + +389 +00:40:29,870 --> 00:40:39,870 +هو محور Yطيب بيجي على المنحنة الأول أربعة ناقص X + +390 +00:40:39,870 --> 00:40:44,670 +تربيع يبقى X تربيع إلى أسفل وشفر إلى أعلى بمقدار + +391 +00:40:44,670 --> 00:40:52,470 +أربعة يبقى لو جيت للمنحنة هذا يبقى المنحنة + +392 +00:40:52,470 --> 00:40:57,410 +بالشكل هذا يبقى + +393 +00:40:57,410 --> 00:41:03,590 +هذا المنحنة Y يساوي أربعة ناقص X تربيعبعد ذلك اذا + +394 +00:41:03,590 --> 00:41:10,330 +كان عندك خط مستقيم y تساوي اتنين ناقص ال x بقول لو + +395 +00:41:10,330 --> 00:41:18,070 +كانت x بيزيرو يبقى y باتنين لو كانت x بيزيرو y + +396 +00:41:18,070 --> 00:41:23,270 +باتنين يعني في نص المسافة فوق اربعة يبقى هات اتنين + +397 +00:41:23,270 --> 00:41:29,880 +واللي بعدهلو كانت Y ب0 يبقى X ب2 + +398 +00:41:46,910 --> 00:41:52,930 +يبقى النقطتين الاتنين يقعني على الخط المستقيم إذا + +399 +00:41:52,930 --> 00:41:59,110 +بجيب المصدر هك و بوصل ما بين النقطتين هدول و بمد + +400 +00:41:59,110 --> 00:42:05,350 +هذا على استقالة ماخلصناش جال بعد هيك في عندك خطين + +401 +00:42:05,350 --> 00:42:11,350 +مستقيمين X يساوي سالب اتنين و X يساوي اتنين X + +402 +00:42:11,350 --> 00:42:16,170 +يساوي سالب اتنين يبقى هذا الخط الطالع رأسي دوري هك + +403 +00:42:18,200 --> 00:42:23,160 +والخط التاني X يساوي اتنين وهو الخط اللي عندنا هذا + +404 +00:42:23,160 --> 00:42:30,100 +تمام يبقى هذا X يساوي اتنين وهذا X يساوي سالب + +405 +00:42:30,100 --> 00:42:36,800 +اتنين يبقى صارتهل هناك ما بين X يساوي 2 ومساحة + +406 +00:42:36,800 --> 00:42:40,940 +تانية فيه محصورة بينه بين المنحنيات؟ لأ التلاتة + +407 +00:42:40,940 --> 00:42:45,020 +اتقطعوا في نفس مين؟ في نفس النقطة إذا ماعنديش + +408 +00:42:45,020 --> 00:42:49,200 +مساحة محددة مع الخط الرأسي الأول لكن مع الخط + +409 +00:42:49,200 --> 00:42:53,580 +الرأسي التاني صار عندي مساحة محددة يبقى أنا في + +410 +00:42:53,580 --> 00:42:59,220 +عندي المساحة دي محصورة ما بين خطين من الخطوط + +411 +00:42:59,220 --> 00:43:00,800 +المستقيمة + +412 +00:43:04,700 --> 00:43:13,180 +المساحة المحصورة بين خطين مستقيمين ومنحنة المساحة + +413 +00:43:13,180 --> 00:43:20,560 +المحصورة بين الخطين + +414 +00:43:20,560 --> 00:43:31,160 +المستقيمين ومنحنة المستقيمين + +415 +00:43:31,180 --> 00:43:34,000 +الخط المالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +416 +00:43:34,000 --> 00:43:35,220 +مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي + +417 +00:43:35,220 --> 00:43:37,800 +يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +418 +00:43:37,800 --> 00:43:38,160 +مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي + +419 +00:43:38,160 --> 00:43:39,800 +يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +420 +00:43:39,800 --> 00:43:44,700 +مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي + +421 +00:43:44,700 --> 00:43:52,800 +يتخيل خط مالي يتخيل خط مالي يتخيل خط مالي يتخيل خط + +422 +00:43:52,800 --> 00:43:58,640 +مالي يتيبقى هذا كل منحنط كل واحد كتب عليه معادلة + +423 +00:43:58,640 --> 00:44:06,010 +إذا ماعناش مساحة واحدة وانما عندنا مجموعمساحتين صح + +424 +00:44:06,010 --> 00:44:10,470 +ولا لا؟ ايوة طب اتنين بدنا نكمل بالنسبة ل X ولا + +425 +00:44:10,470 --> 00:44:16,170 +بالنسبة ل Y تعالى نشوف كل مساحة من هذه المساحات لو + +426 +00:44:16,170 --> 00:44:20,150 +جيت للمساحة اللى عندنا هذه يبقى فى منحنى فوق وفى + +427 +00:44:20,150 --> 00:44:26,430 +منحنى تحت هنا فى منحنى فوق وفى منحنى تحت لكن لو + +428 +00:44:26,430 --> 00:44:31,120 +جيتى يمين وشمال اه ممكنممكن يا مشوال بياخد تروح + +429 +00:44:31,120 --> 00:44:34,260 +ترسم خط أفق بيصير هذا على اليمين و هذا على الشمال + +430 +00:44:34,260 --> 00:44:38,440 +و هذا على اليمين و هذا على الشمال يبدو يتكاملينو + +431 +00:44:38,440 --> 00:44:44,560 +بعد هيك هذه يمين و شمال ماعنديش مش هتظبط هذه لذلك + +432 +00:44:44,560 --> 00:44:49,400 +افضل حاجة خلص بالنسبة ل X و انسى الموضوع تمام يبقى + +433 +00:44:49,400 --> 00:44:54,780 +بروح بكمل اس ال X بس بدي اروح احدد حدود التكوين + +434 +00:44:54,780 --> 00:44:59,720 +بدي اعرف قداش الاحداث تبع نقطة التقاطع هنا يعني + +435 +00:44:59,720 --> 00:45:04,160 +قداش قيم دسك هذه معروفةهذه المعروفة او هذه + +436 +00:45:04,160 --> 00:45:12,060 +المعروفة او هذه المعروفة + +437 +00:45:12,060 --> 00:45:13,400 +او هذه المعروفة او هذه المعروفة او هذه المعروفة او + +438 +00:45:13,400 --> 00:45:14,420 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +439 +00:45:14,420 --> 00:45:14,720 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +440 +00:45:14,720 --> 00:45:16,340 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +441 +00:45:16,340 --> 00:45:17,220 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +442 +00:45:17,220 --> 00:45:19,100 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +443 +00:45:19,100 --> 00:45:22,880 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +444 +00:45:22,880 --> 00:45:25,880 +هذه المعروفة او هذه المعروفة او هذه المعروفة او + +445 +00:45:25,880 --> 00:45:25,980 +هذه المعروفة ا + +446 +00:45:30,240 --> 00:45:37,260 +بدي اخد اربعة ناقص X تربيع يساوي اتنين ناقص X بدي + +447 +00:45:37,260 --> 00:45:41,460 +اعملها معادلة صفريهات لهذه الشجة التانية بيصير X + +448 +00:45:41,460 --> 00:45:49,240 +تربيع بالموجة ناقص X زي ما هي ماتغيراتي اربعة + +449 +00:45:49,240 --> 00:45:55,160 +بتجيلك بالسالب و عندك اتنين بيظل سالب اتنين يساوي + +450 +00:45:55,160 --> 00:45:55,720 +زيرو + +451 +00:46:02,100 --> 00:46:10,840 +هنا اكس وهنا اكس وهنا اتنين وهنا واحد وهنا سالب + +452 +00:46:10,840 --> 00:46:17,820 +وهنا مجد يبقى ناقص اتنين اكس وزاد اكس يبقى ناقص + +453 +00:46:17,820 --> 00:46:22,720 +اكس يبقى بناء عليه الاكس الاولى ساوي سالب واحد + +454 +00:46:22,720 --> 00:46:29,630 +والاكس التانى ساوي قداشرإتنين فعلا نقطة التقاطع + +455 +00:46:29,630 --> 00:46:34,670 +الأولى سالب واحد ونقطة التقاطع التانية جداش اتنين + +456 +00:46:34,670 --> 00:46:39,790 +هي مع الخط والمنحنى يبقى عند اتنين يبقى معناته + +457 +00:46:39,790 --> 00:46:50,200 +عندي تكاملين يبقى ال area المطلوبة ال areaمن سلب 2 + +458 +00:46:50,200 --> 00:46:55,040 +لغاية سلب 1 + +459 +00:46:55,040 --> 00:47:00,060 +يبقى الخط المستقيم هذا اللي فوق اللي هو 2 ناقص X + +460 +00:47:00,600 --> 00:47:06,660 +أتنين ناقص X ناقص المنحنى اللى تحت هذا اللى همين + +461 +00:47:06,660 --> 00:47:13,380 +أربعة ناقص X تربية يبقى أربعة ناقص X تربية وهي + +462 +00:47:13,380 --> 00:47:17,840 +الجزء ودير بالك وانت بتشتغل مش هحط السلب للأربعة و + +463 +00:47:17,840 --> 00:47:21,740 +تسيب التانية يبقى السلب و بتحط الدالة بالكام اللى + +464 +00:47:21,740 --> 00:47:25,060 +بين الجزين مشان شرط السلب تدخل على term من هذه + +465 +00:47:25,060 --> 00:47:28,780 +ترميزة اللى بيسووا بعضكواو بروح بغلط الاشارة و بظل + +466 +00:47:28,780 --> 00:47:32,920 +يخبص و هداك و بتطلع اليوم ماعمش بصبوط هدا إيه نطلع + +467 +00:47:32,920 --> 00:47:38,260 +جواب طيب يبقى هذا الكلام بد يساوي تكامل من سالب + +468 +00:47:38,260 --> 00:47:44,600 +اتنين إلى سالب واحد لمن؟ للاتنين ناقص X ناقص أربعة + +469 +00:47:44,600 --> 00:47:50,000 +زائد X تربيع كله بالنسبة إلى DX من ناقص اتنين + +470 +00:47:50,000 --> 00:47:55,500 +لناقص واحداكس تربية موجبة وهي ناقص اكس ناقص اربعة + +471 +00:47:55,500 --> 00:48:00,680 +زي دي اتنين بيظل جداش ناقص اتنين كله بالنسبة الى + +472 +00:48:00,680 --> 00:48:05,480 +DX بدنا نيجي اه لسه عملنا هيك لسه في تكامل تاني + +473 +00:48:05,480 --> 00:48:10,000 +خلي ا واحد طيب خلي ا واحد ولا يهمك هذه ا واحد + +474 +00:48:10,000 --> 00:48:17,640 +خلينا ماشيين يبقى هذه ا واحد وهذه ا اتنينيبقى بدنا + +475 +00:48:17,640 --> 00:48:26,060 +نحسب هذه يبقى بصير x تكيب على 3 ناقص x تربيع على 2 + +476 +00:48:26,060 --> 00:48:36,080 +ناقص 2x كله من سلب 2 لراية سلب 1عوض بالقيمة اللي + +477 +00:48:36,080 --> 00:48:40,380 +فوق يا شباب يبقى ناقص واحد تكييب اللي هو ناقص واحد + +478 +00:48:40,380 --> 00:48:45,820 +يبقى ناقص طول اللي بعدها ناقص واحد تربيع اللي هو + +479 +00:48:45,820 --> 00:48:50,780 +واحد على اتنين والناقص هذه بتظلها زي ما هي النص + +480 +00:48:50,780 --> 00:48:57,980 +هذه زائد اتنين خلصنا القيمة اللي فوق ناقص افتح قوس + +481 +00:48:58,610 --> 00:49:04,630 +هنا هذا بتعطيك ناقص تمانية على تلاتة يبقى ناقص + +482 +00:49:04,630 --> 00:49:09,510 +تمانية على تلاتة هذي بيصير اربعة على اتنين اللي هو + +483 +00:49:09,510 --> 00:49:15,570 +بيقدرش باتنين بالسالب وهي سالب اتنين هذي بيبقى + +484 +00:49:15,570 --> 00:49:22,450 +زائد اربعة يبقى زائد اربعةيبقى النتيجة كالتالت وهي + +485 +00:49:22,450 --> 00:49:29,030 +سالب طول وهي سالب نص وهي زائد اتنين وهي زائد + +486 +00:49:29,030 --> 00:49:35,870 +تمانية تلاتة وهي زائد اتنين وانا ناقص اربعطلّعلي + +487 +00:49:35,870 --> 00:49:43,610 +هذه وهذه بطل قداش سبعة على تلاتة يبقى هذه يساوي + +488 +00:49:43,610 --> 00:49:49,790 +سبعة على تلاتة وناقص نص مافيش غيره وهذه ناقص نص + +489 +00:49:49,790 --> 00:49:56,370 +بطل عندى اتنين واتنين اربعة مع الأربعة مع السلامة + +490 +00:49:56,790 --> 00:50:03,590 +يبقى هذه سالب أربع مع اتنين و مع اتنين يبقى كله + +491 +00:50:03,590 --> 00:50:09,850 +على قداش على ستة ستة على تلاتة في اتنين في سبعة + +492 +00:50:09,850 --> 00:50:17,510 +باربعتاش نقص ستة على اتنين فيها التلاتة في واحد + +493 +00:50:17,510 --> 00:50:26,220 +بتلاتة يبقى النتيجة يسوى احداشر على ستةبنروح نجيب + +494 +00:50:26,220 --> 00:50:32,580 +اتنين للمساحة الثانية يبقى تكامل من سالب واحد + +495 +00:50:32,580 --> 00:50:37,860 +لغاية اتنين الدالة اللى فوق ناقص الدالة اللى تحت + +496 +00:50:37,860 --> 00:50:43,100 +يبقى اربعة ناقص X تربية ناقص الدالة اللى تحت له + +497 +00:50:43,100 --> 00:50:50,460 +لاتنين ناقص X كله بالنسبة الى DX يبقى تكامل من + +498 +00:50:50,460 --> 00:50:58,150 +سالب واحد لغاية اتنينللمين للاربع ناقص X تربية + +499 +00:50:58,150 --> 00:51:06,070 +ناقص اتنين زائد ال X كل هذا الكلام بالنسبة إلى DX + +500 +00:51:06,070 --> 00:51:13,410 +ويساوينقص اتنين وزايد اربع بيقول قداش اتنين تكامل + +501 +00:51:13,410 --> 00:51:20,890 +من سلب واحد لاتنين لاتنين زايد X ناقص X تربيع كله + +502 +00:51:20,890 --> 00:51:28,190 +بالنسبة الى DX يبقى النتيجة 2X X تربيع على 2 ناقص + +503 +00:51:28,190 --> 00:51:33,950 +X تكيب على 3 كله من ناقص 1 لغاية 2 + +504 +00:51:37,780 --> 00:51:43,620 +يبقى هذه النتيجة تساوي اتنين في اتنين باربع زائد + +505 +00:51:43,620 --> 00:51:50,000 +اربع على اتنين باتنين ناقص تمانية على تلاتة تمانية + +506 +00:51:50,000 --> 00:51:54,460 +على تلاتة ناقص يفتح جوز نعود بالقيمة هذه اللي هي + +507 +00:51:54,460 --> 00:52:03,680 +ناقص اتنين و هنا زائد نص و عندك هنا ناقص و ناقص + +508 +00:52:03,680 --> 00:52:12,420 +بيصير زائد تلتهذا بيصير ستة ناقص تمانية على تلاتة + +509 +00:52:12,420 --> 00:52:21,060 +و هنا زائد اتنين و ناقص نص ناقص تلت و يساوي اتنين + +510 +00:52:21,060 --> 00:52:26,400 +و ستة تمانية عندك ناقص تمانية على تلاتة و ناقص تلت + +511 +00:52:26,400 --> 00:52:33,740 +بناقص تسع على تلاتة يعني قداش ناقص تلاتة و بيظل + +512 +00:52:33,740 --> 00:52:41,040 +عندك هنا ناقص نصيبقى هاي اتنين وستة تمانية تمانية + +513 +00:52:41,040 --> 00:52:47,500 +بدي اشيل منهم تلاتة بضل قداش بضل اللي هو خمسة + +514 +00:52:47,500 --> 00:52:54,670 +يساوي خمسة ناطص نصف الان بدي المساحة الكليةيبقى ال + +515 +00:52:54,670 --> 00:53:01,630 +area اللي بدوا إياها A يسوى A1 زائد A2 A1 طلعناها + +516 +00:53:01,630 --> 00:53:11,850 +مداشر ب 11 عالى 6 زائد 9 عالى 2 كله عالى 6 بضل 11 + +517 +00:53:11,850 --> 00:53:21,790 +زائد 6 عالى 2 ديال 3 في 9بسبعة و عشرين يبقى تمانية + +518 +00:53:21,790 --> 00:53:28,970 +و تلاتين على ستة أو تسعة و عشر على تلاتة هذه + +519 +00:53:28,970 --> 00:53:32,130 +المساحة الكلية المطلوبة + +520 +00:53:51,040 --> 00:53:51,600 +أيوة + +521 +00:53:55,410 --> 00:54:02,850 +وين وي تسوي سالب واحد؟ وي تسوي + +522 +00:54:02,850 --> 00:54:04,830 +سالب واحد، بده يجيلك هنا. + +523 +00:54:08,370 --> 00:54:15,810 +كيف؟ العملية + +524 +00:54:15,810 --> 00:54:20,230 +ليست سهلة، بده يصير عندك وي تسوي سالب أدتك، كمان + +525 +00:54:20,230 --> 00:54:25,400 +مساحة، هيك، هيك، هيكتمام؟ وبعدين تمدوا على + +526 +00:54:25,400 --> 00:54:29,140 +استقانته، فيه كمان هذه مساحة وبعدين تمدوا على هذه + +527 +00:54:29,140 --> 00:54:34,320 +وهنا كمان مساحة وتمدوا هنا وهنا كمان مساحة ان شاء + +528 +00:54:34,320 --> 00:54:35,780 +الله للعصر بنخلص اليوم + +529 +00:54:40,360 --> 00:54:44,760 +بصير ملوش قيمة، ملوش اي اعتبار، ان احنا بندور + +530 +00:54:44,760 --> 00:54:48,200 +المساحة المحصورة بين المنحنات، بتطلعش منها إلا إذا + +531 +00:54:48,200 --> 00:54:51,760 +قال لي بين X يساوي Zero و Y يساوي Zero، اه تدخل + +532 +00:54:51,760 --> 00:54:56,080 +المحاور معاه، مجاليش يبقى أنا مقيد بس بالمنحنات + +533 +00:54:56,080 --> 00:55:00,460 +اللي بنوصل عليها، غيريك مليش علاقة فيه، طبعا، طيب + +534 +00:55:00,460 --> 00:55:07,710 +هذا نمرة B من المثلة نمرة Cنمر ال C بيقول يا سيدي + +535 +00:55:07,710 --> 00:55:16,650 +X يساوي Y تربية and ال X يساوي Y زائد اتنين + +536 +00:55:19,450 --> 00:55:25,350 +يبقى بناروح نرسم المثلة مشان نعرف شو شكلها بالضبط + +537 +00:55:25,350 --> 00:55:31,730 +يبقى باجي بقول هاي المحاور هذا محور X هذا محور Y + +538 +00:55:31,730 --> 00:55:36,990 +هذا نقطة الأصل اللي هي Zero X يسوى Y تربية هو + +539 +00:55:36,990 --> 00:55:44,260 +قنابلة مفتوح جهتي اليمينيبقى هذا ال parabola لأن x + +540 +00:55:44,260 --> 00:55:51,020 +بدي يسوى 100y تربيع يبقى هذا ال x بدي يسوى y تربيع + +541 +00:55:51,020 --> 00:55:58,000 +بداية للخط المستقيم لأن لو كانت y ب0x ب2 يبقى لو + +542 +00:55:58,000 --> 00:56:04,830 +جيت قلت هاي اتنينلو كانت X بزير و Y بسالب اتنين X + +543 +00:56:04,830 --> 00:56:07,830 +بزير و Y بسالب اتنين X بزير و Y بسالب اتنين X بزير + +544 +00:56:07,830 --> 00:56:07,850 +و Y بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +545 +00:56:07,850 --> 00:56:08,050 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +546 +00:56:08,050 --> 00:56:08,790 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +547 +00:56:08,790 --> 00:56:08,930 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +548 +00:56:08,930 --> 00:56:12,830 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +549 +00:56:12,830 --> 00:56:20,910 +بسالب اتنين X بزير و Y بسالب اتنين X بزير و Y + +550 +00:56:20,910 --> 00:56:28,950 +بسالبو بمد الخط على استقامته يبقى هذا اللي هو + +551 +00:56:28,950 --> 00:56:34,210 +تقاطع مع المنحنة يبقى المنطقة المظلة لهذه هي + +552 +00:56:34,210 --> 00:56:40,770 +المنطقة المحصورة ما بين المنحنة اللي عندنا و الخط + +553 +00:56:40,770 --> 00:56:49,940 +المستقيم يبقى الخط المستقيم هذا X يساوي Y زائد 2Y + +554 +00:56:49,940 --> 00:56:56,620 +المنحنى اللي يفوت هو X يساوي Y تربيه بالشكل اللي + +555 +00:56:56,620 --> 00:56:56,980 +عندنا + +556 +00:57:01,010 --> 00:57:07,330 +تمام طيب واضح انه لو تيجي تقوله هذه فوق هذه تحت + +557 +00:57:07,330 --> 00:57:11,390 +هنا تنتل بيصيروا جبال بعض بيصير واحد على يمين واحد + +558 +00:57:11,390 --> 00:57:15,870 +على شمال مش هتظبط معاه لكن واضح انه الخط هذا على + +559 +00:57:15,870 --> 00:57:19,470 +اليمين وهذا الجزء منه منحنى وين عليه شمال يعني + +560 +00:57:19,470 --> 00:57:23,360 +واحد جهة إيدي شمال وواحد جهة إيدياليمين إذا هنا + +561 +00:57:23,360 --> 00:57:27,840 +التكامل بيشير بالنسبة ل Y يبقى بروح بقول لو بدي + +562 +00:57:27,840 --> 00:57:34,600 +أعرف قداش أقل قيمة بتاخدها Y و قداش أكبر قيمة هنا + +563 +00:57:34,600 --> 00:57:39,900 +بتاخدها من Y يبقى معناته بدي أحل المعادلاتين هدول + +564 +00:57:39,900 --> 00:57:46,120 +مع بعضيبقى عندي y تربية بدها تساوي ال y زائدي + +565 +00:57:46,120 --> 00:57:51,300 +اتنين او ال y تربية ناقص y ناقص اتنين بده يساوي + +566 +00:57:51,300 --> 00:57:57,860 +zero وهي قوسين بده يساوي zero يبقى هنا y هنا y هنا + +567 +00:57:57,860 --> 00:58:02,630 +واحد هنا اتنين سالف موجةيبقى موجة بواي و سالب + +568 +00:58:02,630 --> 00:58:07,210 +اتنين واي بيظل سالب واي مظبوط إذا واي تسوى سالب + +569 +00:58:07,210 --> 00:58:12,190 +واحد و واي تسوى قداش اتنين يبقى النقطة هذه سالب + +570 +00:58:12,190 --> 00:58:18,170 +واحد و النقطة هذه قداش اتنينيبقى ال area اللي بدنا + +571 +00:58:18,170 --> 00:58:23,030 +ياها هي تكامل من سالب واحد لغاية مين دالية اتنين + +572 +00:58:23,030 --> 00:58:28,290 +الدالة اللي على اليمين واضح انها Y زي D2 الدالة + +573 +00:58:28,290 --> 00:58:33,150 +اللي على الشمال الييمين Y تربيع كله بالنسبة إلى + +574 +00:58:33,150 --> 00:58:39,860 +مين إلى DYالان التكامل هذا حددت حدود التكامل صح + +575 +00:58:39,860 --> 00:58:46,300 +يبقى الباقي كله بيصير شغل روتيني فقط لغاية يبقى + +576 +00:58:46,300 --> 00:58:53,880 +هذا الكلام بيصير Y تربيه على 2 زي 2Y ناقص Y تكعيب + +577 +00:58:53,880 --> 00:59:00,770 +على 3 كله من سالب 1 لغاية 2نعوض بالقيمة اللى فوق + +578 +00:59:00,770 --> 00:59:05,050 +ناقص القيمة اللى تحت يبقى بيصير اربع على اتنين + +579 +00:59:05,050 --> 00:59:14,110 +باتنين زائد اربع ناقص تمانية على تلاتة ناقص + +580 +00:59:14,110 --> 00:59:19,830 +افتحانوز هنا ناقص واحد تربية لو واحد بيبقى عندي نص + +581 +00:59:21,620 --> 00:59:28,880 +وهنا ناقص اتنين تمام وهنا ناقص واحد بيصير ناقص مع + +582 +00:59:28,880 --> 00:59:36,620 +ناقص بيصير زائد طلت بالشكل اللي عنها يبقى النتيجة + +583 +00:59:36,620 --> 00:59:43,240 +اتنين واربعة ستة ناقص تمانية على تلاتة ناقص نص + +584 +00:59:43,240 --> 00:59:57,190 +زائد اتنين ناقص طلت ويساويتمنية تمنية تمنية + +585 +00:59:57,190 --> 01:00:05,590 +تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية + +586 +01:00:05,590 --> 01:00:14,950 +تمنية تمنية تمنية تمنية تمنية تمنية + +587 +01:00:24,970 --> 01:00:28,490 +هذا النوع الأول من المسائل اللي هو المساحة + +588 +01:00:28,490 --> 01:00:33,910 +المحصورة بين منحنى وخط مستقيم ممكن أن تكون المساحة + +589 +01:00:33,910 --> 01:00:41,470 +موجودة بين منحنيين وليس بين منحنى وخط مستقيم إذا + +590 +01:00:41,470 --> 01:00:44,530 +نذهب إلى المثال رقم 2 + +591 +01:00:52,580 --> 01:00:57,320 +بقول find the + +592 +01:00:57,320 --> 01:01:12,380 +area of the region enclosed by + +593 +01:01:12,380 --> 01:01:13,780 +the following curves + +594 +01:01:23,150 --> 01:01:30,030 +بندى المساحة المحصورة ما بين المنحنيات القاتلة نمر + +595 +01:01:30,030 --> 01:01:42,490 +A X يساوي Y تربيع and X زائد 2Y تربيع بده يساوي + +596 +01:01:42,490 --> 01:01:44,290 +كده؟ بده يساوي 3 + +597 +01:02:13,930 --> 01:02:19,810 +هذه المساحة الموجودة بين المنحنات X يساوي Y تربيع + +598 +01:02:19,810 --> 01:02:26,880 +و X زائد 2Y تربيع يساوي 3بنروح نرسم كل منحنى من + +599 +01:02:26,880 --> 01:02:30,880 +هذه المنحنيات مشان نعرف انها مكمل بالنسبة ل X و + +600 +01:02:30,880 --> 01:02:38,640 +بالنسبة ل Y و نحدد النقاط اللي هي حدود التكامل اذا + +601 +01:02:38,640 --> 01:02:47,740 +لو جيت للمنحنى الأول هذا محور X وهذا محور Y وهذا + +602 +01:02:47,740 --> 01:02:55,080 +نقطة الأصل Zالمنحدر هو X يسوى Y تربيع رسمناه قبل + +603 +01:02:55,080 --> 01:03:01,160 +قليل بالشكل اللي عندنا هذا يبقى هذا ال X يسوى Y + +604 +01:03:01,160 --> 01:03:06,910 +تربيعالمنحنى الثانى هذا عبارة عن ايش؟ عبارة عن x + +605 +01:03:06,910 --> 01:03:13,790 +بده يساوي سالب اتنين y تربية زائد تلاتة يعني هذا + +606 +01:03:13,790 --> 01:03:20,370 +لو روحت قعدت كتابته مرة تانية بمين؟ ب x يساوي سالب + +607 +01:03:20,370 --> 01:03:25,470 +اتنين y تربية زائد تلاتة بقول واسة اتنين والتلاتة + +608 +01:03:26,210 --> 01:03:31,430 +يبقى Y تساوي X يساوي سالب Y تربيع يبقى هذا بس + +609 +01:03:31,430 --> 01:03:36,750 +بعدين اقلبه وين؟ ع الشجة التانية طيب اتنين هذه + +610 +01:03:36,750 --> 01:03:40,510 +بتخليه يقرب على المنحنى او يبعد الرقم اللي عندي + +611 +01:03:40,510 --> 01:03:46,430 +تمام التلاتة هي shift بس ان من ال shift الى اعلى + +612 +01:03:46,430 --> 01:03:50,850 +الرسم يمين وشمال اذا ال shift جهة اليمين بمقدار + +613 +01:03:50,850 --> 01:03:56,050 +تلاتةيبقى المنحنة على الإشمال هكذا و سأعمل shift + +614 +01:03:56,050 --> 01:04:04,930 +للخلف بمقدار 3 لماذا؟ لأن لو كانت Y ب0 يبقى X ب3 + +615 +01:04:04,930 --> 01:04:10,810 +يبقى هذا X ب3 و Y ب0 و الparabola ستصبح بالشكل + +616 +01:04:10,810 --> 01:04:16,760 +اللي عندنا هذا هكذاطبعا يبقى هذا المنحنى اللي هو X + +617 +01:04:16,760 --> 01:04:23,700 +يساوي سالب اتنين Y تربيع زائد تلاتة اذا المنطقة + +618 +01:04:23,700 --> 01:04:29,320 +اللي بينهم هي المنطقة المضللة اللي عندنا ايوة + +619 +01:04:29,320 --> 01:04:32,720 +وشايف + +620 +01:04:32,720 --> 01:04:36,280 +المنحنى اللي عندك ولا لا حق واي بزير قداشك تكون + +621 +01:04:37,860 --> 01:04:42,940 +سمعت بالـ shift تبع الدالة لما كانت y تساوي مثلا x + +622 +01:04:42,940 --> 01:04:47,880 +سربيع او x كام يبقى shift الى اعلى اذا الرقم ل y + +623 +01:04:47,880 --> 01:04:51,260 +بصير shift جهة اليمين او جهة الشمال حسب القيمة + +624 +01:04:51,260 --> 01:04:55,080 +تبعته طيب اذا ماانت مش عارف ال shift ولا حاجة + +625 +01:04:55,080 --> 01:04:59,320 +بقوله حط ال y ب 0 وشوف x وين بتروح يبقى بنحدد + +626 +01:04:59,320 --> 01:05:01,100 +القيمة في هذه الحالة + +627 +01:05:05,430 --> 01:05:13,290 +كيف؟ المثل معطلك X يساوي Y كيف + +628 +01:05:13,290 --> 01:05:19,410 +مش مفروض؟ تلتان معروفات هي X يساوي Y تلتان بدكش حط + +629 +01:05:19,410 --> 01:05:27,210 +ل Y تساوي جدر X جدر X معروف هي جدر X الموجب وجدر X + +630 +01:05:27,210 --> 01:05:33,820 +الثاني صحيح ولا لأ؟ ماعكش خبر مش مشكلةطيب خليكم + +631 +01:05:33,820 --> 01:05:39,180 +معنا يا شباب يبقى هاي رسمنا ال X يساوي Y تربية و + +632 +01:05:39,180 --> 01:05:44,080 +المنحنة تاني X زائد 2Y تربية يساوي 3 رسمناها يبقى + +633 +01:05:44,080 --> 01:05:49,080 +المنطقة المظلة هي المنطقة بين المنحنيين واضح ان في + +634 +01:05:49,080 --> 01:05:53,820 +منحنة عندي على اليمين ومنحنة تاني وين على الشمال + +635 +01:05:53,820 --> 01:05:58,960 +يبقى انا بدي اقل قيمة بتاخدها Y اكبر قيمة هنا + +636 +01:05:58,960 --> 01:05:59,860 +بتاخدها مين + +637 +01:06:03,430 --> 01:06:09,990 +يبقى انا عند X يساوي Y تربية وعندي X التانية ناقص + +638 +01:06:09,990 --> 01:06:18,570 +اتنين Y تربية زائد تلاتة يبقى Y تربية + +639 +01:06:18,570 --> 01:06:23,910 +يساوي اتنين Y تربية زائد تلاتة يبقى Y تساوي زائد + +640 +01:06:23,910 --> 01:06:30,360 +او ناقصإذا هذه سالب واحد وهذه مين وهذه واحد يبقى + +641 +01:06:30,360 --> 01:06:35,400 +النقطة ان هذه سالب واحد والنقطة هذه واحد يبقى ال + +642 +01:06:35,400 --> 01:06:39,900 +area اللي عندنا بدأ تساوي تكمل من سالب واحد إلى + +643 +01:06:39,900 --> 01:06:44,180 +واحد الدالة اللي على اليمين اللي هي اتنين Y تربية + +644 +01:06:44,180 --> 01:06:48,180 +زائد تلاتة ناقص الدالة اللي على الشمال اللي هي مين + +645 +01:06:48,480 --> 01:06:58,220 +x يساوي y تربيع كل هذا بالنسبة لمين الى dy سالب + +646 +01:06:58,220 --> 01:07:05,260 +اتنين y تربيع زي التلاتة سالب y تربيع يبقى كأن + +647 +01:07:05,260 --> 01:07:13,190 +المسألة تكامل من سالب واحد الى واحد لمين لتلاتةنقص + +648 +01:07:13,190 --> 01:07:27,610 +ثلاثة Y تربيع كله بالنسبة الى D1 يبقى + +649 +01:07:27,610 --> 01:07:32,850 +even function ممكن اقول من الصفرلغاية كده؟ لغاية + +650 +01:07:32,850 --> 01:07:36,330 +واحدة انسى مش مشكلة فالمساحة اللى فوق واضحة انها + +651 +01:07:36,330 --> 01:07:40,150 +جد المساحة اللى تحت يعني لو خدت واحدة وضربتها في + +652 +01:07:40,150 --> 01:07:43,650 +اتنين بمشي الحال اجى فى بلد كان فيها مجاش ماعناش + +653 +01:07:43,650 --> 01:07:48,490 +مشكلة يبقى لو خلتها زى ما هو مجاش فى باقيبقول له + +654 +01:07:48,490 --> 01:07:53,730 +هذه تلاتة Y ناقص Y تكيبها تلاتة بتروح و بظل + +655 +01:07:53,730 --> 01:07:58,890 +المساحة من سالب واحد لغاية قداش واحد يبقى بده + +656 +01:07:58,890 --> 01:08:06,830 +يساوي تلاتة ناقص تلاتة هذه Y تكيبها تلاتة بتروح مع + +657 +01:08:06,830 --> 01:08:14,120 +تلاتة يبقى عند الواحد تلاتة ناقص واحد ناقصهنا بصير + +658 +01:08:14,120 --> 01:08:21,540 +ناقص تلاتة وهنا يا سيد العزيز ناقص واحد بصير زائد + +659 +01:08:21,540 --> 01:08:28,460 +واحد يبقى الجواب بيصير تلاتة ناقص واحد زائد تلاتة + +660 +01:08:28,460 --> 01:08:33,300 +كمان ناقص واحد يبقى النتيجة كم؟ أربع يبقى قيمة + +661 +01:08:33,300 --> 01:08:39,380 +المساحة تساوي أربع هذا نمر ايه من المثلة؟ نمر بيه + +662 +01:08:40,960 --> 01:08:51,820 +نمر بيبقى يبقى y تساوي x تربيع and يبقى y ناقص x + +663 +01:08:51,820 --> 01:08:55,720 +تربيع زائد 4x + +664 +01:09:04,920 --> 01:09:09,140 +هذه برضه معادلة من درجة ثانية في X يبقى هذه + +665 +01:09:09,140 --> 01:09:14,120 +Parabola وهذه كذلك Parabola بس هذه ال vertex تبعها + +666 +01:09:14,120 --> 01:09:19,700 +نقطة هذه معمولة لها إيه؟ شوف، بدي أحدد وين ال + +667 +01:09:19,700 --> 01:09:25,500 +vertex تبع هذه ال Parabola فاروح بعمل إكمال المربع + +668 +01:09:25,500 --> 01:09:29,120 +هذه قد إيش بدها مشان يصير إكمال المربع؟ + +669 +01:09:37,320 --> 01:09:45,580 +يبقى هذا الكلام يصبح على الشكل التالي عندك ال Y + +670 +01:09:45,580 --> 01:09:54,660 +يسوى ناقص X تربيع زائد 4 X ناقص 4 زائد 4أو بمعنى + +671 +01:09:54,660 --> 01:10:01,440 +آخر هذه ها ها بد يصير y ناقص أربعة بد يساوي هاي + +672 +01:10:01,440 --> 01:10:07,020 +ناقص أخدناه عام المشترك بظال x تربيه ناقص أربعة x + +673 +01:10:07,020 --> 01:10:12,660 +زائد أربعة هذه الأربعة نعشج هذه هدول التلاتة أخدنا + +674 +01:10:12,660 --> 01:10:18,440 +منهم سالب عام المشترك يبقى بصير ال y ناقص أربعة + +675 +01:10:18,440 --> 01:10:25,790 +يساوي ال x ناقص اتنين لكل تربيهيبقى هذه البرابولة + +676 +01:10:25,790 --> 01:10:31,490 +و ال vertex تبعها هي بين 2 و 4 يبقى انا لو روحت + +677 +01:10:31,490 --> 01:10:37,050 +رسمت الرسمة اللي عندنا هذه فبدي بقوله هذا محور X + +678 +01:10:37,050 --> 01:10:43,350 +وهذا محور Y وهذه نقطة الأصل اللي هي Zero البرابولة + +679 +01:10:43,350 --> 01:10:48,670 +الأولى Y تساوي X تربيع يبقى Y تساوي X تربيع + +680 +01:10:48,670 --> 01:10:56,690 +البرابولة اللي عندنا هذه هيكيبقى هذه اللي هي هذه + +681 +01:10:56,690 --> 01:11:03,650 +فوق X يساوي Y تربيع هذه Y تساوي X تربيعبتدخل ال + +682 +01:11:03,650 --> 01:11:08,490 +parabola التانية ال vertex تبعها اللي هو اتنين + +683 +01:11:08,490 --> 01:11:14,750 +واربعة يبقى اتحرك اتنين هنا على اليمين وده يطالع + +684 +01:11:14,750 --> 01:11:20,710 +فوق اداش اربعة يبقى هذه النقطة اتنين واربعة طب ليش + +685 +01:11:20,710 --> 01:11:25,530 +اجت على المنحنة ولم تجت فوق او جت تحت لأن y تساوي + +686 +01:11:25,530 --> 01:11:28,770 +x تساوي اتنين لما ال x تساوي اتنين تبقى اربعة إذا + +687 +01:11:28,770 --> 01:11:33,870 +انتقى على مين على المنحنة بالضبط تماماطيب هذا ال + +688 +01:11:33,870 --> 01:11:38,070 +vertex تبع اتنين و اربعة open up ولا open down + +689 +01:11:38,070 --> 01:11:43,730 +open down بسبب الإشارة السلبية اتنين يا مربى نقطة + +690 +01:11:43,730 --> 01:11:49,390 +الاصل والله ليه يا مربى نقطة الاصل طلع المعادلة لو + +691 +01:11:49,390 --> 01:11:55,910 +حطيت x ب zero y بقدرش يبقى دي مربى نقطة الاصل غصب + +692 +01:11:55,910 --> 01:12:00,270 +من علمه يرضى يبقى ال parabola هذه بدها تيجي بالشكل + +693 +01:12:00,270 --> 01:12:07,100 +اللي عندنا هذاو من هنا فرابولة بالشكل هذا و من هنا + +694 +01:12:07,100 --> 01:12:13,660 +فرابولة بالشكل هذا يبقى الفرابولة إلى أسفل + +695 +01:12:13,660 --> 01:12:27,760 +الفرابولة + +696 +01:12:27,760 --> 01:12:30,160 +إذا المنطقة اللي بينهم هي + +697 +01:12:39,220 --> 01:12:47,280 +هذا المنطقة المظلة بين الاتنين هي المنطقة المطلوبة + +698 +01:12:53,660 --> 01:12:58,640 +ال X هتتغير من اين لين و اذا انا اريد نسبة Y من + +699 +01:12:58,640 --> 01:13:05,660 +صفر لغاية اربعة ايام طيب ايهم افضل كامل بالنسبة ل + +700 +01:13:05,660 --> 01:13:12,980 +X ولا بالنسبة ل Y انفع الشجتين بس ال X أسهل كتير + +701 +01:13:12,980 --> 01:13:18,340 +لان ال X لسه بيتحول و تاخد جذر و جثة طويلة يبقى + +702 +01:13:18,340 --> 01:13:24,790 +انا لو جيت و قلت ال area Aبدي يساوي تكامل ال X + +703 +01:13:24,790 --> 01:13:30,290 +هتتغير من صفر لين لغاية الاتنين بدي الدالة اللي + +704 +01:13:30,290 --> 01:13:33,970 +فوق الدالة اللي فوق اللي هو المنحنة اللي عندها ده + +705 +01:13:33,970 --> 01:13:38,850 +Y يساوي ناقص X تربيع زي دربيع هذه الدالة اللي فوق + +706 +01:13:38,850 --> 01:13:45,430 +وال X تربيع هي من الدالة اللي تحت يبقى لناقص X + +707 +01:13:45,430 --> 01:13:53,640 +تربيعزائد أربعة X هذه كلها ناقص ال X تربية اللي هي + +708 +01:13:53,640 --> 01:13:58,300 +الدالة التانية كلها بالنسبة إلى مين بالنسبة إلى DX + +709 +01:13:58,300 --> 01:14:04,560 +يبقى هذا الكلام بيساوي تكامل من صفر لإتنين للاربعة + +710 +01:14:04,560 --> 01:14:12,260 +X ناقص اتنين X تربية كل هذا الكلام بالنسبة إلى مين + +711 +01:14:12,260 --> 01:14:19,680 +إلى DXيبقى هذا بده يساوي اللي هو اتنين X تربية + +712 +01:14:19,680 --> 01:14:27,920 +ناقص طولتين X تكيب من صفر لغاية اتنين يبقى هنا + +713 +01:14:27,920 --> 01:14:36,500 +تمانية ناقص هنا تمانية ستاشر على تلاتة ناقص ال + +714 +01:14:36,500 --> 01:14:41,960 +zeroيبقى هذا كله على تلاتة في تمانية باربعة وإشرين + +715 +01:14:41,960 --> 01:14:50,600 +من ستاشر بيظل تمانية على تلاتة فقط لا غير يبقى لما + +716 +01:14:50,600 --> 01:14:55,740 +ترسم صح أو تحدد حدود التكمل صح، باقي الشغل كله + +717 +01:14:55,740 --> 01:14:57,820 +بيصير شغل روتيني أيضا + +718 +01:15:01,970 --> 01:15:06,430 +أنا بقولك الامتحانات اللي بخليها لك بقسمها لك، لكن + +719 +01:15:06,430 --> 01:15:10,970 +الامتحانات اللي بقسمها لك بقسمها لك، ايه نعم؟ لو + +720 +01:15:10,970 --> 01:15:14,850 +طلعت على الامتحانات السابقة، هتلاقي بعض المسائل + +721 +01:15:14,850 --> 01:15:17,970 +اللي على الموضوع هذا ما الرسمينها، ومظللينها مش + +722 +01:15:17,970 --> 01:15:24,230 +هقولك هي المساحة اللي بدنا يعني، ايوة، كده؟ الرسم + +723 +01:15:24,230 --> 01:15:26,130 +التاني، كده؟ + +724 +01:15:31,170 --> 01:15:36,970 +هي رسمة قدامك + +725 +01:15:36,970 --> 01:15:41,490 +رسمة المنحنة التانية ما انتشرفش اللي سوناه مش هي + +726 +01:15:41,490 --> 01:15:46,630 +المنحنة روحت املت و اكمل المربع لغاية ما وصلت لهنا + +727 +01:15:47,440 --> 01:15:51,540 +هذه برابولة بسمعولي لو شيلت الاربعة و اتنين بصير Y + +728 +01:15:51,540 --> 01:15:55,880 +تساوي سالب X تربيع برابولة الى أسفل بس ممكن + +729 +01:15:55,880 --> 01:15:59,120 +تسمعليها زاحة لليمين و زاحة لأعلى مشان الverse X + +730 +01:15:59,120 --> 01:16:04,060 +اتنين و اربعة وبالتالي صلة بسيطة جدا طيب ال هذا + +731 +01:16:04,060 --> 01:16:11,120 +نمر بي من السؤال كان بدنا نروح لنمره C نمره C + +732 +01:16:11,120 --> 01:16:16,240 +بقولي Y تساوي X كيب and + +733 +01:16:18,190 --> 01:16:24,870 +تلاتة X تربيها ناقص Y يساوي اربعة + +734 +01:16:32,700 --> 01:16:37,540 +يبقى بنروح نرسم الرسم اللى عندنا بس قبل انا ارسمها + +735 +01:16:37,540 --> 01:16:43,240 +ها دي ها ها بقدر احطها فى الشكل الطبيعى تبعها يبقى + +736 +01:16:43,240 --> 01:16:47,240 +لو جبت ال Y على اليمين والاربعة الشمال بصير Y + +737 +01:16:47,240 --> 01:16:52,920 +يساوي تلاتة X تربية وناقص اربعة أبدا برضه هذه ال + +738 +01:16:52,920 --> 01:16:56,400 +parabola شيل الاربعة وشيل التلاتة بصير Y تساوي X + +739 +01:16:56,400 --> 01:17:01,850 +تربيةتلاتة تتجرب على محور Y سالب اربعة شفت الاصل + +740 +01:17:01,850 --> 01:17:06,530 +بمقدار اربعة اذا لو جيت رسمت الرسم اللي عندنا + +741 +01:17:06,530 --> 01:17:13,510 +الرسم بالشكل هذا هذا محور X هذا محور Y هذا نقطة + +742 +01:17:13,510 --> 01:17:18,870 +الاصل اللي هي Zero طلعلي كويسة النقطة الأولى Y + +743 +01:17:18,870 --> 01:17:23,690 +تساوي X تكيب مشهور عند المنحنة ومعروف يبقى المنحنة + +744 +01:17:23,690 --> 01:17:25,590 +بده يجيلك X + +745 +01:17:28,980 --> 01:17:38,190 +يبقى هذا المنحنى Y تساوي X تكيببتجي للمنحنة لأن Y + +746 +01:17:38,190 --> 01:17:42,750 +تساوي X تربيه ال Parabola إلى أعلى تلاتة يبقى + +747 +01:17:42,750 --> 01:17:47,690 +بتجرب على محور Y سالب أربعة يبقى shift إلى أسفل + +748 +01:17:47,690 --> 01:17:52,410 +بمقدار سالب أربعة إذا لو روحت قولت هذه اللي هي + +749 +01:17:52,410 --> 01:17:57,630 +main سالب أربعة و ال parabola بتجي أرسمها يبقى ال + +750 +01:17:57,630 --> 01:18:01,830 +parabola بتاخد الشكل التالي اللي عندنا هيك و بتجي + +751 +01:18:01,830 --> 01:18:03,110 +تاخد الشكل هذا + +752 +01:18:06,190 --> 01:18:11,150 +المساحة الموجودة بين المنحنيين هي المساحة اللي + +753 +01:18:11,150 --> 01:18:11,790 +عندنا هنا + +754 +01:18:19,960 --> 01:18:27,140 +واضح أن هناك منحنى أعلى ومنحنى أسفل هذا المنحنى + +755 +01:18:27,140 --> 01:18:34,200 +الأسفل يساوي تلاتة X تربية ناقص أربعة ومنحنى + +756 +01:18:34,200 --> 01:18:39,620 +الأعلى Y تساوي X تتانية إذا هذا تكمل بالنسبة ل X + +757 +01:18:39,620 --> 01:18:46,560 +إذا بلزمني أعرف قدر أقل قيمة ل X هنا وقدر أكبر + +758 +01:18:46,560 --> 01:18:54,060 +قيمة ل X هنابتروح احل المعادلاتين مع بعض بالنسبة + +759 +01:18:54,060 --> 01:19:00,200 +لمين الى X يبقى بالدرجة اقول X تكيب يساوي تلاتة X + +760 +01:19:00,200 --> 01:19:08,760 +تربيع ناقص أربعة او X تكيب ناقص تلاتة X أُص أربعة + +761 +01:19:08,760 --> 01:19:17,160 +زائد أربعة يساوي Zero X تربيع زائد أربعة يساوي + +762 +01:19:17,160 --> 01:19:24,370 +Zeroنقدر نحللها هيك؟ نسأل الموضوع، اه يبقى هذه + +763 +01:19:24,370 --> 01:19:32,870 +معادلة من الدرجة التالتة يبقى شغل مخك مين + +764 +01:19:32,870 --> 01:19:39,310 +قالك not exist يا شاطر انت؟ هو اللي وجهك الامتعان + +765 +01:19:39,310 --> 01:19:43,110 +وقلتلنا does not exist هو اللي بقولك العلامة does + +766 +01:19:43,110 --> 01:19:46,790 +not exist نفس الإجابة + +767 +01:19:52,010 --> 01:20:00,210 +طبعا شو بيزددى؟ بدي أنزل الدرجة بتاعتها من الدرجة + +768 +01:20:00,210 --> 01:20:06,650 +التالتة للدرجة التانية اتفكرا اولا كي بتروح على ال + +769 +01:20:06,650 --> 01:20:12,190 +constant و بتشوف قواسم ال constant واحد سالب واحد + +770 +01:20:12,190 --> 01:20:17,150 +اتنين سالب اتنين اربعة سالب اربعة يبقى ان عندي ستة + +771 +01:20:17,150 --> 01:20:23,410 +قواسم واحد منهم لازم يحقق المعادلةبقول جرب الواحد + +772 +01:20:23,410 --> 01:20:27,990 +والسالب واحد انسى الموضوع تمام والله يمكن يجيبوها + +773 +01:20:27,990 --> 01:20:34,970 +لو قلت هنا واحد واربع خمس سالب تسبطش لو قلت سالب + +774 +01:20:34,970 --> 01:20:40,050 +واحد بصير سالب واحد و هدى السالب تلاته بصير سالب + +775 +01:20:40,050 --> 01:20:41,890 +اه والله سالب واحد تيجي بنفع + +776 +01:20:46,000 --> 01:21:04,500 +ماذا لو انا + +777 +01:21:04,500 --> 01:21:08,200 +انا انا انا انا انا انا انا انا انا انا انا انا + +778 +01:21:08,200 --> 01:21:08,300 +انا انا انا انا انا انا انا انا انا انا انا انا + +779 +01:21:08,300 --> 01:21:08,340 +انا انا انا انا انا انا انا انا انا انا انا انا + +780 +01:21:08,340 --> 01:21:08,340 +انا انا انا انا انا انا انا انا انا انا انا انا + +781 +01:21:08,340 --> 01:21:08,340 +انا انا انا انا انا انا انا انا انا انا انا انا + +782 +01:21:08,340 --> 01:21:08,340 +انا انا انا انا انا انا انا انا انا انا انا انا + +783 +01:21:08,340 --> 01:21:08,340 +انا انا انا انا انا انا انا انا انا انا انا انا + +784 +01:21:08,340 --> 01:21:08,340 +انا انا انا انا انا انا انا انا انا انا انا انا + +785 +01:21:08,340 --> 01:21:09,240 +انا انا انا انا انا انا انا انا انا انا انا انا + +786 +01:21:09,240 --> 01:21:14,600 +اناequation one سميه لهذا ال equation one يعني + +787 +01:21:14,600 --> 01:21:19,600 +معنى هذا الكلام ان ال X نقص اتنين هو احد العوامل + +788 +01:21:19,600 --> 01:21:28,580 +للمعادلة يبقى هنا ال X نقص اتنين is a factor of + +789 +01:21:28,580 --> 01:21:33,400 +equation oneماذا يعني factor of equation one؟ يعني + +790 +01:21:33,400 --> 01:21:39,000 +لو جسمت المعادلة هذه على x نقص اتنين تقبل القسمة + +791 +01:21:39,000 --> 01:21:44,060 +بدون باقيطيب تعالى اتأكد كلامنا صحيح و الله كله + +792 +01:21:44,060 --> 01:21:50,080 +كلام اذا بتروح اقسم اللى عندنا اللى هو main x تكيب + +793 +01:21:50,080 --> 01:21:57,900 +ناقص قداش اتنين ناقص تلاتة x تربية ناقص تلاتة زائد + +794 +01:21:57,900 --> 01:22:05,120 +اربعة كله على x ناقص اتنينبعدين بقولوا x تكييب على + +795 +01:22:05,120 --> 01:22:12,580 +x فيها كده؟ x تربيه طيب x تربيه في x بx تكييب نقص + +796 +01:22:12,580 --> 01:22:18,740 +اتنين x تربيه زائد بصير نقص وهذه زائد مع سلامة + +797 +01:22:18,740 --> 01:22:27,120 +زائد اتنين x تربيه بظل سالب x تربيه زائد اربعةسالب + +798 +01:22:27,120 --> 01:22:34,820 +X تربيع على X بظال جديش سالب X سالب X تربيع زائد + +799 +01:22:34,820 --> 01:22:43,140 +2X زائد ناقص مع السلامة بظال ناقص 2X زائد جديش + +800 +01:22:43,630 --> 01:22:48,490 +أربعة الباقي من الدرجة الأولى والمقصوم عليه من + +801 +01:22:48,490 --> 01:22:54,610 +الدرجة الأولى يبقى بنواصل عملية القسمة يبقى ناقص + +802 +01:22:54,610 --> 01:23:02,450 +اتنين X على X بثالث اتنين بثالث اتنين X زائد أربعة + +803 +01:23:02,450 --> 01:23:09,900 +زائد ناقص بصير Zero فعلا هي قسمت بدون باقييبقى + +804 +01:23:09,900 --> 01:23:15,880 +مسألتي هذه هاها بصير على الشكل التالي هذا المثل + +805 +01:23:15,880 --> 01:23:22,280 +بصير أخدت x ناقص اتنين طالع النتج عندي قداش x + +806 +01:23:22,280 --> 01:23:30,180 +ترابيع ناقص xنقص اتنين كله بده يساوي قداش بده + +807 +01:23:30,180 --> 01:23:36,120 +يساوي زيرو الحين هذه بقدر احللها يبقى هذه x نقص + +808 +01:23:36,120 --> 01:23:46,240 +اتنين وهذا قص وهذا قص ويساوي زيرو x1 2 ناقص زاد + +809 +01:23:46,240 --> 01:23:52,480 +صار الجث هذا هو نفس الجث هذا يبقى صار عندي x ناقص + +810 +01:23:52,480 --> 01:23:58,500 +2 لكل تربية في x زائد واحد بده يساوي zero هذا + +811 +01:23:58,500 --> 01:24:03,500 +معناه ان x بده يساوي 2 والx بده يساوي جدال سالب + +812 +01:24:03,500 --> 01:24:08,660 +واحد إذا النقطة هذه سالب واحد والنقطة هذه 8يعني + +813 +01:24:08,660 --> 01:24:13,140 +النقطة دي لما أقول X نقص اتنين لكل تربية يعني طلعت + +814 +01:24:13,140 --> 01:24:19,740 +نفس النقطة بس إيه مكررة مرتم تمام يبقى معنا هذا + +815 +01:24:19,740 --> 01:24:24,960 +الكلام بدي أقوله ال area إيه بده سوى تكامل من عند + +816 +01:24:24,960 --> 01:24:30,640 +السلب واحد لغاية الإتنين الدالة اللي فوق هي من X + +817 +01:24:30,640 --> 01:24:39,070 +تكيمنقص الدلة التي تحتلت تلاتة X تربية ناقص أربعةY + +818 +01:24:39,070 --> 01:24:45,650 +تساوي تلاتة X تربية ناقص أربعة تلاتة X تربية ناقص + +819 +01:24:45,650 --> 01:24:51,370 +أربعة كله بالنسبة لمين إلى DX يبقى هذا الكلام + +820 +01:24:51,370 --> 01:24:56,630 +يساوي تكامل من سلب واحد لاتنين لل X تكيب ناقص + +821 +01:24:56,630 --> 01:25:03,510 +تلاتة X تربية زائد أربعة كله بالنسبة إلى DX ان + +822 +01:25:03,510 --> 01:25:10,170 +كامل يبقى X أقصى أربعة على أربعةنقص x تكيب على 3 + +823 +01:25:10,170 --> 01:25:19,560 +مع 3 زائد 4x كله من ناقص 1 لغاية 2نعود بالقيمة + +824 +01:25:19,560 --> 01:25:27,100 +اللى فوق ناقص القيمة اللى تحت يبقى يساوي 16 على 4 + +825 +01:25:27,100 --> 01:25:37,240 +ناقص تمانية زائد تمانية ناقص قوس هنا بصير ربع وهنا + +826 +01:25:37,240 --> 01:25:45,200 +زائد واحد وهنا ناقص أربعةهذه ستصبح تمانية و تمانية + +827 +01:25:45,200 --> 01:25:52,320 +مع السلامة هذه ستصبح أربعة ناقص ربع ناقص واحد زائد + +828 +01:25:52,320 --> 01:25:57,780 +أربعة أربعة و أربعة تمانية تمانية بدنا نشيل منها + +829 +01:25:57,780 --> 01:26:06,880 +واحد ثبال سبعة ناقص ربع يعني ستة و تلت أربع يعني + +830 +01:26:06,880 --> 01:26:11,460 +سبعة و عشرين على قداش على أربعة + +831 +01:26:13,950 --> 01:26:20,170 +المثال الأخير بيقول + +832 +01:26:20,170 --> 01:26:29,970 +example 3 find the area + +833 +01:26:29,970 --> 01:26:33,130 +enclosed + +834 +01:26:33,130 --> 01:26:38,010 +by + +835 +01:26:38,010 --> 01:26:41,150 +the + +836 +01:26:41,150 --> 01:26:42,810 +y-axis + +837 +01:26:46,800 --> 01:26:56,180 +والـ curve هو المنحنة x يساوي y ناقص واحد لكل + +838 +01:26:56,180 --> 01:27:07,580 +تربيع و ال x يساوي تلاتة ناقص ال y and ال x يساوي + +839 +01:27:07,580 --> 01:27:20,300 +اتنين جذر ال yas shown in the figure كما هو مبين + +840 +01:27:20,300 --> 01:27:25,600 +بالشكل وراح رسملي طبعا هذا سؤال في الكتاب راح + +841 +01:27:25,600 --> 01:27:33,340 +رسملي هذا الشكل اللي محصور بين هذه المنحنيات وطلب + +842 +01:27:33,340 --> 01:27:35,600 +مساحة هذا الشكل + +843 +01:28:03,030 --> 01:28:05,110 +السلام عليكم و رحمه الله + +844 +01:28:19,970 --> 01:28:24,190 +الله أكبر الله أكبر الله أكبر + +845 +01:28:44,230 --> 01:28:49,510 +قال لي اتلي مساحة المنطقة المغلقة بمحور Y يبقى + +846 +01:28:49,510 --> 01:28:56,030 +محور Y احد المنحنيات X يساوي Y ناقص واحد لكل تربيع + +847 +01:28:56,030 --> 01:29:01,930 +و X يساوي تلاتة ناقص Y و X يساوي اتنين جذر ال Y + +848 +01:29:01,930 --> 01:29:06,990 +يبقى المساحة اللي بينهم هي المساحة المظللة اللي + +849 +01:29:06,990 --> 01:29:12,150 +عندنا هذه و قال لي هنا النقطة بقى لدي الواحد تمام + +850 +01:29:13,460 --> 01:29:17,920 +طبعا الكتاب حط السؤال و رسمك الرسمة و قولك هات ليه + +851 +01:29:17,920 --> 01:29:23,580 +المساحة اللى عندنا بقوله بسيطة منحنى لو جيت قولت + +852 +01:29:23,580 --> 01:29:27,380 +اللى تحت و اللى فوق صار اللى فوق منحنيات اتنين و + +853 +01:29:27,380 --> 01:29:31,620 +اللى تحت منحنى واحد صحيح إذا ماتظبطشلو جيت اللى + +854 +01:29:31,620 --> 01:29:36,280 +علي اليمين و اللى علي الإشمال بيصيروا اتنين علي + +855 +01:29:36,280 --> 01:29:39,960 +اليمين و خط علي الإشمال و بعدين واحد فاجهي من + +856 +01:29:39,960 --> 01:29:46,520 +الخربطة هذه لكن لو جيت قلت بتهيأجسم هذا المنحنى + +857 +01:29:46,520 --> 01:29:52,460 +إلى منطقتين بالشكل اللى عندنا هذا يبقى هاي المنطقة + +858 +01:29:52,460 --> 01:29:56,380 +و + +859 +01:29:56,380 --> 01:30:01,340 +المنطقة التانيةعندما أخذ هذه المنطقة و أخذ هذه + +860 +01:30:01,340 --> 01:30:04,220 +المنطقة و أخد هذه المنطقة و أخد هذه المنطقة و أخد + +861 +01:30:04,220 --> 01:30:05,400 +هذه المنطقة و أخد هذه المنطقة و أخد هذه المنطقة و + +862 +01:30:05,400 --> 01:30:07,160 +أخد هذه المنطقة و أخد هذه المنطقة و أخد هذه + +863 +01:30:07,160 --> 01:30:12,280 +المنطقة و أخد هذه المنطقة و أخد هذه المنطقة و أخد + +864 +01:30:12,280 --> 01:30:18,900 +هذه المنطقة و أخد هذه المنطقة و أخد هذه المنطقة + +865 +01:30:18,950 --> 01:30:24,010 +يبقى انا عند هنا x يساوي y ناقص واحد لكل تربية + +866 +01:30:24,010 --> 01:30:30,150 +وعندي x يساوي تلاتة ناقص y يبقى بقدر اجيب قيمة y + +867 +01:30:30,150 --> 01:30:36,530 +بس انا لازمالي mainلازمالى قيمة X وليس قيمة Y اذا + +868 +01:30:36,530 --> 01:30:43,810 +انا هنا بقدر اقول المنحنى الاول X يساوي Y ناقص + +869 +01:30:43,810 --> 01:30:49,930 +واحد لكل تربية والمنحنى التانى X يساوي تلاتة ناقص + +870 +01:30:49,930 --> 01:30:54,250 +Yحلّيت بالنسبة ل X في الأول وحلّيت بالنسبة ل Y في + +871 +01:30:54,250 --> 01:30:58,990 +الأول، لا تفرق عننا هذي والله هذي السيان يبقى احنا + +872 +01:30:58,990 --> 01:31:02,870 +لو جينا قولنا بدي أخليها زي ما هي مثلا يبقى ال Y + +873 +01:31:02,870 --> 01:31:10,050 +ناقص واحد لكل تربية تسوى تلاتة ناقص Yأو بمعنى آخر + +874 +01:31:10,050 --> 01:31:17,130 +Y تربية ناقص اتنين Y زائد واحد يساوي تلاتة ناقص Y + +875 +01:31:17,130 --> 01:31:23,630 +ممكن نعملها معادلة صفرية بصير Y تربية هات Y هنا + +876 +01:31:23,630 --> 01:31:30,270 +بصير موجة بصير ناقص Y هات هات هنا بصير سالبتلاتة + +877 +01:31:30,270 --> 01:31:34,810 +مع واحد بيبقى سالب اتنين يساوي زيرو هذه لو روحت + +878 +01:31:34,810 --> 01:31:41,950 +حللتها كقوسين يساوي زيرو يبقى هنا Y هنا Y واحد + +879 +01:31:41,950 --> 01:31:47,610 +اتنين سالب اللي هو اتنين Y وموجة بيبقى سالب Y + +880 +01:31:47,610 --> 01:31:54,140 +مظبوط اذا انا عندي Y سالب واحد وY اتنينيبقى هنا y + +881 +01:31:54,140 --> 01:32:01,240 +يساوي سالب واحد و y تساوي اتنين يبقى انا انا حلت + +882 +01:32:01,240 --> 01:32:08,020 +الاتنين هدول مع بعض مرة بدهم يتقفع عند y تساوي + +883 +01:32:08,020 --> 01:32:13,900 +سالب واحد و مرة عند y تساوي من الاتنينإذا للإحداث + +884 +01:32:13,900 --> 01:32:19,300 +النقطة هذه بيكون جداش لإتنين هذا المنحنى لو كملته + +885 +01:32:19,300 --> 01:32:24,380 +أجه هيتقاطع مع مين؟ مع الخط عنده نقطة Y تساوي سالب + +886 +01:32:24,380 --> 01:32:27,800 +واحد إذا ماليش علاقة فيه يبقى أنا إليه علاقة في ال + +887 +01:32:27,800 --> 01:32:34,270 +Y تساوي مين؟ إتنينلو جيت أخدت Y تساوي 2 و عوضت بها + +888 +01:32:34,270 --> 01:32:41,110 +في أي من المعادلتين يبقى هذا بيعطيك ان X بيساوي + +889 +01:32:41,110 --> 01:32:46,210 +تلاتة نقص اتنين اللي هو قداش واحد إذا إحداث النقطة + +890 +01:32:46,210 --> 01:32:52,510 +هذه هو واحد و اتنين يبقى X عند هنا بقداش تساوي + +891 +01:32:52,510 --> 01:32:56,990 +واحد بالدالي النقطة اللي عندنا هذه كمان بدي أعرف + +892 +01:32:56,990 --> 01:32:59,390 +قداش القيمة بتبعتها + +893 +01:33:02,590 --> 01:33:06,690 +يبقى بدى اعرف جداش لحظاتى معناته بدى احل معادلة + +894 +01:33:06,690 --> 01:33:11,290 +المنحنى هذا مع مين مع معادلة المنحنى اللى عندنا + +895 +01:33:11,290 --> 01:33:21,490 +هذا هذا المنحنى اللى همين X بده يساوي تلاتة ناقص Y + +896 +01:33:21,490 --> 01:33:31,470 +and ال X بده يساوي اتنين جذر ال Yبقدر اقول هذه why + +897 +01:33:31,470 --> 01:33:39,720 +تساوي؟تلاتة ناقص X تلاتة ناقص X and هذه لو جيت + +898 +01:33:39,720 --> 01:33:47,820 +ربعت الطرفين بصير Y يساوي ربع ال X يبقى Y تساوي + +899 +01:33:47,820 --> 01:33:55,800 +ربع ال X تربية يبقى لو حلت الاتنين مع بعض ربع X + +900 +01:33:55,800 --> 01:34:02,930 +تربية بدها تساوي تلاتة ناقص Xأضرب كله في أربعة + +901 +01:34:02,930 --> 01:34:10,670 +بيصير عندك مين X تربية يساوي اتناشر ناقص أربعة X + +902 +01:34:10,670 --> 01:34:19,070 +يبقى هذا الكلام بيصير X تربية زائد أربعة X ناقص + +903 +01:34:19,070 --> 01:34:25,440 +اتناشر يساوي كده؟ يساوي Zeroنحلل هذا الكلام كقوسين + +904 +01:34:25,440 --> 01:34:32,680 +يساوي Zero يبقى هنا X هنا X هذي ستة في اتنين ستة + +905 +01:34:32,680 --> 01:34:38,020 +في اتنين هذي زائد و هذي نقص زائد ستة X و نقص اتنين + +906 +01:34:38,020 --> 01:34:42,900 +X يبقى زائد اربع X يبقى بناء ان عليه ال X بده + +907 +01:34:42,900 --> 01:34:50,900 +يساوي اتنين و ال X بده يساوي سالب ستةيبقى هذا + +908 +01:34:50,900 --> 01:34:55,380 +الكلام، لو كملنا المنحة، لو أجى معاه، هذا هيتقطع + +909 +01:34:55,380 --> 01:34:58,900 +عند السلف ستة، ماليش علاقة فيها، إيه اللي علاقة في + +910 +01:34:58,900 --> 01:35:05,180 +جداش؟ فيه ليتنين، يبقى بصير التكامل عندنا بهذا + +911 +01:35:05,180 --> 01:35:12,070 +الشكليبقى الآن حددت حدود التكامل، قسمت المنطقة إلى + +912 +01:35:12,070 --> 01:35:18,850 +منطقتين، إذا بقدر أحسب قداش قيمة هذه المساحة + +913 +01:35:18,850 --> 01:35:25,110 +المحصورة بين المنحنيين، فبروح بقوله الـ A to Z + +914 +01:35:26,800 --> 01:35:31,780 +تكامل من عند ال zero لغاية ال واحد من ال zero + +915 +01:35:31,780 --> 01:35:39,200 +لغاية ال واحد الدالة اللى فوق اه هذه مرتبناش هذه + +916 +01:35:39,200 --> 01:35:48,580 +بدها تصير جذر ال X بده ساوي Y ناقص واحد طبعا هحمل + +917 +01:35:48,580 --> 01:35:49,880 +ال Y السالبة + +918 +01:35:54,960 --> 01:36:04,070 +يبقى هذا معناه ان Y تساوي جذر ال X زائد واحديبقى + +919 +01:36:04,070 --> 01:36:10,530 +الدالة اللي فوق هذه Y تساوي جدر ال X زائد واحد هي + +920 +01:36:10,530 --> 01:36:17,410 +الدالة اللي فوق، يبقى جدر ال X زائد واحد ناقص + +921 +01:36:17,410 --> 01:36:24,410 +الدالة اللي تحت، هذه طلعناها كده؟رابع X تربيع يبقى + +922 +01:36:24,410 --> 01:36:32,130 +ناقص رابع X تربيع كله بالنسبة إلى DX زائد تكمل + +923 +01:36:32,130 --> 01:36:37,440 +المنطقة الثانية من واحد لغاية اتنينالدالة اللى فوق + +924 +01:36:37,440 --> 01:36:45,180 +هذى يقول انه يسوى تلاتة ناقص X تلاتة ناقص X ناقص + +925 +01:36:45,180 --> 01:36:52,180 +اللى هو ربع X تربيع يبقى ناقص ربع X تربيع كله + +926 +01:36:52,180 --> 01:36:58,300 +بالنسبة إلى DX يبقى + +927 +01:36:58,300 --> 01:37:03,660 +هذه ال area ايه تساوي من درجة التكمل الأول يبقى + +928 +01:37:03,660 --> 01:37:05,420 +هذا طول تان + +929 +01:37:08,270 --> 01:37:16,990 +زي الاكس ناقص اكس تكييب على جداش على الاطناع + +930 +01:37:16,990 --> 01:37:22,550 +الحكاية ده من عند ال zero لغاية الواحد نجي للتكامل + +931 +01:37:22,550 --> 01:37:30,680 +اللي بعده ثلاثة اكسنقص x تربيه على اتنين نقص x + +932 +01:37:30,680 --> 01:37:37,740 +تكيب على الاطمعاش كل هذا الكلام من الواحد لغاية + +933 +01:37:37,740 --> 01:37:45,220 +اتنين يبقى هذا بده يساوي تلتين زائد واحد ناقص واحد + +934 +01:37:45,220 --> 01:37:49,800 +على الاطمعاش و ال zero ال باقي كله بطير ب zeroنجي + +935 +01:37:49,800 --> 01:37:56,940 +لبعدها زائد اتنين في تلاتة بستة و هنا ناقص اتنين و + +936 +01:37:56,940 --> 01:38:05,340 +هنا ناقص تمانية على الاتماشر فيها اتنين على تلاتة + +937 +01:38:13,030 --> 01:38:18,050 +خلّصنا ال term اللي فوق ناقص ال term اللي تحت + +938 +01:38:18,050 --> 01:38:27,050 +تلاتة ناقص نص ناقص واحد على الاطمعاش هذا الكلام + +939 +01:38:27,050 --> 01:38:28,930 +يساوي كل term + +940 +01:38:34,510 --> 01:38:41,450 +هذه اتنين ع تلاتة مع سالب اتنين ع تلاتة و عندك هنا + +941 +01:38:41,450 --> 01:38:50,690 +سبعة و سالب اتنين بيضال خمسة خمسة نقص واحد ع + +942 +01:38:50,690 --> 01:38:59,310 +الاطماناسمع يا راجل ناقص ثلاثة زائد نص زائد واحد + +943 +01:38:59,310 --> 01:39:02,950 +على الاطناش ناقص واحد على اطناش وزائد واحد على + +944 +01:39:02,950 --> 01:39:09,490 +اطناش بيروح بيضل عندنا جداش اتنين و نص يبقى خمسة + +945 +01:39:09,490 --> 01:39:17,460 +على اتنين مقدار هذه المساحة، تمام؟طيب لحد هنا + +946 +01:39:17,460 --> 01:39:22,040 +انتهى ال section اللي هو خمسة ستة ويليكم أرقام + +947 +01:39:22,040 --> 01:39:31,000 +المسائل يبقى exercises خمسة ستة المسائل التالية + +948 +01:39:31,000 --> 01:39:35,780 +واحد لتسعة + +949 +01:39:35,780 --> 01:39:44,380 +وستين يعني واحد لتسعة وستين الأدومن تلاتة وسبعين + +950 +01:39:44,380 --> 01:39:50,560 +لغاية تمانية وسبعين وكذلك + +951 +01:39:50,560 --> 01:39:53,320 +من تمانية لتسعين + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/hTfsspApfcQ.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/hTfsspApfcQ.srt new file mode 100644 index 0000000000000000000000000000000000000000..227da22d7e5a05bb9f2e1c791a5fd84dd741f663 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/hTfsspApfcQ.srt @@ -0,0 +1,3426 @@ +1 +00:00:21,670 --> 00:00:27,530 +بسم الله الرحمن الرحيم المرة الماضية ابتدأنا في ال + +2 +00:00:27,530 --> 00:00:31,910 +combining functions ووصلنا إلى ال composition of + +3 +00:00:31,910 --> 00:00:36,010 +functions وعطينا definition لل composition of + +4 +00:00:36,010 --> 00:00:39,590 +functions وكذلك ال domain لل composition of + +5 +00:00:39,590 --> 00:00:44,190 +functions وأخذنا على ذلك مثالا واحدة المثال واحد + +6 +00:00:44,190 --> 00:00:46,730 +كان عبارة عن two functions جيبنا ال composition + +7 +00:00:46,730 --> 00:00:53,280 +فيما بينهما لازمنا في نفس الموضوع وأمثلة ولكن بطرق + +8 +00:00:53,280 --> 00:00:57,700 +أخرى المثال الثاني بيقول لو كانت الدالة f of x + +9 +00:00:57,700 --> 00:01:02,580 +يساوي x plus one على x وكان ال composition ما بين + +10 +00:01:02,580 --> 00:01:07,580 +الـ f والـ g of x بده يساوي الـ x قال هاتلي شكل دالة + +11 +00:01:07,580 --> 00:01:11,680 +g of x المرة اللي فاتت أعطانا two functions وطلبنا + +12 +00:01:11,680 --> 00:01:16,140 +شكل ال composition المرة هذه ما يعطيك إحدى الدالتين + +13 +00:01:16,140 --> 00:01:21,160 +وما يعطيك شكل ال composition وطلبت منه طلبت ال + +14 +00:01:21,160 --> 00:01:26,600 +function الأخرى يبقى لازلنا في نفس الموضوع ولكن + +15 +00:01:26,600 --> 00:01:31,760 +بطريقة فنية شوية يبقى الحل كالتالي + +16 +00:01:35,830 --> 00:01:40,530 +بنبدأ بالشيء المعطى الشيء المعطى اللي هو الـ F + +17 +00:01:40,530 --> 00:01:47,350 +composition G as a function of X قال يساوي الـ X لو + +18 +00:01:47,350 --> 00:01:53,430 +رجعت إلى تعريف ال composition هذا معناه F للـ G of + +19 +00:01:53,430 --> 00:02:02,300 +X بده يساوي X itself هذا معناه أن دالة g of x عبارة + +20 +00:02:02,300 --> 00:02:06,700 +عن element في domain main في domain الـ F إذا الـ F + +21 +00:02:06,700 --> 00:02:11,800 +بدأ تأثر عليه F لما تأثر على ال element عرفناها + +22 +00:02:11,800 --> 00:02:16,140 +بأنه ال element plus one مقسوما على نفس ال element + +23 +00:02:16,140 --> 00:02:21,600 +إذا بدأ أطبخ تعريف ال function هذه على main على ال + +24 +00:02:21,600 --> 00:02:26,690 +function ال N هذه بجمع كان ال X مين أجانب؟ إذا زي + +25 +00:02:26,690 --> 00:02:32,270 +ما شيلت كل X هنا هشيلها هنا وأحط معاها كلمين G of + +26 +00:02:32,270 --> 00:02:40,030 +X يبقى هذه بدها تصير F of G of X هي عبارة عن G of + +27 +00:02:40,030 --> 00:02:46,090 +X plus one على G of X كله بده يستوي قداش؟ بده + +28 +00:02:46,090 --> 00:02:51,910 +يستوي X ممتاز جدا من هذه المعادلة بدي أحاول أجيب + +29 +00:02:51,910 --> 00:02:59,470 +ما هو شكل ال G of X لذلكحضروح نضرب ضرب تبادلي إذا + +30 +00:02:59,470 --> 00:03:05,990 +لو ضربنا ضرب تبادلي بيصير g of x plus one بدي يساوي + +31 +00:03:05,990 --> 00:03:12,950 +الـ x في الـ g of x تمام؟ بدي أخلي اللي فيهم g of x + +32 +00:03:12,950 --> 00:03:17,970 +في جهة واللي باقي فيه ناحية الثانية يبقى لو جيت + +33 +00:03:17,970 --> 00:03:24,330 +قولتها DX في الـ G of X ناقص الـ G of X بتسوي قداش + +34 +00:03:24,330 --> 00:03:30,930 +واحد أو لو أخذنا الـ G of X ك common factor أو عامل + +35 +00:03:30,930 --> 00:03:37,890 +مشترك ما بين الاتنين بتسوي قداش واحد طبعا لو قسمنا + +36 +00:03:37,890 --> 00:03:43,290 +كلا الطرفين على الـ X ناقص الـ one بصير شكل الـ G of + +37 +00:03:43,290 --> 00:03:50,290 +X بدي يصير واحد على X ناقص واحد هذا شكل الـ G of X + +38 +00:03:50,290 --> 00:03:56,750 +وبروح بضيف عليها بقوله X ممنوعة تساوي واحد لأن لو + +39 +00:03:56,750 --> 00:04:03,670 +ساوى واحد بصير الدالة غير معرفة في هذه الحالة طيب + +40 +00:04:03,670 --> 00:04:10,610 +تمام يبقى هاي جبت له المطلوب تبعنا جبت له اللي هو شكل + +41 +00:04:10,610 --> 00:04:14,650 +الـ Geo Vex طبعا زي ما أنت شايف هذا السؤال مباشر + +42 +00:04:14,650 --> 00:04:19,710 +ما فيش فيه فنية ولا حاجة لكن بدي أجرب مش هجيب + +43 +00:04:19,710 --> 00:04:24,490 +الدالة G بدي أروح أجيب شكل الدالة F يعني بدي أعطي + +44 +00:04:24,490 --> 00:04:30,130 +ال composition وأعطي شكل الـ Geo أطلب من شكل الـ F + +45 +00:04:30,130 --> 00:04:41,370 +وهذا هو المثال رقم 3 يبقى example تلاتة بيقول + +46 +00:04:41,370 --> 00:04:50,350 +لي ما يأتي if الـ g of x بده يساوي الـ x plus three + +47 +00:04:50,350 --> 00:04:57,890 +and الـ if composition g as a function of x + +48 +00:05:04,160 --> 00:05:16,960 +السؤال بيقول لي find a formula Find a formula بدنا + +49 +00:05:16,960 --> 00:05:21,340 +صيغة for f of x + +50 +00:05:30,900 --> 00:05:35,160 +الطريقة اللي بدها تبقى حل المثال رقم 2 هبدأ بها حل + +51 +00:05:35,160 --> 00:05:42,000 +كذلك المثال رقم 3 يبقى بدأ بال composition تبع الـ + +52 +00:05:42,000 --> 00:05:47,920 +f composition g as a function of x بده يساوي x² + +53 +00:05:47,920 --> 00:05:54,810 +plus 1 هذا مقطع بدي أرجع لتعريف ال composition يبقى + +54 +00:05:54,810 --> 00:06:03,050 +f of g of x بده يساوي x squared plus one طلع عليه + +55 +00:06:03,050 --> 00:06:07,930 +كويسة الآن الـ g معلومة إذا مدام معلومة بدي أشيلها + +56 +00:06:07,930 --> 00:06:14,330 +وأحط القيمات تبعها إذا هذه f of x plus three + +57 +00:06:14,330 --> 00:06:22,520 +لقيمة الـ g بده يساوي x squared plus one من هذه + +58 +00:06:22,520 --> 00:06:26,060 +المعادلة سأعرف ما هو شكل الـ g + +59 +00:06:30,540 --> 00:06:36,400 +احنا بنقول دائما f of element موجود في الـ domain الـ + +60 +00:06:36,400 --> 00:06:39,400 +x زائد ثلاثة لكن لازم تكون في الـ domain بس احنا + +61 +00:06:39,400 --> 00:06:43,920 +ما نقولش f of x زائد فاحنا بنقول f of x, f of y, f + +62 +00:06:43,920 --> 00:06:48,100 +of z, f of w, f وشغالة زي هيك يعني أنا بدي + +63 +00:06:48,100 --> 00:06:51,890 +variable واحد مش variable مضعف اللي هي رقم يعني + +64 +00:06:51,890 --> 00:06:56,690 +كأنه معمول shift لدالة بمقدار هذا لأ لأ لأ أنا بدي + +65 +00:06:56,690 --> 00:07:03,450 +f of element واحد فقط ايش نعمل كده + +66 +00:07:03,450 --> 00:07:08,410 +ماشي بيقول صاحبنا شيل الـ x زائد تلاتة وحط بدالها + +67 +00:07:08,410 --> 00:07:12,890 +أي variable آخر الـ Variable اللي أعجبك حطه بدلته و + +68 +00:07:12,890 --> 00:07:16,750 +أقول له ماشي الحال يبقى أنا بدأجي على الـ X زائد + +69 +00:07:16,750 --> 00:07:22,830 +تلاتة وأحطها بمين؟ بـ Variable HD يبقى بدأجي أقول له + +70 +00:07:22,830 --> 00:07:30,370 +put حط لي Y زي ما قال هو عبارة عن X زائد تلاتة + +71 +00:07:30,370 --> 00:07:35,870 +بقول له كويس يبقى بدأجي أحول كل المثلة بدلالة مين؟ + +72 +00:07:36,150 --> 00:07:42,570 +بدل الـ Y يبقى هذا معناه أن Y minus 3 بده يساوي + +73 +00:07:42,570 --> 00:07:47,450 +مين؟ بده يساوي الـ X يبقى هذه المسألة بده تصير على + +74 +00:07:47,450 --> 00:07:53,370 +الشكل التالي F of Y يساوي الـ X هشيلها وقت بدالها + +75 +00:07:53,370 --> 00:08:00,900 +مين؟ Y سالب تلاتة لكل تربيع زائد واحديبقى معنى هذا + +76 +00:08:00,900 --> 00:08:09,520 +الكلام أن الـ F of Y يساوي Y squared نقص ستة Y زائد + +77 +00:08:09,520 --> 00:08:16,000 +تسعة زائد واحد أو أن شئتم فاقولوا هذه على الشكل + +78 +00:08:16,000 --> 00:08:25,040 +التالي F of Y بده يساوي Y تربيع نقص ستة Y زائد + +79 +00:08:25,040 --> 00:08:25,640 +عشرة + +80 +00:08:28,690 --> 00:08:35,530 +يبقى هاي وجبت له صيغة أو formula أو شكل لمين لدى + +81 +00:08:35,530 --> 00:08:40,390 +الـ F صارت F of الـ variable Y هي عبارة عن Y تربيع + +82 +00:08:40,390 --> 00:08:45,390 +ناقص ستة Y زائد عشرة H أنا جبت له صيغة اللي هو + +83 +00:08:45,390 --> 00:08:51,890 +طلبها وانتهينا من المثلة واحد يجي يقول طيب إذا + +84 +00:08:51,890 --> 00:08:57,010 +بتقدر تجيب ال composition ما بين الـ F هذه والـ G + +85 +00:08:57,010 --> 00:09:01,310 +هذه اللي في رأس المثلة بقول له أه هدول two + +86 +00:09:01,310 --> 00:09:06,370 +variables، ما ينفعش إذا لازم أحط هذه الدالة بدلالة + +87 +00:09:06,370 --> 00:09:11,430 +مين؟ بدلالة الـ X، بقول له كويس، بسأل السؤال التالي + +88 +00:09:11,430 --> 00:09:16,970 +هذا الـ Y variable محدد أو variable اختياري أيًا + +89 +00:09:16,970 --> 00:09:24,310 +كان شكله؟ محدد يعني ما أقدرش أغيره؟ لا اختياري أغير أي + +90 +00:09:24,310 --> 00:09:28,890 +رمز حاطه يبقى لو شيلت الـ Y وحطيت مكانه الـ Z بصير + +91 +00:09:28,890 --> 00:09:33,950 +شكل الدلة F of Z يساوي Z تربيع نقص ستة Z زائد عشرة + +92 +00:09:33,950 --> 00:09:38,540 +بقدر أعمل composition مع الـ G of X اللي فوق؟ برضه + +93 +00:09:38,540 --> 00:09:44,200 +هدول two variables طيب بديش أحط Z بدي أحط C بدي + +94 +00:09:44,200 --> 00:09:49,060 +أحط L M T اللي بدك إياه، لذا لو حققت الـ X فيه + +95 +00:09:49,060 --> 00:09:56,540 +مشكلة؟ طب لو بدل الـ Y هذه حطيت F of X Capital يساوي + +96 +00:09:56,540 --> 00:10:00,540 +X Capital تربيع ناقص ستة X Capital زائد عشرة في + +97 +00:10:00,540 --> 00:10:05,540 +مشكلة بدل الـ Capital لو حطيتها Smaller بتتغير لأن + +98 +00:10:05,540 --> 00:10:10,640 +هو بده الشكل يتدلق شو صغتها يبقى أنا بناء عليه + +99 +00:10:10,640 --> 00:10:15,440 +بقول له The General Formula تبعت الهند يبقى دي + +100 +00:10:15,440 --> 00:10:16,760 +Formula + +101 +00:10:22,210 --> 00:10:29,090 +بدا الـ F of Y بدي أقول له F of X يساوي X تربيع نقص + +102 +00:10:29,090 --> 00:10:35,330 +6X زائد عشرة يبقى X ولا Y ولا Z ولا الصيغة اللي + +103 +00:10:35,330 --> 00:10:38,670 +بدك إياها الـ variable اللي بدك إن شاء الله تقول لي F + +104 +00:10:38,670 --> 00:10:40,950 +of W ما عنديها مشكلة + +105 +00:10:47,040 --> 00:10:56,240 +مش هدا شكل الـ F يعني إيش أسوي؟ بدء أشيلها وأحط + +106 +00:10:56,240 --> 00:11:00,120 +بدالها Y نقل وأحطها وأشيل بدال X زائد تلاتة يعني + +107 +00:11:00,120 --> 00:11:06,240 +اللي اشتغلت بتكون خربته وبتكون رجعت لمين لشكل هذا + +108 +00:11:06,240 --> 00:11:12,340 +صح؟ وإيش استفدناه؟ أنا بده صيغة لـ F إذا بدي أرجع + +109 +00:11:12,340 --> 00:11:16,880 +وأحط نفس اللي بدك هي القيمة اللي حطيتها مش هذا + +110 +00:11:16,880 --> 00:11:21,860 +صار شكل ال formula صح ولا لا؟ يبقى توس يعني أقول لك + +111 +00:11:21,860 --> 00:11:26,900 +لو شيلت Y وحطيت الـ Z فيه مشكلة؟ يا راجل تاج اللعبة + +112 +00:11:26,900 --> 00:11:31,020 +اسمع لي شوية عارف إيش اللي بدك يعني اللي بدك تشيل + +113 +00:11:31,020 --> 00:11:35,400 +أنت الـ Y تحط بدلها where راح تيه الـ X زي التلاتة + +114 +00:11:35,430 --> 00:11:39,350 +مظبط يجب أن نعود هنا يعني ما اشتغلناه خربناه + +115 +00:11:39,350 --> 00:11:44,930 +وسويناه شي شي مظبوط أو لا أنا جبت شكل الـ F F as a + +116 +00:11:44,930 --> 00:11:48,910 +function of any variable X ولا Y ولا Z ولا W ولا + +117 +00:11:48,910 --> 00:11:55,510 +لا T من ما يكون يكون تفضل ومش هتفرق بس إيه أصلًا + +118 +00:11:55,510 --> 00:11:58,910 +بس لما تيجي تقدر تعمل composition ما بين الـ F والـ + +119 +00:11:58,910 --> 00:12:04,190 +G والجيب لي هذيتقدرش لأنه شدولة وvariables أنا + +120 +00:12:04,190 --> 00:12:08,110 +بدي variable واحد للي اتنين صحيح ولا لا من هنا + +121 +00:12:08,110 --> 00:12:13,450 +بقول لك مدام جبت الشكل العام يبقى هذا ينطبق على أي + +122 +00:12:13,450 --> 00:12:17,190 +variable من واحد لغاية سبعة وعشرين مش الأحرف + +123 +00:12:17,190 --> 00:12:20,810 +المجلسية سبعة وعشرين أخذنا فيهم واحد على الشجة + +124 +00:12:20,810 --> 00:12:24,170 +تانية بيبقى ستة وعشرين يبقى ستة وعشرين حرف حط + +125 +00:12:24,170 --> 00:12:31,980 +الرمز اللي بدك يجبك فيهم شو بتفرج ولا حاجة أيوة يا + +126 +00:12:31,980 --> 00:12:35,760 +راجل احنا بدنا F، بتقول لي G؟ ماشي بدي في G، أنا ما + +127 +00:12:35,760 --> 00:12:40,260 +G عندي، ها هي جاهزة، وأنتي، هاي G جاهزة، أنا اللي + +128 +00:12:40,260 --> 00:12:47,360 +مجهول عندي شكل الـ F، مش شكل الـ G يعني + +129 +00:12:47,360 --> 00:12:51,360 +جيب لي G of Y واطلع لي في الآخر بدلالة Y، ماشي بدي + +130 +00:12:51,360 --> 00:12:55,480 +فيها، أنا المثل عندي بدلالة X إذا بدك كذا تخليها + +131 +00:12:55,480 --> 00:13:00,060 +بداية Y ما عنديش مانع بس بدك تروح تجيب لي جيب دلالة + +132 +00:13:00,060 --> 00:13:07,540 +Y بصير المثل يا عم why ولا T ولا Z ولا هيها نفسها + +133 +00:13:07,540 --> 00:13:15,680 +اه مين بده يسأل تاني تفضل نقول + +134 +00:13:15,680 --> 00:13:21,760 +لك لأ بقى أنا بدي الشكل العام الرمز العام ماشي؟ يلا + +135 +00:13:21,760 --> 00:13:26,760 +غير، في كمان سؤال؟ طب أنا لازلت في نفس النقطة و + +136 +00:13:26,760 --> 00:13:32,720 +بدي أروح أجيب مثال يختلف كليا عن هدول، المثال هذا + +137 +00:13:32,720 --> 00:13:36,600 +بدي أربطه ببداية ال section اللي بدأنا فيه بالـ + +138 +00:13:36,600 --> 00:13:41,310 +section اللي جابله يعني بدي أربط بداية هذا section + +139 +00:13:41,310 --> 00:13:46,410 +بموضوع ال composition بموضوع man بموضوع section + +140 +00:13:46,410 --> 00:13:51,350 +واحد واحد وبدي آخذ منه ال even وال odd function + +141 +00:13:51,350 --> 00:13:57,110 +بدي أربط التلات شغلات دول كلهم بسؤال واحد السؤال + +142 +00:13:57,110 --> 00:14:00,990 +اللي هو مثال رقم 4 يبقى example 4 + +143 +00:14:07,410 --> 00:14:16,090 +example four بقول ما يأتي بقول if الـ if is an even + +144 +00:14:16,090 --> 00:14:26,270 +function and الـ g is an odd function ده الفردية + +145 +00:14:26,270 --> 00:14:35,690 +تمام what can you say about what can you + +146 +00:14:41,580 --> 00:14:45,980 +G composition of F نمرة A + +147 +00:15:20,560 --> 00:15:27,010 +سؤال مرة ثانية ما يعطيني F ده اللي زوجية وما يعطيني G + +148 +00:15:27,010 --> 00:15:31,910 +ده اللي فردية وبعدين تقول لي إيش بتقدر تقول عن + +149 +00:15:31,910 --> 00:15:37,910 +الأربع دول هدول فردية، زوجية، فردية وزوجية في نفس + +150 +00:15:37,910 --> 00:15:42,190 +الوقت neither even nor odd لا فردية ولا زوجية + +151 +00:15:45,820 --> 00:15:50,360 +يبقى أنا بدي أطبق تعريف ال even وال odd اللي عندي + +152 +00:15:50,360 --> 00:15:55,300 +وأشوف إيش بدي يكون النتج وبناء عليه بقدر أحكم على + +153 +00:15:55,300 --> 00:16:00,680 +كل دالة من هذه الدوال شو نوعيتها يبقى في الأول أنا + +154 +00:16:00,680 --> 00:16:07,440 +عندي F is even هذا إيش معناه؟ معناه أن الـ F لو + +155 +00:16:07,440 --> 00:16:14,150 +أثرت على سالب X بدي يعطينا الـ F of X itself والـ X + +156 +00:16:14,150 --> 00:16:20,030 +هذه موجودة في domain مين؟ في domain الـ F بعد هيك + +157 +00:16:20,030 --> 00:16:28,710 +أن الـ G is odd هذا معناه أن الـ G of سالب X يساوي + +158 +00:16:28,710 --> 00:16:35,150 +سالب G of X والـ X موجودة في domain مين؟ إذا احنا + +159 +00:16:35,150 --> 00:16:39,990 +ذكرنا بـ section 1 1 وهو ال even وال odd function + +160 +00:16:39,990 --> 00:16:44,390 +الآن بدي نستخدم هذا الكلام في الحكم على الـ + +161 +00:16:44,390 --> 00:16:48,890 +functions التالية هل هي even ولا odd فبدي آخذ له + +162 +00:16:48,890 --> 00:16:58,160 +نمرة a الآن بدي حاصل ضرب g في f of ناقص x يبقى أنا + +163 +00:16:58,160 --> 00:17:04,600 +بدي الدالة gf كحاصل ضرب احكم عليها هل هي even ولا + +164 +00:17:04,600 --> 00:17:09,380 +odd يبقى بدي أشيل الـ X واحط مكانها سالب X شيلنا وحطينا + +165 +00:17:09,380 --> 00:17:18,650 +يبقى بدي أشوف ما هو الناتج هذا تعتبر حاصل ضرب + +166 +00:17:18,650 --> 00:17:19,370 +دالتين + +167 +00:17:30,620 --> 00:17:36,300 +الـ g of سالب x هي همجداش سالب g of x لأن الـ g + +168 +00:17:36,300 --> 00:17:44,100 +فردية إذا انحكت بهدي سالب g of x مضروبة فيه الـ f + +169 +00:17:44,100 --> 00:17:52,080 +of سالب x همجداش بف of x يبقى هادي f of x تمام؟ لو + +170 +00:17:52,080 --> 00:17:59,280 +أخذت السالب برا من التنتين بظل g of x في الـ f of x + +171 +00:17:59,740 --> 00:18:07,580 +لو رجعتها إلى أصلها يبقى + +201 +00:21:00,260 --> 00:21:04,960 +G composition F of -X هو G composition F of X + +202 +00:21:04,960 --> 00:21:10,020 +يبقى الـ G composition F عبارة عن ايه؟ ممتاز جدا + +203 +00:21:10,020 --> 00:21:13,760 +لأن طبقة التعريف اللي فوق هي تعريف ال even + +204 +00:21:13,760 --> 00:21:19,540 +function يبقى هذا بده يعطينا أن ال G composition + +205 +00:21:19,540 --> 00:21:28,390 +F is an even function يبقى ده اللي زوجية تمام طب + +206 +00:21:28,390 --> 00:21:34,450 +بدنا نروح لنمرسي جال ال جي composition جي بدي أخذه + +207 +00:21:34,450 --> 00:21:40,430 +as a function of -X وشوف ما هو النتيجة يبقى + +208 +00:21:40,430 --> 00:21:47,910 +برجع لتعريف ال composition يبقى جي للجي of -X + +209 +00:21:47,910 --> 00:21:52,730 +مش هيك تعريف ال composition طيب هذه الجي اللي برا + +210 +00:21:52,730 --> 00:21:59,690 +كما هيبنجي اللي جوا بينها قوسين جي of -X + +211 +00:21:59,690 --> 00:22:05,710 +تساوي كده؟ -G of X لإن الجي فردية يبقى هذا + +212 +00:22:05,710 --> 00:22:12,810 +-G of X تمام؟ هذا كله أصبح element في + +213 +00:22:12,810 --> 00:22:17,430 +domain مين؟ في domain الجي وهذا ال element سبق + +214 +00:22:17,430 --> 00:22:23,260 +بإشارة والـ G أدت الـ G لما تأثر على ال element + +215 +00:22:23,260 --> 00:22:28,340 +اللي موجود في دنيا نفسها يبقى سالب بره يبقى السالب + +216 +00:22:28,340 --> 00:22:35,260 +هذا يطلع هنا بره يبقى يبقى ساوي -G للـ G of X + +217 +00:22:35,260 --> 00:22:43,120 +لأن الـ G فردية أرجعها لتعريفها مرة ثانية يبقى هذا + +218 +00:22:43,120 --> 00:22:50,580 +-g composition g as a function of x شوف بيش + +219 +00:22:50,580 --> 00:22:56,100 +بدنا ولوين وصلنا ال g composition g as a function + +220 +00:22:56,100 --> 00:22:57,080 +of -x + +221 +00:23:04,430 --> 00:23:12,310 +طيب يبقى هنا سؤال جي composition جي is an odd + +222 +00:23:12,310 --> 00:23:19,360 +function طيب سؤال شفهي و بده إجابة سريعة لو بدل جي + +223 +00:23:19,360 --> 00:23:25,340 +كومبوزيشن جي قلت لك جي ضرب جي as a product ضرب جي + +224 +00:23:25,340 --> 00:23:31,460 +في جي زي هنا جي في اف لو بدلت الاف بـ جي تتوقع + +225 +00:23:31,460 --> 00:23:37,910 +أنها even لأن بده يطلع -G of x مع ضروبفي + +226 +00:23:37,910 --> 00:23:43,310 +-g of x يعني +g of x في g of x يعني g + +227 +00:23:43,310 --> 00:23:47,350 +مضروبة في g as a function of x يبقى دي بصير even + +228 +00:23:47,350 --> 00:23:52,100 +function شايف ال two functions التنتين قدحاصل + +229 +00:23:52,100 --> 00:23:57,240 +ضربهم even لكن ال composition تبعهم شو طلع؟ odd + +230 +00:23:57,240 --> 00:24:03,900 +تمام؟ كويس يبقى هذه good exercise إليك شوف لبالله + +231 +00:24:03,900 --> 00:24:12,050 +ال G مضروبة في G as a function of -X شو تساوي؟ + +232 +00:24:12,050 --> 00:24:18,010 +هذي good exercise لك، والجواب هنا أجابته عليه + +233 +00:24:18,010 --> 00:24:21,590 +عبارة عن إيش؟ even function، يالا عملها فضلا + +234 +00:24:21,590 --> 00:24:28,190 +براحتك، طب تانيجي للتي؟ بنجي لدى هنا بدنا نشيل كل + +235 +00:24:28,190 --> 00:24:35,510 +X ونحط مكانها -X يبقى هذه بتصير -X لكل + +236 +00:24:35,510 --> 00:24:44,290 +تكييب F على G هنا F على G كله as a function of + +237 +00:24:44,290 --> 00:24:50,930 +-X هذا الكلام يساوي هذه مضروبة في نفسها لثلت + +238 +00:24:50,930 --> 00:24:56,410 +مرات - في - بموجب في - بسالب يبقى اللي + +239 +00:24:56,410 --> 00:25:03,290 +برا بسالب X تقعيد نيجي هذا خارج القسمة يبقى ال bus + +240 +00:25:03,290 --> 00:25:07,630 +هيأثر على ال element و المقام هيأثر على نفس ال + +241 +00:25:07,630 --> 00:25:13,930 +element يبقى هذه مضروبة في ال F و بـ -X مقسومة + +242 +00:25:13,930 --> 00:25:19,210 +على الـG of -X يبقى هذا الكلام بده يساوي + +243 +00:25:19,210 --> 00:25:25,650 +السالب X تكييب فيه ال F even يبقى هذا شو بديجي + +244 +00:25:25,650 --> 00:25:33,900 +بدالها؟ F of X يبقى هذه F of X الـG odd يبقى سالب + +245 +00:25:33,900 --> 00:25:42,920 +برا على -G of X، - على - موجب يبقى + +246 +00:25:42,920 --> 00:25:51,500 +النتيجة تساوي X تكييب في F of X على G of X + +247 +00:25:54,620 --> 00:26:02,640 +بترجعها إلى أصلها يبقى هذا يساوي X تكييب في F على + +248 +00:26:02,640 --> 00:26:09,540 +G as a function of X بدأنا هذه و حطينا السالب طلعت + +249 +00:26:09,540 --> 00:26:14,460 +نفس الدالة بدون سالب يبقى معنى هذا الكلام ندالة + +250 +00:26:14,460 --> 00:26:22,300 +مالها even يبقى سا ال X تكييب F على G as a function + +251 +00:26:22,300 --> 00:26:30,020 +of X is an even function حد اللي هو أي تساؤل هنا + +252 +00:26:30,020 --> 00:26:36,700 +يا شباب؟ حد بيحب يسألني سؤال؟ طيب، غير بالك؟ + +253 +00:26:37,270 --> 00:26:42,910 +المحاضرة دي very important لا يكاد يخلو أي امتحان + +254 +00:26:42,910 --> 00:26:49,070 +فصل من سؤال عليها هي و نصف الثاني من المحاضرة + +255 +00:26:49,070 --> 00:26:54,070 +المرة الماضية اللي و ال section هذا كل واحد اتنين + +256 +00:26:54,070 --> 00:27:00,070 +دائما و أبدا لو مسكت اي امتحان سابق بتلاقي على + +257 +00:27:00,070 --> 00:27:05,250 +الأقل فيه سؤال اللي لم يكن أكثر في هذا ال section + +258 +00:27:06,850 --> 00:27:13,770 +نظرا لأهميته طب + +259 +00:27:13,770 --> 00:27:19,470 +ننتقل الآن إلى النقطة الثانية من هذا ال section + +260 +00:27:19,470 --> 00:27:24,730 +يبقى + +261 +00:27:24,730 --> 00:27:28,470 +shifting a + +262 +00:27:28,470 --> 00:27:34,030 +graph of a function + +263 +00:27:37,240 --> 00:27:43,400 +هنجسمه إلى نقطتين النقطة الأولى نمر ايه ال + +264 +00:27:43,400 --> 00:27:51,540 +vertical shifting الإزاحة الرأسية لمن الإزاحة + +265 +00:27:51,540 --> 00:28:04,140 +الرأسية للدالة يبقى if k is a positive real number + +266 +00:28:12,640 --> 00:28:29,700 +نقطة الأولى y تساوي f of x plus k shifts the graph + +267 +00:28:29,700 --> 00:28:36,760 +of y تساوي f of x up + +268 +00:28:38,480 --> 00:28:43,240 +k units نقطة + +269 +00:28:43,240 --> 00:28:53,340 +ثانية Y تساوي F of X minus k shift the graph of Y + +270 +00:28:53,340 --> 00:29:01,820 +تساوي down k units نمرى + +271 +00:29:01,820 --> 00:29:05,020 +B Horizontal + +272 +00:29:09,380 --> 00:29:21,820 +Shifts أو Horizontal Shifting إزاحات أفقية if ال H + +273 +00:29:21,820 --> 00:29:35,140 +is a positive real number then نقطة + +274 +00:29:35,140 --> 00:29:50,560 +الأولى why to servef of x ناقص h shifts the + +275 +00:29:50,560 --> 00:30:04,040 +graph of y تساوي f of x to the right لليمين + +276 +00:30:04,040 --> 00:30:16,780 +h units النقطة الثانية y تساوي f of x plus h shift the + +277 +00:30:16,780 --> 00:30:32,960 +graph of y تساوي f of x to the left لليسار ال h units examples + +278 +00:30:38,830 --> 00:30:45,830 +مثال واحد سكتش و + +279 +00:30:45,830 --> 00:30:51,690 +اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و + +280 +00:30:51,690 --> 00:30:53,030 +اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و + +281 +00:30:53,030 --> 00:30:53,870 +اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و + +282 +00:30:53,870 --> 00:31:02,490 +اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و اكتش و + +283 +00:31:02,490 --> 00:31:21,390 +اكتش y تساوي 1 على X تربيع after shifting right + +284 +00:31:21,390 --> 00:31:25,990 +2 + +285 +00:31:25,990 --> 00:31:32,930 +and down 1 + +286 +00:31:34,740 --> 00:31:43,520 +نمر بـ X تربيع زائد Y تربيع يساوي 25 + +287 +00:31:43,520 --> 00:31:55,100 +After shifting right 2 After shifting up 3 After + +288 +00:31:55,100 --> 00:32:02,140 +shifting up 3 and left + +289 +00:32:11,540 --> 00:32:16,820 +4 يبقى هذا ال section كان عبارة عن ثلاث نقاط + +290 +00:32:16,820 --> 00:32:21,180 +النقطة الأولى كانت combining functions النقطة + +291 +00:32:21,180 --> 00:32:24,940 +الثانية اللي بدأنا فيها shifting functions والنقطة + +292 +00:32:24,940 --> 00:32:29,840 +الثالثة ال scaling the graph of a function يبقى + +293 +00:32:29,840 --> 00:32:34,500 +shifting a graph of a function هنقسم ال shifting + +294 +00:32:34,500 --> 00:32:40,380 +إلى نقطتين ال shifting إلى أعلى أو إلى أسفل هذا + +295 +00:32:40,380 --> 00:32:44,680 +النقطة الأولى و هنسميه vertical shifting يعني + +296 +00:32:44,680 --> 00:32:51,540 +إزاحة رأسية نقطة ثانية إزاحة أفقية جهة اليمين أو + +297 +00:32:51,540 --> 00:32:56,620 +جهة الشمال وبالتالي بنسميها horizontal shifting + +298 +00:32:56,870 --> 00:33:03,930 +الإزاحة الأفقية بدا نيجي الآن للإزاحة الرأسية وهي + +299 +00:33:03,930 --> 00:33:08,530 +vertical shifting في الأول نحاول نقرا الكلام اللي + +300 +00:33:08,530 --> 00:33:15,610 +مكتوب نفهمه تماما نشوف كيف هنطبقه كويس يبقى بنا + +301 +00:33:15,610 --> 00:33:19,690 +نبدأ بال vertical shifting بدي بقول if ال K is a + +302 +00:33:19,690 --> 00:33:25,490 +positive real number positive real number يبقى عدد + +303 +00:33:25,490 --> 00:33:31,430 +حقيقي موجب ولم أقول عددا صحيحا قد يكون عدد كسري + +304 +00:33:31,430 --> 00:33:36,230 +يعني أنا ممكن أعمل shift للاعلى و للاسفل واحدة + +305 +00:33:36,230 --> 00:33:41,510 +واحدة وحدة و نص وحدة و نصوحتين و تلاتة اربعة + +306 +00:33:41,510 --> 00:33:45,590 +واحدة و ربع إلى آخره يعني ليس بالضرورة ان تكون + +307 +00:33:45,590 --> 00:33:50,570 +الازاحة رقما صحيحا وانما ممكن ان يكون رقم كسري + +308 +00:33:50,570 --> 00:33:56,390 +سواء كانت الإزاحة إلى أعلى أو إلى أسفل سيا نفسنا بنجي + +309 +00:33:56,390 --> 00:34:01,170 +بقول الآن لو كان الكيه positive real number بقى + +310 +00:34:01,170 --> 00:34:06,550 +أنا عندي معادلة y تساوي f of x زائد الـ k شو + +311 +00:34:06,550 --> 00:34:11,090 +معناها هذي؟ هذي shifting the graph of y تساوي f of + +312 +00:34:11,090 --> 00:34:17,530 +x يعني أضفت له لو y تساوي f of x شو عملتله؟ أضفت + +313 +00:34:17,530 --> 00:34:23,310 +الرقم k للدالة ايش معناه هذا shift إلى أعلى يعني + +314 +00:34:23,310 --> 00:34:28,810 +بدي أعمل إزاحة للدالة إلى أعلى بمقدار k من الوحدات + +315 +00:34:28,810 --> 00:34:33,370 +k units k من الوحدات المستخدمة هل هي ال centimeter + +316 +00:34:33,370 --> 00:34:39,410 +ولا متر ولا كيلومتر ولا قدم نظام انجليزي او نظام + +317 +00:34:39,410 --> 00:34:44,090 +فرنسي قدم او يردة او بوصة أو إلى آخره + +318 +00:34:46,670 --> 00:34:51,210 +النقطة الثانية لو قلت y تساوي f of x ناقص ال k + +319 +00:34:51,210 --> 00:34:56,830 +يبقى الرسم هذي بدي أنزله إلى أسفل بمقدار الرقم k + +320 +00:34:56,830 --> 00:35:00,850 +اللي هو اعطاني ليه يبقى إذا أضفنا يضافها معناته + +321 +00:35:00,850 --> 00:35:06,040 +shift إلى أعلى إذا كان إضافة بالسالب بمعنى shift + +322 +00:35:06,040 --> 00:35:10,480 +إلى أسفل يبقى هذه k units الرسمة في الدعمال اللي + +323 +00:35:10,480 --> 00:35:15,960 +هي إزاحة إلى أسفل أعلى هذه k units إزاحة لوام إلى + +324 +00:35:15,960 --> 00:35:20,920 +أسفل بالشكل اللي عندنا هذا نيجي للإزاحة الأفقية + +325 +00:35:20,920 --> 00:35:25,640 +الـ horizontal shifting فباجي بقول لو كان ال H is a + +326 +00:35:25,640 --> 00:35:31,390 +positive real number then يبقى بالداجي لـ Y تساوي F + +327 +00:35:31,390 --> 00:35:38,010 +of X ناقص الـ H معناته إزاحة جهة اليمين بمقدار قداش + +328 +00:35:38,010 --> 00:35:44,470 +H يبقى هادي to the right جهة إيدك اليمين الحالة + +329 +00:35:44,470 --> 00:35:50,550 +الثانية لو بدل ال H حطينا مكانها -H ايش بيصير + +330 +00:35:50,550 --> 00:35:56,170 +هذه؟ - مع - ايش بيصير؟ موجب طيب لما تبقى X + +331 +00:35:56,170 --> 00:35:59,950 +موجب هيقول -H بيتيجي وين؟ في الناحية التانية + +332 +00:35:59,950 --> 00:36:05,450 +لما تبقى H على اتجاه محور X الموجب -H بيتيجي + +333 +00:36:05,450 --> 00:36:13,070 +في اتجاه محور X السالب وبالتالي بيصير f of x زائد + +334 +00:36:13,070 --> 00:36:19,710 +الـ H اللي هو جهة الشمال بمقدار اللي هو الـ H يبقى + +335 +00:36:19,710 --> 00:36:25,330 +بالنقص إزاحة جهة اليمين بالموجبة إزاحة جهة الشمال + +336 +00:36:25,330 --> 00:36:30,370 +طيب تعالي نلزق هذه المعلومة في دماغنا بحيث ما + +337 +00:36:30,370 --> 00:36:36,930 +تطلعش مننا أبدا طلعلي شو الفرق بين الحالة الأولى A + +338 +00:36:36,930 --> 00:36:41,770 +والحالة الثانية B طلع ليه كويس فتح هنا k مكتوب + +339 +00:36:41,770 --> 00:36:46,810 +قدامك على اللوحة في الحالة الأولى الرقم k أضفناه + +340 +00:36:46,810 --> 00:36:51,730 +للمتغير ولا لل function كلها؟ لل function كلها + +341 +00:36:51,730 --> 00:36:59,430 +يبقى الرقم k يضاف لل function وليس للمتغير إن حدث + +342 +00:36:59,430 --> 00:37:04,930 +ذلك يبقى إزاحة رأسية تعال للحالة التانية الـ H هذه + +343 +00:37:04,930 --> 00:37:09,610 +أضفناها أو طرحناها من مين مش كل ال function لأ من + +344 +00:37:09,610 --> 00:37:15,450 +المتغير نفسه يبقى إن حدثت اللي هو الإضافة أو الطرح + +345 +00:37:15,450 --> 00:37:20,350 +من المتغير نفسه بتبقى إزاحة أفقية تحريكة رسمية + +346 +00:37:20,350 --> 00:37:27,380 +يمين أو شمال ومن هنا صار الفرق بين الحالتين ركز هذه + +347 +00:37:27,380 --> 00:37:31,000 +المعلومة في دماغك لكي نستخدمها الآن عندما نبدأ + +348 +00:37:31,000 --> 00:37:37,520 +نرسم الرسومات المختلفة طيب بدنا نطبق هذا الكلام + +349 +00:37:37,520 --> 00:37:40,720 +على أرض الواقعية قبل ما نطبقه حد أيه له سؤال في + +350 +00:37:40,720 --> 00:37:45,020 +النقطة النظرية دي بس قبل ما نبدأ نطبقها؟ في أي + +351 +00:37:45,020 --> 00:37:50,450 +تساؤل؟ طيب نبدأ نحطها على عرض الواقع بأمثلة مختلفة + +352 +00:37:50,450 --> 00:37:55,170 +أول مثال من هذه الأمثلة بيقول sketch and write + +353 +00:37:55,170 --> 00:38:01,530 +ارسم وكذلك اكتب the following questions شو بيكون + +354 +00:38:01,530 --> 00:38:06,710 +شكلها المعادلة الأولى قال لي y تساوي 1 عليك + +355 +00:38:06,710 --> 00:38:16,500 +التربيعية هذا ما نحتاجش بدي أعمله قال لي 2 + +356 +00:38:16,500 --> 00:38:19,580 +و إلى أسفل بمقدار 1 بمقدار 2 بمقدار 2 + +357 +00:38:19,580 --> 00:38:21,520 +بمقدار 2 بمقدار 2 بمقدار 2 بمقدار + +358 +00:38:21,520 --> 00:38:22,800 +2 بمقدار 2 بمقدار 2 بمقدار 2 + +359 +00:38:22,800 --> 00:38:23,140 +بمقدار 2 بمقدار 2 بمقدار 2 بمقدار + +360 +00:38:23,140 --> 00:38:23,460 +2 بمقدار 2 بمقدار 2 بمقدار 2 + +361 +00:38:23,460 --> 00:38:27,760 +بمقدار 2 بمقدار 2 بمقدار 2 بمقدار 2 + +362 +00:38:27,760 --> 00:38:36,720 +بمقدار 2 بمقدار 2 بمقدار + +363 +00:38:38,570 --> 00:38:43,550 +بطلع في المثل اللي قدامي هي ما طيني Y as a function + +364 +00:38:43,550 --> 00:38:50,230 +of X يعني هي Y as a function of X هيها بدون مين ال + +365 +00:38:50,230 --> 00:38:56,750 +K يبقى أصل الدالة 1 على X تربيع وقد سبق لنا رسمها + +366 +00:38:56,750 --> 00:39:03,500 +قبل ذلك يبقى هذه لو جيت ارسمها 1 على X تربيع + +367 +00:39:03,500 --> 00:39:09,460 +بالشكل اللي عندنا هذا محور X هذا محور Y هذه نقطة + +368 +00:39:09,460 --> 00:39:15,580 +الأصل اللي هي Zero 1 على X تربيع بدي ارسمها + +369 +00:39:15,580 --> 00:39:20,560 +منقطة لأن مش هي المطلوبة بالشكل اللي عندنا هذا + +370 +00:39:20,560 --> 00:39:29,820 +يبقى هذه رسمة الدالة 1 على X تربيع يبقى هي + +371 +00:39:29,820 --> 00:39:35,300 +بالشكل اللي عندنا هذا الدالة هذه بدي اعمل لها + +372 +00:39:35,300 --> 00:39:42,260 +shifting جهة اليمين بمقدار 2 يبقى بدي أمسك الرسمة + +373 +00:39:42,260 --> 00:39:47,760 +وازيحها جهة اليمين بمقدار 2 إذا لو روحت قلت هذا + +374 +00:39:47,760 --> 00:3 + +401 +00:42:51,050 --> 00:42:55,970 +مكانها X ناقص H يبقى مكان الـ X ترميها شيلت حاطيتها + +402 +00:42:56,000 --> 00:43:00,820 +X ناقص اتنين كل تربيع بيصير كله تربيع + +403 +00:43:14,650 --> 00:43:18,610 +طيب يبقى هاي رسمنا الرسم هذا، بدنا نيجي للرسم + +404 +00:43:18,610 --> 00:43:23,570 +الرقم بيه، بدي أسالكوا السؤال التالي هل يعني أنا + +405 +00:43:23,570 --> 00:43:30,410 +بدي أفكر بعقليك و بدي أبدأ أجاوب و إجابتي غلط قبل + +406 +00:43:30,410 --> 00:43:42,390 +اللي أجاوبها؟بدا أبدأ بعقلية مشكلتك وبعضكها بيقول + +407 +00:43:42,390 --> 00:43:52,750 +لي ايه ده لأ بمقدار تلاتة تمام تلاتة هنا اللي هي + +408 +00:43:52,750 --> 00:43:58,310 +إضافة للـ F of X يعني إضافة لمين؟إضافة لشكل يعني + +409 +00:43:58,310 --> 00:44:05,390 +إضافة للدالة Y إذا بدي أحط هنا Y زائد تلاتة لكل + +410 +00:44:05,390 --> 00:44:12,010 +تربية مشاكل الظاهرة اللي حكي تمام والـ X هذه جالي + +411 +00:44:12,010 --> 00:44:17,530 +and left بمقدار أربعة يبقى من الشمال يبقى بده أحط + +412 +00:44:17,530 --> 00:44:23,210 +X زائد أربعة يبقى بده أصير X زائد أربعة لكل تربيع + +413 +00:44:23,210 --> 00:44:29,030 +زائد Y زائد تلاتة لكل تربيع يساوي خمسة وعشرين هيك + +414 +00:44:29,030 --> 00:44:35,930 +ظاهرة مظبوط؟ بنقولك لا كلامك غلط والآن بدنا نقول + +415 +00:44:35,930 --> 00:44:43,070 +ليش غلط؟ ايوة + +416 +00:44:43,070 --> 00:44:49,530 +هذه مسألة ضمنية مش محطوطة y في شجة وباقي الـ x في + +417 +00:44:49,530 --> 00:44:55,010 +شجة يبقى هذي y تربيع وليس يبقى الخطوة الأولى بدك + +418 +00:44:55,010 --> 00:45:00,230 +تخلي y as a function of x وبعد هيك تروح تطبق main + +419 +00:45:00,230 --> 00:45:06,170 +الشروط اللي عندك مثلاً احتمال كبير جدا تقع في الخطأ + +420 +00:45:06,170 --> 00:45:10,990 +طيب بدنا نيجي نطبق الكلام اللي قلناه هذه معادلة + +421 +00:45:10,990 --> 00:45:18,450 +إيش؟ دائرة نصف قطرها و مركزها ممتاز جدا يعني هذه ها + +422 +00:45:18,450 --> 00:45:24,910 +لو جيت رسمتها باجي بقوله هذه المحور X وهي محور X + +423 +00:45:24,910 --> 00:45:31,230 +وهي Y وهذه الدائرة اللي عندنا بالشكل اللي عندها + +424 +00:45:31,230 --> 00:45:33,250 +دائرة تمام؟ + +425 +00:45:39,320 --> 00:45:45,480 +طيب استنى شوية هذه مش هي المطلوبة هذه الأصلية قبل + +426 +00:45:45,480 --> 00:45:50,620 +ما نعملها shift طب بدنا نعملها shift بقول اه هذه + +427 +00:45:50,620 --> 00:45:56,540 +معناها ايش؟ أن y تربيع يساوي خمسة وعشرين ناقص x + +428 +00:45:56,540 --> 00:46:02,060 +تربيع أنا بدي y as a function of x يبقى y يساوي + +429 +00:46:02,060 --> 00:46:06,760 +الجذر التربيعي لخمسة وعشرين ناقص x تربيع + +430 +00:46:09,390 --> 00:46:15,130 +بنفعش اقول زاد أو ناقص، يبقى يا زائد يا ناقص، + +431 +00:46:15,130 --> 00:46:20,130 +مظبوط ولا؟ يبقى خليها زي ما هي بالزائد مثلاً، تمام؟ + +432 +00:46:20,480 --> 00:46:25,960 +الحين صارت y function في main في x الحين يعمل ال + +433 +00:46:25,960 --> 00:46:29,780 +shift اللي بدك إياه بجبك كلامك صحيح باجي بتطلع إيش + +434 +00:46:29,780 --> 00:46:35,980 +قلي؟ قلي أربعة جهة الشمال يبقى الـ x إيش بده يصير؟ + +435 +00:46:35,980 --> 00:46:41,740 +x زائد أربعة ولا أقصى أربعة؟ باجي بتطلع قلي هنا + +436 +00:46:41,740 --> 00:46:45,520 +جهة الشمال يبقى تقول إيه؟ بدك تشيل الـ x وتحط + +437 +00:46:45,520 --> 00:46:51,220 +مكانها x زائد الرقم اللي قالك عليه أربعة إذا هذه + +438 +00:46:51,220 --> 00:46:56,440 +بدها تصير الجذر التربيعي لخمسة وعشرين ناقص X زائد + +439 +00:46:56,440 --> 00:47:03,540 +أربعة لكل تربيع يساوي اه بدها تساوي مين؟ Y و Y شو + +440 +00:47:03,540 --> 00:47:10,360 +عملناها؟ قال لي up بمقدار تلاتة يبقى up بمقدار تلاتة + +441 +00:47:10,360 --> 00:47:15,200 +إذا حيلة أعلى بمقدار تلاتة إذا بدنا نيجي نضيف على + +442 +00:47:15,200 --> 00:47:21,700 +الدالة هذه الرقم تلاتة يبقى هيك طب استنى شوية يبقى + +443 +00:47:21,700 --> 00:47:26,240 +هيك طبقتها صحيح؟ حطيت الدلة في الشكل اللي عندنا + +444 +00:47:26,240 --> 00:47:30,560 +الأصلي وبعد هيك أعمل اللي هو الـ shifts اللي + +445 +00:47:30,560 --> 00:47:34,800 +مطلوبة طيب هذه لو جيبتها على الشجة الثانية إيش بصير؟ + +446 +00:47:34,800 --> 00:47:41,200 +Y ناقص تلاتة يساوي الجذر التربيعي لخمسة وعشرين X + +447 +00:47:41,200 --> 00:47:47,430 +زائد أربعة لكل تربيع طب بدنا ننقل على الشجة + +448 +00:47:47,430 --> 00:47:52,930 +الثانية إيش بيصير؟ بيصير Y ناقص تلاتة لكل تربيع + +449 +00:47:52,930 --> 00:48:01,330 +زائد X زائد أربعة لكل تربيع يساوي 125 إذا بدنا نيجيها + +450 +00:48:01,330 --> 00:48:08,450 +لدالة هذه ونعملي لها shift المطلوب يبقى بدنا نزل + +451 +00:48:08,450 --> 00:48:16,680 +الرسم تحت بس مشان تكون أوضح يبقى هذا محور X وهذا Y + +452 +00:48:16,680 --> 00:48:26,700 +وهذا Zero وهذا الدالة الأصلية اللي كانت هنا تمام + +453 +00:48:26,700 --> 00:48:33,280 +يبقى هذه الدرجة كده نص قطرها ومركزها نقطة الأصل + +454 +00:48:33,280 --> 00:48:41,100 +الآن هذه الـ circle هذه الـ circle والـ + +455 +00:48:43,420 --> 00:48:51,840 +سينتر H و K بدو يساوي كداش الـ H عندي هنا سالب + +456 +00:48:51,840 --> 00:48:59,520 +أربعة كداش الـ K عندي هنا اللي هو تلاتة يبقى بدي + +457 +00:48:59,520 --> 00:49:01,800 +أتحرك طبعا هذه هيك + +458 +00:49:06,370 --> 00:49:12,850 +هذا من هنا لهنا كده؟ خمسة يبقى بدي ارجع هنا سالب + +459 +00:49:12,850 --> 00:49:18,150 +أربعة وأطلع فوق كده؟ تلاتة يبقى بدنا نيجي نطلع + +460 +00:49:18,150 --> 00:49:23,690 +فوق هنا بمقدار تلاتة يبقى إشارة النقطة هذه سالب + +461 +00:49:23,690 --> 00:49:29,970 +أربعة وتلاتة اللي هي مركزي الدائرة الجديدة السؤال + +462 +00:49:29,970 --> 00:49:34,470 +هو تتوقع الدائرة هذه تمر بنقطة الأصل؟ + +463 +00:49:39,070 --> 00:49:46,290 +ايوة، شوف يا سيدي، لو جيت قلت هذا ها على فرض إنها + +464 +00:49:46,290 --> 00:49:49,890 +بدأت مر بنقطة الأصل على فرضها، أنا مش عارف، مش + +465 +00:49:49,890 --> 00:49:55,400 +متأكد بتقول المسافة هدى قداش؟ الخط الأحمر هدى Zero + +466 +00:49:55,400 --> 00:49:59,420 +Zero هدى سلب أربعة وتلاتة يبقى أربعة ناقص Zero + +467 +00:49:59,420 --> 00:50:03,240 +لكل تربيع تلاتة ناقص Zero لكل تربيع تحت الجذر ستة + +468 +00:50:03,240 --> 00:50:07,640 +عشر زيت تسعة خمسة قعدين تحت الجذر يبقى بالتأكيد + +469 +00:50:07,640 --> 00:50:13,220 +الدائرة بده تمر وين؟ بنقطة الأصل تمام؟ بدنا نروح + +470 +00:50:13,220 --> 00:50:19,260 +نرسم هذه الدائرة يبقى هي الدائرة اللي عندنا + +471 +00:50:22,550 --> 00:50:30,390 +مش شكل اللي عنها تمام؟ + +472 +00:50:30,390 --> 00:50:38,510 +يبقى أي دائرة مرت بنقطة الأصل تماماً + +473 +00:50:38,510 --> 00:50:45,490 +هذا الشكل ليش؟ لأن نصف القطر يساوي خمسة + +474 +00:50:59,010 --> 00:51:03,670 +يبقى أي دائرة اللي عندنا نصف قطرها يساوي خمسة هذا + +475 +00:51:03,670 --> 00:51:09,770 +المركز تبعها تمام يبقى المنقطة الأساسية مليش ولاقة + +476 +00:51:09,770 --> 00:51:14,970 +فيها والدائرة الحمرا هي الدائرة اللي هي main اللي + +477 +00:51:14,970 --> 00:51:21,330 +هو x زائد أربعة لكل تربيع زائد y ناقص ثلاثة لكل + +478 +00:51:21,330 --> 00:51:27,110 +تربيع يساوي ماين يساوي خمسة وعشرين حاضر فيك قول + +479 +00:51:27,110 --> 00:51:32,990 +ايه؟ اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل + +480 +00:51:32,990 --> 00:51:36,910 +اتفضل + +481 +00:51:36,910 --> 00:51:49,310 +اتفضل اتفضل اتفضل + +482 +00:51:49,310 --> 00:51:56,250 +اتفضل كنت بدك تكتبها y زائد تلاتة لكل تربيع زائد x + +483 +00:51:56,250 --> 00:51:59,410 +زائد أربعة لكل تربيع بيستوى zero هادي قُرصك من + +484 +00:51:59,410 --> 00:52:03,850 +البداية غلط جاب الـ lab ده يبقى مشان أتلاشى الخطأ + +485 +00:52:03,850 --> 00:52:09,370 +رجعت كتبت الـ function اللي عندي y كدالة في x وبعد + +486 +00:52:09,370 --> 00:52:14,670 +هيك عملت shift فروحنا لما كتبناها كتبناها هي Y as + +487 +00:52:14,670 --> 00:52:19,130 +a function of X وعملت الـ shifts وبعدين رجعتها إلى + +488 +00:52:19,130 --> 00:52:25,630 +أصلها فاستبعت بذلك الخطأ تماماً فصرت أهندي Y ناقص + +489 +00:52:25,630 --> 00:52:30,050 +تلاتة بدل التفكير الأول اللي هو Y زي التلاتة اللي + +490 +00:52:30,050 --> 00:52:35,290 +هو كان غلط فضل احنا مش هنعمل الخطوطين ليه؟ يصاروا + +491 +00:52:35,290 --> 00:52:37,410 +الأعلى الخطوط في معدل الأخدام + +492 +00:52:43,750 --> 00:52:48,770 +أنا بدي اعمل + +493 +00:52:48,770 --> 00:52:54,210 +shift على خطوتين قلت له ايوة جالي بدي ارسم دائرة + +494 +00:52:54,210 --> 00:52:59,710 +في الأول مركزها ناقص 4 و 0 لو الـ shift الأول إذا + +495 +00:52:59,710 --> 00:53:04,310 +حاجهة الشمال ناقص 4 و 0 ونصف القطر خمسة بتجيكي + +496 +00:53:04,310 --> 00:53:10,070 +الدائرة هيك وبعدين ودي زيحة لفوق بمقدار تلاتة و + +497 +00:53:10,070 --> 00:53:14,070 +تطلع الدائرة الحمراء، مظبوط، ما عنديش مشكلة، عادي + +498 +00:53:14,070 --> 00:53:18,010 +جدا، مية لمية، ما فيش أي إشكالية، حد بدي سؤال تاني؟ + +499 +00:53:18,010 --> 00:53:25,430 +ايوة، اللي وراك يا راجل، اه؟ احنا كنا في الأول + +500 +00:53:25,430 --> 00:53:30,170 +قلنا إن هي رأيك إن عملنا الزرع العملية + +501 +00:53:33,970 --> 00:53:41,100 +كيف يعني؟ يعني الـ X بدل من كل Y فضالك X زائد أربعة + +502 +00:53:41,100 --> 00:53:45,920 +ماشي الحال والثانية ليش ي وي دالة فيك في هذه + +503 +00:53:45,920 --> 00:53:50,600 +الحلقة اتنين هل هي الـ function بهذا الشكل X + +504 +00:53:50,600 --> 00:53:52,920 +تربيع زائد واي تربيع و ساعة و خمسين هل هذه function + +505 +00:53:52,920 --> 00:53:56,840 +مش function لأن الـ element الواحد له صورتين و + +506 +00:53:56,840 --> 00:54:00,540 +بتالي ليه صورة لكن أنا روحت حولتها لـ function وبعد + +507 +00:54:00,540 --> 00:54:03,680 +هيك اشتغلت الشيء وعملت الـ shift ورجعتها إلى + +508 +00:54:03,680 --> 00:54:05,420 +أصلها ايوة + +509 +00:54:08,750 --> 00:54:13,150 +ما عنديش مشكلة أنا لو طلبت بدي شكل الرسمة النهائية + +510 +00:54:13,150 --> 00:54:17,390 +لكن أنت مشان توصل صح للرسمة النهائية بعمل خطوات + +511 +00:54:17,390 --> 00:54:23,510 +تدلك طيب هذا لسه المثال الأول بننتقل الآن للمثال + +512 +00:54:23,510 --> 00:54:24,890 +الثاني + +513 +00:54:41,240 --> 00:54:46,360 +لذلك بقول لك لما بترسم، بترسم تحط ليه إحداثية، نقط، + +514 +00:54:46,360 --> 00:54:50,360 +دليل على إن أنت فاهم هذا الشغل، مش رسمتي رسم هيك + +515 +00:54:50,360 --> 00:54:55,520 +أي كلام، ايوة أول رسمة اللي كانت في المركز هي + +516 +00:54:55,520 --> 00:55:00,360 +الرسمة والله دائرة دائرة ماشي اللي كانت في المركز + +517 +00:55:00,360 --> 00:55:04,700 +مش كانت تقطع محور السينات في خمسة وسالب خمسة؟ + +518 +00:55:04,700 --> 00:55:07,280 +محور السينات خمسة على اليمين وسالب خمسة على + +519 +00:55:07,280 --> 00:55:11,200 +الشمال، صحيح الرسمة الثانية اللي هي السودة، هذه + +520 +00:55:11,200 --> 00:55:15,980 +الحمرة؟ لأ السودة اللي موجهة السودة هيها، هنا بدي + +521 +00:55:15,980 --> 00:55:21,080 +يكون خمسة وهنا سالب خمسة، هاي سالب أربعة جابلة، اه + +522 +00:55:23,850 --> 00:55:28,610 +بعمل زي هنا درجية الشمال بسالب أربعة وطلعناها فوق + +523 +00:55:28,610 --> 00:55:34,810 +بمقدار تلاتة فصارت الدائرة الحمراء هاله كيف؟ سمعت + +524 +00:55:34,810 --> 00:55:39,070 +صاحبك هذا اللي جالك؟ ممكن نعملها على خطوطين؟ قلش لو + +525 +00:55:39,070 --> 00:55:43,250 +ممكن وقلنا لو ممكن الدائرة السودا نزيح جهة الشمال + +526 +00:55:43,250 --> 00:55:47,970 +بمقدار أربعة وبالتالي بدل ما المركز 00 بده يصير + +527 +00:55:47,970 --> 00:55:52,770 +سالب أربعة وزيرو ونرسم هذه الدائرة وبعدين الدائرة + +528 +00:55:52,770 --> 00:55:56,050 +الجديدة نرفعها فوق بمقدار تلاتة ويصير الدائرة + +529 +00:55:56,050 --> 00:55:58,830 +الحمراء خلاص؟ طيب + +530 +00:56:17,610 --> 00:56:26,270 +بنجعل المثال رقم اتنين يبقى + +531 +00:56:26,270 --> 00:56:27,290 +example two + +532 +00:56:33,270 --> 00:56:53,190 +بقول sketch the graph of the following functions + +533 +00:57:00,020 --> 00:57:08,220 +Y تساوي absolute value اتنين ناقص X ناقص تلاتة نمرة + +534 +00:57:08,220 --> 00:57:18,180 +B Y تساوي اتنين زائد الجذر التربيعي ل X زائد واحد + +535 +00:57:18,180 --> 00:57:28,860 +نمرة C Y تساوي واحد على X ناقص اتنين زائد X ناقص + +536 +00:57:28,860 --> 00:57:38,740 +واحد زائد اتنين نمرة D Y تساوي absolute value لل X + +537 +00:57:38,740 --> 00:57:48,940 +تربيع ناقص واحد نمرة A Y تساوي ناقص X تربيع زائد + +538 +00:57:48,940 --> 00:58:03,700 +ستة X ناقص سبعة خلي + +539 +00:58:03,700 --> 00:58:10,100 +بالكم معايا هنا سؤال بيقول يوصولي كل من الدوال + +540 +00:58:10,100 --> 00:58:16,150 +التالية معطيني بدل الدالة خمسة وبدنا نرسم كل دالة + +541 +00:58:16,150 --> 00:58:21,190 +من الدوالة الخامسة ونستخدم في رسمهم عملية ال + +542 +00:58:21,190 --> 00:58:26,550 +shift التي ذكرناها قبل قليل يبقى بالداجي للدالة + +543 +00:58:26,550 --> 00:58:32,350 +الأولى اللي هي Y تساوي absolute value اتنين ناقص X + +544 +00:58:32,350 --> 00:58:40,110 +ناقص تلاتة اتنين ناقص X ناقص تلاتة + +545 +00:58:42,640 --> 00:58:47,900 +طيب طلع لي في الدالة دي لو روحت أنت للي عندنا هدول + +546 +00:58:47,900 --> 00:58:53,700 +بلاجي اتنين ناقص اكس بلاجي X ناقص اتنين راح ولا + +547 +00:58:53,700 --> 00:58:57,360 +لأ أما أنا ما عنديش الشغل هذه حتى لأ أنا ماخدتش + +548 +00:58:57,360 --> 00:59:02,480 +بقوله بسيطة جدا إذا بدي استخدم خواص الـ absolute + +549 +00:59:02,480 --> 00:59:07,040 +فليه بقوله هاي الـ absolute وبروح باخد ناقص عامل + +550 +00:59:07,040 --> 00:59:12,840 +مشترك من الجذر اللي جوا بصير X ناقص اتنين ناقص + +551 +00:59:12,840 --> 00:59:21,270 +تلاتة بقول له أيوة يبقى هذا الكلام بده يساوي في + +552 +00:59:21,270 --> 00:59:25,390 +عندي خاصية بتقول absolute value للسالب X يساوي + +553 +00:59:25,390 --> 00:59:30,890 +absolute value للـ X صحيح ولا لا؟ إذا هذه تساوي + +554 +00:59:30,890 --> 00:59:36,350 +absolute value للـ X ناقص اتنين ناقص ثلاثة بالشكل + +555 +00:59:36,350 --> 00:59:42,460 +اللي عندنا طبعاً بقول لك بدنا نبدأ نرسم، مشان نبدأ + +556 +00:59:42,460 --> 00:59:48,340 +نرسم باطلع في مسألة كويس، هذه المسألة الأساس تبعها + +557 +00:59:48,340 --> 00:59:52,920 +شيل اتنين وشيل التلاتة يبقى أساسها مين؟ absolute + +558 +00:59:52,920 --> 00:59:58,350 +value للـ X، هذه رسمناها قبل X؟ اه رسمناها قبل هيك + +559 +00:59:58,350 --> 01:00:02,530 +يبقى لو جيت أخدت المحاور بالشكل اللي عندنا هذا + +560 +01:00:02,530 --> 01:00:09,870 +وقلنا هذا محور X وهذا محور Y وهذا نقطة الأصل هي + +561 +01:00:09,870 --> 01:00:16,050 +Zero Absolute value للـ X رسمناها قبل هيك فكانت على + +562 +01:00:16,050 --> 01:00:21,450 +الشكل اللي عندنا هذا بهذا الشكل يبقى هذه Absolute + +563 +01:00:21,450 --> 01:00:27,380 +value للـ X بدنا نتدرج مع الرسم step by step الخطوة + +564 +01:00:27,380 --> 01:00:33,740 +الأولى انسى هذه يبقى قولنا X ناقص اتنين سؤالي هو + +565 +01:00:33,740 --> 01:00:40,560 +اسمع شوية طرحنا اتنين من المتغير والله من الدالة + +566 +01:00:40,560 --> 01:00:45,040 +يعني طرحناها من الـ absolute value للـ X والله + +567 +01:00:45,040 --> 01:00:50,840 +طرحناها من الـ X من الـ X يعني طرحناها من المتغير + +568 +01:00:50,840 --> 01:00:55,480 +وليس من الدالة إذا طرحناها من المتغير يجي shift + +569 +01:00:55,480 --> 01:00:59, + +601 +01:03:52,740 --> 01:04:01,840 +رسمناه قبل ذلك يبقى هذا جذر الـ X يبقى هذا Y تساوي + +602 +01:04:01,840 --> 01:04:09,820 +جذر الـ X طيب جذر الـ X قلنا زائد واحد، الواحد أضافناه + +603 +01:04:09,820 --> 01:04:15,420 +لـ X والله لجذر الـ X لجذر X يبقى إزاحة جهة + +604 +01:04:15,420 --> 01:04:21,140 +الشمال بمقدار واحد، يبقى نظرة اللي إنها زائد مش زي + +605 +01:04:21,140 --> 01:04:26,980 +هذه ناقص، بدي أرجعها للخلف بمقدار واحد يبقى هذه + +606 +01:04:26,980 --> 01:04:31,700 +النقطة سالب واحد وبالتالي بدي يصير المنحنة اللي + +607 +01:04:31,700 --> 01:04:37,720 +عندك بالشكل اللي عندك هذا، يبقى هذا الجذر التربيعي + +608 +01:04:37,720 --> 01:04:43,600 +لـ x زائد واحد، بعد هيك الجذر التربيعي لـ x زائد + +609 +01:04:43,600 --> 01:04:48,500 +واحد، كلها أضفنا لها قداش؟ اثنين، يعني الدالة كلها + +610 +01:04:48,500 --> 01:04:53,940 +أضفنا لها اثنين يبقى إزاحة إلى أعلى بمقدار، يبقى + +611 +01:04:53,940 --> 01:05:00,080 +الرسم الأزرق المنقطة، بدي أطلعها فوق بمقدار تمام يعني + +612 +01:05:00,080 --> 01:05:04,640 +بتيجي للنقطة اللي عندنا هذه فوق واطلع هنا هذا + +613 +01:05:04,640 --> 01:05:10,020 +النقطة اللي عندناها سالب واحد واثنين تمام يعني + +614 +01:05:10,020 --> 01:05:16,300 +اللي جبالة هنا بتبقى اثنين وهنا واحد وهنا صفر + +615 +01:05:17,280 --> 01:05:22,660 +وبالتالي هذه الرسمة بدي أزيحها لفوق بمقدار 2 بيصير + +616 +01:05:22,660 --> 01:05:27,260 +بالشكل اللي عندنا الأزرق هذا، يبقى الشكل الأزرق هذا + +617 +01:05:27,260 --> 01:05:31,720 +اللي هو 2 زائد الجذر التربيعي لـ X زائد 1 اللي هو + +618 +01:05:31,720 --> 01:05:41,620 +بيساوي مين؟ بيساوي Y طيب بدنا نروح لنمرة C، يبقى + +619 +01:05:41,620 --> 01:05:47,220 +نمر أسيلة Y تساوي 1 على X ناقص 1 زائد 2 + +620 +01:05:47,220 --> 01:05:53,740 +شيل الواحد وشيل الاثنين يبدأ أصل ده اللي هي 1 على + +621 +01:05:53,740 --> 01:05:59,940 +X، يبقى لو جيت رسمت المحاور، هي المحاور اللي عندنا + +622 +01:05:59,940 --> 01:06:07,900 +هذا محور X هذا Y هذا نقطة الأصل 1 على X يبقى هي + +623 +01:06:07,900 --> 01:06:16,520 +ومن هنا بنفس الطريقة يبقى الدالة السوداء المنقطة + +624 +01:06:16,520 --> 01:06:25,980 +هذه الدالة 1 على X، الآن الـ X شملنا لها، الـ X + +625 +01:06:25,980 --> 01:06:30,300 +طرحنا منها واحد، الواحد من الدالة والله من + +626 +01:06:30,300 --> 01:06:36,540 +المتغير المتغير إذا shift جهة اليمين بمقدار واحد + +627 +01:06:36,540 --> 01:06:43,780 +يعني لو جينا قلنا هذا الخط الرأسي اللي هو X يساوي + +628 +01:06:43,780 --> 01:06:49,780 +واحد، تمام؟ إذا بدي أزيح الدالة جهة اليمين بمقدار + +629 +01:06:49,780 --> 01:06:57,920 +كده؟ بمقدار واحد، يبقى هذا الخط مده على استقامته هذا + +630 +01:06:57,920 --> 01:07:04,180 +محور X، يبقى كل الرسمة بده حركة جهة اليمين بمقدار + +631 +01:07:04,180 --> 01:07:10,020 +واحد يبقى الخط اللي عندنا بده يصير بهذا الشكل وهذا + +632 +01:07:10,020 --> 01:07:18,460 +بده ييجي لجوس بهذا الشكل، يبقى الخط الأزرق المنقطة + +633 +01:07:18,460 --> 01:07:25,740 +هذا معادلته 1 على X ناقص 1 اللي هي تساوي + +634 +01:07:25,740 --> 01:07:30,740 +مين؟ تساوي Y، طيب هذا المقدار كله يعني الـ function + +635 +01:07:30,740 --> 01:07:37,880 +كلها أضفنا لها قداش؟ يبقى زي اثنين بمقدار، يبقى بدي أجي + +636 +01:07:37,880 --> 01:07:44,120 +اثنين، أزرق المنقطة بدي أرفعهم فوق بمقدار اثنين، وين + +637 +01:07:44,120 --> 01:07:49,760 +اثنين، يبقى هذه النقطة؟ يبقى هنا لو كان هذا خط أفقي + +638 +01:07:49,760 --> 01:07:55,080 +بالشكل اللي عندنا هذا، يبقى هذا الخط Y تساوي 2 + +639 +01:07:55,080 --> 01:08:00,850 +حد فيكم بيقدر يقول لي قداش إحداثي النقطة هذه؟ واحد و + +640 +01:08:00,850 --> 01:08:06,070 +اثنين يبقى هذه النقطة الإحداثي تبعها واحد واثنين + +641 +01:08:06,070 --> 01:08:12,070 +وبالتالي ده اللي أزرق ارفعها فوق بمقدار اثنين + +642 +01:08:12,070 --> 01:08:18,470 +يبقى بده ييجيلك الخط الأحمر هذا جاي من فوق الشكل + +643 +01:08:18,470 --> 01:08:26,190 +هذا ومن هنا هذا جاي من تحت بهذا الشكل تمام يبقى + +644 +01:08:26,190 --> 01:08:33,810 +هذه الدالة Y تساوي 1 على X ناقص 1 زائد 2 + +645 +01:08:33,810 --> 01:08:39,250 +تمام، يبقى خلاصنا من نمرة C، بدنا نيجي لنمرة D وما + +646 +01:08:39,250 --> 01:08:46,680 +أدرك كمان نمرة D يبقى هذه D يقول لي Y تساوي + +647 +01:08:46,680 --> 01:08:53,580 +absolute value للـ X تربيع ناقص 1 وهذا المحاور + +648 +01:08:53,580 --> 01:08:59,420 +وهذا محور X وهذا الرأس اللي عندنا اللي هو محور + +649 +01:08:59,420 --> 01:09:02,280 +main محور Y + +650 +01:09:09,830 --> 01:09:15,610 +وانسى الواحد يبقى أصل الدالة من X تربيع بدنا نروح + +651 +01:09:15,610 --> 01:09:23,570 +نرسم الدالة Y تساوي X تربيع قداش مرات؟ مش مرة كمان + +652 +01:09:23,570 --> 01:09:32,990 +يبقى هذه الدالة اللي عندنا هي Y تساوي X تربيع طيب + +653 +01:09:32,990 --> 01:09:42,380 +هنا بتمر بنقطة الأصل تمام كويس؟ اللي هي Zero طيب + +654 +01:09:42,380 --> 01:09:49,780 +الـ X تربيع شو أعمل لها لها؟ ناقص 1 من الـ X ولا + +655 +01:09:49,780 --> 01:09:56,580 +من الـ X تربيع؟ يعني من المتغير ولا من الدالة؟ + +656 +01:09:58,850 --> 01:10:04,750 +من الدالة، لو كانت من المتغير لقلنا X ناقص 1 + +657 +01:10:04,750 --> 01:10:10,550 +لكل تربيع، تمام؟ هيك بيصير من المتغير لكن من الدالة + +658 +01:10:10,550 --> 01:10:14,490 +طرحنا من الـ X تربيع، مدام طرحنا من الـ X تربيع + +659 +01:10:14,490 --> 01:10:20,710 +معناته بدي أنزل الرسم بمقدار، يبقى بدنا ننزل الرسم + +660 +01:10:20,710 --> 01:10:27,110 +بمقدار واحد، يبقى بدي ييجينا هذا الخط وبدي يجيك + +661 +01:10:27,110 --> 01:10:33,510 +المنحنة هيك ويجي طالع بهذا الشكل، هذه النقطة اللي + +662 +01:10:33,510 --> 01:10:42,570 +هي اتبعها صفر وسالب واحد، يبقى هذا الرسم المنقطة + +663 +01:10:42,570 --> 01:10:48,830 +الزرقى X تربيع ناقص 1 وY تساوي X تربيع ناقص + +664 +01:10:48,830 --> 01:10:56,300 +واحد طيب استنى شوية استنى شوية، الآن بدنا نأخذ + +665 +01:10:56,300 --> 01:11:01,700 +absolute value لهذه الدالة عمرها بتطلع قيمة سالبة + +666 +01:11:01,700 --> 01:11:06,740 +طيب الـ absolute value للقيمة الموجبة مش هي نفس + +667 +01:11:06,740 --> 01:11:11,820 +القيمة الموجبة والله بتتغير، طيب هذا بده يخليني + +668 +01:11:11,820 --> 01:11:17,240 +أسألكم السؤال التالي، الجزء من عند النقطة هذه فما + +669 +01:11:17,240 --> 01:11:22,500 +فوق ومن النقطة هذه فما فوق، بدي يتغير ولا بدي يبقى + +670 +01:11:22,500 --> 01:11:30,940 +كما هو؟ كما هو، كما هو، لن يتغير، إذا هذا الخط يظل + +671 +01:11:30,940 --> 01:11:37,340 +زي ما هو، أي خط غامق لما نأخذه الـ absolute value مش + +672 +01:11:37,340 --> 01:11:44,700 +حيحصله ولا حاجة، تمام؟ باقي دالة الجزء المنقط هذا + +673 +01:11:44,700 --> 01:11:53,340 +أصلًا كل الـ Y تبعته قيم سالبة، لما نأخذها موجبة يعني + +674 +01:11:53,340 --> 01:11:57,540 +اللي تحت الـ X-axis وين بدها تصير؟ فوق الـ X-axis + +675 +01:11:57,540 --> 01:12:02,840 +إذا الجزء هذا بده ينقلب وبده تيجينا النقطة هذه + +676 +01:12:02,840 --> 01:12:08,780 +اللي هي صفر وواحد وبالتالي المنحنة هيجي كذا ويجي + +677 +01:12:08,780 --> 01:12:09,960 +بالشكل هذا + +678 +01:12:14,990 --> 01:12:22,110 +يبقى صارت الرسم الخط الأزرق المتواصل هذا اللي هو + +679 +01:12:22,110 --> 01:12:27,430 +الـ Y تساوي absolute value للـ X تربيع إنها استطعت + +680 +01:12:27,430 --> 01:12:35,210 +رسمها من خلال مفهوم لمين؟ للـ absolute value يبقى + +681 +01:12:35,210 --> 01:12:39,770 +الجزء الأول رسمته من خلال مفهوم للـ shift vertical + +682 +01:12:39,770 --> 01:12:44,740 +إلى أسفل بمقدار واحد، الجزء الثاني فكرنا الـ absolute + +683 +01:12:44,740 --> 01:12:51,480 +مالي بتطلعش إلا قيم موجبة، إذا الجزء الموجب تبع الـ + +684 +01:12:51,480 --> 01:12:57,760 +Y هيبقى كما هو، الجزء السالب هذا كله بدي يتحول لمين؟ + +685 +01:12:57,760 --> 01:13:03,900 +لموجب، يعني لو وصل لك هنا نص وكان سالب نص بيصير نص + +686 +01:13:03,900 --> 01:13:10,080 +وموجب نص كان هذا سالب نص وسالب نص لازال سالب نص و + +687 +01:13:10,080 --> 01:13:14,920 +نص ينقلب فوق وهكذا، يبقى الجزء اللي تحت بيصير جزء + +688 +01:13:14,920 --> 01:13:19,420 +فوق، سؤال واحد و + +689 +01:13:19,420 --> 01:13:26,160 +لزهراء واحد جوا الجزء، تتأكد أنت؟ يعني هذه فيها فرق + +690 +01:13:26,160 --> 01:13:32,530 +بينها وبين X ناقص 1 لكل تربيع؟ هذه كيف بنكمل + +691 +01:13:32,530 --> 01:13:36,370 +إزاحتها؟ اسمع يا رب نتناقش احنا وياه وأنتوا + +692 +01:13:36,370 --> 01:13:43,210 +استفيدوا، هو هذه الأصلية كانت X تربيع ناقص 1 + +693 +01:13:44,290 --> 01:13:48,190 +مظبوط؟ أنت بتقول لي هذه بدي أعملها يمين وشمال، طب + +694 +01:13:48,190 --> 01:13:51,190 +وهذه كيف أعمل فيها؟ لأ أنا قصدي لو كانت مثلًا X + +695 +01:13:51,190 --> 01:13:56,170 +تربيع يا الله دي قصدي خلط، لو X تربيع هي الدالة + +696 +01:13:56,170 --> 01:14:00,410 +وليس المتغير، المتغير X مش X تربيع، رددت + +697 +01:14:00,410 --> 01:14:04,570 +المتغير، أضفت له رقم صار هو الدالة، صحيح ولا لا؟ + +698 +01:14:04,570 --> 01:14:07,590 +يبقى صار هو الدالة، يبقى السلم واحد طرحنا من + +699 +01:14:07,590 --> 01:14:12,920 +الدالة ولا من المتغير هذا الآن لو بدك ترسم هذه + +700 +01:14:12,920 --> 01:14:18,580 +معناته بدك تعمل إزاحة جهة اليمين بمقدار واحد يبقى + +701 +01:14:18,580 --> 01:14:24,060 +هاي الفرق بين هذه وهذه نفس السؤال طيب ماشي حد بده + +702 +01:14:24,060 --> 01:14:30,060 +يسأل ثاني قبل ما نكمل طيب طلّالي كويس يبقى لا هذا + +703 +01:14:30,060 --> 01:14:39,260 +ولا ذاك بدنا نيجي لنمرة ايه؟ طلّالي كويس، بنعمل ايه؟ + +704 +01:14:39,260 --> 01:14:45,500 +هذا بده شغل؟ كيف بده شغل؟ Y تساوي سالب X تربيع زائد + +705 +01:14:45,500 --> 01:14:51,340 +ستة X معادلة من الدرجة الثانية هذه في X من حد ما + +706 +01:14:51,340 --> 01:14:52,540 +تشوف Y + +707 +01:15:06,660 --> 01:15:10,500 +مفتوح إلى أعلى أو مفتوح إلى أسفل + +708 +01:15:14,350 --> 01:15:23,170 +عشان نرسمه بدقة بدنا نروح نحط المعادلة هذه في شكل + +709 +01:15:23,170 --> 01:15:24,210 +آخر + +710 +01:15:44,540 --> 01:15:52,020 +يبقى بقول هي سالب عامل مشترك وهي X تربيع ناقص 6X + +711 +01:15:52,020 --> 01:15:58,750 +وهي ناقص 7 اللي برا، سويتش ايه؟ ولا حاجة، الآن بدنا + +712 +01:15:58,750 --> 01:16:04,690 +نيجي للمقدار بين القوسين، بدنا نعمله إكمال المربع + +713 +01:16:04,690 --> 01:16:12,410 +نيجي للصف الثامن، صف الثامن بقيت واخدت فيه طريقة + +714 +01:16:12,410 --> 01:16:20,770 +إكمال المربع وللسبعة، خلّي التامن مسدقين، التامن اسمع + +715 +01:16:20,770 --> 01:16:25,650 +بس أنت اللي راح في عيدك، كيف بدنا نعمل إكمال المربع + +716 +01:16:25,650 --> 01:16:35,730 +نص معامل X الكل تربيع، نصه قداش؟ 3 ومربعه 9 + +717 +01:16:35,730 --> 01:16:39,430 +أنا بدي أعطيك الكلمة اللي قلته بس بطريقة أخرى + +718 +01:16:43,930 --> 01:16:50,450 +معامل X مقسومًا على أربعة أمثال معامل X تربيع + +719 +01:17:06,640 --> 01:17:17,520 +عشان أعمل مربع كامل بنضيف مربع معامل X مقسومًا على + +720 +01:17:17,520 --> 01:17:27,480 +أربعة أمثال معامل X، يبقى حبها قادة في دماغك وبدنا + +721 +01:17:27,480 --> 01:17:35,680 +نبدأ نشتغل عليها، نيجي معامل X هنا كدهش؟ 6 مربعه 36 + +722 +01:17:35,680 --> 01:17:45,200 +طيب معامل X تربيع أربعة أمثاله 4 × 1 = 4، 36 ÷ 4 يبقى + +723 +01:17:45,200 --> 01:17:52,250 +بالنظيف 9، 9 بيكون عملنا ايش؟ أضفنا صفر وبالتالي + +724 +01:17:52,250 --> 01:17:58,530 +لن تتغير القيمة طيب تعالي هادي بدها تساوي قداش بالك + +725 +01:17:58,530 --> 01:18:10,390 +كويس هي الناقص وX تربيعها ناقص ستة X زائد 9 طيب + +726 +01:18:10,390 --> 01:18:15,590 +هنا ناقص 7 وهنا أكتب ناقص 7 ولا ناقص 9؟ + +727 +01:18:15,590 --> 01:18:21,460 +ناقص 9 غلط، لأن أنت نقصت ساعة هي أضفناها، بصير لك + +728 +01:18:21,460 --> 01:18:27,120 +أضيفها مرتين، هي زائد 9 وفي شريط سالب برا، يبقى + +729 +01:18:27,120 --> 01:18:33,200 +هنا أضفنا كده؟ سالب 9 أيضًا برا بدي زائد 9، + +730 +01:18:33,200 --> 01:18:41,460 +يبقى هذه زائد 9، تمام؟ يبقى هيك هاي ناقص 9 وهي + +731 +01:18:41,460 --> 01:18:46,380 +زي التسعة، ما سوينا شيء إذا المعادلة دي صارت Y + +732 +01:18:46,380 --> 01:18:53,740 +يساوي ناقص (X ناقص 3) لكل تربيع زي دي 2 + +733 +01:19:17,800 --> 01:19:25,680 +ناقص 7 وزائد 9 زائد 2 + +734 +01:19:25,780 --> 01:19:31,420 +الشغل الأولى، الإشارة السالبة هذه، معناته + +735 +01:19:31,420 --> 01:19:35,800 +البربولة مفتوحة لوين؟ لسه، لكن لو كانت الإشارة + +736 +01:19:35,800 --> 01:19:39,700 +موجبة، كان البربولة مفتوحة لوين؟ الأعلى، هي نمرة + +737 +01:19:39,700 --> 01:19:46,810 +واحد، نمرة اثنين هذا 2 والتلاتة هو الـ vertex + +738 +01:19:46,810 --> 01:19:52,670 +الرأس تبع مين؟ تبع القرابل القرابل إلى أسفل وإحداثي + +739 +01:19:52,670 --> 01:19:59,610 +الرأس هو 3 و2، تمام؟ يبقى هذه بدأ تبقى + +740 +01:19:59,610 --> 01:20:05,170 +رسمة قرابل open + +741 +01:20:05,170 --> 01:20:10,510 +down مفتوحة لأسفل with + +742 +01:20:12,990 --> 01:20:24,290 +Vertex H وK يكون 3 و2 يعني لو جيت أخذت + +743 +01:20:24,290 --> 01:20:32,230 +المحاور هنا ورحت قلت هذا محور X وهذا محور Y وهذا + +744 +01:20:32,230 --> 01:20:39,200 +نقطة الأصل اللي هي صفر، أصل المثال هو Y تساوي X + +745 +01:20:39,200 --> 01:20:45,140 +تربيع سبقت بإشارة سالبة مقلوبة إلى أسفل بدي أحركها + +746 +01:20:45,140 --> 01:20:50,920 +جهة اليمين بمقدار 3 وأطلعها إلى أعلى بمقدار + +747 +01:20:50,920 --> 01:20:56,880 +2 يفقه لو قلت هذا 1 وهذا 2 وهذا 3 + +748 +01:20:56,880 --> 01:21:01,920 +وجهها تقول هنا 1 وهنا 2 يبقى الـ parabola + +749 +01:21:01,920 --> 01:21:07,200 +بتحركها إلى أعلى هنا إحداثي النقطة هذه 3 و + +750 +01:21:07,200 --> 01:21:13,120 +2 والـ parabola open down الشكل اللي عندنا هذا + +751 +01:21:13,120 --> 01:21:16,960 +يبقى هي الـ parabola مفتوحة إلى أسفل والـ vertex + +752 +01:21:16,960 --> 01:21:19,280 +سباحة عبارة عن 3 و2 تفضل + +753 +01:21:23,340 --> 01:21:29,520 +وهي احنا أخذنا اشتقاق، بعرفش عنه حاجة ولا حتى الـ + +754 +01:21:29,520 --> 01:21:33,480 +chapter الجاي بعد ما نأخذه بصير بعد هيك مطلق + +755 +01:21:33,480 --> 01:21:37,720 +الحرية إليك أنا بتقيد في حدود المعلومات اللي + +756 +01:21:37,720 --> 01:21:41,560 +أخدتها بحل بها بس فقط لغاية أما اشتقاق حتى الآن + +757 +01:21:41,560 --> 01:21:45,000 +بعرفوش، أما في chapter 3 مارح أقيّدنك أه + +758 +01:21:49,950 --> 01:21:54,050 +ما أخذناش ايه؟ ما أخذناش السالب 7 والتسعة كيف + +759 +01:21:54,050 --> 01:22:01,110 +السالب 7 والتسعة هي؟ طب ما نبدأ نكمل المربع هي + +760 +01:22:01,110 --> 01:22:04,930 +لو إنها جاهزة من فوق ما احتاجت إكمال المربع هل اللي + +761 +01:22:04,930 --> 01:22:09,050 +عندك هذه قبل ما نأخذ فيها التسعة ولا هل هذه + +762 +01:22:09,050 --> 01:22:13,810 +مربع كامل؟ وين السالب اللي أخذناه؟ هو السالب في + +763 +01:22:13,810 --> 01:22:20,360 +البداية محطوط لمين؟ محطوط للـ X تربيع والله بدك تخلي + +764 +01:22:20,360 --> 01:22:24,540 +الـ X ترميها بإشارة سالبة دائمًا أنا أقول X ترميها + +765 +01:22:24,540 --> 01:22:34,640 +بناخدها بإشارة من موجب تمام؟ يالا يعني + + +801 +01:28:19,630 --> 01:28:27,610 +نُمنى اثنين Y to serve F of ذالب X reflect the + +802 +01:28:27,610 --> 01:28:33,290 +graph of across the Y-axis + +803 +01:28:59,940 --> 01:29:11,980 +Sketch the graph of the following functions + +804 +01:29:15,550 --> 01:29:27,110 +نمرة A Y تساوي اثنين ناقص جذر ال X نمرة B Y تساوي + +805 +01:29:27,110 --> 01:29:37,510 +جذر التربيع لخمسة ناقص X نمرة C Y يساوي اثنين X + +806 +01:29:37,510 --> 01:29:49,450 +تربيع و Y يساوي نصف X تربيع نمرة D Y تساوي الجذري + +807 +01:29:49,450 --> 01:29:58,850 +التربيعي للاثنين X زائد واحد نمرة E Y تساوي الجذري + +808 +01:29:58,850 --> 01:30:08,730 +التربيعي للواحد زائد X على اثنين وY تساوي الجذري + +809 +01:30:08,730 --> 01:30:13,530 +التربيعي للواحد ناقص X على اثنين + +810 +01:30:19,910 --> 01:30:23,670 +الآن في هذا ال section أخذنا أول نقطتين والآن بدنا + +811 +01:30:23,670 --> 01:30:27,510 +نأتي للنقطة الثالثة النقطة الأولى كانت combining + +812 +01:30:27,510 --> 01:30:31,990 +النقطة الثانية كانت shifting of functions النقطة + +813 +01:30:31,990 --> 01:30:37,370 +الثالثة لل scaling ال scaling يعني الرسم بنسبة + +814 +01:30:37,370 --> 01:30:42,490 +لنرسم بنسبة ما يعني بدنا نصغر الرسم أو نكبر الرسم + +815 +01:30:42,490 --> 01:30:46,910 +زي ما أنت عندك صورة بتحب تُبرزها بتروح تكبرها و + +816 +01:30:46,910 --> 01:30:51,520 +تحطها في صدر بيجدك كبر د الرسم بدك تسافر و لا تجيب + +817 +01:30:51,520 --> 01:30:56,400 +السفر، بتروح تصغّر من الرسمة بما يتناسب أو بدك تطلع + +818 +01:30:56,400 --> 01:31:00,460 +بطاقة الطالب من القبول والتسجيل، تصغّر الصورة تبعك، + +819 +01:31:00,460 --> 01:31:04,860 +تجيب تصغير أو تكبير طيب، هذا معناه ال scaling + +820 +01:31:04,860 --> 01:31:10,920 +reflecting يعني بدنا نقلب الرسمة عبر محور ما؟ و + +821 +01:31:10,920 --> 01:31:16,060 +سيكون القلبة عنا عبر محور X أو عبر محور Y نبدأ بال + +822 +01:31:16,060 --> 01:31:17,660 +scaling، ماذا الذي أخذته؟ + +823 +01:31:20,650 --> 01:31:25,440 +وزعلان ليش؟ فأنا ميت دكية يا عزيزي يبقى قبل أن نبدأ + +824 +01:31:25,440 --> 01:31:29,860 +Scaling of a graph خلي بالك معايا هنا قال افترض أن + +825 +01:31:29,860 --> 01:31:35,560 +c رقم أكبر من الواحد صحيح عدد حقيقي ليس بضرورة أن + +826 +01:31:35,560 --> 01:31:39,380 +يكون integer integer أو كسر ماعنا مشكلة to obtain + +827 +01:31:39,380 --> 01:31:45,420 +real number to obtain the graph of y تساوي c of x + +828 +01:31:45,420 --> 01:31:49,440 +يبقى احنا عندنا دالة of x ضربناها في رقم وهذا + +829 +01:31:49,440 --> 01:31:54,250 +الرقم أكبر من الواحدة شو معناه stretch the graph + +830 +01:31:54,250 --> 01:31:58,650 +معناه بيجي تنغطى الرسمة بيجي تكبر الرسمة بتعمليه + +831 +01:31:58,650 --> 01:32:03,150 +استطالة للرسمة يبقى stretch the graph of Y تساوي F + +832 +01:32:03,150 --> 01:32:08,590 +of X vertically بمقدار العامل C factor يعني عامل + +833 +01:32:08,910 --> 01:32:14,550 +يبقى أنت بدك تكبر رسمة بمقدار C يعني لو كان C 2 + +834 +01:32:14,550 --> 01:32:20,170 +بيصير رسمة جد اللي جاب المرتين ثلاثة جدها ثلاث مرات + +835 +01:32:20,170 --> 01:32:24,670 +واحد ونصف جدها مرة ونصف وهكذا يبقى هذه المقصود + +836 +01:32:24,670 --> 01:32:29,130 +فيها نمرة اثنين بدل ما ضربناها في C بدي اضرب واحد + +837 +01:32:29,130 --> 01:32:33,570 +على C يبقى واحد على C كسر أقل من واحدة صحية ولا + +838 +01:32:33,570 --> 01:32:39,390 +أكبر؟ أقل لأن C أصلاً أكبر من واحدة اثنين ثلاثة + +839 +01:32:39,390 --> 01:32:43,310 +أربعة أصلاً نصف ثلاثة أرباع وخمسة إذا هذا كسر أقل + +840 +01:32:43,310 --> 01:32:47,630 +من واحدة أصلاً شو بتعملي Galicompress اضغط عليها + +841 +01:32:47,630 --> 01:32:52,030 +خليها تنكمش مش بس أش رأسي يبقى احنا بدل ما كنا نكبر + +842 +01:32:52,030 --> 01:32:53,050 +نفسنا بنروح إيه + +843 +01:33:07,590 --> 01:33:12,550 +لو قلنا f of c x هنا ضربنا c في الدالة هنا ضربناها + +844 +01:33:12,550 --> 01:33:17,600 +في المتغير يبقى بدك تضغط بس horizontally + +845 +01:33:17,600 --> 01:33:23,460 +الأولانية ضغطنا رأسي هدم نضغط وين؟ أفقي يبقى + +846 +01:33:23,460 --> 01:33:28,920 +compress horizontally بمقدار مين؟ بمقدار الـC F of + +847 +01:33:28,920 --> 01:33:33,000 +X على C يعني ضربنا المتغير في واحدة يبقى بدك تعمل + +848 +01:33:33,000 --> 01:33:38,800 +stretch أفقي يبقى بدك تمعط الرسمة أفقي بمقدار + +849 +01:33:38,800 --> 01:33:43,800 +العامل تبعك اللي هو مين؟ C خلاصة مكان تضغط الرسمة + +850 +01:33:43,800 --> 01:33:48,240 +أو تكبر الرسمة أو تكبر الرسمة أو تكبر الرسمة أو + +851 +01:33:48,240 --> 01:33:49,200 +تكبر الرسمة أو تكبر الرسمة أو تكبر الرسمة أو تكبر + +852 +01:33:49,200 --> 01:33:49,440 +الرسمة أو تكبر الرسمة أو تكبر الرسمة أو تكبر + +853 +01:33:49,440 --> 01:33:50,060 +الرسمة أو تكبر الرسمة أو تكبر الرسمة أو تكبر + +854 +01:33:50,060 --> 01:33:51,900 +الرسمة أو تكبر الرسمة أو تكبر الرسمة أو تكبر + +855 +01:33:51,900 --> 01:33:52,460 +الرسمة أو تكبر الرسمة أو تكبر الرسمة أو تكبر + +856 +01:33:52,460 --> 01:33:52,760 +الرسمة أو تكبر الرسمة أو تكبر الرسمة أو تكبر + +857 +01:33:52,760 --> 01:33:57,660 +الرسمة أو تكبر الرسمة أو تكبر الرسمة أو تكبر + +858 +01:33:57,660 --> 01:34:03,800 +الرسمة أو تكبر الرسمة أو تكبر بدل F of X يبقى اللي + +859 +01:34:03,800 --> 01:34:08,180 +كانت موجبة بيصير سالب و اللي كانت سالبة بيصير موجب + +860 +01:34:08,180 --> 01:34:15,420 +يعني بدك تقلب الرسم عبر محور X فلو ال X هذه حطيت + +861 +01:34:15,420 --> 01:34:20,200 +السالب جوه لل X يبقى نقلب الرسم عبر محور Y يعني + +862 +01:34:20,200 --> 01:34:25,380 +اللي كانت X الدالة فوق بيصير F of سالب X يبقى + +863 +01:34:25,380 --> 01:34:28,970 +الدالة وين؟ في الناحية الثانية يبقى قلبنا الرسم عبر + +864 +01:34:28,970 --> 01:34:33,890 +محور X ومن هنا صارت الفروقات اللي عندنا يبقى لو + +865 +01:34:33,890 --> 01:34:38,470 +الدالة كلها ضربتها في إشارة سالب بنجلب الدالة عبر + +866 +01:34:38,470 --> 01:34:44,250 +إيش؟ محور X لكن لو ضربنا المتغير للدالة بنجلب ال + +867 +01:34:44,250 --> 01:34:48,790 +function كلها عبر محور Y بدنا نروح نطبق هذا على + +868 +01:34:48,790 --> 01:34:53,780 +أرض الواقع بدنا نأتي للدالة الأولى نمرة إيه؟ Y تساوي + +869 +01:34:53,780 --> 01:35:00,240 +اثنين ناقص جذر ال X، يبقى أصل الدالة، هذا محور X، + +870 +01:35:00,240 --> 01:35:06,260 +هذا Y، هذا نقطة الأصل، أصل الدالة هي جذر ال X، إيش + +871 +01:35:06,260 --> 01:35:10,580 +هذا قبل جذر ال X؟ يبقى السالب بأجل الدالة والله + +872 +01:35:10,580 --> 01:35:16,460 +للمتغير للدالة قبل الجذر، لو كان المتغير كان + +873 +01:35:16,460 --> 01:35:21,060 +حاطناها تحت الجذر، هذه برا الجذر يبقى السالب أجل + +874 +01:35:21,060 --> 01:35:25,980 +الدالة، يبقى بدأنا نقلب الدالة عبر محور ماذا X يبقى + +875 +01:35:25,980 --> 01:35:32,420 +بدها تصير الدالة هذه نُصمّمها لك بلون آخر، يبقى هذه + +876 +01:35:32,420 --> 01:35:39,060 +بدها تصير سالب جذر X يبقى كأن ال F بكسرت عندي + +877 +01:35:39,060 --> 01:35:41,260 +سالب جذر X، شو أجاها؟ + +878 +01:35:59,360 --> 01:36:07,650 +الخط الأزرق المتواصل هذا اثنين ناقص جذر X وهذا + +879 +01:36:07,650 --> 01:36:12,410 +محور X اللي فوق، تمام؟ طيب، هذا بالنسبة للرسمة + +880 +01:36:12,410 --> 01:36:17,730 +الأولى، هذه نمرة A، بدنا نأتي لنمرة B نمرة B هي + +881 +01:36:17,730 --> 01:36:22,970 +المحاور، هذا محور X، هذا محور Y، هذه نقطة الأصل + +882 +01:36:22,970 --> 01:36:29,790 +يمين Zero أصلي ده لمين؟ جذر ال X، يبقى نفس الرسمة + +883 +01:36:29,790 --> 01:36:41,630 +تبعنا، هذه جذر ال X طيب لو كانت هذه + +884 +01:36:41,630 --> 01:36:48,970 +خمسة زائد جذر ال X يعني X زائد خمسة كلها تحت الجذر + +885 +01:36:48,970 --> 01:36:57,820 +يعني شفت وين؟ جذر التربيع لـ X زائد خمسة جهة + +886 +01:36:57,820 --> 01:37:03,900 +الشمال بمقدار خمسة يعني هذه لو جئت هنا ليه سالب + +887 +01:37:03,900 --> 01:37:10,120 +خمسة، بدّه يصير المنحنى هيك هذا الجذر التربيعي لـ X + +888 +01:37:10,120 --> 01:37:15,860 +زائد خمسة، اللي هو خمسة زائد جذر ال X طيب بدي أشيل + +889 +01:37:15,860 --> 01:37:21,280 +كل X و أحط مكانها ناقص X، بحصل على مسألة دي، صح + +890 +01:37:21,280 --> 01:37:26,640 +ولا لأ؟ لما تشيل ال X و تحط مكانها ناقص X، بتجلب + +891 +01:37:26,640 --> 01:37:32,280 +الرسم عبر مين؟ عبر محور Y، يبقى اللي كانت هذه سالب + +892 +01:37:32,280 --> 01:37:37,720 +بخمسة يبقى سالب بخمسة بتصير النحو التالي يبقى دي + +893 +01:37:37,720 --> 01:37:43,940 +خمسة يبقى بدها تجيلك هنا النقطة اللي هي خمسة و + +894 +01:37:43,940 --> 01:37:48,520 +نقلب الرسم عبر محور Y بهذا الشكل يعني اللي كانت + +895 +01:37:48,520 --> 01:37:52,000 +على الشمال بتحصير على اليمين و اللي كانت على + +896 +01:37:52,000 --> 01:37:56,800 +اليمين انجلبت و صارت وين؟ صارت على الشمال بالشكل + +897 +01:37:56,800 --> 01:38:01,240 +اللي عندنا هذا يقول خط الأزرق المتواصل هذا الجدر + +898 +01:38:01,240 --> 01:38:08,340 +التربيعي لخمسة ناقص X يعني بدك تلعب في الرسمة طبقا + +899 +01:38:08,340 --> 01:38:13,680 +للمعلومات اللي عندك هذا نمرة B نأتي لنمرة C يقول لي + +900 +01:38:13,680 --> 01:38:19,020 +Y يساوي اثنين X تربيع لاحظ لا عملت حتى لها لا + +901 +01:38:19,020 --> 01:38:24,770 +compress ولا stretch برسم الدالة وإيه وبشغل فقط + +902 +01:38:24,770 --> 01:38:30,190 +على ال reflecting يبقى اشتغلت على التنتين هدول بدّه + +903 +01:38:30,190 --> 01:38:33,710 +نأتي نشتغل على الأربعة اللي فوق هدول بدّه اجي + +904 +01:38:33,710 --> 01:38:40,950 +لنمرة C نمرة C هي المحاور هذا محور X هذا محور Y + +905 +01:38:40,950 --> 01:38:47,510 +هذا نقطة الأصل اللي هي Zero اصل الدالة Y تساوي X + +906 +01:38:47,510 --> 01:38:53,230 +تربيع مظبوط اللي ال parabola المشهورة يبقى هذه + +907 +01:38:53,230 --> 01:39:00,350 +الـC هي هنا وهذه اصل الدالة بالشكل هذا يبقى هذه Y + +908 +01:39:00,350 --> 01:39:06,890 +تساوي X تربيع وهذه النقطة الأصل اللي هي Zero + +909 +01:39:06,890 --> 01:39:13,200 +الدالة دي شو حصل لها ضربتها في اثنين في ثلاثة في + +910 +01:39:13,200 --> 01:39:18,540 +أربعة رقم أكبر من الواحد الصحيح إذا لما تضرب + +911 +01:39:18,540 --> 01:39:23,480 +الدالة هذه رقم بدك stretch vertically يعني بدي + +912 +01:39:23,480 --> 01:39:28,880 +أثبت النقطة هذه و أمسك هدول وأشدّهم لوين؟ لفوق + +913 +01:39:28,880 --> 01:39:34,020 +يبقى مجتمع تدالة لوين؟ لفوق إذا الدالة هتأخذ الشكل + +914 +01:39:34,020 --> 01:39:38,540 +التالي parabola + +915 +01:39:38,540 --> 01:39:48,090 +بالشكل اللي عندك هنا يبقى ال parabola بالخط + +916 +01:39:48,090 --> 01:39:52,090 +الأزرق يبقى Y يساوي 2X تربيع + +917 +01:40:00,700 --> 01:40:05,660 +يبقى دي إيش عملتلها؟ vertically stretch، stretch + +918 +01:40:05,660 --> 01:40:12,360 +إلى أعلى، يبقى هنا عملتلها سهم زي هيك وهذا stretch + +919 +01:40:12,360 --> 01:40:19,450 +إلى أعلى، طبعاً، يعني طب شو السبب؟ بقول اه لو كانت Y + +920 +01:40:19,450 --> 01:40:24,970 +تساوي X تربيع و حطيت X بواحد يبقى النقطة واحد و + +921 +01:40:24,970 --> 01:40:29,170 +واحدة تقع على المنحنة لكن عند الواحد اثنين X تربيع + +922 +01:40:29,170 --> 01:40:33,490 +وتكون جدّها إيش اثنين يبقى بتطلع بدل ما كانت هنا بتصير + +923 +01:40:33,490 --> 01:40:37,150 +وين هنا فوق و من هنا الرأس اللي بتيجي منها فوق يعني + +924 +01:40:37,150 --> 01:40:45,110 +stretch إلى أعلى نقطة ثانية جالي بدي نصف X تربيع + +925 +01:40:45,110 --> 01:40:50,150 +بيقول إذا بتضرب في رقم واحد على رقم أكبر ملاحظة + +926 +01:40:50,150 --> 01:40:55,030 +يعني بيصير كسر يبقى compress وين؟ Vertical يبقى + +927 +01:40:55,030 --> 01:41:04,160 +تضغط إلى أسفل يبقى لو كان هذه المحاور هذا محور X + +928 +01:41:04,160 --> 01:41:11,790 +وهذا محور Y وهذا المنحنى اللي عندنا بالشكل هذا يبقى + +929 +01:41:11,790 --> 01:41:18,470 +هذا Y تساوي X تربيع تمام؟ شو بدنا نعمل؟ بدنا نضغط + +930 +01:41:18,470 --> 01:41:21,170 +عليه على أسفل، لما نضغط عليه على أسفل، إيش بدّه + +931 +01:41:21,170 --> 01:41:26,050 +يحدث؟ بدّه يفتح المنحنة، يبقى أنا بدّه أمسك هيك و + +932 +01:41:26,050 --> 01:41:30,950 +أضغط عليه إلى أسفل، يبقى إيش بدّه يحصل؟ بدّه يفتح + +933 +01:41:30,950 --> 01:41:35,790 +المنحنة، يبقى بدّه يصير المنحنة اللي عندك هذا، + +934 +01:41:35,790 --> 01:41:37,510 +بالشكل هذا هيك + +935 +01:41:40,480 --> 01:41:49,200 +طبعاً يبقى هذا نصف X تربيع أو Y يساوي نصف X تربيع يبقى + +936 +01:41:49,200 --> 01:41:54,420 +هنا عملنا لوين إلى أسفل يبقى هذا عملنا إيش + +937 +01:41:54,420 --> 01:41:58,580 +compress في الأول شدينا العل هنا ال compress إلى + +938 +01:41:58,580 --> 01:42:04,000 +أسفل يبقى هنا حصل ضغط عليه اللي هو compress أو + +939 +01:42:04,000 --> 01:42:10,470 +انكماش إلى أسفل يبقى هذا الفرق ما بين الحالتين حتى + +940 +01:42:10,470 --> 01:42:17,130 +الآن خلصنا الحالة الأولى والثانية نمسحهم يا بغى + +941 +01:42:17,130 --> 01:42:22,450 +نمسح الحالة الأولى والثانية عشان نكمل الرسم تابعة + +942 +01:42:24,710 --> 01:42:29,910 +طيب بدنا نأتي لنمرة دال الضايلة D و E يبقى بدنا نأتي + +943 +01:42:29,910 --> 01:42:36,150 +لنمرة دال أصل الدالة قبل الواحد واثنين شو كانت جذر + +944 +01:42:36,150 --> 01:42:45,250 +ال X يبقى هذه المحاور هذا محور X وهذا محور Y وهذا + +945 +01:42:45,250 --> 01:42:52,930 +نقطة الأصل اللي هي Zero وهذا جذر ال X تمام؟ + +946 +01:42:53,380 --> 01:43:01,000 +طيب جذر ال X شو جاله؟ اثنين في الجذر والله في X + +947 +01:43:01,000 --> 01:43:08,740 +بيقول هنا لو ضربت رقم في ال X شو بيحصل؟ بيصير + +948 +01:43:08,740 --> 01:43:12,720 +compress هذه كانت اللي فوق الكلمة اللي فوقها + +949 +01:43:12,720 --> 01:43:19,510 +compress طبعاً يبقى بدك تضغط horizontally يبقى أنا + +950 +01:43:19,510 --> 01:43:23,810 +لما آتي اضغط على هذه أفقي ماشي بدي أحصلها؟ بدي + +951 +01:43:23,810 --> 01:43:29,390 +أسير لفوق يبقى بدّه يجيك الخط اللي عندك هذا فوق هذا + +952 +01:43:29,390 --> 01:43:35,750 +الجذر التربيعي للاثنين X و مش هنأكدلك لو كان هنا + +953 +01:43:35,750 --> 01:43:40,570 +الرقم واحد بيصير جذر الواحد بواحد بيصير النقطة هذه + +954 +01:43:40,570 --> 01:43:46,410 +واحد وواحد هذه بيصير واحد وقداش وجذر اثنين وهكذا + +955 +01:43:46,410 --> 01:43:51,050 +جذر اثنين وواحد وأربعة من عشرة تقريباً يعني أكبر + +956 +01:43:51,050 --> 01:43:56,950 +منها من الواحد وهكذا يبقى هنا حصلنا compress + +957 +01:43:56,950 --> 01:44:00,430 +قمتنا أفقي compress + +958 +01:44:02,160 --> 01:44:08,540 +أفقياً، تمام؟ يبقى خلصنا قصة جذر ال X، الحين بدي + +959 +01:44:08,540 --> 01:44:14,040 +أسأل سؤال وهتجاوبوني عليه غلط، السؤال هذا صارت + +960 +01:44:14,040 --> 01:44:17,900 +الدالة عندنا الجذر التربيعي لاثنين X، روحنا أضفنا + +961 +01:44:17,900 --> 01:44:24,720 +إيش؟ أضفنا إيش يعني؟ عشمال بمقدار؟ يالّا غلط، ماشي + +962 +01:44:24,720 --> 01:44:25,100 +الحاجة + +963 +01:44:28,070 --> 01:44:34,730 +الآن بدنا نعرف ليش غلط، تمام؟ سنة وبعدين عاد، + +964 +01:44:34,730 --> 01:44:39,010 +اسمع شوية إنتوا يعني، يبقى بدنا نعرف ليش كلامنا + +965 +01:44:39,010 --> 01:44:44,670 +هذا صار غلط، بقولك اه تعالَ نحسب، إحنا عندنا الجدر + +966 +01:44:44,670 --> 01:44:51,300 +التربيعي للاثنين X زائد واحد مظبوط هكذا طيب هذا هو + +967 +01:44:51,300 --> 01:44:56,280 +ال generator بيبقى اثنين عامل مشترك بيبقى ال X + +968 +01:44:56,280 --> 01:45:04,860 +زائد نصف مظبوط ولا لا مش ال X زائد نصف إحنا كانت هذه + +969 +01:45:04,860 --> 01:45:10,480 +لما بنطرح رقم أو بنجمعه لل X + +1001 +01:48:19,400 --> 01:48:26,400 +على الدالة و شيلت X و حطيت مكانها سالب X في المثلة + +1002 +01:48:26,400 --> 01:48:33,680 +بتجلب الدالة عبر مين؟ عبر محور Y تمام؟ إذا أنا هذا + +1003 +01:48:33,680 --> 01:48:39,300 +الرسم الحمرا بدي أشيل ال X بس و أحط مكانها سالب X + 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function تمام؟ واحد كان مديوس اللي هنا بطل؟ أيوة كيف كيف؟", "tokens": [6027, 20292, 31439, 2135, 37279, 16572, 5172, 16712, 6027, 1829, 23758, 5296, 28814, 1863, 3224, 7251, 3555, 4587, 7578, 11331, 33546, 1211, 6024, 116, 28480, 23758, 11933, 1829, 8592, 22807, 7251, 34268, 26890, 7251, 34268, 26890, 7401, 2445, 7251, 3555, 4587, 7578, 4724, 39648, 46740, 370, 2423, 290, 8978, 283, 307, 364, 7401, 2445, 46811, 10943, 22807, 36764, 24401, 25961, 3714, 16254, 41779, 13672, 1829, 34105, 4724, 9566, 1211, 22807, 36632, 2407, 3660, 9122, 33911, 9122, 33911, 22807], "avg_logprob": -0.3265427117106281, "compression_ratio": 1.565934065934066, "no_speech_prob": 0.0, "words": [{"start": 1097.21, "end": 1097.67, "word": "اللي", "probability": 0.762939453125}, {"start": 1097.67, "end": 1097.83, "word": " هو", "probability": 0.79052734375}, {"start": 1097.83, "end": 1098.21, "word": " main", "probability": 0.66357421875}, {"start": 1098.21, "end": 1099.19, "word": " تعريف", "probability": 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function", "probability": 0.947265625}, {"start": 1105.03, "end": 1105.73, "word": " يبقى", "probability": 0.9605712890625}, {"start": 1105.73, "end": 1106.23, "word": " بقول", "probability": 0.96044921875}, {"start": 1106.23, "end": 1106.61, "word": " له", "probability": 0.26806640625}, {"start": 1106.61, "end": 1107.05, "word": " so", "probability": 0.160400390625}, {"start": 1107.05, "end": 1107.79, "word": " ال", "probability": 0.51611328125}, {"start": 1107.79, "end": 1108.07, "word": " g", "probability": 0.48876953125}, {"start": 1108.07, "end": 1108.39, "word": " في", "probability": 0.76123046875}, {"start": 1108.39, "end": 1108.85, "word": " f", "probability": 0.849609375}, {"start": 1108.85, "end": 1109.63, "word": " is", "probability": 0.96533203125}, {"start": 1109.63, "end": 1110.69, "word": " an", "probability": 0.923828125}, {"start": 1110.69, "end": 1111.73, "word": " odd", "probability": 0.94091796875}, {"start": 1111.73, "end": 1112.69, "word": " function", 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المرة اللى قبل اللى فاتت فى section واحد و واحد مش جولنا بنشيل ال X و بنحط مكانها سلب X و بنشوف ماهو الناتج وهيه كتبناها لك فوق if of even تعني كذا و if of odd تعني كذا", "tokens": [4117, 33911, 5551, 9778, 3215, 8315, 37279, 16572, 5172, 2423, 754, 4032, 2423, 7401, 9673, 25720, 13672, 7578, 12174, 36150, 13672, 7578, 6156, 9307, 2655, 6156, 7578, 3541, 36764, 24401, 4032, 36764, 24401, 37893, 10874, 12610, 8315, 44945, 8592, 26895, 2423, 1783, 4032, 44945, 5016, 9566, 3714, 41361, 11296, 8608, 46152, 1783, 4032, 44945, 8592, 38688, 19446, 3224, 2407, 28239, 9307, 7435, 37037, 1829, 3224, 9122, 2655, 3555, 8315, 11296, 5296, 4117, 6156, 30543, 498, 295, 754, 37279, 22653, 9122, 15730, 4032, 498, 295, 7401, 37279, 22653, 9122, 15730], "avg_logprob": -0.2960069364971585, "compression_ratio": 1.7105263157894737, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1127.92, "end": 1128.64, "word": "كيف", "probability": 0.54437255859375}, {"start": 1128.64, "end": 1129.06, "word": 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"word": " مكانها", "probability": 0.9930013020833334}, {"start": 1136.88, "end": 1137.22, "word": " سلب", "probability": 0.257080078125}, {"start": 1137.22, "end": 1137.48, "word": " X", "probability": 0.93408203125}, {"start": 1137.48, "end": 1137.62, "word": " و", "probability": 0.8359375}, {"start": 1137.62, "end": 1137.96, "word": " بنشوف", "probability": 0.9801432291666666}, {"start": 1137.96, "end": 1138.34, "word": " ماهو", "probability": 0.80322265625}, {"start": 1138.34, "end": 1139.0, "word": " الناتج", "probability": 0.7171223958333334}, {"start": 1139.0, "end": 1140.24, "word": " وهيه", "probability": 0.7205403645833334}, {"start": 1140.24, "end": 1141.0, "word": " كتبناها", "probability": 0.91015625}, {"start": 1141.0, "end": 1141.3, "word": " لك", "probability": 0.951171875}, {"start": 1141.3, "end": 1141.92, "word": " فوق", "probability": 0.939697265625}, {"start": 1141.92, "end": 1142.74, "word": " if", "probability": 0.58544921875}, {"start": 1142.74, "end": 1143.06, 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6282.323125000039} \ No newline at end of file diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/jcb1zLJ06L8.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/jcb1zLJ06L8.srt new file mode 100644 index 0000000000000000000000000000000000000000..81f72f114ad429ef82de8aeec619116ab9b3f83d --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/jcb1zLJ06L8.srt @@ -0,0 +1,2578 @@ +1 +00:00:31,530 --> 00:00:37,090 +إذا فشلت اختبار المشتقة الثانية بنرجع لمين لاختبار + +2 +00:00:37,090 --> 00:00:41,410 +المشتقة الأولى لكن إحنا في شغلنا في الأمثلة مش + +3 +00:00:41,410 --> 00:00:46,350 +هنحاول نستخدم هذا إلا عند الضرورة ولا أظن أنه يلزم + +4 +00:00:46,350 --> 00:00:50,040 +بس بيلزم لمن لم يكن يقوم بالاستخدام و لمن لم يكن + +5 +00:00:50,040 --> 00:00:54,100 +يقوم بالاستخدام يعني في الغالب أثناء الشغل العملي + +6 +00:00:54,100 --> 00:00:58,720 +هستخدم اختبار المشتقة الأولى لمواضيع النهايات + +7 +00:00:58,720 --> 00:01:02,380 +العظمى والصغرى المعالية هستخدم اختبار المشتقة + +8 +00:01:02,380 --> 00:01:09,210 +الثانية لقياس الـconcavity لدالة ما طيب الآن وصلنا + +9 +00:01:09,210 --> 00:01:17,130 +إلى السؤال اللي إحنا بدنا إياه ضروري جدا كيف بدنا نرسم + +10 +00:01:17,130 --> 00:01:23,230 +المنحنيات مشان نجاوب على هذا السؤال بدنا نعمل اللي + +11 +00:01:23,230 --> 00:01:29,770 +هو عدة خطوات الخطوة الأولى بتقول لي ما يأتي بدنا + +12 +00:01:29,770 --> 00:01:34,810 +find the intercepts with the coordinate axes يعني + +13 +00:01:34,810 --> 00:01:41,230 +بدنا نجيب تقاطع المنحنى تبعنا مع محوري الإحداثيات + +14 +00:01:41,230 --> 00:01:47,030 +كيف بنحصل عليها؟ بحط مرة x بـ zero بجيب قيمة y بحط Y + +15 +00:01:47,030 --> 00:01:52,310 +بـ zero و بجيب قيمة X إن أمكن، إذا مش ممكن، بلاش يعني + +16 +00:01:52,310 --> 00:01:55,110 +إذا العملية شاقة أو صعبة، انسى الموضوع، اللي + +17 +00:01:55,110 --> 00:01:58,690 +السهلة، جيبها صعبة، سيبك منها يبقى الخطوة الأولى، + +18 +00:01:58,690 --> 00:02:02,830 +بدي أجيب نقاط تقاطع المنحنى مع محوري الإحداثيات + +19 +00:02:02,830 --> 00:02:07,270 +النقطة الثانية، بدي أجيب الـasymptotes إذا كانت + +20 +00:02:07,270 --> 00:02:11,150 +موجودة يعني لو كانت الـfunction العادية فيها عندي + +21 +00:02:11,150 --> 00:02:15,360 +asymptote لأ، ما عنديش الاسمتوت، يبقى مش مطالب فيهم، + +22 +00:02:15,360 --> 00:02:20,620 +يبقى أنا مطالب في الاسمتوت إذا كان عندي ده الـ + +23 +00:02:20,620 --> 00:02:24,540 +rational function فيها بسط ومقام، بدي أشوف في + +24 +00:02:24,540 --> 00:02:27,780 +عندي horizontal اسمتوت أم لا، في عندي oblique + +25 +00:02:27,780 --> 00:02:31,920 +اسمتوت أم لا، في عندي vertical اسمتوت أم لا، التي + +26 +00:02:31,920 --> 00:02:36,230 +سابقة دراستها مش في chapter تلاتة، في chapter + +27 +00:02:36,230 --> 00:02:41,270 +اتنين، مظبوط يبقى مدرس في chapter اتنين لازم أن هي + +28 +00:02:41,270 --> 00:02:45,570 +و عندها رسم في chapter أربعة النقطة التالتة بدي + +29 +00:02:45,570 --> 00:02:49,310 +أجيب المشتقة الأولى والثانية، طبعا المشتقة الأولى + +30 +00:02:49,310 --> 00:02:52,690 +منها بجيب الـ interval of increasing و الـ interval + +31 +00:02:52,690 --> 00:02:56,390 +of decreasing زي ما شوفنا في المحاضرة الماضية و + +32 +00:02:56,390 --> 00:02:59,750 +بجيب منها الـ local maximum و الـ local minimum + +33 +00:03:00,170 --> 00:03:03,610 +المشتقة الثانية بجيب منها الـ concave up و الـ + +34 +00:03:03,610 --> 00:03:08,650 +concave down لسه ما أخذناش مثال على تعيين الـ concave + +35 +00:03:08,650 --> 00:03:12,510 +up و الـ concave down لكن اتكلمنا عنها كنظرية في + +36 +00:03:12,510 --> 00:03:17,350 +المرة الماضية و كذلك من خلالها بدنا نحسب الـ + +37 +00:03:17,350 --> 00:03:21,410 +inflection point يبقى من خلال المشتقة الأولى بكون + +38 +00:03:21,410 --> 00:03:24,670 +جيبت أربعة اللي هو الـ local extremely فترات + +39 +00:03:24,670 --> 00:03:29,660 +التزايد والتناقص و الـ local extreme وهذا من وين؟ من + +40 +00:03:29,660 --> 00:03:33,580 +المشتقة الأولى خمسة بدي أجيبها من وين؟ من المشتقة + +41 +00:03:33,580 --> 00:03:38,120 +الثانية يعني ليس بضروري أجيب التنتين ورا بعض لأ + +42 +00:03:38,120 --> 00:03:41,700 +بجيب المشتقة الأولى وبعدين هيك بجيب الـ interval + +43 +00:03:41,700 --> 00:03:44,220 +increasing and decreasing و الـ local maximum و الـ + +44 +00:03:44,220 --> 00:03:47,800 +local minimum بعد هيك بروح بجيب المشتقة الثانية و + +45 +00:03:47,800 --> 00:03:50,840 +بروح بشوف الـ concavity للمنحنى و الـ reflection + +46 +00:03:50,840 --> 00:03:56,420 +points إن وجدت نقوة السلسة والاخيرة كل المعلومات + +47 +00:03:56,420 --> 00:04:00,540 +اللي جمعتها دي بتروح أستخدمها في الرسم أو هي اللي + +48 +00:04:00,540 --> 00:04:04,840 +هتسهلي عملية الرسم بدون ما أروح أعمل جدول زي ما + +49 +00:04:04,840 --> 00:04:09,480 +كنا في الثانوية حط جدول حط قيم السيناتات لقيم + +50 +00:04:09,480 --> 00:04:13,380 +الصادات أبدأ أرسم النقط و أوصل بينهم هذا كلام عفى + +51 +00:04:13,380 --> 00:04:18,070 +عليه الزمن لأ إن خلال فترات التزايد والتناقص + +52 +00:04:18,070 --> 00:04:20,610 +والـlocal maximum والـconcavity والـinfliction + +53 +00:04:20,610 --> 00:04:24,610 +points والتقاطع مع محاور الإحداثيات بتروح أرسم من + +54 +00:04:24,610 --> 00:04:31,590 +الرسمة تبعت هذه المسألة طيب لحد هنا stop انتهى + +55 +00:04:31,590 --> 00:04:35,730 +الجزء النظري تبع هذا الـsection لم يبقى إلا مجموعة + +56 +00:04:35,730 --> 00:04:39,390 +من الأمثلة لكن ضايل نقطة نظرية ببدأ أقولها لك في + +57 +00:04:39,390 --> 00:04:43,800 +حينها طبعا مش موجودة في الكتاب، لكن هي بتلزمني عند + +58 +00:04:43,800 --> 00:04:49,560 +عملية الرسم أول مثال بقول sketch the graph of the + +59 +00:04:49,560 --> 00:04:53,660 +following functions و أعطاني دالة Y تساوي X تكعيب + +60 +00:04:53,660 --> 00:04:59,440 +ناقص تلاتة X زائد تلاتة يبقى هذا منحنى من الدرجة + +61 +00:04:59,440 --> 00:05:05,460 +الثالثة لا في جسمه مطول ولا غيره يبقى أول خطوة بدي + +62 +00:05:05,460 --> 00:05:10,260 +أروح أجيب نقاط تقاطع المنحنى مع محوري الإحداثيات + +63 +00:05:10,460 --> 00:05:17,340 +إذا لو حطيت الـ X تساوي Zero بده تبقى الـ Y تساوي قد + +64 +00:05:17,340 --> 00:05:23,660 +إيش معناه هذا الكلام؟ إن النقطة Zero تلاتة lie on + +65 +00:05:23,660 --> 00:05:31,910 +the graph of الـ function F يبقى النقطة 0 3 طب لو + +66 +00:05:31,910 --> 00:05:37,150 +حطيت Y بـ 0 بصير صعب حالها يقول ليه شغال بحالي ليس + +67 +00:05:37,150 --> 00:05:41,190 +بالضرورة السهلة بيشتغلها مش السهلة بدنا إياها يبقى + +68 +00:05:41,190 --> 00:05:45,450 +انتهينا من الخطوة الأولى الخطوة الثانية جالي هتل + +69 +00:05:45,450 --> 00:05:50,450 +الـ asymptotes إن وجد هدفي الـ asymptote لو بدأ أخد + +70 +00:05:50,450 --> 00:05:53,190 +الـ limit لما الـ X تروح لما لا نهاية تطلع مع لا + +71 +00:05:53,190 --> 00:05:57,320 +نهاية أنا ما عنديش في المقام حتى أقول أخد الـ limit + +72 +00:05:57,320 --> 00:06:01,540 +لما بتروح ليمين وأبلغي يعني ما عنديش functional + +73 +00:06:01,540 --> 00:06:05,800 +function يبقى الخطوة هذه أنسى الموضوع اللي هو + +74 +00:06:05,800 --> 00:06:10,100 +الـassumption يبقى بداجي لمين للخطوة التالتة + +75 +00:06:10,100 --> 00:06:15,700 +المشتقة يبقى باجي بقوله الـ y prime يساوي تلاتة X + +76 +00:06:15,700 --> 00:06:22,280 +تربيع ناقص تلاتة يعني تلاتة في X تربيع ناقص واحد + +77 +00:06:22,280 --> 00:06:29,900 +يعني تلاتة يعني يساوي تلاتة في X ناقص واحد في X + +78 +00:06:29,900 --> 00:06:35,560 +زائد واحد تمام يبقى المشتقة زي ما ينتشر الـ + +79 +00:06:35,560 --> 00:06:40,600 +polynomial إذا معرفة for all X يبقى الـ critical + +80 +00:06:40,600 --> 00:06:46,330 +points باجيبهم فقط من خلال إنه أساوي هذه بقد إيش + +81 +00:06:46,330 --> 00:06:50,610 +بصفر انسى ما قالش لي اتلي critical لكن اللي أزمة + +82 +00:06:50,610 --> 00:06:55,090 +بالضارة بجيبها يبقى باجي بقوله بدي أشوف الإشارات + +83 +00:06:55,090 --> 00:07:00,430 +يبقى بروح بقوله بدي إشارة تلاتة في X ناقص واحد و + +84 +00:07:00,430 --> 00:07:03,790 +بقوله هذا الـ real line و هذا النقطة اللي هي main + +85 +00:07:03,790 --> 00:07:09,580 +لإن واحد بعد الواحد positive و قبلها negative يعني + +86 +00:07:09,580 --> 00:07:13,600 +لو حطيت قيم الـ X بعد الواحد زي اتنين تلاتة أربعة + +87 +00:07:13,600 --> 00:07:17,720 +بلاقي النتيجة موجبة دائما وأبدا لو حطيت قبل الواحد + +88 +00:07:17,720 --> 00:07:21,780 +زي Zero سالب واحد سالب اتنين الأخر بلاقيها سالبة + +89 +00:07:21,780 --> 00:07:25,760 +بعد ذلك بدنا نروح ناخد إشارة القوس الثاني اللي هو + +90 +00:07:25,760 --> 00:07:30,890 +X زائد واحد بياخد الـ zero تبع وين؟ عند السالب واحد + +91 +00:07:30,890 --> 00:07:35,310 +بعد السالب واحد positive و قبل السالب واحد معله + +92 +00:07:35,310 --> 00:07:43,110 +negative الآن بدي أجي أخد إشارة حاصل الضرب حاصل + +93 +00:07:43,110 --> 00:07:47,950 +الضرب اللي هو مين؟ تلاتة في x ناقص واحد في x زائد + +94 +00:07:47,950 --> 00:07:54,080 +واحد وهذا الـ real line وهذه الحدود الإقليمية اللي + +95 +00:07:54,080 --> 00:08:00,120 +عندنا لمن؟ لحاصل الضرب، يبقى هذه عند الواحد وهذه + +96 +00:08:00,120 --> 00:08:07,100 +عند السالب واحد الاثنين مضروبات في بعض ضربهم وبدي أضرب + +97 +00:08:07,100 --> 00:08:11,660 +الإشارات في بعض ضربهم يبقى هنا زائد هنا ناقص هنا + +98 +00:08:11,660 --> 00:08:17,480 +زائد يبقى في هذه الفترة كانت الدالة increasing هنا + +99 +00:08:17,480 --> 00:08:24,380 +صارت decreasing هنا رجعت increasing إذا بروح بقوله + +100 +00:08:24,380 --> 00:08:25,380 +ما يأتي + +101 +00:08:27,890 --> 00:08:36,710 +بعدين بقوله الـ F is increasing دالة تزايدية on + +102 +00:08:36,710 --> 00:08:44,530 +الفترة من سلب infinity لغاية سلب واحد and on و + +103 +00:08:44,530 --> 00:08:52,740 +كذلك على الفترة من واحد لغاية infinity الـ F is + +104 +00:08:52,740 --> 00:09:00,560 +decreasing ده تناقصية على الفترة من سالب واحد + +105 +00:09:00,560 --> 00:09:05,560 +لغاية واحد بعد هيك بدي Local Maximum و Local + +106 +00:09:05,560 --> 00:09:11,620 +Minimum بدي أخد F of سالب واحد يساوي برجع على رأس + +107 +00:09:11,620 --> 00:09:16,040 +المسألة من فوق وبعوض فيها يبقى سالب واحد تكعيب + +108 +00:09:16,040 --> 00:09:22,000 +سالب تلاتة في سالب واحد زائد تلاتة ويساوي سالب + +109 +00:09:22,000 --> 00:09:28,670 +واحد زائد تلاتة زائد تلاتة ويساوي قد إيش خمسة بعد ذلك + +110 +00:09:28,670 --> 00:09:35,190 +البداية يأخذ الـ F of واحد واحد تكعيب ناقص ثلاثة في + +111 +00:09:35,190 --> 00:09:42,290 +واحد زائد تلاتة ويساوي كم؟ واحد إذا بجي بقوله الـ F + +112 +00:09:42,290 --> 00:09:54,300 +has local maximum كم؟ خمسة at x يساوي سالب واحد and + +113 +00:09:54,300 --> 00:10:06,240 +local minimum اللي هو local minimum واحد at x + +114 +00:10:06,240 --> 00:10:12,700 +يساوي قد إيش؟ واحد إذا إنتهينا من مين؟ من الـ local + +115 +00:10:12,700 --> 00:10:17,640 +extrema ولا من الـ increasing و الـ decreasing؟ بيجي + +116 +00:10:17,640 --> 00:10:22,220 +بعد ذلك الـ concavity و الـ inflection points وهذا + +117 +00:10:22,220 --> 00:10:25,940 +يعتبر أول مثال على الـ concavity و الـ inflection + +118 +00:10:25,940 --> 00:10:30,440 +points إذا بدي أجي على مين؟ على المشتقة الأولى + +119 +00:10:30,440 --> 00:10:33,940 +اللي عندنا، شو بدي أعملها؟ بدي أجيب المشتقة + +120 +00:10:33,940 --> 00:10:39,960 +الثانية، إذا بروح باخد الـ F بابلي برايم of X اللي + +121 +00:10:39,960 --> 00:10:46,340 +بيجداش؟ ستة X والتلاتة مع السلامة يبقى هذه بدها + +122 +00:10:46,340 --> 00:10:54,100 +تساوي Zero only at X يساوي جداش Zero إذن احتمالي + +123 +00:10:54,100 --> 00:10:59,110 +الـ Zero هذه تبقى Inflection Point فيه احتمال الله + +124 +00:10:59,110 --> 00:11:04,750 +أعلم قد يكون وقد لا يكون، تمام؟ إذا بدنا نروح + +125 +00:11:04,750 --> 00:11:12,880 +ندرس إشارة اللي هو الـ 6X ما عنديش غيرها هذه الـ zero + +126 +00:11:12,880 --> 00:11:16,600 +بتاخد الـ zero لو جيت بعد الـ zero القيمة هذه مالها + +127 +00:11:16,600 --> 00:11:22,820 +موجبة يبقى هذه موجبة لو جيت قبل الـ zero يعني + +128 +00:11:22,820 --> 00:11:27,520 +المشتقة الثانية سالبة بقى يبقى المنحنى concave + +129 +00:11:27,520 --> 00:11:35,280 +down الثانية موجبة يبقى المنحنى concave up تمام؟ + +130 +00:11:35,280 --> 00:11:38,140 +إذا بروح بقول ما يأتي + +131 +00:11:45,110 --> 00:11:50,970 +طبعا الدالة polynomial فهي متصلة على كل real line + +132 +00:11:50,970 --> 00:11:53,610 +بلا استثناء + +133 +00:12:10,380 --> 00:12:22,920 +is concave down on من سلب infinity لغاية zero and + +134 +00:12:22,920 --> 00:12:33,340 +concave up on الفترة من zero لغاية infinity الدالة + +135 +00:12:33,340 --> 00:12:37,360 +معرفة عند الـ Zero يبقى مجال معرفة يعني الدالة + +136 +00:12:37,360 --> 00:12:42,880 +متصلة عند الـ Zero والدالة غيرت اتجاه الـ Concavity + +137 +00:12:42,880 --> 00:12:50,600 +إذا في Inflection point يبقى الـ F is continuous + +138 +00:12:50,600 --> 00:13:06,320 +for all X معناته إنها كون الـ F is continuous at x + +139 +00:13:06,320 --> 00:13:11,140 +يساوي زيرو and + +140 +00:13:11,140 --> 00:13:19,980 +الـ F it change its concavity at + +141 +00:13:27,590 --> 00:13:39,670 +هنا بده يعطينا there is an inflection point + +142 +00:13:51,490 --> 00:14:00,630 +تلاتة هذا معناه زيرو وتلاتة is an inflection + +143 +00:14:00,630 --> 00:14:06,070 +point طيب + +144 +00:14:06,070 --> 00:14:07,310 +تمام خلصنا + +145 +00:14:10,750 --> 00:14:14,670 +المغنقة في حالة الـ increasing و الـ decreasing قلنا + +146 +00:14:14,670 --> 00:14:19,560 +فقط إذا المشتق أكبر من zero على الـ open interval + +147 +00:14:19,560 --> 00:14:24,460 +يبقى increasing أو decreasing على الـ closed + +148 +00:14:24,460 --> 00:14:29,140 +interval بس في الـ concurrent انسى الموضوع بس باخد + +149 +00:14:29,140 --> 00:14:33,400 +الفترة لأن عند هذه النقطة بصير انقلاب ما بقدر + +150 +00:14:33,400 --> 00:14:37,480 +تعتبرها مع الأولى ولا بتقدر تعتبرها مع مين؟ مع + +151 +00:14:37,480 --> 00:14:43,460 +الثانية طيب هيك إحنا جبنا كل المعلومات من خلال هذه + +152 +00:14:43,460 --> 00:14:48,140 +المعلومات بدنا نروح نرسم الرسمة فبجي بقول هذه + +153 +00:14:48,140 --> 00:14:55,080 +المحاور اللي عندنا هذا محور X هذا محور Y هذه نقطة + +154 +00:14:55,080 --> 00:15:01,990 +الأصل اللي هي Zero عندما ترسم أول خطوة ترسمها هي + +155 +00:15:01,990 --> 00:15:06,930 +الاسمتوتز، لو ما عنديش اسمتوتز، يبقى ثاني الخطوة + +156 +00:15:06,930 --> 00:15:10,770 +بدور على الـ local maximum و الـ local minimum، يبقى + +157 +00:15:10,770 --> 00:15:16,210 +إحنا عندنا local maximum خمسة يعني عندي السلب + +158 +00:15:16,210 --> 00:15:21,130 +واحد وخمسة، وين السلب واحد؟ يبقى باجي بقول له هي + +159 +00:15:21,130 --> 00:15:25,670 +النقطة، هي السلب واحد وبدأ أطلع خمسة، يبقى هذه + +160 +00:15:25,670 --> 00:15:31,210 +السلب واحد وخمسة، يبقى فيها عندي local maximum، + +161 +00:15:31,210 --> 00:15:36,070 +هاي حاطط جوس local maximum في عندي local minimum + +162 +00:15:36,070 --> 00:15:43,250 +عنده نقطة واحد وواحد يبقى باجي النقطة هي النقطة + +163 +00:15:43,250 --> 00:15:47,890 +واحد وهي النقطة الثانية اللي هنا واحد يبقى هذه + +164 +00:15:47,890 --> 00:15:53,150 +واحد وواحد عند local minimum بالشكل اللي عندنا هذا + +165 +00:15:53,700 --> 00:16:02,620 +بعد هيك تعاليش بيقول لي بيقول لي إن الـ F + +166 +00:16:02,620 --> 00:16:08,120 +دل تزايدية من سالب infinity لغاية سالب واحد من + +167 +00:16:08,120 --> 00:16:13,710 +سالب infinity لغاية سالب واحد يبقى دل تزايدية يبقى + +168 +00:16:13,710 --> 00:16:18,530 +المعناته بيجي من تحتنا وضل طالع لغايتها، يبقى + +169 +00:16:18,530 --> 00:16:22,990 +المنحنى هذا بيجيني بالشكل هذا هاي وهيك، دلتة + +170 +00:16:22,990 --> 00:16:28,170 +زيودية، تمام؟ جالي من سالب واحد إلى واحد، + +171 +00:16:28,170 --> 00:16:33,820 +decreasing يبقى الدالة تناقصية، إذا المنحنى هيجيني + +172 +00:16:33,820 --> 00:16:40,640 +هكذا، بالضبط تماما. وبعد ذلك، جالي من واحد إلى + +173 +00:16:40,640 --> 00:16:46,060 +انفينيتي، الدالة كمان تزايدية، يبقى الدالة بتبقى + +174 +00:16:46,060 --> 00:16:51,720 +طالعة إلى ما + +201 +00:20:10,280 --> 00:20:17,140 +الفرحان Y تساوي هذا سؤال اتنين Y تساوي واحد زائد X + +202 +00:20:17,140 --> 00:20:26,280 +تربيع على واحد ناقص X تربيع السؤال + +203 +00:20:26,280 --> 00:20:32,560 +هو هل الدالة معرفة عند الواحد والسالب واحد؟ يبقى + +204 +00:20:32,560 --> 00:20:40,040 +هدول مش هيظهرولي أثناء الرسم يبقى هنا بقوله هذه ال + +205 +00:20:40,040 --> 00:20:45,880 +X ممنوعة تساوي واحد والـ X ممنوعة تساوي سالب واحد + +206 +00:20:45,880 --> 00:20:51,960 +لإن عند هذين الدالة is undefined غير معرفة + +207 +00:20:51,960 --> 00:20:57,920 +طيب بدنا نبدأ نجيب تقاطعاتها مع محوري الإحداثيات + +208 +00:20:57,920 --> 00:21:06,620 +يبقى بدي أجي أخد أنه لو كانت الـ X تساوي Zero ثم Y + +209 +00:21:06,620 --> 00:21:08,540 +تساوي كده؟ واحد + +210 +00:21:13,220 --> 00:21:17,200 +يبقى الـ Y هو اللي بتساوي 0 واحد زي الـ X تربيع ممكن + +211 +00:21:17,200 --> 00:21:22,940 +تساوي 0 يبقى has no solution لا يمكن لمجموعة + +212 +00:21:22,940 --> 00:21:28,800 +كميتين موجبتين أن يساوي صفرا وبالتالي انسى الموضوع + +213 +00:21:28,800 --> 00:21:35,580 +يبقى هاي جبت النقطة هذه واحدة فقط اللي هو 01 on + +214 +00:21:35,580 --> 00:21:44,210 +the graph يبقى هذه النقطة تقع وين تقع على الملحنة + +215 +00:21:48,010 --> 00:21:53,350 +طيب نبدأ الآن نشغل شغلنا في الاشتقاق لكن قلت لك + +216 +00:21:53,350 --> 00:21:57,670 +المرة الماضية إذا عندك دالة numerator و دالة مقام و + +217 +00:21:57,670 --> 00:22:03,350 +درجة الـ numerator أكبر من أو تساوي المقام يبقى أول خطوة + +218 +00:22:03,350 --> 00:22:10,110 +نفضل نعملها قسمة مطولة إذا بيدوّح أجسم الـ X تربيع + +219 +00:22:10,110 --> 00:22:18,670 +زائد واحد على مين؟ على ناقص X تربيع زائد واحد طبعا + +220 +00:22:18,670 --> 00:22:23,730 +أي واحد ناقص X تربيع أنا ناقص X تربيع زي واحد X + +221 +00:22:23,730 --> 00:22:29,590 +تربيع على ناقص X تربيع فيها كم؟ ناقص واحد بيبقى في + +222 +00:22:29,590 --> 00:22:35,410 +سالب X تربيع X تربيع وهنا كم؟ سالب واحد هذه موجبة + +223 +00:22:35,410 --> 00:22:42,260 +بيصير سالبة وهذه بيصير موجبة بيبقى لدي كم؟ إذا صرت + +224 +00:22:42,260 --> 00:22:49,900 +الدالة Y تساوي سالب واحد زائد اتنين على واحد ناقص + +225 +00:22:49,900 --> 00:22:55,880 +X تربيع أو ممكن تحطها على الشكل التالي زائد اتنين + +226 +00:22:55,880 --> 00:23:02,560 +هذه الفرق بين المربعين واحد ناقص X في واحد زائد X + +227 +00:23:02,560 --> 00:23:07,550 +يبقى هي حطيناها بالشكل اللي عندنا هذا يبقى بعد ما + +228 +00:23:07,550 --> 00:23:12,550 +جيبنا النقاط التقاطع أو نقطة التقاطع مع محاور + +229 +00:23:12,550 --> 00:23:18,570 +الإحداثية الـ (0,1) بدأ أجيب من المشتقة الأولى أو + +230 +00:23:18,570 --> 00:23:23,550 +قبلها بدأ أجيب من الـ Asymptotes يبقى باجي بقوله + +231 +00:23:23,550 --> 00:23:28,250 +في عندي Obligate asymptote؟ لأ لإن درجة البسط + +232 +00:23:28,250 --> 00:23:32,980 +درجة المقام ماهياش أعلى منها بمقدار واحد يبقى بتروح + +233 +00:23:32,980 --> 00:23:38,100 +أدور وين؟ على الـ horizontal يبقى بدي أخد limit للـ Y + +234 +00:23:38,100 --> 00:23:43,920 +لما الـ X بدها تروح لزائد أو ناقص infinity أي من + +235 +00:23:43,920 --> 00:23:49,390 +التنتين يبقى هذا الكلام بدي يساوي limit لما الـ X + +236 +00:23:49,390 --> 00:23:54,450 +بدي تروح لزائد أو ناقص infinity طبعا هتحطيني نفس + +237 +00:23:54,450 --> 00:23:58,530 +النتيجة من البسط polynomial والمقام polynomial + +238 +00:23:58,530 --> 00:24:05,370 +يبقى واحد زائد X تربيع على واحد ناقص X تربيع بروح + +239 +00:24:05,370 --> 00:24:11,600 +نقسم كله من البسط والمقام على يبقى X تربيع يبقى هذا + +240 +00:24:11,600 --> 00:24:15,960 +الكلام limit لما الـ X بده يروح لزائد أو ناقص + +241 +00:24:15,960 --> 00:24:22,140 +infinity لواحد على X تربيع زائد واحد واحد على X + +242 +00:24:22,140 --> 00:24:28,900 +تربيع ناقص واحد يبقى النتيجة كده؟ سالب واحد طبعا + +243 +00:24:28,900 --> 00:24:34,380 +هذا بالزيرو وهذا بالزيرو يبقى كده؟ يبقى سالب واحد + +244 +00:24:34,380 --> 00:24:43,420 +يبقى كذلك Y تساوي سالب واحد is a horizontal + +245 +00:24:43,420 --> 00:24:48,220 +asymptote + +246 +00:24:48,220 --> 00:24:51,360 +تمام تمام + +247 +00:24:54,710 --> 00:25:00,810 +الرقم اللي يجعل المقام يساوي 0 إذا احتمال X يساوي + +248 +00:25:00,810 --> 00:25:06,430 +واحد وكذلك X يساوي سالب واحد هذين يكونوا Vertical + +249 +00:25:06,430 --> 00:25:11,890 +Asymptotes إذا بتروح أخد limit لما الـ X بده يساوي + +250 +00:25:11,890 --> 00:25:16,810 +بده تروح لسالب واحد مثلا من جهة اليمين اليمين لل + +251 +00:25:16,810 --> 00:25:21,920 +function اللي عندنا هذه اليمين سالب واحد زائد اتنين + +252 +00:25:21,920 --> 00:25:28,320 +على واحد ناقص x في واحد زائد x هو يساوي المقدار + +253 +00:25:28,320 --> 00:25:33,640 +الثابت هذا مالوش دعوة وهذا زائد اتنين على احنا + +254 +00:25:33,640 --> 00:25:39,700 +رايحين اللي يسلب واحد من جهات اليمين تمام؟ إذا هذا + +255 +00:25:39,700 --> 00:25:45,900 +هذا ماعندوش مشكلة في هذه الحالة، يبقى هذا بظل واحد + +256 +00:25:45,900 --> 00:25:53,280 +سالب سالب واحد، مصبوط؟ يبقى هذا بصير واحد زائد + +257 +00:25:53,280 --> 00:26:02,700 +واحد، لما أروحلي سالب واحد من جهة اليمين يعني أكبر + +258 +00:26:02,700 --> 00:26:07,060 +من سالب واحد يعني سالب تسعة من عشرة مثلا إذا هذا + +259 +00:26:07,060 --> 00:26:15,680 +بيبقى very small positive يبقى very small positive + +260 +00:26:15,680 --> 00:26:19,020 +quantity هذا بيقدّش بصغير + +261 +00:26:26,590 --> 00:26:32,330 +بينفينيتي يبقى سالب واحد زائد انفينيتي بقدّاش + +262 +00:26:32,330 --> 00:26:38,510 +بينفينيتي يبقى بناء عليه الـ X يساوي سالب واحد is a + +263 +00:26:38,510 --> 00:26:43,070 +vertical asymptote وليس بالضرورة انك تروح تحسبها + +264 +00:26:43,070 --> 00:26:47,450 +من وين؟ من عندي الشمال احنا نقول هادي أو هادي سيال + +265 +00:26:47,450 --> 00:26:52,230 +ليس بدنا نروح نحسب الاتنين إذا لو روحت أخدت limit + +266 +00:26:52,230 --> 00:26:57,150 +لما الـ X بدأ تروح للواحد مثلا من جهة الشمال اللي + +267 +00:26:57,150 --> 00:27:00,190 +هي النقطة التانية معناها تخلصنا من السالب واحد بدأ + +268 +00:27:00,190 --> 00:27:05,970 +نروح لمن؟ للواحد لمن؟ لسالب واحد زائد اتنين على + +269 +00:27:05,970 --> 00:27:12,210 +واحد ناقص X في واحد زائد X يبقى هذا الكلام يساوي + +270 +00:27:12,210 --> 00:27:18,940 +سالب واحد زائد اتنين على. احنا رايحين للواحد من جهة + +271 +00:27:18,940 --> 00:27:24,140 +الشمال. من جهة الشمال يعني اقل من واحد بكثير. يبقى + +272 +00:27:24,140 --> 00:27:33,940 +القوس هذا very small positive. يبقى هذا very small + +273 +00:27:33,940 --> 00:27:38,280 +positive quantity. تمام؟ + +274 +00:27:40,930 --> 00:27:48,630 +وهذا واحد زائد واحد طيب، لاحظ في الحالة الأولى لما + +275 +00:27:48,630 --> 00:27:53,690 +قلنا سالب واحد من جهة اليمين سالب واحد من جهة + +276 +00:27:53,690 --> 00:27:58,190 +اليمين يعني سالب تسعة من عشرة لما جهتها الجثة ده + +277 +00:27:58,190 --> 00:28:01,730 +سالب تسعة بقال very small positive وهذا صار سالب + +278 +00:28:01,730 --> 00:28:07,370 +واحد وهنا واحد يعني سالب سالب واحد صار موجب بواحد + +279 +00:28:07,370 --> 00:28:13,250 +وبالتالي أتتني من نفس النتيجة يبقى هذه أتتني سالب + +280 +00:28:13,250 --> 00:28:19,670 +واحد زائد infinity اللي هو infinity معناته الخطين + +281 +00:28:19,670 --> 00:28:26,710 +اللي اتنين هدول are vertical asymptotes يبقى الـ X + +282 +00:28:26,710 --> 00:28:33,910 +يساوي سالب واحد and الـ X بده يساوي واحد are two + +283 +00:28:33,910 --> 00:28:38,990 +vertical asymptotes + +284 +00:28:44,300 --> 00:28:47,940 +يبقى خلاصنا قصة الـ Asymptotes، بدنا نروح لمين + +285 +00:28:47,940 --> 00:28:55,300 +الآن؟ للاشتقاق، يبقى بالدليل الـY'Y أساوي + +286 +00:28:57,900 --> 00:29:02,120 +ممكن نشتق من هذه أو من هذه تماما، لكن لو + +287 +00:29:02,120 --> 00:29:08,120 +نشتقّ منها، ده أسهل شوية، مصبوط؟ يعني هذه كأنها + +288 +00:29:08,120 --> 00:29:13,040 +مشتقة السالب واحد مع السلامة، وبضالي اتنين مالكش + +289 +00:29:13,040 --> 00:29:19,400 +دعوة، وهذا السالب واحد على المقدار تربيع، واحد على + +290 +00:29:19,400 --> 00:29:25,950 +واحد ناقص X تربيع الكل تربيع في مشتقة مداخل القوس + +291 +00:29:25,950 --> 00:29:34,970 +وجدّاش سالب اتنين X، مظبوط؟ يبقى النتيجة صارت أربع + +292 +00:29:34,970 --> 00:29:43,200 +X على واحد ناقص X تربيع لكل تربيع هذه لو سويتها + +293 +00:29:43,200 --> 00:29:49,640 +بالـ Zero معناته ان X تساوي قدّاش؟ يبقى هذا بده يعطيلك + +294 +00:29:49,640 --> 00:29:54,760 +أن X أو خلاص مش لازم ان هذي Critical Points قد + +295 +00:29:54,760 --> 00:29:59,260 +تكون Local Maximum أو قد تكون Local Minimum إذا + +296 +00:29:59,260 --> 00:30:05,750 +بدنا نروح نبحث الإشارات نبحث الإشارات هذه لو روحت + +297 +00:30:05,750 --> 00:30:12,730 +قلت لك أربعة X على واحد ناقص X في واحد زائد X لكل + +298 +00:30:12,730 --> 00:30:18,730 +تربيع يبقى هذه تربيع وهذه إيه؟ تربيع إذا بدي أروح + +299 +00:30:18,730 --> 00:30:24,830 +أخد إشارة الأربعة X وهذا اللي يا الله إني بتاخد الـ + +300 +00:30:24,830 --> 00:30:30,070 +zero تبعها وين؟ عند الـ zero بعد الـ zero positive + +301 +00:30:30,070 --> 00:30:39,000 +وقبل الـ zero إيه؟ نقات، نجي نأخذ إشارة واحد ناقص X + +302 +00:30:39,000 --> 00:30:45,520 +لكل تربيع، إذا أخذت Zero تبعها وين؟ عند الواحد، + +303 +00:30:45,520 --> 00:30:51,700 +بعد الواحد positive، وقبل الواحد positive لأنها + +304 +00:30:51,700 --> 00:30:59,530 +كمية مربعة لكن لو ماكنتش تربيع لأصبحت بعد الواحد + +305 +00:30:59,530 --> 00:31:05,430 +سالب وقبل الواحد موجب تمام؟ طيب يبقى بدّاجي أخد + +306 +00:31:05,430 --> 00:31:11,810 +إشارة الواحد زائد x لكل تربيع تاخد الـ zero تباعها + +307 +00:31:11,810 --> 00:31:18,180 +وين؟ عند السالب واحد بعده برضه positive وجاب له + +308 +00:31:18,180 --> 00:31:25,420 +positive لأن كمية مربعة بدي أخد إشارة الآن اللي هو + +309 +00:31:25,420 --> 00:31:32,160 +أربعة X على واحد ناقص X الكل تربيع واحد زائد X + +310 +00:31:32,160 --> 00:31:38,320 +الكل تربيع ونيجي نحدد الحدود الإقليمية + +311 +00:31:48,450 --> 00:31:56,300 +الأولى positive والثانية negative والثالثة negative + +312 +00:31:56,300 --> 00:32:01,900 +والرابعة negative يبقى الدالة كانت نازلة وظلت نازلة + +313 +00:32:01,900 --> 00:32:04,620 +وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت + +314 +00:32:04,620 --> 00:32:05,020 +نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة + +315 +00:32:05,020 --> 00:32:08,060 +وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت + +316 +00:32:08,060 --> 00:32:18,300 +نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظل + +317 +00:32:25,760 --> 00:32:32,000 +الفترة من عند السالب infinity لغاية قدّاش؟ سالب واحد + +318 +00:32:32,000 --> 00:32:37,620 +as an open interval لأن عند السالب واحد الدالة مش + +319 +00:32:37,620 --> 00:32:45,140 +معرفة حط معاها اتحاد سالب واحد وzero وبدنا نقفلها + +320 +00:32:45,140 --> 00:32:49,940 +من عند الـ zero لأن ده اللي عندها معرفة بعد هيك الـ + +321 +00:32:49,940 --> 00:32:58,600 +if is increasing ده اللي تنقصيه على الفترة من عند + +322 +00:32:58,600 --> 00:33:05,000 +الـ zero لغاية الواحد عند الواحد مش معرفة اتحاد + +323 +00:33:05,000 --> 00:33:13,070 +الواحد و infinity طيب في عندي local maximum هل يوجد + +324 +00:33:13,070 --> 00:33:17,950 +local maximum؟ الله يبعث لك الله يقول ماعنديش إلا + +325 +00:33:17,950 --> 00:33:24,590 +local minimum وين؟ عند zero عند zero حسبناها عند + +326 +00:33:24,590 --> 00:33:31,250 +zero طلعت واي بقدّاش؟ واحد يبقى باجي بقوله الـ F + +327 +00:33:31,250 --> 00:33:41,480 +has local minimum واحد at x يساوي زيرو وانتهينا منها + +328 +00:33:41,480 --> 00:33:45,060 +.الآن الـ increase والـ decrease اللي خلصنا منه + +329 +00:33:45,060 --> 00:33:51,160 +يبقى بدنا نروح لمين؟ للمشتقة الثانية. واين المشتقة + +330 +00:33:51,160 --> 00:33:56,340 +اللي اشتقناها احنا اصلا؟ اللي هي هذه. مصبوط؟ اللي هي + +331 +00:33:56,340 --> 00:33:59,880 +اللي بدّي أروح اشتغل هذه بتطلع روحي، بس هذه أسهل كتير + +332 +00:33:59,880 --> 00:34:05,340 +. مصبوط؟ يبقى بدي أروح أجيبله المشتقة الثانية من + +333 +00:34:05,340 --> 00:34:13,260 +هذه هيها. هذا الجذر اللي بده أخذه هو المشتق اللي + +334 +00:34:13,260 --> 00:34:17,420 +هو اللي بده أجيبه هو المشتق الثاني يبقى باجي بقوله + +335 +00:34:17,420 --> 00:34:26,150 +يبقى الـ Y double prime يبقى المقام أي تربيع؟ في مشتقة + +336 +00:34:26,150 --> 00:34:32,810 +البسط اللي هو باربع ناقص البسط في مشتقة المقام + +337 +00:34:32,810 --> 00:34:39,470 +الأس في القوس مرفوع لنفس الأس مطروح من واحد في + +338 +00:34:39,470 --> 00:34:46,570 +مشتقة مداخل القوس يبقى هذه المقام في مشتقة البسط + +339 +00:34:46,570 --> 00:34:52,750 +ناقص البسط في مشتقة المقام الأس في القوس مرفوع + +340 +00:34:52,750 --> 00:34:57,890 +لنفس الأس مطروح منه واحد في مشتقة مداخل القوس كل + +341 +00:34:57,890 --> 00:35:06,890 +هذا maximum على واحد ناقص X تربيع لكل أس أربعة طيب + +342 +00:35:06,890 --> 00:35:08,930 +تعال نشوف كيف بدأت أصف هذه + +343 +00:35:13,520 --> 00:35:20,120 +إذا بقدر أخد اتنين في اتنين كمان بأربع عامل مشترك + +344 +00:35:20,120 --> 00:35:27,700 +يعني بقدر أخد أربعة في واحد ناقص X تربيع عامل + +345 +00:35:27,700 --> 00:35:33,860 +مشترك كدهش مضال لإن هنا واحد ناقص X تربيع فقط، + +346 +00:35:33,860 --> 00:35:40,370 +نيجي هنا الجذر هذا راح والأربعة دي راحت ضل سالب في + +347 +00:35:40,370 --> 00:35:48,890 +سالب موجب وعندك X تربيع، يبقى ضل عند هنا موجب أربع + +348 +00:35:48,890 --> 00:35:54,010 +X تربيع مظبوط هيك؟ هذه الأربعة عادي برا بقال عندك + +349 +00:35:54,010 --> 00:35:59,070 +اتنين في اتنين بأربع X في X ب X تربيع والسالب + +350 +00:35:59,070 --> 00:36:05,850 +في سالب بموجب تمام؟ كل هذا على مين؟ على واحد ناقص + +351 +00:36:05,850 --> 00:36:10,590 +X تربيع لكل قوس أربعة أظن الجذر هذا بيروح مع + +352 +00:36:10,590 --> 00:36:15,430 +الأربعة اللي تحت هذه وبالتالي بتصفى المسألة إلى + +353 +00:36:15,430 --> 00:36:22,730 +أربعة في مين؟ في واحد زائد ثلاثة X تربيع على واحد + +354 +00:36:22,730 --> 00:36:31,750 +ناقص X تربيع الكل تكعيب طيب تمام هذه لو سويتها بال + +355 +00:36:31,750 --> 00:36:39,000 +zero بتجيب لي نتيجة Has no solution يبقى الآن لو قلت + +356 +00:36:39,000 --> 00:36:46,780 +له yw prime يساوي أربعة في واحد زائد ثلاثة x تربيع + +357 +00:36:46,780 --> 00:36:53,880 +على مين؟ على واحد ناقص x الكل تكعيب واحد زائد x الكل + +358 +00:36:53,880 --> 00:37:03,580 +تكعيب هذه تساوي zero has no solution بتجيب ليش ولا + +359 +00:37:03,580 --> 00:37:09,960 +قيمة ليش؟ لأن لا يمكن لمجموعة كميتين موجبتين + +360 +00:37:09,960 --> 00:37:15,840 +انها تساوي Zero يبقى هذه مالهاش حل بالبلد هيك لو + +361 +00:37:15,840 --> 00:37:20,000 +سويتها بالـ Zero يبقى تصير ثلاثة X تربيع زائد واحد + +362 +00:37:20,000 --> 00:37:25,730 +يساوي Zero يبقى ثلاثة X تربيع يساوي سالب واحد هل + +363 +00:37:25,730 --> 00:37:31,910 +يُعقل كمية مربعة تساوي قيمة سالبة؟ يبقى هذه لا حلول + +364 +00:37:31,910 --> 00:37:35,310 +على الريال في الـ complex ماشي إلا حل بس في + +365 +00:37:35,310 --> 00:37:41,350 +الريال عندنا مالهاش حل تماما هل الـ X يساوي سالب + +366 +00:37:41,350 --> 00:37:46,710 +واحد والـ X يساوي واحد ممكن يكون inflection point؟ + +367 +00:37:47,810 --> 00:37:54,170 +لأنها غير معرفة عندهم يبقى معناها خليني أدرس + +368 +00:37:54,170 --> 00:37:59,470 +الإشارات اللي عندنا ونشوف لون بدنا نوصل يبقى أنا + + +401 +00:41:32,640 --> 00:41:40,760 +أو because دوري because ال + +402 +00:41:40,760 --> 00:41:46,320 +F is not continuous + +403 +00:41:48,530 --> 00:41:55,750 +مع الاكس يساوي سالب واحد عند الاكس يساوي واحد + +404 +00:42:05,390 --> 00:42:09,690 +مشان نرسم يبقى احنا عندنا y تساوي سالب واحد + +405 +00:42:09,690 --> 00:42:14,510 +horizontal واحد و سالب واحد اللي هو ال vertical + +406 +00:42:14,510 --> 00:42:20,550 +asymptotes وعند المنحنية مرضه نقطة zero واحد + +407 +00:42:43,950 --> 00:42:47,790 +خلّي بالك هنا قبل + +408 +00:42:47,790 --> 00:42:50,990 +قليل في السؤال اللي جابله أول شغلة بنفسه من ال + +409 +00:42:50,990 --> 00:42:56,490 +asymptotes يبقى أنا عند ال asymptote ال X يساوي + +410 +00:42:56,490 --> 00:43:04,050 +واحد و سالب واحد يبقى لو روحت قلت هذا الخط الرأسي + +411 +00:43:04,050 --> 00:43:12,300 +اللي هو من ال X يساوي واحد وجيت من الناحية التانية + +412 +00:43:12,300 --> 00:43:20,040 +وعلى نفس البعد وقلت هذا ال X يساوي سالب واحد فيه + +413 +00:43:20,040 --> 00:43:25,440 +كمان horizontal asymptote Y يساوي سالب واحد يبقى + +414 +00:43:25,440 --> 00:43:34,260 +هناك هذا الخط المنقط ل Y تساوي سالب واحد يبقى + +415 +00:43:34,260 --> 00:43:39,130 +هدول ال asymptotes اللي عندنا بعد هيك جال لي في + +416 +00:43:39,130 --> 00:43:44,530 +عندي local minimum عند ال zero والواحد يبقى عند ال + +417 +00:43:44,530 --> 00:43:50,190 +zero والواحد في عندي local minimum يبقى المنحنة + +418 +00:43:50,190 --> 00:43:56,270 +هيكون مفتوح إلى أعلى بهذا الشكل غير هيك انسى طيب هي + +419 +00:43:56,270 --> 00:44:01,110 +عندنا النقطة سالب واحد وهي عندنا النقطة واحد من + +420 +00:44:01,110 --> 00:44:06,710 +سالب واحد إلى زيرو هل الدالة تزايدية ولا تناقصية + +421 +00:44:06,710 --> 00:44:12,890 +يبقى من سالب واحد إلى زيرو الدالة decreasing طيب + +422 +00:44:12,890 --> 00:44:17,890 +تناقصية وهذا ال asymptote إذا بتبقى نازلة مع مين؟ + +423 +00:44:17,890 --> 00:44:22,730 +مع ال asymptote جاية مع ال asymptote منفر وأجت + +424 +00:44:22,730 --> 00:44:28,690 +نازلة بهذا الشكل من Zero لواحد ما لها increasing + +425 +00:44:28,690 --> 00:44:33,070 +يبقى increasing و بتيجي تطلع مع ال asymptote بهذا + +426 +00:44:33,070 --> 00:44:39,630 +الشكل طيب نجي نكمل الآن لو جيت من سالب infinity + +427 +00:44:39,630 --> 00:44:44,430 +لغاية سالب واحد من سالب infinity لسالب واحد + +428 +00:44:44,430 --> 00:44:51,250 +decreasing الدالة تناقصية تناقصية بس أنا مش عارف + +429 +00:44:51,250 --> 00:44:56,310 +هل هي فوق ولا تحت مشان أعرف فوق ولا تحت بروح أنا + +430 +00:44:56,310 --> 00:45:02,000 +بحسبها مثلا عندي سالب اثنين أشوف أين تجي عند السلم + +431 +00:45:02,000 --> 00:45:06,000 +هل فوق إذا فوق بيكون خلاص أنت هنا من الجسر تحت + +432 +00:45:06,000 --> 00:45:10,640 +يبقى أنت هنا يبقى بتروح أشيبله F في جداش وسالب + +433 +00:45:10,640 --> 00:45:18,400 +اثنين يبقى بد ال F of سالب اثنين يبقى واحد ناقص + +434 +00:45:18,400 --> 00:45:24,240 +اثنين لكل تربيع زائد اثنين لكل تربيع على واحد ناقص + +435 +00:45:24,240 --> 00:45:28,660 +ناقص اثنين لكل تربيع مش هذي مثلة ايه ال canon يبقى + +436 +00:45:28,660 --> 00:45:36,020 +هذا الكلام بده يساوي واحد زائد أربعة على واحد ناقص + +437 +00:45:36,020 --> 00:45:43,740 +أربعة يبقى الجواب يساوي الناقص خمسة على ثلاثة يبقى خمسة + +438 +00:45:43,740 --> 00:45:48,980 +على ثلاثة والسالب واحد وثلثين طيب هي السالب واحد + +439 +00:45:48,980 --> 00:45:53,460 +عندنا يبقى بدي أنزل كمان شوية يبقى بتجيلك النقطة + +440 +00:45:53,460 --> 00:45:59,760 +اللي هي عندنا هذه تمام؟ جالي هذا على هذه الفترة + +441 +00:45:59,760 --> 00:46:05,460 +decreasing، الدالة تناقصية، خلي بالك هنا، ممكن + +442 +00:46:05,460 --> 00:46:12,120 +أقول decreasing هك؟ صح؟ وممكن أقول decreasing هك؟ + +443 +00:46:12,780 --> 00:46:16,760 +أريد أن أعرف من هؤلاء هؤلاء هو الـ Concave Up وهو + +444 +00:46:16,760 --> 00:46:22,260 +الـ Concave Down فأنا أرى الـ Concave على الفترة + +445 +00:46:22,260 --> 00:46:27,620 +من سالب Infinity لسالب واحد يبقى من سالب Infinity + +446 +00:46:27,620 --> 00:46:32,520 +لسالب واحد Concave Down فأنا أريد أن تكون الرسمة + +447 +00:46:32,520 --> 00:46:36,420 +من؟ اللي عندنا بالشكل هذا فأنا أريد أن تأتي الرسمة + +448 +00:46:36,420 --> 00:46:41,820 +مع الـ Asymptotic بالشكل هذا وتمشي مع الاسمتوت + +449 +00:46:41,820 --> 00:46:47,520 +التاني بهذا الشكل تمام؟ + +450 +00:46:47,520 --> 00:46:53,580 +طيب، الآن بدي أجي للجزء الثاني من الرسمة، بدي أشوف + +451 +00:46:53,580 --> 00:46:59,740 +بعد الواحد زي اثنين، شو بدي يكون شكل الدالة؟ يبقى + +452 +00:46:59,740 --> 00:47:04,220 +خمسة على جداش، خمسة على ثلاثة بس + +453 +00:47:07,050 --> 00:47:13,530 +Concave تعلّي عليها من واحد إلى انفينيتي وبعد من + +454 +00:47:13,530 --> 00:47:19,470 +واحد إلى انفينيتي اللي هو اللي جافه به is concave + +455 +00:47:19,470 --> 00:47:24,810 +down على الفترة هذه وكذلك على الفترة اللي عندنا + +456 +00:47:24,810 --> 00:47:29,990 +هذه يبقى concave down لو روحت حصها بده تيجي النقطة + +457 +00:47:29,990 --> 00:47:34,130 +تحت وبالتالي بده يجيك المنحنة بالشكل اللي أنا معه + +458 +00:47:34,130 --> 00:47:39,270 +ال asymptote ماشي بهذا الشكل يبقى هي الرسمة اللي + +459 +00:47:39,270 --> 00:47:43,590 +أنا طبعا لو جيت حسبتها هتعطيك نفس النتيجة اللي + +460 +00:47:43,590 --> 00:47:49,470 +عندك هذه يعني لو جينا قولنا ال F of 2 هتلاقيها + +461 +00:47:49,470 --> 00:47:54,640 +كمان ناقص خمسة على ثلاثة وبالتالي المنحنة صار أن + +462 +00:47:54,640 --> 00:48:01,720 +كله تحت بهذا الشكل من + +463 +00:48:01,720 --> 00:48:07,180 +هنا نعطي تعريف جديد اللي وعدناكوا فيه قبل قليل + +464 +00:48:07,180 --> 00:48:13,400 +Definition آه آه هذا كان في الكتاب في الطابعة + +465 +00:48:13,400 --> 00:48:17,600 +التاسعة بس في الطابعة العاشرة مش موجود لكن هنعطيه + +466 +00:48:17,600 --> 00:48:22,320 +عليها رسومات موجودة في التمرين بنعطيك يام عشان نشوف + +467 +00:48:22,320 --> 00:48:33,760 +كيف بنعمل الرسومات هذه the graph of the continuous + +468 +00:48:33,760 --> 00:48:52,930 +function y تساوي f of x has a cusp على x + +469 +00:48:52,930 --> 00:49:05,730 +بديو ساوي C if the concavity is + +470 +00:49:05,730 --> 00:49:12,910 +the same on + +471 +00:49:12,910 --> 00:49:14,050 +both sides + +472 +00:49:18,420 --> 00:49:30,060 +of C and either اما + +473 +00:49:30,060 --> 00:49:40,180 +النقطة الأولى اللي هو ال limit للـ F prime of X لما + +474 +00:49:40,180 --> 00:49:45,100 +الـ X بده يروح الى C من جهة الشمال بده يساوي + +475 +00:49:45,100 --> 00:49:57,040 +Infinity and limit لل F prime of X لما الـ X بده + +476 +00:49:57,040 --> 00:50:03,160 +يروح لـ C من جهة اليمين بده يساوي سالب Infinity or + +477 +00:50:04,560 --> 00:50:11,880 +نقطة ثانية limit لما ال X بده يروح ل C من جهة + +478 +00:50:11,880 --> 00:50:20,160 +الشمال لل F prime of X بده يساوي سالب infinity and + +479 +00:50:20,160 --> 00:50:28,100 +limit لما ال X بده يروح ل C من جهة اليمين لل F + +480 +00:50:28,100 --> 00:50:32,540 +prime of X يساوي infinity + +481 +00:50:37,010 --> 00:50:42,030 +طبعا لو روحنا ورسمنا الرسم هذه نقول بالشكل ان هذا + +482 +00:50:42,030 --> 00:50:49,530 +هذا محور X هذا محور Y هذه النقطة اللي هي Zero ممكن + +483 +00:50:49,530 --> 00:50:53,930 +المنحنة يجيلك بالشكل اللي عندك هذا + +484 +00:51:08,400 --> 00:51:14,220 +يبقى طبعا هنا بيكون الكاسب وهنا هذه النقطة اللي + +485 +00:51:14,220 --> 00:51:22,660 +عندنا اللي هو نقطة C وهنا ال limit لل F prime of X + +486 +00:51:22,660 --> 00:51:28,560 +لما ال X بدها تروح الى C من جهة الشمال بده يساوي + +487 +00:51:28,560 --> 00:51:35,820 +infinity وهنا ال limit لل F prime of X لما ال X بده + +488 +00:51:35,820 --> 00:51:45,240 +يروح ل C من جهة اليمين بدها تساوي سالب infinity أو + +489 +00:51:45,240 --> 00:51:52,440 +ممكن يكون بالشكل اللي عندك هذا محور X وهذا Y وهذا + +490 +00:51:52,440 --> 00:51:59,600 +Zero منحنا جالك كيك ورجع طالع هيك يبقى هذه النقطة + +491 +00:52:00,790 --> 00:52:10,190 +اللي هي C هنا ال limit لل F prime of X لما ال X بده + +492 +00:52:10,190 --> 00:52:16,270 +يروح ل C من جهة الشمال يساوي سالب Infinity أو هنا + +493 +00:52:16,270 --> 00:52:22,490 +ال limit لل F prime of X لما ال X بده يروح ل C من + +494 +00:52:22,490 --> 00:52:29,920 +جهة اليمين بده يساوي من؟ بده يساوي Infinity وهذا + +495 +00:52:29,920 --> 00:52:34,800 +كمان هنا اللي هو الكاسب + +496 +00:53:02,300 --> 00:53:09,880 +نعود للتعريف اللي قبل أن نأخذ مثال على ذلك التعريف + +497 +00:53:09,880 --> 00:53:14,220 +يقول الـ graph of the continuous function يبقى + +498 +00:53:14,220 --> 00:53:18,660 +الشرط الأساسي أن تبقى ده اللي متصل أو Y to the + +499 +00:53:18,660 --> 00:53:26,820 +power of X لديه كسب وعند X يساوي C if the + +500 +00:53:26,820 --> 00:53:32,170 +concavity is the same in both sides of C and يبقى + +501 +00:53:32,170 --> 00:53:38,560 +دالة دالة متصلة على طرفين النقطة المنحنة يا + +502 +00:53:38,560 --> 00:53:44,540 +إما concave up يا إما concave down طلع لهنا هذا + +503 +00:53:44,540 --> 00:53:50,620 +الفرع مفتوح لوين وهذا مفتوح لوين إلى أعلى يبقى هنا + +504 +00:53:50,620 --> 00:53:56,600 +على طرفين نقطة C مفتوح إلى أعلى أو عند النقطة C + +505 +00:53:56,600 --> 00:54:01,660 +الفرع مفتوح لوين إلى أسفل وهذا مفتوح لوين إلى أسفل + +506 +00:54:02,090 --> 00:54:08,050 +يبقى عند طرفين الكاصب الدالة متصلة وعند الطرفين + +507 +00:54:08,050 --> 00:54:12,910 +الدالة إما concave up أو concave down يبقى هذه + +508 +00:54:12,910 --> 00:54:18,810 +الشرطين الثالث لو روحت أخدت limit للمشتقة عند نقطة + +509 +00:54:18,810 --> 00:54:23,340 +الكاصب لما روحلها من طرف الشمال يا إما هتعطيني + +510 +00:54:23,340 --> 00:54:27,700 +infinity، يا إما هتعطيني السالب infinity، بتفرقش + +511 +00:54:27,700 --> 00:54:31,680 +عنا، تطلع في الحالة الأولى أعطبطني infinity + +512 +00:54:31,680 --> 00:54:37,960 +بالموجب، ليش؟ لأن الدالة دالة تزايدية، تمام؟ إذا + +513 +00:54:37,960 --> 00:54:41,980 +المشتقة بتبقى أكبر من ال zero، يبقى ال limit تبعها + +514 +00:54:41,980 --> 00:54:47,330 +بتعطيني infinity في الحالة هذه للجزء الثاني بيكون + +515 +00:54:47,330 --> 00:54:51,750 +ال limit لما تذهب إلى C من جهة اليمين بتبقى ال F + +516 +00:54:51,750 --> 00:54:58,070 +from تناقصية فتعطي من السالب infinity أو في البداية + +517 +00:54:58,070 --> 00:55:01,590 +ممكن تبقى تناقصية تعطي من السالب infinity والثانية + +518 +00:55:01,590 --> 00:55:07,420 +تزايدية تعطي من ال infinity يعني بمعنى آخر بعد ما + +519 +00:55:07,420 --> 00:55:13,260 +ألاقي على طرفين نقطة لها نفس ال concavity بتروح أخد + +520 +00:55:13,260 --> 00:55:17,840 +limit ال F prime لما ال X بده تروح ل C من جهة + +521 +00:55:17,840 --> 00:55:21,960 +الشمال إن طلعت من جهة الشمال بده تساوي ال infinity + +522 +00:55:21,960 --> 00:55:26,220 +لازم تطلع من جهة اليمين جداش سالب infinity وإن + +523 +00:55:26,220 --> 00:55:31,400 +طلعت من جهة الشمال بسالب infinity لازم تطلع من جهة + +524 +00:55:31,400 --> 00:55:37,640 +اليمين يعني أنا بتساوي أربعة limits ولا اثنين؟ اثنين + +525 +00:55:37,640 --> 00:55:42,880 +فقط لا غير، لأنه قال لي هذه or، يا إما الحالة + +526 +00:55:42,880 --> 00:55:47,280 +الأولى يا إما من الحالة الثانية، يبقى درجات + +527 +00:55:47,280 --> 00:55:51,940 +ال concavity على الشجتين نفس الشيء مفتوحة إلى أعلى أو + +528 +00:55:51,940 --> 00:55:57,460 +مفتوحة إلى أسفل بروح باخد ال limit للمشتقة لما ال + +529 +00:55:57,460 --> 00:56:02,560 +X بدها تروح إلى C من جهة الشمال لجاتها infinity + +530 +00:56:02,560 --> 00:56:06,360 +إذا من جهة اليمين بسالب infinity لجاتها من جهة + +531 +00:56:06,360 --> 00:56:11,200 +الشمال بسالب infinity إذا من جهة يعني واحدة منهم بس + +532 +00:56:11,200 --> 00:56:16,040 +يا إما الحالة الأولى يا إما الحالة الثانية وهيها + +533 +00:56:16,040 --> 00:56:22,140 +قدامك على الرسم والآن هنثبتلك هذه المعلومة بمثال + +534 +00:56:22,140 --> 00:56:31,160 +يبقى بداجي أخد example ثلاثة بقول + +535 +00:56:31,160 --> 00:56:32,500 +sketch the graph + +536 +00:56:42,610 --> 00:56:57,490 +F of X يساوي X أس ثلثين X أس ثلثين X ناقص خمسة + +537 +00:57:21,990 --> 00:57:26,310 +يبقى مضاجي كعدد ما أنا ما بعرفش لكسب ولا غيره أنا + +538 +00:57:26,310 --> 00:57:29,550 +بدي أخد مثال وبدي أحل زي ما كنت بحل في المثالين + +539 +00:57:29,550 --> 00:57:35,550 +السابقين هذه الدالة بقدر أكتبها على الشكل التالي X + +540 +00:57:35,550 --> 00:57:45,210 +أس ثلاثة على اثنين؟ ناقص خمسة X أس ثلثين الآن لو كانت ال X + +541 +00:57:45,210 --> 00:57:53,940 +تساوي زيرو then كده ال Y؟ ساوي زيرو طيب لو كانت ال + +542 +00:57:53,940 --> 00:58:04,360 +Y تساوي 0 then بصير X أس ثلثين فاهمين في X ناقص + +543 +00:58:04,360 --> 00:58:10,000 +خمسة تساوي Zero هذا بده يعطيلك ان X يساوي Zero و X + +544 +00:58:10,000 --> 00:58:15,240 +يساوي قداش خمسة معناته أنا من الحالتين بجيب ثلاث + +545 +00:58:15,240 --> 00:58:20,280 +نقط ولا اثنين بس يا راجي قولوا غير اطلعوا فيها كويس + +546 +00:58:20,280 --> 00:58:25,740 +اثنين لأن الحالة الأولى هي الحالة الثانية هذه يبقى + +547 +00:58:25,740 --> 00:58:31,480 +هنا the points النقاط Zero و Zero + +548 +00:58:40,430 --> 00:58:44,110 +بعد ذلك بدي أدي الخطوة اللي بعدها فيه عندي + +549 +00:58:44,110 --> 00:58:51,090 +asymptote هنا أه ماعنديش ماعندي بصيغة وبمقام يبقى + +550 +00:58:51,090 --> 00:58:55,470 +انسى قصة الاسم تت يبقى بناء عليه بدي أروح أجيب له + +551 +00:58:55,470 --> 00:59:02,390 +ال F prime of X مباشرة يبقى خمسة على ثلاثة X أس + +552 +00:59:02,390 --> 00:59:11,520 +ثلثين ناقص عشرة على ثلاثة X أس سالب ثلث أو خمسة X + +553 +00:59:11,520 --> 00:59:22,100 +أس ثلثين على ثلاثة ناقص عشرة على ثلاثة X أس ثلث أو + +554 +00:59:22,100 --> 00:59:29,340 +لو حطيت المقامات للكل ثلاثة X أس ثلث بصير أن هنا + +555 +00:59:29,340 --> 00:59:41,480 +خمسة X ناقص عشرة أو خمسة X ناقص اثنين على ثلاثة X + +556 +00:59:41,480 --> 00:59:42,700 +أس ثلث + +557 +00:59:45,870 --> 00:59:51,490 +احنا ايش كتبناها؟ صفر وخمسة وصفر صفر، أه الثانية + +558 +00:59:51,490 --> 00:59:59,050 +عند X تساوي، أه خمسة وصفر ثانية خمسة وزيرو، مظبوط + +559 +00:59:59,050 --> 01:00:05,130 +كلامك صحيح، تحصل فحسن العائلات عادي جدا، أه نعم + +560 +01:00:05,130 --> 01:00:10,410 +قال صلى الله عليه وسلم رفعن أمتي الخطأ والنسيان + +561 +01:00:10,410 --> 01:00:16,670 +وما استكره عليه نرجع ثاني يبقى بتروح تشوف إشارة كل + +562 +01:00:16,670 --> 01:00:24,070 +term من هذه ال termات يبقى بتروح تأخد إشارة اللي هو + +563 +01:00:24,070 --> 01:00:30,490 +من خمسة في X ناقص اثنين بتاخد ال zero تبعها وين عند + +564 +01:00:30,490 --> 01:00:35,910 +اثنين بعد اثنين positive وقبلها negative طبعا ال + +565 +01:00:35,910 --> 01:00:38,050 +domain تبع الدومين يا شباب + +566 +01:00:40,510 --> 01:00:44,770 +كله بالاستثناء كل الريال يبقى ما عندي مشكلة في هذه + +567 +01:00:44,770 --> 01:00:50,890 +الحالة بروح بقوله بدي آخد إشارة ثلاثة X و أس ثلث + +568 +01:00:50,890 --> 01:00:54,510 +وهذا الريال اللي هي اللي بتاخد ال zero تبعها وهي + +569 +01:00:54,510 --> 01:01:00,910 +عند ال Zero بعد ال Zero positive وقبلها negative + +570 +01:01:02,450 --> 01:01:09,250 +بالدالي أخد إشارة خمسة في X ناقص اثنين على ثلاثة + +571 +01:01:09,250 --> 01:01:15,450 +X وثلث وهذا ال real line ونحدد الحدود الإقليمية + +572 +01:01:15,450 --> 01:01:23,540 +ومنها نحدد main نحدد الإشارات هي Zero هي اثنين + +573 +01:01:23,540 --> 01:01:29,200 +مجسمات على بعض قسمة يبقى موجب على موجب بموجب سالب + +5 + +601 +01:05:13,160 --> 01:05:19,460 +إذا بدي أروح أشوف إشارة هذا المقدار يبقى بدي أروح أخد + +602 +01:05:19,460 --> 01:05:28,420 +إشارة عشرة في X زائد واحد بتاخد الصفر تبعها وين؟ + +603 +01:05:28,420 --> 01:05:35,520 +عند السالب واحد بعد السالب واحد موجبة وقبل السالب + +604 +01:05:35,520 --> 01:05:43,790 +واحد سالبة، بدي ياخد إشارة المقدار تسعة اكس أس أربعة + +605 +01:05:43,790 --> 01:05:50,770 +على تلاتة وهذا اللي بتاخد الصفر تبعها وين؟ عند + +606 +01:05:50,770 --> 01:05:59,610 +الصفر يبقى بعد الصفر موجب وقبل الصفر سالب + +607 +01:05:59,610 --> 01:06:06,420 +التالت لـ X أس أربعة سالب ولا موجب؟ موجب سالب يبقى + +608 +01:06:06,420 --> 01:06:13,420 +كله موجب يمين الصفر وشمال الصفر تمام؟ يبقى + +609 +01:06:13,420 --> 01:06:20,900 +بدي أجي أخد إشارة المقدار عشرة X زائد واحد على تسعة + +610 +01:06:20,900 --> 01:06:29,440 +X أس أربعة على تلاتة هذا الـ real line وهذه الحدود + +611 +01:06:29,440 --> 01:06:36,360 +الإقليمية لأنها سالب واحد وهذه positive وهذه كمان + +612 +01:06:36,360 --> 01:06:43,220 +positive وهذه negative يبقى concave down, concave + +613 +01:06:43,220 --> 01:06:51,700 +up, concave up يبقى عند السالب واحد فقط هو الـ + +614 +01:06:51,700 --> 01:06:55,740 +inflection point لأن الدالة دالة متصلة وعند السالب + +615 +01:06:55,740 --> 01:07:02,970 +واحد الدالة معرفة وغيرت اتجاه من الـ concavity يبقى + +616 +01:07:02,970 --> 01:07:08,710 +بدي أروح أجيب له الـ F of سالب واحد، بدي ارجع لوين + +617 +01:07:08,710 --> 01:07:15,790 +لرأس المثل، هيبقى سالب واحد أس اثنين في سالب واحد + +618 +01:07:15,790 --> 01:07:22,130 +سالب خمسة هذا الجذر التالت لـ-1 تربيع اللي هو بواحد + +619 +01:07:22,130 --> 01:07:30,250 +يبقى الجواب جداش سالب ستة يبقى الـ F has an + +620 +01:07:30,250 --> 01:07:37,910 +inflection point اللي إحداثياته تبعها اللي هو سالب + +621 +01:07:37,910 --> 01:07:46,660 +واحد وسالب ستة حددت الـ inflection point اه ما قلناش + +622 +01:07:46,660 --> 01:07:56,040 +الـ concave طيب يلا الـ if أو the graph of if is + +623 +01:07:56,040 --> 01:08:08,820 +concave down on من سالب infinity لغاية سالب واحد + +624 +01:08:08,820 --> 01:08:12,260 +and ما فيش غيرها + +625 +01:08:16,830 --> 01:08:29,030 +and concave up on سالب واحد وصفر اتحاد صفر و + +626 +01:08:29,030 --> 01:08:33,490 +infinity طيب، + +627 +01:08:33,490 --> 01:08:38,750 +إذا عند الصفر، في احتمال يكون في عندي كسَب، مش + +628 +01:08:38,750 --> 01:08:45,440 +عارف، بقول لك أبداً الدالة عند Zero دالة متصلة، اثنين + +629 +01:08:45,440 --> 01:08:50,120 +الدالة ما غيّرتش اتجاه الـ concavity على يميني الصفر + +630 +01:08:50,120 --> 01:08:56,080 +وعلى شمالي الصفر إذا عشان أتأكد إنه في عندي كسَب + +631 +01:08:56,080 --> 01:09:02,400 +مطلوب إيجاد limit للمشتقة عند الـ X بدأت تروح لـ + +632 +01:09:02,400 --> 01:09:09,680 +Zero من اليمين أو من الشمال طيب إذا بدي أروح أخد الـ + +633 +01:09:09,680 --> 01:09:15,420 +F' موجودة عندنا اه هي موجودة هي وين هي؟ يبقى بدي + +634 +01:09:15,420 --> 01:09:22,690 +أخذ limit للـ F prime of X لما الـ X بدها تروح لـ Zero + +635 +01:09:22,690 --> 01:09:29,290 +من جهة الشمال يبقى هذه الـ limit لما الـ X بدها تروح + +636 +01:09:29,290 --> 01:09:35,690 +لـ Zero من جهة الشمال لخمسة في X ناقص اثنين على + +637 +01:09:35,690 --> 01:09:44,930 +تلاتة X أس تلاتة يساوي خمسة على تلاتة ما لهاش دورة + +638 +01:09:44,930 --> 01:09:50,650 +وهذه لما الـ X بدها تروح لـ Zero من جهة الشمال يبقى + +639 +01:09:50,650 --> 01:09:57,190 +البسط بضل قداش ناقص اثنين، Zero من جهة الشمال + +640 +01:09:57,190 --> 01:10:06,010 +معناته very small negative يبقى very small نجاتيف + +641 +01:10:06,010 --> 01:10:11,710 +اييه quantity تمام، نجاتيف على نجاتيف ايش بيصير + +642 +01:10:11,710 --> 01:10:15,010 +positive يبقى جداش + +643 +01:10:29,080 --> 01:10:36,120 +بتروح تاخد limit للـ F prime of X لما الـ X بده يروح + +644 +01:10:36,120 --> 01:10:41,760 +لـ 0 من جهة اليمين يبقى limit لما الـ X بده يروح لـ 0 + +645 +01:10:41,760 --> 01:10:49,290 +من جهة اليمين X ناقص اثنين على تلاتة X أس تلاتة + +646 +01:10:49,290 --> 01:10:55,690 +على تلاتة ما لهاش دور وهذا بيبقى ناقص اثنين على Zero + +647 +01:10:55,690 --> 01:11:03,530 +من جهة اليمين يعني very small positive quantity + +648 +01:11:04,010 --> 01:11:09,750 +يبقى النتيجة ده قداش بتساوي يبقى من الاثنين هدول + +649 +01:11:09,750 --> 01:11:16,390 +ونفس الـ concavity على يمين الصفر هذا بده يعطيك + +650 +01:11:16,390 --> 01:11:28,770 +ان هناك كسَب at x يساوي Zero اظن هيك احنا خلصنا مش + +651 +01:11:28,770 --> 01:11:35,940 +ضايق إلا الرسم مش هيك يبقى بدنا نشيل المشتقة هذه + +652 +01:11:35,940 --> 01:11:48,720 +هيك وهذه معاها ونيجي نرسم رسمتنا خلي + +653 +01:11:48,720 --> 01:11:51,900 +بالأعلى كده يبقى هي المحاور + +654 +01:11:54,920 --> 01:12:01,080 +هذا محور X وهذا محور Y وهذا نقطة الأصل اللي هي + +655 +01:12:01,080 --> 01:12:07,560 +Zero، الـ symptom ما عندناش تمام يبقى أول شغلة بنرسم الـ + +656 +01:12:07,560 --> 01:12:12,020 +local maximum والـ local minimum عند local maximum + +657 +01:12:12,020 --> 01:12:18,780 +وين عند الـ Zero يبقى Zero واتنين عند Zero فيه كسَب + +658 +01:12:18,780 --> 01:12:25,510 +يبقى بالدرسية الرأس مدبب بالشكل اللي عندنا هنا بعد + +659 +01:12:25,510 --> 01:12:29,770 +ذلك إذا كان عندنا local minimum عند x يساوي 2 له + +660 +01:12:29,770 --> 01:12:37,150 +سالب 4 و6 من 10 يبقى عند x يساوي 2 هذا واحد وهذا + +661 +01:12:37,150 --> 01:12:44,410 +اثنين بدي أنزل لسالب يبقى هذا اثنين وسالب 4 و6 + +662 +01:12:44,410 --> 01:12:52,080 +من 10 وبدي أصبح المنحنى إلى أعلى طيب تمام الآن بدي + +663 +01:12:52,080 --> 01:12:56,960 +أجي من سالب infinity لغاية الـ zero بدي أشوف هل هي + +664 +01:12:56,960 --> 01:13:00,120 +increasing اه من سالب infinity لغاية الـ zero + +665 +01:13:00,120 --> 01:13:05,720 +increasing اه يبقى هذه كلها بيبقى increasing بس + +666 +01:13:05,720 --> 01:13:11,690 +ايش عندي في عندي inflection point وين عندي السالب + +667 +01:13:11,690 --> 01:13:18,350 +واحد وسالب ستة وين السالب واحد؟ هاي سالب واحد وبدي + +668 +01:13:18,350 --> 01:13:25,050 +أنزل سالب ستة هنا يجي هذه السالب واحد وسالب ستة + +669 +01:13:25,050 --> 01:13:29,050 +جاب لي السالب واحد جاب لي السالب واحد بدي أشوف + +670 +01:13:29,050 --> 01:13:34,580 +الـ concavity يبقى من سالب infinity لسالب واحد + +671 +01:13:34,580 --> 01:13:43,500 +concave down يبقى المنحنى كان concave down الشكل + +672 +01:13:43,500 --> 01:13:48,000 +اللي عندنا هذا تمام؟ ومن عند السالب واحد لغاية + +673 +01:13:48,000 --> 01:13:51,260 +الستة concave up + +674 +01:13:58,140 --> 01:14:02,480 +يبقى concave up بالشكل اللي عندنا هنا يبقى النقطة + +675 +01:14:02,480 --> 01:14:07,360 +هذه صارت inflection + +676 +01:14:07,360 --> 01:14:15,200 +point للنقطة اللي عندنا قبلها concave down بعدها + +677 +01:14:15,200 --> 01:14:20,680 +concave up بعدها الآن من zero لـ infinity concave + +678 +01:14:20,680 --> 01:14:27,280 +up وين راح تكون curve up من zero كذلك لوين لغاية + +679 +01:14:27,280 --> 01:14:32,040 +infinity مدام من zero infinity تكون curve up يبقى + +680 +01:14:32,040 --> 01:14:37,960 +هذا بدي يظل نازل هيك وهذا بدي يظل طالع إلى ما شاء + +681 +01:14:37,960 --> 01:14:44,660 +الله لكن جالي في نقطة تقاطع طلعناها قداش؟ هذه اظن + +682 +01:14:44,660 --> 01:14:50,430 +كانت خمسة وzero يبقى هذه النقطة كانت خمسة و Zero و + +683 +01:14:50,430 --> 01:14:55,910 +هذا يبقى كيف up لاحظ increasing من سالب infinity + +684 +01:14:55,910 --> 01:15:01,290 +إلى سالب واحد هل من اثنين إلى infinity increasing + +685 +01:15:01,290 --> 01:15:06,650 +ولا لا؟ تعال نشوف increasing من اثنين لإنفينتي + +686 +01:15:06,650 --> 01:15:13,010 +سليمة هل decreasing من Zero لغاية اثنين ولا لا؟ + +687 +01:15:13,010 --> 01:15:17,970 +يبقى decreasing من Zero لغاية اثنين يبقى رسمتي + +688 +01:15:17,970 --> 01:15:20,130 +سليمة مائة بالمائة + +689 +01:15:31,950 --> 01:15:38,150 +اللي حكمني النقطة هذه إن عند النقطة على يمينها + +690 +01:15:38,150 --> 01:15:41,670 +وعلى شمالها لها نفس الـ concave مش تقول لما + +691 +01:15:41,670 --> 01:15:46,210 +نعرفنا الكسَب وقلنا دالة دالة متصلة عند النقطة وعلى + +692 +01:15:46,210 --> 01:15:51,150 +يمينها وعلى شمالها لها نفس الـ concavity هذه مش + +693 +01:15:51,150 --> 01:15:56,160 +بمزاجي باخد من عندي لا لحكمتنا النقطة هذه وهكذا، + +694 +01:15:56,160 --> 01:15:59,980 +تمام؟ حاجة لو هي تساوي التاني قبل ما نروح للمثال + +695 +01:15:59,980 --> 01:16:06,450 +اللي بعده ايه؟ السؤال لأنه عرفنا للكسَب قلنا بنجيب + +696 +01:16:06,450 --> 01:16:11,110 +الـ limit للـ F prime لازم تطلع عند الـ zero اه، + +697 +01:16:11,110 --> 01:16:13,750 +إذا من اليمين مثلًا infinity من الشمال سالب + +698 +01:16:13,750 --> 01:16:15,630 +infinity طب لو طلع من اليمين ومن الشمال infinity + +699 +01:16:15,630 --> 01:16:20,070 +infinity لا يا أخو ده ممتاز ممتاز عارف ليش؟ + +700 +01:16:20,070 --> 01:16:24,710 +لأن لما أقول لك F prime يعني المماس limit للمماس، + +701 +01:16:24,710 --> 01:16:29,490 +اطلع لهذا لو جيت اللي قلت المماس هنا بيكون + +702 +01:16:29,490 --> 01:16:34,300 +المماس سالب ولا لا لكن لو جيت للمماثل اللي عندك + +703 +01:16:34,300 --> 01:16:39,260 +هذا بيعمل لك زاوية موجبة إذا لا يمكن لازم واحد إن + +704 +01:16:39,260 --> 01:16:42,400 +كان الأول infinity الثاني سالب من الفترة طلعوا + +705 +01:16:42,400 --> 01:16:44,580 +اثنين infinity ما فيش كسَب أصلاً + +706 +01:16:48,510 --> 01:16:56,370 +اسمع يا ابني انت معيار أيوة ايش + +707 +01:16:56,370 --> 01:17:01,350 +يعني بالاسم المحوركس أنا باخد limit للـ F prime ايش + +708 +01:17:01,350 --> 01:17:05,870 +ما يكون شكل هيكون مش فيش حد اسم المحوركس ومحور اكس + +709 +01:17:05,870 --> 01:17:09,870 +أنا باخد limit للـ function لما الـ X بده تروح لهذا + +710 +01:17:09,870 --> 01:17:12,430 +الرقم اللي عنده المشكلة + +711 +01:17:16,200 --> 01:17:19,360 +ايش أنت أنت من الرسمة؟ أنا بقول لك يا راني الـ limit + +712 +01:17:19,360 --> 01:17:22,520 +للمشتقة بقول الـ limit للرسمة يا راني الـ limit + +713 +01:17:22,520 --> 01:17:24,180 +للمشتقة تبع الدالة. + +714 +01:17:26,780 --> 01:17:33,300 +ايش أنت أنت يعني؟ مرسومة + +715 +01:17:33,300 --> 01:17:37,240 +وخالصة ايه؟ اسمع اسمع اسمع تعال على الرسمة + +716 +01:17:37,240 --> 01:17:43,160 +هنا ايه الحاجب نانيه؟ هاي الرسمة قدامك يعني لو + +717 +01:17:43,160 --> 01:17:47,400 +عندي رسم زي محور ... زي محور X هيك؟ هي هي محور X + +718 +01:17:47,400 --> 01:17:47,760 +هيو + +719 +01:17:52,450 --> 01:18:00,270 +خط مستقيم يعني؟ مستقيم ومطلق ماشي يعني اللي هي + +720 +01:18:00,270 --> 01:18:06,710 +ايه؟ يعني أنت أسألك هاي الـ absolute value اسمها + +721 +01:18:06,710 --> 01:18:10,570 +يا ابنيها هاي الـ absolute value اللي قاعد تسأل + +722 +01:18:10,570 --> 01:18:14,930 +عليها صح؟ هذا absolute value X وهذا محور X وهذا + +723 +01:18:14,930 --> 01:18:19,310 +محور Y بدك تاخد limit لـ absolute value X لكي + +724 +01:18:19,310 --> 01:18:20,030 +تروح لوين؟ + +725 +01:18:27,730 --> 01:18:32,710 +الخط هذا بيبقى ماشي إلى ما شاء الله إلى أن يرفع + +726 +01:18:32,710 --> 01:18:38,230 +الله الأرض ومن علينا يعني الـ X بدأت تروح لسالب + +727 +01:18:38,230 --> 01:18:43,710 +Infinity لما الـ X بدأت تروح لسالب Infinity بدأت + +728 +01:18:43,710 --> 01:18:50,030 +يكون الناتج Infinity ولو راحت الـ X للـ Infinity + +729 +01:18:50,030 --> 01:18:55,390 +بدأت تروح كمان هذه للـ Infinity على الشجتين خلاص؟ diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/jcb1zLJ06L8_raw.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/jcb1zLJ06L8_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..dc8009a1724bc8ff66e16df04f823db1105cb4b7 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/jcb1zLJ06L8_raw.srt @@ -0,0 +1,2924 @@ +1 +00:00:31,530 --> 00:00:37,090 +إذا فشلت اختبار المشتقة ثاني بنرجع لمين لاختبار + +2 +00:00:37,090 --> 00:00:41,410 +المشتقة الأولى لكن احنا في شغلنا في الأمثلة مش + +3 +00:00:41,410 --> 00:00:46,350 +هنحاول نستخدم هذا إلا عند ضرورة ولا أظن أنه يلزم + +4 +00:00:46,350 --> 00:00:50,040 +بس بيلزملمن لم يكن يقوم بالاستخدام و لمن لم يكن + +5 +00:00:50,040 --> 00:00:54,100 +يقوم بالاستخدام يعني في الغالب أثناء الشغل العاملي + +6 +00:00:54,100 --> 00:00:58,720 +هستخدم اختبار المشتقة الأولى لمواضيع النهايات + +7 +00:00:58,720 --> 00:01:02,380 +العظمى والصورة المعالية هستخدم اختبار المشتقة + +8 +00:01:02,380 --> 00:01:09,210 +الثانية لقياس الconcavity لدالة ماطيب الان وصلنا + +9 +00:01:09,210 --> 00:01:17,130 +الى السؤال اللى احنا بدناه ضرورى جدا كيف بدنا نرسم + +10 +00:01:17,130 --> 00:01:23,230 +المنحنيات مشان انجاب على هذا السؤال بدنا نعمل اللى + +11 +00:01:23,230 --> 00:01:29,770 +هو عدة خطوات الخطوة الأولىبتقول لي ما ياتي بدنا + +12 +00:01:29,770 --> 00:01:34,810 +find the intercepts with the coordinate axes يعني + +13 +00:01:34,810 --> 00:01:41,230 +بدنا نجيب تقاطة المنحنة تبعنا مع محوري الإحداثيات + +14 +00:01:41,230 --> 00:01:47,030 +كيف بنحصل عليها بحط مرة x ب zero بجيب قيمة yبحط Y + +15 +00:01:47,030 --> 00:01:52,310 +بزير و بجيب قيمة X إن أمكن، إذا مش ممكن، بلاش يعني + +16 +00:01:52,310 --> 00:01:55,110 +إذا العملية شاقة أو صعبة، انسى الموضوع، اللي + +17 +00:01:55,110 --> 00:01:58,690 +السهلة، جيبها صعبة، سيبك منها يبقى الخطوة الأولى، + +18 +00:01:58,690 --> 00:02:02,830 +بدي أجيب نقاط قاطة منحنة مع محوري الإحداثيات + +19 +00:02:02,830 --> 00:02:07,270 +النقطة الثانية، بدي أجيب الـasymptotes إذا كانت + +20 +00:02:07,270 --> 00:02:11,150 +موجودة يعني لو كانت البرنامج العادية فيها عندي + +21 +00:02:11,150 --> 00:02:15,360 +asymptoteلأ، ماعنديش الاسمتوت، يبقى مش مطالب فيهم، + +22 +00:02:15,360 --> 00:02:20,620 +يبقى أنا مطالب في الاسمتوت إذا كان عندي ده ال + +23 +00:02:20,620 --> 00:02:24,540 +rational function فيها بسط و مقام، بدي أشوف في + +24 +00:02:24,540 --> 00:02:27,780 +عندي horizontal اسمتوت ام لا، في عندي oblique + +25 +00:02:27,780 --> 00:02:31,920 +اسمتوت ام لا، في عندي vertical اسمتوت ام لا، اللتي + +26 +00:02:31,920 --> 00:02:36,230 +سابقة دراستهامش في chapter تلاتة، في chapter + +27 +00:02:36,230 --> 00:02:41,270 +اتنين، مظبوط يبقى مدرس في chapter اتنين لازم ان هي + +28 +00:02:41,270 --> 00:02:45,570 +و عندها رسم في chapter اربع النقطة التالتة بدي + +29 +00:02:45,570 --> 00:02:49,310 +أجيب المشتقة الأولى والثانية، طبعا المشتقة الأولى + +30 +00:02:49,310 --> 00:02:52,690 +منها بجيب ال interval of increasing و ال interval + +31 +00:02:52,690 --> 00:02:56,390 +of decreasing زي ما شوفنا في المحاضرة الماضية و + +32 +00:02:56,390 --> 00:02:59,750 +بجيب منها ال local maximum و ال local minimum + +33 +00:03:00,170 --> 00:03:03,610 +المشتقة الثانية بجيب منها ال concave up و ال + +34 +00:03:03,610 --> 00:03:08,650 +concave down لسه ماخمناش مثال على تعيين ال concave + +35 +00:03:08,650 --> 00:03:12,510 +up و ال concave down لكن اتكلمنا عنها كنظري في + +36 +00:03:12,510 --> 00:03:17,350 +المرة الماضية و كذلك من خلالها بدنا نحسب ال + +37 +00:03:17,350 --> 00:03:21,410 +inflection point يبقى من خلال المشتقة الأولى بكون + +38 +00:03:21,410 --> 00:03:24,670 +جيبت أربعة اللي هو ال local extremely فترات + +39 +00:03:24,670 --> 00:03:29,660 +التزايدوالتناقص و ال local extreme وهذا من وين؟ من + +40 +00:03:29,660 --> 00:03:33,580 +المشتقة الأولى خمسة بدي أجيبها من وين؟ من المشتقة + +41 +00:03:33,580 --> 00:03:38,120 +الثانية يعني ليس بضروري أجيب التنتين ورا بعض لأ + +42 +00:03:38,120 --> 00:03:41,700 +بجيب المشتقة الأولى وبعدين هيك بجيب ال interval + +43 +00:03:41,700 --> 00:03:44,220 +increasing and decreasing و ال local maximum و ال + +44 +00:03:44,220 --> 00:03:47,800 +local minimum بعد هيك بروح بجيب المشتقة الثانيةو + +45 +00:03:47,800 --> 00:03:50,840 +بروح بشوف ال concavity للمنحنة و ال reflection + +46 +00:03:50,840 --> 00:03:56,420 +points ان وجدت نقوة السلسة والاخيرة كل المعلومات + +47 +00:03:56,420 --> 00:04:00,540 +اللي جمعتها دي بتروح أستخدمها في الرسم أو هي اللي + +48 +00:04:00,540 --> 00:04:04,840 +هتسهلي عملية الرسم بدون ما أروح أعمل جدول زي ما + +49 +00:04:04,840 --> 00:04:09,480 +كنا في الثانوية حط جدول حط قيم السيناتات لقيم + +50 +00:04:09,480 --> 00:04:13,380 +الصادات ابدا أرسم النقط و أوصل بينهم هذا كلام عفى + +51 +00:04:13,380 --> 00:04:18,070 +عليه الزمن لأمن خلال فترات التزايد والتناقص + +52 +00:04:18,070 --> 00:04:20,610 +والـlocal maximum والـconcavity والـinfliction + +53 +00:04:20,610 --> 00:04:24,610 +points والتقاطة مع محاول الإحداثيات بتروح أرسم من + +54 +00:04:24,610 --> 00:04:31,590 +الرسمة تبعت هذه المسألة طيب لحد هنا stop انتهى + +55 +00:04:31,590 --> 00:04:35,730 +الجزء النظري تبع هذا الsection لم يبقى إلا مجموعة + +56 +00:04:35,730 --> 00:04:39,390 +من الأمثلة لكن ضايل نقطة نظري بدأ أقولها لك في + +57 +00:04:39,390 --> 00:04:43,800 +حينهاطبعا مش موجودة في الكتاب، لكن هي بتلزمني عند + +58 +00:04:43,800 --> 00:04:49,560 +عملية الرسم أول مثال بقول sketch the graph of the + +59 +00:04:49,560 --> 00:04:53,660 +following functions و أعطاني دالة Y تساوي X تكييب + +60 +00:04:53,660 --> 00:04:59,440 +ناقص تلاتة X زائد تلاتة يبقى هذا منحنا من الدرجة + +61 +00:04:59,440 --> 00:05:05,460 +الثالث لا في جسمه مطول ولا غيره يبقى أول خطوة بدي + +62 +00:05:05,460 --> 00:05:10,260 +أروح أجيب نقاط تقاطه المنحنة مع محوري الإحداثيات + +63 +00:05:10,460 --> 00:05:17,340 +اذا لو حطيت ال X تساوي Zero بده تبقى ال Y تساوي قد + +64 +00:05:17,340 --> 00:05:23,660 +ياشي معناه هذا الكلام ان النقطة Zero تلاتة lie on + +65 +00:05:23,660 --> 00:05:31,910 +the graph of ال function Fيبقى النقطة 0 3 طب لو + +66 +00:05:31,910 --> 00:05:37,150 +حطيت Y ب 0 بصير صعب حالها يقول ليه شغال بحالي ليس + +67 +00:05:37,150 --> 00:05:41,190 +بالضرورة السهلة بيشتغلها مش السهلة بدنا اشيها يبقى + +68 +00:05:41,190 --> 00:05:45,450 +انتهينا من الخطوة الأولى الخطوة الثانية جالي هتل + +69 +00:05:45,450 --> 00:05:50,450 +ال asymptotes ان وجد هدفي ال asymptote لو بدأ أخد + +70 +00:05:50,450 --> 00:05:53,190 +ال limit لما ال X تروح لما لا نهاية تطلع مع لا + +71 +00:05:53,190 --> 00:05:57,320 +نهايةأنا ماعنديش في المقام حتى أقول أخد ال limit + +72 +00:05:57,320 --> 00:06:01,540 +لما بتروح ليمين و أبلغي يعني ماعنديش functional + +73 +00:06:01,540 --> 00:06:05,800 +function يبقى الخطوة هذه أنسى الموضوع اللي هو + +74 +00:06:05,800 --> 00:06:10,100 +الassumption يبقى بداجي لمين للخطوة التالتة + +75 +00:06:10,100 --> 00:06:15,700 +المشتقة يبقى باجي بقوله ال y primeيسوي تلاتة X + +76 +00:06:15,700 --> 00:06:22,280 +تربيه ناقص تلاتة يعني تلاتة في X تربيه ناقص واحد + +77 +00:06:22,280 --> 00:06:29,900 +يعني تلاتة يعني يسوي تلاتة في X ناقص واحد في X + +78 +00:06:29,900 --> 00:06:35,560 +زائد واحد تمام يبقى المشتقة زي ما ينتشر ال + +79 +00:06:35,560 --> 00:06:40,600 +polynomial إذا معرفة for all X يبقى ال critical + +80 +00:06:40,600 --> 00:06:46,330 +points باجيبهم فقط من خلالإنه أساوي هذه بقداش + +81 +00:06:46,330 --> 00:06:50,610 +بزيره انسى ماقاليش اتلي critical لكن اللي ازمت + +82 +00:06:50,610 --> 00:06:55,090 +بالديارة بجيبها يبقى باجي بقوله بدي أشوف الإشارات + +83 +00:06:55,090 --> 00:07:00,430 +يبقى بروح بقوله بدي إشارة تلاتة في X ناقص واحد و + +84 +00:07:00,430 --> 00:07:03,790 +بقوله هذا ال real line و هذا النقطة اللي هي main + +85 +00:07:03,790 --> 00:07:09,580 +لإن واحد بعد الواحد positive و قبلها aنجاتف يعني + +86 +00:07:09,580 --> 00:07:13,600 +لو حطيت قيم ال X بعد الواحد زي اتنين تلاتة اربعة + +87 +00:07:13,600 --> 00:07:17,720 +بلاجي النتيجة موجبة دائما وابدا لو حطيت قبل الواحد + +88 +00:07:17,720 --> 00:07:21,780 +زي Zero سالب واحد سالب اتنين الاخر بلاجيها سالبة + +89 +00:07:21,780 --> 00:07:25,760 +بعد ذلك بدنا نروح ناخد إشارة القوس الثاني اللي هو + +90 +00:07:25,760 --> 00:07:30,890 +X زي واحدبياخد الـ zero تبع وين؟ عند السلب واحد + +91 +00:07:30,890 --> 00:07:35,310 +بعد السلب واحد positive و قبل السلب واحد معله + +92 +00:07:35,310 --> 00:07:43,110 +negative الآن بدي أدي أخد إشارة حصل الضرب حصل + +93 +00:07:43,110 --> 00:07:47,950 +الضرب اللي هو مين؟ تلاتة في x ناقص واحد في x زائد + +94 +00:07:47,950 --> 00:07:54,080 +واحد وهذا ال real lineوهذه الحدود الإقليمية اللي + +95 +00:07:54,080 --> 00:08:00,120 +عندنا لمن؟ لحاصل الضرب، يبقى هذه عند الواحد وهذه + +96 +00:08:00,120 --> 00:08:07,100 +عند السالب واحدالجثين مضربات في بعض ضربك وبدي أضرب + +97 +00:08:07,100 --> 00:08:11,660 +الإشارات في بعض ضربك يبقى هنا زائد هنا ناقص هنا + +98 +00:08:11,660 --> 00:08:17,480 +زائد يبقى في هذه الفترة كانت الدالة increasing هنا + +99 +00:08:17,480 --> 00:08:24,380 +صارت decreasing هنا رجعت increasing إذا بروح بقوله + +100 +00:08:24,380 --> 00:08:25,380 +ما يأتي + +101 +00:08:27,890 --> 00:08:36,710 +بعدين بقوله ال F is increasing دالة تزايدية on + +102 +00:08:36,710 --> 00:08:44,530 +الفترة من سلب infinity لغاية سلب واحد and on و + +103 +00:08:44,530 --> 00:08:52,740 +كذلك على الفترة من واحد لغاية infinityالـ F is + +104 +00:08:52,740 --> 00:09:00,560 +decreasing ده لتناقصية على الفترة من سالب واحد + +105 +00:09:00,560 --> 00:09:05,560 +لغاية واحدبعد هيك بدي Local Maximum و Local + +106 +00:09:05,560 --> 00:09:11,620 +Minimum بدي أخد F of سالب واحد يساوي برجع على رأس + +107 +00:09:11,620 --> 00:09:16,040 +المسألة من فوق وبعوض فيها يبقى سالب واحد تكييب + +108 +00:09:16,040 --> 00:09:22,000 +سالب تلاتة في سالب واحد زائد تلاتة ويساوي سالب + +109 +00:09:22,000 --> 00:09:28,670 +واحد زائد تلاتة زائد تلاتة ويساوي كداش خمسةبعد ذلك + +110 +00:09:28,670 --> 00:09:35,190 +البداية يأخذ ال F of واحد واحد تكييب ناقص ثلاثة في + +111 +00:09:35,190 --> 00:09:42,290 +واحد زائد تلاتة ويساوي كم؟ واحد إذا بجي بقوله ال F + +112 +00:09:42,290 --> 00:09:54,300 +has local maximum كم؟ خمسة at x يساوي سالب واحدand + +113 +00:09:54,300 --> 00:10:06,240 +local minimum اللي هو local minimum واحد at x + +114 +00:10:06,240 --> 00:10:12,700 +يساوي كده؟ واحد إذا إنتهينا من مين؟ من ال local + +115 +00:10:12,700 --> 00:10:17,640 +extrema ولا من ال increasing و ال decreasing؟بيجي + +116 +00:10:17,640 --> 00:10:22,220 +بعد ذلك ال concavity و ال inflection points وهذا + +117 +00:10:22,220 --> 00:10:25,940 +يعتبر أول مثال على ال concavity و ال inflection + +118 +00:10:25,940 --> 00:10:30,440 +points إذا بدي أجي على مين؟ على المشتقة الأولى + +119 +00:10:30,440 --> 00:10:33,940 +اللي عندنا، شو بدي أعملها؟ بدي أجيب المشتقة + +120 +00:10:33,940 --> 00:10:39,960 +الثانية، إذا بروح باخدالـ F بابلي برايم of X اللي + +121 +00:10:39,960 --> 00:10:46,340 +يجداش؟ ستة X والتلاتة مع السلامة يبقى هذه بدها + +122 +00:10:46,340 --> 00:10:54,100 +تساوي Zero only at X يساوي جداش Zero إذن احتمالي + +123 +00:10:54,100 --> 00:10:59,110 +الـ Zero هذه تبقى Inflection Point فيه احتمالالله + +124 +00:10:59,110 --> 00:11:04,750 +أعلم قد يكون و قد ذا يكون، تمام؟ إذا بدنا نروح + +125 +00:11:04,750 --> 00:11:12,880 +ندرس إشارة اللي هو ال 6X ماعنديش غيرهاهذه الـ zero + +126 +00:11:12,880 --> 00:11:16,600 +بتاخد الـ zero لو جيت بعد ال zero القيمة هذه مالها + +127 +00:11:16,600 --> 00:11:22,820 +موجبة يبقى هذه موجبة لو جيت قبل ال zero يعني + +128 +00:11:22,820 --> 00:11:27,520 +المشتقة الثانية السالي بقى يبقى المنحنة concave + +129 +00:11:27,520 --> 00:11:35,280 +down التانية موجبة يبقى المنحنة concave up تمام؟ + +130 +00:11:35,280 --> 00:11:38,140 +إذا بروح بقول ما يأتي + +131 +00:11:45,110 --> 00:11:50,970 +طبعا الدالة polynomial فهي متصلة على كل real line + +132 +00:11:50,970 --> 00:11:53,610 +بلا استثناء + +133 +00:12:10,380 --> 00:12:22,920 +is concave down on من سلب infinity لغاية zero and + +134 +00:12:22,920 --> 00:12:33,340 +concave up on الفترة من zero لغاية infinityالدالة + +135 +00:12:33,340 --> 00:12:37,360 +معرفة عند الـ Zero يبقى مدان معرفة يعني الدالة + +136 +00:12:37,360 --> 00:12:42,880 +متصلة عند ال Zero والدالة غيرت اتجاه ال Concavity + +137 +00:12:42,880 --> 00:12:50,600 +إذا في Infliction point يبقى ال F is continuous + +138 +00:12:50,600 --> 00:13:06,320 +for all Xمعناته إنها كون ال F is continuous at x + +139 +00:13:06,320 --> 00:13:11,140 +يساوي زيرو and + +140 +00:13:11,140 --> 00:13:19,980 +ال F it change its concavity at + +141 +00:13:27,590 --> 00:13:39,670 +هنا بده يعطينا there is an inflection point + +142 +00:13:51,490 --> 00:14:00,630 +تلاتة هذا معناه زيرو و تلاتة is an inflection + +143 +00:14:00,630 --> 00:14:06,070 +point طيب + +144 +00:14:06,070 --> 00:14:07,310 +تمام خلصنا + +145 +00:14:10,750 --> 00:14:14,670 +المغنقة في حالة ال increasing و ال decreasing قلنا + +146 +00:14:14,670 --> 00:14:19,560 +فقطإذا المشتق أكبر من zero على ال open interval + +147 +00:14:19,560 --> 00:14:24,460 +يبقى increasing أو decreasing على ال closed + +148 +00:14:24,460 --> 00:14:29,140 +interval بس في ال concurrent انسى الموضوع بس باخد + +149 +00:14:29,140 --> 00:14:33,400 +الفترة لإن عند هذه النقطة بصير انقلاب لابتقدر + +150 +00:14:33,400 --> 00:14:37,480 +تعتبرها مع الأولى ولا بتقدر تعتبرها مع مين؟ مع + +151 +00:14:37,480 --> 00:14:43,460 +الثانية طيب هيك احنا جيبنا كل المعلوماتمن خلال هذه + +152 +00:14:43,460 --> 00:14:48,140 +المعلومات بدنا نروح نرسم الرسمة فبجي بقول هذه + +153 +00:14:48,140 --> 00:14:55,080 +المحاور اللي عندنا هذا محور X هذا محور Y هذه نقطة + +154 +00:14:55,080 --> 00:15:01,990 +الأصل اللي هي Zeroعندما ترسم أول خطوة ترسمها هي + +155 +00:15:01,990 --> 00:15:06,930 +الاسمتوتز، لو ماعنديش اسمتوتز، يبقى ثاني الخطوة + +156 +00:15:06,930 --> 00:15:10,770 +بدور على ال local maximum و ال local minimum، يبقى + +157 +00:15:10,770 --> 00:15:16,210 +احنا عندنا local maximum خمس ساوينيعني عندي السلب + +158 +00:15:16,210 --> 00:15:21,130 +واحد وخمسة، وين السلب واحد؟ يبقى باجي بقول له هي + +159 +00:15:21,130 --> 00:15:25,670 +النقطة، هي السلب واحد وبدأ أطلع خمسة، يبقى هذه + +160 +00:15:25,670 --> 00:15:31,210 +السلب واحد وخمسة، يبقى فيها عندي local maximum، + +161 +00:15:31,210 --> 00:15:36,070 +هاي حاطيت جوس local maximumفي عندى local minimum + +162 +00:15:36,070 --> 00:15:43,250 +عنده نقطة واحد وواحد يبقى باجي النقطة هي النقطة + +163 +00:15:43,250 --> 00:15:47,890 +واحد وهي النقطة التانية اللى هنا واحد يبقى هذه + +164 +00:15:47,890 --> 00:15:53,150 +واحد وواحد عند local minimum بالشكل اللى عندنا هذا + +165 +00:15:53,700 --> 00:16:02,620 +بعد هيك تعاليش بيقوللي بيقوللي ان ال F + +166 +00:16:02,620 --> 00:16:08,120 +دل تزايدية من سالب infinity لغاية سالب واحد من + +167 +00:16:08,120 --> 00:16:13,710 +سالب infinity لغاية سالب واحد يبقى دل تزايديةيبقى + +168 +00:16:13,710 --> 00:16:18,530 +المعناته بيجي من تحتنا وضل طالع لغايتها، يبقى + +169 +00:16:18,530 --> 00:16:22,990 +المنحنة هذا بيجيني بالشكل هذا هاي و هيك، دلتة + +170 +00:16:22,990 --> 00:16:28,170 +زيودية، تمام؟ جالي من سالب واحد إلى واحد، + +171 +00:16:28,170 --> 00:16:33,820 +decreasingيبقى الدالة تناقصية، إذا المنحنة هيجيني + +172 +00:16:33,820 --> 00:16:40,640 +هكذا، بالضبط تماما. وبعد ذلك، جالي من واحد إلى + +173 +00:16:40,640 --> 00:16:46,060 +انفينيتي، الدالة كمان تزايدية، يبقى الدالة بتبقى + +174 +00:16:46,060 --> 00:16:51,720 +طالعة إلى ما شاء الله.طيب السؤال هو ايه ال + +175 +00:16:51,720 --> 00:16:56,340 +inflection point قال لي عند ال zero والتلاتة عند + +176 +00:16:56,340 --> 00:17:01,700 +ال zero والتلاتة هناها هذه ال zero تلاتة اللي هي + +177 +00:17:01,700 --> 00:17:08,360 +ال inflection point لاحظ جبلها concave down بعدها + +178 +00:17:08,360 --> 00:17:13,740 +concave up تعالى نشوف هل من سلب infinity لغاية ال + +179 +00:17:13,740 --> 00:17:18,980 +zero concave down ولا لأبسالب الانفينيتي إلى زيرو + +180 +00:17:18,980 --> 00:17:23,400 +كونكيف دانو كتبنا فوق ومن عند الزيرو إلى + +181 +00:17:23,400 --> 00:17:27,140 +الانفينيتي كونكيف up من الزيرو إلى الانفينيتي + +182 +00:17:27,140 --> 00:17:31,980 +مفتوحة لويا إلى اعلى يبقى راسمنا دقيق مائة بالمائة + +183 +00:17:31,980 --> 00:17:37,240 +ماعناش اي مشكلة يبقى خلاصنا من السؤال حد فيكم يلو + +184 +00:17:37,240 --> 00:17:38,400 +اي تساؤل؟ + +185 +00:17:41,620 --> 00:17:44,640 +كيف؟ إذا وجدت سنانة تراصل من أطرا جديدة، ممكن + +186 +00:17:44,640 --> 00:17:47,340 +أستعمل نقاط يعني لها؟ أه طبعا، هاي النقاط اللي + +187 +00:17:47,340 --> 00:17:51,300 +بنكتبهم، يعني احنا لو كانت الشغلات اللي جيبناها + +188 +00:17:51,300 --> 00:17:56,620 +هذه ما جبتليش، خلتلي شك في بعض الأمور، بروح بحط + +189 +00:17:56,620 --> 00:18:00,860 +نقاط من عندي، و بشوف المنحنة بيه جاي فوق ولا جاي + +190 +00:18:00,860 --> 00:18:02,060 +تحت، إلا آخرين + +191 +00:18:11,720 --> 00:18:17,100 +طبعا هذا يعتبر المثال من أبسط أنواع الأمثل + +192 +00:18:30,230 --> 00:18:33,150 +مباشرة تقعر النطار في الصحيح معاه + +193 +00:18:44,450 --> 00:18:48,310 +بتتأكد بعد ورصة ورقة انك فعلا كنت في دولة على نفس + +194 +00:18:48,310 --> 00:18:52,210 +الفترة وكنت كذب ولا لا لاجئت في شغل مش مظبوط بغير + +195 +00:18:52,210 --> 00:18:58,710 +انك تروح تدقق رسمتك شوية طيب نيجي ناخد مثال ثاني + +196 +00:18:58,710 --> 00:19:04,250 +غير هذا المثال نجي ل example two + +197 +00:19:10,640 --> 00:19:19,360 +Example 2 يقول لي Y تساوي 1 زائد X تربية على 1 + +198 +00:19:19,360 --> 00:19:21,140 +ناقص X تربية + +199 +00:19:48,810 --> 00:19:50,330 +هذه الكلام انتهينا منه + +200 +00:20:04,540 --> 00:20:10,280 +طيب مثال ثاني بيقول ايه انا كتبه فوق عشان نستغل + +201 +00:20:10,280 --> 00:20:17,140 +الفرحان Y تساوي هذا سؤال اتنين Y تساوي واحد زائد X + +202 +00:20:17,140 --> 00:20:26,280 +تربيع على واحد ناقص X تربيع السؤال + +203 +00:20:26,280 --> 00:20:32,560 +هو هل الدالة معرفة عند الواحد والسلب واحد؟يبقى + +204 +00:20:32,560 --> 00:20:40,040 +هدول مش هيظهرولي أثناء الرسم يبقى هنا بقوله هذه ال + +205 +00:20:40,040 --> 00:20:45,880 +X ممنوعة تساوي واحد وال X ممنوعة تساوي سالف واحد + +206 +00:20:45,880 --> 00:20:51,960 +لإن عند اتنين هدول الدالة is undefined غير معرفة + +207 +00:20:51,960 --> 00:20:57,920 +طيب بدنا نبدأ نجيب تقاطعاتها مع محوري الإحداثيات + +208 +00:20:57,920 --> 00:21:06,620 +يبقى بدي أجي أخد أنه لو كانتالـ X تساوي Zero ثم Y + +209 +00:21:06,620 --> 00:21:08,540 +تساوي كده؟ واحد + +210 +00:21:13,220 --> 00:21:17,200 +يبقى ال boss هو اللي فتساوي 0 واحد زي x تربية ممكن + +211 +00:21:17,200 --> 00:21:22,940 +يساوي 0 يبقى has no solution لا يمكن لمجموعة + +212 +00:21:22,940 --> 00:21:28,800 +كميتين موجبتين أن يساوي صفرا وبالتالي انسى الموضوع + +213 +00:21:28,800 --> 00:21:35,580 +يبقى هاي جبت النقطة هذه واحدة فقط اللي هو 01 on + +214 +00:21:35,580 --> 00:21:44,210 +the graph يبقى هذه النقطة تقع وين تقع علىالملحنة + +215 +00:21:48,010 --> 00:21:53,350 +طيب نبدأ الأن نشغل شغلنا في الاشتقاء لكن قلت لك + +216 +00:21:53,350 --> 00:21:57,670 +المرة الماضية إذا عندك دالة bus و دالة مقام و + +217 +00:21:57,670 --> 00:22:03,350 +دارية ال bus أكبر من أو تساوي المقام يبقى أول خطوة + +218 +00:22:03,350 --> 00:22:10,110 +نفضل نعملها قسم المطولة إذا بيدروح أجسم ال X تربية + +219 +00:22:10,110 --> 00:22:18,670 +زائد واحد على مين على ناقص X تربية زائد واحدطبعا + +220 +00:22:18,670 --> 00:22:23,730 +اي واحد ناقص X تربية انا ناقص X تربية زي واحد X + +221 +00:22:23,730 --> 00:22:29,590 +تربية على ناقص X تربية فيها كم؟ ناقص واحد بيبقى في + +222 +00:22:29,590 --> 00:22:35,410 +سلب X تربية X تربية وهنا كم؟ سالب واحد هذه موجة + +223 +00:22:35,410 --> 00:22:42,260 +بيصير سالب وهذه بيصير موجة بيبقى لدي كم؟إذا صرت + +224 +00:22:42,260 --> 00:22:49,900 +الدالة Y تساوي سالب واحد زائد اتنين على واحد ناقص + +225 +00:22:49,900 --> 00:22:55,880 +X تربية او ممكن تحطها على الشكل التالي زائد اتنين + +226 +00:22:55,880 --> 00:23:02,560 +هذه الفرق بين المربعين واحد ناقص X في واحد زائد X + +227 +00:23:02,560 --> 00:23:07,550 +يبقى هي حطيناها بالشكل اللي عندنا هذايبقى بعد ما + +228 +00:23:07,550 --> 00:23:12,550 +جيبنا النقاط التقاطة أو نقطة التقاطة مع محاور + +229 +00:23:12,550 --> 00:23:18,570 +الإحداثية الـ U01 بدأ أجيب من المشتقة الأولى أو + +230 +00:23:18,570 --> 00:23:23,550 +قبلها بدأ أجيب من الـ Asymptotes يبقى باجي بقوله + +231 +00:23:23,550 --> 00:23:28,250 +في عندي Obligate asymptote؟ لأ لإن ضرية البصرة + +232 +00:23:28,250 --> 00:23:32,980 +ضرية المقام ماهياش أعلى منها بمقدار واحديبقى بتروح + +233 +00:23:32,980 --> 00:23:38,100 +ادور وين على ال horizontal يبقى بدي اخد limit لل Y + +234 +00:23:38,100 --> 00:23:43,920 +لما ال X بدها تروح لزائد او ناقص infinity اي من + +235 +00:23:43,920 --> 00:23:49,390 +التنتينيبقى هذا الكلام بدي يساوي limit لما ال X + +236 +00:23:49,390 --> 00:23:54,450 +بدي تروح لزائد او ناقص infinity طبعا هتحطيني نفس + +237 +00:23:54,450 --> 00:23:58,530 +النتيجة من البصد polynomial والمقام polynomial + +238 +00:23:58,530 --> 00:24:05,370 +يبقى واحد زائد X تربية على واحد ناقص X تربية بروح + +239 +00:24:05,370 --> 00:24:11,600 +نقسم كله من البصد والمقام علىيبقى X تربية يبقى هذا + +240 +00:24:11,600 --> 00:24:15,960 +الكلام limit لما ال X بده يروح لزائد او ناقص + +241 +00:24:15,960 --> 00:24:22,140 +infinity لواحد على X تربية زائد واحد واحد على X + +242 +00:24:22,140 --> 00:24:28,900 +تربية ناقص واحد يبقى النتيجة كده؟سالب واحد طبعا + +243 +00:24:28,900 --> 00:24:34,380 +هذا بالزيرو وهذا بالزيرو يبقى كده؟ يبقى سالب واحد + +244 +00:24:34,380 --> 00:24:43,420 +يبقى كذلك Y تساوي سالب واحد is a horizontal + +245 +00:24:43,420 --> 00:24:48,220 +asymptote + +246 +00:24:48,220 --> 00:24:51,360 +تمام تمام + +247 +00:24:54,710 --> 00:25:00,810 +الرقم اللي يجعل المقام يساوي 0 إذا احتمال X يساوي + +248 +00:25:00,810 --> 00:25:06,430 +واحد وكذلك X يساوي سالب واحد هذين يكونوا Vertical + +249 +00:25:06,430 --> 00:25:11,890 +Asymptotes إذا بتروح أخد limit لما ال X بده يساوي + +250 +00:25:11,890 --> 00:25:16,810 +بده تروح لسالب واحد مثلا من جهة اليمين اليمين لل + +251 +00:25:16,810 --> 00:25:21,920 +function اللي عندنا هذه اليمين سالب واحدزائد اتنين + +252 +00:25:21,920 --> 00:25:28,320 +على واحد ناقص x في واحد زائد x هو يساوي المقدار + +253 +00:25:28,320 --> 00:25:33,640 +الثابت هذا مالوش داره وهذا زائد اتنين على احنا + +254 +00:25:33,640 --> 00:25:39,700 +رايحين اللي يسلب واحد من جهات اليمينتمام؟ إذا هذا + +255 +00:25:39,700 --> 00:25:45,900 +هذا ماعندوش مشكلة في هذه الحالة، يبقى هذا بظل واحد + +256 +00:25:45,900 --> 00:25:53,280 +سالب سالب واحد، مصبوط؟ يبقى هذا بصير واحد زائد + +257 +00:25:53,280 --> 00:26:02,700 +واحد، لما أروحلي سالب واحد من جهة اليمينيعني أكبر + +258 +00:26:02,700 --> 00:26:07,060 +من سالب واحد يعني سالب تسعة من عشرة مثلا إذا هذا + +259 +00:26:07,060 --> 00:26:15,680 +بيبقى very small positive يبقى very small positive + +260 +00:26:15,680 --> 00:26:19,020 +quantity هذا بيقدش بصغير + +261 +00:26:26,590 --> 00:26:32,330 +بينفينيتي يبقى سالب واحد زائد انفينيتي بقداش + +262 +00:26:32,330 --> 00:26:38,510 +بينفينيتي يبقى بناء عليه ال X يساوي سالب واحد is a + +263 +00:26:38,510 --> 00:26:43,070 +vertical asymptote وليس بالضرورة انك تروح تحسبها + +264 +00:26:43,070 --> 00:26:47,450 +من وينمن عندي الشمال احنا نقول هادي او هادي سيال + +265 +00:26:47,450 --> 00:26:52,230 +ليس بدنا نروح نحسب الاتنين اذا لو روحت اخدت limit + +266 +00:26:52,230 --> 00:26:57,150 +لما ال X بدأ تروح للواحد مثلا من جهة الشمال اللي + +267 +00:26:57,150 --> 00:27:00,190 +هي النقطة التانية معناها تخلصنا من السالب واحد بدأ + +268 +00:27:00,190 --> 00:27:05,970 +نروح لمن؟ للواحد لمن؟ لسالب واحد زائد اتنين على + +269 +00:27:05,970 --> 00:27:12,210 +واحد ناقص X في واحد زائد X يبقى هذا الكلام يساوي + +270 +00:27:12,210 --> 00:27:18,940 +سالب واحدزائد اتنين على. احنا رايحين للواحد من جهة + +271 +00:27:18,940 --> 00:27:24,140 +الشمال. من جهة الشمال يعني اقل من واحد بكثر. يبقى + +272 +00:27:24,140 --> 00:27:33,940 +القوس هذا very small positive. يبقى هذا very small + +273 +00:27:33,940 --> 00:27:38,280 +positive quantity. تمام؟ + +274 +00:27:40,930 --> 00:27:48,630 +وهذا واحد زائد واحدطيب، لاحظ في الحالة الأولى لما + +275 +00:27:48,630 --> 00:27:53,690 +قلنا سالب واحد من جهة اليمين سالب واحد من جهة + +276 +00:27:53,690 --> 00:27:58,190 +اليمين يعني سالب تسعة من عشرة لما جهتها الجثة ده + +277 +00:27:58,190 --> 00:28:01,730 +سالب تسعة بقال very small positive وهذا صار سالب + +278 +00:28:01,730 --> 00:28:07,370 +واحد وهنا واحد يعني سالب سالب واحد صار موجة بواحد + +279 +00:28:07,370 --> 00:28:13,250 +وبالتالي أتتني من نفس النتيجة يبقى هذه أتتني سالب + +280 +00:28:13,250 --> 00:28:19,670 +واحدزائد infinity اللي هو infinity معناته الخطين + +281 +00:28:19,670 --> 00:28:26,710 +اللي اتنين هدول are vertical asymptotes يبقى ال X + +282 +00:28:26,710 --> 00:28:33,910 +يساوي سالب واحد and ال X بده يساوي واحد are two + +283 +00:28:33,910 --> 00:28:38,990 +vertical asymptotes + +284 +00:28:44,300 --> 00:28:47,940 +يبقى خلاصنا قصة الـ Asymptotes، بدنا نروح لمين + +285 +00:28:47,940 --> 00:28:55,300 +الآن؟ للاشتقاق، يبقى بالدليل الـY'Y أساوي + +286 +00:28:57,900 --> 00:29:02,120 +ممكن نشتاق من هذه أو من هذه تماما، لكن لو + +287 +00:29:02,120 --> 00:29:08,120 +نشتاقينها، ده أسهل شوية، مصبوط؟ يعني هذه كأنها + +288 +00:29:08,120 --> 00:29:13,040 +مشتاقة السالب واحد مع السلامة، وبضالي اتنين مالكش + +289 +00:29:13,040 --> 00:29:19,400 +دعوة، وهذا السالب واحد على المقدار تربية، واحد على + +290 +00:29:19,400 --> 00:29:25,950 +واحد ناقص X تربيةالكل تربية في مشتقت مداخل القسل + +291 +00:29:25,950 --> 00:29:34,970 +وجداش سالي باتنين X، مظبوط؟ يبقى النتيجة صارت أربع + +292 +00:29:34,970 --> 00:29:43,200 +X على واحد ناقص X تربية لكل تربيةهذه لو سويتها + +293 +00:29:43,200 --> 00:29:49,640 +بالـ Zero معناته ان X سوى قداش يبقى هذا بده يعطيلك + +294 +00:29:49,640 --> 00:29:54,760 +ان X أو خلاص مش لازم ان هذي Critical Points قد + +295 +00:29:54,760 --> 00:29:59,260 +تكون Local Maximum او قد تكون Local Minimum اذا + +296 +00:29:59,260 --> 00:30:05,750 +بدنا نروح نبحث الإشاراتنبحث الإشارات هذه لو روحت + +297 +00:30:05,750 --> 00:30:12,730 +قولتلك اربعة X على واحد ناقص X في واحد زائد X لكل + +298 +00:30:12,730 --> 00:30:18,730 +تربية يبقى هذه تربية وهذه ايه؟ تربية اذا بدي اروح + +299 +00:30:18,730 --> 00:30:24,830 +اخد إشارة الاربعة X وهذا اللي يا الله اني بتاخد ال + +300 +00:30:24,830 --> 00:30:30,070 +zero تبعها وين؟ عند ال zero بعد ال zero positive + +301 +00:30:30,070 --> 00:30:39,000 +وقبل ال zero ايه؟نقات، نجي يأخذ إشارة واحد ناقص X + +302 +00:30:39,000 --> 00:30:45,520 +لكل تربيع، إذا أخذت Zero تبعها وين؟ عند الواحد، + +303 +00:30:45,520 --> 00:30:51,700 +بعد الواحد positive، وقبل الواحد positive لأنها + +304 +00:30:51,700 --> 00:30:59,530 +كمية مربعةلكن لو ماكنتش تربية لأصبحت بعد الواحد + +305 +00:30:59,530 --> 00:31:05,430 +سالب و قبل الواحد موجب تمام؟ طيب يبقى بداجي أخد + +306 +00:31:05,430 --> 00:31:11,810 +إشارة الواحد زائد x لكل تربية تاخد ال zero تباعها + +307 +00:31:11,810 --> 00:31:18,180 +وين؟ عند السالب واحد بعده برضه positiveو جاب له + +308 +00:31:18,180 --> 00:31:25,420 +positive لأن كمية مربعة بدي اخد اشارة الان اللي هو + +309 +00:31:25,420 --> 00:31:32,160 +اربعة X على واحد ناقص X الكل تربية واحد زائد X + +310 +00:31:32,160 --> 00:31:38,320 +الكل تربية و نيجي نحدد الحدود الإقليمية + +311 +00:31:48,450 --> 00:31:56,300 +الأولى positive والتانية negativeوالتالتة نيجاتيب + +312 +00:31:56,300 --> 00:32:01,900 +والربعة نيجاتيب يبقى الدلة كانت نازلة وظلت نازلة + +313 +00:32:01,900 --> 00:32:04,620 +وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت + +314 +00:32:04,620 --> 00:32:04,620 +نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة + +315 +00:32:04,620 --> 00:32:04,620 +وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت + +316 +00:32:04,620 --> 00:32:05,020 +نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة + +317 +00:32:05,020 --> 00:32:08,060 +وظلت نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظلت + +318 +00:32:08,060 --> 00:32:18,300 +نازلة وظلت نازلة وظلت نازلة وظلت نازلة وظل + +319 +00:32:25,760 --> 00:32:32,000 +الفترة من عند السلب infinity لغاية جداش سالب واحد + +320 +00:32:32,000 --> 00:32:37,620 +as an open interval لأن عند السلب واحد الدالة مش + +321 +00:32:37,620 --> 00:32:45,140 +معرفةحط معاها اتحاد سالب واحد و zero و بدنا نقفلها + +322 +00:32:45,140 --> 00:32:49,940 +من عند ال zero لأن ده اللي عندها معرفة بعد هيك ال + +323 +00:32:49,940 --> 00:32:58,600 +if is increasing ده اللي تنقصيه على الفترة من عند + +324 +00:32:58,600 --> 00:33:05,000 +ال zero لغاية الواحد عند ال واحد مش معرفة اتحاد + +325 +00:33:05,000 --> 00:33:13,070 +الواحد و infinityطيب في عندي local maximumهل يوجد + +326 +00:33:13,070 --> 00:33:17,950 +local maximum؟ الله يبعث لك الله يقول ماعنديش إلا + +327 +00:33:17,950 --> 00:33:24,590 +local minimum وين؟ عند zero عند zero حسبناها عند + +328 +00:33:24,590 --> 00:33:31,250 +zero طلعت واي بقدراش؟ واحد يبقى باجي بقوله ال F + +329 +00:33:31,250 --> 00:33:41,480 +has local minimum واحد at x يساوي زيروانتهينا منها + +330 +00:33:41,480 --> 00:33:45,060 +.الان ال increase و ال decrease اللي خلصنا منه + +331 +00:33:45,060 --> 00:33:51,160 +يبقى بدنا نروح لمين؟ للمشتقة الثانية.و اين المشتقة + +332 +00:33:51,160 --> 00:33:56,340 +اللي اشتقناها احنا اصلا؟ اللي هي هذه.مصبوط؟ الهي + +333 +00:33:56,340 --> 00:33:59,880 +اللي بدروح اشتغل هذه بتطلع روحي، بس هذه أسهل كتير + +334 +00:33:59,880 --> 00:34:05,340 +.مصبوط؟ يبقى بدي أروح أجيبله المشتقة الثانية من + +335 +00:34:05,340 --> 00:34:13,260 +هذه هيها. هذا الجزر.اللي بده أخذه هو المشتق، اللي + +336 +00:34:13,260 --> 00:34:17,420 +هو اللي بده أجيبه هو المشتق الثاني يبقى باجي بقوله + +337 +00:34:17,420 --> 00:34:26,150 +يبقى ال Y W prime يبقى المقامأي تربية؟ في مشتقة + +338 +00:34:26,150 --> 00:34:32,810 +البصطة اللي هو باربع ناقص البصط في مشتقة المقام + +339 +00:34:32,810 --> 00:34:39,470 +الأس في القوس مرفوع لنفس الأس مطروح من واحد في + +340 +00:34:39,470 --> 00:34:46,570 +مشتقة مداخل القوسيبقى هذه المقام في مشتقة البصد + +341 +00:34:46,570 --> 00:34:52,750 +ناقص البصد في مشتقة المقام الأس في القوس مرفوع + +342 +00:34:52,750 --> 00:34:57,890 +لنفس الأس مطروح منه واحد في مشتقة مداخل القوس كل + +343 +00:34:57,890 --> 00:35:06,890 +هذا maximum على واحد ناقص X تربية لكل أس أربعة طيب + +344 +00:35:06,890 --> 00:35:08,930 +تعالى نشوف كيف بدأت أصف هذه + +345 +00:35:13,520 --> 00:35:20,120 +إذا بقدر اخد اتنين في اتنين كمان باربع عامل مشترك + +346 +00:35:20,120 --> 00:35:27,700 +يعني بقدر اخد اربعة في واحد ناقص X تربية عامل + +347 +00:35:27,700 --> 00:35:33,860 +مشترك، كدهش مضال لإن هنا واحد ناقص X تربية فقط، + +348 +00:35:33,860 --> 00:35:40,370 +نيجي هناالجث هذا راح والاربع دي راحت، ضل سلب في + +349 +00:35:40,370 --> 00:35:48,890 +سلب موجب و عندك X تربية، يبقى ضل عند هنا موجب اربع + +350 +00:35:48,890 --> 00:35:54,010 +X تربية، مظبوط هيك؟هذه الأربعة عادي برا بقال عندك + +351 +00:35:54,010 --> 00:35:59,070 +اتنين في اتنين باربع اكس في اكس باكس تربية والسالب + +352 +00:35:59,070 --> 00:36:05,850 +في سالب بموجب تمام؟ كل هذا على مين؟ على واحد ناقص + +353 +00:36:05,850 --> 00:36:10,590 +اكس تربية لكل قص أربعة اظن الجوز هذا بيروح مع + +354 +00:36:10,590 --> 00:36:15,430 +الأربعة اللي تحت هذه وبالتالي بتصفى المسألة إلى + +355 +00:36:15,430 --> 00:36:22,730 +أربعة في مين؟في واحد زائد تلاتة X تربية على واحد + +356 +00:36:22,730 --> 00:36:31,750 +ناقص X تربية الكل تكيبة طيب تمام هذه لو سويتها بال + +357 +00:36:31,750 --> 00:36:39,000 +zero بتجيبلي نتيجةHas no solution يبقى الآن لو قلت + +358 +00:36:39,000 --> 00:36:46,780 +له yw prime يساوي أربعة في واحد زائد تلاتة x سربيع + +359 +00:36:46,780 --> 00:36:53,880 +على مين على واحد ناقص x الكل تكيب واحد زائد x الكل + +360 +00:36:53,880 --> 00:37:03,580 +تكيب هذه تساوي zero has no solutionبتجيب ليش ولا + +361 +00:37:03,580 --> 00:37:09,960 +قيمة، ليش؟ لأنه لا يمكن لمجموعة كميتين موجابتين + +362 +00:37:09,960 --> 00:37:15,840 +انها تساوي Zero يبقى هذه مالهاش حل، بالبلد هيك لو + +363 +00:37:15,840 --> 00:37:20,000 +سويتها بال Zero يبقى تصير تلاتة X تربية زاد واحد + +364 +00:37:20,000 --> 00:37:25,730 +يساوي Zero يبقى تلاتة X تربية يساوي سالب واحدهل + +365 +00:37:25,730 --> 00:37:31,910 +يُعقل كمية مربعة ساوي قيمة سالبة؟ يبقى هذه لا حلول + +366 +00:37:31,910 --> 00:37:35,310 +على الريال، في ال complex ماشي إلا حل، بس في + +367 +00:37:35,310 --> 00:37:41,350 +الريال عندنا مالهاش حل تماما هل ال X يساوي سالب + +368 +00:37:41,350 --> 00:37:46,710 +واحد وال X يساوي واحد ممكن يكون inflection point؟ + +369 +00:37:47,810 --> 00:37:54,170 +لأنها غير معرفة عندهم يبقى معناها خليني أدرس + +370 +00:37:54,170 --> 00:37:59,470 +الإشارات اللي عندنا و نشوف لون بدنا نوصل يبقى انا + +371 +00:37:59,470 --> 00:38:02,990 +بدى أدرس إشارة ال Y double A prime عشان أشوف ال + +372 +00:38:02,990 --> 00:38:07,560 +concave up و ال concave downوالـ inflection points + +373 +00:38:07,560 --> 00:38:15,740 +يبقى بدى أروح أخد إشارة اللي هو 4 في 1 زائد 3 X + +374 +00:38:15,740 --> 00:38:22,840 +تربية وده ال real line عمرها بتاخد zeroأمرا بتاخد + +375 +00:38:22,840 --> 00:38:29,060 +zero؟ أمرا بتاخد قيمة سالبة؟ يبقى هذه كتبناها و + +376 +00:38:29,060 --> 00:38:33,960 +الله ما كتبناها مش هتفرج عندنا بالمرة هذه موجبة + +377 +00:38:33,960 --> 00:38:39,780 +على طول الخط بداجي أخد إشارة الجوز الثاني لواحد + +378 +00:38:39,780 --> 00:38:46,660 +ناقص X لكل تكيمة بتاخد ال zero تبعها وين؟ عندنا + +379 +00:38:46,660 --> 00:38:48,400 +بعد الواحد + +380 +00:38:50,840 --> 00:38:58,000 +سالبة لأنه سالب تكييب بسالب إذا بعده سالبة و قبله + +381 +00:38:58,000 --> 00:39:04,080 +موجة بالشكل اللي عندنا بعدك بدأت أخد إشارة واحد + +382 +00:39:04,080 --> 00:39:10,360 +زائد X لكل تكييب بتاخد ال zero تبعها ويا عند + +383 +00:39:10,360 --> 00:39:17,940 +السالب واحد بعد سالب واحد موجة بقى يبقى هي موجة + +384 +00:39:17,940 --> 00:39:24,720 +بقى عندنافبجب ليه سالب واحد زي سالي باتنين سالبة، + +385 +00:39:24,720 --> 00:39:29,800 +يبقى هنا سالبة بهذا الشكل، يبقى لاحظ إن النقطة + +386 +00:39:29,800 --> 00:39:33,020 +الثانية على غير ما تعودنا، على اليمين سالب وعلى + +387 +00:39:33,020 --> 00:39:36,880 +الشمال موجب، مش دائما على اليمين موجب وعلى الشمال + +388 +00:39:36,880 --> 00:39:42,780 +سالبيبقى بنروح ناخد إشارة كل المقدار اللي هو أربعة + +389 +00:39:42,780 --> 00:39:48,200 +في واحد زائد تلاتة X تربية على واحد ناقص X لكل + +390 +00:39:48,200 --> 00:39:54,120 +تكييب واحد زائد X لكل تكييب و أقول هذا ال real + +391 +00:39:54,120 --> 00:40:00,110 +lineوهي الحدود الإقليمية اللي عندنا وهي عندنا اللي + +392 +00:40:00,110 --> 00:40:05,570 +هو واحد وهي عندنا اللي هو مين اللي هو سالب واحد + +393 +00:40:05,570 --> 00:40:12,490 +يبقى هذه السالبة هذه موجبة هذه السالبة يبقى هنا + +394 +00:40:12,490 --> 00:40:21,030 +concave downهنا concave up هنا concave down تمام؟ + +395 +00:40:21,030 --> 00:40:29,350 +إذا نبنيه يجي نقول the graph of + +396 +00:40:29,350 --> 00:40:33,930 +F is concave + +397 +00:40:35,110 --> 00:40:41,850 +down, on على الفترة من أول إلى أولين من سالب + +398 +00:40:41,850 --> 00:40:51,530 +infinity لغاية سالب واحد and on وكذلك من عند + +399 +00:40:51,530 --> 00:40:58,470 +الواحد لغاية infinity and concave up + +400 +00:41:01,610 --> 00:41:09,910 +عن الفترة من سالب واحد إلى أحد عند السالب واحد + +401 +00:41:09,910 --> 00:41:16,790 +والواحد no inflection الندالة غير متصلة عندهم يبقى + +402 +00:41:16,790 --> 00:41:26,390 +هنا there is no inflection point + +403 +00:41:32,640 --> 00:41:40,760 +أو because دوري because ال + +404 +00:41:40,760 --> 00:41:46,320 +F is not continuous + +405 +00:41:48,530 --> 00:41:55,750 +مع الاكس يساوي سالب واحد عند الاكس يساوي واحد + +406 +00:42:05,390 --> 00:42:09,690 +مشان نرسم يبقى احنا عندنا y تساوي سالب واحد + +407 +00:42:09,690 --> 00:42:14,510 +horizontal واحد و سالب واحد اللي هو ال vertical + +408 +00:42:14,510 --> 00:42:20,550 +asymptotes وعند المنحنية مرضه نقطة zero واحد + +409 +00:42:43,950 --> 00:42:47,790 +خلّي بالك هنا قبل + +410 +00:42:47,790 --> 00:42:50,990 +قليل في السؤال اللي جابله أول شغلة بنفسه من ال + +411 +00:42:50,990 --> 00:42:56,490 +asymptotes يبقى أنا عند ال asymptote ال X يساوي + +412 +00:42:56,490 --> 00:43:04,050 +واحد و سالب واحد يبقى لو روحت قلت هذا الخط الرأسي + +413 +00:43:04,050 --> 00:43:12,300 +اللي هو من ال X يساوي واحدو جيت من الناحية التانية + +414 +00:43:12,300 --> 00:43:20,040 +وعلى نفس البعد وقلت هذا ال X يساوي سالب واحد فيه + +415 +00:43:20,040 --> 00:43:25,440 +كمان horizontal asymptote Y يساوي سالب واحد يبقى + +416 +00:43:25,440 --> 00:43:34,260 +هناك هذا الخط المنقطة ل Y تساوي سالب واحد يبقى + +417 +00:43:34,260 --> 00:43:39,130 +هدول ال asymptotes اللي عندنا بعد هيكجال لي في + +418 +00:43:39,130 --> 00:43:44,530 +عندي local minimum عند ال zero والواحد يبقى عند ال + +419 +00:43:44,530 --> 00:43:50,190 +zero والواحد في عندي local minimum يبقى المنحنة + +420 +00:43:50,190 --> 00:43:56,270 +هيكون مفتوح الي أعلى بهذا الشكل غير هيك انسىطيب هى + +421 +00:43:56,270 --> 00:44:01,110 +عندنا النقطة سالب واحد وهى عندنا النقطة واحد من + +422 +00:44:01,110 --> 00:44:06,710 +سالب واحد الى زيرو هل الدالة تزايدية ولا تناقصية + +423 +00:44:06,710 --> 00:44:12,890 +يبقى من سالب واحد الى زيرو الدالة decreasing طيب + +424 +00:44:12,890 --> 00:44:17,890 +تناقصية وهذا ال asymptote اذا بتبقى نازلة مع مين؟ + +425 +00:44:17,890 --> 00:44:22,730 +مع ال asymptote جاية مع ال asymptote منفر وأجت + +426 +00:44:22,730 --> 00:44:28,690 +نازلة بهذا الشكلمن Zero لواحد ما لها increasing + +427 +00:44:28,690 --> 00:44:33,070 +يبقى increasing و بتيجي تطلع مع ال asymptote بهذا + +428 +00:44:33,070 --> 00:44:39,630 +الشكلطيب نجي نكمل الان لو جيت من سالب infinity + +429 +00:44:39,630 --> 00:44:44,430 +لغاية سالب واحد من سالب infinity لسالب واحد + +430 +00:44:44,430 --> 00:44:51,250 +decreasing اتدالة تناقصية تناقصية بس انا مش عارف + +431 +00:44:51,250 --> 00:44:56,310 +هل هي فوق ولا تحت مشان اعرف فوق ولا تحت بروح انا + +432 +00:44:56,310 --> 00:45:02,000 +بحسبها مثلا عندي سالب اتنينأشوف أين تجي عند السلم + +433 +00:45:02,000 --> 00:45:06,000 +هل فوق إذا فوق بيكون خلاص انت هنا من الجسر تحت + +434 +00:45:06,000 --> 00:45:10,640 +يبقى انت هنا يبقى بتروح أشيبله F في جداش و سالب + +435 +00:45:10,640 --> 00:45:18,400 +اتنين يبقى بد ال F of سالب اتنين يبقى واحد ناقص + +436 +00:45:18,400 --> 00:45:24,240 +اتنين لكل تربية زائد اتنين لكل تربية على واحد ناقص + +437 +00:45:24,240 --> 00:45:28,660 +ناقص اتنين لكل تربية مش هذي مثلة ايه ال canonيبقى + +438 +00:45:28,660 --> 00:45:36,020 +هذا الكلام بده يساوي واحد زائد أربعة على واحد ناقص + +439 +00:45:36,020 --> 00:45:43,740 +أربعة يبقى الجواب يساوي الناقص خمس أتلات يبقى خمس + +440 +00:45:43,740 --> 00:45:48,980 +أتلات والسالب واحد و تلتين طيب هاي السالب واحد + +441 +00:45:48,980 --> 00:45:53,460 +عندنا يبقى بدي أنزل كمان شوية يبقى بتجيلك النقطة + +442 +00:45:53,460 --> 00:45:59,760 +اللي هي عندنا هذهتمام؟ جالي هذا على هذه الفترة + +443 +00:45:59,760 --> 00:46:05,460 +decreasing، الدالة تناقصية، خلي بالك هنا، ممكن + +444 +00:46:05,460 --> 00:46:12,120 +أقول decreasing هك؟ صح؟ و ممكن أقول decreasing هك؟ + +445 +00:46:12,780 --> 00:46:16,760 +أريد أن أعرف من هؤلاء هؤلاء هو الـ Concave Up وهو + +446 +00:46:16,760 --> 00:46:22,260 +الـ Concave Down فأنا أرى الـ Concave على الفترة + +447 +00:46:22,260 --> 00:46:27,620 +من سالب Infinity لسالب واحد يبقى من سالب Infinity + +448 +00:46:27,620 --> 00:46:32,520 +لسالب واحد Concave Down فأنا أريد أن تكون الرسمة + +449 +00:46:32,520 --> 00:46:36,420 +من؟ اللي عندنا بالشكل هذا فأنا أريد أن تأتي الرسمة + +450 +00:46:36,420 --> 00:46:41,820 +مع الـ Asymptotic بالشكل هذاو تمشي مع الاسمتوت + +451 +00:46:41,820 --> 00:46:47,520 +التاني بهذا الشكل تمام؟ + +452 +00:46:47,520 --> 00:46:53,580 +طيب، الآن بدي أجي للجزء الثاني من الرسمة، بدي أشوف + +453 +00:46:53,580 --> 00:46:59,740 +بعد الواحد زي اتنين، شو بدي يكون شكل الدالة؟ يبقى + +454 +00:46:59,740 --> 00:47:04,220 +خمس على جداش، خمس أتلات بس + +455 +00:47:07,050 --> 00:47:13,530 +Concave تعلّي عليها من واحد إلى انفينيتي وبعد من + +456 +00:47:13,530 --> 00:47:19,470 +واحد إلى انفينيتي اللي هو اللي جافه به is concave + +457 +00:47:19,470 --> 00:47:24,810 +down على الفترة هذه وكذلك على الفترة اللي عندنا + +458 +00:47:24,810 --> 00:47:29,990 +هذهيبقى concave down لو روحت حصها بده تيجي النقطة + +459 +00:47:29,990 --> 00:47:34,130 +تحت وبالتالي بده يجيك المنحنة بالشكل اللي انا معه + +460 +00:47:34,130 --> 00:47:39,270 +ال asymptote ماشي بهذا الشكل يبقى هي الرسمة اللي + +461 +00:47:39,270 --> 00:47:43,590 +انا طبعا لو جيت حسبتها هتعطيك نفس النتيجة اللي + +462 +00:47:43,590 --> 00:47:49,470 +عندك هذه يعني لو جينا قولنا ال F of 2 هتلاقيها + +463 +00:47:49,470 --> 00:47:54,640 +كمان ناقص خمسةعلى ثلاثة و بالتالي المنحنة صار أن + +464 +00:47:54,640 --> 00:48:01,720 +كله تحت بهذا الشكل من + +465 +00:48:01,720 --> 00:48:07,180 +هنا نعطي تعريف جديد اللي وعدناكوا فيه قبل قليل + +466 +00:48:07,180 --> 00:48:13,400 +Definition آه آه هذا كان في الكتاب في الطابعة + +467 +00:48:13,400 --> 00:48:17,600 +التاسعة بس في الطابعة التاشر مش موجود لكن هنعطيه + +468 +00:48:17,600 --> 00:48:22,320 +عليها رسومات موجودة في التمرينبنعطيك يام عشان نشوف + +469 +00:48:22,320 --> 00:48:33,760 +كيف بنعمل الرسومات هذه the graph of the continuous + +470 +00:48:33,760 --> 00:48:52,930 +function y تساوي f of x has a cuspعلى اكس + +471 +00:48:52,930 --> 00:49:05,730 +بديو ساوي C if the concavity is + +472 +00:49:05,730 --> 00:49:12,910 +the same on + +473 +00:49:12,910 --> 00:49:14,050 +both sides + +474 +00:49:18,420 --> 00:49:30,060 +of C and either اما + +475 +00:49:30,060 --> 00:49:40,180 +النقطة الأولى اللي هو ال limitللـ F prime of X لما + +476 +00:49:40,180 --> 00:49:45,100 +الـ X بده يروح الى C من جهة الشمال بده يساوي + +477 +00:49:45,100 --> 00:49:57,040 +Infinity and limit لل F prime of X لما الـ X بده + +478 +00:49:57,040 --> 00:50:03,160 +يروح لـ C من جهة اليمين بده يساوي سالب Infinity or + +479 +00:50:04,560 --> 00:50:11,880 +نقطة ثانية limit لما ال X بده يروح ل C من جهة + +480 +00:50:11,880 --> 00:50:20,160 +الشمال لل F prime of X بده يساوي سالب infinity and + +481 +00:50:20,160 --> 00:50:28,100 +limit لما ال X بده يروح ل C من جهة اليمين لل F + +482 +00:50:28,100 --> 00:50:32,540 +prime of X يساوي infinity + +483 +00:50:37,010 --> 00:50:42,030 +طبعا لو روحنا و رسمنا الرسم هذه نقول بالشكل ان هذا + +484 +00:50:42,030 --> 00:50:49,530 +هذا محور X هذا محور Y هذا النقطة اللي هي Zero ممكن + +485 +00:50:49,530 --> 00:50:53,930 +المنحنة يجيلك بالشكل اللي عندك هذا + +486 +00:51:08,400 --> 00:51:14,220 +يبقى طبعا هنا بيكون الكاسب وهنا هذه النقطة اللى + +487 +00:51:14,220 --> 00:51:22,660 +عندنا اللى هو نقطة C وهنا ال limit لل F prime of X + +488 +00:51:22,660 --> 00:51:28,560 +لما ال X بدها تروح الى C من جهة الشمال بده يساوي + +489 +00:51:28,560 --> 00:51:35,820 +infinityوهنا ال limit لل F prime of X لما ال X بده + +490 +00:51:35,820 --> 00:51:45,240 +يروح ل C من جهة اليمين بدها تساوي سالب infinity او + +491 +00:51:45,240 --> 00:51:52,440 +ممكن يكون بالشكل اللي عندك هذا محور X وهذا Y وهذا + +492 +00:51:52,440 --> 00:51:59,600 +Zero منحنا جالك كيك ورجع طالع هيك يبقى هذه النقطة + +493 +00:52:00,790 --> 00:52:10,190 +اللي هي C هنا I limit لل F prime of X لما ال X بده + +494 +00:52:10,190 --> 00:52:16,270 +يروح ل C من جهة الشمال يساوي سالب Infinity او هنا + +495 +00:52:16,270 --> 00:52:22,490 +I limit لل F prime of X لما ال X بده يروح ل C من + +496 +00:52:22,490 --> 00:52:29,920 +جهة اليمين بده يساوي من؟ بده يساوي Infinityوهذا + +497 +00:52:29,920 --> 00:52:34,800 +كمان هنا اللي هو الكاسب + +498 +00:53:02,300 --> 00:53:09,880 +نعود للتعريف اللى قبل ان نأخد مثال على ذلك التعريف + +499 +00:53:09,880 --> 00:53:14,220 +يقول الـ graph of the continuous function يبقى + +500 +00:53:14,220 --> 00:53:18,660 +الشرف الأساسي ان تبقى ده اللى متصل او Y to the + +501 +00:53:18,660 --> 00:53:26,820 +power of X لديه كسب ويم عند X يساوي C if the + +502 +00:53:26,820 --> 00:53:32,170 +concavity is the same in both sides of C andيبقى + +503 +00:53:32,170 --> 00:53:38,560 +دالة مدالة متصلة اتنين على طرفين النقطةالمنحنة يا + +504 +00:53:38,560 --> 00:53:44,540 +إما concave up يا إما concave down طلع لهنا هذا + +505 +00:53:44,540 --> 00:53:50,620 +الجثم مفتوح لوين وهذا مفتوح لوين إلى أعلى يبقى هنا + +506 +00:53:50,620 --> 00:53:56,600 +على طرفين نقطة C مفتوح إلى أعلى أو عند النقطة C + +507 +00:53:56,600 --> 00:54:01,660 +الجثم مفتوح لوين إلى أسفل وهذا مفتوح لوين إلى أسفل + +508 +00:54:02,090 --> 00:54:08,050 +يبقى عند طرفين الكاصب الدالة متصلة وعند الطرفين + +509 +00:54:08,050 --> 00:54:12,910 +الدالة إما concave up أو concave down يبقى هذه + +510 +00:54:12,910 --> 00:54:18,810 +الشرطين التالت لو روحت أخدت limit للمشتقة عند نقطة + +511 +00:54:18,810 --> 00:54:23,340 +الكاصب لما روحلها من طرف الشماليا إما هتعطيني + +512 +00:54:23,340 --> 00:54:27,700 +infinity، يا إما هتعطيني السالب infinity، بتفريقش + +513 +00:54:27,700 --> 00:54:31,680 +عنا، اتطلع في الحالة الأولى اعطبطني infinity + +514 +00:54:31,680 --> 00:54:37,960 +بالموجب، ليش؟ لأن دالة دالة تزايدية، تمام؟ إذا + +515 +00:54:37,960 --> 00:54:41,980 +المشتقة بتبقى أكبر من ال zero، يبقى ال limit تبعها + +516 +00:54:41,980 --> 00:54:47,330 +بتعطيني infinityفي الحالة هذه للجزء الثاني بيكون + +517 +00:54:47,330 --> 00:54:51,750 +ال limit لما تذهب إلى C من جهة اليمين بتبقى ال F + +518 +00:54:51,750 --> 00:54:58,070 +from تناقصية فتعطي من السلب infinity أو في البداية + +519 +00:54:58,070 --> 00:55:01,590 +ممكن تبقى تناقصية تعطي من السلب infinity والتانية + +520 +00:55:01,590 --> 00:55:07,420 +تزايدية تعطي من ال infinity يعني بمعنى آخربعد ما + +521 +00:55:07,420 --> 00:55:13,260 +ألاقي على طرفين نقطة لها نفس الconcavity بتروح أخد + +522 +00:55:13,260 --> 00:55:17,840 +limit ال F prime لما ال X بده تروح ل C من جهة + +523 +00:55:17,840 --> 00:55:21,960 +الشمال ان طلعت من جهة الشمال بده تساوي ال infinity + +524 +00:55:21,960 --> 00:55:26,220 +لازم تطلع من جهة اليمين جداش سالب infinity وان + +525 +00:55:26,220 --> 00:55:31,400 +طلعت من جهة الشمال بسالب infinity لازم تطلع من جهة + +526 +00:55:31,400 --> 00:55:37,640 +اليمينيعني انا بتسوي اربعة limits ولا تنتين؟ تنتين + +527 +00:55:37,640 --> 00:55:42,880 +فقط لا غير، لأنه قال لي هذه or، يا إما الحالة + +528 +00:55:42,880 --> 00:55:47,280 +الأولى يا إما من الحالة الثانية، يبقى درجات + +529 +00:55:47,280 --> 00:55:51,940 +الconcretyعلى الشجتين نفس الشيء مفتوحة إلى أعلى أو + +530 +00:55:51,940 --> 00:55:57,460 +مفتوحة إلى أسفل بروح باخد ال limit للمشتقة لما ال + +531 +00:55:57,460 --> 00:56:02,560 +X بدها تروح إلى C من جهة الشمال لجاتها infinity + +532 +00:56:02,560 --> 00:56:06,360 +إذا من جهة اليمين بسلب infinity لجاتها من جهة + +533 +00:56:06,360 --> 00:56:11,200 +الشمال بسلب infinity إذا من جهة يعني واحدة منهم بس + +534 +00:56:11,200 --> 00:56:16,040 +يا إما الحالة الأولى يا إما الحالة الثانية وهيها + +535 +00:56:16,040 --> 00:56:22,140 +قدامك على الرسموالان هنثبتلك هذه المعلومة بمثال + +536 +00:56:22,140 --> 00:56:31,160 +يبقى بداجي اخد example تلاتة بقول + +537 +00:56:31,160 --> 00:56:32,500 +sketch the graph + +538 +00:56:42,610 --> 00:56:57,490 +F of X يساوي X أس تلتين X أس تلتين X ناقص خمسة + +539 +00:57:21,990 --> 00:57:26,310 +يبقى مضاجي كعدد ما انا مابعرفش لكسب ولا غيره انا + +540 +00:57:26,310 --> 00:57:29,550 +بدي اخد مثال و بدي احل زي ما كنت بحل في المثالين + +541 +00:57:29,550 --> 00:57:35,550 +السابقين هذه الدالة بقدر اكتبها على الشكل التالي X + +542 +00:57:35,550 --> 00:57:45,210 +أس كده؟ ناقص خمسة X أس تلتين الان لو كانت ال X + +543 +00:57:45,210 --> 00:57:53,940 +تساوي زيرو then كده ال Y؟ ساوي زيروطيب لو كانت ال + +544 +00:57:53,940 --> 00:58:04,360 +Y تساوي 0 then بصير X أس تلتينفاهمين في X ناقص + +545 +00:58:04,360 --> 00:58:10,000 +خمسة تساوي Zero هذا بده يعطيلك ان X يساوي Zero و X + +546 +00:58:10,000 --> 00:58:15,240 +يساوي قداش خمسة معناته انا من الحالتين جيب ثلاث + +547 +00:58:15,240 --> 00:58:20,280 +نقط ولا تنتين بس يا راجي قولوا غير اطلع فيها كويس + +548 +00:58:20,280 --> 00:58:25,740 +تنتين لان الحالة الأولى هي الحالة التانية هذه يبقى + +549 +00:58:25,740 --> 00:58:31,480 +هنا the points النقاط Zero و Zero + +550 +00:58:40,430 --> 00:58:44,110 +بعد ذلك بدي ادى الخطوة اللى بعدها فيه عندى + +551 +00:58:44,110 --> 00:58:51,090 +asymptote هناأه ماعنديش ماعندي بصفة و مقام يبقى + +552 +00:58:51,090 --> 00:58:55,470 +انسى قصة الاسم تت يبقى بناء عليه بدي أروح أجيب له + +553 +00:58:55,470 --> 00:59:02,390 +ال F prime of X مباشرة يبقى خمسة على تلاتة X أس + +554 +00:59:02,390 --> 00:59:11,520 +طولتيننقص عشرة على تلاتة X أس سالب تلت أو خمسة X + +555 +00:59:11,520 --> 00:59:22,100 +أس تلتين على تلاتة ناقص عشرة على تلاتة X أس تلت أو + +556 +00:59:22,100 --> 00:59:29,340 +لو حطت المقامات للكلتلاتة X أس طلت بصير أن هنا + +557 +00:59:29,340 --> 00:59:41,480 +خمسة X ناقص عشرة أو خمسة X ناقص اتنين على تلاتة X + +558 +00:59:41,480 --> 00:59:42,700 +أس طلت + +559 +00:59:45,870 --> 00:59:51,490 +أحنا إيش كتبناها؟ صفر وخمسة وصفر صفر، أه التانية + +560 +00:59:51,490 --> 00:59:59,050 +عند X تساوي، أه خمسة وصفر تانية خمسة وزيهم، مظبوط + +561 +00:59:59,050 --> 01:00:05,130 +كلامك صحيح، تحصل فحسن العائلات عادي جدا، أه نعم + +562 +01:00:05,130 --> 01:00:10,410 +قال صلى الله عليه وسلم رفعن أمتي الخطأ والنسيان + +563 +01:00:10,410 --> 01:00:16,670 +وما استكره عليهنرجع تاني يبقى بتروح اشوف اشارة كل + +564 +01:00:16,670 --> 01:00:24,070 +term من هذه ال termات يبقى بتروح اخد اشارة اللي هو + +565 +01:00:24,070 --> 01:00:30,490 +من خمسة في X نقص اتنين بتاخد ال zero تبعها وين عند + +566 +01:00:30,490 --> 01:00:35,910 +اتنين بعد اتنين positive و قبلها negative طبعا ال + +567 +01:00:35,910 --> 01:00:38,050 +domain تبع الدلمين يا شباب + +568 +01:00:40,510 --> 01:00:44,770 +كله بالاستثناء كل الريال يبقى ماعندي مشكلة في هذه + +569 +01:00:44,770 --> 01:00:50,890 +الحالة بروح بقوله بدي أخد إشارة تلاتة اكس و أس طول + +570 +01:00:50,890 --> 01:00:54,510 +و هدا الريال اللي هي اللي بتاخد ال zero تبعها و هي + +571 +01:00:54,510 --> 01:01:00,910 +عند ال zero بعد ال zero positive و قبلها negative + +572 +01:01:02,450 --> 01:01:09,250 +بالدالي اخد اشارة خمسة في اكس ناقص اتنين على تلاتة + +573 +01:01:09,250 --> 01:01:15,450 +اكس وسطل وهذا ال real line ونحدد الحدود الإقليمية + +574 +01:01:15,450 --> 01:01:23,540 +ومنها نحدد mainنحدد الإشارات هي zero هي اتنين + +575 +01:01:23,540 --> 01:01:29,200 +مجسمات على بعض قسمة يبقى موجب على موجب بموجب سالب + +576 +01:01:29,200 --> 01:01:34,880 +على موجب بسالب سالب على سالب بموجب يبقى الدالة + +577 +01:01:34,880 --> 01:01:40,850 +كانت increasing صارت decreasingرجعت F increasing + +578 +01:01:40,850 --> 01:01:48,130 +يبقى بناء انا عليه بروح بقوله ال F is increasing + +579 +01:01:50,170 --> 01:01:56,230 +دالة تزايدية من عند السالب infinity لغاية ال zero + +580 +01:01:56,230 --> 01:02:04,590 +الدالة طبعا معرفة عند ال zero and on وكذلك على + +581 +01:02:04,590 --> 01:02:11,930 +الفترة من عند اتنين لغاية جداش infinityالـ F is + +582 +01:02:11,930 --> 01:02:20,930 +decreasing دالة تناقصية على الفترة من عند الـ Zero + +583 +01:02:20,930 --> 01:02:26,290 +لغاية مين لغاية اتنين بقى ال local maximum و ال + +584 +01:02:26,290 --> 01:02:31,330 +local minimum إذا بدنا نروح نحسب F of Zero بقدر + +585 +01:02:31,330 --> 01:02:39,980 +حسبناها قبل هي F of Zero تساوي Zero andبدا نحسب F + +586 +01:02:39,980 --> 01:02:47,940 +of اتنين F of اتنين بده يساوي اتنين قصة طولتين في + +587 +01:02:47,940 --> 01:02:56,620 +الاتنين ناقص خمسة ويساوي ناقص تلاتة الجذر التالت + +588 +01:02:56,620 --> 01:03:03,690 +لاربعحسبوني بالله عندكم شوفوا له قداش هتلاقيه + +589 +01:03:03,690 --> 01:03:11,250 +حوالي سالب أربعة وست من عشرة تقريبا يبقى حسبنا مين + +590 +01:03:11,250 --> 01:03:20,070 +لفه باتنين وبناء عليه بقوله ال F has local maximum + +591 +01:03:20,070 --> 01:03:26,710 +zero at x يساوي زيرو and + +592 +01:03:41,760 --> 01:03:47,510 +طيب انت هنا من مين؟من الـ interval of increasing + +593 +01:03:47,510 --> 01:03:51,550 +and decreasing و ال local maximum و ال local + +594 +01:03:51,550 --> 01:03:55,890 +minimum بدنا نيجي ل ال concave up و ال concave + +595 +01:03:55,890 --> 01:03:59,070 +down و ال inflection points + +596 +01:04:18,010 --> 01:04:24,670 +عشرة عشرة عشرة + +597 +01:04:24,670 --> 01:04:32,910 +على تسعة اكس أسالي بتلتهذه ستصبح ازاد عشر على تسعة + +598 +01:04:32,910 --> 01:04:34,410 +X السالب + +599 +01:04:37,970 --> 01:04:46,430 +عشرة على تسعة إكسوس كده؟ أربعة على تلاتة يبقى هذا + +600 +01:04:46,430 --> 01:04:55,050 +الكلام بيصير عشرة على تسعة واحد على إكسوس تلت زائد + +601 +01:04:55,050 --> 01:05:03,490 +واحد على إكسوس أربعة على تلاتةعشرة عالى تسعة كله + +602 +01:05:03,490 --> 01:05:10,590 +على اكس أس اربعة عالى تلاتة بضل اكس زائد واحد + +603 +01:05:13,160 --> 01:05:19,460 +إذا بدروح أشوف إشارة هذا المقدار يبقى بدروح أخد + +604 +01:05:19,460 --> 01:05:28,420 +إشارة عشرة في X زائد واحد بتاخد ال zero تبعها وين؟ + +605 +01:05:28,420 --> 01:05:35,520 +عند السالب واحد بعد السالب واحد موجبة وقبل السالب + +606 +01:05:35,520 --> 01:05:43,790 +واحد سالبةبدا ياخد إشارة المقدار تسعة اكس أس أربعة + +607 +01:05:43,790 --> 01:05:50,770 +على تلاتة وهذا اللي بتاخد ال zero تبعها وين؟ عند + +608 +01:05:50,770 --> 01:05:59,610 +ال zero يبقى بعد ال zero موجب و قبل ال zero الجدر + +609 +01:05:59,610 --> 01:06:06,420 +التالت له اكس أس أربعةسلم ولا موجب؟ موجب سلم يبقى + +610 +01:06:06,420 --> 01:06:13,420 +كله موجب يمين ال zero و إشمال ال zero تمام؟ يبقى + +611 +01:06:13,420 --> 01:06:20,900 +بدي أجي أخد إشارة المقدار عشرة X زي واحد على تسعة + +612 +01:06:20,900 --> 01:06:29,440 +X أس اربعة على تلاتة هذا ال real lineوهذه الحدود + +613 +01:06:29,440 --> 01:06:36,360 +الإقليمية لإنها سالب واحد وهذه positive وهذه كمان + +614 +01:06:36,360 --> 01:06:43,220 +positive وهذه negative يبقى concave down, concave + +615 +01:06:43,220 --> 01:06:51,700 +up, concave upيبقى عند السلب واحد فقط هو الـ + +616 +01:06:51,700 --> 01:06:55,740 +inflection point لأن الدلة دلة متصلة و عند السلب + +617 +01:06:55,740 --> 01:07:02,970 +واحد الدلة معرفة و غيرت اتجاه من الـ concavityيبقى + +618 +01:07:02,970 --> 01:07:08,710 +بدى أروح أجيبله ال F of سالب واحد، بدى أرجع لوين + +619 +01:07:08,710 --> 01:07:15,790 +لرأس المثل، هيبقى سالب واحد أسطلتين في سالب واحد + +620 +01:07:15,790 --> 01:07:22,130 +سالب خمسةهذا الجدر التالت لـ-1 تربية اللي هو بواحد + +621 +01:07:22,130 --> 01:07:30,250 +يبقى الجواب جداش سالب ستة يبقى ال F has an + +622 +01:07:30,250 --> 01:07:37,910 +inflection point اللي احداتي تبعها اللي هو سالب + +623 +01:07:37,910 --> 01:07:46,660 +واحد وسالب ستة حددت ال inflection pointأه ماقلناش + +624 +01:07:46,660 --> 01:07:56,040 +ال concave طيب يالا ال if أو the graph of if is + +625 +01:07:56,040 --> 01:08:08,820 +concave down on من سالب infinity لغاية سالب واحد + +626 +01:08:08,820 --> 01:08:12,260 +and مافيش غيرها + +627 +01:08:16,830 --> 01:08:29,030 +and concave up on سالب واحد و zero اتحاد zero و + +628 +01:08:29,030 --> 01:08:33,490 +infinity طيب، + +629 +01:08:33,490 --> 01:08:38,750 +إذا عند ال zero، في احتمال يكون في عندي كسب، مش + +630 +01:08:38,750 --> 01:08:45,440 +عارفكقولوا أبدا الدالة عند Zero دالة متصلة اتنين + +631 +01:08:45,440 --> 01:08:50,120 +الدالة مغيرتش اتجاه الconcavity على يميني ال Zero + +632 +01:08:50,120 --> 01:08:56,080 +وعلى شمالي ال Zeroإذا عشان أتأكد إنه في عندي class + +633 +01:08:56,080 --> 01:09:02,400 +مظلوم إيجاد limit للمشتقة عند ال X بدأت تروح ل + +634 +01:09:02,400 --> 01:09:09,680 +Zero من اليمين أو من الشمال طيب إذا بدروح أخد ال + +635 +01:09:09,680 --> 01:09:15,420 +F' موجودة عندنا أه هي موجودة هي وين هي يبقى بدأ + +636 +01:09:15,420 --> 01:09:22,690 +أخد limitللـ F prime of X لما X بدها تروح لـ Zero + +637 +01:09:22,690 --> 01:09:29,290 +من جهة الشمال يبقى هذه ال limit لما ال X بدها تروح + +638 +01:09:29,290 --> 01:09:35,690 +ل Zero من جهة الشمال لخمسة في X ناقص اتنين على + +639 +01:09:35,690 --> 01:09:44,930 +تلاتة X أس تلت يساويخمسة على تلاتة ما لهاش دورة + +640 +01:09:44,930 --> 01:09:50,650 +وهذه لما X بدها تروح ل Zero من جهة الشمال يبقى + +641 +01:09:50,650 --> 01:09:57,190 +البصد بضال قداش ناقص اتنين Zero من جهة الشمال + +642 +01:09:57,190 --> 01:10:06,010 +معناته very small negative يبقى very smallنجاتيف + +643 +01:10:06,010 --> 01:10:11,710 +ايه quantity تمام نجاتيف على نجاتيف ايش بيصير + +644 +01:10:11,710 --> 01:10:15,010 +positive يبقى جديش + +645 +01:10:29,080 --> 01:10:36,120 +بتروح اخد limit لل F prime of X لما ال X بده يروح + +646 +01:10:36,120 --> 01:10:41,760 +ل0 من جهة اليمين يبقى limit لما ال X بده تروح ل0 + +647 +01:10:41,760 --> 01:10:49,290 +من جهة اليمينX ناقص اتنين على تلاتة X أسطلت خمسة + +648 +01:10:49,290 --> 01:10:55,690 +على تلاتة مالاش دا و هذا بيبقى ناقص اتنين على Zero + +649 +01:10:55,690 --> 01:11:03,530 +من جهة اليمين يعني very small positive quantity + +650 +01:11:04,010 --> 01:11:09,750 +يبقى النتيجة ده بداش يساوي يبقى من الاتنين هدول + +651 +01:11:09,750 --> 01:11:16,390 +ونفس ال concavity على يمين ال zero هذا بده يعطيلك + +652 +01:11:16,390 --> 01:11:28,770 +ان هناك كاسب at x يساوي zero اظن هيك احنا خلصنا مش + +653 +01:11:28,770 --> 01:11:35,940 +ضايق الا الرسممش هيك يبقى بدنا نشيل المشتقة هذه + +654 +01:11:35,940 --> 01:11:48,720 +هيك و هذه معاها و نيجي نرسم راسمتنا خلّي + +655 +01:11:48,720 --> 01:11:51,900 +بالا كده يبقى هي المحاور + +656 +01:11:54,920 --> 01:12:01,080 +هذا محور X وهذا محور Y وهذا نقطة الأصل اللي هي + +657 +01:12:01,080 --> 01:12:07,560 +Zero ال symptom ماعناش تمام يبقى أول شغلة بنرسم ال + +658 +01:12:07,560 --> 01:12:12,020 +local maximum و ال local minimum عند local maximum + +659 +01:12:12,020 --> 01:12:18,780 +وين عند ال Zero يبقى Zero اتنين عند Zero فيه كسبة + +660 +01:12:18,780 --> 01:12:25,510 +يبقى بالدرسية الرأس مدبب بالشكل اللي عندنا هنابعد + +661 +01:12:25,510 --> 01:12:29,770 +ذلك إذا كان عندنا local minimum عند x يساوي 2 له + +662 +01:12:29,770 --> 01:12:37,150 +سالب 4 و 6 من 10 يبقى عند x يساوي 2 هذا واحد و هذا + +663 +01:12:37,150 --> 01:12:44,410 +اتنين بدي أنزل لسالب يبقى هذا اتنين و سالب 4 و 6 + +664 +01:12:44,410 --> 01:12:52,080 +من 10 و بدي أصبح المنحنة إلى أعلىطيب تمام الان بدي + +665 +01:12:52,080 --> 01:12:56,960 +اجي من سالب infinity لغاية ال zero بدي اشوف هل هي + +666 +01:12:56,960 --> 01:13:00,120 +increasing اه من سالب infinity لغاية ال zero + +667 +01:13:00,120 --> 01:13:05,720 +increasing اه يبقى هذه كلها بيبقى increasing بس + +668 +01:13:05,720 --> 01:13:11,690 +ايش عنديفي اندي inflection point وين عندى السالب + +669 +01:13:11,690 --> 01:13:18,350 +واحد وسالب ستة وين السالب واحد هاي سالب واحد وبدى + +670 +01:13:18,350 --> 01:13:25,050 +أنزل سالب ستة هنا يجي هذه السالب واحد وسالب ستة + +671 +01:13:25,050 --> 01:13:29,050 +جابلي السالب واحد جابلي السالب واحد بدى اشوف + +672 +01:13:29,050 --> 01:13:34,580 +الconcavityيبقى من سالب infinity لسالب واحد + +673 +01:13:34,580 --> 01:13:43,500 +concave down يبقى المنحنة كان concave down الشكل + +674 +01:13:43,500 --> 01:13:48,000 +اللي عندنا هذا تمام؟ ومن عند السالب واحد لغاية + +675 +01:13:48,000 --> 01:13:51,260 +الستة concave up + +676 +01:13:58,140 --> 01:14:02,480 +يبقى concave up بالشكل اللي عندنا هنا يبقى النقطة + +677 +01:14:02,480 --> 01:14:07,360 +هذه صارت inflection + +678 +01:14:07,360 --> 01:14:15,200 +point للنقطة اللي عندنا قبلها concave down بعدها + +679 +01:14:15,200 --> 01:14:20,680 +concave up بعدها الآن من zero ل infinity concave + +680 +01:14:20,680 --> 01:14:27,280 +upوين راح تكون curve up من zero كذلك لوين لغاية + +681 +01:14:27,280 --> 01:14:32,040 +infinity مدام من zero infinity تكون curve up يبقى + +682 +01:14:32,040 --> 01:14:37,960 +هذا بدي يظل نازل هيك وهذا بدي يظل طالع إلى ما شاء + +683 +01:14:37,960 --> 01:14:44,660 +الله لكن جالي في نقطة تقاطع طلعناها جدوش هذه اظن + +684 +01:14:44,660 --> 01:14:50,430 +كانت خمسة و zeroيبقى هذا النقطة كانت خمسة وزير و + +685 +01:14:50,430 --> 01:14:55,910 +هذا يبقى كيف up لاحظ increasing من سالب infinity + +686 +01:14:55,910 --> 01:15:01,290 +إلى سالب واحد هل من اتنين إلى infinity increasing + +687 +01:15:01,290 --> 01:15:06,650 +ولا لاتعالى نشوف increasing من اتنين لإنفينتي + +688 +01:15:06,650 --> 01:15:13,010 +سليمة هل decreasing من Zero لغاية اتنين ولا لا + +689 +01:15:13,010 --> 01:15:17,970 +يبقى decreasing من Zero لغاية اتنين يبقى رسمتي + +690 +01:15:17,970 --> 01:15:20,130 +سليمة مائة بالمائة + +691 +01:15:31,950 --> 01:15:38,150 +اللي حكمني النقطة هذه، ان عند النقطة على يمينها + +692 +01:15:38,150 --> 01:15:41,670 +وعلى شمالها، إلها نفس الـ concave. مش تقل لما + +693 +01:15:41,670 --> 01:15:46,210 +نعرفنا الكاس وقلنا دلّا دلّا متصلة عند النقطة وعلى + +694 +01:15:46,210 --> 01:15:51,150 +يمينها وعلى شمالها، إلها نفس الـ concavity، هذي مش + +695 +01:15:51,150 --> 01:15:56,160 +بمذادي باخد من عندى، لأ لحكمتنا النقطة هذه.وهكذا، + +696 +01:15:56,160 --> 01:15:59,980 +تمام؟ حاجة لو هي تساوي التاني، قبل ما نروح للمثال + +697 +01:15:59,980 --> 01:16:06,450 +اللي بعده، ايه؟السؤال لأنه عرفنا للقاس، قلنا بنجيب + +698 +01:16:06,450 --> 01:16:11,110 +ال limit لل F prime لازم تطلع، عند ال zero، اه، + +699 +01:16:11,110 --> 01:16:13,750 +اذا من اليمين مثلا infinity من الشمال سالب + +700 +01:16:13,750 --> 01:16:15,630 +infinity طب لو طلع من اليمين و من الشمال infinity + +701 +01:16:15,630 --> 01:16:20,070 +infinity؟ لا يا اخو، ده ممتاز، ممتاز، عارف ليش؟ + +702 +01:16:20,070 --> 01:16:24,710 +لإن لما أقولك F prime يعني المماس، limit للمماس، + +703 +01:16:24,710 --> 01:16:29,490 +اتطلع لهذا، لو جيهتي اللي قولي المماس هنا، بيكون + +704 +01:16:29,490 --> 01:16:34,300 +المماس سالب ولا لا؟لكن لو جيت للمماثل اللي عندك + +705 +01:16:34,300 --> 01:16:39,260 +هذا بيعملك ذاوية موجبة، إذا لا يمكن لازم واحد إن + +706 +01:16:39,260 --> 01:16:42,400 +كان الأول infinity التاني السالي من الفترة، طلعوا + +707 +01:16:42,400 --> 01:16:44,580 +اتنين infinity مافيش كسب أصلا + +708 +01:16:48,510 --> 01:16:56,370 +اسمع يا ابني انت معيار ايوة ايش + +709 +01:16:56,370 --> 01:17:01,350 +يعني بالاسم المحوركس انا باخد limit لل F prime اش + +710 +01:17:01,350 --> 01:17:05,870 +ما يكون شكل هيكون مش فيش حد اسم المحوركس ومحوراكس + +711 +01:17:05,870 --> 01:17:09,870 +انا باخد limit لل function لما X بده تروح لهذا + +712 +01:17:09,870 --> 01:17:12,430 +الرقم اللي عنده المشكلة + +713 +01:17:16,200 --> 01:17:19,360 +أيش انت انت من الرسمة؟ أنا بقولك يا راني ال limit + +714 +01:17:19,360 --> 01:17:22,520 +للمشتقة، بقول ال limit للرسمة. يا راني ال limit + +715 +01:17:22,520 --> 01:17:24,180 +للمشتقة تبعت الدالة. + +716 +01:17:26,780 --> 01:17:33,300 +ايش انت انت يعني؟ مرسومة + +717 +01:17:33,300 --> 01:17:37,240 +وخالصة؟ ايه؟ اسمع، اسمع، اسمع، تعال على الرسمة + +718 +01:17:37,240 --> 01:17:43,160 +هنا. ايه الحاجب نانيه؟ هاي الرسمة قدامك.يعني لو + +719 +01:17:43,160 --> 01:17:47,400 +عندي رسم زي محور .. زي محور X هيك؟ هي .. هي محور X + +720 +01:17:47,400 --> 01:17:47,760 +هيو + +721 +01:17:52,450 --> 01:18:00,270 +خط مستقيم يعني؟ مستقيم و مطلق، ماشي يعني، اللي هي + +722 +01:18:00,270 --> 01:18:06,710 +إيه؟ يعني أنت أسألك، هاي الـabsolute value، اسمها + +723 +01:18:06,710 --> 01:18:10,570 +يا ابنيها، هاي الـabsolute value اللي قاعد تسأل + +724 +01:18:10,570 --> 01:18:14,930 +عليها، صح؟ هذا absolute value X وهذا محور X وهذا + +725 +01:18:14,930 --> 01:18:19,310 +محور Y، بدك تاخد limit لـabsolute value X، لكي + +726 +01:18:19,310 --> 01:18:20,030 +تروح لوين؟ + +727 +01:18:27,730 --> 01:18:32,710 +الخط هذا بيبقى ماشي إلى ما شاء الله، إلى أن يرفع + +728 +01:18:32,710 --> 01:18:38,230 +الله الأرض ومن علينا، يعني الـX بدأ تروح لسالب + +729 +01:18:38,230 --> 01:18:43,710 +Infinity. لما الـX بدأ تروح لسالب Infinity، بدأ + +730 +01:18:43,710 --> 01:18:50,030 +يكون الناتج Infinity. ولو راحة الـX للـInfinity، + +731 +01:18:50,030 --> 01:18:55,390 +بدأ تروح كمان هذه للـInfinity على الشجتين. خلاص؟ + diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/lVyOSNqm3DA_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/lVyOSNqm3DA_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..44ea733dac7f7c8c2ee4a6ae743f3b8ac0a2a9ea --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/lVyOSNqm3DA_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 3885, "start": 20.69, "end": 38.85, "text": 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{"start": 1331.63, "end": 1332.49, "word": " على", "probability": 0.6826171875}, {"start": 1332.49, "end": 1332.83, "word": " b", "probability": 0.5693359375}, {"start": 1332.83, "end": 1333.53, "word": " ناقص", "probability": 0.935302734375}, {"start": 1333.53, "end": 1333.79, "word": " ال", "probability": 0.919921875}, {"start": 1333.79, "end": 1334.15, "word": " a", "probability": 0.77587890625}, {"start": 1334.15, "end": 1335.27, "word": " تكمل", "probability": 0.83544921875}, {"start": 1335.27, "end": 1335.57, "word": " من", "probability": 0.99560546875}, {"start": 1335.57, "end": 1335.99, "word": " a", "probability": 0.98681640625}, {"start": 1335.99, "end": 1336.29, "word": " إلى", "probability": 0.779296875}, {"start": 1336.29, "end": 1336.71, "word": " b", "probability": 0.9912109375}, {"start": 1336.71, "end": 1337.39, "word": " للf", "probability": 0.5701904296875}, {"start": 1337.39, "end": 1337.79, "word": " of", "probability": 0.8779296875}, {"start": 1337.79, "end": 1338.27, "word": " x", "probability": 0.97900390625}, {"start": 1338.27, "end": 1338.85, "word": " dx", "probability": 0.89013671875}, {"start": 1338.85, "end": 1340.63, "word": " example", "probability": 0.6552734375}], "temperature": 1.0}, {"id": 61, "seek": 137511, "start": 1347.01, "end": 1375.11, "text": "Find the average value of the function لدالة F of X يساوي X ناقص واحد لكل تربيع over الفترة Zero وتلاتة", "tokens": [37, 471, 264, 4274, 2158, 295, 264, 2445, 5296, 3215, 6027, 3660, 479, 295, 1783, 7251, 3794, 995, 45865, 1783, 8717, 995, 4587, 9381, 36764, 24401, 5296, 28820, 6055, 2288, 21292, 3615, 670, 27188, 2655, 25720, 17182, 34683, 1211, 9307, 3660], "avg_logprob": -0.23232887295030413, "compression_ratio": 1.110236220472441, "no_speech_prob": 0.0, "words": [{"start": 1347.0099999999998, "end": 1348.4099999999999, "word": "Find", "probability": 0.440673828125}, {"start": 1348.4099999999999, "end": 1349.81, "word": " the", "probability": 0.62939453125}, {"start": 1349.81, "end": 1352.07, "word": " average", "probability": 0.7587890625}, {"start": 1352.07, "end": 1354.51, "word": " value", "probability": 0.9794921875}, {"start": 1354.51, "end": 1356.35, "word": " of", "probability": 0.849609375}, {"start": 1356.35, "end": 1356.57, "word": " the", "probability": 0.76513671875}, {"start": 1356.57, "end": 1357.33, "word": " function", "probability": 0.9658203125}, {"start": 1357.33, "end": 1361.73, "word": " لدالة", "probability": 0.72357177734375}, {"start": 1361.73, "end": 1362.25, "word": " F", "probability": 0.491943359375}, {"start": 1362.25, "end": 1362.63, "word": " of", "probability": 0.395751953125}, {"start": 1362.63, "end": 1363.09, "word": " X", "probability": 0.890625}, {"start": 1363.09, "end": 1364.51, "word": " يساوي", "probability": 0.90087890625}, {"start": 1364.51, "end": 1365.63, "word": " X", "probability": 0.8681640625}, {"start": 1365.63, "end": 1366.27, "word": " ناقص", "probability": 0.9154052734375}, {"start": 1366.27, "end": 1366.73, "word": " واحد", "probability": 0.98779296875}, {"start": 1366.73, "end": 1367.27, "word": " لكل", "probability": 0.970947265625}, {"start": 1367.27, "end": 1368.51, "word": " تربيع", "probability": 0.90234375}, {"start": 1368.51, "end": 1369.75, "word": " over", "probability": 0.64208984375}, {"start": 1369.75, "end": 1371.83, "word": " الفترة", "probability": 0.98974609375}, {"start": 1371.83, "end": 1373.51, "word": " Zero", "probability": 0.392578125}, {"start": 1373.51, "end": 1375.11, "word": " وتلاتة", "probability": 0.794677734375}], "temperature": 1.0}, {"id": 62, "seek": 143425, "start": 1409.97, "end": 1434.25, "text": "نعود للتعريف اللي كنا نكتبه يبقى قال لو كانت الدالة قابلة لتكمل على الفترة المغلقة A وB then its average أو its mean يعني المتوسط تبع الدالة أو المعدل تبع الدالة القيمة المتوسطة للدالة على الفترة A وB is defined as", "tokens": [1863, 3615, 23328, 24976, 2655, 3615, 16572, 5172, 13672, 1829, 9122, 8315, 8717, 4117, 2655, 3555, 3224, 7251, 3555, 4587, 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"probability": 0.79638671875}, {"start": 1418.69, "end": 1419.57, "word": " then", "probability": 0.11932373046875}, {"start": 1419.57, "end": 1420.09, "word": " its", "probability": 0.7099609375}, {"start": 1420.09, "end": 1420.77, "word": " average", "probability": 0.82763671875}, {"start": 1420.77, "end": 1421.21, "word": " أو", "probability": 0.55712890625}, {"start": 1421.21, "end": 1421.69, "word": " its", "probability": 0.36962890625}, {"start": 1421.69, "end": 1422.15, "word": " mean", "probability": 0.646484375}, {"start": 1422.15, "end": 1422.51, "word": " يعني", "probability": 0.9169921875}, {"start": 1422.51, "end": 1423.67, "word": " المتوسط", "probability": 0.9818115234375}, {"start": 1423.67, "end": 1424.07, "word": " تبع", "probability": 0.8401692708333334}, {"start": 1424.07, "end": 1424.67, "word": " الدالة", "probability": 0.99169921875}, {"start": 1424.67, "end": 1424.87, "word": " أو", "probability": 0.701171875}, {"start": 1424.87, "end": 1425.55, "word": " المعدل", "probability": 0.9381510416666666}, {"start": 1425.55, "end": 1425.93, "word": " تبع", "probability": 0.9471028645833334}, {"start": 1425.93, "end": 1426.67, "word": " الدالة", "probability": 0.9939778645833334}, {"start": 1426.67, "end": 1429.91, "word": " القيمة", "probability": 0.624725341796875}, {"start": 1429.91, "end": 1430.75, "word": " المتوسطة", "probability": 0.99462890625}, {"start": 1430.75, "end": 1431.23, "word": " للدالة", "probability": 0.943603515625}, {"start": 1431.23, "end": 1431.39, "word": " على", "probability": 0.91357421875}, {"start": 1431.39, "end": 1431.93, "word": " الفترة", "probability": 0.9861653645833334}, {"start": 1431.93, "end": 1432.21, "word": " A", "probability": 0.9404296875}, {"start": 1432.21, "end": 1432.61, "word": " وB", "probability": 0.936767578125}, {"start": 1432.61, "end": 1432.91, "word": " is", "probability": 0.734375}, {"start": 1432.91, "end": 1433.61, "word": " defined", "probability": 0.9111328125}, {"start": 1433.61, "end": 1434.25, "word": " as", "probability": 0.97216796875}], "temperature": 1.0}, {"id": 63, "seek": 146303, "start": 1434.81, "end": 1463.03, "text": "هدّيلها الرمز average لف a v بينقصين f يبقى اختصار the average of the function f average لف واحد على b ناقص ال a لتكامل من a إلى b لل f of x dx يعني ايه؟يعني بدنا نروح نكمل الدالة على الفترة هذه كلها ثم نقسم نتيجة التكمل على طول الدالة تكمل يعني ايش؟ مساحة", "tokens": [3224, 3215, 11703, 26895, 11296, 34892, 2304, 11622, 4274, 5296, 5172, 257, 371, 4724, 9957, 4587, 9381, 9957, 283, 7251, 3555, 4587, 7578, 1975, 46456, 9381, 9640, 264, 4274, 295, 264, 2445, 283, 4274, 5296, 5172, 36764, 24401, 15844, 272, 8717, 995, 4587, 9381, 2423, 257, 5296, 2655, 4117, 10943, 1211, 9154, 257, 30731, 272, 24976, 283, 295, 2031, 30017, 37495, 22653, 1975, 1829, 3224, 22807, 40228, 22653, 47525, 8315, 8717, 32887, 5016, 8717, 24793, 1211, 32748, 6027, 3660, 15844, 27188, 2655, 25720, 29538, 28242, 11296, 38637, 2304, 8717, 4587, 38251, 8717, 31371, 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{"start": 1445.71, "end": 1446.29, "word": " ناقص", "probability": 0.8341064453125}, {"start": 1446.29, "end": 1446.47, "word": " ال", "probability": 0.82568359375}, {"start": 1446.47, "end": 1446.83, "word": " a", "probability": 0.822265625}, {"start": 1446.83, "end": 1447.97, "word": " لتكامل", "probability": 0.96455078125}, {"start": 1447.97, "end": 1448.17, "word": " من", "probability": 0.9921875}, {"start": 1448.17, "end": 1448.47, "word": " a", "probability": 0.9560546875}, {"start": 1448.47, "end": 1448.71, "word": " إلى", "probability": 0.7275390625}, {"start": 1448.71, "end": 1448.97, "word": " b", "probability": 0.9619140625}, {"start": 1448.97, "end": 1449.19, "word": " لل", "probability": 0.5751953125}, {"start": 1449.19, "end": 1449.53, "word": " f", "probability": 0.3271484375}, {"start": 1449.53, "end": 1449.85, "word": " of", "probability": 0.9482421875}, {"start": 1449.85, "end": 1450.31, "word": " x", "probability": 0.9228515625}, {"start": 1450.31, "end": 1451.19, "word": " dx", "probability": 0.8310546875}, {"start": 1451.19, "end": 1451.67, "word": " يعني", "probability": 0.906982421875}, {"start": 1451.67, "end": 1452.95, "word": " ايه؟يعني", "probability": 0.7513020833333334}, {"start": 1452.95, "end": 1453.27, "word": " بدنا", "probability": 0.927001953125}, {"start": 1453.27, "end": 1453.53, "word": " نروح", "probability": 0.9822591145833334}, {"start": 1453.53, "end": 1454.23, "word": " نكمل", "probability": 0.8326822916666666}, {"start": 1454.23, "end": 1454.97, "word": " الدالة", "probability": 0.9622395833333334}, {"start": 1454.97, "end": 1455.19, "word": " على", "probability": 0.91943359375}, {"start": 1455.19, "end": 1455.73, "word": " الفترة", "probability": 0.98974609375}, {"start": 1455.73, "end": 1456.09, "word": " هذه", "probability": 0.83203125}, {"start": 1456.09, "end": 1456.63, "word": " كلها", "probability": 0.950439453125}, {"start": 1456.63, "end": 1457.01, "word": " ثم", "probability": 0.96875}, {"start": 1457.01, "end": 1457.81, "word": " نقسم", "probability": 0.9949544270833334}, {"start": 1457.81, "end": 1458.91, "word": " نتيجة", "probability": 0.9864501953125}, {"start": 1458.91, "end": 1459.61, "word": " التكمل", "probability": 0.8494466145833334}, {"start": 1459.61, "end": 1460.01, "word": " على", "probability": 0.970703125}, {"start": 1460.01, "end": 1460.75, "word": " طول", "probability": 0.996337890625}, {"start": 1460.75, "end": 1461.29, "word": " الدالة", "probability": 0.9676106770833334}, {"start": 1461.29, "end": 1461.81, "word": " تكمل", "probability": 0.8121744791666666}, {"start": 1461.81, "end": 1462.09, "word": " يعني", "probability": 0.98193359375}, {"start": 1462.09, "end": 1462.45, "word": " ايش؟", "probability": 0.7083740234375}, {"start": 1462.45, "end": 1463.03, "word": " مساحة", "probability": 0.9637044270833334}], "temperature": 1.0}, {"id": 64, "seek": 148418, "start": 1463.92, "end": 1484.18, "text": "يعني بدى اقسم جداش المساحة اللى طلعت عندي على طول ال interval بطلع عندى 100 بطلع عندى اللى ال average value او ال mean value ل100 لل function اللى عندنا يعني برجع مرة تانية بقول ال average value لدل F على الفترة المغلقة A وB", "tokens": [40228, 22653, 47525, 7578, 1975, 4587, 38251, 10874, 3215, 33599, 9673, 3794, 39319, 3660, 13672, 7578, 23032, 1211, 34268, 18871, 16254, 15844, 23032, 12610, 2423, 15035, 4724, 9566, 1211, 3615, 43242, 7578, 2319, 4724, 9566, 1211, 3615, 43242, 7578, 13672, 7578, 2423, 4274, 2158, 1975, 2407, 2423, 914, 2158, 5296, 6879, 24976, 2445, 13672, 7578, 43242, 8315, 37495, 22653, 4724, 47341, 3615, 3714, 25720, 6055, 7649, 10632, 4724, 39648, 2423, 4274, 2158, 5296, 3215, 1211, 479, 15844, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 316, 4032, 33], "avg_logprob": -0.31409802118485625, "compression_ratio": 1.7474747474747474, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1463.92, "end": 1464.76, "word": "يعني", "probability": 0.5479736328125}, {"start": 1464.76, "end": 1465.18, "word": " بدى", 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{"start": 3577.3, "end": 3578.06, "word": " تان", "probability": 0.989501953125}, {"start": 3578.06, "end": 3578.34, "word": " ال", "probability": 0.94970703125}, {"start": 3578.34, "end": 3578.82, "word": " X", "probability": 0.99267578125}, {"start": 3578.82, "end": 3580.36, "word": " لواحد", "probability": 0.6079915364583334}, {"start": 3580.36, "end": 3580.8, "word": " على", "probability": 0.77685546875}, {"start": 3580.8, "end": 3581.48, "word": " واحد", "probability": 0.98681640625}, {"start": 3581.48, "end": 3582.32, "word": " زائد", "probability": 0.8108723958333334}, {"start": 3582.32, "end": 3582.62, "word": " T", "probability": 0.7509765625}, {"start": 3582.62, "end": 3583.68, "word": " تربيع", "probability": 0.914306640625}, {"start": 3583.68, "end": 3584.52, "word": " DT", "probability": 0.784912109375}], "temperature": 1.0}, {"id": 150, "seek": 361422, "start": 3606.16, "end": 3614.22, "text": "بنفس الطريقة في السؤال اللي قبل قليل هذه تعتبر function وهذه كلها function 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4253.58, "word": " لواحد", "probability": 0.8912760416666666}, {"start": 4253.58, "end": 4254.16, "word": " زائد", "probability": 0.9620768229166666}, {"start": 4254.16, "end": 4254.72, "word": " cosine", "probability": 0.896484375}, {"start": 4254.72, "end": 4255.14, "word": " ال", "probability": 0.88916015625}, {"start": 4255.14, "end": 4255.62, "word": " X", "probability": 0.97705078125}, {"start": 4255.62, "end": 4256.32, "word": " DX", "probability": 0.72021484375}, {"start": 4256.32, "end": 4259.62, "word": " خلّي", "probability": 0.7567138671875}, {"start": 4259.62, "end": 4259.9, "word": " ملاك", "probability": 0.50732421875}, {"start": 4259.9, "end": 4260.06, "word": " هنا", "probability": 0.95068359375}], "temperature": 1.0}, {"id": 177, "seek": 426891, "start": 4260.85, "end": 4268.91, "text": "هذا تكامل يستوي تكامل واحد بقداش تكامل cosine من ورا الى ورا", "tokens": [3224, 15730, 6055, 4117, 10943, 1211, 7251, 14851, 45865, 6055, 4117, 10943, 1211, 36764, 24401, 4724, 28543, 33599, 6055, 4117, 10943, 1211, 23565, 9154, 4032, 23557, 2423, 7578, 4032, 23557], "avg_logprob": -0.3140120929287326, "compression_ratio": 1.271604938271605, "no_speech_prob": 0.0, "words": [{"start": 4260.85, "end": 4261.27, "word": "هذا", "probability": 0.8564453125}, {"start": 4261.27, "end": 4261.91, "word": " تكامل", "probability": 0.73583984375}, {"start": 4261.91, "end": 4262.57, "word": " يستوي", "probability": 0.7452799479166666}, {"start": 4262.57, "end": 4263.29, "word": " تكامل", "probability": 0.8717041015625}, {"start": 4263.29, "end": 4263.55, "word": " واحد", "probability": 0.918701171875}, {"start": 4263.55, "end": 4264.29, "word": " بقداش", "probability": 0.773681640625}, {"start": 4264.29, "end": 4265.69, "word": " تكامل", "probability": 0.8861083984375}, {"start": 4265.69, "end": 4266.39, "word": " cosine", "probability": 0.479736328125}, {"start": 4266.39, "end": 4268.29, "word": " من", "probability": 0.89453125}, {"start": 4268.29, "end": 4268.55, "word": " ورا", "probability": 0.4735107421875}, {"start": 4268.55, "end": 4268.73, "word": " الى", "probability": 0.59619140625}, {"start": 4268.73, "end": 4268.91, "word": " ورا", "probability": 0.95361328125}], "temperature": 1.0}, {"id": 178, "seek": 429810, "start": 4270.61, "end": 4298.11, "text": "زيرو لغاية باي نجي نعوض بحدود التكامل يبقى باي زائد صين البي ناقص زيرو ناقص صين الزيرو و يساوي باي قداش صين البي زيرو و صين الزيرو يبقى هذا كله باي فقط والباقي كله بأصفر بروح مع السلامة example three", "tokens": [11622, 13546, 2407, 5296, 17082, 995, 10632, 4724, 47302, 8717, 7435, 1829, 8717, 3615, 2407, 11242, 4724, 24401, 23328, 16712, 4117, 10943, 1211, 7251, 3555, 4587, 7578, 4724, 47302, 30767, 16373, 3215, 20328, 9957, 2423, 21292, 8717, 995, 4587, 9381, 30767, 13546, 2407, 8717, 995, 4587, 9381, 20328, 9957, 2423, 11622, 13546, 2407, 4032, 7251, 3794, 995, 45865, 4724, 47302, 12174, 3215, 33599, 20328, 9957, 2423, 21292, 30767, 13546, 2407, 4032, 20328, 9957, 2423, 11622, 13546, 2407, 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mode 100644 index 0000000000000000000000000000000000000000..5921c32048b14ed8dde6bf9188153c344a025141 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/lVyOSNqm3DA_raw.srt @@ -0,0 +1,3012 @@ +1 +00:00:20,690 --> 00:00:25,750 +بسم الله الرحمن الرحيم نواصل ما ابتدأنا به + +2 +00:00:25,750 --> 00:00:30,390 +المحاضرة الماضية فكان في المحاضرة الماضية أخر + +3 +00:00:30,390 --> 00:00:36,650 +تعريف درسناه أو ذكرناه قدامنا هو استخدام المساحة + +4 +00:00:36,650 --> 00:00:41,260 +في حساب قيمة التكاملفلو كانت الدالة دالة متصلة + +5 +00:00:41,260 --> 00:00:46,520 +وقابلة للتكامل على فترة a وb فإن قيمة هذا التكامل + +6 +00:00:46,520 --> 00:00:50,420 +من a إلى b هو عبارة عن المساحة المحصورة بين هذا + +7 +00:00:50,420 --> 00:00:54,780 +المنحنى ومحور x على الفترة a وb هذا آخر definition + +8 +00:00:54,780 --> 00:00:58,780 +كان مكتوب معاك المرة الماضية وهيبدأ ناخد أمثلة + +9 +00:00:58,780 --> 00:01:03,450 +تطبيقية على استخدام هذا التعريبالسؤال بيقول لـ + +10 +00:01:03,450 --> 00:01:08,350 +graph the integrands يبقى أرسم الدوال المراد + +11 +00:01:08,350 --> 00:01:13,490 +تكاملة واستخدم المساحة عشان تحسب كل من التكاملات + +12 +00:01:13,490 --> 00:01:18,070 +التالية بالداجة الآن لتكامل الأول + +13 +00:01:21,220 --> 00:01:25,600 +بنرسم المنحنة اللي عندنا هذا اللي هو الـ Integrand + +14 +00:01:25,600 --> 00:01:30,100 +الدلة المراد تكاملة الدلة اللي عندنا هي مين؟ Y + +15 +00:01:30,100 --> 00:01:34,460 +تساوي الجذر التربية إلى ستاشر ناقص X تربية + +16 +00:01:37,710 --> 00:01:42,490 +دائرة تمام بس هاد ربع دائرة نص دائرة دائرة كلها + +17 +00:01:42,490 --> 00:01:46,830 +الله أعلم اللي بدي أحكمها حدود التكامل اللي عندنا + +18 +00:01:46,830 --> 00:01:51,030 +إذا لو جيت أرسم هذه الدائرة دائرة بتاخد الشكل + +19 +00:01:51,030 --> 00:01:56,870 +التالي هذا محور X هذا محور Y هذه نقطة الأصل اللي + +20 +00:01:56,870 --> 00:02:01,780 +هي Zeroيبقى هذه الدائرة مركزها نقطة الاصب و نص خطر + +21 +00:02:01,780 --> 00:02:07,080 +هيساوي أربع أساط، ممتاز جدا، لكن التكامل من أين + +22 +00:02:07,080 --> 00:02:12,040 +إلى أين؟ من سالب أربعة إلى زيرو، يبقى هاي عندي + +23 +00:02:12,040 --> 00:02:17,080 +سالب أربعة وهي عندي زيرو، وهنا عندي مام، اللي هو + +24 +00:02:17,080 --> 00:02:21,720 +الأربعة، يبقى الدائرة بالشكل اللي عندنا من سالب + +25 +00:02:21,720 --> 00:02:27,070 +أربعة لغاية زيرو، الباقي ماليش علاقة فيهما خلّاني + +26 +00:02:27,070 --> 00:02:31,530 +اوقف؟ ما خلّاني اوقف هو حدود التكامل من ناقص 4 إلى + +27 +00:02:31,530 --> 00:02:38,650 +0 فتوقفنا فصار عندى هذا الجزء فقط لا غير ماعنديش + +28 +00:02:38,650 --> 00:02:45,810 +غير هذاهذه قداش تمثل بالنسبة للدائرة ربع الدائرة + +29 +00:02:45,810 --> 00:02:50,590 +إذا بناء عليه بصير عندنا تكامل من سالب أربعة إلى + +30 +00:02:50,590 --> 00:02:56,330 +زيرو للجذر التربيه الى ستاشر ناقص X تربيه دي X بدي + +31 +00:02:56,330 --> 00:03:02,910 +ساوي الرابع ال area of the circle يبقى هذه أربعة + +32 +00:03:08,730 --> 00:03:14,690 +يبقى مساحة الجزء المظلل يساوي 4πي وهو قيمة التكامل + +33 +00:03:14,690 --> 00:03:19,410 +يبقى أنا حصلت على قيمة التكامل بدون ما أكامل عن + +34 +00:03:19,410 --> 00:03:23,090 +طريق حساب من؟ عن طريق حساب المساحة تبقى لـ + +35 +00:03:23,090 --> 00:03:25,550 +Definition تبع المرة الماضية + +36 +00:03:27,860 --> 00:03:35,100 +نمر بيه ال F of X بدي يسوي 2 ناقص absolute value ل + +37 +00:03:35,100 --> 00:03:41,740 +X تمام؟ بدنا نروح نرسم رسمة هذه الدالة يبقى لو + +38 +00:03:41,740 --> 00:03:47,440 +روحنا رسمنا رسمة الدالة هذه بقول هذا محور X وهذا + +39 +00:03:47,440 --> 00:03:54,580 +محور Y وهذه نقطة الأصل اللي هي Zero absolute value + +40 +00:03:54,580 --> 00:04:00,650 +ل X اللي بالشكل اللي عندنا هناتمام؟ لكن ايش سبقها؟ + +41 +00:04:00,650 --> 00:04:06,130 +يبقى بتنج اللي بيصير وين؟ الى أسفل، يبقى هذه بدها + +42 +00:04:06,130 --> 00:04:11,490 +تصير الى أسفل بالشكل لأن هذا يبقى هذا راحه وهذا + +43 +00:04:11,490 --> 00:04:13,310 +الله سهل عليه مع السلامة + +44 +00:04:31,070 --> 00:04:40,050 +الرسم اللي قدامنا هذه هي من 0 لل 2 وهي رسمة 2 ناقص + +45 +00:04:40,050 --> 00:04:46,050 +absolute value لمن؟ لل Xقال لي بدي اتكامل عليها من + +46 +00:04:46,050 --> 00:04:50,690 +وين؟ من سالب واحد إلى واحد، يبقى النقطة هذه كده يا + +47 +00:04:50,690 --> 00:04:57,210 +شبابمتأكدين ان هذه واحد يبقى هذه اتنين و سالب + +48 +00:04:57,210 --> 00:05:01,930 +اتنين يبقى النقطة هذه سالب اتنين و النقطة هذه + +49 +00:05:01,930 --> 00:05:07,410 +اتنين ليش؟ لأن لو حطيت هذه ب zero بصير absolute + +50 +00:05:07,410 --> 00:05:12,530 +value ل X ساو اتنين يعني X باتنين و سالب اتنين لكن + +51 +00:05:12,530 --> 00:05:16,830 +احنا عند التكمل من سالب واحد الى واحد يبقى السالب + +52 +00:05:16,830 --> 00:05:21,050 +واحد بياتجني في المنتصف هنا و واحد بياتجني في + +53 +00:05:21,050 --> 00:05:26,140 +المنتصف هنايبقى لو جيت طالع رأسي ومن هنا جيت طالع + +54 +00:05:26,140 --> 00:05:30,320 +رأسي بالشكل اللي عندها ده، يبقى المساحة المطلوبة + +55 +00:05:30,320 --> 00:05:35,700 +هي المساحة اللي عندها دي كلها، هذه المساحة + +56 +00:05:35,700 --> 00:05:41,300 +المطلوبة، ترى؟ طيب، شو الشكل هذه؟ + +57 +00:05:44,160 --> 00:05:50,500 +هذه اتصالات اتصالات اتصالات اتصالات اتصالات + +58 +00:05:50,500 --> 00:06:07,900 +اتصالات اتصالات اتصالات + +59 +00:06:07,900 --> 00:06:14,090 +اتصالاتعشان اذكر فيكم مساحة شبه المنحرف؟ + +60 +00:06:17,230 --> 00:06:21,050 +القاعدة المتوسطة في الارتفاع يعني مجموعة القاعدتين + +61 +00:06:21,050 --> 00:06:24,590 +المتوازيتين على اتنين مضروب في مين؟ في الارتفاع. + +62 +00:06:24,670 --> 00:06:29,290 +إذا بدنا نحدد. بدأ أجيب مساحة واحد فيهم. بدأ أجيب + +63 +00:06:29,290 --> 00:06:33,870 +مساحة هذا و مساحة هذا و نروح نضربه في كم؟ في + +64 +00:06:33,870 --> 00:06:37,850 +اتنين، بيكون جيبنا المساحة المطلوبة. المسافة من + +65 +00:06:37,850 --> 00:06:42,870 +هنا لهنا كم؟ واحد. تمام تمام. إذا بدي أعرف كم + +66 +00:06:42,870 --> 00:06:48,510 +المسافة اللي عندناالمسافة هذه من هنا لهنا اللي + +67 +00:06:48,510 --> 00:06:54,730 +هيقداش 2 يبقى ضالة هذه هذه عبارة عن F of سالب واحد + +68 +00:06:54,730 --> 00:07:00,650 +يبقى باجي بقوله ال F of سالب واحد بديه يساوي 2 + +69 +00:07:00,650 --> 00:07:06,490 +سالب سالب absolute value لمن؟ لسالب واحد يبقى هذه + +70 +00:07:06,490 --> 00:07:11,610 +بيساوي 2 سالب واحد وتساوي واحد إذن الطول هذا يساوي + +71 +00:07:11,610 --> 00:07:18,400 +واحدوالطول هذا كله يساوي كده؟ يساوي 2 إذا بقدر + +72 +00:07:18,400 --> 00:07:24,620 +أقول التكامل اللي عندنا من سالب 1 إلى 1 للي 2 ناقص + +73 +00:07:24,620 --> 00:07:31,520 +absolute value لل X DX يساوي هذا 2 في مساحة شبه + +74 +00:07:31,520 --> 00:07:36,440 +المنحرف الأول مساحة شبه المنحرف اللي هو عبارة عن + +75 +00:07:36,440 --> 00:07:43,300 +مجموع القاعدتين المتوازيتينمقسوما على اتنين يبقى + +76 +00:07:43,300 --> 00:07:46,020 +هذه القاعدة الأولى اللي هي واحد هذه القاعدة + +77 +00:07:46,020 --> 00:07:50,440 +التانية اتنين في البعد بينهم اللي هو قد ياش واحد + +78 +00:07:50,440 --> 00:07:55,260 +يبقى الجواب يساوي قد ياش يساوي تلاتة إذا قيمة هذا + +79 +00:07:55,260 --> 00:07:59,980 +التكامل يساوي تلاتة حسبته بدون أن أقوم بإجراء + +80 +00:07:59,980 --> 00:08:06,980 +عملية التكامل ولكن عن طريق من؟ عن طريق المساحةطيب + +81 +00:08:06,980 --> 00:08:12,560 +بدنا نجي للمثل بتابعتنا هذا يبقى بدنا نروح نرسم + +82 +00:08:12,560 --> 00:08:18,120 +هذه الدالة يبقى ال F of X عندي اللي عبارة عن واحد + +83 +00:08:18,120 --> 00:08:24,590 +زائد الجذر التربية لواحد زائد X تربيةأمثل واحد لأن + +84 +00:08:24,590 --> 00:08:32,610 +هذا يبقى واحد ناقص X تربية وليست واحد زاد X تربية + +85 +00:08:32,610 --> 00:08:39,730 +صح هو هم لا شباب يبقى واحد ناقص X تربيةيبقى الجدر + +86 +00:08:39,730 --> 00:08:47,330 +التربية لو واحد ناقص X تربية يبقى انا اعرف معادلة + +87 +00:08:47,330 --> 00:08:51,430 +ايش بروح بقول غطي الواحد لان هذا مالوش دعوة يبقى + +88 +00:08:51,430 --> 00:08:55,230 +اصل هو Y تسوى الجدر التربية لو واحد ناقص X تربية + +89 +00:08:55,230 --> 00:09:00,370 +معادلة ايش؟دائرة ممتاز جدا يبقى دائرة هذه بس مش + +90 +00:09:00,370 --> 00:09:05,050 +عارف نص ولا تلت ولا ربع الله أعلم يبقى لو جينرس + +91 +00:09:05,050 --> 00:09:11,470 +منها بتاخد الشكل التالي يبقى هذا محور X وهذا محور + +92 +00:09:11,470 --> 00:09:17,100 +Y وهذا نقطة الأصل اللي هي Zeroالدائرة اللي عندها + +93 +00:09:17,100 --> 00:09:23,560 +دي نص خطرة جداش و مركزها نقطة الأصل يبقى لو جيت + +94 +00:09:23,560 --> 00:09:28,040 +قلت هذه النقطة اللي هي واحد يبقى الدائرة هتيجيك + +95 +00:09:28,040 --> 00:09:31,340 +بالشكل اللي عندها ده بقى لاعرفش نكمل والله مانكملش + +96 +00:09:31,340 --> 00:09:35,100 +تعالى نشوف حدود التكامل جال من عندنا ناقص واحد + +97 +00:09:35,100 --> 00:09:41,930 +لغايةيبقى من عند الناقص واحد لغاية واحد يبقى يا + +98 +00:09:41,930 --> 00:09:46,430 +اما نصف الدائرة العلوي يا اما نصف الدائرة السفلي + +99 +00:09:46,430 --> 00:09:50,950 +هيكم سالب واحد إلى واحد تمام لكن لو اجي الإشارة + +100 +00:09:50,950 --> 00:09:55,640 +اللي جاب لي الجذر إشارةموجة بقى بيبقى من النصف + +101 +00:09:55,640 --> 00:10:00,540 +العليو وليس النصف السفلي يبقى الرسم اللي أنا رسمها + +102 +00:10:00,540 --> 00:10:06,160 +هذه هي الجدر التربية إلى واحد ناقص X تربية طيب هذه + +103 +00:10:06,160 --> 00:10:11,960 +الدالة شو عملناها shift إلى أعلى بمقدار واحد يبقى + +104 +00:10:11,960 --> 00:10:16,700 +بإننا نمسك هذه الدائرة كلها ونعملها إزاحة إلى أعلى + +105 +00:10:16,700 --> 00:10:23,710 +بمقدار واحد يبقى توصل لهناإتنين يبقى لو جيت تخيلت + +106 +00:10:23,710 --> 00:10:28,310 +فيه خط أفقي هيك بالشكل اللي عندنا هذا يبقى بنتجينا + +107 +00:10:28,310 --> 00:10:36,090 +دائرة هيك بهذا الشكل تمام؟ أو من هنا بهذا الشكل + +108 +00:10:36,090 --> 00:10:40,250 +يبقى هي الدائرة اللي عندنا بالشكل اللي عندنا هنا + +109 +00:10:40,250 --> 00:10:46,730 +يبقى الجزء المنقط الصفلي هذا صار مالوش وجود أبداً + +110 +00:10:48,290 --> 00:10:53,110 +يبقى هي الرصنة بتبعتنا يبقى هذي form اللي هي y + +111 +00:10:53,110 --> 00:10:58,410 +تساوي واحد زائد الجدر التربية لواحد ناقص x تربية + +112 +00:10:58,410 --> 00:11:02,050 +بالشكل اللي عندنا هذا طيب هذا المنحنى اللي فوق + +113 +00:11:02,050 --> 00:11:08,470 +الدائرةحصر مساحة بينه بين محور X يبقى لو جيت نزلتك + +114 +00:11:08,470 --> 00:11:13,690 +عمود على سالب واحد وهنا عمود على واحد يبقى صار + +115 +00:11:13,690 --> 00:11:20,410 +عندنا في مساحة مستطيل هنا زائد مساحة من نصف + +116 +00:11:20,410 --> 00:11:24,920 +الدائرة اللي عندناإذا قيمة التكامل تساوي مساحة + +117 +00:11:24,920 --> 00:11:30,060 +المستطيل زائد مساحة الدائرة ليش ان التكامل قال + +118 +00:11:30,060 --> 00:11:35,320 +المساحة اللي موجودة ما بين المنحناء محور X بقوله + +119 +00:11:35,320 --> 00:11:42,820 +تمام إذا التكامل من سالب واحد إلى واحد للواحد زائد + +120 +00:11:42,820 --> 00:11:48,080 +الجدر التربية إلى واحد ناقص X تربية كله في دي X + +121 +00:11:48,080 --> 00:12:00,930 +بده يساوي ال areaof the rectangle المستطيل + +122 +00:12:00,930 --> 00:12:09,750 +زائد ال area of the circle و الله نص ال area of + +123 +00:12:09,750 --> 00:12:14,690 +the circle يبقى هذا الكلام بده يساوي مسحت المستطيل + +124 +00:12:14,690 --> 00:12:18,010 +الطول في العرض العرض قداش + +125 +00:12:21,310 --> 00:12:25,470 +الارض والطول يبقى المسافة هذه كلها من هنا إلى هنا + +126 +00:12:25,470 --> 00:12:28,900 +اتنين هذه واحدة و هذه واحدة يبقى هذا اتنينيبقى هذا + +127 +00:12:28,900 --> 00:12:34,100 +الكلام بده يساوي اتنين الطول في العرض اللي هو قداش + +128 +00:12:34,100 --> 00:12:41,960 +واحد صحيح زائد هذه النص مساحة الدائرة ودائرة الطه + +129 +00:12:41,960 --> 00:12:49,400 +ونق قداش مسافة من هنا لهنا اللي هو واحد يبقى واحد + +130 +00:12:49,400 --> 00:12:55,300 +تربيع يبقى النتيجة اتنين زائد باي على اتنين او + +131 +00:12:55,300 --> 00:13:00,580 +انشرتم فيقولوا اربعأصبعي كله على اتنين، اللي هي + +132 +00:13:00,580 --> 00:13:07,640 +المساحة المطلوبة. أيوة. اتكمل دائرة نفسي. إيش رأيك + +133 +00:13:07,640 --> 00:13:13,540 +أنت؟ ما عارفش اتكمل الدائرة. إيش رأيك في هذه؟ + +134 +00:13:16,260 --> 00:13:22,200 +مش هيها ولا رابعة دائرة انت + +135 +00:13:22,200 --> 00:13:26,300 +بتعرف تكملها تبقى لها دي حتى هذه اللحظة ما شاء + +136 +00:13:26,300 --> 00:13:30,260 +الله في كل كل أسباب نكملها لك وبدغشش اكملها الحين + +137 +00:13:30,260 --> 00:13:38,100 +حط لل X يسوى أربعة صين ثيتاتعويضة تتكامل معاك بطير + +138 +00:13:38,100 --> 00:13:42,240 +الجذر بتقدر تتكاملها لسه هذا خارج نطاق دراستك ان + +139 +00:13:42,240 --> 00:13:45,920 +شاء الله او مرحبا بك في calculus بيه لكن احنا + +140 +00:13:45,920 --> 00:13:50,300 +بنحسب قيمة التكامل هذا عن طريق من؟ عن طريق المساحة + +141 +00:13:50,300 --> 00:13:55,260 +لسه احنا في اول الطريق فيا لبعض التكاملات اللي + +142 +00:13:55,260 --> 00:14:03,580 +بنستخدمها كثير اللي عندك هنا some basic integrals + +143 +00:14:06,800 --> 00:14:11,540 +بعض التكاملات الأساسية اللى هتمر معانا كتير و لابد + +144 +00:14:11,540 --> 00:14:18,320 +منها بنواصل حكينا في نفس الموضوع وبندى لها some + +145 +00:14:18,320 --> 00:14:23,660 +basic integrals بعض التكاملات الأساسية اللى هتمر + +146 +00:14:23,660 --> 00:14:28,690 +معانا كتير خلال هذا sectionتكمل أول تكمل من Zero + +147 +00:14:28,690 --> 00:14:34,630 +إلى بي لل X DX يبقى النتيجة بي تربيه على اتنين + +148 +00:14:34,630 --> 00:14:38,910 +منذكر بالثانوية بقيني اقول X تربيه على اتنين و + +149 +00:14:38,910 --> 00:14:41,930 +بنعوض بالقيم اللي فوق ناقص اللي تحت اللي تحت بصير + +150 +00:14:41,930 --> 00:14:46,570 +Zero يبقى بي تربيه عليها على اتنين لو بدل Zero + +151 +00:14:46,570 --> 00:14:51,560 +حطينا رقم تاني وليكن Aيبقى integration من a إلى b + +152 +00:14:51,560 --> 00:14:57,820 +إلى x dx بنفس الطريقة يبقى b تربية على اتنين ناقص + +153 +00:14:57,820 --> 00:15:01,400 +a تربية على اتنين يبقى هذه الزادة يعني اللي جاب + +154 +00:15:01,400 --> 00:15:05,780 +الأبناء بسالب a تربية على اتنين يعني بنعوض بالقيمة + +155 +00:15:05,780 --> 00:15:10,960 +اللي فوق ناقص القيمة المتعة لو بدل ال x كانت x + +156 +00:15:10,960 --> 00:15:13,340 +تربية تكمل x تربية برع ناشر + +157 +00:15:16,170 --> 00:15:19,990 +يبقى النتيجة بالقيم اللى فوق ناقص اللى تحت يبقى B + +158 +00:15:19,990 --> 00:15:24,950 +تكيب على تلاتة ناقص A تكيب على تلاتة والـA أقل من + +159 +00:15:24,950 --> 00:15:29,430 +مين من B يعني ال index اللى تحت في التكامل أصغر من + +160 +00:15:29,430 --> 00:15:34,630 +مين من ال index اللى فوق دائما عرضا النقطة الرابعة + +161 +00:15:34,630 --> 00:15:39,370 +لو كان تكامل على constant بقول يبقى ال constant في + +162 +00:15:39,370 --> 00:15:42,590 +طول ال interval C في ال B ناقص + +163 +00:15:55,030 --> 00:15:59,630 +الاربع نقاط هذول خليهم في دماغك نبدأ نشتغل عليهم + +164 +00:15:59,630 --> 00:16:05,050 +عملياهو راح قال لي احسبلي كل من التكاملات التالية + +165 +00:16:05,050 --> 00:16:11,810 +واطني التكامل لرقم ايه فبجي بقوله تكامل لرقم ايه + +166 +00:16:11,810 --> 00:16:18,030 +اللي يتكامل من 2 5 ل X تكييب DXطبقًا للكلام اللي + +167 +00:16:18,030 --> 00:16:28,050 +هو قاله في رقم تلاتة يبقى باجي بقوله X تربية يبقى + +168 +00:16:28,050 --> 00:16:33,130 +X تربية اللي هي رقم تلاتة زي ما قلنا يبقى هذه بدها + +169 +00:16:33,130 --> 00:16:40,310 +تساوي خمس تكييب على تلاتة ناقص اتنين تكييب على + +170 +00:16:40,310 --> 00:16:48,060 +تلاتةيعني كأنه هذا تلت عامل مشترك وخمسة تكييب ليه؟ + +171 +00:16:48,060 --> 00:16:54,660 +مية خمسة وعشرين ناقص اتنين تكييب ليه جداش؟ تمانية. + +172 +00:16:54,980 --> 00:16:58,360 +المية وخمسة وعشرين بتشيل منهم تمانية بيبقى لجداش؟ + +173 +00:16:58,360 --> 00:17:05,520 +مية وسبعة عشر على جداش على تلاتة. بتيجي؟ تلاتة في + +174 +00:17:05,520 --> 00:17:11,300 +تلاتة بتسعة، بتيجي.يبقى هنا بصير تلاتة و سبعة و + +175 +00:17:11,300 --> 00:17:16,180 +اتنين او تلاتة فيها تسعة يبقى النتيجة تساوي تسعة و + +176 +00:17:16,180 --> 00:17:23,020 +تلاتين نمرة B نمرة B قال تكمل من Zero لواحد لاتنين + +177 +00:17:23,020 --> 00:17:30,520 +X ناقص X تكعيب DXحسب خواص التكامل بقدر أجازة + +178 +00:17:30,520 --> 00:17:35,340 +التكامل هذا إلى تكاملين والمقدار الثابت بقوله برة + +179 +00:17:35,340 --> 00:17:41,480 +يبقى هذا الكلام يساوي 2 تكامل من 0 إلى 1 لل X DX + +180 +00:17:41,480 --> 00:17:49,030 +ناقص تكامل من 0 إلى 1 لل X تكعيب DXالإثنان مالكش + +181 +00:17:49,030 --> 00:17:54,250 +دعوة وهذه عبارة عن الاكس اللي هي عبارة عن اكس + +182 +00:17:54,250 --> 00:18:00,250 +تربية بده اشيل اكس وحط مكانه واحد يبقى واحد تربية + +183 +00:18:00,250 --> 00:18:05,970 +عليها على الإثنان كونها زرع يبقى مطبق عليها من؟ + +184 +00:18:05,970 --> 00:18:12,250 +القاعدة الأولىخلاصنا منها نجي للي بعدها يبقى هاي + +185 +00:18:12,250 --> 00:18:19,070 +اتنين وهادي ناقص بنفس الطريقة يبقى أس أربع على + +186 +00:18:19,070 --> 00:18:25,730 +أربع يبقى واحد أس أربع على أربع يبقى هذا الكلام + +187 +00:18:25,730 --> 00:18:29,990 +بده يسهل مص مع اتنين الله يسهل عليها واحد تربيع + +188 +00:18:29,990 --> 00:18:35,210 +اللي هو بواحدنقص واحد اقص اربعة اللي هو واحد على + +189 +00:18:35,210 --> 00:18:42,060 +اربعة يبقى واحد ناقص ربع اللي هو تلات اربعةنجي + +190 +00:18:42,060 --> 00:18:49,040 +للنقطة رقم C بيقوللي تكامل من واحد للاتنين لل X + +191 +00:18:49,040 --> 00:18:56,420 +على اتنين زائد اتنين X على اتنين زائد اتنين كله + +192 +00:18:56,420 --> 00:19:02,580 +بالنسبة إلى من؟ إلى DX بقدر اجزء هذا التكامل إلى + +193 +00:19:02,580 --> 00:19:09,140 +تكاملينيبقى هذا الكلام بده يسون نص برا وتكامل من + +194 +00:19:09,140 --> 00:19:16,820 +واحد لليتنين لل X DX زائد تكامل من واحد لليتنين + +195 +00:19:16,820 --> 00:19:25,790 +لليتنين DXهذا الكلام يساوي مص خليك ثابت برا بيظهر + +196 +00:19:25,790 --> 00:19:32,510 +لنا من هذا ال X من القاعدة الرقم اتنين تمام؟ يبقاش + +197 +00:19:32,510 --> 00:19:39,410 +باجي بقوله هذه في اتنين تربية عالمية على اتنين + +198 +00:19:39,410 --> 00:19:47,830 +ناقص واحد تربية على الاتنين اللي بعده زاد فاللي + +199 +00:19:47,830 --> 00:19:54,880 +علله القاعدة رقم اربعةيبقى تكامل المقدار ثابت يبقى + +200 +00:19:54,880 --> 00:20:01,340 +المقدار الثابت زي ما هو في الـB ناقص الـA يبقى هذا + +201 +00:20:01,340 --> 00:20:08,270 +الكلام بده يساوي هذا نص زي ما هوببقى لإن اتنين + +202 +00:20:08,270 --> 00:20:12,150 +تربية على اتنين يعني اربعة على الاتنين اللي يبقى + +203 +00:20:12,150 --> 00:20:16,650 +جديش باتنين ناقص واحد تربية اللي هو واحد اللي هو + +204 +00:20:16,650 --> 00:20:23,250 +جديش نص زائد بلّع لإن اتنين ناقص واحد بواحد في + +205 +00:20:23,250 --> 00:20:32,770 +اتنين باتنين يبقى يساويهنا نص في اتنين ناقص نص + +206 +00:20:32,770 --> 00:20:38,350 +بيظل واحد و نص يعني كده ايش؟ تلاتة على اتنين وهنا + +207 +00:20:38,350 --> 00:20:49,190 +زائد اتنين ويساوي تلاتة ربع زائد اتنين يبقى احداشر + +208 +00:20:49,190 --> 00:20:57,660 +على اربعة شكلها نهنةلا يزال في ال section باقي + +209 +00:20:57,660 --> 00:21:03,660 +باقي نقطة أخيرة النقطة الأخيرة بتتحدث عن ال + +210 +00:21:03,660 --> 00:21:09,660 +average value لدولار نعطي تعريف ثم مثال عليها + +211 +00:21:09,660 --> 00:21:13,900 +definition if + +212 +00:21:13,900 --> 00:21:19,940 +ال if is integrable + +213 +00:21:21,370 --> 00:21:30,130 +ده اللي قابل الاتكامل على الفترة المغلقة A وB then + +214 +00:21:30,130 --> 00:21:44,810 +it's average then it's average average + +215 +00:21:44,810 --> 00:21:50,870 +أو mean يمكن نسميها average value + +216 +00:21:53,950 --> 00:22:07,710 +on the closed interval a وb is defined as average + +217 +00:22:07,710 --> 00:22:15,990 +لدالة f بده ساوي واحد على b ناقص ال a تكمل من a + +218 +00:22:15,990 --> 00:22:20,630 +إلى b للf of x dx example + +219 +00:22:27,010 --> 00:22:41,730 +Find the average value of the function لدالة + +220 +00:22:41,730 --> 00:22:51,830 +F of X يساوي X ناقص واحد لكل تربيع over الفترة + +221 +00:22:51,830 --> 00:22:55,110 +Zero وتلاتة + +222 +00:23:29,970 --> 00:23:34,530 +نعود للتعريف اللي كنا نكتبه يبقى قال لو كانت + +223 +00:23:34,530 --> 00:23:39,570 +الدالة قابلة لتكمل على الفترة المغلقة A وB then + +224 +00:23:39,570 --> 00:23:44,870 +its average أو its mean يعني المتوسط تبع الدالة أو + +225 +00:23:44,870 --> 00:23:49,910 +المعدل تبع الدالة القيمة + +226 +00:23:49,910 --> 00:23:54,250 +المتوسطة للدالة على الفترة A وB is defined as + +227 +00:23:54,810 --> 00:24:00,750 +هدّيلها الرمز average لف a v بينقصين f يبقى اختصار + +228 +00:24:00,750 --> 00:24:05,470 +the average of the function f average لف واحد على + +229 +00:24:05,470 --> 00:24:11,670 +b ناقص ال a لتكامل من a إلى b لل f of x dx يعني + +230 +00:24:11,670 --> 00:24:16,630 +ايه؟يعني بدنا نروح نكمل الدالة على الفترة هذه كلها + +231 +00:24:16,630 --> 00:24:22,450 +ثم نقسم نتيجة التكمل على طول الدالة تكمل يعني ايش؟ + +232 +00:24:22,450 --> 00:24:27,940 +مساحةيعني بدى اقسم جداش المساحة اللى طلعت عندي على + +233 +00:24:27,940 --> 00:24:32,960 +طول ال interval بطلع عندى 100 بطلع عندى اللى ال + +234 +00:24:32,960 --> 00:24:36,460 +average value او ال mean value ل100 لل function + +235 +00:24:36,460 --> 00:24:40,320 +اللى عندنا يعني برجع مرة تانية بقول ال average + +236 +00:24:40,320 --> 00:24:45,460 +value لدل F على الفترة المغلقة A وBهي عبارة عن + +237 +00:24:45,460 --> 00:24:49,060 +واحد على بي نقص اللي هي تكامل من A إلى B لل F of X + +238 +00:24:49,060 --> 00:24:53,080 +DX يعني تكامل يتدالى مقسوما على مين على طول + +239 +00:24:53,080 --> 00:24:56,820 +الانترال واحد على بي نقص ال A يعني التكامل كله + +240 +00:24:56,820 --> 00:25:02,180 +مقسوما على طول الفترة من A إلى B اللي هو B نقص ال + +241 +00:25:02,180 --> 00:25:06,420 +A نجي نظر مثال عامل يقول هات ال average value + +242 +00:25:06,420 --> 00:25:10,500 +لدالة F of X سوى X نقص واحد لكل تربيع على الفترة + +243 +00:25:10,500 --> 00:25:17,370 +من Zero إلى تلاتةيبقى باجي بقوله الـ Average لدلة + +244 +00:25:17,370 --> 00:25:24,570 +F بده يساوي واحد على تلاتة ناقص Zero تكامل من Zero + +245 +00:25:24,570 --> 00:25:33,600 +لغاية تلاتة لل X ناقص واحد لكل تربيع DXتمام طيب + +246 +00:25:33,600 --> 00:25:40,400 +هذه تساوي اللي هي تلت تكامل من zero إلى تلتة بده + +247 +00:25:40,400 --> 00:25:48,500 +افك التربيه هذا يبقى x تربيه نقص 2x زائد واحد كله + +248 +00:25:48,500 --> 00:25:56,320 +في dx يبقى هذا الكلام يساوي تلت فيه التكامل بده + +249 +00:25:56,320 --> 00:26:02,140 +وزرهيبقى تكامل من Zero إلى تلاتة لل X تربيه DX + +250 +00:26:02,140 --> 00:26:08,760 +ناقص اتنين تكامل من Zero إلى تلاتة لل X DX زائد + +251 +00:26:08,760 --> 00:26:13,580 +تكامل من Zero إلى تلاتة لل واحد في Main في DX + +252 +00:26:13,580 --> 00:26:18,380 +بالشكل اللي عندنا هذا طيب هذا الكلام بده يسوى + +253 +00:26:18,380 --> 00:26:24,580 +تلاتة فيبدا جلودة هذا هو القاعدة رقم تلاتة اللي + +254 +00:26:24,580 --> 00:26:31,020 +كانت قبل قليل يبقى هذا شو بيصير بيصير تلاتة تكعيب + +255 +00:26:31,020 --> 00:26:38,820 +على تلاتة قلصنا منها الان ناقص اتنين مالكش دعوة + +256 +00:26:38,820 --> 00:26:43,720 +هذه لو كانت اكس تربيع على اتنين يعني تلاتة تربيع + +257 +00:26:43,720 --> 00:26:51,760 +على اتنين يبقى تلاتة تربيع على اتنيناللي بعدها + +258 +00:26:51,760 --> 00:26:57,860 +زائد ال constant C في تلاتة ناقص zero هاي جفلنا + +259 +00:26:57,860 --> 00:27:04,900 +الجوز تمام؟ يبقى هاي التلت اللي برا تلاتة مع تلاتة + +260 +00:27:04,900 --> 00:27:11,730 +بتروح بظل تسعةنقص اتنين مع اتنين بيروح بيظل كمان + +261 +00:27:11,730 --> 00:27:19,010 +تسعة زائد تلاتة هذه مع هذه الله يسهل عليها بل تلت + +262 +00:27:19,010 --> 00:27:24,250 +في تلاتة يبقى ال average value للدالة على كل + +263 +00:27:24,250 --> 00:27:29,510 +الفترة هذه تساوي مين؟ تساوي واحد، صحيح انتهينا من + +264 +00:27:29,510 --> 00:27:35,210 +هذا ال section وعليكم ال exercises ل section خمسة + +265 +00:27:35,210 --> 00:27:35,850 +تلاتة + +266 +00:27:44,530 --> 00:27:53,630 +Exercises خمسة تلاتة المسائل التالية من واحد لتسعة + +267 +00:27:53,630 --> 00:27:59,470 +و ستين الاد من واحد لتسعة و ستين الاد و من تلاتة و + +268 +00:27:59,470 --> 00:28:00,970 +سبعين لتمانين + +269 +00:28:16,120 --> 00:28:21,260 +قبل الحقيقة ما يخش في section خمسة أربعة ياجوا بعض + +270 +00:28:21,260 --> 00:28:28,500 +الطلاب وسألوني في تكامل لcos x أس تسعمية يعني + +271 +00:28:28,500 --> 00:28:35,010 +تفاضل cos x تفاضل الرقم تسعمية وتسعة وتسعينيعني زي + +272 +00:28:35,010 --> 00:28:40,490 +الانتخابات العربية، تمام؟ أنا بتعطيك قاعدة لمشتقة + +273 +00:28:40,490 --> 00:28:44,570 +ال sine وال cosine مهما كان الرقم اللي عندك تسعة + +274 +00:28:44,570 --> 00:28:48,670 +مية و تسعة و تسعين، تسعة تلاف، ميت ألف، قد ما + +275 +00:28:48,670 --> 00:28:54,510 +يكون، بتعطيك القاعدة التالية، القاعدة هذه بتقول لي + +276 +00:28:54,510 --> 00:29:04,440 +ما ياتي نمرة واحدبد المشتقة رقم N الـDN على DXN + +277 +00:29:04,440 --> 00:29:13,160 +لمين لصين ال X؟ كويس، هذه إلها أحد أمرين يا إما + +278 +00:29:13,160 --> 00:29:20,380 +ناقص واحد قس N ناقص واحد على اتنين ليه قصين ال X + +279 +00:29:20,380 --> 00:29:27,790 +إذا كان ال N is odd؟يا إما ناقص واحد أس N على + +280 +00:29:27,790 --> 00:29:36,310 +اتنين لصين ال X لما ال N is evenالقاعدة الثانية + +281 +00:29:36,310 --> 00:29:43,490 +بدي المشتقة النونية لل x in ل cosine ال x اللي كان + +282 +00:29:43,490 --> 00:29:48,150 +عليها السؤال في الكتاب تمام يبقى هذه كمان أحد + +283 +00:29:48,150 --> 00:29:54,190 +أمرين يا إما ناقص واحد أس n زائد واحد على اتنين + +284 +00:29:54,190 --> 00:30:02,890 +لصين ال x لما ال n is odd يا إما ناقص واحد أس n + +285 +00:30:02,890 --> 00:30:04,210 +على اتنين + +286 +00:30:16,130 --> 00:30:21,910 +سؤال موجود في الكتاب سقسن تلاتة خمسة سؤال تسعة + +287 +00:30:21,910 --> 00:30:30,090 +وخمسينيبقى سؤال تسعة و خمسين من section تلاتة خمسة + +288 +00:30:30,090 --> 00:30:37,870 +طلب المشتق رقم تلت تسعات لمن؟ + +289 +00:30:37,870 --> 00:30:41,810 +ل cosine ال X شكله أن هذا كان السؤال + +290 +00:30:48,230 --> 00:30:53,350 +هذا الكلام بده يساوي بجيب اطلع الرقم اللي عند مين + +291 +00:30:53,350 --> 00:30:59,010 +odd وانا عندي هذه ال cosine ولو كانت ال N أزد يبقى + +292 +00:30:59,010 --> 00:31:05,230 +هي النتيجة يبقى بقوله ناقص واحد أس تسعة تسعة تسعة + +293 +00:31:05,480 --> 00:31:14,060 +زائد واحد على اتنين + +294 +00:31:14,910 --> 00:31:20,570 +تلات تسعة زياد واحد كدهش؟ الف على اتنين خمسمية عدد + +295 +00:31:20,570 --> 00:31:26,190 +زوجي والله فاردين سالب واحد قص عدد زوجي واحد في + +296 +00:31:26,190 --> 00:31:31,010 +صين ال X صين ال X يبقى عرفت من وين الكتاب جاب + +297 +00:31:31,010 --> 00:31:36,490 +الجواب صين ال X يبقى هذه خدها قاعدة دائما و أبدا + +298 +00:31:36,490 --> 00:31:42,390 +معاك واستعملها لل sign و ال cosine مهما كان الأس + +299 +00:31:42,390 --> 00:31:48,410 +الف مليونتسعات، خمسمية، زي ما بدك، كويس؟ يبقى هذه + +300 +00:31:48,410 --> 00:31:52,950 +صحيحة in general ننتقل الآن لل section اللي بعده + +301 +00:31:52,950 --> 00:31:58,710 +اللي هو section خمسة أربع وهذا ال section very + +302 +00:31:58,710 --> 00:32:05,310 +important ولا يخلو الامتحان النهائي دائما وأبدا من + +303 +00:32:05,310 --> 00:32:06,790 +سؤال عليه + +304 +00:32:18,020 --> 00:32:31,380 +هذا خلاص نمسح؟ شوية؟ خليه شويتين و لا يهمك يبقى + +305 +00:32:31,380 --> 00:32:38,680 +بدنا نيدي خمسة أربعة The Fundamental + +306 +00:32:38,680 --> 00:32:44,200 +Theorem + +307 +00:32:44,200 --> 00:32:47,360 +of Calculus + +308 +00:32:58,170 --> 00:33:16,890 +قبل ان ناخد هذه النظرية ناخد نظرية اخرى نظرية + +309 +00:33:16,890 --> 00:33:25,110 +القيمة المتوسطة for definite integrals + +310 +00:33:28,630 --> 00:33:40,670 +بتقول ما يأتي if ال if is continuous دالة + +311 +00:33:40,670 --> 00:33:52,570 +متصلة على الفترة المغلقة a و b then at some point + +312 +00:33:52,570 --> 00:33:56,110 +at some point c + +313 +00:33:59,710 --> 00:34:08,170 +اللي موجودة في الفترة المغلقة A وB ال + +314 +00:34:08,170 --> 00:34:20,890 +F of C بده يساوي واحد على B ناقص ال A تكامل من A + +315 +00:34:20,890 --> 00:34:24,510 +إلى B لل F of X DX + +316 +00:34:35,070 --> 00:34:37,630 +طبعا احنا خدنا ال fundamental theorem of calculus + +317 +00:34:37,630 --> 00:34:42,990 +لمين؟ لـ derivatives قبل ذلك تمام؟ هذه لمين؟ لـ + +318 +00:34:42,990 --> 00:34:48,530 +definite integrals لتكاملات المحدودة اطلعلي في + +319 +00:34:48,530 --> 00:34:53,690 +النص تبع هذه النظرية واطلعلي في تعريف ال average + +320 +00:34:53,690 --> 00:34:59,670 +value اللي قبل قليل شوف له ميات نفس الشيء و الله + +321 +00:34:59,670 --> 00:35:05,560 +بختلفوا عن بعضطلع عليه فيه كويس فتح في التعريف و + +322 +00:35:05,560 --> 00:35:11,240 +طلع في النظرية هذه هناك بيقول ال average تبع + +323 +00:35:11,240 --> 00:35:16,140 +الدالة F يساوي واحد علبي نقص لف تكمل A علبي لF of + +324 +00:35:16,140 --> 00:35:21,000 +X DX هذه بيقول لو كانت الدالة دالة متواصلة الفترة + +325 +00:35:21,000 --> 00:35:26,620 +لازم تلاقي نقطة sum يعني مش كل النقارةيعني ممكن + +326 +00:35:26,620 --> 00:35:31,700 +تكون نقطة لازم تلاقي some point هتلاقي نقطة موجودة + +327 +00:35:31,700 --> 00:35:36,480 +في ال interval a و b بحيث ال f of c بدو يسوى 1 على + +328 +00:35:36,480 --> 00:35:42,680 +b نقص ال a في التكامل من a إلى b لل f of x dx حد + +329 +00:35:42,680 --> 00:35:46,640 +بديكم يقدر يقولي يعني ما هو المقصود من هذه النظرية + +330 +00:35:46,640 --> 00:35:51,410 +يعني ايش جصد يقولي بالظبط هيكمن خلال النص اللى + +331 +00:35:51,410 --> 00:35:54,870 +قدامنا ايه الطرق المتصل .. بدي واحد يحكي مش بديش + +332 +00:35:54,870 --> 00:35:58,330 +مجموعة واحد يحكي من أجل ان نتناقش هنا ويقول انه في + +333 +00:35:58,330 --> 00:36:02,550 +اي طرق متصل فيه نقطة فيها نقطة فيها وعن ذلك + +334 +00:36:02,550 --> 00:36:10,360 +المساحةيعني المعدل او المعدل ال average تبع الدالة + +335 +00:36:10,360 --> 00:36:16,180 +بيحصل او بيحدث عند نقطة يعني لازم الاجي النقطة في + +336 +00:36:16,180 --> 00:36:21,220 +ال domain تبع الدالة عند هذه النقطة بيحصل من ال + +337 +00:36:21,220 --> 00:36:24,360 +average هذا قال في average و سكت لكن ماقالش وين + +338 +00:36:24,360 --> 00:36:28,360 +بيحصل اجت هذه النقطة جلت لل average بيحصل عند + +339 +00:36:28,360 --> 00:36:31,040 +النقطة C بالضبط تماما + +340 +00:36:44,220 --> 00:36:51,060 +أنا ممكن أصيغ هذه بصيغة أخرى، ما هي الصيغة الأخرى؟ + +341 +00:36:51,300 --> 00:36:58,020 +ممكن اقول لك هذه اذا تكامل من a الى b لل f of x دي + +342 +00:36:58,020 --> 00:37:04,180 +x بده يساوي مين اللي هو ال b ناقص ال a في ال f of + +343 +00:37:04,180 --> 00:37:07,600 +c صح + +344 +00:37:07,600 --> 00:37:11,300 +ضربت الطرفين في b ناقص ال a بس مش أكتر + +345 +00:37:15,070 --> 00:37:20,350 +هذا التكامل من A الى B لل F of X DX شو يسوي + +346 +00:37:20,350 --> 00:37:25,510 +التكامل؟ ال average تبع الدالة مضروب فى طول الفترة + +347 +00:37:26,230 --> 00:37:30,510 +يبقى هذه أفادتني كمان شغلة تانية ان قيمة التكامل + +348 +00:37:30,510 --> 00:37:33,750 +من A إلى B هو عبارة عن ال average تبع الدالة مش ال + +349 +00:37:33,750 --> 00:37:36,990 +F of C هو ال average تبع الدالة ال average تبع + +350 +00:37:36,990 --> 00:37:42,170 +الدالة بيبقى تضربه بس في طول الفترة بيعطيك فعلا + +351 +00:37:42,170 --> 00:37:48,790 +قيمة هذا من هذا التكامل هذا اللي قصدنا من هذا نعطي + +352 +00:37:48,790 --> 00:37:49,610 +مثال توضيح + +353 +00:37:59,410 --> 00:38:08,790 +بقول let ال F of X تساوي اللي هو ال X تربيع و ال X + +354 +00:38:08,790 --> 00:38:16,010 +هذه موجودة في الفترة من Zero من Zero لغاية تسعة + +355 +00:38:16,010 --> 00:38:20,210 +المطلوب + +356 +00:38:20,210 --> 00:38:23,630 +الأول بقول find + +357 +00:38:28,690 --> 00:38:37,810 +On the given interval يعني كأننا بناخد مثال تاني + +358 +00:38:37,810 --> 00:38:44,880 +على ال average مطموعة ثانيةبقول find a point find + +359 +00:38:44,880 --> 00:38:55,960 +a point c in الفترة المغلقة zero وتسعة at which + +360 +00:38:55,960 --> 00:39:04,140 +the given function at which the given function + +361 +00:39:04,140 --> 00:39:14,090 +الدلة المعطاةأخذ هذا القيم عادي + +362 +00:39:21,840 --> 00:39:25,800 +يبقى هذا السؤال على النظرية هذه وعلى مين على ال + +363 +00:39:25,800 --> 00:39:30,420 +average اللي قبل قليل نقطة الأولى المطولة قال لي + +364 +00:39:30,420 --> 00:39:35,240 +هاتلي ال average جداش تبع ال function اتنين هاتلي + +365 +00:39:35,240 --> 00:39:39,100 +ال average بيحصل وين عند اي نقطة على الفترة من + +366 +00:39:39,100 --> 00:39:44,280 +zero الى تسعة بيحصل هذا مين هذا ال average بنقوله + +367 +00:39:44,280 --> 00:39:45,700 +بسيطة اي solution + +368 +00:39:49,260 --> 00:39:53,940 +بدنا ال average تبع الدالة بقول له ال average تبع + +369 +00:39:53,940 --> 00:40:02,520 +الدالة F يسوى واحد على B ناقص ال A يبقى تسعة ناقص + +370 +00:40:02,520 --> 00:40:09,840 +Zero تكامل من Zero إلى تسعة لل F of X DX يعني X + +371 +00:40:09,840 --> 00:40:18,380 +تربيه DX شكر ال average؟ طيب هذا الكلام يساوي + +372 +00:40:24,920 --> 00:40:33,760 +يبقى تسعة تكييب على تلاتة يبقى هذه تسعة تكييب على + +373 +00:40:33,760 --> 00:40:40,270 +مين؟ على تلاتةأظن تسعة مع تسعة تكعيب يبقى كم؟ تسعة + +374 +00:40:40,270 --> 00:40:47,010 +تربيع يبقى تسعة تربيع على تلاتة يعني واحد و تمانين + +375 +00:40:47,010 --> 00:40:52,210 +على تلاتة يعني كم؟ سبعة و عشرين يبقى ال average + +376 +00:40:52,210 --> 00:40:56,230 +تبع الدالة على الفترة من صفر لتسعة هو سبعة و عشرين + +377 +00:40:56,230 --> 00:41:00,760 +ايش بيقول ليه؟قال يشوف ال average هذا وين بيحصل + +378 +00:41:00,760 --> 00:41:04,700 +find the point C هتلي النقطة C اللي موجودة في ال + +379 +00:41:04,700 --> 00:41:08,880 +interval هذه اللي ال average هذا بيحصل عندها بقوله + +380 +00:41:08,880 --> 00:41:14,900 +بسيطة هي النظرية قدامنا هي عندك ال F of C اللي + +381 +00:41:14,900 --> 00:41:22,540 +يجداش بدها ساوي واحد على B ناقص ال A تكامل من A + +382 +00:41:22,540 --> 00:41:30,430 +إلى B لل F of X DXمش هذا هو ال average طيب هذا بده + +383 +00:41:30,430 --> 00:41:35,790 +يعطينا mean ال F of C هي ال F of X معطعة يبقى بده + +384 +00:41:35,790 --> 00:41:41,550 +يشيل X ويحط مكانها مين؟ C يبقى هذا معناته C تربيع + +385 +00:41:41,550 --> 00:41:47,210 +هذا عبارة عن ال average يبقى بده يساوي ال average + +386 +00:41:47,210 --> 00:41:52,820 +ل$Fمظبوط؟ لأنه تعريف من؟ تعريف الـ Leverage طب هذا + +387 +00:41:52,820 --> 00:41:57,640 +احنا حسبناه فوق طالع كدهش؟ سبعة و عشرين، اذا هذا + +388 +00:41:57,640 --> 00:42:03,020 +معناه ان الـC تربية بده يساوي سبعة و عشرين هذا + +389 +00:42:03,020 --> 00:42:08,540 +معناه ان الـC بده يساوي زائد او ناقص تلاتة جذر + +390 +00:42:08,540 --> 00:42:14,480 +تلاتة، طب سالب تلاتة جذر التلاتة موجودة في الفترة؟ + +391 +00:42:14,640 --> 00:42:22,740 +إذا هذه مرفوضة يبقى هنا سة C تساوي تلاتة جذر تلاتة + +392 +00:42:22,740 --> 00:42:28,900 +اللي موجودة في الفترة Zero وتسعة والاخر مالها + +393 +00:42:28,900 --> 00:42:38,640 +مرفوضة لإنها مش موجودة داخل هذه الفترة تقدر + +394 +00:42:38,640 --> 00:42:45,180 +تقول C تساوي becauseيعني احنا رفضنا التانية اللي + +395 +00:42:45,180 --> 00:42:51,940 +هو C تساوي سالب تلاتة جذر تلاتة but not belong ل + +396 +00:42:51,940 --> 00:42:56,840 +ال interval 0 9 يعني أخدنا الأولى و هملنا التانية + +397 +00:42:56,840 --> 00:43:02,500 +لإنها مش موجودة داخل هذه الفترة ابنجي الآن للنظرية + +398 +00:43:02,500 --> 00:43:05,840 +اللي احنا حاطينها العنوان اللي فوق تبع هذا section + +399 +00:43:05,840 --> 00:43:11,500 +اللي ال fundamental theorem of calculusنجي الأن لـ + +400 +00:43:11,500 --> 00:43:17,320 +Fundamental Theorem + +401 +00:43:17,320 --> 00:43:20,860 +of + +402 +00:43:20,860 --> 00:43:27,200 +Calculus Part + +403 +00:43:27,200 --> 00:43:31,420 +1 هنقسمها + +404 +00:43:31,420 --> 00:43:37,550 +إلى جزئين، فنجي للجزء الأولبتقول لما ياتي لو كانت + +405 +00:43:37,550 --> 00:43:45,810 +ال F is continuous + +406 +00:43:45,810 --> 00:43:50,350 +على ال closed interval a و b + +407 +00:43:53,540 --> 00:44:03,060 +Capital F of X يساوي تكامل من A إلى X لل F of T دي + +408 +00:44:03,060 --> 00:44:12,340 +تي لل F of T دي تي + +409 +00:44:12,340 --> 00:44:25,330 +is continuous is continuous onالـ class interval a + +410 +00:44:25,330 --> 00:44:31,170 +و b and differentiable + +411 +00:44:31,170 --> 00:44:45,030 +على الفترة المفتوحة a و b and ال f prime of + +412 +00:44:45,030 --> 00:44:56,330 +x بدي سوى d على dxلتكامل من A إلى X للـF of T دي T + +413 +00:44:56,330 --> 00:45:03,250 +ويساوي F of X لأن + +414 +00:45:03,250 --> 00:45:08,090 +هنا نحن نتكلم عن نظرية الأساسية للتفاضل والتكامل + +415 +00:45:08,090 --> 00:45:14,500 +Fundamental theorem of calculus الجزء الأولبقول لو + +416 +00:45:14,500 --> 00:45:18,960 +كانت الدالة F small continuous على الفترة المغلقة + +417 +00:45:18,960 --> 00:45:25,500 +A وB وكان capital F هو عبارة عن تكامل ال F small + +418 +00:45:25,500 --> 00:45:33,220 +على الفترة من A إلى X يبقى مرة تانية بقول لو كانت + +419 +00:45:33,220 --> 00:45:38,710 +F small دالة متصلة على الفترة المغلقة A وBيبقى + +420 +00:45:38,710 --> 00:45:43,890 +capital F of X كانت كذلك تسوي تكامل من A إلى X لل + +421 +00:45:43,890 --> 00:45:49,230 +F of T DT يعني تكامل محدود على الفترة من A إلى X + +422 +00:45:49,230 --> 00:45:53,570 +كانت دالة متصلة كذلك على الفترة الـA وB المغلقة + +423 +00:45:53,570 --> 00:45:58,270 +وقابلة للتفاضل على الفترة المفتوحة يبقى ال F prime + +424 +00:45:58,270 --> 00:46:04,090 +of X يبقى يسوي D على DX لهذا التكامل يبقى شو + +425 +00:46:04,090 --> 00:46:09,750 +بيعمل؟التفاضل ده هيلغي التكمل وترجع الدالة الى + +426 +00:46:09,750 --> 00:46:15,450 +أصلها اللي هي main f of x طلعليها كويس تحت ال a + +427 +00:46:15,450 --> 00:46:21,420 +مقدار ثابت ال a constantوالـ X هو المتغير لما انا + +428 +00:46:21,420 --> 00:46:25,160 +اجي أفاضلها بطير يتكامل فبتظهر F of X الدالة من + +429 +00:46:25,160 --> 00:46:30,980 +الدالة الأصلية والله هذه بسيطة جدا يعني لو قلت لك + +430 +00:46:30,980 --> 00:46:36,320 +تكامل من عشرة لل X لل F of X دي X وبدي اجي أفاضلها + +431 +00:46:36,320 --> 00:46:39,720 +يبقى بتقول الجواب هو F of X قد ما تكون تكون، + +432 +00:46:39,720 --> 00:46:45,080 +مظبوط؟ بناء على هذه النظرية السؤال هولو بدل ال X + +433 +00:46:45,080 --> 00:46:50,420 +هذا اللي فوق كانت دالة في X مش X كانت G of X كي + +434 +00:46:50,420 --> 00:46:57,340 +بنسويه بقولك ولا حاجة بيصير بيصير طبقة لتشين رول + +435 +00:46:57,340 --> 00:47:04,800 +بتقولي F of G of X في G prime of X يبقى هذه بدي + +436 +00:47:04,800 --> 00:47:10,000 +اقول كأنها result نتيجة او crollery نتيجة عليها اه + +437 +00:47:10,000 --> 00:47:12,280 +لو جيه تقول crollery + +438 +00:47:14,530 --> 00:47:23,490 +نتيجة الرقم واحد لو بدي D على DX لتكامل من A للـG + +439 +00:47:23,490 --> 00:47:32,570 +of X لل F of T DT بقوله بسيطة جدا طبقا للكلام اللي + +440 +00:47:32,570 --> 00:47:39,450 +فوق F of G of X مضروبة في مشتقة الـG طبقا للـchain + +441 +00:47:39,450 --> 00:47:46,970 +rule اللي هو G prime of X تمام؟أجي واحد تاني قال + +442 +00:47:46,970 --> 00:47:51,150 +لي ايش رأيك لو خلتي التكامل هذا زي ما هو بدل + +443 +00:47:51,150 --> 00:47:56,890 +constant حطيت دالة تانية في X كيف بنسوّمها؟ بسيطة + +444 +00:47:56,890 --> 00:48:00,330 +جدا ايه اللي عملت دالة اللي فوق؟ قلت عمل دالة اللي + +445 +00:48:00,330 --> 00:48:08,830 +تساعد بإشارة مخالفة كيف يعني؟ يعني D على DXلتكامل + +446 +00:48:08,830 --> 00:48:17,680 +من H of X لل G of X لل F of T ديبدي افاضي ليه + +447 +00:48:17,680 --> 00:48:21,540 +التكمل مش بدي اتكامل و بعدين اتفاضل لأ انا بدي + +448 +00:48:21,540 --> 00:48:27,760 +افاضي التكمل مباشرة يبقى باجي بقوله هذا الجزء اللي + +449 +00:48:27,760 --> 00:48:33,080 +فوق هو اللي رمناه واحد يبقى باجي بقوله هذا هو f of + +450 +00:48:33,080 --> 00:48:39,780 +g of x في ال g prime of x ناقص ماحدش أحسن من حد + +451 +00:48:39,780 --> 00:48:43,080 +اللي عملته للدلة اللي فوق يطلع تعمله للدلة اللي + +452 +00:48:43,080 --> 00:48:50,160 +تحت يبقى بروح بقوله ال fof H of X في H prime of X + +453 +00:48:50,160 --> 00:48:53,200 +سؤال + +454 +00:48:53,200 --> 00:48:56,200 +على هذا الـ Fundamental بتكرر كتير في الامتحانات + +455 +00:48:56,200 --> 00:49:00,940 +تمام؟ يبقى ركزي كويسة، الآن بدنا نيجي ناخد أمثلة + +456 +00:49:00,940 --> 00:49:04,560 +مختلفة، طبعا الكتاب ما جالش للنتيجة الأولى ولا + +457 +00:49:04,560 --> 00:49:09,140 +التانية اللي كانت، حط مسائل عليها حط النظرية ومن + +458 +00:49:09,140 --> 00:49:12,080 +ضمن المسائل حط مسائل على نتيجتها الأتنين هذو + +459 +00:49:35,410 --> 00:49:42,110 +نبدأ في الأمثلة يبقى example one + +460 +00:49:52,590 --> 00:49:54,550 +بقول find the derivative of the following + +461 +00:49:54,550 --> 00:50:06,510 +functions find the derivatives of the following + +462 +00:50:06,510 --> 00:50:15,790 +functions نمر ايه؟ + +463 +00:50:15,790 --> 00:50:29,260 +Y تساويY تساوي التكامل من X الى 1 ل T cos T dt + +464 +00:50:29,260 --> 00:50:32,440 +بدنا + +465 +00:50:32,440 --> 00:50:37,000 +نشتق هذه الدالة فاجب أن نتطلع في هذه النظرية + +466 +00:50:37,000 --> 00:50:42,260 +والنتاج لا شبه النظرية ولا شبه النتاج لأنه متغير + +467 +00:50:42,260 --> 00:50:46,760 +تحت مش فوق لكن احنا نخدم الخواص التكامل المحدودإنه + +468 +00:50:46,760 --> 00:50:51,600 +بقدر أقلب حدود التكمل و أحط إشارة سالب بقوله كويس + +469 +00:50:51,600 --> 00:50:58,070 +يبقى solutionيبقى باجي بقوله ال Y يساوي سالب تكامل + +470 +00:50:58,070 --> 00:51:05,150 +من واحد الى X ل T Cos T DT يبقى اللي فوق بس قلبت + +471 +00:51:05,150 --> 00:51:10,550 +حدود التكامل و حطيت اشارة سالب الان بقدر اشتق يبقى + +472 +00:51:10,550 --> 00:51:16,350 +هذه قال هات ال derivative يبقى Y prime يساوي سالب + +473 +00:51:16,350 --> 00:51:21,430 +مالكش دعوةمش هروح اكمل هذى طب انا هقولك ده لابتجه + +474 +00:51:21,430 --> 00:51:26,190 +اعرفش اتكملها تمام الا اذا كنت خبيرا فى التكمل اه + +475 +00:51:26,190 --> 00:51:29,130 +ممكن تكملها وبعدين تفاضل لكن احنا مابتناش نضيع + +476 +00:51:29,130 --> 00:51:33,430 +وقتك لأ انا مابتش تقدورى باجى بقطل عليه فوق X يبقى + +477 +00:51:33,430 --> 00:51:37,350 +هذى مباشر على مين على النظر يبقى ماعليك الا تشيل + +478 +00:51:37,350 --> 00:51:41,490 +كل T و تحط مكانها مين X لدالة اللى عندك يبقى + +479 +00:51:41,490 --> 00:51:46,230 +الدالة T Cos T يبقى سالب X Cos X الله يعطيك + +480 +00:51:46,230 --> 00:51:52,220 +العافية خلصهايبقى هاي المشتقة تمام طيب نمر بي + +481 +00:51:52,220 --> 00:52:01,540 +انتقل شوية نمر بي بيقولي Y يساوي تكامل من جدر ال X + +482 +00:52:01,540 --> 00:52:07,640 +لغاية ال zero ل sign T تربيع DT + +483 +00:52:11,220 --> 00:52:16,160 +قبل ما اشتق بدي ارتب المثال اللي عندي اظن ولا واحد + +484 +00:52:16,160 --> 00:52:21,360 +بيقدر يكملها هذه ولا انا كمان بهذا الشكل sin t + +485 +00:52:21,360 --> 00:52:25,860 +تربيع ولا واحد فين بيقدر يكملها يبقى باجي بقوله + +486 +00:52:25,860 --> 00:52:34,380 +هذه سالب تكامل من zero الى جدر ال X ل sin t تربيع + +487 +00:52:34,380 --> 00:52:42,020 +DTأنا بدى أشتق يبقى Y' يساوي سالب برا مالكش دعوة + +488 +00:52:42,020 --> 00:52:47,720 +تمام يبقى ماعليه اللي أشيل كل T و أحط مكانها جذر + +489 +00:52:47,720 --> 00:52:55,860 +ال X يبقى ال sign لجذر ال X الكل تاربية في مشتقة + +490 +00:52:55,860 --> 00:53:01,840 +جذر ال X هالمرة هذه بدى أكتبها لك تفصيلا مشان اه + +491 +00:53:01,840 --> 00:53:07,930 +ماتوهش تاني مرةخلصنا يبقى هاي المشتقة يبقى النتيجة + +492 +00:53:07,930 --> 00:53:14,710 +تساوي سالب sign ال X مشتقة جذر ال X اللي هو اتنين + +493 +00:53:14,710 --> 00:53:19,750 +او واحد على اتنين جذر ال X يبقى هاي النتيجة اللي + +494 +00:53:19,750 --> 00:53:29,050 +عندنا نعم ليش جذر X بتتربط مش انت تحت الجذر و + +495 +00:53:29,050 --> 00:53:35,640 +طلعتهابطيلة الجدر مباشرة يبقى عندك جدر ال X و بدك + +496 +00:53:35,640 --> 00:53:44,760 +تروح اتربعه نمر ال C بيقول Y يساوي تكامل من 2 إلى + +497 +00:53:44,760 --> 00:53:50,720 +سك X التي ناقص 1 على T + +498 +00:53:55,170 --> 00:54:00,710 +يبقى بدنا ايه؟ بدنا الروح نشتق، جاهزين، هذا مافيش + +499 +00:54:00,710 --> 00:54:07,730 +فيها شيء يبقى هذا الكلام بده يعطيلك Y' تساوي بدك + +500 +00:54:07,730 --> 00:54:14,770 +تشيل كل T و تحط مكانها سك ال X يبقى هاي سك ال X + +501 +00:54:14,770 --> 00:54:22,530 +ناقص واحد على سك ال X في مشتقة سك ال X، بقدرش + +502 +00:54:22,530 --> 00:54:29,020 +مشتقة سك ال X؟انت قدمت امتحان اليوم يبقى هذا سك ال + +503 +00:54:29,020 --> 00:54:36,300 +X في تان ال X تمام في اختصارات بنحاول نختصر يبقى + +504 +00:54:36,300 --> 00:54:40,040 +انا بده افك الجثة بده ادخل السك جوه بده اخلي التان + +505 +00:54:40,040 --> 00:54:48,020 +برا يبقى بصير عندي سك تربيع ال X ناقص واحد في تان + +506 +00:54:48,020 --> 00:54:57,680 +ال X سك تربيع ناقص واحدتان تربيع يبقى تان تربيع ال + +507 +00:54:57,680 --> 00:55:19,660 +X في تان ال X ويساوي تان تكييب ال X طيب + +508 +00:55:19,660 --> 00:55:31,010 +النمرة دينمره دي بيقول لي Y يسوى تكامل من تاني ال + +509 +00:55:31,010 --> 00:55:39,810 +X لإتنين X التي الجدرى التربية لواحد زائد T تربية + +510 +00:55:39,810 --> 00:55:47,580 +DT يبقى هذه علامة على النتيجة رقم اتنينيبقى بدهش + +511 +00:55:47,580 --> 00:55:55,640 +اقوله ال Y' تساوي بده أشيل كل T و أحط مكانها 2X + +512 +00:55:55,640 --> 00:56:03,360 +يبقى هذا 2X في الجذر التربيعي اللي هو 1 زائد 4X + +513 +00:56:03,360 --> 00:56:03,940 +تربيع + +514 +00:56:19,050 --> 00:56:27,790 +نقص تان ال X في الجذر التربيعي ناقص تان ال X في + +515 +00:56:27,790 --> 00:56:34,980 +الجذر التربيعي ناقص تان ال X في الجذر التربيعيبسك + +516 +00:56:34,980 --> 00:56:42,060 +تربيع ال X نعيد ترتيبها يبقى اربعة X واحد زائد + +517 +00:56:42,060 --> 00:56:49,420 +اربعة X تربيع ناخص واحد زائد تان تربيع سك تربيع + +518 +00:56:49,420 --> 00:56:57,720 +تطلع من تحت الجدر بسك يبقى بصيغة تان ال X في سك + +519 +00:56:57,720 --> 00:57:05,510 +تكعيب ال X الله عطاك العافية خلصك نمر أيه؟نمر أيه + +520 +00:57:05,510 --> 00:57:16,210 +بيقولي Y تساوي X تربيع تكامل من اتنين ل X تربيع ل + +521 +00:57:16,210 --> 00:57:24,790 +cosine T تكعيب كله DT ايوة + +522 +00:57:24,790 --> 00:57:29,590 +استنى شوية يعني هذه ولا زي السؤال من المثال اللي + +523 +00:57:29,590 --> 00:57:36,040 +جابها اه ممتاز جدايبقى هذه تعتبر function وهذه + +524 +00:57:36,040 --> 00:57:41,720 +كلها function تانية إذا هذه مشتقة حاصل ضرب دالتين + +525 +00:57:41,720 --> 00:57:47,640 +يبقى احنا بدنا ال y prime يبقى باجي بقوله ال y + +526 +00:57:47,640 --> 00:57:52,980 +prime يساوي الدالة الأولى في مشتقة الدالة تانية + +527 +00:57:52,980 --> 00:57:59,180 +بدي أشيل كل T و أحط مكانها X تربيع يبقى cosine X + +528 +00:57:59,180 --> 00:58:06,400 +تربيع الكلتكيب في مشتقة الدالة اللى فوق الهو بقدرش + +529 +00:58:06,400 --> 00:58:17,090 +باتنين X خلصنا الجزء الاولهذا الأول يبقى في مشتقة + +530 +00:58:17,090 --> 00:58:24,150 +الثاني خلاصنا من تمام مية لمية زائد مشتقة الأول + +531 +00:58:24,150 --> 00:58:30,590 +قداش اتنين X في تكامل من اتنين لل X تربيع ل cosine + +532 +00:58:30,590 --> 00:58:33,690 +T تكعيب DT + +533 +00:58:36,460 --> 00:58:46,040 +يبقى هذه اتنين اكس تكعيب cosine اكس أُس ستة زائد + +534 +00:58:46,040 --> 00:58:54,450 +اتنين اكستكامل من اتنين لل X تربية لكو صين T تكيب + +535 +00:58:54,450 --> 00:59:01,030 +DT يبقى إذا عندك حاصل ضرب دالتين بدك تروح تستخدم + +536 +00:59:01,030 --> 00:59:06,090 +مشتقة حاصل ضرب دالتين حسب ما اتعلمت في chapter + +537 +00:59:06,090 --> 00:59:15,150 +تلاتة طيب هذا هو المثال الأول ننتقل الآن للمثال + +538 +00:59:15,150 --> 00:59:26,500 +رقم اتنينيبقى example two بيقول + +539 +00:59:26,500 --> 00:59:38,340 +if y تساوي صين ال X تكامل من كتان ال X إلى تان ال + +540 +00:59:38,340 --> 00:59:44,520 +X لواحد على واحد زائد T تربيع DT + +541 +01:00:06,160 --> 01:00:11,200 +بنفس الطريقة في السؤال اللي قبل قليل هذه تعتبر + +542 +01:00:11,200 --> 01:00:15,780 +function وهذه كلها function تانيةاذا انا مشتقت + +543 +01:00:15,780 --> 01:00:22,080 +ايه؟ اصل ضرب دالي تاني يبقى بالدي ال Y prime سنة + +544 +01:00:22,080 --> 01:00:28,440 +الدالة الأولى تمام؟ في مشتقت الدالة الثانية يبقى + +545 +01:00:28,440 --> 01:00:32,520 +هاي فتح نقص الدالة الثانية بدي أشيل كل T و أحط + +546 +01:00:32,520 --> 01:00:40,060 +مكانها تان ال X يبقى واحد على واحد زائد تان تربيع + +547 +01:00:40,060 --> 01:00:48,450 +ال X في مشتقت التان جداش؟تربيع ال X خلصنا الدالة + +548 +01:00:48,450 --> 01:00:51,350 +اللى فوق اللى عملنا الدالة اللى فوق بدنا نعمل + +549 +01:00:51,350 --> 01:00:56,910 +الدالة اللى تاعة واحد على واحد زائد كتان تربيع ال + +550 +01:00:56,910 --> 01:01:06,730 +X في طفول كتان بسالب كسكن تربيع ال X خلصنا هذا لسه + +551 +01:01:06,730 --> 01:01:12,090 +الأول في مشتقة الثانية زائد الثانية في مشتقة + +552 +01:01:12,090 --> 01:01:19,790 +الأولى زائدالأولى اللى مشتقتها cosine ال X في + +553 +01:01:19,790 --> 01:01:27,490 +تكامل لكتان ال X إلى تان ال X واحد زائد T تقريبا + +554 +01:01:27,490 --> 01:01:38,200 +DT هنا ايه الترتيبيبقى ال Y' يساوي صين X فيه واحد + +555 +01:01:38,200 --> 01:01:44,000 +زائد تان تربيع سك تربيع مع سك تربيع بواحد يبقى هذا + +556 +01:01:44,000 --> 01:01:49,750 +الله يسهل عليك مع السلامة بواحد صحيح وهي ناقصناقص + +557 +01:01:49,750 --> 01:01:56,210 +مع ناقص بزائد تمام واحد زائد كتان تربية كسكت تربية + +558 +01:01:56,210 --> 01:02:01,990 +مع كسكت تربية مع السلامة يبقى صارب واحد بالشكل + +559 +01:02:01,990 --> 01:02:05,250 +اللي عندنا ما شاء الله ليه انا كبير انا طلعت ولا + +560 +01:02:05,250 --> 01:02:13,810 +حاجة يبقى هنا زائد cosine ال Xتكامل لكتان ال X إلى + +561 +01:02:13,810 --> 01:02:19,310 +تان ال X واحد على واحد زائد T تربية DT واحد زائد + +562 +01:02:19,310 --> 01:02:28,330 +واحد يسوى اتنين يبقى اتنين sin X زائد cos X تكامل + +563 +01:02:28,540 --> 01:02:36,480 +كتان ال X لتان ال X لواحد زائد T تربيع DT خلصنا + +564 +01:02:36,480 --> 01:02:41,860 +المطلوب الأول قال لي احسبلي المشتق هذي وين عند X + +565 +01:02:41,860 --> 01:02:46,420 +يسوى باي على مين على أربعة إذا هشيل كل X و أحط + +566 +01:02:46,420 --> 01:02:52,220 +مكانها باية على أربعة يبقى ال Y prime عند ال باية + +567 +01:02:52,220 --> 01:02:57,640 +على أربعة بده يساويSin باية على أربعة يعني جيب + +568 +01:02:57,640 --> 01:03:03,180 +الخمسة وأربعين جداش؟ واحد على جذر اتنين يبقى اتنين + +569 +01:03:03,180 --> 01:03:10,420 +في واحد على جذر اتنينزيت كوصاين الواحد على جدري + +570 +01:03:10,420 --> 01:03:17,140 +اتنين تمام وظل الخمسة واربعين يبقى صار هذا واحد + +571 +01:03:17,140 --> 01:03:24,120 +وظل تمام الخمسة واربعين واحد على واحد زائد T ترميع + +572 +01:03:24,120 --> 01:03:31,780 +DT أول خاصية أخدناها من خواص التكمل الحدود أنه إذا + +573 +01:03:31,780 --> 01:03:37,880 +تساوى حدات تكملفإن قيمة التكمل تساوي يبقى هذا كله + +574 +01:03:37,880 --> 01:03:43,500 +بسلامته مع السلامة ب zero يبقى الجواب اتنين على + +575 +01:03:43,500 --> 01:03:49,200 +جذر اتنينطب ايش رايك لو ضربت في جذر اتنين و جسمت + +576 +01:03:49,200 --> 01:03:55,960 +على جذر اتنين فى اتنين على اتنين تحت الجذر بيبقى + +577 +01:03:55,960 --> 01:04:01,480 +القداش جذر اتنين هو الجواب يبقى يا اما اتنين على + +578 +01:04:01,480 --> 01:04:08,420 +جذر اتنين يا اما جذر اتنين اي واحدة فيهم بتقدر دور + +579 +01:04:08,420 --> 01:04:09,980 +المطلوب + +580 +01:04:13,440 --> 01:04:18,600 +هذا السؤال مرة جيبناه في احدى الامتحانات لنشوفك + +581 +01:04:18,600 --> 01:04:21,920 +ليش لأن هذا جاب ال fundamental theorem و جاب + +582 +01:04:21,920 --> 01:04:26,380 +الخواص تبع التكاملات المحدودة لنشوفك بتعرف تطبق + +583 +01:04:26,380 --> 01:04:27,480 +الخواص ولا لا + +584 +01:04:41,770 --> 01:04:45,250 +بنا نيجي للجزء الثاني من ال fundamental theorem + +585 +01:04:45,250 --> 01:04:53,630 +يبقى بنا نيجي لل fundamental theorem + +586 +01:04:53,630 --> 01:05:05,370 +part two اللي + +587 +01:05:05,370 --> 01:05:09,050 +هم يسميها the calculation + +588 +01:05:14,290 --> 01:05:23,450 +النظرية الحسابات بتقول لما ياتي if ال if is + +589 +01:05:23,450 --> 01:05:36,190 +continuous at every point في + +590 +01:05:36,190 --> 01:05:57,990 +الفترة a و b andcapital F is an antiderivative of + +591 +01:05:57,990 --> 01:06:07,430 +ال F على الفترة المغلقة A وB then تكامل + +592 +01:06:07,950 --> 01:06:17,910 +من A إلى B لل F of X DX بدي يسوي capital F of X من + +593 +01:06:17,910 --> 01:06:26,150 +عند ال A لغاية ال B ويسوي F of B ناقص F of A + +594 +01:06:26,150 --> 01:06:29,470 +Example + +595 +01:06:29,470 --> 01:06:34,890 +Calculate + +596 +01:06:38,970 --> 01:06:45,870 +The following integrals + +597 +01:06:45,870 --> 01:06:49,730 +احسب + +598 +01:06:49,730 --> 01:06:57,490 +للتكاملات التالية نمر واحد تكمل من zero لواحد لل X + +599 +01:06:57,490 --> 01:07:01,710 +تربيع زائد جدر ال X في DX + +600 +01:07:31,060 --> 01:07:35,140 +الجزء الأول من fundamental theorem of calculus كان + +601 +01:07:35,140 --> 01:07:41,780 +بتكلم عن التفاضل للتكامل المحدود عندي تكامل محدود + +602 +01:07:41,780 --> 01:07:47,250 +لدالة لو بدناانفاض لهذا التكامل الجزء الثاني بتكلم + +603 +01:07:47,250 --> 01:07:53,030 +عن كيفية حساب التكامل المحدود لدالة ما يعني كيفية + +604 +01:07:53,030 --> 01:07:59,910 +تحسب هذا التكامل عمليا بدون ما نحسب مساحة ولا نحسب + +605 +01:07:59,910 --> 01:08:04,890 +ال average ولا غيره دورة كامل بقول لو كانت الدالة + +606 +01:08:04,890 --> 01:08:10,340 +دالة متصلة عند كل نقطة في ال interval a وbوكان + +607 +01:08:10,340 --> 01:08:16,200 +capital F هو الـ antiderivative لدالة F على الفترة + +608 +01:08:16,200 --> 01:08:23,480 +المغلقة A وBيبقى تكامل من A إلى B لل F of X DX هو + +609 +01:08:23,480 --> 01:08:29,040 +عبارة عن كابتل F of X اللي قلنا عليها بروح بنعوض + +610 +01:08:29,040 --> 01:08:33,660 +في النتيجة اللي حصلت عندنا القيمة العلوية ناقص + +611 +01:08:33,660 --> 01:08:38,380 +القيمة السفلية يبقى هي اللي بتقوله من هنا سمنها ال + +612 +01:08:38,380 --> 01:08:42,700 +calculation theorem نظرية الحسابات يعني كيف بدك + +613 +01:08:42,700 --> 01:08:49,350 +تحسب التكامل المحدود عملياًيبقى هاي المقصود من هذه + +614 +01:08:49,350 --> 01:08:52,950 +النظرية طبعا قبل قلي كنا بنشغل الشغل هاد بس ايش + +615 +01:08:52,950 --> 01:08:56,010 +أخدنا ال sum basic integral للأربع تكاملات و بكنا + +616 +01:08:56,010 --> 01:08:59,230 +بنستخدمها اللي هاي من هنا بطل بدنا نكمل و نعود + +617 +01:08:59,230 --> 01:09:03,430 +دغري على طول القط تمام نعطي بعض الأمثلة جالي + +618 +01:09:03,430 --> 01:09:07,850 +أحسبلي كل من تكاملات التالية و أطاني أول تكامل هذا + +619 +01:09:07,850 --> 01:09:12,610 +بقوله دغري هذا الكلام بده يساوي تكامل من zero إلى + +620 +01:09:12,610 --> 01:09:16,910 +واحد لل X تربية زائد X أص نص + +621 +01:09:23,510 --> 01:09:32,770 +X تركيب على تلاتة X تركيب على تلاتة X تركيب على + +622 +01:09:32,770 --> 01:09:37,270 +تلاتة + +623 +01:09:37,300 --> 01:09:42,060 +لإتنين كل هذا الكلام من Zero لغاية كده اش واحد + +624 +01:09:42,060 --> 01:09:47,220 +يبقى لو بدي احسبه عملي بقول هذا الكلام بده يساوي + +625 +01:09:47,220 --> 01:09:54,620 +هاي X تكييب على تلاتة زي طولتين X أس تلاتة على + +626 +01:09:54,620 --> 01:09:59,500 +اتنين من Zero لغاية واحد يبقى انا بتعود بالقيم + +627 +01:09:59,500 --> 01:10:06,490 +اللي فوق ناقص القيم اللي تحت يبقى واحد تكييبعلى + +628 +01:10:06,490 --> 01:10:13,550 +تلاتة زي دي اتنين على تلاتة لواحد أس تلاتة على + +629 +01:10:13,550 --> 01:10:19,630 +اتنين هيعوضها بمين بالقيمة اللي فوق لل F of B يبقى + +630 +01:10:19,630 --> 01:10:27,510 +ناقص ال F of A يبقى ناقص Zero ناقص Zero طبعا طيب + +631 +01:10:27,510 --> 01:10:33,690 +هذا الكلام بده يساوي اظن ان هذا تلت مظبوط و هذا + +632 +01:10:33,690 --> 01:10:42,360 +تلتينبطلع واحد صحيح طيب نجي ناخد كمان مثال نمر + +633 +01:10:42,360 --> 01:10:49,120 +اتنين بدنا تكامل لمين؟ لواحد زائد cosine ال X + +634 +01:10:49,120 --> 01:10:56,320 +تكامل من Zero إلى Pi لواحد زائد cosine ال X DX + +635 +01:10:56,320 --> 01:10:59,620 +خلّي + +636 +01:10:59,620 --> 01:11:05,690 +ملاك هناهذا تكامل يستوي تكامل واحد بقداش تكامل + +637 +01:11:05,690 --> 01:11:14,250 +cosine من ورا الى ورازيرو لغاية باي نجي نعوض بحدود + +638 +01:11:14,250 --> 01:11:22,550 +التكامل يبقى باي زائد صين البي ناقص زيرو ناقص صين + +639 +01:11:22,550 --> 01:11:29,130 +الزيرو و يساوي باي قداش صين البي زيرو و صين الزيرو + +640 +01:11:29,130 --> 01:11:35,630 +يبقى هذا كله باي فقط والباقي كله بأصفر بروح مع + +641 +01:11:35,630 --> 01:11:38,110 +السلامة example three + +642 +01:11:42,140 --> 01:11:50,740 +بنتكامل من واحد لغاية اتنين لل X زائد واحد على X + +643 +01:11:50,740 --> 01:11:56,020 +الكل ترابيع DX كيف نتكامل هذا + +644 +01:11:58,850 --> 01:12:04,150 +فك التربية مش هيك طيب هذا الكلام بده يصير تكمل من + +645 +01:12:04,150 --> 01:12:11,270 +واحد للاتنين لل X تربية زائد اتنين فقط صح ولا لأ + +646 +01:12:11,270 --> 01:12:20,420 +حصل ضربهما زائد واحد على X تربية كله في DXيعني كأن + +647 +01:12:20,420 --> 01:12:26,460 +المسألة هي تكامل من واحد إلى اتنين لل X تربية زائد + +648 +01:12:26,460 --> 01:12:32,520 +اتنين زائد X أُس ناقص اتنين DX هالحيط بدنا نكامل + +649 +01:12:32,520 --> 01:12:40,720 +يبقى هذه تساوي X تكيب على تلاتة زائد اتنين X ناقص + +650 +01:12:40,720 --> 01:12:43,320 +X أُس ناقص واحد صحيح؟ + +651 +01:12:46,810 --> 01:12:53,210 +بلاش هاي زائد وهي على ناقص واحد والكلام هذا من + +652 +01:12:53,210 --> 01:12:59,370 +واحد لإتنين يعني كأنها X تكييب على تلاتة زائد + +653 +01:12:59,370 --> 01:13:07,510 +اتنين X ناقص واحد على X من واحد لغاية اتنين بتدعوك + +654 +01:13:07,510 --> 01:13:13,150 +بالقيمة اللي فوق اتنين تكييب بقداشتمانية ع تلاتة + +655 +01:13:13,150 --> 01:13:19,190 +زائد أربع ناقص نصف هيعوضنا القيمة اللي فوق ناقص + +656 +01:13:19,190 --> 01:13:23,030 +القيمة اللي تحت يبقى ناقص واحد تكيب ع تلاتة اللي + +657 +01:13:23,030 --> 01:13:29,350 +هو بواحد ناقص اتنين في واحد باتنين ناقص بيصير زائد + +658 +01:13:29,350 --> 01:13:35,880 +واحد ع واحد اللي هو بواحدواضحة؟ واضح طيب نيجي نجمع + +659 +01:13:35,880 --> 01:13:42,600 +هدول هذا الكلام يساوي عندك أربعة صحيح واحد خمسة + +660 +01:13:42,600 --> 01:13:50,120 +وناقص اتنين بيظل تلاتة عدد صحيح وعندك هنا ناقص تلت + +661 +01:13:50,120 --> 01:13:57,080 +و تمانية ع تلاتة بيظل سبعة تلاتة ناقص نص زائد سبعة + +662 +01:13:57,080 --> 01:14:03,820 +على تلاتة ناقص نص مظبوط هيك؟الاربعة و سالب اتنين و + +663 +01:14:03,820 --> 01:14:08,880 +واحد خمسة و اتنين تلاتة سالب تلت و تمانية ع تلاتة + +664 +01:14:08,880 --> 01:14:12,920 +بيبقى سبعة تلاتة هو يناقص نص زي مهم المضاعف + +665 +01:14:12,920 --> 01:14:19,800 +المشترك للكل كله قداش ستة في تلاتة تمانتاش ستة ع + +666 +01:14:19,800 --> 01:14:24,520 +تلاتة في اتنين في سبعة اربعة اتاش ستة على اتنين + +667 +01:14:24,520 --> 01:14:30,700 +اللي هو بتلاتةاربعتاش و تمانتاش بقداش اتنين و + +668 +01:14:30,700 --> 01:14:37,740 +تلاتين شيل منهم تلاتة بظل تسعة و عشرين على ستة + +669 +01:14:37,740 --> 01:14:45,420 +قيمة هذا التكامل طيب هذا النقطة التالتة النقطة + +670 +01:14:45,420 --> 01:14:54,110 +الرابعةبنتكامل من Zero لغاية Pi على ستة لسك ال X + +671 +01:14:54,110 --> 01:15:01,910 +زائد تاني ال X لكل تربيع DX يساوي + +672 +01:15:01,910 --> 01:15:09,690 +تكامل من Zero لPi على ستة شو رأيك في هذا نفك + +673 +01:15:09,690 --> 01:15:17,600 +التربيع يبقاش بصير بصير سك تربيع ال Xزي دي اتنين + +674 +01:15:17,600 --> 01:15:25,980 +سك ال X في تان ال X زي التان تربيع ال X كله + +675 +01:15:25,980 --> 01:15:32,240 +بالنسبة الى DX اظن هذه بقدر اكملها و هذه بقدر + +676 +01:15:32,240 --> 01:15:40,330 +اكملها و التان تربيعبحول في دلالة سك تربيع ناقص + +677 +01:15:40,330 --> 01:15:47,390 +واحد يبقى هذه تكامل من zero ل by على ستة ل سك + +678 +01:15:47,390 --> 01:15:55,030 +تربيع ال X زائد اتنين سك ال X في تان ال X زائد سك + +679 +01:15:55,030 --> 01:16:02,820 +تربيع ال X ناقص واحد كله في DXعندي سك تربيه وعندي + +680 +01:16:02,820 --> 01:16:07,680 +سك تربيه بيصير كده؟ نان سكت كل هذا قبل التكامل + +681 +01:16:07,680 --> 01:16:14,320 +يبقى هاي التكامل من Zero لPi على ستة لاتنين سك + +682 +01:16:14,320 --> 01:16:22,320 +تربيه ال X زيدي اتنين سك ال X في تاني ال X ناقص + +683 +01:16:22,320 --> 01:16:31,650 +واحد كله DX هذا الكلام يساويإن كامل يتنم لكش ده و + +684 +01:16:31,650 --> 01:16:40,090 +تكامل سكتة ربيع X اللي هو سكتك أيه بعد تلاتة؟ تان + +685 +01:16:40,090 --> 01:16:45,110 +يعني؟ طب صح صح كويس تفضل تان بسكت ربيع إذا انت + +686 +01:16:45,110 --> 01:16:53,030 +كامل السكت ربيع بتان ال Xزائد اتنان وتكامل سك في + +687 +01:16:53,030 --> 01:17:01,490 +تان بسك ال X وهذا ناقص X والحكي هذا كله من عند ال + +688 +01:17:01,490 --> 01:17:08,330 +zero لغاية باي على ستة يبقى هذا يساوي اتنان بدنا + +689 +01:17:08,330 --> 01:17:14,910 +نيجي لظل التلاتين درجة يعني جا تلاتين على جتا + +690 +01:17:14,910 --> 01:17:19,610 +تلاتينواحد على جذر تلاتة الكل اه واحد على جذر + +691 +01:17:19,610 --> 01:17:29,130 +تلاتة بس يبقى هذا واحد على جذر تلاتة زائد اتنين سك + +692 +01:17:29,130 --> 01:17:35,370 +ال X يعني واحد على cosine ال X cosine التلاتين في + +693 +01:17:35,370 --> 01:17:41,410 +جذر تلاتة يعني اتنين على جذر تلاتةيبقى في اتنين + +694 +01:17:41,410 --> 01:17:48,690 +على جدر تلاتة ناقص باي على ستة هاي خلصنا القيمة + +695 +01:17:48,690 --> 01:17:56,290 +اللي فوق ناقص اللي تحت يبقى ناقص تاني زيرو بزيرو و + +696 +01:17:56,290 --> 01:18:03,910 +سك زيرو بواحد وضل زائد لهمين زيرو + +697 +01:18:07,080 --> 01:18:14,620 +ما هو واحد في اتنين؟ خلّي بالك هنا، هذه ناقص + +698 +01:18:14,620 --> 01:18:17,140 +اتنين، هذه ناقص اتنين، هذه ناقص اتنين، هذه ناقص + +699 +01:18:17,140 --> 01:18:19,380 +اتنين، هذه ناقص اتنين، هذه ناقص اتنين، هذه ناقص + +700 +01:18:19,380 --> 01:18:24,780 +اتنين، هذه ناقص اتنين، هذه ناقص اتنين، هذه ناقص + +701 +01:18:24,780 --> 01:18:25,620 +اتنين، هذه ناقص اتنين، هذه ناقص اتنين، هذه ناقص + +702 +01:18:25,620 --> 01:18:25,620 +اتنين، هذه ناقص اتنين، هذه ناقص اتنين، هذه ناقص + +703 +01:18:25,620 --> 01:18:27,500 +اتنين، هذه ناقص اتنين، هذه ناقص اتنين، هذه ناقص + +704 +01:18:27,500 --> 01:18:29,830 +اتنين، هذه ناقص اتنين، هذه ناقص اكويس؟ يبقى ده شو + +705 +01:18:29,830 --> 01:18:35,830 +بيصير؟ بيصير اتنين على جذر تلاتة زاد اربع على جذر + +706 +01:18:35,830 --> 01:18:43,930 +تلاتة ناقص باية على ستة ناقص اتنين ويساوي هدول ستة + +707 +01:18:43,930 --> 01:18:53,410 +على جذر تلاتة ستة على جذر تلاتة ناقص باية على ستة + +708 +01:18:53,410 --> 01:19:00,220 +ناقص اتنينهذه لو ضربت في جذر تلاتة وقسمتها على جذر + +709 +01:19:00,220 --> 01:19:09,780 +تلاتة بصير اتنين جذر تلاتة ناقص باية على ستة ناقص + +710 +01:19:09,780 --> 01:19:18,870 +اتنين طيب هذا تكمل رقم اربع تكمل رقم خمسةخمسة + +711 +01:19:18,870 --> 01:19:26,450 +بيقول تكامل من باي على اتنين لغاية باي لصين اتنين + +712 +01:19:26,450 --> 01:19:33,470 +X على اتنين صين ال X كوالب النسبة الى DX + +713 +01:19:40,030 --> 01:19:45,990 +هذه اتنين صين مع اتنين صين تكامل ال cosine بصين ال + +714 +01:19:45,990 --> 01:19:54,090 +X فقط لغير من باي على اتنين الى باي يبقى صين ال + +715 +01:19:54,090 --> 01:20:00,410 +باي ناقص صين ال باي على اتنين صين باي صين باي على + +716 +01:20:00,410 --> 01:20:06,810 +اتنين جات الصين جات الصين يبقى واحد ولا بنص + +717 +01:20:12,140 --> 01:20:23,320 +أخر تكامل رقم ستة اللي هو تكامل من zero لغاية باي + +718 +01:20:23,320 --> 01:20:32,540 +لنص ل cosine ال X زائد absolute value ل cosine ال + +719 +01:20:32,540 --> 01:20:33,560 +X في DX + +720 +01:20:39,330 --> 01:20:45,230 +كوصين او absolute value لكوصين مشكلة دي ولا لا او + +721 +01:20:45,230 --> 01:20:50,670 +او + +722 +01:20:50,670 --> 01:20:50,670 +او او او او او او او او او او او او او او او او او + +723 +01:20:50,670 --> 01:20:51,250 +او او او او او او او او او او او او او او او او او + +724 +01:20:51,250 --> 01:20:51,250 +او او او او او او او او او او او او او او او او او + +725 +01:20:51,250 --> 01:20:51,430 +او او او او او او او او او او او او او او او او او + +726 +01:20:51,430 --> 01:20:52,150 +او او او او او او او او او او او او او او او او او + +727 +01:20:52,150 --> 01:20:56,570 +او او او او او او او او او او او او او او او + +728 +01:21:06,260 --> 01:21:14,080 +تكامل من zero إلى πاية على اتنين لنص في cos x زائد + +729 +01:21:14,080 --> 01:21:22,050 +absolute value لcos xكله في DX زائد تكامل من باي + +730 +01:21:22,050 --> 01:21:29,530 +على اتنين إلى باي لنص في cosine ال X زائد absolute + +731 +01:21:29,530 --> 01:21:35,510 +value ل cosine ال X كله ل DX خلي بالك هذا السؤال + +732 +01:21:35,510 --> 01:21:41,570 +في الكتاب في الآخر بس طبعا يبقى هذا الكلام بده + +733 +01:21:41,570 --> 01:21:47,830 +يساوي هي تكامل من zero ل باي على اتنين ل نصهذا + +734 +01:21:47,830 --> 01:21:52,950 +الربع الأول كل النسبة المثلثية موجبة إذا هذا ال + +735 +01:21:52,950 --> 01:21:57,510 +absolute كتبت و الله شلته مابتفرجش مصبوط ولا لا + +736 +01:21:57,510 --> 01:22:06,110 +يبقى بصير cosine ال x زائد cosine ال x في dxزي + +737 +01:22:06,110 --> 01:22:12,650 +التكامل من باي على اتنين إلى باي لنص في cosine ال + +738 +01:22:12,650 --> 01:22:20,290 +X هذا الرابع الرابع ال cosine سالب يبقى بشيل ال + +739 +01:22:20,290 --> 01:22:27,230 +absolute و بكتب سالب cosine ال X كله في DX اظن هذا + +740 +01:22:27,230 --> 01:22:36,340 +راح ب zeroمظبوط؟ يبقى بضل باسمين ال term الأول فقط + +741 +01:22:36,340 --> 01:22:37,180 +لا غير + +742 +01:22:48,250 --> 01:22:53,410 +طيب هذا الكلام بده يساوي integration من zero لغاية + +743 +01:22:53,410 --> 01:23:00,790 +باي على اتنين لكوصين ال X DX فقط لغير اتنين مع نص + +744 +01:23:00,790 --> 01:23:08,170 +بيروح و بيبقى كوصين ال Xيبقى هذا صين ال X من Zero + +745 +01:23:08,170 --> 01:23:14,310 +لغاية باي على اتنين يبقى صين باي على اتنين ناقص + +746 +01:23:14,310 --> 01:23:19,350 +صين ال Zero صين ال Zero ب Zero و صين باي على اتنين + +747 +01:23:19,350 --> 01:23:25,090 +يبقى داشلو كان عندك absolute value طلعلي فيه هذا + +748 +01:23:25,090 --> 01:23:30,250 +المثال absolute value أول ما بفكر كيف بدي أتخلص من + +749 +01:23:30,250 --> 01:23:35,490 +ال absolute value بطلع لحدود التكامل و بشوف وين + +750 +01:23:35,490 --> 01:23:39,950 +الأبدال هذه اللي داخلة absolute موجبة و اكتشفت كون + +751 +01:23:39,950 --> 01:23:45,860 +سالبة و بنال عليها بنشتغللا يزال في في ال section + +752 +01:23:45,860 --> 01:23:51,260 +نقطة ليه total area للمرة القادمة ان شاء الله + +753 +01:23:51,260 --> 01:23:51,860 +تعالى + diff 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" c", "probability": 0.71630859375}, {"start": 95.65, "end": 95.91, "word": " بده", "probability": 0.8515625}, {"start": 95.91, "end": 96.37, "word": " يساوي", "probability": 0.9439697265625}, {"start": 96.37, "end": 96.95, "word": " f", "probability": 0.8232421875}, {"start": 96.95, "end": 97.57, "word": " of", "probability": 0.92626953125}, {"start": 97.57, "end": 97.97, "word": " c", "probability": 0.87060546875}], "temperature": 1.0}, {"id": 5, "seek": 12719, "start": 98.61, "end": 127.19, "text": "يبقى معنى هذا الكلام إن الدالة متصلة عند نقطة إذا كانت نهاية الدالة عند تلك النقطة تساوي قيمة الدالة عند تلك النقطة إن حدث ذلك يبقى بقول الدالة متصلة عند هذه النقطة واضح كلام اظنك؟ طيب الكلام هذا بنحاول أنصيه صيغة أخرى بدل ما هو شرط واحد بدي أحاول أحط هذا الشرط على ثلاثة شروط", "tokens": [1829, 3555, 4587, 7578, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 36145, 32748, 6027, 3660, 44650, 36520, 3660, 43242, 8717, 47432, 3660, 11933, 15730, 25961, 2655, 8717, 11296, 10632, 32748, 6027, 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"probability": 0.83135986328125}, {"start": 119.51, "end": 120.01, "word": " أنصيه", "probability": 0.78936767578125}, {"start": 120.01, "end": 120.57, "word": " صيغة", "probability": 0.7930908203125}, {"start": 120.57, "end": 121.13, "word": " أخرى", "probability": 0.9431966145833334}, {"start": 121.13, "end": 121.51, "word": " بدل", "probability": 0.986083984375}, {"start": 121.51, "end": 121.65, "word": " ما", "probability": 0.943359375}, {"start": 121.65, "end": 121.85, "word": " هو", "probability": 0.966796875}, {"start": 121.85, "end": 122.29, "word": " شرط", "probability": 0.9581705729166666}, {"start": 122.29, "end": 122.77, "word": " واحد", "probability": 0.961181640625}, {"start": 122.77, "end": 123.53, "word": " بدي", "probability": 0.61279296875}, {"start": 123.53, "end": 123.97, "word": " أحاول", "probability": 0.9105224609375}, {"start": 123.97, "end": 124.39, "word": " أحط", "probability": 0.8919270833333334}, {"start": 124.39, "end": 124.73, "word": " هذا", "probability": 0.982421875}, {"start": 124.73, "end": 125.27, "word": " الشرط", "probability": 0.9744466145833334}, {"start": 125.27, "end": 125.69, "word": " على", "probability": 0.9619140625}, {"start": 125.69, "end": 126.77, "word": " ثلاثة", "probability": 0.93837890625}, {"start": 126.77, "end": 127.19, "word": " شروط", "probability": 0.935546875}], "temperature": 1.0}, {"id": 6, "seek": 14619, "start": 127.47, "end": 146.19, "text": "بحيث إذا اختل أي شرط من الشروط التلاتة يبقى ده اللي بتبطل يصير continuous ومن هنا يصير discontinuous يعني ده اللي غير متصلة تمام الشروط التلاتة بدي أجيبهم من نفس ال definition اللي قدامي هذا مش هطلع برا تماما", "tokens": [3555, 5016, 1829, 12984, 11933, 15730, 1975, 46456, 1211, 36632, 13412, 2288, 9566, 9154, 25124, 32887, 9566, 16712, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 11778, 3224, 13672, 1829, 39894, 3555, 9566, 1211, 7251, 9381, 13546, 10957, 4032, 27842, 34105, 7251, 9381, 13546, 31420, 12549, 37495, 22653, 11778, 3224, 13672, 1829, 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130.15, "end": 130.89, "word": " التلاتة", "probability": 0.9326171875}, {"start": 130.89, "end": 131.57, "word": " يبقى", "probability": 0.7325439453125}, {"start": 131.57, "end": 131.81, "word": " ده", "probability": 0.5074462890625}, {"start": 131.81, "end": 131.97, "word": " اللي", "probability": 0.8681640625}, {"start": 131.97, "end": 132.57, "word": " بتبطل", "probability": 0.81427001953125}, {"start": 132.57, "end": 132.85, "word": " يصير", "probability": 0.70556640625}, {"start": 132.85, "end": 133.35, "word": " continuous", "probability": 0.94384765625}, {"start": 133.35, "end": 133.65, "word": " ومن", "probability": 0.577392578125}, {"start": 133.65, "end": 133.89, "word": " هنا", "probability": 0.50048828125}, {"start": 133.89, "end": 134.17, "word": " يصير", "probability": 0.8125813802083334}, {"start": 134.17, "end": 135.81, "word": " discontinuous", "probability": 0.925537109375}, {"start": 135.81, "end": 136.45, "word": " يعني", "probability": 0.824462890625}, {"start": 136.45, "end": 136.79, "word": " ده", "probability": 0.982421875}, {"start": 136.79, "end": 137.01, "word": " اللي", "probability": 0.98388671875}, {"start": 137.01, "end": 137.69, "word": " غير", "probability": 0.9873046875}, {"start": 137.69, "end": 138.77, "word": " متصلة", "probability": 0.704345703125}, {"start": 138.77, "end": 139.37, "word": " تمام", "probability": 0.811279296875}, {"start": 139.37, "end": 140.43, "word": " الشروط", "probability": 0.9563802083333334}, {"start": 140.43, "end": 141.01, "word": " التلاتة", "probability": 0.97021484375}, {"start": 141.01, "end": 141.23, "word": " بدي", "probability": 0.574951171875}, {"start": 141.23, "end": 141.65, "word": " أجيبهم", "probability": 0.905859375}, {"start": 141.65, "end": 141.81, "word": " من", "probability": 0.96484375}, {"start": 141.81, "end": 142.57, "word": " نفس", "probability": 0.84619140625}, {"start": 142.57, "end": 142.71, "word": " ال", "probability": 0.8662109375}, {"start": 142.71, "end": 143.27, "word": " definition", "probability": 0.8486328125}, {"start": 143.27, "end": 143.59, "word": " اللي", "probability": 0.958251953125}, {"start": 143.59, "end": 144.13, "word": " قدامي", "probability": 0.8592529296875}, {"start": 144.13, "end": 144.41, "word": " هذا", "probability": 0.84375}, {"start": 144.41, "end": 144.83, "word": " مش", "probability": 0.78857421875}, {"start": 144.83, "end": 145.23, "word": " هطلع", "probability": 0.9090576171875}, {"start": 145.23, "end": 145.55, "word": " برا", "probability": 0.76220703125}, {"start": 145.55, "end": 146.19, "word": " تماما", "probability": 0.9925130208333334}], "temperature": 1.0}, {"id": 7, "seek": 16443, "start": 146.61, "end": 164.43, "text": "فبجي بقول ده ال F is continuous at A لسه قبل ما نروح لهدا بدنا نيجي هنا جالي at an interior point يعني عند النقطة الداخلية بده أجي عند طرفي ال interven يعني لما أقول interior point يعني open interven", "tokens": [5172, 3555, 7435, 1829, 4724, 39648, 11778, 3224, 2423, 479, 307, 10957, 412, 316, 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"word": " continuous", "probability": 0.89111328125}, {"start": 149.05, "end": 149.47, "word": " at", "probability": 0.6953125}, {"start": 149.47, "end": 149.77, "word": " A", "probability": 0.340087890625}, {"start": 149.77, "end": 150.27, "word": " لسه", "probability": 0.8688151041666666}, {"start": 150.27, "end": 150.55, "word": " قبل", "probability": 0.850830078125}, {"start": 150.55, "end": 151.15, "word": " ما", "probability": 0.8212890625}, {"start": 151.15, "end": 151.47, "word": " نروح", "probability": 0.8050130208333334}, {"start": 151.47, "end": 151.95, "word": " لهدا", "probability": 0.72705078125}, {"start": 151.95, "end": 152.67, "word": " بدنا", "probability": 0.594970703125}, {"start": 152.67, "end": 153.03, "word": " نيجي", "probability": 0.9273681640625}, {"start": 153.03, "end": 153.29, "word": " هنا", "probability": 0.96533203125}, {"start": 153.29, "end": 153.65, "word": " جالي", "probability": 0.67236328125}, {"start": 153.65, "end": 154.01, "word": " at", "probability": 0.94384765625}, {"start": 154.01, "end": 154.51, "word": " an", "probability": 0.9033203125}, {"start": 154.51, "end": 155.03, "word": " interior", "probability": 0.595703125}, {"start": 155.03, "end": 155.59, "word": " point", "probability": 0.99267578125}, {"start": 155.59, "end": 156.03, "word": " يعني", "probability": 0.9228515625}, {"start": 156.03, "end": 156.25, "word": " عند", "probability": 0.9931640625}, {"start": 156.25, "end": 157.13, "word": " النقطة", "probability": 0.9407552083333334}, {"start": 157.13, "end": 158.07, "word": " الداخلية", "probability": 0.9931640625}, {"start": 158.07, "end": 158.83, "word": " بده", "probability": 0.556396484375}, {"start": 158.83, "end": 158.99, "word": " أجي", "probability": 0.7726236979166666}, {"start": 158.99, "end": 159.27, "word": " عند", "probability": 0.87353515625}, {"start": 159.27, "end": 159.95, "word": " طرفي", "probability": 0.85107421875}, {"start": 159.95, "end": 160.05, "word": " ال", "probability": 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اللي بعد ان الدالة if is continuous at left end point X يساوي A هي ال A يبقى هذه جاية على طرف الانترفال الشمال", "tokens": [1211, 19452, 5296, 15042, 8717, 7435, 1829, 28239, 47432, 3660, 11778, 1829, 45164, 4032, 4587, 34268, 15844, 41950, 28480, 9957, 2423, 7649, 2655, 2288, 5172, 6027, 4724, 16254, 5551, 8592, 38688, 8032, 1211, 39896, 10957, 43242, 28239, 47432, 3660, 16247, 12610, 7578, 4032, 4117, 33911, 39894, 30544, 10957, 43242, 28239, 47432, 3660, 6024, 104, 7649, 10632, 1975, 2407, 20193, 6156, 3555, 2655, 39648, 1829, 28239, 47432, 3660, 13672, 1829, 39182, 16472, 2423, 3215, 6027, 3660, 498, 307, 10957, 412, 1411, 917, 935, 1783, 7251, 3794, 995, 45865, 316, 39896, 2423, 316, 7251, 3555, 4587, 7578, 29538, 10874, 995, 10632, 15844, 23032, 28480, 2423, 7649, 2655, 2288, 5172, 6027, 25124, 2304, 6027], "avg_logprob": -0.24874441352273738, "compression_ratio": 1.8951965065502183, "no_speech_prob": 0.0, "words": [{"start": 164.71, "end": 165.11, "word": "لكن", "probability": 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16, "seek": 35093, "start": 321.77, "end": 350.93, "text": "فبعدين بقول الدالة if is continuous at x يساوي c if and only if the following three conditions are satisfied يعني لو كانت الدالة متصلة يجب أن تتحقق الشروط الثالثة أو الثلاثة و بالعكس لو تحققت الشروط الثلاثة إذا الدالة تبقى continuous ليش؟ لأن قلنا هنا if and only if معناته للاتجاهين أو الاتجاهان الصحيحة", "tokens": [5172, 3555, 22488, 9957, 4724, 39648, 32748, 6027, 3660, 498, 307, 10957, 412, 2031, 7251, 3794, 995, 45865, 269, 498, 293, 787, 498, 264, 3480, 1045, 4487, 366, 11239, 37495, 22653, 45164, 25961, 2655, 32748, 6027, 3660, 44650, 36520, 3660, 7251, 7435, 3555, 14739, 6055, 2655, 5016, 4587, 4587, 25124, 32887, 9566, 6024, 104, 6027, 12984, 3660, 34051, 6024, 104, 1211, 5718, 104, 3660, 4032, 20666, 3615, 4117, 3794, 45164, 6055, 5016, 4587, 38149, 25124, 32887, 9566, 6024, 104, 1211, 5718, 104, 3660, 11933, 15730, 32748, 6027, 3660, 6055, 3555, 4587, 7578, 10957, 32239, 8592, 22807, 5296, 33456, 12174, 1211, 8315, 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بيصير تساوي اتنين بدي اقول limit ال F of X لما ال X بيروح ل C كذلك exist", "tokens": [3555, 1863, 8592, 38688, 19446, 39896, 25124, 32887, 9566, 16712, 1211, 9307, 3660, 4724, 26108, 1829, 9154, 16712, 3615, 16572, 5172, 5296, 15042, 1975, 39648, 8032, 3215, 12610, 1975, 2655, 1863, 9957, 47525, 16095, 7251, 2655, 3794, 995, 2407, 7578, 20449, 8315, 47395, 2423, 479, 295, 383, 2514, 20328, 5016, 49429, 5296, 10721, 45164, 25961, 2423, 775, 406, 2514, 4724, 1829, 9381, 13546, 6055, 3794, 995, 45865, 1975, 2655, 1863, 9957, 4724, 16254, 1975, 39648, 4948, 2423, 479, 295, 1783, 5296, 15042, 2423, 1783, 4724, 1829, 32887, 5016, 5296, 383, 9122, 8848, 23275, 2514], "avg_logprob": -0.25115130888788323, "compression_ratio": 1.64321608040201, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 352.0, "end": 352.72, "word": "بنشوف", "probability": 0.3889923095703125}, {"start": 352.72, "end": 352.94, "word": " ما", "probability": 0.51220703125}, {"start": 352.94, "end": 353.2, "word": 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0.95361328125}, {"start": 368.72, "end": 368.84, "word": " ال", "probability": 0.9443359375}, {"start": 368.84, "end": 369.02, "word": " X", "probability": 0.95849609375}, {"start": 369.02, "end": 369.4, "word": " بيروح", "probability": 0.838134765625}, {"start": 369.4, "end": 369.54, "word": " ل", "probability": 0.8349609375}, {"start": 369.54, "end": 370.02, "word": " C", "probability": 0.485595703125}, {"start": 370.02, "end": 370.86, "word": " كذلك", "probability": 0.9803059895833334}, {"start": 370.86, "end": 371.42, "word": " exist", "probability": 0.88427734375}], "temperature": 1.0}, {"id": 18, "seek": 40020, "start": 372.02, "end": 400.2, "text": "تلاتة مدام هذا موجود وهذا موجود يمكن يتساوي ويمكن لا يتساوي إن حدثت تساوي بقول يبقى ده اللي هذي معلها continuous إذا لم يحدث تساوي بقول discontinuous يبقى الشرط التالت كlimit ال F of X لما ال X بيروح إلى C بدي سواء منين F of C وبالتالي ال function بقول عليها continuous function نظرا لتحقق الشروط التلاتة", "tokens": [2655, 1211, 9307, 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" function", "probability": 0.8642578125}, {"start": 394.16, "end": 394.52, "word": " بقول", "probability": 0.93212890625}, {"start": 394.52, "end": 394.94, "word": " عليها", "probability": 0.9755859375}, {"start": 394.94, "end": 396.1, "word": " continuous", "probability": 0.94140625}, {"start": 396.1, "end": 397.44, "word": " function", "probability": 0.8359375}, {"start": 397.44, "end": 398.28, "word": " نظرا", "probability": 0.7242024739583334}, {"start": 398.28, "end": 399.0, "word": " لتحقق", "probability": 0.89892578125}, {"start": 399.0, "end": 399.64, "word": " الشروط", "probability": 0.908203125}, {"start": 399.64, "end": 400.2, "word": " التلاتة", "probability": 0.9437255859375}], "temperature": 1.0}, {"id": 19, "seek": 42278, "start": 400.98, "end": 422.78, "text": "لو جيت عند الشرط الأول ولا جيته غير متحقق أروح أدور على التاني والتالت ليه خلاص بيقول الدالة discontinuous وانتهينا يعني إذا الدالة غير معرفة عندها نقطة إذا الدالة عند هذه النقطة بيكون عندنا discontinuity عدم 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هنا", "probability": 0.95458984375}, {"start": 760.96, "end": 761.42, "word": " الدالة", "probability": 0.8883463541666666}, {"start": 761.42, "end": 762.22, "word": " معرفة", "probability": 0.9845377604166666}, {"start": 762.22, "end": 762.92, "word": " والنهاية", "probability": 0.900146484375}, {"start": 762.92, "end": 763.38, "word": " الموجودة", "probability": 0.9267578125}, {"start": 763.38, "end": 763.9, "word": " واثنين", "probability": 0.7912109375}, {"start": 763.9, "end": 764.38, "word": " are", "probability": 0.5595703125}, {"start": 764.38, "end": 764.96, "word": " not", "probability": 0.96044921875}, {"start": 764.96, "end": 765.56, "word": " equal", "probability": 0.90478515625}, {"start": 765.56, "end": 766.1, "word": " يبقى", "probability": 0.84588623046875}, {"start": 766.1, "end": 766.2, "word": " لا", "probability": 0.7685546875}, {"start": 766.2, "end": 766.56, "word": " هادي", "probability": 0.7236328125}, {"start": 766.56, "end": 766.74, "word": " ولا", 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" فكان", "probability": 0.605712890625}, {"start": 780.44, "end": 780.7, "word": " F", "probability": 0.6943359375}, {"start": 780.7, "end": 781.08, "word": " A", "probability": 0.1439208984375}, {"start": 781.08, "end": 781.78, "word": " بساوي", "probability": 0.659698486328125}, {"start": 781.78, "end": 782.58, "word": " المتصل", "probability": 0.8414713541666666}, {"start": 782.58, "end": 782.8, "word": " من", "probability": 0.96875}, {"start": 782.8, "end": 783.3, "word": " اليمين", "probability": 0.8167317708333334}, {"start": 783.3, "end": 786.16, "word": " شوفت", "probability": 0.6070963541666666}, {"start": 786.16, "end": 786.66, "word": " التسايل", "probability": 0.54443359375}, {"start": 786.66, "end": 786.76, "word": " من", "probability": 0.986328125}, {"start": 786.76, "end": 787.08, "word": " اليمين", "probability": 0.8553059895833334}, {"start": 787.08, "end": 787.16, "word": " و", "probability": 0.984375}, {"start": 787.16, "end": 787.3, "word": " من", "probability": 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0.720458984375}, {"start": 794.0, "end": 794.5, "word": " يساوي", "probability": 0.78680419921875}, {"start": 794.5, "end": 795.64, "word": " بساوي", "probability": 0.82061767578125}, {"start": 795.64, "end": 796.38, "word": " هاين", "probability": 0.623046875}, {"start": 796.38, "end": 797.06, "word": " اطلع", "probability": 0.62152099609375}, {"start": 797.06, "end": 797.36, "word": " فرن", "probability": 0.69970703125}, {"start": 797.36, "end": 797.78, "word": " اسمها", "probability": 0.8084309895833334}, {"start": 797.78, "end": 798.04, "word": " هذي", "probability": 0.5323893229166666}], "temperature": 1.0}, {"id": 36, "seek": 81562, "start": 799.96, "end": 815.62, "text": "الدالة من جهة اليمين ال limit يساوي قيمة بسميها ال right continuous. لكن هذي بقدر أقول left continuous؟ لأ لأن ده غير معرفة عندها أو معرفة ولا تساوي ال limit.", "tokens": [6027, 3215, 6027, 3660, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 2423, 4948, 7251, 3794, 995, 45865, 12174, 32640, 3660, 4724, 38251, 1829, 11296, 2423, 558, 10957, 13, 44381, 8032, 8848, 1829, 4724, 28543, 2288, 5551, 39648, 1411, 10957, 22807, 5296, 10721, 5296, 33456, 11778, 3224, 32771, 13546, 20449, 28480, 3660, 43242, 11296, 34051, 20449, 28480, 3660, 49429, 6055, 3794, 995, 45865, 2423, 4948, 13], "avg_logprob": -0.3027935709917184, "compression_ratio": 1.5185185185185186, "no_speech_prob": 0.0, "words": [{"start": 799.96, "end": 800.88, "word": "الدالة", "probability": 0.70196533203125}, {"start": 800.88, "end": 801.32, "word": " من", "probability": 0.78125}, {"start": 801.32, "end": 801.84, "word": " جهة", "probability": 0.9685872395833334}, {"start": 801.84, "end": 802.84, "word": " اليمين", "probability": 0.8779296875}, {"start": 802.84, "end": 803.54, "word": " ال", "probability": 0.139892578125}, {"start": 803.54, "end": 804.02, "word": " limit", "probability": 0.8935546875}, {"start": 804.02, "end": 804.78, "word": " يساوي", "probability": 0.8212890625}, {"start": 804.78, "end": 805.12, "word": " قيمة", 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"probability": 0.68359375}, {"start": 811.82, "end": 812.02, "word": " ده", "probability": 0.72119140625}, {"start": 812.02, "end": 812.3, "word": " غير", "probability": 0.84033203125}, {"start": 812.3, "end": 813.02, "word": " معرفة", "probability": 0.9122721354166666}, {"start": 813.02, "end": 813.38, "word": " عندها", "probability": 0.8896484375}, {"start": 813.38, "end": 813.88, "word": " أو", "probability": 0.5517578125}, {"start": 813.88, "end": 814.5, "word": " معرفة", "probability": 0.9602864583333334}, {"start": 814.5, "end": 814.68, "word": " ولا", "probability": 0.81787109375}, {"start": 814.68, "end": 815.22, "word": " تساوي", "probability": 0.97021484375}, {"start": 815.22, "end": 815.32, "word": " ال", "probability": 0.88916015625}, {"start": 815.32, "end": 815.62, "word": " limit.", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 37, "seek": 84413, "start": 816.07, "end": 844.13, "text": "يبقى هنا في discontinuity عند هذه النقطة لكن هنا في right continuous لكن تلعب بعضها بقدر اقول continuous لا بقدرش اقول continuous وممكن هذا هنا تبقى غير معرفة تمام وبالتالي لا عندي right continuous ولا عندي left continuous لكن عندي jump discontinuity بيحصل قفزة في هذه الحالة حد لو يسأل اخر قبل ان ادخل الامثلة", "tokens": [1829, 3555, 4587, 7578, 34105, 8978, 31420, 21757, 43242, 29538, 28239, 47432, 3660, 44381, 34105, 8978, 558, 10957, 44381, 6055, 1211, 3615, 3555, 45030, 11242, 11296, 4724, 28543, 2288, 1975, 39648, 10957, 20193, 4724, 28543, 2288, 8592, 1975, 39648, 10957, 4032, 2304, 43020, 23758, 34105, 6055, 3555, 4587, 7578, 32771, 13546, 20449, 28480, 3660, 46811, 10943, 46599, 6027, 2655, 6027, 1829, 20193, 18871, 16254, 558, 10957, 49429, 18871, 16254, 1411, 10957, 44381, 18871, 16254, 3012, 31420, 21757, 4724, 1829, 5016, 36520, 12174, 5172, 11622, 3660, 8978, 29538, 21542, 6027, 3660, 11331, 3215, 45164, 7251, 3794, 10721, 1211, 1975, 34740, 12174, 36150, 16472, 1975, 3215, 9778, 1211, 2423, 10943, 12984, 37977], "avg_logprob": 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{"start": 1069.34, "end": 1070.02, "word": " لا", "probability": 0.61572265625}, {"start": 1070.02, "end": 1070.92, "word": " تساوي", "probability": 0.9654541015625}, {"start": 1070.92, "end": 1071.56, "word": " limit", "probability": 0.64453125}, {"start": 1071.56, "end": 1072.28, "word": " لل", "probability": 0.81201171875}, {"start": 1072.28, "end": 1072.72, "word": " F", "probability": 0.8349609375}, {"start": 1072.72, "end": 1073.06, "word": " of", "probability": 0.97265625}, {"start": 1073.06, "end": 1073.42, "word": " X", "probability": 0.95556640625}, {"start": 1073.42, "end": 1074.12, "word": " لما", "probability": 0.934326171875}, {"start": 1074.12, "end": 1074.28, "word": " ال", "probability": 0.89599609375}, {"start": 1074.28, "end": 1074.58, "word": " X", "probability": 0.96240234375}, {"start": 1074.58, "end": 1074.98, "word": " بده", "probability": 0.800537109375}, {"start": 1074.98, "end": 1075.32, "word": " يروح", "probability": 0.9915364583333334}, {"start": 1075.32, 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discontinuity", "probability": 0.70263671875}, {"start": 1083.63, "end": 1084.01, "word": " يعني", "probability": 0.933349609375}, {"start": 1084.01, "end": 1084.65, "word": " ايه؟", "probability": 0.77783203125}, {"start": 1084.65, "end": 1084.97, "word": " يعني", "probability": 0.8388671875}, {"start": 1084.97, "end": 1085.63, "word": " الشرط", "probability": 0.9715169270833334}, {"start": 1085.63, "end": 1086.31, "word": " التالت", "probability": 0.95361328125}, {"start": 1086.31, "end": 1086.61, "word": " لم", "probability": 0.96044921875}, {"start": 1086.61, "end": 1087.51, "word": " يتحقق", "probability": 0.99541015625}, {"start": 1087.51, "end": 1087.69, "word": " في", "probability": 0.978515625}, {"start": 1087.69, "end": 1088.15, "word": " هذه", "probability": 0.974609375}, {"start": 1088.15, "end": 1088.95, "word": " الحالة", "probability": 0.9869791666666666}, {"start": 1088.95, "end": 1089.51, "word": " ومن", "probability": 0.906005859375}, {"start": 1089.51, "end": 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1099.07, "end": 1099.35, "word": " هذا", "probability": 0.861328125}, {"start": 1099.35, "end": 1099.61, "word": " صار", "probability": 0.921630859375}, {"start": 1099.61, "end": 1099.87, "word": " عندي", "probability": 0.8798828125}, {"start": 1099.87, "end": 1101.37, "word": " discontinuity،", "probability": 0.7945963541666666}, {"start": 1101.37, "end": 1101.65, "word": " واحنا", "probability": 0.6971435546875}, {"start": 1101.65, "end": 1102.27, "word": " قبل", "probability": 0.6678466796875}, {"start": 1102.27, "end": 1102.87, "word": " قليل", "probability": 0.9860026041666666}, {"start": 1102.87, "end": 1103.47, "word": " حطينا", "probability": 0.8876953125}, {"start": 1103.47, "end": 1104.17, "word": " ثلاثة", "probability": 0.9564453125}, {"start": 1104.17, "end": 1104.81, "word": " أنواع", "probability": 0.96533203125}, {"start": 1104.81, "end": 1105.03, "word": " لل", "probability": 0.79833984375}, {"start": 1105.03, "end": 1106.37, "word": " discontinuity،", "probability": 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"end": 1125.4, "word": " limit", "probability": 0.9541015625}, {"start": 1125.4, "end": 1125.96, "word": " exist", "probability": 0.92529296875}, {"start": 1125.96, "end": 1126.34, "word": " لكن", "probability": 0.80029296875}, {"start": 1126.34, "end": 1127.04, "word": " اتنين", "probability": 0.7764892578125}], "temperature": 1.0}, {"id": 51, "seek": 115618, "start": 1128.3, "end": 1156.18, "text": "الـ f of تلاتة لا تساوي اللي هو limit للـ f of x لمين للـ x ثلاثة يبقى so this is a removable discontinuity", "tokens": [6027, 39184, 283, 295, 6055, 1211, 9307, 3660, 20193, 6055, 3794, 995, 45865, 13672, 1829, 31439, 4948, 24976, 39184, 283, 295, 2031, 32767, 9957, 24976, 39184, 2031, 38637, 1211, 5718, 104, 3660, 7251, 3555, 4587, 7578, 370, 341, 307, 257, 44060, 31420, 21757], "avg_logprob": -0.46413353288715536, "compression_ratio": 1.2352941176470589, "no_speech_prob": 0.0, "words": [{"start": 1128.3000000000002, "end": 1129.4, "word": "الـ", "probability": 0.244842529296875}, 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هذا discontinuity يمكن إزالته السؤال هو هل يمكن الآن تعريف الدالة بطريقة جديدة بحيث الدالة تبقى continuous الإجابة نعم لو شيلت الأربعة و حطيت بدلك أداشة قيمة ال limit بصير ال limit", "tokens": [1829, 3555, 4587, 7578, 23758, 31420, 21757, 7251, 43020, 11933, 11622, 6027, 47395, 21136, 33604, 6027, 31439, 8032, 1211, 7251, 43020, 6024, 48506, 37279, 16572, 5172, 32748, 6027, 3660, 4724, 9566, 16572, 28671, 10874, 16254, 41891, 4724, 5016, 1829, 12984, 32748, 6027, 3660, 6055, 3555, 4587, 7578, 10957, 33688, 7435, 16758, 3660, 8717, 25957, 45164, 13412, 26895, 2655, 16247, 25513, 27884, 4032, 11331, 9566, 36081, 47525, 1211, 4117, 5551, 3215, 33599, 3660, 12174, 32640, 3660, 2423, 4948, 4724, 9381, 13546, 2423, 4948], "avg_logprob": -0.18260542420019588, "compression_ratio": 1.6397849462365592, "no_speech_prob": 0.0, "words": [{"start": 1161.84, "end": 1162.48, "word": "يبقى", "probability": 0.743499755859375}, {"start": 1162.48, "end": 1162.88, "word": " هذا", "probability": 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جديدة", "probability": 0.99072265625}, {"start": 1171.94, "end": 1172.8, "word": " بحيث", "probability": 0.961669921875}, {"start": 1172.8, "end": 1173.62, "word": " الدالة", "probability": 0.9679361979166666}, {"start": 1173.62, "end": 1173.96, "word": " تبقى", "probability": 0.962890625}, {"start": 1173.96, "end": 1174.58, "word": " continuous", "probability": 0.88720703125}, {"start": 1174.58, "end": 1175.88, "word": " الإجابة", "probability": 0.843505859375}, {"start": 1175.88, "end": 1176.74, "word": " نعم", "probability": 0.977294921875}, {"start": 1176.74, "end": 1177.42, "word": " لو", "probability": 0.70947265625}, {"start": 1177.42, "end": 1177.96, "word": " شيلت", "probability": 0.8798828125}, {"start": 1177.96, "end": 1178.56, "word": " الأربعة", "probability": 0.8937174479166666}, {"start": 1178.56, "end": 1178.72, "word": " و", "probability": 0.978515625}, {"start": 1178.72, "end": 1179.24, "word": " حطيت", "probability": 0.8133138020833334}, {"start": 1179.24, "end": 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ناقص تلاتة لما ال X لا تساوي تلاتة وهنا ستة لما ال X تساوي تلاتة is continuous", "tokens": [2655, 3794, 995, 45865, 5551, 24401, 5551, 29973, 9957, 35186, 11933, 15042, 2423, 1783, 6055, 2288, 21292, 3224, 8717, 995, 4587, 9381, 6055, 3794, 27884, 15844, 2423, 1783, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 5296, 15042, 2423, 1783, 20193, 6055, 3794, 995, 45865, 6055, 1211, 9307, 3660, 37037, 8315, 8608, 2655, 3660, 5296, 15042, 2423, 1783, 6055, 3794, 995, 45865, 6055, 1211, 9307, 3660, 307, 10957], "avg_logprob": -0.16259058057398035, "compression_ratio": 1.682170542635659, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 1202.83, "end": 1203.81, "word": "تساوي", "probability": 0.73248291015625}, {"start": 1203.81, "end": 1204.37, "word": " أحد", "probability": 0.792236328125}, {"start": 1204.37, "end": 1205.13, "word": " أمرين", "probability": 0.9215494791666666}, {"start": 1205.13, "end": 1205.81, "word": " يا", "probability": 0.1851806640625}, {"start": 1205.81, "end": 1206.25, "word": " إما", "probability": 0.970458984375}, {"start": 1206.25, "end": 1206.45, "word": " ال", "probability": 0.80224609375}, {"start": 1206.45, "end": 1206.71, "word": " X", "probability": 0.5205078125}, {"start": 1206.71, "end": 1207.31, "word": " تربيه", "probability": 0.806884765625}, {"start": 1207.31, "end": 1207.81, "word": " ناقص", "probability": 0.8338623046875}, {"start": 1207.81, "end": 1208.25, "word": " تسعة", "probability": 0.82763671875}, {"start": 1208.25, "end": 1208.45, "word": " على", "probability": 0.74951171875}, {"start": 1208.45, "end": 1208.67, "word": " ال", "probability": 0.472412109375}, {"start": 1208.67, "end": 1208.93, "word": " X", "probability": 0.99072265625}, {"start": 1208.93, "end": 1209.49, "word": " ناقص", "probability": 0.991455078125}, {"start": 1209.49, "end": 1210.07, "word": " تلاتة", "probability": 0.946533203125}, {"start": 1210.07, "end": 1210.93, "word": " لما", "probability": 0.837646484375}, {"start": 1210.93, "end": 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1218.69, "word": " is", "probability": 0.6962890625}, {"start": 1218.69, "end": 1220.79, "word": " continuous", "probability": 0.91455078125}], "temperature": 1.0}, {"id": 55, "seek": 124755, "start": 1232.05, "end": 1247.55, "text": "تعريف جديد الدالة الجديدة هي دالة متصلة عند x يساوي تلتة وبالتالي أزلنا ال discontinuity تبع ال function الان", "tokens": [2655, 3615, 16572, 5172, 10874, 16254, 3215, 32748, 6027, 3660, 25724, 16254, 41891, 39896, 11778, 6027, 3660, 44650, 9381, 37977, 43242, 2031, 7251, 3794, 995, 45865, 6055, 1211, 2655, 3660, 46599, 6027, 2655, 6027, 1829, 5551, 11622, 1211, 8315, 2423, 31420, 21757, 6055, 3555, 3615, 2423, 2445, 2423, 7649], "avg_logprob": -0.41031248688697813, "compression_ratio": 1.390625, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 1232.05, "end": 1233.45, "word": "تعريف", "probability": 0.49072265625}, {"start": 1233.45, "end": 1234.23, "word": " جديد", "probability": 0.8605143229166666}, {"start": 1234.23, "end": 1235.31, "word": " الدالة", "probability": 0.6892903645833334}, {"start": 1235.31, "end": 1235.97, "word": " الجديدة", "probability": 0.62890625}, {"start": 1235.97, "end": 1236.95, "word": " هي", "probability": 0.339111328125}, {"start": 1236.95, "end": 1237.65, "word": " دالة", "probability": 0.92138671875}, {"start": 1237.65, "end": 1238.41, "word": " متصلة", "probability": 0.8191731770833334}, {"start": 1238.41, "end": 1238.73, "word": " عند", "probability": 0.92138671875}, {"start": 1238.73, "end": 1239.15, "word": " x", "probability": 0.38330078125}, {"start": 1239.15, "end": 1240.25, "word": " يساوي", "probability": 0.78619384765625}, {"start": 1240.25, "end": 1241.01, "word": " تلتة", "probability": 0.7623291015625}, {"start": 1241.01, "end": 1242.17, "word": " وبالتالي", "probability": 0.874755859375}, {"start": 1242.17, "end": 1242.93, "word": " أزلنا", "probability": 0.859130859375}, {"start": 1242.93, "end": 1243.03, "word": " ال", "probability": 0.6923828125}, {"start": 1243.03, "end": 1244.19, "word": " discontinuity", "probability": 0.7841796875}, {"start": 1244.19, "end": 1244.63, "word": " تبع", "probability": 0.8582356770833334}, {"start": 1244.63, "end": 1245.11, "word": " ال", "probability": 0.412353515625}, {"start": 1245.11, "end": 1246.61, "word": " function", "probability": 0.367919921875}, {"start": 1246.61, "end": 1247.55, "word": " الان", "probability": 0.436767578125}], "temperature": 1.0}, {"id": 56, "seek": 126200, "start": 1248.44, "end": 1262.0, "text": "طيب نعطي مثال اخر يبقى هذا المثال كان على الحالة الأولى .. ايه اللي عندي؟ مثال اخر بيسأل بس حاول اتدور اثر بس سمحت و انت ال .. على ال jump و ال ..", "tokens": [9566, 1829, 3555, 8717, 3615, 9566, 1829, 50113, 6027, 1975, 34740, 7251, 3555, 4587, 7578, 23758, 9673, 12984, 6027, 25961, 15844, 21542, 6027, 3660, 16247, 12610, 7578, 4386, 1975, 1829, 3224, 13672, 1829, 18871, 16254, 22807, 50113, 6027, 1975, 34740, 4724, 1829, 3794, 10721, 1211, 4724, 3794, 11331, 995, 12610, 1975, 2655, 3215, 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1262.0, "word": " ..", "probability": 0.100341796875}], "temperature": 1.0}, {"id": 57, "seek": 128883, "start": 1269.84, "end": 1288.84, "text": "لأ ال infinity صارت ال limit من اليمين وال limit من الشمال، يا بدها تروح لما لا نهاية، يا واحدة ما لا نهاية، والثانية سالب ما لا نهاية، وطيتك الشكل على الرسم، تمام؟ طيب، يبقى example two، بدنا ال f of x", "tokens": [1211, 10721, 2423, 13202, 20328, 9640, 2655, 2423, 4948, 9154, 2423, 32640, 9957, 16070, 4948, 9154, 25124, 2304, 6027, 12399, 35186, 47525, 11296, 6055, 32887, 5016, 5296, 15042, 20193, 8717, 11296, 10632, 12399, 35186, 36764, 24401, 3660, 19446, 20193, 8717, 11296, 10632, 12399, 16070, 12984, 7649, 10632, 8608, 6027, 3555, 19446, 20193, 8717, 11296, 10632, 12399, 4032, 9566, 36081, 4117, 25124, 28820, 15844, 34892, 38251, 12399, 46811, 10943, 22807, 23032, 1829, 3555, 12399, 7251, 3555, 4587, 7578, 1365, 732, 12399, 47525, 8315, 2423, 283, 295, 2031], "avg_logprob": -0.3220186733651435, "compression_ratio": 1.7891891891891891, 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هو", "probability": 0.990234375}, {"start": 1359.99, "end": 1360.63, "word": " الواحد", "probability": 0.90087890625}, {"start": 1360.63, "end": 1361.29, "word": " صحيح", "probability": 0.8087158203125}], "temperature": 1.0}, {"id": 61, "seek": 138700, "start": 1369.36, "end": 1387.0, "text": "يبقى هاي قيمة الدالة بعد الـ0 بواحد وقبل الـ0 سالب واحد لكن هل الدالة معرفة عند الـ0؟ لأ يبقى باجي بقوله هنا ال F of 0 او هنا solution في الأول", "tokens": [1829, 3555, 4587, 7578, 8032, 47302, 12174, 32640, 3660, 32748, 6027, 3660, 39182, 2423, 39184, 15, 4724, 14407, 24401, 4032, 4587, 36150, 2423, 39184, 15, 8608, 6027, 3555, 36764, 24401, 44381, 8032, 1211, 32748, 6027, 3660, 20449, 28480, 3660, 43242, 2423, 39184, 15, 22807, 5296, 10721, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 34105, 2423, 479, 295, 1958, 1975, 2407, 34105, 3827, 8978, 16247, 12610], "avg_logprob": -0.31567028985507245, "compression_ratio": 1.5751633986928104, "no_speech_prob": 1.1920928955078125e-07, 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discontinuous", "probability": 0.830078125}, {"start": 1411.37, "end": 1413.65, "word": " at", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 63, "seek": 144074, "start": 1415.42, "end": 1440.74, "text": "X يساوي Zero طيب هذا ال discontinuity مين من الأنواع Jump لإن ال limit من اليمين لا تساوي ال limit من الشمال يبقى this is a jump discontinuity السبب because", "tokens": [55, 7251, 3794, 995, 45865, 17182, 23032, 1829, 3555, 23758, 2423, 31420, 21757, 3714, 9957, 9154, 16247, 1863, 14407, 3615, 18697, 5296, 28814, 1863, 2423, 4948, 9154, 45595, 2304, 9957, 20193, 6055, 3794, 995, 45865, 2423, 4948, 9154, 25124, 2304, 6027, 7251, 3555, 4587, 7578, 341, 307, 257, 3012, 31420, 21757, 21136, 3555, 3555, 570], "avg_logprob": -0.287667414439576, "compression_ratio": 1.476510067114094, "no_speech_prob": 0.0, "words": [{"start": 1415.42, "end": 1415.94, "word": "X", "probability": 0.0950927734375}, {"start": 1415.94, "end": 1416.72, "word": " يساوي", "probability": 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"seek": 185192, "start": 1847.78, "end": 1851.92, "text": "ماله؟ الاحمر هذا ال .. اخر صورة فهو zero انت واحد", "tokens": [2304, 6027, 3224, 22807, 2423, 39319, 29973, 23758, 2423, 4386, 1975, 34740, 20328, 13063, 3660, 6156, 3224, 2407, 4018, 16472, 2655, 36764, 24401], "avg_logprob": -0.6927083109815916, "compression_ratio": 1.025, "no_speech_prob": 0.0, "words": [{"start": 1847.7800000000002, "end": 1848.3400000000001, "word": "ماله؟", "probability": 0.3790130615234375}, {"start": 1848.3400000000001, "end": 1848.9, "word": " الاحمر", "probability": 0.8435872395833334}, {"start": 1848.9, "end": 1849.14, "word": " هذا", "probability": 0.58544921875}, {"start": 1849.14, "end": 1849.4, "word": " ال", "probability": 0.51953125}, {"start": 1849.4, "end": 1849.44, "word": " ..", "probability": 0.2393798828125}, {"start": 1849.44, "end": 1849.68, "word": " اخر", "probability": 0.703857421875}, {"start": 1849.68, "end": 1850.08, "word": " صورة", "probability": 0.72314453125}, {"start": 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"temperature": 1.0}, {"id": 84, "seek": 193031, "start": 1904.91, "end": 1930.31, "text": "أحنا قلنا if of 0 does not exist يبقى discontinuous تمام؟ discontinuous عند 0 لكن ما نوعية ال discontinuous؟ هل هو jump؟ والله removable؟ والله infinite discontinuity؟ مش أنا أعرف منهم، قلت ال limit من الأمامي بسوية ال limit يبقى jump، هاي السبب أما بداية، قبل ما وصلت تحت، قلنا هنا discontinuous، أيوة", "tokens": [10721, 5016, 8315, 12174, 1211, 8315, 498, 295, 1958, 775, 406, 2514, 7251, 3555, 4587, 7578, 31420, 12549, 6055, 15042, 2304, 22807, 31420, 12549, 43242, 1958, 44381, 19446, 8717, 45367, 10632, 2423, 31420, 12549, 22807, 8032, 1211, 31439, 3012, 22807, 16070, 43761, 44060, 22807, 16070, 43761, 13785, 31420, 21757, 22807, 37893, 41850, 5551, 3615, 28480, 9154, 16095, 12399, 12174, 1211, 2655, 2423, 4948, 9154, 16247, 2304, 10943, 1829, 4724, 3794, 2407, 10632, 2423, 4948, 7251, 3555, 4587, 7578, 3012, 12399, 8032, 47302, 21136, 3555, 3555, 5551, 15042, 4724, 28259, 10632, 12399, 12174, 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5296, 10721, 3794, 34051, 5551, 9778, 3215, 2655, 1211, 11296, 25724, 8848, 2288, 28239, 11536, 1829, 34051, 10874, 38251, 2655, 1975, 12984, 29399, 9957, 15844, 45030, 11242, 28242, 4724, 1829, 30544, 11778, 6027, 3660, 44650, 36520, 3660, 4724, 3794], "avg_logprob": -0.17299107142857142, "compression_ratio": 1.5955882352941178, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2311.33, "end": 2311.67, "word": "أو", "probability": 0.763916015625}, {"start": 2311.67, "end": 2312.57, "word": " ضربناهم", "probability": 0.9296875}, {"start": 2312.57, "end": 2313.21, "word": " ضرب", "probability": 0.98974609375}, {"start": 2313.21, "end": 2314.19, "word": " أو", "probability": 0.79150390625}, {"start": 2314.19, "end": 2315.23, "word": " كونستان", "probability": 0.7677001953125}, {"start": 2315.23, "end": 2315.51, "word": " في", "probability": 0.51708984375}, {"start": 2315.51, "end": 2316.67, "word": " إحداهما", "probability": 0.8472900390625}, {"start": 2316.67, "end": 2317.47, "word": " أو", "probability": 0.93994140625}, {"start": 2317.47, "end": 2318.33, "word": " رفعتها", "probability": 0.9869384765625}, {"start": 2318.33, "end": 2318.81, "word": " لأس", "probability": 0.7285970052083334}, {"start": 2318.81, "end": 2319.13, "word": " أو", "probability": 0.833984375}, {"start": 2319.13, "end": 2319.85, "word": " أخدتلها", "probability": 0.9417317708333334}, {"start": 2319.85, "end": 2320.39, "word": " الجذر", "probability": 0.8937174479166666}, {"start": 2320.39, "end": 2321.05, "word": " النوني", "probability": 0.9046223958333334}, {"start": 2321.05, "end": 2321.67, "word": " أو", "probability": 0.96142578125}, {"start": 2321.67, "end": 2322.37, "word": " جسمت", "probability": 0.9332682291666666}, {"start": 2322.37, "end": 2323.01, "word": " اثنتين", "probability": 0.728271484375}, {"start": 2323.01, "end": 2323.33, "word": " على", "probability": 0.8154296875}, {"start": 2323.33, "end": 2323.89, "word": " بعض", "probability": 0.98779296875}, {"start": 2323.89, "end": 2324.53, "word": " كل", "probability": 0.71044921875}, {"start": 2324.53, "end": 2325.03, "word": " بيكون", "probability": 0.83349609375}, {"start": 2325.03, "end": 2325.43, "word": " دالة", "probability": 0.8463541666666666}, {"start": 2325.43, "end": 2326.05, "word": " متصلة", "probability": 0.8601888020833334}, {"start": 2326.05, "end": 2326.39, "word": " بس", "probability": 0.9287109375}], "temperature": 1.0}, {"id": 101, "seek": 235452, "start": 2326.6, "end": 2354.52, "text": "عند القسمة بد المقام ممنوع يساوي zero عند النقطة اللى بنحسب قيمة الدالة عندها أو اللى بنحسب قيمة ال limit عندها يبقى أول خاصية من هذه الخواص على الشكل التالي if ال if and ال g are continuous functions are continuous", "tokens": [3615, 41260, 25062, 38251, 3660, 47525, 9673, 4587, 10943, 3714, 27842, 45367, 7251, 3794, 995, 45865, 4018, 43242, 28239, 47432, 3660, 13672, 7578, 44945, 5016, 35457, 12174, 32640, 3660, 32748, 6027, 3660, 43242, 11296, 34051, 13672, 7578, 44945, 5016, 35457, 12174, 32640, 3660, 2423, 4948, 43242, 11296, 7251, 3555, 4587, 7578, 5551, 12610, 16490, 33546, 10632, 9154, 29538, 33962, 14407, 9381, 15844, 25124, 28820, 16712, 6027, 1829, 498, 2423, 498, 293, 2423, 290, 366, 10957, 6828, 366, 10957], "avg_logprob": -0.198674844412864, "compression_ratio": 1.7604166666666667, "no_speech_prob": 0.0, "words": [{"start": 2326.6, "end": 2327.12, "word": "عند", "probability": 0.634033203125}, {"start": 2327.12, "end": 2327.68, "word": " القسمة", "probability": 0.82470703125}, {"start": 2327.68, "end": 2327.84, "word": " بد", "probability": 0.1724853515625}, {"start": 2327.84, "end": 2328.48, "word": " المقام", "probability": 0.927734375}, {"start": 2328.48, "end": 2328.92, "word": " ممنوع", "probability": 0.9739583333333334}, {"start": 2328.92, "end": 2329.58, "word": " يساوي", "probability": 0.9432373046875}, {"start": 2329.58, "end": 2330.36, "word": " zero", "probability": 0.137451171875}, {"start": 2330.36, "end": 2330.7, "word": " عند", "probability": 0.9267578125}, {"start": 2330.7, "end": 2331.24, "word": " النقطة", "probability": 0.9599609375}, {"start": 2331.24, "end": 2331.36, "word": " اللى", "probability": 0.70703125}, {"start": 2331.36, "end": 2331.82, "word": " بنحسب", "probability": 0.9208984375}, {"start": 2331.82, "end": 2332.26, "word": " قيمة", "probability": 0.9912109375}, {"start": 2332.26, "end": 2332.68, "word": " الدالة", "probability": 0.7747395833333334}, {"start": 2332.68, "end": 2333.2, "word": " عندها", "probability": 0.950439453125}, {"start": 2333.2, "end": 2333.72, "word": " أو", "probability": 0.6630859375}, {"start": 2333.72, "end": 2333.88, "word": " اللى", "probability": 0.932861328125}, {"start": 2333.88, "end": 2334.36, "word": " بنحسب", "probability": 0.9710286458333334}, {"start": 2334.36, "end": 2335.14, "word": " قيمة", "probability": 0.9905598958333334}, {"start": 2335.14, "end": 2335.38, "word": " ال", "probability": 0.350830078125}, {"start": 2335.38, "end": 2335.8, "word": " limit", "probability": 0.80224609375}, {"start": 2335.8, "end": 2336.48, "word": " عندها", "probability": 0.8837890625}, {"start": 2336.48, "end": 2337.28, "word": " يبقى", "probability": 0.956298828125}, {"start": 2337.28, "end": 2337.6, "word": " أول", "probability": 0.8515625}, {"start": 2337.6, "end": 2338.22, "word": " خاصية", "probability": 0.9943033854166666}, {"start": 2338.22, "end": 2338.42, "word": " من", "probability": 0.97216796875}, {"start": 2338.42, "end": 2338.72, "word": " هذه", "probability": 0.94482421875}, {"start": 2338.72, "end": 2339.54, "word": " الخواص", "probability": 0.7443033854166666}, {"start": 2339.54, "end": 2339.86, "word": " على", "probability": 0.91162109375}, {"start": 2339.86, "end": 2340.62, "word": " الشكل", "probability": 0.932861328125}, {"start": 2340.62, "end": 2341.64, "word": " التالي", "probability": 0.9298502604166666}, {"start": 2341.64, "end": 2342.82, "word": " if", "probability": 0.38818359375}, {"start": 2342.82, "end": 2345.52, "word": " ال", "probability": 0.79150390625}, {"start": 2345.52, "end": 2346.0, "word": " if", "probability": 0.65283203125}, {"start": 2346.0, "end": 2347.14, "word": " and", "probability": 0.947265625}, {"start": 2347.14, "end": 2348.24, "word": " ال", "probability": 0.77880859375}, {"start": 2348.24, "end": 2348.72, "word": " g", "probability": 0.56103515625}, {"start": 2348.72, "end": 2350.1, "word": " are", "probability": 0.869140625}, {"start": 2350.1, "end": 2350.72, "word": " continuous", "probability": 0.892578125}, {"start": 2350.72, "end": 2351.74, "word": " functions", "probability": 0.8388671875}, {"start": 2351.74, "end": 2352.86, "word": " are", "probability": 0.8740234375}, {"start": 2352.86, "end": 2354.52, "word": " continuous", "probability": 0.91064453125}], "temperature": 1.0}, {"id": 102, "seek": 238241, "start": 2356.47, "end": 2382.41, "text": "function at x يساوي c then ال f زائد او ناقص g و ال f في g و حاصل ضرب مقدار ثابت في احدى الدالتين where ال k is constant", "tokens": [69, 32627, 412, 2031, 7251, 3794, 995, 45865, 269, 550, 2423, 283, 30767, 16373, 3215, 1975, 2407, 8717, 995, 4587, 9381, 290, 4032, 2423, 283, 8978, 290, 4032, 11331, 33546, 1211, 48812, 25513, 3714, 28543, 9640, 38637, 16758, 2655, 8978, 1975, 24401, 7578, 32748, 6027, 2655, 9957, 689, 2423, 350, 307, 5754], "avg_logprob": -0.30454010108731827, "compression_ratio": 1.2962962962962963, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2356.47, "end": 2357.31, "word": "function", "probability": 0.078399658203125}, {"start": 2357.31, "end": 2358.85, "word": " at", "probability": 0.5478515625}, {"start": 2358.85, "end": 2359.61, "word": " x", "probability": 0.93994140625}, {"start": 2359.61, "end": 2360.51, "word": " يساوي", "probability": 0.739166259765625}, {"start": 2360.51, "end": 2361.17, "word": " c", "probability": 0.72021484375}, {"start": 2361.17, "end": 2364.17, "word": " then", "probability": 0.309814453125}, {"start": 2364.17, "end": 2366.97, "word": " ال", "probability": 0.513671875}, {"start": 2366.97, "end": 2367.51, "word": " f", "probability": 0.482421875}, {"start": 2367.51, "end": 2368.63, "word": " زائد", "probability": 0.78466796875}, {"start": 2368.63, "end": 2368.93, "word": " او", "probability": 0.831298828125}, {"start": 2368.93, "end": 2369.51, "word": " ناقص", "probability": 0.896728515625}, {"start": 2369.51, "end": 2369.89, "word": " g", "probability": 0.72705078125}, {"start": 2369.89, "end": 2370.67, "word": " و", "probability": 0.47216796875}, {"start": 2370.67, "end": 2370.89, "word": " ال", "probability": 0.61474609375}, {"start": 2370.89, "end": 2371.31, "word": " f", "probability": 0.794921875}, {"start": 2371.31, "end": 2371.71, "word": " في", "probability": 0.89794921875}, {"start": 2371.71, "end": 2372.03, "word": " g", "probability": 0.890625}, {"start": 2372.03, "end": 2372.81, "word": " و", "probability": 0.90966796875}, {"start": 2372.81, "end": 2373.45, "word": " حاصل", "probability": 0.7772623697916666}, {"start": 2373.45, "end": 2373.77, "word": " ضرب", "probability": 0.9501953125}, {"start": 2373.77, "end": 2374.49, "word": " مقدار", "probability": 0.87646484375}, {"start": 2374.49, "end": 2375.05, "word": " ثابت", "probability": 0.9934895833333334}, {"start": 2375.05, "end": 2375.31, "word": " في", "probability": 0.9248046875}, {"start": 2375.31, "end": 2375.87, "word": " احدى", "probability": 0.8091634114583334}, {"start": 2375.87, "end": 2376.83, "word": " الدالتين", "probability": 0.91650390625}, {"start": 2376.83, "end": 2378.09, "word": " where", "probability": 0.568359375}, {"start": 2378.09, "end": 2379.13, "word": " ال", "probability": 0.81201171875}, {"start": 2379.13, "end": 2379.49, "word": " k", "probability": 0.75634765625}, {"start": 2379.49, "end": 2380.75, "word": " is", "probability": 0.93017578125}, {"start": 2380.75, "end": 2382.41, "word": " constant", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 103, "seek": 241076, "start": 2386.04, "end": 2410.76, "text": "مقدار ثابت وكذلك ال F على G بشرط ان ال G of C ممنوع يساوي Zero و ال F مرفوعة لل N and الجذر النوني ل F where", "tokens": [2304, 28543, 9640, 38637, 16758, 2655, 4032, 4117, 8848, 23275, 2423, 479, 15844, 460, 4724, 46309, 9566, 16472, 2423, 460, 295, 383, 3714, 27842, 45367, 7251, 3794, 995, 45865, 17182, 4032, 2423, 479, 3714, 28480, 2407, 27884, 24976, 426, 293, 25724, 8848, 2288, 28239, 11536, 1829, 5296, 479, 689], "avg_logprob": -0.17812500268220902, "compression_ratio": 1.2352941176470589, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 2386.04, "end": 2386.92, "word": "مقدار", "probability": 0.775634765625}, {"start": 2386.92, "end": 2387.74, "word": " ثابت", "probability": 0.9886067708333334}, {"start": 2387.74, "end": 2389.5, "word": " وكذلك", "probability": 0.8653564453125}, {"start": 2389.5, "end": 2390.18, "word": " ال", "probability": 0.85693359375}, {"start": 2390.18, "end": 2390.62, "word": " F", "probability": 0.568359375}, {"start": 2390.62, "end": 2391.88, "word": " على", "probability": 0.6572265625}, {"start": 2391.88, "end": 2392.34, "word": " G", "probability": 0.935546875}, {"start": 2392.34, "end": 2394.04, "word": " بشرط", "probability": 0.9313151041666666}, {"start": 2394.04, "end": 2394.38, "word": " ان", "probability": 0.69873046875}, {"start": 2394.38, "end": 2394.64, "word": " ال", "probability": 0.7841796875}, {"start": 2394.64, "end": 2394.94, "word": " G", "probability": 0.9013671875}, {"start": 2394.94, "end": 2395.3, "word": " of", "probability": 0.748046875}, {"start": 2395.3, "end": 2395.8, "word": " C", "probability": 0.94384765625}, {"start": 2395.8, "end": 2397.04, "word": " ممنوع", "probability": 0.9871419270833334}, {"start": 2397.04, "end": 2397.7, "word": " يساوي", "probability": 0.9180908203125}, {"start": 2397.7, "end": 2398.4, "word": " Zero", "probability": 0.4443359375}, {"start": 2398.4, "end": 2399.72, "word": " و", "probability": 0.65673828125}, {"start": 2399.72, "end": 2400.78, "word": " ال", "probability": 0.53564453125}, {"start": 2400.78, "end": 2401.24, "word": " F", "probability": 0.982421875}, {"start": 2401.24, "end": 2402.22, "word": " مرفوعة", "probability": 0.9395751953125}, {"start": 2402.22, "end": 2403.02, "word": " لل", "probability": 0.8740234375}, {"start": 2403.02, "end": 2403.58, "word": " N", "probability": 0.89453125}, {"start": 2403.58, "end": 2405.1, "word": " and", "probability": 0.65673828125}, {"start": 2405.1, "end": 2406.66, "word": " الجذر", "probability": 0.8562825520833334}, {"start": 2406.66, "end": 2407.86, "word": " النوني", "probability": 0.8499348958333334}, {"start": 2407.86, "end": 2408.2, "word": " ل", "probability": 0.86572265625}, {"start": 2408.2, "end": 2408.84, "word": " F", "probability": 0.865234375}, {"start": 2408.84, "end": 2410.76, "word": " where", "probability": 0.794921875}], "temperature": 1.0}, {"id": 104, "seek": 244129, "start": 2413.55, "end": 2441.29, "text": "الـ N is a positive integer كلهم هدول مالهم are continuous functions يبقى كلهم هدول دوال متصلة at X يساوي C", "tokens": [6027, 39184, 426, 307, 257, 3353, 24922, 28242, 16095, 8032, 3215, 12610, 3714, 6027, 16095, 366, 10957, 6828, 7251, 3555, 4587, 7578, 28242, 16095, 8032, 3215, 12610, 11778, 2407, 6027, 44650, 9381, 37977, 412, 1783, 7251, 3794, 995, 45865, 383], "avg_logprob": -0.2841082433374917, "compression_ratio": 1.2314049586776858, "no_speech_prob": 0.0, "words": [{"start": 2413.55, "end": 2414.03, "word": "الـ", "probability": 0.42108154296875}, {"start": 2414.03, "end": 2414.39, "word": " N", "probability": 0.55615234375}, {"start": 2414.39, "end": 2415.35, "word": " is", "probability": 0.139892578125}, {"start": 2415.35, "end": 2416.35, "word": " a", "probability": 0.84130859375}, {"start": 2416.35, "end": 2417.45, "word": " positive", "probability": 0.916015625}, {"start": 2417.45, "end": 2419.85, "word": " integer", "probability": 0.91552734375}, {"start": 2419.85, "end": 2424.01, "word": " كلهم", 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" x", "probability": 0.951171875}, {"start": 2892.34, "end": 2892.88, "word": " إن", "probability": 0.5146484375}, {"start": 2892.88, "end": 2893.32, "word": " كانت", "probability": 0.98095703125}, {"start": 2893.32, "end": 2893.46, "word": " C", "probability": 0.441162109375}, {"start": 2893.46, "end": 2893.84, "word": " بشيل", "probability": 0.9544270833333334}, {"start": 2893.84, "end": 2894.08, "word": " X", "probability": 0.60205078125}, {"start": 2894.08, "end": 2894.24, "word": " و", "probability": 0.7373046875}, {"start": 2894.24, "end": 2894.76, "word": " بحط", "probability": 0.9822591145833334}, {"start": 2894.76, "end": 2895.12, "word": " C", "probability": 0.9423828125}, {"start": 2895.12, "end": 2896.04, "word": " وبالتالي", "probability": 0.902734375}, {"start": 2896.04, "end": 2897.12, "word": " تعويض", "probability": 0.94189453125}, {"start": 2897.12, "end": 2897.68, "word": " مباشر", "probability": 0.9954833984375}, {"start": 2897.68, "end": 2898.18, "word": " هذا", 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"text": "تجهت إلى الـinfinity و روحت من جهة الـ limit وتجهت نزلت لويا لسالب infinity وهكذا يبقى ال limit does not exist لأنه عنده infinite discontinuity عند هذه النقاط يبقى الدلة دلة متصلة لما عدا عند النقاط هذا اللي صار عند infinite discontinuity غير هيك لا الدلة معرفة عند هذه النقاط ولا حتى ال limit", "tokens": [2655, 7435, 3224, 2655, 30731, 2423, 39184, 259, 5194, 507, 4032, 12602, 2407, 33753, 9154, 10874, 3224, 3660, 2423, 39184, 4948, 34683, 7435, 3224, 2655, 8717, 11622, 1211, 2655, 45164, 25528, 5296, 3794, 6027, 3555, 13202, 37037, 4117, 15730, 7251, 3555, 4587, 7578, 2423, 4948, 775, 406, 2514, 5296, 33456, 3224, 43242, 3224, 13785, 31420, 21757, 43242, 29538, 28239, 4587, 41193, 7251, 3555, 4587, 7578, 32748, 37977, 11778, 37977, 44650, 36520, 3660, 5296, 15042, 6225, 28259, 43242, 28239, 4587, 41193, 23758, 13672, 1829, 20328, 9640, 43242, 13785, 31420, 21757, 32771, 13546, 39896, 4117, 20193, 32748, 37977, 20449, 28480, 3660, 43242, 29538, 28239, 4587, 41193, 49429, 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هي 2X زي التلاتة يبقى 2X زي التلاتة H لما تأثر على ال element يساوي الجذر التالت لل element مش هذه هي F of X تبعدنا", "tokens": [3224, 15730, 47525, 3224, 7251, 3794, 995, 45865, 2423, 389, 295, 460, 295, 1783, 23758, 47525, 3224, 37495, 9566, 1829, 4117, 2423, 389, 295, 2423, 460, 13672, 1829, 39896, 568, 55, 30767, 1829, 16712, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 568, 55, 30767, 1829, 16712, 1211, 9307, 3660, 389, 5296, 15042, 6055, 10721, 49115, 15844, 2423, 4478, 7251, 3794, 995, 45865, 25724, 8848, 2288, 16712, 6027, 2655, 24976, 4478, 37893, 29538, 39896, 479, 295, 1783, 6055, 3555, 22488, 8315], "avg_logprob": -0.23148148148148148, "compression_ratio": 1.729559748427673, "no_speech_prob": 0.0, "words": [{"start": 3662.48, "end": 3663.02, "word": "هذا", "probability": 0.830078125}, {"start": 3663.02, "end": 3663.44, "word": " بده", "probability": 0.2821044921875}, {"start": 3663.44, "end": 3664.2, "word": " يساوي", "probability": 0.930419921875}, {"start": 3664.2, "end": 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3757.23, "word": " all", "probability": 0.9580078125}, {"start": 3757.23, "end": 3757.87, "word": " X", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 158, "seek": 379845, "start": 3779.15, "end": 3798.45, "text": "طيب حتى الآن احنا اخدنا اللي هو خواص الدوال المتصلة واخدنا امثلة على كيفية استخدام هذه الخواص للدوال المختلفة طيب كل اللي اتحدثنا فيه اللي هو كان ال continuity عند نقطة", "tokens": [9566, 1829, 3555, 11331, 49975, 6024, 48506, 1975, 5016, 8315, 1975, 9778, 3215, 8315, 13672, 1829, 31439, 16490, 2407, 33546, 32748, 2407, 6027, 9673, 2655, 36520, 3660, 4032, 47283, 3215, 8315, 1975, 2304, 12984, 37977, 15844, 9122, 33911, 10632, 44713, 9778, 3215, 10943, 29538, 33962, 2407, 33546, 24976, 3215, 2407, 6027, 9673, 46456, 46538, 3660, 23032, 1829, 3555, 28242, 13672, 1829, 1975, 2655, 24401, 12984, 8315, 8978, 3224, 13672, 1829, 31439, 25961, 2423, 23807, 43242, 8717, 47432, 3660], "avg_logprob": -0.17434730824035935, "compression_ratio": 1.7309941520467835, 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"word": " امثلة", "probability": 0.877685546875}, {"start": 3787.61, "end": 3787.83, "word": " على", "probability": 0.4306640625}, {"start": 3787.83, "end": 3788.33, "word": " كيفية", "probability": 0.9884440104166666}, {"start": 3788.33, "end": 3789.17, "word": " استخدام", "probability": 0.9676513671875}, {"start": 3789.17, "end": 3789.97, "word": " هذه", "probability": 0.98095703125}, {"start": 3789.97, "end": 3791.07, "word": " الخواص", "probability": 0.9329427083333334}, {"start": 3791.07, "end": 3791.81, "word": " للدوال", "probability": 0.812255859375}, {"start": 3791.81, "end": 3792.83, "word": " المختلفة", "probability": 0.9969482421875}, {"start": 3792.83, "end": 3793.53, "word": " طيب", "probability": 0.7390950520833334}, {"start": 3793.53, "end": 3793.85, "word": " كل", "probability": 0.97705078125}, {"start": 3793.85, "end": 3793.97, "word": " اللي", "probability": 0.965087890625}, {"start": 3793.97, "end": 3794.61, "word": " اتحدثنا", "probability": 0.9734375}, {"start": 3794.61, "end": 3795.19, "word": " فيه", "probability": 0.9873046875}, {"start": 3795.19, "end": 3795.59, "word": " اللي", "probability": 0.77783203125}, {"start": 3795.59, "end": 3795.75, "word": " هو", "probability": 0.896484375}, {"start": 3795.75, "end": 3796.03, "word": " كان", "probability": 0.77392578125}, {"start": 3796.03, "end": 3796.17, "word": " ال", "probability": 0.94873046875}, {"start": 3796.17, "end": 3797.15, "word": " continuity", "probability": 0.9111328125}, {"start": 3797.15, "end": 3797.93, "word": " عند", "probability": 0.98583984375}, {"start": 3797.93, "end": 3798.45, "word": " نقطة", "probability": 0.8984375}], "temperature": 1.0}, {"id": 159, "seek": 382525, "start": 3798.75, "end": 3825.25, "text": "توقع قبل قليل قلنا ممكن تقسيم الـ discontinuity نعمله removable تمام هذا بنسمي continuous extension عند نقطة يعني الدالة ممكن تكون متصلة عند هذه النقطة ممكن تخليها تصير متصلة عند هذه النقطة وهذا بنسمي continuous extension للدالة عند نقطة يبقى فاجل continuous", 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3822.31, "end": 3822.91, "word": " نقطة", "probability": 0.9773763020833334}, {"start": 3822.91, "end": 3823.71, "word": " يبقى", "probability": 0.9320068359375}, {"start": 3823.71, "end": 3824.23, "word": " فاجل", "probability": 0.5525716145833334}, {"start": 3824.23, "end": 3825.25, "word": " continuous", "probability": 0.82421875}], "temperature": 1.0}, {"id": 160, "seek": 385270, "start": 3828.86, "end": 3852.7, "text": "extension extension to a point تعميم اتصال الدالة عند نقطة definition بيقول معنى f ال f of x is undefined", "tokens": [3828, 3378, 10320, 281, 257, 935, 37279, 2304, 32640, 1975, 2655, 9381, 6027, 32748, 6027, 3660, 43242, 8717, 47432, 3660, 7123, 4724, 1829, 39648, 20449, 1863, 7578, 283, 2423, 283, 295, 2031, 307, 674, 5666, 2001], "avg_logprob": -0.2565456081081081, "compression_ratio": 1.219298245614035, "no_speech_prob": 0.0, "words": [{"start": 3828.8599999999997, "end": 3830.2599999999998, "word": "extension", "probability": 0.679931640625}, {"start": 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3870.71, "end": 3870.93, "word": " ال", "probability": 0.90283203125}, {"start": 3870.93, "end": 3871.25, "word": " x", "probability": 0.81298828125}, {"start": 3871.25, "end": 3871.67, "word": " بده", "probability": 0.39697265625}, {"start": 3871.67, "end": 3871.99, "word": " يروح", "probability": 0.9814453125}, {"start": 3871.99, "end": 3872.33, "word": " إلى", "probability": 0.5556640625}, {"start": 3872.33, "end": 3872.85, "word": " c", "probability": 0.92578125}, {"start": 3872.85, "end": 3873.75, "word": " بده", "probability": 0.834228515625}, {"start": 3873.75, "end": 3874.39, "word": " يساوي", "probability": 0.970947265625}, {"start": 3874.39, "end": 3874.63, "word": " ال", "probability": 0.89892578125}, {"start": 3874.63, "end": 3875.09, "word": " L", "probability": 0.69580078125}, {"start": 3875.09, "end": 3876.95, "word": " exists", "probability": 0.71533203125}, {"start": 3876.95, "end": 3878.35, "word": " يبقى", "probability": 0.722808837890625}, {"start": 3878.35, "end": 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"probability": 0.95556640625}], "temperature": 1.0}, {"id": 165, "seek": 397381, "start": 3965.71, "end": 3973.81, "text": "and then it was extension of f to x يساوي c", "tokens": [474, 550, 309, 390, 10320, 295, 283, 281, 2031, 7251, 3794, 995, 45865, 269], "avg_logprob": -0.40546875397364296, "compression_ratio": 0.8421052631578947, "no_speech_prob": 0.0, "words": [{"start": 3965.71, "end": 3965.99, "word": "and", "probability": 0.0693359375}, {"start": 3965.99, "end": 3966.19, "word": " then", "probability": 0.689453125}, {"start": 3966.19, "end": 3966.27, "word": " it", "probability": 0.42724609375}, {"start": 3966.27, "end": 3966.43, "word": " was", "probability": 0.9296875}, {"start": 3966.43, "end": 3967.33, "word": " extension", "probability": 0.853515625}, {"start": 3967.33, "end": 3968.69, "word": " of", "probability": 0.96142578125}, {"start": 3968.69, "end": 3970.41, "word": " f", "probability": 0.494384765625}, {"start": 3970.41, "end": 3971.45, "word": " to", 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"duration_after_vad": 4734.0025000000005} \ No newline at end of file diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/wEzmV3DYYdg.srt b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/wEzmV3DYYdg.srt new file mode 100644 index 0000000000000000000000000000000000000000..f895fa0101f62e89a3c311d98e0a150cc070b906 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/wEzmV3DYYdg.srt @@ -0,0 +1,3163 @@ +1 +00:00:21,230 --> 00:00:26,570 +بسم الله الرحمن الرحيم المُقَلّم الآن في ال section + +2 +00:00:26,570 --> 00:00:31,190 +رقم اثنين اثنين وهو يتحدث عن limit of a function + +3 +00:00:31,190 --> 00:00:36,990 +and limit laws يبقى نهاية دالة ما، وكذلك بنا نأخذ + +4 +00:00:36,990 --> 00:00:42,310 +في هذه ال section بعض قواعد النهايات، هنبدأ أول شيء + +5 +00:00:42,310 --> 00:00:49,490 +ب concept of a limit يبقى بنا نتعرض إلى مفهوم ال + +6 +00:00:49,490 --> 00:00:53,950 +limit يعني ما معنى ال limit لـ function أو نهاية + +7 +00:00:53,950 --> 00:00:59,850 +function ما عند نقطة ما، هذا اللي متعرض له الآن، يبقى + +8 +00:00:59,850 --> 00:01:06,830 +نحن لسنا بصدد حساب النهايات، وإنما بصدد فهم معنى + +9 +00:01:06,830 --> 00:01:11,390 +النهاية هل نهاية function هي قيمة function عند + +10 +00:01:11,390 --> 00:01:15,890 +نقطة؟ والله قيمة ال function هي شيء ونهاية ال + +11 +00:01:15,890 --> 00:01:21,190 +function هي شيء آخر، هذا الذي نود أن نعرفه من خلال + +12 +00:01:21,190 --> 00:01:26,970 +مجموعة من الأمثلة، نبدأ بالمثال الأول، والمثال الأول + +13 +00:01:26,970 --> 00:01:32,530 +عبارة عن ثلاث نقاط زي ما أنت شايف، وهناك أمثلة أخرى + +14 +00:01:32,530 --> 00:01:37,830 +من خلالها سنتعرف على الفرق بين نهاية الدالة عند + +15 +00:01:37,830 --> 00:01:42,850 +نقطة وقيمة الدالة عند تلك النقطة، المثال بيقول لي + +16 +00:01:42,850 --> 00:01:46,310 +how does the following functions behave near x + +17 +00:01:46,310 --> 00:01:52,470 +بدها تساوي ثلاثة، وصف لي أو بيّن لي كيف بد يكون سلوك + +18 +00:01:52,470 --> 00:01:57,590 +الدالة اللي عندنا بالقرب من x يساوي ثلاثة، يعني عند + +19 +00:01:57,590 --> 00:02:02,050 +x يساوي ثلاثة، إيش بد يكون وضع ال function بالضبط + +20 +00:02:02,050 --> 00:02:05,870 +هذا أو إيش سلوك هذا، اللي احنا عايزين نعرفه الآن + +21 +00:02:06,540 --> 00:02:10,180 +أعطاني ثلاث نقاط، النقطة الأولى بيقول لو كانت f of + +22 +00:02:10,180 --> 00:02:16,320 +x هي x square minus 9 على x minus 3، نمر بي جي of x + +23 +00:02:16,320 --> 00:02:21,060 +يساوي piecewise function، ده اللي مقسم إلى جزئين + +24 +00:02:21,060 --> 00:02:25,800 +الجزء الأول هو الجزء الأول اللي عندنا هنا، مع العلم + +25 +00:02:25,800 --> 00:02:31,020 +أن x ممنوع يساوي 3، هنا لو كانت x يساوي 3، فقيمة ال + +26 +00:02:31,020 --> 00:02:36,890 +function تساوي 4، إن H of X زي 3 لا يوجد عليها أي + +27 +00:02:36,890 --> 00:02:37,650 +قيود + +28 +00:02:47,480 --> 00:02:53,120 +هذه الدالة مُعرّفة عند X يساوي ثلاثة، يعني معنى هذا + +29 +00:02:53,120 --> 00:02:58,100 +الكلام إن X يساوي ثلاثة ليست موجودة في domain ال + +30 +00:02:58,100 --> 00:03:02,240 +function، مدام ليست موجودة في domainها، إذن الدالة + +31 +00:03:02,240 --> 00:03:09,080 +غير معرفة عند X يساوي ثلاثة، فبروح بقول له ال F is + +32 +00:03:09,080 --> 00:03:21,300 +undefined at X يساوي ثلاثة، that is أي أن ال F of + +33 +00:03:21,300 --> 00:03:25,820 +ثلاثة does not exist + +34 +00:03:28,220 --> 00:03:34,520 +يبقى ال f of ثلاثة ما لهاش وجود، تمام؟ طيب، باجي + +35 +00:03:34,520 --> 00:03:40,580 +بقوله but ولكن ال f of x بقدر أكتبها على الشكل + +36 +00:03:40,580 --> 00:03:45,580 +التالي اللي هي ال x minus three بحللها كفرق بين + +37 +00:03:45,580 --> 00:03:52,140 +المربعين على x ناقص three، لما كانت ال x ممنوعة + +38 +00:03:52,140 --> 00:03:58,130 +تساوي ثلاثة، إذا المقام هذا لا يمكن أن يساوي zero، ما + +39 +00:03:58,130 --> 00:04:02,050 +دام لما يمكن أن يساوي zero، إذا ممكن أن يكون هناك + +40 +00:04:02,050 --> 00:04:07,430 +اختصارات بين البسط والمقام، ويبقى عندنا x plus + +41 +00:04:07,430 --> 00:04:13,710 +three وبشرط إن ال x ما لها ممنوعة تساوي ثلاثة، يبقى + +42 +00:04:13,710 --> 00:04:19,120 +ال function الأولى اللي عندنا نمر أيه، حطيتها في شكل + +43 +00:04:19,120 --> 00:04:25,800 +جديد، هذا الشكل الجديد هو X زائد ثلاثة، علما بأن X + +44 +00:04:25,800 --> 00:04:31,260 +مالها لا تساوي ثلاثة، السؤال هو لما أقول لك F of X + +45 +00:04:31,260 --> 00:04:36,540 +يساوي X زائد ثلاثة، معدلتيش هذه قط مستقيم، طب خليني + +46 +00:04:36,540 --> 00:04:41,460 +نرسم الخط المستقيم ونحاول نتعرف على بعض الشغلات من + +47 +00:04:41,460 --> 00:04:47,220 +خلال هذا الخط المستقيم، إذا لو روحت قلت هذا محور X + +48 +00:04:47,220 --> 00:04:54,280 +هذا محور Y، هذه نقطة الأصل، وحبينا نرسم هذا الخط + +49 +00:04:54,280 --> 00:04:58,460 +المستقيم، مشان نرسم الخط المستقيم بناروح ناخد + +50 +00:04:58,460 --> 00:05:03,420 +نقطتين موجودتين عليه، ونروح نوصل فيما بينهم + +51 +00:05:03,420 --> 00:05:07,820 +وبالتالي بنرسم هذا الخط المستقيم، فباجي بقول لو + +52 +00:05:07,820 --> 00:05:13,460 +كانت X يساوي Zero، يبقى F of Zero بيساوي كده؟ ثلاثة + +53 +00:05:13,460 --> 00:05:17,560 +إذا عندي ال Zero هذه بيبقى تساوي ثلاثة، يبقى هذه + +54 +00:05:17,560 --> 00:05:22,900 +النقطة اللي هي Zero وثلاثة، لو كانت ال F of X كلها + +55 +00:05:22,900 --> 00:05:27,740 +بـ 0 يبقى X بتساوي سالب ثلاثة، يعني لما Y تساوي 0، X + +56 +00:05:27,740 --> 00:05:33,100 +يساوي سالب ثلاثة، الهمين النقطة اللي عندنا هذه تمام؟ + +57 +00:05:33,100 --> 00:05:38,780 +إذا أنا لو روحت وصلت فيما بين النقطتين هذه ومديت + +58 +00:05:38,780 --> 00:05:43,880 +الخط المستقيم على استقامته، و روحت أشوف إيش اللي + +59 +00:05:43,880 --> 00:05:47,820 +بدي يحصل عند الثلاثة، فباجي بقول له هذا النقطة + +60 +00:05:47,820 --> 00:05:51,320 +واحد، هذا النقطة اثنين، هذا النقطة اثنين، هذا + +61 +00:05:51,320 --> 00:05:51,340 +هذا النقطة اثنين، هذا النقطة اثنين، هذا النقطة + +62 +00:05:51,340 --> 00:05:51,800 +اثنين، هذا النقطة اثنين، هذا النقطة اثنين، هذا + +63 +00:05:51,800 --> 00:05:52,240 +النقطة اثنين، هذا النقطة اثنين، هذا النقطة اثنين، + +64 +00:05:52,240 --> 00:05:55,540 +هذا النقطة اثنين، هذا النقطة اثنين، هذا النقطة + +65 +00:05:55,540 --> 00:06:01,660 +اثنين، هذا النقطة اثنين، هذا النقطة اثنين، هذا + +66 +00:06:01,660 --> 00:06:07,560 +النقطة اثنين، هذا يعني الخط المستقيم هذا لما + +67 +00:06:07,560 --> 00:06:13,800 +يكون ماشي هكذا، هنلاقي هذا الثقب موجود في هذا الخط + +68 +00:06:13,800 --> 00:06:21,540 +المستقيم، تمام؟ عشان يبقى الـ function اللي عندنا + +69 +00:06:21,540 --> 00:06:26,240 +هذه، روحت رسمت، رسمتها لما انحطيتها في الشكل هذا + +70 +00:06:26,240 --> 00:06:31,160 +فطلع الرسمة تبعتها هو الخط المستقيم باللون الأحمر + +71 +00:06:31,160 --> 00:06:35,640 +اللي موجود عندنا في الرسمة، لكن عند النقطة X يساوي + +72 +00:06:35,640 --> 00:06:41,210 +ثلاثة دالة غير معربة، طب لو كانت الدالة معرفة عندي + +73 +00:06:41,210 --> 00:06:47,130 +الثلاثة، بيكون هذا قداش القيمة؟ ستة، يبقى على محور Y + +74 +00:06:47,130 --> 00:06:53,250 +لو جيت ماشي أفق هيك، بتكون النقطة هذه ستة، تمام، تمام + +75 +00:06:53,250 --> 00:06:59,330 +طيب، تعالى نشوف، الآن أنا بقول الدالة غير معرفة عند x + +76 +00:06:59,330 --> 00:07:04,350 +يساوي ثلاثة، يعني f of ثلاثة does not exist، طيب + +77 +00:07:04,350 --> 00:07:10,030 +كويس، بالداجة أشوف لو أنا اقتربت من الدالة، قيمة + +78 +00:07:10,030 --> 00:07:15,660 +الدالة بتقترب من مين؟ بمعنى إن أنا هنا روحت أجرب + +79 +00:07:15,660 --> 00:07:21,340 +على الثلاثة من أي جهة كانت، بدي أشوف قيمة الدالة + +80 +00:07:21,340 --> 00:07:27,720 +وين بتروح، فأنا كل ما أقترب من الثلاثة بلاقي قيمة + +81 +00:07:27,720 --> 00:07:32,780 +الدالة بتقترب من مين؟ من ستة، أو من ناحية كل ما + +82 +00:07:32,780 --> 00:07:39,180 +أقرب من الدالة الدالة بتقترب من مين؟ بتقترب من ستة + +83 +00:07:39,180 --> 00:07:46,070 +إذا، بنال عليه بقدر أقول إن كل ما كنت قريب جدا من X + +84 +00:07:46,070 --> 00:07:50,610 +يساوي ثلاثة، كل ما كانت قيمة الدالة قريبة جدا من + +85 +00:07:50,610 --> 00:07:56,370 +ستة، هذا الكلام اللي أنا بصيغه، بتعبر عنه بصيغة + +86 +00:07:56,370 --> 00:08:01,110 +رياضية جديدة، وهي أن ال limit لل function اللي عندها + +87 +00:08:01,110 --> 00:08:06,460 +لما ال X بدها تساوي ثلاثة، بدها تساوي ستة، الدالة غير + +88 +00:08:06,460 --> 00:08:13,480 +معرفة عند الـ 6، لكن لها قيمة وهي قداش؟ ستة، ولكن ليست + +89 +00:08:13,480 --> 00:08:19,400 +لها قيمة، يبقى الدالة تقترب من الـ 6، كل ما اقتربت X + +90 +00:08:19,400 --> 00:08:23,160 +من مين؟ من ثلاثة، يبقى بروح بقول، يبقى ال limit + +91 +00:08:23,160 --> 00:08:28,880 +نهاية ال function لما ال X بتروح لثلاثة هي ستة، لكن + +92 +00:08:28,880 --> 00:08:34,650 +الدالة غير معرفة عند X يساوي ثلاثة، إذا قيمة الدالة + +93 +00:08:34,650 --> 00:08:40,030 +شيء ونهاية الدالة ما له شيء آخر، الكلام اللي سمعته + +94 +00:08:40,030 --> 00:08:43,910 +بدي أروح أُصيغه حتى لما تروح تذاكر هذا الكلام تفهم + +95 +00:08:43,910 --> 00:08:49,830 +إيش الكلام اللي أنت ابتغره عنه، فباجي بقول the + +96 +00:08:49,830 --> 00:09:00,290 +graph الرسم البياني، the graph of the function F is + +97 +00:09:00,290 --> 00:09:01,070 +shown + +98 +00:09:06,030 --> 00:09:13,010 +مبين بالرسم الخط المستقيم الأحمر اللي عنده with + +99 +00:09:13,010 --> 00:09:16,210 +removed + +100 +00:09:16,210 --> 00:09:21,170 +point + +101 +00:09:21,170 --> 00:09:25,090 +at + +102 +00:09:25,090 --> 00:09:30,870 +x يساوي ثلاثة، عند الثلاثة النقطة هذه مزالة تماما + +103 +00:09:35,650 --> 00:09:44,990 +But we can + +104 +00:09:44,990 --> 00:09:55,130 +make the value of f of x + +105 +00:10:07,550 --> 00:10:21,010 +if x was very close to ثلاثة + +106 +00:10:21,010 --> 00:10:23,650 +this means that + +107 +00:10:29,860 --> 00:10:41,080 +هذا يعني أن ال F approaches ستة + +108 +00:10:41,080 --> 00:10:52,640 +as X approaches ثلاثة and we write + +109 +00:10:58,750 --> 00:11:07,490 +بنكتب أن ال limit لل X تربيع ناقص تسعة على ال X + +110 +00:11:07,490 --> 00:11:12,370 +ناقص ثلاثة، لما ال X بدها تروح إلى ثلاثة بدها تساوي + +111 +00:11:12,370 --> 00:11:20,590 +كده؟ بدها تساوي ستة، مرة + +112 +00:11:20,590 --> 00:11:27,420 +ثانية بقول الكلام اللي قلناه شفوي قبل قليل، وروح + +113 +00:11:27,420 --> 00:11:32,400 +نصغناه على اللوح بهذا الشكل، فبعدين بقول الرسم + +114 +00:11:32,400 --> 00:11:37,620 +البياني للدالة هي قدامنا الخط الأحمر with removed + +115 +00:11:37,620 --> 00:11:42,380 +point at x يساوي ثلاثة، and x يساوي ثلاثة، النقطة دي + +116 +00:11:42,380 --> 00:11:50,090 +هيها مزالة مش موجودة وين على الرسم، but we can make + +117 +00:11:50,090 --> 00:11:55,330 +the value of f of x very + +118 +00:11:55,330 --> 00:12:02,590 +close to ستة، قريبة جدا من ستة، بايت شوز باختيار x very + +119 +00:12:02,590 --> 00:12:08,290 +close لثلاثة، بعدين نخلي x قريبة جدا من ثلاثة، بمعنى كل ما + +120 +00:12:08,290 --> 00:12:15,040 +اقتربت x من ثلاثة كل ما اقتربت قيمة الدالة من ستة، this + +121 +00:12:15,040 --> 00:12:19,440 +means that، هذا يعني أنه يجب أن يُصاغ الكلام بصيغة + +122 +00:12:19,440 --> 00:12:24,700 +أخرى، فباجي بقول هذا معناه أن f approaches ستة، الـ f + +123 +00:12:24,700 --> 00:12:33,930 +تقترب من ستة as x approaches ثلاثة كل ما تجرب X على ثلاثة + +124 +00:12:33,930 --> 00:12:41,570 +تجرب F of X على مين؟ على ستة، تجرب F of X على مين؟ + +125 +00:12:41,570 --> 00:12:45,010 +على ستة، تجرب F of X على مين؟ على ستة، تجرب F of X + +126 +00:12:45,010 --> 00:12:48,830 +على مين؟ على ستة، تجرب F of X على مين؟ على ستة، تجرب F + +127 +00:12:48,830 --> 00:12:51,870 +of X على مين؟ على ستة، تجرب F of X على مين؟ على ستة + +128 +00:12:51,870 --> 00:12:52,550 +تجرب F of X على مين؟ على ستة، تجرب F of X على مين؟ + +129 +00:12:52,550 --> 00:12:54,550 +of X على مين؟ على ستة، تجرب F of X على مين؟ على ستة + +130 +00:12:54,550 --> 00:12:58,470 +تجرب F of X على مين؟ على ستة، تجرب F of X على مين؟ + +131 +00:12:58,470 --> 00:13:01,100 +على ستة، تجرب F ستة، يبقى نهاية الدالة يساوي ستة، لكن + +132 +00:13:01,100 --> 00:13:06,140 +قيمة الدالة عن تلك النقطة غير معرفة، هذا يبين أن + +133 +00:13:06,140 --> 00:13:11,080 +قيمة الدالة شيء ونهاية الدالة شيء آخر، تعال خد + +134 +00:13:11,080 --> 00:13:18,030 +نمر بي، لو جيت لنمر بي، نمر بي الجزء الأول اللي فيها + +135 +00:13:18,030 --> 00:13:22,950 +هذا هو الجزء الأول اللي عندنا، مظبوط، هي نمر أ، لكن + +136 +00:13:22,950 --> 00:13:28,370 +الجزء الثاني راح خلالي الدالة معرفة عند X تساوي + +137 +00:13:28,370 --> 00:13:31,530 +ثلاثة، وبالتالي أعطاها القيمة اللي هي قداش؟ أربعة + +138 +00:13:31,530 --> 00:13:35,950 +يعني لو روحت رسمت ال function هذه اللي هي نمر بي + +139 +00:13:35,950 --> 00:13:43,590 +بيكون رسمتها على الشكل التالي، هذا محور X، هذه نقطة + +140 +00:13:43,590 --> 00:13:48,670 +الأصل هي Zero، وهذا محور Y، وهذا الخط المستقيم اللي + +141 +00:13:48,670 --> 00:13:54,770 +موجود عندنا تمام؟ وهذا النقطة واحد وهذه اثنين وهذه + +142 +00:13:54,770 --> 00:14:00,730 +ثلاثة، وجينا طالعين هنا صار هذا ثقب موجود في الخط + +143 +00:14:00,730 --> 00:14:06,550 +المستقيم، وهذا المستقيم موجود على استقامته، جينا + +144 +00:14:06,550 --> 00:14:13,110 +عند X يساوي ثلاثة، لجيت قيمة الذلة تساوي كم؟ تساوي + +145 +00:14:13,110 --> 00:14:18,890 +أربعة، يعني النقطة هذه اللي كانت هنا كم؟ ستة، أجت + +146 +00:14:18,890 --> 00:14:23,230 +هذه النقطة اللي هي كم؟ أربعة، يعني لو مشيت أفقي + +147 +00:14:23,230 --> 00:14:28,870 +بلاقي النقطة هذه، الإحداثي تبعها ثلاثة، والثاني كم؟ + +148 +00:14:28,870 --> 00:14:38,990 +أربعة، هل الـ function هذه في الحالة نمر بي معرفة + +149 +00:14:38,990 --> 00:14:44,790 +عند اكس يساوي ثلاثة؟ كده؟ ومن هنا صار خلاف بينه + +150 +00:14:44,790 --> 00:14:49,570 +وبين النقطة إيه؟ هنا أصبحت الدالة معرفة، بروح + +151 +00:14:49,570 --> 00:14:54,310 +بقوله ال F is defined + +152 +00:14:56,100 --> 00:15:05,820 +defined at x يساوي ثلاثة، that is أي أن ال F of + +153 +00:15:05,820 --> 00:15:14,300 +ثلاثة يساوي كده أربعة، but ولكن ال limit لمين؟ للـ + +154 +00:15:14,300 --> 00:15:19,240 +G of X لما الـ X بدها تروح إلى الثلاثة بدها تساوي + +155 +00:15:19,240 --> 00:15:24,880 +كده؟ ستة، اللي هي الحالة الأولى، طيب، يساوي ستة، إذا + +156 +00:15:24,880 --> 00:15:30,520 +أصبحت قيمة الدالة شيء ونهاية الدالة شيء آخر + +157 +00:15:30,520 --> 00:15:34,800 +يبقى هذا بيختلف عن اللي قبله أن الدالة معرفة لكن + +158 +00:15:34,800 --> 00:15:39,700 +قيمة الدالة عند هذه النقطة لا تساوي نهاية الدالة + +159 +00:15:39,700 --> 00:15:48,240 +عند تلك النقطة سواء الـ G of ثلاثة، الـ G of ثلاثة لا + +160 +00:15:48,240 --> 00:15:53,980 +تساوي limit الـ G of X لما الـ X بدها تروح لثلاثة + +161 +00:15:53,980 --> 00:15:58,540 +قيمة الدالة تساوي أربعة لكن الـ limit يساوي ستة + +162 +00:15:58,540 --> 00:16:03,330 +هذا يؤكد الكلام اللي قلناه في النقطة الأولى إن قيمة + +163 +00:16:03,330 --> 00:16:06,670 +الدالة شيء ونهاية الدالة شيء آخر + +164 +00:16:10,430 --> 00:16:15,270 +نجي نطلع لنمر سي، نمر سي جالس الـ H of X يساوي الـ + +165 +00:16:15,270 --> 00:16:21,250 +X مالها؟ زائد ثلاثة، عليها قيود؟ ما عليهاش قيود، إذا + +166 +00:16:21,250 --> 00:16:25,430 +أنا لو روحت رسمت الرسمة تابعة الدالة الثانية H + +167 +00:16:25,430 --> 00:16:32,210 +بقولها المحور، وهذا محور X، وهذا محور Y، وهذا Zero + +168 +00:16:32,210 --> 00:16:38,010 +وهذا واحد اثنين ثلاثة، فروحت رسمت الخط المستقيم اللي + +169 +00:16:38,010 --> 00:16:43,690 +عندنا هذا، هذا الخط ماشي دغري هيك، وإن الثلاثة + +170 +00:16:43,690 --> 00:16:49,550 +أطلع عند الثلاثة هنا، لجيت الدالة معرفة يعني + +171 +00:16:49,550 --> 00:16:54,530 +النقطة هذه مغلقة وليست على شكل تجويف كما كانت في + +172 +00:16:54 + +201 +00:20:29,970 --> 00:20:37,930 +بقى الـ G هذه بدل الـ F، G is defined صحيح كيف؟ + +202 +00:20:37,930 --> 00:20:43,330 +في نفس ال .. اه، G of تلتة صحيح معاك حق + +203 +00:20:47,210 --> 00:20:52,770 +طيب، لازمنا في نفس النقطة، لكن بدنا نجيب مثال آخر + +204 +00:20:52,770 --> 00:21:00,790 +بنقطتين حتى نثبت هذا المفهوم، بدأجي للدالة الأولى + +205 +00:21:00,790 --> 00:21:08,310 +و نشوف شو هو المطلوب من السؤال، بيقول لي ناقش لي سلوك كل + +206 +00:21:08,310 --> 00:21:13,150 +من الدوال التالية وين عند X لما تروح ل Zero لما + +207 +00:21:13,150 --> 00:21:17,850 +ال X تقترب من ال Zero، ناقش لي سلوك كل دالة من هتين + +208 +00:21:17,850 --> 00:21:24,190 +الدالتين، بيقول لي بسيطة بالداجلة الدالة الأولى F of X + +209 +00:21:24,190 --> 00:21:32,000 +يساوي هذه اللوغاريتمات كتبتها بطريقة أخرى، يبقى هذه إما x + +210 +00:21:32,000 --> 00:21:37,760 +على x لما ال x أكبر من ال zero، يا إما ال x على + +211 +00:21:37,760 --> 00:21:42,760 +ناقص x لما ال x أقل من ال zero، عند ال zero هل هي + +212 +00:21:42,760 --> 00:21:49,860 +معرفة؟ لأ، يبقى هذه إما واحد لما ال x أكبر من ال + +213 +00:21:49,860 --> 00:21:56,660 +zero أو سالب واحد لما ال x أقل من ال zero، الآن if + +214 +00:21:56,660 --> 00:22:08,280 +of 0 أو ال if is undefined غير معرفة at x يساوي 0 + +215 +00:22:08,280 --> 00:22:14,070 +تمام؟ طيب بدنا نشوف هل ال limit exist ولا لأ، مشان + +216 +00:22:14,070 --> 00:22:19,030 +نشوف ال limit exist ولا لأ، بدنا نروح نرسم رسمة هذه + +217 +00:22:19,030 --> 00:22:25,610 +الدالة، يبقى هذا محور X، هذا محور Y، هذا لقطة الأصل + +218 +00:22:25,610 --> 00:22:30,390 +اللي هي ال zero، الـ Range تبع هذه الدالة عبارة عن + +219 +00:22:30,390 --> 00:22:38,350 +قيمتين فقط، لهما الهمين واحد و سالب واحد، إذا كل + +220 +00:22:38,350 --> 00:22:44,850 +X لما تبقى أكبر من Zero، قيمة الدالة كم؟ واحد، لكن + +221 +00:22:44,850 --> 00:22:51,590 +عند Zero غير معرفة، يبقى على شكل تجويف، فالرسمة يكون + +222 +00:22:51,590 --> 00:22:58,740 +هذا هو الخط المستقيم، تمام؟ عند قبل الـ zero برضه + +223 +00:22:58,740 --> 00:23:04,800 +بيكون عندنا تجويف بهذا الشكل، تمام، والرسمة خط + +224 +00:23:04,800 --> 00:23:11,250 +مستقيم موازن له، هذه النقطة الهمين ناقص واحد، طيب + +225 +00:23:11,250 --> 00:23:16,950 +كويس، احنا بيقولوا دالة غير معرفة عند X يساوي Zero + +226 +00:23:16,950 --> 00:23:21,530 +بدنا نيجي نشوف هل ال limit موجودة ولا لأ، بيقولوا + +227 +00:23:21,530 --> 00:23:26,690 +تعالي نقترب من ال Zero، لنا جالي X بدها تروح ل Zero + +228 +00:23:26,690 --> 00:23:31,170 +فلو جيت من الناحية هذه، كل مجرب على Zero، الدالة + +229 +00:23:31,170 --> 00:23:36,070 +رايحة لوين؟ سالب واحد، إذا جيت بعد ال Zero، كل مجرب + +230 +00:23:36,070 --> 00:23:41,320 +على Zero الدالة رايحة لوين؟ لواحد، يبقى عند ال zero + +231 +00:23:41,320 --> 00:23:47,300 +صار jump قافزة من وين لوين؟ من سالب infinity إلى + +232 +00:23:47,300 --> 00:23:51,820 +infinity، يبقى ال limit موجودة ولا غير موجودة؟ غير + +233 +00:23:51,820 --> 00:23:55,740 +موجودة، بقيت تقولوا في الثانوية إذا عند ال limit من + +234 +00:23:55,740 --> 00:23:58,760 +اليمين، بالسويسي ال limit من الشمال، يبقى ال limit + +235 +00:23:58,760 --> 00:24:04,050 +does not exist، احنا بنقول إذا النقطة حصلت قفزة من + +236 +00:24:04,050 --> 00:24:06,950 +دالة من قيمة إلى قيمة أخرى، بيقول ال limit مالها + +237 +00:24:06,950 --> 00:24:15,390 +غير موجودة، يبقى باقي بقول limit ال X على absolute + +238 +00:24:15,390 --> 00:24:21,870 +value ل X لما ال X بتروح ل zero does not exist، ما + +239 +00:24:21,870 --> 00:24:29,930 +هو السبب، because ال + +240 +00:24:29,930 --> 00:24:42,470 +F jumped تعمل قفزة from سالب واحد to واحد at x + +241 +00:24:42,470 --> 00:24:48,090 +تساوي Zero، نظراً لإنها عند إعصار jump يبقى limit ما + +242 +00:24:48,090 --> 00:24:53,390 +لها does not exist، يبقى هذا المثال بيبين إنه لدالة + +243 +00:24:53,390 --> 00:24:58,270 +معرفة عندها نقطة ولا حتى limit إيه موجودة، يبقى هذه + +244 +00:24:58,270 --> 00:25:03,210 +كمان حالة رابعة غير التلات حالات اللي خدها موين في + +245 +00:25:03,210 --> 00:25:07,810 +المثال الأول، طب تعالى ناخد نمرة بيه و نشوف شو اللي + +246 +00:25:07,810 --> 00:25:13,240 +بدى يصير لو جيت لي نمرة بيه، نمر بيه خليني أرسمها في + +247 +00:25:13,240 --> 00:25:18,620 +الأول، يبقى باجي بقولها هي المحاور، هذا محور X، هذا + +248 +00:25:18,620 --> 00:25:25,000 +محور Y، هذا نقطة الأصل اللي هي Zero، F of X رسمناها + +249 +00:25:25,000 --> 00:25:31,040 +قبل ذلك وكان المنحنى على الشكل التالي، يبقى هذا + +250 +00:25:31,040 --> 00:25:35,200 +المنحنى بيجينا هيك ومن هنا بيجي طالع بالشكل اللي + +251 +00:25:35,200 --> 00:25:40,260 +عندنا هنا الدالة is undefined عند Zero، بتتذكروا + +252 +00:25:40,570 --> 00:25:44,890 +قلنا لك ال domain يساوي ال range يساوي كل ال real + +253 +00:25:44,890 --> 00:25:51,230 +line ما عدا ال zero، هنا قال لها هذه piecewise + +254 +00:25:51,230 --> 00:25:57,950 +function عند zero راح خلالي قيمتها كده؟ Zero، يمقصر + +255 +00:25:57,950 --> 00:26:02,610 +ال domain يساوي ال range يساوي كل ال real line + +256 +00:26:02,610 --> 00:26:08,760 +تمام؟ إذا هل تتدلى معرف عند ال zero ولا لا؟ يبقى + +257 +00:26:08,760 --> 00:26:15,460 +في نمرة B الـ F مُعرّفة + +258 +00:26:15,460 --> 00:26:21,140 +مُعرّفة at + +259 +00:26:21,140 --> 00:26:31,140 +X بده يساوي Zero، that is أي أن F of zero يساوي + +260 +00:26:31,140 --> 00:26:34,540 +Zero، تمام؟ طيب تعالى ناخد ال limit + +261 +00:26:37,540 --> 00:26:45,380 +ولكن اللي هو limit لل F of X لما ال X بده يروح لل + +262 +00:26:45,380 --> 00:26:51,300 +zero exist ولا does not exist، تعالى شوف إذا اتحركت + +263 +00:26:51,300 --> 00:26:56,180 +لل zero من الناحية اليمين بلاقي هذا يا حلوين، لما لا + +264 +00:26:56,180 --> 00:27:00,940 +نهاية، وإذا اتحركت للـ zero من جهة الشمال بلاقي هذه + +265 +00:27:00,940 --> 00:27:07,420 +مالها نازلة لسالب infinity، يبقى دالة have two + +266 +00:27:07,420 --> 00:27:15,020 +infinite limits، يبقى تنتين مختلفتين يبقى limit f + +267 +00:27:15,020 --> 00:27:22,420 +of x does not exist because + +268 +00:27:25,720 --> 00:27:36,600 +الـ F has two different infinite + +269 +00:27:36,600 --> 00:27:41,240 +limits + +270 +00:27:41,240 --> 00:27:48,220 +يعني عندي واحدة infinity والتانية سالب infinity + +271 +00:27:48,220 --> 00:27:51,340 +وبالتالي يعني that is + +272 +00:27:54,490 --> 00:28:02,850 +اللي هي infinity and سالب infinity، يبقى من هذا + +273 +00:28:02,850 --> 00:28:08,450 +المثال بنخلص إلى ما يأتي أن الدالة معرفة عند نقطة لكن + +274 +00:28:08,450 --> 00:28:13,630 +النهاية غير موجودة، إذا لو جيت للخمسة أمثلة مع بعض + +275 +00:28:13,630 --> 00:28:19,060 +بلاقي ما يأتي، الدالة غير معرفة عند نقطة لكن النهاية + +276 +00:28:19,060 --> 00:28:25,000 +موجودة، الدالة معرفة والنهاية موجودة واثنين are not + +277 +00:28:25,000 --> 00:28:29,260 +equal، الحالة التالتة الدالة معرفة والنهاية موجودة + +278 +00:28:29,260 --> 00:28:34,180 +واثنين are equal، الحالة التالتة اللي لا دالة معرفة + +279 +00:28:34,180 --> 00:28:38,620 +عندها نقطة ولا نهاية موجودة، الحالة الخامسة دالة + +280 +00:28:38,620 --> 00:28:43,260 +معرفة ولا نهاية غير موجودة، هذا بيخليني أسأل السؤال + +281 +00:28:43,260 --> 00:28:49,490 +التالي، ضع علامة صح أو خطأ أمام العبارة التالية، إذا + +282 +00:28:49,490 --> 00:28:55,790 +كانت الدالة معرفة عند X يساوي A، فإذا كانت دالة + +283 +00:28:55,790 --> 00:28:58,490 +معرفة عند X يساوي A، فإذا كانت دالة معرفة عند X + +284 +00:28:58,490 --> 00:28:58,970 +يساوي A، فإذا كانت دالة معرفة عند X يساوي A، فإذا + +285 +00:28:58,970 --> 00:28:58,990 +كانت دالة معرفة عند X يساوي A، فإذا كانت دالة + +286 +00:28:58,990 --> 00:28:59,050 +معرفة عند X يساوي A، فإذا كانت دالة معرفة عند X + +287 +00:28:59,050 --> 00:28:59,290 +يساوي A، فإذا كانت دالة معرفة عند X يساوي A، فإذا + +288 +00:28:59,290 --> 00:28:59,530 +كانت دالة معرفة عند X يساوي A، فإذا كانت دالة + +289 +00:28:59,530 --> 00:29:00,470 +معرفة عند X يساوي A، فإذا كانت دالة معرفة عند X + +290 +00:29:00,470 --> 00:29:04,490 +يساوي A، فإذا كانت دالة معرفة عند X يسا + +291 +00:29:04,970 --> 00:29:11,150 +خطأ، خطأ وهي وهي أكبر مثال عليها، هيها معرفة + +292 +00:29:11,150 --> 00:29:15,950 +والنهاية غير موجودة، يجب أن توقف نفسك كويس في هذا + +293 +00:29:15,950 --> 00:29:20,490 +المفهوم، لما تبقى الدالة معرفة عند نقطة، ليس + +294 +00:29:20,490 --> 00:29:27,040 +بالضرورة أن تبقى النهاية موجودة، الدالة معرفة لكن + +295 +00:29:27,040 --> 00:29:33,040 +النهاية غير موجودة و هذا و هذا طبيعي، طيب بدنا نشوف + +296 +00:29:33,040 --> 00:29:38,460 +هل المعنى هذا ترسخ في ذهنك ولا لا، نحاول نعطيك مثال + +297 +00:29:38,460 --> 00:29:43,920 +عملي و نشوف إيش بدك تقولنا من خلال هذا المثال + +298 +00:29:43,920 --> 00:29:45,140 +العملي + +299 +00:30:05,320 --> 00:30:15,360 +تفجر مثال من + +300 +00:30:15,360 --> 00:30:28,320 +الرسم + +301 +00:30:28,320 --> 00:30:30,120 +المقابل + +302 +00:30:34,990 --> 00:30:40,650 +the following limits + +303 +00:30:40,650 --> 00:30:44,790 +if + +304 +00:30:44,790 --> 00:30:53,370 +it exists، نعمل + +305 +00:30:53,370 --> 00:31:02,150 +واحد، بدي ال limit لما ال X بدي تروح لل واحد لل F + +306 +00:31:02,150 --> 00:31:12,980 +of X، نمر اتنين بدي limit ال F of X لما ال X بده + +307 +00:31:12,980 --> 00:31:21,240 +تروح للاتنين، نمر تلاتة بدنا limit لما ال X تروح لل + +308 +00:31:21,240 --> 00:31:31,690 +zero لل F of X، نمر اربعة بدنا limit لل F of X لما + +309 +00:31:31,690 --> 00:31:40,470 +ال X بدها تروح لسالب واحد، نمرا خمسة بدنا limit لل + +310 +00:31:40,470 --> 00:31:51,070 +F of X لما ال X بدها تروح لسالب اتنين، نمرا ستة + +311 +00:31:51,070 --> 00:32:00,350 +بدنا جدش ال domain للدالة F، نمر السابعة بدنا نقدرش + +312 +00:32:00,350 --> 00:32:10,210 +ال range لدى ال F، نرسم + +313 +00:32:10,210 --> 00:32:20,290 +الرسمة، هذا محور X، هذا Y، وهذا نقطة الأصل اللي عندنا + +314 +00:32:20,290 --> 00:32:34,310 +هاي واحد، هاي اتنين، هاي تلاتة، هاي أربعة، سالب واحد، + +315 +00:32:34,310 --> 00:32:44,790 +سالب اتنين، سالب تلاتة، واحد، اتنين، تلاتة، أربعة، + +316 +00:32:44,790 --> 00:32:53,570 +إلى آخره، سالب واحد، سالب اتنين، سالب تلاتة، سالب + +317 +00:32:53,570 --> 00:32:54,130 +أربعة + +318 +00:33:34,080 --> 00:33:36,700 +ماذا حصل؟ + +319 +00:34:15,140 --> 00:34:22,100 +الرسم اللي قدامي هذي من الرسم + +320 +00:34:22,100 --> 00:34:28,340 +المناظر أو الرسم المقابل، احسب لي + +321 +00:34:28,340 --> 00:34:36,450 +قداش، قل جداش limit لكل دالة عند كل نقطة مناظرة if it + +322 +00:34:36,450 --> 00:34:40,530 +exists إذا موجودة، بدنا نعرف جداش ال limit ماهيش + +323 +00:34:40,530 --> 00:34:43,730 +موجودة خلاص بتقري بلي it does not exist واتريحنا + +324 +00:34:43,730 --> 00:34:49,190 +من هذه الشغل، هذه من خلال الرسم، بدي أحاول أجيب عشان + +325 +00:34:49,190 --> 00:34:52,930 +أدير بالك فاتح معايا كويس كتير في الامتحان، الناس + +326 +00:34:52,930 --> 00:34:56,730 +في الأول بنجيب رسمة من هذا القبيل و بنطلب طلبات + +327 +00:34:56,730 --> 00:35:02,220 +مثل هذه الطلبات، ففتح هناك إيه كويس، الآن بيقول لي + +328 +00:35:02,220 --> 00:35:06,180 +بدي قداش limit ال F of X لما ال X بده تروح لوين؟ + +329 +00:35:06,180 --> 00:35:10,860 +للواحد، بدي ع الرسمة وين الواحد؟ هاي الواحد، روحت + +330 +00:35:10,860 --> 00:35:15,900 +يمين و الله شمالي، الدالة ومعرفة والقيمة موجودة و + +331 +00:35:15,900 --> 00:35:20,140 +النهاية موجودة، هذه نازلة للصفر وهذه طالعة لوين؟ + +332 +00:35:20,140 --> 00:35:26,210 +للصفر، إذا ال limit يساوي قداش؟ يساوي Zero، تمام، طيب + +333 +00:35:26,210 --> 00:35:31,390 +بدي آجي لل limit عند X يساوي اتنين، عند اتنين واحد + +334 +00:35:31,390 --> 00:35:37,490 +ولا اتنين، القيمة اتنين لكن ال limit هذه من هنا و + +335 +00:35:37,490 --> 00:35:42,530 +من هنا طالع لمين؟ للواحد، يبقى ال limit هذه تساوي + +336 +00:35:42,530 --> 00:35:47,530 +واحد، صحيح، دي البلك مش هتروح تكتب اتنين، اتنين قيمة + +337 +00:35:47,530 --> 00:35:52,110 +تتدلة وليست نهاية، تتدلة زي الرسم اللي كنا رسمينها + +338 +00:35:52,110 --> 00:35:57,070 +قبل شوية وكانت القيمة أربعة وال limit إيه؟ ستة، طيب + +339 +00:35:57,070 --> 00:36:00,650 +نمرة تلاتة بـdelimit الـ F of X لما الـ X بتروح + +340 +00:36:00,650 --> 00:36:05,990 +للـ Zero، عند الـ Zero هذه نازلة لسلب Infinity وهذه + +341 +00:36:05,990 --> 00:36:10,270 +طالعة لإيه؟ لإنفينيتي، يبقى هذه بقول عليها معنها + +342 +00:36:10,270 --> 00:36:20,070 +does not exist، هذه مش موجودة، طب بدنا نيجي عند + +343 +00:36:20,070 --> 00:36:25,190 +السالب واحد كدهش؟ + +344 +00:36:26,450 --> 00:36:31,470 +متاكدين؟ يعني لو جيت متحرك من اليمين و رايح على + +345 +00:36:31,470 --> 00:36:35,450 +الشمال Zero و جيت من الشمال رايحة limit لجه واحد + +346 +00:36:35,450 --> 00:36:40,570 +يبقى قفزت من Zero إلى واحد، يبقى limit كمان does + +347 +00:36:40,570 --> 00:36:49,630 +not exist، يبقى هذه كمان does not exist، طيب لو جيت + +348 +00:36:49,630 --> 00:36:54,810 +عند ال X بتروح ل سالب اتنين، يبقى ال limit إن جيت + +349 +00:36:54,810 --> 00:36:59,130 +من اليمين و جيت من الشمال كله نزل لقداش؟ ل zero + +350 +00:36:59,130 --> 00:37:03,510 +يبقى ال limit هذه بتساوي ال zero، طب بدي domain + +351 +00:37:03,510 --> 00:37:10,890 +الدالة F، سالب تلاتة إلى تلاتة، يعني الدالة هذه + +352 +00:37:10,890 --> 00:37:18,670 +معرفة كل الفترة هذه ما عدا Zero، عند Zero الدالة مش + +353 +00:37:18,670 --> 00:37:24,850 +معرفة، يبقى بجي بقول الدمين هذا يساوي اللي هو سالب + +354 +00:37:24,850 --> 00:37:32,610 +تلاتة لغاية Zero اتحاد Zero وتلاتة بشكل أو + +355 +00:37:44,660 --> 00:37:46,060 +-33333333333333333333333333333333333333333333 + +356 +00:37:48,980 --> 00:37:54,540 +تأخذ القيمة Zero ولا لا؟ تأخد الـ Zero، هي الدالة + +357 +00:37:54,540 --> 00:37:59,240 +ماخدة Zero هنا وماخدة Zero هنا وماخدة Zero هنا وماخدة + +358 +00:37:59,240 --> 00:38:03,360 +Zero هنا، اتنين، هذا القوس اللي هنا بيجيب لي + +359 +00:38:03,360 --> 00:38:07,000 +كل القيام السالبة، هذا القوس اللي طالع بيجيب كل + +360 +00:38:07,000 --> 00:38:10,940 +القيام الموجودة، والباقي من الملحقات بجمع المبكر + +361 +00:38:10,940 --> 00:38:17,160 +السالب كله من سالب infinity الى infinity، كل ال + +362 +00:38:17,160 --> 00:38:21,060 +number، الواحد الواحد الواحد، ر + +363 +00:38:42,840 --> 00:38:49,760 +طيب، أيوة، مين اللي بدأ يسأل؟ رقم اتنين؟ مالها؟ هي + +364 +00:38:49,760 --> 00:38:54,320 +ال X بتروح للإتنين، احنا ما نتكلمش على قيمة الدالة، + +365 +00:38:54,320 --> 00:38:57,600 +قيمة الدالة اتنين صحيحة، احنا موافقين، هي قيمة + +366 +00:38:57,600 --> 00:39:01,760 +الدالة، احنا ما نتكلم على مين؟ على ال limit، صح ولا + +367 +00:39:01,760 --> 00:39:06,960 +لأ؟ يبقى وين اتنين؟ هيها، كل ما تقترب من اتنين من + +368 +00:39:06,960 --> 00:39:12,150 +هنا، الدالة مقتربة من مين؟ من الواحد، إذا اقتربت + +369 +00:39:12,150 --> 00:39:18,390 +لاتنين من هنا بتلاقي الدالة مقتربة من مين؟ خلاص، طيب + +370 +00:39:18,390 --> 00:39:30,610 +ننتقل الآن الى some limits بعض النهايات some limits + +371 +00:39:30,610 --> + +401 +00:43:54,480 --> 00:44:01,260 +ثاني الثيتا وبشرط أن ثاني الثيتا ما تسويش ال zero + +402 +00:44:39,800 --> 00:44:46,540 +واضح أن عدة طرق لحساب النهايات المختلفة حتى الآن + +403 +00:44:46,540 --> 00:44:51,510 +لم نأخذ أي طريقة هذا المقصود بالـ sum limits بعض + +404 +00:44:51,510 --> 00:44:55,570 +النهايات اللي هو الطريقة الأولى في حساب النهايات + +405 +00:44:55,570 --> 00:45:00,510 +هي التعويض المباشر بحيث التعويض المباشر ما يجيبليش + +406 +00:45:00,510 --> 00:45:05,950 +zero على zero أو infinity على infinity أو zero أو + +407 +00:45:05,950 --> 00:45:11,350 +الأمور هذه يعني بها ال limit تبقى defined يعني + +408 +00:45:11,350 --> 00:45:17,510 +معرفة يبقى هذه تعويض مباشر زي مين؟ زي الخمس حالات + +409 +00:45:17,510 --> 00:45:22,260 +اللي قدامنا هذه بدا يجي للحالة الأولى for the + +410 +00:45:22,260 --> 00:45:26,620 +identity function لدالة الواحدة شو دالة الواحدة f of + +411 +00:45:26,620 --> 00:45:31,500 +x يساوي x يبقى لو بدي أخد limit لل f of x لما ال x + +412 +00:45:31,500 --> 00:45:37,160 +بتروح لأي قيمة x0 بدي أساوي limit ال x لما ال x + +413 +00:45:37,160 --> 00:45:41,820 +بتروح ل ال x0 يبقى تعويض مباشر اللي هو بدي اعطيني + +414 +00:45:41,820 --> 00:45:46,600 +main x node الآن for the constant function f of x + +415 +00:45:46,600 --> 00:45:51,360 +يساوي k لو بدي limit ال k لما ال x بدي يروح لل x + +416 +00:45:51,360 --> 00:45:56,380 +node هل المقدار الثابت يعتمد على تغير ال x إذا لا + +417 +00:45:56,380 --> 00:46:00,020 +يعتمد يبقى limit المقدار الثابت بالمقدار الثابت + +418 +00:46:00,020 --> 00:46:07,650 +itself يمكن جمع اتنين هدول بحالة واحدة لو عندي + +419 +00:46:07,650 --> 00:46:13,910 +linear function f of x يساوي x زائد k يبقى limit + +420 +00:46:13,910 --> 00:46:20,870 +تعويض مباشر يبقى بقوله x naught زائد k تمام بدل + +421 +00:46:20,870 --> 00:46:25,070 +ما هي linear لو بدي أعّمها أكثر من ذلك فاروح تقول + +422 +00:46:25,070 --> 00:46:30,230 +لو عندي polynomial كثيرة حدود و احنا بنعرف أن ال + +423 +00:46:30,230 --> 00:46:33,870 +polynomial اللي هدول ال a n و ال a n منصول ال a + +424 +00:46:33,870 --> 00:46:40,130 +one و ال a naught كلهم معاملات يعني أرقام لكن الأس + +425 +00:46:40,130 --> 00:46:46,310 +اللي عند الأسس كلها أرقام صحيحة موجبة تمام يبقى + +426 +00:46:46,310 --> 00:46:49,990 +هذه صارت مش linear لا ممكن من الدرجة الثانية + +427 +00:46:49,990 --> 00:46:53,590 +الدرجة الثالثة الدرجة الرابعة الدرجة العاشرة + +428 +00:46:53,590 --> 00:46:57,480 +الدرجة المائة قد ما تكون تكون يبقى لما بدي أحسب ال + +429 +00:46:57,480 --> 00:47:01,900 +limit لها برضه تعويض مباشر بشيل ال X و بحط مكانها + +430 +00:47:01,900 --> 00:47:06,980 +مين C بصير P of C يعني بدك تيجي على X هنا كل X و + +431 +00:47:06,980 --> 00:47:12,040 +تحط مكانها C و اجمع كل النتج اللي عندنا بصير H هذا + +432 +00:47:12,040 --> 00:47:17,240 +قيمة limit لل polynomial يبقى الثلاث هدول ممكن + +433 +00:47:17,650 --> 00:47:23,290 +أخذهم كلهم بمين؟ برقم ثلاثة لأن رقم ثلاثة احتوى + +434 +00:47:23,290 --> 00:47:26,890 +على الحالة الثانية واحتوى على مين؟ على الحالة + +435 +00:47:26,890 --> 00:47:30,990 +الأولى طيب الآن الحالة الرابعة بدي أخليها تعتمد + +436 +00:47:30,990 --> 00:47:34,430 +على الحالة الثالثة بيقول لو عندك rational function + +437 +00:47:34,430 --> 00:47:38,250 +و احنا سابقا عرفنا ال rational function قلنا هي + +438 +00:47:38,250 --> 00:47:43,260 +دالة بسط ومقام بهذا الـ bus polynomial والمقام + +439 +00:47:43,260 --> 00:47:48,520 +polynomial يبقى هنا بقول we have limit ال P of X + +440 +00:47:48,520 --> 00:47:53,140 +على ال Q of X لما ال X بدي روح إلى ال C يبقى ما + +441 +00:47:53,140 --> 00:47:58,540 +علي إلا أشيل كل X و أحط مكانها C بشرف أن المقام + +442 +00:47:58,540 --> 00:48:02,780 +هذا ماله ممنوع يستوي Zero حتى تكون هذه ال limit + +443 +00:48:02,780 --> 00:48:07,590 +مالها exist بالنسبة للـ trigonometric functions + +444 +00:48:07,590 --> 00:48:12,430 +الدوال المثلثية الستة يبقى لما بدا أخد مثلا sin x + +445 +00:48:12,430 --> 00:48:16,090 +لما ال x بدي أذهب إلى θ ماعليك إلا تشيل ال x و تحط + +446 +00:48:16,090 --> 00:48:20,990 +مكانها تتعويض مباشر كما في الحالات الأربع السابقة + +447 +00:48:20,990 --> 00:48:26,190 +لكل الدوال المثلثية الستة أو لو كان عندي ثمانية + +448 +00:48:26,190 --> 00:48:31,310 +ناقص cos x مثلا على تان ال x يبقى كذلك تعويض مباشر + +449 +00:48:31,310 --> 00:48:37,640 +بحيث أن المقام ما يسويش عندها Zero يبقى هادية قصده + +450 +00:48:37,640 --> 00:48:42,740 +من هذا الكلام أن الدوال المثلثية تعويض مباشرة إذا + +451 +00:48:42,740 --> 00:48:47,720 +قابلتني أي دالة من الدوال الخامس بروح بعوض تعويض + +452 +00:48:47,720 --> 00:48:53,900 +مباشرة طيب احنا الآن حتى الآن خلصنا النقطة الأولى + +453 +00:48:53,900 --> 00:48:59,160 +من هذا ال section اللي هي the concept of limit لكن + +454 +00:48:59,160 --> 00:49:04,080 +هل أخذنا limit loss لما أخذناش قوانين النهايات، + +455 +00:49:04,080 --> 00:49:06,460 +القوانين النهائية اللي بدنا نأخذها من الآن هي + +456 +00:49:06,460 --> 00:49:11,640 +القوانين اللي أخذتها في الثانوية العامة، هما هما لن + +457 +00:49:11,640 --> 00:49:16,580 +نغيّر فيهم حرفا واحدا يبقى بدنا نروح ونحط القوانين + +458 +00:49:16,580 --> 00:49:20,800 +كما أخذتهم دون برهان، في التنويه كلام البرهان من + +459 +00:49:20,800 --> 00:49:25,280 +القيامهم، مظبوط؟ أيه احنا بدنا إيش برهان؟ بدنا النص + +460 +00:49:25,280 --> 00:49:36,760 +العملي لهم يبقى هنا the limit logic قوانين + +461 +00:49:36,760 --> 00:49:41,680 +النهايات بجي + +462 +00:49:41,680 --> 00:49:54,680 +بقول F يبقى F ال L و ال M و ال C and ال K are real + +463 +00:49:54,680 --> 00:50:09,300 +numbers are real numbers and و كذلك limit لل F of + +464 +00:50:09,300 --> 00:50:18,390 +X لما ال X بده تروح الى C بده يساوي ال L and limit + +465 +00:50:18,390 --> 00:50:26,210 +لل G of X لما ال X بده يروح الى C بده يعطينا ال M + +466 +00:50:26,210 --> 00:50:34,630 +then بدنا نيجي للنقطة الأولى limit لما ال X بدي روح + +467 +00:50:34,630 --> 00:50:42,770 +إلى C لل F of X زائد أو ناقص G of X يبقى هذا + +468 +00:50:42,770 --> 00:50:51,890 +الكلام بدي أساوي ال L زائد أو ناقص M نمرة + +469 +00:50:51,890 --> 00:51:03,000 +اثنين بدي limit لأ لما ال X بدي روح الى C لـ K + +470 +00:51:03,000 --> 00:51:10,660 +مضروبة في الـ F of X يساوي K اللي هو المقدار + +471 +00:51:10,660 --> 00:51:17,240 +الثابت فاهمين؟ في limit ال F of X اللي هو L كما هي + +472 +00:51:17,240 --> 00:51:25,920 +نمرة ثلاثة عن طريق الـ Limit لما الـ X بدها تروح + +473 +00:51:25,920 --> 00:51:34,860 +إلى C لـ F of X في الـ G of X يبقى هذا الكلام + +474 +00:51:34,860 --> 00:51:42,990 +بيساوي الـ L في M نمر أربعة بدنا limit لما ال X بده + +475 +00:51:42,990 --> 00:51:53,950 +يروح ل C لل F of X على ال G of X بده يساوي L على M + +476 +00:51:53,950 --> 00:52:02,510 +وبشرط أن ال M ما لها ممنوعة تساوي Zero نمر خمسة + +477 +00:52:02,510 --> 00:52:12,770 +limit لما ال X بده تروح الى C لل F of X مرفوعة لل + +478 +00:52:12,770 --> 00:52:21,130 +أس N بده يساوي الأس N و ال N is a positive integer + +479 +00:52:33,040 --> 00:52:43,080 +نمرة ستة بدنا limit لما ال X بده يروح الى C للجذر + +480 +00:52:43,080 --> 00:52:52,960 +النوني لل F of X يساوي الجذر النوني ل L يساوي L أس + +481 +00:52:52,960 --> 00:53:02,400 +واحد على N و ال N is a positive integer + +482 +00:53:27,080 --> 00:53:28,600 +أنت جاي من هنا؟ + +483 +00:55:07,670 --> 00:55:13,430 +يجب أن نعود لقواعد النهايات أو قوانين النهايات + +484 +00:55:13,430 --> 00:55:20,590 +بقول لو أن ال و M و C و K أعداد حقيقية وفي نفس + +485 +00:55:20,590 --> 00:55:24,650 +الوقت روحت حسبت limit f of x لما ال X بيذهب ل C + +486 +00:55:24,650 --> 00:55:32,700 +لجهته L طبعا ال عدد حقيقي و كذلك limit g of x لما ال + +487 +00:55:32,700 --> 00:55:39,360 +x بيروح الى c سواء m و ال m عدد حقيقي then بيجي + +488 +00:55:39,360 --> 00:55:44,580 +نقطة الأولى limit لما ال x بيروح الى c لل f of x + +489 +00:55:44,580 --> 00:55:51,420 +زائد أو ناقص g of x بيقول يساوي ال L زائد أو ناقص M + +490 +00:55:51,420 --> 00:55:57,710 +كانت معاكم القاعدة في الثانوية العامة كتالة نهاية + +491 +00:55:57,710 --> 00:56:02,910 +المجموع الجبري لدالتين يساوي المجموع الجبري + +492 +00:56:02,910 --> 00:56:08,570 +للنهايتين يعني + +493 +00:56:08,570 --> 00:56:12,670 +إيش قصدوا بهذه العبارة؟ قصدوا أن لو كان عندي مجموع + +494 +00:56:12,670 --> 00:56:17,210 +دالتين ال limit هتخش على الدالة الأولى وكذلك تخش + +495 +00:56:17,210 --> 00:56:20,530 +على مين؟ على الدالة الثانية، يعني limit الدالة + +496 +00:56:20,530 --> 00:56:24,160 +الأولى زائد أو ناقص limit الدالة الثانية Limited + +497 +00:56:24,160 --> 00:56:27,820 +دالة الأولى بـ N Limited دالة الثانية بـ N يبقى زائد + +498 +00:56:27,820 --> 00:56:33,710 +و ناقص زائد يزاد و ناقص هي ناقص النقطة الثانية نهاية + +499 +00:56:33,710 --> 00:56:39,030 +مقدار ثابت في دالة يساوي المقدار الثابت مضروبا في + +500 +00:56:39,030 --> 00:56:43,930 +نهاية الدالة كان معاكم بهذا النص يبقى احنا روحنا + +501 +00:56:43,930 --> 00:56:47,170 +و قلنا نفس الكلام limit لما الاكس فو احنا سي اللي + +502 +00:56:47,170 --> 00:56:51,610 +هي K في F of X يساوي نهاية المقدار الثابت كنا + +503 +00:56:51,610 --> 00:56:56,290 +كاتبناها قبل قليل بالمقدار الثابت itself + +504 +00:57:03,740 --> 00:57:10,200 +نهاية المجموع الجبري لحاصل ضرب دالتين يساوي لحاصل + +505 +00:57:10,200 --> 00:57:16,110 +ضرب النهايتين يبقى نهاية حاصل ضرب دالتين يساوي حاصل + +506 +00:57:16,110 --> 00:57:20,510 +ضرب النهايتين يعني معنى هذا الكلام أن ال limit + +507 +00:57:20,510 --> 00:57:25,090 +هتخش على الدالة الأولى ضرب ال limit لمين للدالة + +508 +00:57:25,090 --> 00:57:30,050 +الثانية وبالتالي الفي أم الضرب مش أحسن من الجسم بس + +509 +00:57:30,050 --> 00:57:35,460 +الجسم ممكن تحط عليه condition زيادة نهاية خارج قسم + +510 +00:57:35,460 --> 00:57:41,180 +الدالتين تساوي خارج قسم النهايتين بالشرط أن نهاية + +511 +00:57:41,180 --> 00:57:44,580 +دالة المقام ممنوعة تساوي zero لأن النهاية بيصير + +512 +00:57:44,580 --> 00:57:46,580 +بهياش معرفة + +513 +00:57:55,020 --> 00:58:00,980 +حيث أن عدد صحيح موجب يعني القوس مرفوع للقوس مثلا + +514 +00:58:00,980 --> 00:58:08,020 +عشرين ال limit هذه very important person معها vip + +515 +00:58:08,020 --> 00:58:13,560 +كده بتسيب القوس و بتدخل على مين؟ على الدالة اللي جوا، + +516 +00:58:13,560 --> 00:58:16,540 +يعني لو دخلت على الدالة اللي جوا، ال limit اللي + +517 +00:58:16,540 --> 00:58:22,320 +هتجدها شالـ IUL و الـ N اللي فوق بضلت هي Main الـ N + +518 +00:58:22,320 --> 00:58:29,140 +اللي فوق بشرط أن عدد صحيح موجب لو كان سالب عدد صحيح + +519 +00:58:29,140 --> 00:58:35,340 +سالب يقصر واحد على نفس الدالة وطبق للقاعدة اللي + +520 +00:58:35,340 --> 00:58:39,240 +عندنا هذه limit الconstant بالconstant itself و + +521 +00:58:39,240 --> 00:58:42,620 +limit هذه بنجيبها من هنا و بندخل عليها بشرط ما + +522 +00:58:42,620 --> 00:58:48,080 +تسويش ال zero تمام؟ يبقى صارتك هنا حلقة خاصة منها + +523 +00:58:48,260 --> 00:58:55,480 +نجي لستة نهاية الجذر النوني يعني جذر تربيعي، جذر + +524 +00:58:55,480 --> 00:59:00,420 +تكعيبي، جذر رابعي، جذر خامس، إلى آخره برضه لا تزال + +525 +00:59:00,420 --> 00:59:04,820 +ال limit معها ال Vip زي ما دخلت داخل ال course + +526 +00:59:05,010 --> 00:59:10,310 +بتدخل تحت مين؟ تحت الجذر التربيعي والجذر التكعيبي + +527 +00:59:10,310 --> 00:59:15,150 +و كل الجذور ما عندها مشكلة فيها لأن لو دخلت صابت + +528 +00:59:15,150 --> 00:59:19,630 +الجذر و دخلت عليه فبصير limit ال F of X هو بجدهش ب + +529 +00:59:19,630 --> 00:59:25,810 +L بصير L تحت الجذر النوني أو L أس واحد على L حيث + +530 +00:59:25,810 --> 00:59:32,220 +أن هنا عدد صحيح موجب الكلام اللي قلته هذا بنوحه + +531 +00:59:32,220 --> 00:59:38,280 +أنطبقه عمليا مع مذاكرة ما سبق دراسته في الثانوية + +532 +00:59:38,280 --> 00:59:43,840 +على العام أول مثال بيقول يحسب لي limit لهذه الدالة + +533 +00:59:43,840 --> 00:59:48,880 +بقول له طبقا للكلام اللي احنا جايلينه هنا هذا + +534 +00:59:48,880 --> 00:59:54,400 +يعتبر الجذر الثالث صحيح ولا لا؟ إذا ال limit هتدخل + +535 +00:59:54,400 --> 01:00:00,280 +جوا، إذا طبقا لهذا الجذر الثالث يساوي هذا ال limit + +536 +01:00:00,280 --> 01:00:07,780 +لما ال X بدها تروح ل 0 لمين لخمسة X ناقص ثمانية + +537 +01:00:07,780 --> 01:00:16,130 +و هي كلها أسطل طبقا لمين لرقم ستة، بقوله كويس هذه + +538 +01:00:16,130 --> 01:00:21,610 +صارت معادلة خطية تمام توقف قبل شوية اقول المعادلة + +539 +01:00:21,610 --> 01:00:26,710 +الخطية بتروح تعوض تعويضا مباشرا يبقى هذه بدها + +540 +01:00:26,710 --> 01:00:36,620 +تساوي صفر ناقص ثمانية أس قداش الجذر الثالث يبقى + +541 +01:00:36,620 --> 01:00:40,700 +سالب اثنين يبقى سالب اثنين يبقى سالب اثنين يبقى + +542 +01:00:40,700 --> 01:00:40,780 +سالب اثنين يبقى سالب اثنين يبقى سالب اثنين يبقى + +543 +01:00:40,780 --> 01:00:44,220 +سالب اثنين يبقى سالب اثنين يبقى سالب اثنين يبقى + +544 +01:00:44,220 --> 01:00:49,620 +سالب اثنين يبقى سالب اثنين يبقى سالب اثنين يبقى + +545 +01:00:49,620 --> 01:00:51,640 +سالب اثنين يبقى سالب + +546 +01:00:54,720 --> 01:00:59,780 +نمر يا بي بيقول لي ال limit لما ال x بيروح لل + +547 +01:00:59,780 --> 01:01:08,600 +اثنين لمين؟ لل x تربيع ناقص سبعة x زائد عشرة على x + +548 +01:01:08,600 --> 01:01:17,290 +ناقص اثنين بقوله كويس ال X رايح على اثنين هل الدالة + +549 +01:01:17,290 --> 01:01:21,910 +هذه معرفة على الاثنين؟ معرفة ولا مش معرفة بهمليش + +550 +01:01:21,910 --> 01:01:26,710 +قيمة الدالة شيء و النهاية شيء آخر بقوله كويس تعالى + +551 +01:01:26,710 --> 01:01:31,970 +نجرب نحط هذه أو نعوض تعويض مباشر لو عوضنا تعويض + +552 +01:01:31,970 --> 01:01:37,410 +مباشر بصير البسط و المقام يبقى الدالةصلة غير + +553 +01:01:37,410 --> 01:01:43,550 +معرفة بهمنيش معرفة والله غير معرفة إذا مشان هيك + +554 +01:01:43,550 --> 01:01:49,390 +باجي بعمل ما يأتي بشوف هل البسط يمكن تحليله ولا لأ + +555 +01:01:49,390 --> 01:01:55,850 +بقول أه هاي جوز و هاي جوز ثاني و المقام زي ما هو X + +556 +01:01:55,850 --> 01:02:03,530 +ناقص اثنين يبقى هذه X هذه X هذه خمسة في اثنين يبقى + +557 +01:02:03,530 --> 01:02:11,490 +اثنين وهنا خمسة وهذا ناقص وهذا ناقص وهذا ناقص وهذا + +558 +01:02:11,490 --> 01:02:15,370 +ناقص + +559 +01:02:15,370 --> 01:02:16,750 +وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص + +560 +01:02:16,750 --> 01:02:16,790 +وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص + +561 +01:02:16,790 --> 01:02:17,790 +وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص + +562 +01:02:17,790 --> 01:02:17,970 +وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص + +563 +01:02:17,970 --> 01:02:20,670 +وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص وهذا ناقص + +564 +01:02:20,670 --> 01:02:28,480 +وهذا ناقص و على صفر إذا هذا ما هذا الله سهّل عليه + +565 +01:02:28,480 --> 01:02:34,020 +يبقى آلة المسألة إلى limit لما ال X بيروح للثنين + +566 +01:02:34,020 --> 01:02:40,240 +لل X ناقص خمسة صارت هذه دالة خطية من الدرجة الأولى + +567 +01:02:40,240 --> 01:02:43,980 +يعني polynomial من الدرجة الأولى يبقى تعويضا + +568 +01:02:43,980 --> 01:02:51,300 +مباشرا اثنين ناقص خمسة بيعطينا مين سالب ثلاثة بعد + +569 +01:02:51,300 --> 01:02:52,900 +المثال الثالث + +570 +01:02:55,270 --> 01:03:03,490 +المثال C بيقول لي بدي ال limit لما ال X بدها تروح + +571 +0 + +601 +01:06:02,550 --> 01:06:10,510 +يعترض عليك طيب نروح لمثال رقم D دي بيقول لي بيديه + +602 +01:06:10,510 --> 01:06:18,980 +limit لما الـ X بدها تروح للأربعة للـ 4 X ناقص X + +603 +01:06:18,980 --> 01:06:27,960 +تربيع على الـ 2 ناقص جذر الـ X اقتراح + +604 +01:06:27,960 --> 01:06:31,720 +واحد بسمعه بيقول نضرب في المرافق ونقول له كلامي + +605 +01:06:31,720 --> 01:06:38,440 +كويس واحد ثاني قال لي لا دي حل التحليل هدي الصح + +606 +01:06:38,440 --> 01:06:43,750 +وهدي الصح الاتنين are the same بقوله كويس هذه ال + +607 +01:06:43,750 --> 01:06:50,350 +limit لما ال X بدأت تروح للـ 4 هنا لو أخذت X عامل + +608 +01:06:50,350 --> 01:06:58,490 +مشترك بيظل عندي 4 ناقص X وهنا 2 ناقص جذر ال + +609 +01:06:58,490 --> 01:07:05,030 +X حتى الآن اختصارات ما فيش لكن الـ guess الأول هذا + +610 +01:07:05,030 --> 01:07:11,940 +بقدر أحلله كذلك فرق بين المربعين يبقى هذا الـ limit + +611 +01:07:11,940 --> 01:07:20,200 +لما الـ x بدها تروح للـ 4 للـ x في 2 ناقص جذر الـ x 2 + +612 +01:07:20,200 --> 01:07:28,360 +زائد جذر الـ x على الـ 2 ناقص جذر الـ x هذا الجسم مع + +613 +01:07:28,360 --> 01:07:34,740 +هذا يبقى آلة المسألة إلى limit لما الـ X بدها تروح + +614 +01:07:34,740 --> 01:07:45,410 +للـ 4 لمن؟ للـ X في 2 زائد جذر الـ X نقوله ماشي يبقى + +615 +01:07:45,410 --> 01:07:48,890 +تعالى نعوض طيب مباشرة ونشوف نجيب نتيجة ولا لا + +616 +01:07:48,890 --> 01:07:57,030 +يبقى لو الـ X راحت للـ 4 بيصير 4×2 زائد جذر الأربعة + +617 +01:07:57,030 --> 01:08:04,490 +جذر الأربعة اللي هو قداش بـ 2 4×4 16 يبقى قيمة الـ + +618 +01:08:04,490 --> 01:08:12,050 +limit يساوي 16 حتى الآن كلها أسئلة بسيطة ولم نأتي + +619 +01:08:12,050 --> 01:08:19,310 +بأي جديد فيها مجرد + +620 +01:08:19,310 --> 01:08:28,430 +تذكير ليس إلا طيب + +621 +01:08:28,430 --> 01:08:33,890 +السؤال اللي بعده نمرة إيه نمرة + +622 +01:08:33,890 --> 01:08:42,910 +إيه بيقول ليه بده الـ limit لما الـ X بدها تروح للـ 4 + +623 +01:08:42,910 --> 01:08:53,330 +كذلك لمن؟ للـ 4 ناقص الـ X على 5 ناقص الجذر التربيعي + +624 +01:08:53,330 --> 01:08:59,190 +لـ X تربيع زي التسعة كبرناها شوية أظن عن السؤال اللي + +625 +01:08:59,190 --> 01:09:05,750 +قبله طيب تعالى شوف يبقى لو عوضت عميد مباشر بطلع + +626 +01:09:05,750 --> 01:09:10,770 +قداش Zero على Zero إذا عوضتوا من حد ما تشوف الجذر + +627 +01:09:10,770 --> 01:09:14,950 +سواء إن الجذر في البسط والمقام تضرب في المرافق + +628 +01:09:14,950 --> 01:09:19,770 +إذا لو ضربنا في المرافق بدي يصير هذا الـ limit + +629 +01:09:26,890 --> 01:09:34,950 +على خمسة ناقص الجذر التربيعي لـ X تربيع زائد تسعة + +630 +01:09:34,950 --> 01:09:41,930 +ضربناها في خمسة زائد الجذر التربيعي لـ X تربيع زائد + +631 +01:09:41,930 --> 01:09:49,230 +تسعة على خمسة الجذر التربيعي لـ X تربيع زائد تسعة + +632 +01:09:49,230 --> 01:09:54,150 +بالشكل اللي عندنا هذا يبقى هذه بدها تساوي limit + +633 +01:09:54,150 --> 01:10:00,700 +لما الـ X بدها تروح للـ 4 البسط 4 ناقص X كما + +634 +01:10:00,700 --> 01:10:06,920 +هو وهنا خمسة زائد الجذر التربيعي إلى X تربيع زائد + +635 +01:10:06,920 --> 01:10:15,110 +تسعة على هذا بالنسبة للـ 4 يصبح 25 ناقص X + +636 +01:10:15,110 --> 01:10:20,330 +تربيع زائد تسعة فرق بين المربعين رجعته إلى أصله + +637 +01:10:20,330 --> 01:10:26,410 +مربع الأول ناقص مربع الثاني يبقى هذا الكلام بده + +638 +01:10:26,410 --> 01:10:32,410 +يساوي الـ limit لما الـ X بدها تروح للـ 4 للـ 4 + +639 +01:10:32,410 --> 01:10:38,990 +ناقص X خمسة زائد الجذر التربيعي إلى X تربيع زائد + +640 +01:10:38,990 --> 01:10:46,120 +تسعة كله مقسومًا على هذه ناقص X تربيع وناقص تسعة + +641 +01:10:46,120 --> 01:10:53,100 +ناقص تسعة وزاد 25 بيصير 16 ناقص X + +642 +01:10:53,100 --> 01:10:59,740 +تربيع برضه هذه بقدر أحللها مقام كفرق بين المربعين + +643 +01:11:00,040 --> 01:11:07,080 +يبقى limit لما الـ X بدها تقول للـ 4 للـ 4 + +644 +01:11:07,080 --> 01:11:14,460 +ناقص X في خمسة زائد الجذر التربيعي X تربيع زائد التسعة + +645 +01:11:14,460 --> 01:11:22,960 +4 ناقص X 4 زائد X نختصر يبقى أولًا في المسألة + +646 +01:11:22,960 --> 01:11:30,180 +limit لما الـ X بدّه يروح للـ 4 للخمسة زائد الجذر + +647 +01:11:30,180 --> 01:11:37,840 +التربيعي لـ X تربيع زائد 9 على 4 زائد X الساوي لأ لو + +648 +01:11:37,840 --> 01:11:45,700 +عوضنا X بـ 4 بصير 16 و9 و25 تحت الجذر بصير 5 زائد + +649 +01:11:45,700 --> 01:11:56,300 +5 على 4 زائد 4 يعني 10 على 8 يعني 5 على + +650 +01:11:56,300 --> 01:12:01,880 +4 قيمة النهاية يعني هذه مش سهلة روحنا ضربنا في + +651 +01:12:01,880 --> 01:12:08,220 +المرافق وبعد المرافق اختصرنا بعد ما حللنا كذلك فرق + +652 +01:12:08,220 --> 01:12:13,540 +بين المرافق يعني بيجي عمليتين في آن واحد طب أنت + +653 +01:12:13,540 --> 01:12:22,530 +قلت الكل شوية و ليش ما يجيش ممنوع؟ طيب نمرة A نمرة F + +654 +01:12:22,530 --> 01:12:32,830 +بدنا limit لما الـ X بده يروح لـ 0 لتان الـ X ناقص + +655 +01:12:32,830 --> 01:12:42,250 +sign الـ X كله على sign تكعيب الـ X هذا + +656 +01:12:42,250 --> 01:12:51,830 +سؤالي شوية بدنا نتجل الكلام عوض عوض مباشر Zero على + +657 +01:12:51,830 --> 01:13:01,530 +Zero شو نسوي شغل مخك يبقى وزعنا + +658 +01:13:01,530 --> 01:13:08,090 +بيصير عندي واحد على sin تربيع في cosine تربيع + +659 +01:13:08,090 --> 01:13:14,000 +الأول والتربيع الثاني واحد على sin تربيع لا يزال واحد + +660 +01:13:14,000 --> 01:13:17,680 +على صفر بماء لنهاية وواحد على صفر بماء لنهاية ناقص + +661 +01:13:17,680 --> 01:13:25,820 +ماء لنهاية الله أعلم طيب + +662 +01:13:25,820 --> 01:13:30,280 +ماشي بعدين أو كل الأقالي يعني اللي جالك وزع نفس + +663 +01:13:30,280 --> 01:13:31,540 +الجثة + +664 +01:13:38,570 --> 01:13:43,670 +يبقى نجرب هل اقتراح حد ونشوف نوصل لنتيجة ولا لأ + +665 +01:13:43,670 --> 01:13:49,970 +يبقى بيجي يقولي هذا الـ limit لما الـ X تروح لـ + +666 +01:13:49,970 --> 01:13:55,420 +zero فاتح معايا كويس والله بدي أكتب الـ tan بدلالة الـ + +667 +01:13:55,420 --> 01:14:00,120 +sign و الـ cosine وبالتالي حولت المسألة كلها بدلالة + +668 +01:14:00,120 --> 01:14:07,720 +sign و cosine يبقى هذه الـ sign الـ x على cosine الـ + +669 +01:14:07,720 --> 01:14:15,220 +x ناقص sign الـ x وكله مقسومًا على sign تكعيب الـ x + +670 +01:14:16,380 --> 01:14:23,560 +طبعًا هذا الكلام يساوي لو جيت وحدت المقامات كله على + +671 +01:14:23,560 --> 01:14:26,200 +مين؟ على cosine + +672 +01:14:47,030 --> 01:14:53,930 +خذ الـ cosine عامل مشترك موافقين يبقى هاي الـ limit لما + +673 +01:14:53,930 --> 01:15:00,770 +الـ X بدّه يروح لـ zero لـ cosine الـ X واحد ناقص cosine الـ + +674 +01:15:00,770 --> 01:15:10,030 +X على cosine الـ X في cosine تكعيب الـ X في اختصار مش + +675 +01:15:10,030 --> 01:15:15,440 +هيك؟ يبقى هذا الكلام بده يساوي الـ limit لما الـ x + +676 +01:15:15,440 --> 01:15:21,840 +بده يروح لـ zero لواحد ناقص cosine الـ x على cosine + +677 +01:15:21,840 --> 01:15:33,190 +الـ x في sin تربيع الـ x هنجرب cosine صفر + +678 +01:15:33,190 --> 01:15:40,990 +بواحد ناقص واحد بصفر cosine صفر بواحد في الصفر بصفر + +679 +01:15:40,990 --> 01:15:47,790 +لا تزال Zero على Zero ولا مرافق ولا هجيب للمرافق بس + +680 +01:15:47,790 --> 01:15:52,150 +فابتهك و assign تربيع بحاول أبني الـ cosine + +681 +01:15:52,150 --> 01:15:57,550 +تربيع وأبتدى أن حلّت المشكلة تمام يبقى الاقتراح + +682 +01:15:57,550 --> 01:16:05,130 +كتالي ويساوي limit لما الـ x بدها تروح لـ zero لواحد + +683 +01:16:05,130 --> 01:16:12,940 +ناقص cosine الـ x كما هي في cosine الـ x cosine تربيع + +684 +01:16:12,940 --> 01:16:21,140 +لواحد ناقص cosine تربيع الـ X المقام فرق بين المربعين + +685 +01:16:21,610 --> 01:16:29,310 +ويساوي limit لما الـ X بده تروح للـ zero واحد ناقص + +686 +01:16:29,310 --> 01:16:36,650 +cosine الـ X cosine الـ X واحد ناقص cosine الـ X واحد + +687 +01:16:36,650 --> 01:16:43,290 +زائد cosine الـ X هذا مع هذا يبقى النتيجة قالت إلى + +688 +01:16:43,290 --> 01:16:48,770 +الـ limit لما الـ X بدها تروح للـ zero للـ واحد على + +689 +01:16:48,770 --> 01:16:49,930 +cosine + +690 +01:16:56,880 --> 01:17:04,740 +نرجع طاولة مباشرة يبقى هاي واحد على cosine صفر بواحد + +691 +01:17:04,740 --> 01:17:11,620 +في واحد زائد واحد ويساوي قداش نصف يبقى الـ limit ده + +692 +01:17:11,620 --> 01:17:16,180 +الداّلي هادي يساوي إن وصلت من حد ما تشوف حساب + +693 +01:17:16,180 --> 01:17:20,940 +المثلثات بيبقى النوب دي يرفع لكن امشي بتوصل + +694 +01:17:20,940 --> 01:17:22,460 +بسهولة + +695 +01:17:42,980 --> 01:17:48,940 +طيب لازلنا في نفس الـ limits وخد هذا المثال بيختلف عن + +696 +01:17:48,940 --> 01:17:55,600 +هدول بدي أشوف شو وجد نظرك فيه إيه أقول اللي + +697 +01:17:55,600 --> 01:18:01,880 +إيه؟ لحد هنا تمام؟ شيل الـ cosine تربيع حق بدلها واحد + +698 +01:18:01,880 --> 01:18:07,340 +ناقص cosine تربيع أو المتطابقة المثلثية ما الخلاص؟ + +699 +01:18:07,340 --> 01:18:12,720 +فرق بالمربعين خلصنا إيه يا عزيزي سؤال ثاني؟ اسأل + +700 +01:18:12,720 --> 01:18:16,260 +قل + +701 +01:18:16,260 --> 01:18:24,600 +يعني سؤال سؤال بعد المحاضرة سأليه بدكية طبعًا؟ + +702 +01:18:24,600 --> 01:18:34,480 +طيب الآن نصل إلى مثال آخر يختلف نوعيًا عن هدول + +703 +01:18:34,480 --> 01:18:43,210 +وهو أحد أسئلة الكتاب بيقول Flimit إذا كانت نهاية + +704 +01:18:43,210 --> 01:18:50,530 +لما الـ X بده يروح للـ 2 للـ F of X ناقص خمسة + +705 +01:18:50,530 --> 01:19:02,350 +على X ناقص 2 يساوي 3 Fine وجدنا limit الـ + +706 +01:19:02,350 --> 01:19:07,250 +F of X لما الـ X بدها تروح للـ 2 + +707 +01:19:11,090 --> 01:19:16,450 +يلا فاكر في السؤال كويس وبدي أبدأ أسمع مقترحات + +708 +01:19:16,450 --> 01:19:34,910 +منكم لكيفية الحل يلا + +709 +01:19:34,910 --> 01:19:39,690 +مين بدي أفكر أنا في الموضوع أنا بدي أحكي + +710 +01:19:45,080 --> 01:19:50,420 +بس تصبر يا عزيزي نمشي مع اقتراحك اللي هو نشوفه صح + +711 +01:19:50,420 --> 01:19:55,440 +ولا خطأ يبقى هذا حسب مفهوم الـ limit limit الـ bus + +712 +01:19:55,440 --> 01:20:00,460 +على limit المقار 100% كانها حياة رياضية صحية limit + +713 +01:20:00,460 --> 01:20:05,880 +الـ 5 limit الـ dollar ناقص limit الـ 5 صح limit + +714 +01:20:05,880 --> 01:20:13,030 +هذه بقداش ممنوع مش هيك شرطنا يبقى هذه التقسيمة + +715 +01:20:13,030 --> 01:20:19,930 +أصحابها بنوقف إيه بقول؟ بقول اه ضرب مقص هو أنا + +716 +01:20:19,930 --> 01:20:24,490 +عندي هنا يا راجل هذه قيمة وهذه limit كيف مقص + +717 +01:20:24,490 --> 01:20:28,530 +ولا مش طلب تيجي لمقصه؟ يعني بقى تقول الـ limit + +718 +01:20:28,530 --> 01:20:33,970 +هادي على الـ limit هادي وتضرب هكذا كتابة تظهر في X + +719 +01:20:33,970 --> 01:20:37,670 +ناقص 2 أو اتنين؟ هذا لسه داخل الـ limit + +720 +01:20:48,420 --> 01:20:53,040 +من اللي وراك فجأت المقام بيبقى إنه بيساوي صفر والـ + +721 +01:20:53,040 --> 01:20:56,800 +... اه المقام بيساوي صفر وعندنا قيمة للنهاية إذا + +722 +01:20:56,800 --> 01:21:00,260 +نزل بس تكون صفر عشان تطلع صفر على صفر قيمة غير معينة + +723 +01:21:00,260 --> 01:21:03,860 +ونخسر صفر مع الصفر تطلع 3 إذا Fx بيساوي + +724 +01:21:03,860 --> 01:21:08,780 +5 يا راجل خليك تم الكلام وبعدين ما .. Fx نخس + +725 +01:21:08,780 --> 01:21:13,530 +5 .. هو بيحكي كلام ربما يكون صحيح عيد ثاني من + +726 +01:21:13,530 --> 01:21:16,290 +أول اجازة حتى اللي كان برفع إيده اسمه عشان تقوله + +727 +01:21:16,290 --> 01:21:20,070 +وفكر وإيش في الكلام اللي بيقوله ثاني اقتب هي الـ + +728 +01:21:20,070 --> 01:21:23,790 +limit بالساعة و5 الـ limit تساوي 3 5 + +729 +01:21:23,790 --> 01:21:28,930 +5 الـ Fx في حالة بالساعة و5 شرطنا ما هو مقام + +730 +01:21:28,930 --> 01:21:32,010 +عندك صفر إذا لازم بس تكون صفر عشان تطلع عندك 3 + +731 +01:21:32,010 --> 01:21:35,790 +هذا سنتاج فلسفة أنا بدي شغل رياضي وبعد ما هي 5 + +732 +01:21:35,790 --> 01:21:40,610 +أصلًا أنا بقول بما أنك كذا إذا لا هذا شغل فلسفة اه + +733 +01:21:50,690 --> 01:21:55,470 +تفكيري كويس تفكيري كويس بيقول يا زميلكم كلامه + +734 +01:21:55,470 --> 01:21:59,650 +صحيح بيقول بدي أنا هذا هو المطلوب بدي أمسك في + +735 +01:21:59,650 --> 01:22:05,350 +المطلوب لغاية ما أخلق في هذا المطلوب المعطى هذا + +736 +01:22:05,350 --> 01:22:09,610 +وبعدين الله بيفرجها مش هاي قصدك؟ تمام يبقى يا + +737 +01:22:09,610 --> 01:22:12,670 +أهل مني امشي على تفكير ونشوف لو أنا نوصل يبقى + +738 +01:22:12,670 --> 01:22:13,210 +solution + +739 +01:22:17,640 --> 01:22:21,220 +تفتح معايا كويس في عندك 4 مسائل في الكتاب + +740 +01:22:21,220 --> 01:22:25,400 +منها الموديل هذا واحد منهم كله بنفس التفكير + +741 +01:22:25,400 --> 01:22:31,260 +الآن أنا بدي الـ limit لما الـ X بدي أروح للـ 2 للـ + +742 +01:22:31,260 --> 01:22:36,560 +F of X هذا هو المطلوب عندي معطيات تقولي تبادل + +743 +01:22:36,560 --> 01:22:42,230 +تقولي طرفين وسطين كله غلط هذا الكلام الآن أنا + +744 +01:22:42,230 --> 01:22:47,210 +مشان أخلق هذا الـ term هنا بدي أضيف رقمه وأطرح هذا + +745 +01:22:47,210 --> 01:22:52,570 +الرقم بقول له اه يبقى بدي أجي أقوله هذا الـ limit لما + +746 +01:22:52,570 --> 01:23:00,590 +الـ x بدها تروح للـ 2 للـ f of x ناقص 5 زائد 5 + +747 +01:23:01,280 --> 01:23:04,860 +الكلام صحيح 100% يبقى أنا أضفت للدالة + +748 +01:23:04,860 --> 01:23:09,920 +كمية صفر ولا عادي أنا ما سويتش ولا عادي أنا ما عملتش + +749 +01:23:09,920 --> 01:23:16,720 +شيء كلام مصبوط طيب هذا الكلام يساوي limit لما الـ X + +750 +01:23:16,720 --> 01:23:21,900 +بدي أروح للـ 2 لمين؟ بدي أجي للـ term اللي عندي + +751 +01:23:21,900 --> 01:23:25,780 +أو بدي أوزع الـ limit لهذه في الأول يبقى هذا الـ + +752 +01:23:25,780 --> 01:23:34,620 +limit الـ F of X ناقص 5 زائد limit الـ 5 لما الـ + +753 +01:23:34,620 --> 01:23:39,240 +X بدي أروح للـ 2 حسب قواعد النهاية السليمة وزعت + +754 +01:23:39,240 --> 01:23:46,540 +limit الـ two terms بدي أخلق هذه في السؤال اللي عندنا + +755 +01:23:46,940 --> 01:23:52,260 +بأجي بقول لك كويس هذه الـ limit لما الـ X بدها تروح للـ + +756 +01:23:52,260 --> 01:23:57,640 +2 للـ F of X ناقص 5 مش أنا أخلق هذا المقدار + +757 +01:23:57,640 --> 01:24:02,080 +بدي X ناقص 2 في المقام إذا بضرب فيها وبقسم + +758 +01:24:02,080 --> 01:24:10,060 +عليها يبقى صار هذا X ناقص 2 وهنا هذا كله بدي + +759 +01:24:10,060 --> 01:24:14,980 +أضرب في X ناقص 2 قداش نهاية المقدار الثابت + +760 +01:24:15,310 --> 01:24:20,150 +بالمقدار الثابت Excel يبقى هذه حسبناها بل مشكلتنا + +761 +01:24:20,150 --> 01:24:26,130 +مع من؟ مع هذه هذه بدي أجزئها لجزئين بدي أخذ هذه + +762 +01:24:26,130 --> 01:24:31,230 +function لحالها وهذه function لحالها وأوزع عليهم + +763 +01:24:31,230 --> 01:24:39,500 +الـ limit هذا الكلام يساوي limit لما الـ X بدّه يروح + +764 +01:24:39,500 --> 01:24:46,500 +للـ 2 للـ F of X ناقص 5 على X ناقص 2 في + +765 +01:24:46,500 --> 01:24:51,740 +limit لما الـ X بدّه يروح للـ 2 للـ X ناقص 2 + +766 +01:24:51,740 --> 01:24:54,020 + +801 +01:29:51,200 --> 01:29:56,800 +أقل من مين من التالتة بيقولي except possibly + +802 +01:29:56,800 --> 01:30:03,620 +that X وسوى C itself يعني ما عدا عند X وسوى C + +803 +01:30:03,620 --> 01:30:09,180 +itself إيش يعني ما عدا يعني ممكن الدالة هذه + +804 +01:30:09,180 --> 01:30:14,340 +ماتفجهاش معرفة عند X يساوي C في مشكلة؟ ماعديش + +805 +01:30:14,340 --> 01:30:18,820 +مشكلة لأنه أنا بدور على limit والـ limit لا تعتمد + +806 +01:30:18,820 --> 01:30:23,160 +هل الدالة عند هذه النقطة معرفة أو غير معرفة إذا + +807 +01:30:23,160 --> 01:30:27,580 +معرفة كان بها مش معرفة برضه كان بها ومن هنا أقول + +808 +01:30:27,580 --> 01:30:32,800 +لك except possibly يعني ممكن عند X يساوي C بعض + +809 +01:30:32,800 --> 01:30:38,490 +الدول هدول ماتفجهاش معرفة تمام؟ وبالتالي لا يقدح في + +810 +01:30:38,490 --> 01:30:44,170 +نتيجة الـ limit بيقول إن كان الأمر كذلك رحت حسبت + +811 +01:30:44,170 --> 01:30:49,290 +limit الدالة الأولى اللي هي الصغر فيهما و limit + +812 +01:30:49,290 --> 01:30:54,970 +الدالة الكبرى الكبرى فيهما ولقيت اتنين are equal + +813 +01:30:55,670 --> 01:30:59,730 +إن حدث ذلك يبقى limit الدالة اللي في الـ مُص بدها + +814 +01:30:59,730 --> 01:31:06,270 +تساوي مين؟ بدها تساوي نفس القيمة تمام؟ أيوة يبقى + +815 +01:31:06,270 --> 01:31:10,250 +إذا limit الدالة الأولى تساوي limit الدالة الأخيرة + +816 +01:31:10,250 --> 01:31:13,350 +إذا limit الدالة اللي في الـ مُص بدها تساوي نفس + +817 +01:31:13,350 --> 01:31:19,050 +القيمة تبعت الدالتين طب هيسأل واحد سؤال ويقول طب + +818 +01:31:19,050 --> 01:31:24,490 +احنا واجتيش بنستخدم sandwich theorem مقولك والله + +819 +01:31:24,490 --> 01:31:29,550 +إذا جربت تعويض مباشر وما قدرتش إذا روحت حللت + +820 +01:31:29,550 --> 01:31:34,630 +وما قدرتش أو مافيش عندك تحليل في المثلة ما قدرتش + +821 +01:31:34,630 --> 01:31:39,370 +أضرب في مرافق لإن ماعنديش جدور اتعجدت كل الطرق + +822 +01:31:39,370 --> 01:31:44,730 +اللي اتعلمناها في حساب هذه الـ limit بنلجأ لمين + +823 +01:31:44,730 --> 01:31:50,370 +لساند واشتغل أو إذا كانت نتيجة التعويض مش شغل غير + +824 +01:31:50,370 --> 01:31:55,180 +معينة أنا بعرفاش ممكن نلجأ لسان ونشير له نقول له طيب + +825 +01:31:55,180 --> 01:31:59,460 +كويس تعالى نشوف الدالة اللي عندنا دي لو بدي أعوض + +826 +01:31:59,460 --> 01:32:04,160 +تعويض مباشر ليش؟ لإن الدالة الأولى polynomial من + +827 +01:32:04,160 --> 01:32:09,280 +الدرجة الثانية تعويض مباشر هذه الـ sign تعويض مباشر + +828 +01:32:09,280 --> 01:32:15,300 +زي ما قلنا طيب أعوض واحد على الصفر غير معروف قول + +829 +01:32:15,300 --> 01:32:20,580 +infinity sign infinity بعرفها؟ بعرفاش هذه موجة طالع + +830 +01:32:20,580 --> 01:32:24,740 +عنها وأين بتنتهي أنا بعرفش إذا هذه بقدرش أحددها + +831 +01:32:24,740 --> 01:32:30,540 +لكن هذه بيصير Zero في Infinity كمية غير معينة + +832 +01:32:30,540 --> 01:32:34,660 +الكميات الغير معينة صفر في Infinity واحد قصر + +833 +01:32:34,660 --> 01:32:39,000 +Infinity Infinity سالب Infinity Zero على Zero + +834 +01:32:39,000 --> 01:32:43,330 +Infinity على Zero كل هذه قيم غير معينة بعرفاش بقدرش + +835 +01:32:43,330 --> 01:32:47,570 +أحضره نتيجة إذا التعويض المباشر بيعطيني الـ zero في + +836 +01:32:47,570 --> 01:32:53,190 +infinity بعرفاش يبقى ورطنا طب تعالي نحلل نحلل إيش + +837 +01:32:53,190 --> 01:32:57,290 +وفي تحليل مافيش فيها تحليل هذه طيب بنسوي ما انتش + +838 +01:32:57,290 --> 01:33:01,850 +عارفين نتحرك نتململ بقول طب بس فكر بطريقة أخرى + +839 +01:33:01,850 --> 01:33:07,450 +احنا رسمنا منحنى الـ sign قبل ذلك وقلنا مهما تكون + +840 +01:33:07,450 --> 01:33:11,830 +الزاوية كبيرة صغيرة مجمعة في السرير مش عارف ايه + +841 +01:33:11,830 --> 01:33:15,890 +قداش أكبر قيمة بياخدوا الـ sign واحد وأقل قيمة + +842 +01:33:15,890 --> 01:33:21,410 +يبقى هذه الـ sign كل اللي بقدر أقوله في الهامش sign + +843 +01:33:21,410 --> 01:33:27,290 +واحد أقل من أو يساوي واحد وأكبر من أو يساوي + +844 +01:33:27,290 --> 01:33:33,840 +واحد قاعدة رياضية سليمة مئة بالمئة الـ X تربيع الـ + +845 +01:33:33,840 --> 01:33:38,180 +X تذهب إلى الـ Zero يبقى X لا يمكن أن يساوي Zero + +846 +01:33:38,180 --> 01:33:41,700 +لأنه يمكن أن يتدالى عند Zero غير معرفة وأنا + +847 +01:33:41,700 --> 01:33:49,400 +اكتشفنا أن Zero غير معرفة يبقى بقى يقول F X لا + +848 +01:33:49,400 --> 01:33:55,760 +تساوي Zero إذا الـ X تربيع اللي عندي هذه قيمة موجبة + +849 +01:33:58,860 --> 01:34:02,520 +القيمة الموجبة لو ضربتها في الـ equality تتغير الـ + +850 +01:34:02,520 --> 01:34:07,700 +equality؟ لأ يبقى بدي أروح أضرب هذه في X تربيع إذا + +851 +01:34:07,700 --> 01:34:12,940 +لو ضربتها في X تربيع بيصير سالم X تربيع أقل من أو + +852 +01:34:12,940 --> 01:34:21,040 +يساوي X تربيع في sin 1 على X أقل من أو يساوي من X + +853 +01:34:21,040 --> 01:34:26,450 +تربيع هيخرجت من؟ في الـ Inquality المسألة اللي عندي + +854 +01:34:26,450 --> 01:34:33,020 +تمام؟ بتروح آخذ الـ limit للثلاثة أطراف فبدأ آخذ الـ + +855 +01:34:33,020 --> 01:34:40,600 +limit لـ -x تربيع لما الـ x بدها تروح للـ 0 أقل من أو + +856 +01:34:40,600 --> 01:34:45,580 +يساوي الـ limit لما الـ x بدها تروح للـ 0 للـ x تربيع + +857 +01:34:45,580 --> 01:34:50,560 +في الـ sign 1 على x أقل من أو يساوي الـ limit لما الـ + +858 +01:34:50,560 --> 01:34:56,640 +x بدها تروح للـ 0 لمام للـ x تربيع بروح نعوض تعويض + +859 +01:34:56,640 --> 01:35:02,260 +مباشر ليش؟ لأن هذه polynomial يبقى الـ سالب zero + +860 +01:35:02,260 --> 01:35:09,780 +zero هاي zero أقل من أو يساوي هذه اللي بديها X بده + +861 +01:35:09,780 --> 01:35:15,280 +تروح للـ zero للـ X تربيع في الـ sign واحد على X أقل + +862 +01:35:15,280 --> 01:35:22,370 +من أو يساوي zero يبقى صارت طرف الشمال يساوي مين الطرف + +863 +01:35:22,370 --> 01:35:27,750 +اليمين يبقى اللي في النص يساوي طبقا لـ Sandwich + +864 +01:35:27,750 --> 01:35:33,650 +theorem يبقى بين أنا عليه بروح بقوله buy sandwich + +865 +01:35:33,650 --> 01:35:41,260 +theorem اللي هو الـ limit لما الـ X بدها تروح للـ zero + +866 +01:35:41,260 --> 01:35:46,780 +للـ X تربيع الـ sine واحد على X بتساوي قد إيه؟ هي zero + +867 +01:35:46,780 --> 01:35:50,020 +لإن الأولى بـ zero والأخيرة الـ limit اللي لها مين + +868 +01:35:50,020 --> 01:35:55,660 +بـ zero طب بدي أعطيك كمان مثال زيّه بس فني أكثر شوية + +869 +01:35:55,660 --> 01:36:02,160 +كمان يبقى نمرة اثنين نمرة اثنين بيقول لي ما يأتي + +870 +01:36:02,160 --> 01:36:10,640 +given إذا أعطيته given absolute value للـ G of X + +871 +01:36:10,640 --> 01:36:20,480 +ناقص الأربعة أقل من أو يساوي خمسة في X ناقص اثنين + +872 +01:36:20,480 --> 01:36:31,650 +لكل تربيع for all x لجميع قيم x find limit لما الـ x + +873 +01:36:31,650 --> 01:36:37,070 +بدها تروح للاثنين للـ g of x + +874 +01:37:01,250 --> 01:37:07,050 +طبعا مادام absolute value يبقى أول تفكير يطرق على + +875 +01:37:07,050 --> 01:37:11,480 +ذهني أن أتخلص من الـ absolute حتى أقدر أحسب الـ limit + +876 +01:37:11,480 --> 01:37:15,640 +مظبوط ولا لا يبقى برجع على خواص الـ absolute value + +877 +01:37:15,640 --> 01:37:19,400 +هذه عمرها ما هتكون قيمة سالبة ودايما أنا أبدأ + +878 +01:37:19,400 --> 01:37:24,360 +القيمة موجبة وقد تكون صفر ماعندنا مشكلة طب كويس إذا + +879 +01:37:24,360 --> 01:37:28,860 +بناء أنا عليه بدي أكتب هذه بصيغة أخرى فلما أكتبها + +880 +01:37:28,860 --> 01:37:35,010 +بصيغة أخرى بيصير g of x ناقص أربعة أقل من أو يساوي + +881 +01:37:35,010 --> 01:37:40,050 +خمسة في X ناقص اثنين لكل تربيع أكبر من أو يساوي + +882 +01:37:40,050 --> 01:37:47,420 +سالب خمسة في X ناقص اثنين لكل تربيع أنا بدي limit + +883 +01:37:47,420 --> 01:37:52,380 +للـ G يبقى الأربعة بديش إياها فبروح بضيف أربعة + +884 +01:37:52,380 --> 01:37:57,400 +لثلاثة أطراف يبقى لو ضفت أربعة بيصير عندي أربعة + +885 +01:37:57,400 --> 01:38:03,780 +ناقص خمسة في X ناقص اثنين لكل تربيع أقل من أو يساوي + +886 +01:38:03,780 --> 01:38:09,160 +G of X أقل من أو يساوي أربعة زائد خمسة في X ناقص + +887 +01:38:09,160 --> 01:38:15,130 +اثنين لكل تربيع هي خلّي الجيل L حالها إذا بقدر آخذ + +888 +01:38:15,130 --> 01:38:20,070 +الـ limit لمن؟ لثلاثة أطراف يبقى باجي بقول limit + +889 +01:38:20,070 --> 01:38:25,650 +لما الـ X بدها تروح للـ اثنين للـ أربعة ناقص خمسة في + +890 +01:38:25,650 --> 01:38:31,650 +X ناقص اثنين لكل تاربية أقل من أو يساوي limit لما + +891 +01:38:31,650 --> 01:38:37,210 +الـ X بدها تروح للـ اثنين للـ G of X أقل من أو يساوي + +892 +01:38:37,210 --> 01:38:42,580 +limit لما الـ X بدها تروح للـ اثنين للـ أربعة زائد خمسة + +893 +01:38:42,580 --> 01:38:49,100 +في X ناقص اثنين لكل تاربيع هذه الآن polynomial من + +894 +01:38:49,100 --> 01:38:54,740 +الدرجة الثانية تتعويض مباشرة بجي بقول نهاية + +895 +01:38:54,740 --> 01:39:00,700 +المقدار الثابت بالمقدار الثابت itself وهذه الناقص + +896 +01:39:00,700 --> 01:39:02,420 +كم؟ Zero + +897 +01:39:07,690 --> 01:39:12,690 +أقل من أو يساوي الـ limit لما الـ X بدها تروح + +898 +01:39:12,690 --> 01:39:19,150 +للإثنين الـ G of X أقل من أو يساوي أربعة زائد زيرو + +899 +01:39:19,640 --> 01:39:23,320 +يبقى سبعة الطرف الشمال يبقى كم؟ أربعة والطرف + +900 +01:39:23,320 --> 01:39:29,120 +اليمين يبقى صارت عندنا أربعة أقل من أو يساوي الـ + +901 +01:39:29,120 --> 01:39:34,040 +limit لما الـ X بتروح للـ اثنين للـ G of X أقل من أو + +902 +01:39:34,040 --> 01:39:40,300 +يساوي مين؟ أربعة بقدر أستخدم الآن من؟ Sandwich theorem و + +903 +01:39:40,300 --> 01:39:46,380 +نوصل لمين؟ لإجابة السؤال اللي مطلوبة فبروح بقوله + +904 +01:39:46,380 --> 01:39:46,940 +bye + +905 +01:39:49,530 --> 01:39:54,790 +Sandwich theorem limit + +906 +01:39:56,060 --> 01:40:01,360 +للـ g of x لما الـ x بيروح للاثنين بيساوي مين؟ + +907 +01:40:01,360 --> 01:40:07,580 +بيساوي أربعة لا يزال عندنا في الـ section نقطة أخرى + +908 +01:40:07,580 --> 01:40:12,340 +لكن وبها ينتهي الـ section لك قبل أن أعطيك أرقام + +909 +01:40:12,340 --> 01:40:18,160 +مسائل تبعات exercises اثنين اثنين أتمشي حالك فيهم + +910 +01:40:18,160 --> 01:40:25,570 +يبقى باجي بقول exercises اثنين اثنين المسائل + +911 +01:40:25,570 --> 01:40:35,910 +التالية من واحد لخمسة وستين والأد وكذلك من خمسة + +912 +01:40:35,910 --> 01:40:42,870 +وسبعين لتمانين، من خمسة وسبعين لغاية ثمانين diff --git a/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/wEzmV3DYYdg_raw.json b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/wEzmV3DYYdg_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..97856ae64563539b3ff0578e3d392e79db5f3063 --- /dev/null +++ b/PL9fwy3NUQKwY6bGFmuJGxU8kL7vx3U133/wEzmV3DYYdg_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 4975, "start": 21.23, "end": 49.75, "text": "بسم الله الرحمن الرحيم المقلم الان في ال section رقم اتنين اتنين وهو يتحدث عن limit of a function and limit loss يبقى نهاية دالة ما و كذلك بنا ناخد في هذه ال section بعض قواعد النهايات هنبدأ أول شيء ب concept of a limit يبقى بنا نتعرض 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محور X هذا محور Y هذا لقطة الاصل اللي هي ال zero", "tokens": [2304, 8592, 7649, 8717, 8592, 38688, 2423, 4948, 2514, 49429, 5296, 10721, 47525, 8315, 8717, 32887, 5016, 8717, 2288, 38251, 12602, 38251, 3660, 29538, 32748, 6027, 3660, 7251, 3555, 4587, 7578, 23758, 3714, 5016, 13063, 1783, 23758, 3714, 5016, 13063, 398, 23758, 5296, 47432, 3660, 2423, 33546, 1211, 13672, 1829, 39896, 2423, 4018], "avg_logprob": -0.2728588106455626, "compression_ratio": 1.434782608695652, "no_speech_prob": 0.0, "words": [{"start": 1333.51, "end": 1334.07, "word": "مشان", "probability": 0.6737060546875}, {"start": 1334.07, "end": 1334.49, "word": " نشوف", "probability": 0.8313802083333334}, {"start": 1334.49, "end": 1334.67, "word": " ال", "probability": 0.25}, {"start": 1334.67, "end": 1334.95, "word": " limit", "probability": 0.71142578125}, {"start": 1334.95, "end": 1335.53, "word": " exist", "probability": 0.7158203125}, {"start": 1335.53, "end": 1335.83, "word": " ولا", "probability": 0.87744140625}, 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نمرة", "probability": 0.7532552083333334}, {"start": 1569.44, "end": 1569.82, "word": " B", "probability": 0.494873046875}, {"start": 1569.82, "end": 1570.94, "word": " الـ", "probability": 0.51025390625}, {"start": 1570.94, "end": 1571.4, "word": " F", "probability": 0.5283203125}, {"start": 1571.4, "end": 1575.46, "word": " مُعرّفة", "probability": 0.7228306361607143}, {"start": 1575.46, "end": 1577.02, "word": " مُعرّفة", "probability": 0.8431919642857143}, {"start": 1577.02, "end": 1581.14, "word": " at", "probability": 0.37060546875}, {"start": 1581.14, "end": 1584.02, "word": " X", "probability": 0.5869140625}, {"start": 1584.02, "end": 1584.74, "word": " بده", "probability": 0.3271484375}, {"start": 1584.74, "end": 1585.24, "word": " يساوي", "probability": 0.85595703125}, {"start": 1585.24, "end": 1586.06, "word": " زيرو،", "probability": 0.50555419921875}, {"start": 1586.06, "end": 1586.52, "word": " that", "probability": 0.634765625}, {"start": 1586.52, "end": 1587.22, "word": 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"word": " does", "probability": 0.8369140625}, {"start": 1636.32, "end": 1638.82, "word": " not", "probability": 0.9619140625}, {"start": 1638.82, "end": 1640.26, "word": " exist", "probability": 0.9736328125}, {"start": 1640.26, "end": 1642.42, "word": " because", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 72, "seek": 167134, "start": 1645.72, "end": 1671.34, "text": "الـ F has two different infinite limits يعني عندي واحدة infinity والتانية سالب infinity وبالتالي يعني that is", "tokens": [6027, 39184, 479, 575, 732, 819, 13785, 10406, 37495, 22653, 18871, 16254, 36764, 24401, 3660, 13202, 16070, 2655, 7649, 10632, 8608, 6027, 3555, 13202, 46599, 6027, 2655, 6027, 1829, 37495, 22653, 300, 307], "avg_logprob": -0.22162223738782547, "compression_ratio": 1.3070175438596492, "no_speech_prob": 0.0, "words": [{"start": 1645.72, "end": 1646.2, "word": "الـ", "probability": 0.707275390625}, {"start": 1646.2, "end": 1646.64, "word": " F", "probability": 0.65234375}, {"start": 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"word": " بـdelimit", "probability": 0.57197265625}, {"start": 2158.71, "end": 2158.89, "word": " الـ", "probability": 0.4188232421875}, {"start": 2158.89, "end": 2159.01, "word": " F", "probability": 0.316650390625}, {"start": 2159.01, "end": 2159.23, "word": " of", "probability": 0.76708984375}, {"start": 2159.23, "end": 2159.47, "word": " X", "probability": 0.97607421875}, {"start": 2159.47, "end": 2159.81, "word": " لما", "probability": 0.85400390625}, {"start": 2159.81, "end": 2160.03, "word": " الـ", "probability": 0.862060546875}, {"start": 2160.03, "end": 2160.21, "word": " X", "probability": 0.9521484375}, {"start": 2160.21, "end": 2160.65, "word": " بتروح", "probability": 0.6927083333333334}, {"start": 2160.65, "end": 2161.07, "word": " للـ", "probability": 0.5703125}, {"start": 2161.07, "end": 2161.41, "word": " Zero", "probability": 0.51708984375}, {"start": 2161.41, "end": 2162.59, "word": " عند", "probability": 0.94091796875}, {"start": 2162.59, "end": 2162.91, "word": " الـ", "probability": 0.786376953125}, {"start": 2162.91, "end": 2163.11, "word": " Zero", "probability": 0.93505859375}, {"start": 2163.11, "end": 2163.43, "word": " هذه", "probability": 0.64111328125}, {"start": 2163.43, "end": 2164.03, "word": " نازلة", "probability": 0.8304036458333334}, {"start": 2164.03, "end": 2164.95, "word": " لسلب", "probability": 0.6818033854166666}, {"start": 2164.95, "end": 2165.57, "word": " Infinity", "probability": 0.61328125}, {"start": 2165.57, "end": 2165.99, "word": " وهذه", "probability": 0.75390625}, {"start": 2165.99, "end": 2166.31, "word": " طالع", "probability": 0.7161458333333334}, {"start": 2166.31, "end": 2166.97, "word": " لإيه؟", "probability": 0.4990478515625}, {"start": 2166.97, "end": 2168.17, "word": " لإنفينيتي", "probability": 0.8001534598214286}, {"start": 2168.17, "end": 2168.61, "word": " يبقى", "probability": 0.845458984375}, {"start": 2168.61, "end": 2168.99, "word": " هذه", "probability": 0.7197265625}, {"start": 2168.99, 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بحسبها", "probability": 0.9906005859375}, {"start": 2377.67, "end": 2378.41, "word": " بالتعويض", "probability": 0.913671875}, {"start": 2378.41, "end": 2379.33, "word": " المباشر", "probability": 0.994384765625}], "temperature": 1.0}, {"id": 99, "seek": 240654, "start": 2379.86, "end": 2406.54, "text": "تمام؟ Direct Substitution مين هي هذه الدوال؟ فباجي بقول نمرة واحد For For the Identity Function لدلة الوحدة F of X بده سوى X We have", "tokens": [2655, 15042, 2304, 22807, 18308, 42090, 6518, 3714, 9957, 39896, 29538, 32748, 2407, 6027, 22807, 6156, 3555, 26108, 1829, 4724, 39648, 8717, 2304, 25720, 36764, 24401, 1171, 1171, 264, 25905, 507, 11166, 882, 5296, 3215, 37977, 2423, 2407, 24401, 3660, 479, 295, 1783, 47525, 3224, 8608, 2407, 7578, 1783, 492, 362], "avg_logprob": -0.3191105889586302, "compression_ratio": 1.2171052631578947, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2379.86, "end": 2380.46, "word": "تمام؟", "probability": 0.48355865478515625}, {"start": 2380.46, "end": 2381.0, "word": " Direct", "probability": 0.66064453125}, {"start": 2381.0, "end": 2382.56, "word": " Substitution", "probability": 0.82177734375}, {"start": 2382.56, "end": 2382.94, "word": " مين", "probability": 0.6844482421875}, {"start": 2382.94, "end": 2383.12, "word": " هي", "probability": 0.80859375}, {"start": 2383.12, "end": 2383.5, "word": " هذه", "probability": 0.98046875}, {"start": 2383.5, "end": 2384.64, "word": " الدوال؟", "probability": 0.7838134765625}, {"start": 2384.64, "end": 2385.3, "word": " فباجي", "probability": 0.7628173828125}, {"start": 2385.3, "end": 2385.78, "word": " بقول", "probability": 0.9560546875}, {"start": 2385.78, "end": 2386.22, "word": " نمرة", "probability": 0.7864583333333334}, {"start": 2386.22, "end": 2386.82, "word": " واحد", "probability": 0.976318359375}, {"start": 2386.82, "end": 2387.26, "word": " For", "probability": 0.376953125}, {"start": 2387.26, "end": 2390.3, "word": " For", "probability": 0.455078125}, {"start": 2390.3, "end": 2391.64, "word": " the", "probability": 0.67431640625}, {"start": 2391.64, "end": 2396.02, "word": " Identity", "probability": 0.793701171875}, {"start": 2396.02, "end": 2398.16, "word": " Function", "probability": 0.83251953125}, {"start": 2398.16, "end": 2399.86, "word": " لدلة", "probability": 0.8758138020833334}, {"start": 2399.86, "end": 2401.02, "word": " الوحدة", "probability": 0.9642333984375}, {"start": 2401.02, "end": 2401.76, "word": " F", "probability": 0.671875}, {"start": 2401.76, "end": 2402.24, "word": " of", "probability": 0.80419921875}, {"start": 2402.24, "end": 2402.78, "word": " X", "probability": 0.97021484375}, {"start": 2402.78, "end": 2403.44, "word": " بده", "probability": 0.73046875}, {"start": 2403.44, "end": 2404.0, "word": " سوى", "probability": 0.6886393229166666}, {"start": 2404.0, "end": 2404.62, "word": " X", "probability": 0.9912109375}, {"start": 2404.62, "end": 2405.6, "word": " We", "probability": 0.8193359375}, {"start": 2405.6, "end": 2406.54, "word": " have", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 100, "seek": 243690, "start": 2408.28, "end": 2436.9, "text": "limit لل X لما ال X بدها تروح إلى X node بده يساوي X node itself نمرة اتنين for the constant function الدالة الثابتة F of X بده يساوي K we have limit", "tokens": [4197, 270, 24976, 1783, 5296, 15042, 2423, 1783, 47525, 11296, 6055, 32887, 5016, 30731, 1783, 9984, 47525, 3224, 7251, 3794, 995, 45865, 1783, 9984, 2564, 8717, 2304, 25720, 1975, 2655, 1863, 9957, 337, 264, 5754, 2445, 32748, 6027, 3660, 6024, 104, 16758, 2655, 3660, 479, 295, 1783, 47525, 3224, 7251, 3794, 995, 45865, 591, 321, 362, 4948], "avg_logprob": -0.21538254156194883, "compression_ratio": 1.3486842105263157, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2408.28, "end": 2409.26, "word": "limit", "probability": 0.65673828125}, {"start": 2409.26, "end": 2410.24, "word": " لل", "probability": 0.42529296875}, {"start": 2410.24, "end": 2410.78, "word": " X", "probability": 0.367919921875}, {"start": 2410.78, "end": 2411.6, "word": " لما", "probability": 0.905517578125}, {"start": 2411.6, "end": 2411.84, "word": " ال", "probability": 0.68994140625}, {"start": 2411.84, "end": 2412.26, "word": " X", "probability": 0.91650390625}, {"start": 2412.26, "end": 2413.22, "word": " بدها", "probability": 0.922607421875}, {"start": 2413.22, "end": 2413.8, "word": " تروح", "probability": 0.9939778645833334}, {"start": 2413.8, "end": 2414.1, "word": " إلى", "probability": 0.435791015625}, {"start": 2414.1, "end": 2414.46, "word": " X", "probability": 0.916015625}, {"start": 2414.46, "end": 2414.96, "word": " node", "probability": 0.67041015625}, {"start": 2414.96, "end": 2416.0, "word": " بده", "probability": 0.767578125}, {"start": 2416.0, "end": 2416.4, "word": " يساوي", "probability": 0.82452392578125}, {"start": 2416.4, "end": 2416.84, "word": " X", "probability": 0.97216796875}, {"start": 2416.84, "end": 2417.34, "word": " node", "probability": 0.9404296875}, {"start": 2417.34, "end": 2418.24, "word": " itself", "probability": 0.556640625}, {"start": 2418.24, "end": 2419.82, "word": " نمرة", "probability": 0.5411783854166666}, {"start": 2419.82, "end": 2420.52, "word": " اتنين", "probability": 0.87890625}, {"start": 2420.52, "end": 2421.42, "word": " for", "probability": 0.74267578125}, {"start": 2421.42, "end": 2422.6, "word": " the", "probability": 0.87548828125}, {"start": 2422.6, "end": 2424.28, "word": " constant", "probability": 0.9541015625}, {"start": 2424.28, "end": 2426.46, "word": " function", "probability": 0.97119140625}, {"start": 2426.46, "end": 2427.94, "word": " الدالة", "probability": 0.9083658854166666}, {"start": 2427.94, "end": 2428.9, "word": " الثابتة", "probability": 0.963671875}, {"start": 2428.9, "end": 2429.44, "word": " F", "probability": 0.59228515625}, {"start": 2429.44, "end": 2429.8, "word": " of", "probability": 0.7158203125}, {"start": 2429.8, "end": 2430.32, "word": " X", "probability": 0.99169921875}, {"start": 2430.32, "end": 2431.36, "word": " بده", "probability": 0.927001953125}, {"start": 2431.36, "end": 2431.88, "word": " يساوي", "probability": 0.9764404296875}, {"start": 2431.88, "end": 2432.46, "word": " K", "probability": 0.94921875}, {"start": 2432.46, "end": 2433.62, "word": " we", "probability": 0.53955078125}, {"start": 2433.62, "end": 2434.64, "word": " have", "probability": 0.970703125}, {"start": 2434.64, "end": 2436.9, "word": " limit", "probability": 0.94384765625}], "temperature": 1.0}, {"id": 101, "seek": 246140, "start": 2437.54, "end": 2461.4, "text": "للـ K لما ال X بدي يروح لل X node بدي يشوي K itself نمرة تلاتة For the polynomial لكثيرة الحدود P of X", "tokens": [1211, 1211, 39184, 591, 5296, 15042, 2423, 1783, 4724, 16254, 7251, 32887, 5016, 24976, 1783, 9984, 4724, 16254, 7251, 8592, 45865, 591, 2564, 8717, 2304, 25720, 6055, 1211, 9307, 3660, 1171, 264, 26110, 5296, 4117, 12984, 48923, 21542, 3215, 23328, 430, 295, 1783], "avg_logprob": -0.2993607852946628, "compression_ratio": 1.1574803149606299, "no_speech_prob": 0.0, "words": [{"start": 2437.54, "end": 2438.22, "word": "للـ", "probability": 0.5585123697916666}, {"start": 2438.22, "end": 2438.48, "word": " K", "probability": 0.63671875}, {"start": 2438.48, "end": 2438.92, "word": " لما", "probability": 0.872802734375}, {"start": 2438.92, "end": 2439.14, "word": " ال", "probability": 0.82470703125}, {"start": 2439.14, "end": 2439.56, "word": " X", "probability": 0.87646484375}, {"start": 2439.56, "end": 2440.58, "word": " بدي", "probability": 0.695556640625}, {"start": 2440.58, "end": 2440.98, "word": " يروح", "probability": 0.783935546875}, {"start": 2440.98, "end": 2441.2, "word": " لل", "probability": 0.63232421875}, {"start": 2441.2, "end": 2441.6, "word": " X", "probability": 0.65478515625}, {"start": 2441.6, "end": 2442.0, "word": " node", "probability": 0.18701171875}, {"start": 2442.0, "end": 2442.34, "word": " بدي", "probability": 0.8056640625}, {"start": 2442.34, "end": 2442.8, "word": " يشوي", "probability": 0.7176106770833334}, {"start": 2442.8, "end": 2443.22, "word": " K", "probability": 0.89892578125}, {"start": 2443.22, "end": 2444.0, "word": " itself", "probability": 0.480712890625}, {"start": 2444.0, "end": 2446.08, "word": " نمرة", "probability": 0.630126953125}, {"start": 2446.08, "end": 2447.72, "word": " تلاتة", "probability": 0.9295654296875}, {"start": 2447.72, "end": 2449.74, "word": " For", "probability": 0.367431640625}, {"start": 2449.74, "end": 2451.42, "word": " the", "probability": 0.8583984375}, {"start": 2451.42, "end": 2453.52, "word": " polynomial", "probability": 0.92041015625}, {"start": 2453.52, "end": 2457.76, "word": " لكثيرة", "probability": 0.950927734375}, {"start": 2457.76, "end": 2458.84, "word": " الحدود", "probability": 0.9933268229166666}, {"start": 2458.84, "end": 2460.46, "word": " P", "probability": 0.951171875}, {"start": 2460.46, "end": 2460.88, "word": " of", "probability": 0.609375}, {"start": 2460.88, "end": 2461.4, "word": " X", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 102, "seek": 248403, "start": 2462.15, "end": 2484.03, "text": "بدي يساوي a n x to the power n a n minus one x to the power n minus one زائد a one x زائد a naught we have limit", "tokens": [3555, 16254, 7251, 3794, 995, 45865, 257, 297, 2031, 281, 264, 1347, 297, 257, 297, 3175, 472, 2031, 281, 264, 1347, 297, 3175, 472, 30767, 16373, 3215, 257, 472, 2031, 30767, 16373, 3215, 257, 13138, 321, 362, 4948], "avg_logprob": -0.2786458302766849, "compression_ratio": 1.3473684210526315, "no_speech_prob": 0.0, "words": [{"start": 2462.15, "end": 2462.55, "word": "بدي", "probability": 0.41497802734375}, {"start": 2462.55, "end": 2463.15, "word": " يساوي", "probability": 0.65771484375}, {"start": 2463.15, "end": 2463.57, "word": " a", "probability": 0.36376953125}, {"start": 2463.57, "end": 2463.95, "word": " n", "probability": 0.349365234375}, {"start": 2463.95, "end": 2464.35, "word": " x", "probability": 0.7451171875}, {"start": 2464.35, "end": 2464.61, "word": " to", "probability": 0.63330078125}, {"start": 2464.61, "end": 2464.79, "word": " the", "probability": 0.908203125}, {"start": 2464.79, "end": 2465.21, "word": " power", "probability": 0.9091796875}, {"start": 2465.21, "end": 2465.75, "word": " n", "probability": 0.8095703125}, {"start": 2465.75, "end": 2466.49, "word": " a", "probability": 0.7822265625}, {"start": 2466.49, "end": 2466.95, "word": " n", "probability": 0.9658203125}, {"start": 2466.95, "end": 2467.41, "word": " minus", "probability": 0.83642578125}, {"start": 2467.41, "end": 2467.81, "word": " one", "probability": 0.8046875}, {"start": 2467.81, "end": 2468.19, "word": " x", "probability": 0.9619140625}, {"start": 2468.19, "end": 2468.41, "word": " to", "probability": 0.96240234375}, {"start": 2468.41, "end": 2468.59, "word": " the", "probability": 0.9169921875}, {"start": 2468.59, "end": 2468.93, "word": " power", "probability": 0.88037109375}, {"start": 2468.93, "end": 2469.29, "word": " n", "probability": 0.83154296875}, {"start": 2469.29, "end": 2469.75, "word": " minus", "probability": 0.9853515625}, {"start": 2469.75, "end": 2470.27, "word": " one", "probability": 0.9375}, {"start": 2470.27, "end": 2471.89, "word": " زائد", "probability": 0.8463541666666666}, {"start": 2471.89, "end": 2472.51, "word": " a", "probability": 0.9091796875}, {"start": 2472.51, "end": 2473.19, "word": " one", "probability": 0.90478515625}, {"start": 2473.19, "end": 2474.01, "word": " x", "probability": 0.9833984375}, {"start": 2474.01, "end": 2475.23, "word": " زائد", "probability": 0.9689127604166666}, {"start": 2475.23, "end": 2475.67, "word": " a", "probability": 0.9736328125}, {"start": 2475.67, "end": 2476.17, "word": " naught", "probability": 0.52490234375}, {"start": 2476.17, "end": 2477.93, "word": " we", "probability": 0.37109375}, {"start": 2477.93, "end": 2478.67, "word": " have", "probability": 0.97216796875}, {"start": 2478.67, "end": 2484.03, "word": " limit", "probability": 0.9462890625}], "temperature": 1.0}, {"id": 103, "seek": 251119, "start": 2485.92, "end": 2511.2, "text": "للـ P of X لما الـ X بده يروح الى C بده يسوي P of C و لو بده يسوي A N C to the power N A minus one C to the power N minus one زائد A one C زائد ال A naught نمرا أربعة", "tokens": [1211, 1211, 39184, 430, 295, 1783, 5296, 15042, 2423, 39184, 1783, 47525, 3224, 7251, 32887, 5016, 2423, 7578, 383, 47525, 3224, 7251, 3794, 45865, 430, 295, 383, 4032, 45164, 47525, 3224, 7251, 3794, 45865, 316, 426, 383, 281, 264, 1347, 426, 316, 3175, 472, 383, 281, 264, 1347, 426, 3175, 472, 30767, 16373, 3215, 316, 472, 383, 30767, 16373, 3215, 2423, 316, 13138, 8717, 2304, 23557, 5551, 25513, 27884], "avg_logprob": -0.3002232198204313, "compression_ratio": 1.5136986301369864, "no_speech_prob": 0.0, "words": [{"start": 2485.92, "end": 2486.6, "word": "للـ", "probability": 0.5075276692708334}, {"start": 2486.6, "end": 2486.8, "word": " P", "probability": 0.55078125}, {"start": 2486.8, "end": 2487.26, "word": " of", "probability": 0.70361328125}, {"start": 2487.26, "end": 2487.72, "word": " X", "probability": 0.96044921875}, {"start": 2487.72, "end": 2488.08, "word": " لما", "probability": 0.8251953125}, {"start": 2488.08, "end": 2488.3, "word": " الـ", "probability": 0.714111328125}, {"start": 2488.3, "end": 2488.56, "word": " X", "probability": 0.9482421875}, {"start": 2488.56, "end": 2488.96, "word": " بده", "probability": 0.42236328125}, {"start": 2488.96, "end": 2489.26, "word": " يروح", "probability": 0.9905598958333334}, {"start": 2489.26, "end": 2489.62, "word": " الى", "probability": 0.5989990234375}, {"start": 2489.62, "end": 2490.02, "word": " C", "probability": 0.8486328125}, {"start": 2490.02, "end": 2490.96, "word": " بده", "probability": 0.7139892578125}, {"start": 2490.96, "end": 2491.3, "word": " يسوي", "probability": 0.7970377604166666}, {"start": 2491.3, "end": 2491.72, "word": " P", 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ناخدها من الآن هي القوانين اللي خدتها في الثانوية العامة، هما هما لن نغي فيهم حرفا واحدا", "tokens": [1211, 10721, 19446, 47283, 3215, 8315, 8592, 12174, 2407, 7649, 9957, 28239, 11296, 1829, 9307, 12399, 25062, 2407, 7649, 9957, 28239, 3224, 16373, 10632, 13672, 1829, 47525, 8315, 8717, 47283, 3215, 11296, 9154, 6024, 48506, 39896, 25062, 2407, 7649, 9957, 13672, 1829, 16490, 3215, 2655, 11296, 8978, 6024, 104, 7649, 2407, 10632, 18863, 10943, 3660, 12399, 8032, 15042, 8032, 15042, 5296, 1863, 8717, 17082, 1829, 8978, 16095, 11331, 28480, 995, 36764, 24401, 995], "avg_logprob": -0.19562922639621272, "compression_ratio": 1.9275362318840579, "no_speech_prob": 0.0, "words": [{"start": 2941.6, "end": 2941.96, "word": "لأ", "probability": 0.593017578125}, {"start": 2941.96, "end": 2942.46, "word": " مااخدناش", "probability": 0.7228515625}, {"start": 2942.46, "end": 2942.98, "word": " قوانين", "probability": 0.9859619140625}, {"start": 2942.98, "end": 2944.08, "word": " النهايات،", 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العملي لهم يبقى هنا the limit logic قوانين النهايات بجي بقول F", "tokens": [1829, 3555, 4587, 7578, 47525, 8315, 8717, 32887, 5016, 4032, 1863, 5016, 9566, 25062, 2407, 7649, 9957, 9122, 15042, 5551, 9778, 3215, 2655, 16095, 11778, 11536, 4724, 2288, 3224, 7649, 12399, 8978, 16712, 1863, 2407, 10632, 28242, 10943, 2423, 26890, 3224, 20498, 9154, 25062, 25528, 16095, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 1975, 1829, 3224, 1975, 5016, 8315, 47525, 8315, 1975, 8592, 1829, 4724, 2288, 16095, 22807, 47525, 8315, 28239, 9381, 18863, 2304, 20292, 5296, 16095, 7251, 3555, 4587, 7578, 34105, 264, 4948, 9952, 12174, 2407, 7649, 9957, 28239, 11296, 1829, 9307, 4724, 7435, 1829, 4724, 39648, 479], "avg_logprob": -0.2804687529802322, "compression_ratio": 1.6767676767676767, "no_speech_prob": 0.0, "words": [{"start": 2954.36, "end": 2954.84, "word": "يبقى", "probability": 0.77734375}, {"start": 2954.84, "end": 2955.1, "word": " بدنا", "probability": 0.829345703125}, {"start": 2955.1, "end": 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يقصر واحد على نفس الدالة وطبق للقاعدة اللي عندنا هذه limit الconstant بالconstant itself و limit هذه بنجيبها من هنا و بندخل عليها بشر ما تسويش ال zero تمام؟ يبقى صارتك هنا حلقة خاصة منها", "tokens": [3615, 3215, 3215, 20328, 5016, 1829, 5016, 8608, 6027, 5172, 7251, 4587, 9381, 2288, 36764, 24401, 15844, 8717, 36178, 32748, 6027, 3660, 4032, 9566, 3555, 4587, 24976, 4587, 995, 22488, 3660, 13672, 1829, 43242, 8315, 29538, 4948, 2423, 1671, 372, 394, 20666, 25279, 394, 2564, 4032, 4948, 29538, 44945, 7435, 1829, 3555, 11296, 9154, 34105, 4032, 44945, 3215, 9778, 1211, 25894, 11296, 4724, 8592, 2288, 19446, 6055, 3794, 45865, 8592, 2423, 4018, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 20328, 9640, 2655, 4117, 34105, 11331, 1211, 28671, 16490, 33546, 3660, 9154, 11296], "avg_logprob": -0.34811829238809566, "compression_ratio": 1.5951219512195123, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3508.26, "end": 3508.72, "word": "عدد", "probability": 0.4353841145833333}, 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"probability": 0.91162109375}, {"start": 4515.22, "end": 4515.44, "word": " x", "probability": 0.482177734375}, {"start": 4515.44, "end": 4515.8, "word": " بده", "probability": 0.6751708984375}, {"start": 4515.8, "end": 4516.04, "word": " يروح", "probability": 0.98388671875}, {"start": 4516.04, "end": 4516.22, "word": " ل", "probability": 0.82421875}, {"start": 4516.22, "end": 4516.76, "word": " zero", "probability": 0.51611328125}, {"start": 4516.76, "end": 4518.04, "word": " لوحد", "probability": 0.568115234375}, {"start": 4518.04, "end": 4518.62, "word": " ناقص", "probability": 0.8953857421875}, {"start": 4518.62, "end": 4519.26, "word": " cosine", "probability": 0.80615234375}, {"start": 4519.26, "end": 4519.56, "word": " ال", "probability": 0.56689453125}, {"start": 4519.56, "end": 4519.98, "word": " x", "probability": 0.86962890625}, {"start": 4519.98, "end": 4520.96, "word": " على", "probability": 0.5302734375}, {"start": 4520.96, "end": 4521.84, "word": " cosine", "probability": 0.86865234375}, {"start": 4521.84, "end": 4522.58, "word": " ال", "probability": 0.87548828125}, {"start": 4522.58, "end": 4523.14, "word": " x", "probability": 0.95947265625}, {"start": 4523.14, "end": 4523.66, "word": " في", "probability": 0.6357421875}, {"start": 4523.66, "end": 4524.08, "word": " mean", "probability": 0.480712890625}, {"start": 4524.08, "end": 4524.72, "word": " في", "probability": 0.912109375}, {"start": 4524.72, "end": 4525.7, "word": " sin", "probability": 0.436767578125}, {"start": 4525.7, "end": 4527.2, "word": " تربيع", "probability": 0.8280029296875}, {"start": 4527.2, "end": 4527.62, "word": " ال", "probability": 0.89306640625}, {"start": 4527.62, "end": 4527.98, "word": " x", "probability": 0.9228515625}, {"start": 4527.98, "end": 4529.2, "word": " هبنجرب", "probability": 0.722119140625}], "temperature": 1.0}, {"id": 186, "seek": 454349, "start": 4530.95, "end": 4543.49, "text": "كوصين صفر بواحد ناقص واحد بصفر كوصين صفر بواحد في الصفر صفر لا تزال zero على zero", "tokens": [4117, 2407, 9381, 9957, 20328, 5172, 2288, 4724, 14407, 24401, 8717, 995, 4587, 9381, 36764, 24401, 4724, 9381, 5172, 2288, 9122, 2407, 9381, 9957, 20328, 5172, 2288, 4724, 14407, 24401, 8978, 31767, 5172, 2288, 20328, 5172, 2288, 20193, 6055, 11622, 6027, 4018, 15844, 4018], "avg_logprob": -0.26961806615193684, "compression_ratio": 1.5681818181818181, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 4530.950000000001, "end": 4532.35, "word": "كوصين", "probability": 0.508148193359375}, {"start": 4532.35, "end": 4533.19, "word": " صفر", "probability": 0.8776041666666666}, {"start": 4533.19, "end": 4534.51, "word": " بواحد", "probability": 0.7464192708333334}, {"start": 4534.51, "end": 4534.99, "word": " ناقص", "probability": 0.884765625}, {"start": 4534.99, "end": 4535.61, "word": " واحد", "probability": 0.9892578125}, {"start": 4535.61, "end": 4536.47, "word": " بصفر", "probability": 0.90087890625}, {"start": 4536.47, "end": 4537.47, "word": " كوصين", "probability": 0.8236083984375}, {"start": 4537.47, "end": 4538.17, "word": " صفر", "probability": 0.9757486979166666}, {"start": 4538.17, "end": 4539.07, "word": " بواحد", "probability": 0.9853515625}, {"start": 4539.07, "end": 4539.29, "word": " في", "probability": 0.58935546875}, {"start": 4539.29, "end": 4539.99, "word": " الصفر", "probability": 0.9072265625}, {"start": 4539.99, "end": 4540.99, "word": " صفر", "probability": 0.790283203125}, {"start": 4540.99, "end": 4541.27, "word": " لا", "probability": 0.4833984375}, {"start": 4541.27, "end": 4542.09, "word": " تزال", "probability": 0.9415690104166666}, {"start": 4542.09, "end": 4542.65, "word": " zero", "probability": 0.405517578125}, {"start": 4542.65, "end": 4543.03, "word": " على", "probability": 0.86083984375}, {"start": 4543.03, "end": 4543.49, "word": " zero", "probability": 0.86767578125}], "temperature": 1.0}, {"id": 187, "seek": 457107, "start": 4545.09, "end": 4571.07, "text": "ولا مرافق ولا هجاب للمرافق بس فابتهك و ي assign تربية بحاول أبنائي ال cosine تربية و أبتدى ان حلت المشكلة تمام يبقى الاقتراح كتالي و يساوي limit لما ال x بدى روح ل zero لواحد ناقص cosine ال x كما هي high cosine ال x", "tokens": [12610, 995, 3714, 23557, 5172, 4587, 49429, 8032, 7435, 16758, 5296, 19528, 23557, 5172, 4587, 4724, 3794, 6156, 16758, 47395, 4117, 4032, 7251, 6269, 6055, 2288, 21292, 3660, 4724, 5016, 995, 12610, 5551, 3555, 1863, 16373, 1829, 2423, 23565, 6055, 2288, 21292, 3660, 4032, 5551, 3555, 2655, 3215, 7578, 16472, 11331, 1211, 2655, 9673, 8592, 28820, 3660, 46811, 10943, 7251, 3555, 4587, 7578, 42963, 38149, 23557, 5016, 9122, 2655, 6027, 1829, 4032, 7251, 3794, 995, 45865, 4948, 5296, 15042, 2423, 2031, 47525, 7578, 12602, 2407, 5016, 5296, 4018, 5296, 14407, 24401, 8717, 995, 4587, 9381, 23565, 2423, 2031, 9122, 15042, 39896, 1090, 23565, 2423, 2031], "avg_logprob": -0.31810142381011314, "compression_ratio": 1.674757281553398, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 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{"start": 4557.55, "end": 4558.57, "word": " كتالي", "probability": 0.8167724609375}, {"start": 4558.57, "end": 4558.87, "word": " و", "probability": 0.91064453125}, {"start": 4558.87, "end": 4559.73, "word": " يساوي", "probability": 0.86865234375}, {"start": 4559.73, "end": 4560.77, "word": " limit", "probability": 0.9150390625}, {"start": 4560.77, "end": 4561.67, "word": " لما", "probability": 0.9267578125}, {"start": 4561.67, "end": 4561.85, "word": " ال", "probability": 0.955078125}, {"start": 4561.85, "end": 4562.13, "word": " x", "probability": 0.40283203125}, {"start": 4562.13, "end": 4562.51, "word": " بدى", "probability": 0.80517578125}, {"start": 4562.51, "end": 4562.99, "word": " روح", "probability": 0.8502604166666666}, {"start": 4562.99, "end": 4563.21, "word": " ل", "probability": 0.85107421875}, {"start": 4563.21, "end": 4563.77, "word": " zero", "probability": 0.501953125}, {"start": 4563.77, "end": 4565.13, "word": " لواحد", "probability": 0.7599283854166666}, {"start": 4565.13, "end": 4566.13, "word": " ناقص", "probability": 0.9825439453125}, {"start": 4566.13, "end": 4566.71, "word": " cosine", "probability": 0.85791015625}, {"start": 4566.71, "end": 4566.91, "word": " ال", "probability": 0.78564453125}, {"start": 4566.91, "end": 4567.15, "word": " x", "probability": 0.8369140625}, {"start": 4567.15, "end": 4567.65, "word": " كما", "probability": 0.921630859375}, {"start": 4567.65, "end": 4568.15, "word": " هي", "probability": 0.890625}, {"start": 4568.15, "end": 4569.05, "word": " high", "probability": 0.359375}, {"start": 4569.05, "end": 4570.03, "word": " cosine", "probability": 0.97119140625}, {"start": 4570.03, "end": 4570.73, "word": " ال", "probability": 0.8193359375}, {"start": 4570.73, "end": 4571.07, "word": " x", "probability": 0.87744140625}], "temperature": 1.0}, {"id": 188, "seek": 458114, "start": 4571.54, "end": 4581.14, "text": "قصين تربية لواحد ناقص قصين تربية ال X المقام فرق بين المربعين", "tokens": [4587, 9381, 9957, 6055, 25513, 10632, 5296, 14407, 24401, 8717, 995, 4587, 9381, 12174, 9381, 9957, 6055, 25513, 10632, 2423, 1783, 9673, 4587, 10943, 6156, 2288, 4587, 49374, 9673, 25513, 3615, 9957], "avg_logprob": -0.29521780303030304, "compression_ratio": 1.3580246913580247, "no_speech_prob": 0.0, "words": [{"start": 4571.54, "end": 4572.24, "word": "قصين", "probability": 0.4198404947916667}, {"start": 4572.24, "end": 4572.94, "word": " تربية", "probability": 0.8963216145833334}, {"start": 4572.94, "end": 4574.38, "word": " لواحد", "probability": 0.7111002604166666}, {"start": 4574.38, "end": 4575.72, "word": " ناقص", "probability": 0.9796142578125}, {"start": 4575.72, "end": 4576.8, "word": " قصين", "probability": 0.8330078125}, {"start": 4576.8, "end": 4577.34, "word": " تربية", "probability": 0.9749348958333334}, {"start": 4577.34, "end": 4577.52, "word": " ال", "probability": 0.1939697265625}, {"start": 4577.52, "end": 4577.74, "word": " X", "probability": 0.630859375}, {"start": 4577.74, "end": 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+7 +00:00:29,440 --> 00:00:35,940 +qualitative معناها فحوصات نوعية أو جودة تعطي نتيجة + +8 +00:00:35,940 --> 00:00:41,640 +positive أو negative ظهور لون أو عدم ظهور لون، لا + +9 +00:00:41,640 --> 00:00:45,140 +تعطي رقم في عندنا نوعتان من الفحوصات اللي هو + +10 +00:00:45,140 --> 00:00:51,030 +quantitative testQuantitative معناها كمية تحليل كم + +11 +00:00:51,030 --> 00:00:55,670 +يعني بديطلع عندك كمية أو مقدار يعني هيطلع عندك في + +12 +00:00:55,670 --> 00:00:59,850 +الآخر عدد تركيز بس اللي احنا هنتعرف عليه اليوم هو + +13 +00:00:59,850 --> 00:01:06,210 +qualitative test for amino acid فحوصات نوعية للكشف + +14 +00:01:06,210 --> 00:01:12,950 +عن الأحمض الأمينيةفي البداية نحكي مقدمة عن الأحماض + +15 +00:01:12,950 --> 00:01:17,130 +الأمينية و هذه الأشياء حكيناها في المعمل الماضي + +16 +00:01:17,130 --> 00:01:21,850 +حكينا إن الطعام ينقسم إلى تلاتة إلى carbohydrate و + +17 +00:01:21,850 --> 00:01:25,270 +lipid و protein حكينا ال carbohydrate هو مصدر + +18 +00:01:25,270 --> 00:01:29,470 +الطاقة ال lipid هو مخزن الطاقة و ال protein هو + +19 +00:01:29,470 --> 00:01:34,250 +طاقة الخلايا لبناء الخلايا و للتجد حكيناها المرة + +20 +00:01:34,250 --> 00:01:39,900 +الماضيةبرضه حكينا عن الأحماض الأمينية إنه هي عبارة + +21 +00:01:39,900 --> 00:01:44,180 +عن الوحدة البنائية للبروتين وحكينا إنها بترتبط مع + +22 +00:01:44,180 --> 00:01:47,680 +بعض بـprotein bond حكينا الصيغة العامة للأحماض + +23 +00:01:47,680 --> 00:01:51,240 +الأمينية عبارة عن H وإن كل حمض أمين بيختلف عن + +24 +00:01:51,240 --> 00:01:57,580 +الآخر بال R ال side ال chain حكينا كمان المرة + +25 +00:01:57,580 --> 00:01:59,780 +الماضية إن الأحماض الأمينية + +26 +00:02:03,760 --> 00:02:06,880 +وين بتيجي الرابط اللي بيبتديها؟ بين مجموع كربوكسيل + +27 +00:02:06,880 --> 00:02:11,700 +من حمض أميني ومجموع أمين من حمض أميني آخر يتم نزع + +28 +00:02:11,700 --> 00:02:15,960 +جزء ماء في هذه العملية فسمينا التفاعلات تكون + +29 +00:02:15,960 --> 00:02:20,800 +الرابط اللي بيبتديها بـ Condensation Reaction لأنه + +30 +00:02:20,800 --> 00:02:24,500 +بينتج عنها ماء حكينا على الأطراف بيظل عند Free + +31 +00:02:24,500 --> 00:02:28,920 +Amino Group بنسميها الـ N Terminus و Free Carboxyl + +32 +00:02:28,920 --> 00:02:35,040 +Group سميناها الـ C Terminusهنا كمان إن الأحماض + +33 +00:02:35,040 --> 00:02:39,000 +الأمنية تنقسم حسب المصدر إلى essential و non + +34 +00:02:39,000 --> 00:02:43,320 +-essential ال essential الجسم غير قادر على تصنيعها + +35 +00:02:43,320 --> 00:02:47,040 +يجب توفيرها في الواجبات ال non-essential الجسم + +36 +00:02:47,040 --> 00:02:51,420 +قادر على تصنيحها فمش ضرور تكون موجودة في الواجبات + +37 +00:02:51,420 --> 00:02:58,610 +اليوميةو هنا حكينا أن أبسط حمض أميني هو ال glycine + +38 +00:02:58,610 --> 00:03:02,590 +ليش؟ لأن ال side-chain أو ال R-group هي عبارة عن + +39 +00:03:02,590 --> 00:03:06,730 +طرد هيدروجين فقط و حكينا كمان أن الحمض الأمين + +40 +00:03:06,730 --> 00:03:10,990 +الشاز أو الفريد باختلف عن غيره من الأحماض الأمينية + +41 +00:03:10,990 --> 00:03:16,430 +هو البرولينلأنه ماعندهوش amino group حرة اللي + +42 +00:03:16,430 --> 00:03:19,890 +متصلة في الـ central carbon سمناها primary amino + +43 +00:03:19,890 --> 00:03:24,530 +group في كل الأحماض الأمينية تسمى مجموعة الـ amino + +44 +00:03:24,530 --> 00:03:30,030 +group هي primary amino group أو free alpha amino + +45 +00:03:30,030 --> 00:03:35,030 +group إلا في حالة البرولين تسمى secondary amino + +46 +00:03:35,030 --> 00:03:39,270 +group أو amino group لأنها متصلة بالـ central + +47 +00:03:39,270 --> 00:03:47,470 +carbon من جهة بالـ sided chainمن جهة أخرى حكينا عن + +48 +00:03:47,470 --> 00:03:51,670 +الأحماض الأمنية وتقسيمها حسب ال polarity إلى polar + +49 +00:03:51,670 --> 00:03:53,050 +و non polar + +50 +00:03:56,470 --> 00:04:00,650 +charge و ال charge في منها positive charge و في + +51 +00:04:00,650 --> 00:04:04,790 +منها negative charge فهذه التقسيمة كلها سواء polar + +52 +00:04:04,790 --> 00:04:09,510 +او non polar تعتمد على ال side chain بتطلع على ال + +53 +00:04:09,510 --> 00:04:13,430 +side chain حكينا حكي ان اذا في بس كربون و هيدروجين + +54 +00:04:13,430 --> 00:04:18,930 +بتكون non polar اذا فيها مجموعات قطبية بتكون polar + +55 +00:04:18,930 --> 00:04:22,670 +بتطلع اذا كانت مشحونة بتكون charge و اذا غير + +56 +00:04:22,670 --> 00:04:25,390 +مشحونة بتكون uncharged + +57 +00:04:27,110 --> 00:04:31,130 +حكينا عن هذه الصورة اللي بتقسم للأحماض الأمينية + +58 +00:04:31,130 --> 00:04:35,610 +إلى non-polar و polar ال polar في منها uncharged و + +59 +00:04:35,610 --> 00:04:39,950 +في منها charged و في positive و في negative حكينا + +60 +00:04:39,950 --> 00:04:43,510 +في أحماض أمينية بنسميها aromatic amino acid + +61 +00:04:43,510 --> 00:04:47,070 +aromatic اللي هي بتحتوي في ال side chain على حلقة + +62 +00:04:47,070 --> 00:04:50,650 +بنزين إذا كان في ال side chain في حلقة بنسميها + +63 +00:04:50,650 --> 00:04:53,290 +aromatic amino acid + +64 +00:04:56,910 --> 00:05:00,770 +ويجي نحكي عن حاجة اسمها Ionization Ionization + +65 +00:05:00,770 --> 00:05:05,110 +معناها كيف يتصرف الحمض الأميني في الأوساط + +66 +00:05:05,110 --> 00:05:10,190 +المختلفة، في وسط قاعدي، في وسط حمضي، في neutral، + +67 +00:05:10,190 --> 00:05:15,330 +في اتش، في وسط المتعانيهلجت لو جينا و اتفرج على + +68 +00:05:15,330 --> 00:05:19,210 +المعادلة هاي اللي فوق في الوسط هذا حمض أميني موجود + +69 +00:05:19,210 --> 00:05:24,350 +في وسط متعدد الصيغة العامة لحمض أميني موجود في وسط + +70 +00:05:24,350 --> 00:05:29,790 +متعدد بتكون عدد الشحنات الموجبة بتساوي عدد الشحنات + +71 +00:05:29,790 --> 00:05:33,690 +السالمة ان هنا مكتوب CH2 هو الصيغة العامة للحمض + +72 +00:05:33,690 --> 00:05:38,150 +الأميني Central Carbon و Hydrogen و ال R group هي + +73 +00:05:38,150 --> 00:05:41,250 +عبارة عن ذرة الهيدروجين المعتبرينها هناوانقدش + +74 +00:05:41,250 --> 00:05:45,670 +three plus و COO minus هي الصيغة العامة للحمد + +75 +00:05:45,670 --> 00:05:49,090 +الأميني في الوسط المتعادل تكون الشحنات الموجبة + +76 +00:05:49,090 --> 00:05:54,830 +بتساوي الشحنات السالمةالجهاد الـ net charge بتكون + +77 +00:05:54,830 --> 00:05:59,330 +زيه لو جيت أخدت هذا الحمض الأميني حاطيته في وسط + +78 +00:05:59,330 --> 00:06:07,010 +حمضي وسط حمضي يعني جلالة الـ pH يعني أنه كان فيه + +79 +00:06:07,010 --> 00:06:11,130 +زيادة في أيونات الهيدروجين يعني هذا الوسط مليء بـ + +80 +00:06:11,130 --> 00:06:16,620 +H plus زيادةفالحمض الأمينى دخلته من المتعدل وحطيته + +81 +00:06:16,620 --> 00:06:20,120 +في وسط الحمضي وسط الحمضي فيه زيادة في أيونات + +82 +00:06:20,120 --> 00:06:24,400 +الهيدروجين الجاتمين بده يحتاج الهيدروجين هياخد من + +83 +00:06:24,400 --> 00:06:28,920 +الوسط COO- محتاج الهيدروجين فبتستحب من الوسط + +84 +00:06:28,920 --> 00:06:37,990 +هيدروجين و بتتشبع ب CRCOOHفبتصير CH2 COOH NH3 Plus + +85 +00:06:37,990 --> 00:06:44,990 +بصير الشكل العام له CH2 COOH NH3 Plus فأخذ ذرة + +86 +00:06:44,990 --> 00:06:49,960 +هيدروجيني صارت النت تشارج عليه positive chargeاللي + +87 +00:06:49,960 --> 00:06:53,040 +موجودة في المعادلة على اليسار هذا اللي هو الصيغة + +88 +00:06:53,040 --> 00:06:59,480 +العامة الحمض الأميني في وسط حمضي CH2COHNH3Plus + +89 +00:06:59,480 --> 00:07:03,580 +إنه الكربوكسيل أخدت أيون هيدروجين أو بروتون + +90 +00:07:03,580 --> 00:07:08,720 +هيدروجين من الوسط الحمضي اللي هي فيه فصارت COH نت + +91 +00:07:08,720 --> 00:07:13,960 +تشارج في الوسط الحمضي صارتPositive charge طبعا لو + +92 +00:07:13,960 --> 00:07:18,060 +أخدتها الوسط من الوسط المتعدد وحطته في وسط قاعدي + +93 +00:07:18,060 --> 00:07:25,280 +الوسط القاعدي مليء بـ OH- وسط بيكون مليء بـ OH- OH + +94 +00:07:25,280 --> 00:07:30,140 +- هي تحتاج إلى ذرة هيدروجين عشان تتكون جزئنا + +95 +00:07:30,140 --> 00:07:35,920 +فبتروح على أي ذر جزية بتنزع منه هيدروجين عشان + +96 +00:07:35,920 --> 00:07:40,320 +تتكوننا من عندنا بنقدر ننزع منه هيدروجين لأن اتش 3 + +97 +00:07:40,320 --> 00:07:46,960 +plusتاخد منه هيدروجين فبصير NH2 COO minus هتتغير؟ + +98 +00:07:46,960 --> 00:07:52,300 +لأ مش هتتغير فالوسط المتعدل CH2 NH3 plus COO minus + +99 +00:07:52,300 --> 00:07:57,360 +لما يروح على القاعدة اللي هي على اليمين بيصير NH2 + +100 +00:07:57,360 --> 00:08:02,860 +و COO minus اتغيرت من الـ NH3 نزعنا منها هيدروجين + +101 +00:08:02,860 --> 00:08:07,600 +و صارت NH2الـ net charge إيه لو بيكون minus ففي + +102 +00:08:07,600 --> 00:08:11,920 +حالة الوسط الحمضي .. في حالة وسط متعادل ال net + +103 +00:08:11,920 --> 00:08:16,360 +charge بتكون zero فحالة وسط حمضي بيكون ال net + +104 +00:08:16,360 --> 00:08:20,100 +charge positive في حالة الوسط القاعدي ال net + +105 +00:08:20,100 --> 00:08:24,700 +charge negativeهلجد؟ الحمض الأميني اللي بتكون + +106 +00:08:24,700 --> 00:08:29,120 +متساوي عليه الشحنات الموجبة و الشحنات السالبة و ال + +107 +00:08:29,120 --> 00:08:32,960 +net charge بتكون بتساوي zero بسميه Zwitterion + +108 +00:08:32,960 --> 00:08:37,580 +Zwitterion هو الحمض الأميني اللي تتساوي عليه + +109 +00:08:37,580 --> 00:08:42,180 +الشحنة الموجبة و الشحنة السالبة يعني الشحنة الكلية + +110 +00:08:42,180 --> 00:08:46,280 +تكون صفر وين موجود ال Zwitterion؟ في الوسط + +111 +00:08:46,280 --> 00:08:50,650 +المتعادل كان موجودبالوسط المتعدل الحمض الأميني + +112 +00:08:50,650 --> 00:08:54,790 +بيكون الشحن الموجبة بتساوي الشحن السالي يعني الشحن + +113 +00:08:54,790 --> 00:08:59,950 +الكلية بتساوي سفر وهذا بسميه Zwitterion Zwitterion + +114 +00:08:59,950 --> 00:09:03,870 +هو الحمض الأميني الذي تتساوي عليه الشحن الموجبة + +115 +00:09:03,870 --> 00:09:10,520 +والشحن السالي وندت شهر Zeroعند الوسط المتعادل هذا، + +116 +00:09:10,520 --> 00:09:13,240 +عند تكون الحمض الأميني اللي بتكون شحنات الموجبة + +117 +00:09:13,240 --> 00:09:16,340 +السالبة بتساوي الموجبة، في حاجة بنتسميها + +118 +00:09:16,340 --> 00:09:21,100 +isoelectric point أو الـ PR الـ PI أو الـ + +119 +00:09:21,100 --> 00:09:26,540 +isoelectric point هي قيمة BH بتتساوي عند الشحن + +120 +00:09:26,540 --> 00:09:32,320 +الموجبة والسالبة على سطح الحمض الأمينيوبالتالي، + +121 +00:09:32,320 --> 00:09:38,620 +شحنة الكلية صفر قيمة BH تتساوى عندها شحنة الموجبة + +122 +00:09:38,620 --> 00:09:43,760 +والسالبة على سطح الحمض الأمين وبالتالي، شحنة + +123 +00:09:43,760 --> 00:09:47,640 +الكلية بتساوي صفر هاي الـ Isoelectric point، + +124 +00:09:47,640 --> 00:09:53,260 +الإفتصار بـI تمام، في حاجة بنسميها protonated + +125 +00:09:53,260 --> 00:09:57,740 +معناها إنه اكتساب بروتون أو H plus في حاجة بنسميها + +126 +00:09:57,740 --> 00:10:02,780 +Deprotonated يعني فقد بروتوناللي بياخد H plus يعني + +127 +00:10:02,780 --> 00:10:07,800 +في الوسط الحمض زي COO minus اكتسبت H فهذه gain of + +128 +00:10:07,800 --> 00:10:12,800 +البروتون يعني صارلها protonated Deprotonated يعني + +129 +00:10:12,800 --> 00:10:16,760 +loss of البروتون زي الـ NH3 plus في الوسط القاعدة + +130 +00:10:16,760 --> 00:10:22,060 +لما حضيتها صارت NH2 نزعت منها H فبسميها .. بقول + +131 +00:10:22,060 --> 00:10:26,600 +عنها نصارلها Deprotonated فقدت البروتون + +132 +00:10:30,550 --> 00:10:34,490 +هنا بيحكيلي أن الـ Isoelectric point أو الـ PI هي + +133 +00:10:34,490 --> 00:10:39,090 +قيمة BH اللي بيكون فيها الانيونك بتساوي الكاتيونك + +134 +00:10:39,090 --> 00:10:45,350 +النت تشارج بتكون Zero كل حمض أميني له PI أو + +135 +00:10:45,350 --> 00:10:49,490 +Isoelectric point بتختلف عن غيره حسب شو؟ حسب ال + +136 +00:10:49,490 --> 00:10:52,830 +side chain فهو حاكي أن كل حمض أميني بيميزه عن غيره + +137 +00:10:52,830 --> 00:10:54,110 +side chain + +138 +00:10:56,690 --> 00:11:01,790 +نحكي في الجزء العملي للمعمل الأول جزء العملي بيحكي + +139 +00:11:01,790 --> 00:11:06,930 +عن qualitative test for amino acid بحوصات جودة + +140 +00:11:06,930 --> 00:11:10,710 +لالكشف عن الأحماض الأمينية النتيجة عندنا هتكون + +141 +00:11:10,710 --> 00:11:16,330 +positive أو negative«ظهور لون» أو «عدم ظهور لون» + +142 +00:11:16,330 --> 00:11:19,450 +في عندنا number of tests to detect the presence of + +143 +00:11:19,450 --> 00:11:23,210 +amino acid هذه الفحوصات الكاشف عن الأحمان الأمينية + +144 +00:11:23,210 --> 00:11:26,830 +largely depend on the nature of sided chain علشان + +145 +00:11:26,830 --> 00:11:29,770 +بيعتمدوا على الـsided chain لأنه حكي أن البيميز + +146 +00:11:29,770 --> 00:11:34,090 +حمض أمين عن الآخر هو الـsided chain الجد احنا + +147 +00:11:34,090 --> 00:11:38,210 +الفحوصات اللي هنشتغلها بيطلع معنا لون يتغير أو + +148 +00:11:38,210 --> 00:11:44,060 +مايتغيرهذا اللون له شدة intensity of color شدة + +149 +00:11:44,060 --> 00:11:47,940 +اللون هي بتكون تختلف يعني ممكن هو يتلون بس على + +150 +00:11:47,940 --> 00:11:52,580 +درجات من حاجة لتانية تكون درجة بتختلف شدة اللون هي + +151 +00:11:52,580 --> 00:11:56,860 +علشان بتعتمد بتعتمد على أول شي number of reacting + +152 +00:11:56,860 --> 00:12:00,900 +unit number of reacting unit اللي هي ال reacting + +153 +00:12:00,900 --> 00:12:05,040 +unit هي عبارة عن المادة الفعالةقداش عدد المادة + +154 +00:12:05,040 --> 00:12:08,780 +الفعالة الموجودة؟ إيش هي المادة الفعالة؟ دي الاشي + +155 +00:12:08,780 --> 00:12:12,940 +اللي بدور عليها الفحص أنا بشتغل فحص مثلا بيدور على + +156 +00:12:12,940 --> 00:12:15,980 +peptide bond إذا موجودة ال peptide bond، يعطيني + +157 +00:12:15,980 --> 00:12:19,900 +لون إذا مش موجودة، مش هيتغير اللون طب ال peptide + +158 +00:12:19,900 --> 00:12:23,160 +bond هذي ممكن تكون بس رابطتين، ويعطيني لون ممكن + +159 +00:12:23,160 --> 00:12:26,400 +تكون تلاتة ويعطيني لون بس هل اللون هيكون نفسه إذا + +160 +00:12:26,400 --> 00:12:30,080 +كانوا تنتين وإذا كانوا تلاتة؟ شدة اللون هتختلف + +161 +00:12:30,080 --> 00:12:34,810 +بناء على number of reacting unitالحاجة التانية + +162 +00:12:34,810 --> 00:12:37,890 +اللي بتعتمد عليها شدة اللون هي الـ accessibility + +163 +00:12:37,890 --> 00:12:42,050 +to reaction هل هذه المادة الفعالة الـ acting unit + +164 +00:12:42,050 --> 00:12:46,350 +قريبة من التفاعل، هل هي حرة، free، بتقدر تيجي + +165 +00:12:46,350 --> 00:12:48,990 +ترتبط، تشتغل مع التفاعل، مع الـ agent اللي أنا + +166 +00:12:48,990 --> 00:12:52,910 +حطيته، تشتغل و تتغير اللون، ولا إنها مشغولة، مش + +167 +00:12:52,910 --> 00:12:56,930 +هتقدر في حواجز، مش هتقدر تيجي ترتبطهي بتسميها + +168 +00:12:56,930 --> 00:13:00,810 +accessibility to reaction إذا تشدت اللون تعتمد على + +169 +00:13:00,810 --> 00:13:04,450 +حاشتين على ال number of reacting unit وعلى + +170 +00:13:04,450 --> 00:13:10,470 +accessibility to reaction إيش + +171 +00:13:10,470 --> 00:13:13,570 +هي الفحصات اللي هنستخدمها للكشف عن الأحماض + +172 +00:13:13,570 --> 00:13:19,070 +الأمينية؟ هنا فحص اسمه ninhydrin test for 3-alpha + +173 +00:13:19,070 --> 00:13:24,160 +amino groupعلى Free Alpha Amino Group إذا موجودة + +174 +00:13:24,160 --> 00:13:27,280 +بيتغير اللون وبيعطى positive إذا مش موجودة مش + +175 +00:13:27,280 --> 00:13:30,880 +هيتغير اللون فالـ Free Alpha Amino Group هاي + +176 +00:13:30,880 --> 00:13:35,000 +بسميها الـ Reacting Unit فحص التاني اسمه Bio-Red + +177 +00:13:35,000 --> 00:13:39,240 +Test بتدور على ال-peptide bond لإنه فحص ال + +178 +00:13:39,240 --> 00:13:45,040 +-xanthoproteic testZanto Proteic Test for Aromatic + +179 +00:13:45,040 --> 00:13:51,240 +Amino Acid لأ + +180 +00:13:51,240 --> 00:13:55,300 +الأحماض الأمنية اللي تحتوي على حلقة بنزين نشطة + +181 +00:13:55,300 --> 00:14:00,720 +نضيف هنا Activated Aromatic Amino Acidهنا فحص اسمه + +182 +00:14:00,720 --> 00:14:05,240 +hopkincol أو glycosilic acid reaction اللي هو اسمه + +183 +00:14:05,240 --> 00:14:09,580 +hopkincol، glycosilic acid reaction بيدور على الـ + +184 +00:14:09,580 --> 00:14:13,920 +Indole group الـ melons test for amino acid + +185 +00:14:13,920 --> 00:14:18,800 +containing hydroxylفينال جروب للفينول جروب الأمينو + +186 +00:14:18,800 --> 00:14:23,100 +أسد اللي بيحتوي على فينول جروب ساكيجوشي test for + +187 +00:14:23,100 --> 00:14:28,160 +ليجوانيديام جروب لليجوانيديام جروب ليد سالفايت + +188 +00:14:28,160 --> 00:14:33,080 +test بيدور على ال self-hydraile group للحمض الأمين + +189 +00:14:33,080 --> 00:14:36,240 +اللي يحتوي على self-hydraile group هو اللي هيعطيني + +190 +00:14:36,240 --> 00:14:39,360 +positive غير هيك مش هيعطيني positive + +191 +00:14:42,170 --> 00:14:46,290 +نجي نحكي عن أول فحص، أول فحص هو الـ Nenhedrine الـ + +192 +00:14:46,290 --> 00:14:49,010 +Nenhedrine إيش ال objective للفحص، إيش الهدف من + +193 +00:14:49,010 --> 00:14:52,730 +الفحص؟ to detect the presence of free alpha amino + +194 +00:14:52,730 --> 00:14:56,950 +group، بيدور على الـ free alpha amino group إذا + +195 +00:14:56,950 --> 00:15:00,970 +موجود free alpha amino group، هيتغير اللون، + +196 +00:15:00,970 --> 00:15:04,330 +بيعطيني لون بارد، في حالات اللي موجودة في free + +197 +00:15:04,330 --> 00:15:07,930 +alpha amino groupمين عنده free alpha amino group؟ + +198 +00:15:07,930 --> 00:15:11,390 +إذا ذاكرين الحمض الأميني، أيش الصيغة العامة له؟ + +199 +00:15:11,390 --> 00:15:14,750 +تكون من center carbon ومن الهيدروجينة ومن ال side + +200 +00:15:14,750 --> 00:15:18,530 +chain ومن carboxyl group ومن amino group amino + +201 +00:15:18,530 --> 00:15:23,350 +group هاي سميناها primary amino group أو alpha + +202 +00:15:23,350 --> 00:15:27,530 +amino group معادة في حالة البرولين سميناها amino + +203 +00:15:27,530 --> 00:15:32,840 +groupيعني الأحماض الأمينية كلها تحتوي على free + +204 +00:15:32,840 --> 00:15:37,700 +alpha amino group ما عدا لبرولين عنده amino group + +205 +00:15:37,700 --> 00:15:40,760 +يعني مين هيعطيني positive مع هذا الفحص لو أنا + +206 +00:15:40,760 --> 00:15:44,440 +اشتغلت مجموعة أحماض أمينية على هذا الفحص؟ كلهم + +207 +00:15:44,440 --> 00:15:47,540 +هيعطوني positive لأنهم كلهم بيحتوي على free alpha + +208 +00:15:47,540 --> 00:15:53,040 +amino group تمام؟طيب، إذا ال objective to detect + +209 +00:15:53,040 --> 00:15:55,520 +the presence of free alpha amino group هل موجود + +210 +00:15:55,520 --> 00:15:58,420 +free alpha amino group أو لا؟ إذا تغير اللغة يعني + +211 +00:15:58,420 --> 00:16:01,560 +موجود، إذا ما تغيرش يعني مش موجود طيب إيش ال + +212 +00:16:01,560 --> 00:16:05,620 +principle؟ مبتدأ العمل للفحص؟ كيف يشتغل الفحص؟ ال + +213 +00:16:05,620 --> 00:16:08,520 +principle لو نعملها على نظام معادلات بيسهل عليه + +214 +00:16:08,520 --> 00:16:12,380 +كيف هذا الفحص له ال principle؟ إنه عندنا amino + +215 +00:16:12,380 --> 00:16:15,940 +acid أنا بضيف حمض أميني، بضيف عليه نينهيدرينرياشا + +216 +00:16:15,940 --> 00:16:17,240 +إيش بيعمل ال + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/MUWHefMMBZ4.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/MUWHefMMBZ4.srt new file mode 100644 index 0000000000000000000000000000000000000000..dabbc6da96b0cef69132769ef0c6e78704b757f3 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/MUWHefMMBZ4.srt @@ -0,0 +1,1597 @@ +1 +00:00:00,220 --> 00:00:03,140 +عملنا qualitative analytical test for + +2 +00:00:03,140 --> 00:00:08,500 +carbohydrates اللي هي ما عملنا بيحكي عن أنه فحوصات + +3 +00:00:08,500 --> 00:00:14,360 +نوعية فحوصات جودة للكشف عن الـ carbohydrates عن + +4 +00:00:14,360 --> 00:00:18,800 +السكريات اليوم فحوصاتنا للكشف عن الـ carbohydrate + +5 +00:00:18,800 --> 00:00:23,180 +وهي فحوصات qualitative فحوصات جودة يعني بيطلع + +6 +00:00:23,180 --> 00:00:26,940 +معايا في الآخر لون هيكون positive أو negative مش + +7 +00:00:26,940 --> 00:00:32,480 +هيطلع معايا كمية أو رقم ماشي أهداف معملنا اليوم + +8 +00:00:32,480 --> 00:00:35,660 +بشكل عام المعمل كله بدنا نطلع منه general + +9 +00:00:35,660 --> 00:00:38,760 +information about carbohydrates بدنا نطلع منه + +10 +00:00:38,760 --> 00:00:41,740 +بمعلومات عامة عن الكربوهيدرات نعرف شو هي + +11 +00:00:41,740 --> 00:00:44,840 +الكربوهيدرات differentiate between carbohydrates + +12 +00:00:44,840 --> 00:00:49,420 +أني بدي أقارن .. بدي أفرد من أنواع الكربوهيدرات + +13 +00:00:49,420 --> 00:00:53,320 +أنواع السكريات qualitative analysis of + +14 +00:00:53,320 --> 00:00:57,000 +carbohydrates بعدين نشوف الفحوصات أو الجزء العملي + +15 +00:00:57,000 --> 00:01:02,240 +اللي هو فحوصات qualitative للكشف عن السكريات + +16 +00:01:03,510 --> 00:01:06,930 +Qualitative Test of Amino Acids Qualitative + +17 +00:01:06,930 --> 00:01:10,790 +Analytical Test إيش هي qualitative؟ it is + +18 +00:01:10,790 --> 00:01:13,810 +concerned with determining the identity of a + +19 +00:01:13,810 --> 00:01:17,930 +substance لمعرفة هوية هذه المادة بس بدي أعرف هل + +20 +00:01:17,930 --> 00:01:21,050 +هذه المادة موجودة أو لا مثلا سكر موجود أو لا + +21 +00:01:21,050 --> 00:01:25,710 +enable us to detect the presence of things برضه + +22 +00:01:25,710 --> 00:01:30,230 +نفس الكلام إنه أعرف هل هذه الموجودة الأشياء أو لا + +23 +00:01:30,950 --> 00:01:37,030 +بحوصاتك qualitative يعني موجود أو غير موجود بداية + +24 +00:01:37,030 --> 00:01:40,330 +بدنا نتعرف على الـ carbohydrates على السكرية + +25 +00:01:40,330 --> 00:01:45,070 +السكرية تم قسم إلى قسمين في منها simple saccharide + +26 +00:01:45,070 --> 00:01:47,930 +هي السكرية يعني simple سكرية وفي منها + +27 +00:01:47,930 --> 00:01:53,060 +polysaccharide سكرية بسيطة وسكرية تعدينة في البداية + +28 +00:01:53,060 --> 00:01:56,020 +نيجي نحكي عن الـ simple saccharide الـ saccharide + +29 +00:01:56,020 --> 00:02:00,420 +هي من خصائصها إنه إلها low molecular weight الـ + +30 +00:02:00,420 --> 00:02:03,780 +molecular weight الوزن الجزائي إلها قليل وكمان هي + +31 +00:02:03,780 --> 00:02:08,600 +soluble in water بتتوق في الميه وكمان هي sweet to + +32 +00:02:08,600 --> 00:02:13,840 +طارس طعمها حلو إذا الـ saccharide الوزن الجزائي + +33 +00:02:13,840 --> 00:02:19,310 +إلها قليل ذائبة في الماء وطعمها حلوبتنقسم إلى .. + +34 +00:02:19,310 --> 00:02:23,170 +أنا مكتبت قسمياً هما تلاتة في منها mono-saccharide + +35 +00:02:23,170 --> 00:02:28,750 +سكريات أحادية في di-saccharide سكريات ثنائية في + +36 +00:02:28,750 --> 00:02:33,990 +oligosaccharide ألاقيت mono-saccharide سكر واحد، + +37 +00:02:33,990 --> 00:02:37,250 +دي بس واحد، سكر واحد، simple sugar di-saccharide + +38 +00:02:37,250 --> 00:02:40,970 +هي double sugar، بيكون سكر ثنائي اتنين من الـ mono + +39 +00:02:40,970 --> 00:02:45,070 +بيتحدوا مع بعض oligo بتكون من تلاتة إلى تسعة، عدد + +40 +00:02:45,070 --> 00:02:49,480 +السكريات فيها من تلاتة إلى تسعة الـ Monosaccharide + +41 +00:02:49,480 --> 00:02:54,140 +هي simple sugar هو سكر واحد بيكون الصيغة العامة له + +42 +00:02:54,140 --> 00:03:04,170 +(CH2O)n لكل N N هي عدد ذرات الكعك الصيغة له (CH2O)n كل N N + +43 +00:03:04,170 --> 00:03:07,670 +هي عدد الذرات الكربون مثال عليها الـ + +44 +00:03:07,670 --> 00:03:12,330 +glyceraldehyde وهذا الـ glyceraldehyde فيه 3 ذرات + +45 +00:03:12,330 --> 00:03:18,390 +كربون فبتكون الصيغة العامة له C3H6O3 + +46 +00:03:19,600 --> 00:03:24,400 +في عندنا جيليكوز، فراكتوز، جالاكتوز، هدولة mono + +47 +00:03:24,400 --> 00:03:29,120 +-saccharide، سكريات إحادية، hexose بنسميها هم + +48 +00:03:29,120 --> 00:03:32,860 +التلاتة الجيليكوز و فراكتوز و جالاكتوز، بنسميهم + +49 +00:03:32,860 --> 00:03:36,720 +hexose، سكرية simple-saccharide، mono-saccharide، + +50 +00:03:36,720 --> 00:03:41,460 +ولكن سوداسي، عدد ذرّات الكربون فيه 6 في عندنا الـ + +51 +00:03:41,460 --> 00:03:46,080 +ribose و الـ manose و الـ xylose و الـ arabinose + +52 +00:03:46,080 --> 00:03:50,860 +هدولة فيهم خمس ذرات كربون بنطلق عليهم باسم Pentose + +53 +00:03:50,860 --> 00:03:55,340 +لذالن الـ monosaccharide هي simple sugar فيها سكر + +54 +00:03:55,340 --> 00:04:00,880 +واحد الصيغة العامة يلها (CH2O)n كل M أمثل عليها + +55 +00:04:00,880 --> 00:04:04,580 +اللي هو الـ glyceraldehyde بتكون من تلت ذرات كربون + +56 +00:04:05,010 --> 00:04:08,970 +ويعنى Gelicose وFructose وGalactose هدولة هكسوز + +57 +00:04:08,970 --> 00:04:13,630 +وكريات فيها 6 ذرات كاربوم نسميها هكسوز فيعنى + +58 +00:04:13,630 --> 00:04:20,330 +Ribose ومالنوز Ribose ومالنوز زيلوز أرابينوز هدولة + +59 +00:04:20,330 --> 00:04:26,280 +خماسي نسميها Pentose أما الـ Disaccharide هو Double + +60 +00:04:26,280 --> 00:04:29,960 +Sugar سكة تنائية بتكون من اتنين Monosaccharide + +61 +00:04:29,960 --> 00:04:37,580 +بيتتحدوا مع بعض الصيغة العامة له C12H22O11 + +62 +00:04:37,580 --> 00:04:42,980 +هي سكرين تنائيين بيجوا بيتتحدوا مع بعض بتكون من ست + +63 +00:04:42,980 --> 00:04:46,980 +ذرات كاربون يعني الصيغة أصلاً لكل واحد منهم هي + +64 +00:04:46,980 --> 00:04:49,700 +C6H12O6 + +65 +00:04:53,840 --> 00:04:57,420 +C6H12O6 إذن الـ «تايسا كرايد» هو اتحاد سكريين + +66 +00:04:57,420 --> 00:05:01,340 +تنائيين عبارة عن «هيكسوز» عبارة عن «سوداسي» C6 للـ + +67 +00:05:01,340 --> 00:05:04,920 +«رات كاربون» يعني الصيغة لكل واحد منهم من هدول + +68 +00:05:04,920 --> 00:05:11,200 +الوحيد اللي قاشوا اتحدوا مع بعض هي «C6H12O6» + +69 +00:05:11,880 --> 00:05:17,200 +يجي اتنين مع بعض C6H12O6 + C6H12O6 بيتحدوا + +70 +00:05:17,200 --> 00:05:22,520 +مع بعض افترض يعطيني Dice Caride سيغته العامة C12 + +71 +00:05:22,520 --> 00:05:28,880 +H24O12 طب هنا مكتوب ان الـ Dice Caride السيغة + +72 +00:05:28,880 --> 00:05:36,810 +العامة له C12H22O11 موين راحت؟ ذرتين هيدروجين + +73 +00:05:36,810 --> 00:05:41,770 +وذرة أكسوجين مفقودين مفقودين في تكوين الرابط + +74 +00:05:41,770 --> 00:05:48,110 +السكرية بين السكريان والوحديان ارتباط سكريان + +75 +00:05:48,110 --> 00:05:53,130 +ووحديان مع بعض عشان يكونوا السكر التنائي بيرتبطوا + +76 +00:05:53,130 --> 00:05:59,080 +مع بعض برابط سكرية اسمها glycosidic bond هاي الـ + +77 +00:05:59,080 --> 00:06:05,840 +glycosidic point عندما تتكون ينتج عنها جزء ماء، + +78 +00:06:05,840 --> 00:06:11,380 +نزع جزء ماء فاسم التفاعل اللي بينتج عنه نزع جزء + +79 +00:06:11,380 --> 00:06:17,200 +ماء هو Condensation Reaction نفس التفاعل تكون + +80 +00:06:17,200 --> 00:06:21,470 +الرابط الـ PPD اللي حكينا عنه فعشان هي صيغة + +81 +00:06:21,470 --> 00:06:27,410 +السكريات السونية صارت C12H22O11 + +82 +00:06:27,410 --> 00:06:32,610 +ونزعنا جزء ماء لتكوين الرابط السكرية اللي اسمها + +83 +00:06:32,610 --> 00:06:36,760 +glycosidic bond طيب، إيش الأمثلة على الـ + +84 +00:06:36,760 --> 00:06:41,400 +Disaccharide؟ عندنا Maltose، Saccharose و Lactose، + +85 +00:06:41,400 --> 00:06:45,680 +هدول سكريات و نايم حكينا إن هما عبارة عن اتحاد + +86 +00:06:45,680 --> 00:06:49,900 +سكريين أحدين مع بعض لو جينا حكينا عن الـ Maltose، + +87 +00:06:49,900 --> 00:06:53,680 +الـ Maltose هو عبارة عن اتحاد جليكوز مع جليكوز، + +88 +00:06:53,680 --> 00:06:57,900 +بيتحدوا مع بعض، بيكونولي Maltose الـ Saccharose هو + +89 +00:06:57,900 --> 00:07:03,060 +عبارة عن اتحاد جليكوز مع Fructose الـ Lactose هو + +90 +00:07:03,060 --> 00:07:09,080 +عبارة عن اتحاد جليكوز مع Galactose لذا الملتوز + +91 +00:07:09,080 --> 00:07:14,440 +جليكوز و جليكوز السكاروز جليكوز و فراكتوز اللاكتوز + +92 +00:07:14,440 --> 00:07:19,300 +هو جليكوز و Galactose والـ Oligo حكينا عنها أنها + +93 +00:07:19,300 --> 00:07:24,080 +بتتكون من 3 إلى 9 سكريات مع بعض أما بالنسبة لـ + +94 +00:07:24,080 --> 00:07:27,920 +Polysaccharide اللي هي عديدة التسكر هي Complex + +95 +00:07:27,920 --> 00:07:34,330 +Sugar هي سكريات معقدة من خصائصها إنه إلها high + +96 +00:07:34,330 --> 00:07:38,790 +molecular weight الوزن الجزائي لها عالي Insoluble + +97 +00:07:38,790 --> 00:07:42,350 +in water ما بتدوب في الماء لأنها عبارة عن سنسلة + +98 +00:07:42,350 --> 00:07:47,670 +طويلة بتفرعات فبيكون Insoluble كمان هي tasteless + +99 +00:07:47,670 --> 00:07:53,240 +لا طعم لها حكينا إنه هي multiple sugar تكون فيها + +100 +00:07:53,240 --> 00:07:57,740 +تفارع صيغة العامة ليها غير مطلوبة أمثلة عليها هي + +101 +00:07:57,740 --> 00:08:02,460 +الـ starch اللي هو النشا النباتي و الـ glycogen هو + +102 +00:08:02,460 --> 00:08:07,020 +النشا الحيواني الـ cellulose اللي بتستخدم النبات + +103 +00:08:07,020 --> 00:08:11,660 +لبناء الـ cell wall اللِّينِن والكايتن اللي بتستخدم + +104 +00:08:11,660 --> 00:08:15,620 +الحشرات لبناء الـ cell wall ده من الأمثل على ال + +105 +00:08:15,620 --> 00:08:20,320 +polysaccharide starch نشا النباتي وجلايكوجن نشا + +106 +00:08:20,320 --> 00:08:24,340 +حيواني cellulose اللي بيستخدم في النبات لبناء ال + +107 +00:08:24,340 --> 00:08:29,640 +cell wall اللِّينِن والكايتن اللي بيستخدم في الحشرات + +108 +00:08:29,640 --> 00:08:34,900 +لبناء الـ cell wall بينهاج اسمها الـ functional + +109 +00:08:34,900 --> 00:08:39,520 +group functional group هي منطقة في المُركّب تحدد + +110 +00:08:39,520 --> 00:08:43,720 +خصائصه هي region of molecules that give it a + +111 +00:08:43,720 --> 00:08:48,860 +particular property single molecule can have more + +112 +00:08:48,860 --> 00:08:51,620 +than one functional group as parts of its + +113 +00:08:51,620 --> 00:08:55,380 +structure ممكن يكون عنده أكتر من functional group + +114 +00:08:56,660 --> 00:08:59,560 +الـ active part أو الـ functional group اللي + +115 +00:08:59,560 --> 00:09:04,620 +موجودة في السكريات هي الديهيد أو كيتون group بتكون + +116 +00:09:04,620 --> 00:09:09,540 +الديهيد أو كيتون الديهيد أو كيتون and هيدروكسيل + +117 +00:09:09,540 --> 00:09:13,980 +group لذلك اللي موجود بيكون الديهيد أو كيتون أو + +118 +00:09:13,980 --> 00:09:16,700 +هيدروكسيل group هذا اللي بيكونوا موجودين في + +119 +00:09:16,700 --> 00:09:21,800 +السكريات هي الـ functional group طلع تحت إيش الفرق + +120 +00:09:21,800 --> 00:09:25,440 +بين الـ Aldehyde وإيش الفرق بينه وبين الـ Ketone + +121 +00:09:25,440 --> 00:09:31,620 +الـ Aldehyde بتكون عندنا C مرتبطة مع الـ double + +122 +00:09:31,620 --> 00:09:37,540 +bond O من جهة مرتبطة بذرة هيدروجين ومن الجهة + +123 +00:09:37,540 --> 00:09:42,510 +التانية مرتبطة بـ R group، بمجموعة إذاً في الـ + +124 +00:09:42,510 --> 00:09:47,230 +aldehyde بتكون عنا الـ C=O مرتبطة من + +125 +00:09:47,230 --> 00:09:53,150 +جهة بذرة هيدروجين ومن جهة تانية مرتبطة بـ R group + +126 +00:09:53,150 --> 00:09:57,470 +مجموعة مش بذرة هيدروجين بسيطة فقط وإنما بمجموعة + +127 +00:09:57,470 --> 00:10:00,970 +إذا لاجينا الـ C=O من جهة مرتبطة بذرة + +128 +00:10:00,970 --> 00:10:04,950 +هيدروجين ومن جهة تانية بمجموعة بـ R group بسميها + +129 +00:10:04,950 --> 00:10:10,330 +aldehyde أما إذا شوفت الـ C=O مرتبطة من + +130 +00:10:10,330 --> 00:10:14,690 +جهة بـ R-group مجموعة ومن جهة التانية كمان R-group + +131 +00:10:14,690 --> 00:10:19,930 +مجموعة بسميها كيتون لذن الـ aldehyde بتكون الـC=O + +132 +00:10:19,930 --> 00:10:24,970 +مرتبطة من جهة بـH ومن جهة بـR أما الكيتون بتكون + +133 +00:10:24,970 --> 00:10:31,990 +الـC=O مرتبطة من جهة بـR ومن جهة بـR تاني زي تحت + +134 +00:10:31,990 --> 00:10:35,410 +مثل عن الـGlucose و الـFructose لو جينا تلالنا على + +135 +00:10:35,410 --> 00:10:38,190 +الـ Structure للـ Glycose نيجي نطلع الـ C= + +136 +00:10:38,190 --> 00:10:42,290 +O وينها، هي على الشمال، C=O محوطة + +137 +00:10:42,290 --> 00:10:47,450 +عليها، إيش مرتبطة من جهة مرتبطة بضارة هيدروجين؟ من + +138 +00:10:47,450 --> 00:10:51,610 +الجهة التانية مرتبطة بمجموعة، بـ R group، اللي هي C + +139 +00:10:51,610 --> 00:10:57,640 +-O-H-H إذا من جهة مرتبطة بـ H ومن جهة بـ R مين يبقى + +140 +00:10:57,640 --> 00:11:01,500 +هيكون Aldehyde ولا كيتون الجليكوز؟ أكيد هيكون + +141 +00:11:01,500 --> 00:11:05,360 +Aldehyde لأنه مرتبطة C=O من جهة بـ R + +142 +00:11:05,360 --> 00:11:10,060 +ومن جهة بـ H لو جينا للفركتوز مكتوب بالناس بال + +143 +00:11:10,060 --> 00:11:13,260 +structure C=O اللي هي محوط عليها من + +144 +00:11:13,260 --> 00:11:19,130 +جهة مرتبطةبـ R group اللي هي CHHOH من الجهة + +145 +00:11:19,130 --> 00:11:23,650 +التانية مرتبطة بـ CHOH برضه R تانية إذا الـ C + +146 +00:11:23,650 --> 00:11:27,630 +=O في الفركتوز متصلة من الجهتين بـ R من + +147 +00:11:27,630 --> 00:11:33,250 +جهة و R من جهة يبقى هتكون كيتون تمام؟ إذا الجليكوز + +148 +00:11:33,250 --> 00:11:37,850 +عبارة عن الديهايد والفركتوز عبارة عن كيتون أصبحنا + +149 +00:11:37,850 --> 00:11:42,230 +عارفين إيش الفرق بين الالديهايد وكيتون بحكينا إن + +150 +00:11:42,230 --> 00:11:47,970 +الالديهايد بتكون على كربونا رقم 1 والكيتون بيكون + +151 +00:11:47,970 --> 00:11:52,170 +على كربونا رقم 2 إنه بدي أرقم تقول لو جينا على + +152 +00:11:52,170 --> 00:11:55,330 +الجليكوز نيجي الرقم من الكربون نبدأ الترقيم من + +153 +00:11:55,330 --> 00:12:00,850 +الجهة الأقرب للـ C=O الترقيم يبدأ من الجهة الأقرب + +154 +00:12:00,850 --> 00:12:04,730 +للـ C=O من ضهر هذه الجهة من عند الـ functional + +155 +00:12:04,730 --> 00:12:07,390 +group من الجهة الأقرب للـ functional group من عند + +156 +00:12:07,390 --> 00:12:10,770 +الـ C=O من ضهر هتطلع كربونا رقم واحد ومتصلة من جهة + +157 +00:12:10,770 --> 00:12:15,110 +الـ H ومن جهة المجموعة فالالدهيد في الجلوكوز الـ + +158 +00:12:15,110 --> 00:12:19,540 +C=O من ضهر موجود على رقم كربونا رقم واحد لو جينا على + +159 +00:12:19,540 --> 00:12:22,760 +الـ Fructose جينا الرقم من اليسارها، الرقم هي في + +160 +00:12:22,760 --> 00:12:26,580 +عندي كربونا رقم 1، وبعدين 2 كربونا اللي هي C + +161 +00:12:26,580 --> 00:12:31,440 +=O في الـ Ketone، في الـ Fructose اللي + +162 +00:12:31,440 --> 00:12:37,860 +هي موجودة على كربونا رقم 2 هنا حاجة اسمها Sugar + +163 +00:12:37,860 --> 00:12:43,560 +Nomenclature اللي هي السكر وصورته كأنه انعكسه في + +164 +00:12:43,560 --> 00:12:47,700 +المرايا كأنه mirror image أن السكر له انعكاس نفس + +165 +00:12:47,700 --> 00:12:53,820 +السكر موجود على شكلين في منه الـD وأقل بنسميهم + +166 +00:12:53,820 --> 00:12:56,760 +يعني مثلا الـGelicose في منه الـD-Gelicose وأقل + +167 +00:12:56,760 --> 00:13:00,940 +الـGelicose كيف هذا بدي أقرر هل هو الـD ولا الأقل؟ + +168 +00:13:01,480 --> 00:13:05,080 +لما نكتب السكر الـ structure له بشكل linear بشكل + +169 +00:13:05,080 --> 00:13:10,540 +خطي بشكل عمودي بدي أرقم الـ carbon بيطلع على + +170 +00:13:10,540 --> 00:13:18,020 +carbonة رقم 5 بيطلع على carbonة رقم 5 إذا الـ OH + +171 +00:13:18,020 --> 00:13:23,560 +موجودة إلى جهة الـ left إلى جهة اليسار بيكون الـ L + +172 +00:13:24,460 --> 00:13:29,280 +دي هتطلع على كربونا رقم 5 فنطلع على الـ Hydroxyl + +173 +00:13:29,280 --> 00:13:32,160 +group اللي متصلة فيها اللي هي الـ OH اللي متصلة + +174 +00:13:32,160 --> 00 + +201 +00:15:19,430 --> 00:15:25,570 +ولا إلى ال-right؟ لل-left إذا هندقها left إذا هو + +202 +00:15:25,570 --> 00:15:31,380 +الـfour في عندنا السُكر لما بدي أرسم الـ structure + +203 +00:15:31,380 --> 00:15:35,580 +للسُكريات في منها شكل إيه؟ في منها شكل Linear خطي + +204 +00:15:35,580 --> 00:15:41,040 +عمودي بيكون وفي منها شكل حلقة هلجيت الشكل الـ + +205 +00:15:41,040 --> 00:15:44,180 +Linear اللي عندي؟ حكينا بنقدر نكتب عليه هو الـ D + +206 +00:15:44,180 --> 00:15:47,720 +أو R هلجيت لو عند الـ Linear هذا وبتعمل منه حلقة + +207 +00:15:47,720 --> 00:15:54,590 +كيف؟ بربط Carbon رقم 5 مع الـ functional group كيف + +208 +00:15:54,590 --> 00:16:00,070 +بدأ أحول من Linear أو عمودي لمغلق برابط Carbon رقم + +209 +00:16:00,070 --> 00:16:03,330 +5 مع الـ Functional Group ألقيت عندي حلقتين + +210 +00:16:03,330 --> 00:16:07,070 +هايومها، احكيلي الحلقة لما نسميها، بنسميها Alpha + +211 +00:16:07,070 --> 00:16:10,490 +أو Beta، هل هي Alpha أو Beta كيف بدها تكون Alpha + +212 +00:16:10,490 --> 00:16:16,490 +أو Beta، كيف بدأ أميز هل هي Alpha أو Beta؟ بحكي ليه + +213 +00:16:16,490 --> 00:16:21,970 +بنطلع على Carbon رقم 1؟ أشوف الـ OH المتصل فيها، + +214 +00:16:21,970 --> 00:16:26,130 +هل هي إلى الأسفل أو للأعلى؟ إذا الـ OH المتصلة مع + +215 +00:16:26,130 --> 00:16:30,870 +Carbon رقم 1 كانت below، كانت للأسفل، أسفل + +216 +00:16:30,870 --> 00:16:36,060 +الحلقة، بنسميها Alpha إذا كانت الـ OH متصلة في + +217 +00:16:36,060 --> 00:16:40,880 +الكربونة رقم 1 للأعلى، بسميه Beta يعني لو جينا + +218 +00:16:40,880 --> 00:16:45,640 +الحلقتين الموجودين عندنا، بنرقم الكربون عند كل + +219 +00:16:45,640 --> 00:16:48,580 +نقطة، عند كل زاوية، بيكون فيها ذرة كربون في + +220 +00:16:48,580 --> 00:16:52,120 +الحلقة هلجيت هذه الكربون، بدي أرقمها، من أين نبدأ + +221 +00:16:52,120 --> 00:16:55,340 +ترقيم حكينا؟ من عند الـ functional group كيف تتعرف + +222 +00:16:55,340 --> 00:16:57,700 +في الـ functional group في الحلقة؟ بتكون مرتبطة في + +223 +00:16:57,700 --> 00:17:00,500 +الـC double bond O مش هي بتكون مرتبطة في الـA + +224 +00:17:00,500 --> 00:17:04,540 +فهي الـA هي الكربونة المتصلة فيها هي كربونة رقم 1 + +225 +00:17:04,540 --> 00:17:10,860 +برقم 1,2,3,4,5,6 مركزين معايا على الحلقة الأولى + +226 +00:17:10,860 --> 00:17:15,430 +اللي علي الشمال أول حلقة هي مرقمة من عند الـ + +227 +00:17:15,430 --> 00:17:20,770 +Functional Group 1,2,3,4,5,6 كربونة رقم 1 اللي + +228 +00:17:20,770 --> 00:17:24,690 +قد تطلع عليها When الـ OH هي بالأزرق الـ OH هل هي + +229 +00:17:24,690 --> 00:17:28,810 +للأسفل ولا للأعلى؟ للأسفل، إذن هو Alpha-Glucose + +230 +00:17:29,520 --> 00:17:33,320 +جينا على الحلقة الثانية، بدي أرقم الـ Carbon، من + +231 +00:17:33,320 --> 00:17:36,500 +وين أرقم؟ من عند الـ Functional Group، واحد، + +232 +00:17:36,500 --> 00:17:41,000 +اثنين، ثلاثة، أربعة، خمسة، ستة، هجد أشوف الـ OH + +233 +00:17:41,000 --> 00:17:44,540 +المتصلة في Carbon رقم واحد، هيو معلم ليها بالازرق + +234 +00:17:45,010 --> 00:17:49,150 +وين موجودة للأعلى أو للأسفل؟ موجودة الـ OH للأعلى + +235 +00:17:49,150 --> 00:17:53,550 +above the ring إذا هو Beta Glucose إذا لما بدي + +236 +00:17:53,550 --> 00:17:57,590 +أسمي الحلقة Alpha ولا Beta بناءً على الـ OH + +237 +00:17:57,590 --> 00:18:03,430 +المتصلة بكربونة رقم 1 هل هي للأعلى ولا للأسفل؟ + +238 +00:18:04,720 --> 00:18:08,600 +بنحكي عن الـ mono-saccharide الـ mono-saccharide + +239 +00:18:08,600 --> 00:18:12,700 +حكينا إن هي سكريات وحيدة وبتختلف في عدد الراتد + +240 +00:18:12,700 --> 00:18:16,760 +الكربون في منها هكسوس سداسية وفي منها خماسية بنتوز + +241 +00:18:16,760 --> 00:18:20,220 +بيحكي لي في منها كمان السكريات إحنا حكينا بشكل عام + +242 +00:18:20,220 --> 00:18:23,740 +في منها عندها تحتوي على aldehyde group في منها + +243 +00:18:23,740 --> 00:18:27,540 +تحتوي على كيتون كيتونيجون فالـ mono-saccharide بيحكي لي + +244 +00:18:27,540 --> 00:18:32,260 +بتنقسم إلى قسمين في منها aldose وفي منها ketose + +245 +00:18:33,210 --> 00:18:37,510 +ماشي يعني الـ Dose؟ يعني تحتوي على Aldehyde group + +246 +00:18:37,510 --> 00:18:41,770 +الـ Dose معناها إنه عندها Aldehyde group طب و + +247 +00:18:41,770 --> 00:18:45,030 +حكينا وين الـ Aldehyde group بتكون؟ حكينا بتكون + +248 +00:18:45,030 --> 00:18:50,870 +موجودة على كربونة رقم 1 أما Ketose معناها إنه + +249 +00:18:50,870 --> 00:18:55,970 +تحتوي على كيتون group وحكينا إن الكيتون بتكون على + +250 +00:18:55,970 --> 00:19:00,850 +كربونة رقم 2 إذن الـ Dose اللي بتحتوي على الديهيد + +251 +00:19:00,850 --> 00:19:05,330 +جروب بتكون على كربونة رقم واحد أشهر مثال على الـ ال + +252 +00:19:05,330 --> 00:19:09,670 +Dose هو الجلوكوز سكر الجلوكوز يحتوي على الديهيد + +253 +00:19:09,670 --> 00:19:15,470 +جروب فبسميه الـ Dose وأصلا الـ جلوكوز هو سكر هو + +254 +00:19:15,470 --> 00:19:20,630 +هكسوز يحتوي على ست ذرات كربون حكينا عنه هكسوز فبقدر + +255 +00:19:20,630 --> 00:19:26,470 +أطلق عليه اسم الـ Aldohexose الجلوكوز بقدر أطلق عليه + +256 +00:19:26,470 --> 00:19:30,530 +اسم Aldohexose من هون أجت كلمة Aldo لأنه عنده + +257 +00:19:30,530 --> 00:19:36,250 +Aldehyde group وhexose لأنه ست ذرات كربون فبالكيتوز + +258 +00:19:36,250 --> 00:19:40,270 +اللي تحتوي على كيتون group أشهر مثال عليها هو + +259 +00:19:40,270 --> 00:19:46,600 +الفركتوز والـ Fructose أصلا هو هكسوز هو يحتوي على + +260 +00:19:46,600 --> 00:19:52,300 +6 ذرات كربون اللي هو سداسي فبقدر أطلق عليه اسم + +261 +00:19:52,300 --> 00:19:58,280 +كيتوهكسوز كيتوهكسوز معناه أنه يحتوي على كيتون جروب + +262 +00:19:58,280 --> 00:20:05,110 +وهو سداسي يحتوي على 6 ذرات كربون بنحكي عن الـ + +263 +00:20:05,110 --> 00:20:08,190 +polysaccharide الـ polysaccharide حكينا هي العديد + +264 +00:20:08,190 --> 00:20:12,130 +من التسكر من الأمثلة عليها، عندنا أول مثال الـ + +265 +00:20:12,130 --> 00:20:16,190 +amylose الـ amylose هو عبارة عن سلسلة من سكر + +266 +00:20:16,190 --> 00:20:20,430 +الجلوكوز جليكوز بوليمر، هي الرسمة عندنا الـ + +267 +00:20:20,430 --> 00:20:24,690 +structure له للـ amylose أنه عبارة عن سكر الجليكوز + +268 +00:20:24,690 --> 00:20:29,620 +متصل مع بعض و لبعض، بوليمر من الجليكوز ألفا واحد + +269 +00:20:29,620 --> 00:20:34,200 +لأربعة لينكش ان هي الرابط الموجودة بينهم اسمها الفا + +270 +00:20:34,200 --> 00:20:38,500 +واحد لأربعة ليش كيف سميناها الفا واحد لأربعة؟ هلجيت + +271 +00:20:38,500 --> 00:20:41,420 +الفا من وين أجت؟ حكينا من الطلع على كربونة رقم + +272 +00:20:41,420 --> 00:20:45,040 +واحد لو جينا على الحلقة الأولى على اليسار تيجي على + +273 +00:20:45,040 --> 00:20:49,380 +الكربونة لو طلعت على الـ OH هل هي below ولا above؟ + +274 +00:20:49,380 --> 00:20:55,470 +لاجي الـ OH below الـ OH لتحت اسمها Alpha طيب واحد + +275 +00:20:55,470 --> 00:20:59,750 +لأربعة هذا اسم الموقع الرابطة بين الجلوكوز الأول + +276 +00:20:59,750 --> 00:21:03,370 +والجلوكوز الثاني لو جينا على الجلوكوز الأول هيوم + +277 +00:21:03,370 --> 00:21:07,970 +رقم اللي على الشمال عندك واحد كربونة رقم واحد اتصلت + +278 +00:21:07,970 --> 00:21:12,540 +مع كربونة رقم أربعة من الجلوكوز الثاني باسم الرابط + +279 +00:21:12,540 --> 00:21:18,560 +ألفا واحد لأربعة ألفا عشان الـ OH لتحت واحد لأربعة + +280 +00:21:18,560 --> 00:21:22,840 +لأن كربونة رقم واحد من جلوكوزي الأول اتصلت مع + +281 +00:21:22,840 --> 00:21:28,090 +كربونة رقم أربعة من جلوكوزي الثاني مثال ثاني على + +282 +00:21:28,090 --> 00:21:31,530 +الـ polysaccharide اللي هو الـ amylobectin الـ + +283 +00:21:31,530 --> 00:21:35,850 +amylobectin بيشبه الـ amylose هو عبارة عن مجموعة + +284 +00:21:35,850 --> 00:21:39,670 +من الجلوكوز متصل مع بعض و لبعض فهو جلوكوز بوليمر + +285 +00:21:39,670 --> 00:21:43,810 +برابط ألفا وواحد لأربعة وعرفنا ألفا جاية الـ OH + +286 +00:21:43,810 --> 00:21:47,410 +لتحت واحد لأربعة اللي هي كربونة رقم واحد السكر + +287 +00:21:47,410 --> 00:21:50,830 +الأول مع كربونة رقم أربعة من السكر الثاني ارتبطوا + +288 +00:21:50,830 --> 00:21:54,690 +مع بعض بس الزيادة على الـ Amylose إنه عنده branch + +289 +00:21:54,690 --> 00:22:00,830 +عنده تفرع من سكر الجلوكوز مكون رابطة اسمها Alpha 1 + +290 +00:22:00,830 --> 00:22:06,090 +لـ 6 Alpha 1 ل 6 Alpha من وين جاي؟ إنه الـ OH لتحت + +291 +00:22:06,090 --> 00:22:12,130 +1 ل 6 إنه التفرع جاي وين؟ عند Carbon رقم 1 من + +292 +00:22:12,130 --> 00:22:16,250 +الحلقة اللي فوق مع Carbon رقم 6 من الحلقة اللي + +293 +00:22:16,250 --> 00:22:21,180 +تحت إذن الـ Amylose هو polysaccharide عبارة عن + +294 +00:22:21,180 --> 00:22:25,680 +جلوكوز بوليمر الرابطة ألفا واحد لأربعة Amylopectin + +295 +00:22:25,680 --> 00:22:29,920 +برضه هو polysaccharide جليكوز بوليمر عنده ألفا + +296 +00:22:29,920 --> 00:22:36,700 +لواحد لأربعة وعنده كمان branch رابطة ألفا واحد لستة + +297 +00:22:40,600 --> 00:22:43,920 +مثال آخر على الـ polysaccharide اللي هي عديد + +298 +00:22:43,920 --> 00:22:47,360 +التسكر هو الـ Glycogen الـ Glycogen زي الـ + +299 +00:22:47,360 --> 00:22:51,040 +amylobectin عنده رابط عنده polymer من جلوكوز ألفا + +300 +00:22:51,040 --> 00:22:54,880 +واحد لأربعة وعنده branch ألفا واحد لستة لكن + +301 +00:22:54,880 --> 00:22:58,980 +التفرعات اللي عنده أكثر من تفرعات الـ amylobectin + +302 +00:22:58,980 --> 00:23:03,280 +زي الـ I-Glycogen more ألفا واحد لستة branch + +303 +00:23:03,280 --> 00:23:08,800 +التفرعات زيادة وكل ما زادت التفرعات في السكر، هذا + +304 +00:23:08,800 --> 00:23:14,000 +بيجعل السكر ضعيف ويكون سهل التكسّر، فالـ Glycogen + +305 +00:23:14,000 --> 00:23:18,160 +عشان تفرعاته أكثر، فهذا بيخليه Rapid glucose + +306 +00:23:18,160 --> 00:23:22,620 +release from Glycogen، لما الجسم يحتاج glucose، + +307 +00:23:22,620 --> 00:23:26,660 +أسرع يجي أنه يكسّر الـ Glycogen ويعطيني glucose، + +308 +00:23:26,660 --> 00:23:31,520 +لأنه عنده تفرعات زيادة، فهذا بيتكسر بسرعة وبيحرر + +309 +00:23:31,520 --> 00:23:36,260 +سكر الـ glucose لما يحتاجه الجسم، ليش سهل التكسّر + +310 +00:23:36,260 --> 00:23:41,980 +بسبب زيادة التفرعات مثال آخر هو الـ cellulose + +311 +00:23:41,980 --> 00:23:45,520 +حكينا الـ cellulose يستخدم في الـ plant cell wall + +312 +00:23:45,520 --> 00:23:49,800 +في بناء الـ cell wall للـ plant للنبات هو عبارة عن + +313 +00:23:49,800 --> 00:23:55,000 +linear chain سلسلة طويلة من السكر ولكن هي الرابطة + +314 +00:23:55,000 --> 00:24:01,030 +Beta 1L4 بيتا ليش؟ لأن الـ OH للحلقة موجودة above + +315 +00:24:01,030 --> 00:24:07,550 +بوجودة للأعلى OH للأعلى، إذا بيكون بيتا 1 ل 4 لأن + +316 +00:24:07,550 --> 00:24:11,410 +الرابط بين كل حلقة والثانية جاية من كربون رقم واحد + +317 +00:24:11,410 --> 00:24:15,510 +من الحلقة الأولى مع كربون رقم أربعة من الحلقة + +318 +00:24:15,510 --> 00:24:20,170 +الثانية إذا الـ cellulose بيكون لينيار من الـ + +319 +00:24:20,170 --> 00:24:27,700 +glucose بوليمر من الـ glucose برابطة بيتا 1 ل 4 فيه + +320 +00:24:27,700 --> 00:24:31,280 +إنه تقسيم للسكريات بناء على الـ reducing هل هو + +321 +00:24:31,280 --> 00:24:35,240 +reducing sugar أو non-reducing sugar في البداية + +322 +00:24:35,240 --> 00:24:37,500 +نحكي إيش يعني oxidation وإيش يعني reduction + +323 +00:24:37,500 --> 00:24:42,080 +oxidation معناها loss of electron إنه فقد إلكترون + +324 +00:24:42,080 --> 00:24:46,080 +بسميه oxidation reduction معناها gain of electron + +325 +00:24:46,080 --> 00:24:53,170 +إنه كسب إلكترون السكر المختزل هو السكر بسميه مختزل + +326 +00:24:53,170 --> 00:25:02,030 +السكر + +327 +00:25:02,030 --> 00:25:05,870 +المختزل هو السكر الذي يحتوي على functional group + +328 +00:25:05,870 --> 00:25:10,930 +سواء كيتون أو ألدهيد بس تكون free تكون حرة قادرة + +329 +00:25:10,930 --> 00:25:16,100 +على المشاركة في تفاعلات الأكسدة والاختزال تمام، + +330 +00:25:16,100 --> 00:25:19,380 +reducing sugar هو السكر اللي بيحتوي على free + +331 +00:25:19,380 --> 00:25:23,860 +aldehyde أو free ketone functional group يكون عنده + +332 +00:25:23,860 --> 00:25:28,360 +functional group free قادر على المشاركة في تفاعلات + +333 +00:25:28,360 --> 00:25:32,480 +الأكسدة والاختزال، لذا الشرط عشان أقول عن هذا + +334 +00:25:32,480 --> 00:25:36,700 +السكر أن هو reducing أو non-reducing وجود free + +335 +00:25:36,700 --> 00:25:41,260 +aldehyde أو ketone أجل جيت السكر هو reducing + +336 +00:25:41,260 --> 00:25:46,620 +sugar هو عامل مختزل يعني هو هيختزل غيره وهو + +337 +00:25:46,620 --> 00:25:52,770 +هيصير له أكسدة reducing sugar يعني سكر مختزل مختزل + +338 +00:25:52,770 --> 00:25:57,150 +يعني هو بده يختزل غيره بده يعمل اختزال لغيره وهو + +339 +00:25:57,150 --> 00:26:01,470 +نفسه بده يصير له أكسدة مين بده يأكسده؟ أكيد عامل + +340 +00:26:01,470 --> 00:26:06,270 +مؤكسد بده يجي يأكسد هذا السكر وهو يصير له اختزال + +341 +00:26:06,270 --> 00:26:10,010 +فعشان مكتوب sugar can be oxidized by mild + +342 +00:26:10,010 --> 00:26:16,850 +oxidizing agent السكر بيتأكسد بوجود عامل مؤكسد + +343 +00:26:17,410 --> 00:26:22,390 +والعامل المؤكسد هذا and oxidizing agent is reduced + +344 +00:26:22,390 --> 00:26:25,770 +in the reaction هيصير له اختزاة، إذا العامل + +345 +00:26:25,770 --> 00:26:31,050 +المختزل اللي هو السكر هذا بيختزل غيره، هو بيصير له + +346 +00:26:31,050 --> 00:26:37,150 +أكسدة، العامل المؤكسد بيأكسد غيره، هو بيصير له + +347 +00:26:37,150 --> 00:26:43,200 +اختزاة أجيت لما يتأكسد السكر هيتأكسد إلى acid + +348 +00:26:43,200 --> 00:26:47,220 +ويعطيني مركب ثاني من السكريات اللي هي reducing + +349 +00:26:47,220 --> 00:26:50,700 +sugar بيحكي لي reducing sugar هم كل الـ mono + +350 +00:26:50,700 --> 00:26:55,400 +-saccharide كل السكريات الأحادية دي هي عبارة عن + +351 +00:26:55,400 --> 00:26:59,950 +reducing sugar والـ maltose والـ lactose كل + +352 +00:26:59,950 --> 00:27:04,990 +السكريات الأحادية وبالإضافة عليهم الـ maltose والـ + +353 +00:27:04,990 --> 00:27:08,430 +lactose من الـ disaccharide كل الـ monosaccharide + +354 +00:27:08,430 --> 00:27:10,950 +وعندنا الـ maltose والـ lactose من الـ + +355 +00:27:10,950 --> 00:27:17,420 +disaccharide هدول بس هم يعتبروا reducing sugar زي + +356 +00:27:17,420 --> 00:27:20,620 +ما حكينا، مين هم الـ Oxidized اللي هم الـ Reducing + +357 +00:27:20,620 --> 00:27:26,080 +Sugar اللي بيقدر يصير لهم أكسدة وهم يختزلوا غيرهم + +358 +00:27:26,080 --> 00:27:30,400 +كل الـ Monosaccharide والـ Disaccharide بنعتبرهم + +359 +00:27:30,400 --> 00:27:35,580 +Reducing Sugar، بيصير لهم أكسدة، لأن السكريات بتكون + +360 +00:27:35,580 --> 00:27:39,740 +موجودة في المحلول، بتكون على شكل خلية متوازن من + +361 +00:27:39,740 --> 00:27:43,940 +open chain و closed ring في منها بتكون open مفتوحة + +362 +00:27:43,940 --> 00:27:48,190 +خطية وفي منها بتكون حلقية كل الـ Monosaccharide + +363 +00:27:48,190 --> 00:27:52,150 +بتكون open و closed لكن الـ Oligosaccharide بس فيه + +364 +00:27:52,150 --> 00:27:55,890 +منه closed structure، only closed when cyclic + +365 +00:27:55,890 --> 00:27:58,690 +structure open، the aldehyde group is available + +366 +00:27:58,690 --> 00:28:02,290 +for oxidation مدى ما تكون عندي حلقة وأعملها open، + +367 +00:28:02,290 --> 00:28:05,890 +أفتحها وتصير خطية، بتكون الـ functional group فيها + +368 +00:28:05,890 --> 00:28:10,770 +تقدر تدخل في تفاعلات الأكسدة والاختزال، يعني بتصير + +369 +00:28:10,770 --> 00:28:11,470 +free + +370 +00:28:14,480 --> 00:28:18,080 +حينها الشكل للـ Open ولـ Closed Structure of + +371 +00:28:18,080 --> 00:28:21,340 +Monosaccharide كيف بيكون شكلها على اليسار عندنا + +372 +00:28:21,340 --> 00:28:25,120 +شكل الـ Open كيف شكل الـ Linear للـ Structure + +373 +00:28:25,120 --> 00:2 + +401 +00:30:12,090 --> 00:30:17,410 +يكون reducing sugar هو وجود free carbonyl group أو + +402 +00:30:17,410 --> 00:30:21,650 +free functional group وهي موجودة هنا في هذا السكر + +403 +00:30:21,650 --> 00:30:25,010 +في اللاكتوز إذا واحد من السكريات عنده free + +404 +00:30:25,010 --> 00:30:29,710 +functional group عشان هيك هو يعتبر reducing sugar + +405 +00:30:29,710 --> 00:30:33,290 +لأنه عنده free carbonyl group صحيح الثاني مشغولة + +406 +00:30:33,290 --> 00:30:37,830 +بس المهم في واحدة free بتشارك في تفاعلات الأكسدة + +407 +00:30:37,830 --> 00:30:42,870 +والاختزال من عندنا الـ non-reducing sugar؟ non + +408 +00:30:42,870 --> 00:30:46,230 +-reducing sugar معناها إنه not oxidized by mild + +409 +00:30:46,230 --> 00:30:51,150 +oxidizing agent يعني مش هيصير لهم أكسدة بوجود عامل + +410 +00:30:51,150 --> 00:30:55,030 +مؤكسد، لا هم هيختزلوا غيرهم ولا هم يصير لهم أكسدة، + +411 +00:30:55,030 --> 00:31:00,110 +من هم؟ هم السكروز وكل ال polysaccharides السكروز + +412 +00:31:00,110 --> 00:31:04,370 +وكل ال polysaccharides يعتبروا non-reducing sugar + +413 +00:31:05,600 --> 00:31:09,620 +طيب السكروز is not reducing sugar, why؟ ليش + +414 +00:31:09,620 --> 00:31:13,900 +السكروز مش reducing sugar؟ بيحكيلي السكروز هو + +415 +00:31:13,900 --> 00:31:19,700 +سكر ثنائي عبارة عن اتحاد سكر الجلوكوز والفركتوز + +416 +00:31:19,700 --> 00:31:24,020 +اتحاد سكر الجلوكوز بالفركتوز بحكي لما ييجوا هدول + +417 +00:31:24,020 --> 00:31:27,560 +السكرين يتحدوا عشان يكونوا للـSaccharose بيرتبطوا + +418 +00:31:27,560 --> 00:31:30,480 +مع بعض وبتيجي الرابطة السكرية بينهم بين + +419 +00:31:30,480 --> 00:31:33,740 +الـfunctional group للسكر الأول والـfunctional + +420 +00:31:33,740 --> 00:31:37,220 +group للسكر الثاني، إذا الرابطة السكرية دي بتيجي + +421 +00:31:37,220 --> 00:31:40,680 +بين الـfunctional group للسكر الأول والـfunctional + +422 +00:31:40,680 --> 00:31:44,140 +group للسكر الثاني، يعني الكربونيل group من السكر + +423 +00:31:44,140 --> 00:31:48,480 +الأول بتيجي مع الكربونيل group من السكر الثاني فما + +424 +00:31:48,480 --> 00:31:51,000 +إنهم مرتبطين من عند الـ functional group في + +425 +00:31:51,000 --> 00:31:55,380 +الحالتين يبقى ما فيش free functional group وبالتالي + +426 +00:31:55,380 --> 00:31:59,300 +بتكون الـ carbonyl group are busy in the two sides + +427 +00:31:59,300 --> 00:32:04,200 +بتكون مشغولة في الجهتين فما فيش free functional group + +428 +00:32:04,470 --> 00:32:09,410 +تشارك في تفاعلات الأكسدة والاختزال فالسكروز not + +429 +00:32:09,410 --> 00:32:13,010 +reducing sugar لأنه اختل شرط أن يكون reducing + +430 +00:32:13,010 --> 00:32:17,190 +sugar وهو وجود free functional group ما فيش عنده + +431 +00:32:17,190 --> 00:32:20,170 +free functional group، they are busy in the two + +432 +00:32:20,170 --> 00:32:24,410 +sides، في السكرين مشغولة في تكوين الرابطة السكرية + +433 +00:32:26,160 --> 00:32:30,680 +إيش هي ال oxidizing agent اللي ممكن استخدمها لكشف + +434 +00:32:30,680 --> 00:32:35,920 +عن وجود reducing sugar لازم يكون عنده سكر بيختزل + +435 +00:32:35,920 --> 00:32:39,520 +غيره وعامل مؤكسد عشان هو ي access ال sugar مين + +436 +00:32:39,520 --> 00:32:42,300 +هم العوامل المؤكسدة اللي ممكن استخدمها؟ هي + +437 +00:32:42,300 --> 00:32:47,780 +البنديكت سولوشن، فيه فيلينج سولوشن، تولنز ريجنت و بيكريك + +438 +00:32:47,780 --> 00:32:53,260 +أسد سولوشن Bendects, Filling, Tolens, Bacaric Acid + +439 +00:32:53,260 --> 00:32:57,480 +إيش هو الـ Oxidizing Agent؟ الـ Oxidizing Agent هو + +440 +00:32:57,480 --> 00:33:01,680 +العامل اللي اسمه تاني Oxidizer or Oxidant العامل + +441 +00:33:01,680 --> 00:33:06,380 +اللي بيأكسد غيره هو نفسه بيختزل تعريفه Chemical + +442 +00:33:06,380 --> 00:33:10,920 +Compound That Transfers Oxygen Atom هو مركب كيميائي + +443 +00:33:10,920 --> 00:33:16,740 +ينقل ذرة أكسجين أو هو اللي بيكسب إلكترون إلكترون + +444 +00:33:16,740 --> 00:33:21,710 +in Redox chemical reaction هدا الـ reduction طيب + +445 +00:33:21,710 --> 00:33:24,490 +الألدوز اللي جينا احنا لما يصير عندنا oxidation + +446 +00:33:24,490 --> 00:33:28,030 +reduction reaction السكر reducing sugar ليش هيتحول + +447 +00:33:28,030 --> 00:33:31,610 +لما يصير له oxidation؟ لأن السكر هو عامل مختزل، + +448 +00:33:31,610 --> 00:33:35,790 +بدي يصير له أكسدة، فالسكر هيختزل إلى إيه؟ هيتأكسد + +449 +00:33:35,790 --> 00:33:39,490 +إلى أيش؟ إذا كان السكر نوع ألدوز عنده aldehyde + +450 +00:33:39,490 --> 00:33:42,830 +group زي الجلوكوز، لما يصير له oxidation، بتحول + +451 +00:33:42,830 --> 00:33:47,770 +إلى حاجة اسمها carboxylate أما إذا كان السكر نوعه + +452 +00:33:47,770 --> 00:33:52,190 +كيتوز عنده كيتون جروب زي الفركتوز ما يصير + +453 +00:33:52,190 --> 00:33:56,810 +oxidation بتحول لحاجة اسمها hydroxylcarboxylate diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/MUWHefMMBZ4_raw.json b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/MUWHefMMBZ4_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..87403e9bdc2c4dd1a75a2107098a50e18c5fa0d1 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/MUWHefMMBZ4_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 2928, "start": 0.22, "end": 29.28, "text": "عملنا qualitative analytical test for carbohydrates اللي هي ما عملنا بيحكي عن أنه فحوصات نوعية فحوصات جودة للكشف عن ال carbohydrates عن السكريات اليوم فحوصاتنا للكشف عن ال carbohydrate وهي فحوصات qualitative فحوصات جودة يعني بيطلع معايا في الآخر لون هيكون positive أو negative مش هيطلع معايا كمية أو رقم", "tokens": [25957, 1211, 8315, 31312, 29579, 1500, 337, 36817, 13672, 1829, 39896, 19446, 6225, 42213, 8315, 4724, 1829, 5016, 4117, 1829, 18871, 14739, 3224, 6156, 5016, 2407, 9381, 9307, 8717, 45367, 10632, 6156, 5016, 2407, 9381, 9307, 10874, 23328, 3660, 24976, 4117, 8592, 5172, 18871, 2423, 36817, 18871, 21136, 4117, 16572, 9307, 45595, 20498, 6156, 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0.98388671875}, {"start": 86.17, "end": 86.69, "word": " الكلام", "probability": 0.9475911458333334}, {"start": 86.69, "end": 87.09, "word": " إنه", "probability": 0.74169921875}, {"start": 87.09, "end": 87.55, "word": " أعرف", "probability": 0.98681640625}, {"start": 87.55, "end": 87.79, "word": " هل", "probability": 0.9775390625}, {"start": 87.79, "end": 87.99, "word": " هذه", "probability": 0.5908203125}, {"start": 87.99, "end": 89.21, "word": " الموجودة", "probability": 0.9031982421875}, {"start": 89.21, "end": 89.77, "word": " الأشياء", "probability": 0.87261962890625}, {"start": 89.77, "end": 90.05, "word": " أو", "probability": 0.9013671875}, {"start": 90.05, "end": 90.23, "word": " لا", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 5, "seek": 11197, "start": 90.95, "end": 111.97, "text": "بحوصاتك qualitative يعني موجود أو غير موجود بداية بدنا نتعرف على ال carbohydrates على السكرية السكرية تم قسم إلى قسمين في منها simple saccharide هي السكرية يعني simple سكرية وفي 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وكمان هي sweet to طارس طعمها حلو إذا الـ saccharide الوزن الجزائي إلها قليل ذائبة في الماء وطعمها حلو", "tokens": [41185, 29739, 28259, 10632, 8717, 1829, 7435, 1829, 8717, 5016, 4117, 1829, 18871, 2423, 39184, 2199, 4899, 7374, 482, 2423, 39184, 4899, 7374, 482, 39896, 9154, 16490, 9381, 16373, 9381, 11296, 36145, 3224, 11933, 1211, 11296, 2295, 19046, 3364, 2423, 39184, 19046, 3364, 2423, 2407, 11622, 1863, 25724, 11622, 16373, 1829, 11933, 1211, 11296, 12174, 20292, 1211, 4032, 24793, 7649, 39896, 24807, 638, 294, 1281, 39894, 2655, 30543, 8978, 9673, 1829, 3224, 4032, 24793, 7649, 39896, 3844, 281, 23032, 9640, 3794, 23032, 25957, 11296, 11331, 1211, 2407, 11933, 15730, 2423, 39184, 4899, 7374, 482, 2423, 2407, 11622, 1863, 25724, 11622, 16373, 1829, 11933, 1211, 11296, 12174, 20292, 1211, 29910, 16373, 49401, 8978, 9673, 16606, 4032, 9566, 25957, 11296, 11331, 1211, 2407], "avg_logprob": -0.21439549693318663, "compression_ratio": 1.9260869565217391, "no_speech_prob": 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"end": 135.72, "word": " في", "probability": 0.98388671875}, {"start": 135.72, "end": 136.06, "word": " الماء", "probability": 0.9658203125}, {"start": 136.06, "end": 136.86, "word": " وطعمها", "probability": 0.96240234375}, {"start": 136.86, "end": 137.16, "word": " حلو", "probability": 0.9881184895833334}], "temperature": 1.0}, {"id": 7, "seek": 16737, "start": 137.93, "end": 167.37, "text": "بتنقسم إلى .. أنا مكتبت قسمياً هما تلاتة في منها mono-saccharide سكريات أحادية في di-saccharide سكريات ثنائية في oligosaccharide ألاقيت mono-saccharide سكر واحد، دي بس واحد، سكر واحد، simple sugar di-saccharide هي double sugar، بيكون سكر ثنائي اتنين من الـ mono بيتحدوا مع بعض oligo بتكون من تلاتة إلى تسعة، عدد السكريات فيها من تلاتة إلى تسعة", "tokens": [3555, 2655, 1863, 4587, 38251, 30731, 4386, 41850, 3714, 4117, 2655, 3555, 2655, 12174, 38251, 25528, 14111, 8032, 15042, 6055, 1211, 9307, 3660, 8978, 9154, 11296, 35624, 12, 82, 326, 7374, 482, 8608, 37983, 1829, 9307, 5551, 5016, 18513, 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Monosaccharide هي simple sugar هو سكر واحد بيكون الصيغة العامة له CH2O لكل N N هي عدد ذرات الكعك", "tokens": [6027, 39184, 4713, 329, 326, 7374, 482, 39896, 2199, 5076, 31439, 8608, 37983, 36764, 24401, 4724, 1829, 30544, 31767, 1829, 17082, 3660, 18863, 10943, 3660, 46740, 5995, 17, 46, 5296, 28820, 426, 426, 39896, 6225, 3215, 3215, 29910, 2288, 9307, 33251, 3615, 4117], "avg_logprob": -0.22816050729968332, "compression_ratio": 1.1029411764705883, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 167.9, "end": 168.52, "word": "الـ", "probability": 0.953369140625}, {"start": 168.52, "end": 169.48, "word": " Monosaccharide", "probability": 0.82744140625}, {"start": 169.48, "end": 169.7, "word": " هي", "probability": 0.76611328125}, {"start": 169.7, "end": 170.16, "word": " simple", "probability": 0.286865234375}, {"start": 170.16, "end": 170.68, "word": " sugar", "probability": 0.7216796875}, {"start": 170.68, "end": 170.86, "word": " هو", "probability": 0.6142578125}, 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له", "probability": 0.953125}, {"start": 194.69, "end": 198.39, "word": " C3H6O3", "probability": 0.9484049479166666}], "temperature": 1.0}, {"id": 10, "seek": 21960, "start": 199.6, "end": 219.6, "text": "في عندنا جيليكوز، فراكتوز، جالاكتوز، هدولة mono-saccharide، سكريات إحادية، hexose بنسميها هم التلاتة الجيليكوز و فراكتوز و جالاكتوز، بنسميهم hexose، سكرية simple-saccharide، mono-saccharide، ولكن سوداسي، عدد ذرّات الكربون فيه 6", "tokens": [41185, 43242, 8315, 10874, 1829, 20292, 4117, 2407, 11622, 12399, 6156, 23557, 4117, 2655, 2407, 11622, 12399, 10874, 6027, 995, 4117, 2655, 2407, 11622, 12399, 8032, 3215, 12610, 3660, 35624, 12, 82, 326, 7374, 482, 12399, 8608, 4117, 16572, 9307, 11933, 5016, 18513, 10632, 12399, 23291, 541, 44945, 38251, 1829, 11296, 8032, 2304, 16712, 1211, 9307, 3660, 25724, 1829, 20292, 4117, 2407, 11622, 4032, 6156, 23557, 4117, 2655, 2407, 11622, 4032, 10874, 6027, 995, 4117, 2655, 2407, 11622, 12399, 44945, 38251, 1829, 16095, 23291, 541, 12399, 8608, 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"probability": 0.79150390625}, {"start": 205.16, "end": 205.7, "word": " سكريات", "probability": 0.8740234375}, {"start": 205.7, "end": 207.08, "word": " إحادية،", "probability": 0.728125}, {"start": 207.08, "end": 207.72, "word": " hexose", "probability": 0.56683349609375}, {"start": 207.72, "end": 208.56, "word": " بنسميها", "probability": 0.84820556640625}, {"start": 208.56, "end": 209.12, "word": " هم", "probability": 0.78369140625}, {"start": 209.12, "end": 209.64, "word": " التلاتة", "probability": 0.92041015625}, {"start": 209.64, "end": 210.32, "word": " الجيليكوز", "probability": 0.870361328125}, {"start": 210.32, "end": 210.48, "word": " و", "probability": 0.91015625}, {"start": 210.48, "end": 211.16, "word": " فراكتوز", "probability": 0.8779296875}, {"start": 211.16, "end": 211.28, "word": " و", "probability": 0.9384765625}, {"start": 211.28, "end": 212.28, "word": " جالاكتوز،", "probability": 0.87420654296875}, {"start": 212.28, "end": 212.86, "word": " بنسميهم", 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اسمها glycosidic bond", "tokens": [5172, 3615, 8592, 7649, 39896, 20328, 1829, 17082, 3660, 21136, 4117, 16572, 9307, 21136, 11536, 10632, 20328, 9640, 2655, 383, 4762, 39, 7490, 46, 5348, 4032, 1863, 11622, 3615, 8315, 10874, 11622, 38207, 3714, 16606, 5296, 2655, 4117, 2407, 9957, 34892, 16758, 9566, 21136, 37983, 10632, 13672, 1829, 24525, 2304, 11296, 22633, 6877, 327, 299, 6086], "avg_logprob": -0.19010416248388456, "compression_ratio": 1.2605633802816902, "no_speech_prob": 1.9669532775878906e-06, "words": [{"start": 380.31, "end": 380.81, "word": "فعشان", "probability": 0.80462646484375}, {"start": 380.81, "end": 380.93, "word": " هي", "probability": 0.69287109375}, {"start": 380.93, "end": 381.47, "word": " صيغة", "probability": 0.8994140625}, {"start": 381.47, "end": 382.09, "word": " السكريات", "probability": 0.90869140625}, {"start": 382.09, "end": 382.51, "word": " السونية", "probability": 0.7003580729166666}, {"start": 382.51, "end": 382.93, "word": " صارت", "probability": 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نشا حيواني cellulose اللي بيستخدم في النبات لبناء ال cell wall اللينن والكايتن اللي بيستخدم في الحشرات لبناء ال cell wall", "tokens": [6027, 1211, 9957, 1863, 16070, 4117, 995, 36081, 1863, 13672, 1829, 39894, 14851, 9778, 40448, 21542, 46309, 9307, 5296, 3555, 1863, 16606, 2423, 2815, 2929, 11778, 3224, 9154, 16247, 2304, 12984, 1211, 15844, 2423, 6754, 82, 326, 7374, 482, 3543, 10874, 1863, 33599, 28239, 3555, 9307, 1829, 4032, 7435, 15040, 1829, 4117, 29245, 1863, 8717, 8592, 995, 11331, 1829, 2407, 7649, 1829, 2815, 425, 541, 13672, 1829, 4724, 1829, 14851, 9778, 40448, 8978, 28239, 3555, 9307, 5296, 3555, 1863, 16606, 2423, 2815, 2929, 13672, 9957, 1863, 16070, 4117, 995, 36081, 1863, 13672, 1829, 4724, 1829, 14851, 9778, 40448, 8978, 21542, 46309, 9307, 5296, 3555, 1863, 16606, 2423, 2815, 2929], "avg_logprob": -0.13941761390729385, "compression_ratio": 2.108108108108108, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 488.92, "end": 489.56, "word": "اللينن", 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{"start": 602.57, "end": 603.05, "word": " تانية", "probability": 0.9658203125}, {"start": 603.05, "end": 603.81, "word": " بمجموعة", "probability": 0.9383951822916666}, {"start": 603.81, "end": 604.05, "word": " بـ", "probability": 0.961669921875}, {"start": 604.05, "end": 604.19, "word": " R", "probability": 0.7998046875}, {"start": 604.19, "end": 604.41, "word": " group", "probability": 0.970703125}, {"start": 604.41, "end": 604.95, "word": " بسميها", "probability": 0.935302734375}, {"start": 604.95, "end": 605.67, "word": " aldehyde", "probability": 0.8426513671875}, {"start": 605.67, "end": 607.17, "word": " أما", "probability": 0.964111328125}, {"start": 607.17, "end": 607.45, "word": " إذا", "probability": 0.98779296875}, {"start": 607.45, "end": 607.81, "word": " شوفت", "probability": 0.7389322916666666}, {"start": 607.81, "end": 607.97, "word": " الـ", "probability": 0.972412109375}, {"start": 607.97, "end": 608.11, "word": " C", "probability": 0.92138671875}, {"start": 608.11, "end": 608.35, "word": " double", "probability": 0.95458984375}, {"start": 608.35, "end": 608.79, "word": " bond", "probability": 0.96337890625}, {"start": 608.79, "end": 609.09, "word": " O", "probability": 0.986328125}], "temperature": 1.0}, {"id": 28, "seek": 63395, "start": 609.49, "end": 633.95, "text": "مرتبطة من جهة بـ R-group مجموعة ومن جهة التانية كمان R-group مجموعة بسميها كيتون لذن الـ aldehyde بتكون الـCWO مرتبطة من جهة بـH ومن جهة بـR أما الكيتون بتكون الـCWO مرتبطة من جهة بـR ومن جهة بـR تاني زي تحت مثل عن الـGlucose و الـFructose", "tokens": [29973, 2655, 3555, 9566, 3660, 9154, 10874, 3224, 3660, 4724, 39184, 497, 12, 17377, 3714, 7435, 2304, 2407, 27884, 4032, 27842, 10874, 3224, 3660, 16712, 7649, 10632, 9122, 2304, 7649, 497, 12, 17377, 3714, 7435, 2304, 2407, 27884, 4724, 38251, 1829, 11296, 9122, 36081, 11536, 5296, 8848, 1863, 2423, 39184, 16798, 68, 3495, 1479, 39894, 30544, 2423, 39184, 34, 54, 46, 3714, 43500, 3555, 9566, 3660, 9154, 10874, 3224, 3660, 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729.39, "word": " رقم", "probability": 0.97998046875}, {"start": 729.39, "end": 729.87, "word": " واحد", "probability": 0.661376953125}, {"start": 729.87, "end": 730.43, "word": " ومتصلة", "probability": 0.8326171875}, {"start": 730.43, "end": 730.55, "word": " من", "probability": 0.96875}, {"start": 730.55, "end": 730.77, "word": " جهة", "probability": 0.9842122395833334}, {"start": 730.77, "end": 730.91, "word": " الـ", "probability": 0.5345458984375}, {"start": 730.91, "end": 731.11, "word": " H", "probability": 0.578125}, {"start": 731.11, "end": 731.31, "word": " ومن", "probability": 0.820068359375}, {"start": 731.31, "end": 731.47, "word": " جهة", "probability": 0.9734700520833334}, {"start": 731.47, "end": 732.11, "word": " المجموعة", "probability": 0.8986328125}, {"start": 732.11, "end": 733.39, "word": " فالالدهيد", "probability": 0.7779947916666666}, {"start": 733.39, "end": 733.61, "word": " في", "probability": 0.9443359375}, {"start": 733.61, "end": 734.67, "word": " الجلوكوز", "probability": 0.7933756510416666}, {"start": 734.67, "end": 735.11, "word": " الـ", "probability": 0.490875244140625}, {"start": 735.11, "end": 735.63, "word": " CW", "probability": 0.8720703125}, {"start": 735.63, "end": 735.87, "word": " من", "probability": 0.93505859375}, {"start": 735.87, "end": 736.05, "word": " ضهر", "probability": 0.9869791666666666}, {"start": 736.05, "end": 736.47, "word": " موجود", "probability": 0.8634440104166666}, {"start": 736.47, "end": 736.65, "word": " على", "probability": 0.90380859375}, {"start": 736.65, "end": 737.11, "word": " رقم", "probability": 0.9508463541666666}, {"start": 737.11, "end": 737.61, "word": " كربونا", "probability": 0.92822265625}, {"start": 737.61, "end": 737.93, "word": " رقم", "probability": 0.9918619791666666}, {"start": 737.93, "end": 738.29, "word": " واحد", "probability": 0.939208984375}], "temperature": 1.0}, {"id": 34, "seek": 75456, "start": 738.78, "end": 754.56, "text": "لو جينا على الـ Fructose جينا الرقم من اليسارها، الرقم هي في عندي كربونا رقم 1، وبعدين 2 كربونا اللي هي C double bond 1 في الـ Ketone، في الـ Fructose اللي هي موجودة على كربونا رقم 2", "tokens": [1211, 2407, 10874, 1829, 8315, 15844, 2423, 39184, 479, 1757, 541, 10874, 1829, 8315, 34892, 4587, 2304, 9154, 45595, 3794, 9640, 11296, 12399, 34892, 4587, 2304, 39896, 8978, 18871, 16254, 9122, 25513, 2407, 8315, 12602, 4587, 2304, 502, 12399, 46599, 22488, 9957, 568, 9122, 25513, 2407, 8315, 13672, 1829, 39896, 383, 3834, 6086, 502, 8978, 2423, 39184, 591, 302, 546, 12399, 8978, 2423, 39184, 479, 1757, 541, 13672, 1829, 39896, 3714, 29245, 23328, 3660, 15844, 9122, 25513, 2407, 8315, 12602, 4587, 2304, 568], "avg_logprob": -0.22191220504187403, "compression_ratio": 1.7261904761904763, "no_speech_prob": 1.239776611328125e-05, "words": [{"start": 738.78, "end": 739.06, "word": "لو", "probability": 0.689208984375}, {"start": 739.06, "end": 739.32, "word": " جينا", "probability": 0.9694010416666666}, {"start": 739.32, "end": 739.54, "word": " على", "probability": 0.890625}, {"start": 739.54, "end": 739.76, "word": " الـ", "probability": 0.929443359375}, {"start": 739.76, "end": 740.36, "word": " Fructose", "probability": 0.7013346354166666}, {"start": 740.36, "end": 740.66, "word": " جينا", "probability": 0.8124186197916666}, {"start": 740.66, "end": 741.26, "word": " الرقم", "probability": 0.97265625}, {"start": 741.26, "end": 741.52, "word": " من", "probability": 0.88916015625}, {"start": 741.52, "end": 742.14, "word": " اليسارها،", "probability": 0.79365234375}, {"start": 742.14, "end": 742.48, "word": " الرقم", "probability": 0.935546875}, {"start": 742.48, "end": 742.62, "word": " هي", "probability": 0.329833984375}, {"start": 742.62, "end": 742.76, "word": " في", "probability": 0.646484375}, {"start": 742.76, "end": 743.02, "word": " عندي", "probability": 0.636962890625}, {"start": 743.02, "end": 743.34, "word": " كربونا", "probability": 0.7689208984375}, {"start": 743.34, "end": 743.68, "word": " رقم", "probability": 0.9773763020833334}, {"start": 743.68, "end": 744.52, "word": " 1،", "probability": 0.62109375}, {"start": 744.52, "end": 744.9, "word": " وبعدين", "probability": 0.7861328125}, {"start": 744.9, "end": 745.26, "word": " 2", "probability": 0.71044921875}, {"start": 745.26, "end": 746.0, "word": " كربونا", "probability": 0.81549072265625}, {"start": 746.0, "end": 746.12, "word": " اللي", "probability": 0.79296875}, {"start": 746.12, "end": 746.32, "word": " هي", "probability": 0.87841796875}, {"start": 746.32, "end": 746.58, "word": " C", "probability": 0.70556640625}, {"start": 746.58, "end": 746.86, "word": " double", "probability": 0.53271484375}, {"start": 746.86, "end": 747.22, "word": " bond", "probability": 0.90283203125}, {"start": 747.22, "end": 747.54, "word": " 1", "probability": 0.7705078125}, {"start": 747.54, "end": 748.1, "word": " في", "probability": 0.42236328125}, {"start": 748.1, "end": 748.76, "word": " الـ", "probability": 0.90478515625}, {"start": 748.76, "end": 749.5, "word": " Ketone،", "probability": 0.72210693359375}, {"start": 749.5, "end": 749.58, "word": " في", "probability": 0.8876953125}, {"start": 749.58, "end": 749.9, "word": " الـ", "probability": 0.95947265625}, {"start": 749.9, "end": 750.8, "word": " Fructose", "probability": 0.9147135416666666}, {"start": 750.8, "end": 751.44, "word": " اللي", "probability": 0.788818359375}, {"start": 751.44, "end": 751.6, "word": " هي", "probability": 0.74462890625}, {"start": 751.6, "end": 752.24, "word": " موجودة", "probability": 0.98828125}, {"start": 752.24, "end": 752.6, "word": " على", "probability": 0.93798828125}, {"start": 752.6, "end": 753.58, "word": " كربونا", "probability": 0.9693603515625}, {"start": 753.58, "end": 754.14, "word": " رقم", "probability": 0.9954427083333334}, {"start": 754.14, "end": 754.56, "word": " 2", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 35, "seek": 78094, "start": 756.4, "end": 780.94, "text": "هنا حاجة اسمها Sugar Nomenclature اللي هي السكر وصورته كأنه انعكسه في المرايا كأنه mirror image أن السكر له انعكاس نفس السكر موجود على شكلين في منه الـD وأقل بنسميهم يعني مثلا الـGelicose في منه الـD-Gelicose وأقل الـGelicose كيف هذا بدي أقرر هل هو الـD ولا الأقل؟", "tokens": [3224, 8315, 11331, 26108, 3660, 24525, 2304, 11296, 24576, 426, 4726, 3474, 1503, 13672, 1829, 39896, 21136, 37983, 4032, 9381, 13063, 47395, 9122, 33456, 3224, 16472, 3615, 4117, 3794, 3224, 8978, 9673, 23557, 25528, 9122, 33456, 3224, 8013, 3256, 14739, 21136, 37983, 46740, 16472, 3615, 4117, 32277, 8717, 36178, 21136, 37983, 3714, 29245, 23328, 15844, 13412, 28820, 9957, 8978, 9154, 3224, 2423, 39184, 35, 4032, 10721, 4587, 1211, 44945, 38251, 1829, 16095, 37495, 22653, 50113, 15040, 2423, 39184, 38, 338, 299, 541, 8978, 9154, 3224, 2423, 39184, 35, 12, 38, 338, 299, 541, 4032, 10721, 4587, 1211, 2423, 39184, 38, 338, 299, 541, 9122, 33911, 23758, 4724, 16254, 5551, 4587, 2288, 2288, 8032, 1211, 31439, 2423, 39184, 35, 49429, 16247, 4587, 1211, 22807], "avg_logprob": -0.21774193476284703, "compression_ratio": 1.775, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 756.4, "end": 756.62, "word": "هنا", "probability": 0.56793212890625}, {"start": 756.62, "end": 757.04, "word": " حاجة", "probability": 0.99169921875}, {"start": 757.04, "end": 757.52, "word": " اسمها", "probability": 0.9679361979166666}, {"start": 757.52, "end": 757.86, "word": " Sugar", "probability": 0.48876953125}, {"start": 757.86, "end": 759.0, "word": " Nomenclature", "probability": 0.8741455078125}, {"start": 759.0, "end": 759.8, "word": " اللي", "probability": 0.884521484375}, {"start": 759.8, "end": 760.06, "word": " هي", "probability": 0.900390625}, {"start": 760.06, "end": 761.32, "word": " السكر", "probability": 0.749267578125}, {"start": 761.32, "end": 762.44, "word": " وصورته", "probability": 0.8314208984375}, {"start": 762.44, "end": 762.84, "word": " كأنه", "probability": 0.83544921875}, {"start": 762.84, "end": 763.44, "word": " انعكسه", "probability": 0.854296875}, {"start": 763.44, "end": 763.56, "word": " في", "probability": 0.9580078125}, {"start": 763.56, "end": 763.98, "word": " المرايا", "probability": 0.8310546875}, {"start": 763.98, "end": 764.34, "word": " كأنه", "probability": 0.9235026041666666}, {"start": 764.34, "end": 764.64, "word": " mirror", "probability": 0.480224609375}, {"start": 764.64, "end": 765.24, "word": " image", "probability": 0.82421875}, {"start": 765.24, "end": 765.74, "word": " أن", "probability": 0.53173828125}, {"start": 765.74, "end": 766.24, "word": " السكر", "probability": 0.9384765625}, {"start": 766.24, "end": 766.46, "word": " له", "probability": 0.2177734375}, {"start": 766.46, "end": 767.14, "word": " انعكاس", "probability": 0.8890380859375}, {"start": 767.14, "end": 767.7, "word": " نفس", "probability": 0.94921875}, {"start": 767.7, "end": 768.2, "word": " السكر", "probability": 0.97607421875}, {"start": 768.2, "end": 768.66, "word": " موجود", "probability": 0.9890950520833334}, {"start": 768.66, "end": 769.0, "word": " على", "probability": 0.93115234375}, {"start": 769.0, "end": 770.76, "word": " شكلين", "probability": 0.8719075520833334}, {"start": 770.76, "end": 771.26, "word": " في", "probability": 0.7509765625}, {"start": 771.26, "end": 771.72, "word": " منه", "probability": 0.87158203125}, {"start": 771.72, "end": 772.0, "word": " الـD", "probability": 0.6569010416666666}, {"start": 772.0, "end": 772.78, "word": " وأقل", "probability": 0.736663818359375}, {"start": 772.78, "end": 773.82, "word": " بنسميهم", "probability": 0.8736572265625}, {"start": 773.82, "end": 774.08, "word": " يعني", "probability": 0.905517578125}, {"start": 774.08, "end": 774.36, "word": " مثلا", "probability": 0.974853515625}, {"start": 774.36, "end": 775.0, "word": " الـGelicose", "probability": 0.6989339192708334}, {"start": 775.0, "end": 775.18, "word": " في", "probability": 0.609375}, {"start": 775.18, "end": 775.42, "word": " منه", "probability": 0.98486328125}, {"start": 775.42, "end": 775.58, "word": " الـD", "probability": 0.8140462239583334}, {"start": 775.58, "end": 776.26, "word": "-Gelicose", "probability": 0.9103515625}, {"start": 776.26, "end": 776.76, "word": " وأقل", "probability": 0.81488037109375}, {"start": 776.76, "end": 777.54, "word": " الـGelicose", "probability": 0.9364420572916666}, {"start": 777.54, "end": 778.54, "word": " كيف", "probability": 0.982666015625}, {"start": 778.54, "end": 778.74, "word": " هذا", "probability": 0.56884765625}, {"start": 778.74, "end": 778.94, "word": " بدي", "probability": 0.607177734375}, {"start": 778.94, "end": 779.36, "word": " أقرر", "probability": 0.9127197265625}, {"start": 779.36, "end": 779.5, "word": " هل", "probability": 0.897705078125}, {"start": 779.5, "end": 779.7, "word": " هو", "probability": 0.9921875}, {"start": 779.7, "end": 780.08, "word": " الـD", "probability": 0.9759114583333334}, {"start": 780.08, "end": 780.4, "word": " ولا", "probability": 0.438232421875}, {"start": 780.4, "end": 780.94, "word": " الأقل؟", "probability": 0.829345703125}], "temperature": 1.0}, {"id": 36, "seek": 80356, "start": 781.48, "end": 803.56, "text": "لما نكتب السكر الـ structure له بشكل linear بشكل خطي بشكل عمودي بدي أرقم الـ carbon بيطلع على carbonة رقم 5 بيطلع على carbonة رقم 5 إذا الـ OH موجودة إلى جهة الـ left إلى جهة اليسار بيكون الـ 4", "tokens": [1211, 15042, 8717, 4117, 2655, 3555, 21136, 37983, 2423, 39184, 3877, 46740, 4724, 8592, 28820, 8213, 4724, 8592, 28820, 16490, 9566, 1829, 4724, 8592, 28820, 6225, 2304, 2407, 16254, 4724, 16254, 5551, 2288, 4587, 2304, 2423, 39184, 5954, 4724, 1829, 9566, 1211, 3615, 15844, 5954, 3660, 12602, 4587, 2304, 1025, 4724, 1829, 9566, 1211, 3615, 15844, 5954, 3660, 12602, 4587, 2304, 1025, 11933, 15730, 2423, 39184, 13931, 3714, 29245, 23328, 3660, 30731, 10874, 3224, 3660, 2423, 39184, 1411, 30731, 10874, 3224, 3660, 45595, 3794, 9640, 4724, 1829, 30544, 2423, 39184, 1017], "avg_logprob": -0.17663043899380643, "compression_ratio": 1.7329545454545454, "no_speech_prob": 9.179115295410156e-06, "words": [{"start": 781.48, "end": 781.84, "word": "لما", "probability": 0.8203125}, {"start": 781.84, "end": 782.42, "word": " نكتب", "probability": 0.965087890625}, {"start": 782.42, "end": 782.98, "word": " السكر", "probability": 0.79541015625}, {"start": 782.98, "end": 783.18, "word": " الـ", "probability": 0.823486328125}, {"start": 783.18, "end": 783.6, "word": " structure", "probability": 0.46630859375}, {"start": 783.6, "end": 783.92, "word": " له", "probability": 0.2366943359375}, {"start": 783.92, "end": 784.32, "word": " بشكل", "probability": 0.9571940104166666}, {"start": 784.32, "end": 784.68, "word": " linear", "probability": 0.3466796875}, {"start": 784.68, "end": 785.08, "word": " بشكل", "probability": 0.8673502604166666}, {"start": 785.08, "end": 785.56, "word": " خطي", "probability": 0.9659830729166666}, {"start": 785.56, "end": 785.98, "word": " بشكل", "probability": 0.7647298177083334}, {"start": 785.98, "end": 786.56, "word": " عمودي", "probability": 0.98486328125}, {"start": 786.56, "end": 787.62, "word": " بدي", "probability": 0.772216796875}, {"start": 787.62, "end": 788.82, "word": " أرقم", "probability": 0.9285888671875}, {"start": 788.82, "end": 789.18, "word": " الـ", "probability": 0.69482421875}, {"start": 789.18, "end": 789.56, "word": " carbon", "probability": 0.61572265625}, {"start": 789.56, "end": 790.26, "word": " بيطلع", "probability": 0.80830078125}, {"start": 790.26, "end": 790.54, "word": " على", "probability": 0.890625}, {"start": 790.54, "end": 791.3, "word": " carbonة", "probability": 0.6025390625}, {"start": 791.3, "end": 791.6, "word": " رقم", "probability": 0.9928385416666666}, {"start": 791.6, "end": 792.1, "word": " 5", "probability": 0.61328125}, {"start": 792.1, "end": 794.4, "word": " بيطلع", "probability": 0.9162109375}, {"start": 794.4, "end": 794.62, "word": " على", "probability": 0.92626953125}, {"start": 794.62, "end": 795.36, "word": " carbonة", "probability": 0.974365234375}, {"start": 795.36, "end": 795.66, "word": " رقم", "probability": 0.9964192708333334}, {"start": 795.66, "end": 796.16, "word": " 5", "probability": 0.95361328125}, {"start": 796.16, "end": 797.36, "word": " إذا", "probability": 0.94091796875}, {"start": 797.36, "end": 797.7, "word": " الـ", "probability": 0.96484375}, {"start": 797.7, "end": 798.02, "word": " OH", "probability": 0.71240234375}, {"start": 798.02, "end": 799.04, "word": " موجودة", "probability": 0.9820556640625}, {"start": 799.04, "end": 799.22, "word": " إلى", "probability": 0.83154296875}, {"start": 799.22, "end": 799.74, "word": " جهة", "probability": 0.9884440104166666}, {"start": 799.74, "end": 800.08, "word": " الـ", "probability": 0.890869140625}, {"start": 800.08, "end": 800.46, "word": " left", "probability": 0.8017578125}, {"start": 800.46, "end": 800.8, "word": " إلى", "probability": 0.73388671875}, {"start": 800.8, "end": 801.16, "word": " جهة", "probability": 0.9720052083333334}, {"start": 801.16, "end": 801.86, "word": " اليسار", "probability": 0.99169921875}, {"start": 801.86, "end": 802.66, "word": " بيكون", "probability": 0.84912109375}, {"start": 802.66, "end": 803.32, "word": " الـ", "probability": 0.579833984375}, {"start": 803.32, "end": 803.56, "word": " 4", "probability": 0.435791015625}], "temperature": 1.0}, {"id": 37, "seek": 82334, "start": 804.46, "end": 823.34, "text": "دي هتطلع على كربونا رقم 5 فنطلع على الـ Hydroxyl group اللي متصلة فيها اللي هي الـ OH اللي متصلة فيها إذا كانت على جهة الـ Left بيكون Alpha إذا كانت الـ Hydroxyl group على كربونا 5 إلى جهة الـ Right إلى جهة اليمين", "tokens": [16254, 8032, 2655, 9566, 1211, 3615, 15844, 9122, 25513, 2407, 8315, 12602, 4587, 2304, 1025, 6156, 1863, 9566, 1211, 3615, 15844, 2423, 39184, 24231, 340, 87, 5088, 1594, 13672, 1829, 44650, 36520, 3660, 8978, 11296, 13672, 1829, 39896, 2423, 39184, 13931, 13672, 1829, 44650, 36520, 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احكيلي الحلقة لما نسميها، بنسميها Alpha أو Beta، هل هي Alpha أو Beta كيف بدها تكون Alpha أو Beta، كيف بدأ أميز هل هي Alpha أو Beta؟", "tokens": [4117, 33911, 47525, 10721, 5551, 5016, 12610, 9154, 14670, 289, 34051, 6225, 2304, 2407, 16254, 32767, 17082, 1211, 4587, 4724, 2288, 16758, 9566, 31453, 12602, 4587, 2304, 1025, 20449, 2423, 39184, 11166, 41048, 10500, 5551, 1211, 4587, 36081, 18871, 16254, 11331, 1211, 38149, 9957, 8032, 47302, 20498, 11296, 12399, 1975, 5016, 4117, 1829, 20292, 21542, 1211, 28671, 5296, 15042, 8717, 38251, 1829, 11296, 12399, 44945, 38251, 1829, 11296, 20588, 34051, 33286, 12399, 8032, 1211, 39896, 20588, 34051, 33286, 9122, 33911, 47525, 11296, 6055, 30544, 20588, 34051, 33286, 12399, 9122, 33911, 47525, 10721, 5551, 2304, 1829, 11622, 8032, 1211, 39896, 20588, 34051, 33286, 22807], "avg_logprob": -0.23407452596494785, "compression_ratio": 1.688073394495413, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 954.25, "end": 954.59, "word": "كيف", 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"word": " أو", "probability": 0.939453125}, {"start": 970.67, "end": 971.05, "word": " Beta،", "probability": 0.734619140625}, {"start": 971.05, "end": 971.15, "word": " كيف", "probability": 0.94580078125}, {"start": 971.15, "end": 971.37, "word": " بدأ", "probability": 0.608154296875}, {"start": 971.37, "end": 972.97, "word": " أميز", "probability": 0.6878662109375}, {"start": 972.97, "end": 973.13, "word": " هل", "probability": 0.79638671875}, {"start": 973.13, "end": 973.29, "word": " هي", "probability": 0.93017578125}, {"start": 973.29, "end": 973.57, "word": " Alpha", "probability": 0.990234375}, {"start": 973.57, "end": 973.77, "word": " أو", "probability": 0.958984375}, {"start": 973.77, "end": 974.29, "word": " Beta؟", "probability": 0.958984375}], "temperature": 1.0}, {"id": 44, "seek": 99245, "start": 975.61, "end": 992.45, "text": "بحكي ليه بنطلع على Carbona رقم 1؟ أشوف الـ OH المتصل فيها، هل هي إلى الأسفل أو للأعلى؟ إذا الـ OH المتصلة مع Carbona رقم 1 كانت below، كانت 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وhexose لأنه ست ذرات كرم فبالكيتوز اللي تحتوي على كيتون group أشهر مثال عليها هو الفركتوز", "tokens": [6027, 7435, 26895, 2407, 4117, 2407, 11622, 4724, 28543, 2288, 5551, 9566, 1211, 4587, 47356, 24525, 2304, 24031, 78, 675, 87, 541, 9154, 8032, 11536, 5551, 7435, 2655, 9122, 19528, 3660, 24031, 78, 5296, 33456, 3224, 43242, 3224, 24031, 68, 3495, 1479, 1594, 4032, 675, 87, 541, 5296, 33456, 3224, 8608, 2655, 29910, 2288, 9307, 9122, 2288, 2304, 6156, 3555, 6027, 4117, 36081, 2407, 11622, 13672, 1829, 6055, 33753, 45865, 15844, 9122, 36081, 11536, 1594, 5551, 8592, 3224, 2288, 50113, 6027, 25894, 11296, 31439, 27188, 2288, 4117, 2655, 2407, 11622], "avg_logprob": -0.22252746663250766, "compression_ratio": 1.5326086956521738, "no_speech_prob": 3.6954879760742188e-06, "words": [{"start": 1163.99, "end": 1165.17, "word": "الجيلوكوز", "probability": 0.6825474330357143}, {"start": 1165.17, "end": 1165.91, "word": " بقدر", "probability": 0.9571940104166666}, {"start": 1165.91, "end": 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"seek": 141448, "start": 1385.5, "end": 1414.48, "text": "وكل ما زادت التفرعات في السكر، هذا بيجعل السكر ضعيف ويكون سهل تكسّم، فالـ Glycogen عشان تفرعاته أكتر، فهذا بيخليه Rapid glucose release from Glycogen، لما الجسم يحتاج glucose، أسرع يجي أنه يكسّر الـ Glycogen ويعطيني glucose، لأنه عنده تفرعات زيادة، فهذا بيتكسر بسرعة وبيحرر سكر الـ glucose لما يحتاجه الجسم،", "tokens": [2407, 28820, 19446, 30767, 18513, 2655, 16712, 5172, 2288, 3615, 9307, 8978, 21136, 37983, 12399, 23758, 4724, 1829, 7435, 30241, 21136, 37983, 48812, 3615, 33911, 4032, 1829, 30544, 8608, 3224, 1211, 6055, 4117, 3794, 11703, 2304, 12399, 6156, 6027, 39184, 460, 356, 66, 8799, 6225, 8592, 7649, 6055, 5172, 2288, 3615, 9307, 3224, 5551, 4117, 2655, 2288, 12399, 6156, 3224, 15730, 4724, 1829, 9778, 20292, 3224, 44580, 23997, 4374, 490, 460, 356, 66, 8799, 12399, 5296, 15042, 25724, 38251, 7251, 33753, 26108, 23997, 12399, 5551, 3794, 2288, 3615, 7251, 7435, 1829, 14739, 3224, 7251, 4117, 3794, 11703, 2288, 2423, 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أسرع", "probability": 0.9932861328125}, {"start": 1403.08, "end": 1403.34, "word": " يجي", "probability": 0.6754557291666666}, {"start": 1403.34, "end": 1403.54, "word": " أنه", "probability": 0.706787109375}, {"start": 1403.54, "end": 1404.1, "word": " يكسّر", "probability": 0.937890625}, {"start": 1404.1, "end": 1404.3, "word": " الـ", "probability": 0.92333984375}, {"start": 1404.3, "end": 1404.92, "word": " Glycogen", "probability": 0.8551025390625}, {"start": 1404.92, "end": 1405.76, "word": " ويعطيني", "probability": 0.86044921875}, {"start": 1405.76, "end": 1406.66, "word": " glucose،", "probability": 0.749755859375}, {"start": 1406.66, "end": 1406.96, "word": " لأنه", "probability": 0.9285481770833334}, {"start": 1406.96, "end": 1407.16, "word": " عنده", "probability": 0.98974609375}, {"start": 1407.16, "end": 1407.9, "word": " تفرعات", "probability": 0.9853515625}, {"start": 1407.9, "end": 1409.06, "word": " زيادة،", "probability": 0.88310546875}, {"start": 1409.06, "end": 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في الـ plant cell wall في بناء الـ cell wall للـ plant للنبات هو عبارة عن linear chain سلسلة طويلة من السكر ولكن هي الرابطة Beta 1L4", "tokens": [20292, 8592, 8608, 3224, 1211, 16712, 4117, 3794, 2288, 4724, 35457, 3555, 30767, 1829, 18513, 3660, 16712, 5172, 2288, 3615, 9307, 50113, 6027, 19753, 34740, 31439, 2423, 39184, 2815, 425, 541, 11331, 4117, 1829, 8315, 2423, 39184, 2815, 425, 541, 7251, 14851, 9778, 40448, 8978, 2423, 39184, 3709, 2815, 2929, 8978, 44945, 16606, 2423, 39184, 2815, 2929, 24976, 39184, 3709, 24976, 1863, 3555, 9307, 31439, 6225, 3555, 9640, 3660, 18871, 8213, 5021, 8608, 1211, 3794, 37977, 23032, 2407, 26895, 3660, 9154, 21136, 37983, 35525, 19452, 39896, 34892, 16758, 9566, 3660, 33286, 502, 43, 19], "avg_logprob": -0.1733552590796822, "compression_ratio": 1.5674418604651164, "no_speech_prob": 6.139278411865234e-06, "words": [{"start": 1414.8, "end": 1415.22, "word": "ليش", "probability": 0.6953125}, {"start": 1415.22, "end": 1415.54, "word": " سهل", 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"word": " للـ", "probability": 0.622314453125}, {"start": 1427.28, "end": 1427.64, "word": " plant", "probability": 0.93359375}, {"start": 1427.64, "end": 1428.38, "word": " للنبات", "probability": 0.86669921875}, {"start": 1428.38, "end": 1429.14, "word": " هو", "probability": 0.83447265625}, {"start": 1429.14, "end": 1429.6, "word": " عبارة", "probability": 0.99365234375}, {"start": 1429.6, "end": 1429.8, "word": " عن", "probability": 0.9951171875}, {"start": 1429.8, "end": 1430.12, "word": " linear", "probability": 0.80078125}, {"start": 1430.12, "end": 1430.74, "word": " chain", "probability": 0.93505859375}, {"start": 1430.74, "end": 1431.4, "word": " سلسلة", "probability": 0.98046875}, {"start": 1431.4, "end": 1432.46, "word": " طويلة", "probability": 0.97509765625}, {"start": 1432.46, "end": 1432.94, "word": " من", "probability": 0.98583984375}, {"start": 1432.94, "end": 1433.56, "word": " السكر", "probability": 0.90380859375}, {"start": 1433.56, "end": 1434.06, "word": " ولكن", 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"probability": 0.869140625}, {"start": 1616.34, "end": 1616.92, "word": " و", "probability": 0.80419921875}, {"start": 1616.92, "end": 1617.18, "word": " ال", "probability": 0.6962890625}, {"start": 1617.18, "end": 1617.94, "word": " maltose", "probability": 0.8125}, {"start": 1617.94, "end": 1618.38, "word": " و", "probability": 0.96875}, {"start": 1618.38, "end": 1618.72, "word": " ال", "probability": 0.71484375}, {"start": 1618.72, "end": 1619.3, "word": " lactose", "probability": 0.753173828125}], "temperature": 1.0}, {"id": 73, "seek": 163553, "start": 1619.51, "end": 1635.53, "text": "كل السكريات الأحادية وبالإضافة عليهم الـ maltose والـ lactose من الـ disaccharide كل الـ monosaccharide وعندنا الـ maltose والـ lactose من الـ disaccharide هدولة بس هم يعتبروا reducing sugar", "tokens": [28820, 21136, 4117, 16572, 9307, 16247, 5016, 18513, 10632, 46599, 6027, 28814, 11242, 31845, 3660, 25894, 16095, 2423, 39184, 45654, 541, 16070, 39184, 34042, 541, 9154, 2423, 39184, 717, 326, 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a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/OOPghZ3VTGI_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/OOPghZ3VTGI_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..75518e492f936367a3844f87dac9a5816c436b6c --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/OOPghZ3VTGI_postprocess.srt @@ -0,0 +1,740 @@ +1 +00:00:00,000 --> 00:00:04,560 +الـ Solution هو جهاز لفصل المواد حسب الكثافة + +2 +00:00:04,560 --> 00:00:10,780 +الثقيل ينزل تحت والخفيف يكون في الأعلى جهاز لفصل + +3 +00:00:10,780 --> 00:00:14,580 +المواد بناء على الكثافة Separate material of + +4 +00:00:14,580 --> 00:00:19,000 +varying density تستيتيوط قنابيب نستخدمها عشان + +5 +00:00:19,000 --> 00:00:22,800 +نشتغل فيها الفحوصات نحط فيها small amount of + +6 +00:00:22,800 --> 00:00:28,880 +solution قنابيب تحتوي على أو تتسع إلى كميات قليلة + +7 +00:00:28,880 --> 00:00:33,930 +من المحلينThermometer بجيس فيه الحرارة measure + +8 +00:00:33,930 --> 00:00:39,670 +temperature وير جوز هي شبكة موزعة للحرارة وير جوز + +9 +00:00:39,670 --> 00:00:43,670 +شبكة موزعة للحرارة بحطها فوق اللهب بتعمل spread + +10 +00:00:43,670 --> 00:00:50,430 +heat بتوزع الحرارة اللي بيوريت هي الصحاحة كده + +11 +00:00:50,430 --> 00:00:54,430 +استخدمتوها في الكيميا اللي بنستخدمها في عمليات ال + +12 +00:00:54,430 --> 00:00:59,750 +titrationنحط فيها جواه سائل بنسميه titrant الـ + +13 +00:00:59,750 --> 00:01:04,330 +«بيريت» ساحةها تستخدم للمعايرة للـ titration تحتوي + +14 +00:01:04,330 --> 00:01:08,370 +على السائل في داخلها بنسميه titrant كيف بدي أقرأ + +15 +00:01:08,370 --> 00:01:13,550 +منها major volume نقرأ القراءة من سطح التقعر من + +16 +00:01:13,550 --> 00:01:19,220 +سطح التقعر كتم القراءةهنا حاجة بنتسميها certainty + +17 +00:01:19,220 --> 00:01:22,700 +و حاجة بنتسميها uncertainty اللي هي القيمة اللي + +18 +00:01:22,700 --> 00:01:26,820 +أنا متأكدة منها طويق مشاك فيها هو أنا مثلا في + +19 +00:01:26,820 --> 00:01:30,260 +البيوت في الصحاحة بدي أجي أقرأ ال volume حكي أنا + +20 +00:01:30,260 --> 00:01:33,560 +بنقرأ من سطح التقاعو لو جينا شوفنا الصورة اللي على + +21 +00:01:33,560 --> 00:01:38,000 +الجنب في ال slide هلجيت القراءة جاي فوق ال 36 + +22 +00:01:38,000 --> 00:01:43,750 +بشويةتمام؟ هي هي 35 الشرطة اللي فوقها 36 هي بعيدها + +23 +00:01:43,750 --> 00:01:48,510 +بشوية يعني القيمة القراعة هتكون 36 و إشي ممكن + +24 +00:01:48,510 --> 00:01:51,810 +واحدة تيجي تقولي إنها 36 و نصف واحدة تانية تقولي + +25 +00:01:51,810 --> 00:01:56,770 +36 و 6 واحدة تقولي 36 و 4 لكن القيمة اللي أنا + +26 +00:01:56,770 --> 00:02:01,320 +متأكدة منها ال certainty إنها 36والقيمة اللى فيها + +27 +00:02:01,320 --> 00:02:05,040 +الشك اللى هيتختلف من one ل two اللى هى الأعشار + +28 +00:02:05,040 --> 00:02:08,320 +اللى جنبها اللى هى الخمسة من عشرة ستة من عشرة + +29 +00:02:08,320 --> 00:02:14,400 +أربعة من عشرة فالفرق بيكون زائد أو ناقص واحد من + +30 +00:02:14,400 --> 00:02:18,720 +عشرة هاي بتكون القيمة ال uncertaintyTamam + +31 +00:02:18,720 --> 00:02:21,400 +certainty اللي أنا متأجدة منها في الصورة مثلا + +32 +00:02:21,400 --> 00:02:26,000 +للقراءة هاي أنها 36 Uncertainty هي الأعشار اللي + +33 +00:02:26,000 --> 00:02:29,100 +جنبها، اللي هو أنا .. هي مش على ال 36 بالظبط، هي + +34 +00:02:29,100 --> 00:02:33,000 +فوقها في شويه، يعني ممكن تكون 36 و نص، ممكن 36 و + +35 +00:02:33,000 --> 00:02:38,350 +6، ممكن 36 و أعملالـ Certainty بتعتمد على حاجة + +36 +00:02:38,350 --> 00:02:42,370 +بنسميها precision على الدقة الـ Certainty و الـ + +37 +00:02:42,370 --> 00:02:45,890 +Measurement depends on the precision بتعتمد على + +38 +00:02:45,890 --> 00:02:50,010 +الدقة يعني الدقة مثلا في الأدوات اللي مقسمة أكتر + +39 +00:02:50,010 --> 00:02:54,410 +هتكون الدقة أكتر فيها مجسمة لا عشار ولا مجسمة بس + +40 +00:02:54,410 --> 00:02:58,650 +لعداد صحيحة مين هتكون أدق؟ أكيد اللي مجسمة لا عشار + +41 +00:02:58,650 --> 00:02:59,710 +هي الأدق + +42 +00:03:02,280 --> 00:03:06,680 +هنا مصطلحين مهمين اللي هم بتسميهم accuracy و + +43 +00:03:06,680 --> 00:03:11,220 +precision تجي نتعرف على accuracy ماذا تعني؟ + +44 +00:03:11,220 --> 00:03:16,000 +accuracy تعني مدى قرب النتيجة من النتيجة الحقيقية + +45 +00:03:16,000 --> 00:03:20,900 +درجة الانتباه من الحقيقة ال degree of conformity + +46 +00:03:20,900 --> 00:03:26,080 +to the truth and experiment مدى قرب النتيجة من + +47 +00:03:26,080 --> 00:03:31,950 +النتيجة الحقيقيةكيف يعني؟ يعني انا بحكيلك ان فيها + +48 +00:03:31,950 --> 00:03:36,290 +نفاح السكر اشتغلت و طلعت مية خد اشتغليها و شوفيها + +49 +00:03:36,290 --> 00:03:39,710 +قيمة الحقيقية انا حكيتلك انها مية و انت اشتغلتيها + +50 +00:03:39,710 --> 00:03:44,070 +و طلعت معاكي سبعين هل السبعين قريبة من المية؟ لأ + +51 +00:03:44,070 --> 00:03:47,890 +فهي بنسميها inaccurate result انت ما طلعتيهاش + +52 +00:03:47,890 --> 00:03:51,750 +accurate لكن لو طلعت معاكي تسعة و تسعين تسعة و + +53 +00:03:51,750 --> 00:03:55,770 +تسعين قريبة من المية اذا accurate result accuracy + +54 +00:03:55,770 --> 00:04:00,820 +مدى قرب النتيجة من النتيجة الحقيقيةفبالـ Precision + +55 +00:04:00,820 --> 00:04:05,080 +الـ Precision هي مادة قُرب النتائج من بعضها البعض + +56 +00:04:05,080 --> 00:04:09,380 +degree of agreement between replicated experiments + +57 +00:04:12,600 --> 00:04:17,340 +وطلعت النتاج في كل مرة يعني نفس الفحص اشتغلته خمس + +58 +00:04:17,340 --> 00:04:21,900 +مرات تمام؟ طلعت معايا القيمة الأولى 72 القيمة + +59 +00:04:21,900 --> 00:04:28,500 +التانية 74 القيمة التالتة 71 القيمة الرابعة 73 هل + +60 +00:04:28,500 --> 00:04:31,980 +هما قريبين من بعض؟ هو كلهم قريبين من بعض فهي + +61 +00:04:31,980 --> 00:04:37,180 +precise result نتائجك كانت precisePrecision مدى + +62 +00:04:37,180 --> 00:04:40,760 +قربها من بعضها البعض إن أنا أعيد الفحص أكتر من مرة + +63 +00:04:40,760 --> 00:04:44,560 +و أشوف النتائج هل قريبة من بعض ولا لا Accuracy قرب + +64 +00:04:44,560 --> 00:04:47,500 +النتيجة من النتيجة الحقيقية أنا بكون معطياكي + +65 +00:04:47,500 --> 00:04:51,100 +النتيجة و أنت اشتغليها هل طلعت نتيجتي مقاربة + +66 +00:04:51,100 --> 00:04:55,280 +لنتيجتي فهنا بتكون accurate result إذا طلعت بعيد + +67 +00:04:55,280 --> 00:05:00,780 +عنها بتكون not accurate، inaccurate result طبعا؟ + +68 +00:05:00,780 --> 00:05:05,000 +طب أنا حكيتلك إنه عندي أنا فحص اشتغلت و طلعت 100 + +69 +00:05:05,760 --> 00:05:09,160 +وانت اشتغلي ليها اكتر من مرة وشوفي ليها accurate + +70 +00:05:09,160 --> 00:05:13,460 +or precise اشتغلتي انا وحكيتلك انها 100، انت + +71 +00:05:13,460 --> 00:05:19,020 +اشتغلتيها خمس مرة، طلعت معاكي مرة 101، مرة 99، مرة + +72 +00:05:19,020 --> 00:05:24,380 +102، مرة 98، هلجيت النتائج قريبة من بعض، كانت 101، + +73 +00:05:24,380 --> 00:05:31,000 +99، 102، 98ما أنها قريبة من بعض هتكون precise طب + +74 +00:05:31,000 --> 00:05:34,520 +النتيجة الحقيقية كانت مية وكانوا جراب على المية + +75 +00:05:34,520 --> 00:05:38,700 +كلهم، لذا هي precise و accurate جمعت من الإتنين + +76 +00:05:38,700 --> 00:05:42,080 +كانت precise و accurate مع بعض + +77 +00:05:45,090 --> 00:05:48,870 +نحكي عن الـ chemical reaction التفاعل الكيميائي + +78 +00:05:48,870 --> 00:05:54,390 +التفاعل الكيميائي هو تفاعل تدخل فيه مادة تطلع عنها + +79 +00:05:54,390 --> 00:06:00,210 +مادة جديدة بصفات جديدة تغيير مادتك إلى مادة جديدة + +80 +00:06:00,210 --> 00:06:03,310 +بخصائص + +81 +00:06:03,310 --> 00:06:08,410 +مختلفة تدخل مادة جديدة بخصائص مختلفةSign of + +82 +00:06:08,410 --> 00:06:13,110 +chemical reaction علامات حدوث التفاعل أول شيء ممكن + +83 +00:06:13,110 --> 00:06:16,950 +يتكون عندي راسم هذا يدل على حدوث التفاعل Formation + +84 +00:06:16,950 --> 00:06:20,910 +of precipitate Color change ممكن يتغير اللون + +85 +00:06:20,910 --> 00:06:26,070 +Evolution of gas يعني تصاعد غاز تصاعد غاز يعني + +86 +00:06:26,070 --> 00:06:30,130 +الحدث عندي تغير Temperature change تتغير درجة + +87 +00:06:30,130 --> 00:06:35,120 +الحرارة برضه هو علامة من علامات حدوث التفاعلكيف + +88 +00:06:35,120 --> 00:06:38,720 +تتغير درجة الحرارة؟ في عندنا نوعين من التفاعل في + +89 +00:06:38,720 --> 00:06:44,020 +تفاعل اسمه Exothermic Reaction يعني طارد للحرارة + +90 +00:06:44,020 --> 00:06:48,640 +يعني بيحتاجش الحرارة، بيطلع الحرارة لبرا فبتكون + +91 +00:06:48,640 --> 00:06:52,280 +الأنبوبة لما تحسيها من برا بتكون ساخنةto get + +92 +00:06:52,280 --> 00:06:56,140 +hotter surrounding to get hot هوته يكون الخارج + +93 +00:06:56,140 --> 00:07:00,520 +المحيط الخارجي ساخن لأنه طارد للحرارة endothermic + +94 +00:07:00,520 --> 00:07:05,860 +reaction ماصل الحرارة تفاعل ماصل الحرارة تحتاج + +95 +00:07:05,860 --> 00:07:10,560 +لحرارة بتاخد حرارة فبيكون المحيط الخارجي بارد cool + +96 +00:07:13,910 --> 00:07:17,050 +عشان معاها ال biochemical compound اللى هنتعرف + +97 +00:07:17,050 --> 00:07:21,190 +عليها هنتعرف على ال carbohydrates على ال amino + +98 +00:07:21,190 --> 00:07:25,130 +acid و ال protein هنتعرف على ال lemon نيوكليك + +99 +00:07:25,130 --> 00:07:31,180 +تايبز والنيوكليك أسد هتاخدوها في مادة تانيةبدنا + +100 +00:07:31,180 --> 00:07:35,400 +اليه ندخل في مقدمة بسيطة عن الـ amino acid الأحماض + +101 +00:07:35,400 --> 00:07:39,220 +الأمينية وإن شاء الله المرة اللي جاي هنكملها هذا + +102 +00:07:39,220 --> 00:07:44,440 +الموضوع الأحماض الأمينية الـ amino acid إيش هي؟ هي + +103 +00:07:44,440 --> 00:07:48,880 +الـ building blocks of البروتين هي الوحدة البنائية + +104 +00:07:48,880 --> 00:07:53,760 +لتركيب البروتين تكون مرتبطة مع بعضها linked to + +105 +00:07:53,760 --> 00:07:58,240 +peptide Iأحماد أمينية مجموعة أحماد أمينية بتكون + +106 +00:07:58,240 --> 00:08:02,420 +مرتبطة مع بعض في peptide bond في رابطة بيبتيدية + +107 +00:08:02,420 --> 00:08:06,680 +لما يرتبطوا مع بعض هدول بيكونولي البروتين فالحمض + +108 +00:08:06,680 --> 00:08:12,180 +الأميني هو الوحدة البنائية لتركيب البروتين وترتبط + +109 +00:08:12,180 --> 00:08:17,930 +مع بعضها بروابط بيبتيدية بـ peptide bondإيش تركيب + +110 +00:08:17,930 --> 00:08:21,690 +هذا الحمض الأمين؟ لو نطلع على الصورة اللي عندنا + +111 +00:08:21,690 --> 00:08:26,530 +كيف تركيبها بتكون بالنص في عندنا ذرة Carbon هذه + +112 +00:08:26,530 --> 00:08:30,090 +الـCarbon بنسميها Central Carbon اللي هي الكربون + +113 +00:08:30,090 --> 00:08:34,970 +المركزية أو إلها اسم تاني Alpha Carbon أو اسمها + +114 +00:08:34,970 --> 00:08:38,900 +التالت Primary Carbonهي عندنا في الوسط في تركيب + +115 +00:08:38,900 --> 00:08:41,660 +الحمض الأميني بتكون عندنا الـ Central Carbon + +116 +00:08:41,660 --> 00:08:46,960 +كربونا مركزية او ايه تسميها تاني Alpha Carbon او + +117 +00:08:46,960 --> 00:08:50,900 +Primary Carbon هاي الـ Central Carbon بتكون مرتبطة + +118 +00:08:50,900 --> 00:08:56,080 +باربع روابط بتكون مرتبطة بجهة بمجموعة بنسميها + +119 +00:08:56,080 --> 00:09:01,950 +Carboxyl Group Carboxyl Group اللي هي COOHالـ + +120 +00:09:01,950 --> 00:09:06,050 +Carboxyl group و بتكون من جهة التانية مرتبطة + +121 +00:09:06,050 --> 00:09:11,050 +بمجموعتها .. بضارة هيدروجين بـ H و من جهة بتكون + +122 +00:09:11,050 --> 00:09:15,330 +مرتبطة بـ Aminogroup لأن H3I plus بسميها + +123 +00:09:15,330 --> 00:09:20,150 +Aminogroup و من الأسفل بتكون مرتبطة بالـ R group + +124 +00:09:20,150 --> 00:09:24,890 +الـ R group هاي اسمها الـ sided chainالـ side + +125 +00:09:24,890 --> 00:09:28,970 +chain هذه هي اللي بتميز الحمض الأميني عن غيره هي + +126 +00:09:28,970 --> 00:09:32,330 +عبارة عن مجموعة بتكون مرتبطة ممكن تكون ذرة واحدة + +127 +00:09:32,330 --> 00:09:37,250 +وممكن تكون مجموعةهي اللي بتميز كل حمض أميني عن + +128 +00:09:37,250 --> 00:09:41,290 +الآخر كل الأحماض الأمينية لها نفس التركيب بتكون + +129 +00:09:41,290 --> 00:09:45,730 +ذرة كربون و هيدروجين و كربوكسيل و أمينو و الـR + +130 +00:09:45,730 --> 00:09:49,590 +group هذي هي اللي بتختلف من حمض أميني للآخر يعني + +131 +00:09:49,590 --> 00:09:54,570 +اللي بيميز حمض أميني عن الآخر هي الـR group تمام؟ + +132 +00:09:55,130 --> 00:09:59,930 +وكل الأحماض الأمينية عندها amino group او primary + +133 +00:09:59,930 --> 00:10:03,650 +amino group اللي هي مجموعة الأمين العجبى بنسميها + +134 +00:10:03,650 --> 00:10:10,130 +amino group او primary amino group ماعدى حمض أمين + +135 +00:10:10,130 --> 00:10:14,750 +واحد اسمه البرولين البرولين ماعندهوش amino عنده + +136 +00:10:14,750 --> 00:10:19,830 +حاجة بنسميها amino group او secondary amino group + +137 +00:10:21,080 --> 00:10:26,960 +كلهم عندهم amino group مع ده البرولين عنده amino + +138 +00:10:26,960 --> 00:10:31,480 +group أو secondary amino group ليش سموها هكذا؟ + +139 +00:10:31,480 --> 00:10:34,920 +عشان مجموعة ال amino هاي اللي على الجنب الـ NH3 + +140 +00:10:34,920 --> 00:10:38,880 +plus بتكون مرتبطة مع الـR و مع الـC عاملة حلقة + +141 +00:10:38,880 --> 00:10:44,210 +بينها و بين نفسهاتكون الـ Amino Group مرتبطة مع + +142 +00:10:44,210 --> 00:10:47,550 +الـ R من جهة مع الـ Side Chain ومع الكربون + +143 +00:10:47,550 --> 00:10:50,910 +المركزية من جهة، متكونش مربوطة برابطة واحدة مع + +144 +00:10:50,910 --> 00:10:54,090 +الكربون زي الصورة وخلاص، لأ، بتكون مربوطة من + +145 +00:10:54,090 --> 00:10:58,390 +جهتها، جهة مع الكربون وجهة مع الـ R، مع الـ Side + +146 +00:10:58,390 --> 00:11:03,030 +Chain، هنا ماضلتش اسمها Primary Amino Group زي أي + +147 +00:11:03,030 --> 00:11:06,410 +حمض أميني مرتبطة بجهة واحدة، ساميها Primary، زي + +148 +00:11:06,410 --> 00:11:10,910 +مرتبطة في الكربونة وخلاصإذا مرتبطة مع الكربونة ومع + +149 +00:11:10,910 --> 00:11:15,690 +الـR زي في حالة لبرولين وهو الحالة الوحيدة الحمض + +150 +00:11:15,690 --> 00:11:21,790 +الوحيد بنتسميها amino group أو secondary amino + +151 +00:11:21,790 --> 00:11:28,130 +groupفي عندنا الـ food are divided into three + +152 +00:11:28,130 --> 00:11:31,510 +classes طعام مقسم إلى تلاتة في عندنا carbohydrate + +153 +00:11:31,510 --> 00:11:35,310 +و lipid و protein طعام بتكون من تلاتة + +154 +00:11:35,310 --> 00:11:39,270 +carbohydrate، lipid و protein ال carbohydrate + +155 +00:11:39,270 --> 00:11:43,770 +تعتبر هي مصدر الطاقة source of energy ال lipid + +156 +00:11:43,770 --> 00:11:49,250 +تعتبر مخزن الطاقة energy reserve ال protein هي + +157 +00:11:49,250 --> 00:11:53,830 +energy for growth and cellular maintenanceهي عبارة + +158 +00:11:53,830 --> 00:11:59,190 +عن طاقة الخلايا المستخدمة للنمو لبناء الجسم إذا + +159 +00:11:59,190 --> 00:12:03,410 +عندنا تلاتة نجد إحنا حكينا إنه البروتين كيف بتكون + +160 +00:12:03,410 --> 00:12:07,550 +بتيجي مجموعة أحماض أمينية ترتبط مع بعضها البعض + +161 +00:12:07,550 --> 00:12:11,450 +بيهرتبط high point في روابط بيبتدية بتكوين + +162 +00:12:11,450 --> 00:12:14,750 +البروتين لو جينا على الصورة هذه على الخط اللي فوق + +163 +00:12:14,750 --> 00:12:17,830 +أول شيء احنا عرفنا الصيغة العامة و ال structure + +164 +00:12:17,830 --> 00:12:21,050 +العامة للحمض الأميني إنه بيتكون من مجموعة carbon + +165 +00:12:21,050 --> 00:12:26,390 +مركزيةمرتبطة بهيدروجين وباردشين وكربوكسين + +166 +00:12:26,390 --> 00:12:32,070 +وامينوبرون توجينها الخط اللي فوقها على رموز جيت + +167 +00:12:32,070 --> 00:12:36,810 +عنه أول خط أحمر فوق اللي هي ال repeat units فيه + +168 +00:12:36,810 --> 00:12:39,770 +عندنا صيغة العاملة الحمد الأميني فيه في النص + +169 +00:12:39,770 --> 00:12:44,870 +مجموعة كاربون من فوق مرتبط فيها مجموعة هيدروجينمن + +170 +00:12:44,870 --> 00:12:47,530 +الأسفل مرتبط فيها الـ R group اللي هي الـ side + +171 +00:12:47,530 --> 00:12:51,890 +chain على اليمين مرتبط فيها الـ C double bond O + +172 +00:12:51,890 --> 00:12:56,890 +اللي هي الكربوكسيل group على اليسار مرتبط فيها NH + +173 +00:12:56,890 --> 00:13:01,510 +اللي هي مجموعة الأمين الأمينو group تمام؟ هي أول + +174 +00:13:01,510 --> 00:13:06,420 +حمض أميني جنبه مرتبط فيه حمض أميني تاني اللي هيالـ + +175 +00:13:06,420 --> 00:13:10,120 +Carbona المركزية و Hydrogen في الأعلى و R في + +176 +00:13:10,120 --> 00:13:13,720 +الأسفل وعلى اليمين Carboxyl group وعلى الجمال + +177 +00:13:13,720 --> 00:13:18,580 +Amino group هدول مجموعة أحماض أمينية أجت اترتبت + +178 +00:13:18,580 --> 00:13:22,860 +جانب بعض مرتبطة مع بعضها البعض في peptide bond + +179 +00:13:22,860 --> 00:13:28,460 +رابطة ببتدية فكونتلي البروتين طب وين ال peptide + +180 +00:13:28,460 --> 00:13:33,820 +bond جاية؟ ال peptide bond أجت وارتبطت بيهمجموعة + +181 +00:13:33,820 --> 00:13:38,480 +كربوكسيل من الحمض الأمين الأول ومجموعة أمين من + +182 +00:13:38,480 --> 00:13:42,600 +الحمض الأمين التاني إذا 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"word": " الأول", "probability": 0.978515625}, {"start": 829.2, "end": 829.44, "word": " عن", "probability": 0.91650390625}, {"start": 829.44, "end": 830.14, "word": " التاني", "probability": 0.9801432291666666}, {"start": 830.14, "end": 831.1, "word": " بنسميها", "probability": 0.8798828125}, {"start": 831.1, "end": 831.72, "word": " peptide", "probability": 0.82275390625}, {"start": 831.72, "end": 832.0, "word": " bond", "probability": 0.91845703125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 832.73725, "duration_after_vad": 807.2047187500011} \ No newline at end of file diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/QSsLWVqy8CU_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/QSsLWVqy8CU_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..31a3b1182e3e6f9801100642d427a8e73f6b6226 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/QSsLWVqy8CU_postprocess.srt @@ -0,0 +1,944 @@ +1 +00:00:00,000 --> 00:00:04,390 +يكون positive، إذا لا يحتوي، هيكون negativeفكيف + +2 +00:00:04,390 --> 00:00:08,530 +الـ principle مبدأ عمل الفحص أنه بيجي عنده amino + +3 +00:00:08,530 --> 00:00:13,290 +acid with aromatic ring حمض أميني بيحتوي على حلقة + +4 +00:00:13,290 --> 00:00:17,070 +بنزين بحط عليه concentrated nitric acid + +5 +00:00:17,070 --> 00:00:23,130 +concentrated nitric acid HNO3 في وجود قاعدة قوية + +6 +00:00:23,130 --> 00:00:27,870 +زي الـ NaO2 في وجود NaO2 ليش هييجي يعمل الـ nitric + +7 +00:00:27,870 --> 00:00:32,290 +acid لحمض الأميني اللي يحتوي على بنزين ring؟بيعمل + +8 +00:00:32,290 --> 00:00:37,190 +Nitration of Benzene Ring بيضيف Nitration of + +9 +00:00:37,190 --> 00:00:42,370 +Benzene Ring بيضيف NO3 على حلقة البنزين Nitric + +10 +00:00:42,370 --> 00:00:46,110 +Acid بيضيف NO3 على حلقة البنزين بيسميها Nitration + +11 +00:00:46,110 --> 00:00:49,870 +of Benzene Ring إذن هو Amino Acid with Benzene + +12 +00:00:49,870 --> 00:00:54,510 +Ring زائد Concentrated Nitric Acid مع Concentrated + +13 +00:00:54,510 --> 00:00:59,530 +HNO3 في وجود NOH بيصير Nitration of Benzene Ring + +14 +00:01:02,100 --> 00:01:05,200 +بنزين ريال يحتوي على يلو color إذا صار يلو color + +15 +00:01:05,200 --> 00:01:11,200 +إذا positive إذا negative إذا لا يحتوي على بنزين + +16 +00:01:11,200 --> 00:01:15,720 +ريالفي الملاحظة اللي تحت بيحكيلي عن الأحماض + +17 +00:01:15,720 --> 00:01:18,920 +الأمنية اللي بتحتوي على بنزين رينج، مين هم الأحماض + +18 +00:01:18,920 --> 00:01:22,340 +الأمنية اللي بتحتوي على بنزين رينج؟ هم تلات، في + +19 +00:01:22,340 --> 00:01:27,500 +الـTyrosine وTryptophan وPhenylalanine، تلت أحماض + +20 +00:01:27,500 --> 00:01:30,980 +أمنية فقط تحتوي على بنزين رينج، هم الـTyrosine + +21 +00:01:30,980 --> 00:01:35,030 +وTryptophan وPhenylalanineفي حالة التيروزين + +22 +00:01:35,030 --> 00:01:38,670 +والتريبتوفان بتكون activated، contain activated + +23 +00:01:38,670 --> 00:01:43,330 +بنزين ريكو حلقة البنزين بتكون نشطة فبتقدر تتفاعل + +24 +00:01:43,330 --> 00:01:47,690 +بسهولة مع الـnitric acid مع الـconcentrated nitric + +25 +00:01:47,690 --> 00:01:52,460 +acid بيصيريلها نيتراشن بيعطين لون يلولكن في حالة + +26 +00:01:52,460 --> 00:01:56,680 +الفلن الألانين لا تتفاعل مع نيترك أسن لأنها بتكون + +27 +00:01:56,680 --> 00:02:03,800 +حلقة البنزين غير ناشطة فمش هيتفاعل ولا هيعطيني لهم + +28 +00:02:03,800 --> 00:02:07,640 +إذا الأحمض الأمينية تلاتة عند حلقة البنزين هم + +29 +00:02:07,640 --> 00:02:12,260 +التيروزينTryptophan فين الألانين؟ ولكن مين النشطة + +30 +00:02:12,260 --> 00:02:15,600 +و هيعطيني positive مع فحص ال Xanthopretic test بس + +31 +00:02:15,600 --> 00:02:20,240 +تيروزين لـ Tryptophan أما الفين الألانين هيعطيني + +32 +00:02:20,240 --> 00:02:25,100 +negative مش هيتغير اللون لأن حلقة البنزين غير نشطة + +33 +00:02:25,680 --> 00:02:28,660 +فى فحص الـ xantoproteic test من هيعطينى positive + +34 +00:02:28,660 --> 00:02:35,280 +فقط التيروزين والتريبتوفان وكمان أي بروتيل يحتوي + +35 +00:02:35,280 --> 00:02:39,780 +على التيروزين أو التريبتوفان فى تركيبه فالبروتين + +36 +00:02:39,780 --> 00:02:42,980 +هو عبارة عن مجموعة من الأحماض الأمنية مرتبطة مع + +37 +00:02:42,980 --> 00:02:47,080 +بعضها البعض بروابط مبتدية إذا كان أحد الأحماض + +38 +00:02:47,080 --> 00:02:50,880 +الأمنية هذه تيروزين أو تريبتوفان أو الأثنين معاها + +39 +00:02:50,880 --> 00:02:57,410 +هيعطينى positiveأوضح بمعادلة إن الـ Thyrosine مع + +40 +00:02:57,410 --> 00:03:00,270 +Concentrated Nitric Acid مش مهم إن الـ Structure + +41 +00:03:00,270 --> 00:03:04,810 +إنه يعطيني Nitration of بنزين رنج Yellow Color + +42 +00:03:04,810 --> 00:03:08,130 +وإذا اتفاعل برضه الـ Tryptophan مع Concentrated + +43 +00:03:08,130 --> 00:03:11,770 +Nitric Acid هيصير برضه عمليت Nitration of بنزين + +44 +00:03:11,770 --> 00:03:14,750 +رنج وهيعطيني Yellow Color لأن الـ Thyrosine و الـ + +45 +00:03:14,750 --> 00:03:17,930 +Tryptophan يحتوي على Activated Benzene Ring لكن لو + +46 +00:03:17,930 --> 00:03:21,190 +اتفاعلنا الفل الأليان مع الـ Concentrated Nitric + +47 +00:03:21,190 --> 00:03:25,530 +Acid مايتفعلش، مش هيعطيني Yellow Colorليش؟ لأن + +48 +00:03:25,530 --> 00:03:28,990 +حلقة البنزين اللي موجودة في الفيلم الألانين غير + +49 +00:03:28,990 --> 00:03:30,950 +ناشطة، من أكتر + +50 +00:03:33,620 --> 00:03:38,140 +طب كيف خطوات العمل؟ خطوات العمل بجيب لتيوب، glass + +51 +00:03:38,140 --> 00:03:41,680 +tube، بحط عليها واحد مل من الحمض الأميني أو من + +52 +00:03:41,680 --> 00:03:44,140 +المحلول اللي أنا أعطاتكيا، أنا مش عارف حمض أميني + +53 +00:03:44,140 --> 00:03:47,400 +أو بروتين، مهم محلول اللي أنا أعطاتكيا، بتحط منه + +54 +00:03:47,400 --> 00:03:51,000 +واحد مل، بتحط عليه واحد مل من ال nitric acid من ال + +55 +00:03:51,000 --> 00:03:55,970 +HNO3، بعدين بتسخنيه على اللهةلما نيسخن على اللهب + +56 +00:03:55,970 --> 00:04:00,390 +بحطه في الراك يبرد بعد ما تبرد شوية لـ tube بضيف + +57 +00:04:00,390 --> 00:04:04,130 +عليها اتنين نيل من الانهيواتش من القاعدة ليش هذه + +58 +00:04:04,130 --> 00:04:08,330 +الانهيواتش؟ عشان تزود شدة اللون بضيف انهيواتش + +59 +00:04:08,330 --> 00:04:13,590 +لزيادة شدة اللون والله إذا تغير اللون إلى yellow + +60 +00:04:13,590 --> 00:04:18,310 +إذا هذا حمض أميني أو بروتين يحتوي على بنزين ريل + +61 +00:04:18,310 --> 00:04:23,090 +إذا ماتغيرش اللون إذا لا يحتوي على بنزين ريل + +62 +00:04:25,930 --> 00:04:29,010 +الفحص اللي بعد هيك هو الـ Hopkin Cool أو الـ + +63 +00:04:29,010 --> 00:04:32,730 +Glycosilic Acid Reaction اللي هو اسمها؟ Hopkin + +64 +00:04:32,730 --> 00:04:36,250 +Cool أو Glycosilic Acid Reaction إيش الهدف من + +65 +00:04:36,250 --> 00:04:41,130 +الفحص؟ لكشف عن وجود لتريبتوفعل بيكشف عن + +66 +00:04:41,130 --> 00:04:43,950 +لتريبتوفعل، مش معناه لتريبتوفعل لأنه هذا بيدور على + +67 +00:04:43,950 --> 00:04:49,730 +حاجة نسميهاالدول جروب هي مجموع موجودة بس في الـ + +68 +00:04:49,730 --> 00:04:52,870 +tryptophan إذا موجود ال tryptophan هيعطيني + +69 +00:04:52,870 --> 00:04:55,970 +positive إذا مش موجود هيعطيني negative فهو + +70 +00:04:55,970 --> 00:04:59,790 +positive مع ال tryptophan أو أي بروتين يحتوي في + +71 +00:04:59,790 --> 00:05:03,990 +تركيبه على ال tryptophan هبقاش ال principle المبدأ + +72 +00:05:03,990 --> 00:05:07,410 +إنه بجيب الحمض الأمين اللي عندسي ال tryptophan أو + +73 +00:05:07,410 --> 00:05:13,330 +البروتين و أضيف عليه cooking pool reagent مع H2SO4 + +74 +00:05:13,330 --> 00:05:17,400 +concentrated sulfuric acidبتكوّنلي هذا الـ + +75 +00:05:17,400 --> 00:05:20,360 +Sulfuric Acid هي مسؤولة عن تكوين to formation of + +76 +00:05:20,360 --> 00:05:24,420 +violet ring بتكوّنلي حلقة في الوسط، تفصل solution + +77 +00:05:24,420 --> 00:05:28,960 +من الأيلى جزاين، بتكون حلقة لون هموم، violet ring، + +78 +00:05:28,960 --> 00:05:32,600 +الـ Sulfuric Acid بتكوّنلي violet ring، بتكوّنلي + +79 +00:05:32,600 --> 00:05:36,900 +حلقة لون هموم، إذا اتكوّنت هذه الحلقة، معناها إنه + +80 +00:05:36,900 --> 00:05:40,100 +فحص positive، معناه إنه هذا المركب هو tryptophan + +81 +00:05:40,100 --> 00:05:45,440 +أو بروتين يحتوي على tryptophanإذا لم تتكون إذا أنه + +82 +00:05:45,440 --> 00:05:52,040 +نيجاتيف لا يحتوي على الـ tryptophan طب + +83 +00:05:52,040 --> 00:05:55,520 +كيف ال procedure في وقت العمل؟ بجيب ال class tube + +84 +00:05:55,520 --> 00:05:58,900 +بحط فيها واحد mil من ال solution من المحلول اللي + +85 +00:05:58,900 --> 00:06:02,560 +انا اعطيتكيها سواء tryptophan او غيرها و بحط عليها + +86 +00:06:02,560 --> 00:06:06,460 +واحد mil من ال hook and pull reaction و بعمل mix + +87 +00:06:06,460 --> 00:06:09,800 +أجيب ال tube و بحط عليها واحد mil من ال solution + +88 +00:06:09,800 --> 00:06:13,630 +مع واحد mil من ال hook and pull و بعمل mixبعدين + +89 +00:06:13,630 --> 00:06:18,630 +بمسك التيوب بميلها بشكل مائل و بحط فيها من 3 إلى 4 + +90 +00:06:18,630 --> 00:06:23,510 +مل من ال H2SO4 Concentrated Sulphuric Acid على + +91 +00:06:23,510 --> 00:06:26,930 +الجدار بضيفه ال Sulphuric Acid و بشكل تدريجي مش + +92 +00:06:26,930 --> 00:06:31,750 +مرة واحدة و بحرص على أني ما أرجش التيوببمسك لتيوب + +93 +00:06:31,750 --> 00:06:35,890 +بشكل ما واضيف على الجدار من 3 إلى 4 مل من ال + +94 +00:06:35,890 --> 00:06:39,770 +concentrated sulphuric acid بشكل تدريجي بدون رج + +95 +00:06:39,770 --> 00:06:44,510 +لتيوب بعد ما اخلص باعدل لتيوب شواش بدون معرجها + +96 +00:06:44,510 --> 00:06:49,630 +باعدلها إذا دونت عندي حلقة لونها violetإذا هذا + +97 +00:06:49,630 --> 00:06:52,670 +positive، يحتوي على الـ tryptophan، هو tryptophan، + +98 +00:06:52,670 --> 00:06:55,550 +يمكن أن يناسب الـ tryptophan أو protein يحتوي على + +99 +00:06:55,550 --> 00:06:58,410 +tryptophan، إذا ما اتكونتش الحلقة، إذا الـ + +100 +00:06:58,410 --> 00:07:02,430 +negative، لا يوجد tryptophan، لا يحتوي على الـ + +101 +00:07:02,430 --> 00:07:03,230 +tryptophan + +102 +00:07:06,060 --> 00:07:09,800 +بس اللي بعد هيك هو ال melons test ال melons test + +103 +00:07:09,800 --> 00:07:14,120 +هو للكشف عن وجود التيروزين objective to detect the + +104 +00:07:14,120 --> 00:07:17,200 +presence of tyrosine ليش؟ لأن التيروزين يحتوي على + +105 +00:07:17,200 --> 00:07:19,600 +phenol group هو بالت ال phenol group اللي في + +106 +00:07:19,600 --> 00:07:23,160 +التيروزين إذا موجود أنا تيروزين عنده هيعطيني + +107 +00:07:23,160 --> 00:07:26,240 +positive إذا مش موجود هيعطيني negative فهو + +108 +00:07:26,240 --> 00:07:30,260 +positive مع التيروزين أو أي بروتين يحتوي على + +109 +00:07:30,260 --> 00:07:34,820 +التيروزين غير هيك بيعطيني negativeايش هي الـ + +110 +00:07:34,820 --> 00:07:39,900 +Phenol Group؟ هي حلقة بنزين مرتبطة بـ OH، Hydroxyl + +111 +00:07:39,900 --> 00:07:43,300 +Group Attached to Benzene Ring إذا عندى حلقة بنزين + +112 +00:07:43,300 --> 00:07:46,640 +مرتبطة بـ Hydroxyl Group، فهذه بيسميها Phenol + +113 +00:07:46,640 --> 00:07:50,840 +Group، وهي موجودة في حالة تيروزين، بيحكي للـ Melon + +114 +00:07:50,840 --> 00:07:55,210 +Reagent عبارة عن مكونات contain mercury andNitric + +115 +00:07:55,210 --> 00:07:59,110 +acid هتش أنوادري و Mercury و هدول المكونين هم + +116 +00:07:59,110 --> 00:08:03,710 +toxic و corrosive و بسبب حروب و مهيج irritant + +117 +00:08:03,710 --> 00:08:10,330 +فبدنا نتعامل مع ال Mercury reaction بحوار طب ايش + +118 +00:08:10,330 --> 00:08:11,270 +ال principle اللي + +119 +00:08:19,710 --> 00:08:22,810 +التيروسين زي الـmineral reagent حكينا الـmineral + +120 +00:08:22,810 --> 00:08:26,670 +reagent هو عبارة عن مكونات نيترك أسد أتشانودري و + +121 +00:08:26,670 --> 00:08:30,410 +مالك مجرد ما أضيف الـmineral reagent على التيروسين + +122 +00:08:30,410 --> 00:08:35,090 +تيجي أول مكون اللي هو الـnitric acid يعمل نيتراشن + +123 +00:08:35,090 --> 00:08:38,930 +للبنزين يعمل نيتراشن لحلقة البنزين الموجودة في + +124 +00:08:38,930 --> 00:08:42,620 +التيروسينبعد ما يصيرلها نيتراشن بيجي الـ mercury + +125 +00:08:42,620 --> 00:08:47,220 +بيرتبط معها وبيتكون عندي لون أحمر طوبي إذا ان هو + +126 +00:08:47,220 --> 00:08:51,640 +تيروسين مع ميلون رياجينت وبيتكون عندي نيتراتي + +127 +00:08:51,640 --> 00:08:55,800 +تيروسين ميركاري كومبكس اللي هو تيروسين بيصيرله + +128 +00:08:55,800 --> 00:08:59,560 +نيتراشن ومرتبط معه mercury بنسميها نيتراتي تيروسين + +129 +00:08:59,560 --> 00:09:05,160 +ميركاري كومبكس شو اللونه بيكون بركره لون أحمر طوبي + +130 +00:09:05,160 --> 00:09:08,180 +إذا أن هو positive إذا أن هو التيروسين أو أي + +131 +00:09:08,180 --> 00:09:12,530 +بروتين يحتوي على التيروسيننحكي للملاحظة أن كل + +132 +00:09:12,530 --> 00:09:16,690 +الفينول اللى بتحتوي كل الفينول كل المركبات اللى + +133 +00:09:16,690 --> 00:09:20,530 +عندها فينول ال group اللى حلقة بنزينة مرتبطة ب OH + +134 +00:09:20,530 --> 00:09:26,190 +هتعطينا positive مع الفينول ريجال ان احنا حكينا بس + +135 +00:09:26,190 --> 00:09:28,570 +طب ايش ال principle + +136 +00:09:34,850 --> 00:09:38,270 +طيروسين طيروسين واضيف عليه melon reagent طيروسين + +137 +00:09:38,270 --> 00:09:40,950 +زي الـ melon reagent حكينا الـ melon reagent هو + +138 +00:09:40,950 --> 00:09:45,790 +عبارة عن مكونات نيترك أسد أتشانواتري و مركز مجرد + +139 +00:09:45,790 --> 00:09:49,130 +ما أضيف الـ melon reagent على الطيروسين تيجي اول + +140 +00:09:49,130 --> 00:09:52,710 +ايه؟ اول مكون اللي هو الـ nitric acid يعمل نيتراشن + +141 +00:09:52,710 --> 00:09:56,560 +للبنزينبيعمل Nitration لحلقة البنزين الموجودة في + +142 +00:09:56,560 --> 00:09:59,980 +الـ Tyrosine، بعد ما يصير لها Nitration، بيجي الـ + +143 +00:09:59,980 --> 00:10:04,440 +Mercury بيرتبط معها، وبيتكون عندى لون أحمر طوف، + +144 +00:10:04,440 --> 00:10:08,280 +اذا ان هو Tyrosine مع ميلونرياجنت، بيتكون عندى + +145 +00:10:08,280 --> 00:10:12,860 +Nitrated Tyrosine Mercury Complexاللي هو تيروسين + +146 +00:10:12,860 --> 00:10:15,760 +بسيريلو نيتراشن ومرتبط معاه ميركري، بتسميها + +147 +00:10:15,760 --> 00:10:19,960 +نيتراتي تيروسين ميركري كومبلاز، شو لونه؟ بيكون + +148 +00:10:19,960 --> 00:10:24,560 +فريكري، لون أحمر، طوبي، إذا ان هو positive، إذا ان + +149 +00:10:24,560 --> 00:10:28,860 +هو التيروسين أو أي بلوتين يحتوي على التيروسينبحكي + +150 +00:10:28,860 --> 00:10:33,420 +للملاحظة أن كل الفينول اللى بتحتوي كل الفينول كل + +151 +00:10:33,420 --> 00:10:37,080 +المراكبات اللى عندها فينول group هي حلقة بنزين + +152 +00:10:37,080 --> 00:10:41,800 +مرتبطة بهواتف متعطين positive مع الميلونريال أن + +153 +00:10:41,800 --> 00:10:45,460 +إحنا حكينا بس من الأحماض الأمنية التيروسين هو + +154 +00:10:45,460 --> 00:10:48,400 +الوحيد اللى عنده فينول group عنده حلقة بنزين + +155 +00:10:48,400 --> 00:10:52,400 +مرتبطة فيه هواتف لكن هل الطبيعة كلها في المراكبات + +156 +00:10:52,400 --> 00:10:56,000 +الكيميائية كلها فش غير التيروسين صح وفي الأحماض + +157 +00:10:56,000 --> 00:11:01,350 +الأمنية بسالثانية فيه مركبات تانية عند حلقة بنزين + +158 +00:11:01,350 --> 00:11:04,970 +مرتبطة بواعي فلو جيت اشتغلت عليها ال melon test + +159 +00:11:04,970 --> 00:11:09,010 +هتعطيني positive طب على فرض انا أعطيتك محلول + +160 +00:11:09,010 --> 00:11:12,810 +حكيتلك شوفيلي إيش هذا المحلول يسيغليلي عليها ال + +161 +00:11:12,810 --> 00:11:16,630 +melon شوفي تايروسين positive ولا نجده فجيت ان انت + +162 +00:11:16,630 --> 00:11:20,330 +اشتغلتيه و أعطاكي positive إذا هو هتتوقع إنه مركب + +163 +00:11:20,330 --> 00:11:24,960 +يحتوي على phenolgo تمام؟طب هل هو تيروسين ولا + +164 +00:11:24,960 --> 00:11:29,400 +مُركّب تاني؟ كيف بتتأكد هل هو تيروسين أو لا؟ لأن + +165 +00:11:29,400 --> 00:11:32,920 +في مُركّبات تانية تحتوي على Phenol Group؟ بشتغل + +166 +00:11:32,920 --> 00:11:36,720 +فحص الـNihidrine، مش الـNihidrine أول فحص أخدنا هو + +167 +00:11:36,720 --> 00:11:40,980 +مُخصص لـ Free Alpha Amino Group اللي موجودة في كل + +168 +00:11:40,980 --> 00:11:45,310 +الأحماض الأمنية، الـAmino Acidأنا هشتغل فحص الـ + +169 +00:11:45,310 --> 00:11:49,610 +Ninhydrin لما تشتغلي فحص الـ Ninhydrin إذا أعطاكي + +170 +00:11:49,610 --> 00:11:52,810 +positive إذا هو تيروسين لأن حمض أميني يحتوي على + +171 +00:11:52,810 --> 00:11:55,830 +free alpha amino group إذا أعطاني negative إذا هو + +172 +00:11:55,830 --> 00:12:00,030 +مرنكب تيميائي آخر يحتوي على phenol group غير + +173 +00:12:00,030 --> 00:12:00,770 +التيروسين + +174 +00:12:04,290 --> 00:12:07,210 +كيف ال procedure؟ خدت وقت إجراء التجربة، بجيب + +175 +00:12:07,210 --> 00:12:10,410 +التيور، بحط فيها واحد ميل من ال solution اللي أنا + +176 +00:12:10,410 --> 00:12:14,410 +أعطيتها على تلاتة drop من ال melon raisin و بعدين + +177 +00:12:14,410 --> 00:12:17,470 +بحطه في ال water bath لمدة خمسة minutes، في ماء + +178 +00:12:17,470 --> 00:12:20,430 +مغليه لمدة خمسة minutes، بعدين بطلع، إذا تغير + +179 +00:12:20,430 --> 00:12:24,210 +اللون و اتكون عندي break red، إذا هو positive، إذا + +180 +00:12:24,210 --> 00:12:27,750 +ما تغيرش اللون، ماعطانيش ال precipitate break red، + +181 +00:12:27,750 --> 00:12:29,210 +إذا هو negative + +182 +00:12:32,100 --> 00:12:35,780 +الفحص اللي بعد هي اسمه Sakaguchi Test Sakaguchi + +183 +00:12:35,780 --> 00:12:39,500 +Test ال objective منه لكشف عن الأحماض الأمنية اللي + +184 +00:12:39,500 --> 00:12:44,160 +بتحتوي على Iguanidia Migrum وهو فقط ال Arginine + +185 +00:12:44,160 --> 00:12:48,860 +موجودة في Iguanidia Migrum في ال Arginine فحص خاص + +186 +00:12:48,860 --> 00:12:53,780 +لل Arginine أنه بيحتوي على Iguanidia Migrumال + +187 +00:12:53,780 --> 00:12:56,280 +ساكيا جوشي تيست اناش ناخد لا لبرنسيب اللي هو + +188 +00:12:56,280 --> 00:13:00,020 +للطريقة بس انه ال objective هو لل guanidine مجروم + +189 +00:13:00,020 --> 00:13:03,360 +اللي موجودة فيه اللي هجنين و ال positive انه + +190 +00:13:03,360 --> 00:13:05,320 +يعطيني لون red color + +191 +00:13:10,120 --> 00:13:14,200 +الفحص اللي بعد هي اسمه lip sulfite test أو sulfur + +192 +00:13:14,200 --> 00:13:18,340 +test ايش ال objective منه؟ للكشف عن ال self + +193 +00:13:18,340 --> 00:13:22,520 +-hydrayl group تدور على ال self-hydryl group + +194 +00:13:22,520 --> 00:13:25,740 +الموجودة وين ال self-hydryl group؟ في الحمض + +195 +00:13:25,740 --> 00:13:29,260 +الأميني cysteine وموجودة كمان في ال cysteine + +196 +00:13:29,260 --> 00:13:33,160 +وموجودة في الميثيونين ال self-hydryl group موجودة + +197 +00:13:33,160 --> 00:13:38,380 +في ثلاثة، cysteine, cysteine, methionineولكن بتكون + +198 +00:13:38,380 --> 00:13:42,960 +في الـ cysteine و الـ cysteine free ال مثيولين + +199 +00:13:42,960 --> 00:13:47,640 +بتكون not free بتقدرش تتفاعل لأنه بيكون مربوطة + +200 +00:13:47,640 --> 00:13:51,280 +برابطتين carbon من جهة و carbon أخرى من جهة أخرى + +201 +00:13:51,280 --> 00:13:55,280 +فغير قادر على كسر الرابط و أنه يتفاعل فهو negative + +202 +00:13:55,280 --> 00:13:58,540 +في حالة ال مثيولين و positive في حالة ال cysteine + +203 +00:13:58,540 --> 00:14:04,180 +و ال cysteine و أي بروتين يحتوي عليهتمام إذا للـ + +204 +00:14:04,180 --> 00:14:06,700 +lead sulphide test أو الـ sulphur test اللي كاشف + +205 +00:14:06,700 --> 00:14:10,040 +عن ال sulphohydryl group الموجودة في ال 16 أو ال + +206 +00:14:10,040 --> 00:14:14,340 +16 مثيلين نيجاتر لإنها not freeماشي ال principle + +207 +00:14:14,340 --> 00:14:18,980 +أني بجيب الحمض الأميني مثلا سيستين أو سيستان بضيف + +208 +00:14:18,980 --> 00:14:24,480 +عليها 10% من ال NaOH في وجود حرارة heat بيعطيني + +209 +00:14:24,480 --> 00:14:30,440 +Sodium Sulphate بجيب سيستين أو سيستان مع 10% NaOH + +210 +00:14:30,440 --> 00:14:34,880 +في وجود حرارة بتكون عندي Sodium Sulphate بضيف + +211 +00:14:34,880 --> 00:14:40,060 +عليها 10% Lead Acetate بيعطيني حاجة بتسميها Lead + +212 +00:14:40,060 --> 00:14:44,260 +Sulphateالليد سالفايت هذا عبارة عن ال precipitates + +213 +00:14:44,260 --> 00:14:50,260 +لونه أسود، 60 أو سيستان، مع 10% النيوهاتش في وجود + +214 +00:14:50,260 --> 00:14:55,180 +حرارة، بيعطيني Sodium Sulfate، بضيف عليه 10% ليد + +215 +00:14:55,180 --> 00:14:59,360 +أسيتات، بيعطيني Lead Sulfide ب precipitates لونه + +216 +00:14:59,360 --> 00:15:03,720 +أسود، يعني positive، يعني بتحتوي على 60 أو سيستان + +217 +00:15:07,940 --> 00:15:11,080 +هنا بيوضحنى ان الميثيونين وال سيستين التنتين + +218 +00:15:11,080 --> 00:15:14,240 +بيحتوى على sulfur group بس ليش الـ 16 بس هي اللى + +219 +00:15:14,240 --> 00:15:17,300 +بتعطينى positive لو دينا ال structure الميثيونين + +220 +00:15:17,300 --> 00:15:22,380 +تشوفوا ال S و N مرتبطة في CH2 من جهة و CH3 من جهة + +221 +00:15:22,380 --> 00:15:25,880 +فهي مرتبطة من الجهتين و صعب تكسير هذه الرابطة + +222 +00:15:26,100 --> 00:15:29,880 +فبنقدرش نكسرها عشان تتفاعل ما يتفاعل فهي not free + +223 +00:15:29,880 --> 00:15:33,980 +أما في حالة ال cysteine فهي free هي الأس فوق + +224 +00:15:33,980 --> 00:15:37,860 +مرتبطة في H من جهة و free من جهة أخرى تقدر تتفاعل + +225 +00:15:37,860 --> 00:15:42,780 +و تحت معادلات لبرنسبل الفحص cysteine مضيف عليه + +226 +00:15:42,780 --> 00:15:47,180 +النيوهاتش في وجود حرارة بيعطيني صوديوم سالفايت + +227 +00:15:47,180 --> 00:15:52,240 +مضيف عليها lead 10% من lead أسيتات بيعطيني lead + +228 +00:15:52,240 --> 00:15:56,600 +سالفايت ال precipitate لونه أسوديكون ال recipe + +229 +00:15:56,600 --> 00:16:02,600 +اللي هو هنا اسمهكيف خطوات العمل؟ بحط واحد مل من ال + +230 +00:16:02,600 --> 00:16:06,300 +solution أنا أعطيتكيا في تيووب بحط واحد مل منه على + +231 +00:16:06,300 --> 00:16:10,480 +واحد مل من ال sodium hydroxide ده نيو هاتش مع خمسة + +232 +00:16:10,480 --> 00:16:13,580 +دروب من عشرة فالمية lead acetate بحطهم كلهم مع بعض + +233 +00:16:13,580 --> 00:16:17,160 +و بعمل math بعدين بحطه في ال water bath لمدة خمسة + +234 +00:16:17,160 --> 00:16:21,020 +منه بطلعه من ال water bath إذا صار لونه أسود فيه + +235 +00:16:21,020 --> 00:16:24,400 +نراسب أسود is a positive يحتوي على ال system إذا + +236 +00:16:24,400 --> 00:16:28,940 +ما اتغيرش اللون is a negative ليحتوي على ال system + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/QSsLWVqy8CU_raw.json b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/QSsLWVqy8CU_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..3e74dabc0c6c45c69e6242df0733dbc4218585d8 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/QSsLWVqy8CU_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 288, "start": 0.0, "end": 2.88, "text": "يكون positive، إذا لا يحتوي، هيكون negative", "tokens": [1829, 30544, 3353, 12399, 11933, 15730, 20193, 7251, 33753, 45865, 12399, 39896, 30544, 3671], "avg_logprob": -0.294531246026357, "compression_ratio": 1.0491803278688525, "no_speech_prob": 5.960464477539063e-08, "words": 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0.81591796875}, {"start": 114.84, "end": 115.42, "word": " نيترك", "probability": 0.6895751953125}, {"start": 115.42, "end": 115.8, "word": " أسن", "probability": 0.65673828125}, {"start": 115.8, "end": 116.18, "word": " لأنها", "probability": 0.7289225260416666}, {"start": 116.18, "end": 116.68, "word": " بتكون", "probability": 0.776611328125}, {"start": 116.68, "end": 117.2, "word": " حلقة", "probability": 0.9562174479166666}, {"start": 117.2, "end": 117.94, "word": " البنزين", "probability": 0.9625244140625}, {"start": 117.94, "end": 118.98, "word": " غير", "probability": 0.6331787109375}, {"start": 118.98, "end": 121.34, "word": " ناشطة", "probability": 0.7145233154296875}, {"start": 121.34, "end": 121.84, "word": " فمش", "probability": 0.8557942708333334}, {"start": 121.84, "end": 122.52, "word": " هيتفاعل", "probability": 0.90625}, {"start": 122.52, "end": 122.8, "word": " ولا", "probability": 0.90234375}, {"start": 122.8, "end": 123.46, "word": " هيعطيني", "probability": 0.84658203125}, {"start": 123.46, "end": 123.8, "word": " لهم", "probability": 0.529296875}, {"start": 123.8, "end": 124.52, "word": " إذا", "probability": 0.731201171875}, {"start": 124.52, "end": 124.96, "word": " الأحمض", "probability": 0.778564453125}, {"start": 124.96, "end": 125.44, "word": " الأمينية", "probability": 0.8521728515625}, {"start": 125.44, "end": 125.84, "word": " تلاتة", "probability": 0.907958984375}, {"start": 125.84, "end": 126.02, "word": " عند", "probability": 0.99169921875}, {"start": 126.02, "end": 126.4, "word": " حلقة", "probability": 0.9503580729166666}, {"start": 126.4, "end": 126.94, "word": " البنزين", "probability": 0.861572265625}, {"start": 126.94, "end": 127.64, "word": " هم", "probability": 0.807373046875}, {"start": 127.64, "end": 128.44, "word": " التيروزين", "probability": 0.79853515625}], "temperature": 1.0}, {"id": 8, "seek": 14510, "start": 128.7, "end": 145.1, "text": "Tryptophan فين الألانين؟ ولكن مين النشطة و هيعطيني positive مع فحص ال Xanthopretic test بس تيروزين لـ Tryptophan أما الفين الألانين هيعطيني negative مش هيتغير اللون لأن حلقة البنزين غير نشطة", "tokens": [51, 627, 662, 404, 3451, 8978, 1863, 16247, 1211, 7649, 9957, 22807, 35525, 19452, 3714, 9957, 28239, 8592, 9566, 3660, 4032, 39896, 3615, 9566, 9957, 1829, 3353, 20449, 6156, 5016, 9381, 2423, 1783, 282, 392, 404, 1505, 299, 1500, 4724, 3794, 6055, 13546, 2407, 11622, 9957, 5296, 39184, 6526, 662, 404, 3451, 5551, 15042, 27188, 9957, 16247, 1211, 7649, 9957, 39896, 3615, 9566, 9957, 1829, 3671, 37893, 8032, 36081, 17082, 13546, 13672, 11536, 5296, 33456, 11331, 1211, 28671, 29739, 1863, 11622, 9957, 32771, 13546, 8717, 8592, 9566, 3660], "avg_logprob": -0.22401685393258428, "compression_ratio": 1.5935828877005347, "no_speech_prob": 1.1324882507324219e-05, "words": [{"start": 128.7, "end": 129.6, "word": "Tryptophan", "probability": 0.89169921875}, {"start": 129.6, "end": 130.16, "word": " فين", "probability": 0.528564453125}, {"start": 130.16, "end": 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"text": "أوضح بمعادلة إن الـ Thyrosine مع Concentrated Nitric Acid مش مهم إن الـ Structure إنه يعطيني Nitration of بنزين رنج Yellow Color وإذا اتفاعل برضه الـ Tryptophan مع Concentrated Nitric Acid هيصير برضه عمليت Nitration of بنزين رنج وهيعطيني Yellow Color لأن الـ Thyrosine و الـ Tryptophan يحتوي على Activated Benzene Ring لكن لو اتفاعلنا الفل الأليان مع الـ Concentrated Nitric Acid مايتفعلش، مش هيعطيني Yellow Color", "tokens": [10721, 2407, 11242, 5016, 4724, 2304, 3615, 18513, 37977, 36145, 2423, 39184, 40010, 2635, 533, 20449, 2656, 2207, 5468, 37942, 1341, 5097, 327, 37893, 3714, 16095, 36145, 2423, 39184, 745, 2885, 36145, 3224, 7251, 3615, 9566, 9957, 1829, 37942, 2405, 295, 44945, 11622, 9957, 12602, 1863, 7435, 17550, 10458, 4032, 28814, 15730, 1975, 2655, 5172, 995, 30241, 4724, 43042, 3224, 2423, 39184, 6526, 662, 404, 3451, 20449, 2656, 2207, 5468, 37942, 1341, 5097, 327, 39896, 9381, 13546, 4724, 43042, 3224, 6225, 42213, 36081, 37942, 2405, 295, 44945, 11622, 9957, 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cooking pool reagent مع H2SO4 concentrated sulfuric acid", "tokens": [6027, 3215, 12610, 10874, 32887, 3555, 39896, 3714, 7435, 2304, 45367, 3714, 29245, 23328, 3660, 4724, 3794, 8978, 2423, 39184, 853, 662, 404, 3451, 11933, 15730, 3714, 29245, 23328, 2423, 853, 662, 404, 3451, 39896, 3615, 9566, 9957, 1829, 3353, 11933, 15730, 37893, 3714, 29245, 23328, 39896, 3615, 9566, 9957, 1829, 3671, 6156, 3224, 2407, 3353, 20449, 2423, 853, 662, 404, 3451, 34051, 36632, 4724, 32887, 31371, 1863, 7251, 33753, 45865, 8978, 6055, 31747, 1829, 3555, 3224, 15844, 2423, 853, 662, 404, 3451, 8032, 3555, 4587, 33599, 2423, 8665, 9673, 44510, 10721, 36145, 3224, 4724, 7435, 1829, 3555, 21542, 2304, 11242, 16247, 2304, 9957, 13672, 1829, 43242, 3794, 1829, 2423, 853, 662, 404, 3451, 34051, 2423, 26890, 35473, 9957, 4032, 5551, 11242, 33911, 47356, 6361, 7005, 26949, 317, 20449, 389, 17, 17188, 19, 21321, 33831, 299, 8258], "avg_logprob": -0.2129755443420963, "compression_ratio": 1.7894736842105263, 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التيوب", "tokens": [3555, 22488, 9957, 4724, 2304, 3794, 4117, 2423, 31371, 37746, 4724, 2304, 26895, 11296, 4724, 8592, 28820, 3714, 16373, 1211, 4032, 4724, 5016, 9566, 8978, 11296, 9154, 805, 30731, 1017, 3714, 1211, 9154, 2423, 389, 17, 17188, 19, 2656, 2207, 5468, 35897, 950, 374, 299, 5097, 327, 15844, 25724, 3215, 9640, 4724, 11242, 33911, 3224, 2423, 35897, 950, 374, 299, 5097, 327, 4032, 4724, 8592, 28820, 6055, 3215, 16572, 7435, 1829, 37893, 3714, 25720, 36764, 24401, 3660, 4032, 4724, 5016, 2288, 9381, 15844, 14739, 1829, 19446, 5551, 47341, 8592, 2423, 31371, 37746], "avg_logprob": -0.20530914427131736, "compression_ratio": 1.495, "no_speech_prob": 2.9802322387695312e-06, "words": [{"start": 373.19, "end": 373.63, "word": "بعدين", "probability": 0.9392903645833334}, {"start": 373.63, "end": 374.07, "word": " بمسك", "probability": 0.8516845703125}, {"start": 374.07, "end": 374.41, "word": " التيوب", "probability": 0.5616048177083334}, {"start": 374.41, "end": 374.91, 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"text": "بمسك لتيوب بشكل ما واضيف على الجدار من 3 إلى 4 مل من ال concentrated sulphuric acid بشكل تدريجي بدون رج لتيوب بعد ما اخلص باعدل لتيوب شواش بدون معرجها باعدلها إذا دونت عندي حلقة لونها violet", "tokens": [3555, 2304, 3794, 4117, 5296, 31371, 37746, 4724, 8592, 28820, 19446, 4032, 46958, 33911, 15844, 25724, 3215, 9640, 9154, 805, 30731, 1017, 3714, 1211, 9154, 2423, 21321, 47286, 374, 299, 8258, 4724, 8592, 28820, 6055, 3215, 16572, 7435, 1829, 47525, 11536, 12602, 7435, 5296, 31371, 37746, 39182, 19446, 1975, 9778, 1211, 9381, 4724, 995, 22488, 1211, 5296, 31371, 37746, 13412, 2407, 33599, 47525, 11536, 20449, 47341, 11296, 4724, 995, 22488, 1211, 11296, 11933, 15730, 11778, 11536, 2655, 18871, 16254, 11331, 1211, 28671, 5296, 11536, 11296, 46480], "avg_logprob": -0.2742456841742855, "compression_ratio": 1.6455026455026456, "no_speech_prob": 3.6776065826416016e-05, "words": [{"start": 390.87, "end": 391.41, "word": "بمسك", "probability": 0.671875}, {"start": 391.41, "end": 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"end": 423.23, "text": "إذا هذا positive، يحتوي على الـ tryptophan، هو tryptophan، يمكن أن يناسب الـ tryptophan أو protein يحتوي على tryptophan، إذا ما اتكونتش الحلقة، إذا الـ negative، لا يوجد tryptophan، لا يحتوي على الـ tryptophan", "tokens": [28814, 15730, 23758, 3353, 12399, 7251, 33753, 45865, 15844, 2423, 39184, 853, 662, 404, 3451, 12399, 31439, 853, 662, 404, 3451, 12399, 7251, 43020, 14739, 7251, 8315, 35457, 2423, 39184, 853, 662, 404, 3451, 34051, 7944, 7251, 33753, 45865, 15844, 853, 662, 404, 3451, 12399, 11933, 15730, 19446, 1975, 2655, 30544, 2655, 8592, 21542, 1211, 28671, 12399, 11933, 15730, 2423, 39184, 3671, 12399, 20193, 7251, 29245, 3215, 853, 662, 404, 3451, 12399, 20193, 7251, 33753, 45865, 15844, 2423, 39184, 853, 662, 404, 3451], "avg_logprob": -0.20740327309994472, "compression_ratio": 1.8875, "no_speech_prob": 8.821487426757812e-06, "words": [{"start": 408.79, "end": 409.19, "word": "إذا", "probability": 0.73095703125}, {"start": 409.19, "end": 409.63, 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"end": 851.42, "word": " مثيلين", "probability": 0.4820149739583333}, {"start": 851.42, "end": 851.86, "word": " نيجاتر", "probability": 0.76279296875}, {"start": 851.86, "end": 852.16, "word": " لإنها", "probability": 0.73553466796875}, {"start": 852.16, "end": 852.36, "word": " not", "probability": 0.68798828125}, {"start": 852.36, "end": 852.64, "word": " free", "probability": 0.343017578125}], "temperature": 1.0}, {"id": 40, "seek": 88100, "start": 853.38, "end": 881.0, "text": "ماشي ال principle أني بجيب الحمض الأميني مثلا سيستين أو سيستان بضيف عليها 10% من ال NaOH في وجود حرارة heat بيعطيني Sodium Sulphate بجيب سيستين أو سيستان مع 10% NaOH في وجود حرارة بتكون عندي Sodium Sulphate بضيف عليها 10% Lead Acetate بيعطيني حاجة بتسميها Lead Sulphate", "tokens": [2304, 33599, 1829, 2423, 8665, 14739, 1829, 4724, 7435, 1829, 3555, 21542, 2304, 11242, 16247, 2304, 9957, 1829, 50113, 15040, 8608, 1829, 14851, 9957, 34051, 8608, 1829, 14851, 7649, 4724, 11242, 33911, 25894, 11296, 1266, 4, 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"word": " بجيب", "probability": 0.985595703125}, {"start": 855.58, "end": 856.22, "word": " الحمض", "probability": 0.89404296875}, {"start": 856.22, "end": 856.7, "word": " الأميني", "probability": 0.81103515625}, {"start": 856.7, "end": 856.94, "word": " مثلا", "probability": 0.952392578125}, {"start": 856.94, "end": 857.42, "word": " سيستين", "probability": 0.678985595703125}, {"start": 857.42, "end": 857.6, "word": " أو", "probability": 0.86376953125}, {"start": 857.6, "end": 858.14, "word": " سيستان", "probability": 0.8253173828125}, {"start": 858.14, "end": 858.98, "word": " بضيف", "probability": 0.8932291666666666}, {"start": 858.98, "end": 859.28, "word": " عليها", "probability": 0.6700439453125}, {"start": 859.28, "end": 859.52, "word": " 10", "probability": 0.61328125}, {"start": 859.52, "end": 859.94, "word": "%", "probability": 0.97607421875}, {"start": 859.94, "end": 860.26, "word": " من", "probability": 0.98486328125}, {"start": 860.26, "end": 860.38, "word": " ال", "probability": 0.8291015625}, {"start": 860.38, "end": 861.28, "word": " NaOH", "probability": 0.572265625}, {"start": 861.28, "end": 861.92, "word": " في", "probability": 0.884765625}, {"start": 861.92, "end": 862.3, "word": " وجود", "probability": 0.96923828125}, {"start": 862.3, "end": 862.86, "word": " حرارة", "probability": 0.9903564453125}, {"start": 862.86, "end": 863.24, "word": " heat", "probability": 0.5966796875}, {"start": 863.24, "end": 864.48, "word": " بيعطيني", "probability": 0.782421875}, {"start": 864.48, "end": 865.26, "word": " Sodium", "probability": 0.738037109375}, {"start": 865.26, "end": 865.92, "word": " Sulphate", "probability": 0.5308430989583334}, {"start": 865.92, "end": 866.92, "word": " بجيب", "probability": 0.9375}, {"start": 866.92, "end": 867.44, "word": " سيستين", "probability": 0.9664306640625}, {"start": 867.44, "end": 867.68, "word": " أو", "probability": 0.92333984375}, {"start": 867.68, "end": 868.24, "word": " سيستان", "probability": 0.968994140625}, {"start": 868.24, "end": 868.84, "word": " مع", "probability": 0.393798828125}, {"start": 868.84, "end": 869.16, "word": " 10", "probability": 0.97509765625}, {"start": 869.16, "end": 869.62, "word": "%", "probability": 0.98974609375}, {"start": 869.62, "end": 870.44, "word": " NaOH", "probability": 0.96044921875}, {"start": 870.44, "end": 870.62, "word": " في", "probability": 0.99169921875}, {"start": 870.62, "end": 870.96, "word": " وجود", "probability": 0.97802734375}, {"start": 870.96, "end": 871.72, "word": " حرارة", "probability": 0.9964599609375}, {"start": 871.72, "end": 872.34, "word": " بتكون", "probability": 0.6097412109375}, {"start": 872.34, "end": 872.64, "word": " عندي", "probability": 0.7196044921875}, {"start": 872.64, "end": 873.32, "word": " Sodium", "probability": 0.96728515625}, {"start": 873.32, "end": 873.92, "word": " Sulphate", "probability": 0.93896484375}, {"start": 873.92, "end": 874.88, "word": " بضيف", "probability": 0.96044921875}, {"start": 874.88, "end": 875.32, "word": " عليها", "probability": 0.878173828125}, {"start": 875.32, "end": 875.66, "word": " 10", "probability": 0.97216796875}, {"start": 875.66, "end": 876.24, "word": "%", "probability": 0.99609375}, {"start": 876.24, "end": 876.52, "word": " Lead", "probability": 0.415283203125}, {"start": 876.52, "end": 877.4, "word": " Acetate", "probability": 0.9287109375}, {"start": 877.4, "end": 878.94, "word": " بيعطيني", "probability": 0.85537109375}, {"start": 878.94, "end": 879.32, "word": " حاجة", "probability": 0.9972330729166666}, {"start": 879.32, "end": 879.8, "word": " بتسميها", "probability": 0.825439453125}, {"start": 879.8, "end": 880.06, "word": " Lead", "probability": 0.82958984375}, {"start": 880.06, "end": 881.0, "word": " Sulphate", "probability": 0.7360026041666666}], "temperature": 1.0}, {"id": 41, "seek": 90372, "start": 881.68, "end": 903.72, "text": "الليد سالفايت هذا عبارة عن ال precipitates لونه أسود، 60 أو سيستان، مع 10% النيوهاتش في وجود حرارة، بيعطيني Sodium Sulfate، بضيف عليه 10% ليد أسيتات، بيعطيني Lead Sulfide ب precipitates لونه أسود، يعني positive، يعني بتحتوي على 60 أو سيستان", "tokens": [6027, 20292, 3215, 8608, 6027, 5172, 995, 36081, 23758, 6225, 3555, 9640, 3660, 18871, 2423, 23354, 30035, 5296, 11536, 3224, 5551, 3794, 23328, 12399, 4060, 34051, 8608, 1829, 14851, 7649, 12399, 20449, 1266, 4, 2423, 22653, 2407, 3224, 9307, 8592, 8978, 49610, 23328, 11331, 2288, 9640, 3660, 12399, 4724, 40228, 9566, 9957, 1829, 42059, 2197, 318, 5757, 473, 12399, 4724, 11242, 33911, 47356, 1266, 4, 5296, 25708, 5551, 3794, 36081, 9307, 12399, 4724, 40228, 9566, 9957, 1829, 441, 2056, 318, 5757, 482, 4724, 23354, 30035, 5296, 11536, 3224, 5551, 3794, 23328, 12399, 37495, 22653, 3353, 12399, 37495, 22653, 39894, 33753, 45865, 15844, 4060, 34051, 8608, 1829, 14851, 7649], "avg_logprob": -0.34002293796714295, "compression_ratio": 1.6771300448430493, "no_speech_prob": 2.8192996978759766e-05, "words": [{"start": 881.68, 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914.0, "end": 914.1, "word": " هي", "probability": 0.8681640625}, {"start": 914.1, "end": 914.24, "word": " اللى", "probability": 0.848876953125}, {"start": 914.24, "end": 914.64, "word": " بتعطينى", "probability": 0.830126953125}, {"start": 914.64, "end": 915.16, "word": " positive", "probability": 0.87744140625}, {"start": 915.16, "end": 915.62, "word": " لو", "probability": 0.8271484375}, {"start": 915.62, "end": 915.9, "word": " دينا", "probability": 0.89794921875}, {"start": 915.9, "end": 916.02, "word": " ال", "probability": 0.96435546875}, {"start": 916.02, "end": 916.4, "word": " structure", "probability": 0.720703125}, {"start": 916.4, "end": 917.3, "word": " الميثيونين", "probability": 0.8642578125}, {"start": 917.3, "end": 917.86, "word": " تشوفوا", "probability": 0.84716796875}, {"start": 917.86, "end": 917.94, "word": " ال", "probability": 0.9365234375}, {"start": 917.94, "end": 918.26, "word": " S", "probability": 0.11785888671875}, {"start": 918.26, "end": 918.62, 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تعريف ال lipid ال lipid هي group of naturally + +5 +00:00:21,550 --> 00:00:25,030 +occurring substance consisting of higher fatty + +6 +00:00:25,030 --> 00:00:28,710 +acid وهي naturally occurring substance أو compound + +7 +00:00:30,320 --> 00:00:35,920 +مركبات أو مجموعة من المكو.. من المركبات تتكون من + +8 +00:00:35,920 --> 00:00:41,060 +نسبة عالية من الأحماض الدهنية، لذلك الدهون هي + +9 +00:00:41,060 --> 00:00:46,760 +عبارة عن مركبات تحتوي على نسبة عالية من الأحماض + +10 +00:00:46,760 --> 00:00:50,440 +الدهنية، من ال fatty acid، من الأحماض الدهنية، وهي + +11 +00:00:50,440 --> 00:00:53,200 +in the generally occurring substance هي مواد + +12 +00:00:53,200 --> 00:00:59,020 +موجودة طبيعيا في طعامنا اليوم Organic substance + +13 +00:00:59,020 --> 00:01:02,140 +relatively insoluble in water but soluble in + +14 +00:01:02,140 --> 00:01:05,780 +organic solvent بيحكي لأن اللي بتطبيعتها هي + +15 +00:01:05,780 --> 00:01:11,780 +organic هي مواد عضوية هي non-polar هي مواد عضوية + +16 +00:01:11,780 --> 00:01:16,580 +non-polar لا تدوب في الماء مادامها non-polar إذا مش + +17 +00:01:16,580 --> 00:01:20,860 +هتدوب في الماء في الماء وين هتدوب؟ بتدوب بيحكي لي + +18 +00:01:20,860 --> 00:01:25,400 +في ال organic solvent في اللي بيشبهها المبدأ like, + +19 +00:01:25,500 --> 00:01:30,580 +dissolve like المتشابهات تذيب بعضها فهي بتدوب في + +20 +00:01:30,580 --> 00:01:34,280 +المواد العضوية اللي زيها زي مين مواد عضوية بتدوب + +21 +00:01:34,280 --> 00:01:39,430 +فيها ال lipid؟ زي chloroform, ether, benzene على + +22 +00:01:39,430 --> 00:01:45,250 +مبدأ like dissolve like إن المتشابهات تذيب بعضها + +23 +00:01:45,250 --> 00:01:50,790 +function of lipid لو جينا نتعرف على وظائف اللبد + +24 +00:01:50,790 --> 00:01:55,210 +أول وظيفة حكينا عنها في أول معمل إنها storage form + +25 +00:01:55,210 --> 00:02:00,510 +of energy هي مخزن الطاقة ال lipid تعتبر مخزن + +26 +00:02:00,510 --> 00:02:04,510 +الطاقة الوظيفة الثانية هي structural component of + +27 +00:02:04,510 --> 00:02:09,460 +cell membrane هي بتدخل في تركيب ال cell membrane في + +28 +00:02:09,460 --> 00:02:14,860 +تركيب الغلاف الخلوي الجدار الخلوي بتدخل فيه تركيبه + +29 +00:02:14,860 --> 00:02:19,140 +اللبد ثالثة هي precursor of many steroid hormone + +30 +00:02:19,140 --> 00:02:25,380 +as estrogen و vitamin D هي اللبد الأساسية في تركيب + +31 +00:02:25,380 --> 00:02:29,000 +الهرمونات الاسترويدية اللي هي نفسها ال sex hormone + +32 +00:02:29,000 --> 00:02:33,600 +زي الاستروجين و vitamin D اللي برضه هي بتدخل فيه + +33 +00:02:33,600 --> 00:02:39,160 +تركيبه protection of internal organs تعمل على حماية + +34 +00:02:39,160 --> 00:02:44,180 +الأعضاء الداخلية الدهون تعمل على حماية الأعضاء + +35 +00:02:44,180 --> 00:02:44,980 +الداخلية + +36 +00:02:47,330 --> 00:02:51,990 +هنا فيه إنه رسمة ل cell membrane بدي أوضح لي إنه + +37 +00:02:51,990 --> 00:02:54,730 +أغلب مكونات ال cell membrane هي عبارة عن lipid + +38 +00:02:54,730 --> 00:02:58,210 +يعني outside of cell اللي خارج الخلية فيها + +39 +00:02:58,210 --> 00:03:01,550 +سفينجومايلين هذا lipid ال glycolipid برضه lipid + +40 +00:03:01,550 --> 00:03:05,670 +و ال phosphatidylcholine فيها كولسترول كل هذه المكونات + +41 +00:03:05,670 --> 00:03:09,210 +عبارة عن lipid فأغلب مكونات ال cell membrane هي + +42 +00:03:09,210 --> 00:03:14,290 +عبارة عن lipid فهو التركيبة الأساسية ل ال cell + +43 +00:03:14,290 --> 00:03:14,830 +membrane + +44 +00:03:17,980 --> 00:03:22,760 +أنواع الدهون type of lipid إيش أنواع الدهون الدهون + +45 +00:03:22,760 --> 00:03:28,360 +قُسّمت بشكل عام إلى lipid with fatty acid و lipid + +46 +00:03:28,360 --> 00:03:34,060 +without fatty acid يعني الدهون بشكل عام قُسّمت إلى + +47 +00:03:34,060 --> 00:03:39,620 +قسمين دهون تحتوي على fatty acid ودهون لا تحتوي على + +48 +00:03:39,620 --> 00:03:42,940 +fatty acid lipid with fatty acid و lipid without + +49 +00:03:42,940 --> 00:03:46,680 +fatty acid اللي with fatty acid تحتوي على fatty + +50 +00:03:46,680 --> 00:03:51,280 +acid من الأمثلة عليها ال waxes، fat and oil، الزبدة + +51 +00:03:51,280 --> 00:03:55,640 +والزيت، phospholipid، sphingolipid، lipid + +52 +00:03:55,640 --> 00:03:59,900 +without fatty acid زي الستيرويد، هذه التقسيمة بشكل + +53 +00:03:59,900 --> 00:04:04,790 +عام وهذه هيها نبدأ نفرع منها هذه اللي حكينا هنا a + +54 +00:04:04,790 --> 00:04:08,350 +classification هنا of lipid نبدأ نفصلها اللبد بشكل + +55 +00:04:08,350 --> 00:04:12,490 +عام تنقسم إلى lipid with fatty acid تحتوي على + +56 +00:04:12,490 --> 00:04:16,330 +fatty acid و lipid without fatty acid هذه تحتوي على + +57 +00:04:16,330 --> 00:04:19,870 +fatty acid نأخذ الجزء الأول اللي هي اللبد with + +58 +00:04:19,870 --> 00:04:24,770 +fatty acid اللي بتحتوي على fatty acid اللبد التي + +59 +00:04:24,770 --> 00:04:28,470 +تحتوي على fatty acid تنقسم إلى قسمين في منها + +60 +00:04:28,470 --> 00:04:33,780 +simple lipid و في منها conjugate في simple وفي + +61 +00:04:33,780 --> 00:04:36,920 +conjugate هذه ال lipid with fatty acid تنقسم إلى + +62 +00:04:36,920 --> 00:04:41,260 +simple و conjugate نحكي عن ال simple بيحكي إنه ال + +63 +00:04:41,260 --> 00:04:45,320 +simple lipid تركيبتها الأساسية عبارة عن fatty acid + +64 +00:04:45,320 --> 00:04:50,340 +مع كحول إذا كان بس عبارة عن fatty acid و كحول + +65 +00:04:50,340 --> 00:04:53,840 +تركيب الأساسية إليه fatty acid و كحول نسميه + +66 +00:04:53,840 --> 00:04:58,320 +simple lipid بيحكي إنه الكحول هذا ممكن يكون + +67 +00:04:58,320 --> 00:05:03,780 +glycerol أو كحول نوع ثاني غير ال glycerol إذا fatty + +68 +00:05:03,780 --> 00:05:07,980 +أسيد متصلة بكحول نسميها سم باللبد طب الكحول هذا إما + +69 +00:05:07,980 --> 00:05:11,680 +بيكون ممكن يكون نوعه إيش هيكون نوعه ممكن يكون + +70 +00:05:11,680 --> 00:05:16,240 +glycerol أو حاجة ثانية كحول نوع ثاني غير ال + +71 +00:05:16,240 --> 00:05:21,160 +glycerol كيف بيرتبط ال fatty acid مع الكحول ب ester + +72 +00:05:21,160 --> 00:05:24,560 +bond by ester bond اللي هي الرابطة الدهنية هذا + +73 +00:05:24,560 --> 00:05:28,980 +اسم الرابطة الدهنية بيرتبط ال fatty acid مع الكحول + +74 +00:05:28,980 --> 00:05:34,530 +برابطة دهنية لو الكحول هذا كان glycerol الناتج من + +75 +00:05:34,530 --> 00:05:38,970 +اللي بدهات نسميه إما oil أو fat يعني إذا fatty + +76 +00:05:38,970 --> 00:05:44,110 +acid مرتبط معها glycerol نسميها oil هينتج عنها oil + +77 +00:05:44,110 --> 00:05:48,290 +أو fat ال oil هو عبارة عن ال tri-glyceride rich in + +78 +00:05:48,290 --> 00:05:51,830 +unsaturated fatty acid و بيكون liquid at room + +79 +00:05:51,830 --> 00:05:55,210 +temperature الزيت ال oil هو عبارة عن ال tri + +80 +00:05:55,210 --> 00:05:58,630 +-glyceride tri معناها ثلاثة يعني ثلاثة fatty acid + +81 +00:05:58,900 --> 00:06:03,120 +مرتبطين مع glycerol مع الكحول try معناها ثلاثة + +82 +00:06:03,120 --> 00:06:07,420 +fatty acid مع glycerol الكحول هذا ال oil بيكون + +83 +00:06:07,420 --> 00:06:11,460 +بيحكي ليهو unsaturated fatty acid يحتوي على + +84 +00:06:11,460 --> 00:06:15,880 +unsaturated fatty acid إيش يعني unsaturated يعني + +85 +00:06:15,880 --> 00:06:21,940 +أحماض دهنية غير مشبعة يعني تحتوي على رابطة ثنائية + +86 +00:06:21,940 --> 00:06:27,670 +أو أكثر وال oil هذا بيكون liquid قوامه بيكون سائل أما + +87 +00:06:27,670 --> 00:06:31,290 +الفت فهو برضه triglyceride ثلاثة fatty acid مع + +88 +00:06:31,290 --> 00:06:35,750 +glycerol ولكن هو غني بال saturated fatty acid + +89 +00:06:35,750 --> 00:06:40,630 +أحماض دهنية مشبعة وبيكون على درجة حرارة الغرفة + +90 +00:06:40,630 --> 00:06:43,810 +بيكون عبارة عن solid أو semi solid بيكون صلب أو + +91 +00:06:43,810 --> 00:06:50,530 +شبه الصلب هذه الفت الزبدة طيب لو الكحول كانت + +92 +00:06:50,530 --> 00:06:53,610 +حاجة غير ال glycerol كان عبارة عن fatty acid + +93 +00:06:53,610 --> 00:06:57,850 +أحماض دهنية مرتبط معها كحول غير ال glycerol بينتج + +94 +00:06:57,850 --> 00:07:02,690 +عندي حاجة اسمها waxes اللي هينتج عندي حاجة اسمها + +95 +00:07:02,690 --> 00:07:07,150 +waxes إذا أول نوع من احنا اللي بتقسمها بشكل عام + +96 +00:07:07,150 --> 00:07:10,010 +إلى with fatty acid و without fatty acid ال with + +97 +00:07:10,010 --> 00:07:13,590 +fatty acid في منها simple و في منها conjugate ال + +98 +00:07:13,590 --> 00:07:17,010 +simple اللي هذا بيكون عبارة عن fatty acid مع كحول + +99 +00:07:17,010 --> 00:07:21,530 +إذا الكحول كان glycerol بيعطيني oil و fat إذا حاجة + +100 +00:07:21,530 --> 00:07:25,170 +ثانية غير ال glycerol بيعطيني حاجة اسمها waxes + +101 +00:07:28,030 --> 00:07:30,930 +القسم الثاني من اللبد with fatty acid هي ال + +102 +00:07:30,930 --> 00:07:36,930 +conjugate لبن conjugate لبن هي عبارة عن اللبد في + +103 +00:07:36,930 --> 00:07:41,350 +تركيبته بيكون بيحتوي على fatty acid مع كحول مع + +104 +00:07:41,350 --> 00:07:45,390 +additional group مع group كمان زيادة بيكون عبارة + +105 +00:07:45,390 --> 00:07:50,410 +عن تركيبته fatty acid أحمد دهنية مرتبطة مع الكحول + +106 +00:07:50,410 --> 00:07:54,570 +ومرتبط عليها كمان group زيادة additional group + +107 +00:07:55,420 --> 00:07:59,700 +fatty acid مع كحول مع additional group مع group + +108 +00:07:59,700 --> 00:08:07,500 +ثانية لو الكحول لو مع additional group sorry مع + +109 +00:08:07,500 --> 00:08:10,780 +additional group مع group ثاني جُد بناء على ال + +110 +00:08:10,780 --> 00:08:14,740 +group اللي بتتصل في هذا ال lipid نسميه lipid فإذا + +111 +00:08:14,740 --> 00:08:17,240 +ال group اللي اتصلت معاه كانت phosphate group + +112 +00:08:17,240 --> 00:08:21,400 +نسميه phospholipid phospholipid هو عبارة عن + +113 +00:08:21,400 --> 00:08:25,750 +conjugate lipid يحتوي على fatty acid مع كحول مع + +114 +00:08:25,750 --> 00:08:31,690 +phosphoric acid الـ glycolipid هو عبارة عن لبد + +115 +00:08:31,690 --> 00:08:36,010 +يحتوي.. كونجيوجيت لبد يحتوي على fatty acid مع كحول مع + +116 +00:08:36,010 --> 00:08:39,230 +carbohydrate الـ glyco جاية من carbohydrate اللي + +117 +00:08:39,230 --> 00:08:44,930 +هي السكر الـ sulfolipid هو عبارة عن fatty acid مع + +118 +00:08:44,930 --> 00:08:50,490 +كحول مع sulfate group فوسفوليبيد فوسفات جروب بتكون + +119 +00:08:50,490 --> 00:08:54,930 +متصلة فيهم الجلايكو بتكون carbohydrate صلفو بيكون + +120 +00:08:54,930 --> 00:08:59,790 +كبريتات جروب ليبوبروتين بيكون متصل معها البروتين + +121 +00:08:59,790 --> 00:09:06,090 +عبارة عن fatty acid مع كحول والبروتين متصلة فيها + +122 +00:09:06,090 --> 00:09:10,290 +لذلك ال conjugate lipid هو عبارة عن fatty acid مع + +123 +00:09:10,290 --> 00:09:14,830 +كحول مع جروب كمان مضافة عليها هذه ال group هي اللي + +124 +00:09:14,830 --> 00:09:17,630 +أعطته الاسم إذا هي phosphate group نسميها + +125 +00:09:17,630 --> 00:09:21,710 +phospholipid إذا carbohydrate نسميها glycolipid + +126 +00:09:21,710 --> 00:09:25,510 +إذا sulfate نسميها sulfolipid وإذا ال protein + +127 +00:09:25,510 --> 00:09:33,150 +نسميها lipoprotein هنا عندنا مخطط بيوضح لي تقسيمة + +128 +00:09:33,150 --> 00:09:36,330 +أنه كيف بتقسم اللبد هو بشكل عام احنا هذه ال + +129 +00:09:36,330 --> 00:09:39,730 +structures مش مطلوبة مننا لكن بشكل عام نعرف إن + +130 +00:09:39,730 --> 00:09:44,380 +اللبد مقسم إلى with fatty acid without fatty acid + +131 +00:09:44,380 --> 00:09:47,640 +ال with fatty acid اللي اتفرعنا فيها في منها + +132 +00:09:47,640 --> 00:09:51,680 +simple و في منها conjugate ال simple هي عبارة عن + +133 +00:09:51,680 --> 00:09:55,700 +fatty acid مع كحول والكحول هذا إما يكون glycerol + +134 +00:09:55,700 --> 00:09:59,100 +أو حاجة ثانية غير ال glycerol إذا كان glycerol + +135 +00:09:59,100 --> 00:10:02,520 +بيعطيني fat و oil إذا حاجة ثانية غير ال glycerol + +136 +00:10:02,520 --> 00:10:07,500 +بيعطيني waxes، waxes lipid أما الكنجوجيت lipid هي + +137 +00:10:07,500 --> 00:10:11,720 +عبارة عن fatty acid مع كحول، مع other group، مع + +138 +00:10:11,720 --> 00:10:16,980 +group ثانية متصلة فيها وبناء على هذه ال group + +139 +00:10:16,980 --> 00:10:19,540 +نسميها phospholipid يعني phosphate group + +140 +00:10:19,540 --> 00:10:23,240 +glycolipid يعني carbohydrate sulfolipid يعني + +141 +00:10:23,240 --> 00:10:28,340 +sulfate group ليبوبروتين يعني متصل فيها بروتين ال + +142 +00:10:28,340 --> 00:10:31,660 +without fatty acid، lipid without fatty acid مش + +143 +00:10:31,660 --> 00:10:35,020 +متصل فيها fatty acid هي هذه الجزء اللي تحت هنا + +144 +00:10:35,020 --> 00:10:38,560 +الجزء + +145 +00:10:38,560 --> 00:10:43,200 +اللي تحت ماض لطويل ونازل لتحت مكتوب عندها steroid + +146 +00:10:45,230 --> 00:10:48,590 +مكتوب بـ steroids فاللبد الـ without fatty acid + +147 +00:10:48,590 --> 00:10:53,510 +نسميها steroids تحتوي على steroid nucleus تحتوي + +148 +00:10:53,510 --> 00:10:57,910 +على steroid nucleus من الأمثلة على اللبد التي لا + +149 +00:10:57,910 --> 00:11:02,170 +تحتوي fatty acid تحتوي على steroid nucleus زي + +150 +00:11:02,170 --> 00:11:08,750 +الكولسترول و bile salt و steroid hormone الكولسترول و + +151 +00:11:08,750 --> 00:11:13,010 +bile salt و steroid hormone هدول لبد without + +152 +00:11:13,010 --> 00:11:18,390 +fatty acid طب اليوم الشغل العملي هو عبارة عن + +153 +00:11:18,390 --> 00:11:27,330 +qualitative test for لبن لنعمل فحوصات جودة + +154 +00:11:27,330 --> 00:11:32,440 + ونوعية للكشف عن اللبد فحوصات qualitative يعني جودة + +155 +00:11:32,440 --> 00:11:36,780 +ونوعية زي فحوصات الكشف عن الأحماض الأمينية فهنا + +156 +00:11:36,780 --> 00:11:40,380 +مجموعة فحوصات ممكن يتغير اللون أو ما يتغيرش اللون + +157 +00:11:40,380 --> 00:11:46,600 +ونشوف فحوصات للكشف عن ال lipids زي مين أول فحص + +158 +00:11:46,600 --> 00:11:49,660 +هنتعرف عليه هو solubility in polar and nonpolar + +159 +00:11:49,660 --> 00:11:54,600 +solvent فهنا فحص اسمه emulsification test اللي هو + +160 +00:11:54,600 --> 00:11:58,540 +الاستحلاب فهنا فحص ال oxidation of unsaturated + +161 +00:11:58,540 --> 00:12:03,480 +fatty acid أكسدة الـ unsaturated fatty acid ويعني + +162 +00:12:03,480 --> 00:12:07,140 +فحص qualitative analysis of detection in natural + +163 +00:12:07,140 --> 00:12:12,400 +product اللي هو فحص اسمه سالكا ويسكي reaction هنجي + +164 +00:12:12,400 --> 00:12:17,640 +نتعرف على كل فحص على حدى أول فحص هو solubility in + +165 +00:12:17,640 --> 00:12:22,200 +polar and nonpolar solvent solubility in polar and + +166 +00:12:22,200 --> 00:12:27,570 +nonpolar يعني بدي أجيب ال lipid بدي أدوبه في + +167 +00:12:27,570 --> 00:12:32,650 +مواد.. بدي أجيبه وأحطه في مواد عضوية وغير عضوية + +168 +00:12:32,650 --> 00:12:36,250 +وأشوف وين يدوب يعني أنت جيب له مواد polar و non + +169 +00:12:36,250 --> 00:12:39,850 +-polar حاجات اللي بتحكي إن هو non-polar بيدوب في + +170 +00:12:39,850 --> 00:12:43,310 +ال non-polar فإذا جبت له non-polar بيدوب فيه إذا + +171 +00:12:43,310 --> 00:12:47,370 +جبت له polar مش هيدوب فيه احنا في هذا الفحص بدنا + +172 +00:12:47,370 --> 00:12:51,990 +نجيب ماء نجيب chloroform نجيب ether نجيب إيثانول + +173 +00:12:51,990 --> 00:12:55,630 +ندوب ال lipid فيهم الزيت مثلًا نجيب زيت ندوبه في الماء + +174 +00:12:55,630 --> 00:12:59,810 +نشوف إنه يدوب ولا يدوبش بعدين بدنا نجيب الزيت و + +175 +00:12:59,810 --> 00:13:05,270 +ندوبه في إيه نشوف هل هيدوب ولا مش هيدوب بعدين نجيب + +176 +00:13:05,270 --> 00:13:09,530 +chloroform وندوبه فيه نشوف هل ال lipid هيدوب ولا مش + +177 +00:13:09,530 --> 00:13:14,790 +هيدوب هنلاحظ إن ال lipid يدوب فيهم كلهم تم هذا ال + +178 +00:13:14,790 --> 00:13:19,010 +distill water لأنه عبارة عن polar و ال lipid non + +179 +00:13:19,010 --> 00:13:25,110 +polar فبيدوبش فيه فمبدأ عمل الفحص الـ principle هو + +180 +00:13:25,110 --> 00:13:29,650 +على أي مبدأ بناء على إيش هيدوب اللبط في الماء، + +181 +00:13:29,650 --> 00:13:33,150 +هيدوب في المركبة العضوية ومش هيدوب في الماء، بناء + +182 +00:13:33,150 --> 00:13:37,510 + +201 +00:14:52,660 --> 00:14:56,320 +الكيوب التانية بدي أحط عليها drop من الـ oil على واحد + +202 +00:14:56,320 --> 00:15:01,060 +من الـ ether بدي أحط منها drop من الزيت على واحد من + +203 +00:15:01,060 --> 00:15:05,330 +الـ ether و أشوف بيدوب ولا بيدوب، بشجيب الـ tube + +204 +00:15:05,330 --> 00:15:09,290 +التالت فيها chloroform حط واحد drop من الزيت على + +205 +00:15:09,290 --> 00:15:13,510 +واحد من الـ chloroform هشوف بيدوب ولا لأ، الـ tube + +206 +00:15:13,510 --> 00:15:16,850 +الرابع ده حط فيها drop من الـ oil على واحد من الـ + +207 +00:15:16,850 --> 00:15:21,960 +ethanol، هشوف بيدوب ولا بيدوب، نفس الخطوات بدي أجيب + +208 +00:15:21,960 --> 00:15:25,580 +أربعة توب تانية و أعمل فيها نفس الخطوات اللي هي + +209 +00:15:25,580 --> 00:15:28,480 +واحدة distilled water واحدة ether واحدة chloroform + +210 +00:15:28,480 --> 00:15:32,020 +واحدة ethanol بس بدل الزيت بدي أحط butter، بدي أحط + +211 +00:15:32,020 --> 00:15:35,240 +زبدة، زبدة مع distilled water شوف بيدوب ولا بيدوبش + +212 +00:15:35,240 --> 00:15:39,200 +ether مع زبدة شوف بيدوب ولا بيدوبش، chloroform مع + +213 +00:15:39,200 --> 00:15:42,880 +زبدة شوف بيدوب ولا بيدوبش، ethanol مع زبدة هل بيدوب + +214 +00:15:42,880 --> 00:15:47,380 +ولا ما بيدوبش، ده شوف هدول بيدوبوا ولا ما بيدوبوا مش + +215 +00:15:47,380 --> 00:15:52,060 +بنتوقع؟ بنتوقع إنه يدوب في كل ما عدا الـ distilled + +216 +00:15:52,060 --> 00:15:58,640 +water، مش هيدوب في الـ distilled water، هدر بالنسبة + +217 +00:15:58,640 --> 00:16:02,880 +للفحص الأول، الفحص التاني هو اسمه الـ emulsification + +218 +00:16:02,880 --> 00:16:08,440 +emulsification معناه استحلاب، emulsification معناها + +219 +00:16:08,440 --> 00:16:14,780 +استحلاب، إيش يعني استحلاب؟ يعني جعل مادتين ما + +220 +00:16:14,780 --> 00:16:18,540 +بيدوبوا ببعض طبيعي، اللي هي دوبوا ببعض، بدي أخليهم + +221 +00:16:18,540 --> 00:16:24,480 +بيدوبوا ببعض بمساعدة emulsifying agent، بمساعدة + +222 +00:16:24,480 --> 00:16:29,270 +عامل مستحلب، إذا الـ emulsification أنه أنا بدي أخلي + +223 +00:16:29,270 --> 00:16:33,550 +مادتين هم أصلا ما بيدوبوا ببعض، بدي أخليهم يدوبوا + +224 +00:16:33,550 --> 00:16:39,210 +بواسطة عامل مستحلب، بمساعدة عامل مستحلب، زي مين + +225 +00:16:39,210 --> 00:16:42,650 +مادتين بدوبوش ببعض، مثلا الزيت مع الميه بدوبوش ببعض، + +226 +00:16:42,650 --> 00:16:47,490 +أنا بدي أجيب عامل مستحلب بيساعد على أنه الزيت يدوب + +227 +00:16:47,490 --> 00:16:52,150 +في الميه، زي مثلا هلجيت لو عندنا مجلة، المجلة هي هاد + +228 +00:16:52,150 --> 00:16:56,150 +فيه زيت و أنت تجيتي تجليه، تخسليه، لو حطيت الميه و + +229 +00:16:56,150 --> 00:17:00,890 +خلاص، هالخلاص هينظف و انه هيروح الزيت منه؟ لأ، + +230 +00:17:00,890 --> 00:17:04,710 +بتحس انه الزيت يتكوم زي قطرات في هذا المجلة، أنت + +231 +00:17:04,710 --> 00:17:08,010 +شو بتعمل عشان تشيلي هذا الزيت و تنظفيه خالص؟ بتحطي + +232 +00:17:08,010 --> 00:17:12,830 +صابون، الصابون بيساعد على إنه يدوب الزيت في المي و + +233 +00:17:12,830 --> 00:17:16,470 +يشيل الزيت من المجلة، كان جابل الزيت مش راضي يروح + +234 +00:17:16,470 --> 00:17:19,850 +بالمي، لما حطيتي صابونة، الصابونة ساعدت، فهنا + +235 +00:17:19,850 --> 00:17:24,830 +الصابونة بسميها كإنها emulsifying agent، عامل + +236 +00:17:24,830 --> 00:17:31,580 +مستحلب، ساعد على دوبان الزيت في المي و إنه يختفي، مش + +237 +00:17:31,580 --> 00:17:34,480 +بيحكيلي أن الـ emulsion هو mixture of two or more + +238 +00:17:34,480 --> 00:17:38,100 +liquids are normally immiscible، الـ emulsion هو + +239 +00:17:38,100 --> 00:17:42,520 +عبارة عن خليط من مادتين أو أكثر طبيعيين ما بيدوبوا + +240 +00:17:42,520 --> 00:17:47,780 +بالمي زي زيت مع مي و بدوبوش في بعض طبيعيين، + +241 +00:17:47,780 --> 00:17:52,840 +هبسميه emulsion، هلجيت الـ bile salt هيش هي الـ bile + +242 +00:17:52,840 --> 00:17:56,760 +salt؟ الـ bile salt هي ملح العصارة الصفراوية بتنتج + +243 +00:17:56,760 --> 00:18:01,060 +من الكوليسترول، تصنع من الكوليسترول وتخزن في الجالب + +244 +00:18:01,060 --> 00:18:08,260 +لدر في المثانة في المرارة، تخزن في المرارة، لما ان + +245 +00:18:08,260 --> 00:18:11,500 +احنا الجسم الحين في جسم الإنسان أغلب مكوناته ماي، + +246 +00:18:11,500 --> 00:18:14,680 +طب اللي الإنسان لما ياكل واجب الدهون كيف هيبدأ + +247 +00:18:14,680 --> 00:18:18,570 +تدوب و تمشي في جسم الإنسان اللي أغلبه ماي؟ بحكي إنه + +248 +00:18:18,570 --> 00:18:22,290 +إحنا في جسم الإنسان when you eat fat لما تاكلي + +249 +00:18:22,290 --> 00:18:26,370 +وجبة دهون، في عندنا الـ bile salt بتشتغل في الجسم + +250 +00:18:26,370 --> 00:18:30,670 +كصابونة، زي صابونة كأنها، بتدوب الـ bile salt و + +251 +00:18:30,670 --> 00:18:34,910 +بتخليها ماشية في الجسم بسهولة بين الماء، كيف؟ الـ + +252 +00:18:34,910 --> 00:18:38,590 +bile salt هاي .. هاي الأصفر اللي تحت أصفر و الها + +253 +00:18:38,590 --> 00:18:42,850 +طرف أخضر، مكتوب عليها أنها bile salt، إيش هاي الطرف + +254 +00:18:42,850 --> 00:18:46,810 +الأخضر؟ هاي bile salt إلها جزءين، جزء بكون .. بكون + +255 +00:18:46,810 --> 00:18:49,550 +منها hydrophilic اللي هو الأخضر، الجزء الأخضر + +256 +00:18:49,550 --> 00:18:52,570 +hydrophilic، والجزء الأصفر بيكون عبارة عن + +257 +00:18:52,570 --> 00:18:57,410 +hydrophobic، جزء بيكون منها محب للماء وجزء بيكون + +258 +00:18:57,410 --> 00:19:01,390 +كاره للماء، كيف تيجي تعمل هاي الـ bile salt؟ بتيجي + +259 +00:19:01,390 --> 00:19:04,310 +على وجبة الدهون اللي عندها، هاي الزرقة الكبيرة + +260 +00:19:04,310 --> 00:19:09,710 +بتحوت عليها من جميع الاتجاهات بحيث أنه جزء الكاره + +261 +00:19:09,710 --> 00:19:14,770 +للماء يكون للداخل منها والجزء اللي بيحب الماء يكون + +262 +00:19:14,770 --> 00:19:19,790 +للخارج، فالحين هي كأنها كورة ماشية في الجسم من جوا + +263 +00:19:19,790 --> 00:19:24,450 +بتدوبش في الماء لكن من برا محبة للماء، فمهما تمشي + +264 +00:19:24,450 --> 00:19:28,750 +في الجسم هتبين كأنها دائبة في الماء، فالدهون كيف + +265 +00:19:28,750 --> 00:19:32,850 +بتمشي في الجسم عن طريق الـ bile salt اللي بتعمل + +266 +00:19:32,850 --> 00:19:38,310 +كسبونة بتحوت عليها من الداخل بجزء مكاره للماء + +267 +00:19:38,310 --> 00:19:46,910 +هيدروفوبك ومن الخارج بجزء هيدروفليك محب للماء، طيب + +268 +00:19:46,910 --> 00:19:50,130 +هلجيت الـ emulsification اللي هو الاستحلاب فيه منه + +269 +00:19:50,130 --> 00:19:53,250 +نوعين، ننزل تحت على آخر الـ slide في emulsification + +270 +00:19:53,250 --> 00:19:57,440 +type، أنواع الاستحلاب، في منه permanent وفي منه + +271 +00:19:57,440 --> 00:20:01,520 +temporary، permanent يعني بيكون استحلاب بشكل دائم + +272 +00:20:01,520 --> 00:20:06,040 +يعني الزيت مع مي ودائبي بشكل دائم، مهما أسيب الـ tube + +273 +00:20:06,040 --> 00:20:09,800 +أرجها و أرجع أسيبها بخلق بلاجيهم دايما منتشرين + +274 +00:20:09,800 --> 00:20:14,680 +الزيت منتشر في المي، temporary انه الزيت مع مي + +275 +00:20:14,680 --> 00:20:18,940 +بتعملي mix بدوبوا ببعض، مجرد ما تسيب التيوب بيرجع + +276 +00:20:18,940 --> 00:20:23,070 +يفصل طبقتين، الزيت لحال و المي لحال، فالـ permanent + +277 +00:20:23,070 --> 00:20:26,990 +بيكون viscous and stable، they don't separate، بيكون + +278 +00:20:26,990 --> 00:20:30,630 +لزج، قوامه لزج لأنه مادتين غير دائبين، كإن إساره + +279 +00:20:30,630 --> 00:20:35,470 +دائبين بيكون stable مستقر، ومهما تسيبيه، don't + +280 +00:20:35,470 --> 00:20:38,590 +separate، ما بيفصلوش برجعوش يفصلوا الطبقتين وإنما + +281 +00:20:38,590 --> 00:20:42,790 +بيضلهم دائبين بعض، permanent بشكل ده، أما الـ + +282 +00:20:42,790 --> 00:20:46,540 +temporary جاي from shaking، بيحكي لإنت بتمسكي الـ tube + +283 +00:20:46,540 --> 00:20:50,080 +و بتحطي زيت على الماء، اعملي mix، رشجي لتيوب بإيدك + +284 +00:20:50,080 --> 00:20:53,780 +بتحس إنه الزيت انتشر في الماء، بمجرد ما تسيبي + +285 +00:20:53,780 --> 00:20:58,840 +الـ tube بيرجع يفصل لطبقتين، الزيت لحال و المي لحال + +286 +00:20:58,840 --> 00:21:03,600 +هذا بيكون temporary بشكل معقده، هو رجعنا على الـ slide + +287 +00:21:03,600 --> 00:21:07,500 +من أولها من فوق، بيحكيلي هنا في عندنا أربع أربع + +288 +00:21:07,500 --> 00:21:13,180 +شكال على الجانب A وB وC وD، في A موجودة عندي حاطين + +289 +00:21:13,180 --> 00:21:17,460 +خليط من مادتين سائلين ما بدوبوش ببعض زي الزيت والمي + +290 +00:21:17,460 --> 00:21:20,820 +لو اعتبرنا انه الجزء اللي فوق هو الزيت والجزء اللي + +291 +00:21:20,820 --> 00:21:24,640 +تحت مي، ففي أش في صورة A شايفين two immiscible + +292 +00:21:24,640 --> 00:21:29,040 +liquids not yet emulsified، انه خليطين من خليط من + +293 +00:21:29,040 --> 00:21:33,550 +مادتين أصلا بدوبوش بعض، immiscible لا يختلطوا ولا + +294 +00:21:33,550 --> 00:21:36,250 +حطينا لهم emulsifying agent عشان نعملهم + +295 +00:21:36,250 --> 00:21:40,950 +emulsification، ما حطيناهاش عامل مستحيل، بيساعد على + +296 +00:21:40,950 --> 00:21:45,030 +أنهم يدوبوا أبعاد، بحكي اللي في بيه لو طلعت عليها + +297 +00:21:45,030 --> 00:21:48,250 +بتحس أنه الجزء اللي كان فوق انتشر في اللي تحت، يعني + +298 +00:21:48,250 --> 00:21:52,630 +الزيت انتشر في الماء، قطارات الزيت انتشرت في الماء + +299 +00:21:52,630 --> 00:21:56,430 +بحكي لإن emulsion of phase two disappears in phase + +300 +00:21:56,430 --> 00:22:00,130 +one، أنه انتشرت الجزء اللي فوق في الجزء اللي تحت + +301 +00:22:00,130 --> 00:22:05,490 +مبين كأنهم ذائبين، في C بيحكيلي unstable emulsion + +302 +00:22:05,490 --> 00:22:09,450 +separate، كان هذا الـ emulsion الاستحلاب كان مؤقت + +303 +00:22:09,450 --> 00:22:13,610 +كان temporary، جاي من عملية shaking، فمجرد ما سيبنا + +304 +00:22:13,610 --> 00:22:17,790 +الـ tube في C على طول فصل، رجع فصل طبقتين، طبقة اللي فوق + +305 +00:22:17,790 --> 00:22:22,590 +لحال و اللي تحت لحال، الزيت فوق و المي تحت، في D + +306 +00:22:22,590 --> 00:22:27,450 +بيحكيلي استخدمنا surfactant، surfactant هو نفسه + +307 +00:22:27,450 --> 00:22:33,560 +emulsifying agent، هو عامل مستحلب، استخدم في C في D + +308 +00:22:33,560 --> 00:22:37,320 +استخدم surfactant، عامل مستحلب، emulsifying agent + +309 +00:22:37,320 --> 00:22:42,280 +إيش عمل هذا العامل؟ عمل على حشر نفسه، position + +310 +00:22:42,280 --> 00:22:46,200 +itself on interface between face one و face two + +311 +00:22:46,200 --> 00:22:52,170 +حشر نفسه بين الطبقة اللي فوق و الطبقة اللي تحت، يعني + +312 +00:22:52,170 --> 00:22:55,130 +كأنه زي الصابونة زي الـ Bile Salt اللي تاوم حكينا + +313 +00:22:55,130 --> 00:22:58,990 +عنها أنها بتربط بجزء من الداخل Hydrophobic ومن + +314 +00:22:58,990 --> 00:23:03,190 +الخارج Hydrophilic، بتربط في الزيت بحيث أنه يمشي + +315 +00:23:03,190 --> 00:23:07,010 +بالمي كأنه دائب، ففي دي أنا استخدمت emulsifying + +316 +00:23:07,010 --> 00:23:10,870 +agent، حشر نفسه في الزيت بين الزيت والمي وخلّى + +317 +00:23:10,870 --> 00:23:15,560 +الزيت كأنه دائب في المي، و هذا كان بشكل permanent + +318 +00:23:15,560 --> 00:23:20,900 +بشكل دائم، فمهما سبتيها مش هيفصل عن بعض بسبب وجود + +319 +00:23:20,900 --> 00:23:22,920 +الـ emulsifying agent + +320 +00:23:25,960 --> 00:23:30,420 +كيف نعمل فحصنا لليوم؟ لنستخدم emulsifying agent ده، + +321 +00:23:30,420 --> 00:23:35,020 +أجيب زيت و أحط عليه مي، لو رجيتهم هم هيدوبوا و + +322 +00:23:35,020 --> 00:23:38,480 +بعدين هترجع تفصل لطبقتين تاني، بس عشان يرجع تلت يوم + +323 +00:23:38,480 --> 00:23:42,120 +بدي أستخدم في هذا الفحص emulsifying agent، أحط زيت + +324 +00:23:42,120 --> 00:23:46,520 +على مي و أستخدم عامل مستحلب يساعد على دوابنيتهم + +325 +00:23:46,520 --> 00:23:50,800 +ببعض، إيش العامل المستحلب اللي بدي أستخدمه؟ هو نصف + +326 +00:23:50,800 --> 00:23:56,640 +المية، Na2CO3 Sodium Bicarbonate، هذا إيش وظيفته في + +327 +00:23:56,640 --> 00:24:01,800 +هذا الفحص؟ وظيفته emulsifying agent، عامل مستحل + +328 +00:24:01,800 --> 00:24:06,900 +وبدنا نشتغل الفحص على زيت زيتون طبيعي Natural Olive + +329 +00:24:06,900 --> 00:24:11,740 +Oil وعلى Rancid Olive Oil، على زيت زيتون طبيعي وزيت + +330 +00:24:11,740 --> 00:24:17,180 +الزيتون المتزنخ، natural olive oil زيت الزيتون + +331 +00:24:17,180 --> 00:24:20,640 +الطبيعي و نستخدم rancid olive oil اللي هو زيت + +332 +00:24:20,640 --> 00:24:24,420 +الزيتون المتزنخ، إيش الفرق بين الاتنين؟ بيحكي للـ + +333 +00:24:24,420 --> 00:24:27,040 +natural olive oil اللي هو زيت الزيتون الطبيعي + +334 +00:24:27,040 --> 00:24:31,200 +بيكون جديد، بيكون لسه مش ساير عليه عمليات أكسدة، + +335 +00:24:31,200 --> 00:24:34,380 +بيكون سايرله بس partial oxidation، عمليات أكسدة + +336 +00:24:34,380 --> 00:24:39,770 +بسيطة، جزئية، لما تأكسدى انتهى أي جزاء تأكسدى هذا + +337 +00:24:39,770 --> 00:24:44,810 +الزيت بينتج عنه تكسير للفاتي أسد، بتتكسر بتتفكك عن + +338 +00:24:44,810 --> 00:24:48,510 +بعضها، الفاتي أسد وبتتحرر فبيصير عندي فيه free + +339 +00:24:48,510 --> 00:24:52,330 +fatty acid، في الـ natural olive oil بيكون partially + +340 +00:24:52,330 --> 00:24:57,690 +الـ oxidation عمليات أكسدة جزئية بسيطة، فكمية الفاتي + +341 +00:24:57,690 --> 00:25:02,370 +أسد الحرة بتكون قليلة، يحتوي على few of free fatty + +342 +00:25:02,370 --> 00:25:06,280 +acid، لكن في الـ Rancid Olive Oil في زيت الزيتون + +343 +00:25:06,280 --> 00:25:10,060 +المتزنخ اللي هو مجلة فيه أكتر من مرة عاملينه + +344 +00:25:10,060 --> 00:25:14,160 +مستخدمينه أكتر من مرة بيكون صاير عليه Complete + +345 +00:25:14,160 --> 00:25:19,720 +Oxidation عمليات أكسدة كاملة، بتأدي إلى تحرير جميع + +346 +00:25:19,720 --> 00:25:23,360 +الفاتي أسد فبيكون عندنا many of free fatty acid + +347 +00:25:23,360 --> 00:25:28,980 +الفاتي أسد بتكون الـ free الحرة بتكون بشكل أكبر، إيش + +348 +00:25:28,980 --> 00:25:33,120 +هي Rancidity؟ Rancidity معناها التزنخ، Rancidity + +349 +00:25:33,120 --> 00:25:38,840 +معناها التزنخ، هي ظهور رائحة كريهة أو غير مرغوب + +350 +00:25:38,840 --> 00:25:43,800 +فيها على الزيت والزبدة، وهي الرائحة غالبا بتكون + +351 +00:25:43,800 --> 00:25:49,680 +مصحوبة بتغير في القوام والشكل، لذن الـ Rancidity هو + +352 +00:25:49,680 --> 00:25:55,860 +التزنخ وظهور رائحة غير مرغوب فيها، مصحوبة بتغيير في + +353 +00:25:55,860 --> 00:25:59,740 +القوام والشكل على الزيت والزبدة + +354 +00:26:02,130 --> 00:26:05,870 +مش خطواتنا كيف نشتغل الفحص تبع الـ emulsification + +355 +00:26:05,870 --> 00:26:09,650 +إذا انفهمنا أن الـ objective من الفحص أن أنا بدي + +356 +00:26:09,650 --> 00:26:14,150 +أعمل emulsified oil and water in each other by + +357 +00:26:14,150 --> 00:26:18,410 +emulsifying agent، بدي أساعد الـ oil والـ water، المي + +358 +00:26:18,410 --> 00:26:22,530 +والزيت ان هم يصيروا emulsified بعض بمساعدة من؟ + +359 +00:26:22,530 --> 00:26:27,150 +emulsifying agent، اللي هو عبارة عن الـ Sodium + +360 +00:26:27,150 --> 00:26:30,870 +Bicarbonate، فلو كتبتوا .. كتبنا لبرنزميل عن النظام + +361 +00:26:30,870 --> 00:26:35,730 +معادلة ده، هذا الفحص أحكي fat أو oil اللي هو الزيت + +362 +00:26:35,730 --> 00:26:39,690 +مع water، بدي أضيف عليه ميه في وجود emulsifying + +363 +00:26:39,690 --> 00:26:42,950 +agent اللي هو Sodium Bicarbonate، إيش بدي يصير + +364 +00:26:42,950 --> 00:26:46,490 +عندي؟ بدي يصير عندي emulsification، بدي يصير عندي + +365 +00:26:46,490 --> 00:26:50,740 +emulsification، الناتج، خطوات العمل، بدي أجيب تلاتة + +366 +00:26:50,740 --> 00:26:54,320 +تيوب بقى، تيوب الأول بدي أشتغل عليه بدي أحط فيه + +367 +00:26:54,320 --> 00:26:58,020 +drop من الـ oil، زيت زيتون مع 2 ml distilled water و + +368 +00:26:58,020 --> 00:27:02,740 +أعمل mix، بس حطيت زيت مع مي و عملتي mix، إيش + +401 +00:29:18,500 --> 00:29:22,780 +unsaturated fatty acidبعدين في أكسدة في تفاعلات + +402 +00:29:22,780 --> 00:29:26,220 +أكسدة واختزال إذا أنا محتاجة لـ oxidizing agent + +403 +00:29:26,220 --> 00:29:31,180 +لعامل مؤكسد عشان يoxidize الـ unsaturated fatty + +404 +00:29:31,180 --> 00:29:35,080 +acid إيش يعني unsaturated fatty acid حكينا + +405 +00:29:35,080 --> 00:29:39,000 +unsaturated معناها أنه بيحتوي على double bond على + +406 +00:29:39,000 --> 00:29:43,480 +one or more double bond عنده double bond واحدة أو + +407 +00:29:43,480 --> 00:29:47,860 +أكثر في عندنا نوعين من الـ Acid هدول اللي بنستخدمهم + +408 +00:29:47,860 --> 00:29:51,040 +في عندنا Oleic Acid هو عبارة عن Unsaturated Fatty + +409 +00:29:51,040 --> 00:29:55,620 +Acid وفي Stearic Acid هو Saturated Fatty Acid + +410 +00:29:55,620 --> 00:29:59,260 +بنستخدم هدول الاتنين في هذا الفحص اليوم مين اللي + +411 +00:29:59,260 --> 00:30:02,940 +هيعطيني positive بس الـ Unsaturated Fatty Acid اللي + +412 +00:30:02,940 --> 00:30:06,800 +هو الـ Oleic Acid الـ Oleic Acid هيتغير لونه ويعطيني + +413 +00:30:06,800 --> 00:30:10,720 +positive لأنه بيصير له أكسدة أما الـ stearic acid + +414 +00:30:10,720 --> 00:30:14,940 +بيصيرش عليه أكسدة لأنه عبارة عن saturated fatty + +415 +00:30:14,940 --> 00:30:20,230 +acid كيف بيدعم الـ Oxidation؟ بدي Oxidizing agent + +416 +00:30:20,230 --> 00:30:24,230 +اللي هو عامل مؤكسد العامل المؤكسد اللي بنستخدمه في + +417 +00:30:24,230 --> 00:30:27,590 +فحصنا لليوم في هذا الفحص هو الـ potassium + +418 +00:30:27,590 --> 00:30:34,150 +permanganate KMnO4 potassium permanganate لو حكيت الـ + +419 +00:30:34,150 --> 00:30:38,070 +objective لهذا الفحص to oxidize oleic acid by + +420 +00:30:38,070 --> 00:30:42,450 +potassium permanganate بيدعم الأكسدة للـ acid + +421 +00:30:42,450 --> 00:30:46,830 +باستخدام البوتاسيوم بيرمانجانات ولو بدك تكتب الـ + +422 +00:30:46,830 --> 00:30:50,470 +principle على شكل معادلة بحكي أن الـ acid اللي أنا + +423 +00:30:50,470 --> 00:30:54,690 +بده أعمله أكسدة زي الـ potassium permanganate بيحكي + +424 +00:30:54,690 --> 00:30:58,930 +اللي بيعطيني لون brown الأولك أسد مع بوتاسيوم + +425 +00:30:58,930 --> 00:31:02,990 +بيرمانجانات العامل المؤكسد يعمل على أكسدة الأولك + +426 +00:31:02,990 --> 00:31:06,870 +أسد ويتحول اللون إلى لون براون البوتاسيوم + +427 +00:31:06,870 --> 00:31:10,610 +بيرمانجانات أصلا لونه violet لونه move لونه purple + +428 +00:31:10,610 --> 00:31:15,150 +على violet move لما تحطيه على الأولك أسد بيعمل + +429 +00:31:15,150 --> 00:31:21,000 +عملية أكسدة للأولك أسد بيحوله إلى لون براون كيف + +430 +00:31:21,000 --> 00:31:24,420 +خطوات إجراء التجربة؟ بدي أشوف بالتيوب بدي أشتغل + +431 +00:31:24,420 --> 00:31:27,180 +فيها أوليك أسد والتيوب بدي أشتغل فيها ستيريك أسد + +432 +00:31:27,180 --> 00:31:31,160 +وأشوف من يغير أول تيوب بدي أشتغل فيها أوليك أسد + +433 +00:31:31,160 --> 00:31:34,520 +بدي أشتغل فيه one drop of oleic acid على تلاتة مل + +434 +00:31:34,520 --> 00:31:38,120 +من الـ sodium bicarbonate على اتنين مل من + +435 +00:31:38,120 --> 00:31:44,670 +البوتاسيوم بيرمانجانات تمام ده حاط واحد drop من + +436 +00:31:44,670 --> 00:31:48,090 +الـ olic acid على 3 مل من الـ sodium bicarbonate على + +437 +00:31:48,090 --> 00:31:51,690 +2 مل من الـ potassium permanganate الـ olic acid هو + +438 +00:31:51,690 --> 00:31:55,470 +عبارة عن unsaturated fatty acid ييجي الـ potassium + +439 +00:31:55,470 --> 00:31:59,550 +permanganate بيعمله أكسدة يفترض يتحول اللون إلى + +440 +00:31:59,550 --> 00:32:04,390 +brown إذا positive إذا هو olic acid التيوب الثانية + +441 +00:32:04,390 --> 00:32:08,470 +بده أحط drop من الـ stearic acid على 3 مل من الـ + +442 +00:32:08,470 --> 00:32:12,670 +sodium bicarbonate على 2 مل من الـ potassium + +443 +00:32:12,670 --> 00:32:16,530 +permanganate بيحكي اللي لما تحطي الـ stearic acid + +444 +00:32:16,530 --> 00:32:20,150 +هو عبارة عن unsaturated fatty acid فلما تحط عليه + +445 +00:32:20,150 --> 00:32:24,550 +الـ potassium permanganate بيتغيرش اللون وإنما بيظل + +446 +00:32:24,550 --> 00:32:31,930 +لونه violet مش هيتغير مش هيتحول للون brown آخر + +447 +00:32:31,930 --> 00:32:35,790 +فحص هو السلكا ويسكي reaction هذا السلكا ويسكي + +448 +00:32:35,790 --> 00:32:41,530 +reaction هو فحص للكشف عن الزيت بستخدم زيت بدي أشوف + +449 +00:32:41,530 --> 00:32:45,590 +هل هذا الزيت مخشوش مضعف عليه الكلسترول ولا مش مضعف + +450 +00:32:45,590 --> 00:32:51,280 +هذا خاص للكشف هذا الفحص السلكا ويسكي reaction للكشف + +451 +00:32:51,280 --> 00:32:55,020 +عن الكوليسترول، هل الكوليسترول موجود ولا لا؟ في + +452 +00:32:55,020 --> 00:32:58,320 +ناس بتغش الزيت، بتضيف عليه كوليسترول أنا بدي أشوف + +453 +00:32:58,320 --> 00:33:01,380 +هل هذا الزيت مضاف عليه كوليسترول ولا هو زيت زيتون + +454 +00:33:01,380 --> 00:33:07,040 +طبيعي؟ كيف مبدأ عمله؟ هذا الفحص مبدأ عمله بيتم على + +455 +00:33:07,040 --> 00:33:12,880 +استخدام concentrated sulfuric acid H2SO4 نستخدم + +456 +00:33:12,880 --> 00:33:18,420 +concentrated sulfuric acid اللي هو H2SO4 هذا حساس + +457 +00:33:18,420 --> 00:33:22,900 +للرطوبة «highly hygroscopic» هو حساس للرطوبة لا + +458 +00:33:22,900 --> 00:33:25,720 +يمكن للطيوبات اللي أشتغل فيها يكون فيها ماء لازم + +459 +00:33:25,720 --> 00:33:31,080 +تكون جافة لأن أصلا مبدأ عمله يعمل على «removal of + +460 +00:33:31,080 --> 00:33:33,880 +two molecules of water from two molecules of + +461 +00:33:33,880 --> 00:33:38,120 +cholesterol» إن إذا الكوليسترول موجود في الزيت إذا + +462 +00:33:38,120 --> 00:33:43,260 +كان في عندي في الزيت موجود كوليسترول بيجي الـ H2SO4 + +463 +00:33:43,260 --> 00:33:46,720 +الـ concentrated sulfuric acid هاد بيقوم بنزع + +464 +00:33:46,720 --> 00:33:51,660 +جزيئين ماء من جزيئين كوليسترول إذا في كوليسترول + +465 +00:33:51,660 --> 00:33:58,020 +بيجي الـ H2SO4 بينزع جزيئين ماء من هذا الكوليسترول + +466 +00:33:58,020 --> 00:34:03,310 +من position من موقع تلاتة وتلاتة نزع جزيئين ماء من + +467 +00:34:03,310 --> 00:34:07,650 +اتنين كولسترول من موقع تلاتة وتلاتة بينتج النتج + +468 +00:34:07,650 --> 00:34:10,950 +بيتحول لكلسترول لما تنزع منه جزئين ماء بيتحول + +469 +00:34:10,950 --> 00:34:16,050 +لحاجة اسمها bi-cholestadine الـ H2SO4 كمان مرة + +470 +00:34:16,050 --> 00:34:20,750 +السلفيوريك أسد هذا بيشتغل على البيكلستادين بيعمله + +471 +00:34:20,750 --> 00:34:26,930 +سلفيونات بيكلستادين at position 7 و7 بيعمل سلفيونات + +472 +00:34:26,930 --> 00:34:31,150 +للبيكلستادين بيضيف عليه سلفيونية الـ group بتحول إلى + +473 +00:34:31,150 --> 00:34:36,090 +حاجة اسمها bi-sulfonic acid bi-cholestadine لونه + +474 +00:34:36,090 --> 00:34:41,200 +red color إذا بفحص السلكا whisk reaction وفحص + +475 +00:34:41,200 --> 00:34:44,420 +للكشف عن الكوليسترول هل موجود في زيتا المضاف عليه + +476 +00:34:44,420 --> 00:34:50,260 +كوليسترول ولا لأ؟ كيف باستخدام Sulphuric Acid؟ إيش + +477 +00:34:50,260 --> 00:34:53,900 +وظيفة Sulphuric Acid في فحص السلكويسكي reaction؟ + +478 +00:34:53,900 --> 00:34:58,280 +الوظيفتين أول وظيفة remove two molecules of water + +479 +00:34:58,280 --> 00:35:02,440 +from two molecules of كوليسترول نزع جزيئين ماء من + +480 +00:35:02,440 --> 00:35:06,520 +الـ ... من اتنين كوليسترول من موقع تلاتة ويتحول + +481 +00:35:06,520 --> 00:35:10,590 +الكوليسترول لحاجة اسمها bi-cholestadine بعدين + +482 +00:35:10,590 --> 00:35:13,990 +الوظيفة الثانية يعمل سلفيونات بيكلستادين at + +483 +00:35:13,990 --> 00:35:18,350 +position 7 و7 اللي هي إضافة سلفيونية الـ group على + +484 +00:35:18,350 --> 00:35:22,450 +position 7 و7 في البيكلستادين بتكون حاجة اسمها + +485 +00:35:22,450 --> 00:35:27,810 +bisulfonic acid bicolestidine لونها red color إذا + +486 +00:35:27,810 --> 00:35:30,650 +الـ objective من هذا الفحص to detect the presence + +487 +00:35:30,650 --> 00:35:35,890 +of cholesterol كيف مبدأ أعمله؟ إنه بيكون عندي + +488 +00:35:35,890 --> 00:35:39,590 +اتنين كولسترول إذا عندي مركبين كولسترول بنحط عليهم + +489 +00:35:39,590 --> 00:35:44,590 +concentrated sulfuric acid H2SO4 بيتحول النتج لـ + +490 +00:35:44,590 --> 00:35:49,210 +ليه؟ by sulfonate by كولستادين لونه red + +491 +00:35:54,630 --> 00:35:58,110 +هنا عملنا structure لبيكولستادين كيف شكله و + +492 +00:35:58,110 --> 00:36:02,390 +بيسالفونك أسد بيكولستادين كيف شكله عشان أطلب مننا + +493 +00:36:02,390 --> 00:36:07,650 +الـ structure إيش الـ ... كيف خطوات التجربة أو إيش + +494 +00:36:07,650 --> 00:36:10,670 +نستخدم الـ agent نستخدم زيت زيتون مضاعف عليه + +495 +00:36:10,670 --> 00:36:15,030 +الكوليسترول نستخدم زيت زيتون طبيعي وزيت زيتون مضاعف + +496 +00:36:15,030 --> 00:36:18,430 +عليه الكوليسترول عشان نشوف الفارق ونستخدم الـ + +497 +00:36:18,430 --> 00:36:22,330 +chloroform عشان ندوّب بس الزيت عشان أقدر أدوّب + +498 +00:36:22,330 --> 00:36:28,350 +الزيت ونتجنب استنشاق كمية من هذا الـ chloroform + +499 +00:36:28,350 --> 00:36:31,550 +لأن هذا بيأثر على الـ central nervous system على + +500 +00:36:31,550 --> 00:36:37,080 +الجهاز العصبي بسبب نزلة و headache و business صداع + +501 +00:36:37,080 --> 00:36:43,900 +وغثيان وكوم داخل وبدنا نستخدم الـ sulfuric acid + +502 +00:36:43,900 --> 00:36:48,640 +اللي له وظيفتين في هذا الفحص حكينا عنهم كيف طريقة + +503 +00:36:48,640 --> 00:36:52,920 +إجراء التجربة ده جيب كيبين واحد أستغل فيها الزيت + +504 +00:36:52,920 --> 00:36:56,620 +الزيتون من غير كلسترول وواحدة بدأ أستخدم فيها زيت + +505 +00:36:56,620 --> 00:37:00,920 +زيتون مضاف عليه كلسترول عشان أشوف الفارق أول تيوب + +506 +00:37:00,920 --> 00:37:07,920 +سأضع عليها 1ml كلوروفارم 1ml كلوروفارم على 2 drop + +507 +00:37:07,920 --> 00:37:13,720 +من الزيت 1ml كلوروفارم على 2 drop من الزيت ثم أضع + +508 +00:37:13,720 --> 00:37:18,300 +2ml من H2SO4 هجد زيت زيتون إذا كان طبيعي مش + +509 +00:37:18,300 --> 00:37:22,340 +هيتغير إشي وهيكون negative في الشلون تيوب التاني + +510 +00:37:22,340 --> 00:37:27,400 +سأضع عليها 1ml كلوروفارم واتنين drop من + +511 +00:37:27,400 --> 00:37:30,820 +الكوليسترول زيت زيتون مضاف عليه كوليسترول وأحط + +512 +00:37:30,820 --> 00:37:35,460 +اتنين مل من H2SO4 فان بلاحظ أن اللون عندي بيتحول + +513 +00:37:35,460 --> 00:37:39,620 +إلى red إذا تكونت الـ red اللون الأحمر إذا هذا + +514 +00:37:39,620 --> 00:37:47,590 +الزيت مضاف عليه كوليسترول إذا ما اتحولش إذا هو زيت + +515 +00:37:47,590 --> 00:37:51,410 +زيتون طبيعي بدون كوليسترول بيحكي لي في أول إشي أنه + +516 +00:37:51,410 --> 00:37:56,050 +أنه تكون الـ dry test tube تكون التيوبات جافة ضروري + +517 +00:37:56,050 --> 00:37:59,190 +للتيوبات تكون جافة لأنه هذا حكينا أنه highly + +518 +00:37:59,190 --> 00:38:03,530 +hygroscopic حساس للرطوبة لأن أصلا المبدأ عامله أنه + +519 +00:38:03,530 --> 00:38:07,350 +بده جزيئين ماء ينزع جزيئين ماء إذا التيوب فيها ماء + +520 +00:38:07,350 --> 00:38:11,250 +هياخد الماء الموجودة في التيوب مش هيشتغل على + +521 +00:38:11,250 --> 00:38:15,510 +الكوليسترول إذا موجود إنما هيشتغل على الماء اللي في + +522 +00:38:15,510 --> 00:38:21,410 +التيوب بدل الكوليسترول هيك بنكون خلصنا هذا المعمل، + +523 +00:38:21,410 --> 00:38:25,010 +المعمل الليبد إن شاء الله نشتغل عملي فيه المعمل، + +524 +00:38:25,010 --> 00:38:30,680 +مطلوب منك تكتب لي الـ principle لكل فحص على شكل + +525 +00:38:30,680 --> 00:38:35,640 +معادلات واللي مش معادلة تكتب لي المبدأ برضه + +526 +00:38:35,640 --> 00:38:37,080 +يعطيكم العافية diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/ejpJCjHaqTg_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/ejpJCjHaqTg_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..614bc907f46ed48aac57e8356088f568af0a7269 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/ejpJCjHaqTg_postprocess.srt @@ -0,0 +1,1544 @@ +1 +00:00:00,000 --> 00:00:04,920 +بنحكي في موضوع جديد هو موضوع الفيتامينات، أتحدث عن + +2 +00:00:04,920 --> 00:00:10,570 +الفيتامينات و عن أقسام الفيتاميناتأولش نحكي عن + +3 +00:00:10,570 --> 00:00:15,190 +خصائص ال vitamins characteristics of vitamins أولش + +4 +00:00:15,190 --> 00:00:19,930 +ال vitamins هي عبارة عن micro nutrients هي مغذيات + +5 +00:00:19,930 --> 00:00:24,530 +صغيرة أول خاصية انها تعتبر micro nutrients مغذيات + +6 +00:00:24,530 --> 00:00:29,530 +صغيرة ليش بيعتبرها micro لأن very small amount are + +7 +00:00:29,530 --> 00:00:34,620 +needed by the body الجسم بيحتاجها بكميات قليلةvery + +8 +00:00:34,620 --> 00:00:38,820 +small amount are contained in food و الأطعمة تحتوى + +9 +00:00:38,820 --> 00:00:43,380 +على الفيتامينات بكميات قليلة، إذن هي مغاديات صغيرة + +10 +00:00:43,380 --> 00:00:47,840 +لأنه بيحتاجها الجسم بكميات قليلة و كمان موجودة في + +11 +00:00:47,840 --> 00:00:52,360 +الأطعمة بكميات قليلةبعد هيك ال vitamins are + +12 +00:00:52,360 --> 00:00:57,160 +essential الفيتامينات ضرورية ومهمة للجسم لأنها + +13 +00:00:57,160 --> 00:01:02,100 +بتلعب دور مهم في الجسم play important role in the + +14 +00:01:02,100 --> 00:01:06,380 +body most vitamins are obtained from the food we + +15 +00:01:06,380 --> 00:01:10,680 +eat من ورا الجسم بياخد الفيتامينات معظم + +16 +00:01:10,680 --> 00:01:15,260 +الفيتامينات بياخدها من الطعام الطعام اللي بيتناوره + +17 +00:01:15,260 --> 00:01:20,790 +بيحتوي على الفيتاميناتفي بعض الفيتامينات بتصنحها + +18 +00:01:20,790 --> 00:01:25,870 +بكتيريا موجودة في الأمعاء زي ال normal flora بتصنع + +19 +00:01:25,870 --> 00:01:30,680 +vitamin Kبعض الفيتامينات بتصنعها بكتيريا موجودة + +20 +00:01:30,680 --> 00:01:35,260 +فيه لما و أما معظم الفيتامينات بناخدها من الطعام + +21 +00:01:35,260 --> 00:01:38,600 +there is no perfect food that contain all the + +22 +00:01:38,600 --> 00:01:43,000 +vitamins in the right amount فش طعام واحد مثلا + +23 +00:01:43,000 --> 00:01:47,820 +أقولك الطماطم تحتوي على كل أنواع الفيتامينات لأ + +24 +00:01:47,820 --> 00:01:51,880 +الفيتامين منتشر في أطعم مختلفة لكن فش طعام واحد + +25 +00:01:51,880 --> 00:01:53,980 +يحتوي كل أنواع الفيتامين + +26 +00:01:58,030 --> 00:02:02,990 +هي الفيتامينات لا تحتوي سعرات حرارية، not contain + +27 +00:02:02,990 --> 00:02:06,470 +kilo calories، لا تحتوي سعرات حرارية وبالتالي هي + +28 +00:02:06,470 --> 00:02:12,270 +لا تعطي طاقة ولا تنتج الطاقة vitamin are + +29 +00:02:12,270 --> 00:02:15,270 +classified according to how soluble they are in + +30 +00:02:15,270 --> 00:02:19,530 +fat or water الفيتامينات مقسمة حسب دوبانيتها، في + +31 +00:02:19,530 --> 00:02:24,980 +منها تدوب في الدهون وفي منها تدوب في الماءعنا هاد + +32 +00:02:24,980 --> 00:02:28,960 +الجدول بيفرق بين ال vitamins اللي هم على قسمين + +33 +00:02:28,960 --> 00:02:32,440 +العمودي الأول اللي هى ال water soluble vitamins + +34 +00:02:32,440 --> 00:02:37,140 +وفيه عنا fat soluble vitamins أنثى على water + +35 +00:02:37,140 --> 00:02:41,860 +soluble vitamins عنا vitamin B وC أما ال fat + +36 +00:02:41,860 --> 00:02:48,160 +soluble vitamins عنا vitamin A DE و K مجموعين في + +37 +00:02:48,160 --> 00:02:53,920 +كلمة أكيد أو أديك، لذا الفات سوليوبين في عندنا و + +38 +00:02:53,920 --> 00:02:57,160 +في عندنا water soluble vitamin ال water soluble هي + +39 +00:02:57,160 --> 00:03:03,550 +ال B و ال C، الفات سوليوبين هم A و D و E و Kطيب + +40 +00:03:03,550 --> 00:03:06,570 +نيجي نفرق بينهم أول إشي من ناحية ال absorption + +41 +00:03:06,570 --> 00:03:11,370 +مدام هو water soluble vitamins ال water soluble + +42 +00:03:11,370 --> 00:03:15,690 +vitamins يعني بتدوب في المي والجسم على طول أغلب + +43 +00:03:15,690 --> 00:03:19,730 +مكوناته مي فهي على طول directly into the blood بتم + +44 +00:03:19,730 --> 00:03:24,970 +إمتصاصها مباشرة عبر الدم أما الفات سوليوبل لازم + +45 +00:03:24,970 --> 00:03:29,510 +بأول تروح على ال lymph و بعدين تيجي على الدم عشان + +46 +00:03:29,510 --> 00:03:35,190 +يتم تحميلوهي تنقلها، إذاً الامتصاص ال water + +47 +00:03:35,190 --> 00:03:38,590 +soluble يتم امتصاصها مباشرة في الدم أما الفاة + +48 +00:03:38,590 --> 00:03:42,370 +soluble vitamins لازم تروح على اللنف وبعدين يتم + +49 +00:03:42,370 --> 00:03:48,380 +نقلها للبلادطيب transport كيف بدها تتنقل هاي ال + +50 +00:03:48,380 --> 00:03:52,140 +water soluble مدى ما خصائصها زي خصائص الجسم فهي + +51 +00:03:52,140 --> 00:03:56,260 +travel freely بتنتقل بحرية، بتمشي بحرية من غير أي + +52 +00:03:56,260 --> 00:04:00,200 +معوقة أما ال fat soluble vitamins لأن خصائصها + +53 +00:04:00,200 --> 00:04:05,270 +بتغير عن الجسمفبتحتاج إلى نواقل require carrier + +54 +00:04:05,270 --> 00:04:09,030 +proteins بتحتاج إلى نواقل عشان تنجولها وعشان تمشي + +55 +00:04:09,030 --> 00:04:13,590 +في داخل الجسم ال storage التخزين هل بيتم تخزينها + +56 +00:04:13,590 --> 00:04:18,430 +ولا لا ال water soluble vitamins بتمش تخزينها بدل + +57 +00:04:18,430 --> 00:04:22,150 +هذا كل اللي مكتوب circulated freely لنكتب not + +58 +00:04:22,150 --> 00:04:27,150 +stored لاتخزن ما بيتم تخزينها أما ال fat soluble + +59 +00:04:27,150 --> 00:04:31,240 +vitamin بتم تخزينها it is storedwhen بتخزن في + +60 +00:04:31,240 --> 00:04:36,400 +الأنسجة الدهنية، في الخلايا الدهنية حسنا طبيعة + +61 +00:04:36,400 --> 00:04:40,480 +خلايا الجسم دهنية فهتتخزن ال fat soluble vitamins + +62 +00:04:40,480 --> 00:04:45,060 +اللي بتشبهها، إذا ال water لا تخزن أما الفات تخزن + +63 +00:04:45,060 --> 00:04:50,390 +excretion هجيت الإخراجمدام ال water لا تخزن في + +64 +00:04:50,390 --> 00:04:55,710 +الجسم فاللي هيكون زائد عن حاجة الجسم هيتم إخراجه + +65 +00:04:55,710 --> 00:05:00,530 +ال kidney هتعمل ال detection هتعمله فلترة وتعمله + +66 +00:05:00,530 --> 00:05:04,130 +remove excess in urine وهتعمله إخراج مع ال urine + +67 +00:05:04,130 --> 00:05:08,330 +ال excretion معناه الإخراج ال water soluble + +68 +00:05:08,330 --> 00:05:12,340 +vitamins مدام مافيش تخزين لهامش هيتخزن في الجسم + +69 +00:05:12,340 --> 00:05:16,960 +فالكمية الزائدة عن حاجة الجسم هيتم إخراجها مع + +70 +00:05:16,960 --> 00:05:21,660 +اليورو أما الفات سوليوبل vitamins مدامها بتخزن إذا + +71 +00:05:21,660 --> 00:05:26,620 +الكمية الزائدة عن حاجة الجسم بتم تخزينها في + +72 +00:05:26,620 --> 00:05:30,880 +الأنسجة و الخلايا الدهنية إذا في ال execution في + +73 +00:05:30,880 --> 00:05:34,360 +الفوتر سوليوبل بتم execution أما في الفات no + +74 +00:05:34,360 --> 00:05:40,650 +executionال toxicity اللي هو السمية أنه يوصل لحد + +75 +00:05:40,650 --> 00:05:44,490 +السمية كمية الفيتامين في الجسم صارت زيادة كمية + +76 +00:05:44,490 --> 00:05:49,710 +كبيرة ووصلت لحد السمية هلجت ال water soluble + +77 +00:05:49,710 --> 00:05:52,470 +possible to reach toxic level؟ + +78 +00:05:54,740 --> 00:05:59,740 +الـ toxicity حكينا السمية أن يوصل لحد السمية ال + +79 +00:05:59,740 --> 00:06:03,000 +water soluble بتتم إخراجها أصلا خارج الجسم فممكن + +80 +00:06:03,000 --> 00:06:08,720 +توصل لحد السمية ولكن يعني احتمال قليل و بيحكي إن + +81 +00:06:08,720 --> 00:06:12,440 +هذه ال toxicity بتيجي من consumed from supplement + +82 +00:06:12,440 --> 00:06:17,840 +لما ياخد supplement مدعمات أو أقراص vitamins ممكن + +83 +00:06:17,840 --> 00:06:21,580 +هنا نوصل لحد السمية في ال fat soluble vitamins + +84 +00:06:21,910 --> 00:06:26,890 +السمية عالية احتمال انه نوصل لحد السمية likely ليش + +85 +00:06:26,890 --> 00:06:31,290 +لأنه اصلا بيخزن في الجسمطب ال requirements اللي هو + +86 +00:06:31,290 --> 00:06:34,750 +حاجة الجسم إلها من جداش لجداش الفترة أنا لازم + +87 +00:06:34,750 --> 00:06:38,630 +أتناول هذه الفيتامينة ال water soluble vitamins + +88 +00:06:38,630 --> 00:06:43,450 +بنحتاجه frequent dose يعني من كل يوم لتلت أيام بدي + +89 +00:06:43,450 --> 00:06:47,710 +منه لأنه بيتم إخراجه لكن ال fat soluble لأنه بيتم + +90 +00:06:47,710 --> 00:06:52,770 +تخزينه في داخل الجسم ففترات متباعدة خلال periodic + +91 +00:06:52,770 --> 00:06:58,240 +dose ممكن من أسبوع لشهراحتاج ال fat soluble + +92 +00:06:58,240 --> 00:07:01,820 +vitamin اذا هنا عندنا نوعين من انواع ال vitamins + +93 +00:07:01,820 --> 00:07:06,220 +water soluble و ال fat soluble vitamin خدنا مثال + +94 +00:07:06,220 --> 00:07:09,760 +على هاي و مثال على هاي و مقارنة بينهم فالجيت هنفصل + +95 +00:07:09,760 --> 00:07:14,040 +كل واحدة اول اش ان نحكي عن ال fat soluble vitamin + +96 +00:07:14,040 --> 00:07:19,220 +اللي حكينا هم اربعة مجموعين في كلمة اكيد او اديك + +97 +00:07:20,670 --> 00:07:23,910 +الخصائص العامة لل fats, soluble vitamins هذا ملخص + +98 +00:07:23,910 --> 00:07:26,550 +الجدول اللي خاص في ال fats, soluble vitamins + +99 +00:07:26,550 --> 00:07:30,490 +الأطعمة اللي بتكون موجودة فيها الفات و ال soluble + +100 +00:07:30,490 --> 00:07:33,290 +vitamins بتكون موجودة في الأطعمة الدهنية و في + +101 +00:07:33,290 --> 00:07:38,050 +الزيت in fats and oil require piles for absorption + +102 +00:07:38,050 --> 00:07:42,490 +بتحتاج .. لازم نحتاج حاجة عشان تساعد على امتصاصها + +103 +00:07:42,490 --> 00:07:47,450 +حكينا فبتحتاج ال piles للامتصاص إذا فاكرين حكينا + +104 +00:07:47,450 --> 00:07:51,350 +في معمل ال cholesterolإنه ال bio اللي بتشتغل ك + +105 +00:07:51,350 --> 00:07:56,530 +soap كصابونة بتعمل على امتصاص الفات كيف بده ينهضم + +106 +00:07:56,530 --> 00:08:01,380 +في الجسم و يتم امتصاصه عبر ال bioEnter the lymph + +107 +00:08:01,380 --> 00:08:05,220 +in the blood تدخل الليم في العقد وبعدين بتروح على + +108 +00:08:05,220 --> 00:08:09,980 +الدم وبتم تخزينها في الفاتي تشوف الخلايا الدهنية + +109 +00:08:09,980 --> 00:08:15,120 +need in small amount وبنحتاجها بكميات قليلة ممكن + +110 +00:08:15,120 --> 00:08:20,200 +نوصل لحد السمية لأنه فش إلها إخراج not readily + +111 +00:08:20,200 --> 00:08:22,460 +executed ما بتم إخراجها + +112 +00:08:25,100 --> 00:08:28,700 +طب أول نوع من أنواع الفات سوليوبيل فيتامين فيتامين + +113 +00:08:28,700 --> 00:08:34,700 +A فيتامين A في منه تلت أشكال تلت أشكال من فيتامين + +114 +00:08:34,700 --> 00:08:39,520 +A موجود في الجسم على تلت أشكال ريتينول ريتينال + +115 +00:08:39,520 --> 00:08:45,060 +ريتينوك أسن إذا الفات ال فيتامين A موجود في الجسم + +116 +00:08:45,060 --> 00:08:51,210 +على تلت أشكال ريتينول ريتينالretinoic acid كلهم مع + +117 +00:08:51,210 --> 00:08:55,390 +بعض collectively known as retinoid كلهم مع بعض + +118 +00:08:55,390 --> 00:09:00,170 +بنسميهم retinoid ال precursor اللي هي الوحدة + +119 +00:09:00,170 --> 00:09:03,910 +البنائية في تكوين vitamin A في تكوين ال retinoid + +120 +00:09:03,910 --> 00:09:09,830 +الوحدة الأساسية والبنائية هو ال beta carotene ال + +121 +00:09:09,830 --> 00:09:15,330 +beta carotene هو الوحدة البنائية لتكوين vitamin A + +122 +00:09:17,900 --> 00:09:21,400 +derived from plant food من وين بدى احصل على هذا ال + +123 +00:09:21,400 --> 00:09:25,040 +beta carotene عشان يكون لفيتامين a يكون لريتينول + +124 +00:09:25,040 --> 00:09:29,500 +ريتينويد بحصل عليه من ال plant food من الأطعمة + +125 +00:09:29,500 --> 00:09:34,180 +النباتية وكمان can split and form retinol in + +126 +00:09:34,180 --> 00:09:38,500 +intestine and liver وبتم تصنيع في ال liver و ال + +127 +00:09:38,500 --> 00:09:43,240 +intestineالبيتا كاروتين one الأطعمة بنلاقيها في + +128 +00:09:43,240 --> 00:09:48,060 +الخضروات الورقية الخضراء بنلاقيها في الخضروات اللي + +129 +00:09:48,060 --> 00:09:53,140 +نونها برتقالي وفي الفواكه اللي هو البرتقال ال + +130 +00:09:53,140 --> 00:09:57,580 +orange fruit vitamin + +131 +00:09:57,580 --> 00:10:01,860 +A function إيش وظيفة vitamin A أهم وظيفة لvitamin + +132 +00:10:01,860 --> 00:10:05,520 +A ال vision اللي هو في النظر في الرؤية يستخدم في + +133 +00:10:05,520 --> 00:10:10,210 +الرؤية maintain epithelial tissue and skinبحافظ + +134 +00:10:10,210 --> 00:10:14,810 +على الأنسجة و الخلايا support reproduction and + +135 +00:10:14,810 --> 00:10:19,830 +growth بيدعم النمو و البلوغ بساعد في النمو و + +136 +00:10:19,830 --> 00:10:24,890 +البلوغ immune system الوظائف في جهاز المناعة bone + +137 +00:10:24,890 --> 00:10:31,270 +development الوظائف في نمو و تطور العظم + +138 +00:10:33,520 --> 00:10:37,340 +هلجيت vitamin A deficiency اللي هي النقص هلجيت هل + +139 +00:10:37,340 --> 00:10:40,640 +في احتمال ايش احتماليته انه يتم نقص vitamin A في + +140 +00:10:40,640 --> 00:10:44,680 +الجسم الاحتمال انه يتم نقص vitamin A هو احتمال + +141 +00:10:44,680 --> 00:10:48,680 +ضعيف لانه حكينا ان vitamin A من الفات سوليو + +142 +00:10:48,680 --> 00:10:52,380 +بالفيتامين و الفات سوليو بالفيتامين بتتم تخزينها + +143 +00:10:52,380 --> 00:10:56,200 +في الخلايا الدهنية في الجسم ما بتتم اخراجها + +144 +00:10:56,200 --> 00:11:00,740 +فاحتمال النقص احتمال ضعيف لانه بتم تخزينه في الجسم + +145 +00:11:00,740 --> 00:11:05,580 +فهو rare ال deficiency rareلكن إذا صار deficiency، + +146 +00:11:05,580 --> 00:11:09,860 +إيش بيسبب أمراض؟ بسبب infectious disease، أمراض + +147 +00:11:09,860 --> 00:11:14,460 +معضية، زي الـ pneumonia اللي هي الالتهاب الرئوي، + +148 +00:11:14,460 --> 00:11:20,510 +measles حصبة، ودياريا shكمان ممكن يسبب + +149 +00:11:20,510 --> 00:11:24,970 +keratinization لإنه حكينا إنه من وضع ال vitamin A + +150 +00:11:24,970 --> 00:11:29,370 +إنه بيحافظ على الأنسجة و الخلايا الجلد فبيصير إذا + +151 +00:11:29,370 --> 00:11:34,130 +نقص هيصير keratinization اللي هو تأثير على + +152 +00:11:34,500 --> 00:11:38,400 +keratinization يعني هيصير تأثير على الجلد بيصير + +153 +00:11:38,400 --> 00:11:42,900 +تراكم للكيراتين تحت الجلد تراكم للكيراتين تحت + +154 +00:11:42,900 --> 00:11:47,140 +الجلد فبيصير الجلد عبارة عن ال dry جاف و rough + +155 +00:11:47,140 --> 00:11:51,080 +بيكون خشن و بيكون scaly جلد باهت لذا ال + +156 +00:11:51,080 --> 00:11:54,560 +keratinization تراكم الكيراتين تحت الجلد فبيكون + +157 +00:11:54,560 --> 00:12:00,280 +الجلد باهت و خشن و جاف كمان فقد او دفشانس ل + +158 +00:12:00,280 --> 00:12:04,970 +vitamin A بيعمل night blindnessاللي هو العشاء + +159 +00:12:04,970 --> 00:12:10,310 +الليلي ان الرؤية بالليل بتكون خافتة طب نيجي + +160 +00:12:10,310 --> 00:12:13,270 +للفيتامين التاني من الفات سوليو بالفيتامين اللي هو + +161 +00:12:13,270 --> 00:12:18,670 +فيتامين دهفيتامين دال بيصنع في الجسم body can make + +162 +00:12:18,670 --> 00:12:23,070 +فيتامين دال من أشعة الشمس بياخد من أشعة الشمس و + +163 +00:12:23,070 --> 00:12:26,570 +بيقوم فيتامين دال و كمان حكينا قبل هيك أنه + +164 +00:12:26,570 --> 00:12:31,670 +الكلسترول يعتبر الوحدة البنائية لتكوين فيتامين دال + +165 +00:12:31,670 --> 00:12:35,690 +إذا ففيتامين دال بياخدوا من أشعة الشمس و من + +166 +00:12:35,690 --> 00:12:40,570 +الكلسترول بتم تصنيع في الكيليا و الكبد in liver + +167 +00:12:40,570 --> 00:12:45,410 +and kidneyلو صار عندى اى مرض فى ال liver و ال + +168 +00:12:45,410 --> 00:12:49,150 +kidney هاد هيأثر على ال activation على تكوين + +169 +00:12:49,150 --> 00:12:53,610 +فيتامين ده لذن اذا صار اى مرض فى الكلية و الكبد + +170 +00:12:53,610 --> 00:12:59,470 +هيأثر على إنتاج فيتامين ده source of vitamin ده + +171 +00:12:59,470 --> 00:13:03,570 +لون الليمون موجود في vitamin ده لون موجود؟ موجود + +172 +00:13:03,570 --> 00:13:07,310 +فى ال fortified food فى الملك فى ال margarine فى + +173 +00:13:07,310 --> 00:13:10,750 +ال beef فى ال eggفي ال sun، من أشعة الشمس، في + +174 +00:13:10,750 --> 00:13:15,210 +الحليب، في ال margarine، في ال بيف البقرية، موجود + +175 +00:13:15,210 --> 00:13:19,810 +في أماكن، في أطعمة متعددة، مش مطلوب مننا نحفظ هذه + +176 +00:13:19,810 --> 00:13:26,630 +الأطعمة هذه صورة بتوضح كيف يتم إنتاج فيتامين دال، + +177 +00:13:26,630 --> 00:13:30,310 +مش مطلوبة مننا برضه، بس مطلوب مننا أن نعرف أن + +178 +00:13:30,310 --> 00:13:34,210 +فيتامين دال بيصنع في الجسم من أشعة الشمس و من + +179 +00:13:34,210 --> 00:13:36,950 +الكوليسترول في ال liver و ال kidney + +180 +00:13:39,720 --> 00:13:44,840 +vitamin dal function إيش وظائف vitamin dal؟ أول + +181 +00:13:44,840 --> 00:13:49,220 +وظيفة part of the bone making maintenance team هو + +182 +00:13:49,220 --> 00:13:54,300 +أحد عضاء فريق المحافظة على العضم، إله دور مهم في + +183 +00:13:54,300 --> 00:14:00,010 +المحافظة على العظامكيف بيحافظ على العضام؟ maintain + +184 +00:14:00,010 --> 00:14:03,330 +blood concentration of calcium and phosphorus + +185 +00:14:03,330 --> 00:14:07,890 +بيحافظ على مستوى مناسب من الكالسيوم و الفوسفوراس + +186 +00:14:07,890 --> 00:14:14,490 +في الدم و + +187 +00:14:14,490 --> 00:14:18,130 +الكالسيوم عضو مهم لبناء العضم و الفوسفوراس + +188 +00:14:18,510 --> 00:14:23,250 +mineralization of bone بيعمل على تمادن العظام + +189 +00:14:23,250 --> 00:14:28,210 +تمادن العظيم إيش يعني تمادن العظيم تمادن العظيم + +190 +00:14:28,210 --> 00:14:31,430 +raise blood calcium and phosphorus by increasing + +191 +00:14:31,430 --> 00:14:35,990 +absorption from gas digestive tract أنه بيرفع + +192 +00:14:35,990 --> 00:14:40,430 +مستوى ال calcium و ال phosphorus بزيادة انتصاصه عن + +193 +00:14:40,430 --> 00:14:46,310 +طريق انه يزيد انتصاصهإذا تمعدن العظم أني أزود كمية + +194 +00:14:46,310 --> 00:14:49,750 +الكالسيوم الفوسفوراس في العظام اللي بتجوه العظم + +195 +00:14:49,750 --> 00:14:54,070 +كيف بدي أرفع هذه؟ بعمل على زيادة امتصاص الكالسيوم + +196 +00:14:54,070 --> 00:14:58,130 +الفوسفوراس من الأمعاء للدم ان امتص الكالسيوم + +197 +00:14:58,130 --> 00:15:02,130 +الفوسفوراس من الأمعاء للدم Deposition of calcium + +198 +00:15:02,130 --> 00:15:05,850 +and phosphorus into bone ويسحب الكالسيوم + +199 +00:15:05,850 --> 00:15:10,710 +الفوسفوراس ويعملهم Deposition تراكم في العظم إنهم + +200 +00:15:10,710 --> 00:15:16,440 +ييجوا على العظمStimulating retention by kidney شو + +201 +00:15:16,440 --> 00:15:19,800 +يعني stimulating retention؟ ال retention أني أسحب + +202 +00:15:19,800 --> 00:15:23,900 +الكالسيوم و الفوسفرس من الكيلية للدم بدل ما يتم + +203 +00:15:23,900 --> 00:15:29,400 +إخراجه مع البال لكي الكيلية ال kidney توصلها فضلات + +204 +00:15:29,400 --> 00:15:32,570 +و بقايا الجسم اللي بتعملها يخرج مع ال urineجابل ما + +205 +00:15:32,570 --> 00:15:37,010 +تعمل إخراج هب يعمل فيتامين دال على ال retention + +206 +00:15:37,010 --> 00:15:41,370 +أنه يسحب الكالسيوم و الفوسفورس من الكيليا إلى الدم + +207 +00:15:41,370 --> 00:15:47,060 +يرجع تاني بدل ما يتم إخراجه مع ال bonedeficiency + +208 +00:15:47,060 --> 00:15:51,500 +لو قال فيتامين دال أهم الأسباب الأمراض اللى هتسير + +209 +00:15:51,500 --> 00:15:56,340 +أنه هيأثر على العظم هو بيصير infection بيصير عندى + +210 +00:15:56,340 --> 00:16:01,480 +عدوى و أهم إشي أنه بيصير عندى ostomalgia أو ركيزيا + +211 +00:16:01,480 --> 00:16:04,960 +إيش هي ال ostomalgia و الركيزيا؟ هذا الكساح + +212 +00:16:04,960 --> 00:16:09,480 +الركيزيا هو الكساح عند ال child و ال infant عند + +213 +00:16:09,480 --> 00:16:15,190 +الصغار السان ركيزيايطلق على الكساح عند صغار السن + +214 +00:16:15,190 --> 00:16:20,210 +استريو ماليزيا هو الكساح عند كبار السن عند ال + +215 +00:16:20,210 --> 00:16:26,550 +adult بيكون عند ال adult طب نحكي عن فيتمين E تالت + +216 +00:16:26,550 --> 00:16:30,850 +واحد من الفئة السليف الفيتامين هو فيتمين E فيتمين + +217 +00:16:30,850 --> 00:16:36,630 +E يعتبر antioxidant يعتبر antioxidant ايش يعني + +218 +00:16:36,630 --> 00:16:42,970 +antioxidant؟Antioxidant يعني ضد الأكسدة ضد الأكسدة + +219 +00:16:42,970 --> 00:16:47,230 +ضد الأكسدة يعني بتتطبط عملية الأكسدة Antioxidant + +220 +00:16:47,230 --> 00:16:49,950 +is a molecule that inhibit the oxidation of + +221 +00:16:49,950 --> 00:16:53,570 +another molecule بتطبط عملية الأكسدة Defender + +222 +00:16:53,570 --> 00:16:57,270 +against free radical كيف هي ال antioxidant بتكون + +223 +00:16:57,270 --> 00:17:01,950 +ضرورية للجسم؟انها بتدافع عن الجسم ضد ال free + +224 +00:17:01,950 --> 00:17:06,390 +radical ايش هي ال free radical انه لما يدخل فيروس + +225 +00:17:06,390 --> 00:17:10,130 +او بكتيريا للجسم لداخل الجسم يدخل كأن غريب زي + +226 +00:17:10,130 --> 00:17:14,270 +فيروس او بكتيريا الجسم بيروح بيقاوم هذا الفيروس او + +227 +00:17:14,270 --> 00:17:19,100 +بكتيريا كبدي قاومه وبينتج ال free radicalfree + +228 +00:17:19,100 --> 00:17:22,820 +radical هي دي عشان يتهاجم الفيروس و البكتيريا لكن + +229 +00:17:22,820 --> 00:17:26,860 +عيوبها انها بتهاجم كمان خلايا الجسم هي هتهاجم + +230 +00:17:26,860 --> 00:17:30,900 +الفيروس و البكتيريا و تقضي عليه و تهاجم كمان خلايا + +231 +00:17:30,900 --> 00:17:36,520 +الجسم يعني هتضر خلايا الجسم فإيش بيجي vitamin E + +232 +00:17:36,520 --> 00:17:41,140 +بيعمل اختزال لهذه free radical هو ضد ال X ده فإيش + +233 +00:17:41,140 --> 00:17:45,960 +هيعمل اختزال بيختزل ال free radical و بيوقف نشاطها + +234 +00:17:47,260 --> 00:17:51,680 +فهو Defender against free radical بيدافع عن الجسم + +235 +00:17:51,680 --> 00:17:55,520 +من ال free radical عشان ما تأثرش عليه may reduce + +236 +00:17:55,520 --> 00:18:00,020 +the risk of heart disease بقلل خطر الإصابة بأمراض + +237 +00:18:00,020 --> 00:18:04,540 +القلب widespread in food منتشر بشكل واسع في أطعمة + +238 +00:18:04,540 --> 00:18:09,760 +كثيرةeasily destroyed by heat processing الحرارة + +239 +00:18:09,760 --> 00:18:14,920 +بتأثر عليه vitamin E الحرارة بتأثر عليه وحساس + +240 +00:18:14,920 --> 00:18:20,120 +للحرارة بنطلق عليه heat sensitive ال deficiency ال + +241 +00:18:20,120 --> 00:18:24,000 +deficiency له برضه rare نادرة ما يحدث deficiency + +242 +00:18:24,000 --> 00:18:29,040 +لأن هو عبارة عن fat soluble vitamins بتم تخزين ال + +243 +00:18:29,040 --> 00:18:33,160 +excess منه بتم تخزينه في الجسم فإن يفقده أو أنه + +244 +00:18:33,160 --> 00:18:38,650 +يتم نقص فيه هذانادرا إيه لو صار deficientiation + +245 +00:18:38,650 --> 00:18:42,170 +مرض ممكن يصير بيصير عندي erythrocyte hemolysis + +246 +00:18:42,170 --> 00:18:47,670 +erythrocyte hemolysis هي تكسير لخلايا الدم الحمراء + +247 +00:18:47,670 --> 00:18:56,550 +تعني تكسير لخلايا الدم الحمراء vitamin K vitamin K + +248 +00:18:56,550 --> 00:19:00,250 +برضه fat-soluble vitamin aid in blood declutting + +249 +00:19:00,250 --> 00:19:04,750 +and bone mineralization بيلعب دور في تجلوت الدم + +250 +00:19:05,020 --> 00:19:11,380 +وتمادن العظم دور vitamin K بيلعب دور في تجلط الدم + +251 +00:19:11,380 --> 00:19:16,040 +وتمادن العظم deficiency causes hemorrhagic disease + +252 +00:19:16,040 --> 00:19:22,480 +إذا صار فيه نقص هيصير أمراض نزيفية أمراض نزف ليش + +253 +00:19:22,480 --> 00:19:25,680 +لأن دوره أنه يلعب دور في تجلط الدم وتخسر الدم إذا + +254 +00:19:25,680 --> 00:19:30,190 +نقص بديصير أمراض نزيف مش تجلط للدم فيه نزيفsource + +255 +00:19:30,190 --> 00:19:34,610 +من وين بنحصل على vitamin K هو vitamin بتم تصنيعه + +256 +00:19:34,610 --> 00:19:37,450 +من البكتيريا الموجودة في اللمعاء من ال + +257 +00:19:37,450 --> 00:19:41,990 +gastrointestinal tract و بتم امتصاصه وتخزينه في ال + +258 +00:19:41,990 --> 00:19:47,050 +liver إذا مصدره من بكتيريا موجودة في اللمعاء و بتم + +259 +00:19:47,050 --> 00:19:52,270 +امتصاصه وتخزينه في ال liver بيستخدم لتصنيع عوامل + +260 +00:19:52,270 --> 00:19:57,630 +التجلط ال clothing factorهك بنقول خلصنا الفات + +261 +00:19:57,630 --> 00:20:01,130 +سوليوبل فيتامين و حكينا عن كل واحد منهم على السريع + +262 +00:20:01,130 --> 00:20:03,810 +اللي هتنيجي على القسم التاني اللي هم ال water + +263 +00:20:03,810 --> 00:20:08,170 +soluble vitamin ال water soluble vitamin هم + +264 +00:20:08,170 --> 00:20:13,590 +vitamin B و C بس B بيحكوا عنها B complex لأنهم + +265 +00:20:13,590 --> 00:20:19,010 +عبارة عن 8 أنواع من B بس بنطلق عليهم باسم B كلهم B + +266 +00:20:19,010 --> 00:20:23,630 +لكن هم B complex عددهم 8 مع vitamin C عن ال water + +267 +00:20:23,630 --> 00:20:29,450 +soluble vitamin بيطلعوا 9خصائص الـ water soluble + +268 +00:20:29,450 --> 00:20:33,890 +vitamins اللي حكيناها في الجدول إنها لا تلعب دور + +269 +00:20:33,890 --> 00:20:38,870 +في إنتاج الطاقة إنه هي non energy producing لا + +270 +00:20:38,870 --> 00:20:45,010 +تنتج الطاقة ولكن تساهم في إنتاج الطاقةهي بتساعد كـ + +271 +00:20:45,010 --> 00:20:49,010 +Co-factor بتساعد الإنزيم على إنتاج الطاقة + +272 +00:20:49,010 --> 00:20:52,630 +بيكومplex فيتمين are often associated with giving + +273 +00:20:52,630 --> 00:20:57,770 +a person more energy بتساهم في إنتاج الطاقة فبتزود + +274 +00:20:57,770 --> 00:21:01,030 +طاقة this is due to the fact this vitamin each + +275 +00:21:01,030 --> 00:21:04,370 +play different role in energy metabolism أنها + +276 +00:21:04,370 --> 00:21:08,570 +بتلعب كيف بتساهم بإعطاء الشخص الطاقة ليس عن طريق + +277 +00:21:08,570 --> 00:21:13,840 +إنتاج الطاقة وإنهي بتنتجش الطاقة من نفسها، هي + +278 +00:21:13,840 --> 00:21:17,920 +نفسها تزوّد الجسم بالطاقة، لأ وإنما إنها تساهم كـ + +279 +00:21:17,920 --> 00:21:24,640 +Co-factor كمساعد لإنتاج الطاقةبالرغم من أن هذه + +280 +00:21:24,640 --> 00:21:31,460 +الفيطامينات مميزة بالماء، لا تتم تخزينها في الجسم + +281 +00:21:31,460 --> 00:21:35,740 +حكيينة، بتم إخراج الزائد منها عبر الكدن مع + +282 +00:21:35,740 --> 00:21:39,440 +اليورين، تتدخل في الماء، وتتدخل في الماء، وتتم + +283 +00:21:39,440 --> 00:21:42,840 +إكسكريتها من الجسم من خلال اليورين، من خلال + +284 +00:21:42,840 --> 00:21:46,600 +اليورين، لذلك، من المهم أن تتناول الطعام مليء في + +285 +00:21:46,600 --> 00:21:51,280 +هذه الفيطامينات كل يوم، لكي توفر الجسم ما يحتاجه + +286 +00:21:51,760 --> 00:21:55,880 +إذا ان هي حاجة ان انا ولا تخزن في الجسم بدوف المي + +287 +00:21:55,880 --> 00:21:59,580 +يتم إخراجها مع ال urine لازم أتناولها كل فترة من + +288 +00:21:59,580 --> 00:22:06,260 +يوم لتلت أيام عشان أقضي حاجة الجسممن الأمثلة على + +289 +00:22:06,260 --> 00:22:09,100 +ال water-soluble vitamin في عندنا ال بيكمبليكس + +290 +00:22:09,100 --> 00:22:15,340 +فيتامين ال بيكمبليكس يعتبر ك coenzyme يعني بيحفظ + +291 +00:22:15,340 --> 00:22:20,440 +ال انزيم found in the same food ال بيكمبليكس + +292 +00:22:20,440 --> 00:22:25,410 +فيتامين هم كمبليكس عبارة عن تمانيةكلهم موجودين في + +293 +00:22:25,410 --> 00:22:29,490 +نفس الطعام يعني لو قلتلك واحدة نوع مثلا في ال B + +294 +00:22:29,490 --> 00:22:32,990 +-complex الثيامين إذا الثيامين موجود في الجزر يبدأ + +295 +00:22:32,990 --> 00:22:36,710 +كل ال B-complex التمانية كلهم موجودين في الجزر فال + +296 +00:22:36,710 --> 00:22:40,970 +single deficiency rare أني أفقد واحد منهم هذا إشي + +297 +00:22:40,970 --> 00:22:46,580 +نادر Act together in metabolism بتلعب دورفي الـ + +298 +00:22:46,580 --> 00:22:50,920 +Metabolism في إنتاج الطاقة Metabolic pathway used + +299 +00:22:50,920 --> 00:22:54,960 +by protein, carbohydrate and fat حكينا قبل هيك أن + +300 +00:22:54,960 --> 00:22:58,180 +مصدر الطاقة الـ carbohydrate ومخزن الطاقة هي + +301 +00:22:58,180 --> 00:23:01,980 +الدهون وطاقة الخلايا للبناء هي البروتين يعني هدول + +302 +00:23:01,980 --> 00:23:07,550 +مسئولين عن إنتاج الطاقة للجسم الـ Vitaminبتساهم في + +303 +00:23:07,550 --> 00:23:10,030 +إنتاج الطاقة، بتساعد هدول الـ carbohydrate + +304 +00:23:10,030 --> 00:23:13,730 +والبروتين والفت على إنهم يعطوا الطاقة للجسم، لكن + +305 +00:23:13,730 --> 00:23:19,110 +هي بنفسها لا تنتج الطاقة مين هما الـ B-complex + +306 +00:23:19,110 --> 00:23:22,830 +vitamin؟ فيها الناس صيامين، اللي هو B1, riboflavin + +307 +00:23:22,830 --> 00:23:28,830 +B2, niacin B3, pantothenic acid, biotin, pyridoxin + +308 +00:23:28,830 --> 00:23:33,570 +B6 و الـ folate و vitamin B12، هدولة كلهم vitamin + +309 +00:23:33,570 --> 00:23:38,380 +Bفهم أكتر من نوع أطلقنا عليهم B Complex Vitamin + +310 +00:23:38,380 --> 00:23:45,280 +وكلهم موجودين في نفس نوع الطعام إيش وظائف ال B + +311 +00:23:45,280 --> 00:23:49,720 +Complex؟ أول وظيفة هي Energy Metabolism حكينا أنها + +312 +00:23:49,720 --> 00:23:54,670 +بتساهم في إنتاج الطاقةو هنجسم اللي هيهم مين منهم + +313 +00:23:54,670 --> 00:23:57,830 +اللي بتساهم في إنتاج الطاقة و هذا مش مطلوب منها، + +314 +00:23:57,830 --> 00:24:02,110 +مطلوب منها نعرف بس الوظائف كعنوين ال بيك كومبليكس + +315 +00:24:02,110 --> 00:24:05,490 +أول وظيفة إلها energy metabolism إنتاج الطاقة + +316 +00:24:05,490 --> 00:24:09,910 +تساهم في إنتاج الطاقة red blood cell sensitives + +317 +00:24:09,910 --> 00:24:13,970 +إنه بتساهم في إنتاج خلايا الدم الحمراء كوريات الدم + +318 +00:24:13,970 --> 00:24:18,960 +الحمراءHomocysteine Metabolism اللي هو عملية + +319 +00:24:18,960 --> 00:24:23,100 +Metabolism لحاجة نسميها الـ Homocysteine + +320 +00:24:26,000 --> 00:24:31,860 +vitamin C اسمه الكيميائي بنطلق عليه اسم ascorbic + +321 +00:24:31,860 --> 00:24:36,820 +acid ascorbic acid او vitamin C senses by most + +322 +00:24:36,820 --> 00:24:42,060 +animal بتتم تصنيعه من معظم الحيوانات لكن الإنسان + +323 +00:24:42,060 --> 00:24:47,000 +لأ كل الحيوانات بتصنعه ما عدا الإنسان الإنسان غير + +324 +00:24:47,000 --> 00:24:51,460 +قادر على تصنيع vitamin Cdecrease absorption with + +325 +00:24:51,460 --> 00:24:56,220 +high intake اكيد هيقلل الامتصاص اذا انا عند زيادة + +326 +00:24:56,220 --> 00:24:59,900 +التناولة اذا الجسم حاسس ان هو موجود بكميات كافية + +327 +00:24:59,900 --> 00:25:04,620 +هيقلل الامتصاص ال excess منه الكميات الزائدة هيصير + +328 +00:25:04,620 --> 00:25:10,660 +execution عملية اخراج لها food source of vitamin C + +329 +00:25:10,660 --> 00:25:16,890 +وين موجود؟ موجود في الcitrus .. citrus fruit اللي + +330 +00:25:16,890 --> 00:25:20,890 +هي الفواكه الحمضية موجود في ال .. في ال potato، في + +331 +00:25:20,890 --> 00:25:24,230 +ال green pepper، في الفلفل الأخضر، في الزهرة، في + +332 +00:25:24,230 --> 00:25:27,470 +ال broccoli، في ال strawberry، فالورة، في ال + +333 +00:25:27,470 --> 00:25:31,350 +romaine lettuce، الخس، في ال spinach، السبانخ، مش + +334 +00:25:31,350 --> 00:25:36,830 +مطلوب إننا نحفظ اللي أطعمهاfunction of vitamin C، + +335 +00:25:36,830 --> 00:25:41,650 +إيش وظائف vitamin C؟ vitamin C يعتبر ضي vitamin E، + +336 +00:25:41,650 --> 00:25:46,950 +إن هو reducing agent، يعني antioxidant، vitamin C + +337 +00:25:46,950 --> 00:25:53,350 +و E يعتبروا antioxidant reducing agentأيش وظيفته؟ + +338 +00:25:53,350 --> 00:25:58,170 +بيحفظ ال iron absorption enhanced يحفظ انتصاص + +339 +00:25:58,170 --> 00:26:03,550 +الحديد، يحفظ انتصاص الحديد عشان هيك مثلا لو واحد + +340 +00:26:03,550 --> 00:26:07,590 +عنده نقص في الحديد، بيعطوه حبوب حديد، بيحكولي يفضل + +341 +00:26:07,590 --> 00:26:11,850 +لو تتناول الحبوب الحديد مع عصير برتقال عشان عصير + +342 +00:26:11,850 --> 00:26:16,130 +البرتقال يحتوي على vitamin C و vitamin C بيحفظ + +343 +00:26:16,130 --> 00:26:21,280 +الانتصاصSynthesis of collagen كمان هو مسئول عن + +344 +00:26:21,280 --> 00:26:25,060 +تصنيع الكولاجين اللى موجود فى الجلد Immune + +345 +00:26:25,060 --> 00:26:29,940 +function اللى وظائف منعية ايش وظيفته المنعية بيحكى + +346 +00:26:29,940 --> 00:26:33,160 +اللى doesn't prevent common cold or flu but may + +347 +00:26:33,160 --> 00:26:37,420 +reduce duration of symptom day by day ان هو راجيت + +348 +00:26:37,420 --> 00:26:40,700 +لما الواحد يصير معاه influenza بيحكوله اشرب عصير + +349 +00:26:40,700 --> 00:26:46,520 +برتقال او اتناول البرتقال هذا بيجلل اللى هو الفترة + +350 +00:26:47,240 --> 00:26:50,940 +Vitamin C الموجود في عصير البرتقال بيجلل فترة + +351 +00:26:50,940 --> 00:26:55,760 +أعراض المرض ولا يمنع ال influenza وعراض ال burn + +352 +00:26:55,760 --> 00:27:01,280 +وإنما يقلل فترة هذه الأعراضإذا لا يقضي على الفيروس + +353 +00:27:01,280 --> 00:27:05,420 +وإنما يقلل الفترة كمان و من وضع فيه wound healing + +354 +00:27:05,420 --> 00:27:09,280 +اللي هو التقام الجروح يساعد في التقام الجروح + +355 +00:27:09,280 --> 00:27:12,840 +easily lost through cooking برضه هو عبارة عن heat + +356 +00:27:12,840 --> 00:27:17,880 +sensitive حساس للحرارة فبيفقد مع درجات الحرارة + +357 +00:27:17,880 --> 00:27:22,500 +العالية لإن لو عصير البرتقال سخنتي خلاص vitamin C + +358 +00:27:22,500 --> 00:27:26,400 +بيتكسر بيروح مش هيدل موجود sensitive to heat + +359 +00:27:28,720 --> 00:27:33,140 +vitamin C deficiency إذا صار عندي فقد أو نقص فيه + +360 +00:27:33,140 --> 00:27:38,620 +vitamin C أشهر مرض بينتج عن نقص vitamin C هو مرض + +361 +00:27:38,620 --> 00:27:42,860 +الـscurvy الاسقربوت مرض scurvy disease اللي هو + +362 +00:27:42,860 --> 00:27:47,620 +الاسقربوت disease characterized by weakness, small + +363 +00:27:47,620 --> 00:27:52,960 +hemorrhage throughout the body that cause gum and + +364 +00:27:52,960 --> 00:27:58,030 +skin to bleedهو مرض بيكون عبارة عن خصائصه أنه + +365 +00:27:58,030 --> 00:28:03,690 +بيكون ضعف عام في الجسم، بيكون فيه نزيف في مسامات + +366 +00:28:03,690 --> 00:28:08,390 +الجلد، مسامات الجلد بتفرز دم، ممكن نزيف في اللثة و + +367 +00:28:08,390 --> 00:28:14,580 +سقوط الأسنانفي عندنا صورة تحت مثلا Sclerotic + +368 +00:28:14,580 --> 00:28:18,580 +Rosary، هاي من المرض أنه بيكون عندنا بروز للقفص + +369 +00:28:18,580 --> 00:28:22,840 +الصدري، القفص الصدري بارز للأمام، في عندنا بيكون + +370 +00:28:22,840 --> 00:28:28,460 +نزيف في اللثة، تساقط للأسنان، في عندنا Volicular + +371 +00:28:28,460 --> 00:28:32,580 +Hemorrhage، اللي هو نزيف في مسامات الجلب، تحت + +372 +00:28:32,580 --> 00:28:38,820 +الجلب بيلاقي بُقع زي نزيفVitamin C excess لو كان + +373 +00:28:38,820 --> 00:28:43,940 +في عندنا كميات زائدة من vitamin C اللي هو زيادة في + +374 +00:28:43,940 --> 00:28:47,940 +حاجة الجسم وهي زيادة أكيد rare لأن هو water + +375 +00:28:47,940 --> 00:28:51,740 +soluble vitamin بيصيرله excretion بيصيرله إخراج بس + +376 +00:28:51,740 --> 00:28:56,920 +إذا كان بكميات زائدة بسبب خلال ماء بيصير عندي مرض + +377 +00:28:56,920 --> 00:29:02,710 +hemochromatosisHemochromatosis معناها زيادة نسبة + +378 +00:29:02,710 --> 00:29:07,150 +الحديد في الجسم زيادة تخزين الحديد Iron overload + +379 +00:29:07,150 --> 00:29:12,250 +لأنه حكينا أن Vitamin C بيحفظ امتصاص الحديد فإذا + +380 +00:29:12,250 --> 00:29:16,710 +زاد Vitamin C هيمتص كمية من الحديد الزيادة هيزود + +381 +00:29:16,710 --> 00:29:20,910 +كمية امتصاص الحديد وسبب مرض اسمه Hemochromatosis + +382 +00:29:20,910 --> 00:29:27,600 +اللي هو Iron overload زيادة الحديدأجزالات كيدنستون + +383 +00:29:27,600 --> 00:29:32,140 +اللي هي حصاوي في الكيلة من نوع أجزالات أجزالات + +384 +00:29:32,140 --> 00:29:35,900 +كيدنستون اللي هي حصاوي من نوع أجزالات ايه ال tooth + +385 +00:29:35,900 --> 00:29:40,720 +enamel؟ اللي هو تآكل للأسنان، بيصير عندي تآكل + +386 +00:29:40,720 --> 00:29:42,080 +للأسنان + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/hVJVg6dDeBU_raw.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/hVJVg6dDeBU_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..8c6082c5a1cf35077eb0ba45f883534b3bb1263a --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/hVJVg6dDeBU_raw.srt @@ -0,0 +1,828 @@ +1 +00:00:00,000 --> 00:00:03,080 +هنا على الصورة هذه، على الخط اللي فوق أول شيء، هنا + +2 +00:00:03,080 --> 00:00:05,680 +عرفنا الصيغة العامة والـ structure العامة للحمض + +3 +00:00:05,680 --> 00:00:09,900 +الأميني إنه بيتكون من جمعة كاربو المركزية مرتبطة + +4 +00:00:09,900 --> 00:00:15,820 +بهيدروجين وارتشين وكاربوكسين وامينوبرونلو جينا + +5 +00:00:15,820 --> 00:00:21,540 +هالخط اللي فوقها على رموز جيت عنه أن أول خط أحمر + +6 +00:00:21,540 --> 00:00:25,100 +فوق اللي هي ال repeat units في عندنا صيغة عاملة + +7 +00:00:25,100 --> 00:00:29,320 +الحمد للأمين في في النص مجموعة carbon من فوق مرتبط + +8 +00:00:29,320 --> 00:00:33,620 +فيها مجموعة هيدروجين من الأسفل مرتبط فيها ال R + +9 +00:00:33,620 --> 00:00:37,340 +group اللي هي ال side chain على اليمين مرتبط فيها + +10 +00:00:37,340 --> 00:00:41,320 +ال C double bond O اللي هي الكربوكسيل group على + +11 +00:00:41,320 --> 00:00:46,250 +اليسارمرتبط فيها N-H اللي هي مجموعة الأمين + +12 +00:00:46,250 --> 00:00:51,070 +الأمينوجروب تمام؟ هي أول حمض أميني جنبه مرتبط فيه + +13 +00:00:51,070 --> 00:00:55,550 +حمض أميني تاني اللي هي الكربونة المركزية وهيدروجين + +14 +00:00:55,550 --> 00:00:59,730 +في الأعلى وR في الأسفل وعلى اليمين كاربوكسيل جروب + +15 +00:00:59,730 --> 00:01:04,810 +وعلى الجمال أمينوجروب هدول مجموعة أحماض أمينية أجت + +16 +00:01:04,810 --> 00:01:08,730 +اترتبت جانب بعض مرتبطة مع بعضها البعض في + +17 +00:01:08,730 --> 00:01:14,740 +بيبتايدبونرابطة بيبتيديا فكونتلي البروتين طب وين + +18 +00:01:14,740 --> 00:01:19,040 +ال peptide bond جاية؟ ال peptide bond أجت ورتبطت + +19 +00:01:19,040 --> 00:01:24,780 +بيهمجموعة كربوكسيل من الحمض الأميني الأول ومجموعة + +20 +00:01:24,780 --> 00:01:28,680 +أمين من الحمض الأميني التاني إذا ملاحظين الحمض + +21 +00:01:28,680 --> 00:01:32,300 +الأميني الأول و الحمض الأميني التاني في بينهم + +22 +00:01:32,300 --> 00:01:35,300 +رابطة هي الرابطة اللي في النص اللي فصلت الحمض + +23 +00:01:35,300 --> 00:01:39,680 +الأميني الأول عن التاني بنسميها peptide bond و + +24 +00:01:39,680 --> 00:01:45,880 +موقعها تيجي بين مجموعة كربوكسيل من حمض أميني + +25 +00:01:45,880 --> 00:01:51,230 +ومجموعة أمين من حمض أميني آخرماش عملة هاي + +26 +00:01:51,230 --> 00:01:55,850 +الـpeptide bond هي المفروض ان الـCOOH الكربوكسيلي + +27 +00:01:55,850 --> 00:02:01,490 +جروب و الـN و الـAmino group NH2 هي بتعمل على نزع + +28 +00:02:01,490 --> 00:02:09,530 +جزء ما تنزع H2O تنزع جزء ما بتاخد من الكربوكسيلي + +29 +00:02:09,530 --> 00:02:14,290 +جروب بتاخد منها OH تبدلها C double bond O و بتاخد + +30 +00:02:14,290 --> 00:02:19,410 +من الـNH2 بتاخد مجموعة هيدروجينفهيك الصراطين + +31 +00:02:19,410 --> 00:02:23,990 +ياخدوا OH من هنا و Hydrogen من هنا يعني H2O اللي + +32 +00:02:23,990 --> 00:02:28,450 +هو جزء ماء فالرابطة البيبتيدية تكون الرابطة + +33 +00:02:28,450 --> 00:02:34,410 +البيبتيدية بينتج عنها خروج ماء وهذا التفاعل يسمى + +34 +00:02:34,410 --> 00:02:39,870 +Condensation Reaction تفاعلات اللي بتنتج عنها خروج + +35 +00:02:39,870 --> 00:02:45,970 +ماء بنسميها Condensation Reaction لأنه كون عنها + +36 +00:02:45,970 --> 00:02:52,090 +جزء ماءإذا انتفاع التكون الرابط البيبتيدية يعتبر + +37 +00:02:52,090 --> 00:02:59,980 +Condensation Reaction لأنه نتج عنه جزيع ماء H2Oطيب + +38 +00:02:59,980 --> 00:03:03,820 +تمام، إذا البروتين بيتكون عن طريق مجموعة أحماض + +39 +00:03:03,820 --> 00:03:08,840 +أمينية ترتبط في روابط بيبتيدية وين بتيجي الرابطة + +40 +00:03:08,840 --> 00:03:14,260 +بين مجموعة كربوكسيل ومجموعة أمين؟ إيش بينتج عنها + +41 +00:03:14,260 --> 00:03:19,440 +خروج ماء، نزع جزء ماء؟ لذلك سمينا التفاعل تكون + +42 +00:03:19,440 --> 00:03:25,990 +رابط البيبتيدية بـ Condensation Reactionاللي جيت + +43 +00:03:25,990 --> 00:03:29,370 +على الأطراف في البروتين في البروتين هذا اللي اتكون + +44 +00:03:29,370 --> 00:03:32,070 +في السلسلة اللي فوق اللي انتوا شايفينها على + +45 +00:03:32,070 --> 00:03:35,910 +الأطراف في حمض أميني فيه مجموعة أمين و group + +46 +00:03:35,910 --> 00:03:40,650 +مرتبطتش بحمض أميني آخر وعلى الطرف من الجهة التانية + +47 +00:03:40,650 --> 00:03:44,190 +من اليمين في عندنا مجموعة حمض أميني فيه مجموعة + +48 +00:03:44,190 --> 00:03:48,290 +Carboxyl مرتبطتش يعني في عندنا مجموعة Carboxyl + +49 +00:03:48,290 --> 00:03:53,330 +free حرة في مجموعة أمين free برضه حرة على الأطراف + +50 +00:03:53,330 --> 00:03:57,000 +بتكونهذه بنسميها مجموعة الأمين الحرة بنسميها + +51 +00:03:57,000 --> 00:04:02,500 +Anterminous Anterminous هو الحمض الأميني الذي + +52 +00:04:02,500 --> 00:04:09,020 +يحتوي على free amino group لم تشارك في تكوين + +53 +00:04:09,020 --> 00:04:14,360 +الرابطة البيبتدية إذا مجموعة الأمين الـ free بتكون + +54 +00:04:14,360 --> 00:04:18,700 +الحرة التي لم تشارك في تكوين الرابطة بنسميها + +55 +00:04:18,700 --> 00:04:24,380 +Anterminousطب و الـ C-terminus .. C-terminus برضه + +56 +00:04:24,380 --> 00:04:29,540 +هي الحمض الأميني اللي يحتوي على free carboxyl + +57 +00:04:29,540 --> 00:04:35,580 +group لم تشارك في تكوين الرابط اللي بيبتديهايعني + +58 +00:04:35,580 --> 00:04:39,320 +بنفهم احنا عند تكول ال protein تيجي مجموعة أحماض + +59 +00:04:39,320 --> 00:04:44,720 +أمينية ترتبط مع بعضها البعض في روابط بيبتيدية وين + +60 +00:04:44,720 --> 00:04:48,440 +بتتكون الروابط البيبتيدية؟ بين Carboxyl group من + +61 +00:04:48,440 --> 00:04:53,510 +حمض أميني أميني group من حمض أميني آخروشو بتعمل + +62 +00:04:53,510 --> 00:04:57,730 +على نزع جزاق ماء؟ بسمّينا التفاعل Condensation + +63 +00:04:57,730 --> 00:05:03,110 +Reaction لأنه بينتج عنه جزاق ماء في مجموعة الأحمض + +64 +00:05:03,110 --> 00:05:07,350 +الأميني هاي بيضل على الأطراف مجموعة أمينو جروب مش + +65 +00:05:07,350 --> 00:05:12,070 +مرتبطة على الطرف من جهة مجموعة كربوكسيل جروب مش + +66 +00:05:12,070 --> 00:05:16,930 +مرتبطة على جهةالمجموعة الكربوكسيلة الحرة اللتي لم + +67 +00:05:16,930 --> 00:05:20,450 +ترتبط ولم تشارك في تكوين الرابطة اللي بيبتديها + +68 +00:05:20,450 --> 00:05:25,450 +بسميها C-terminus ومجموعة ال amino group الحرة ال + +69 +00:05:25,450 --> 00:05:30,030 +free اللتي لم تشارك في تكوين الرابطة بسميها N + +70 +00:05:30,030 --> 00:05:30,950 +-terminus + +71 +00:05:33,570 --> 00:05:37,230 +وانا classification of amino acid according source + +72 +00:05:37,230 --> 00:05:41,910 +تقسيم الأحماض الأمينية بناء على مصدر بيقسموها + +73 +00:05:41,910 --> 00:05:46,330 +لقسمين في عندنا أحماض أمينية أساسية essential + +74 +00:05:46,330 --> 00:05:51,470 +amino acid وفي non-essential amino acid غير ضرورية + +75 +00:05:51,470 --> 00:05:55,690 +أحماض الأمينية الأساسية هي الأحماض اللي بيكون + +76 +00:05:55,690 --> 00:06:01,130 +الجسم غير قادر على تصنيعها لازم تكون موجودة في + +77 +00:06:01,130 --> 00:06:06,020 +الوجبةincapable of forming requests and must be + +78 +00:06:06,020 --> 00:06:11,840 +required in time الجسم غير قادر على تصنيعها و لازم + +79 +00:06:11,840 --> 00:06:15,340 +تكون موجودة في الواجبات، في الأكل اليومي اللي + +80 +00:06:15,340 --> 00:06:21,390 +بيتناوله، فعددها تسعةالـ Non-essential أمينواسد + +81 +00:06:21,390 --> 00:06:26,090 +الغير ضرورية الجسم قادر على تصنيحها بيقدر يصنحها + +82 +00:06:26,090 --> 00:06:32,130 +مش ضروري أني أتأكد أنها موجودة في وجباتي وعددها 11 + +83 +00:06:32,130 --> 00:06:36,570 +Non-essential الجسم قادر على تصنيحها Essential + +84 +00:06:36,570 --> 00:06:40,610 +الجسم غير قادر على تصنيحها لازم أتأكد أن أنا + +85 +00:06:40,610 --> 00:06:46,140 +أخدتها عن طريق الوجبات اليومية وعددها 9الـ get non + +86 +00:06:46,140 --> 00:06:51,240 +-essential أكتر 11 يعني صح ولا خطأ إذا حكيت الجسم + +87 +00:06:51,240 --> 00:06:57,480 +قادر على تصنيع معظم الأحماض الأمنية صح الجسم قادر + +88 +00:06:57,480 --> 00:07:05,310 +على تصنيع معظم الأحماض الأمنية اللي هي عددها 11طيب + +89 +00:07:05,310 --> 00:07:10,110 +عندنا أبسط حمض أميني هو simplest and smallest + +90 +00:07:10,110 --> 00:07:14,050 +amino acid هو عبارة عن ال glycine ال glycine هو + +91 +00:07:14,050 --> 00:07:19,010 +أبسط حمض أميني ليش؟ لأنه احنا حكينا كل حمض أميني + +92 +00:07:19,010 --> 00:07:22,950 +يختلف عن التاني بال side chain بال R وال R في ال + +93 +00:07:22,950 --> 00:07:27,710 +glycine هي عبارة عن ذرة هيدروجين فقط عبارة عن H + +94 +00:07:27,710 --> 00:07:33,210 +ذرة هيدروجين فهو بسيط جدا يكون عبارة عن كربونة + +95 +00:07:33,210 --> 00:07:33,950 +مركزية + +96 +00:07:39,760 --> 00:07:43,140 +زرّة هيدروجين من الجهة الأخرى الـ R-group هي عبارة + +97 +00:07:43,140 --> 00:07:47,900 +عن زرّة هيدروجين فهو أبسط حمض أميني لـ glycine أما + +98 +00:07:47,900 --> 00:07:52,600 +الحمض الأمين الشهد الفريد هو البرولين حكينا + +99 +00:07:52,600 --> 00:07:57,640 +البرولين هو الحمض الأمين الوحيد الذي يحتوي على + +100 +00:07:57,640 --> 00:08:03,070 +amino group وليس amino groupماحتويش على مجموعة + +101 +00:08:03,070 --> 00:08:06,490 +بنسميها amino group بإنما بنسميها amino group أو + +102 +00:08:06,490 --> 00:08:10,630 +secondary amino group بنسميها، ليش؟ لأنه بتكون فيه + +103 +00:08:10,630 --> 00:08:15,050 +مجموعة الأمين مرتبطة في الكربون المركزية ومرتبطة + +104 +00:08:15,050 --> 00:08:18,730 +مع الـR، مع الـside chain، مع مجموعة الـside chain + +105 +00:08:18,730 --> 00:08:23,030 +اللي بتكون موجودة، فهي بنسميها amino group مش + +106 +00:08:23,030 --> 00:08:24,610 +amino group + +107 +00:08:27,190 --> 00:08:32,330 +بنجي لتصنيف الأحماض الأمنية بناء على ال polarity + +108 +00:08:32,330 --> 00:08:36,290 +كيف بدي أحدد ال polarity القطبية للأحماض الأمنية؟ + +109 +00:08:36,290 --> 00:08:39,310 +من خلال النظر إلى ال sided chain إلى ال R group + +110 +00:08:39,310 --> 00:08:44,010 +هذه مجموعة ال R إيش أجي مكانها؟أول شيء تصنيف + +111 +00:08:44,010 --> 00:08:47,530 +الأحماض الأمينية بناء على الـ polarity تُقسم إلى + +112 +00:08:47,530 --> 00:08:53,250 +قسمين في منها polar قطبية في منها non polar non + +113 +00:08:53,250 --> 00:08:57,790 +polar يعني غير قطبية يعني هي الأحماض الأمينية + +114 +00:08:57,790 --> 00:09:06,520 +تحتوي على C وH في ال side chain فقطالنانبولان هي + +115 +00:09:06,520 --> 00:09:10,420 +الـ amino acid that contains C وH in their side + +116 +00:09:10,420 --> 00:09:14,100 +chain لما أجى أطلع على الاري جروب هاي إيش فيها + +117 +00:09:14,100 --> 00:09:19,520 +بلاقي فيها بس يا ذرات كربون يا هيدروجين أو كربون + +118 +00:09:19,520 --> 00:09:24,470 +وهيدروجينالألاجي في الـ side-chain كربون وهيدروجين + +119 +00:09:24,470 --> 00:09:29,050 +فقط، لا تحتوي أي مجموعة قطبية أخرى، وهي غير قادرة + +120 +00:09:29,050 --> 00:09:34,250 +على تكوين روابط أيونية ولا هيدروجينية ولا قادرة + +121 +00:09:34,250 --> 00:09:39,430 +على كسب أو فقد الإلكترونات، هي الـ non-polar amino + +122 +00:09:39,430 --> 00:09:42,930 +acidتكون تحتوي في الـ sided chain على كاربون + +123 +00:09:42,930 --> 00:09:47,830 +وهيدروجين فقط غير قادر على تكوين روابط هيدروجينية + +124 +00:09:47,830 --> 00:09:54,170 +ولا ايونية ولا قادر على فقد وكسب الالكترونال الجزء + +125 +00:09:54,170 --> 00:09:57,730 +التاني من الأحماض الأمينية هي الـ polar القطبية + +126 +00:09:57,730 --> 00:10:03,810 +القطبية مقسمة لقسمين في منها بتكون قطبية مشحونة + +127 +00:10:03,810 --> 00:10:08,050 +وفي قطبية غير مشحونة يعني في منها polar charged + +128 +00:10:08,050 --> 00:10:13,530 +وفي polar unchargedالـ Bowler سواء كانت charged أو + +129 +00:10:13,530 --> 00:10:17,850 +uncharged الـ side chain بيكون يحتوي على مجموعة + +130 +00:10:17,850 --> 00:10:22,030 +قطبية لو جيتي على الـ R على الـ side chain تطلع + +131 +00:10:22,030 --> 00:10:26,850 +عليه بتلاقي يحتوي على مجموعة قطبية إيش هي + +132 +00:10:26,850 --> 00:10:30,930 +المجموعات القطبية؟ ممكن تكون OH اللي هي Hydroxyl + +133 +00:10:30,930 --> 00:10:36,290 +group هي مجموعة قطبية OH Hydroxyl group معناها C + +134 +00:10:36,290 --> 00:10:42,090 +double bond O اللي هي الكربوني ال groupCWO هي + +135 +00:10:42,090 --> 00:10:46,190 +الكربوني للجروب فهي عندنا الـ sulfhydryl للجروب + +136 +00:10:46,190 --> 00:10:51,130 +الـ sulfhydryl للجروب اللي هي الـSH في عندنا + +137 +00:10:51,130 --> 00:10:56,450 +الأمين للجروب اللي هي الـH2 أمين للجروب هدولة كلهم + +138 +00:10:56,450 --> 00:11:00,650 +مجموعات قطبيةلو شوفتهم في الـ sided chain بعرف إنه + +139 +00:11:00,650 --> 00:11:06,150 +هذا بولا طب هل هو charged ولا uncharged? uncharged + +140 +00:11:06,150 --> 00:11:09,110 +يعني ماعلهوش شحنة لا عليه positive ولا عليه + +141 +00:11:09,110 --> 00:11:13,170 +negative فيه مجموعة قطبية لكن لا هي positive ولا + +142 +00:11:13,170 --> 00:11:17,370 +هي negative طب ليه charged؟ charged معناه إنه + +143 +00:11:17,370 --> 00:11:21,470 +يحتوي على مجموعة قطبية بشحنة إما بتكون الشحنة + +144 +00:11:21,470 --> 00:11:26,200 +positive لـcharged إذا كانت positive يعني باسأو + +145 +00:11:26,200 --> 00:11:32,520 +negative charge يعني أسل، إذا الأحماض الأمنية تقسم + +146 +00:11:32,520 --> 00:11:37,400 +حسب ال polarity إلى polar أو non-polar، non-polar + +147 +00:11:37,400 --> 00:11:45,790 +لا يحتوي على مجموعة قطبيةوإنما يحتوي على بس كربون + +148 +00:11:45,790 --> 00:11:49,450 +وهيدروجين في الـ sided chain طب البولر يحتوي على + +149 +00:11:49,450 --> 00:11:55,290 +مجموعة قطبية إما حكينا هيدروكسيل أو كربونيل أو + +150 +00:11:55,290 --> 00:12:00,430 +sulfahydride أو أمين إجروم هدول المجموعات القطبية + +151 +00:12:00,430 --> 00:12:06,150 +إما تكون uncharged أو charged عليها شحنة أو معلهاش + +152 +00:12:06,150 --> 00:12:06,910 +شحنة + +153 +00:12:10,230 --> 00:12:13,090 +لو جينا نتفرج على الصور الموجودة هان أو على الـ + +154 +00:12:13,090 --> 00:12:17,190 +structure الأحماض الأمنية موجودة هان هذه الصور + +155 +00:12:17,190 --> 00:12:21,270 +مقسمة لأحماض الأمنية لـ polar و non-polar في منها + +156 +00:12:21,270 --> 00:12:25,310 +charged و في منها uncharged، تمام؟ هلجيت؟ لو جينا + +157 +00:12:25,310 --> 00:12:29,890 +على الصورة من فوق لليسار، في عندنا مجموعة، هلجيت؟ + +158 +00:12:29,890 --> 00:12:33,190 +أنا كيف بتعرف polar ولا non-polar، حاجة هنا؟ نتطلع + +159 +00:12:33,190 --> 00:12:35,750 +على الـside chain، على القعر اللي بتكون في الأسفل، + +160 +00:12:35,750 --> 00:12:40,190 +هي الملونةلجيت أول حمض أمين لو جينا تطلعنا بنلاقي + +161 +00:12:40,190 --> 00:12:43,630 +الـR هي عبارة عن أتش عن هيدروجين حكينا اللي بيكون + +162 +00:12:43,630 --> 00:12:47,810 +عنده الـR الـR group عبارة عن هيدروجين أو كربونا + +163 +00:12:47,810 --> 00:12:52,400 +أو الاتنين مع بعض بيكون non-polarفهذه المجموعة + +164 +00:12:52,400 --> 00:12:57,780 +كلها الجزء اللي فار من اليسار هي non-polar amino + +165 +00:12:57,780 --> 00:13:02,980 +acid لأن الـR group تحتوي على كربون وهيدروجين فقط، + +166 +00:13:02,980 --> 00:13:08,240 +تمام؟ الجتلة تحت منها على اليسار للأسفل لو طلعنا + +167 +00:13:08,240 --> 00:13:14,040 +على الـR group اللي تحت بنلاقيها تحتوي على مجموعة + +168 +00:13:14,040 --> 00:13:20,350 +قطبية تحتوي على مجموعة قطبيةفي منها بتحتوي على + +169 +00:13:20,350 --> 00:13:24,670 +هيدروكسيل جروب في منها بتحتوي على أمين جروب في + +170 +00:13:24,670 --> 00:13:29,770 +منها بتحتوي على صلفهيدرال جروب S-H المهم كلهم في + +171 +00:13:29,770 --> 00:13:34,870 +الـR group يحتوي على واحدة من المجموعات القطرية + +172 +00:13:35,420 --> 00:13:39,800 +يعني الأول يحتوي OH، التاني OH، التالت الستين + +173 +00:13:39,800 --> 00:13:43,440 +يحتوي على SH، self-hydraulic group يعني فيه إنه + +174 +00:13:43,440 --> 00:13:47,940 +مجموعات قطبية، يبقى هو polar طب هل عليه شحنة؟ لأ + +175 +00:13:47,940 --> 00:13:51,580 +فيش شحنات ولا موجم ولا سائل، إذا هو polar + +176 +00:13:51,580 --> 00:13:57,400 +uncharged R groupBowler Uncharged Amino Acid لو + +177 +00:13:57,400 --> 00:14:00,480 +جينا على جهة اليمين للأسفل، المجمعتين اللي في + +178 +00:14:00,480 --> 00:14:04,480 +الأسفل، بنلاقي إن فيهم في الـR group، في عندهم + +179 +00:14:04,480 --> 00:14:11,200 +مجموعات قطبية أغلبهم عندهم أمينوجروب أو Carboxyl + +180 +00:14:11,200 --> 00:14:15,650 +groupCarbonyl group Amino group او Carbonyl group + +181 +00:14:15,650 --> 00:14:20,050 +هدول مجموعات قطبية يبقى polar لكن عليهم شحنات اللي + +182 +00:14:20,050 --> 00:14:23,350 +في الأسفل عليهم شحنة سالمة و اللي في الأعلى عليهم + +183 +00:14:23,350 --> 00:14:27,490 +شحنة موجبة فبنسميها negatively charged polar و في + +184 +00:14:27,490 --> 00:14:32,090 +positively charged polar أما اللي فاض هدولة + +185 +00:14:32,090 --> 00:14:36,790 +aromatic لأنه بيحتووا على حلقة إذا كان عندى حمض + +186 +00:14:36,790 --> 00:14:42,340 +أمين يحتو على حلقة بنسميه aromaticلو جينا في هذه + +187 +00:14:42,340 --> 00:14:45,520 +الصورة بس عشان نرجع لقى اللي قبل حكيناها عشان + +188 +00:14:45,520 --> 00:14:49,900 +تفهموه أكتر لو جيتوا على البرولين البرولين موجود + +189 +00:14:49,900 --> 00:14:55,080 +في .. على الجهة اليسار في الأسفل في أن حمض الأمين + +190 +00:14:55,080 --> 00:14:59,840 +مكتوب تحته برولين طلعوا على الاري جروب إله بنلاقي + +191 +00:14:59,840 --> 00:15:05,170 +إنه الاري جروبعمل حلقة مع الـ Amino group يعني + +192 +00:15:05,170 --> 00:15:09,110 +عندك ضارة الكربون في النص و فوق مرتبط فيها كربوكسي + +193 +00:15:09,110 --> 00:15:12,950 +لـ group COO و من الجانب ضارة هيدروجين و على + +194 +00:15:12,950 --> 00:15:16,510 +الأسفل المفروض أن الـ R group من الجانب الـ Amino + +195 +00:15:16,510 --> 00:15:21,060 +groupالـ Amino Group هاي مرتبطة مع الـ R مش حرة زي + +196 +00:15:21,060 --> 00:15:24,220 +الباقي الأحماض الأمينية لو طلعت على كل الأحماض + +197 +00:15:24,220 --> 00:15:28,760 +الأمينية بنلاقي الـ NH2 هاي أو الـ NH3 Plus اللي + +198 +00:15:28,760 --> 00:15:31,920 +هي الـ Amino Group حرة بس مرتبطة مع الكربونة + +199 +00:15:31,920 --> 00:15:36,290 +المرجزيةإلا في حالة البروتين، في حالة البرولين + +200 +00:15:36,290 --> 00:15:41,370 +مرتبطة مع الكربونة المركزية ومرتبطة كمان مع الـR، + +201 +00:15:41,370 --> 00:15:45,770 +مع الـside chain عشان هيك سميناها amino group أو + +202 +00:15:45,770 --> 00:15:50,830 +secondary amino group مش primary amino group فهو + +203 +00:15:50,830 --> 00:15:52,870 +الحمض الأميني الشاد + +204 +00:15:58,770 --> 00:16:03,530 +لمّا نشتغل العمل ان شاء الله راح نسير نكتب تقرير + +205 +00:16:03,530 --> 00:16:07,230 +نكتب report تقرير عن المعمل اللي احنا اشتغلناه ده + +206 +00:16:07,230 --> 00:16:12,330 +نكتب فيه اسم الفحص، الهدف منه، المبدأ العام، خطوات + +207 +00:16:12,330 --> 00:16:17,690 +إجارة التجربة، نكتب النتيجة ونكتب تعليق عليها كمّة + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/iXxjfqDroRk_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/iXxjfqDroRk_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..e02b2b385b2a372d027e0c3aa88339d64bbbac35 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/iXxjfqDroRk_postprocess.srt @@ -0,0 +1,920 @@ +1 +00:00:05,480 --> 00:00:09,280 +أول فحص هو الـ Nihidrine الـ Nihidrine إيش ال + +2 +00:00:09,280 --> 00:00:12,700 +objective لو فحصتش الهدف من الفحص to detect the + +3 +00:00:12,700 --> 00:00:16,300 +presence of a free alpha amino group بيدور على ال + +4 +00:00:16,300 --> 00:00:20,680 +free alpha amino group إذا موجود free alpha amino + +5 +00:00:20,680 --> 00:00:25,180 +group هيتغير اللون، بيعطيني اللون purple في حالات + +6 +00:00:25,180 --> 00:00:28,800 +اللي موجودة في free alpha amino groupمين عنده فيه + +7 +00:00:28,800 --> 00:00:31,740 +Alpha Amino Group؟ إذا ذاكرين الحمض الأميني، عيش + +8 +00:00:31,740 --> 00:00:35,040 +الصيغة العامة له، تكون من Center Carbon ومن + +9 +00:00:35,040 --> 00:00:38,640 +الهيدروجينة، من ال Side Chain ومن Carboxyl Group + +10 +00:00:38,640 --> 00:00:43,160 +ومن Amino Group Amino Group هاي سميناها Primary + +11 +00:00:43,160 --> 00:00:47,720 +Amino Group أو Alpha Amino Group، معادة في حالة + +12 +00:00:47,720 --> 00:00:51,920 +البرولين سميناها Amino Groupيعني الأحماض الأمينية + +13 +00:00:51,920 --> 00:00:57,380 +كلها تحتوي على free alpha amino group ما يعدى + +14 +00:00:57,380 --> 00:01:01,600 +لبرولين عنده amino group يعني مين هيعطيني positive + +15 +00:01:01,600 --> 00:01:04,880 +مع هذا الفحص لو أنا اشتغلت مجموعة أحماض أمينية على + +16 +00:01:04,880 --> 00:01:08,400 +هذا الفحص؟ كلهم هيعطوني positive لأنهم كلهم بيحتوي + +17 +00:01:08,400 --> 00:01:13,800 +على free alpha amino group تمام؟طيب، لذا ال + +18 +00:01:13,800 --> 00:01:16,260 +objective to detect the presence of free alpha + +19 +00:01:16,260 --> 00:01:19,360 +amino group هل موجود free alpha amino group أو لا؟ + +20 +00:01:19,360 --> 00:01:21,940 +إذا تغير اللغة يعني موجود، إذا ما تغيرش يعني مش + +21 +00:01:21,940 --> 00:01:25,680 +موجود طيب إيش ال principle؟ مبدأ العمل للفحص؟ كيف + +22 +00:01:25,680 --> 00:01:29,120 +يشتغل الفحص؟ ال principle لو نعملها على نظام + +23 +00:01:29,120 --> 00:01:32,320 +معادلات بيسهل عليهكيف هي هذا الفحص الهو الـ + +24 +00:01:32,320 --> 00:01:35,840 +principle أنه عندنا أمينو أسد أنا بضيف حمض أميني + +25 +00:01:35,840 --> 00:01:38,980 +بضيف عليه نهيدرينرياجانت إيش بيعمل + +26 +00:01:38,980 --> 00:01:43,200 +النهيدرينرياجانت؟ بيشتغل على الـ free amino group + +27 +00:01:43,200 --> 00:01:47,060 +بيعطيني amino group لحالها أنا تشتريه وبيعطيني + +28 +00:01:47,060 --> 00:01:51,120 +هيدريندنتينإذا الأمينو أسد بضيف عليه نينهيدرين + +29 +00:01:51,120 --> 00:01:55,300 +بيعطيني أن أتش تري و هيدرين دانتين مركب اسمه + +30 +00:01:55,300 --> 00:02:00,960 +هيدرين دانتين نجيب الان أتش تري و الهيدرين دانتين + +31 +00:02:00,960 --> 00:02:05,100 +هاي و نحط عليهم كمان مرة نينهيدرين بيتفاعلوا مع + +32 +00:02:05,100 --> 00:02:08,920 +بعض و بيعطيني حاجة اسمها Romans Complex Romans + +33 +00:02:08,920 --> 00:02:15,420 +Complex هذا لونه purple colorإذا موجود الحنانة حمض + +34 +00:02:15,420 --> 00:02:18,100 +أميني، إذا كان يحتوي على Free Amino Alpha + +35 +00:02:18,100 --> 00:02:22,320 +Aminogram، بضيف عليه الـNahydrin Reagent، المحصلة + +36 +00:02:22,320 --> 00:02:25,740 +كلها أنه في الآخر هيعطيني Romans Complex، + +37 +00:02:25,740 --> 00:02:29,280 +الـNahydrin يشتغل على الـAmino Acid، اللي يحتوي + +38 +00:02:29,280 --> 00:02:32,860 +على Free Alpha Aminogram، يعطيني حاجة بنسميها + +39 +00:02:32,860 --> 00:02:37,440 +Romans Complex، إيش لونها؟ لون بيربونإذا إذا + +40 +00:02:37,440 --> 00:02:41,140 +اتغيرت تغييرت الفحص وتغير اللون ل purple إذا هاي + +41 +00:02:41,140 --> 00:02:46,540 +المركب يحتوي على free alpha amino group إذا هو + +42 +00:02:46,540 --> 00:02:50,280 +positive يحتوي على free alpha amino group وهو + +43 +00:02:50,280 --> 00:02:50,900 +positive + +44 +00:02:54,400 --> 00:02:58,660 +هنا عندنا ال principle على شكل معادلة مرسوم فيها + +45 +00:02:58,660 --> 00:03:01,040 +structure احنا مش مطلوب منها ال structure بس على + +46 +00:03:01,040 --> 00:03:04,620 +شكل معادلة حتى نلخص ال principle و يكون أثناء ال + +47 +00:03:04,620 --> 00:03:08,220 +principle أنه عندي حمض أميني أمينو أسد بضيف عليها + +48 +00:03:08,220 --> 00:03:14,020 +نهيدرين راجع بيعطيني هيدرين دنتينو Anacetrate باخد + +49 +00:03:14,020 --> 00:03:16,920 +الهيدرين دنتين و ال Anacetrate باطيف عليهم كمان + +50 +00:03:16,920 --> 00:03:20,840 +مرانين هيدرين رياجان بيعطيني حاجة بنسميها romance + +51 +00:03:20,840 --> 00:03:25,540 +complex لغنها purple هذا إذا كان المركب ال amino + +52 +00:03:25,540 --> 00:03:29,000 +acid يحتوي على free alpha amino group بيعطيني + +53 +00:03:29,000 --> 00:03:33,700 +romance complex لغنه purple هذه المحصلة النهائية + +54 +00:03:41,910 --> 00:03:45,930 +البرولين يحتوي على amino group او secondary amino + +55 +00:03:45,930 --> 00:03:50,030 +group لأن البرولين يتفاعل مع ال نهيدرين ال amino + +56 +00:03:50,030 --> 00:03:53,450 +group اللي عنده بتتفاعل مع ال نهيدرين بس لها طريقة + +57 +00:03:53,450 --> 00:03:57,370 +خاصة للتفاعل فبدل ما تعطيني لون purple بيعطيني لون + +58 +00:03:57,370 --> 00:04:02,090 +yellow لذن كل الأحماض الأمينية تعطي قيمة positive + +59 +00:04:02,090 --> 00:04:06,570 +مع ال نهيدرينلكن هالكلها بتعطي لون purple؟ لأ، كل + +60 +00:04:06,570 --> 00:04:10,230 +الأحمد الأمنية بتعطي لون purple معادا البرولين + +61 +00:04:10,230 --> 00:04:13,950 +بيعطيني لون yellow، زفاعل معنين هيدرين بيعطيني لون + +62 +00:04:13,950 --> 00:04:18,770 +yellowأمينو أسد برولين and هيدروكس برولين react + +63 +00:04:18,770 --> 00:04:23,290 +with ninhydrin but give yellow color من يعطيني + +64 +00:04:23,290 --> 00:04:26,610 +positive غير الأمينو أسد besides أمينو أسد من + +65 +00:04:26,610 --> 00:04:29,550 +هييعطيني positive أحمد الأمينية تعطيني positive مع + +66 +00:04:29,550 --> 00:04:33,070 +ال ninhydrin كمان ال peptides البروتين ال + +67 +00:04:33,070 --> 00:04:35,950 +structure ال primary structure of البروتين يسميه + +68 +00:04:35,950 --> 00:04:36,530 +peptides + +69 +00:04:40,710 --> 00:04:44,290 +مرتبطة مع بعضها البعض في peptide bond محماض أمينية + +70 +00:04:44,290 --> 00:04:47,230 +مرتبطة مع بعضها في peptide bond حكينا في جهة من + +71 +00:04:47,230 --> 00:04:51,030 +الجهات بيكون فيه free amino group وجهة تانية فيه + +72 +00:04:51,030 --> 00:04:54,450 +free carboxyl group إذا متوفر عندي free amino + +73 +00:04:54,450 --> 00:04:57,990 +group، يعني إذا انتوفر ال objective لإنين هيدرين، + +74 +00:04:57,990 --> 00:05:01,720 +يعني هيعطيني positiveالأمينو أسد هتعطيني positive + +75 +00:05:01,720 --> 00:05:05,540 +من النيلهيدرين ال peptides اللي هي عبارة عن ترتيب + +76 +00:05:05,540 --> 00:05:09,680 +من أحماض أمينية مرتبطة مع بعضها البعض ب peptide + +77 +00:05:09,680 --> 00:05:14,500 +bond هتعطيني برضه positive ال peptone هو عبارة عن + +78 +00:05:14,500 --> 00:05:17,420 +ال protein مكسّرالحين أنا لما أكسر البروتين إيش + +79 +00:05:17,420 --> 00:05:21,560 +هينتج عندى؟ بينتج من البروتين peptide bond و amino + +80 +00:05:21,560 --> 00:05:24,960 +acid بدأ من نتج amino acid و ال amino acid تحتكوي + +81 +00:05:24,960 --> 00:05:27,420 +على free alpha amino group هيعطيني positive مع ال + +82 +00:05:27,420 --> 00:05:30,620 +نينهيدرين أو لا، هيعطيني positive إذا أن ال + +83 +00:05:30,620 --> 00:05:35,580 +peptide و ال peptone و البروتين و ال amino acid هم + +84 +00:05:35,580 --> 00:05:40,160 +الأربع بيعطوني positive مع ال نينهيدرين نينهيدرين + +85 +00:05:40,160 --> 00:05:44,480 +هيعطيني positive معاهاطيب، أحكيلي تحت إن النهيدرين + +86 +00:05:44,480 --> 00:05:48,480 +فيه إيثانول وهو «flammable» قابل الإشتعال الـ + +87 +00:05:48,480 --> 00:05:51,780 +«regent» هذا قابل الإشتعال «toxic sam» و + +88 +00:05:51,780 --> 00:05:55,560 +«irritant» مهيج فبدنا نحفظه بعيد عن اللهب عشان هو + +89 +00:05:55,560 --> 00:05:59,120 +قابل الإشتعال، بعيد عن العينين وعن الجلد لأنه مهيج + +90 +00:05:59,120 --> 00:06:05,100 +وبعيد عن الملابس وبدنا نتجنب استنشاق كمية كبيرة + +91 +00:06:05,100 --> 00:06:08,800 +منه لأنه مهيج فبدنا نتعامل معاه بحذر + +92 +00:06:12,040 --> 00:06:15,700 +هنا معادلة لاتفاعل البرولين مع ال نينهيدرين حكينا + +93 +00:06:15,700 --> 00:06:19,480 +إله خاص يقاله طريقة خاصة لاتفاعل مع ال نينهيدرين + +94 +00:06:19,480 --> 00:06:22,260 +بيعطينيش romance complex اللونه purple وإنما + +95 +00:06:22,260 --> 00:06:26,280 +يعطيني yellow product ناتج لونه yellow إذا تفاعل + +96 +00:06:26,280 --> 00:06:29,820 +البرولين مع ال نينهيدرين بيعطيني لون yellow + +97 +00:06:33,100 --> 00:06:37,080 +هنا عنا سؤال بيحكي لي ليش كل الأحماض الأمينية with + +98 +00:06:37,080 --> 00:06:40,880 +all amino acid منها يدرين give purple but with + +99 +00:06:40,880 --> 00:06:43,120 +proline يدرين give yellow ليش ميعتنين yellow مع + +100 +00:06:43,120 --> 00:06:46,680 +البرولين و مع الباقي بيعطيني purple حكينا لأن + +101 +00:06:46,680 --> 00:06:51,520 +البرولين it have amino group but البرولين have + +102 +00:06:51,520 --> 00:06:56,350 +amino group not alpha amino groupالـ Amino group + +103 +00:06:56,350 --> 00:06:59,910 +هاي بتخلي .. بتعطيه rigid confirmation .. + +104 +00:06:59,910 --> 00:07:03,310 +confirmation .. rigid confirmation بتاعة المركب + +105 +00:07:03,310 --> 00:07:08,370 +صلابة فبيقلل ال flexibility لإنه بيخليه صعب التكسر + +106 +00:07:08,370 --> 00:07:11,770 +فبدل ما يتكسر لهيدر اندانتينو الأمينو group + +107 +00:07:11,770 --> 00:07:16,130 +الأناتشي تريه ويعطيني romance complex لأ صعب إنه + +108 +00:07:16,130 --> 00:07:20,110 +يتكسر فإله طريقة خاصة في التفاعل بيعطيني لون + +109 +00:07:20,110 --> 00:07:20,610 +yellow + +110 +00:07:23,370 --> 00:07:27,170 +فى ال procedure خطوات العمل انه نجيب تيوب glass + +111 +00:07:27,170 --> 00:07:30,030 +تيوب بحط فيها واحد مل من ال solution اللى انا + +112 +00:07:30,030 --> 00:07:33,390 +اعطاتكى يعنى اعطاتك محلول مجهول بديك تفحصى هل + +113 +00:07:33,390 --> 00:07:37,090 +يحتوي على فيه alpha منوبروب ولا لأ نحط واحد مل من + +114 +00:07:37,090 --> 00:07:40,510 +هذا ال solution مع خمسة دروب من ال nonhydric agent + +115 +00:07:41,650 --> 00:07:45,270 +و بتحطيه في ال water bath اللي بيحتوي على ماء مغلي + +116 +00:07:45,270 --> 00:07:50,410 +على boil water bath بحطه لمدة دقيقتهم بعد دقيقتهم + +117 +00:07:50,410 --> 00:07:53,970 +بطلّع ال tube من ال water bath إذا اتغير اللون ل + +118 +00:07:53,970 --> 00:07:58,130 +purple color إذا هذا المركب يحتوي على free alpha + +119 +00:07:58,130 --> 00:08:02,710 +amino group إذا مااتحولش اللون ل purple color إذا + +120 +00:08:02,710 --> 00:08:06,290 +لا يحتوي على free alpha amino group طب إذا أعطاني + +121 +00:08:06,290 --> 00:08:11,920 +yellow color إذا بعرف أنه brûléPurple color هيكون + +122 +00:08:11,920 --> 00:08:15,080 +أي مركب يحتوي على 3000 amino group ممكن يكون amino + +123 +00:08:15,080 --> 00:08:19,380 +acid، ممكن peptide، ممكن peptone، ممكن البروتين، + +124 +00:08:19,380 --> 00:08:24,160 +مهم يحتوي على free 1000 amino group لكن if أعطاني + +125 +00:08:24,160 --> 00:08:27,060 +yellow color، بعرف إنه هذا Proline + +126 +00:08:29,890 --> 00:08:33,650 +الفحص التاني هو فحص ال bio-retest، bio-retest ايش + +127 +00:08:33,650 --> 00:08:36,290 +ال objective من الفحص؟ to take the presence of + +128 +00:08:36,290 --> 00:08:40,290 +peptide bond، يدور على ال peptide bond، اذا موجودة + +129 +00:08:40,290 --> 00:08:43,490 +ال peptide bond، بيعطينا positive، اذا مش موجودة، + +130 +00:08:43,490 --> 00:08:48,590 +هيعطينا negative ومش هيتغير اللونإذا كيف .. وين + +131 +00:08:48,590 --> 00:08:51,410 +موجودة الـ peptide bond هتكون؟ هل موجودة في الحمض + +132 +00:08:51,410 --> 00:08:54,130 +الأميني؟ single amino acid؟ هل ال structure فيه + +133 +00:08:54,130 --> 00:08:58,150 +peptide bond؟ ال structure العام للأمينو أسد؟ لأ، + +134 +00:08:58,150 --> 00:09:01,430 +إذا أن الأمينو أسد كلها هتعطيني negative مع ال bio + +135 +00:09:01,430 --> 00:09:06,050 +rate test مين هيعطيني positive؟ ال protein، لأن ال + +136 +00:09:06,050 --> 00:09:10,010 +protein هو عبارة عن ترتيب الأحماض الأمينية مرتبطة + +137 +00:09:10,010 --> 00:09:13,530 +مع بعضها البعض في peptide bond فال protein هيعطيني + +138 +00:09:13,530 --> 00:09:20,910 +positive، كمانعندما يتكسر البروتين في بيبتايد بون، + +139 +00:09:20,910 --> 00:09:23,950 +فهي يعطيني positive، لذلك البروتين والبيبتون + +140 +00:09:23,950 --> 00:09:28,030 +هيعطوني positive قبل ال principle، المبدأ العام + +141 +00:09:28,030 --> 00:09:28,650 +للفحص + +142 +00:09:33,660 --> 00:09:37,800 +بضيف عليه bio-retriation إيش هو ال bio-retriation؟ + +143 +00:09:37,800 --> 00:09:43,340 +مايبقى حاجته كبر صلفات with strong base كبر صلفات + +144 +00:09:43,340 --> 00:09:49,200 +CUSO4 في وجود strong base قاعدة قوية NaOH أو KOH + +145 +00:09:50,000 --> 00:09:53,660 +بيجي الـ bioretary agent الكبر اللي فيه بيروح على + +146 +00:09:53,660 --> 00:09:56,960 +الـ peptide هون بروبوتها كلها يتهم مع بعضها + +147 +00:09:56,960 --> 00:10:02,200 +ويعملهم كإنه مشبكة، بيعمل الكبر ك-chelating agent، + +148 +00:10:02,200 --> 00:10:06,500 +الكبر يشتغل، بيشتغل ك-chelating agent، كعامل + +149 +00:10:06,500 --> 00:10:11,590 +متمخلقعامل متمخلب، يعني عامل زي مخ ضبوط، إله أكتر + +150 +00:10:11,590 --> 00:10:14,630 +من إيه؟ في mid من هنا و من هنا و من هنا، بيروبوت + +151 +00:10:14,630 --> 00:10:18,390 +كل الروابط البيبجية الموجودة مع بعضها البعض، في + +152 +00:10:18,390 --> 00:10:23,570 +وجود القاعدة القوية، بيعمل gelating agent لكبر، + +153 +00:10:23,570 --> 00:10:26,670 +بيعمل gelating agent، عامل متمخلب + +154 +00:10:32,700 --> 00:10:37,240 +لونه violet إذا تغير اللون لviolet إذا موجود عندي + +155 +00:10:37,240 --> 00:10:40,780 +ال peptide bond إذا ما تغيرش إذا ال negative مش + +156 +00:10:40,780 --> 00:10:45,040 +موجودة بحكيلي هذا اللون this color is dependent on + +157 +00:10:45,040 --> 00:10:48,200 +the number of peptide bond بيعتمد على عدد ال + +158 +00:10:48,200 --> 00:10:51,400 +peptide bond إذا ال peptide bond موجودة عندى تنتين + +159 +00:10:51,400 --> 00:10:54,860 +بيكون violet بس بشدة أخف من لما يكون عندى مثلا + +160 +00:10:54,860 --> 00:10:59,460 +أربع روابط بيبتدية فكل ما زادت عدد روابط البيبتدية + +161 +00:10:59,460 --> 00:11:01,880 +كل ما زادت شدت اللون + +162 +00:11:06,510 --> 00:11:09,350 +في الـ Reagent البيوريد حاكينا بيحتوي على كبر + +163 +00:11:09,350 --> 00:11:14,030 +صلفات with a strong base NaOH أو KOH ليش موجودة + +164 +00:11:14,030 --> 00:11:17,730 +الـ strong base الـ NaOH is there to raise the pH + +165 +00:11:17,730 --> 00:11:22,530 +عشان ترفع الـ pH لتوفير alkaline media لتوفير + +166 +00:11:22,530 --> 00:11:26,330 +alkaline media الـ pH اللي نحتاجها لتوفير alkaline + +167 +00:11:26,330 --> 00:11:30,870 +media طيب الميني المركب المهم في هذه الـ في هذا + +168 +00:11:30,870 --> 00:11:31,930 +الـ Reagent الـ circular + +169 +00:11:39,380 --> 00:11:43,180 +المركب المهم هو الـ cover ال cover حاكينا هو أهم + +170 +00:11:43,180 --> 00:11:47,440 +مركب موجود في ال region بيجي من ال cover صلفية في + +171 +00:11:47,440 --> 00:11:51,740 +وجود alkaline solution إذا وجدت ال peptide bond و + +172 +00:11:51,740 --> 00:11:54,660 +ال peptide bond are present ال alkaline solution + +173 +00:11:54,660 --> 00:11:58,220 +ال cover من ال cover صلفية بيجي بيعطيني complex + +174 +00:11:58,220 --> 00:12:03,600 +لونه violetبيحكيلي إنه two peptide bonds at least + +175 +00:12:03,600 --> 00:12:07,220 +are required for the formation of this complex على + +176 +00:12:07,220 --> 00:12:11,660 +الأقل يكون موجود في المُركّب two peptide bonds إذا + +177 +00:12:11,660 --> 00:12:15,660 +كان موجود رابطتين ببتديات أو أكتر بيشتغل ال + +178 +00:12:15,660 --> 00:12:19,620 +reagent وبيعطيني لهم إذا رابطة ببتدية واحدة بيقدرش + +179 +00:12:19,620 --> 00:12:23,000 +يشتغل ويعطيني negative لأنه لو أجل كبر على رابطة + +180 +00:12:23,000 --> 00:12:26,260 +ببتدية واحدةالكيب دي عمل عامل متمخلب وبإنه بدي + +181 +00:12:26,260 --> 00:12:29,760 +ربطهم كلهم مع بعض مافيش غير رابط واحد يربطها مع + +182 +00:12:29,760 --> 00:12:33,580 +مين فمش هيعطيني لون فعلى الأقل لازم يكون موجود + +183 +00:12:33,580 --> 00:12:35,260 +رابطتين فأكثر + +184 +00:12:38,260 --> 00:12:41,960 +إيش هو الكليات؟ الكليات هو chemical compound مركب + +185 +00:12:41,960 --> 00:12:47,320 +كيميائي بيتكون من metal ion مع كليات انجازان مركب + +186 +00:12:47,320 --> 00:12:52,380 +بيتكون من metal ion مع كليات انجازان طب مين الكلية + +187 +00:12:52,380 --> 00:12:55,820 +انجازان؟ هو ال substance whose molecule can form + +188 +00:12:55,820 --> 00:13:00,040 +several bonds to a single metal ion هو المركب اللي + +189 +00:13:00,040 --> 00:13:06,060 +له ID كثيرة هو المركب القادر على عمل عدة روابط + +190 +00:13:15,860 --> 00:13:19,240 +إيش الـ procedure خطوات عمل الفحص أني بجيب الـ + +191 +00:13:19,240 --> 00:13:21,820 +tube بحط فيها واحد مل من ال solution اللي أنا + +192 +00:13:21,820 --> 00:13:25,320 +أعطاتكيها سواء أعطاتكي protein أو amino acid تحطي + +193 +00:13:25,320 --> 00:13:29,420 +واحد منه على اتنين مل من ال bioretarian بتحطي + +194 +00:13:29,420 --> 00:13:33,920 +بتعملي mix إذا تغير اللون ل violet إذا هذا المركب + +195 +00:13:33,920 --> 00:13:37,400 +اللي أنا أعطاتكيه يحتوي على peptide bond إذا ما + +196 +00:13:37,400 --> 00:13:44,430 +تغيرش إذا ال negative له يحتوي على peptide bondطيب + +197 +00:13:44,430 --> 00:13:47,990 +هنا جدول يحتوي على الألوان اللي ممكن تظهر لما أنا + +198 +00:13:47,990 --> 00:13:50,990 +أشتغل فحص ال بيرون، بحكيلي if a note changed، + +199 +00:13:50,990 --> 00:13:54,170 +الفحص هو لون ال بيروترياجنت الطبيعي، يعني لونه + +200 +00:13:54,170 --> 00:13:57,990 +أزرق، فإذا كان negative هيظل لون أزرق زي ما هو، + +201 +00:13:57,990 --> 00:14:01,810 +إذا positive هيتغير لviolinفإذا ما تغيرش اللون + +202 +00:14:01,810 --> 00:14:05,230 +وضلوا أزرق، معناها البروتين مش موجود يعني ممكن + +203 +00:14:05,230 --> 00:14:08,370 +يكون موجود عندي حمض أمين، المهم الـbutyde bond مش + +204 +00:14:08,370 --> 00:14:13,110 +موجودة، فاللون ما تغيرش، ماصارش تفاعل إذا اللون + +205 +00:14:13,110 --> 00:14:17,470 +اتغير، بيحكيلي إلى violet من blue لviolet لدرجة ال + +206 +00:14:17,470 --> 00:14:21,710 +purple، الغامق، إذا البروتين موجود طب إذا اتغير لل + +207 +00:14:21,710 --> 00:14:25,930 +pink لدرجة أفتح من الviolet، اللون pink، إذا اللي + +208 +00:14:25,930 --> 00:14:30,900 +موجود بـbutyde bond، ولكن عددها قليل، أقليعني ممكن + +209 +00:14:30,900 --> 00:14:35,280 +يكون موجود وعندي بيبتون اللي هو عند بروتين مكسّة، + +210 +00:14:35,280 --> 00:14:39,460 +عدد البيبتايد فوق الـ bond اللي فيه قليل، فدرجة + +211 +00:14:39,460 --> 00:14:40,980 +اللون بتكون أقل. + +212 +00:14:43,720 --> 00:14:48,300 +البحث اللي بعد هيك هو الـ xanthoproteic test الـ + +213 +00:14:48,300 --> 00:14:51,140 +xanthoproteic test إيش ال objective منه؟ to + +214 +00:14:51,140 --> 00:14:55,720 +differentiate between aromatic and amino acidلأ، + +215 +00:14:55,720 --> 00:14:59,320 +بس ده الـ amino acid اللي بيحتوي على benzene ring + +216 +00:14:59,320 --> 00:15:02,660 +على حلقة بنزين، إذا فاكرين الصورة دي اللي حكينا + +217 +00:15:02,660 --> 00:15:05,880 +إنه في بعض الأحماض الأمينية تسميها aromatic amino + +218 +00:15:05,880 --> 00:15:10,250 +acid تحتوي على حلقة بنزينبس مانضيف هنا إنها تكون + +219 +00:15:10,250 --> 00:15:14,350 +Activated Aromatic Amino Acid تكون حلقة البنزين + +220 +00:15:14,350 --> 00:15:18,270 +مشطعة أنه في حمض أمينة، حلقة البنزين اللي عنده + +221 +00:15:18,270 --> 00:15:22,790 +بتكون Inactive إذا يحتوي على Aromatic Activated + +222 +00:15:22,790 --> 00:15:26,610 +Aromatic Benzene Ring أو Aromatic Amino Acid بيكون + +223 +00:15:26,610 --> 00:15:29,570 +.. بيعطيني لون Yellow، بيكون Positive إذا لا + +224 +00:15:29,570 --> 00:15:33,690 +يحتوي، هيكون Negativeفكيف الـ principle مبدأ عمل + +225 +00:15:33,690 --> 00:15:38,950 +الفحص أنه بيجي عنده amino acid with aromatic ring + +226 +00:15:38,950 --> 00:15:42,930 +حمض أميني بيحتوي على حلقة بنزين بحط عليه + +227 +00:15:42,930 --> 00:15:47,190 +concentrated nitric acid concentrated nitric acid + +228 +00:15:47,190 --> 00:15:54,110 +HNO3 في وجود قاعدة قوية زي الـNaO2 في وجود NaO2 + +229 +00:15:54,110 --> 00:15:58,050 +ليش هييجي يعمل الـ nitric acid لحمض الأميني اللي + +230 +00:15:58,050 --> 00:16:02,910 +يحتوي على بنزين ring؟يعمل نيترياشيل of بنزين ريكو + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/nTcz4I3nh3A_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/nTcz4I3nh3A_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..a1d5404c6113ca3f49e247ce206c1f204295d48c --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/nTcz4I3nh3A_postprocess.srt @@ -0,0 +1,1660 @@ +1 +00:00:01,890 --> 00:00:06,410 +اليوم راح نحكي بمعمل هو isolation of casein from + +2 +00:00:06,410 --> 00:00:10,890 +milk اللي هو عزل ال protein ال casein من الحليب + +3 +00:00:10,890 --> 00:00:15,770 +وهذا يعتبر تطبيق على المعمل الماضي إن أحنا صارنا + +4 +00:00:15,770 --> 00:00:19,710 +عارفين ال isoelectric point لل casein بدنا نوصل + +5 +00:00:19,710 --> 00:00:24,150 +البيت لحليب لل isoelectric point بتبعت ال casein + +6 +00:00:24,150 --> 00:00:29,350 +وبالتالي بيترسب ال protein ال casein و تبقى باقي + +7 +00:00:29,350 --> 00:00:30,410 +ال proteinات + +8 +00:00:33,330 --> 00:00:37,510 +في البداية بدنا نحكي عن البروتين أنه ينقسم إلى + +9 +00:00:37,510 --> 00:00:40,830 +قسمين نوع البروتين في simple protein و في + +10 +00:00:40,830 --> 00:00:45,530 +conjugated protein بروتينات بسيطة أو بروتينات + +11 +00:00:45,530 --> 00:00:52,330 +معقدة simple protein هي عبارة عن حماض أمينية + +12 +00:00:52,330 --> 00:00:56,750 +مرتبطة مع بعضها البعض بروابط بيبتديايعني لو كسرتها + +13 +00:00:56,750 --> 00:01:01,030 +هيدرولايزed to yield only amino acid زي الألبومين + +14 +00:01:01,030 --> 00:01:04,690 +والجلوبيلين لو كسرتها بس منتج منها أحماط أمينية + +15 +00:01:04,690 --> 00:01:09,260 +مثال عليها الألبومين والجلوبيلينconjugated protein + +16 +00:01:09,260 --> 00:01:13,780 +بروتينات معقدة اللي بتحتوي على أحماض أمنية ومتصل + +17 +00:01:13,780 --> 00:01:18,820 +فيها another group other chemical group بروتين + +18 +00:01:18,820 --> 00:01:21,440 +that function in interaction with other chemical + +19 +00:01:21,440 --> 00:01:24,940 +group attached by covalent bond or by weak + +20 +00:01:24,940 --> 00:01:28,780 +interaction المتصل مع الأحماض الأمنية مجموعة تانية + +21 +00:01:28,780 --> 00:01:32,240 +مجموعة group تانية ممكن تكون هذه المجموعة في صفية + +22 +00:01:32,240 --> 00:01:36,220 +group ممكن تكون carbohydrate ممكنوالـ lipid ممكن + +23 +00:01:36,220 --> 00:01:39,740 +مجموعة هيم فعش ما نسميها أو some example of + +24 +00:01:39,740 --> 00:01:43,400 +conjugated protein هو زي الـ lipoprotein اللي هو + +25 +00:01:43,400 --> 00:01:47,620 +protein متصل فيه مجموعة lipid الـ glycoprotein + +26 +00:01:47,620 --> 00:01:51,920 +اللي هو protein متصل فيه carbohydrate سكريات الـ + +27 +00:01:51,920 --> 00:01:54,660 +phosphoprotein هو عبارة عن protein مرتبط فيه + +28 +00:01:54,660 --> 00:01:59,300 +مجموعة فسفان والـ hemoprotein هو protein متصل فيه + +29 +00:01:59,570 --> 00:02:04,010 +مجموعة E إذا كانت أحماض أمينية متصلة معها group + +30 +00:02:04,010 --> 00:02:08,290 +تانية ساميها conjugated protein إذا كان بس أحماض + +31 +00:02:08,290 --> 00:02:12,510 +أمينية متصلة مع بعض البعض بسميه simple protein + +32 +00:02:15,400 --> 00:02:18,960 +ممكن نحكي عن الـ Phosphoprotein حكينا إن هو عبارة + +33 +00:02:18,960 --> 00:02:22,500 +عن بروتين أو عن أحماض أمينيا bonded to a substance + +34 +00:02:22,500 --> 00:02:25,540 +containing phosphoric acid متصلة فيه مجموعة + +35 +00:02:25,540 --> 00:02:30,040 +phosphate group أو أي مركّب مادة تحتوي على + +36 +00:02:30,040 --> 00:02:33,540 +phosphoric acid إذا كان موجود مجموعة phosphate + +37 +00:02:33,540 --> 00:02:38,870 +بسميه phosphoproteinلو جبنا أيونات الكالسيوم + +38 +00:02:38,870 --> 00:02:42,310 +أيونات الكالسيوم معروفة أنها بيكون plus والفوسفات + +39 +00:02:42,310 --> 00:02:46,370 +نجمة الفوسفات تكون minus إذا حطينا أيونات + +40 +00:02:46,370 --> 00:02:50,890 +الكالسيوم على بروتين يحتوي على فوسفات جروم بيصير + +41 +00:02:50,890 --> 00:02:56,190 +عملية ionization تأيّن للفوسفات جروم موجب مع سلب + +42 +00:02:56,190 --> 00:03:00,370 +الكلسيوم موجب و الفوسفات سلب فبأي نوع الكالسيوم + +43 +00:03:00,370 --> 00:03:04,070 +بأيّن الفوسفات تصير شحنات الموجب والسلبة متساوية + +44 +00:03:04,070 --> 00:03:07,660 +الشحنة الكل هي zeroفهذا بيزود الـ hydrophobic + +45 +00:03:07,660 --> 00:03:13,460 +interaction بيزود أنه يكون كاره للماء أو أنه يكون + +46 +00:03:13,460 --> 00:03:17,820 +غير قطبي فهذا بيأد إلى ال precipitation Ionized + +47 +00:03:17,820 --> 00:03:20,920 +phosphate group by calcium ion increase + +48 +00:03:20,920 --> 00:03:24,040 +hydrophobic interaction which lead to + +49 +00:03:24,040 --> 00:03:27,680 +precipitationإذا جيبت أيانات الكالسيوم، بحطها على + +50 +00:03:27,680 --> 00:03:31,200 +بروتين يحتوي على فوسفات، تكون الكالسيوم موجب + +51 +00:03:31,200 --> 00:03:35,720 +والفوسفات minus، بتأين الشحنات، بتعادلوا يعني، + +52 +00:03:35,720 --> 00:03:39,380 +الشحنات الموجبة أو السالبة، بزود الـhydrophobic، و + +53 +00:03:39,380 --> 00:03:44,900 +بيصير ال precipitation بترسب هذا البروتينطيب هنا + +54 +00:03:44,900 --> 00:03:48,160 +الصورة بتوضح ال milk composition اللي هي مكونات + +55 +00:03:48,160 --> 00:03:51,460 +الحليب ليش بتكون الحليب؟ بيتكون من carbohydrates + +56 +00:03:51,460 --> 00:03:56,400 +بيحتوي على سكريات و هو سكر اللاكتوز يحتوي على واطر + +57 +00:03:56,400 --> 00:04:00,020 +على ميه وهي أكبر نسبة في الحليب هي ميه منيرال + +58 +00:04:00,020 --> 00:04:03,660 +بيحتوي على منيرال على معادن زي الكالسيوم بوتاسيوم + +59 +00:04:03,660 --> 00:04:08,440 +صادم صادم فوسفرست يحتوي على فيتمين اللي هي فيتمين + +60 +00:04:08,440 --> 00:04:14,260 +A وD وKبيحتوي على proteins زي بروتين الكازين + +61 +00:04:14,260 --> 00:04:20,790 +بيحتوي على lipid على دهونزي ما حكينا تكرار إن + +62 +00:04:20,790 --> 00:04:25,530 +الحليب يتكون من فيتامين، فيتامين A وD وK، يتكون من + +63 +00:04:25,530 --> 00:04:28,590 +مينيرال زي الكالسيوم، بوتاسيوم، صوديوم، and + +64 +00:04:28,590 --> 00:04:32,570 +فوسفرس، يتكون من البروتين، و البروتين هذا يحتوي + +65 +00:04:32,570 --> 00:04:35,690 +على كل الأحمض الأمينية الأساسية، all essential + +66 +00:04:35,690 --> 00:04:38,570 +amino acid، يعني كل الأحمض الأمينية الأساسية + +67 +00:04:38,570 --> 00:04:42,070 +موجودة في الحليب، يحتوي على carbohydrates، على + +68 +00:04:42,070 --> 00:04:46,440 +سكريات، وأشهرها، و السكر الموجود في الحليب هوسكر + +69 +00:04:46,440 --> 00:04:51,460 +اللاكتوز وهو عبارة عن Dysaccharide سكر تنائي عبارة + +70 +00:04:51,460 --> 00:04:55,620 +عن اتحاد سكر الـ Galactose مع الـ Glucose ويحتوي + +71 +00:04:55,620 --> 00:05:02,010 +على لبنأهم عنصرين مش موجودين في الحليب مفقدين هو + +72 +00:05:02,010 --> 00:05:06,750 +الحديد و vitamin C إذا الحليب يعتبر مغد رئيسي + +73 +00:05:06,750 --> 00:05:11,670 +يحتوي على مكونات كتيرة يحتاجها للجسم لكن في عنصرين + +74 +00:05:11,670 --> 00:05:15,450 +أساسيا رئيسيا يحتاجه الجسم و غير موجودة في الحليب + +75 +00:05:18,800 --> 00:05:22,540 +in which milk is deficient are iron and vitamin C + +76 +00:05:22,540 --> 00:05:26,720 +هو الحديد و vitamin C طب بيحكي للبعبي ال infants + +77 +00:05:26,720 --> 00:05:30,640 +are usually born كف البعبي الراطية بيعتمد بس على + +78 +00:05:30,640 --> 00:05:33,940 +حليب الأم بياخد كل الأشياء الأساسية طب من وين + +79 +00:05:33,940 --> 00:05:37,960 +بيجيب الحديد و من وين بيجيب vitamin C بيحكي للحديد + +80 +00:05:37,960 --> 00:05:43,350 +موجود في جسمه منذ الولادة بكمية تكفيهلأ عدة أسابيع + +81 +00:05:43,350 --> 00:05:48,390 +عنده مخزن born with a storage supply of iron large + +82 +00:05:48,390 --> 00:05:52,130 +enough to meet their need for several weeks إنه + +83 +00:05:52,130 --> 00:05:56,050 +عنده مخزن في جسمه حديد كميات كبيرة تكفيه لعدة + +84 +00:05:56,050 --> 00:06:00,650 +أسابيع أما vitamin C سهل الحصول عليه عن طريق أنه + +85 +00:06:00,650 --> 00:06:06,810 +تتناول الوم عصير البرتقال وبيتزود في الحليب للطفل + +86 +00:06:09,270 --> 00:06:12,530 +الواش البروتينات الموجودة في الحليب في أن تلت + +87 +00:06:12,530 --> 00:06:16,730 +أنواع من البروتينات موجودة في الحليب هو الكازين، + +88 +00:06:16,730 --> 00:06:21,610 +lactalbumin و lactoglobulin البروتين الكازين بيشكل + +89 +00:06:21,610 --> 00:06:26,390 +في الحليب نسبة 80% من البروتينة أما lactalbumin و + +90 +00:06:26,390 --> 00:06:31,490 +lactoglobulin بتسميهم واي بروتين تشكل 20% من نسبة + +91 +00:06:31,490 --> 00:06:35,430 +البروتينات الموجودة في الحليب فالنسبة الكبرى + +92 +00:06:35,430 --> 00:06:37,610 +للبروتينات هي للكازين + +93 +00:06:39,720 --> 00:06:43,680 +ممكن نتعرف على الـ casein، structure of casein ال + +94 +00:06:43,680 --> 00:06:48,300 +casein يعتبر phosphoprotein، إذا هو conjugated + +95 +00:06:48,300 --> 00:06:52,720 +protein، not simply protein، هو conjugate مثلًا + +96 +00:06:52,720 --> 00:06:55,800 +على phosphoprotein، وهو conjugate، ليش؟ بتتصل فيه + +97 +00:06:55,800 --> 00:06:59,380 +مجموعة phosphate group attached to some of the + +98 +00:06:59,380 --> 00:07:02,940 +amino acid مرتبطة مع بعض الأحمض الأمينية الموجودة + +99 +00:07:02,940 --> 00:07:07,210 +فيهأي أحمض أمينية مرتبطة فيها الـ Phosphate Group + +100 +00:07:07,210 --> 00:07:12,670 +خالباً عند الحمض الأميني سيرين وثريونين مرتبطة + +101 +00:07:12,670 --> 00:07:15,610 +مجموعة الـ Phosphate Group في الحمض الأميني + +102 +00:07:15,610 --> 00:07:20,860 +السيرين وثريونين الموجودين في تركيبة الكازينبحكي + +103 +00:07:20,860 --> 00:07:24,580 +لي إن الكازين هو mixture of at least three similar + +104 +00:07:24,580 --> 00:07:30,140 +proteins وعبارة عن خليط من تلت بروتينات الكازين هو + +105 +00:07:30,140 --> 00:07:34,020 +خليط من تلت بروتينات هذه التلت بروتينات الفرق + +106 +00:07:34,020 --> 00:07:38,540 +بينها بتختلف هما متشابهين بس بيختلفوا في الـ + +107 +00:07:38,540 --> 00:07:43,600 +molecular weight الوزن الجزائي بتختلف في كمية الـ + +108 +00:07:43,600 --> 00:07:46,900 +phosphorus اللي بتحتويها number of phosphate group + +109 +00:07:46,900 --> 00:07:48,420 +amount of phosphorus + +110 +00:07:51,160 --> 00:07:54,460 +بينهم، اللي هي كمية الـ Phosphate group و الـ + +111 +00:07:54,460 --> 00:07:58,280 +Molecular weight إيش هم التلاتة البروتينات؟ هم + +112 +00:07:58,280 --> 00:08:04,120 +Alpha-Casein و Beta-Casein و Kappa-Casein تلاتة، + +113 +00:08:04,120 --> 00:08:08,420 +Alpha-Casein و Beta-Casein و Kappa-Casein بحكيلي + +114 +00:08:08,420 --> 00:08:12,180 +هدول التلاتة كمان اللي هم different hydrophobic + +115 +00:08:12,180 --> 00:08:15,640 +and hydrophilic regions بختلف اللي هو + +116 +00:08:20,490 --> 00:08:23,670 +في منها كاره للماء، في منها محب للماء، في منها + +117 +00:08:23,670 --> 00:08:29,390 +بيثوف في الماء، وفي لا نيجي + +118 +00:08:29,390 --> 00:08:33,090 +نحكي عن التلات البروتينات المقاومة للكازين Alpha + +119 +00:08:33,090 --> 00:08:36,890 +-Casein هو ال major casein هو الأكبر أعلى + +120 +00:08:36,890 --> 00:08:40,350 +molecular weight أعلى من بيتا و أعلى من كعبة + +121 +00:08:40,350 --> 00:08:44,950 +بيتكون من تمانية إلى عشرة فسفات جروم ال Alpha + +122 +00:08:44,950 --> 00:08:50,220 +-Casein هو أكترهو الـ major هو الـ highest + +123 +00:08:50,220 --> 00:08:53,020 +molecular weight عدد الـ phosphate group فيه من + +124 +00:08:53,020 --> 00:08:57,620 +تمانية لعشرة الـ beta casein هو أقل molecular + +125 +00:08:57,620 --> 00:09:01,260 +weight من ألفة وأعلى من كامة molecular weight له + +126 +00:09:01,260 --> 00:09:06,080 +أقل من ألفة وأعلى من كامة بيتكون من خمسة phosphate + +127 +00:09:06,080 --> 00:09:10,610 +group متصلة فيهبحكيلي الـ Beta-Casein more + +128 +00:09:10,610 --> 00:09:14,910 +hydrophobic than Alpha-Casein and Kappa-Casein الـ + +129 +00:09:14,910 --> 00:09:20,290 +Beta-Casein أعلى هيدروفوبك من Alpha ومن Kappa الـ + +130 +00:09:20,290 --> 00:09:24,410 +Beta أعلى هيدروفوبك كاره للماء أكتر من Alpha و + +131 +00:09:24,410 --> 00:09:28,750 +أكتر من Kappa ليش؟ لأن الأحماض الأمينية المكونة + +132 +00:09:28,750 --> 00:09:33,650 +إلي أغلبها non-polar أغلبها هيدروفوبك كاره للماء + +133 +00:09:34,660 --> 00:09:38,960 +حكيلي، بسبب أن ألفا كازين وبيتا كازين مرتبطين + +134 +00:09:38,960 --> 00:09:45,860 +بالكالسيوم هم مرتبطين بالكالسيوم لأنهم مرتبطين + +135 +00:09:45,860 --> 00:09:50,240 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +136 +00:09:50,240 --> 00:09:53,080 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +137 +00:09:53,080 --> 00:09:54,960 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +138 +00:09:54,960 --> 00:09:57,260 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +139 +00:09:57,260 --> 00:10:00,740 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +140 +00:10:00,740 --> 00:10:04,480 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +141 +00:10:04,480 --> 00:10:09,090 +بالكحطيت عليهم كالسيوم، هيترسبه، ليش؟ لأنه بيصير + +142 +00:10:09,090 --> 00:10:13,110 +ionization للفوسفات، ووجود الكالسيوم، فبيصير + +143 +00:10:13,110 --> 00:10:17,770 +مترسب، بيبطل soluble، بيصير insoluble زي المعادل + +144 +00:10:17,770 --> 00:10:20,670 +اللي تحت مكتوب، أن البروتين موطنه لسه فيه + +145 +00:10:20,670 --> 00:10:23,850 +phosphate group، يعني phosphoprotein، زائد + +146 +00:10:23,850 --> 00:10:27,190 +كالسيوم، لو ضفنا عليه كالسيوم، بيصير ionization + +147 +00:10:27,190 --> 00:10:30,930 +للفوسفات في وجود الكالسيوم، فبيصير insoluble + +148 +00:10:34,010 --> 00:10:39,450 +طب بالنسبة ل كابا كازين الكابا كازين مش زي Alpha و + +149 +00:10:39,450 --> 00:10:43,470 +Beta كازين يحتوي فقط هو أقل Molecular weight و + +150 +00:10:43,470 --> 00:10:46,930 +يحتوي فقط على 2 Phosphate Group بس على 2 Phosphate + +151 +00:10:46,930 --> 00:10:51,270 +Group النسبة الأكبر فيه هي Carbohydrate هي التأول + +152 +00:10:51,270 --> 00:10:56,910 +من Carbohydrate مليء بالسُكَر الكابا كازين مش زي + +153 +00:10:56,910 --> 00:11:02,270 +Alpha و Beta كازين يحتوي فقط هو أقلبيحتوي فقط على + +154 +00:11:02,270 --> 00:11:04,710 +two phosphate group بس على اتنين من ال phosphate + +155 +00:11:04,710 --> 00:11:09,550 +group النسب الأكبر فيه هي carbohydrate التكون من + +156 +00:11:09,550 --> 00:11:14,950 +carbohydrate مليء بالسكر فبسموه glycoprotein + +157 +00:11:14,950 --> 00:11:19,890 +الكعبة تزين هو glycoprotein يحتوي على سكر ياد فهو + +158 +00:11:19,890 --> 00:11:24,530 +hydrophilicThey are stable in the presence of + +159 +00:11:24,530 --> 00:11:28,250 +calcium لأنه فيه بس دنتين فوسفات جروب أما الأغلبه + +160 +00:11:28,250 --> 00:11:32,310 +هو سكريات فهو stable هو ثابت في وجود الكالسيوم + +161 +00:11:32,310 --> 00:11:36,830 +مابتأثرش في الكالسيوم زي الألفة والبيتا لو حصلهم + +162 +00:11:36,830 --> 00:11:40,610 +كالسيوم حاجة بيصيروا insoluble بيترسبوا لأنه عندهم + +163 +00:11:40,610 --> 00:11:43,910 +فوسفات جروب بيصيرلها ionized بالكالسيوم مابترسبوا + +164 +00:11:43,910 --> 00:11:48,290 +لكن القعبة كازين لأن كمية الفوسفات عنده أقلين + +165 +00:11:48,290 --> 00:11:51,920 +وإنما كمية الكاربوهيدرات السكر هي اللي عاليةأنا لو + +166 +00:11:51,920 --> 00:11:56,500 +حطيت calcium مابيتأثر، بيكون steric وهذا بيلعب دور + +167 +00:11:56,500 --> 00:12:00,520 +في حماية ال alpha و ال beta كزين + +168 +00:12:06,820 --> 00:12:10,580 +أن هما المفروض يكونوا مترسبين مش ضايبين في الحليب + +169 +00:12:10,580 --> 00:12:13,880 +بس احنا لما نشوف الحليب هل بنشوف فيه حاجة مترسبة + +170 +00:12:13,880 --> 00:12:17,880 +تحت ولا كله خليط مع بعض، بنشوفه كله خليط، مانشوفش + +171 +00:12:17,880 --> 00:12:20,340 +أنه فيه حاجة مترسبة تحت، يعني Alpha و Beta ما + +172 +00:12:20,340 --> 00:12:23,180 +بيكونوا مترسبين، ليش Alpha و Beta ما بيكونوا + +173 +00:12:23,180 --> 00:12:27,760 +مترسبين؟ لأن الكاباكازين التي لا تتأثر في وجود + +174 +00:12:27,760 --> 00:12:33,380 +الكالسيوم تعمل على حماية Alpha و Beta من الترسب + +175 +00:12:33,840 --> 00:12:37,820 +they protecting play a role in protecting other + +176 +00:12:37,820 --> 00:12:41,460 +casein from precipitation and make casein more + +177 +00:12:41,460 --> 00:12:46,220 +soluble كيف بتكوين حاجة اسمها الـ mecells؟ كيف + +178 +00:12:46,220 --> 00:12:49,720 +بتحمي Alpha و Beta بتكوين حاجة بتسميها الـ + +179 +00:12:49,720 --> 00:12:54,000 +mecells؟ الـ mecells هذه هي large molecule هي مركب + +180 +00:12:54,000 --> 00:12:58,880 +كبير بيتكون من Kappa casein و Alpha casein و Beta + +181 +00:12:58,880 --> 00:13:05,370 +casein مع بعض كيف أجوا؟ انه كانوا دائماالألفة + +182 +00:13:05,370 --> 00:13:10,130 +والبيتا كازين وبرا محوط عليهم ومغطيهم من برا كلها + +183 +00:13:10,130 --> 00:13:15,170 +كابا كازين فمين ظاهر للملك من برا بتكون الكابا برا + +184 +00:13:15,170 --> 00:13:18,150 +والألفة والبيتا جوجل مش ظاهرين للكالسيون + +185 +00:13:18,150 --> 00:13:21,870 +فالكالسيون مابيقدر يشوفهم ويروح يأين مجموعات + +186 +00:13:21,870 --> 00:13:25,650 +الفوسفات الموجودة فيها فبتعمل الكابا على حماية + +187 +00:13:25,650 --> 00:13:30,230 +ألفة وبيتا بيحكي لي neither the alpha nor the beta + +188 +00:13:30,230 --> 00:13:32,890 +-casein is soluble in milk singly or in + +189 +00:13:32,890 --> 00:13:36,990 +combinationولا Alpha ولا Beta بيدوبوا في الحليب + +190 +00:13:36,990 --> 00:13:41,210 +سواء واحد فيهم أو اتنين مع بعض، بيدوبوش في الحليب + +191 +00:13:41,210 --> 00:13:44,370 +لأنه إذا وجود ال calcium في الحليب، خلاص هم + +192 +00:13:44,370 --> 00:13:47,790 +الاتنين insoluble سواء واحد منهم أو اتنين معاك، + +193 +00:13:47,790 --> 00:13:51,770 +لكن إذا اضفت كابا، if kaba casein isadded to + +194 +00:13:51,770 --> 00:13:55,330 +either one or to the combination of the two لو + +195 +00:13:55,330 --> 00:13:59,310 +ضفتي الكابا كزين على الألفة والبيتا اتنين مع بعض + +196 +00:13:59,310 --> 00:14:04,090 +او على واحد منهم، لذا الكزين complex is soluble + +197 +00:14:04,090 --> 00:14:08,970 +فهالكزين هيعمل complex يكون ذائب في الحليب، هذا ال + +198 +00:14:08,970 --> 00:14:11,010 +complex بنسميه ميسم + +199 +00:14:14,240 --> 00:14:19,960 +ما هي الـ Measles؟ مصطلح + +200 +00:14:19,960 --> 00:14:25,020 +الـ Measles هو مصطلح كيميائي واطلق على التركيب + +201 +00:14:25,020 --> 00:14:30,560 +المركبات الكبيرة للـ Very Very Large Molecules الـ + +202 +00:14:30,560 --> 00:14:32,800 +Very Very Large Molecules + +203 +00:14:37,840 --> 00:14:41,800 +أما المركبات الكبيرة، حقيقة هي كبيرة جدا أنها تكون + +204 +00:14:41,800 --> 00:14:44,380 +ضائبة في الماء، المركبات كبيرة كيف بدأت تدوب في + +205 +00:14:44,380 --> 00:14:49,280 +الماء، بل هذه الملكولات الكبيرة ستصبح مصطلحات تسمح + +206 +00:14:49,280 --> 00:14:51,880 +لهم بالدخول في الماء + +207 +00:15:06,030 --> 00:15:10,890 +ماء لأنها مُركّبات كبيرة فتوزيع هذه الـ large + +208 +00:15:10,890 --> 00:15:14,590 +structure in water dispersion أو انتشار this large + +209 +00:15:14,590 --> 00:15:18,570 +mole structure in water is known as a colloidal + +210 +00:15:18,570 --> 00:15:22,410 +suspension بنسميها توزيع هذه المُركّب الكبير اللي + +211 +00:15:22,410 --> 00:15:26,230 +هم القعبة كازين برا ال فوبيتا بتكون في الداخل + +212 +00:15:26,230 --> 00:15:29,670 +فهدولة كون مُركّب كامل كأنه دائرة جواها + +213 +00:15:35,820 --> 00:15:40,240 +ماشى فى الميّه و هو كبير فكيف هو توزع فى الماء هى؟ + +214 +00:15:40,240 --> 00:15:43,240 +هل هو دائب فى الماء؟ بيبين كأنه colloidal + +215 +00:15:43,240 --> 00:15:47,460 +suspension كأنه محلول غروي أو محلول معلق فى الماء + +216 +00:15:47,460 --> 00:15:51,340 +لأنه بيسمحسمعه الـ structure that allow large + +217 +00:15:51,340 --> 00:15:54,520 +molecules to remain colloidally suspended in water + +218 +00:15:54,520 --> 00:15:58,300 +هذا المركب اللى بيكون معلق فى الماء our term + +219 +00:15:58,300 --> 00:16:02,940 +بنسميه الـ measles الـ measles هو المركب المعلق فى + +220 +00:16:02,940 --> 00:16:08,760 +الماءطيب، دي حالة الكازينة بيحكي ليه؟ اللي هو + +221 +00:16:08,760 --> 00:16:12,500 +الـmesons اللي بتتكونها الكازين اللي بتلت انواع من + +222 +00:16:12,500 --> 00:16:16,160 +البروتينات بيكون للخارج the part of the casein + +223 +00:16:16,160 --> 00:16:19,760 +molecule that have an affinity for water from the + +224 +00:16:19,760 --> 00:16:24,020 +outside of casein meson اللي بيكون محبب للماء، + +225 +00:16:24,020 --> 00:16:25,200 +وعنده جاذبية للماء + +226 +00:16:30,120 --> 00:16:33,700 +في خارج الـ mesons ومن هو هنا في حالة الـ casein + +227 +00:16:33,700 --> 00:16:38,120 +كل الخارج هو الـ carbacasein على العكس ال part of + +228 +00:16:38,120 --> 00:16:40,720 +casein molecules that are hidden ده هو طرف اللي + +229 +00:16:40,720 --> 00:16:44,140 +بيكره الميه اللي بيحبش الميه، بيذوبش في الميه، + +230 +00:16:44,140 --> 00:16:47,740 +form the inner core of the mesons، بيكون في + +231 +00:16:47,740 --> 00:16:51,480 +الداخل، في الجزء الداخلي ومن هم اللي بيكره الميه + +232 +00:16:51,480 --> 00:16:56,980 +كل الداخل هي الـ α و الـ beta caseinبحكيلي الكزين + +233 +00:16:56,980 --> 00:17:00,300 +is present as كزينات which mean that it's bind to + +234 +00:17:00,300 --> 00:17:04,340 +calcium and magnesium الكزين لما يترسب إذا صار + +235 +00:17:04,340 --> 00:17:08,840 +لترسيب بنسميه كزينات بتحول اللي عادي اسمها كزينات + +236 +00:17:08,840 --> 00:17:13,940 +يعني هو الكزين المترسب متى هاد هيترسب إذا جدرت + +237 +00:17:13,940 --> 00:17:18,540 +ترتبط مع كالسيوم أو مغنيسيوم بتعمل ionization و + +238 +00:17:18,540 --> 00:17:20,060 +بترسب الكزين + +239 +00:17:23,090 --> 00:17:26,910 +طب هنا عندنا صور للألفة والبيتا والكابا كزي في + +240 +00:17:26,910 --> 00:17:30,570 +عندنا لليمين الصورة اللي تحت الأبيض بالأسم ده هي + +241 +00:17:30,570 --> 00:17:35,010 +عبارة عن صور ل ال measles للكزين measles اللي هو + +242 +00:17:35,010 --> 00:17:39,130 +الكابا والبيتا والألفا كزي مع بعض كيف شكل ال + +243 +00:17:39,130 --> 00:17:44,250 +measles تحت المجهد ممكنها كرة كريات تحتوي من + +244 +00:17:44,250 --> 00:17:48,190 +الكابا من الخارج وبيتا وألفا في الداخل + +245 +00:17:50,410 --> 00:17:55,170 +هنا صورة الـ Measles الكورة هذه الكتلة تتكوين من + +246 +00:17:55,170 --> 00:17:58,950 +Alpha و Beta و Kappa Alpha لأو Beta للداخل و Kappa + +247 +00:17:58,950 --> 00:18:04,130 +للخارج هي مكبرة بالإلكترون مايكروسكوبي تحت المجهر + +248 +00:18:04,130 --> 00:18:09,750 +الإلكتروني صورة من المجهر الإلكتروني حكينا في + +249 +00:18:09,750 --> 00:18:12,730 +المعمل السابق أن الـ isoelectric point لمعظم + +250 +00:18:12,730 --> 00:18:18,470 +البروتينات تتروح من pH 4 إلى 6اللي بترى الـ Y كمان + +251 +00:18:18,470 --> 00:18:22,970 +من البروتينات هي من BH 4 إلى 6 طيب ليش ال كازين + +252 +00:18:22,970 --> 00:18:27,630 +دائب في الحليب؟ why casein is solvent in milk؟ + +253 +00:18:27,630 --> 00:18:31,650 +هلجد؟ هو هيتوب حكينا بيكون دائب إذا ال BH أعلى من + +254 +00:18:31,650 --> 00:18:36,230 +ال BI أو أقل من ال PR لكن متى فاتساوة ال BH مع ال + +255 +00:18:36,230 --> 00:18:42,690 +BI يترسم؟ هلجد؟ الحليب بيحكيني أنه ليش هو دائب + +256 +00:18:42,690 --> 00:18:50,050 +لأنه ال BI للوالـ pH للحليب هي 6 و 6 الـ Bi + +257 +00:18:50,050 --> 00:18:55,590 +للكازين 4 و 7 الـ pH للحليب هي القاعدي 6 و 6 فالـ + +258 +00:18:55,590 --> 00:19:00,570 +pH للحليب أعلى من الـ Bi مش متساوية، هي أعلى، بما + +259 +00:19:00,570 --> 00:19:01,290 +أنها أعلى + +260 +00:19:04,750 --> 00:19:08,190 +بتكون الشحنات نيجاتيف اللي على الكزيد، pH أعلى من + +261 +00:19:08,190 --> 00:19:14,830 +الـPI، شحنات متشابه حاجانة بتتنافر، بيصير قوة + +262 +00:19:14,830 --> 00:19:17,450 +تنافر، بتتوزع فيه السائل و بتكون + +263 +00:19:22,570 --> 00:19:27,230 +بالانمال فكيف بدي أداوبها لازم أوصل الـ pH تاعت + +264 +00:19:27,230 --> 00:19:32,150 +الحنيب للبيئة I للكازين ممكن هادي أعملها عن طريق + +265 +00:19:32,150 --> 00:19:35,110 +ال bacterial action بفعل البكتيريا وحكينا في + +266 +00:19:35,110 --> 00:19:36,010 +المعمل السابق + +267 +00:19:39,810 --> 00:19:44,030 +بتجي بكتيريا تحول سكر اللاكتوز اللي موجود في + +268 +00:19:44,030 --> 00:19:48,530 +الحليب إلى lactic acid اللاكتك أسد هو عبارة عن حمض + +269 +00:19:48,530 --> 00:19:52,850 +والحمض هذا بيقلل ال pH فهيقلل ال pH بتاعة الملك من + +270 +00:19:52,850 --> 00:19:57,870 +6.6 اللي هو الطبيعي إلى 4.7 ال pH بتاعة الحليب + +271 +00:19:57,870 --> 00:20:04,450 +هيتقل من 6.6 إلى 4.7 4.7 صارت ال pH للحليب هي 4.7 + +272 +00:20:04,450 --> 00:20:08,470 +طب و ال ISO electrical point بتاعة الكازين 4.7 + +273 +00:20:08,940 --> 00:20:13,100 +فصارت الـ pH للحليب مساوية للـ PI تاعت الكازين + +274 +00:20:13,100 --> 00:20:17,500 +وبالتالي بيترسب لأن حكينا ما تمت ساوية الـ pH مع + +275 +00:20:17,500 --> 00:20:20,160 +الـ PI، لذا بيترسب + +276 +00:20:24,520 --> 00:20:29,420 +طرق ترسيب الكازين كيف ممكن أعمل precipitation of + +277 +00:20:29,420 --> 00:20:33,520 +casein؟ أول طريقة ممكن بإضافة excess calcium أيون، + +278 +00:20:33,520 --> 00:20:37,760 +إنه إضافة كميات كبيرة من أيونات الكالسيون بحيث + +279 +00:20:37,760 --> 00:20:41,520 +إنها توصل للـAlpha والـBeta كازين وتأين + +280 +00:20:41,520 --> 00:20:46,400 +الفسويتجروب اللي موجودة فيها ويترسبيصير Intolerant + +281 +00:20:46,400 --> 00:20:50,640 +طريقة تانية ممكن بإضافة acid أنه أضيف حمض زي ال + +282 +00:20:50,640 --> 00:20:55,280 +HCl أو ال Acetic acid لأن وسط الحليب حكينا أنه وسط + +283 +00:20:55,280 --> 00:21:00,520 +قاعده بيكون alkaline 6 و 6 ال pH للملك و ال PI + +284 +00:21:00,520 --> 00:21:06,720 +للكازين هي 4.7 فانا بدي أوصل ال pH بتاع الملك من 6 + +285 +00:21:06,720 --> 00:21:11,400 +و 6 إلى 4 و 7 كيف بدي أجللها أنه أضيف حمض الحمض + +286 +00:21:11,400 --> 00:21:17,290 +هيقلل ال pH فتوصل ال pH لللـ «بي آي» للـ «كازين» + +287 +00:21:17,290 --> 00:21:21,490 +ويترسب الـ «كازين» هذا مبدأ عملنا لليوم إن أنا بدأ + +288 +00:21:21,490 --> 00:21:26,150 +أضيف حمق عشان يقلل ال «بي آي» و أرسب ال «كازين» + +289 +00:21:26,150 --> 00:21:29,330 +طريقة التالتة ممكن بضعفة الـ «رنين» للـ «إنزاين» + +290 +00:21:29,330 --> 00:21:33,390 +طريقة الرابعة بضعفة عن طريقة الـ «باكتيريا الأكشن» + +291 +00:21:33,390 --> 00:21:37,010 +اللي حكينا عنه إنه كيف تشتغل الباكتيريا وتحويل سكر + +292 +00:21:37,010 --> 00:21:41,190 +اللاكتوز إلى «لاكتك أسد» مدام و أسد بيقلل ال «بي + +293 +00:21:41,190 --> 00:21:46,650 +آي» لحليببسبب الـ Renin enzyme كيف بيشتغل، كيف + +294 +00:21:46,650 --> 00:21:50,250 +بيرسل بالكاتين الـ Renin enzyme هو أنزين باللاجئ + +295 +00:21:50,250 --> 00:21:54,270 +موجود فيه الـ calves و ال goats موجود فيه العجل و + +296 +00:21:54,270 --> 00:21:58,830 +العنزة أو الماعز، هو عبارة عن هيدروليسز أنزين هو + +297 +00:21:58,830 --> 00:22:02,590 +أنزين مكسر، بيطلق عليه peptidase، peptidase يعني + +298 +00:22:02,590 --> 00:22:06,410 +أنزيمات بتكسر، هو بيكسر الـpeptide bond بين + +299 +00:22:06,410 --> 00:22:12,710 +الأحماض الأمانيةطب كيف يشتغل؟ كيف الميكانيزم للـ + +300 +00:22:12,710 --> 00:22:16,150 +Renin؟ الـ Renin هو إنزايم حكينا Hydrolysis + +301 +00:22:16,150 --> 00:22:19,950 +إنزايم، إنزين مكسب، بيروح على الكاباكازين، على + +302 +00:22:19,950 --> 00:22:22,170 +الموجود اللي يمين للخارج، اللي بالظهر، + +303 +00:22:22,170 --> 00:22:25,330 +الكاباكازين، بيروح على الـ Renin، الكاباكازين + +304 +00:22:25,330 --> 00:22:28,470 +بيعمل عليها تكسيرها، بيعمل Hydrolysis breaking the + +305 +00:22:28,470 --> 00:22:33,250 +peptide bond، بيحولها لحاجة بسميها Paracabacazine + +306 +00:22:34,590 --> 00:22:38,790 +هو كان عامل حماية كجدار حماية للـ Beta والـ Alpha + +307 +00:22:38,790 --> 00:22:42,810 +اللي في داخله لما يتكسر ويتحول لبارك كابا كازين + +308 +00:22:42,810 --> 00:22:46,530 +اللي هو عبارة عن كازين مكسر فيه فتحات يعني صارت + +309 +00:22:46,530 --> 00:22:51,310 +Alpha و Beta ظاهرين للخالرفهو بيقدرش يحميهم، + +310 +00:22:51,310 --> 00:22:55,770 +Cannot prevent casein from precipitate فالبرا كابا + +311 +00:22:55,770 --> 00:22:58,430 +كازين هذا مادوش قدرة أنه يحمي الكازين من الترس + +312 +00:22:58,430 --> 00:23:02,910 +بليش؟ لأنه ربعا كابا كازين مكسر لدهرة الألفة + +313 +00:23:02,910 --> 00:23:06,530 +والباتا لوجود الكالسيوم اللي موجود في الحليب بيقدر + +314 +00:23:06,530 --> 00:23:11,350 +يدخل لجوا ويعمل ionization للألفة والباتا كازين + +315 +00:23:11,350 --> 00:23:16,070 +لمجموعات الفسبات الموجودة فيه مدام اتأينه خلاص + +316 +00:23:16,070 --> 00:23:19,910 +بيصير ال precipitate بيترسبحكي ليه لو الـ Calcium + +317 +00:23:19,910 --> 00:23:23,070 +removed from milk، the renin cannot form a + +318 +00:23:23,070 --> 00:23:26,390 +precipitate to milk. إذا الـ Calcium شيلته أنا من + +319 +00:23:26,390 --> 00:23:30,190 +الحليب، وكسر .. واجه الـ renin انزعي، كسر الكابا + +320 +00:23:30,190 --> 00:23:33,230 +كازين، خلاص، مافيش Calcium، مش هيدخل على الـ Alpha + +321 +00:23:33,230 --> 00:23:36,650 +والـ Beta، ومش هيعمل الـ precipitation. لكن الـ + +322 +00:23:36,650 --> 00:23:40,050 +renin لازم مين يشتغل معاه؟ الـ renin يكسر ويجي الـ + +323 +00:23:40,050 --> 00:23:43,470 +Calcium، يعمل Ionization، عشان يعمل ال + +324 +00:23:43,470 --> 00:23:48,430 +precipitation لكازين.طب البكتيريا الـ Action إيه + +325 +00:23:48,430 --> 00:23:52,290 +عادة اللي ما حكيناها؟ البكتيريا اللي حكيناها إنها + +326 +00:23:52,290 --> 00:23:56,430 +بتيجي على الحليب، بتعمل على هضم اللاكتوز، بتكون + +327 +00:23:56,430 --> 00:23:59,910 +منه lactic acid، بتحول سكر اللاكتوز اللي موجود في + +328 +00:23:59,910 --> 00:24:04,340 +الحليب إلى lactic acidLactic acid هذا حمض فبقلل + +329 +00:24:04,340 --> 00:24:10,260 +الـ pH للحليب من 6.6 إلى 4.7 تصير الـ pH للحليب 4 + +330 +00:24:10,260 --> 00:24:14,240 +.7 4.7 هي نفسها الـ isoelectric point بتاعة + +331 +00:24:14,240 --> 00:24:19,240 +الكازين بدل من الـ pH تساوي الـ PI إذا بيترسم + +332 +00:24:19,240 --> 00:24:25,050 +الكازيناللي إذا جلت البيئة و المبيئة ليه في ال + +333 +00:24:25,050 --> 00:24:28,530 +degrees of milk جلت البيئة تحت الحليب ووصلت إلى ال + +334 +00:24:28,530 --> 00:24:32,170 +isoelectric point بتاعت الكازين صاروا متساوين + +335 +00:24:32,170 --> 00:24:36,270 +بينفصل الحليب إلى طبقتين حاجة بتسميها Curds and + +336 +00:24:36,270 --> 00:24:40,600 +Whey بينفصل الحليب إلى Curds and Wheyالـ Curds هي + +337 +00:24:40,600 --> 00:24:43,160 +عبارة عن الكازين هو اللي بيكون بالأسفل، الـ + +338 +00:24:43,160 --> 00:24:45,500 +precipitate اللي بينزل للأسفل اللي هو بروتين + +339 +00:24:45,500 --> 00:24:48,560 +الكازين اللي هو الـ dairy product obtained by + +340 +00:24:48,560 --> 00:24:51,440 +precipitation of milk with renin or acidic + +341 +00:24:51,440 --> 00:24:56,400 +substance and then the draining of the liquid + +342 +00:24:56,400 --> 00:25:00,610 +versionالـ Curds هاد عبارة عن المنتج اليومي اللي + +343 +00:25:00,610 --> 00:25:04,030 +بينتج من تلصيب الحليب باستخدام سواء الـ renin + +344 +00:25:04,030 --> 00:25:09,050 +enzyme أو باستخدام مادة أستيتك فتنزل لتحت هذا + +345 +00:25:09,050 --> 00:25:12,110 +البريس الكيردس و تكون فيه liquid portion في الأعلى + +346 +00:25:12,110 --> 00:25:16,110 +ال liquid portion هذا اللي في الأعلى بيسوي way أو + +347 +00:25:16,110 --> 00:25:19,930 +milk serum is the liquid remaining after milk has + +348 +00:25:19,930 --> 00:25:23,670 +been coagulated and removal of curdsالحليب إذا + +349 +00:25:23,670 --> 00:25:27,730 +قللت ال pH ووصلتها ل ال PI تاعت الكازين ينفصل إلى + +350 +00:25:27,730 --> 00:25:31,250 +طبق تان حاجة بتسميها كيرتز بتكون في الأسفل اللي هو + +351 +00:25:31,250 --> 00:25:34,690 +الطبقة السميكة اللي بتكون في الأسفل اللي هي المنتج + +352 +00:25:34,690 --> 00:25:38,550 +اليومي اللي هو عبارة عن الكازين في الأعلى بيكون ال + +353 +00:25:38,550 --> 00:25:41,610 +whey أو الملك السيروم اللي هو الجزء السائل اللي هو + +354 +00:25:41,610 --> 00:25:43,130 +باقي المكونات + +355 +00:25:45,120 --> 00:25:49,760 +طيب إيش هو معملنا لليوم؟ معملنا لليوم هو عبارة عن + +356 +00:25:49,760 --> 00:25:54,260 +إيش هو يعني ال objective منه إنه isolate casein + +357 +00:25:54,260 --> 00:25:57,980 +from milk and calculate a percentage إن أنا بتعزل + +358 +00:25:57,980 --> 00:26:01,960 +ال casein من الحليب وود أحسبله قداش النسبة + +359 +00:26:01,960 --> 00:26:04,600 +المقاوية اللي هو ال percentage، قداش نسبة موجودة + +360 +00:26:04,600 --> 00:26:08,460 +في الحليببنان على أي مبتدأ الـ principle استخدام + +361 +00:26:08,460 --> 00:26:11,260 +Acetic Acid اللي أنا بتستخدم حمض هو الـ Acetic + +362 +00:26:11,260 --> 00:26:16,440 +Acid أضيفه على الكازين يعطيني كازينات اللي هو + +363 +00:26:16,440 --> 00:26:20,980 +ترسيب للكازين، لذا هو المبتدأ ان الـ principle أن + +364 +00:26:20,980 --> 00:26:27,450 +أنا أضيفPacific Acid زي كزين يعطيني كزينة طيب كيف + +365 +00:26:27,450 --> 00:26:32,450 +الخطوات؟ بدي أجيب cup أحط عليه فيه عشرة مل من + +366 +00:26:32,450 --> 00:26:37,950 +الحليب و أحطه في ال water bath على أربعين درجة + +367 +00:26:37,950 --> 00:26:41,710 +سيليزياس لخمسة minutes أحطها على درجة حرارة في + +368 +00:26:41,710 --> 00:26:45,370 +الميه على درجة حرارة عارفين درجة لمدة خمس دقائق + +369 +00:26:45,370 --> 00:26:51,160 +هذا بس عشان أدفع الحليببعدين هطلعه و هضيف عليه 15 + +370 +00:26:51,160 --> 00:26:55,460 +drop من ال Acetic Acid هضيف عليه Acetic Acid حمض + +371 +00:26:55,460 --> 00:26:59,240 +عشان يقلق البيئة عشان هيبقى على 15 drop Acetic + +372 +00:26:59,240 --> 00:27:03,720 +Acid لتقليل البيئة و أعمل mix هلاجي الحليب فصل + +373 +00:27:03,720 --> 00:27:08,320 +عندى لطبقتين بيكون كل المكونات فوق و تحت بينزل + +374 +00:27:08,320 --> 00:27:12,740 +عندى casein مع lipidبكون عندي نازل فيه الأسفل + +375 +00:27:12,740 --> 00:27:17,260 +casein و lipid و فوق بتكون هنا بدي أجيب الصفين بدي + +376 +00:27:17,260 --> 00:27:21,740 +أعمل filtration عاملينيه فلترة بجيب tube و funnel + +377 +00:27:21,740 --> 00:27:25,720 +محجن و filter paper اللي هي ورقة من ال filter فيها + +378 +00:27:25,720 --> 00:27:29,960 +أجيب ال tube بحط فيها funnel محجن المحجن هذا بحط + +379 +00:27:29,960 --> 00:27:33,320 +فيه ال filter paper اللي هي ورقة الفلترة و بدي + +380 +00:27:33,320 --> 00:27:36,100 +أدير ال cup اللي أنا حدرت اللي هو العشرة مل من + +381 +00:27:36,100 --> 00:27:40,340 +الملك مع خمس عشر دروب أسيتكاسةبفلتر بينزل تحت + +382 +00:27:40,340 --> 00:27:44,660 +الميه وبطل عندى فى ال filter paper الكازين مع اللى + +383 +00:27:44,660 --> 00:27:49,310 +بدهالموجود باخدهم من الورجها دول و بحطهم في cup + +384 +00:27:49,310 --> 00:27:54,710 +بحطهم في cup لجهة ال cup هذا صرفيه casein و lipid + +385 +00:27:54,710 --> 00:27:57,810 +أنا بدي بس ال casein مابديش ال lipid كيف بدي أتخلص + +386 +00:27:57,810 --> 00:28:01,270 +من ال lipid؟ ده أجيب مادة بيدوب فيها ال lipid على + +387 +00:28:01,270 --> 00:28:05,390 +مبدأ like dissolve like إن المضيبات بديبانه إيش + +388 +00:28:05,390 --> 00:28:08,150 +المادة اللي بتجيبها ال lipid؟ زي ال ethanol أو + +389 +00:28:08,150 --> 00:28:11,790 +ether ethanol فبدي أضيف على ال cup على ال casein و + +390 +00:28:11,790 --> 00:28:15,920 +ال lipid ده أضيف خمسة من ال ethanolو 5 مل إيثر + +391 +00:28:15,920 --> 00:28:20,480 +إيثانول و بعمل mix هدول هيدوبوا الدهون .. الدهون + +392 +00:28:20,480 --> 00:28:24,580 +هيدوبوا الليبد هيعملوه على إدابة الليبد فبيدوب + +393 +00:28:24,580 --> 00:28:28,220 +الليبد و بيضل عند الكازين هو اللي مترسم أعمل كمان + +394 +00:28:28,220 --> 00:28:32,480 +مرة فالترة لهذا ال cup بجيب ال tube بحط فيه funnel + +395 +00:28:32,480 --> 00:28:36,780 +محجن بحط في .. في ال funnel هذا filter بابا بحط + +396 +00:28:36,780 --> 00:28:40,960 +فيه ورقة الفلترة و بقعدير ال cup هينزل الساعة كله + +397 +00:28:40,960 --> 00:28:43,780 +لتحت اللي هو عبارة عن إيثانول و لبد فهينزل في ال + +398 +00:28:43,780 --> 00:28:47,420 +tubeويتضل في ال filter paper في الورقة هيضل فيها + +399 +00:28:47,420 --> 00:28:52,420 +الكازين بخلي الورقة تجف شوية عشان يتطير ال Ethanol + +400 +00:28:52,420 --> 00:28:54,920 +أو الاتر Ethanol اللى موجود فيها الكحول اللى انا + +401 +00:28:54,920 --> 00:28:58,880 +حطيتها اللى اجت فيها بتطير فبيضل بس عليها الكازين + +402 +00:28:58,880 --> 00:29:03,720 +بعد ما تجف بوزلها في الميزان بحطها و بسجل عندي + +403 +00:29:03,720 --> 00:29:06,200 +الوزنة كتاش الوزنة عندي + +404 +00:29:09,850 --> 00:29:12,190 +يعني الوزن اللي أنا طلعتها بتحسب منها ال + +405 +00:29:12,190 --> 00:29:16,050 +percentage of casein in milk قداش نسبة ال casein + +406 +00:29:16,050 --> 00:29:19,450 +الموجود في الحليب ال percentage of casein بتساوي + +407 +00:29:19,450 --> 00:29:22,530 +ال gram of casein قداش أنا وزنة ال casein اللي + +408 +00:29:22,530 --> 00:29:27,030 +طلعتها على ال gram of milk وزنة الحليب درمية في + +409 +00:29:27,030 --> 00:29:30,220 +الميةالـ gram of casein هذه الوزن اللي أنا وزنتها + +410 +00:29:30,220 --> 00:29:32,520 +في الآخر اللي كانت على الورقة ووزنتها على الميزان + +411 +00:29:32,520 --> 00:29:36,240 +جديش طلعت ماني ال gram of milk اللي هي الحليب جديش + +412 +00:29:36,240 --> 00:29:39,540 +أنا أخد كمية أول شي عشرة mil من الحليب فهو عشرة + +413 +00:29:39,540 --> 00:29:44,020 +ضرب مية في المية و بطلع النسبة و بال normal range + +414 +00:29:44,020 --> 00:29:49,160 +المفروض تطلع معنا نسبة ال casein من تلاتة إلى خمسة + +415 +00:29:49,160 --> 00:29:52,000 +في المية تلاتة إلى خمسة في المية + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/nTcz4I3nh3A_raw.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/nTcz4I3nh3A_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..a1d5404c6113ca3f49e247ce206c1f204295d48c --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/nTcz4I3nh3A_raw.srt @@ -0,0 +1,1660 @@ +1 +00:00:01,890 --> 00:00:06,410 +اليوم راح نحكي بمعمل هو isolation of casein from + +2 +00:00:06,410 --> 00:00:10,890 +milk اللي هو عزل ال protein ال casein من الحليب + +3 +00:00:10,890 --> 00:00:15,770 +وهذا يعتبر تطبيق على المعمل الماضي إن أحنا صارنا + +4 +00:00:15,770 --> 00:00:19,710 +عارفين ال isoelectric point لل casein بدنا نوصل + +5 +00:00:19,710 --> 00:00:24,150 +البيت لحليب لل isoelectric point بتبعت ال casein + +6 +00:00:24,150 --> 00:00:29,350 +وبالتالي بيترسب ال protein ال casein و تبقى باقي + +7 +00:00:29,350 --> 00:00:30,410 +ال proteinات + +8 +00:00:33,330 --> 00:00:37,510 +في البداية بدنا نحكي عن البروتين أنه ينقسم إلى + +9 +00:00:37,510 --> 00:00:40,830 +قسمين نوع البروتين في simple protein و في + +10 +00:00:40,830 --> 00:00:45,530 +conjugated protein بروتينات بسيطة أو بروتينات + +11 +00:00:45,530 --> 00:00:52,330 +معقدة simple protein هي عبارة عن حماض أمينية + +12 +00:00:52,330 --> 00:00:56,750 +مرتبطة مع بعضها البعض بروابط بيبتديايعني لو كسرتها + +13 +00:00:56,750 --> 00:01:01,030 +هيدرولايزed to yield only amino acid زي الألبومين + +14 +00:01:01,030 --> 00:01:04,690 +والجلوبيلين لو كسرتها بس منتج منها أحماط أمينية + +15 +00:01:04,690 --> 00:01:09,260 +مثال عليها الألبومين والجلوبيلينconjugated protein + +16 +00:01:09,260 --> 00:01:13,780 +بروتينات معقدة اللي بتحتوي على أحماض أمنية ومتصل + +17 +00:01:13,780 --> 00:01:18,820 +فيها another group other chemical group بروتين + +18 +00:01:18,820 --> 00:01:21,440 +that function in interaction with other chemical + +19 +00:01:21,440 --> 00:01:24,940 +group attached by covalent bond or by weak + +20 +00:01:24,940 --> 00:01:28,780 +interaction المتصل مع الأحماض الأمنية مجموعة تانية + +21 +00:01:28,780 --> 00:01:32,240 +مجموعة group تانية ممكن تكون هذه المجموعة في صفية + +22 +00:01:32,240 --> 00:01:36,220 +group ممكن تكون carbohydrate ممكنوالـ lipid ممكن + +23 +00:01:36,220 --> 00:01:39,740 +مجموعة هيم فعش ما نسميها أو some example of + +24 +00:01:39,740 --> 00:01:43,400 +conjugated protein هو زي الـ lipoprotein اللي هو + +25 +00:01:43,400 --> 00:01:47,620 +protein متصل فيه مجموعة lipid الـ glycoprotein + +26 +00:01:47,620 --> 00:01:51,920 +اللي هو protein متصل فيه carbohydrate سكريات الـ + +27 +00:01:51,920 --> 00:01:54,660 +phosphoprotein هو عبارة عن protein مرتبط فيه + +28 +00:01:54,660 --> 00:01:59,300 +مجموعة فسفان والـ hemoprotein هو protein متصل فيه + +29 +00:01:59,570 --> 00:02:04,010 +مجموعة E إذا كانت أحماض أمينية متصلة معها group + +30 +00:02:04,010 --> 00:02:08,290 +تانية ساميها conjugated protein إذا كان بس أحماض + +31 +00:02:08,290 --> 00:02:12,510 +أمينية متصلة مع بعض البعض بسميه simple protein + +32 +00:02:15,400 --> 00:02:18,960 +ممكن نحكي عن الـ Phosphoprotein حكينا إن هو عبارة + +33 +00:02:18,960 --> 00:02:22,500 +عن بروتين أو عن أحماض أمينيا bonded to a substance + +34 +00:02:22,500 --> 00:02:25,540 +containing phosphoric acid متصلة فيه مجموعة + +35 +00:02:25,540 --> 00:02:30,040 +phosphate group أو أي مركّب مادة تحتوي على + +36 +00:02:30,040 --> 00:02:33,540 +phosphoric acid إذا كان موجود مجموعة phosphate + +37 +00:02:33,540 --> 00:02:38,870 +بسميه phosphoproteinلو جبنا أيونات الكالسيوم + +38 +00:02:38,870 --> 00:02:42,310 +أيونات الكالسيوم معروفة أنها بيكون plus والفوسفات + +39 +00:02:42,310 --> 00:02:46,370 +نجمة الفوسفات تكون minus إذا حطينا أيونات + +40 +00:02:46,370 --> 00:02:50,890 +الكالسيوم على بروتين يحتوي على فوسفات جروم بيصير + +41 +00:02:50,890 --> 00:02:56,190 +عملية ionization تأيّن للفوسفات جروم موجب مع سلب + +42 +00:02:56,190 --> 00:03:00,370 +الكلسيوم موجب و الفوسفات سلب فبأي نوع الكالسيوم + +43 +00:03:00,370 --> 00:03:04,070 +بأيّن الفوسفات تصير شحنات الموجب والسلبة متساوية + +44 +00:03:04,070 --> 00:03:07,660 +الشحنة الكل هي zeroفهذا بيزود الـ hydrophobic + +45 +00:03:07,660 --> 00:03:13,460 +interaction بيزود أنه يكون كاره للماء أو أنه يكون + +46 +00:03:13,460 --> 00:03:17,820 +غير قطبي فهذا بيأد إلى ال precipitation Ionized + +47 +00:03:17,820 --> 00:03:20,920 +phosphate group by calcium ion increase + +48 +00:03:20,920 --> 00:03:24,040 +hydrophobic interaction which lead to + +49 +00:03:24,040 --> 00:03:27,680 +precipitationإذا جيبت أيانات الكالسيوم، بحطها على + +50 +00:03:27,680 --> 00:03:31,200 +بروتين يحتوي على فوسفات، تكون الكالسيوم موجب + +51 +00:03:31,200 --> 00:03:35,720 +والفوسفات minus، بتأين الشحنات، بتعادلوا يعني، + +52 +00:03:35,720 --> 00:03:39,380 +الشحنات الموجبة أو السالبة، بزود الـhydrophobic، و + +53 +00:03:39,380 --> 00:03:44,900 +بيصير ال precipitation بترسب هذا البروتينطيب هنا + +54 +00:03:44,900 --> 00:03:48,160 +الصورة بتوضح ال milk composition اللي هي مكونات + +55 +00:03:48,160 --> 00:03:51,460 +الحليب ليش بتكون الحليب؟ بيتكون من carbohydrates + +56 +00:03:51,460 --> 00:03:56,400 +بيحتوي على سكريات و هو سكر اللاكتوز يحتوي على واطر + +57 +00:03:56,400 --> 00:04:00,020 +على ميه وهي أكبر نسبة في الحليب هي ميه منيرال + +58 +00:04:00,020 --> 00:04:03,660 +بيحتوي على منيرال على معادن زي الكالسيوم بوتاسيوم + +59 +00:04:03,660 --> 00:04:08,440 +صادم صادم فوسفرست يحتوي على فيتمين اللي هي فيتمين + +60 +00:04:08,440 --> 00:04:14,260 +A وD وKبيحتوي على proteins زي بروتين الكازين + +61 +00:04:14,260 --> 00:04:20,790 +بيحتوي على lipid على دهونزي ما حكينا تكرار إن + +62 +00:04:20,790 --> 00:04:25,530 +الحليب يتكون من فيتامين، فيتامين A وD وK، يتكون من + +63 +00:04:25,530 --> 00:04:28,590 +مينيرال زي الكالسيوم، بوتاسيوم، صوديوم، and + +64 +00:04:28,590 --> 00:04:32,570 +فوسفرس، يتكون من البروتين، و البروتين هذا يحتوي + +65 +00:04:32,570 --> 00:04:35,690 +على كل الأحمض الأمينية الأساسية، all essential + +66 +00:04:35,690 --> 00:04:38,570 +amino acid، يعني كل الأحمض الأمينية الأساسية + +67 +00:04:38,570 --> 00:04:42,070 +موجودة في الحليب، يحتوي على carbohydrates، على + +68 +00:04:42,070 --> 00:04:46,440 +سكريات، وأشهرها، و السكر الموجود في الحليب هوسكر + +69 +00:04:46,440 --> 00:04:51,460 +اللاكتوز وهو عبارة عن Dysaccharide سكر تنائي عبارة + +70 +00:04:51,460 --> 00:04:55,620 +عن اتحاد سكر الـ Galactose مع الـ Glucose ويحتوي + +71 +00:04:55,620 --> 00:05:02,010 +على لبنأهم عنصرين مش موجودين في الحليب مفقدين هو + +72 +00:05:02,010 --> 00:05:06,750 +الحديد و vitamin C إذا الحليب يعتبر مغد رئيسي + +73 +00:05:06,750 --> 00:05:11,670 +يحتوي على مكونات كتيرة يحتاجها للجسم لكن في عنصرين + +74 +00:05:11,670 --> 00:05:15,450 +أساسيا رئيسيا يحتاجه الجسم و غير موجودة في الحليب + +75 +00:05:18,800 --> 00:05:22,540 +in which milk is deficient are iron and vitamin C + +76 +00:05:22,540 --> 00:05:26,720 +هو الحديد و vitamin C طب بيحكي للبعبي ال infants + +77 +00:05:26,720 --> 00:05:30,640 +are usually born كف البعبي الراطية بيعتمد بس على + +78 +00:05:30,640 --> 00:05:33,940 +حليب الأم بياخد كل الأشياء الأساسية طب من وين + +79 +00:05:33,940 --> 00:05:37,960 +بيجيب الحديد و من وين بيجيب vitamin C بيحكي للحديد + +80 +00:05:37,960 --> 00:05:43,350 +موجود في جسمه منذ الولادة بكمية تكفيهلأ عدة أسابيع + +81 +00:05:43,350 --> 00:05:48,390 +عنده مخزن born with a storage supply of iron large + +82 +00:05:48,390 --> 00:05:52,130 +enough to meet their need for several weeks إنه + +83 +00:05:52,130 --> 00:05:56,050 +عنده مخزن في جسمه حديد كميات كبيرة تكفيه لعدة + +84 +00:05:56,050 --> 00:06:00,650 +أسابيع أما vitamin C سهل الحصول عليه عن طريق أنه + +85 +00:06:00,650 --> 00:06:06,810 +تتناول الوم عصير البرتقال وبيتزود في الحليب للطفل + +86 +00:06:09,270 --> 00:06:12,530 +الواش البروتينات الموجودة في الحليب في أن تلت + +87 +00:06:12,530 --> 00:06:16,730 +أنواع من البروتينات موجودة في الحليب هو الكازين، + +88 +00:06:16,730 --> 00:06:21,610 +lactalbumin و lactoglobulin البروتين الكازين بيشكل + +89 +00:06:21,610 --> 00:06:26,390 +في الحليب نسبة 80% من البروتينة أما lactalbumin و + +90 +00:06:26,390 --> 00:06:31,490 +lactoglobulin بتسميهم واي بروتين تشكل 20% من نسبة + +91 +00:06:31,490 --> 00:06:35,430 +البروتينات الموجودة في الحليب فالنسبة الكبرى + +92 +00:06:35,430 --> 00:06:37,610 +للبروتينات هي للكازين + +93 +00:06:39,720 --> 00:06:43,680 +ممكن نتعرف على الـ casein، structure of casein ال + +94 +00:06:43,680 --> 00:06:48,300 +casein يعتبر phosphoprotein، إذا هو conjugated + +95 +00:06:48,300 --> 00:06:52,720 +protein، not simply protein، هو conjugate مثلًا + +96 +00:06:52,720 --> 00:06:55,800 +على phosphoprotein، وهو conjugate، ليش؟ بتتصل فيه + +97 +00:06:55,800 --> 00:06:59,380 +مجموعة phosphate group attached to some of the + +98 +00:06:59,380 --> 00:07:02,940 +amino acid مرتبطة مع بعض الأحمض الأمينية الموجودة + +99 +00:07:02,940 --> 00:07:07,210 +فيهأي أحمض أمينية مرتبطة فيها الـ Phosphate Group + +100 +00:07:07,210 --> 00:07:12,670 +خالباً عند الحمض الأميني سيرين وثريونين مرتبطة + +101 +00:07:12,670 --> 00:07:15,610 +مجموعة الـ Phosphate Group في الحمض الأميني + +102 +00:07:15,610 --> 00:07:20,860 +السيرين وثريونين الموجودين في تركيبة الكازينبحكي + +103 +00:07:20,860 --> 00:07:24,580 +لي إن الكازين هو mixture of at least three similar + +104 +00:07:24,580 --> 00:07:30,140 +proteins وعبارة عن خليط من تلت بروتينات الكازين هو + +105 +00:07:30,140 --> 00:07:34,020 +خليط من تلت بروتينات هذه التلت بروتينات الفرق + +106 +00:07:34,020 --> 00:07:38,540 +بينها بتختلف هما متشابهين بس بيختلفوا في الـ + +107 +00:07:38,540 --> 00:07:43,600 +molecular weight الوزن الجزائي بتختلف في كمية الـ + +108 +00:07:43,600 --> 00:07:46,900 +phosphorus اللي بتحتويها number of phosphate group + +109 +00:07:46,900 --> 00:07:48,420 +amount of phosphorus + +110 +00:07:51,160 --> 00:07:54,460 +بينهم، اللي هي كمية الـ Phosphate group و الـ + +111 +00:07:54,460 --> 00:07:58,280 +Molecular weight إيش هم التلاتة البروتينات؟ هم + +112 +00:07:58,280 --> 00:08:04,120 +Alpha-Casein و Beta-Casein و Kappa-Casein تلاتة، + +113 +00:08:04,120 --> 00:08:08,420 +Alpha-Casein و Beta-Casein و Kappa-Casein بحكيلي + +114 +00:08:08,420 --> 00:08:12,180 +هدول التلاتة كمان اللي هم different hydrophobic + +115 +00:08:12,180 --> 00:08:15,640 +and hydrophilic regions بختلف اللي هو + +116 +00:08:20,490 --> 00:08:23,670 +في منها كاره للماء، في منها محب للماء، في منها + +117 +00:08:23,670 --> 00:08:29,390 +بيثوف في الماء، وفي لا نيجي + +118 +00:08:29,390 --> 00:08:33,090 +نحكي عن التلات البروتينات المقاومة للكازين Alpha + +119 +00:08:33,090 --> 00:08:36,890 +-Casein هو ال major casein هو الأكبر أعلى + +120 +00:08:36,890 --> 00:08:40,350 +molecular weight أعلى من بيتا و أعلى من كعبة + +121 +00:08:40,350 --> 00:08:44,950 +بيتكون من تمانية إلى عشرة فسفات جروم ال Alpha + +122 +00:08:44,950 --> 00:08:50,220 +-Casein هو أكترهو الـ major هو الـ highest + +123 +00:08:50,220 --> 00:08:53,020 +molecular weight عدد الـ phosphate group فيه من + +124 +00:08:53,020 --> 00:08:57,620 +تمانية لعشرة الـ beta casein هو أقل molecular + +125 +00:08:57,620 --> 00:09:01,260 +weight من ألفة وأعلى من كامة molecular weight له + +126 +00:09:01,260 --> 00:09:06,080 +أقل من ألفة وأعلى من كامة بيتكون من خمسة phosphate + +127 +00:09:06,080 --> 00:09:10,610 +group متصلة فيهبحكيلي الـ Beta-Casein more + +128 +00:09:10,610 --> 00:09:14,910 +hydrophobic than Alpha-Casein and Kappa-Casein الـ + +129 +00:09:14,910 --> 00:09:20,290 +Beta-Casein أعلى هيدروفوبك من Alpha ومن Kappa الـ + +130 +00:09:20,290 --> 00:09:24,410 +Beta أعلى هيدروفوبك كاره للماء أكتر من Alpha و + +131 +00:09:24,410 --> 00:09:28,750 +أكتر من Kappa ليش؟ لأن الأحماض الأمينية المكونة + +132 +00:09:28,750 --> 00:09:33,650 +إلي أغلبها non-polar أغلبها هيدروفوبك كاره للماء + +133 +00:09:34,660 --> 00:09:38,960 +حكيلي، بسبب أن ألفا كازين وبيتا كازين مرتبطين + +134 +00:09:38,960 --> 00:09:45,860 +بالكالسيوم هم مرتبطين بالكالسيوم لأنهم مرتبطين + +135 +00:09:45,860 --> 00:09:50,240 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +136 +00:09:50,240 --> 00:09:53,080 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +137 +00:09:53,080 --> 00:09:54,960 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +138 +00:09:54,960 --> 00:09:57,260 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +139 +00:09:57,260 --> 00:10:00,740 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +140 +00:10:00,740 --> 00:10:04,480 +بالكالسيوم لأنهم مرتبطين بالكالسيوم لأنهم مرتبطين + +141 +00:10:04,480 --> 00:10:09,090 +بالكحطيت عليهم كالسيوم، هيترسبه، ليش؟ لأنه بيصير + +142 +00:10:09,090 --> 00:10:13,110 +ionization للفوسفات، ووجود الكالسيوم، فبيصير + +143 +00:10:13,110 --> 00:10:17,770 +مترسب، بيبطل soluble، بيصير insoluble زي المعادل + +144 +00:10:17,770 --> 00:10:20,670 +اللي تحت مكتوب، أن البروتين موطنه لسه فيه + +145 +00:10:20,670 --> 00:10:23,850 +phosphate group، يعني phosphoprotein، زائد + +146 +00:10:23,850 --> 00:10:27,190 +كالسيوم، لو ضفنا عليه كالسيوم، بيصير ionization + +147 +00:10:27,190 --> 00:10:30,930 +للفوسفات في وجود الكالسيوم، فبيصير insoluble + +148 +00:10:34,010 --> 00:10:39,450 +طب بالنسبة ل كابا كازين الكابا كازين مش زي Alpha و + +149 +00:10:39,450 --> 00:10:43,470 +Beta كازين يحتوي فقط هو أقل Molecular weight و + +150 +00:10:43,470 --> 00:10:46,930 +يحتوي فقط على 2 Phosphate Group بس على 2 Phosphate + +151 +00:10:46,930 --> 00:10:51,270 +Group النسبة الأكبر فيه هي Carbohydrate هي التأول + +152 +00:10:51,270 --> 00:10:56,910 +من Carbohydrate مليء بالسُكَر الكابا كازين مش زي + +153 +00:10:56,910 --> 00:11:02,270 +Alpha و Beta كازين يحتوي فقط هو أقلبيحتوي فقط على + +154 +00:11:02,270 --> 00:11:04,710 +two phosphate group بس على اتنين من ال phosphate + +155 +00:11:04,710 --> 00:11:09,550 +group النسب الأكبر فيه هي carbohydrate التكون من + +156 +00:11:09,550 --> 00:11:14,950 +carbohydrate مليء بالسكر فبسموه glycoprotein + +157 +00:11:14,950 --> 00:11:19,890 +الكعبة تزين هو glycoprotein يحتوي على سكر ياد فهو + +158 +00:11:19,890 --> 00:11:24,530 +hydrophilicThey are stable in the presence of + +159 +00:11:24,530 --> 00:11:28,250 +calcium لأنه فيه بس دنتين فوسفات جروب أما الأغلبه + +160 +00:11:28,250 --> 00:11:32,310 +هو سكريات فهو stable هو ثابت في وجود الكالسيوم + +161 +00:11:32,310 --> 00:11:36,830 +مابتأثرش في الكالسيوم زي الألفة والبيتا لو حصلهم + +162 +00:11:36,830 --> 00:11:40,610 +كالسيوم حاجة بيصيروا insoluble بيترسبوا لأنه عندهم + +163 +00:11:40,610 --> 00:11:43,910 +فوسفات جروب بيصيرلها ionized بالكالسيوم مابترسبوا + +164 +00:11:43,910 --> 00:11:48,290 +لكن القعبة كازين لأن كمية الفوسفات عنده أقلين + +165 +00:11:48,290 --> 00:11:51,920 +وإنما كمية الكاربوهيدرات السكر هي اللي عاليةأنا لو + +166 +00:11:51,920 --> 00:11:56,500 +حطيت calcium مابيتأثر، بيكون steric وهذا بيلعب دور + +167 +00:11:56,500 --> 00:12:00,520 +في حماية ال alpha و ال beta كزين + +168 +00:12:06,820 --> 00:12:10,580 +أن هما المفروض يكونوا مترسبين مش ضايبين في الحليب + +169 +00:12:10,580 --> 00:12:13,880 +بس احنا لما نشوف الحليب هل بنشوف فيه حاجة مترسبة + +170 +00:12:13,880 --> 00:12:17,880 +تحت ولا كله خليط مع بعض، بنشوفه كله خليط، مانشوفش + +171 +00:12:17,880 --> 00:12:20,340 +أنه فيه حاجة مترسبة تحت، يعني Alpha و Beta ما + +172 +00:12:20,340 --> 00:12:23,180 +بيكونوا مترسبين، ليش Alpha و Beta ما بيكونوا + +173 +00:12:23,180 --> 00:12:27,760 +مترسبين؟ لأن الكاباكازين التي لا تتأثر في وجود + +174 +00:12:27,760 --> 00:12:33,380 +الكالسيوم تعمل على حماية Alpha و Beta من الترسب + +175 +00:12:33,840 --> 00:12:37,820 +they protecting play a role in protecting other + +176 +00:12:37,820 --> 00:12:41,460 +casein from precipitation and make casein more + +177 +00:12:41,460 --> 00:12:46,220 +soluble كيف بتكوين حاجة اسمها الـ mecells؟ كيف + +178 +00:12:46,220 --> 00:12:49,720 +بتحمي Alpha و Beta بتكوين حاجة بتسميها الـ + +179 +00:12:49,720 --> 00:12:54,000 +mecells؟ الـ mecells هذه هي large molecule هي مركب + +180 +00:12:54,000 --> 00:12:58,880 +كبير بيتكون من Kappa casein و Alpha casein و Beta + +181 +00:12:58,880 --> 00:13:05,370 +casein مع بعض كيف أجوا؟ انه كانوا دائماالألفة + +182 +00:13:05,370 --> 00:13:10,130 +والبيتا كازين وبرا محوط عليهم ومغطيهم من برا كلها + +183 +00:13:10,130 --> 00:13:15,170 +كابا كازين فمين ظاهر للملك من برا بتكون الكابا برا + +184 +00:13:15,170 --> 00:13:18,150 +والألفة والبيتا جوجل مش ظاهرين للكالسيون + +185 +00:13:18,150 --> 00:13:21,870 +فالكالسيون مابيقدر يشوفهم ويروح يأين مجموعات + +186 +00:13:21,870 --> 00:13:25,650 +الفوسفات الموجودة فيها فبتعمل الكابا على حماية + +187 +00:13:25,650 --> 00:13:30,230 +ألفة وبيتا بيحكي لي neither the alpha nor the beta + +188 +00:13:30,230 --> 00:13:32,890 +-casein is soluble in milk singly or in + +189 +00:13:32,890 --> 00:13:36,990 +combinationولا Alpha ولا Beta بيدوبوا في الحليب + +190 +00:13:36,990 --> 00:13:41,210 +سواء واحد فيهم أو اتنين مع بعض، بيدوبوش في الحليب + +191 +00:13:41,210 --> 00:13:44,370 +لأنه إذا وجود ال calcium في الحليب، خلاص هم + +192 +00:13:44,370 --> 00:13:47,790 +الاتنين insoluble سواء واحد منهم أو اتنين معاك، + +193 +00:13:47,790 --> 00:13:51,770 +لكن إذا اضفت كابا، if kaba casein isadded to + +194 +00:13:51,770 --> 00:13:55,330 +either one or to the combination of the two لو + +195 +00:13:55,330 --> 00:13:59,310 +ضفتي الكابا كزين على الألفة والبيتا اتنين مع بعض + +196 +00:13:59,310 --> 00:14:04,090 +او على واحد منهم، لذا الكزين complex is soluble + +197 +00:14:04,090 --> 00:14:08,970 +فهالكزين هيعمل complex يكون ذائب في الحليب، هذا ال + +198 +00:14:08,970 --> 00:14:11,010 +complex بنسميه ميسم + +199 +00:14:14,240 --> 00:14:19,960 +ما هي الـ Measles؟ مصطلح + +200 +00:14:19,960 --> 00:14:25,020 +الـ Measles هو مصطلح كيميائي واطلق على التركيب + +201 +00:14:25,020 --> 00:14:30,560 +المركبات الكبيرة للـ Very Very Large Molecules الـ + +202 +00:14:30,560 --> 00:14:32,800 +Very Very Large Molecules + +203 +00:14:37,840 --> 00:14:41,800 +أما المركبات الكبيرة، حقيقة هي كبيرة جدا أنها تكون + +204 +00:14:41,800 --> 00:14:44,380 +ضائبة في الماء، المركبات كبيرة كيف بدأت تدوب في + +205 +00:14:44,380 --> 00:14:49,280 +الماء، بل هذه الملكولات الكبيرة ستصبح مصطلحات تسمح + +206 +00:14:49,280 --> 00:14:51,880 +لهم بالدخول في الماء + +207 +00:15:06,030 --> 00:15:10,890 +ماء لأنها مُركّبات كبيرة فتوزيع هذه الـ large + +208 +00:15:10,890 --> 00:15:14,590 +structure in water dispersion أو انتشار this large + +209 +00:15:14,590 --> 00:15:18,570 +mole structure in water is known as a colloidal + +210 +00:15:18,570 --> 00:15:22,410 +suspension بنسميها توزيع هذه المُركّب الكبير اللي + +211 +00:15:22,410 --> 00:15:26,230 +هم القعبة كازين برا ال فوبيتا بتكون في الداخل + +212 +00:15:26,230 --> 00:15:29,670 +فهدولة كون مُركّب كامل كأنه دائرة جواها + +213 +00:15:35,820 --> 00:15:40,240 +ماشى فى الميّه و هو كبير فكيف هو توزع فى الماء هى؟ + +214 +00:15:40,240 --> 00:15:43,240 +هل هو دائب فى الماء؟ بيبين كأنه colloidal + +215 +00:15:43,240 --> 00:15:47,460 +suspension كأنه محلول غروي أو محلول معلق فى الماء + +216 +00:15:47,460 --> 00:15:51,340 +لأنه بيسمحسمعه الـ structure that allow large + +217 +00:15:51,340 --> 00:15:54,520 +molecules to remain colloidally suspended in water + +218 +00:15:54,520 --> 00:15:58,300 +هذا المركب اللى بيكون معلق فى الماء our term + +219 +00:15:58,300 --> 00:16:02,940 +بنسميه الـ measles الـ measles هو المركب المعلق فى + +220 +00:16:02,940 --> 00:16:08,760 +الماءطيب، دي حالة الكازينة بيحكي ليه؟ اللي هو + +221 +00:16:08,760 --> 00:16:12,500 +الـmesons اللي بتتكونها الكازين اللي بتلت انواع من + +222 +00:16:12,500 --> 00:16:16,160 +البروتينات بيكون للخارج the part of the casein + +223 +00:16:16,160 --> 00:16:19,760 +molecule that have an affinity for water from the + +224 +00:16:19,760 --> 00:16:24,020 +outside of casein meson اللي بيكون محبب للماء، + +225 +00:16:24,020 --> 00:16:25,200 +وعنده جاذبية للماء + +226 +00:16:30,120 --> 00:16:33,700 +في خارج الـ mesons ومن هو هنا في حالة الـ casein + +227 +00:16:33,700 --> 00:16:38,120 +كل الخارج هو الـ carbacasein على العكس ال part of + +228 +00:16:38,120 --> 00:16:40,720 +casein molecules that are hidden ده هو طرف اللي + +229 +00:16:40,720 --> 00:16:44,140 +بيكره الميه اللي بيحبش الميه، بيذوبش في الميه، + +230 +00:16:44,140 --> 00:16:47,740 +form the inner core of the mesons، بيكون في + +231 +00:16:47,740 --> 00:16:51,480 +الداخل، في الجزء الداخلي ومن هم اللي بيكره الميه + +232 +00:16:51,480 --> 00:16:56,980 +كل الداخل هي الـ α و الـ beta caseinبحكيلي الكزين + +233 +00:16:56,980 --> 00:17:00,300 +is present as كزينات which mean that it's bind to + +234 +00:17:00,300 --> 00:17:04,340 +calcium and magnesium الكزين لما يترسب إذا صار + +235 +00:17:04,340 --> 00:17:08,840 +لترسيب بنسميه كزينات بتحول اللي عادي اسمها كزينات + +236 +00:17:08,840 --> 00:17:13,940 +يعني هو الكزين المترسب متى هاد هيترسب إذا جدرت + +237 +00:17:13,940 --> 00:17:18,540 +ترتبط مع كالسيوم أو مغنيسيوم بتعمل ionization و + +238 +00:17:18,540 --> 00:17:20,060 +بترسب الكزين + +239 +00:17:23,090 --> 00:17:26,910 +طب هنا عندنا صور للألفة والبيتا والكابا كزي في + +240 +00:17:26,910 --> 00:17:30,570 +عندنا لليمين الصورة اللي تحت الأبيض بالأسم ده هي + +241 +00:17:30,570 --> 00:17:35,010 +عبارة عن صور ل ال measles للكزين measles اللي هو + +242 +00:17:35,010 --> 00:17:39,130 +الكابا والبيتا والألفا كزي مع بعض كيف شكل ال + +243 +00:17:39,130 --> 00:17:44,250 +measles تحت المجهد ممكنها كرة كريات تحتوي من + +244 +00:17:44,250 --> 00:17:48,190 +الكابا من الخارج وبيتا وألفا في الداخل + +245 +00:17:50,410 --> 00:17:55,170 +هنا صورة الـ Measles الكورة هذه الكتلة تتكوين من + +246 +00:17:55,170 --> 00:17:58,950 +Alpha و Beta و Kappa Alpha لأو Beta للداخل و Kappa + +247 +00:17:58,950 --> 00:18:04,130 +للخارج هي مكبرة بالإلكترون مايكروسكوبي تحت المجهر + +248 +00:18:04,130 --> 00:18:09,750 +الإلكتروني صورة من المجهر الإلكتروني حكينا في + +249 +00:18:09,750 --> 00:18:12,730 +المعمل السابق أن الـ isoelectric point لمعظم + +250 +00:18:12,730 --> 00:18:18,470 +البروتينات تتروح من pH 4 إلى 6اللي بترى الـ Y كمان + +251 +00:18:18,470 --> 00:18:22,970 +من البروتينات هي من BH 4 إلى 6 طيب ليش ال كازين + +252 +00:18:22,970 --> 00:18:27,630 +دائب في الحليب؟ why casein is solvent in milk؟ + +253 +00:18:27,630 --> 00:18:31,650 +هلجد؟ هو هيتوب حكينا بيكون دائب إذا ال BH أعلى من + +254 +00:18:31,650 --> 00:18:36,230 +ال BI أو أقل من ال PR لكن متى فاتساوة ال BH مع ال + +255 +00:18:36,230 --> 00:18:42,690 +BI يترسم؟ هلجد؟ الحليب بيحكيني أنه ليش هو دائب + +256 +00:18:42,690 --> 00:18:50,050 +لأنه ال BI للوالـ pH للحليب هي 6 و 6 الـ Bi + +257 +00:18:50,050 --> 00:18:55,590 +للكازين 4 و 7 الـ pH للحليب هي القاعدي 6 و 6 فالـ + +258 +00:18:55,590 --> 00:19:00,570 +pH للحليب أعلى من الـ Bi مش متساوية، هي أعلى، بما + +259 +00:19:00,570 --> 00:19:01,290 +أنها أعلى + +260 +00:19:04,750 --> 00:19:08,190 +بتكون الشحنات نيجاتيف اللي على الكزيد، pH أعلى من + +261 +00:19:08,190 --> 00:19:14,830 +الـPI، شحنات متشابه حاجانة بتتنافر، بيصير قوة + +262 +00:19:14,830 --> 00:19:17,450 +تنافر، بتتوزع فيه السائل و بتكون + +263 +00:19:22,570 --> 00:19:27,230 +بالانمال فكيف بدي أداوبها لازم أوصل الـ pH تاعت + +264 +00:19:27,230 --> 00:19:32,150 +الحنيب للبيئة I للكازين ممكن هادي أعملها عن طريق + +265 +00:19:32,150 --> 00:19:35,110 +ال bacterial action بفعل البكتيريا وحكينا في + +266 +00:19:35,110 --> 00:19:36,010 +المعمل السابق + +267 +00:19:39,810 --> 00:19:44,030 +بتجي بكتيريا تحول سكر اللاكتوز اللي موجود في + +268 +00:19:44,030 --> 00:19:48,530 +الحليب إلى lactic acid اللاكتك أسد هو عبارة عن حمض + +269 +00:19:48,530 --> 00:19:52,850 +والحمض هذا بيقلل ال pH فهيقلل ال pH بتاعة الملك من + +270 +00:19:52,850 --> 00:19:57,870 +6.6 اللي هو الطبيعي إلى 4.7 ال pH بتاعة الحليب + +271 +00:19:57,870 --> 00:20:04,450 +هيتقل من 6.6 إلى 4.7 4.7 صارت ال pH للحليب هي 4.7 + +272 +00:20:04,450 --> 00:20:08,470 +طب و ال ISO electrical point بتاعة الكازين 4.7 + +273 +00:20:08,940 --> 00:20:13,100 +فصارت الـ pH للحليب مساوية للـ PI تاعت الكازين + +274 +00:20:13,100 --> 00:20:17,500 +وبالتالي بيترسب لأن حكينا ما تمت ساوية الـ pH مع + +275 +00:20:17,500 --> 00:20:20,160 +الـ PI، لذا بيترسب + +276 +00:20:24,520 --> 00:20:29,420 +طرق ترسيب الكازين كيف ممكن أعمل precipitation of + +277 +00:20:29,420 --> 00:20:33,520 +casein؟ أول طريقة ممكن بإضافة excess calcium أيون، + +278 +00:20:33,520 --> 00:20:37,760 +إنه إضافة كميات كبيرة من أيونات الكالسيون بحيث + +279 +00:20:37,760 --> 00:20:41,520 +إنها توصل للـAlpha والـBeta كازين وتأين + +280 +00:20:41,520 --> 00:20:46,400 +الفسويتجروب اللي موجودة فيها ويترسبيصير Intolerant + +281 +00:20:46,400 --> 00:20:50,640 +طريقة تانية ممكن بإضافة acid أنه أضيف حمض زي ال + +282 +00:20:50,640 --> 00:20:55,280 +HCl أو ال Acetic acid لأن وسط الحليب حكينا أنه وسط + +283 +00:20:55,280 --> 00:21:00,520 +قاعده بيكون alkaline 6 و 6 ال pH للملك و ال PI + +284 +00:21:00,520 --> 00:21:06,720 +للكازين هي 4.7 فانا بدي أوصل ال pH بتاع الملك من 6 + +285 +00:21:06,720 --> 00:21:11,400 +و 6 إلى 4 و 7 كيف بدي أجللها أنه أضيف حمض الحمض + +286 +00:21:11,400 --> 00:21:17,290 +هيقلل ال pH فتوصل ال pH لللـ «بي آي» للـ «كازين» + +287 +00:21:17,290 --> 00:21:21,490 +ويترسب الـ «كازين» هذا مبدأ عملنا لليوم إن أنا بدأ + +288 +00:21:21,490 --> 00:21:26,150 +أضيف حمق عشان يقلل ال «بي آي» و أرسب ال «كازين» + +289 +00:21:26,150 --> 00:21:29,330 +طريقة التالتة ممكن بضعفة الـ «رنين» للـ «إنزاين» + +290 +00:21:29,330 --> 00:21:33,390 +طريقة الرابعة بضعفة عن طريقة الـ «باكتيريا الأكشن» + +291 +00:21:33,390 --> 00:21:37,010 +اللي حكينا عنه إنه كيف تشتغل الباكتيريا وتحويل سكر + +292 +00:21:37,010 --> 00:21:41,190 +اللاكتوز إلى «لاكتك أسد» مدام و أسد بيقلل ال «بي + +293 +00:21:41,190 --> 00:21:46,650 +آي» لحليببسبب الـ Renin enzyme كيف بيشتغل، كيف + +294 +00:21:46,650 --> 00:21:50,250 +بيرسل بالكاتين الـ Renin enzyme هو أنزين باللاجئ + +295 +00:21:50,250 --> 00:21:54,270 +موجود فيه الـ calves و ال goats موجود فيه العجل و + +296 +00:21:54,270 --> 00:21:58,830 +العنزة أو الماعز، هو عبارة عن هيدروليسز أنزين هو + +297 +00:21:58,830 --> 00:22:02,590 +أنزين مكسر، بيطلق عليه peptidase، peptidase يعني + +298 +00:22:02,590 --> 00:22:06,410 +أنزيمات بتكسر، هو بيكسر الـpeptide bond بين + +299 +00:22:06,410 --> 00:22:12,710 +الأحماض الأمانيةطب كيف يشتغل؟ كيف الميكانيزم للـ + +300 +00:22:12,710 --> 00:22:16,150 +Renin؟ الـ Renin هو إنزايم حكينا Hydrolysis + +301 +00:22:16,150 --> 00:22:19,950 +إنزايم، إنزين مكسب، بيروح على الكاباكازين، على + +302 +00:22:19,950 --> 00:22:22,170 +الموجود اللي يمين للخارج، اللي بالظهر، + +303 +00:22:22,170 --> 00:22:25,330 +الكاباكازين، بيروح على الـ Renin، الكاباكازين + +304 +00:22:25,330 --> 00:22:28,470 +بيعمل عليها تكسيرها، بيعمل Hydrolysis breaking the + +305 +00:22:28,470 --> 00:22:33,250 +peptide bond، بيحولها لحاجة بسميها Paracabacazine + +306 +00:22:34,590 --> 00:22:38,790 +هو كان عامل حماية كجدار حماية للـ Beta والـ Alpha + +307 +00:22:38,790 --> 00:22:42,810 +اللي في داخله لما يتكسر ويتحول لبارك كابا كازين + +308 +00:22:42,810 --> 00:22:46,530 +اللي هو عبارة عن كازين مكسر فيه فتحات يعني صارت + +309 +00:22:46,530 --> 00:22:51,310 +Alpha و Beta ظاهرين للخالرفهو بيقدرش يحميهم، + +310 +00:22:51,310 --> 00:22:55,770 +Cannot prevent casein from precipitate فالبرا كابا + +311 +00:22:55,770 --> 00:22:58,430 +كازين هذا مادوش قدرة أنه يحمي الكازين من الترس + +312 +00:22:58,430 --> 00:23:02,910 +بليش؟ لأنه ربعا كابا كازين مكسر لدهرة الألفة + +313 +00:23:02,910 --> 00:23:06,530 +والباتا لوجود الكالسيوم اللي موجود في الحليب بيقدر + +314 +00:23:06,530 --> 00:23:11,350 +يدخل لجوا ويعمل ionization للألفة والباتا كازين + +315 +00:23:11,350 --> 00:23:16,070 +لمجموعات الفسبات الموجودة فيه مدام اتأينه خلاص + +316 +00:23:16,070 --> 00:23:19,910 +بيصير ال precipitate بيترسبحكي ليه لو الـ Calcium + +317 +00:23:19,910 --> 00:23:23,070 +removed from milk، the renin cannot form a + +318 +00:23:23,070 --> 00:23:26,390 +precipitate to milk. إذا الـ Calcium شيلته أنا من + +319 +00:23:26,390 --> 00:23:30,190 +الحليب، وكسر .. واجه الـ renin انزعي، كسر الكابا + +320 +00:23:30,190 --> 00:23:33,230 +كازين، خلاص، مافيش Calcium، مش هيدخل على الـ Alpha + +321 +00:23:33,230 --> 00:23:36,650 +والـ Beta، ومش هيعمل الـ precipitation. لكن الـ + +322 +00:23:36,650 --> 00:23:40,050 +renin لازم مين يشتغل معاه؟ الـ renin يكسر ويجي الـ + +323 +00:23:40,050 --> 00:23:43,470 +Calcium، يعمل Ionization، عشان يعمل ال + +324 +00:23:43,470 --> 00:23:48,430 +precipitation لكازين.طب البكتيريا الـ Action إيه + +325 +00:23:48,430 --> 00:23:52,290 +عادة اللي ما حكيناها؟ البكتيريا اللي حكيناها إنها + +326 +00:23:52,290 --> 00:23:56,430 +بتيجي على الحليب، بتعمل على هضم اللاكتوز، بتكون + +327 +00:23:56,430 --> 00:23:59,910 +منه lactic acid، بتحول سكر اللاكتوز اللي موجود في + +328 +00:23:59,910 --> 00:24:04,340 +الحليب إلى lactic acidLactic acid هذا حمض فبقلل + +329 +00:24:04,340 --> 00:24:10,260 +الـ pH للحليب من 6.6 إلى 4.7 تصير الـ pH للحليب 4 + +330 +00:24:10,260 --> 00:24:14,240 +.7 4.7 هي نفسها الـ isoelectric point بتاعة + +331 +00:24:14,240 --> 00:24:19,240 +الكازين بدل من الـ pH تساوي الـ PI إذا بيترسم + +332 +00:24:19,240 --> 00:24:25,050 +الكازيناللي إذا جلت البيئة و المبيئة ليه في ال + +333 +00:24:25,050 --> 00:24:28,530 +degrees of milk جلت البيئة تحت الحليب ووصلت إلى ال + +334 +00:24:28,530 --> 00:24:32,170 +isoelectric point بتاعت الكازين صاروا متساوين + +335 +00:24:32,170 --> 00:24:36,270 +بينفصل الحليب إلى طبقتين حاجة بتسميها Curds and + +336 +00:24:36,270 --> 00:24:40,600 +Whey بينفصل الحليب إلى Curds and Wheyالـ Curds هي + +337 +00:24:40,600 --> 00:24:43,160 +عبارة عن الكازين هو اللي بيكون بالأسفل، الـ + +338 +00:24:43,160 --> 00:24:45,500 +precipitate اللي بينزل للأسفل اللي هو بروتين + +339 +00:24:45,500 --> 00:24:48,560 +الكازين اللي هو الـ dairy product obtained by + +340 +00:24:48,560 --> 00:24:51,440 +precipitation of milk with renin or acidic + +341 +00:24:51,440 --> 00:24:56,400 +substance and then the draining of the liquid + +342 +00:24:56,400 --> 00:25:00,610 +versionالـ Curds هاد عبارة عن المنتج اليومي اللي + +343 +00:25:00,610 --> 00:25:04,030 +بينتج من تلصيب الحليب باستخدام سواء الـ renin + +344 +00:25:04,030 --> 00:25:09,050 +enzyme أو باستخدام مادة أستيتك فتنزل لتحت هذا + +345 +00:25:09,050 --> 00:25:12,110 +البريس الكيردس و تكون فيه liquid portion في الأعلى + +346 +00:25:12,110 --> 00:25:16,110 +ال liquid portion هذا اللي في الأعلى بيسوي way أو + +347 +00:25:16,110 --> 00:25:19,930 +milk serum is the liquid remaining after milk has + +348 +00:25:19,930 --> 00:25:23,670 +been coagulated and removal of curdsالحليب إذا + +349 +00:25:23,670 --> 00:25:27,730 +قللت ال pH ووصلتها ل ال PI تاعت الكازين ينفصل إلى + +350 +00:25:27,730 --> 00:25:31,250 +طبق تان حاجة بتسميها كيرتز بتكون في الأسفل اللي هو + +351 +00:25:31,250 --> 00:25:34,690 +الطبقة السميكة اللي بتكون في الأسفل اللي هي المنتج + +352 +00:25:34,690 --> 00:25:38,550 +اليومي اللي هو عبارة عن الكازين في الأعلى بيكون ال + +353 +00:25:38,550 --> 00:25:41,610 +whey أو الملك السيروم اللي هو الجزء السائل اللي هو + +354 +00:25:41,610 --> 00:25:43,130 +باقي المكونات + +355 +00:25:45,120 --> 00:25:49,760 +طيب إيش هو معملنا لليوم؟ معملنا لليوم هو عبارة عن + +356 +00:25:49,760 --> 00:25:54,260 +إيش هو يعني ال objective منه إنه isolate casein + +357 +00:25:54,260 --> 00:25:57,980 +from milk and calculate a percentage إن أنا بتعزل + +358 +00:25:57,980 --> 00:26:01,960 +ال casein من الحليب وود أحسبله قداش النسبة + +359 +00:26:01,960 --> 00:26:04,600 +المقاوية اللي هو ال percentage، قداش نسبة موجودة + +360 +00:26:04,600 --> 00:26:08,460 +في الحليببنان على أي مبتدأ الـ principle استخدام + +361 +00:26:08,460 --> 00:26:11,260 +Acetic Acid اللي أنا بتستخدم حمض هو الـ Acetic + +362 +00:26:11,260 --> 00:26:16,440 +Acid أضيفه على الكازين يعطيني كازينات اللي هو + +363 +00:26:16,440 --> 00:26:20,980 +ترسيب للكازين، لذا هو المبتدأ ان الـ principle أن + +364 +00:26:20,980 --> 00:26:27,450 +أنا أضيفPacific Acid زي كزين يعطيني كزينة طيب كيف + +365 +00:26:27,450 --> 00:26:32,450 +الخطوات؟ بدي أجيب cup أحط عليه فيه عشرة مل من + +366 +00:26:32,450 --> 00:26:37,950 +الحليب و أحطه في ال water bath على أربعين درجة + +367 +00:26:37,950 --> 00:26:41,710 +سيليزياس لخمسة minutes أحطها على درجة حرارة في + +368 +00:26:41,710 --> 00:26:45,370 +الميه على درجة حرارة عارفين درجة لمدة خمس دقائق + +369 +00:26:45,370 --> 00:26:51,160 +هذا بس عشان أدفع الحليببعدين هطلعه و هضيف عليه 15 + +370 +00:26:51,160 --> 00:26:55,460 +drop من ال Acetic Acid هضيف عليه Acetic Acid حمض + +371 +00:26:55,460 --> 00:26:59,240 +عشان يقلق البيئة عشان هيبقى على 15 drop Acetic + +372 +00:26:59,240 --> 00:27:03,720 +Acid لتقليل البيئة و أعمل mix هلاجي الحليب فصل + +373 +00:27:03,720 --> 00:27:08,320 +عندى لطبقتين بيكون كل المكونات فوق و تحت بينزل + +374 +00:27:08,320 --> 00:27:12,740 +عندى casein مع lipidبكون عندي نازل فيه الأسفل + +375 +00:27:12,740 --> 00:27:17,260 +casein و lipid و فوق بتكون هنا بدي أجيب الصفين بدي + +376 +00:27:17,260 --> 00:27:21,740 +أعمل filtration عاملينيه فلترة بجيب tube و funnel + +377 +00:27:21,740 --> 00:27:25,720 +محجن و filter paper اللي هي ورقة من ال filter فيها + +378 +00:27:25,720 --> 00:27:29,960 +أجيب ال tube بحط فيها funnel محجن المحجن هذا بحط + +379 +00:27:29,960 --> 00:27:33,320 +فيه ال filter paper اللي هي ورقة الفلترة و بدي + +380 +00:27:33,320 --> 00:27:36,100 +أدير ال cup اللي أنا حدرت اللي هو العشرة مل من + +381 +00:27:36,100 --> 00:27:40,340 +الملك مع خمس عشر دروب أسيتكاسةبفلتر بينزل تحت + +382 +00:27:40,340 --> 00:27:44,660 +الميه وبطل عندى فى ال filter paper الكازين مع اللى + +383 +00:27:44,660 --> 00:27:49,310 +بدهالموجود باخدهم من الورجها دول و بحطهم في cup + +384 +00:27:49,310 --> 00:27:54,710 +بحطهم في cup لجهة ال cup هذا صرفيه casein و lipid + +385 +00:27:54,710 --> 00:27:57,810 +أنا بدي بس ال casein مابديش ال lipid كيف بدي أتخلص + +386 +00:27:57,810 --> 00:28:01,270 +من ال lipid؟ ده أجيب مادة بيدوب فيها ال lipid على + +387 +00:28:01,270 --> 00:28:05,390 +مبدأ like dissolve like إن المضيبات بديبانه إيش + +388 +00:28:05,390 --> 00:28:08,150 +المادة اللي بتجيبها ال lipid؟ زي ال ethanol أو + +389 +00:28:08,150 --> 00:28:11,790 +ether ethanol فبدي أضيف على ال cup على ال casein و + +390 +00:28:11,790 --> 00:28:15,920 +ال lipid ده أضيف خمسة من ال ethanolو 5 مل إيثر + +391 +00:28:15,920 --> 00:28:20,480 +إيثانول و بعمل mix هدول هيدوبوا الدهون .. الدهون + +392 +00:28:20,480 --> 00:28:24,580 +هيدوبوا الليبد هيعملوه على إدابة الليبد فبيدوب + +393 +00:28:24,580 --> 00:28:28,220 +الليبد و بيضل عند الكازين هو اللي مترسم أعمل كمان + +394 +00:28:28,220 --> 00:28:32,480 +مرة فالترة لهذا ال cup بجيب ال tube بحط فيه funnel + +395 +00:28:32,480 --> 00:28:36,780 +محجن بحط في .. في ال funnel هذا filter بابا بحط + +396 +00:28:36,780 --> 00:28:40,960 +فيه ورقة الفلترة و بقعدير ال cup هينزل الساعة كله + +397 +00:28:40,960 --> 00:28:43,780 +لتحت اللي هو عبارة عن إيثانول و لبد فهينزل في ال + +398 +00:28:43,780 --> 00:28:47,420 +tubeويتضل في ال filter paper في الورقة هيضل فيها + +399 +00:28:47,420 --> 00:28:52,420 +الكازين بخلي الورقة تجف شوية عشان يتطير ال Ethanol + +400 +00:28:52,420 --> 00:28:54,920 +أو الاتر Ethanol اللى موجود فيها الكحول اللى انا + +401 +00:28:54,920 --> 00:28:58,880 +حطيتها اللى اجت فيها بتطير فبيضل بس عليها الكازين + +402 +00:28:58,880 --> 00:29:03,720 +بعد ما تجف بوزلها في الميزان بحطها و بسجل عندي + +403 +00:29:03,720 --> 00:29:06,200 +الوزنة كتاش الوزنة عندي + +404 +00:29:09,850 --> 00:29:12,190 +يعني الوزن اللي أنا طلعتها بتحسب منها ال + +405 +00:29:12,190 --> 00:29:16,050 +percentage of casein in milk قداش نسبة ال casein + +406 +00:29:16,050 --> 00:29:19,450 +الموجود في الحليب ال percentage of casein بتساوي + +407 +00:29:19,450 --> 00:29:22,530 +ال gram of casein قداش أنا وزنة ال casein اللي + +408 +00:29:22,530 --> 00:29:27,030 +طلعتها على ال gram of milk وزنة الحليب درمية في + +409 +00:29:27,030 --> 00:29:30,220 +الميةالـ gram of casein هذه الوزن اللي أنا وزنتها + +410 +00:29:30,220 --> 00:29:32,520 +في الآخر اللي كانت على الورقة ووزنتها على الميزان + +411 +00:29:32,520 --> 00:29:36,240 +جديش طلعت ماني ال gram of milk اللي هي الحليب جديش + +412 +00:29:36,240 --> 00:29:39,540 +أنا أخد كمية أول شي عشرة mil من الحليب فهو عشرة + +413 +00:29:39,540 --> 00:29:44,020 +ضرب مية في المية و بطلع النسبة و بال normal range + +414 +00:29:44,020 --> 00:29:49,160 +المفروض تطلع معنا نسبة ال casein من تلاتة إلى خمسة + +415 +00:29:49,160 --> 00:29:52,000 +في المية تلاتة إلى خمسة في المية + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY.srt new file mode 100644 index 0000000000000000000000000000000000000000..44b163d7efebd9ce421e9d98ddc3110e4e3b0672 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY.srt @@ -0,0 +1,794 @@ +1 +00:00:01,300 --> 00:00:05,160 +اليوم إن شاء الله بنحكي بموضوع جديد اللي هو + +2 +00:00:05,160 --> 00:00:08,660 +precipitation of the protein at isoelectric point + +3 +00:00:08,660 --> 00:00:13,140 +عملية ترسيب ال protein عند نقطة ال isoelectric + +4 +00:00:13,140 --> 00:00:16,900 +point يعني ما عملنا اليوم غير عن ترسيب ال protein + +5 +00:00:16,900 --> 00:00:23,480 +عند نقطة ال isoelectric point نحكي + +6 +00:00:23,480 --> 00:00:27,080 +في البداية مقدمة عن البروتينات إيش هي البروتينات + +7 +00:00:27,080 --> 00:00:32,450 +بشكل عام البروتين حكينا إنه هو عبارة عن polymers of + +8 +00:00:32,450 --> 00:00:35,610 +amino acids حكي إنه إنه بتيجي ال amino acids ترتبط + +9 +00:00:35,610 --> 00:00:40,230 +ببعض بروابط ببتدية بتكون ال protein فال protein هو + +10 +00:00:40,230 --> 00:00:44,750 +polymers من الأحماض الأمينية من ال amino acids our + +11 +00:00:44,750 --> 00:00:48,290 +substance of high molecular weight الوزن الجزائي + +12 +00:00:48,290 --> 00:00:51,910 +له عالي molecular weight لها عالية بنحكي عنها + +13 +00:00:51,910 --> 00:00:55,910 +macromolecules مركبات كبيرة وزنها الجزائي عالي + +14 +00:00:55,910 --> 00:00:59,810 +بنحكي عنها macromolecules الـ molecular weight إلها + +15 +00:00:59,810 --> 00:01:06,480 +من خمسة آلاف إلى مليون ألف كل البروتينات بشكل عام في + +16 +00:01:06,480 --> 00:01:10,840 +ال structure بتتكون من كربون، هيدروجين، أكسجين + +17 +00:01:10,840 --> 00:01:14,300 +ونيتروجين كلها كل البروتينات ال structure فيه + +18 +00:01:14,300 --> 00:01:20,200 +كربون، هيدروجين، أكسجين ونيتروجين معظمها يحتوي على + +19 +00:01:20,200 --> 00:01:25,280 +كبريت وبعضها some contain phosphorus يحتوي على فسفرة + +20 +00:01:25,280 --> 00:01:28,940 +إذا كلها فيها كربون وهيدروجين وأكسجين ونيتروجين + +21 +00:01:28,940 --> 00:01:33,430 +all the proteins most اللي هم معظمها بتحتوي على كبريت + +22 +00:01:33,430 --> 00:01:37,770 +some contain phosphorus يعني بعضها تحتوي على فسفرة + +23 +00:01:37,770 --> 00:01:42,130 +and few have mineral elements و القليل منها بتحتوي + +24 +00:01:42,130 --> 00:01:46,090 +على معادن زي الحديد، مغنيسيوم، كالسيوم + +25 +00:01:46,090 --> 00:01:51,290 +serve as a structural component غنمًا تدخل في تركيب + +26 +00:01:51,290 --> 00:01:55,930 +الكائنات الحية تدخل البروتينات في تركيب الكائنات + +27 +00:01:55,930 --> 00:02:01,990 +الحية هنا عندنا توضيح كيف بيتكون البروتين هنا بيجي + +28 +00:02:01,990 --> 00:02:06,890 +حمضين حمض أميني بيرتبط مع حمض أميني آخر ب peptide + +29 +00:02:06,890 --> 00:02:11,090 +bond أين تتكون ال peptide bond؟ بين كربوكسيل من + +30 +00:02:11,090 --> 00:02:16,370 +حمض أميني الأول و amino group من حمض أميني آخر + +31 +00:02:16,370 --> 00:02:19,450 +بتيجي الرابطة بالنص بين الكربوكسيل و ال amino + +32 +00:02:19,450 --> 00:02:23,630 +group بين الحمضيين الأمينية نسميها رابطة peptide + +33 +00:02:23,630 --> 00:02:28,330 +bond حكينا بيكون الناتج منها نزع جزاء ماء فسمينا + +34 +00:02:28,330 --> 00:02:32,850 +التفاعل Condensation Reaction لأنه بينتج عنه جزاء + +35 +00:02:32,850 --> 00:02:37,570 +ماء بشكل عام البروتينات تتكون من ترتيب من الأحمض + +36 +00:02:37,570 --> 00:02:41,890 +الأمينية ترتبط مع بعضها البعض بـ peptide bond أين + +37 +00:02:41,890 --> 00:02:45,910 +موقع الرابطة اللي بيبتديها؟ بتيجي بين Carboxyl من + +38 +00:02:45,910 --> 00:02:50,030 +حمض أميني و Aminogroup من حمض أميني آخر بتيجي + +39 +00:02:50,030 --> 00:02:51,890 +الرابطة في الوسط بينهم + +40 +00:02:54,980 --> 00:02:58,400 +نحكي عن ال protein function، إيش وظائف البروتين؟ + +41 +00:02:58,400 --> 00:03:03,400 +تتنوع الوظائف للبروتين، أول وظيفة structure، تركيب، + +42 +00:03:03,400 --> 00:03:06,800 +بروتينات تركيبية إنها بتدخل هذه البروتينات في + +43 +00:03:06,800 --> 00:03:10,760 +تركيب خلايا الجسم، some proteins provide structural + +44 +00:03:10,760 --> 00:03:14,760 +support، زي مين زي الكولاجين، يدخل في خلايا ال + +45 +00:03:14,760 --> 00:03:18,620 +muscle، كيراتين في ال hair وكرستالين في ال eyes + +46 +00:03:20,360 --> 00:03:24,000 +الثانية وظيفة هي ال transport transport إن البروتين + +47 +00:03:24,000 --> 00:03:28,940 +يعمل كناقل لنقل المواد من مكان لآخر في الجسم some + +48 +00:03:28,940 --> 00:03:31,600 +proteins are responsible for the transportation of + +49 +00:03:31,600 --> 00:03:34,480 +smaller molecules from one part of the body to + +50 +00:03:34,480 --> 00:03:38,820 +another تعمل كناقل لنقل المركبات الصغيرة من مكان + +51 +00:03:38,820 --> 00:03:42,860 +لآخر في الجسم مثال على الـ transportation البروتين + +52 +00:03:42,860 --> 00:03:46,520 +هو الـ hemoglobin الـ hemoglobin يعمل كنقل ينقل + +53 +00:03:46,520 --> 00:03:54,800 +الأكسجين من الرئتين إلى الخلايا عبر الجسم مش كمان + +54 +00:03:54,800 --> 00:03:59,060 +وظائف البروتين البروتين يعمل ك catalysis إنزيم + +55 +00:03:59,060 --> 00:04:03,380 +إنزيم محفز في بعضهم بيشتغل بعض البروتينات تعمل + +56 +00:04:03,380 --> 00:04:07,380 +كإنزيمات محفظة بتسرع التفاعل catalysis the + +57 +00:04:07,380 --> 00:04:11,930 +chemical reaction وظيفة اللي بعد هي storage تعمل + +58 +00:04:11,930 --> 00:04:16,490 +كبروتينات تخزينية للتخزين أشهر مثال على بروتينات + +59 +00:04:16,490 --> 00:04:19,750 +التخزين هو ال myoglobin ال myoglobin هو storage + +60 +00:04:19,750 --> 00:04:23,750 +protein بيخزن ال oxygen in muscles أثناء ال + +61 +00:04:23,750 --> 00:04:27,330 +exercise بيخزن ال oxygen في العضلات إذا الجسم مثلا + +62 +00:04:27,330 --> 00:04:31,990 +في أثناء التمرين الشاق نقص الـ Oxygen على العضلة، + +63 +00:04:31,990 --> 00:04:35,630 +مين بيزود بال Oxygen؟ الـ Myoglobin بيكون خزين من + +64 +00:04:35,630 --> 00:04:40,270 +ال Oxygen، بيوزعه على العضلات و للجسم عند الحاجة. + +65 +00:04:40,990 --> 00:04:44,630 +Hormones، بتعمل لبروتينات كهرمون، some hormones + +66 +00:04:44,630 --> 00:04:48,090 +are proteins، بعض الهرمونات هي عبارة عن بروتين، + +67 +00:04:48,090 --> 00:04:52,110 +وأشهر مثال على بروتين .. على هرمون يعمل .. يعتبر + +68 +00:04:52,110 --> 00:04:56,720 +البروتين هو الانسولين الانسولين هو example على + +69 +00:04:56,720 --> 00:05:02,080 +هرمون و protein إيش هو الهرمون؟ هرمون serve as + +70 +00:05:02,080 --> 00:05:05,800 +chemical messenger carrying signals from one part + +71 +00:05:05,800 --> 00:05:11,540 +of the body to another الهرمون هو عبارة عن إشارة + +72 +00:05:11,540 --> 00:05:17,280 +أو رسالة كيميائية لنقل الإشارة من مكان إلى آخر في + +73 +00:05:17,280 --> 00:05:17,900 +الجسم + +74 +00:05:21,150 --> 00:05:25,010 +هنا بيحكي إن كيف تتكون الرابطة البيبتيدية أو + +75 +00:05:25,010 --> 00:05:28,070 +البروتين كيف بتتكون polypeptide and the protein + +76 +00:05:28,070 --> 00:05:32,210 +are formed by amino acids held together by amide + +77 +00:05:32,210 --> 00:05:36,550 +bond بتتكون البروتينات من ارتباط أحماض أمينية مع + +78 +00:05:36,550 --> 00:05:40,710 +بعضها البعض ب amide bond هي نفسها ال peptide bond + +79 +00:05:40,710 --> 00:05:44,010 +إذن الرابطة اللي بينهم بتكون اسمها peptide bond أو + +80 +00:05:44,010 --> 00:05:47,580 +amide bond between أين بتيجي هذه الرابطة؟ between + +81 +00:05:47,580 --> 00:05:51,100 +the amino end of one amino acid molecule and + +82 +00:05:51,100 --> 00:05:54,800 +carboxyl end of another amino acid molecule الرابطة + +83 +00:05:54,800 --> 00:05:58,500 +الـ amide bond او الـ peptide bond بتيجي بين ال + +84 +00:05:58,500 --> 00:06:02,000 +amino end ال amino group من حمض أميني مع ال + +85 +00:06:02,000 --> 00:06:04,800 +carboxyl end اللي هي carboxyl group of another + +86 +00:06:04,800 --> 00:06:08,960 +amino acid بتيجي الرابطة باه ال amino group و ال + +87 +00:06:08,960 --> 00:06:11,940 +carboxyl group amino group من حمض أميني مع + +88 +00:06:11,940 --> 00:06:14,960 +carboxyl group من حمض أميني أخر بتيجي الرابطة باه + +89 +00:06:14,960 --> 00:06:20,200 +بتنزع جزء ما و تتكون الرابطة بنسميها it's called a + +90 +00:06:20,200 --> 00:06:23,300 +peptide bond this amide bond is called peptide + +91 +00:06:23,300 --> 00:06:26,700 +bond وحكينا إنه في حاجة بتنتج منها لما يتكون ال + +92 +00:06:26,700 --> 00:06:30,320 +protein بيكون في عندنا حاجة اسمها N-terminus و + +93 +00:06:30,320 --> 00:06:34,430 +حاجة اسمها C-terminus حكينا الـ N-terminus هو الحمض + +94 +00:06:34,430 --> 00:06:39,010 +الأميني اللي بيحتوي على amino group لم تشارك في + +95 +00:06:39,010 --> 00:06:42,890 +تكوين الرابطة البيبتدية not involved in a peptide + +96 +00:06:42,890 --> 00:06:46,350 +bond free amino group اللي بيكون على الطرف فيه + +97 +00:06:46,350 --> 00:06:49,330 +free amino group مش مشاركة في تكوين الرابطة + +98 +00:06:49,330 --> 00:06:53,950 +البيبتدية بتكون في النهاية بنسميها N-terminus الـ C + +99 +00:06:53,950 --> 00:06:58,150 +-terminus هي الحمض الأميني اللي بيحتوي على كربوكسيل + +100 +00:06:58,150 --> 00:07:01,950 +group not involved in a peptide bond يحتوي على + +101 +00:07:01,950 --> 00:07:06,930 +كربوكسيل group لم تشارك في تكوين الرابطة البيبتدية + +102 +00:07:06,930 --> 00:07:12,510 +free carboxyl group طب إيش لنا ال protein + +103 +00:07:12,510 --> 00:07:15,910 +structure؟ و أكيد أخدته بالنظرى في منه primary + +104 +00:07:15,910 --> 00:07:19,690 +structure secondary structure tertiary و + +105 +00:07:19,690 --> 00:07:24,620 +quaternary لو حكينا على السريع الـ Primary Structure هو + +106 +00:07:24,620 --> 00:07:27,560 +عبارة عن سلسلة الأحماض الأمينية بتكون مرتبطة مع + +107 +00:07:27,560 --> 00:07:31,560 +بعضها بروابط ببتدية هذه السلسلة اللي بتكون مرتبطة + +108 +00:07:31,560 --> 00:07:34,080 +مع بعضها بروابط ببتدية هذا بيكون ما بسميه الـ + +109 +00:07:34,080 --> 00:07:37,840 +Primary Structure الـ Secondary Structure بتيجي + +110 +00:07:37,840 --> 00:07:40,620 +اللي هي سلسلة الأحماض الأمينية بترتبط مع بعضها البعض + +111 +00:07:40,620 --> 00:07:45,960 +بروابط ببتدية وفي بينها H bonds روابط هيدروجينية في + +112 +00:07:45,960 --> 00:07:51,170 +منه جزاين Alpha Helix وفي Beta Sheet الـ Tertiary + +113 +00:07:51,170 --> 00:07:55,210 +Structure بتكون عبارة عن شكل كروي، 3D شكل كروي زي + +114 +00:07:55,210 --> 00:07:59,890 +ال myoglobin بتكون three dimensional shape ال + +115 +00:07:59,890 --> 00:08:03,570 +quaternary هي عبارة عن many segments مع بعض + +116 +00:08:03,570 --> 00:08:07,450 +association أكثر من domain مع بعض، يجي يرتبطوا مع + +117 +00:08:07,450 --> 00:08:10,810 +بعض، زي ال hemoglobin بتكون من أربعة، من اثنين + +118 +00:08:10,810 --> 00:08:12,670 +beta و اثنين alpha + +119 +00:08:15,870 --> 00:08:19,550 +اللي عندنا أشكال الـ secondary structure كيف شكل + +120 +00:08:19,550 --> 00:08:22,630 +الـ Alpha Helix بتكون و كيف شكل الـ Beta Sheet + +121 +00:08:22,630 --> 00:08:26,610 +بتكون زي الصورة اللي فوق على اليسار هذه بتكون .. + +122 +00:08:26,610 --> 00:08:29,710 +هذه عبارة عن الـ Beta Sheet اللي جنبها عبارة عن + +123 +00:08:29,710 --> 00:08:36,090 +الـ Alpha Helix طب بدنا نحكي هنا عن .. نحكي اللي + +124 +00:08:36,090 --> 00:08:41,450 +إنه خواص الأحماض الأمينية اللي موجودة في البروتين + +125 +00:08:41,450 --> 00:08:46,120 +و الـpeptide كيف بتم تحديدها؟ جداً البروتين كيف + +126 +00:08:46,120 --> 00:08:49,580 +بتتعرف خصائصه؟ باعرفها من الأحماض الأمينية + +127 +00:08:49,580 --> 00:08:52,620 +المكونة إليه كيف بدي أطلع على الحمض الأميني؟ على + +128 +00:08:52,620 --> 00:08:56,620 +إيش بدي أطلع؟ أطلع على الـR-group اللي بتميز كل + +129 +00:08:56,620 --> 00:09:01,120 +حمض أميني عن الآخر إذا كيف بدي أعرف خصائص البروتين + +130 +00:09:01,120 --> 00:09:04,760 +من الأحماض الأمينية المكونة إليه؟ شو اللي بيميز كل + +131 +00:09:04,760 --> 00:09:09,200 +حمض أميني؟ هي الـR-group فخصائص الحمض الأميني + +132 +00:09:09,200 --> 00:09:12,840 +الموجود في البروتين و الـpeptide تتحدد من خلال + +133 +00:09:13,700 --> 00:09:20,320 +الجروب كمان بيحكيلي شحنة ال terminal groups من هما + +134 +00:09:20,320 --> 00:09:24,340 +ال terminal groups هو ال amino group و الكربوكسيلي + +135 +00:09:24,340 --> 00:09:27,540 +group اللي موجودة في الحمض الأميني ال structure + +136 +00:09:27,540 --> 00:09:31,240 +بتاع الحمض الأميني هي كانت بيتكون من أعلى جروب و + +137 +00:09:31,240 --> 00:09:35,340 +هيدروجين و central carbon فيها كربوكسيلي group و + +138 +00:09:35,340 --> 00:09:39,200 +amino group ال Amino group و ال Carboxyl group + +139 +00:09:39,200 --> 00:09:43,100 +الشحنات اللي عليهم هكذا بتختلف حسب الوسط اللي أنا + +140 +00:09:43,100 --> 00:09:47,180 +بحطها فيه هل هي في وسط حمضي، في وسط قاعدي، في وسط + +141 +00:09:47,180 --> 00:09:53,320 +متعادل فأنا خصائص الحمض الأميني بدي أحددها من خلال + +142 +00:09:53,320 --> 00:09:58,080 +الـ R group وشحنة الـ Amino group and Carboxyl + +143 +00:09:58,080 --> 00:10:04,040 +group عشان هيك بيحكيلي it's important to know which + +144 +00:10:04,040 --> 00:10:07,720 +group of peptides and proteins will be protonated + +145 +00:10:07,720 --> 00:10:12,860 +at certain بيئات ضروري أن أعرف أنا موجودة في أي + +146 +00:10:12,860 --> 00:10:16,440 +وسط في أي بيئات في acidic ولا في alkaline ولا في + +147 +00:10:16,440 --> 00:10:20,180 +neutral طب مين صار عليها protonated؟ ومين صار لها + +148 +00:10:20,180 --> 00:10:24,720 +deprotonated؟ مين فقدت ومين كسبت؟ الشحنة هنا صارت + +149 +00:10:24,720 --> 00:10:27,940 +جديش net charge وهنا جديش net charge لأن + +150 +00:10:27,940 --> 00:10:32,100 +حاجة الشحنة بتحدد خصائص الحمض الأميني وبالتالي + +151 +00:10:32,100 --> 00:10:36,750 +هيعرف خاصية خصائص البروتين protein molecules carry + +152 +00:10:36,750 --> 00:10:40,670 +charge according to their amino acid sequence and + +153 +00:10:40,670 --> 00:10:44,070 +the aqueous solvent pH they are dissolved in + +154 +00:10:44,070 --> 00:10:48,310 +بحكيلي شحنة البروتين كيف بده أحددها من خلال + +155 +00:10:48,310 --> 00:10:50,930 +الأحماض الأمينية المكونة لها the amino acid + +156 +00:10:50,930 --> 00:10:54,060 +sequence بجمع الشحنات كلها اللي موجودة على كل حمض + +157 +00:10:54,060 --> 00:10:58,160 +أميني مثلا الأول positive واحد، الثاني minus واحد، + +158 +00:10:58,160 --> 00:11:01,920 +الثالث هي positive اثنين، بجمعهم مع بعض، بشوف ال + +159 +00:11:01,920 --> 00:11:06,080 +net charge للبروتين كامل جديش الشحنة، كمان عشان + +160 +00:11:06,080 --> 00:11:09,400 +الحاجة الثانية اللي بتحدد هي ال pH اللي موجود + +161 +00:11:09,400 --> 00:11:14,300 +فيها، ما هي ال pH هتغير ال charge اللي موجودة على + +162 +00:11:14,300 --> 00:11:17,860 +ال amino group و ال carboxyl group، بجمع محصلة هذه + +163 +00:11:17,860 --> 00:11:22,500 +الشحنة، و أشوف الشحنة الكلية للبروتين قد ايش هتصير + +164 +00:11:22,500 --> 00:11:26,340 +بما + +165 +00:11:26,340 --> 00:11:29,240 +أن تجربتنا التي اليوم هي عبارة عن ال precipitation + +166 +00:11:29,240 --> 00:11:32,500 +of the protein at the isoelectric point أن أنا بدي + +167 +00:11:32,500 --> 00:11:36,380 +أرسب ال protein عند نقطة ال isoelectric point حتى + +168 +00:11:36,380 --> 00:11:39,180 +نعرف ليش أنا برسب ال protein عند نقطة ال + +169 +00:11:39,180 --> 00:11:42,280 +isoelectric point، لماذا أنا اخترت هذه النقطة، بدنا + +170 +00:11:42,280 --> 00:11:46,350 +نعرف حاجات عن ال protein solubility بحكيلي there + +171 +00:11:46,350 --> 00:11:48,690 +are many factors that contribute to protein + +172 +00:11:48,690 --> 00:11:53,650 +solubility يعني إن عدة عوامل بتلعب دور في ذائبية + +173 +00:11:53,650 --> 00:11:56,450 +البروتين يعني أنا كده بدي أحدد هل هات البروتين + +174 +00:11:56,450 --> 00:12:00,570 +soluble in water أو not soluble the most important + +175 +00:12:00,570 --> 00:12:04,990 +determinants is electrostatic charge أهم عامل بحدد + +176 +00:12:04,990 --> 00:12:10,200 +ذائبية البروتين هي شحنة البروتين إذا كان البروتين + +177 +00:12:10,200 --> 00:12:13,360 +مثلا شحنته موجبة أو شحنته سالبة net charge اللي + +178 +00:12:13,360 --> 00:12:17,740 +عليه جديش Solubility of البروتين كمان بتعتمد على + +179 +00:12:17,740 --> 00:12:22,180 +distribution of hydrophilic and hydrophobic amino + +180 +00:12:22,180 --> 00:12:25,840 +acids on the protein surface، هي اللي بحدد شحنة + +181 +00:12:25,840 --> 00:12:29,280 +البروتين حكينا هي ال amino acid sequence، ترتيب + +182 +00:12:29,2 + +201 +00:13:51,360 --> 00:13:54,940 +بحكي ليه هناك هي أن أمثلة على Hydrophilic Amino + +202 +00:13:54,940 --> 00:13:58,600 +Acid و Hydrophobic Amino Acid زي مين Hydrophilic و + +203 +00:13:58,600 --> 00:14:03,350 +مين Hydrophobic و هذا غير مطلوب أن تكون نفسهم بعد هيك + +204 +00:14:03,350 --> 00:14:07,010 +بيحكيني إنه إذا كانت charged and polar surfaces، + +205 +00:14:07,010 --> 00:14:10,430 +إذا كان سطح البروتين بتكون من أحماض أمينية + +206 +00:14:10,430 --> 00:14:14,770 +مشحونة و polar، قطبية، إذن القطبية هتتفاعل مع + +207 +00:14:14,770 --> 00:14:17,430 +جزيئات الماء، مع الـ solvent، interact with the + +208 +00:14:17,430 --> 00:14:21,370 +solvent and increase solubility وهتزود الذائبية، + +209 +00:14:21,370 --> 00:14:25,330 +وهيكون ذائب، إيش هي الـ net charge of البروتين؟ إيش + +210 +00:14:25,330 --> 00:14:28,850 +تخريف الـ net charge المحصلة النهائية للشحنات؟ هي + +211 +00:14:28,850 --> 00:14:33,110 +average of all charges هي محصلة كل الشحنات، بجمع كل + +212 +00:14:33,110 --> 00:14:37,310 +الشحنات مع بعضها، بشوف الشحنة النهائية at a + +213 +00:14:37,310 --> 00:14:41,650 +certain pH للبروتين net charge و الـ pI، this is + +214 +00:14:41,650 --> 00:14:44,650 +called the isoelectric point حكينا إن الـ + +215 +00:14:44,650 --> 00:14:47,790 +isoelectric point في نقطة اسمها الـ isoelectric point، + +216 +00:14:47,790 --> 00:14:52,390 +وهي قيمة pH اللي عندها بيكون الـ net charge بتساوي + +217 +00:14:52,390 --> 00:14:55,010 +zero الشحنة الكلية بتساوي صفر diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..aaf57f40502b02fb35290223b0e33faeb31d148c --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY_postprocess.srt @@ -0,0 +1,868 @@ +1 +00:00:01,300 --> 00:00:05,160 +اليوم ان شاء الله بنحكي بموضوع جديد اللي هو + +2 +00:00:05,160 --> 00:00:08,660 +precipitation of ال protein at isoelectric bond + +3 +00:00:08,660 --> 00:00:13,140 +عملية ترسيب ال protein عند نقطة ال isoelectric + +4 +00:00:13,140 --> 00:00:16,900 +bond يعني ما عملنا اليوم غير عن ترسيب ال protein + +5 +00:00:16,900 --> 00:00:23,480 +عند نقطة ال isoelectric bond نحكي + +6 +00:00:23,480 --> 00:00:27,080 +في البداية مقدمة عن البروتينات إيش هي البروتينات + +7 +00:00:27,080 --> 00:00:32,450 +بشكل عام البروتين حكيناإن هو عبارة عن polymers of + +8 +00:00:32,450 --> 00:00:35,610 +amino acid حكي إن أنه بتيجي ال amino acid ترتبط + +9 +00:00:35,610 --> 00:00:40,230 +بعض بروابط ببتدية بتكون ال protein فال protein هو + +10 +00:00:40,230 --> 00:00:44,750 +polymers من الأحماض الأمينية من ال amino acid our + +11 +00:00:44,750 --> 00:00:48,290 +substance of high molecular weight الوزن الجزائي + +12 +00:00:48,290 --> 00:00:51,910 +له عالي molecular weight لها عالية بنحكي عنها + +13 +00:00:51,910 --> 00:00:55,910 +macro molecule مركبات كبيرة وزنها الجزائي عالي + +14 +00:00:55,910 --> 00:00:59,810 +بنحكي عنها macro moleculeالـ molecular weight إلها + +15 +00:00:59,810 --> 00:01:06,480 +من خمس تلاف إلى مليون تلفكل البروتينات بشكل عام في + +16 +00:01:06,480 --> 00:01:10,840 +ال structure بتتكون من كربون، هيدروجين، أكسجين + +17 +00:01:10,840 --> 00:01:14,300 +ونيتروجين كلها كل البروتينات ال structure فيه + +18 +00:01:14,300 --> 00:01:20,200 +كربون، هيدروجين، أكسجين ونيتروجين معظمها يحتوي على + +19 +00:01:20,200 --> 00:01:25,280 +سلفة وبعضها some contain فسفرة استحتوي على فسفرة + +20 +00:01:25,280 --> 00:01:28,940 +إذا كلها فيها كربون وهيدروجين وأكسجين ونيتروجين + +21 +00:01:28,940 --> 00:01:33,430 +all ال proteinmost اللي هم معظمها بتحتوي على سالفة + +22 +00:01:33,430 --> 00:01:37,770 +some contain phosphorus يعني بعضها تحتوي على فسفرة + +23 +00:01:37,770 --> 00:01:42,130 +و few have mineral elements و القليل منها بتحتوي + +24 +00:01:42,130 --> 00:01:46,090 +على مينيرال زي الأثيل حديد زي مغنيسيوم زي الكبار + +25 +00:01:46,090 --> 00:01:51,290 +safe as a structural component غنما تدخل في تركيب + +26 +00:01:51,290 --> 00:01:55,930 +الكائنات الحية تدخل البروتينات في تركيب الكائنات + +27 +00:01:55,930 --> 00:02:01,990 +الحيةهنا عندنا توضيح كيف بيتكون البروتين هنا بيجي + +28 +00:02:01,990 --> 00:02:06,890 +حمضيين حمض أميني بيرتبط مع حمض أميني آخر ب peptide + +29 +00:02:06,890 --> 00:02:11,090 +bond وين بتتكون ال peptide bond؟ بين كربوكسيل من + +30 +00:02:11,090 --> 00:02:16,370 +حمض أميني الأول و amino group من حمض أميني آخر + +31 +00:02:16,370 --> 00:02:19,450 +بتيجي الرابطة بالنص بين الكربوكسيل و ال amino + +32 +00:02:19,450 --> 00:02:23,630 +group بين الحمضيين الأمينية نسميها رابطة peptide + +33 +00:02:23,630 --> 00:02:28,330 +bondحكينا بيكون الناتج منها نزع جزاء ماء فسمينا + +34 +00:02:28,330 --> 00:02:32,850 +التفاعل Condensation Reaction لأنه بينتج عنه جزاء + +35 +00:02:32,850 --> 00:02:37,570 +ماء بشكل عام البروتينات تتكون من ترتيب من الأحمض + +36 +00:02:37,570 --> 00:02:41,890 +الأمينية ترتبط مع بعضها البعض بـ peptide bond وين + +37 +00:02:41,890 --> 00:02:45,910 +موقع الرابطة اللي بيبتديها؟ بتيجي بين Carboxyl من + +38 +00:02:45,910 --> 00:02:50,030 +حمض أميني و Aminogroup من حمض أميني آخر بتيجي + +39 +00:02:50,030 --> 00:02:51,890 +الرابطة في الوسط بينهم + +40 +00:02:54,980 --> 00:02:58,400 +نحكي عن ال protein function، إيش وظائف البروتين؟ + +41 +00:02:58,400 --> 00:03:03,400 +تقنع الوظائف للبروتين، أول وظيفة structure، تركيب، + +42 +00:03:03,400 --> 00:03:06,800 +بروتينات تركيبية إنها بتدخل هذه البروتينات في + +43 +00:03:06,800 --> 00:03:10,760 +تركيب خلايا الجسم، some protein provide structural + +44 +00:03:10,760 --> 00:03:14,760 +support، زي مين زي الكولاجين، يدخل في خلايا ال + +45 +00:03:14,760 --> 00:03:18,620 +muscle، كيراتين في ال hair وكرستالين في ال eyes + +46 +00:03:20,360 --> 00:03:24,000 +التاني وظيفة هي ال transport transport إن البروتين + +47 +00:03:24,000 --> 00:03:28,940 +يعمل كناقل لنقل المواد من مكان لآخر في الجسم some + +48 +00:03:28,940 --> 00:03:31,600 +proteins are responsible for the transportation of + +49 +00:03:31,600 --> 00:03:34,480 +smaller molecules from one part of the body to + +50 +00:03:34,480 --> 00:03:38,820 +another تعمل كناقل لنقل المركبات الصغيرة من مكان + +51 +00:03:38,820 --> 00:03:42,860 +لآخر في الجسممثال على الـ transportation البروتين + +52 +00:03:42,860 --> 00:03:46,520 +هو الـ hemoglobin الـ hemoglobin يعمل كنقل بينجل + +53 +00:03:46,520 --> 00:03:54,800 +الأكسجين من الرئتين إلى الخلايا عبر الجسم مش كمان + +54 +00:03:54,800 --> 00:03:59,060 +وظائف البروتين البروتين يعمل ك catalysis إنزان + +55 +00:03:59,060 --> 00:04:03,380 +إنزين محفظ في بعضهم بيشتغل بعض البروتينات تعمل + +56 +00:04:03,380 --> 00:04:07,380 +كإنزيمات محفظة بتسرع التفاعل catalysis the + +57 +00:04:07,380 --> 00:04:11,930 +chemical reactionوظيفة اللي بعد هي storage تعمل + +58 +00:04:11,930 --> 00:04:16,490 +كبروتينات تخزينية للتخزين أشهر مثال على بروتينات + +59 +00:04:16,490 --> 00:04:19,750 +التخزين هو ال myoglobin ال myoglobin هو storage + +60 +00:04:19,750 --> 00:04:23,750 +بروتيين بيخزن ال oxygen in muscle أثناء ال + +61 +00:04:23,750 --> 00:04:27,330 +exercise بيخزن ال oxygen في العضلاتإذا الجسم مثلا + +62 +00:04:27,330 --> 00:04:31,990 +في أثناء التمرين الشاق نقص الـ Oxygen على العضلة، + +63 +00:04:31,990 --> 00:04:35,630 +مين بيزود بال Oxygen؟ الـ Myoglobin بيكون خزين من + +64 +00:04:35,630 --> 00:04:40,270 +ال Oxygen، بيوزح على العضلات و للجسم عند الحاجة. + +65 +00:04:40,990 --> 00:04:44,630 +Hormones، بتعمل لبروتينات كهرمون، some hormones + +66 +00:04:44,630 --> 00:04:48,090 +are البروتين، بعض الهرمونات هي عبارة عن البروتين، + +67 +00:04:48,090 --> 00:04:52,110 +و أشهر مثال على بروتين .. على هرمون يعمل .. يعتبر + +68 +00:04:52,110 --> 00:04:56,720 +البروتين هوالانسولين الانسولين هو example على + +69 +00:04:56,720 --> 00:05:02,080 +هرمون و protein إيش هو الهرمون؟ هرمون serve as + +70 +00:05:02,080 --> 00:05:05,800 +chemical messenger carrying signals from one part + +71 +00:05:05,800 --> 00:05:11,540 +of the body to another الهرمون هو عبارة عن إشارة + +72 +00:05:11,540 --> 00:05:17,280 +أو رسالة كيميائية لنقل الإشارة من مكان إلى آخر في + +73 +00:05:17,280 --> 00:05:17,900 +الجسم + +74 +00:05:21,150 --> 00:05:25,010 +هنا بيحكي إن كيف تتكون الرابطة البيبتيدية أو + +75 +00:05:25,010 --> 00:05:28,070 +البروتين كيف بتتكون polypeptide and the protein + +76 +00:05:28,070 --> 00:05:32,210 +are formed by amino acid held together by amide + +77 +00:05:32,210 --> 00:05:36,550 +bond بتتكون البروتينات من ارتباط أحماد أمينية مع + +78 +00:05:36,550 --> 00:05:40,710 +بعضها البعض ب amide bond هي نفسها ال peptide bond + +79 +00:05:40,710 --> 00:05:44,010 +إذن الرابطة اللي بينهم بتكون اسمها peptide bond أو + +80 +00:05:44,010 --> 00:05:47,580 +amide bondbetween وين بتيجي هذه الرابطة؟ between + +81 +00:05:47,580 --> 00:05:51,100 +the amino end of one amino acid molecule and + +82 +00:05:51,100 --> 00:05:54,800 +carboxyl end of another amino acid molecule الرابط + +83 +00:05:54,800 --> 00:05:58,500 +الـ amide bond او الـ peptide bond بتيجي بين ال + +84 +00:05:58,500 --> 00:06:02,000 +amino end ال amino group منه حمض أميني مع ال + +85 +00:06:02,000 --> 00:06:04,800 +carboxyl end اللي هي carboxyl group of another + +86 +00:06:04,800 --> 00:06:08,960 +amino acidبتيجي الرابطة باه ال amino group و ال + +87 +00:06:08,960 --> 00:06:11,940 +carboxyl group amino group من حمض أميني مع + +88 +00:06:11,940 --> 00:06:14,960 +carboxyl group من حمض أميني أخر بتيجي الرابطة باه + +89 +00:06:14,960 --> 00:06:20,200 +بتنزع جزء ما و تتكون الرابطة بنسميها it's called a + +90 +00:06:20,200 --> 00:06:23,300 +peptide bond this amide bond is called peptide + +91 +00:06:23,300 --> 00:06:26,700 +bond وحكينا إنه في حاجة بتنتج منها لما يتكون ال + +92 +00:06:26,700 --> 00:06:30,320 +protein بيكون في عندنا حاجة اسمها N-terminus و + +93 +00:06:30,320 --> 00:06:34,430 +حاجة اسمها C-terminusحكينا الـ N-terminus هو الحمض + +94 +00:06:34,430 --> 00:06:39,010 +الأميني اللي بيحتوي على amino group لم تشارك في + +95 +00:06:39,010 --> 00:06:42,890 +تكوين الرابطة البيبتدية not involved in a peptide + +96 +00:06:42,890 --> 00:06:46,350 +bond free amino group اللي بيكون على الطرف فيه + +97 +00:06:46,350 --> 00:06:49,330 +free amino group مش مشاركة في تكوين الرابطة + +98 +00:06:49,330 --> 00:06:53,950 +البيبتدية بتكون في النهاية بنسميها N-terminusالـ C + +99 +00:06:53,950 --> 00:06:58,150 +-terminus هي الحمض الأمين اللي بيحتوي على كربوكسيل + +100 +00:06:58,150 --> 00:07:01,950 +جروب not involved in a peptide bond يحتوي على + +101 +00:07:01,950 --> 00:07:06,930 +كربوكسيل جروب لم تشارك في تكوين الرابطة البيبتدية + +102 +00:07:06,930 --> 00:07:12,510 +free carboxyl group طب إيش لنا ال protein + +103 +00:07:12,510 --> 00:07:15,910 +structure؟ و أكيد أخدته بالنظرى في منه primary + +104 +00:07:15,910 --> 00:07:19,690 +structure secondary structure tertiary و + +105 +00:07:19,690 --> 00:07:24,620 +quaternaryلو حكينا على السريع الـ Primary Show هو + +106 +00:07:24,620 --> 00:07:27,560 +عبارة عن سلسة الأحمد الأمينية بتكون مرتبطة مع + +107 +00:07:27,560 --> 00:07:31,560 +بعضها بروابط ببتدية هذه السلسة اللي بتكون مرتبطة + +108 +00:07:31,560 --> 00:07:34,080 +مع بعضها بروابط ببتدية هذا بيكون ما بسميه الـ + +109 +00:07:34,080 --> 00:07:37,840 +Primary Structure الـ Secondary Structure بتيجي + +110 +00:07:37,840 --> 00:07:40,620 +اللي هي سلسة الأحمد الأمينية بترتبط مع بعضها البعض + +111 +00:07:40,620 --> 00:07:45,960 +بروابط ببتدية وفي بينها H bond روابط هيدروجينية في + +112 +00:07:45,960 --> 00:07:51,170 +منه جزاين Alpha Helical وفي Beta Chitالـ Texture + +113 +00:07:51,170 --> 00:07:55,210 +Structure بتكون عبارة عن شكل كروي، دو شكل كروي زي + +114 +00:07:55,210 --> 00:07:59,890 +ال myoglobin بتكون three dimensional shape ال + +115 +00:07:59,890 --> 00:08:03,570 +quaternary هي عبارة عن many segment مع بعض + +116 +00:08:03,570 --> 00:08:07,450 +association أكثر من domain مع بعض، يجي يرتبطوا مع + +117 +00:08:07,450 --> 00:08:10,810 +بعض، زي ال hemoglobin بتكون من أربعة، من اتنين + +118 +00:08:10,810 --> 00:08:12,670 +beta و اتنين alpha + +119 +00:08:15,870 --> 00:08:19,550 +اللي عندنا أشكال الـ secondary structure كيف شكل + +120 +00:08:19,550 --> 00:08:22,630 +الـ Alpha Helix بتكون و كيف شكل الـ Beta Sheet + +121 +00:08:22,630 --> 00:08:26,610 +بتكون زي الصورة اللي فوق على اليسار هذه بتكون .. + +122 +00:08:26,610 --> 00:08:29,710 +هذه عبارة عن الـ Beta Sheet اللي جنبها عبارة عن + +123 +00:08:29,710 --> 00:08:36,090 +الـ Alpha Helix طب بدنا نحكي هنا عن .. نحكي اللي + +124 +00:08:36,090 --> 00:08:41,450 +إنه غصائص الأحماض الأمينية اللي موجودة في البروتين + +125 +00:08:41,450 --> 00:08:46,120 +و الـpeptideكيف بتم تحددها؟ جدان البروتين كيف + +126 +00:08:46,120 --> 00:08:49,580 +بتدعي عرف خصائصه؟ باعرفها من الأحماض الأمينية + +127 +00:08:49,580 --> 00:08:52,620 +المكونة إليه كيف بدي أطلع على الحمض الأميني؟ على + +128 +00:08:52,620 --> 00:08:56,620 +إيش بدي أطلع؟ أطلع على الـR-group اللي بتميز كل + +129 +00:08:56,620 --> 00:09:01,120 +حمض أميني عن الآخر إذا كيف بدي أعرف خصائص البروتين + +130 +00:09:01,120 --> 00:09:04,760 +من الأحماض الأمينية المكونة إليه؟ شو اللي بيميز كل + +131 +00:09:04,760 --> 00:09:09,200 +حمض أميني؟ هي الـR-group فخصائص الحمض الأميني + +132 +00:09:09,200 --> 00:09:12,840 +الموجود في البروتين و الـpeptide تتحدد من خلال + +133 +00:09:13,700 --> 00:09:20,320 +الجروب كمان بيحكيلي شحنة التتراتبل جروب من هما + +134 +00:09:20,320 --> 00:09:24,340 +التتراتبل جروب هو ال amino group و الكربوكسيلي + +135 +00:09:24,340 --> 00:09:27,540 +group اللي موجودة في الحمض الأميني ال structure + +136 +00:09:27,540 --> 00:09:31,240 +بتاع الحمض الأميني هي كانت بيتكون من أعلى جروب و + +137 +00:09:31,240 --> 00:09:35,340 +هيدروجين و central carbon فيها كربوكسيلي group و + +138 +00:09:35,340 --> 00:09:39,200 +amino groupالـ Amino group والـ Carboxyl group + +139 +00:09:39,200 --> 00:09:43,100 +الشحنات اللي عليهم هكذا بتختلف حسب الوسط اللي أنا + +140 +00:09:43,100 --> 00:09:47,180 +بحطها فيه هل هي في وسط حمضي، في وسط قاعدي، في وسط + +141 +00:09:47,180 --> 00:09:53,320 +متعدد فأنا خصائص الحمض الأميني بدي أحددها من خلال + +142 +00:09:53,320 --> 00:09:58,080 +الـ R group وشحنة الـ Amino group and Carboxyl + +143 +00:09:58,080 --> 00:10:04,040 +groupعشان هيك بيحكيلي it's important to know which + +144 +00:10:04,040 --> 00:10:07,720 +group of peptides and proteins will be protonated + +145 +00:10:07,720 --> 00:10:12,860 +at certain بيئات فضروري ان اعرف انا موجودة في اي + +146 +00:10:12,860 --> 00:10:16,440 +وسط في اي بيئات في acidic ولا في alkaline ولا في + +147 +00:10:16,440 --> 00:10:20,180 +neutral طب مين صار عليها protonated؟ومين صار لها + +148 +00:10:20,180 --> 00:10:24,720 +deprotonated؟ مين فقدت ومين كسبت؟ الشحنة هنا صارت + +149 +00:10:24,720 --> 00:10:27,940 +جديش النت ت charge وهنا جديش النت ت charge لأن + +150 +00:10:27,940 --> 00:10:32,100 +حاجة الشحنة بتحدد خصائص الحمض الأميني وبالتالي + +151 +00:10:32,100 --> 00:10:36,750 +هيعرف خاصية خصائص البروتينprotein molecules carry + +152 +00:10:36,750 --> 00:10:40,670 +charge according to their amino acid sequence and + +153 +00:10:40,670 --> 00:10:44,070 +the aqueous solvent pH they are dissolved in + +154 +00:10:44,070 --> 00:10:48,310 +بحكيلي شحنة البروتين كيف بده أحددها من خلال + +155 +00:10:48,310 --> 00:10:50,930 +الأحماض الأمينية المكونة لها ال amino acid + +156 +00:10:50,930 --> 00:10:54,060 +sequenceبجمع الشحنات كلها اللي موجودة على كل حمض + +157 +00:10:54,060 --> 00:10:58,160 +أميني مثلا الأول positive واحد، التاني minus واحد، + +158 +00:10:58,160 --> 00:11:01,920 +البعد هي positive اتنين، بجمعهم مع بعض، بشوف ال + +159 +00:11:01,920 --> 00:11:06,080 +net charge للبروتين كامل جداش الشحنة، كمان عشان + +160 +00:11:06,080 --> 00:11:09,400 +الحاجة التانية اللي بتحدد هي ال pH اللي موجود + +161 +00:11:09,400 --> 00:11:14,300 +فيها، ما هي ال pH هتغير ال charge اللي موجودة على + +162 +00:11:14,300 --> 00:11:17,860 +ال amino group و ال carboxyl group، بجمع محكم هذه + +163 +00:11:17,860 --> 00:11:22,500 +الشحنة، و أشوف الشحنة الكلية للبروتينقداش هتسيق + +164 +00:11:22,500 --> 00:11:26,340 +بما + +165 +00:11:26,340 --> 00:11:29,240 +ان تجربتنا اللى اليوم هي عبارة عن ال precipitation + +166 +00:11:29,240 --> 00:11:32,500 +و في ال protein ال isoelectric point ان انا بدي + +167 +00:11:32,500 --> 00:11:36,380 +ارسب ال protein عن نقطة ال isoelectric point حتى + +168 +00:11:36,380 --> 00:11:39,180 +نعرف ليش انا برسب ال protein عن نقطة ال + +169 +00:11:39,180 --> 00:11:42,280 +isoelectric point، شما انا اخترت هذه النقطة، بدنا + +170 +00:11:42,280 --> 00:11:46,350 +نعرف حاجات عن ال protein solubilityبحكيلي there + +171 +00:11:46,350 --> 00:11:48,690 +are many factors that contribute to protein + +172 +00:11:48,690 --> 00:11:53,650 +solubility يعني إن عدة عوامل بتلعب دور في ذائبية + +173 +00:11:53,650 --> 00:11:56,450 +البروتين يعني أنا كده بده أحدد هل هات البروتين + +174 +00:11:56,450 --> 00:12:00,570 +soluble in water أو not soluble the most important + +175 +00:12:00,570 --> 00:12:04,990 +determinants is electrostatic charge أهم عامل بحد + +176 +00:12:04,990 --> 00:12:10,200 +ذائبية البروتين هي شحنة البروتينإذا كان البروتين + +177 +00:12:10,200 --> 00:12:13,360 +مثلا شحنته موجبة أو شحنته سلب، انت تشارجي اللي + +178 +00:12:13,360 --> 00:12:17,740 +عليه جداش Solubility of البروتين كمان بتعتمد على + +179 +00:12:17,740 --> 00:12:22,180 +distribution of hydrophilic and hydrophobic amino + +180 +00:12:22,180 --> 00:12:25,840 +acid on the protein surface، هي اللي بحدد شحنة + +181 +00:12:25,840 --> 00:12:29,280 +البروتين حكينا هي ال amino acid sequence، ترتيب + +182 +00:12:29,280 --> 00:12:34,240 +الأحمار الأمينية اللي عليهاهذه الشحنة كمان هتحدد + +183 +00:12:34,240 --> 00:12:37,660 +الـ solubility للبروتين من خلال توزيع + +184 +00:12:37,660 --> 00:12:41,280 +الـhydrophilic وhydrophobic أمينو أسد الموجودين + +185 +00:12:41,280 --> 00:12:44,600 +على البروتين البروتين هو عبارة عن sequence من + +186 +00:12:44,600 --> 00:12:48,260 +أمينو أسد هتطلع هاي الأحمض الأمينية شو شحنتها + +187 +00:12:48,260 --> 00:12:51,540 +هتطلع إيش الأحمض الأمينية المكونة له هل هي + +188 +00:12:51,540 --> 00:12:55,080 +hydrophilic ولا hydrophobic مين الأغلب عنده + +189 +00:12:55,080 --> 00:12:58,380 +hydrophilic ولا hydrophobic موجود الـhydrophobic + +190 +00:12:58,380 --> 00:13:03,040 +مثلا للداخل متخبيه والـhydrophilic للخارجولا كيف + +191 +00:13:03,040 --> 00:13:07,500 +توزيعتها بحكي لي ال proteins that have high + +192 +00:13:07,500 --> 00:13:12,680 +hydrophobic amino acid content on the surface have + +193 +00:13:12,680 --> 00:13:17,100 +low solubility in aqueous solvent فجدت hydrophobic + +194 +00:13:17,100 --> 00:13:21,990 +معناها كاره للماءHydrophobic كاره للماء فإذا + +195 +00:13:21,990 --> 00:13:26,810 +البروتين بيتكون من أحماض أمينية كارهة للماء وده + +196 +00:13:26,810 --> 00:13:30,930 +كرمية كبيرة من أحماض أمينية كارهة للماء موجودة على + +197 +00:13:30,930 --> 00:13:36,430 +السطح فهذا بيقلل الذائبية على مبدأ like dissolve + +198 +00:13:36,430 --> 00:13:39,890 +like المديبات مديب بعضها اللي لهم نفس الخصائص + +199 +00:13:39,890 --> 00:13:43,350 +بدوبوا ببعض إذا كان هذا الحمض الأميني كاره للماء + +200 +00:13:43,350 --> 00:13:46,750 +كيف بيدوب في الماء إذا هيكون له solubility + +201 +00:13:51,360 --> 00:13:54,940 +بحكي ليه هناك هي أن أمثلة على Hydrophilic Amino + +202 +00:13:54,940 --> 00:13:58,600 +Acid و Hydrophobic Amino Acid زي مين Hydrophilic و + +203 +00:13:58,600 --> 00:14:03,350 +مين Hydrophobic و هذا مش مطلوب أنها نفسهابعد هيك + +204 +00:14:03,350 --> 00:14:07,010 +بيحكيني إنه إذا كانت charged and polar surfaced، + +205 +00:14:07,010 --> 00:14:10,430 +إذا كان الحمق للبروتينة بتكون من أحماض أمينية + +206 +00:14:10,430 --> 00:14:14,770 +مشفونة و polar، قطبية، إذن القطبية هيتفاعل مع + +207 +00:14:14,770 --> 00:14:17,430 +جزيئات الماء، مع ال solvent، interact with the + +208 +00:14:17,430 --> 00:14:21,370 +solvent and increase solubility وهتزود الذائبية، + +209 +00:14:21,370 --> 00:14:25,330 +وهيكون ذائبإيش هي الـ net charge of البروتين؟ إيش + +210 +00:14:25,330 --> 00:14:28,850 +تخريف الـ net charge المحصلة النهائية للشحنات؟ هي + +211 +00:14:28,850 --> 00:14:33,110 +average of all charge هي محصلة كل الشحنات، بجمع كل + +212 +00:14:33,110 --> 00:14:37,310 +الشحنات مع بعضها، بشوف الشحنة النهائية at a + +213 +00:14:37,310 --> 00:14:41,650 +certain pH بروتين نت charge والـ P0، this is + +214 +00:14:41,650 --> 00:14:44,650 +called the isoelectric point حكينا إن الـ + +215 +00:14:44,650 --> 00:14:47,790 +isoelectric في نقطة اسمها الـ isoelectric point، + +216 +00:14:47,790 --> 00:14:52,390 +وهي قيمة pHاللي عندها بيكون ال mid charge بتساوي + +217 +00:14:52,390 --> 00:14:55,010 +zero الشحنة الكلية بتساوي صفر + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY_raw.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..aaf57f40502b02fb35290223b0e33faeb31d148c --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/pG0PJIJ68bY_raw.srt @@ -0,0 +1,868 @@ +1 +00:00:01,300 --> 00:00:05,160 +اليوم ان شاء الله بنحكي بموضوع جديد اللي هو + +2 +00:00:05,160 --> 00:00:08,660 +precipitation of ال protein at isoelectric bond + +3 +00:00:08,660 --> 00:00:13,140 +عملية ترسيب ال protein عند نقطة ال isoelectric + +4 +00:00:13,140 --> 00:00:16,900 +bond يعني ما عملنا اليوم غير عن ترسيب ال protein + +5 +00:00:16,900 --> 00:00:23,480 +عند نقطة ال isoelectric bond نحكي + +6 +00:00:23,480 --> 00:00:27,080 +في البداية مقدمة عن البروتينات إيش هي البروتينات + +7 +00:00:27,080 --> 00:00:32,450 +بشكل عام البروتين حكيناإن هو عبارة عن polymers of + +8 +00:00:32,450 --> 00:00:35,610 +amino acid حكي إن أنه بتيجي ال amino acid ترتبط + +9 +00:00:35,610 --> 00:00:40,230 +بعض بروابط ببتدية بتكون ال protein فال protein هو + +10 +00:00:40,230 --> 00:00:44,750 +polymers من الأحماض الأمينية من ال amino acid our + +11 +00:00:44,750 --> 00:00:48,290 +substance of high molecular weight الوزن الجزائي + +12 +00:00:48,290 --> 00:00:51,910 +له عالي molecular weight لها عالية بنحكي عنها + +13 +00:00:51,910 --> 00:00:55,910 +macro molecule مركبات كبيرة وزنها الجزائي عالي + +14 +00:00:55,910 --> 00:00:59,810 +بنحكي عنها macro moleculeالـ molecular weight إلها + +15 +00:00:59,810 --> 00:01:06,480 +من خمس تلاف إلى مليون تلفكل البروتينات بشكل عام في + +16 +00:01:06,480 --> 00:01:10,840 +ال structure بتتكون من كربون، هيدروجين، أكسجين + +17 +00:01:10,840 --> 00:01:14,300 +ونيتروجين كلها كل البروتينات ال structure فيه + +18 +00:01:14,300 --> 00:01:20,200 +كربون، هيدروجين، أكسجين ونيتروجين معظمها يحتوي على + +19 +00:01:20,200 --> 00:01:25,280 +سلفة وبعضها some contain فسفرة استحتوي على فسفرة + +20 +00:01:25,280 --> 00:01:28,940 +إذا كلها فيها كربون وهيدروجين وأكسجين ونيتروجين + +21 +00:01:28,940 --> 00:01:33,430 +all ال proteinmost اللي هم معظمها بتحتوي على سالفة + +22 +00:01:33,430 --> 00:01:37,770 +some contain phosphorus يعني بعضها تحتوي على فسفرة + +23 +00:01:37,770 --> 00:01:42,130 +و few have mineral elements و القليل منها بتحتوي + +24 +00:01:42,130 --> 00:01:46,090 +على مينيرال زي الأثيل حديد زي مغنيسيوم زي الكبار + +25 +00:01:46,090 --> 00:01:51,290 +safe as a structural component غنما تدخل في تركيب + +26 +00:01:51,290 --> 00:01:55,930 +الكائنات الحية تدخل البروتينات في تركيب الكائنات + +27 +00:01:55,930 --> 00:02:01,990 +الحيةهنا عندنا توضيح كيف بيتكون البروتين هنا بيجي + +28 +00:02:01,990 --> 00:02:06,890 +حمضيين حمض أميني بيرتبط مع حمض أميني آخر ب peptide + +29 +00:02:06,890 --> 00:02:11,090 +bond وين بتتكون ال peptide bond؟ بين كربوكسيل من + +30 +00:02:11,090 --> 00:02:16,370 +حمض أميني الأول و amino group من حمض أميني آخر + +31 +00:02:16,370 --> 00:02:19,450 +بتيجي الرابطة بالنص بين الكربوكسيل و ال amino + +32 +00:02:19,450 --> 00:02:23,630 +group بين الحمضيين الأمينية نسميها رابطة peptide + +33 +00:02:23,630 --> 00:02:28,330 +bondحكينا بيكون الناتج منها نزع جزاء ماء فسمينا + +34 +00:02:28,330 --> 00:02:32,850 +التفاعل Condensation Reaction لأنه بينتج عنه جزاء + +35 +00:02:32,850 --> 00:02:37,570 +ماء بشكل عام البروتينات تتكون من ترتيب من الأحمض + +36 +00:02:37,570 --> 00:02:41,890 +الأمينية ترتبط مع بعضها البعض بـ peptide bond وين + +37 +00:02:41,890 --> 00:02:45,910 +موقع الرابطة اللي بيبتديها؟ بتيجي بين Carboxyl من + +38 +00:02:45,910 --> 00:02:50,030 +حمض أميني و Aminogroup من حمض أميني آخر بتيجي + +39 +00:02:50,030 --> 00:02:51,890 +الرابطة في الوسط بينهم + +40 +00:02:54,980 --> 00:02:58,400 +نحكي عن ال protein function، إيش وظائف البروتين؟ + +41 +00:02:58,400 --> 00:03:03,400 +تقنع الوظائف للبروتين، أول وظيفة structure، تركيب، + +42 +00:03:03,400 --> 00:03:06,800 +بروتينات تركيبية إنها بتدخل هذه البروتينات في + +43 +00:03:06,800 --> 00:03:10,760 +تركيب خلايا الجسم، some protein provide structural + +44 +00:03:10,760 --> 00:03:14,760 +support، زي مين زي الكولاجين، يدخل في خلايا ال + +45 +00:03:14,760 --> 00:03:18,620 +muscle، كيراتين في ال hair وكرستالين في ال eyes + +46 +00:03:20,360 --> 00:03:24,000 +التاني وظيفة هي ال transport transport إن البروتين + +47 +00:03:24,000 --> 00:03:28,940 +يعمل كناقل لنقل المواد من مكان لآخر في الجسم some + +48 +00:03:28,940 --> 00:03:31,600 +proteins are responsible for the transportation of + +49 +00:03:31,600 --> 00:03:34,480 +smaller molecules from one part of the body to + +50 +00:03:34,480 --> 00:03:38,820 +another تعمل كناقل لنقل المركبات الصغيرة من مكان + +51 +00:03:38,820 --> 00:03:42,860 +لآخر في الجسممثال على الـ transportation البروتين + +52 +00:03:42,860 --> 00:03:46,520 +هو الـ hemoglobin الـ hemoglobin يعمل كنقل بينجل + +53 +00:03:46,520 --> 00:03:54,800 +الأكسجين من الرئتين إلى الخلايا عبر الجسم مش كمان + +54 +00:03:54,800 --> 00:03:59,060 +وظائف البروتين البروتين يعمل ك catalysis إنزان + +55 +00:03:59,060 --> 00:04:03,380 +إنزين محفظ في بعضهم بيشتغل بعض البروتينات تعمل + +56 +00:04:03,380 --> 00:04:07,380 +كإنزيمات محفظة بتسرع التفاعل catalysis the + +57 +00:04:07,380 --> 00:04:11,930 +chemical reactionوظيفة اللي بعد هي storage تعمل + +58 +00:04:11,930 --> 00:04:16,490 +كبروتينات تخزينية للتخزين أشهر مثال على بروتينات + +59 +00:04:16,490 --> 00:04:19,750 +التخزين هو ال myoglobin ال myoglobin هو storage + +60 +00:04:19,750 --> 00:04:23,750 +بروتيين بيخزن ال oxygen in muscle أثناء ال + +61 +00:04:23,750 --> 00:04:27,330 +exercise بيخزن ال oxygen في العضلاتإذا الجسم مثلا + +62 +00:04:27,330 --> 00:04:31,990 +في أثناء التمرين الشاق نقص الـ Oxygen على العضلة، + +63 +00:04:31,990 --> 00:04:35,630 +مين بيزود بال Oxygen؟ الـ Myoglobin بيكون خزين من + +64 +00:04:35,630 --> 00:04:40,270 +ال Oxygen، بيوزح على العضلات و للجسم عند الحاجة. + +65 +00:04:40,990 --> 00:04:44,630 +Hormones، بتعمل لبروتينات كهرمون، some hormones + +66 +00:04:44,630 --> 00:04:48,090 +are البروتين، بعض الهرمونات هي عبارة عن البروتين، + +67 +00:04:48,090 --> 00:04:52,110 +و أشهر مثال على بروتين .. على هرمون يعمل .. يعتبر + +68 +00:04:52,110 --> 00:04:56,720 +البروتين هوالانسولين الانسولين هو example على + +69 +00:04:56,720 --> 00:05:02,080 +هرمون و protein إيش هو الهرمون؟ هرمون serve as + +70 +00:05:02,080 --> 00:05:05,800 +chemical messenger carrying signals from one part + +71 +00:05:05,800 --> 00:05:11,540 +of the body to another الهرمون هو عبارة عن إشارة + +72 +00:05:11,540 --> 00:05:17,280 +أو رسالة كيميائية لنقل الإشارة من مكان إلى آخر في + +73 +00:05:17,280 --> 00:05:17,900 +الجسم + +74 +00:05:21,150 --> 00:05:25,010 +هنا بيحكي إن كيف تتكون الرابطة البيبتيدية أو + +75 +00:05:25,010 --> 00:05:28,070 +البروتين كيف بتتكون polypeptide and the protein + +76 +00:05:28,070 --> 00:05:32,210 +are formed by amino acid held together by amide + +77 +00:05:32,210 --> 00:05:36,550 +bond بتتكون البروتينات من ارتباط أحماد أمينية مع + +78 +00:05:36,550 --> 00:05:40,710 +بعضها البعض ب amide bond هي نفسها ال peptide bond + +79 +00:05:40,710 --> 00:05:44,010 +إذن الرابطة اللي بينهم بتكون اسمها peptide bond أو + +80 +00:05:44,010 --> 00:05:47,580 +amide bondbetween وين بتيجي هذه الرابطة؟ between + +81 +00:05:47,580 --> 00:05:51,100 +the amino end of one amino acid molecule and + +82 +00:05:51,100 --> 00:05:54,800 +carboxyl end of another amino acid molecule الرابط + +83 +00:05:54,800 --> 00:05:58,500 +الـ amide bond او الـ peptide bond بتيجي بين ال + +84 +00:05:58,500 --> 00:06:02,000 +amino end ال amino group منه حمض أميني مع ال + +85 +00:06:02,000 --> 00:06:04,800 +carboxyl end اللي هي carboxyl group of another + +86 +00:06:04,800 --> 00:06:08,960 +amino acidبتيجي الرابطة باه ال amino group و ال + +87 +00:06:08,960 --> 00:06:11,940 +carboxyl group amino group من حمض أميني مع + +88 +00:06:11,940 --> 00:06:14,960 +carboxyl group من حمض أميني أخر بتيجي الرابطة باه + +89 +00:06:14,960 --> 00:06:20,200 +بتنزع جزء ما و تتكون الرابطة بنسميها it's called a + +90 +00:06:20,200 --> 00:06:23,300 +peptide bond this amide bond is called peptide + +91 +00:06:23,300 --> 00:06:26,700 +bond وحكينا إنه في حاجة بتنتج منها لما يتكون ال + +92 +00:06:26,700 --> 00:06:30,320 +protein بيكون في عندنا حاجة اسمها N-terminus و + +93 +00:06:30,320 --> 00:06:34,430 +حاجة اسمها C-terminusحكينا الـ N-terminus هو الحمض + +94 +00:06:34,430 --> 00:06:39,010 +الأميني اللي بيحتوي على amino group لم تشارك في + +95 +00:06:39,010 --> 00:06:42,890 +تكوين الرابطة البيبتدية not involved in a peptide + +96 +00:06:42,890 --> 00:06:46,350 +bond free amino group اللي بيكون على الطرف فيه + +97 +00:06:46,350 --> 00:06:49,330 +free amino group مش مشاركة في تكوين الرابطة + +98 +00:06:49,330 --> 00:06:53,950 +البيبتدية بتكون في النهاية بنسميها N-terminusالـ C + +99 +00:06:53,950 --> 00:06:58,150 +-terminus هي الحمض الأمين اللي بيحتوي على كربوكسيل + +100 +00:06:58,150 --> 00:07:01,950 +جروب not involved in a peptide bond يحتوي على + +101 +00:07:01,950 --> 00:07:06,930 +كربوكسيل جروب لم تشارك في تكوين الرابطة البيبتدية + +102 +00:07:06,930 --> 00:07:12,510 +free carboxyl group طب إيش لنا ال protein + +103 +00:07:12,510 --> 00:07:15,910 +structure؟ و أكيد أخدته بالنظرى في منه primary + +104 +00:07:15,910 --> 00:07:19,690 +structure secondary structure tertiary و + +105 +00:07:19,690 --> 00:07:24,620 +quaternaryلو حكينا على السريع الـ Primary Show هو + +106 +00:07:24,620 --> 00:07:27,560 +عبارة عن سلسة الأحمد الأمينية بتكون مرتبطة مع + +107 +00:07:27,560 --> 00:07:31,560 +بعضها بروابط ببتدية هذه السلسة اللي بتكون مرتبطة + +108 +00:07:31,560 --> 00:07:34,080 +مع بعضها بروابط ببتدية هذا بيكون ما بسميه الـ + +109 +00:07:34,080 --> 00:07:37,840 +Primary Structure الـ Secondary Structure بتيجي + +110 +00:07:37,840 --> 00:07:40,620 +اللي هي سلسة الأحمد الأمينية بترتبط مع بعضها البعض + +111 +00:07:40,620 --> 00:07:45,960 +بروابط ببتدية وفي بينها H bond روابط هيدروجينية في + +112 +00:07:45,960 --> 00:07:51,170 +منه جزاين Alpha Helical وفي Beta Chitالـ Texture + +113 +00:07:51,170 --> 00:07:55,210 +Structure بتكون عبارة عن شكل كروي، دو شكل كروي زي + +114 +00:07:55,210 --> 00:07:59,890 +ال myoglobin بتكون three dimensional shape ال + +115 +00:07:59,890 --> 00:08:03,570 +quaternary هي عبارة عن many segment مع بعض + +116 +00:08:03,570 --> 00:08:07,450 +association أكثر من domain مع بعض، يجي يرتبطوا مع + +117 +00:08:07,450 --> 00:08:10,810 +بعض، زي ال hemoglobin بتكون من أربعة، من اتنين + +118 +00:08:10,810 --> 00:08:12,670 +beta و اتنين alpha + +119 +00:08:15,870 --> 00:08:19,550 +اللي عندنا أشكال الـ secondary structure كيف شكل + +120 +00:08:19,550 --> 00:08:22,630 +الـ Alpha Helix بتكون و كيف شكل الـ Beta Sheet + +121 +00:08:22,630 --> 00:08:26,610 +بتكون زي الصورة اللي فوق على اليسار هذه بتكون .. + +122 +00:08:26,610 --> 00:08:29,710 +هذه عبارة عن الـ Beta Sheet اللي جنبها عبارة عن + +123 +00:08:29,710 --> 00:08:36,090 +الـ Alpha Helix طب بدنا نحكي هنا عن .. نحكي اللي + +124 +00:08:36,090 --> 00:08:41,450 +إنه غصائص الأحماض الأمينية اللي موجودة في البروتين + +125 +00:08:41,450 --> 00:08:46,120 +و الـpeptideكيف بتم تحددها؟ جدان البروتين كيف + +126 +00:08:46,120 --> 00:08:49,580 +بتدعي عرف خصائصه؟ باعرفها من الأحماض الأمينية + +127 +00:08:49,580 --> 00:08:52,620 +المكونة إليه كيف بدي أطلع على الحمض الأميني؟ على + +128 +00:08:52,620 --> 00:08:56,620 +إيش بدي أطلع؟ أطلع على الـR-group اللي بتميز كل + +129 +00:08:56,620 --> 00:09:01,120 +حمض أميني عن الآخر إذا كيف بدي أعرف خصائص البروتين + +130 +00:09:01,120 --> 00:09:04,760 +من الأحماض الأمينية المكونة إليه؟ شو اللي بيميز كل + +131 +00:09:04,760 --> 00:09:09,200 +حمض أميني؟ هي الـR-group فخصائص الحمض الأميني + +132 +00:09:09,200 --> 00:09:12,840 +الموجود في البروتين و الـpeptide تتحدد من خلال + +133 +00:09:13,700 --> 00:09:20,320 +الجروب كمان بيحكيلي شحنة التتراتبل جروب من هما + +134 +00:09:20,320 --> 00:09:24,340 +التتراتبل جروب هو ال amino group و الكربوكسيلي + +135 +00:09:24,340 --> 00:09:27,540 +group اللي موجودة في الحمض الأميني ال structure + +136 +00:09:27,540 --> 00:09:31,240 +بتاع الحمض الأميني هي كانت بيتكون من أعلى جروب و + +137 +00:09:31,240 --> 00:09:35,340 +هيدروجين و central carbon فيها كربوكسيلي group و + +138 +00:09:35,340 --> 00:09:39,200 +amino groupالـ Amino group والـ Carboxyl group + +139 +00:09:39,200 --> 00:09:43,100 +الشحنات اللي عليهم هكذا بتختلف حسب الوسط اللي أنا + +140 +00:09:43,100 --> 00:09:47,180 +بحطها فيه هل هي في وسط حمضي، في وسط قاعدي، في وسط + +141 +00:09:47,180 --> 00:09:53,320 +متعدد فأنا خصائص الحمض الأميني بدي أحددها من خلال + +142 +00:09:53,320 --> 00:09:58,080 +الـ R group وشحنة الـ Amino group and Carboxyl + +143 +00:09:58,080 --> 00:10:04,040 +groupعشان هيك بيحكيلي it's important to know which + +144 +00:10:04,040 --> 00:10:07,720 +group of peptides and proteins will be protonated + +145 +00:10:07,720 --> 00:10:12,860 +at certain بيئات فضروري ان اعرف انا موجودة في اي + +146 +00:10:12,860 --> 00:10:16,440 +وسط في اي بيئات في acidic ولا في alkaline ولا في + +147 +00:10:16,440 --> 00:10:20,180 +neutral طب مين صار عليها protonated؟ومين صار لها + +148 +00:10:20,180 --> 00:10:24,720 +deprotonated؟ مين فقدت ومين كسبت؟ الشحنة هنا صارت + +149 +00:10:24,720 --> 00:10:27,940 +جديش النت ت charge وهنا جديش النت ت charge لأن + +150 +00:10:27,940 --> 00:10:32,100 +حاجة الشحنة بتحدد خصائص الحمض الأميني وبالتالي + +151 +00:10:32,100 --> 00:10:36,750 +هيعرف خاصية خصائص البروتينprotein molecules carry + +152 +00:10:36,750 --> 00:10:40,670 +charge according to their amino acid sequence and + +153 +00:10:40,670 --> 00:10:44,070 +the aqueous solvent pH they are dissolved in + +154 +00:10:44,070 --> 00:10:48,310 +بحكيلي شحنة البروتين كيف بده أحددها من خلال + +155 +00:10:48,310 --> 00:10:50,930 +الأحماض الأمينية المكونة لها ال amino acid + +156 +00:10:50,930 --> 00:10:54,060 +sequenceبجمع الشحنات كلها اللي موجودة على كل حمض + +157 +00:10:54,060 --> 00:10:58,160 +أميني مثلا الأول positive واحد، التاني minus واحد، + +158 +00:10:58,160 --> 00:11:01,920 +البعد هي positive اتنين، بجمعهم مع بعض، بشوف ال + +159 +00:11:01,920 --> 00:11:06,080 +net charge للبروتين كامل جداش الشحنة، كمان عشان + +160 +00:11:06,080 --> 00:11:09,400 +الحاجة التانية اللي بتحدد هي ال pH اللي موجود + +161 +00:11:09,400 --> 00:11:14,300 +فيها، ما هي ال pH هتغير ال charge اللي موجودة على + +162 +00:11:14,300 --> 00:11:17,860 +ال amino group و ال carboxyl group، بجمع محكم هذه + +163 +00:11:17,860 --> 00:11:22,500 +الشحنة، و أشوف الشحنة الكلية للبروتينقداش هتسيق + +164 +00:11:22,500 --> 00:11:26,340 +بما + +165 +00:11:26,340 --> 00:11:29,240 +ان تجربتنا اللى اليوم هي عبارة عن ال precipitation + +166 +00:11:29,240 --> 00:11:32,500 +و في ال protein ال isoelectric point ان انا بدي + +167 +00:11:32,500 --> 00:11:36,380 +ارسب ال protein عن نقطة ال isoelectric point حتى + +168 +00:11:36,380 --> 00:11:39,180 +نعرف ليش انا برسب ال protein عن نقطة ال + +169 +00:11:39,180 --> 00:11:42,280 +isoelectric point، شما انا اخترت هذه النقطة، بدنا + +170 +00:11:42,280 --> 00:11:46,350 +نعرف حاجات عن ال protein solubilityبحكيلي there + +171 +00:11:46,350 --> 00:11:48,690 +are many factors that contribute to protein + +172 +00:11:48,690 --> 00:11:53,650 +solubility يعني إن عدة عوامل بتلعب دور في ذائبية + +173 +00:11:53,650 --> 00:11:56,450 +البروتين يعني أنا كده بده أحدد هل هات البروتين + +174 +00:11:56,450 --> 00:12:00,570 +soluble in water أو not soluble the most important + +175 +00:12:00,570 --> 00:12:04,990 +determinants is electrostatic charge أهم عامل بحد + +176 +00:12:04,990 --> 00:12:10,200 +ذائبية البروتين هي شحنة البروتينإذا كان البروتين + +177 +00:12:10,200 --> 00:12:13,360 +مثلا شحنته موجبة أو شحنته سلب، انت تشارجي اللي + +178 +00:12:13,360 --> 00:12:17,740 +عليه جداش Solubility of البروتين كمان بتعتمد على + +179 +00:12:17,740 --> 00:12:22,180 +distribution of hydrophilic and hydrophobic amino + +180 +00:12:22,180 --> 00:12:25,840 +acid on the protein surface، هي اللي بحدد شحنة + +181 +00:12:25,840 --> 00:12:29,280 +البروتين حكينا هي ال amino acid sequence، ترتيب + +182 +00:12:29,280 --> 00:12:34,240 +الأحمار الأمينية اللي عليهاهذه الشحنة كمان هتحدد + +183 +00:12:34,240 --> 00:12:37,660 +الـ solubility للبروتين من خلال توزيع + +184 +00:12:37,660 --> 00:12:41,280 +الـhydrophilic وhydrophobic أمينو أسد الموجودين + +185 +00:12:41,280 --> 00:12:44,600 +على البروتين البروتين هو عبارة عن sequence من + +186 +00:12:44,600 --> 00:12:48,260 +أمينو أسد هتطلع هاي الأحمض الأمينية شو شحنتها + +187 +00:12:48,260 --> 00:12:51,540 +هتطلع إيش الأحمض الأمينية المكونة له هل هي + +188 +00:12:51,540 --> 00:12:55,080 +hydrophilic ولا hydrophobic مين الأغلب عنده + +189 +00:12:55,080 --> 00:12:58,380 +hydrophilic ولا hydrophobic موجود الـhydrophobic + +190 +00:12:58,380 --> 00:13:03,040 +مثلا للداخل متخبيه والـhydrophilic للخارجولا كيف + +191 +00:13:03,040 --> 00:13:07,500 +توزيعتها بحكي لي ال proteins that have high + +192 +00:13:07,500 --> 00:13:12,680 +hydrophobic amino acid content on the surface have + +193 +00:13:12,680 --> 00:13:17,100 +low solubility in aqueous solvent فجدت hydrophobic + +194 +00:13:17,100 --> 00:13:21,990 +معناها كاره للماءHydrophobic كاره للماء فإذا + +195 +00:13:21,990 --> 00:13:26,810 +البروتين بيتكون من أحماض أمينية كارهة للماء وده + +196 +00:13:26,810 --> 00:13:30,930 +كرمية كبيرة من أحماض أمينية كارهة للماء موجودة على + +197 +00:13:30,930 --> 00:13:36,430 +السطح فهذا بيقلل الذائبية على مبدأ like dissolve + +198 +00:13:36,430 --> 00:13:39,890 +like المديبات مديب بعضها اللي لهم نفس الخصائص + +199 +00:13:39,890 --> 00:13:43,350 +بدوبوا ببعض إذا كان هذا الحمض الأميني كاره للماء + +200 +00:13:43,350 --> 00:13:46,750 +كيف بيدوب في الماء إذا هيكون له solubility + +201 +00:13:51,360 --> 00:13:54,940 +بحكي ليه هناك هي أن أمثلة على Hydrophilic Amino + +202 +00:13:54,940 --> 00:13:58,600 +Acid و Hydrophobic Amino Acid زي مين Hydrophilic و + +203 +00:13:58,600 --> 00:14:03,350 +مين Hydrophobic و هذا مش مطلوب أنها نفسهابعد هيك + +204 +00:14:03,350 --> 00:14:07,010 +بيحكيني إنه إذا كانت charged and polar surfaced، + +205 +00:14:07,010 --> 00:14:10,430 +إذا كان الحمق للبروتينة بتكون من أحماض أمينية + +206 +00:14:10,430 --> 00:14:14,770 +مشفونة و polar، قطبية، إذن القطبية هيتفاعل مع + +207 +00:14:14,770 --> 00:14:17,430 +جزيئات الماء، مع ال solvent، interact with the + +208 +00:14:17,430 --> 00:14:21,370 +solvent and increase solubility وهتزود الذائبية، + +209 +00:14:21,370 --> 00:14:25,330 +وهيكون ذائبإيش هي الـ net charge of البروتين؟ إيش + +210 +00:14:25,330 --> 00:14:28,850 +تخريف الـ net charge المحصلة النهائية للشحنات؟ هي + +211 +00:14:28,850 --> 00:14:33,110 +average of all charge هي محصلة كل الشحنات، بجمع كل + +212 +00:14:33,110 --> 00:14:37,310 +الشحنات مع بعضها، بشوف الشحنة النهائية at a + +213 +00:14:37,310 --> 00:14:41,650 +certain pH بروتين نت charge والـ P0، this is + +214 +00:14:41,650 --> 00:14:44,650 +called the isoelectric point حكينا إن الـ + +215 +00:14:44,650 --> 00:14:47,790 +isoelectric في نقطة اسمها الـ isoelectric point، + +216 +00:14:47,790 --> 00:14:52,390 +وهي قيمة pHاللي عندها بيكون ال mid charge بتساوي + +217 +00:14:52,390 --> 00:14:55,010 +zero الشحنة الكلية بتساوي صفر + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/qvn-U_MgMmU_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/qvn-U_MgMmU_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..587e0ca4a208af1e07f357e837e89e9734ccb6bb --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/qvn-U_MgMmU_postprocess.srt @@ -0,0 +1,884 @@ +1 +00:00:00,000 --> 00:00:03,860 +At the active site هذا كيف بيثبت الـ non + +2 +00:00:03,860 --> 00:00:07,100 +-competitive؟ الـ non-competitive بيجي بيرتبط في + +3 +00:00:07,100 --> 00:00:11,560 +موقع اسمه الـ steric site موجود في الإنزع تمام؟ + +4 +00:00:12,150 --> 00:00:16,930 +مجرد ما يرتبط الـ Non-competitive Act بيعمل تغيير + +5 +00:00:16,930 --> 00:00:21,110 +وتحوير لشكل الـ Active Site بيغير شكل الـ Active + +6 +00:00:21,110 --> 00:00:24,790 +Site فبيبطل الـ Active Site شكله ملائم للـ + +7 +00:00:24,790 --> 00:00:27,930 +Substrate بتيجي الـ Substrate ده ترتبط بتلاقي + +8 +00:00:27,930 --> 00:00:32,250 +الموقع مختلف الـ Active Site مش ملائم لها، غير + +9 +00:00:32,250 --> 00:00:36,850 +ملائم للارتباط فبتقدرش ترتبطفبيثبت ارتباط الـ + +10 +00:00:36,850 --> 00:00:41,550 +«substrate» مع الـ «enzyme» في موقع الـ «active + +11 +00:00:41,550 --> 00:00:46,410 +site» من غلال تغيير شكل الـ «active site» فبيغير + +12 +00:00:46,410 --> 00:00:49,150 +شكل الـ «active site» وبدرش يرتبط فيها الـ + +13 +00:00:49,150 --> 00:00:51,650 +«substrate» طب هل أنا لو زودت تركيز الـ + +14 +00:00:51,650 --> 00:00:55,050 +«substrate» بدي تنحل المشكلة؟ لأ، بتنحلش لأن + +15 +00:00:55,050 --> 00:01:00,190 +المشكلة أساسها ارتباطه في موقع آخر وتغيير شكل الـ + +16 +00:01:00,190 --> 00:01:01,690 +«active site» + +17 +00:01:05,860 --> 00:01:09,660 +الكلمة «KM» لم تتغير «KM» اللي بتعبر عن تركيز + +18 +00:01:09,660 --> 00:01:14,100 +السبسترات في حالة non-competitive inhibitor ما + +19 +00:01:14,100 --> 00:01:17,700 +بتتغير، ليش؟ هاي non-competitive inhibitor don't + +20 +00:01:17,700 --> 00:01:20,660 +interfere with the binding of substrate to enzyme + +21 +00:01:20,660 --> 00:01:26,980 +ما بتأثر على ارتباط السبسترات مع الانزانالأنزين + +22 +00:01:26,980 --> 00:01:30,620 +يظهر نفس الـKM في الـprisons أو عدم وجود + +23 +00:01:30,620 --> 00:01:34,580 +نانكومبيتيف انهيبتور بيحكي إن في حال وجود + +24 +00:01:34,580 --> 00:01:39,580 +نانكومبيتيف انهيبتور أو عدم وجوده، KM نفسها، KM مش + +25 +00:01:39,580 --> 00:01:42,380 +هتتغير، لأنه أنا مهما أزود مش زي الأولى + +26 +00:01:42,380 --> 00:01:45,400 +الـcompetitive inhibitor، مش هنحل المشكلة، حيث أنا + +27 +00:01:45,400 --> 00:01:49,260 +بنزود تركيز السبستريات، فبتغير KM، بتزيد، لكن في + +28 +00:01:49,260 --> 00:01:52,300 +هذه الحالة أنا مافيش داعي أزود أصلا تركيز + +29 +00:01:52,300 --> 00:01:55,920 +السبستريات لأن أنا مش هتأثر، مش هتحل المشكلةفـ KM + +30 +00:01:55,920 --> 00:02:02,140 +نفسها Vmax بتجلب هلجيت أنا لو فيش عندى inhibitor + +31 +00:02:02,140 --> 00:02:05,200 +هاصل لـ Vmax لكن لو في عندى non-competitive + +32 +00:02:05,200 --> 00:02:08,760 +inhibitor خلاص شوّه شكل الـ active site مش هتقدر + +33 +00:02:08,760 --> 00:02:12,960 +ترتبط الـ substrate فانا مش هاصل لـ Vmax فVmax في + +34 +00:02:12,960 --> 00:02:16,520 +حالة non-competitive inhibitor هتجلب increasing + +35 +00:02:16,520 --> 00:02:19,380 +the concentration of substrate doesn't over count + +36 +00:02:19,380 --> 00:02:23,640 +non-competitive inhibitorNon-competitive inhibitor + +37 +00:02:23,640 --> 00:02:26,480 +decreases the Vmax of the reaction الـ Non + +38 +00:02:26,480 --> 00:02:30,600 +-competitive inhibitor بيجلل الـ Vmax Non + +39 +00:02:30,600 --> 00:02:33,680 +-competitive inhibitor therefore simply reduces + +40 +00:02:33,680 --> 00:02:37,880 +the amount of active enzyme بيجلل كمية الإنزين + +41 +00:02:37,880 --> 00:02:41,560 +النشطة اللي هو موقع الـ Active enzyme فهيجلل الـ + +42 +00:02:41,560 --> 00:02:49,490 +Vmax ولكن مش هيؤثر على KMهنا مخطط بيوضح في حال + +43 +00:02:49,490 --> 00:02:53,150 +وجود non-inhibitor أو non-competitive inhibitor + +44 +00:02:53,150 --> 00:02:56,210 +إذا ما في حالة وجود أو عدم وجود inhibitor في حالة + +45 +00:02:56,210 --> 00:02:59,990 +وجود non-competitive inhibitor في حالة عدم وجود + +46 +00:02:59,990 --> 00:03:03,710 +inhibitor القاعدة المعروفة اللي حكينا عنها إنه كل + +47 +00:03:03,710 --> 00:03:07,330 +ما زاد تركيز الـsubstrate بتزيد سرعة التفاعل + +48 +00:03:07,330 --> 00:03:12,330 +الكيميائي ونشاط الإنزيموصولًا إلى نقطة التشبع + +49 +00:03:12,330 --> 00:03:16,250 +للـSaturation Point اللي هي عندها Vmax يثبت + +50 +00:03:16,250 --> 00:03:19,970 +المنحنة وصولًا إلى Vmax طيب، في حال وجود Non + +51 +00:03:19,970 --> 00:03:24,350 +-competitive inhibitor لكن هذا بيأثر على الـActive + +52 +00:03:24,350 --> 00:03:28,110 +site فما بتقدر ترتبط الـSubstrate في الـActive + +53 +00:03:28,110 --> 00:03:35,030 +siteفهيجيل الـ Vmax هل هتتأثر KM هتتأثر تركيز الـ + +54 +00:03:35,030 --> 00:03:39,630 +Substrate لأ نفسها وانما مين اللي هتقول الـ Vmax + +55 +00:03:39,630 --> 00:03:43,330 +اللي هي سرعة التفاعل اقصى سرعة الا انا مش هقدر + +56 +00:03:43,330 --> 00:03:46,130 +اصلا اللي هتجيل Vmax + +57 +00:03:47,790 --> 00:03:50,750 +في النهاية الملخص «competitive inhibitor» عندنا + +58 +00:03:50,750 --> 00:03:53,070 +أنواع الـ «inhibitor» «competitive» و «non + +59 +00:03:53,070 --> 00:03:55,610 +-competitive» في حالة الـ «competitive»، إيش + +60 +00:03:55,610 --> 00:04:00,010 +هيتغير؟ «KM» بتزيد، تركيز الـ «substrate» بزيد أما + +61 +00:04:00,010 --> 00:04:04,070 +«Vmax» ما بتتغير، أقصى سرعة التفاعل هي نفسها «non + +62 +00:04:04,070 --> 00:04:08,430 +-competitive inhibitor» «KM» ما بتتغير، no change، + +63 +00:04:08,430 --> 00:04:15,040 +بط «Vmax» بتجيلب، لكن أقصى سرعة التفاعل بيتجيلببعض + +64 +00:04:15,040 --> 00:04:18,500 +المصطلحات الأغلبية حكينا عنها أولاً الـ Active + +65 +00:04:18,500 --> 00:04:22,580 +site الـ Active site حكينا هو موقع في الإنزيم + +66 +00:04:22,580 --> 00:04:26,920 +بيرتبط فيها الـ substrate لحدوث التفاعل region of + +67 +00:04:26,920 --> 00:04:30,340 +enzyme molecule find the substrate and carry the + +68 +00:04:30,340 --> 00:04:33,920 +catalytic reaction موقع في الإنزيم بيرتبط فيها الـ + +69 +00:04:33,920 --> 00:04:37,540 +substrate لحدوث التفاعل فبالإنزيم، حكي أنا تعرفي + +70 +00:04:37,540 --> 00:04:41,540 +الإنزيم هو محفز بيولوجي غالباً بيكون globular + +71 +00:04:41,540 --> 00:04:45,760 +protein عبارة عن البروتينبينتج من أجسام الكائنات + +72 +00:04:45,760 --> 00:04:50,640 +الحية لتسريع التفاعل الكيميائي وبيطلع بعد التفاعل + +73 +00:04:50,640 --> 00:04:56,520 +كما هو، بدون حدوث أي تدمير أو تغيير على شكله طيب، + +74 +00:04:56,520 --> 00:05:00,100 +«KM»، «KM» برضه حكي هنا إنه هي عبارة عن تركيز + +75 +00:05:00,100 --> 00:05:03,920 +الـsubstrate عند نص Vmax عند الـhalf maximum + +76 +00:05:03,920 --> 00:05:07,540 +velocity substrate concentration at half maximum + +77 +00:05:07,540 --> 00:05:12,620 +velocity«Vmax» حكينا إنه هي أقصى سرعة للتفاعل + +78 +00:05:12,620 --> 00:05:17,240 +«Maximum initial velocity of enzyme reaction» أقصى + +79 +00:05:17,240 --> 00:05:21,680 +سرعة لمعدل حدود التفاعل الكيميائي ولعمل الإنزين + +80 +00:05:21,680 --> 00:05:26,720 +عندها بموصل إلى نقطة الـ «saturation point» إنه + +81 +00:05:26,720 --> 00:05:30,680 +بيصير التفاعل constant تابت بيصير خلاص بيثبت + +82 +00:05:30,680 --> 00:05:34,740 +التفاعل لأنه عندنا «saturating substrate level» + +83 +00:05:34,740 --> 00:05:39,530 +عنده نقطة تشبع من السبستراتالـ catalyst اللي هو + +84 +00:05:39,530 --> 00:05:45,570 +المحفز وأي مادة بتسرق حدوط التفاعل البطيء anything + +85 +00:05:45,570 --> 00:05:47,930 +that speeds up a chemical reaction that is + +86 +00:05:47,930 --> 00:05:52,890 +occurring slowly أي مادة بتسرق حدوط التفاعل اللي + +87 +00:05:52,890 --> 00:05:57,990 +كان يمشي ببطء بسميها catalyst محفز اليوم تطبيقنا + +88 +00:05:57,990 --> 00:06:01,030 +العمل هيكون على أنزيم اسمه alkaline phosphate + +89 +00:06:04,010 --> 00:06:07,170 +الـ alkaline phosphatase هذا بيعمل على تكسير فصفات + +90 +00:06:07,170 --> 00:06:10,030 +جروب بيشتغل على المادة اللي بتحتوي على مجموعة + +91 +00:06:10,030 --> 00:06:13,710 +فصفات بيكسر هذه الفصفات إذا member of + +92 +00:06:13,710 --> 00:06:17,390 +phosphomonoesterase group هو أحد أعضاء مجموعة + +93 +00:06:17,390 --> 00:06:22,180 +إنزيمات يطلق عليها phosphomonoesterase groupThey + +94 +00:06:22,180 --> 00:06:25,880 +are highly specific and act on only one substrate + +95 +00:06:25,880 --> 00:06:31,300 +ومتخصص هيشتغل بس على substrates معين حكينا كل + +96 +00:06:31,300 --> 00:06:34,620 +أنزين متخصص بsubstrate معين وهذا لقناع + +97 +00:06:34,620 --> 00:06:38,680 +الانفسفاتياز متخصص بsubstrate معينهذه الـ + +98 +00:06:38,680 --> 00:06:42,100 +Substrate اللي بتحتوي على فوسفات جروب «الكالاين + +99 +00:06:42,100 --> 00:06:46,180 +فوسفاتيز» لديه فوسفات كبير بشكل خاص بـ Ccf3 عنده + +100 +00:06:46,180 --> 00:06:49,960 +Range واسع من خصوصيته على الـ Substrate كيف يعني؟ + +101 +00:06:49,960 --> 00:06:53,560 +هو متخصص بـ Substrate واحد لكن هذا الـ Substrate + +102 +00:06:53,560 --> 00:06:56,960 +اللي هو متخصص فيه يحتوي على فوسفات جروب ففي أكتر + +103 +00:06:56,960 --> 00:07:00,560 +من مادة في الجسم في أكتر من مكان بتحتوي على فوسفات + +104 +00:07:00,560 --> 00:07:05,690 +جروب عشان هيك هو له Broad Range واسعIt is named + +105 +00:07:05,690 --> 00:07:08,390 +alkaline phosphatase ليش بيسموها alkaline + +106 +00:07:08,390 --> 00:07:14,070 +phosphatase؟ لأنه بيشتغل عن BH9، BH alkaline في + +107 +00:07:14,070 --> 00:07:18,490 +عنده مجموعة أخرى بتشتغل عن BH7 بيسموها acid + +108 +00:07:18,490 --> 00:07:24,060 +phosphatase، بتشتغل عن BH7بيتعمل دراسة للـ + +109 +00:07:24,060 --> 00:07:27,620 +«Alkaline Phosphatase in Vitro» ندرست أو نحدد الـ + +110 +00:07:27,620 --> 00:07:30,380 +«Alkaline Phosphatase» في المعنى «Alkaline + +111 +00:07:30,380 --> 00:07:33,680 +Phosphatase activity by following the rate of + +112 +00:07:33,680 --> 00:07:36,300 +formation of a product» كيف بتتبر «Alkaline + +113 +00:07:36,300 --> 00:07:39,740 +Phosphatase»؟ من خلال متابعة تكون الـ product، + +114 +00:07:39,740 --> 00:07:43,040 +النواتج، إني بدي أجيب اللينزين هاد أحطله الـ + +115 +00:07:43,040 --> 00:07:46,700 +substrate المتخصص فيه يرتبطوا مع بعض ويحولوا إلى + +116 +00:07:46,700 --> 00:07:50,960 +product أشوف هذا ال product الناتج من خلالها بدرست + +117 +00:07:50,960 --> 00:07:54,450 +اللي هو هذا اللينزينالـ Alkaline Phosphatase اللي + +118 +00:07:54,450 --> 00:07:57,730 +بيشتغل على حكاية هنا الـ substrate تحتوي على فسفات + +119 +00:07:57,730 --> 00:08:02,570 +grow على alkaline media على pH alkaline تكون بينجل + +120 +00:08:02,570 --> 00:08:05,910 +مجموعة الفسفات ي grow فأنا بدي أحطله اليوم + +121 +00:08:05,910 --> 00:08:10,770 +substrate هو أربع نيتروفينال فسفات تمام؟ و أحطله + +122 +00:08:10,770 --> 00:08:15,310 +alkaline pH وبيشتغل عليها ويحولني إياها الأربع + +123 +00:08:15,310 --> 00:08:19,720 +نيتروفينالهذه الأربع نيتروفينول بقراها على جهاز + +124 +00:08:19,720 --> 00:08:25,300 +Spectrophotometer على طول موجي 400 نانومتر بقراها + +125 +00:08:25,300 --> 00:08:29,040 +بجيس كمية الضوء اللي امتصتها العين لأن لونها بتكون + +126 +00:08:29,040 --> 00:08:33,660 +bright yellow ولكن باقي المكونات والنواياتش بتكون + +127 +00:08:33,660 --> 00:08:37,540 +لونها بتكون colorless فانا بدي أقرا بس للأربع + +128 +00:08:37,540 --> 00:08:42,160 +نيتروفينول فبشوف من خلال هذه القراعات بعرف نشاط + +129 +00:08:42,160 --> 00:08:46,610 +الانزينإذا أنا عندي إنزيم ألكالينفوسفاتيز بحطله + +130 +00:08:46,610 --> 00:08:50,470 +substrate وتتكون عندي product زي المعادل اللي + +131 +00:08:50,470 --> 00:08:53,790 +حكيناها أولاً بإنزايم زائد substrate بيعطيني + +132 +00:08:53,790 --> 00:08:57,050 +إنزايم substrate complex وبعدين بيبتدي عندي إنزايم + +133 +00:08:57,050 --> 00:09:00,210 +و product مين أنا عند الإنزايم والsubstrate؟ + +134 +00:09:00,210 --> 00:09:03,670 +الإنزايم هو ألكالينفوسفاتيز زائد substrate أربعة + +135 +00:09:03,670 --> 00:09:07,530 +نيتروفين والفوسفات إيش الناتج بدي يطلع عندي؟ بدي + +136 +00:09:07,530 --> 00:09:10,270 +يطلع عندي إنزيم و product الإنزيم هو + +137 +00:09:10,270 --> 00:09:14,010 +للكلينفوسفاتيز، هيطلع زي ما هوزائد مجموعة الـ + +138 +00:09:14,010 --> 00:09:18,430 +Phosphate Group بيكسّرها هذا الإنزيم، زاد 4 + +139 +00:09:18,430 --> 00:09:22,190 +نيتروفينول. الأربع نيتروفينول هذه اللي هي yellow + +140 +00:09:22,190 --> 00:09:25,630 +color، بكلها أصفر، بقرأ الـ absorption، read + +141 +00:09:25,630 --> 00:09:30,310 +absorption، لها 400 نانومتر، بقرألها الانتصاص على + +142 +00:09:30,310 --> 00:09:36,560 +400 نانومتر، طول موجي 400.كيف بدأ أجيز نسمة الـ + +143 +00:09:36,560 --> 00:09:39,360 +«measurement of alkaline phosphatase activity» + +144 +00:09:39,360 --> 00:09:42,080 +بناء على مادة الـ«substrate» اللي هي هذه + +145 +00:09:42,080 --> 00:09:45,260 +الـ«artificial» المصنعة هي الـ«نيتروفينالفوسفات» + +146 +00:09:45,260 --> 00:09:47,560 +هذا الـ«substrate» بيرتبط مع الـ«alkaline + +147 +00:09:47,560 --> 00:09:50,520 +phosphatase» وبيعطينا product حكينا الـ«product» + +148 +00:09:50,520 --> 00:09:55,430 +ينتج لون يلوبيحكيلي إن شدة اللون، intensity of + +149 +00:09:55,430 --> 00:09:58,930 +yellow color شدة اللون هذا الأصفر بتعبّرلي عن + +150 +00:09:58,930 --> 00:10:02,130 +degree to which enzyme has acted upon a substrate + +151 +00:10:02,130 --> 00:10:07,430 +عن درجة ارتباط الانزين مع ال substrate، درجة عمل + +152 +00:10:07,430 --> 00:10:12,590 +الانزين شدة اللون تعبّر على درجة عمل الانزين + +153 +00:10:14,750 --> 00:10:17,630 +في عندنا هنا تعريف الـ enzyme kinetic وهذا حكينا + +154 +00:10:17,630 --> 00:10:20,490 +عنه في الأول أنه ي study في rate at which enzyme + +155 +00:10:20,490 --> 00:10:24,690 +works دراسة معدل حدوث التفاعل طب أنا كيف بدي أدرس + +156 +00:10:24,690 --> 00:10:27,770 +هنا معدل حدوث التفاعل؟ اليوم الدراسة بتكون على + +157 +00:10:27,770 --> 00:10:31,630 +أنزيم الألقالي الفوسفاتينبدي أدرس معدل حدوث + +158 +00:10:31,630 --> 00:10:35,570 +الـAlkaline Phosphatase بناءً على أيش؟ اليوم بدي + +159 +00:10:35,570 --> 00:10:38,850 +أدرس بناءً على تغيير في تركيز الـsubstrate يعني + +160 +00:10:38,850 --> 00:10:43,830 +أنا في نهاية المعمل بعد شغلي بدي أشوف العلاقة ما + +161 +00:10:43,830 --> 00:10:47,860 +بين تركيز الـsubstrate وسرعة التفاعل الكيميائيأحنا + +162 +00:10:47,860 --> 00:10:52,040 +حكينا إن هذه العلاقة خطية وصولا إلى Vmax إلى نقطة + +163 +00:10:52,040 --> 00:10:55,320 +التشبوع اللي هي الـ saturation point بتبطل العلاقة + +164 +00:10:55,320 --> 00:10:58,460 +خطية وإنما بيسبق فأنا اليوم بدأ أدرس هذه العلاقة + +165 +00:10:58,460 --> 00:11:03,880 +كيف بدأ أدرسها؟محكيلة إن نجيب أدت يوبات ونحط فيها + +166 +00:11:03,880 --> 00:11:07,340 +تركيز مختلفة من الـ substrates يعني مثلا الأولى + +167 +00:11:07,340 --> 00:11:12,560 +بدي أحط فيها تركيز substrates خمسة التانى تركيز + +168 +00:11:12,560 --> 00:11:15,160 +الـ substrates يكون فيها عشرة واللي بعدها تركيز + +169 +00:11:15,160 --> 00:11:19,160 +الـ substrates مثلا خمستاشر بعدها عشرين بعدها خمسة + +170 +00:11:19,160 --> 00:11:23,140 +وعشرين بعدها بدي أحط تلاتين خمسة وتلاتين وها كده + +171 +00:11:23,140 --> 00:11:26,320 +كل تيوب ده تكون تركيز الـ substrates فيها أعلى من + +172 +00:11:26,320 --> 00:11:29,770 +الـ tube اللي جابلهصار عندى تيوبات فيها Substrate + +173 +00:11:29,770 --> 00:11:34,250 +بتركيز معين بدي هجيبى الـ Enzyme عشان يرتبط مع الـ + +174 +00:11:34,250 --> 00:11:37,330 +Substrate ويكوّن لـ Product هلجيت بحط على الـ Tube + +175 +00:11:37,330 --> 00:11:39,950 +الأول كلهم نفس الكمية من الـ Enzyme بدي أحط عليها + +176 +00:11:39,950 --> 00:11:43,230 +Enzyme ييجى الـ Enzyme بيرتبط مع الـ Substrate في + +177 +00:11:43,230 --> 00:11:46,510 +الـ Tube الأول وبيعطيني Product بدي أقرأه في جهاز + +178 +00:11:46,510 --> 00:11:49,570 +الـ Spectrophotometer أقرأله الـ Absorbent بعدين + +179 +00:11:49,570 --> 00:11:52,690 +باخد الـ Tube التانى و أقرأ الـ Absorbentأخد الـ + +180 +00:11:52,690 --> 00:11:54,930 +tube التالتة أحط عليها أنزين و أقرأ الـ absorption + +181 +00:11:54,930 --> 00:11:58,750 +و الـ tube الرابع و هكذا لكل tube بيصير كل tube + +182 +00:11:58,750 --> 00:12:02,230 +فيها أنزين و substrate حطيت بالأول بعدين أنزين و + +183 +00:12:02,230 --> 00:12:05,510 +بعدين ده اقرأ بيتكون عندي بسيبها شوية حتى يتفاعل + +184 +00:12:05,510 --> 00:12:08,650 +الانزين مع ال substrate و يعطيني product اتكون ال + +185 +00:12:08,650 --> 00:12:11,270 +product باخدها بقراها في جهاز الـ + +186 +00:12:11,270 --> 00:12:15,510 +spectrophotometerالجهاز الـ Spectrophotometer + +187 +00:12:15,510 --> 00:12:20,250 +هيعطيني Absorbance قراية الانتصار وانا عندي معروف + +188 +00:12:20,250 --> 00:12:23,670 +عرفت تركيز الـ Substrate لكل تيوب مختلف عن التانية + +189 +00:12:23,670 --> 00:12:26,730 +حكينا على فرض الأولى خمسة، التانية عشرة، التلبعيدة + +190 +00:12:26,730 --> 00:12:29,930 +خمستاشر، عشرين، وخمسة وعشرين تركيز الـ Substrate + +191 +00:12:29,930 --> 00:12:35,110 +هلجت الـ Absorbance لكل تيوب هيختلف عن التانيةوهذا + +192 +00:12:35,110 --> 00:12:38,350 +الـ Absorbance حكينا بيختلف حسب شدة اللون، حسب عمل + +193 +00:12:38,350 --> 00:12:42,450 +الانزين فجيتي؟ مثلا الأولى قرأت الـ Absorbance + +194 +00:12:42,450 --> 00:12:45,590 +إليها point واحد، التانية point اتنين، اللي بعدها + +195 +00:12:45,590 --> 00:12:49,470 +point تلاتة، اللي بعدها point أربع كل مزود تركيز + +196 +00:12:49,470 --> 00:12:53,770 +الـ substrate بزيد ارتباط الانزين مع الـ substrate + +197 +00:12:53,770 --> 00:12:58,270 +فهيزيد العمل، هيزيد التفاعل، هتزيد الـ Absorbance، + +198 +00:12:58,270 --> 00:13:02,190 +تمام؟وصولا إلى وين هذا؟ هي هي تظل يزيد لما لا + +199 +00:13:02,190 --> 00:13:06,670 +نهاية؟ لأ، حكينا أول المعمل إنه بيظل يزيد لوصوله + +200 +00:13:06,670 --> 00:13:10,070 +إلى نقطة الـ Saturation Point يعني أنا في النهاية + +201 +00:13:10,070 --> 00:13:13,750 +بعد ما أشتغل شغلي وبعد ما أحط التيوبات، أحط فيها + +202 +00:13:13,750 --> 00:13:17,290 +تركيز مختلف من الـ Substrate أضيف عليها Enzyme، + +203 +00:13:17,290 --> 00:13:20,410 +كمية Enzyme، يتفاعلوا مع بعض ويعطيني Product + +204 +00:13:20,410 --> 00:13:24,130 +أقراها على جهاز الـ Spectrum، تطلع عندي Absorbance + +205 +00:13:24,130 --> 00:13:26,830 +صار عندي معروف Concentration للـ Substrate و + +206 +00:13:26,830 --> 00:13:31,770 +Absorbanceبدي أرسم مخطط، Standard K هل أنت كيف + +207 +00:13:31,770 --> 00:13:35,210 +متوقع أنه يكون شكل المدخول مخطط؟ بناء على العلاقة + +208 +00:13:35,210 --> 00:13:37,890 +اللي حكينا عنها اللي هي العلاقة بين الـSubstrate + +209 +00:13:37,890 --> 00:13:43,310 +Concentration وسرعة التفاعل أو معدل حدوث التفاعل + +210 +00:13:43,310 --> 00:13:47,390 +العلاقة الحكينا عنها الطرضية وصولا إلى Vmax، إلى + +211 +00:13:47,390 --> 00:13:51,410 +الـMaximum Velocity فبناء عليها، هشوف النتاج بتظل + +212 +00:13:51,410 --> 00:13:56,130 +هتزيد معي وفجأة بتثبت النتاج، هوصل إلى نقطة + +213 +00:13:56,130 --> 00:14:01,090 +Saturation Pointالى ثباتالنتاج احنا في النهاية + +214 +00:14:01,090 --> 00:14:06,350 +بنرسم هذا المخطط بدي أرسم على الخط الصيني اللي هي + +215 +00:14:06,350 --> 00:14:09,890 +نقطة الخط الصيني بدي أرسم عليها الـ Concentration + +216 +00:14:09,890 --> 00:14:13,030 +للـ Substrate الخط الصادى بدي أرسم الـ Absorbance + +217 +00:14:13,030 --> 00:14:15,950 +كل نقطة جديش إليها Concentration وجديش إليها + +218 +00:14:15,950 --> 00:14:20,170 +Substrate وأرسمها وأرسم اللي يطلع معايا المنحنة + +219 +00:14:20,170 --> 00:14:25,230 +هيطلع معايا علاقة ترضية وفجأة بيثبت المنحنة متى + +220 +00:14:25,230 --> 00:14:31,060 +هيثبت عند وصول إلى Saturation Pointطريقة العمل + +221 +00:14:31,060 --> 00:14:35,340 +بالتفصيل هنحكي عنها لما نشتغلها في المعمل + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/tYZzyB0o5Ps_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/tYZzyB0o5Ps_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..3a2bcfe8b44a03c6ac54094fc579aa5b71c52383 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/tYZzyB0o5Ps_postprocess.srt @@ -0,0 +1,2588 @@ +1 +00:00:04,790 --> 00:00:08,130 +اليوم بدنا نحكي بموضوع الـ quantitative test for + +2 +00:00:08,130 --> 00:00:14,030 +protein هو فحوصات للكشف عن البروتين ولكن هذه + +3 +00:00:14,030 --> 00:00:19,030 +الفحوصات نوعها quantitative quantitative معناها كم + +4 +00:00:19,030 --> 00:00:23,730 +يعني الفحوصات كميةيعني بدي يطلع معانا في الآخر + +5 +00:00:23,730 --> 00:00:27,530 +تركيز للبروتين مش انه ظهور لون positive أو + +6 +00:00:27,530 --> 00:00:32,010 +negative زي ال qualitative انما quantitative يعني + +7 +00:00:32,010 --> 00:00:36,010 +بدي يظهر عندي تركيز للبروتين بدي يطلع عندي رقم + +8 +00:00:36,010 --> 00:00:43,650 +للبروتين جداش نسبة البروتين بدنا نحكي عن إيش اسمه + +9 +00:00:43,650 --> 00:00:48,630 +colorimetric assay colorimetric assay معناها تحليل + +10 +00:00:48,630 --> 00:00:54,260 +اللون فحوصات تحليل اللونلا كيف هذه الفحوصات هي + +11 +00:00:54,260 --> 00:00:59,340 +مجموعة من الفحوصات من خلالها بعرف تركيز أي مادة + +12 +00:00:59,340 --> 00:01:04,820 +بناء على التغير في اللون مجموعة من الفحوصات من + +13 +00:01:04,820 --> 00:01:10,520 +خلالها بعرف تركيز أي مادة بناء على التغير في اللون + +14 +00:01:10,520 --> 00:01:14,180 +ال law for indirect determination of specific + +15 +00:01:14,180 --> 00:01:20,000 +concentration تسمح بمعرفة تركيز المواد زي إيش هي + +16 +00:01:20,000 --> 00:01:24,500 +المواد الممكن تعرف تركيزهابروتين كربوهيدرات أو + +17 +00:01:24,500 --> 00:01:28,460 +انزين بناء على ياش color exchange بناء على التغير + +18 +00:01:28,460 --> 00:01:32,420 +باللون this reaction can be performed directly + +19 +00:01:32,420 --> 00:01:35,900 +inside the spectrophotometer طب وين هي لجيت أنا + +20 +00:01:35,900 --> 00:01:39,360 +بحط المواد و بتغير لونها؟ طب مين بدي يجيس كمية + +21 +00:01:39,360 --> 00:01:43,080 +التغير في هذا اللون و يطلعلي التركيز؟ بناء على + +22 +00:01:43,080 --> 00:01:48,420 +جهاز اسمه جهاز spectrophotometer جهاز + +23 +00:01:48,420 --> 00:01:56,330 +spectrophotometerوهو جهاز قياس الطيف الضوء جهاز + +24 +00:01:56,330 --> 00:02:03,710 +Spectrophotometer هو جهاز لقياس كمية الضوء التي + +25 +00:02:03,710 --> 00:02:10,290 +تنتصها العينة بناء على قانون Beer-Lambert Law هو + +26 +00:02:10,290 --> 00:02:16,070 +جهاز لقياس كمية الضوء التي تنتصها العينة بناء على + +27 +00:02:16,070 --> 00:02:21,520 +قانون Beer-Lambert Lawوقانون هذا إيش بيحكي؟ بيحكي + +28 +00:02:21,520 --> 00:02:26,440 +الـ intensity of color and absorption is directly + +29 +00:02:26,440 --> 00:02:30,720 +proportional to the concentration إنه كتافة لون + +30 +00:02:30,720 --> 00:02:34,900 +المادة اللون اللي أنا بحطه بحب بعد ما أخلط المادة + +31 +00:02:34,900 --> 00:02:38,800 +المراد قياسة على ال reaction اللون اللي بيظهر عندي + +32 +00:02:38,800 --> 00:02:43,700 +كتافة اللون هاي بتتناسب تناسب ترضي مع تركيز المادة + +33 +00:02:43,700 --> 00:02:48,110 +يعني كل ما زادت شدية اللونهيكون تركيز المادة + +34 +00:02:48,110 --> 00:02:56,790 +الموجود أعلى كل ما قلت شدة اللون هيقل + +35 +00:02:56,790 --> 00:03:02,290 +تركيز المادة علاقة ترضية بين كتافة لون المادة و + +36 +00:03:02,290 --> 00:03:04,790 +تركيز هذه المادة + +37 +00:03:07,450 --> 00:03:11,870 +إيش هي الطرق لتحديد تركيز البروتين؟ method for + +38 +00:03:11,870 --> 00:03:16,010 +protein determination طرق تحديد تركيز البروتين كيف + +39 +00:03:16,010 --> 00:03:19,750 +أنا بدي عندي عينة و بدي أعرف تركيز البروتين فيها؟ + +40 +00:03:19,750 --> 00:03:22,890 +في أن عدة طرق في أن أحد الطرق هي الـ + +41 +00:03:22,890 --> 00:03:27,630 +spectrophotometry based on UV on ultraviolet light + +42 +00:03:27,630 --> 00:03:31,110 +اللي هو طريقة الـ spectrophotometry جهاز الـ + +43 +00:03:31,110 --> 00:03:35,830 +spectrophotometerبناء على مشاعر فوضوى نفسجية + +44 +00:03:35,830 --> 00:03:43,090 +Ultraviolet-Law هي طريقة تقليدية وقديمة البروتين + +45 +00:03:43,090 --> 00:03:48,190 +اكسيرت Ultraviolet-Light في 280 نانومتربتم قياسة + +46 +00:03:48,190 --> 00:03:54,530 +الضوء الممتاز عند ضوء طول موجي 280 نانو متر لكن + +47 +00:03:54,530 --> 00:03:58,010 +اكتشفوا ان الـ ultraviolet light هذي بتأثر على صحة + +48 +00:03:58,010 --> 00:04:03,230 +الإنسان وانها شعة ضارة فلجأوا إلى وجود طريقة أخرى + +49 +00:04:03,230 --> 00:04:06,710 +اللي هي الطريقة التانية الـ dye binding assay أو + +50 +00:04:06,710 --> 00:04:12,570 +اسمها barford assay dye binding assay أو barford + +51 +00:04:12,570 --> 00:04:17,820 +assayتعتمد على وجود صبغة ترتبط مع البروتين زي ما + +52 +00:04:17,820 --> 00:04:21,420 +وجود البروتين في العينة تيجي هذه الصبغة ترتبط مع + +53 +00:04:21,420 --> 00:04:26,520 +البروتين و بتعطيني لون و بجيس هذا اللون دي بند on + +54 +00:04:26,520 --> 00:04:30,500 +dye which bind to protein and give color هذه طريقة + +55 +00:04:30,500 --> 00:04:34,880 +اسمها dye binding assay أو parford assay و بعدين + +56 +00:04:34,880 --> 00:04:39,840 +اكتوروها لطريقة اخرى هي ال cover based assayالـ + +57 +00:04:39,840 --> 00:04:43,800 +cover-based assay هي فحوصات تعتمد على وجود الـ + +58 +00:04:43,800 --> 00:04:48,940 +cover بيجيسه كمية البروتين بناء على وجود الـ cover + +59 +00:04:48,940 --> 00:04:52,920 +وهي تلت طرق تعتمد على وجود الـ cover اللي هي أول + +60 +00:04:52,920 --> 00:04:58,280 +طريقة الـ Lawry-fullin method بيكنك كونك أسد أساي + +61 +00:04:58,280 --> 00:05:03,100 +Lawry-fullin method بيكنك كونك أسد أساي فيه هنا + +62 +00:05:03,100 --> 00:05:08,960 +الـ biuret methodوهدول الطرق اللي بتعتمد على وجود + +63 +00:05:08,960 --> 00:05:14,160 +الـ cover هي مستخدمة هي الـ routine use ال bio-red + +64 +00:05:14,160 --> 00:05:17,720 +هي الأكتر واحدة مستخدمة وهي اللي بيستخدموها هي + +65 +00:05:17,720 --> 00:05:22,360 +simple بسيطة وسهلة جمال وسريعة بتعتمد على أنه + +66 +00:05:22,360 --> 00:05:26,760 +يتكون لون هذا اللون بيعتمد على قانون Beer's law + +67 +00:05:26,760 --> 00:05:31,860 +أنه تتناسب تناسل ترضي شدت اللون مع تركيز المادة كل + +68 +00:05:31,860 --> 00:05:36,960 +ما زاد شدت اللون بزيد تركيز المادةكل هذه الطرق + +69 +00:05:36,960 --> 00:05:39,820 +اللي هي الـ copper based assay بتحتمد all this + +70 +00:05:39,820 --> 00:05:43,320 +method depends on the presence of cupric ion يعني + +71 +00:05:43,320 --> 00:05:46,800 +سواء الـ Lawry-fullon method الـ bicniconic acid + +72 +00:05:46,800 --> 00:05:51,380 +والبيروت method هدول التلات الطرق بتحتمد على وجود + +73 +00:05:51,380 --> 00:05:56,280 +ال cupric ion أن هو ريج إيري أيجاند من مكوناته ال + +74 +00:05:56,280 --> 00:06:01,130 +cupric ionحكينا قبل هيك إنه الـ Capric الـ Capar + +75 +00:06:01,130 --> 00:06:07,410 +بيعمل Cachelating Agent عامل متمخلب بيقدر يعمل عدة + +76 +00:06:07,410 --> 00:06:11,950 +روابط فبيجي على الروابط الببتيدية الموجودة في + +77 +00:06:11,950 --> 00:06:17,590 +البروتين وبيربط فيها من جميع الجهات تمام؟ فهذا الـ + +78 +00:06:17,590 --> 00:06:21,990 +Capric Ion بيكون موجود في الـ Reagent بيجي بيعمل + +79 +00:06:21,990 --> 00:06:25,050 +Cachelate Agent بيرتبط مع الـ peptide bond + +80 +00:06:25,050 --> 00:06:29,980 +وبيعطيني لهبحكي ليه إنه الـ Capric Ion اللي بيكون + +81 +00:06:29,980 --> 00:06:33,140 +موجود في الـ Reaction بيكون على شكل Capric Ion + +82 +00:06:33,140 --> 00:06:39,460 +اللي هي Cu Plus 2 بمجرد ما يرتبط في البروتين إذا + +83 +00:06:39,460 --> 00:06:43,440 +موجود البروتين في العينة أجل Capric Ion هذا ارتبط + +84 +00:06:43,440 --> 00:06:46,840 +مع البروتين وربط الروابط اللي بيبتديها مع بعضها + +85 +00:06:46,840 --> 00:06:52,320 +البعض بيصير له reduction إلى Capric Ionالـ Capric + +86 +00:06:52,320 --> 00:06:55,420 +Ion اللي موجود في الـ reagent بيكون موجود على شكل + +87 +00:06:55,420 --> 00:07:00,020 +Capric Ion Cu Plus II مجرد ما يرتبط مع البروتين + +88 +00:07:00,020 --> 00:07:03,960 +بيصير له reduction اختزال إلى Capric Ion Cu Plus + +89 +00:07:03,960 --> 00:07:09,760 +ففي عندنا تلت طرق لتحديد تركيز البروتين أول طريقة + +90 +00:07:09,760 --> 00:07:13,580 +الـ spectrophotometry وتاني طريقة اللي هي الـ dye + +91 +00:07:13,580 --> 00:07:17,960 +binding assay أو Barford Assay والتالتة الـ copper + +92 +00:07:17,960 --> 00:07:19,540 +based assay + +93 +00:07:23,090 --> 00:07:26,190 +هيش الـ aim and significance اللي هي الهدف + +94 +00:07:26,190 --> 00:07:31,930 +والأهمية لما عملنا اليوم أول شي الأهداف الـ aim to + +95 +00:07:31,930 --> 00:07:36,550 +perform bioretest for البروتين لقدرة على إجراء فحص + +96 +00:07:36,550 --> 00:07:40,790 +ال bio to estimate the amount of total proteins in + +97 +00:07:40,790 --> 00:07:45,470 +sample قدرة على تقدير كمية البروتين الموجود في + +98 +00:07:45,470 --> 00:07:50,990 +العينة وآخر شي to make standard كافي لقدرة على رسم + +99 +00:07:50,990 --> 00:07:55,360 +المنحنة المعياريالـ Standard K اللي هنحكي عنه + +100 +00:07:55,360 --> 00:07:59,860 +لقدام طيب الـ significance اللي همية أنا ليش بدي + +101 +00:07:59,860 --> 00:08:03,800 +أقدر تركيز البروتين أهمية هذا المعمل أني أعرف + +102 +00:08:03,800 --> 00:08:08,080 +quantization of البروتين لأن هذا is important and + +103 +00:08:08,080 --> 00:08:10,960 +has many applications in clinical laboratory + +104 +00:08:10,960 --> 00:08:15,640 +practice لتقدير الأهمية من معملنا أني أقدر تركيز + +105 +00:08:15,640 --> 00:08:19,920 +البروتينلأن كمية هذا البروتين أني أعرفها إلها + +106 +00:08:19,920 --> 00:08:25,060 +أهميات وإلها ضرورة تساعدني في تقييم حالة المريض، + +107 +00:08:25,060 --> 00:08:28,020 +هل في نقص في البروتين معين، يعني الخلل من عند هذا + +108 +00:08:28,020 --> 00:08:31,780 +البروتين في شركات معينة مثلا، لما في عندها مواد + +109 +00:08:31,780 --> 00:08:35,740 +تعرف كم تركيز البروتين فيها أو نسبة البروتين في + +110 +00:08:35,740 --> 00:08:39,260 +الجسم، بدي أعرف كم نسبة البروتين عند هذا الشخص + +111 +00:08:39,260 --> 00:08:44,760 +فإني أقدر كمية البروتين و أعرف كمية البروتين، هذا + +112 +00:08:44,760 --> 00:08:51,990 +إيش مهمفهي الأهمية من معملنا هنا بنحكي عن الـ + +113 +00:08:51,990 --> 00:08:56,630 +Bioret reagent إذا فاكرين في معمل qualitative test + +114 +00:08:56,630 --> 00:09:00,570 +of amino acid كان من ضمن الفحوصات فحص الـ Bioret + +115 +00:09:00,570 --> 00:09:05,370 +test الـ Bioret test كنا بنحط المادة على Bioret + +116 +00:09:05,370 --> 00:09:10,500 +reagent إذا اتغير اللون لأ الviolet إذا هذاإن هو + +117 +00:09:10,500 --> 00:09:13,480 +positive إنه البروتين موجود إنه فيه peptide bond + +118 +00:09:13,480 --> 00:09:16,860 +كنا بس نشوف هل اتغير اللون ولا لأ إذا اتغير + +119 +00:09:16,860 --> 00:09:20,160 +positive إذا ما اتغيرش negative هنا نفس الأشياء + +120 +00:09:20,160 --> 00:09:24,260 +إننا نشتغل على فحص بيور ال test ولكن بعد تغير + +121 +00:09:24,260 --> 00:09:27,600 +اللون بدلاش احنا عارفين إنه فيه بروتين بس هذا + +122 +00:09:27,600 --> 00:09:30,800 +اللون بدنا ناخده نجيسه في جهاز ال + +123 +00:09:30,800 --> 00:09:35,570 +spectrophotometerانجيزه على طول موجي معين عشان + +124 +00:09:35,570 --> 00:09:40,270 +يطلعلي رقم يطلعلي اللي هو كمية الضوء اللي انتصها + +125 +00:09:40,270 --> 00:09:45,190 +العينة بيطلعلي رقم بيطلعلي absorption انتصاص جديش + +126 +00:09:45,190 --> 00:09:49,310 +كمية الانتصاص عشان اعرف تركيز العينة انا في الآخر + +127 +00:09:49,310 --> 00:09:54,790 +بدي اطلع بتركيز للعينة مش بس تغير في لون positive + +128 +00:09:54,790 --> 00:09:58,100 +ولا negativeلأن حكينا بالأول إن اليوم فحصنا + +129 +00:09:58,100 --> 00:10:02,180 +quantitative test of a protein طب مين من الفحوصات + +130 +00:10:02,180 --> 00:10:05,100 +اللي أخدناها في أول معمل تكشف عن وجود ال protein + +131 +00:10:05,100 --> 00:10:09,560 +هو فحص ال bio rate test أخدناها في أول معمل إنه + +132 +00:10:09,560 --> 00:10:12,460 +بيكشف على وجود الرابط ال BPD الموجودة في ال + +133 +00:10:12,460 --> 00:10:16,120 +protein اليوم إننا نشتغل هذا ال bio rate ولكن بعد + +134 +00:10:16,120 --> 00:10:21,300 +ما نشتغله ناخده ونجيس كمية اللون أو تركيز المادة + +135 +00:10:21,300 --> 00:10:25,340 +بناء على التغير في اللون في جهاز spectrophotometer + +136 +00:10:26,480 --> 00:10:29,900 +إذا فاكرين حكينا إن الـ Bioretary agent بيتكون من + +137 +00:10:29,900 --> 00:10:34,720 +أدة مكونات حكينا إن هو عبارة عن قبر صلفات في وجود + +138 +00:10:34,720 --> 00:10:41,500 +alkaline media اللي هي NaOH أو KOHوفي مكون تالت ما + +139 +00:10:41,500 --> 00:10:45,120 +حكينا عنه اللي هو بوتاسيوم صوديوم ترتريت لذا الـ + +140 +00:10:45,120 --> 00:10:48,560 +bioreactient بيتكون من تلت مكونات اللي هم + +141 +00:10:48,560 --> 00:10:52,220 +الكبرسالفيت بوتاسيوم هيدروكسايد أو صوديوم + +142 +00:10:52,220 --> 00:10:56,880 +هيدروكسايد و بوتاسيوم صوديوم ترتريت بيجي الأول + +143 +00:10:56,880 --> 00:11:02,000 +مكون اللي هو الكبرسالفيت الكبرسالفيت هذا it's this + +144 +00:11:02,000 --> 00:11:06,300 +provides a capric ion which form chelate complex + +145 +00:11:06,930 --> 00:11:09,530 +والـ Capric Ion gives the reagent its + +146 +00:11:09,530 --> 00:11:13,730 +characteristic blue color إذا الكبرسالفيات وظيفته + +147 +00:11:13,730 --> 00:11:16,630 +ليش موجود في ال reagent عشان يعطيهم ال Capric Ion + +148 +00:11:16,630 --> 00:11:21,810 +بيزوّتني بال Capric Ion اللي حكينا إنه هذا أهم + +149 +00:11:21,810 --> 00:11:26,650 +عامل لازم يكون موجود عشان يشتغل ككلّات agent اللي + +150 +00:11:26,650 --> 00:11:30,730 +هو عامل متمخلب يربط الروابط اللي بيبتديها مع بعضها + +151 +00:11:30,730 --> 00:11:36,770 +لبعض تكوين كلّات complexإذا فاكرين لما شوفتوا لون + +152 +00:11:36,770 --> 00:11:40,650 +الـ bioretary agent لونه أزرق مين أعطاه هذا اللون + +153 +00:11:40,650 --> 00:11:44,010 +هو الـ capric ion هو المسؤول عن اللون الأزرق + +154 +00:11:44,010 --> 00:11:49,270 +الموجود في الـ reaction المكون التاني بوتاسيوم + +155 +00:11:49,270 --> 00:11:52,970 +هيدروكسيد أو صوديوم هيدروكسيد هذا ما بيساهم + +156 +00:11:52,970 --> 00:11:57,150 +بالتفاعل doesn't participate in the reaction but + +157 +00:11:57,150 --> 00:12:01,530 +provides the alkaline medium وإنما بيرفع البيئة مش + +158 +00:12:01,530 --> 00:12:06,560 +بس عشان يعطيني alkalineبيئة في الإعطاء وسط قاعدة + +159 +00:12:06,560 --> 00:12:10,780 +Potassium Sodium ترتريت المكون التالت اللي قد + +160 +00:12:10,780 --> 00:12:14,920 +تتواظهان أول وظيفة Stabilize the chelate complex + +161 +00:12:14,920 --> 00:12:19,140 +بيحافظ على ثباتية ال complex بعد ما يتكون ال + +162 +00:12:19,140 --> 00:12:22,640 +chelate complex ييجي الكبر يرتبط مع الرواد + +163 +00:12:22,640 --> 00:12:26,420 +البروتينية الموجودة في البروتين ويكون complex اسم + +164 +00:12:26,420 --> 00:12:30,560 +ال chelate اللي هو هذا بيحول اللور من أزرق إلى + +165 +00:12:30,560 --> 00:12:34,800 +violetإذا positive اتحول كان لـviolet من blue to + +166 +00:12:34,800 --> 00:12:38,900 +violet فالميلي اللي خلّاه يتحول الهول كابر أجر طبط + +167 +00:12:38,900 --> 00:12:43,360 +مع الروابط البوكتيرية وكوان الكليات كامة الـ + +168 +00:12:43,360 --> 00:12:46,680 +Potassium Sodium Tertarate بيحافظ على ثباتية هذا + +169 +00:12:46,680 --> 00:12:49,300 +ال complex إنه بعد ما يتكون هذا ال complex + +170 +00:12:49,300 --> 00:12:54,020 +مايتفككش، مايتكسرش تاني، يظل متكون، يظل ثابت عشان + +171 +00:12:54,020 --> 00:12:58,140 +أظن اللون موجود أحافظ على اللون و أروح أجهز تركيز + +172 +00:12:58,810 --> 00:13:02,050 +تاني وظيفة prevent precipitation of copper + +173 +00:13:02,050 --> 00:13:07,950 +hydroxide بيمنع ترصب الكبر لأنه لو ترصبها دو نزل + +174 +00:13:07,950 --> 00:13:11,810 +في القائز مش هيقدر يجي يرتبط مع الروابط الببتدية + +175 +00:13:11,810 --> 00:13:16,230 +ولا يقدر يعمل الكلات complex فهو بيحافظ على أنه + +176 +00:13:16,230 --> 00:13:20,890 +يمنع ترصبالـ cover بوتاسيوم بـ prevent auto + +177 +00:13:20,890 --> 00:13:25,790 +reduction of cover البوتاسيوم الموجود بهذه المكوّن + +178 +00:13:25,790 --> 00:13:30,150 +بيمنع الاختزال الذاتي للـ cover انه يصير ان الـ + +179 +00:13:30,150 --> 00:13:33,570 +Capric Ion اللي موجود في الـ reagent يختزل بدون ما + +180 +00:13:33,570 --> 00:13:36,830 +يرتبط في البروتين يصير الاختزال الذاتي ويتحول إلى + +181 +00:13:36,830 --> 00:13:40,690 +Capric Ion نحكي لبي مجرد ما الـ Capric Ion هذا + +182 +00:13:40,690 --> 00:13:44,530 +اللي موجود في الـ reagent يرتبط مع البروتين بيتحول + +183 +00:13:44,530 --> 00:13:50,250 +إلى Capric Ionوبيتغير اللون فمجرد ما يرتبط لازم + +184 +00:13:50,250 --> 00:13:55,440 +يصير اختزال ويتغير اللونطب ممكن يصير له auto + +185 +00:13:55,440 --> 00:13:58,860 +reduction اختزال ذاتي من نفسه يختزل حاله بدون ما + +186 +00:13:58,860 --> 00:14:02,900 +يرتبط يتحول من Capric Ion لCapric Ion ويتغير اللون + +187 +00:14:02,900 --> 00:14:06,880 +وممكن ما يكونش موجود البروتين لكنه اختزل ذاتيا + +188 +00:14:06,880 --> 00:14:10,840 +فعطاني false positive فعطاني نتيجة positive و + +189 +00:14:10,840 --> 00:14:15,020 +البروتين مش موجود فمين بده يمنح حدوث هذا الاختزال + +190 +00:14:15,020 --> 00:14:19,620 +الذاتي هو البوتاسيوم الموجود فيه مكون من مكونات + +191 +00:14:19,620 --> 00:14:23,150 +الـ reagentاللي هو الـ Potassium Sodium Tertiary + +192 +00:14:23,150 --> 00:14:30,710 +فعنا تلت وظائف للـ Potassium Sodium Tertiary إيش + +193 +00:14:30,710 --> 00:14:35,810 +ال principle اللي عملنا اليوم ال principle أنه أنا + +194 +00:14:35,810 --> 00:14:40,890 +بدي أجيس كمية ال protein determining total protein + +195 +00:14:40,890 --> 00:14:43,570 +in sample is the biorhythm method by biorhythm + +196 +00:14:43,570 --> 00:14:46,830 +method أن أنا بدي أجيس كمية البروتين الموجودة في + +197 +00:14:46,830 --> 00:14:51,620 +العينة بطريقة ال biorhythm methodالـ Biuret Method + +198 +00:14:51,620 --> 00:14:56,200 +حكي أنها بتعتمد على وجود الـ Capric Ion الـ Capric + +199 +00:14:56,200 --> 00:15:00,200 +بيجي بيعمل Complexation to the peptide bond in the + +200 +00:15:00,200 --> 00:15:03,080 +protein بيروح الـ Capric Ion اللي موجود في + +201 +00:15:03,080 --> 00:15:06,980 +الرياجان بيرتبط مع الـ peptide bond بيعمل كلات + +202 +00:15:06,980 --> 00:15:11,820 +Complex Formation of Capric Protein Complex اللي + +203 +00:15:11,820 --> 00:15:14,700 +هو الكبر مع البروتين بيعملوله Complex بيحتاج إلى + +204 +00:15:14,700 --> 00:15:19,100 +two peptide bondsحكينا إنه بحتاج إلى رابطتين + +205 +00:15:19,100 --> 00:15:23,240 +بتدياتين على الأقل عشان يعمل ال complex بيتحول + +206 +00:15:23,240 --> 00:15:27,290 +اللون إلى violet colorكلية البروداكت هذا اللون + +207 +00:15:27,290 --> 00:15:30,610 +اللي اتكون ال complex اللي اتكون ولونه violet + +208 +00:15:30,610 --> 00:15:35,370 +بجيثه measured by absorption spectroscopy at 540 + +209 +00:15:35,370 --> 00:15:40,630 +nanometer بروح باجيث كمية امتصاص اللون الدوق اللي + +210 +00:15:40,630 --> 00:15:44,710 +امتصها العينة على جهاز spectrophotometer على طول + +211 +00:15:44,710 --> 00:15:50,740 +موجي 540 nanometerبحكي للـ molecule containing two + +212 +00:15:50,740 --> 00:15:53,620 +or more peptide bonds associated with the capric + +213 +00:15:53,620 --> 00:16:02,190 +ion to form a complexبيربول قرر تحوي على + +214 +00:16:02,190 --> 00:16:08,790 +رابطتين ببتديتين وأكتر بيرتبط مع الـ Capric Ion + +215 +00:16:08,790 --> 00:16:14,070 +وبيعمل لي كمبليكس كيلية كمبليكس لونه بيربول بجيسه + +216 +00:16:14,070 --> 00:16:19,690 +على خمسمية وأربعين نانو متر في وجود alkaline pH + +217 +00:16:19,690 --> 00:16:24,390 +حكينا لازم يكون أن alkaline pH الكبرك ايون الموجود + +218 +00:16:24,390 --> 00:16:29,970 +في ال regionبيرتبط مع الـ peptide bond بمجرد ما + +219 +00:16:29,970 --> 00:16:34,270 +يرتبط بيصير له reduction of من capric ion to + +220 +00:16:34,270 --> 00:16:38,930 +caprous ion يعني ملخص الـ principle لأن هو نفس الـ + +221 +00:16:38,930 --> 00:16:42,950 +principle تبع ال bio-test اللي أخدناه في معمل الـ + +222 +00:16:42,950 --> 00:16:46,690 +quality test of amino acid أخدنا أن الـ principle + +223 +00:16:46,690 --> 00:16:52,080 +حكيتبناه على شكل معادلة لأن الـ proteinزائد copper + +224 +00:16:52,080 --> 00:16:58,520 +sulfate في وجود قاعدة اللي هي NAH أو KOH كمان ضفنا + +225 +00:16:58,520 --> 00:17:01,880 +عليها اليوم Sodium Potassium Tertarate المكون + +226 +00:17:01,880 --> 00:17:07,620 +التالت بيعطينا كلية Complex Lonoviolet هذا الـ + +227 +00:17:07,620 --> 00:17:10,300 +принцип اللي أخدناه في أول معمل إيش بده أضيف عليه؟ + +228 +00:17:10,300 --> 00:17:13,660 +إنه كلية Complex هذا اللي Lonoviolet ريد + +229 +00:17:13,660 --> 00:17:19,420 +absorption at 540 نانومتران انا مش بس بدي اشوف + +230 +00:17:19,420 --> 00:17:23,940 +اللون لأ بدي اقرأ الانتصاص لهذا اللون عند خمسمية + +231 +00:17:23,940 --> 00:17:28,920 +واربعين نانو متر لانه فحصنا اليوم quantitative بدي + +232 +00:17:28,920 --> 00:17:31,720 +اطلع عندي كمية مش qualitative + +233 +00:17:34,470 --> 00:17:37,890 +حكينا إنه في طرقتين تانيات كمان بيعتمدوا على الـ + +234 +00:17:37,890 --> 00:17:40,590 +CABAR-Based السائلي حكينا إنه إحنا عندنا الـ + +235 +00:17:40,590 --> 00:17:43,790 +Bioret في عندنا الـ Bicnic Conic Acid وفي عندنا + +236 +00:17:43,790 --> 00:17:48,090 +الـ Lowry Method إيش هي ال Lowry Method؟ ال Lowry + +237 +00:17:48,090 --> 00:17:52,590 +Method هو فحص بيعتمد على وجود الـ CABAR إنه فيه + +238 +00:17:52,590 --> 00:17:56,690 +Reagent اسمه الـ Falling Reagentنوكابرس ايون + +239 +00:17:56,690 --> 00:18:01,810 +detected with فلين كيوكالتيو فلين reagent هذا + +240 +00:18:01,810 --> 00:18:06,830 +الفلين reagent منه مكوّنين يتكون من حشتين من + +241 +00:18:06,830 --> 00:18:13,390 +فوسفوموليبدك و فوسفوتانجستك أسنإذا استخدمت فولين + +242 +00:18:13,390 --> 00:18:16,430 +رياجانت اللي بيتكون من فوسفوموليبديك أسد و + +243 +00:18:16,430 --> 00:18:20,150 +فوسفوتانجستيك أسن بنسمي هذه الطريقة الـ Lowry + +244 +00:18:20,150 --> 00:18:24,510 +method this method is commonly referred to as the + +245 +00:18:24,510 --> 00:18:28,470 +Lowry method كيف هي بتشتغل؟ بتعمل على تحويل زي + +246 +00:18:28,470 --> 00:18:33,880 +البييروت بتحول كابريك أيون إلى كابرس أيونبيعمل + +247 +00:18:33,880 --> 00:18:37,780 +كلات مع الرابط الـ PPD الموجودة في البروتين + +248 +00:18:37,780 --> 00:18:42,820 +بيعطيني لون blue Capric ion reduction of following + +249 +00:18:42,820 --> 00:18:46,740 +reagent produce a blue color الـ blue color هي + +250 +00:18:46,740 --> 00:18:49,640 +اللون الأزرق اللي بيظهر عندي بروح بقرأ له ال + +251 +00:18:49,640 --> 00:18:56,280 +absorption بس على طول موجي 650 إلى 750 nanometer + +252 +00:18:58,100 --> 00:19:02,160 +بحكيلي كمية اللون اللى زهرت عندى او شدة اللون + +253 +00:19:02,160 --> 00:19:06,280 +تعتمد على كمية الرابطة البيبتيدية الـ peptide bond + +254 +00:19:06,280 --> 00:19:09,980 +amount of peptide bond كل ما زادت الـ peptide bond + +255 +00:19:09,980 --> 00:19:15,520 +عدد رابط البيبتيدية اكيد هتزيد عندى شدة اللون يعني + +256 +00:19:15,520 --> 00:19:20,000 +هيزيد تركيز المادة لان كمية البروتين اللى موجوده + +257 +00:19:20,000 --> 00:19:25,820 +هيكون اعلىDisadvantage of biuret test في عندنا + +258 +00:19:25,820 --> 00:19:29,700 +عيوب لطريقة الـ biuret test الـ biuret test هي + +259 +00:19:29,700 --> 00:19:34,340 +طريقة لقياس البروتين في الهيوم أول مشكلة هي إنه + +260 +00:19:34,340 --> 00:19:38,560 +this method required large amount of protein for + +261 +00:19:38,560 --> 00:19:43,980 +detection إن هاي الطريقة تحتاج إلى كميات كبيرة من + +262 +00:19:43,980 --> 00:19:48,920 +البروتين عشان تقدر تكشفانه يعني هي بتجيس من واحد + +263 +00:19:48,920 --> 00:19:53,610 +لعشرين milligram per minuteبتجيس كميات البروتين + +264 +00:19:53,610 --> 00:19:57,910 +واحد لعشرين إذا كان في العينة في بروتين ولكن أقل + +265 +00:19:57,910 --> 00:20:01,950 +من واحد ملي جرام لكل ميل بتقدرش هذه الطريقة تجيسه + +266 +00:20:01,950 --> 00:20:07,870 +بتعطيني كميات خاطرإذاً هذه الطريقة بتحتاج لكميات + +267 +00:20:07,870 --> 00:20:11,370 +كبيرة من البروتين عشان تقدر تجيسها لو جبت عينة + +268 +00:20:11,370 --> 00:20:14,810 +فيها كمية بروتين من واحد لعشرين ميلي جرام لكل ملت + +269 +00:20:14,810 --> 00:20:19,050 +بتقدر تجيسها لو فيها أقل من واحد، بتقدرش تجيسها + +270 +00:20:19,050 --> 00:20:22,730 +إذا العينة فيها بروتين ولكن أقل من واحد ميلي جرام + +271 +00:20:22,730 --> 00:20:27,250 +برمال، بتقدرش تجيسها مش هتعطيكي قرار وهذه بنسميها + +272 +00:20:27,250 --> 00:20:33,270 +sensitivity sensitivity تعريفها أقل كمية قادر + +273 +00:20:33,270 --> 00:20:39,700 +الفحص على قياسهاأقل كمية بيقدر الفحص يجيسها بسميها + +274 +00:20:39,700 --> 00:20:43,560 +الـ sensitivity فلو سألت ال sensitivity للفحص ال + +275 +00:20:43,560 --> 00:20:49,000 +bio retest يداش هي الـ 1 milligram برميل أقل كمية + +276 +00:20:49,000 --> 00:20:52,080 +بيقدر ال bio retest يجيسها هي 1 milligram برميل + +277 +00:20:52,080 --> 00:20:55,740 +إذا ال sensitivity لل bio retest هي 1 milligram + +278 +00:20:55,740 --> 00:21:00,820 +برميل تعتبر ال sensitivity له قليلة أول عيوب هذه + +279 +00:21:00,820 --> 00:21:06,030 +الطريقة أن ال sensitivity له قليلةتاني من عيوبه ان + +280 +00:21:06,030 --> 00:21:09,530 +هي sensitive to a variety of nitrogen-containing + +281 +00:21:09,530 --> 00:21:15,590 +substances ان هذه طريقة حساسة لأي مركب كيميائي + +282 +00:21:15,590 --> 00:21:21,150 +يحتوي على رابطتين بيبتديتين فاكترالجيت هو بيتمد + +283 +00:21:21,150 --> 00:21:25,450 +على وجود رابطة بيبتدية تنتن في أكتر بيجي في الـ + +284 +00:21:25,450 --> 00:21:28,730 +Cupric Ion اللي موجود في الرياجان ويرتبط مع هذه + +285 +00:21:28,730 --> 00:21:33,430 +الرابطة البيبتدية وبيكوّن لكلات Complex اللي لون + +286 +00:21:33,430 --> 00:21:38,800 +violet وبجيسه على طول موجي 540 نانومترالرابطتين + +287 +00:21:38,800 --> 00:21:42,360 +البيبتيديتين هدول موجودين في البروتين بحط على + +288 +00:21:42,360 --> 00:21:46,980 +البروتين bio-retraction وبجيس كمية الكلية ال + +289 +00:21:46,980 --> 00:21:50,040 +complex اللي اتكون وعطاني اللون بجيس شدت هذا اللون + +290 +00:21:50,040 --> 00:21:55,080 +في الجهات ممكن في مركبات تانية تحتوي على رابطتين + +291 +00:21:55,080 --> 00:21:59,140 +بيبتيديتين فعلا زي مين؟ زي المركب اسمه الـ Bioria + +292 +00:21:59,140 --> 00:22:03,360 +بيوريا معناهت ان مركبين يوريا بيرتبطوا مع بعض + +293 +00:22:03,360 --> 00:22:07,930 +بيقدروا يرتبطوا مع بعضبيتكون بينهم رابطتين + +294 +00:22:07,930 --> 00:22:12,270 +بيبتديتين فبما أن هذا المراكب خلصار فيه رابطتين + +295 +00:22:12,270 --> 00:22:16,930 +بيبتديتين إذا أن العينة إذا فيها بيوريا بيوريا هذه + +296 +00:22:16,930 --> 00:22:20,630 +فيها رابطتين بيبتديتين حطيت عليها بيوري تريجين + +297 +00:22:20,630 --> 00:22:25,110 +بيجي الكبر كعادي بيرتبط مع الرابط البيبتديةبيكون + +298 +00:22:25,110 --> 00:22:29,350 +كلات Complex لونه violet بجيس شديد اللون هذا على + +299 +00:22:29,350 --> 00:22:33,650 +540 نانومتر وبيعطيني قراعه طب هذه القراع اللي طلعت + +300 +00:22:33,650 --> 00:22:37,670 +معايا مش هتكون لبروتين هتكون لمركب اسمه الـ Bioria + +301 +00:22:37,670 --> 00:22:41,630 +مابهناش يعرفني هل هي للـ Bioria ولا للبروتين يعني + +302 +00:22:41,630 --> 00:22:47,060 +ممكن تعطيني نتائج خاطئةإنه لحساسة لوجود مُركّبات + +303 +00:22:47,060 --> 00:22:51,560 +أخرى غير البروتين يعني هذه الطريقة مش خاصة بس + +304 +00:22:51,560 --> 00:22:55,140 +للبروتين إنها تعطيني قراءة بس للبروتين not + +305 +00:22:55,140 --> 00:23:00,120 +specific، specificity عندها قليلة إنها مش خاصة بس + +306 +00:23:00,120 --> 00:23:04,620 +للبروتين وإنما لأي مُركّب يحتوي على رابطتين + +307 +00:23:04,620 --> 00:23:10,530 +ببتديتين فأكتر زي البيوريأذن طريق العيوب الـ + +308 +00:23:10,530 --> 00:23:14,370 +Biorhythm test أنه ال sensitivity له قليلة و ال + +309 +00:23:14,370 --> 00:23:19,370 +specificity له قليلة أقل كمية قادرة على قياسها + +310 +00:23:19,370 --> 00:23:23,850 +قليلة ال specificity الخصوصية له برضه قليلة أنه + +311 +00:23:23,850 --> 00:23:29,950 +ممكن تختلط مواد أخرى و يعطيني إليها قراءة إيش هو + +312 +00:23:29,950 --> 00:23:33,530 +ال standard curve؟ ال standard curve هو عبارة عن + +313 +00:23:33,530 --> 00:23:37,190 +type of graph used for quantitative research + +314 +00:23:37,190 --> 00:23:43,540 +techniqueهو رسم بياني لمعرفة تركيز أي مادة مجهولة + +315 +00:23:43,540 --> 00:23:48,680 +رسم بياني برسمه عشان أعرف تركيز أي مادة مجهولة + +316 +00:23:48,680 --> 00:23:52,380 +standard care for protein concentration is often + +317 +00:23:52,380 --> 00:23:56,520 +created using non-concentration of bovine serum + +318 +00:23:56,520 --> 00:24:00,320 +أنه كيف أنا بدي استخدم هذا الرسم البياني لمعرفة + +319 +00:24:00,320 --> 00:24:04,120 +تركيز أي مادة مجهولة باستخدام حاجة اسمها standard + +320 +00:24:04,120 --> 00:24:09,430 +مرجعاللي هو عبارة عن البروتين بيكون معروف التركيز + +321 +00:24:09,430 --> 00:24:15,490 +هذا البروتين بيكون موجود في الجسم البروتين اللي + +322 +00:24:15,490 --> 00:24:22,150 +هنستخدمه هو الـ bovine serum + +323 +00:24:22,150 --> 00:24:28,910 +albumin وبروتين الألبومن من عجل صغيرالألبومين هو + +324 +00:24:28,910 --> 00:24:33,210 +عبارة عن سيرام البروتين اللي يترانسبورت الفاتي أسد + +325 +00:24:33,210 --> 00:24:42,310 +ومهم في تحفظ بلازمة BH هو بروتين موجود في الدم + +326 +00:24:42,310 --> 00:24:48,070 +يعمل كناقل لبعض المواد زي الفاتي أسد ويحافظ على + +327 +00:24:48,070 --> 00:24:53,940 +الـ BHفي الـ Protein Quantization Assay بوفاين + +328 +00:24:53,940 --> 00:24:58,900 +سيرام ألبومين تعمل كـ Reference Protein تستخدم + +329 +00:24:58,900 --> 00:25:04,060 +لإصلاح الـ Protein Standard Camp في فحوصات لمعرفة + +330 +00:25:04,060 --> 00:25:08,400 +تركيز البروتين نستخدم البروتين للـ Bovine Serum + +331 +00:25:08,400 --> 00:25:13,860 +البروتين كبروتين مرجع كستاندر كما ده بتكون عارفين + +332 +00:25:13,860 --> 00:25:18,540 +تركيزها ومن خلالها بتدعرف تركيز العينة اللي موجودة + +333 +00:25:18,540 --> 00:25:24,690 +عندههي مادة معروفة التركيز بستخدمها كمرجع لتقدير + +334 +00:25:24,690 --> 00:25:30,350 +تركيز مادة مجهولة الـ standard solution هو non + +335 +00:25:30,350 --> 00:25:34,330 +-concentration of sample الـ standard هو مادة + +336 +00:25:34,330 --> 00:25:40,910 +بتكون معروفة التركيز، مادة أنا عارفة تركيزهاالـ + +337 +00:25:40,910 --> 00:25:44,050 +standard curve حاكي هنا إن هو رسم بياني لمعرفة + +338 +00:25:44,050 --> 00:25:48,790 +تركيز أي مادة مجهولة بناء على إياش، بناء على وجود + +339 +00:25:48,790 --> 00:25:54,870 +standard مادة معروفة التركيزفجيت أنا ضروري أرسم + +340 +00:25:54,870 --> 00:25:58,170 +للـStandard Curve عشان أعرف التركيز العين المجهولة + +341 +00:25:58,170 --> 00:26:01,450 +اللي بتكون عندى كيف بدأ أعرف هذا التركيز؟ بناء على + +342 +00:26:01,450 --> 00:26:05,990 +وجود مادة معروف التركيز، مادة كمرجع المادة هذه + +343 +00:26:05,990 --> 00:26:09,410 +المعروفة التركيز اسمها الـStandard بتجيني من + +344 +00:26:09,410 --> 00:26:13,310 +الشركة هي بتجينها من الشركة بيكون معروف تركيزها + +345 +00:26:13,310 --> 00:26:17,190 +مكتوب عليها أن هو الـStandard وتركيزها هالجانإما + +346 +00:26:17,190 --> 00:26:21,350 +بتجيني من الشركة مخففة، منه هذا الـ standard نفسه + +347 +00:26:21,350 --> 00:26:25,450 +مخفف ومعمول منه عدة تخفيفات، كل تخفيف له تركيز + +348 +00:26:25,450 --> 00:26:28,850 +مختلف، مثلا الأولى بيكون مكتوب عليها إنه هي 5 + +349 +00:26:28,850 --> 00:26:32,570 +milligram per meal، تانية 10 milligram per meal، + +350 +00:26:32,570 --> 00:26:36,510 +25 milligram per meal، 50 milligram per meal، إنه + +351 +00:26:36,510 --> 00:26:41,210 +مخفف واجازةأو بتجيني standard مركز مثلا مكتوب عليه + +352 +00:26:41,210 --> 00:26:44,510 +ان هو 2 milligram per ml و احنا مطلوب منه ان احنا + +353 +00:26:44,510 --> 00:26:49,270 +نعمل منه عدة تخفيفات عشان نشتغل عليه لو انا عملت + +354 +00:26:49,270 --> 00:26:53,150 +عدة تخفيفات كيف بدي احسب التخفي في الـ dilution + +355 +00:26:53,150 --> 00:27:02,430 +بالقانون C1V1 بتساوي C2V2الهو التركيز الأول تركيز + +356 +00:27:02,430 --> 00:27:05,890 +ال standard كده كان جبتلي الشركة أنه 2 milligram + +357 +00:27:05,890 --> 00:27:10,210 +في ال volume ضرب ال volume كده حجم اللي أنا أخدته + +358 +00:27:10,210 --> 00:27:14,310 +من هذا ال standard بساوي C2 التركيز اللي بعد ما + +359 +00:27:14,310 --> 00:27:17,860 +خففته هذا اللي أنا بتاعه عرفه مجهولدرب الـ Volume + +360 +00:27:17,860 --> 00:27:22,220 +2 اللي هو جدّيش أنا أخدت من الـ Distilled water و + +361 +00:27:22,220 --> 00:27:24,760 +جدّيش أخدت من الـ Standard يعني الـ Volume الـ + +362 +00:27:24,760 --> 00:27:28,260 +Total، الكلّي اللي هو حاجة جدّيش أنا أخدت من الـ + +363 +00:27:28,260 --> 00:27:32,840 +Standard و جدّيش أضفت عليه Distilled water، الـ + +364 +00:27:32,840 --> 00:27:35,960 +Volume الكلّي هذا هيوضح معنا إن شاء الله في المعمل + +365 +00:27:35,960 --> 00:27:38,540 +هنوضح كيف هذا القانون + +366 +00:27:40,920 --> 00:27:43,600 +How to calculate the concentration كيف نحسب + +367 +00:27:43,600 --> 00:27:47,460 +التركيز حكي هنا بناء على قانون الـPierre Lambert's + +368 +00:27:47,460 --> 00:27:52,680 +law اللي بيحكي إنه في علاقة بين تركيز المادة وكمية + +369 +00:27:52,680 --> 00:27:56,240 +الضوء الممتص إن الـconcentration of substance + +370 +00:27:56,240 --> 00:27:59,080 +directly proportional to the amount of light + +371 +00:27:59,080 --> 00:28:03,440 +absorbedانه تركيز المادة بيتناسب تناسط طرطي مع + +372 +00:28:03,440 --> 00:28:07,840 +كمية الضوء الممتص أهم نقطة هي النقطة الأخيرة في + +373 +00:28:07,840 --> 00:28:11,360 +هاي ال slide انه ال reference range for total + +374 +00:28:11,360 --> 00:28:18,540 +protein كمية البروتين الطبيعية هي من 66.6 ل 81.4 + +375 +00:28:18,540 --> 00:28:24,460 +gram per liter او 6.6 ل 8.1 gram per deciliter + +376 +00:28:24,460 --> 00:28:30,420 +تختلف هنا الوحدات فركزوا على الوحداتكيف بدي أعمل + +377 +00:28:30,420 --> 00:28:33,860 +الـ Standard Curve اللي هو المخطط أو الرسم البياني + +378 +00:28:33,860 --> 00:28:37,100 +كيف بدي أعمله؟ كيف بدي يساعدني في معرفة تركيز + +379 +00:28:37,100 --> 00:28:41,020 +المادة المجهولة؟ حاجة الـ Standard Curve بينعمل + +380 +00:28:41,020 --> 00:28:44,540 +بناء على وجود مادة معروفة التركيز اسمها الـ + +381 +00:28:44,540 --> 00:28:49,000 +Standard إنه عندي مادة صار معروف تركيزها هذه + +382 +00:28:49,000 --> 00:28:52,160 +المادة سواء أجتني من الشركة بخففها وجهزة أو أنا + +383 +00:28:52,160 --> 00:28:56,580 +عملتلها تخفيفات وعرفت تركيز كل تخفيف المهم في + +384 +00:28:56,580 --> 00:29:01,720 +النهاية إنه عنديالـ Standard بيدّي التخفيفات مثلًا + +385 +00:29:01,720 --> 00:29:06,000 +أنا عندي أربعة standard واحد تخفيف وخمسة milligram + +386 +00:29:06,000 --> 00:29:11,820 +per ml milligram per ml وعشرة gram per ml وخمسة + +387 +00:29:11,820 --> 00:29:15,300 +وعشرين وخمسين هي عندي أربعة standard تخفيفات + +388 +00:29:15,300 --> 00:29:18,580 +مختلفة معروفة أن هي تركيزة التركيز الأول خمسة + +389 +00:29:18,580 --> 00:29:24,140 +والتاني عشرة التالت خمسة وعشرين الرابع خمسينإذا + +390 +00:29:24,140 --> 00:29:27,560 +عندي multiple sample with non-properties بياخدها + +391 +00:29:27,560 --> 00:29:31,980 +وبيعملها measure هذه العينات العدة اللي هي الـ + +392 +00:29:31,980 --> 00:29:37,460 +standard لمعروف خصائصها، معروف تركيزها بروح بجيسها + +393 +00:29:37,460 --> 00:29:41,840 +في جهاز الـ spectrophotometer باخدها، بقراها على + +394 +00:29:41,840 --> 00:29:45,320 +جهاز الـ spectrophotometer إيش بده أقرألها؟ بده + +395 +00:29:45,320 --> 00:29:49,220 +أقرألها الـ absorption هذا الجهاز بيجيس كمية الضوء + +396 +00:29:49,220 --> 00:29:53,090 +اللي بتمطسها العينة يعني بيجيس الـ absorptionبعد + +397 +00:29:53,090 --> 00:29:56,390 +ما حط طبعا ال reagent عليها بكون حاطة على هذا ال + +398 +00:29:56,390 --> 00:30:01,680 +standard باخده بحط عليه من ال reagent تمام؟هلجان + +399 +00:30:01,680 --> 00:30:05,920 +باخده بحط أول واحدة اللي هي تركيزها الخمسة أنا + +400 +00:30:05,920 --> 00:30:08,540 +عارفة تركيزها الخمسة بحطها في جهاز الـ + +401 +00:30:08,540 --> 00:30:12,640 +spectrophotometer و بقرأ ال absorption ال + +402 +00:30:12,640 --> 00:30:16,400 +absorption على فرض الأولى طلعت point واحد اتنين + +403 +00:30:16,400 --> 00:30:21,160 +تلاتة تمام بطلعها باخد التاني اللي هي تركيزها عشر + +404 +00:30:21,160 --> 00:30:24,860 +بقرأ ال absorption على فرض point واحد خمسة أربع + +405 +00:30:25,570 --> 00:30:30,090 +باخد 25 لتركيزها 25 وبقرألها الـ absorption على + +406 +00:30:30,090 --> 00:30:35,490 +فرد point 2 3 5 بعدين باخد لتركيزها 50 وبقرأ أعلى + +407 +00:30:35,490 --> 00:30:41,130 +فرد point 3 3تمام؟ هالجهة أنا بيصير عندي معروف + +408 +00:30:41,130 --> 00:30:44,690 +تركيز لهذه المادة وأخدتها قرأتها في جهاز + +409 +00:30:44,690 --> 00:30:47,310 +Spectrophotometer فصار عندي معروف اللي هي + +410 +00:30:47,310 --> 00:30:51,130 +absorption إذا عندي معروف تركيز، concentration و + +411 +00:30:51,130 --> 00:30:55,830 +absorption بجي برسم الـStandard Curve الـStandard + +412 +00:30:55,830 --> 00:31:00,850 +Curve كيف بدي أرسمه؟ بعبارة عن تقاطع صيني مع صعب + +413 +00:31:00,850 --> 00:31:06,710 +على الخط الصيني بيمثل الـconcentrationوالخط الصعدي + +414 +00:31:06,710 --> 00:31:10,790 +يمثل ال absorption is a standard curve الرسم + +415 +00:31:10,790 --> 00:31:15,630 +وعبارة عن تقاطع سيني وصعدي على الخط السيني بحط ال + +416 +00:31:15,630 --> 00:31:20,090 +concentration وعلى الصعدي بحط ال absorptionبحط + +417 +00:31:20,090 --> 00:31:25,210 +تقسيمة لخط الصيني وخط الصيني وبجيب أرسم مثلا أول + +418 +00:31:25,210 --> 00:31:27,870 +نقطة اللي هي خمسة من الصيني من ال concentration + +419 +00:31:27,870 --> 00:31:31,910 +تركيزها كان خمسة مع تقاطع من ال absorption طلعت + +420 +00:31:31,910 --> 00:31:35,510 +point واحد اتنين تلاتة بحط النقطة الأولى اللي هي + +421 +00:31:35,510 --> 00:31:38,890 +تقاطع خمسة مع point واحد اتنين تلاتة النقطة + +422 +00:31:38,890 --> 00:31:41,730 +التانية اللي هي تركيزها عشرة مع point واحد خمسة + +423 +00:31:41,730 --> 00:31:46,430 +أربعة بحط النقطة التالتة خمسة وعشرين تركيزها من ال + +424 +00:31:46,430 --> 00:31:51,200 +concentration مع point اتنين تلاتة خمسةالرابع + +425 +00:31:51,200 --> 00:31:56,540 +تركيزها الخمسين مع point تلاتة تلاتة بحط النقطة + +426 +00:31:56,540 --> 00:32:01,300 +وبعدين بوصل النقاط أكبر عدد من النقاط بحيث يمثل خط + +427 +00:32:01,300 --> 00:32:07,000 +مستقيم برسم خط مستقيم يمر بأكبر عدد من النقاط بوصل + +428 +00:32:07,000 --> 00:32:12,300 +النقاط مع بعض على بعض بحيث يمثل خط مستقيم بتكون + +429 +00:32:12,300 --> 00:32:18,280 +عندى من ضمن هدول في عندى عينة مجهولة التركيزفي + +430 +00:32:18,280 --> 00:32:21,480 +عندي عينة ماخدينها من مريض مثلًا لأعرف تركيز + +431 +00:32:21,480 --> 00:32:24,720 +البروتين فيها بحط عليها الـReagent و باخدها على + +432 +00:32:24,720 --> 00:32:28,760 +جهاز الـSpectrophotometer بقرا إليها absorption، + +433 +00:32:28,760 --> 00:32:32,360 +انتصار في هذه المادة بيصير عندي معروف إليها + +434 +00:32:32,360 --> 00:32:37,360 +الـabsorption بس مش معروف التركيز باجي على التقاط + +435 +00:32:37,360 --> 00:32:40,940 +عصاد اللي بيمثل الـabsorption على فرض العينة مثلًا + +436 +00:32:40,940 --> 00:32:47,990 +طلعت point1.7 بأجي على point 1.7 من الـ absorption + +437 +00:32:47,990 --> 00:32:53,230 +بوصل خط اللي وصولا إلى الخط المستقيم اللي في الوسط + +438 +00:32:53,230 --> 00:32:58,910 +وبنزل عمود على الخط الساني وبشوف جداش .. وين وين + +439 +00:32:58,910 --> 00:33:03,430 +وصلت عنديا تركيز وبكتب تركيز هذه العينة المجهولة + +440 +00:33:04,260 --> 00:33:09,080 +أنا عارف إنه صعب عليكم تفهموه هنا لكن هنوضحه في + +441 +00:33:09,080 --> 00:33:11,880 +المعمل ونورسمه إن شاء الله على الصجورة ونوضح كيف + +442 +00:33:11,880 --> 00:33:17,810 +بينعمل الـ Standard Kشايفين هنا الرسم اللي تحت + +443 +00:33:17,810 --> 00:33:22,110 +اللي هو تقاطع سيني مع صعدي خط السيني بيمثل الـ + +444 +00:33:22,110 --> 00:33:25,790 +concentration والخط الصعدي بيمثل الـ absorption + +445 +00:33:25,790 --> 00:33:30,350 +يكون عندي مواد جياني معروف تركيزها كل واحدة إلاها + +446 +00:33:30,350 --> 00:33:34,030 +concentration مختلف وabsorption على الخط الصعدي + +447 +00:33:34,030 --> 00:33:36,890 +أنا أخدت هذه العينات وقرأتها في جهاز + +448 +00:33:36,890 --> 00:33:40,860 +Spectrophotometer وطلع معايا absorptionهتبقى اشي + +449 +00:33:40,860 --> 00:33:45,160 +بمثل اول نقطة مثلا على فرقة خمسة من الصيني ال + +450 +00:33:45,160 --> 00:33:48,300 +concentration و من الصادر طلع ال absorption الها + +451 +00:33:48,300 --> 00:33:52,800 +point واحد نات بقى بحط نقطة النقطة اللي بعدها لكل + +452 +00:33:52,800 --> 00:33:56,360 +عينة جداش تركيزها ماجداش ال absorption بحط النقطة + +453 +00:33:56,360 --> 00:34:02,940 +بوصل خط مستقيم يمر بمعظم النقاطفي عندي عيناة بتكون + +454 +00:34:02,940 --> 00:34:07,600 +unknown عيناة مثلا ماخدها من مريض وفيها بروتين بدي + +455 +00:34:07,600 --> 00:34:10,920 +أعرف كمية هذه البروتين بحط عليها من الـ reagent زي + +456 +00:34:10,920 --> 00:34:14,700 +الـ standard بعملها معاملة الـ standard بحط عليها + +457 +00:34:14,700 --> 00:34:17,020 +reagent و بعدين باخدها على جهاز الـ + +458 +00:34:17,020 --> 00:34:20,580 +spectrophotometerوفي الجهاز بيعطيني absorption + +459 +00:34:20,580 --> 00:34:24,800 +بيعطيني امتصاد باجي على الخط الصعدي اللي هي ال + +460 +00:34:24,800 --> 00:34:27,500 +absorption أنا عارفة ال absorption لهذه العينة + +461 +00:34:27,500 --> 00:34:31,720 +قرأتها على الجهاز وعلى فرض طلعت point 1 3 5 يعني + +462 +00:34:31,720 --> 00:34:36,270 +ده كلمة signal الخط الأحمرعلى فرض هي أنها طلعت الـ + +463 +00:34:36,270 --> 00:34:39,790 +absorption بوصل خط إلى الخط المستقيم اللي في + +464 +00:34:39,790 --> 00:34:43,670 +المنتصف وبسقط عمود من عند النقطة اللي وصلت عندها + +465 +00:34:43,670 --> 00:34:48,790 +بسقط عمود على الصانع وإن ما سقط هذا العمود بيكون + +466 +00:34:48,790 --> 00:34:53,570 +هذا الـ concentration هذا عبارة عنتركيز هذه المادة + +467 +00:34:53,570 --> 00:34:57,430 +عفارة طلعت مثلا بين خمسين وخمسة وعشرين بقدر انه + +468 +00:34:57,430 --> 00:35:01,750 +ممكن تكون هي خمسة واربعين ممكن تكون خمسة وتلاتين + +469 +00:35:01,750 --> 00:35:08,330 +فشوف وين وقعت بالظبط اذا هذا هو تركيز المادة وهي + +470 +00:35:08,330 --> 00:35:13,190 +عندنا هنا مخطط تاني على الخط الصيني بحط الـ + +471 +00:35:13,190 --> 00:35:16,250 +Concentration وهنا على الخط الصدي بحط الـ + +472 +00:35:16,250 --> 00:35:21,270 +Absorptionكل عينة أنا قرأتها جداش إلها absorption + +473 +00:35:21,270 --> 00:35:25,410 +مع جداش concentration بحط نقطة، النقطة اللي بعلى، + +474 +00:35:25,410 --> 00:35:31,050 +بعدين بحط خط مستقيم بيمر بمعظم النقاط، والعينة + +475 +00:35:31,050 --> 00:35:35,890 +المجهولة بشوف عندهاجدّش هي الـ absorption بكون أنا + +476 +00:35:35,890 --> 00:35:38,370 +قرأها على الجهاز وعارفة إيه لها الـ absorption + +477 +00:35:38,370 --> 00:35:43,030 +جدّش الإمتصاص طلع بوصل على الخط المستقيم وبسقط + +478 +00:35:43,030 --> 00:35:47,150 +عمودة على الـ concentration وبشوف وين يطلع تركيزها + +479 +00:35:47,150 --> 00:35:52,250 +عند أي رقم هيك بكون أنا عارفة تركيز هذه المادة + +480 +00:35:52,250 --> 00:35:57,390 +وبرضه هنرجع نوضح في المعمل كيف المخطط نرسمه وكيف + +481 +00:35:57,390 --> 00:36:05,170 +نعمل على إيجاد تركيز أي مادة مشهولةهنا عندنا مجموع + +482 +00:36:05,170 --> 00:36:09,550 +من التعريفات عندنا تعريف الـ sensitivity حكينا + +483 +00:36:09,550 --> 00:36:14,390 +عنها sensitivity هي أقل كمية أو أقل تركيز من + +484 +00:36:14,390 --> 00:36:19,190 +الانالايت قادر لفحصها لقياسه أقل كمية بيقدر يجيسها + +485 +00:36:19,190 --> 00:36:22,990 +بنسميها sensitivity lowest amount of analyte in + +486 +00:36:22,990 --> 00:36:27,110 +sample which can be detectedأما ال specificity + +487 +00:36:27,110 --> 00:36:31,990 +اللي هي الخصوصية الخصوصية هي قدرة الفحص إنه يكون + +488 +00:36:31,990 --> 00:36:36,730 +خاص أو فريد فقط لـ Analyte معين اللي أنا ببحث عنه + +489 +00:36:36,730 --> 00:36:41,710 +is the ability to assess uniquely vocally the + +490 +00:36:41,710 --> 00:36:45,490 +analyte in the presence of components which may be + +491 +00:36:45,490 --> 00:36:49,150 +expected to be present إنه عندي مثلا عينة أنا عندي + +492 +00:36:49,150 --> 00:36:52,720 +هذا الفحص بدي فحص السكرطب هى العين اللى أنا أخدتها + +493 +00:36:52,720 --> 00:36:56,780 +فيها عدة مكونات من ضمنها السكر لكن فيه حاجات تانية + +494 +00:36:56,780 --> 00:37:01,080 +فيه مثلا البروتين وفيه carbohydrate سكر لكن أنا + +495 +00:37:01,080 --> 00:37:04,600 +هذا الفحص إذا كان عنده specificity عالية فهو بس + +496 +00:37:04,600 --> 00:37:08,600 +قادر على قياس السكر مالوش دخل في المكونات التانية + +497 +00:37:08,600 --> 00:37:13,520 +مايجسنيش غير السكر بس قدرة الفحص على أنه يرتبط مع + +498 +00:37:13,520 --> 00:37:17,240 +الانالايت اللى أنا ببحث عنه مع حاجة واحدة بدون + +499 +00:37:17,240 --> 00:37:22,040 +الاختلاعات مع المكونات الأخرىالـ Linearity + +500 +00:37:22,040 --> 00:37:37,000 +Linearity of Analytical Procedure هي علاقة + +501 +00:37:37,000 --> 00:37:40,600 +الترضية اللي حكينا عنها بالـ absorption و الـ + +502 +00:37:40,600 --> 00:37:43,990 +concentrationهي ال directly proportional اللي هي + +503 +00:37:43,990 --> 00:37:48,450 +العلاقة الخطية معناها العلاقة الترضية اللي بين + +504 +00:37:48,450 --> 00:37:55,150 +تركيز المادة وكمية الضوء اللي بيمتصها ايه شغلنا + +505 +00:37:55,150 --> 00:37:59,270 +لليوم؟ اليوم هو فحصنا ال virus test لنشتغل virus + +506 +00:37:59,270 --> 00:38:03,370 +test ولكن ك quantitative اللي بدي اقرأه في جهاز + +507 +00:38:03,370 --> 00:38:06,990 +spectrophotometer و بالنهاية بدي اعمل standard + +508 +00:38:06,990 --> 00:38:10,330 +curve بس اعمل هذا ال standard curve + +509 +00:38:15,570 --> 00:38:26,610 +تركيز المادة المجهولة تركيز + +510 +00:38:26,610 --> 00:38:27,770 +المادة المجهولة تركيز المادة المجهولة تركيز المادة + +511 +00:38:27,770 --> 00:38:32,350 +المجهولة تركيز المادة المجهولة تركيز المادة + +512 +00:38:32,350 --> 00:38:40,390 +المجهولة تركيز المادة المجهولة تركيز المادة + +513 +00:38:40,390 --> 00:38:46,400 +المجهولةفكيف بدي أخففه؟ بنيعمل من هذا الـ Standard + +514 +00:38:46,400 --> 00:38:51,700 +6 تيوبات بحكي للتيوب الأول، احنا بشو بنخفف؟ بنحط + +515 +00:38:51,700 --> 00:38:54,600 +من المادة المركزة، بنخففها في الـ distilled water + +516 +00:38:54,600 --> 00:38:57,860 +فبحكي للتيوب الأول، حطي عليه من الـ distilled + +517 +00:38:57,860 --> 00:39:02,560 +water خمسة من عشرة مل فلجيت احنا بشو بنستخدم لما + +518 +00:39:02,560 --> 00:39:08,420 +نحط؟ بنستخدم بايبت والبايبت هي بالمايكرون كل واحد + +519 +00:39:08,420 --> 00:39:14,710 +مل بيعطيني ألف مايكرونيعني الخمسة مل تعطيني خمسمية + +520 +00:39:14,710 --> 00:39:18,710 +مايكرون كل هدول الأرقام اللي بالجدول بالمل بتحولهم + +521 +00:39:18,710 --> 00:39:24,450 +لمايكرون كاب كل واحد مل بيعطيني الف مايكرون خمسة + +522 +00:39:24,450 --> 00:39:28,370 +من عشرة مل يعني خمسمية مايكرون تطلع فالـ tube + +523 +00:39:28,370 --> 00:39:32,890 +الأول بحكيلي نحط عليها خمسمية مايكرون من الـ + +524 +00:39:32,890 --> 00:39:36,130 +distilled water و بدناش نحط عليها من ال protein + +525 +00:39:36,130 --> 00:39:40,960 +standard، نحط صفرطب أنا ماحطتش ال protein خالص + +526 +00:39:40,960 --> 00:39:43,560 +ماجددش تركيز ال protein في ال tube الأول + +527 +00:39:43,560 --> 00:39:49,200 +concentration له سفر أكيد سفر أنا عندي ال tube + +528 +00:39:49,200 --> 00:39:53,600 +الأول بس حقيت عليه distill water ماحطيتش عليه من + +529 +00:39:53,600 --> 00:39:59,600 +ال standard فإذا تركيزه هيكون سفر مافيش تركيز له + +530 +00:39:59,600 --> 00:40:05,240 +سفر milligram per ml لأنه ماحطناش عليه ولا إشي من + +531 +00:40:05,240 --> 00:40:10,030 +ال standard«تيوب» رقم 2 بدي أحط عليها من الـ + +532 +00:40:10,030 --> 00:40:14,730 +«دستيل واتر» 4 من 10 مل يعني 400 مايكرون ومن الـ + +533 +00:40:14,730 --> 00:40:20,690 +«بروتين ستاندرد» بدي أحط عليها 100 مايكرون 1 من 10 + +534 +00:40:20,690 --> 00:40:24,350 +مل يعني 100 مايكرون لذلك هذه خففة الـ «ستاندرد» + +535 +00:40:24,350 --> 00:40:28,270 +الأول إن حطيت 4 من 10 «دستيل واتر» يعني 400 + +536 +00:40:28,270 --> 00:40:32,450 +مايكرون على الـ «ستاندرد» الـ «بروتين ستاندرد» 1 + +537 +00:40:32,450 --> 00:40:38,760 +من 10 مل يعني 100 مايكرونقدش تركيزه بيطلع بعد + +538 +00:40:38,760 --> 00:40:42,500 +تخفيف 4 من 10؟ كيف حسبتي التركيز؟ رجزوا معايا فيها + +539 +00:40:42,500 --> 00:40:47,880 +حكينا بنحسب تركيز الـ Standard المخفف بناء على + +540 +00:40:47,880 --> 00:40:55,340 +قانونC1 V1 سواء C2 V2 خلّينا في تيوب رقم 2 ركزوا + +541 +00:40:55,340 --> 00:41:00,140 +معايا على تيوب رقم 2 كيف بده أحسب التركيز؟ C1 اللي + +542 +00:41:00,140 --> 00:41:04,160 +هو التركيز للـ Standard قبل التخفير احنا حكينا إنه + +543 +00:41:04,160 --> 00:41:07,360 +جاينا من الشركة الـ Standard جدا تركيزه 2 + +544 +00:41:07,360 --> 00:41:13,740 +milligram برميل، إذا C1 هي 2 milligram برميلدرب V1 + +545 +00:41:13,740 --> 00:41:18,800 +الـ V1 هذا كداش أنا أخدت من الـ Standard كداش حطيت + +546 +00:41:18,800 --> 00:41:21,080 +على تيوب اتنين من الـ Standard البروتين الـ + +547 +00:41:21,080 --> 00:41:24,920 +Standard هكالي واحد من عشرة مل يعني مائة مايكرو + +548 +00:41:24,920 --> 00:41:29,580 +اذاً C1 اللي هو تركيزه الأصلي تركيز الـ Standard + +549 +00:41:29,580 --> 00:41:36,320 +كداش كان عندي اتنين درب V1 V1 هي كمية الحجم اللي + +550 +00:41:36,320 --> 00:41:39,940 +أنا أخدته من الـ Standard كداش أخدت مية اذا صار + +551 +00:41:39,940 --> 00:41:45,800 +عندي اتنين درب ميةبساوي C2، إيش هي C2؟ هو التركيز + +552 +00:41:45,800 --> 00:41:49,120 +اللي أنا بتعرفه، جدّاش صارت بعد، جدّاش تركيزها + +553 +00:41:49,120 --> 00:41:53,680 +بعد، فهي و سيبنا مجهولة، لسه بديها، V2 هو الـ + +554 +00:41:53,680 --> 00:41:57,020 +Total، الحجم الكل، جدّاش حطيت من الـDistilled + +555 +00:41:57,020 --> 00:42:00,640 +water مع الـStandard، في Tube 2، جدّاش حطيت، حكي + +556 +00:42:00,640 --> 00:42:03,420 +أنا حطينا من الـDistilled water، 4 من 10 ميلي، + +557 +00:42:03,420 --> 00:42:07,550 +يعني 400 مايكروومن الـ Standard حطيت 1 من 10 مل + +558 +00:42:07,550 --> 00:42:10,950 +يعني 100 مايكرون يعني 400 مايكرون و100 مايكرون + +559 +00:42:10,950 --> 00:42:16,550 +يعني الـ total كله قداش 500 مايكرون، إذا الـ V2 هي + +560 +00:42:16,550 --> 00:42:21,550 +500 مايكرون، إذا صرت بعرف C1 2 عبارة عن 2 ميلي + +561 +00:42:21,550 --> 00:42:28,990 +جرام، V1 هي 100 مايكرون، C2 بتديها، V2 هي 500 + +562 +00:42:28,990 --> 00:42:34,730 +مايكرونمن المعادلة 2 ضرب 100 على 500 بتطلع التركيز + +563 +00:42:34,730 --> 00:42:39,530 +4 من 10 فهمنا كيف جيبنا الـ Concentration لـ Tube + +564 +00:42:39,530 --> 00:42:47,410 +2 من القانون C1 V1 سواء C2 V2 منهي C1 هو تركيز الـ + +565 +00:42:47,410 --> 00:42:50,830 +Standard اللي بدون تخفيف الأصل اللي جانب الشركة + +566 +00:42:50,830 --> 00:42:56,050 +جدش كان 2 milligram per minuteالـ V1 هي التركيز + +567 +00:42:56,050 --> 00:42:58,570 +اللي أنا أخدته من الـ Standard كده أخدتي حجم من + +568 +00:42:58,570 --> 00:43:03,250 +الـ Standard؟ أخدنا 100 مايكرو الـ C2 هذا بتديها + +569 +00:43:03,250 --> 00:43:07,390 +مجهولة الـ V2 هي عبارة عن الحجم الكل ديستل واتر + +570 +00:43:07,390 --> 00:43:11,970 +زائد للـ Standard أخدت 400 مع 100 يعني 500 مايكرو + +571 +00:43:11,970 --> 00:43:16,690 +بيطلع عند الـ concentration 4 من 10نجي على تيوب 3 + +572 +00:43:16,690 --> 00:43:20,950 +تيوب 3 حطيت عليها 3 من 10 مل من الـ distilled + +573 +00:43:20,950 --> 00:43:25,290 +water يعني 300 مايكرون و 2 من 10 مل من الـ + +574 +00:43:25,290 --> 00:43:30,150 +standard يعني 200 مايكرون عليكوا تحسبولي إيها الـ + +575 +00:43:30,150 --> 00:43:33,790 +concentration و تسلمونيها هو التركيز أنا طلع 8 من + +576 +00:43:33,790 --> 00:43:38,170 +10 إليها بدي أكم تعرفولي كيف طلع 8 من 10 بناء على + +577 +00:43:38,170 --> 00:43:43,450 +القانون زي ما حسبنا لتيوب 2 لنحسب ل3ولا أربعة ولا + +578 +00:43:43,450 --> 00:43:49,110 +خمسة وتعطوني الإجابة تسلموني الواجب إنه تحسبولي + +579 +00:43:49,110 --> 00:43:54,850 +لتيوب رقم تلاتة واربعة وخمسة تيوب رقم تلاتة بيحكي + +580 +00:43:54,850 --> 00:43:57,850 +إننا نحط عليها تلاتة من عشرة distilled water يعني + +581 +00:43:57,850 --> 00:44:02,230 +300 مايكرون واتنين من عشرة من البروتين ال standard + +582 +00:44:02,230 --> 00:44:08,380 +يعني 200 مايكرونوبعد أن تيوب رقم 4 بتحط عليها 2 من + +583 +00:44:08,380 --> 00:44:11,640 +10 ميلي من الـ distilled water يعني 2 مايكرون + +584 +00:44:11,640 --> 00:44:15,060 +ديستل واتر تلاتة من عشرة من البروتين ال standard + +585 +00:44:15,060 --> 00:44:21,380 +يعني 300 مايكرونتيوب رقم 5 بدي أحط عليها 1 من 10 + +586 +00:44:21,380 --> 00:44:25,100 +ملي من الـ distilled water 1 من 10 ملي يعني 100 + +587 +00:44:25,100 --> 00:44:29,060 +مايكرون ومن الـ protein standard بدي أحط 4 من 10 + +588 +00:44:29,060 --> 00:44:34,760 +ملي يعني 400 مايكرون تيوب رقم 6 بديش أحط عليها + +589 +00:44:34,760 --> 00:44:38,540 +distilled water بس بدي أحط عليها من الـ protein + +590 +00:44:38,540 --> 00:44:42,920 +standardخمسة من عشرة ملي، يعني خمسمائة مايكرون، + +591 +00:44:42,920 --> 00:44:46,100 +إذا انتيوب رقم ست، أنا ماعملتلهااش تخفيف، حطيتها + +592 +00:44:46,100 --> 00:44:49,120 +زي مياه، خدت بس ماحطش عليها دستل ووتر، يعني + +593 +00:44:49,120 --> 00:44:53,020 +ماخففتاش، يعني من الأصل، الـ standard الأصل، حطيت + +594 +00:44:53,020 --> 00:44:58,080 +عليها خمسمائة مايكرون، فتركيزها جداش هيكون، أكيد + +595 +00:44:58,080 --> 00:45:02,380 +مدام ماخففتاش، بجي تركيزها نفس تركيز الأصلي، اللي + +596 +00:45:02,380 --> 00:45:08,800 +هو اتنين ملي جرام per mil، ماتغيرش تركيزها،أخر + +597 +00:45:08,800 --> 00:45:13,500 +تيوب أحنا نجيب سبعة تيوبات، ستة منهم هم تخفيفات + +598 +00:45:13,500 --> 00:45:19,040 +للـStandard والسبعة هي Unknown، هي عينة مريض بتاعه + +599 +00:45:19,040 --> 00:45:22,640 +عارف كمية البروتين فيها، بديش أحط عليها ولايش من + +600 +00:45:22,640 --> 00:45:25,740 +الـDistilled water ولا من الـStandard، وإنما من + +601 +00:45:25,740 --> 00:45:29,960 +العينة اللي جاية عندي تحط خمسة من عشرة مل، يعني + +602 +00:45:29,960 --> 00:45:35,240 +خمسمية مايكروم هل أنا عارف كمية تركيزها، كمية + +603 +00:45:35,240 --> 00:45:39,740 +البروتين لهذا المريض؟ لأبنحكي لبعد ما نحضر هدول + +604 +00:45:39,740 --> 00:45:43,840 +التيوبات كلهم بنحط واحد مل من الـ bioretary agent + +605 +00:45:43,840 --> 00:45:48,860 +على كل التيوبات بنحط واحد مل من الـ bioretary + +606 +00:45:48,860 --> 00:45:53,940 +agent على كل التيوبات و أعمل mix بعدين بتعملها + +607 +00:45:53,940 --> 00:45:59,900 +incubation لمدة عشرين منه تخليها مدة عشرين دقيقة + +608 +00:45:59,900 --> 00:46:06,340 +على الـ room تنبرجها عشان يصير ارتفاعبعدين بدي أخد + +609 +00:46:06,340 --> 00:46:09,920 +كل تيوب من هذه التيوبات و أقرأها على جهاز + +610 +00:46:09,920 --> 00:46:14,780 +Spectrophotometer على طول موجي خمسمية و أربعين + +611 +00:46:14,780 --> 00:46:19,260 +نانو متر، إيش هيطلعلي؟ هيطلعلي absorb، يعني كل + +612 +00:46:19,260 --> 00:46:23,710 +تيوب بحطبيعطيني قراءة absorption الـ tube اللي + +613 +00:46:23,710 --> 00:46:28,550 +بعدها بيعطيني absorption وهكذا للسبعة tubeات فصار + +614 +00:46:28,550 --> 00:46:31,510 +عندي لل tubeات من واحد لستة معروف الـ + +615 +00:46:31,510 --> 00:46:35,550 +concentration ومعروف عندي absorption بس ال tube + +616 +00:46:35,550 --> 00:46:39,790 +رقم سبعة ال unknown بس معروف عندي absorption قرأت + +617 +00:46:39,790 --> 00:46:43,410 +على جهاز الـ spectrophotometer وعرفت ال absorption + +618 +00:46:43,410 --> 00:46:50,350 +ماقدرتش أعرف ال concentrationتمام هالجيت بعمل ال + +619 +00:46:50,350 --> 00:46:53,530 +standard curve برسم ال curve اللي هو عبارة عن + +620 +00:46:53,530 --> 00:46:57,450 +مضحنة حكاية سيني وصادي على الخط السيني بدي أرسم ال + +621 +00:46:57,450 --> 00:47:01,550 +concentration وعلى الصادي بدي أرسم ال absorption + +622 +00:47:02,360 --> 00:47:07,940 +بحط النقاط لـ Standard و بعدين بطلّع تركيز المادة + +623 +00:47:07,940 --> 00:47:11,640 +المجهولة أنا عارفة إيه لها absorption و بدي أطلّع + +624 +00:47:11,640 --> 00:47:15,440 +تركيزها من الـ standard gap إن شاء الله هذا كله + +625 +00:47:15,440 --> 00:47:21,460 +هيوضح معناه بالشغل و لما نوضحها بالمعنى بيحكيلي في + +626 +00:47:21,460 --> 00:47:25,820 +حاجة اسمها blank solution هو solution محلول بيحتوي + +627 +00:47:25,820 --> 00:47:29,140 +على little to no alkaline usually used to + +628 +00:47:29,140 --> 00:47:33,060 +calibrate an instrumentإنه هذا هو عبارة عن محلول، + +629 +00:47:33,060 --> 00:47:36,480 +بحطش فيه ولا أي شيء، ولا standard ولا sample، بس + +630 +00:47:36,480 --> 00:47:40,560 +بحط فيه الـreagent عشان الـreagent إيه اللون، إذا + +631 +00:47:40,560 --> 00:47:44,200 +فاتبين الـbio-reagent، لونه أزرق فجيت أنا لو هذا + +632 +00:47:44,200 --> 00:47:47,460 +اللون أنا حاططه على جهاز الـSpectrum، هيقرألي هذا + +633 +00:47:47,460 --> 00:47:52,960 +اللون الأزرقفهي يتلخبط ويعطيني قراءة زيادة من + +634 +00:47:52,960 --> 00:47:56,520 +اللون الأزرق الـ Reagent نفسه واللون بتاع التفاعل + +635 +00:47:56,520 --> 00:48:00,260 +مش الجهاز اللي بيقرأ كمية اللون فهيقرأ لون الـ + +636 +00:48:00,260 --> 00:48:05,920 +Reagent العصني وهيقرأ لون التفاعل فأنا بحط الـ + +637 +00:48:05,920 --> 00:48:09,720 +Tube بس تحتوي على الـ Reagent عشان أصفر عليها + +638 +00:48:09,720 --> 00:48:14,020 +الجهازإن الجهاز يقرأ كمية هذا اللون و بعد هي + +639 +00:48:14,020 --> 00:48:17,980 +يخصومها كأنه بده يخصومها من التيوبات التانية زي + +640 +00:48:17,980 --> 00:48:21,300 +إذا خدتوا في المقدمة كيف نوزن على الميزان كيف + +641 +00:48:21,300 --> 00:48:25,540 +بنستخدم الميزان بحط ال cup مثلا اللي بدي أوزن فيه + +642 +00:48:25,540 --> 00:48:28,660 +بدي أحط فيه المادة أول أجي بحط ال cup عشان إيه + +643 +00:48:28,660 --> 00:48:34,740 +الوزن بصفر عليه و بعدين بحط المادة عشان يشيل وزنة + +644 +00:48:34,740 --> 00:48:40,800 +ال cupوأنا بصفر على لون الـ region عشان بعد هيك + +645 +00:48:40,800 --> 00:48:46,240 +أشيل لون الـ region عشان يعملني calibration فالمرة + +646 +00:48:46,240 --> 00:48:50,620 +الجاي لما نشتغل هذه التجربة بدنا معانا ورق رسم + +647 +00:48:50,620 --> 00:48:55,260 +بياني عشان نرسم عليه الـ standard curve + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/vUaw7lH8dOs_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/vUaw7lH8dOs_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..4d754bdb8f22e2ed6aa5dd7e673ad9cce37977b5 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/vUaw7lH8dOs_postprocess.srt @@ -0,0 +1,748 @@ +1 +00:00:01,150 --> 00:00:05,090 +اليوم إن شاء الله راح نحكي في أول معمل من معامل + +2 +00:00:05,090 --> 00:00:09,690 +الكيميا الحيوية هيكون عبارة عن مقدمة عامة عن + +3 +00:00:09,690 --> 00:00:14,390 +المادة تعريف الكيميا الحيوية الأهداف العامة من + +4 +00:00:14,390 --> 00:00:20,150 +دراسة المصاق وليش احنا بندرسه هنتعرف فيه على ال + +5 +00:00:20,150 --> 00:00:23,910 +safe rule داخل المعمل قواعد السلامة والأمان داخل + +6 +00:00:23,910 --> 00:00:28,220 +المعملهنتعرف فيه على بعض الأدوات اللي هنستخدمها في + +7 +00:00:28,220 --> 00:00:34,100 +المعمل و هندخل في مقدمة بسيطة عن الأحماض الأمينية + +8 +00:00:34,100 --> 00:00:40,520 +في البداية خلينا نتعرف على تعريف ال biochemistry + +9 +00:00:40,520 --> 00:00:44,930 +اللي هي الكيميا الحيويةلما نحكي كيميا حيوية، إيش + +10 +00:00:44,930 --> 00:00:49,450 +بنستنتج منها؟ كيميا، كلمة كيميا معناها تفاعلات + +11 +00:00:49,450 --> 00:00:54,270 +كيميائية بدها تكون حيوية يعني تحدث في داخل جسم + +12 +00:00:54,270 --> 00:00:58,950 +الإنسان أو جسم الكائن الحي فهي تفاعلات كيميائية + +13 +00:00:58,950 --> 00:01:03,820 +تحدث في داخل أجسام الكائنات الحيةمش مكتوب هنا + +14 +00:01:03,820 --> 00:01:07,480 +مكتوب ان ال biochemistry is the application of + +15 +00:01:07,480 --> 00:01:10,680 +chemistry to study biological processes at the + +16 +00:01:10,680 --> 00:01:15,160 +cellular and molecular level هي تطبيق كيميائي + +17 +00:01:15,160 --> 00:01:21,440 +لدراسة العمليات الحيوية في داخل الخلايا تطبيق + +18 +00:01:21,440 --> 00:01:27,060 +كيميائي لدراسة العمليات الحيوية في داخل الخلايا + +19 +00:01:28,100 --> 00:01:31,500 +بحكي لي كمان إن ال biochemistry is also concerned + +20 +00:01:31,500 --> 00:01:34,800 +with the study of structure and function of + +21 +00:01:34,800 --> 00:01:39,100 +cellular components إن الكيميا الحيوية بتركز على + +22 +00:01:39,100 --> 00:01:47,580 +دراسة التركيب والوظيفةهي تطبيق يركز على دراسة + +23 +00:01:47,580 --> 00:01:50,700 +التركيب والوظيفة Structural and Function of + +24 +00:01:50,700 --> 00:01:54,360 +Cellular Components اللي هي المكونات الخلوية تركز + +25 +00:01:54,360 --> 00:01:58,960 +على دراسة التركيب ووظيفة المكونات الخلوية زي إيش + +26 +00:01:58,960 --> 00:02:02,600 +المكونات الخلوية؟ زي الـ protein، carbohydrates + +27 +00:02:02,600 --> 00:02:08,570 +واللبن اللي هنتعرف عليهم لقدامال biochemistry + +28 +00:02:08,570 --> 00:02:12,890 +مستنتج من هذه التعريف إنها عبارة عن both life + +29 +00:02:12,890 --> 00:02:17,800 +science and chemical scienceإنها علم كيميائي وعلم + +30 +00:02:17,800 --> 00:02:22,700 +حيوي هي علم كيميائي وعلم حيوي في داخل أجسام + +31 +00:02:22,700 --> 00:02:26,160 +الكائنات الحية عبارة عن دراسة التفاعلات الكيميائية + +32 +00:02:26,160 --> 00:02:30,860 +هي علم كيميائي وعلم حيوي life science and chemical + +33 +00:02:30,860 --> 00:02:35,000 +science it has provided explanation for the causes + +34 +00:02:35,000 --> 00:02:39,640 +of many diseases in humans بتخلينا نتعرف على + +35 +00:02:39,640 --> 00:02:44,200 +مسببات الأمراضمن خلال الكيميا الحيوية بقدر أعرف + +36 +00:02:44,200 --> 00:02:49,240 +مسببات أمرها مثلا إن عندي خلال فيه البروتين لو ما + +37 +00:02:49,240 --> 00:02:52,020 +جيست مستوى البروتين لاجيت فيه خلال فيه فبعرف إن + +38 +00:02:52,020 --> 00:02:57,820 +فيه منطقة لاتصنع بشكل صحيح Biochemistry is the + +39 +00:02:57,820 --> 00:03:00,420 +study of molecular structure and interaction + +40 +00:03:00,420 --> 00:03:03,770 +living organisms حكي هنا إنها بتدرسالتركيب + +41 +00:03:03,770 --> 00:03:07,270 +والوظيفة الـ structure و الـ function للمكونات + +42 +00:03:07,270 --> 00:03:11,350 +الخلوية Biochemists اللي هم الكيميائيين أخصائي + +43 +00:03:11,350 --> 00:03:18,510 +الكيميا seek to understand يسعوا إلى فهمالأجسام من + +44 +00:03:18,510 --> 00:03:23,550 +خلال التفاعلات الكيمية biochemist seek to + +45 +00:03:23,550 --> 00:03:26,730 +understand living organism in term of chemical + +46 +00:03:26,730 --> 00:03:31,430 +reaction أخصائي الكيميا يسعى إلى فهم طبيعة الأجسام + +47 +00:03:31,430 --> 00:03:37,270 +من خلال ال chemical reactionنيجي نتعرف على أهداف + +48 +00:03:37,270 --> 00:03:42,770 +دراسة المصاق ليش أنا بدرس مصاق الكيميا الحيوية؟ + +49 +00:03:42,770 --> 00:03:46,510 +objective of this course أول شيء to learn + +50 +00:03:46,510 --> 00:03:49,330 +fundamental technique used in biochemistry + +51 +00:03:49,330 --> 00:03:53,830 +لمعارفات التقنيات اللي بتفيد في الكيميا الحيوية + +52 +00:03:53,830 --> 00:03:59,410 +إيش أنا بستخدم تقنيات في الكيميا الحيوية؟تنين to + +53 +00:03:59,410 --> 00:04:02,930 +learn some biochemical procedure and experiments + +54 +00:04:02,930 --> 00:04:06,970 +commonly used in biochemistry laboratory عشان أعرف + +55 +00:04:06,970 --> 00:04:11,230 +الخطوات ال procedure يعني الخطوات اللي بستخدمها + +56 +00:04:11,230 --> 00:04:16,230 +لإجراء التجارب المختلفة أيش الخطوات المتبعة لإجراء + +57 +00:04:16,230 --> 00:04:21,670 +التجارب المختلفةتالت إشي to provide a basis for + +58 +00:04:21,670 --> 00:04:25,090 +understanding how biochemical data obtained + +59 +00:04:25,090 --> 00:04:31,470 +analyzed and presented عشان أعرف القواعد لتحليل + +60 +00:04:31,470 --> 00:04:37,310 +النتائج وأوضيها to provide a basis عشان تزودنا + +61 +00:04:37,310 --> 00:04:43,770 +بالقواعد لفهم المعلومات وتحليل النتائج هاي الأهداف + +62 +00:04:43,770 --> 00:04:44,610 +المصاق + +63 +00:04:47,260 --> 00:04:51,880 +بالنسبة لقواعد السلامة والأمان داخل المجتمع بيه ال + +64 +00:04:51,880 --> 00:04:56,400 +safety rules قواعد السلامة والأمان داخل المجتمع + +65 +00:04:56,400 --> 00:05:03,060 +عشان أحمي نفسي فبدنا نتعرف على قواعد السلامة أول + +66 +00:05:03,060 --> 00:05:07,040 +شي لازم ألبس ال coat ال coat بدي يكون طويل طوله + +67 +00:05:07,040 --> 00:05:12,460 +مناسبالشالة بحطها في داخل ال coat مخليهاش لبرا بدي + +68 +00:05:12,460 --> 00:05:16,520 +ألبس gloves قبل لا أشتغل بعد هيك إيش بيحكيلي + +69 +00:05:16,520 --> 00:05:19,780 +listen to or read instruction carefully before + +70 +00:05:19,780 --> 00:05:24,440 +attempting to do anything بدنا نستمع و نقرأ جيدا + +71 +00:05:24,440 --> 00:05:28,940 +الخطوات أكتر من مرة و أشوف المواد اللي أنا بحتاجها + +72 +00:05:28,940 --> 00:05:34,000 +و أحضر كل إشي clean up your lab area at the + +73 +00:05:34,000 --> 00:05:39,050 +conclusion of the laboratory periodبعد ما أخلص من + +74 +00:05:39,050 --> 00:05:43,050 +الشغل و كل شيء بدي أنظف ورايا يعني ال «بنش» بدي + +75 +00:05:43,050 --> 00:05:48,410 +أمسحها إذا خلصت إذا فيها نبيب بدي أغسلها إذا + +76 +00:05:48,410 --> 00:05:53,050 +الأدوات اللي أنا استخدمتها بدي أرجحها مكانها بدي + +77 +00:05:53,050 --> 00:05:56,990 +أرتب كل إشي مكاني after handling chemical remove + +78 +00:05:56,990 --> 00:05:59,970 +gloves and always wash your hands with soap and + +79 +00:05:59,970 --> 00:06:04,210 +water بعد ما أخلص خلصت كل الشغل بدي أشلح ال gloves + +80 +00:06:04,210 --> 00:06:07,130 +و بدي أغسل إيدي بالماء والصبون + +81 +00:06:09,630 --> 00:06:13,610 +هنا هنا قاعدة تحكي لي never trust any chemical you + +82 +00:06:13,610 --> 00:06:16,930 +should never trust anything in the lab ممنوع نطوق + +83 +00:06:16,930 --> 00:06:22,050 +أي مادة كيميائية أو أي مادة موجودة داخل المعمل لأي + +84 +00:06:22,050 --> 00:06:27,390 +سبب إن كان ممنوع نطوق أي مادة كيميائية كمان ممنوع + +85 +00:06:27,390 --> 00:06:32,810 +الأكل والشرب في داخل المعمل ممنوع منعم بادة للأكل + +86 +00:06:32,810 --> 00:06:39,620 +والشرب داخل المعملفيه هنا هنا حاجة بنسميها sign + +87 +00:06:39,620 --> 00:06:44,180 +for caution اللي هي إشارات الخطر إشارات الخطر هذه + +88 +00:06:44,180 --> 00:06:49,520 +عبارة عن رموز استخدمت لتسهيل التعامل بين الشركات + +89 +00:06:49,520 --> 00:06:55,060 +أو البلدان المختلفة عشاناللغة إشارات استعملة + +90 +00:06:55,060 --> 00:06:59,240 +لتسهيل التعامل تكون محطوطة على ججاجة المادة + +91 +00:06:59,240 --> 00:07:03,240 +الكيميائية فهو الإشارة flameable معناها قابل + +92 +00:07:03,240 --> 00:07:07,480 +للاشتعال إن المادة الكيميائية هي قابلة للاشتعال + +93 +00:07:07,480 --> 00:07:11,920 +فلازم أبعدها عن أي مصدر لهاالإشارة التانية بتدل + +94 +00:07:11,920 --> 00:07:15,400 +على إنها poison، يعني إنها سام، إن هذه المادة سام + +95 +00:07:15,400 --> 00:07:20,700 +الإشارة التالتة، biohazard، إنها خطر على الحياة إن + +96 +00:07:20,700 --> 00:07:24,840 +هذه المادة خطر، فيها infection، فيها عدوى مثلا زي + +97 +00:07:24,840 --> 00:07:30,110 +بكتيريا أو فيروس أو برزانالإشارة الرابعة معناها + +98 +00:07:30,110 --> 00:07:33,870 +corrosive corrosive معناها أنها مادة آكلة يعني + +99 +00:07:33,870 --> 00:07:38,370 +بتسبب تآكل الجلد لو أجي على الجلد بتسبب التآكل + +100 +00:07:38,370 --> 00:07:43,390 +الإشارة الأخيرة معناها radioactive radioactive + +101 +00:07:43,390 --> 00:07:49,510 +يعني إشعاع يعني أنها مادة مشعة أن هذه المادة مشعة + +102 +00:07:51,050 --> 00:07:54,890 +بنحكي عن حاجة بنسميها chemical hazard chemical + +103 +00:07:54,890 --> 00:07:59,670 +hazard معناها مخاطر كيميائية ما أني بتعامل مع مواد + +104 +00:07:59,670 --> 00:08:04,430 +كيميائية بجه فيه مخاطر ممكن تصير معايا أول إشي + +105 +00:08:04,430 --> 00:08:09,090 +بيحكيني never mix chemical together يعني ممنوع + +106 +00:08:09,090 --> 00:08:13,810 +نخلط المواد الكيميائية مع بعض إلا إذا أنا حكيتلك + +107 +00:08:13,810 --> 00:08:18,610 +اخلطي المادة هذه على هذه ممنوع أنتي تخلطي مادة + +108 +00:08:18,610 --> 00:08:23,430 +كيميائية على التانيةوإذا حكيتلك اخلطي مادة واحد + +109 +00:08:23,430 --> 00:08:27,470 +على مادة اتنين يعني تحطي واحد على اتنين مش هحط + +110 +00:08:27,470 --> 00:08:31,130 +اتنين على واحد زي ما حكيتلك على الترتيب بتعمل + +111 +00:08:31,130 --> 00:08:36,850 +العكس مينفعش لإن هاي مواد كيميائية حاجة تانية نفع + +112 +00:08:36,850 --> 00:08:41,590 +pure water and concentrated acid مينفعش أضيف المي + +113 +00:08:41,590 --> 00:08:45,990 +على الحمض إذا بدي أحط مي على الحمض بحط الحمض على + +114 +00:08:45,990 --> 00:08:53,730 +الماء مش الماء على الحمضالحمد يضاف على الماء وليس + +115 +00:08:53,730 --> 00:09:00,350 +الماء على الحمد تالت اشي بيحكيلي check labels on + +116 +00:09:00,350 --> 00:09:05,010 +container twice to make sure you use the right + +117 +00:09:05,010 --> 00:09:10,380 +chemicalلمّا بدي أستخدم مادة كيميائية بحكيلي تأكدي + +118 +00:09:10,380 --> 00:09:14,440 +و اقرأ مرة و اتنين الإشارة أو الورقة اللي بتكون + +119 +00:09:14,440 --> 00:09:17,480 +مكتوبة على الـ bottle عشان أتأكد أن هذه المادة + +120 +00:09:17,480 --> 00:09:21,860 +الصح اللي أنا بدي إياها و بدي أتأكد كمان من تاريخ + +121 +00:09:21,860 --> 00:09:24,960 +الإنتاج و تاريخ الانتهاء و إذا في إشارات خطر + +122 +00:09:24,960 --> 00:09:28,950 +موجودة على الـ bottleإذا بما إني بتعامل مع مواد + +123 +00:09:28,950 --> 00:09:32,830 +كيميائية، ممكن تواجهني مخاطر كيميائية، فأنا بدي + +124 +00:09:32,830 --> 00:09:39,830 +أكون حريصة و ألتزم بكل التعليمات طب إذا أنا عندي + +125 +00:09:39,830 --> 00:09:44,010 +مهنتة كيميائية و ضرورة أنا بدي أعرف شو هي، ممنوع + +126 +00:09:44,010 --> 00:09:45,370 +إحنا حاكينا نتوقع + +127 +00:09:49,560 --> 00:09:53,460 +لو احتجنا if you need to smell the odor of a + +128 +00:09:53,460 --> 00:09:58,540 +chemical كيف بتعمل برجع الججاجة أو البوتل للخلف + +129 +00:10:04,380 --> 00:10:09,320 +بحط إيدي عند الفوهة، كف الإيد و بعمل تقريب للأبخرة + +130 +00:10:09,320 --> 00:10:14,340 +تجيني أبخرة مخففة عن ناحية الفأنف و بشمها زي + +131 +00:10:14,340 --> 00:10:18,120 +الصورة الموجودة عندنا كيف حط إيده حط إيده على + +132 +00:10:18,120 --> 00:10:21,660 +الفوهة بيعمل تقريب لأبخرة مخففة عن ناحية الأنف + +133 +00:10:21,660 --> 00:10:26,590 +عشان يشم الريحةطيب before leaving the lab قبل ما + +134 +00:10:26,590 --> 00:10:31,130 +أغادر من المعمل لازم أعمل workplace reagent and + +135 +00:10:31,130 --> 00:10:34,310 +equipment should be put in order يعني ده رتب + +136 +00:10:34,310 --> 00:10:37,550 +المعمل وراي بدي أرجع المواد اللي استخدمتها و + +137 +00:10:37,550 --> 00:10:41,850 +الأدوات و أرتبها زي ما كانت و مش ده لعبة glass بدي + +138 +00:10:41,850 --> 00:10:46,050 +أخسم الأدوات اللي استخدمتها و بدي أ .. إذا استخدمت + +139 +00:10:46,050 --> 00:10:52,310 +الغاز بدي أسكس أمام الغاز و بدي أشتغل كفريق team + +140 +00:10:52,310 --> 00:10:58,930 +warبحكيلي هنا الأدوات اللي ممكن أستخدمها أولاشي + +141 +00:10:58,930 --> 00:11:02,290 +the only type of glassware that may safely be + +142 +00:11:02,290 --> 00:11:06,710 +heated is either chymex or pyrex أنه أنا هستخدم + +143 +00:11:06,710 --> 00:11:11,150 +زجاجيات هضطر لتسخين المواد اللي أنا بحتاجها فإذا + +144 +00:11:11,150 --> 00:11:15,730 +بدي أسخنها فالأكتر أمان أن أستخدم مواد مصنوعة من + +145 +00:11:15,730 --> 00:11:19,810 +مادة ال chymex أو ال pyrex هدول مواد مقاومة + +146 +00:11:19,810 --> 00:11:24,130 +للحرارة إذا عرضتها للهب بتكون مقاومة للحرارةطيب + +147 +00:11:24,130 --> 00:11:27,330 +النقطتين اللي بعد هيك بتحكوني أنه أنا لو بدي أسخن + +148 +00:11:27,330 --> 00:11:31,110 +المادة إيش بدي أعمل؟ كيف بدي أسخنها؟ أجيت المادة + +149 +00:11:31,110 --> 00:11:35,190 +بحطها في التيوب المصنعة من مواد مقاومة للحرارة + +150 +00:11:35,190 --> 00:11:39,030 +اللهب باجي لمصدر اللهب لازم يكون في وسط الbench + +151 +00:11:39,030 --> 00:11:44,530 +مايكونش على الطرف فأشغل اللهب و بعدين باجي للتيوب + +152 +00:11:44,530 --> 00:11:48,970 +اللي أنا بدي أسخنها فامسكها بملقط خشبي أو مصنوع من + +153 +00:11:48,970 --> 00:11:53,940 +الاستهلزو بمسك القنبوبة في هذا الملقطة و بحطها على + +154 +00:11:53,940 --> 00:11:58,900 +اللهب بشكل مائل و بضن أحرك فيها بركزهاش على اللهب + +155 +00:11:58,900 --> 00:12:04,860 +ولا بحطها بشكل عمودي و انما بشكل مائل و بضن أحرك + +156 +00:12:04,860 --> 00:12:10,120 +فيها لحد ما تسخن و بشيلها للوقت المحدد الفتحة تاعة + +157 +00:12:10,120 --> 00:12:11,980 +القنبوب بتكون على + +158 +00:12:16,030 --> 00:12:20,630 +المهم مش باتجاهي أو باتجاه زميلي لإن لو غلطت + +159 +00:12:20,630 --> 00:12:24,470 +المادة الكيميائية وطلعت ماتطلعش في وجه حدا أو + +160 +00:12:24,470 --> 00:12:30,120 +يتأذى حدامش هنحكي عن بعض الأدوات اللي هنستخدمها + +161 +00:12:30,120 --> 00:12:35,700 +أول أداة اسمها volumetric flask volumetric flask + +162 +00:12:35,700 --> 00:12:40,040 +مبوب زجاجي بناخد فيه حجم محدد بتكون في عنده علامة + +163 +00:12:40,040 --> 00:12:43,800 +فوق اللي هي الإشارة إذا عبّت لعندها معناها دي ساعة + +164 +00:12:43,800 --> 00:12:47,600 +كل ال volumetric flask كل مكتوب عليها ساعتها 250، + +165 +00:12:47,600 --> 00:12:51,580 +500، 150، اللي عند العلامة اللي عبيها يعني هذه + +166 +00:12:51,580 --> 00:12:56,340 +الساعة الليلةاسمها volumetric flask في عندنا + +167 +00:12:56,340 --> 00:13:00,480 +dropper، في عندنا كمان test tube لنحكي عن بعض + +168 +00:13:00,480 --> 00:13:04,360 +الأدوات اللي هنستخدمها volumetric flask مبوق زجاجي + +169 +00:13:04,360 --> 00:13:08,200 +علامة فوق اللي هي الإشارة إذا عبّت لعندها معناها + +170 +00:13:08,200 --> 00:13:11,260 +دي ساعة كل ال volumetric flask كل مكتوب عليها + +171 +00:13:11,260 --> 00:13:16,360 +ساعتها 250، 500، 150، اللي عند العلمة معبيها يعني + +172 +00:13:16,360 --> 00:13:21,350 +هذه الساعة الليلةاسمها volumetric flux في عندنا + +173 +00:13:21,350 --> 00:13:26,170 +دروبر، الدروبر هادي باخد فيه حجوم عشوائية في عندنا + +174 +00:13:26,170 --> 00:13:31,110 +balance ميزان أكيد بوزن فيه في عندنا سيلندر، هاد + +175 +00:13:31,110 --> 00:13:36,820 +عبارة عن أنبوب استواني مدرج باخد فيه حجمفي عندنا + +176 +00:13:36,820 --> 00:13:40,860 +funnel محجن زجاجي بينحط فيه حاجة بنسميها filter + +177 +00:13:40,860 --> 00:13:44,340 +paper اللي هي للفلترة بنستخدمهم ال funnel و ال + +178 +00:13:44,340 --> 00:13:48,940 +filter paper محجن زجاجي بستخدم فيه ورقة للفلترة + +179 +00:13:48,940 --> 00:13:53,880 +ورقة مسامية بتسمح بنزول السوائل دون الشوائب + +180 +00:13:53,880 --> 00:14:00,020 +بنسميها filter paperهنا كمان test tube brush اللى + +181 +00:14:00,020 --> 00:14:03,460 +هى الفرشاية اللى بنظف فيها القنابيب بعد ما اخلص من + +182 +00:14:03,460 --> 00:14:07,680 +الشغل بتهى نظف القنبوب بداخل الفرشاية بنظفها فهى + +183 +00:14:07,680 --> 00:14:10,840 +ان حاجة بنسميها clamps اللى هو الملقط اللى بمسك + +184 +00:14:10,840 --> 00:14:14,880 +فيه القنابيب لما نسخنها فهى ان حاجة 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"text": "الـ net charge في الوسط الحمدي صارت", "tokens": [6027, 39184, 2533, 4602, 8978, 2423, 41779, 9566, 21542, 2304, 16254, 20328, 9640, 2655], "avg_logprob": -0.234374996026357, "compression_ratio": 0.9482758620689655, "no_speech_prob": 0.0, "words": [{"start": 139.2, "end": 139.46, "word": "الـ", "probability": 0.5062255859375}, {"start": 139.46, "end": 139.58, "word": " net", "probability": 0.6123046875}, {"start": 139.58, "end": 140.06, "word": " charge", "probability": 0.90087890625}, {"start": 140.06, "end": 140.26, "word": " في", "probability": 0.7802734375}, {"start": 140.26, "end": 140.64, "word": " الوسط", "probability": 0.9778645833333334}, {"start": 140.64, "end": 141.1, "word": " الحمدي", "probability": 0.7699381510416666}, {"start": 141.1, "end": 141.72, "word": " صارت", "probability": 0.9778645833333334}], "temperature": 1.0}, {"id": 8, "seek": 17155, "start": 141.95, "end": 171.55, "text": "Positive charge لو أخدت هاد الوسط من الوسط المتعادل وحطته في وسط قاعده الوسط 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"temperature": 1.0}, {"id": 10, "seek": 21207, "start": 195.31, "end": 212.07, "text": "الـ net charge له بيكون minus ففي حالة الوسط الحمضي .. في حالة وسط متعادل ال net charge بتكون zero في حالة وسط حمضي بيكون ال net charge positive في حالة الوسط القاعدي ال net charge negative", "tokens": [6027, 39184, 2533, 4602, 46740, 4724, 1829, 30544, 3175, 6156, 41185, 11331, 6027, 3660, 2423, 41779, 9566, 21542, 2304, 11242, 1829, 4386, 8978, 11331, 6027, 3660, 46952, 9566, 44650, 3615, 18513, 1211, 2423, 2533, 4602, 39894, 30544, 4018, 8978, 11331, 6027, 3660, 46952, 9566, 11331, 2304, 11242, 1829, 4724, 1829, 30544, 2423, 2533, 4602, 3353, 8978, 11331, 6027, 3660, 2423, 41779, 9566, 25062, 995, 22488, 1829, 2423, 2533, 4602, 3671], "avg_logprob": -0.17352553320602632, "compression_ratio": 1.86, "no_speech_prob": 1.2814998626708984e-05, "words": [{"start": 195.31, "end": 195.57, "word": "الـ", "probability": 0.552978515625}, {"start": 195.57, "end": 195.67, "word": " net", "probability": 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688.21625, "duration_after_vad": 670.7228437500005} \ No newline at end of file diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/yXtOjcfTgyE_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/yXtOjcfTgyE_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..0d3b4b410419430e95577a40c528b19138843448 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/yXtOjcfTgyE_postprocess.srt @@ -0,0 +1,1392 @@ +1 +00:00:00,930 --> 00:00:05,190 +اليوم ده نحكي بموضوع الإنزيمات إيش انهاء + +2 +00:00:05,190 --> 00:00:09,450 +الإنزيمات، إيش العوامل اللي بتأثر على الإنزيم اللي + +3 +00:00:09,450 --> 00:00:14,990 +بتزيد من سرعة عمل الإنزيم والعوامل المثبتة للإنزيم + +4 +00:00:14,990 --> 00:00:19,990 +اللي بتقلل من عمل الإنزيم، اللي بتثبت الإنزيم + +5 +00:00:19,990 --> 00:00:24,270 +بيحكي ليه إن all chemical reactions in living + +6 +00:00:24,270 --> 00:00:27,930 +organisms require أنزيمto work for building + +7 +00:00:27,930 --> 00:00:32,150 +breaking down molecule or speed up the reaction ان + +8 +00:00:32,150 --> 00:00:37,250 +كل التفاعلات في جسم الإنسان تحتاج لوجود إنزين سواء + +9 +00:00:37,250 --> 00:00:41,850 +بناء سواء هدم كل هذه for speed up the reaction + +10 +00:00:41,850 --> 00:00:47,690 +لتسريع التفاعل في عندنا حاجة اسمها enzyme kinetics + +11 +00:00:47,690 --> 00:00:54,660 +enzyme kinetics هي دراسةمعدل حدوث التفاعل to study + +12 +00:00:54,660 --> 00:00:59,900 +the rate at which an enzyme works تفاعلات معدل + +13 +00:00:59,900 --> 00:01:06,560 +حدوث الانزيم معدل عمل الانزيم الانزيم هو عبارة عن + +14 +00:01:06,560 --> 00:01:11,120 +biological catalyst ومحفظ بيولوجي usually a + +15 +00:01:11,120 --> 00:01:16,840 +globular protein عادة هو عبارة عن بروتينproduced + +16 +00:01:16,840 --> 00:01:21,180 +by living organism يصنع في جسم الكائن الحي for + +17 +00:01:21,180 --> 00:01:24,640 +speed up specific chemical reaction without itself + +18 +00:01:24,640 --> 00:01:30,080 +destroyed or changed in any way بدون بيسرع التفاعل + +19 +00:01:30,080 --> 00:01:35,100 +وظيفته إنه يسرع التفاعل الكيميائي بدون ما يستهلك + +20 +00:01:35,100 --> 00:01:40,320 +أو إنه يتدمر أو يصير عليه تغيير في هذا التفاعل إذن + +21 +00:01:40,320 --> 00:01:45,440 +هو محفز بيولوجي عادة بيكون عبارة عن البروتينبينتج + +22 +00:01:45,440 --> 00:01:49,860 +في أجسام الكائنات الحية لتسريع التفاعل بدون ما + +23 +00:01:49,860 --> 00:01:54,380 +يصير عليه استهلاك أو تدمير أو تغيير، إنما بيخرج من + +24 +00:01:54,380 --> 00:01:58,520 +التفاعل زي ما دخل. They are reproduced by the + +25 +00:01:58,520 --> 00:02:01,280 +living organism and are usually present in only + +26 +00:02:01,280 --> 00:02:05,040 +very small amount in various cells، بينتج في أجسام + +27 +00:02:05,040 --> 00:02:08,780 +الكائنات الحية وبالعادة بيكون بكميات قليلة. + +28 +00:02:11,180 --> 00:02:19,500 +ما هي خصائص الانزيم؟ خصائص الانزيم الانزيم + +29 +00:02:19,500 --> 00:02:23,960 +لا يستهلك في التفاعل، بيدخل على التفاعل بيعمل على + +30 +00:02:23,960 --> 00:02:28,080 +تسريع التفاعل الكيميائي بدون ما يستهلك في التفاعل، + +31 +00:02:28,080 --> 00:02:33,040 +بعد ما يخلص التفاعل، بيطلع منه زي ما دخل انزيم لا + +32 +00:02:33,040 --> 00:02:38,120 +يتغير من نفسه، ولا بيسير عليه حتى أي تغيير، زي ما + +33 +00:02:38,120 --> 00:02:42,740 +دخله بيطلعreused again for the same reaction with + +34 +00:02:42,740 --> 00:02:46,640 +other molecules أقدر أستخدمه مرة تانية لنفس + +35 +00:02:46,640 --> 00:02:51,740 +التفاعل مع مادة تانية بستخدمه مرة تانية لنفس + +36 +00:02:51,740 --> 00:02:56,160 +التفاعل مع مادة تانية most enzyme are a protein + +37 +00:02:56,160 --> 00:02:59,800 +حكينا أنه usually عادة الإنزين بيكون عبارة عن + +38 +00:02:59,800 --> 00:03:04,600 +بروتين وglobular protein يعني بيكونtertiary أو + +39 +00:03:04,600 --> 00:03:08,560 +equaternal act as a catalyst to accelerate the + +40 +00:03:08,560 --> 00:03:13,600 +reaction انه بيعمل كمحفز لتسريع التفاعل are + +41 +00:03:13,600 --> 00:03:18,060 +specific for what they will catalyze وهو متخصص + +42 +00:03:18,060 --> 00:03:26,540 +لتفاعل معين كل إنزيم متخصص لإنه يسرع تفاعل معينكيف + +43 +00:03:26,540 --> 00:03:30,980 +بيشتغل الـ enzyme؟ الـ enzyme بيشتغل إنه عندنا الـ + +44 +00:03:30,980 --> 00:03:34,640 +enzyme فيه موقع اسمه الـ active site الـ active + +45 +00:03:34,640 --> 00:03:38,600 +site هو موقع نشط بترتبط فيه ال substrate اللي بدنا + +46 +00:03:38,600 --> 00:03:43,100 +نسرع إليها التفاعل في موقع في ال enzyme اسمه الـ + +47 +00:03:43,100 --> 00:03:47,300 +active site هذا بيشبه الإشي اللي أنا بدي أسرعه، + +48 +00:03:47,300 --> 00:03:51,080 +بيشبه ال substrate يعني كل enzyme متخصص حاجتنا + +49 +00:03:51,080 --> 00:03:55,670 +لتفاعل معينكيف متخصص إنه فيه موقع «active site» + +50 +00:03:55,670 --> 00:03:59,050 +بيشبه المادة اللي بدي أسرها؟ يعني على فرض في هذه + +51 +00:03:59,050 --> 00:04:02,190 +المعادلة، في هذه الدوران، إيش عندي؟ على الجنب، + +52 +00:04:02,190 --> 00:04:06,830 +بالأخطر، على الشمال، عندي substrate اسمه الساكروز، + +53 +00:04:06,830 --> 00:04:10,450 +سكر الساكروز، هذا سكر ثونائي عبارة عن اتحاد + +54 +00:04:10,450 --> 00:04:14,470 +جوليكوز والفراكتور، نعمله تكسير، نعمله عملية + +55 +00:04:14,470 --> 00:04:19,210 +breakdown عشان نتكون جوليكوز والفراكتورفبيجي هذا + +56 +00:04:19,210 --> 00:04:21,470 +الـ substrate اللي هو الـ Saccharose بيروح على + +57 +00:04:21,470 --> 00:04:25,970 +الإنزيم المتخصص له بيرتبط في الموقع اللي اسمه + +58 +00:04:25,970 --> 00:04:30,230 +active site في الفراغ اللي بالوسط، الإنزيم، + +59 +00:04:30,230 --> 00:04:34,150 +الإنزيم هو هذا اللي موقف فيه في الوسط فراغ، بيشبه + +60 +00:04:34,150 --> 00:04:36,790 +هذا الفراغ بيشبه مين؟ بيشبه الـ Saccharose، الـ + +61 +00:04:36,790 --> 00:04:39,950 +substrate بتيجي هذه الـ Saccharose بترتبط في هذا + +62 +00:04:39,950 --> 00:04:42,990 +الموقع، في الـ active site بيكوّن الإنزيم مع + +63 +00:04:42,990 --> 00:04:46,900 +substrate complexبيصير التفاعل اللي هو عبارة عن + +64 +00:04:46,900 --> 00:04:50,100 +تكسير الـ substrates فبتتحول الـ substrates إلى + +65 +00:04:50,100 --> 00:04:54,200 +product دخلت و بدأت تتحول الحين ل product، لنواتج + +66 +00:04:54,200 --> 00:04:57,840 +نواتج هي مرتبطة في الانزيم، فبنسميه انزيم مع + +67 +00:04:57,840 --> 00:05:02,060 +product بعد هي بتتحرر ال product هذه النواتج بتطلع + +68 +00:05:02,060 --> 00:05:06,340 +برا الانزيم والانزيم بيطلع زي ما دخل بدون أي تغيير + +69 +00:05:06,340 --> 00:05:11,540 +ال product بتتحرر من الانزيم والانزيم بيطلع زي ما + +70 +00:05:11,540 --> 00:05:16,650 +هو بدون أي تغييرعنا المعادلة اللي كيف بيشتغل + +71 +00:05:16,650 --> 00:05:20,230 +الانزيم أول حاجة بتيجي انزيم ترتبط مع substrate + +72 +00:05:20,230 --> 00:05:23,730 +انزيم زائد substrate بيعطيني انزيم و substrate + +73 +00:05:23,730 --> 00:05:27,190 +complex بعدين substrate تحول ل product فبيعطيني + +74 +00:05:27,190 --> 00:05:31,810 +انزيم زائد product ال substrate اتحولت إلى نواتر + +75 +00:05:31,810 --> 00:05:37,240 +إلى productكيف بيشتغل الانزين مع الـ Substrate؟ + +76 +00:05:37,240 --> 00:05:41,020 +كيف بيرتبطه؟ حكينا بموقع اسمه الـ ActiveCyan هذا + +77 +00:05:41,020 --> 00:05:46,200 +الموقع بس له تركيب مشابه لتركيب الـ Substrate اللي + +78 +00:05:46,200 --> 00:05:52,600 +خاص في هذا الانزينعلى مبدأ اسمه look and key + +79 +00:05:52,600 --> 00:05:57,200 +hypothesis اللي هو خاصية القفل والمفتاح زي مثلا + +80 +00:05:57,200 --> 00:06:01,160 +عندنا لما يكون عندنا جفن القفل هاد بس وإله مفتاح + +81 +00:06:01,160 --> 00:06:05,700 +واحد بيفتحه بيدخل فيه وبيقدر يفتحه والإنزيم زي هاد + +82 +00:06:05,700 --> 00:06:09,900 +عنده موقع اسمه active site ترتبط معاه substrate + +83 +00:06:09,900 --> 00:06:13,820 +متخصصة فيه بس هو إله بيشبهه هذا الموقع اللي بيشبه + +84 +00:06:13,820 --> 00:06:17,260 +زي إن هنا الجطعة اللي اللونها زهر هي اللي على + +85 +00:06:17,260 --> 00:06:21,690 +الجنبهذا الـ substrate والأصفر الانزين طالع على + +86 +00:06:21,690 --> 00:06:24,910 +الانزين من الجنب فيه موقع اسمه الـ Active site + +87 +00:06:24,910 --> 00:06:29,210 +بيشبه تركيب الـ substrate بتيجي السبستريات بترتبط + +88 +00:06:29,210 --> 00:06:33,750 +في هذا الموقع بيكوّن انزين substrate complex تكون + +89 +00:06:33,750 --> 00:06:37,330 +هذا ال complex بيصير التفاعل ان السبستريات هيدا + +90 +00:06:37,330 --> 00:06:41,970 +تتحول لبردعبتتحول ل product مرتبطة في الانزيم + +91 +00:06:41,970 --> 00:06:46,090 +فبتكون الانزيم و product بعد هيك بيتحرر ال product + +92 +00:06:46,090 --> 00:06:50,970 +بتطلع و بيطلع الانزيم زي ما هو زي ما دخل و بيطلع و + +93 +00:06:50,970 --> 00:06:57,850 +بقدر استخدمه مرة تانية في تفاعل تانيأجيت أنا عندي + +94 +00:06:57,850 --> 00:07:02,330 +تفاعل أي تفاعل كيف بدي أخليه يكون سريع making + +95 +00:07:02,330 --> 00:07:06,310 +reaction go faster يعني بدي أسرع التفاعل بيحكيلي + +96 +00:07:06,310 --> 00:07:10,230 +عند رفع درجة الحرارة الجزيئات بتتحرك أسرع + +97 +00:07:10,230 --> 00:07:12,950 +increasing the temperature make molecule move + +98 +00:07:12,950 --> 00:07:17,410 +faster إذا أنا رفعت درجة الحرارة الجزيئات بتتحرك + +99 +00:07:17,410 --> 00:07:24,120 +أسرع فالتفاعل هيكون أسرعلكن biological systems are + +100 +00:07:24,120 --> 00:07:27,660 +very sensitive to temperature change إن جسم + +101 +00:07:27,660 --> 00:07:32,180 +الإنسان حساس للتغير في درجة الحرارة إذا قالت في + +102 +00:07:32,180 --> 00:07:35,280 +عندي تفاعل في جسم الإنسان، في داخل جسم الإنسان + +103 +00:07:35,280 --> 00:07:39,140 +وهذا التفاعل أنا بدي أسرعلو رفعتي درجة الحرارة + +104 +00:07:39,140 --> 00:07:43,340 +هيأثر على جسم الإنسان فإن رفع درجات الحرارة + +105 +00:07:43,340 --> 00:07:48,060 +لتفاعلات بتحدث داخل جسم الإنسان بتأثر و تأثير عنها + +106 +00:07:48,060 --> 00:07:52,340 +تأثيرات، بينتج عنها تأثيرات فكيف بدي أسرع التفاعل + +107 +00:07:52,340 --> 00:07:56,380 +في داخل جسم الإنسان؟ بالإنزيم enzymes can increase + +108 +00:07:56,380 --> 00:07:58,760 +the rate of reaction without increasing the + +109 +00:07:58,760 --> 00:08:03,500 +temperature استخدم إنزيم بيرفع معدل حدوث التفاعل + +110 +00:08:03,500 --> 00:08:09,040 +بدون ما يزود درجة الحرارةwithout increasing the + +111 +00:08:09,040 --> 00:08:13,400 +temperature النزيم بيسرع التفاعل بدون زيادة درجة + +112 +00:08:13,400 --> 00:08:16,740 +الحرارة طب كيف بيشتغل النزيم؟ بيزودش درجة الحرارة، + +113 +00:08:16,740 --> 00:08:21,280 +شو بيسوي؟ بيقلل حاجة بنسميها ال activation energy، + +114 +00:08:21,280 --> 00:08:26,480 +اللي هي طاقة التنشيط، بيقلل الطاقة اللازمة لحدوث + +115 +00:08:26,480 --> 00:08:32,100 +التفاعللذن الإنزيم بيقلل وجود حدوث التفاعل عن طريق + +116 +00:08:32,100 --> 00:08:36,900 +تقليل الطاقة اللازمة وبالتالي بيسرع التفاعل بدون + +117 +00:08:36,900 --> 00:08:41,960 +تغيير درجة الحرارة لأنه إذا غيرت درجة الحرارة داخل + +118 +00:08:41,960 --> 00:08:45,880 +جسم الإنسان لها تأثيرات ممكن يصير denaturation + +119 +00:08:45,880 --> 00:08:50,380 +تدمير للإنزيمات لأن معظم الإنزيمات هي بروتينات + +120 +00:08:50,380 --> 00:08:58,010 +فهتتأثر بدرجة الحرارةهنا عندنا رسم، رسم ليه؟ إنه + +121 +00:08:58,010 --> 00:09:02,870 +التفاعل كده هيستهلك طاقة لو كان موجود الإنزيم، ولو + +122 +00:09:02,870 --> 00:09:05,870 +التفاعل ماشي بدون وجود الإنزيم، كده هياخد طاقة + +123 +00:09:05,870 --> 00:09:10,890 +الخط المتقطع، اللي هو قمة أعلى، عند القمة، الخط + +124 +00:09:10,890 --> 00:09:15,490 +المتقطع مش مكتوب activation energy without انزعج، + +125 +00:09:15,490 --> 00:09:21,360 +إنه هانحدوث التفاعل بدون وجود الانزيم استهلك طاقة + +126 +00:09:21,360 --> 00:09:25,200 +أعلى إذا الطاقة اللي استهلاكها التفاعل في عدم وجود + +127 +00:09:25,200 --> 00:09:29,480 +الانزيم هتكون أعلى يعني هيمشي التفاعل أبطأ في الخط + +128 +00:09:29,480 --> 00:09:33,440 +اللي تحته مكتوب انه activation energy with enzyme + +129 +00:09:33,440 --> 00:09:38,540 +جديش استهلك طاقة في وجود الانزيم كانت الطاقة أقل + +130 +00:09:38,540 --> 00:09:44,440 +فبنستنتج أن الانزيم يعمل على تقليل الطاقة اللازمة + +131 +00:09:44,440 --> 00:09:50,290 +للتفاعلوبسرع التفاعل بدون الحاجة إلى تغيير درجة + +132 +00:09:50,290 --> 00:09:55,960 +الحرارةعوامل بتأثر على نشاط الإنزين factor + +133 +00:09:55,960 --> 00:10:00,380 +affecting enzyme activity ما هي العوامل اللي بتأثر + +134 +00:10:00,380 --> 00:10:04,040 +على نشاط الإنزين؟ في عندنا عدة عوامل أول عامل + +135 +00:10:04,040 --> 00:10:07,820 +substrate concentration تركيز ال substrate اللي هي + +136 +00:10:07,820 --> 00:10:11,220 +المادة اللي بدأ ترتبط مع الإنزين عشان ينشطها عشان + +137 +00:10:11,220 --> 00:10:15,020 +يسرع التفاعل فالتركيز المادة بيأثر على نشاط + +138 +00:10:15,020 --> 00:10:20,410 +الإنزينالـ pH درجة الـ pH بتأثر على نشاط الانزين + +139 +00:10:20,410 --> 00:10:25,170 +temperature درجة الحرارة بتأثر ال inhibitor اللي + +140 +00:10:25,170 --> 00:10:31,730 +هي المثبتات بتثبت عمل الانزين هتأثر أكيد على نشاط + +141 +00:10:31,730 --> 00:10:37,130 +الانزين هندرس واحدة واحدة من هدول العوامل نيجي + +142 +00:10:37,130 --> 00:10:39,650 +لأول عامل من العوامل اللي هو ال substrate + +143 +00:10:39,650 --> 00:10:44,490 +concentration تركيز ال substrate كيف يؤثر على نشاط + +144 +00:10:44,490 --> 00:10:49,200 +الانزيناللي جيت لو نعتبر أنه عندي أنزيمات موجودة + +145 +00:10:49,200 --> 00:10:53,040 +هاي الانزيم كل انزيم له substrate ييجي الانزيم + +146 +00:10:53,040 --> 00:10:56,820 +الهول بيرتبط مع ال substrate في موقع الactive site + +147 +00:10:56,820 --> 00:11:01,300 +بيرتبط الانزيم بال substrate لما ما هيسرع التفاعل + +148 +00:11:01,300 --> 00:11:05,060 +إذا أجى انزيم تاني ويرتبط بال substrate هيزمش + +149 +00:11:05,060 --> 00:11:09,040 +التفاعل أسرع من الأول من واحد لحاله لما يكونوا + +150 +00:11:09,040 --> 00:11:12,340 +اتنينهل هيكون التفاعل أسرع لما يكون اندي أنزيم + +151 +00:11:12,340 --> 00:11:16,040 +واحد مرتبط بsubstrate أو أنزيمين وكل واحد مرتبط + +152 +00:11:16,040 --> 00:11:19,980 +بsubstrate أكيد وجود أنزيمين هيسرع التفاعل أكتر + +153 +00:11:19,980 --> 00:11:23,580 +ولو جيبت كمان أنزيم تالت مرتبط بsubstrate هيسرع + +154 +00:11:23,580 --> 00:11:28,040 +التفاعل أكتر والرابع برضه هيسرع التفاعل أكتر وهكذا + +155 +00:11:28,820 --> 00:11:33,180 +فكل ما زاد الـ substrate concentration تركيز الـ + +156 +00:11:33,180 --> 00:11:37,300 +substrate كل ما زاد تركيز الـ substrate هيزيد + +157 +00:11:37,300 --> 00:11:42,240 +الإرتباط بين أنزيمه و substrate هيسرع التفاعل أكتر + +158 +00:11:42,240 --> 00:11:48,260 +يعني العلاقة ترضية ما بين تركيز ال substrate و + +159 +00:11:48,260 --> 00:11:54,420 +سرعة التفاعلكل ما أضيف substrate بتزيد سرعة + +160 +00:11:54,420 --> 00:11:59,600 +التفاعل فالعلاقة ترضية the increase in velocity is + +161 +00:11:59,600 --> 00:12:03,200 +proportional to the substrate concentration إن + +162 +00:12:03,200 --> 00:12:08,020 +سرعة التفاعل زيادة سرعة التفاعل هي علاقة ترضية مع + +163 +00:12:08,020 --> 00:12:14,130 +تركيز ال substrateهنا المخطط التاني اللي حكيناه + +164 +00:12:14,130 --> 00:12:18,130 +بالأول ان العلاقة ترضي بين تركيز ال substrate + +165 +00:12:18,130 --> 00:12:24,340 +وصورة التفاعل الكيمياطيب، هل هذه العلاقة ترضية إلى + +166 +00:12:24,340 --> 00:12:28,580 +ما لنهايها تستمر ترضية إن أنا كل ما أضيف substrate + +167 +00:12:28,580 --> 00:12:32,660 +هتزيد سرعة التفاعل كل ما أضيف substrate بتزيد سرعة + +168 +00:12:32,660 --> 00:12:38,040 +التفاعل؟ لأ، هذه العلاقة إلها حد معين كافي يعني، + +169 +00:12:38,040 --> 00:12:42,340 +أنا جيتلى نفرض إن هذا المكان فيه أربع إنزيمات بس، + +170 +00:12:42,340 --> 00:12:46,520 +لو أنا أضفت substrate، بيتصبط مع الإنزيم الأول و + +171 +00:12:46,520 --> 00:12:51,020 +بيسرع التفاعللو ضفتني substrate تاني بيرتبط مع + +172 +00:12:51,020 --> 00:12:55,140 +الانزيم التاني والتفاعل بيمشي أسرع أكتر طب لو ضفت + +173 +00:12:55,140 --> 00:12:58,360 +substrate تالت برضه هيرتبط مع الانزيم التالت + +174 +00:12:58,360 --> 00:13:03,060 +الموجود ويسرع التفاعل أكتر يعني كل ما أضيف + +175 +00:13:03,060 --> 00:13:05,900 +substrate بيرتبط مع الانزيم بيسرع التفاعل بيصير + +176 +00:13:05,900 --> 00:13:09,960 +أسرع حتى الآن العلاقة ترضيه طب عندي أخر انزيم Dial + +177 +00:13:09,960 --> 00:13:14,020 +الرابع لو ضفت عليه substrate هيرتبط مع الانزيم + +178 +00:13:14,020 --> 00:13:17,830 +ويسرع التفاعل أسرعهلقيت؟ خلصوا الانزيمات + +179 +00:13:17,830 --> 00:13:22,670 +الموجودات، كل انزيم صار مرتبط ب substrate و سرعوا + +180 +00:13:22,670 --> 00:13:26,950 +التفاعل، هلقيت؟ أنا لو ضفت substrate خامس، هلفي + +181 +00:13:26,950 --> 00:13:30,890 +انزيم إنه ييجي يرتبط فيه هذا ال substrate؟ لأ، فال + +182 +00:13:30,890 --> 00:13:33,670 +substrate اللي أنا ضفته، هلقيت؟ الخامس مشيله + +183 +00:13:33,670 --> 00:13:38,540 +انزيم، فمش هيرتبط ولا هيمشي التفاعل أسرعالجد فانا + +184 +00:13:38,540 --> 00:13:43,680 +خلاص ان كل الانزيمات صارت متشبعة كل انزيم مرتبط ب + +185 +00:13:43,680 --> 00:13:47,720 +substrate فمهما أضيف substrate مش هيلاجي انزيم + +186 +00:13:47,720 --> 00:13:51,600 +يرتبط فيه فهنا أنا بكون وصلت لنقطة اسمها + +187 +00:13:51,600 --> 00:13:57,000 +saturation pointSaturation point هي نقطة التشبع + +188 +00:13:57,000 --> 00:14:02,280 +اللى عندها بتكون كل الانزيمات مرتبطة بالsubstrate + +189 +00:14:02,280 --> 00:14:06,160 +فانا لو ضفت substrate جديد مش هيلاقي انزيم يرتبط + +190 +00:14:06,160 --> 00:14:10,720 +فيه فمش هيسرها التفاعل فخلاص عند الانزيم الرابع كل + +191 +00:14:10,720 --> 00:14:14,980 +الانزيمات مرتبطة هيأقصى سرعة للتفاعل الكيميائي + +192 +00:14:14,980 --> 00:14:22,090 +نسميها VmaxVmax هي أقصى سرعة يصل إليها التفاعل + +193 +00:14:22,090 --> 00:14:26,310 +الكيميائي هذه الـ maximum velocity هي أقصى سرعة + +194 +00:14:26,310 --> 00:14:30,290 +بيصل إليها التفاعل الكيميائي عند هذه الـ Vmax + +195 +00:14:30,290 --> 00:14:34,650 +بتكون كل الإنزيمات مرتبطة بـ substrate ومسارعة + +196 +00:14:34,650 --> 00:14:39,170 +للتفاعل بتكون كلها متشبعة كل الإنزيمات saturation + +197 +00:14:39,170 --> 00:14:43,410 +with substrate كل إنزيم مرتبط بـ substrate مهما + +198 +00:14:43,410 --> 00:14:47,290 +أضيف substrate مش هلاجي إنزيم مرتبط فيهفخلاص مش + +199 +00:14:47,290 --> 00:14:50,910 +هيأثر على سرعته التفاعل إيش بده يعمل في التفاعل؟ + +200 +00:14:50,910 --> 00:14:54,830 +مافيش إنزيم يرتبط فيه، مش هيأثر أنا عندما تتشبع كل + +201 +00:14:54,830 --> 00:14:59,710 +إنزيم substrate مهما أضيف substrate مش هيأثر على + +202 +00:14:59,710 --> 00:15:04,030 +سرعته التفاعل الكيميائي فكون أنا وصلت لحاجة اسمها + +203 +00:15:04,030 --> 00:15:09,590 +الـ Vmaxالـ maximum velocity هي أقصى سرعة يصل + +204 +00:15:09,590 --> 00:15:14,350 +إليها التفاعل الكيميائي و عندها بتكون كل الإنزيمات + +205 +00:15:14,350 --> 00:15:19,470 +متشبعة مرتبطة بـ substrate هل جيت بيحكيلي عن نص + +206 +00:15:19,470 --> 00:15:24,710 +Vmax نص Vmax نص السرعة القصوة هاي يعني نصها في + +207 +00:15:24,710 --> 00:15:31,830 +حاجة اسمها KM يعني نص Vmax في حاجة اسمها KM إيش هي + +208 +00:15:31,830 --> 00:15:38,510 +KM؟KM هي تركيز الـ substrate اللازم للوصول إلى نُص + +209 +00:15:38,510 --> 00:15:44,530 +سرعة التفاعل الكيميائي KM هي تركيز الـ substrate + +210 +00:15:44,530 --> 00:15:50,230 +اللازم للوصول إلى نُص سرعة التفاعل الـ factor + +211 +00:15:50,230 --> 00:15:54,730 +reaction faster reaction but it reach a saturation + +212 +00:15:54,730 --> 00:15:58,730 +point when all the enzyme molecules are occupied + +213 +00:15:58,730 --> 00:16:03,280 +للـ Vmaxبحكي لأن العلاقة ترضية صحيح بين + +214 +00:16:03,280 --> 00:16:06,620 +الـSubstration، بين الـSubstrate، Concentration، + +215 +00:16:06,620 --> 00:16:10,700 +بين تركيز الـSubstrate وسرعة التفاعل، إنه هيسرع + +216 +00:16:10,700 --> 00:16:15,700 +التفاعل، ولكن لعند متى الوصول إلى نقطة + +217 +00:16:15,700 --> 00:16:20,280 +الـSaturation Point، نقطة التشبط، عندها بتكون كل + +218 +00:16:20,280 --> 00:16:25,600 +الإنزيمات مرتبطة بـSubstrate، فبتكون، بنسميها، + +219 +00:16:25,600 --> 00:16:31,270 +«High V Map»في عندنا ميشيل و مينتن اللي هم معالمين + +220 +00:16:31,270 --> 00:16:34,470 +حطوا قانون بيحكي أنه at low substrate + +221 +00:16:34,470 --> 00:16:37,970 +concentration the enzyme is not saturated with the + +222 +00:16:37,970 --> 00:16:41,430 +substrate and the reaction is not proceeding at + +223 +00:16:41,430 --> 00:16:45,010 +maximum velocity whereas when the enzyme is + +224 +00:16:45,010 --> 00:16:48,410 +saturated with substrate maximum velocity is + +225 +00:16:48,410 --> 00:16:53,160 +observedعايش ملخص هذا الحكي أنه لما يكون تركيز ال + +226 +00:16:53,160 --> 00:16:57,260 +substrate قليل الإنزيمات بتكونش متشبعة بال + +227 +00:16:57,260 --> 00:17:00,860 +substrate بتكونش كل الإنزيمات مرتبطة بال substrate + +228 +00:17:00,860 --> 00:17:05,420 +مهما كل substrate بيرتبط مع أنزيم ولكن غير متشبع + +229 +00:17:05,420 --> 00:17:09,310 +لأن تركيز ال substrate لسه قليلفي هذه الحالة مش + +230 +00:17:09,310 --> 00:17:13,090 +هنوصل للـ maximum velocity إلى أقصى سرعة للتفاعل + +231 +00:17:13,090 --> 00:17:17,930 +مش هنوصلها بينما لما تكون الانزيمات متشبعة بال + +232 +00:17:17,930 --> 00:17:21,190 +substrate خلاص كل الانزيمات مرتبطة بال substrate + +233 +00:17:21,190 --> 00:17:25,510 +فأنا باصل لـ maximum velocity اللي عندها بتكون + +234 +00:17:25,510 --> 00:17:31,110 +نقطة تتشبع ليه الـ saturated pointعشان هيك العلاقة + +235 +00:17:31,110 --> 00:17:35,370 +طردية ما بين تركيز الـsubstrate وسرعة التفاعل + +236 +00:17:35,370 --> 00:17:39,210 +الكيميائي لكنها مش علاقة طردية لما لا نهاية ولا + +237 +00:17:39,210 --> 00:17:43,910 +انما وصولها إلى نقطة الـsaturated point إلى نقطة + +238 +00:17:43,910 --> 00:17:49,390 +التشبع بيثبت المنحنة وتبطل العلاقة طردية بيصيرش كل + +239 +00:17:49,390 --> 00:17:55,030 +ما يزيد تركيز الـsubstrate انه يزيد سرعة التفاعل + +240 +00:17:56,370 --> 00:18:00,070 +هنا عندنا القانون «ميشيلز أنمينتين إكوايشن» هذا + +241 +00:18:00,070 --> 00:18:03,590 +القانون مش مطلوب منها بس ضروري أننا نعرفه الـKM + +242 +00:18:03,590 --> 00:18:08,630 +اللي هي تركيز السبسترات عند نص Vmax الـKM حكينا + +243 +00:18:08,630 --> 00:18:13,990 +عنها قبل هيك اللي هي تركيز السبسترات عند نص Vmax + +244 +00:18:13,990 --> 00:18:17,870 +عامل التاني من العوامل اللي بتأثر على نشاط الإنزيم + +245 +00:18:17,870 --> 00:18:21,770 +هو الـpH الـpH بيحكي الـextreme pH level + +246 +00:18:21,770 --> 00:18:26,180 +والـdenaturated enzymeالـ pH التغيير في الـ pH + +247 +00:18:26,180 --> 00:18:31,080 +بيعمل denaturation للإنزيم بيعمل تشوّه لشكل + +248 +00:18:31,080 --> 00:18:35,080 +الإنزيم بيعمل denaturation يعني تشوّه لشكل الإنزيم + +249 +00:18:35,080 --> 00:18:40,060 +معظم إنزيمات اللي في جسم الإنسان بتشتغل عند pH من + +250 +00:18:40,060 --> 00:18:45,160 +6 إلى 8 most human enzyme work at pH من 6 إلى 80 + +251 +00:18:45,160 --> 00:18:49,240 +بناء على عش أنه هي من 6 إلى 8depend on its + +252 +00:18:49,240 --> 00:18:52,780 +location in the body في إنزيمات برضه بتختلف، + +253 +00:18:52,780 --> 00:18:57,320 +بتشتغلش من 6 ل 8، بناء على موقعها في جسم الإنسان، + +254 +00:18:57,320 --> 00:19:00,940 +وين هي موجودة، في أي مكان زي مثلا الـPepsin، هذا + +255 +00:19:00,940 --> 00:19:05,120 +موجود في الـstomach، في المعدة، ولمّا المعدة وسطها + +256 +00:19:05,120 --> 00:19:08,860 +حمضي، فهو بيشتغل على pH زي المكان اللي هو فيه، + +257 +00:19:08,860 --> 00:19:13,120 +بيعمل على pH 3الـ Trypsin موجود في الـ small + +258 +00:19:13,120 --> 00:19:17,140 +intestine في الأمعاء والأمعاء وسطها قاعدة فهذا + +259 +00:19:17,140 --> 00:19:21,040 +بيشتغل عند pH 8 زي المكان اللي هو موجود فيه + +260 +00:19:21,040 --> 00:19:24,880 +فالإنزيمات الموجودة في الـ GSM تشتغل عند pH حسب + +261 +00:19:24,880 --> 00:19:29,850 +المكان اللي هي موجودة فيه معظمها عند 6 لـ 8طب لو + +262 +00:19:29,850 --> 00:19:33,130 +اتغيرت ال pH لهذا الانزيم يعني مثلا ال بيبسين + +263 +00:19:33,130 --> 00:19:36,630 +بيشتغل عند تلاتة لو حطته على تمانية يشتغل عند pH + +264 +00:19:36,630 --> 00:19:40,370 +تمانية بيحكي اللي بيصير تشوه في شكل الانزيم بيصير + +265 +00:19:40,370 --> 00:19:43,690 +عليه denaturation فال structure of انزيم is + +266 +00:19:43,690 --> 00:19:48,190 +changed شكل الانزيم وتركيبته هتختلف لما يصير تشوه + +267 +00:19:48,190 --> 00:19:53,150 +للانزيم تركيب هذا الانزيم ممكن يختلف، هيختلفإيش + +268 +00:19:53,150 --> 00:19:55,910 +ممكن يختلف فيه؟ الـ Active site موقع الـ Active + +269 +00:19:55,910 --> 00:19:59,930 +site حكينا هذا ملائم للـ Substrate شكله زي شكل الـ + +270 +00:19:59,930 --> 00:20:02,190 +Substrate بتيجي ال Substrate بترتبط في هذا الـ + +271 +00:20:02,190 --> 00:20:06,890 +Active site إذا تغيرت الـ pH بيصير فينا تشوة فشكل + +272 +00:20:06,890 --> 00:20:11,490 +الـ Active site هذا مع التشوة هيتغير هيبطل ملائم + +273 +00:20:11,490 --> 00:20:14,410 +لل Substrate بتيجي ال Substrate ده ترتبط مع + +274 +00:20:14,410 --> 00:20:18,250 +الانزيم في موقع الـ Active site بتلاقي بتقدرش + +275 +00:20:18,250 --> 00:20:21,850 +ترتبط فيه لأنه مش ملائم لشكلها بتقدرش تيجي ترتبط + +276 +00:20:21,850 --> 00:20:25,510 +فيهالـ active site is distorted and the substrate + +277 +00:20:25,510 --> 00:20:29,510 +molecule will no longer fit in it أنه ال active + +278 +00:20:29,510 --> 00:20:33,510 +site صار عليه تشوي وصار تدمين فال substrate + +279 +00:20:33,510 --> 00:20:37,810 +molecule مش ملائم لها هذا الشكل مش هتقدر تيجي + +280 +00:20:37,810 --> 00:20:39,510 +ترتبط مع الانزين + +281 +00:20:43,260 --> 00:20:49,000 +هنا مخطط بيوضّح أن الـ pH، optimum pH للبيبسين، + +282 +00:20:49,000 --> 00:20:52,420 +هيله بالأحمر البيبسين القمة اللي هو هين بيشتغل عند + +283 +00:20:52,420 --> 00:20:56,360 +تلاتة أعلى اللي عمل لهذا الانزيم عند pH تلاتة + +284 +00:20:56,360 --> 00:21:00,160 +لتريبسين أعلى pH اللي هو الأزراج القمة اللي هو + +285 +00:21:00,160 --> 00:21:03,380 +أعلى يشير عند تمانية أعلى reaction اللي هو بيكون + +286 +00:21:03,380 --> 00:21:09,640 +عند pH تمانية العامل اللي بعدين بيأثر على رشاط + +287 +00:21:09,640 --> 00:21:13,850 +الانزيم هو الـ temperature، درجة الحرارةبحكي لدرجة + +288 +00:21:13,850 --> 00:21:18,030 +الحرارة اللي بتأثر على معدل الإنزيم optimum + +289 +00:21:18,030 --> 00:21:21,890 +temperature أفضل درجة حرارة لعمل الإنزيم ويكون + +290 +00:21:21,890 --> 00:21:25,490 +نشيط اللي هو نشاط الإنزيم في عالة نشاطهم الـ human + +291 +00:21:25,490 --> 00:21:29,290 +enzyme work at 35 درجة إلى 40 درجة سليزيا اللي هي + +292 +00:21:29,290 --> 00:21:34,310 +ال body temperature 37 درجة سليزيا ببعين ال range + +293 +00:21:34,310 --> 00:21:38,190 +درجة حرارة جسم الإنسان من 35 إلى 40 درجة سليزيا + +294 +00:21:39,320 --> 00:21:43,900 +بيعمل الانزين بيكون optimum temperature إليه بيكون + +295 +00:21:43,900 --> 00:21:48,420 +أعلى نشاط للانزين طب لو ارتفعت درجة الحرارة ريز ال + +296 +00:21:48,420 --> 00:21:52,500 +temperature أعلى من 40 درجة سليزيا بيصير عندنا + +297 +00:21:52,500 --> 00:21:56,800 +denaturation للانزين لأنه أحكي إن بعض الانزين ماتي + +298 +00:21:56,800 --> 00:21:59,140 +عبارة عن البروتين بيصير الـdenaturation + +299 +00:21:59,140 --> 00:22:03,110 +الـdenaturation يعني اتشوهيعني تركيب اختلاف unfold + +300 +00:22:03,110 --> 00:22:07,930 +تركيب تختلفات lose shape هيفقد شكله إذا شكل الـ + +301 +00:22:07,930 --> 00:22:12,090 +active site مش هيكون ملائم لل substrate طيب لو + +302 +00:22:12,090 --> 00:22:15,950 +lower temperature لو قلة درجة الحرارة أقل من 35 + +303 +00:22:15,950 --> 00:22:22,030 +المركبات هتكون بتتحرك ببطء molecules move slower + +304 +00:22:22,030 --> 00:22:28,010 +هتتحرك المركبات ببطء بتكون تمشي بشكل باطينوبالتالي + +305 +00:22:28,010 --> 00:22:32,870 +التصادمات ما بين الـ substrate والإنزيم هتجل هيكون + +306 +00:22:32,870 --> 00:22:37,410 +لأن المراكبات بتتحرك ببطء فهي بتتحرك و تروح على + +307 +00:22:37,410 --> 00:22:42,110 +الإنزيم فلما تروح تتحرك ببطء هتقل التصادمات بينها + +308 +00:22:42,110 --> 00:22:45,970 +وبين الإنزيم هيقل التقاء ال substrate مع الإنزيم + +309 +00:22:45,970 --> 00:22:50,030 +فمش هيرتبطوا مع بعض فبتجل سرعات التفاعل الكيميائي + +310 +00:22:50,030 --> 00:22:54,390 +ويجل نشاط الإنزيم إذا درجة الحرارة بتأثر إذا + +311 +00:22:54,390 --> 00:22:58,990 +ارتفعت بيصيب دي نات يوراجينإذا قلت، بتقل التصادمات + +312 +00:22:58,990 --> 00:23:02,050 +ما بين الـ substrate والإنزيم optimum temperature + +313 +00:23:02,050 --> 00:23:05,870 +بيعمل عليها الجسم عليها الهيمينزيمات هي زي درجة + +314 +00:23:05,870 --> 00:23:12,710 +حرارة الجسم ما هي ما بين 35 و40 درجة سيليزياهنا + +315 +00:23:12,710 --> 00:23:16,070 +عندنا مخطط رسم لـ temperature ونشاط الانزيم + +316 +00:23:16,070 --> 00:23:19,350 +temperature and enzyme activity in human زي ما + +317 +00:23:19,350 --> 00:23:22,770 +حكينا أنه أعلى نشاط للانزيم optimum temperature + +318 +00:23:22,770 --> 00:23:26,470 +for enzyme activity عند القمة أعلى إشي بيكون عند + +319 +00:23:26,470 --> 00:23:31,850 +37 درجة سليزيا عند هذه الدرجة بتكون الأعلى نشاط + +320 +00:23:31,850 --> 00:23:36,570 +للانزيم نفس درجة حرارة جسم الإنسان وهو هيشتغل + +321 +00:23:36,570 --> 00:23:41,260 +ويكون منيح بين 35 و40لكن إذا ارتفعت بيصير تشوّل + +322 +00:23:41,260 --> 00:23:45,740 +شكل الانزيم فيفقد شكله مش هيقدر يرتبط وإذا قلت + +323 +00:23:45,740 --> 00:23:49,100 +هتقل التصادمات ما بين الانزيم و ال substrate + +324 +00:23:49,100 --> 00:23:54,120 +application ان تطبيقات أخرى مش على جسم الإنسان + +325 +00:23:54,120 --> 00:23:58,200 +مثلا many are a lot lower بتعيش على درجة حرارة + +326 +00:23:58,200 --> 00:24:02,780 +منخفضةCold water fish will die at 30°C because + +327 +00:24:02,780 --> 00:24:07,340 +their enzyme denaturation مثلا سمك بيعيش في مياه + +328 +00:24:07,340 --> 00:24:13,020 +باردة لو انت حططيه على درجة حرارة 30°C هو اصلا + +329 +00:24:13,020 --> 00:24:17,500 +جسمه بيعيش في ماء باردة اقل من 30 فانت لو حططيه في + +330 +00:24:17,500 --> 00:24:21,380 +30°C يعني اقل اعلى من الحرارة اللي هو بيعيش فيها + +331 +00:24:21,380 --> 00:24:24,620 +يعني raise temperature يعني ارتفعت درجة الحرارة + +332 +00:24:24,620 --> 00:24:28,680 +لكن اذا ارتفعت بيصير عنده denaturation لل enzyme + +333 +00:24:29,560 --> 00:24:32,320 +فالسمك اللى بيعيش فى المياه المتجمدة فى المياه + +334 +00:24:32,320 --> 00:24:36,480 +الباردة لو حاططى فى اعلى تلاتين نجالتى على درجة + +335 +00:24:36,480 --> 00:24:40,300 +حرارة تلاتين درجة سيليزياس هيصير عنده denaturation + +336 +00:24:40,300 --> 00:24:44,080 +للإنزين طيب فى عندنا بكتيريا few bacteria have + +337 +00:24:44,080 --> 00:24:47,180 +enzyme very high temperature up to مية درجة + +338 +00:24:47,180 --> 00:24:51,310 +سيليزياسهي أن بعض البكتيريا بتعيش في درجات حرارة + +339 +00:24:51,310 --> 00:24:54,830 +عالي بتعيش على 100 درجة سليزياس فانت لو أخدتها + +340 +00:24:54,830 --> 00:24:58,450 +وحطتيها في درجة حرارة قليلة أقل من 100 درجة + +341 +00:24:58,450 --> 00:25:01,730 +سليزياس هتقل التصادمات بين الانزيم وال substrate + +342 +00:25:01,730 --> 00:25:06,290 +ويجي نشاط الانزيم عندهابحكي لـ Most enzymes are + +343 +00:25:06,290 --> 00:25:09,930 +fully denaturated at 70 درجة سليزياس، معظم + +344 +00:25:09,930 --> 00:25:13,690 +الانزيمات بيصير اللي هتشوه denaturation على درجة + +345 +00:25:13,690 --> 00:25:18,250 +حرارة 70 درجة سليزياس، أكيد لإن رفعتها عنها أكتر + +346 +00:25:18,250 --> 00:25:20,690 +من 40، حينها بيصير denaturation، fully + +347 +00:25:20,690 --> 00:25:26,530 +denaturation على 70 بيكون معظم خلاصة اللي هتشوه + +348 +00:25:26,530 --> 00:25:27,930 +بشكل كامل + diff --git a/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/zJp2OlvRd8A_postprocess.srt b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/zJp2OlvRd8A_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..b30e0a98cfd13802791123ae44634cb839d62078 --- /dev/null +++ b/PL9fwy3NUQKwZ1Q7zOg1ObgufPMjRI3WY1/zJp2OlvRd8A_postprocess.srt @@ -0,0 +1,1040 @@ +1 +00:00:03,620 --> 00:00:06,680 +أو وين بيدوب وين بيكون soluble وين بيكون + +2 +00:00:06,680 --> 00:00:09,900 +precipitate يذا فاكرين لما حكينا عن ال ionization + +3 +00:00:09,900 --> 00:00:13,060 +عن ال amino acid كيف بيتصرف في الأوساط المختلفة + +4 +00:00:13,060 --> 00:00:16,480 +لما حاطنا فيه alkaline و فيه neutral و فيه acidic + +5 +00:00:16,480 --> 00:00:21,000 +pHنفسها للبروتين، لأن البروتين هو عبارة عن سلسلة + +6 +00:00:21,000 --> 00:00:24,320 +من الأحماض الأمينية أنا لو جبت بروتين وحطيته في + +7 +00:00:24,320 --> 00:00:28,140 +الـ neutral pH الـ neutral pH حكينا شو بتكون ال + +8 +00:00:28,140 --> 00:00:31,220 +net charge في الأمين واسد، بتكون Zero ال net + +9 +00:00:31,220 --> 00:00:35,240 +charge Zero يعني عدد الشحنات الموجبة بتساوي عدد + +10 +00:00:35,240 --> 00:00:39,240 +الشحنات السالبة، فإذا كان عدد الشحنات فيها نموجة + +11 +00:00:39,240 --> 00:00:43,020 +وفيها سالبة، بتكون في ال neutral pHفي شحنات موجبة + +12 +00:00:43,020 --> 00:00:48,500 +وفي شحنات سالبة الشحنات المختلفة تتجادب مع بعضها + +13 +00:00:48,500 --> 00:00:52,240 +معروف عن الشحنات المختلفة أنها تتجادب و الشحنات + +14 +00:00:52,240 --> 00:00:56,300 +المتشابهة تتنافس في الـ neutral بيكون فيه موجب و + +15 +00:00:56,300 --> 00:01:00,980 +فيه سالب فبيتجادبوا مع بعض بسبب aggregation أو + +16 +00:01:00,980 --> 00:01:05,450 +precipitationفإذا الوين هيترسّب البروتين عند الـ + +17 +00:01:05,450 --> 00:01:08,690 +neutral pH اللي هي بتكون فيها الـ pH عند الـ + +18 +00:01:08,690 --> 00:01:12,950 +isoelectric point بتساوي الـ isoelectric point + +19 +00:01:12,950 --> 00:01:17,330 +فنقطة الـ isoelectric point هيترسّب البروتين لكن + +20 +00:01:17,330 --> 00:01:22,410 +مثلا لو حطته في acidic media يعني الـ pH كانت أقل + +21 +00:01:22,410 --> 00:01:27,100 +من الـ isoelectric pointacidic يعني pH أقل من الـ + +22 +00:01:27,100 --> 00:01:31,300 +isoelectric bond حكينا الشحنات بتكون موجبة بتكون + +23 +00:01:31,300 --> 00:01:35,260 +ال net charge موجبة في ال acidic ال net charge + +24 +00:01:35,260 --> 00:01:38,840 +بتكون موجبة الأحمد الأمينية المكونة للبروتين هتكون + +25 +00:01:38,840 --> 00:01:43,010 +شحنتها موجبةيعني شحنات متشابهة positive charge + +26 +00:01:43,010 --> 00:01:47,370 +الشحنات المتشابهة إيش هي بيصير بينها؟ بيصير تنافر + +27 +00:01:47,370 --> 00:01:52,550 +تنافر و بتبعد عن بعضها و بتتوزع فيه المحلول فبتصير + +28 +00:01:52,550 --> 00:01:56,310 +soluble ما بتترسب و انما بيصير soluble طب لو + +29 +00:01:56,310 --> 00:02:01,250 +حطيتها في alkaline ميلياجيبت هذا البروتين مكونة من + +30 +00:02:01,250 --> 00:02:04,770 +أحمض أمينية حاطته في الـAlkaline يعني الـBH أعلى + +31 +00:02:04,770 --> 00:02:08,990 +من الـBi الـBH بتكون أعلى من الـBi على الـAlkaline + +32 +00:02:08,990 --> 00:02:12,950 +لإن الـBhi نتش هاجحة كده بتكون في الـAlkaline + +33 +00:02:12,950 --> 00:02:16,770 +نيجاتيف فكل الشحنات اللي على أحمض الأمينية نيجاتيف + +34 +00:02:16,770 --> 00:02:21,710 +شحنات متشابهة، إيش بيصير بينها؟ بتتنافر، بتتنافر و + +35 +00:02:21,710 --> 00:02:26,290 +بتتوزع فيه المحلول وبالتالي بتصير soluble، بتكون + +36 +00:02:26,290 --> 00:02:30,800 +soluble مش ابتتجادالو جينا قرا عن هذه النقاط نفس + +37 +00:02:30,800 --> 00:02:34,780 +اللي حكيناها تحكيلي ال solution pH is above the PI + +38 +00:02:34,780 --> 00:02:38,780 +ال pH أعلى من ال PI مدام ال pH أعلى يعني أنا وصلت + +39 +00:02:38,780 --> 00:02:42,300 +ل alkaline media في ال alkaline ال charge، ال net + +40 +00:02:42,300 --> 00:02:44,260 +charge بتكون negatively charged + +41 +00:02:49,890 --> 00:02:53,510 +الشحنات المتشابهة لـ like charge عندها قوة تنافر + +42 +00:02:53,510 --> 00:02:57,530 +لذلك البروتين والبولسوليو بالادس BH فالبروتين + +43 +00:02:57,530 --> 00:03:03,330 +هيكون ذائب likewise برضه بنفس الطريقة لما تكون + +44 +00:03:03,330 --> 00:03:07,430 +البروتين positive charge وين بيكون positive charge + +45 +00:03:07,430 --> 00:03:13,430 +لما تكون ال BH أقل من الBI اللي في acidic BHبيكون + +46 +00:03:13,430 --> 00:03:17,070 +برضه عندنا شحنات متشابهة بتصير في بينهم repulsion + +47 +00:03:17,070 --> 00:03:22,010 +قوة تنافذ فبيكون البروتين والـB سوليو بالاديس this + +48 +00:03:22,010 --> 00:03:26,710 +BH التبيئة عند الـ isoelectric point بالظبط اللي + +49 +00:03:26,710 --> 00:03:30,150 +هي عند الـ neutral BH هي نقطة الـ isoelectric + +50 +00:03:30,150 --> 00:03:33,170 +point بيكون عندنا negative و positive charge + +51 +00:03:33,170 --> 00:03:37,610 +negative و positive هيقلل ال repulsive repulsive + +52 +00:03:37,610 --> 00:03:42,320 +أو electrostatic or reduceفماذا سيحصل؟ هو الـ + +53 +00:03:42,320 --> 00:03:44,500 +Cause Aggregation and Precipitation + +54 +00:03:48,230 --> 00:03:52,130 +مع بعض تتجمع ويصير precipitation أو aggregation + +55 +00:03:52,130 --> 00:03:56,150 +للبروتين فإذا أنا بدي أدوب أي بروتين أنا أعطيتك + +56 +00:03:56,150 --> 00:03:59,930 +حاجات لك دا و بيلي هذا البروتين بدور على نقطة الـ + +57 +00:03:59,930 --> 00:04:02,490 +isoelectric point له بكون عارفة نقطة الـ + +58 +00:04:02,490 --> 00:04:06,910 +isoelectric point بجيب مثلا buffer يضبطلي الـ pH + +59 +00:04:06,910 --> 00:04:09,690 +عند هذه الـ isoelectric point ويدوب البروتين + +60 +00:04:09,690 --> 00:04:14,130 +بيحكيلي الـ isoelectric point لمعظم البروتين بتكون + +61 +00:04:14,130 --> 00:04:18,610 +بين pH 4الى 6 + +62 +00:04:22,760 --> 00:04:27,400 +إذا بدي أعمل أني أرسب أي بروتين أسف على المعلومة + +63 +00:04:27,400 --> 00:04:31,200 +اللي جابل إذا بدي أرسب أي بروتين مش أدوب أي بروتين + +64 +00:04:31,200 --> 00:04:36,900 +بضبط ال pH عند نقطة ال PI إذا بدي أرسبه بضبط ال pH + +65 +00:04:36,900 --> 00:04:40,780 +عند ال PI أما إذا بدي أدوبه بدي أرفع ال pH أو + +66 +00:04:40,780 --> 00:04:44,420 +أوصلها لل acid أو بدي أقلل .. بدي أقللها أووصلها + +67 +00:04:44,420 --> 00:04:48,370 +لل acid أو أرفعها أني أوصلها لل alkalineلكن إذا + +68 +00:04:48,370 --> 00:04:53,570 +بدي أرسبه بدي أضبط ال bh عند ال bi مش إني أدوبه + +69 +00:04:53,570 --> 00:05:03,370 +ماذا هيترسب إذا ضبطت ال bh عند ال bi احكيلي + +70 +00:05:03,370 --> 00:05:07,810 +أنه solubility of ال protein ثقابية ال protein في + +71 +00:05:07,810 --> 00:05:10,630 +بعض ال protein ثقابيتها لا تتأثر بالحرارة يعني + +72 +00:05:10,630 --> 00:05:14,870 +حاليا احكيلي بدي أدوبه بالحرارةلايتأثر بالحرارة + +73 +00:05:14,870 --> 00:05:19,110 +بسبب تركيبته زي الـ Casein فأنا كيف بدي أزوج وصف + +74 +00:05:19,110 --> 00:05:22,270 +الـ ability of casein؟ تحتمل على الـ pH، يعني أوصل + +75 +00:05:22,270 --> 00:05:27,910 +الـ pH للـ BI يعني أبط الـ pH توصل للـ isoelectric + +76 +00:05:27,910 --> 00:05:31,990 +point لأن حكينا لما متى ما كانت الـ pH بتساوي الـ + +77 +00:05:31,990 --> 00:05:36,510 +BI، يترسب الـ protein فإذا أنا بدي أرسبه، بدي ألعب + +78 +00:05:36,510 --> 00:05:39,670 +في الـ pH إذا بدي أدوبه، برفع الـ pH، بخليه أعلىمن + +79 +00:05:39,670 --> 00:05:43,370 +ال بي اي او اقل من ال بي اي يكون في ال acidity او + +80 +00:05:43,370 --> 00:05:47,550 +ال alkalinity هذا بيدوم بس اذا وصلت ال بي اتش لل + +81 +00:05:47,550 --> 00:05:52,530 +بي اي بدي يتحسن ال intermediate pH at which + +82 +00:05:52,530 --> 00:05:55,370 +protein molecule has charge of 0 نسميها ال + +83 +00:05:55,370 --> 00:05:58,590 +isoelectric point حتى هنا ان ال isoelectric point + +84 +00:05:58,590 --> 00:06:03,130 +هي قيمة بي اتش اللي عندها بتكون ان انت charge 0عند + +85 +00:06:03,130 --> 00:06:07,190 +هذه النقطة، يعني نقطة الـ isoelectric point دائمية + +86 +00:06:07,190 --> 00:06:11,590 +البروتين تكون أقل ما يمكن، solubility is minimal + +87 +00:06:11,590 --> 00:06:17,110 +كيف بدأ أزود الدائمية؟ أني يا إما بأزود الـ pH يا + +88 +00:06:17,110 --> 00:06:21,530 +بقلل الـ pH حكينا إن كانت الـ pH أعلى من الـ PI أو + +89 +00:06:21,530 --> 00:06:25,030 +أقل من الـ PI، بكون soluble بس متى ما كانت عند الـ + +90 +00:06:25,030 --> 00:06:30,180 +PI، بيكون precipitatePrecipitation or coagulation + +91 +00:06:30,180 --> 00:06:33,500 +of milk protein casein at low pH as milk becomes + +92 +00:06:33,500 --> 00:06:37,200 +white بيحكي الفيلم إنها تطبيق على ترسيب البروتين + +93 +00:06:37,200 --> 00:06:41,800 +له فساد الحليب، فيه هنا ظاهرة، ظاهرة فساد الحليب + +94 +00:06:41,800 --> 00:06:44,860 +كيف فساد الحليب؟ فالجهة الحليب معروفة عنه إن هو + +95 +00:06:44,860 --> 00:06:48,820 +وسطه قاعي تمام؟ ومن مكونات الحليب فيه عدة + +96 +00:06:48,820 --> 00:06:51,960 +بروتينات، منها البروتين الكازيني وجدوا إن + +97 +00:06:51,960 --> 00:06:55,840 +الـisoelectric point للكازين هي حوالي أربعة وسبعة + +98 +00:06:57,200 --> 00:07:01,780 +وهي أقل الـ 4.7 أقل من الـ pH بتاعة الحليب فجد + +99 +00:07:01,780 --> 00:07:05,960 +الحليب وسط قاي فبال isoelectric point للكازين اللي + +100 +00:07:05,960 --> 00:07:10,660 +موجود في الحليب 4.7 مين أعلى ال pH قاي ولا ال 4.7 + +101 +00:07:10,660 --> 00:07:14,980 +لأ ال pH لذن ال pH للحليب أعلى من ال PI يعني + +102 +00:07:14,980 --> 00:07:18,540 +الشحنة هتكون ال net charge negative فهيكون ال + +103 +00:07:18,540 --> 00:07:20,000 +protein that kept بتكون في الحليب + +104 +00:07:25,940 --> 00:07:29,740 +الكزين اللي موجود في الحليب اربعة وسبعة مينها على + +105 +00:07:29,740 --> 00:07:31,760 +البيئة توقعي ولا الاربعة وسبعة + +106 +00:07:46,290 --> 00:07:51,150 +سالبة فبتصير طنافر فهيكون سلبة لما يصير فساد + +107 +00:07:51,150 --> 00:07:55,190 +للحليب يلمع فيه أورجانيزم يتم تلمع فيه بكتيريا مش + +108 +00:07:55,190 --> 00:07:58,970 +هاي الترمال بتحول سكر اللاكتوز الموجود في الحليب ل + +109 +00:07:58,970 --> 00:08:04,210 +Lactic Acid و Lactic Acid هذا حمق لأن هو وسط قاعد + +110 +00:08:04,210 --> 00:08:07,230 +الحليب مع ال بكتيريا اللي نمت فيه هو القوانات + +111 +00:08:07,230 --> 00:08:11,730 +للاكتك أسد Lactic Acid هذا هيقلل البيئات اللي هو + +112 +00:08:11,730 --> 00:08:14,650 +اللي بيقللها بيقللها وصولا إلى الأرض + +113 +00:08:18,250 --> 00:08:22,230 +مجد خسارة الحليب هو الـ Lactic Acid وهو ربعاً حمق + +114 +00:08:22,230 --> 00:08:27,970 +والحليب أصلا وسط القاعدة فجد قاعدة محمق بيقلل الـ + +115 +00:08:27,970 --> 00:08:34,550 +pH من قاعدة الحليب وصولا إلى درجة الحموظة فبتقترب + +116 +00:08:34,550 --> 00:08:40,470 +من الـBi للكازين اللي هي 4 و7 مدام الـBi وصلت + +117 +00:08:40,470 --> 00:08:45,070 +الـBH صاروا متساويين إذا بيترسب الكازين فبيصير فيه + +118 +00:08:45,070 --> 00:08:46,590 +تنسيق للكازين + +119 +00:09:13,180 --> 00:09:17,340 +فكيف بتعرف الـ isoelectric point للكازين؟ بناء على + +120 +00:09:17,340 --> 00:09:20,960 +ال principle اللي هو المبدأ إنه بدي أستخدم أسيتات + +121 +00:09:20,960 --> 00:09:26,720 +buffer بستخدم buffer اللي قيم BH مختلفة عشان أكشف + +122 +00:09:26,720 --> 00:09:29,740 +عن الـ isoelectric point of كازين يعني أنا بدي + +123 +00:09:29,740 --> 00:09:33,740 +ألعب بالـ BH بغير الـ BH حكيمة مدى ما بدي أعرف الـ + +124 +00:09:33,740 --> 00:09:37,840 +isoelectric point بعرف بغير الـ BH مثلا بستخدم + +125 +00:09:37,840 --> 00:09:42,280 +تسعة نبيب و أحط عليهم روتين الكازين وكل نبوبة فيها + +126 +00:09:54,070 --> 00:09:58,670 +الأول تانية تلاتة و تمانية بعدها اربعة و واحد اربع + +127 +00:09:58,670 --> 00:10:03,350 +واربع اربع وسبعة خمسة خمسة و تلاتة خمسة و ستة خمسة + +128 +00:10:03,350 --> 00:10:07,470 +و جسد عنده قيم بيقات مختلفة تمام انا استخدمت هذه + +129 +00:10:07,470 --> 00:10:13,050 +القنادير و حطيت فيهم كمية من الحمب بتركيز مختلفة + +130 +00:10:29,150 --> 00:10:33,990 +معادلة بحسم من خلالها دياتي أنا عندى عدة قنابيل + +131 +00:10:33,990 --> 00:10:38,590 +تحتوي على protein الكازين ومحطوط معاها buffer ال + +132 +00:10:38,590 --> 00:10:43,470 +buffer هذه تعمل من حمض وقاعد تركيز الحمض مختلفة + +133 +00:10:43,470 --> 00:10:47,410 +أنا عاملانا تخفيف كل انبوب عن التعنى ليش؟ عشان + +134 +00:10:47,410 --> 00:10:51,470 +أغير البيات بعدين بنسك هذه القنابيل باخد الانبوب + +135 +00:10:51,470 --> 00:10:51,950 +الأول + +136 +00:11:10,940 --> 00:11:14,340 +الأنبوبة المترسّب فيها البروتين الكازيين من هذه + +137 +00:11:14,340 --> 00:11:17,180 +الأنبوبة هي قيمة الـ pH + +138 +00:11:42,230 --> 00:11:47,330 +الـ BKA للي + +139 +00:11:47,330 --> 00:11:55,310 +احنا مستخدمينها هي معروفة 4.75 BKA 4.75 ال base + +140 +00:11:55,310 --> 00:11:58,290 +القاعد اللي أنا استخدمتها اللي بستخدمها في التجربة + +141 +00:11:58,290 --> 00:12:02,690 +هي كازين أسيتات صوبيوم مش مفهوم منكوا تعرفوا + +142 +00:12:11,800 --> 00:12:15,740 +الكزين أسيتات Sodium الـ Milk Base تركيزها 1 من 10 + +143 +00:12:15,740 --> 00:12:19,460 +مين اللي غير تركيزه الـ Acetic Acid فكل أنفور + +144 +00:12:19,460 --> 00:12:25,200 +هيكون له تركيز لبحن مختلف عن التاني عشان يتغير قيم + +145 +00:12:25,200 --> 00:12:30,220 +البيعات معروفة أن هذه التركيز موجودة في آخر في قبل + +146 +00:12:30,220 --> 00:12:33,220 +الأخيرة سواء في قبل الأخيرة في جدول موجودة + +147 +00:12:35,490 --> 00:12:39,350 +جداش تركيزة في النبوب الأول مثلا 1 و 6، للنبوب + +148 +00:12:39,350 --> 00:12:43,090 +التالت 8 من 10، للنبوب التالت 4 من 10 و هكذا، هذه + +149 +00:12:43,090 --> 00:12:47,030 +محسوبة اللي هي تركيز الحمض، بحطها في المعادلة، صار + +150 +00:12:47,030 --> 00:12:51,430 +عندي معروف تركيز الـBKA جداش، والبس 1 من 10، + +151 +00:12:51,430 --> 00:12:54,590 +والacetic acid بتاخدها من الجدول، واحسب الـBH + +152 +00:12:54,590 --> 00:12:58,670 +للنبوب الأول، BH للنبوب التاني، للتالت، فهذا + +153 +00:12:58,670 --> 00:13:03,660 +الجدول اللي في الأخرهو تركيز الحمض في الجداش في كل + +154 +00:13:03,660 --> 00:13:10,020 +انبوبة وال pH جداش موجودة لكل محسوبة لكل انبوبة + +155 +00:13:10,020 --> 00:13:12,780 +كيف حسبها من خلال المعادلة اللي فوق اللي طبعا + +156 +00:13:12,780 --> 00:13:18,100 +حكينا عنها + +157 +00:13:18,100 --> 00:13:22,440 +اكررنا ان حكينا ان البروتينات عشان اخليها تترسب + +158 +00:13:22,440 --> 00:13:26,460 +لازم اوصيها لل isoelectric bond to aggregate and + +159 +00:13:26,460 --> 00:13:27,120 +dissipate + +160 +00:13:32,930 --> 00:13:35,510 +أحنا مختلفة تتجادل مع بعضها + +161 +00:13:47,940 --> 00:13:51,160 +حسب مين؟ حسب الـ Amino Acid Sequence حسب عدد الـ + +162 +00:13:51,160 --> 00:13:55,060 +Anionic والكاتيونيك الـ Growth فأنا بحكي لي هدفات + +163 +00:13:55,060 --> 00:14:00,100 +بستخدمها و بستفيد منها لو بدي أفصل البروتين من عدة + +164 +00:14:00,100 --> 00:14:03,320 +بروتينات يعني مثلا عندي حليب يحتوي على عدة + +165 +00:14:03,320 --> 00:14:07,420 +بروتينات من ضمنها البروتين الكازين كيف بدي أخد من + +166 +00:14:07,420 --> 00:14:11,200 +الحليب بس البروتين الكازين و أسيب الباقي؟ بعرف + +167 +00:14:11,200 --> 00:14:15,220 +الـBI للكازين و بوصلها الـBH للـBI + +168 +00:14:35,740 --> 00:14:42,140 +ساوى للـ VI هالوراسة في تجربتنا لليوم مش البدوات + +169 +00:14:42,140 --> 00:14:45,560 +اللى بدي استخدمها بستخدم acidic acid اللى هو الحمض + +170 +00:14:45,560 --> 00:14:48,480 +بستخدم البروتين الكازين اللى هو اللى أنا بدورله + +171 +00:14:48,480 --> 00:14:50,980 +على ال isoelectric point اللى بتعرفه isoelectric + +172 +00:14:50,980 --> 00:14:54,760 +point بستخدم NA watch عشان ارفع البيئات عشان + +173 +00:14:54,760 --> 00:14:58,260 +اوصلها على القاعدة الحمض بدي نزل البيئات NA watch + +174 +00:14:58,260 --> 00:14:58,920 +بيرفع + +175 +00:15:04,450 --> 00:15:09,090 +عشان أعمل dilution و أغير قيم الـ pH عشان أتغير و + +176 +00:15:09,090 --> 00:15:12,950 +أعرف أن الـ pH تساوي الـ isoelectric bond و بدي + +177 +00:15:12,950 --> 00:15:17,430 +أستخدم تسع تيوبات ليش تسع تيوبات؟ عشان كل تيوب + +178 +00:15:17,430 --> 00:15:21,470 +تكون فيها قيمة الـ pH مختلفة عن التانية عشان أعرف + +179 +00:15:21,470 --> 00:15:30,150 +وين هو ترثبت أي pH من هذه التيوبات كيف + +180 +00:15:30,150 --> 00:15:33,290 +حطوات إجراء التجربة؟ أول شيء مضاجينه + +181 +00:15:38,210 --> 00:15:42,510 +عارفة من فوق تقولها زي رجب من فوق ساعتها تكون + +182 +00:15:42,510 --> 00:15:45,550 +خمسين مل اذا حضر فيها ال buffer اللي انا بدي + +183 +00:15:45,550 --> 00:15:49,630 +استخدمه ايش بدي احط فيها كيف بدي احضر ال buffer + +184 +00:15:49,630 --> 00:15:54,210 +بحط عشرين مل من ديستل واتر على خمسة وعشرين من مية + +185 +00:15:54,210 --> 00:16:01,110 +جرام كزينعلى خمسة مل نا واتش وخمسة مل أسيتك أسد + +186 +00:16:01,110 --> 00:16:05,010 +وعشرين مل ديستل واتر يعني أنا بحط البروتين اللي + +187 +00:16:05,010 --> 00:16:08,150 +أنا بدورله على ال isoelectric point مع أسد و base + +188 +00:16:08,150 --> 00:16:11,150 +مش ال buffer هو عبارة عن أسد مع conjugate base + +189 +00:16:11,150 --> 00:16:16,230 +أضيفهم عليه و ديستل واتر عشان أدورهم فيهو اعمل mix + +190 +00:16:16,230 --> 00:16:19,410 +هان اتكون عندي ال buffer اللي هو عبارة عن ال base + +191 +00:16:19,410 --> 00:16:25,290 +بتركيز 1 من 10 بحضره و بحطه على جنب و بعدين بجيب 9 + +192 +00:16:25,290 --> 00:16:31,770 +تيوبات منابيب برقمهم من 1 ل 9 نحط فيهم دولة + +193 +00:16:31,770 --> 00:16:35,970 +distilled water اول اشي بتقضيف عليها تيوب رقم 1 + +194 +00:16:35,970 --> 00:16:41,920 +distilled water مقدار 6.8وبعدين القنابيب من رقم 2 + +195 +00:16:41,920 --> 00:16:47,020 +ل 9 بتضيف عليهم 5 مل ديسترواتا رقم 1 بتضيف عليه 86 + +196 +00:16:47,020 --> 00:16:51,480 +مل ديسترواتا أما القنابيب من 2 ل 9 بتضيف عليهم 5 + +197 +00:16:51,480 --> 00:16:56,120 +مل ديسترواتا بعدين بتضيف عليه acidic acid اللي هو + +198 +00:16:56,120 --> 00:17:00,880 +الحمد والحمد هذا بتضيفه بتركيز مختلفة عشان أغير + +199 +00:17:00,880 --> 00:17:07,870 +قيم ال pH لكل tube ف tube رقم 1 تضيف عليها 3 و 2من + +200 +00:17:07,870 --> 00:17:11,550 +الـ acetic acid تلاتة و اتنين في تلاتة فاصلة اتنين + +201 +00:17:11,550 --> 00:17:15,370 +من الحمض من الحمض من ال acetic acid لأن نبيب + +202 +00:17:15,370 --> 00:17:18,490 +التاني ماليش يحط عليها من الحمض كيف بدي اعمل بتاخد + +203 +00:17:18,490 --> 00:17:22,940 +من انبوب واحد خمسة ميل على انبوب اتنينأبوب واحد + +204 +00:17:22,940 --> 00:17:26,320 +صار فيه ستة و تمانية ديستل واتر و تلاتة و اتنين + +205 +00:17:26,320 --> 00:17:30,340 +راسيتي كهسان أما باجي الأناديفش فيها خمسة مل من + +206 +00:17:30,340 --> 00:17:34,120 +ديستل واتر بدي اجي على أبوب واحد اللي فيه ديستل + +207 +00:17:34,120 --> 00:17:41,460 +واتر محاني بدي اعمل تخفيفات للحم فبدي اخدعامل mix + +208 +00:17:41,460 --> 00:17:48,120 +واخد خمسة مل من انبوب تلاتة + +209 +00:17:48,120 --> 00:17:52,800 +لاربع وعامل mix واخد خمسة مل من انبوب اربع لخمسة + +210 +00:17:52,800 --> 00:17:58,370 +وخمسة مل من خمسة لستة واخد خمسة مل من ستة لسبعةو + +211 +00:17:58,370 --> 00:18:01,990 +بعدين خمسة مل من سبعة ل تمانية و بعدين خمسة مل من + +212 +00:18:01,990 --> 00:18:06,290 +تمانية لتسعة صارت كل الأنابيب تحتوي على خمسة مل + +213 +00:18:06,290 --> 00:18:10,870 +ديستر واطر من رقم اتنين لتسعة تحتوي خمسة مل ديستر + +214 +00:18:10,870 --> 00:18:16,150 +واطر و خمسة مل من الأنبوب اللي جابنا عملتلهم mix + +215 +00:18:16,150 --> 00:18:19,830 +مع بعض و contango الخمسة فظل المحصلة بس خمسة مل + +216 +00:18:19,830 --> 00:18:24,850 +ديستر واطر مع حمض مع بعض هل جيت معادة الأنبوب + +217 +00:18:24,850 --> 00:18:29,260 +الأخيرة؟من الأنبوب الأخيرة صار فيها خمسة مل زيادة + +218 +00:18:29,260 --> 00:18:32,680 +لإن أنا ما نجلتش لحد بعدها فبدي أطلع منها خمسة مل + +219 +00:18:32,680 --> 00:18:36,540 +و أكرها، خلاص بتتخلص منها، أجيت أنا صرت عاملة + +220 +00:18:36,540 --> 00:18:40,700 +تخفيفات تدريجيية Serial Delusion للأنبي و للحمة + +221 +00:18:40,700 --> 00:18:44,500 +اللي أناضفته للـacetic acidأنا بس على الأول أضفت + +222 +00:18:44,500 --> 00:18:48,680 +أستيك أسد و بعدين بلشت أنجل من النبوب 1 ل2، 2 ل3، + +223 +00:18:48,680 --> 00:18:53,060 +3 ل4، و هكذا وصلت للآخر الـ TUE فعملت Serial + +224 +00:18:53,060 --> 00:18:56,980 +Dilution، تخفيف تدريجي للحم ليش هدى التخفيف؟ عشان + +225 +00:18:56,980 --> 00:19:01,400 +أغير قيم الـ pH عشان أعرف وين الـ pH متساوي للـ + +226 +00:19:01,400 --> 00:19:07,300 +isoelectric bond بعد هيك باجي بتحط في كل TUE بات + +227 +00:19:07,300 --> 00:19:10,880 +من 1 ل 9 من ال buffer اللي أنا حضرته في ال flask + +228 +00:19:14,160 --> 00:19:19,180 +بعدين مل حضرت بفر حكاية بتاخد منه واحد مل على تيوب + +229 +00:19:19,180 --> 00:19:22,720 +واحد وبعدين من ال flask نفسه واحد مل على تيوب + +230 +00:19:22,720 --> 00:19:26,260 +اتنين وبعدين من ال flask نفسه واحد مل على تيوب + +231 +00:19:26,260 --> 00:19:30,900 +تلاتي وهكذا لآخر تيوب بتقدر نضيف واحد مل من ال + +232 +00:19:30,900 --> 00:19:36,920 +flask على كل تيوبها وبتركه لمدة نص ساعة بترك كل + +233 +00:19:36,920 --> 00:19:41,200 +القنابيب لمدة نص ساعة بعد نص ساعة بجلد القنابيب + +234 +00:19:41,200 --> 00:19:45,150 +بشوف همسك تيوب تيوب تيوب واحدهمسكها، شوف فيها + +235 +00:19:45,150 --> 00:19:48,590 +precipitate تحت ولا مافيش فيها إذا ترسّب، يبقى ال + +236 +00:19:48,590 --> 00:19:52,890 +protein هنا مترسّب عند قيمة الـ pH هذه إذا هنا هو + +237 +00:19:52,890 --> 00:19:56,570 +بترسّب، إذا هذه هي الـ PR إذا مش مترسّب، بدي أنتج + +238 +00:19:56,570 --> 00:20:00,090 +إلى اللي بعدها، بشوف كل الأنابيب، أي أنبوب مترسّب + +239 +00:20:00,090 --> 00:20:04,410 +عندها، إذا عند هذه الـ pH متساوي الـ PR + +240 +00:20:13,210 --> 00:20:17,230 +أما بيحكي إن هم لما اشتغلوا التجربة وجدوا أن الـ + +241 +00:20:17,230 --> 00:20:24,010 +«بي» الـ «بي» الـ isoelectric point للكازين هي 4 و + +242 +00:20:24,010 --> 00:20:29,390 +7 يعني المفروض تطلع معناه الـ «به» الـ precipitate + +243 +00:20:29,390 --> 00:20:34,350 +للكازين هي «به» 4 و 7 لأن الـ «بي» للكازين هي 4 و + +244 +00:20:34,350 --> 00:20:39,410 +7 ففي الجدول أي tube عندها الـ «به» 4 و 7 هي tube + +245 +00:20:39,410 --> 00:20:45,680 +رقم 5هو المعنى فيها أعلى precipitates كيف احنا + +246 +00:20:45,680 --> 00:20:50,660 +هنسجل النتيجة نحكي ال result ال BKA حكي انها 4.75 + +247 +00:20:50,660 --> 00:20:54,340 +النتيجة هسجلها همسك تيوب واحد يفترض ان مايكونش + +248 +00:20:54,340 --> 00:20:57,440 +فيها precipitates و اكتب عليها negative اتنين + +249 +00:20:57,440 --> 00:21:02,280 +مافيش فيها negative تلاتة negative اربع قريبة من + +250 +00:21:02,280 --> 00:21:06,940 +ال BH للكزي من ال BY من اربعة وسبعة لكن مش هي + +251 +00:21:06,940 --> 00:21:08,860 +فهتكون ممكن تكون plus واحد + +252 +00:21:12,560 --> 00:21:15,720 +الـ Precision أعلى لـ Preceptive maximum decision + +253 +00:21:15,720 --> 00:21:19,420 +plus 3 إذا كان الـ Preceptive بسيط plus 1 إذا + +254 +00:21:19,420 --> 00:21:25,400 +واصلت plus 2هو أسجل النتيجة المفروض أن حياتيه برقم + +255 +00:21:25,400 --> 00:21:29,060 +5 هي اللي تطلع عندنا أعلى precipitate إذا طلع + +256 +00:21:29,060 --> 00:21:32,920 +عندنا خطأ بنحسب نسبة الخطأ الـError اللي هي + +257 +00:21:32,920 --> 00:21:37,020 +الـExperimental Value ناقص الـTheoretical Value + +258 +00:21:37,020 --> 00:21:40,500 +على الـTheoretical Value ضارب 100 اللي هي القيمة + +259 +00:21:40,500 --> 00:21:43,220 +المحسوبة ناقص القيمة العملية اللي أنا أشتغلتها على + +260 +00:21:43,220 --> 00:21:45,400 +القيمة المحسوبة ضارب 100 +