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eb55c837-bb39-44bd-9cc9-e835a6446582
multivariable_calculus
false
null
Use the method of Lagrange multipliers to find the maximum and minimum values of the function $f(x,y,z) = y \cdot z + x \cdot y$ subject to the constraints $x \cdot y = 1$ and $y^2 + z^2 = 1$.
A minimum of $f(x,y,z)$ is $\frac{1}{2}$ A maximum of $f(x,y,z)$ is $\frac{3}{2}$
eb966639-1939-4210-945f-05a52370964f
algebra
true
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
Estimate the intervals where the function is increasing or decreasing:
The final answer: 1. Interval(s) of increase: $(-\infty,-3)\cup(3,\infty)$ 2. Interval(s) of decrease: $(-3,3)$
ebce3086-94ba-4f5d-a9eb-d41c4104e62a
differential_calc
false
null
Sketch the curve: $$ y = 25 \cdot x^2 \cdot e^{\frac{ 1 }{ 5 \cdot x }} $$ Submit as your final answer: 1. The domain (in interval notation) 2. Vertical asymptotes 3. Horizontal asymptotes 4. Slant asymptotes 5. Intervals where the function is increasing 6. Intervals where the function is decreasing 7. Intervals where the function is concave up 8. Intervals where the function is concave down 9. Points of inflection
1. The domain (in interval notation): $(-\infty,0)\cup(0,\infty)$ 2. Vertical asymptotes: $x=0$ 3. Horizontal asymptotes: None 4. Slant asymptotes: None 5. Intervals where the function is increasing: $\left(\frac{1}{10},\infty\right)$ 6. Intervals where the function is decreasing: $(-\infty,0)$, $\left(0,\frac{1}{10}\right)$ 7. Intervals where the function is concave up: $(0,\infty)$, $(-\infty,0)$ 8. Intervals where the function is concave down: None 9. Points of inflection: None
ebd03078-271e-4a68-af4e-459266d93331
integral_calc
true
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
Find the areas enclosed by the curves $y^2 = 4 \cdot x$ and $y^2 = 8 \cdot x - x^2$ using integration with respect to $x$: 1. The area of the smaller, shaded region. 2. The area of the larger, yellow region.
1. The area of the smaller, shaded region is $8\cdot\left(\pi-\frac{8}{3}\right)$ 2. The area of the larger, yellow region is $8\cdot\left(\pi+\frac{8}{3}\right)$
ecc3ece9-4782-446c-a583-bf68cbb20da0
algebra
false
null
1 cup = 8 fluid oz 1 pint = 2 cups = 16 fl oz 1 quart = 2 pints = 4 cups = 32 fluid oz 1 gal = 4 quarts = 8 pints = 16 cups = 128 fl oz 1 lb = 16 oz 1 ton = 2,000 lbs 1 kg = 1,000 g 1 metric ton = 1,000 kg 1 m = 100 cm 1 km = 1,000 m 1. Miles has a bag of peanuts that weighs 64 oz. How many lbs of peanuts does he have? 2. Michelle has 8 pints of milk. How many quarts of milk does she have? 3. Peter needs 8 cups of water for his drink mix. How many pints is this? 4. What is 1 metric ton and 500 kg multiplied by 4? 5. What is 50 lb and 20 oz divided by 5?
1. $4$ 2. $4$ 3. $4$ 4. $6,000$ 5. $10.25$
ed054e0e-5292-4e76-a784-4603be66e688
multivariable_calculus
false
null
Evaluate the integral by interchanging the order of integration: $$ \int_{1}^{27} \int_{1}^2 \left(\sqrt[3]{x} + \sqrt[3]{y}\right) \, dy \, dx $$
$\int_{1}^{27} \int_{1}^2 \left(\sqrt[3]{x} + \sqrt[3]{y}\right) \, dy \, dx$ = $39\cdot\sqrt[3]{2}+\frac{81}{2}$
ed1c56f4-e389-41c3-a2dd-34b41b6cfc41
differential_calc
false
null
For the function $y = \ln\left(x^2 - \frac{ 3 }{ 2 }\right) - 4 \cdot x$ determine the intervals, where the function is increasing and decreasing. Submit as your final answer: 1. Interval(s) where the function is increasing 2. Interval(s) where the function is decreasing
1. Interval(s) where the function is increasing: $\left(\sqrt{\frac{3}{2}},\frac{3}{2}\right)$ 2. Interval(s) where the function is decreasing: $\left(-\infty,-\sqrt{\frac{3}{2}}\right)$, $\left(\frac{3}{2},\infty\right)$
ed2645bb-1dfa-4a91-ae3e-019819072602
differential_calc
true
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ZofGYZwhMIO/eb8oWirgwch8u90r1DLuvXL+o3PVQ68GU0TdmMOofFKFEG6FrqbSa9MiQiNfO+QZNvv/QmMxTldtntV9nO73C5PMFNf2nVjeeZwsrtcgrEEkNrg8WgDYqKGzL1jgHjZoqk8qu80O10uB3dmBucxxde4R5T0FtQbhfl6saYcnkCHl94/fKAd7mdjm7NFMYXCLmXu2/YzQaVrhv4QrEyJKKl4gLTQaCrdK0NzRUXHDbL0OmLEsdM5/EFPL5AKJWL/v+5DBwWs/63+0cRQiQKlef8jCvxXG13vULDFZg6WmryT/BFouRbZiWPn83l8nkCoUgqF4glV/9Cb9F3WPT/O2wnDwi5emOT+gdKVbiNb69mNeouvRWY3D/k6hNYSP38pf4YU9YwdrRcejmLKiTy0uMqfyQPDOvWgXhfhUrXDTweTySRE0LsFqNF3yEQSbhcrlihYjoXXBHldrmdDpqmc/ZuP3fgC8LhEELC4wcmjZ3Rf9RfOByOQCgO7ZvUUlnstFuddqvnhFyRROaZkt6sbbfotVwuTyCSiBUqt9PRXltKPOfRS662WwiuB8rtdtptdpMh7/sdBYe+Jp7h6zMgefysmEEjO0+mvpRUFeAfEattqLbbLC6ngy8QEkLEcj8Oj08I0bc22Yw6p90qkiqEUrndbNA11xFChCKJQHiZrQHjhGKpf3gsIcRls9lt/zsdXiSVcXl8Qoi2vpKmqI76qoDIPsRzgVRzLSGELxQJL/cvBHoVqSpAERBGCLFbzJceORHL/QiHQ7ld2vpql8Nu1rV7Lk806zTGjlZCiFAi5QuxZx2XR3SHQCzzTJDYcPHczufv+fylpQ2l+UyHgqtRhUZFpwyX+QW4XU6n3eq0WR1Wc+XZY99vfub4528SQrgCgedXg8NiNne0/foyDic4tr9cFWTqaNn5/D3vPjyzubKYEEJRlLG9hRAilCr8QqIYe1c3K0VQeELGJL5Q3DmaZr2mPPfIng2PFx7a5bzcXd5FYplnqjmrvt3+243DORxO1IA0gViqa6nb+sDEnc8v8eyjddptFn0HIUSmCsZeul6KwxFJZDJVkMXQYdI0k99On1IEqRUBIVw+v+zM4c33jPr8paWe5S6HzaRpIYSI5UqpMoix2NA1HA5X7OcvkvsZWhttRh357dInlTpGpgyi3O7cHz7Zcs+og9te8Sy3m/Q2g5YQoggIE+JrNipdtwgl0sQx08YsWBEY2VeiUAVHx/sF4ehbr2bRazR1FQ67ZfSChx5698gjn55evP7zoKh4mqby9m4nhAhE0tC+yYQQi0HT0VTT+cLBU/46LHPp/wY6MJQQ4nbamsoKCSESP1XQb5PZwg1jM+taqop5AsGo25et+PD4I5+eXvDCuyGx/SnKffHEj47LXc8oVQV6duroWhpMl8w7M3bhyiFT71AEhEgVAcExCVJlACHEYujQ1FcQwlEGh/sFhd2otwX/IxRLZf5BMlWQRK7qvGLJL0gt9w9Whf76JUqqDAiJ7U8IMbQ1dd7ZUyiRTf7bqgFjZigCQyRyVd/0cZ7lVoO2teoih8vzC1JjTG8wvlAkUwXJVEEShT9P8OthcZkySOYf7K+OudJFEv5hkaqQSELo9oZK629fw8Ryv9ueeTM6ZbjUL0ARpI5MHEoIoWla39agbann8vgB4bESHDHDgdfukvoFDJ973/C59zEdBLqk4eLZ8tyjMv+gwMh+ngNzfsHqgPCYjvoKz7zkfKEoODqOxxeYdZr2uvI+Q8Z4ztgQiCRpMxalzVh06dbsFnNjaT5PIPQPi1aGRTLyjm5abperqazwQtbekD6JIX0TeTwBTdOBUf08bYzHF5DLnWojkav8Q6O4PL62qUbf3hjaN8mzmlAqH7fokXGLHulck6Yps7a9ra5MKJEGRPb13D0MbrCQ2MTZj7/+u4Xj73ly/D1Pdj4VK1SB0XFV57L1bY2G9kbP7NCEEL/QiKnLX7n0hS6nvaOx2mLo8A+LCYtLvt7h4Xf8gsMn/e3ZSX979tKFw2bfM2z2PVd9VYRfcHhL5QVNbbnNqO+8zWtgVL/5q9+5dE272ahtqrWbDer4gZ7bOQIqHfgyl9PuctjsFmNlbhZfJBZLFbVFp2sKTlI03WfIGEIIl8dTqaND+iQ1lRW0VhXbzIbO3yC/Q7ndzWWFZl27IigsOmX4jX0fQCjK5bBaeAKhvrWh/PRhvkDE5fGrzh1vqy7hC0Tq+EGXPTueLxIHxcT7q6M19ZWa2nLnoFGdU9L/jsNiaqkqthn1Yf2SQ/r0v87vBnpOIleGxPYXSmTaxmpNXWVE/yFX2t9jN5saLp4lHI4yJDw4BmPKDn5BYYERfaqEoubyQqOmWRUWdaULIwyapvbaMg6HExzbXxmMI2aEoNKBbwtPGJw4emr1uV+Ksr4r+OlrQghPIJQqA0L7JY/+60OedWSq4ISMyc0V542aFm1jtSRh0GU35Xa7yk7/xOXyVKFRkQPSbtx7AEIIIQKhOCJxSJ8hY1oqijpH03Nkp9+w8cm3zLrSHdmDo/tHDUjvaKjWNFSZtG3+6pjLrmbRd9QV5fAEwpDYxODohOv4TuDacHn80NjE6ORh5TlHNA2VNrPhskfcaJo2a9uq838RSWShfQcoQ3GzH3bgCYTRqcOrC040l5/X1Feq41Mve+WT5yKY5ooiqTJQHZcsVeLkV0JQ6cC3BUX1GznvwfD+gxtLztlMBkKIRK5UJ6TGDBzpua0nIUQklfcZPKq1+qLUz/8qc2FwCBHJlIljpsYMHOkXpL5BbwAuEaCOHr/4idrzp1oqL3hu7iRVBkT0HxyZnC5XBV/pq7w8ILhv2i12s1GlvuLXfUIIh8v1C1YnB89KyJjkOZgLvZZfSETi6GlcvkAZEnHF2ctoiqYpdfxARWBowsgpfAEmkmSN0D5JiaP+4hekFskUV5r0m3K7+EJRZFJacEx81IBhXD7KDCGodODzFEFhKePnpIyfc5V1gqLjZ6xce/Xt8IWiyQ+s8mo06B4Ol6cKi1SFRRIyr1sv7Dt0bN+hY6++jios+i/LXux5OLiBBCJJ4phpiWOmXWUdDpcX2nfA7Mc33LBU4C0imV/6rKudb0cI4QmEccMmxA2bcGMisQWueAW4GUWoxDGBV5tOGQB6j5hAaYQK8+rBn0ClA7gZ9QmSJYZhsnUAdkgMU/QNvvzZogCdUOkAAAAAWA+VDgAAAID1UOkAAAAAWA+VDgAAAID1UOkAAAAAWA+VDgAAAID1vDbVcGqkcvXMJG9tDXqJzwy5eVQjRtbH7NCduVDYOi4+aEQf3CbBp2ytDtXrRM/gA+tb3qoKdVjNf0kOndA/mOks4E2v5gV5d4McmqavfSt79+697bbbpFLMXOprHA6H2+2WSDDFpU/BsPoqu91O07RYLGY6CHiT3W4nhIhEuKeZr7HZbP/6179WrlzprQ16bS/dggULtm/f7q2tQS+xffv2M2fObN68mekg4E0fffRRXl7eG2+8wXQQ8LJNmzbpdLoXX3yR6SDgTRs3bjQajatXr2Y6CHiZ18cU59IBAAAAsB4qHQAAAADrodIBAAAAsB4qHQAAAADrodIBAAAAsB4qHQAAAADrodIBAAAAsB4qHQDcXN56662mpiamUwAAeBkqHQDcXD777LP29namUwAAeBkqHQAAAADrodIBAAAAsB4qHQAAAADrodIBAAAAsB4qXTfU1dXdc889ERERERERGRkZu3fvZjoReIFWq127du2QIUPefffd3/3om2++GTp0qGfEp0yZwkg8uBb5+fnz5s2L+M22bdusVivTocCbampq7rjjjqFDhxYWFjKdBbxj586dw4YN83xm77///tbWVqYTsQYqXVfV19cvXry4tbW1tLQ0Nzf3lltuWbVq1d69e5nOBT3ndrsPHToUHR398ssvNzc3m83mS3/6zjvvPProo6tXr75w4UJpaemxY8emTJlC0zRTaaG79u/fP3ny5KSkpNLfLFmyRCKRMJ0LvIOm6dWrV6ekpOzatau5udnpdDKdCK4VTdPbtm179NFHlyxZUlpa+u233545c+aJJ57Q6XRMR2MHVLousdvtP/30U2Nj46pVq2QyWVhY2NKlS5OSkvbv39/c3Mx0OughrVb79NNPz5s378CBA6GhoZf+qLGx8bPPPps1a9aYMWOUSqVMJtu7d29eXt53333HVFroltLS0k2bNk2bNu2f//yn7DcCgYDpXOA133zzzd69e7ds2fLyyy8HBQUxHQe8oLS09ODBg/Pmzbv99ttlMll6evqSJUv27dt3/vx5fJ3uClS6LrHb7d9//31wcPDo0aM9S9RqdURERF5eXlVVFbPZoMeCgoJycnI+/PDDP/4oJyenqalp3LhxSqXSsyQ9Pd1ut6PSsYLdbs/Nza2pqVm4cCHTWeB6mTt3bl5e3pIlS5gOAl7T3NxcW1vr+RbtWTJp0iSlUnn27Fm3281sNlbgMx2AHVwuV2NjY1RUVOcShULh7+9vMBh+d7QOfENra6vT6QwLC+vcr8PlcqOiohobG5kNBl1htVqLi4sVCoVCoTh37pxnYXBwcGhoKJ+PX3oAvRSPx+PxeFKpVCQSeZYEBATweLz6+nrspesK/HbrEoqiNBrN0KFDL12oVCrlcjlTkeC60mq1Mpms89cKIYTL5YaHhzMYCbrO7XZrNBq9Xv/5558XFBQQQpqbm4cPH/7YY4+lpKQwnQ4ALi8oKEitVhcVFdXU1MTFxRFC6urqHA5Hc3MzRVFMp2MBHHgFAN9kNBr79+9/5MiRI0eObNy4sbCw8L333sPVcwC9VnR09JQpU2pra7dv375nz549e/bs2LFDr9dLJBIOh8N0OhbAXrquoijKYrFcusRut3M4HJxwzQo2my07O7vzsGlYWNikSZOu/jvCarVeevYGTdMWiyUgIOD6BgXv6du375w5czyPx40bN2TIkHPnzqHSsZHT6fzss888j/l8fnx8fHp6OrOR4Nr9blgTEhLS0tLuuusugUBw+PBhz3nqo0aNksvl0dHRqHRdgUrXJRwORyQS1dbWdi5xOBwdHR0ymUyhUDAYDLrI5XKVlJRcuHDB8zQhIeHWW2+9yu8IiURiNpu1Wq3b7ebxeIQQiqLq6uo6r4+B3ozL5UqlUrvdrtFoIiMjCSEymUwikRgMBofDwXQ66Da3233q1CnPY6FQKBQKUel8gMvlunRYRSJRWlqaVCq999577733Xs/y06dP83i8+Ph4LhcHFf8cKl2XCIXCYcOG5ebmtrW1BQcHE0IaGhrq6ur69OnjeQq9nFwuf+ihh7q+fmJiYmBgYGVlpc1m81x7dfHiRbPZnJaWdt0ygtcIhcI+ffp89913tbW1gwYNIoTo9XqTyRQdHY3vYGwkFovffPNNplOAl0kkkj8d1r179yoUioEDB6LSdQX+H3WJRCKZP3++wWB47733CCF2u/3IkSP19fVjxoz53Xxm4BuGDh2alpb2zTfflJeXe07LfeWVV1JSUiZMmMB0NPhzYrF4yJAhSqXy4MGDGo2GELJ///6CgoLJkydfet06APRmX3755a5dux544AEceO0i7KXrEj6fP3LkyPvvv/+TTz6prq52Op0mk2nOnDmTJk0SCoVMp4MeMhqNa9as0Wq1TU1N9fX1X3zxRXFxcXp6+uzZs0NCQpYvX/7iiy++9NJLQUFBXC7Xbre/9NJLaPCswOPxkpOTH3zwwZ07dz788MN+fn5tbW0zZsyYPXs2rlL3GTk5Od988017e/u5c+caGhrWrFkTFBQ0bdq0GTNmYKoaltLr9Xv37j127JjnqUajueuuuxYvXoybvnQR/t13lZ+f37JlyxITE202GyEkODh40KBBmLKc1QQCwciRIz1XvXTOSRsdHe359ZGenv7Pf/6zvLzc5XIRQh588MEhQ4YwmBa6xc/Pb968eX379vXc3yUwMHDw4ME4TcKXhISEjBgxwmw2jx8/vnNhnz59cISOvYRCYUJCguf0ZUJIeHj40KFD8TWs61DpukGlUmVmZjKdArxGLBbPnj37KisMHjx48ODBNyoOeJlSqbz0jz34mOjo6OjoaKZTgDdJJJJhw4YNGzaM6SBshW8zAAAAAKyHSgcAAADAeqh0AAAAAKyHc+kA4Oby448/4gI6APA9qHQAcHPxzB0NAOBjcOAVAAAAgPVQ6QAAAABYD5UOAAAAgPVQ6QAAAABYD5UOAAAAgPVQ6QAAAABYz2uTmBQVFa1fv95bW4NeIi8vr76+HiPrY3JzcxsaGjCsvuf48eM2mw0j62OOHTvmcDgwrL4nOzt7zpw5Xtyg1yodTdMURXlra9BL0DSNkfU9NE0TQjCsvgcfWF+FYYWu8FqlS0lJeeaZZ7y1Negltm/ffubMGYysj/noo4/y8vIwrL5n06ZNOp0OI+tjNm7caDQaMay+x2q1eneDOJcOAAAAgPVQ6QAAAABYD5UOAAAAgPVQ6QAAAABYD5UOAAAAgPVQ6QAAAABYD5UOAAAAgPVQ6QAAAABYD5UOAAAAgPVQ6QAAAABYD5UOAAAAgPVQ6QAAAABYj890AJaxWCz5+fmVlZVpaWmJiYlMxwFvslgsZ8+eLSoq8jzt379/WlqaXC5nNhVcC5PJlJeX19DQMHz48H79+jEdB7zJbDafPn26rKzM8zQ5OTktLU0sFjObCnqmtrb2xx9/vHRJXFzcsGHDFAoFU5HYCJWuqyiKqqio2L59++HDh6urq1evXo1K50ucTmd2dvauXbsEAoFYLK6oqNi1a9fSpUtnzJghlUqZTgfd5nK5Ll68uHPnzkOHDrW1ta1duxaVzpc4HI6ffvrp+++/F4lEIpGopKRk9+7dK1asmDx5slAoZDoddI/L5Tpx4sTTTz89ZsyYzj+scrnc6XQyG4x1UOm6qqOj47XXXjtz5kxqampbWxvTccDLaJqWSqUzZ8689dZbxWJxeXn5vffeu3Xr1uHDh8fExDCdDrqtsbHxtddeKy0tjY2NNZvNTMcBL6NpWiaTzZ8/f8yYMSKRqLi4eMGCBZs3b87IyAgMDGQ6HXSPy+UyGo3BwcGLFi1asGAB03FYDJWuqwQCwejRo+fPn+90OgsLC5mOA14mFApHjx7d+TQuLi4mJiY7O9tqtTKYCnpMIpFMnDhx6dKl9fX1lZWVTMcBLxOJRLfeemvn06SkpKioqAsXLmC/DtzMcHlEVymVyrvvvnvSpElMB4EbwWAwmM3mmJgYnJrDUsHBwXfffffYsWOZDgI3gl6vt1gscXFxAoGA6SwAjEGlA7iMnTt35uTkzJ49GwdxAHq/d999t6io6K9//atMJmM6C/SQ52SJzMzMzMzM9evX19fXM52IfXDgFeBXFovl008/3bFjByGkoqLizjvvxF8IgF7LZDJt27Ztz549hJCSkpIVK1bMmTNHJBIxnQu6TSgUzpgxIy4uzvM0Pz9/165dtbW1Tz31FE5l7hZUOoBfiUSiGTNmpKenE0IKCgp27Njx9NNPr1+/PiIiguloAPB7Eonk9ttvHz9+PCEkNzf3008/raqq2rhxo0qlYjgZdBOXy1Wr1Wq12vPU80v4nXfeueWWW9RqNS5h7jpUOrhJJSYmulwuQohQKJw1a9b69et5PF54eHh4eDghJCkpyeVyrVu37ttvv12yZAnmMQFgkNlsHjRokOexWCy+4447Vq1axePxoqKioqKiCCGJiYk2m239+vV79uxZtGgRj8djNC9cE7lcPmzYsB07djQ0NDgcDlS6rkOlg5tUdnY2TdOEEA6H88eDNWKxePjw4VKp1GQyeVYDAKZIpdKTJ096HnM4nD9etCSRSEaPHs3n8/GB9Q1ms9nhcFAUhdHsFlQ6uEn97roHiqJcLheHw/FcMUfTdHFxsclkUqvVfD4+JgBM4nA4QUFBly7xfGC5XK7n40lRVEFBgd1uj4iI4HA4DMWEHqJp2jOant2rFEWdP3++vb09JSUFd4/oFvyt6iq3263RaNxud0dHh9Pp1Ov1TU1NUqlULpdjJ78PqKys3LBhQ0hIyLJlyzxPt27dGh8ff8stt+CEazZyOp1ardbtdut0OqfTqdPpmpqaZDKZTCbDB9YHXLhw4fXXX09OTr7zzjsJISUlJVu2bElLSxs7dizGl3Wqq6v/+9//Jicne6YJO3HixJ49e5YsWTJ48GCmo7EMKl1XNTY2Ll68uKWlxfP0vffee++99+bOnbt8+XKcPu8D4uLiFi5cuHbt2i+++MKzZO7cuStXrgwLC2M2GPRMWVnZsmXLOm/0smnTpk2bNi1atOiBBx4ICQlhNhtcu5SUlPnz57/++uvvvvuuZ8nChQsffvhhf39/ZoNBD4SHh6enpz///PNr1qzxLHnxxRdxG4keQKXrqqioqCNHjjCdAq6jcePGjRs3jukU4B0DBgzIyspiOgVcR9OmTZs2bRrTKcALRCLR7bfffvvttzMdhPUw1TAAAAAA66HSAQAAALAeKh0AAAAA66HSAQAAALAeKh0AAAAA66HSAQAAALAeKh0AAAAA66HSAQAAALAeKh0AAAAA66HSAQAAALAeKh0AAAAA63Fomr72rezdu3f+/PlKpfLaNwW9itVqdblcCoWC6SDgTRhWX2WxWCiKksvlTAcBb8Kw+iqTybRmzZqVK1d6a4N8b21o7ty577//vre2Br3Ejh07cnNzN2zYwHQQ8KZPPvnk3Llzr732GtNBwMvefPNNnU63atUqpoOAN23ZssVoND777LNMBwEve/nll727Qa9VOh6PJxaLvbU16CUEAgFG1vdgWH0Vn8/n8/kYWR+DYfVVfL7XOpgHzqUDAAAAYD1UOgAAAADWQ6UDAAAAYD1UOgAAAADWQ6UDAAAAYD1UOgAAAADWQ6UDAAAAYD1UOgAAAADWQ6UDAAAAYD1UOgAAAADWQ6UDAAAAYD1UOgAAAOiNysrK5s6de/ToUYqimM7CAqh0XWU2m//zn/8k/ebvf/97eXk506HAmy5evLhs2bKkpKS33nrLYrEwHQd6wu1279y5My0tbd26dZddIScnZ/r06UlJSQcOHHC73Tc4HnhdXV3dfffdN27cuAsXLjCdBbqHoqjc3NykpKTFixdfaZ2DBw+Wl5fHxMRwub/WFY1G88ILLyQlJf3f//2fTqe7QVlZgs90AHZwOp379+/fuXPnzz//TAg5c+bMv/71r3Xr1j377LN9+/ZlOh14x4kTJz788EO73d7e3o5vhGxUX18/cuRIo9HodrtbWlouu87HH3+clZVlNpuNRuMNjgdet2bNmjfeeEOv1wcEBNhsNqbjQPeMGjWqvLxco9EEBwdfaZ2vvvoqMTFRqVR2Lqmvr3/ttdcsFktycjK+lf0O9tJ1iUAgmD179v79+9VqtVqtnjlz5uzZs48dO3b+/Hmmo4F35OXl7dmzZ9q0abfccgvTWaCHFi1aFBgYePbs2cjIyMuu8P333//888+PPvrolVYAFtm1a9f27duff/75Z599NjAwkOk40D3PPfdcWVnZ3r17b7vttiutk5WV1dDQMGvWLJlM5lnS3t6+cePGoUOH3nnnnTcqKZug0nUVn88Xi8Wex1wuNyAggKIovV7PbCrwCpPJdPjwYbvdPmvWLB6Px3Qc6KGjR4+eO3dOKpVyOJw//tRut3/yySdjx45NSEi47ArALrfddltxcfGKFSuEQiEGlHVeffVVjUaTkJDA51/+aCFFUfv27ZNKpaNHjxYKhYQQl8t15syZkydPLlu27Eqvusmh0vWE2+12OByBgYEBAQFMZ4FrRVFUfn7+gQMH5s6dm5KSwnQcuC4oivr0009bWloWLVoUHh7OdBwA+BMNDQ2//PLLrbfe2vl3tqOj49///vfcuXPHjh3LbLZeC5WuJ6qqqrKzsyMiIvr168d0FrhWOp3u0KFDEolk6tSpTGeB66W+vv7AgQMjRozo378/01kA4M9lZWVptdoJEybI5XJCCE3T33//fVNT05IlS5iO1nuh0nWbxWLZv3//iRMnJk+enJiYyHQcuCYul6uoqCg7O3vOnDlRUVFMx4Hrwm63HzhwwGw2T5ky5SonYgNAL2G1Wg8fPtynT5/+/fsLBAJCSEtLy7Zt2+644w58K7sKHI3uHrvdfuzYMc959NOnT2c6DlwrnU63c+fOwMDAq5yiC2xXUlJy8ODBUaNGDRkyhOks0BMul2vfvn2ex3w+PyYmBudIsEhFRUVJSYnT6fQ8nTBhgp+f39Vfcv78+QsXLtx2220hISGeJdu2bTObzcuXL7++WVkOla4bnE5nXl7e22+/LRaL77333ujoaKYTwTWhabqhoeGHH34YO3bsnj17CCEVFRXNzc35+fm7d++ePHlyWFgY0xnBC3JycoqLiyMiIjyjXFRUZDabjx49ajKZ7rnnHqbTwZ9zuVxff/2157FIJBo/fjwqHYuUlZXt2bOnc7LPoUOH/mmlO378uNVqHTFihGdNs9n8wQcfJCUl/fDDD4QQjUZTWVlpt9t37949evTopKSk6/0W2AKVrqsoiiorK9u0aZNGo3nllVfS09OZTgTXiqZpkUg0c+ZMQsjp06cJIS0tLQaDoaGhoaCgYMSIEah0viEqKuqWW25xOp2eUa6vr3c4HOXl5RRFodKxglgs/vjjj5lOAT00derUbp2p3N7efvr06YEDB3buN3E4HHPnznU4HJ6PsNFobG9vdzqdBQUFcXFxqHSdUOm6SqPRvPrqq/n5+a+99tr48eOZjgNewOVyExMTt2zZ0rnk9OnTzzzzzLhx4x5//HHPObngAyZPnjx58uTOpz/99FNubu7SpUszMzOZCwUAl5eTk1NXV3f33Xd3HnX19/ffsGFD5wq1tbXPP/+82Wx+4YUXMCXhpVDpusThcPz44487duyIjY3NysrKysryLB8wYMC0adNCQ0OZjQcAhJDNmzc3NDSYzebW1tZjx4499dRTsbGxs2fPxsTCPik/P/+HH37o6Og4depUc3PzG2+8ERoaOnHixMmTJ2N2yd5v7969WVlZNputoKDAZDI99dRTwcHBU6ZMSUhIOHnypFgsTk1NlUgkTMdkGVS6LuFyufHx8f/9739/t1ytVnumQATfEBsb++ijj6rVapFIxHQW6LbIyEjPfOADBw70LAkNDf3jUCYmJq5du3bo0KGdd40ENpLL5TExMQEBAXFxcZ0LAwMDMe0wKwQGBnoGrvO0SKVSKZfLa2pqzp07l5qaepWbbQYEBCxZssTlcnXeVQI8UOm6hM/nZ2RkZGRkMB0Erq+QkBDPqXXARl28bDkiImLRokXXOwxcb/369cPMoOw1cuTIkSNH/nH5Z5991traOn/+/KscUZXL5RMmTLie6dgKX1IBAACAeR0dHbm5uaGhoampqbjlVw/gfxkAAAAwTy6XL1u2jKIoTPzeM6h0AAAAwDyhUIiD6dcCB14BAAAAWA+VDgAAAID1UOkAAAAAWA+VDgAAAID1UOkAAAAAWA+VDgAAAID1UOkAAAAAWA+VDgAAAID1vDbVcGlp6dtvv+2trUEvcerUqZqaGoysjzl58mRdXR2G1fdkZ2dbrVaMrI/Jzs622+0YVt+Tk5MzdepUL27Qa5XObDbX1tZ6a2vQS2g0GqPRiJH1MRhWX6XVau12O0bWx+h0OofDgWH1PQaDwbsb9FqlGzJkyNq1a721Negltm/ffubMGYysj/noo4/y8vIwrL5n06ZNOp3uxRdfZDoIeNPGjRuNRuPq1auZDgJe5vUxxbl0AAAAAKyHSgcAAADAeqh0AAAAAKyHSgcAAADAeqh0AAAAAKyHSgcAAADAeqh0AAAAAKyHSgcAAADAeqh0AAAAAKyHSgcAAADAeqh0AAAAAKyHSgcAAADAenymA7CGy+UqKSkpLCz0PA0PDx80aJBSqWQ2FVw7u91eUlJy4cIFz9Po6OjU1FSFQsFsKugxm8124MABgUAwatSoK31Cm5qaTp48abfbO5cEBgaOHTtWLBbfqJhwrSwWS0FBQXV1tedpfHx8SkqKSCRiNBT0UGNjY1ZW1qVLYmJiBg4cKJPJmIrERqh0XUJR1MWLF9944w0ej0cIaW5uNpvNixcvnjNnDlodq7lcroKCgnfeecczsvX19RRFLVmyZNq0aWh1bJSVlXX69Ok1a9ZERER89tlnV/p4/vLLLw888EBGRkZUVJRnSWxs7IgRI1Dp2MLhcGRlZe3atcvlcgmFwsrKSpFItHLlyvHjxwsEAqbTQfe43e7jx48vW7Zs2LBh/fr18ywcNmxYfHw8Kl23oNJ1CU3TTqdz0KBBK1asIISUlpY+//zz77//fnx8/MiRI5lOBz1H07Tb7c7IyFi6dCkhpKys7Nlnn33//fcTEhIGDx7MdDronrKysueee87f33/QoEHt7e1XWdNgMFAUtXLlyr/85S83LB54EUVRFEVlZmZOnDhRLBYXFhY+8MADb775ZlpaWkBAANPpoHucTqfBYAgNDf3b3/62YMECpuOwGM6l6xIejzdkyBBPnyOExMbGpqamNjQ0tLa2MhsMrpFAIOjsc4SQ+Pj4wYMHV1VVNTY2MhsMeoCiqFmzZr3yyiszZsxgOgtcX2KxePr06dOnT/fsWE1NTU1JSTl16pTNZmM6GgBjUOl6wmazWSyWoKAgf39/prOAl0kkEolEwuFwmA4C3da/f/+nnnoqISGB6SDAAIVCIRQKmU4BwCQceO2JX375ZdeuXVOmTElJSWE6C3hTR0dHbW1tWFhYcHAw01nguvv3v//96aefEkLCw8P/8Y9/4Bsae+n1+pKSkqSkJFwewV7Nzc1vvfXWvn37CCHp6enz589Xq9VMh2IZVLqucjgcR44ceeuttwghtbW1SUlJK1aswEkbPubYsWMHDhyYP39+//79mc4C19Gtt966Y8cOp9NJCNFoNK+88oper3/22Wc7r5YAdvn666/z8/NfeOEFnE3PRkKhcPLkydu3b/c8PX/+/K5du2pqah555BF8JLsFla6r+Hx+amrqY489RgipqKj48ccfN27c+OCDD+Ikep9RUVGxa9euqKio6dOn43JX3xYdHR0dHe15bLfbBQLBU089lZKSsnz5cmaDQQ8UFRXt2LFj5MiRkyZNwl46NuJyuTExMTExMZ6n48aNEwgEH3/88ahRo0JDQ3E8vetQ6bqKy+Wq1WrPfuDhw4dLJJLXX389NDQ0Ojoa++p8QHNz83vvvVdcXPzII4+gpvd+WVlZb731VllZmefpCy+8MG3atJ796heJRBkZGZGRkcXFxV7NCF5jNpvHjh3reSwWi2+77bYnnnjC87S+vn79+vVarXb16tVRUVE4C9YHqFSqkSNHfvnll3V1dQ6HA5Wu61DpekIikaSmpqrVar1e73K5mI4D10qv1+/cufPrr79+8MEHMzMz8UW/90tPT9+wYYPD4fA8DQ4OvpbZyNxut8Fg8ByHhV5IIpF89dVXnsdcLrdzJ7pOp1u3bt2RI0c2btyYkZHB5+Mvmo+w2WxOp9PtdtM0zXQWNsEHoIdaW1ubm5sHDx6MuUnZzuFw7Nu3b+3atffcc8/y5cvR51hBKpVKpVKvbMrlclVVVZlMptTUVK9sELyOy+X27dv3j8s3b9787rvvvvnmm7Nnz8YMw76kpKSktbU1MTFRLpcznYVNMIlJlxiNxocffnjlypVms9lsNp8/f/6DDz4Qi8WTJk3y8/NjOh30HE3TZ86cufvuu8eMGbN69WqXy+UZYrvdTlEU0+mge9xut9lstlgsDoeDoiir1ep5TAg5duzY2LFj77rrrsrKSkLI8OHDf/rpJ6PRaDabq6urH3744eTk5IceeojpdwBdRVHU22+/vWnTpieeeGLWrFkOh6Pzk8t0NOi2ysrKp59+eteuXZ5BPHDgwOeff75w4cKhQ4fiSHq3YC9dlygUiieeeGLevHmdU15NmjRp27ZtuC6S7XQ63ffffx8aGnrq1KnExMTO5bNnz/7HP/4RGxvLXDTotgMHDtx///2dR2rmzJkjlUrvv//+p556SiAQ+Pv7+/n5ee789vjjj69YscJgMBBCZDKZ5wsbk9Ghm2prawsLCyUSyQcffPDBBx90Lp83b95rr72Gs6/YJSIiYuDAgQ8//HDnknXr1i1evJjBSCyFStdVMTExOTk5TKcAL/P393/11VdfffVVpoOAF0ybNq2+vv6yP8rIyNizZ0/n0wULFuC+Q6wWGxu7devWrVu3Mh0EvEAkEt1555133nkn00FYDwdeAQAAAFgPlQ4AAACA9VDpAAAAAFgPlQ4AAACA9VDpAAAAAFgPlQ4AAACA9VDpAAAAAFgPlQ4AAACA9VDpAAAAAFgPlQ4AAACA9VDpAAAAAFgPlQ4AAACA9Tg0TV/7Vvbu3Tt//nw/P79r3xT0Kjabzel0KhQKpoOAN2FYfZXFYqFpWiaTMR0EvAnD6qvMZvOaNWtWrlzprQ3yvbWh22677f333/fW1qCX2LFjR05Ozuuvv850EPCmTz755OzZsxs2bGA6CHjZli1b9Hr9qlWrmA4C3rR582aj0fjcc88xHQS87OWXX/buBr1W6bhcrkgk8tbWoJfg8/k8Hg8j62MwrL4KI+uT+Hw+n8/HsPoeHo/n3Q3iXDoAAAAA1kOlAwAAAGA9VDoAAAAA1kOlAwAAAGA9VDoAAAAA1kOlAwAAAGA9VDoAAAAA1kOlAwAAAGA9VDoAAAAA1kOlAwAAAGA9VDoAAAAA1kOlAwAAtiouLr7//vu/++47h8PBdBYAhqHSdVtVVdX//d//JSYmrlu3zmg0Mh0HvKC8vHzp0qWJiYmJiYlTp079+eefmU4EXnD+/PnMzEzPsGZkZHz33XdMJ4JuO3/+fFpa2pw5c660QnZ2dk1Njb+/v0AgyMrKysjI8Iz46NGjjx8/fiOjwrWrqal57LHHpk2bdvToUaazsBIqXbedO3funXfeKSkpaW1tpSiK6ThwrcrLy5ctW2YwGA4fPvztt99GRkY+88wzx44dYzoXXJPCwsIlS5aEh4cfPnz48OHDGRkZjzzyyIEDB5jOBd0wefLkCRMmnD17trq6+rIr6HS648ePBwQEhIWFFRcXr1y58j//+c/hw4f37dsXHh6+YsUKtDq2sFqt77zzzrBhw95+++3Kykqz2cx0IlZCpeue4uLinTt3Tpw4cerUqUxnAS+wWCw///yzRqNZuXKlWq1OSEhYvny5Uqk8ePBgR0cH0+mghywWy4kTJ9xu98KFC9VqtVqtnjNnTkhIyIkTJ7RaLdPpoEtWr1599uzZrKyszMxMDodz2XUKCgpKS0szMjLUanViYuLJkycHDRqkVqv79ev36quvVlVV7d279wbHhp45c+bM5s2bly1btm7dOqVSyXQctkKl6waLxXL8+PGWlpb58+fzeDym44AXGAyGH3/8Ua1Wjx07lhDC4XBiY2PVavXx48fr6+uZTgc95HK5NBqNy+XqPL/K7XYTQvCxZZGXX365vb09KSnpSqNGUVR2djaXy01LS5PJZFwuVywWd5Y/iUQSEhLS0NBwAyNDz40bN+78+fMvv/yyUCi8UoOHP4VK11U0TZeVlX355Zdz584dOnQo03HAOxwOR1tbW0REROcSf39/lUrV0dFhsVgYDAbXws/Pb8qUKU1NTZs2baqpqamtrf3mm294PN6kSZP8/f2ZTgfeUV1dffbs2UGDBvXt2/d3P6Jp2maz8fn82NhYJqIBMIPPdADWMJlMBw4ccLvdmZmZBoOB6TjgHU6nU6vVhoSEXLowICBAJpMxFQm8IjExccOGDatWrRoxYoRn583GjRszMjKYzgVek5+fX1FRMX369Eu/knk4nc59+/ZZLJbRo0czkg2AEdhL1yUURZWVlf3www/z5s3D1z6A3o/D4cTFxd11111hYWFyuXzAgAE0Tet0OqZzgXdYrdbc3NyAgICUlJQ//rS0tHTDhg3p6ek46RluKqh0XWKxWD7++GOpVLpw4UKms4CXURRls9kuXWK323k8Hs67Yi+Hw3H48OGVK1c2NjZ++OGH//3vfyUSyUsvvbR7925cSecbSkpKCgoK0tLS+vXr97sfNTQ0rF27Njw8fNWqVYxkA2AKDrx2SVtb265du0aOHOmZ2qqurq6+vt7lcu3evXvixInR0dFMB4Qe4nK5HA7n0nOo7Xa7RqNRKBQ49speWq12x44dKpVq1apV8fHxhBCFQvHkk09+9913o0ePTkhIYDogXBOXy1VQUKDRaNLS0n53cmR7e/u///3vU6dOrV+/fsiQIUwlBGAEKt2fo2maw+FkZmYSQnJycggh7e3ter2ew+EUFhYOHToUlY69pFJpampqS0uLVqv1/G2oq6trbm6Oi4vDefTsZbfba2trIyIiPH2OEBIZGRkSEtLc3Ix7DPiA9vb2nJycsLCwQYMGXbrcZDJt2bJlx44d69atmzdvHlPxAJiCSvfnPBNbbN68uXNJQUHBs88+m5CQsHr1asygw2oqlSozM/Oll1764osvHnzwQZvNdujQIY1Gc9dddwUFBTGdDnpIJBLFxMSUlJScO3du8ODBhJDS0tKamprk5GSVSsVwOLhmlZWVRUVF48eP/93X6bfffvv1119/7rnn7rvvPqayATAIlQ5uaiKRaOLEiXl5ee+++255ebndbm9tbc3MzBwzZoxAIGA6HfSQSqVaunTptm3bnnnmGc/p85WVlUlJSUuXLg0NDWU6HXTJvn37Tpw4YbfbCwoKtFrtk08+qVAoZs2alZiYmJ+f73A4PNcyd65/9uzZrVu3mkympqamJ5980rMwMDBw5syZl72EAnqVioqKTz75xGQynTt3rq6u7v333z98+PDEiRPHjRuHc2C6DpWuJyIjI1esWKFUKiUSCdNZ4FqFhIQ89thjAwcO9ExEFxUVNWzYMOyiYzWRSDR69OjAwMCTJ096lqSmpo4aNSouLo7ZYNB1QUFBcXFxDofj8ccf9yyRSqUKhaK5uTk7OzsmJiYtLe3S9RUKxSuvvPK76ST9/PzkcvmNCw09JZFI+vbta7Va4+Pj58+f71kYGBiIy9S6BZWuJwICAnBtvC8JCwu76667mE4B3iQUCgcOHDhw4ECmg0APjRgxYsSIEX9cfuTIkaKiovvuuy8wMPDS5XFxcajs7BUeHr548WKmU7AeJjEBAAB2MBgMp06dkslkmEMY4I+wlw4AANhBKpXecccds2bN+uNNwAAAlQ4AANiBz+fHxMQwnQKgl8KBVwAAAADWQ6UDAAAAYD1UOgAAAADWQ6UDAAAAYD1UOgAAAADWQ6UDAAAAYD1UOgAAAADWQ6UDAAAAYD2vTTVcWlq6detWb20NeonTp0/X1NRgZH3MyZMn6+rqMKy+5/jx41arFSPrY7Kzs202G4bV9+Tk5Hj3fvEcmqavfSsXL178+OOPr307AAAAADeJmTNnjho1yltb806lAwAAAAAG4Vw6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANZDpQMAAABgPVQ6AAAAANb7f4WfK5OMDTEcAAAAAElFTkSuQmCC
Given $f(t) = 2 \cdot t^3 \cdot h(t)$, find $f'(2)$ using the table below:
$f'(2)$ = $-28$
ed6590ad-a3e5-4993-8bb9-046bd2baed10
precalculus_review
false
null
Evaluate the definite integral. Express answer in exact form whenever possible: $$ \int_{0}^\pi \sin\left(\frac{ 1 }{ 2 } \cdot x\right) \cdot \cos\left(\frac{ 1 }{ 4 } \cdot x\right) \, dx $$
$\int_{0}^\pi \sin\left(\frac{ 1 }{ 2 } \cdot x\right) \cdot \cos\left(\frac{ 1 }{ 4 } \cdot x\right) \, dx$ = $\frac{8-2\cdot\sqrt{2}}{3}$
edd9644b-fd02-4a1a-a1f2-e7bca71a8d16
multivariable_calculus
false
null
Calculate the second-order partial derivatives. (Treat $A$,$B$,$C$,$D$ as constants.) $f(x,y,z) = \arctan(x \cdot y \cdot z)$.
$f_{xx}(x,y,z)$ = $\frac{-2\cdot x\cdot y^3\cdot z^3}{\left(1+x^2\cdot y^2\cdot z^2\right)^2}$ $f_{xy}(x,y,z)$ = $f_{yx}(x,y,z)$ = $\frac{z-x^2\cdot y^2\cdot z^3}{\left(1+x^2\cdot y^2\cdot z^2\right)^2}$ $f_{yy}(x,y,z)$ = $\frac{-2\cdot x^3\cdot y\cdot z^3}{\left(1+x^2\cdot y^2\cdot z^2\right)^2}$ $f_{yz}(x,y,z)$ = $f_{zy}(x,y,z)$ = $\frac{x-x^3\cdot y^2\cdot z^2}{\left(1+x^2\cdot y^2\cdot z^2\right)^2}$ $f_{zz}(x,y,z)$ = $\frac{-2\cdot x^3\cdot y^3\cdot z}{\left(1+x^2\cdot y^2\cdot z^2\right)^2}$ $f_{xz}(x,y,z)$ = $f_{zx}(x,y,z)$ = $\frac{y-x^2\cdot y^3\cdot z^2}{\left(1+x^2\cdot y^2\cdot z^2\right)^2}$
ede288d5-dc9e-40cc-8a71-19739dead514
differential_calc
false
null
For the function $f(x) = x^3 + x^4$, determine: 1. Intervals where $f$ is increasing or decreasing, 2. Local minima and maxima of $f$, 3. Intervals where $f$ is concave up and concave down, and 4. The inflection points of $f$.
1. Increasing over $\left(-\frac{3}{4},0\right)\cup(0,\infty)$; decreasing over $\left(-\infty,-\frac{3}{4}\right)$ 2. Local maxima at None; local minima at $x=-\frac{3}{4}$ 3. Concave up for $x<-\frac{1}{2}$, $x>0$; concave down for $-\frac{1}{2}<x<0$ 4. Inflection points at $P\left(-\frac{1}{2},-\frac{1}{16}\right)$
ee44cdc7-c5a2-4805-89a4-1ab2303c9f5f
integral_calc
false
null
Find the area of the figure enclosed between the curves $y = 3 \cdot x^2$, $y = \frac{ x^2 }{ 6 }$, and $y = 2$.
Area: $\frac{48-8\cdot\sqrt{2}}{3\cdot\sqrt{3}}$
ee5612f3-dfe9-48e0-923c-6283b47e7047
sequences_series
false
null
Compute $\sqrt[5]{1000}$ with accuracy $10^{-5}$.
The final answer: $3.981072$
ee885838-2669-4456-821d-5bf3b8ec639c
differential_calc
false
null
Given the curve $y = 2 \cdot x - \arccos\left(\frac{ 1 }{ x }\right)$, find all 1. horizontal asymptotes, 2. vertical asymptotes, 3. slant asymptotes.
1. horizontal asymptotes: None 2. vertical asymptotes: None 3. slant asymptotes: $y=2\cdot x-\frac{\pi}{2}$
ef10d9c3-512a-450c-af52-3c11bd8c7b53
algebra
false
null
Find the area of a triangle bounded by the x-axis, the line $f(x) = 12 - \frac{ 1 }{ 3 } \cdot x$, and the line perpendicular to $f(x)$ that passes through the origin.
The area of the triangle is $\frac{972}{5}$
ef27aab9-82a3-4029-ad59-88207a0aa73d
precalculus_review
false
null
Use properties of the natural logarithm to write the expression $\ln\left(\frac{ 6 }{ \sqrt{e^3} }\right)$ as an expression of $\ln(6)$.
$\ln\left(\frac{ 6 }{ \sqrt{e^3} }\right)$ = $\ln(6)-\frac{3}{2}$
ef4c1961-77eb-4ec9-9674-8d37ac5fb76d
sequences_series
false
null
Find the Fourier integral of the function $q(x) = \begin{cases} 0, & x < 0 \\ \pi \cdot x, & 0 \le x \le 2 \\ 0, & x > 2 \end{cases}$
$q(x) = $\int_0^\infty\left(\frac{\left(2\cdot\alpha\cdot\sin\left(2\cdot\alpha\right)+\cos\left(2\cdot\alpha\right)-1\right)\cdot\cos\left(\alpha\cdot x\right)+\left(\sin\left(2\cdot\alpha\right)-2\cdot\alpha\cdot\cos\left(2\cdot\alpha\right)\right)\cdot\sin\left(\alpha\cdot x\right)}{\alpha^2}\right)d\alpha$
ef891729-6f14-49d4-9e8b-5359940d9704
algebra
false
null
The population $P$ of a koi pond over $x$ months is modeled by the function $P(x) = \frac{ 68 }{ 1 + 16 \cdot e^{-0.28 \cdot x} }$. How many months will it take before there are $20$ koi in the pond?
$x$: $\frac{\ln(0.15)}{-0.28}$
ef9db5b2-252c-4e24-b0bc-60680edcc39f
sequences_series
false
null
Find the Fourier series of the function $\varphi(x) = \frac{ x }{ 2 }$ in the interval $(0, 2 \cdot \pi)$.
The Fourier series is: $\frac{\pi}{2}-\frac{\sin(x)}{1}-\frac{\sin(2\cdot x)}{2}-\frac{\sin(3\cdot x)}{3}-\cdots$
efa9f4b4-8a9e-4f58-9671-8a0e93572e95
algebra
false
null
Find the area of a triangle bounded by the x-axis, the line $f(x) = 12 - \frac{ 1 }{ 5 } \cdot x$, and the line perpendicular to $f(x)$ that passes through the origin.
The area of the triangle is $\frac{4500}{13}$
efadedf0-ebaf-4ce0-b95e-58234f0c05d5
differential_calc
false
null
Find the derivative of $y = \sin(2 \cdot x) \cdot \cos(3 \cdot x) - \frac{ \ln(x-1) }{ \ln(x+1) } + c$
The final answer: $y'=2\cdot\cos(5\cdot x)-\sin(3\cdot x)\cdot\sin(2\cdot x)-\frac{(x+1)\cdot\ln(x+1)-(x-1)\cdot\ln(x-1)}{(x-1)\cdot(x+1)\cdot\left(\ln(x+1)\right)^2}$
efdc4110-cf56-4f37-bf54-40fdd5d58145
differential_calc
false
null
Compute the limit using L'Hopital's Rule: $$ \lim_{x \to \infty} \left(x - x^2 \cdot \ln\left(1 + \frac{ 1 }{ x }\right)\right) $$
The final answer: $\frac{1}{2}$
efe8b07b-20ef-4acb-a3a8-924f76bbb728
differential_calc
false
null
Find all values of the constant $c$ such that the limit $$ \lim_{x \to -\infty} \left(\frac{ 3^{c \cdot x}+1 }{ 3^{2 \cdot x}+1 }\right) $$ exists. Enter the range for the constant $c$ as an interval of the real line.
The final answer: $[0,\infty)$
f04a641b-4ad9-445a-99a6-43a8def62a2f
integral_calc
false
null
Compute the integral: $$ \int \frac{ 1 }{ (x+4) \cdot \sqrt{x^2+2 \cdot x+5} } \, dx $$
$\int \frac{ 1 }{ (x+4) \cdot \sqrt{x^2+2 \cdot x+5} } \, dx$ = $C+\frac{1}{\sqrt{13}}\cdot\ln\left(\sqrt{13}-4-x-\sqrt{x^2+2\cdot x+5}\right)-\frac{1}{\sqrt{13}}\cdot\ln\left(4+\sqrt{13}+x+\sqrt{x^2+2\cdot x+5}\right)$
f05e9aaf-c4af-4097-b180-bbbce6a70c0a
precalculus_review
false
null
Use the Rational Zero Theorem to find all real zeros of the following polynomial: $p(x) = x^3 - 8 \cdot x^2 + 17 \cdot x - 10$
The real zeros are $1$, $2$, $5$
f06583ca-72cf-40eb-a419-128a961eea6e
integral_calc
false
null
Compute the integral: $$ -\int \frac{ \sin\left(\frac{ x }{ 3 }\right)^4 }{ \cos\left(\frac{ x }{ 3 }\right)^2 } \, dx $$
$-\int \frac{ \sin\left(\frac{ x }{ 3 }\right)^4 }{ \cos\left(\frac{ x }{ 3 }\right)^2 } \, dx$ = $-\frac{3\cdot\sin\left(\frac{x}{3}\right)^3}{\cos\left(\frac{x}{3}\right)}+\frac{3}{2}\cdot x-\frac{9}{4}\cdot\sin\left(\frac{2\cdot x}{3}\right)+C$
f0abc5d4-cb46-4522-a5e4-08a47caf8212
integral_calc
false
null
Compute the integral: $$ \int \sqrt[3]{x \cdot \left(8-x^2\right)} \, dx $$
$\int \sqrt[3]{x \cdot \left(8-x^2\right)} \, dx$ = $C+\frac{1}{3}\cdot\left(2\cdot\ln\left(\left|1+\sqrt[3]{\frac{8}{x^2}-1}^2-\sqrt[3]{\frac{8}{x^2}-1}\right|\right)-4\cdot\ln\left(\left|1+\sqrt[3]{\frac{8}{x^2}-1}\right|\right)-4\cdot\sqrt{3}\cdot\arctan\left(\frac{1}{\sqrt{3}}\cdot\left(2\cdot\sqrt[3]{\frac{8}{x^2}-1}-1\right)\right)\right)+\frac{4\cdot\sqrt[3]{\frac{8}{x^2}-1}}{1+\sqrt[3]{\frac{8}{x^2}-1}^3}$
f0b46da5-b7cf-4d8a-81ae-e3ff591ba59c
precalculus_review
false
null
Solve $|3 \cdot x - 11| = 4 \cdot x - 3$.
The final answer: $x=2$
f12059b7-639d-4813-96ca-8ce7814a6f55
multivariable_calculus
false
null
Find points on the curve at which the tangent line is horizontal or vertical: $$ x = \frac{ 3 \cdot t }{ 1+t^3 }, \quad y = \frac{ 3 \cdot t^2 }{ 1+t^3 } $$
1. Horizontal: $P(0,0)$, $P\left(\sqrt[3]{2},\sqrt[3]{4}\right)$ 2. Vertical: $P\left(\sqrt[3]{4},\sqrt[3]{2}\right)$
f124cb60-bc4d-44b2-b851-fd1aef9a1bfb
integral_calc
false
null
Solve the integral: $$ \int 22 \cdot \cot(-11 \cdot x)^5 \, dx $$
$\int 22 \cdot \cot(-11 \cdot x)^5 \, dx$ = $C+\frac{1}{2}\cdot\left(\cot(11\cdot x)\right)^4+\ln\left(1+\left(\cot(11\cdot x)\right)^2\right)-\left(\cot(11\cdot x)\right)^2$
f1283a97-29cb-42c8-a96e-42213e587522
differential_calc
false
null
Calculate the derivative of the function $r = 2 \cdot \ln\left(\sqrt[6]{\frac{ 1+\tan(3 \cdot \varphi) }{ 1-\tan(3 \cdot \varphi) }}\right)$.
$r'$ = $2\cdot\sec(6\cdot\varphi)$
f13796c5-a85c-4895-983c-ead174a245bc
multivariable_calculus
false
null
Find the moment of inertia of one arch of the cycloid $x = a \cdot \left(t - \sin(t)\right)$, $y = a \cdot \left(1 - \cos(t)\right)$ relative to the x-axis.
Moment of Inertia: $\frac{256}{15}\cdot a^3$
f1e83625-9780-41d5-9516-ace9a7d12801
precalculus_review
false
null
Suppose a function $f(x)$ is periodic with the period $T$. What is the period of the function $f(a \cdot x + b)$, when $a > 0$?
The final answer: $\frac{T}{a}$
f1efd818-8385-44fb-ac8f-8bf513dfc2e8
algebra
false
null
Solve the equation for $x$: $$ \frac{ 3 }{ \log_{2}(10) }-\log_{10}(x-9)=\log_{10}(44) $$
$x$ = $\frac{101}{11}$
f22f4c69-3c17-40de-9b09-9d9e2366f174
sequences_series
false
null
Suppose that $\sum_{n=0}^\infty\left(a_{n} \cdot x^n\right)$ converges to a function $y$ such that $y'' - y' + y = 0$ where $y(0) = 1$ and $y'(0) = 0$. Compute $a_{0}$, ..., $a_{5}$.
The final answer: $a_{0}$: $1$ $a_{1}$: $0$ $a_{2}$: $\frac{1}{2}$ $a_{3}$: $\frac{1}{6}$ $a_{4}$: $0$ $a_{5}$: $-\frac{1}{120}$
f26b7d10-ebe6-4a28-b7ac-df7c888f2ccf
precalculus_review
false
null
Solve the logarithmic equation exactly, if possible: $\ln(x) + \ln(x-2) = \ln(4)$ If the solution does not exist, enter undefined.
$x$ = $1+\sqrt{5}$
f29b52bc-52d0-49f7-977d-cf9effc0cd00
algebra
false
null
Given the rational function $f(x) = \frac{ x^2-1 }{ x^3+9 \cdot x^2+14 \cdot x }$, find 1. the domain (in interval notation), 2. vertical asymptotes (in the form $x=a$), 3. horizontal asymptotes (in the form $y=c$).
1. The domain in interval notation is $(-\infty,-7)\cup(-7,-2)\cup(-2,0)\cup(0,\infty)$ 2. Vertical asymptotes of $f(x)$: $x=-7$, $x=0$, $x=-2$ 3. Horizontal asymptotes of $f(x)$: $y=0$
f2ac69f4-7404-4834-a8cc-1658a2cdda96
sequences_series
false
null
Evaluate $\int_{0}^{\frac{ \pi }{ 2 }}{\sin\left(\theta\right)^4 d \theta}$ and $\int_{0}^{\frac{ \pi }{ 2 }}{\sin\left(\theta\right)^2 d \theta}$ in the approximation $T=4 \cdot \sqrt{\frac{ L }{ g }} \cdot \int_{0}^{\frac{ \pi }{ 2 }}{\left(1+\frac{ 1 }{ 2 } \cdot k^2 \cdot \sin\left(\theta\right)^2+\frac{ 3 }{ 8 } \cdot k^4 \cdot \sin\left(\theta\right)^4\right) d \theta}$ to obtain an improved estimate for $T$.
$T$: $2\cdot\pi\cdot\sqrt{\frac{L}{g}}\cdot\left(1+\frac{k^2}{4}+\frac{9\cdot k^4}{64}\right)$
f3483e15-54ea-41ca-9681-11eb71d774d0
differential_calc
true
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
Given $f(t) = g(t) \cdot h(t)$, find $f'(2)$ using the table below:
$f'(2)$ = $-15$
f38c8513-234c-4b70-b306-880df56aa4e9
integral_calc
false
null
Evaluate the integral: $$ I = \int 3 \cdot \ln\left(\sqrt{2-x}+\sqrt{2+x}\right) \, dx $$
The final answer: $3\cdot x\cdot\ln\left(\sqrt{2-x}+\sqrt{2+x}\right)-\frac{3}{2}\cdot\left((C+x)-2\cdot\arcsin\left(\frac{x}{2}\right)\right)$
f395b144-92c4-40f4-8eb6-84b365bd4f7c
algebra
false
null
Use the vertex $P(h,k) = P(-4,-5)$ and a point $P(x,y) = P(-2,7)$ on the graph of $f(x)$ to find the general form of the quadratic function.
The final answer: $f(x)=3\cdot x^2+24\cdot x+43$
f3c9a461-3a76-4213-94ae-ea4760b8a013
differential_calc
true
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
| | $x$ | $f$ | $f'$ | | --- | --- | --- | --- | | $0$ | $3$ | $-1$ | The function $f$ is a differentiable function. The table above shows values of $f$ and $f'$, the derivative of $f$, at selected values of $x$. The graph of $g$ is shown at right. Given $h(x) = (3 \cdot g(x) + 2 \cdot x) \cdot (f(x) - 2)$, find $h'(0)$. | | | --- | --- | --- | --- | --- | --- | --- | --- |
$h'(0)$ = $\frac{1}{2}$
f3e17598-93ba-4014-916f-e790a5525c7a
algebra
true
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
The graph below illustrates the decay of a radioactive substance over $t$ days: Use the graph to estimate the average decay rate from $t=5$ to $t=10$.
The final answer: $-\frac{4}{5}$
f4126597-791b-4deb-99db-5c16af183608
multivariable_calculus
false
null
Consider points $A(3,-1,2)$, $B(2,1,5)$, and $C(1,-2,-2)$. 1. Find the area of parallelogram $ABCD$ with adjacent sides $\vec{AB}$ and $\vec{AC}$. 2. Find the area of triangle $ABC$. 3. Find the distance from point $A$ to line $BC$.
1. $A$ = $5\cdot\sqrt{6}$ 2. $A$ = $\frac{5\cdot\sqrt{6}}{2}$ 3. $d$ = $\frac{5\cdot\sqrt{6}}{\sqrt{59}}$
f46c0483-d278-4a55-af5b-bc6b958126ff
integral_calc
false
null
Solve the integral: $$ \int \left(\frac{ x+2 }{ x-2 } \right)^{\frac{ 3 }{ 2 }} \, dx $$
$\int \left(\frac{ x+2 }{ x-2 } \right)^{\frac{ 3 }{ 2 }} \, dx$ = $C+\sqrt{\frac{x+2}{x-2}}\cdot(x-10)-6\cdot\ln\left(\left|\frac{\sqrt{x-2}-\sqrt{x+2}}{\sqrt{x-2}+\sqrt{x+2}}\right|\right)$
f47cb838-a60c-461f-8c9b-9143e021222f
integral_calc
false
null
Use integration by substitution and/or by parts to compute the integral: $$ \int x \cdot \ln(5+x) \, dx $$
The final answer: $D+5\cdot(x+5)+\left(\frac{1}{2}\cdot(x+5)^2-5\cdot(x+5)\right)\cdot\ln(x+5)-\frac{1}{4}\cdot(x+5)^2$
f4aa6ca1-ce0a-4dd9-bd2d-056d17e9d173
precalculus_review
false
null
Find the period of the function $f(x) = \left(\sin(x)\right)^4 + \left(\cos(x)\right)^4$.
The final answer: $T=\frac{\pi}{2}$
f4bc1799-6bb0-4f5b-8914-a951b5560142
multivariable_calculus
false
null
Find the moment of inertia of one arch of the cycloid $x=a \cdot \left(3 \cdot t-\sin(3 \cdot t)\right)$, $y=a \cdot \left(1-\cos(3 \cdot t)\right)$ relative to the x-axis.
Moment of Inertia: $\frac{256}{15}\cdot a^3$
f50abb06-3b30-462d-b87a-b921c7c38f0c
multivariable_calculus
false
null
For the function $f(x,y) = 2 \cdot x \cdot y \cdot e^{-x^2-y^2}$, use the second derivative test to identify any critical points and determine whether each critical point is a local minimum, local maximum, saddle point, or none of these.
$f$ has a local minimum at $P\left(-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)$, $P\left(\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right)$ . $f$ has a local maximum at $P\left(-\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right)$, $P\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)$ . $f$ has a saddle point at $P(0,0)$ . The second derivative test is inconclusive at None .
f61c3d0e-e73d-42ec-9f3a-0c30d2022bef
precalculus_review
false
null
Identify the set of real numbers for which $x \cdot (x-1) \cdot (x-4) \le 0$.
The final answer: $(-\infty,0]\cup[1,4]$
f6a631ca-4b2b-4716-be3b-538b249f543e
multivariable_calculus
false
null
Calculate the average lengths of all vertical chords of the parabola $\frac{ x^2 }{ a^2 } - \frac{ y^2 }{ b^2 } = 1$ over the interval $a \le x \le 2 \cdot a$.
The final answer: $\mu=b\left(2\cdot\sqrt{3}-\ln\left(2+\sqrt{3}\right)\right)$
f6ce3b4f-29e4-44a8-832c-9912388bdc0f
differential_calc
true
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
Graph of $f$: Let $f$ be a function whose graph, consisting of four line segments, is shown in the figure above. Let $g$ be the function defined by $g(x) = x + f(x)$. At what value of $x$ does $g(x)$ attain its absolute maximum on the interval $[-3,5]$?
The function $g(x)$ attains its absolute maximum on the interval $[-3,5]$ at $x$ = $5$
f6f3fc6f-7ebb-4b8d-8bf9-3dee49a8e6c6
integral_calc
true
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
Let $R$ and $S$ in the figure above be defined as follows: $R$ is the region in the first and second quadrants bounded by the graphs of $y = (x-1)^2 \cdot (x+2)$ and $y = \ln(x+3)$. $S$ is the shaded region in the first quadrant bounded by the two graphs, the $x$-axis, and the $y$-axis. The region $R$ is the base of a solid. For this solid, each cross section perpendicular to the $x$-axis is an isosceles right triangle with one leg across the base of the solid. Write, but do not evaluate, an integral expression that gives the volume of the solid.
$V$ = $\frac{1}{2}\cdot\int_{-2}^{0.278}\left((x-1)^2\cdot(x+2)-\ln(x+3)\right)^2dx$
f715864e-78fd-4609-a76c-00ec0430b38f
multivariable_calculus
false
null
Given $\vec{r}(t) = \left\langle e^t \cdot \cos(t), e^t \cdot \sin(t), e^t \right\rangle$. Find the tangential and normal components of acceleration.
The final answer: 1. The tangential component of acceleration, $a_{t}$, is: $\sqrt{3}\cdot e^t$ 2. The normal component of acceleration, $a_{N}$, is: $\sqrt{2}\cdot e^t$
f73136c7-5fe8-4f38-8765-b1ec63b449af
sequences_series
false
null
Expand the function $f(x) = e^x$ in terms of powers of $x + 1$.
The final answer: $e^x=\frac{1}{e}+(x+1)\cdot\frac{1}{e}+\frac{(x+1)^2}{2!}\cdot\frac{1}{e}+\frac{(x+1)^3}{3!}\cdot\frac{1}{e}+\frac{(x+1)^4}{4!}\cdot e^{\xi}$
f75e7bcb-5148-4043-96cb-45ed33624be4
precalculus_review
false
null
If $y=100$ at $t=4$ and $y=10$ at $t=8$, when does $y=1$? Use $y=y_{0} \cdot e^{k \cdot t}$, where $y_{0}$ is the beginning amount, $y$ is the ending amount, $k$ is the growth or decay rate, and $t$ is time.
$y$ = 1 at $t$ = $12$
f79b682d-3c4b-4608-9f46-0f999d9bc010
differential_calc
true
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tXT3fffbdSU1P15JNPlu62BQBwl5J1elfr0KGD46YVAosRECCMrFmzxnHGh1T+6VeSlJCQoObNm+vw4cOltaKiIu3atcvVc2iffPJJn9GMqmjVqpWeeOIJPfHEE375egCA4DCN2DP6EXyMgABhxDT60aNHD7Vr165CX8fLC9EBAOHLtAOWm2+ehSoaECCMVGX3q6uZ3qzdtg6kqKjIdgQAgMswAuIONCBAmFi6dKl27drlqFdk/UcJ05u12xqQvLw82xEAAC5SVFREA+ISNCBAmDCNfvTv31/NmjWr8NcyLUQ3rS0BAMAt9u7d69gwJSEhQY0aNbKUKHzRgABhwrT+ozLTrySpTZs2jp2ecnJydPTo0Up9PQAAAs20VrFkN0MEFw0IEAYWLlyojIwMR72yDYhkHgVhIToAwK1M1yjTtQyBRwMChAHT6MfQoUNVv379Sn9NrxxICACARAPiJjQgQIi7ePGi33a/uhojIAAAL9m0aZOjxgJ0O2hAgBC3aNEiHTlyxFGvagPCWSAAAK84ceKEcnJyfGoxMTHq2LGjpUThjQYECHGm0Y/Ro0crLi6uSl83MTHRUdu/f79jhxEAAGwz3SBLTExUZCS/CtvAsw6EsLNnzxrXf1Tm7I9rxcbGGk9QZzteAIDbcP6Hu9CAACFs8eLFOnXqlKM+ZcoUv3x9L5yIDgDAl19+6aiZrmEIDhoQIISZRj8mT56smJgYv3x9L5yIDgAAIyDuQgMChKiTJ0/69fBBExaiAwDcLj8/X/v27XPUe/XqZSENJBoQIGQtWrRI586d86lFR0dr0qRJfvsepuFr0zA3AAC2bN++XUVFRT61li1bKjY21lIi0IAAIcq0+5U/Fp9frUmTJkpISPCp5eXlKTMz06/fBwCAyjKNzDP9yi4aECAEZWVlBXz6VYmePXs6aqwDAQC4hemaxAnodtGAACFo8eLFunz5sk+tVq1aGjVqlN+/l+lNnAYEAOAWpqnBNCB20YAAIShYox+SeRibdSAAALdgByz3oQEBQsz+/fuDsv6jRI8ePRw1GhAAgBtkZmbq/PnzPrX4+Hi1bt3aUiJINCBAyDGNfjRo0EA33XRTQL5fly5dVL16dZ/a4cOHdfr06YB8PwAAyosF6O5EAwKEGNPoR6CmX5UwzaXlPBAAgG2mEfnExEQLSXA1GhAghKSnp2v58uWOuo0GZOvWrQH9ngAA3Mi2bdscNRag20cDAoQQ0+hHixYt1K9fv4B+X9M6ENObPgAAwWQaATFdsxBcNCBACAnm7ldXM52ITgMCALDp5MmTOn78uE8tMjKSKVguQAMChIgtW7Zo7dq1jnowGpBu3bopMtL37WT//v3Ky8sL+PcGAMDEdCOsS5cuiomJsZAGV6MBAUKEafSjffv2xtEJf4uJiVHnzp0ddUZBAAC2MP3KvWhAgBARzLM/TDgPBADgJqabYDQg7kADAoSAtWvXavPmzY56MKZflWAdCADATUw3wYIxKwA3RgMChADT6Ee3bt3UoUOHoGVgJywAgFvk5eUpMzPTUWcExB1oQIAQYGv3q6v17NnTUdu5c6fy8/ODmgMAgE2bNjlq7du3V2xsrIU0uBYNCOBxK1asUHp6uqMe7AYkNjZWbdu29akVFRUZswEAEEimEXimX7kHDQjgcabRj6SkJLVs2TLoWViIDgBwA3bAcjcaEMDjTOs/gj36UYIGBADgBjQg7kYDAnjY4sWLtW/fPkfdVgPCTlgAANvy8/O1Z88eR71Xr14W0sCEBgTwMNPox+DBg9WwYUMLaaQ+ffo4alu3blVRUZGFNACAcLRt2zbHdad58+ZKSEiwlAjXogEBPKqwsNC4/iOYhw9eKyEhQU2bNvWp5efna+/evZYSAQDCDQcQuh8NCOBRCxYsUFZWlqM+depUC2n+jXUgAACbOIDQ/WhAAI8yjX7cfPPN1oeYaUAAADYxAuJ+0Rs2bLCdoUK8dqaA1/KWnBrqldeF157fElXNffHiRc2cOdNxyF+PHj0C8m9Xkbw1atRw5Fq2bFlQX1Nee11kZWWVPmdZWVn8/AUIeQPLa3m9dr0r4bXnOdh5i4uLtWXLFhUUFDjq5fm35vkNDkZAAA9as2aNTp8+7agPGzbMQhpf7du3d9RMO3UBAOBvGRkZjuajVq1aql+/vqVEMIlOSkqynaFSvJbbK3lL7g54JW8Jr+UtUdnc//d//6eYmBif2sSJEzVo0CB/xCpTefPWr19fOTk5pX++dOmSGjZsqFatWgUqmpFXXhepqaml/54tWrTwTO4S5A0s8gaGV693JbyWO1h59+7d67g+Dho0qMLfn+c3sBgBATwmOzvbuP7D1tkfJr1793bUWAcCAAg0DiD0BhoQwGMWLVqks2fP+tQiIyM1efJkS4mcTLuN0IAAAALNtACdHbDchwYE8Jiyzv6IiIiwkMasZ8+ejhonogMAAo0dsLyBBgTwkKNHj7p++pXECAgAIPj279+vvLw8n1psbKzatGljJxDKRAMCeMiiRYt08eJFn1rNmjU1ZswYS4nM2rVrp9jYWJ/a8ePHdfLkSUuJAAChznSjy7QmEfbRgAAesnjxYkfNbaMfJUxD3kzDAgAECus/vIMGBPCIjIwMT0y/KsGJ6ACAYGL9h3fQgAAesXjxYhUVFfnU6tWr54rDB01Md50YAQEABMrmzZsdNUZA3IkGBPAIL41+SOadsBgBAQAEwpEjR3wOwJWkmJgYderUyVIiXA8NCOABu3fv1tKlSx11NzcgnTt3dpxGm5mZ6dihBACAqjLd4OrevbsiI/lV1434VwE8wDT60bRpUw0YMMBCmvKJjIxU165dHfVNmzZZSAMACGWs//AWGhDAA0y7X02fPj34QSqI80AAAMHADljeQgMCuNy2bdu0evVqR93N069KsBUvACAYTDe3GAFxLxoQwOVMox9t27Y1LvJ2G0ZAAACBlpOToyNHjvjUypoGDHegAQFczmu7X12tR48ejgWAe/bsUX5+vqVEAIBQY9p+17QRCtyDBgRwsQ0bNmjjxo2OuhfWf0hXtkDs2LGjT62oqIhpWAAAv2EBuvfQgAAuZhr9SExM9NS+5pyIDgAIJBoQ76EBAVzMtP7DK9OvSnAiOgAgkNgBy3toQACXWrVqlXGkwGsNCCMgAIBAycvL04EDBxx1L2zUEs5oQACXMo1+9OnTR61bt7aQpvJ69+7tqO3YsUNFRUXBDwMACCmm0Y927dopNjbWQhqUFw0I4FJe3v3qarGxsWrTpo1PLT8/X7t27bITCAAQMph+5U00IIALpaamas+ePY761KlTLaSpOtaBAAACwTSll+lX7kcDAriQafRj4MCBatKkiYU0VceJ6ACAQNi6daujxgiI+9GAAC4UKtOvSnAiOgDA38qazmtaewh3oQEBXGb+/Pk6ePCgo+7V6VeSlJSU5KiZ7loBAFBepg1NmjVrpoSEBEuJUF40IIDLmHa/GjFihOrWrWshjX8kJCSoadOmPrW8vDzt3bvXUiIAgNdt377dUWP9hzfQgAAucvny5ZCbflXCtA5ky5YtFpIAAEKB6RrC+g9voAEBXGT+/Pk6duyYoz558mQLafzLdFdq8+bNwQ8CAAgJpgbEdLML7kMDAriIafRj/PjxiouLs5DGv0wNCCMgAIDKyM/PV3p6uqPep08fC2lQUTQggEvk5OSE7PQrybwryZdffsmJ6ACACktPT1d+fr5PrXHjxmrQoIGlRKgIGhDAJRYsWKDTp0876pMmTbKQxv8aNGjgWIh+8eJFTkQHAFSYaQS9V69eFpKgMmhAAJcw7X41bdo0RUdHW0gTGKZpWGzHCwCoKFMDwg5Y3kEDArjAyZMnjdOvpk+fHvwwAWS6O8U6EABARZluXjEC4h00IIALLFy4UOfPn/ep1ahRQ+PGjbOUKDBYiA4AqKr8/Hzt2LHDUacB8Q4aEMAFQnnx+dX69evnqLEQHQBQEabrRrNmzViA7iE0IIBlhw4dCpsGJCEhQc2bN/eplbWVIgAAJky/8j4aEMCyRYsWqaCgwKdWp04djRgxwk6gAGMaFgCgKliA7n00IIBlZe1+FapYiA4AqAq24PU+GhDAor179+qLL75w1EO5AWEEBABQWfn5+cbzo/r27WshDSqLBgSwyDT60bhxYw0cONBCmuAwXSRMJ9oCAHCtrVu3Ohagt2zZUgkJCZYSoTJoQACLwmXx+dUSEhLUsmVLn1pZWyoCAHA10wJ01n94Dw0IYMn+/fu1cuVKRz3UDh80YRoWAKAyWP8RGmhAAEvWrl3rqLVu3Vq9e/cOfpggYyE6AKAy2II3NNCAAJaYGpBQn35VwjQCYrqoAABQ4uLFi9q9e7ejTgPiPTQggAW7du0yrnkIlwbENMrDQnQAwPVs27bNsQC9devWLED3IBoQwALT6Efnzp2VmJhoIU3wJSQkqHXr1j61oqIibdu2zVIiAIDbMf0qdNCAABaE8/SrEixEBwBUBCegh47oDRs22M5QIenp6bYjVIjX8mZmZkqSvPK68NrzK0lffvmlMXe7du1c+7wH4nmuW7euY8rVwoUL/XIx8drrIisrq/S5yMrKcu3r4Fpee57JG1hey+u1610Jrz3P/sy7cuVKx3WjRo0afv03DOfnN5gYAQGCzDT60bFjRzVv3txCGns6duzoqO3Zs8dCEgCA212+fFmHDh1y1MNl6nKoiU5KSrKdoVK8ltsreUvuInglbwkv5f3xj3+s6OhoSVJMTIwk6Z577vHE38GfGTt27Kgnn3zSp3b06FF169ZNNWrU8Mv38MJzKkmpqamlr4UWLVp4JncJ8gYWeQPDq9e7El7LXdW8aWlppdfOEm3bttWgQYOq9HXLEm7Pb7AxAgIE0bJly7Rr1y5HfcqUKRbS2JWQkKA2bdr41FiIDgAw4QDC0EIDAgTR4sWLHbUBAwaE3fSrEpwHAgAoD3bACi00IEAQLVq0yFELt92vrsaJ6ACA8mAEJLTQgABBsmjRIh04cMBRnzx5soU07sBWvACAG7l48aL27dvnqJsOtYU30IAAQWIa/Rg2bJgaNmxoIY07mBbN7dmzRxcvXrSQBgDgRps2bXLUOnTo4LcNSxB8NCBAEBQVFTH9yqBGjRpq166do7558+bghwEAuBLTr0IPDQgQBHPnztWRI0cc9UmTJllI4y5MwwIAXA8NSOihAQGCwLT71cCBA5WQkGAhjbuwEB0AcD3sgBV6aECAAMvLyzNOvxo+fLiFNO7DCAgAoCw5OTmODVwiIyPVo0cPS4ngDzQgQIDNmzdPX331laN+0003WUjjPn369HHUDhw4oJycHAtpAABuYhr96NixIwvQPY4GBAiwsna/qlatmoU07lOjRg116NDBUedEdAAA069CEw0IEECnT59m+lU5MA0LAGBCAxKaaECAAJo/f75yc3N9atWqVdPgwYMtJXIn08XEdNEBAIQX080o000reAsNCBBApt2vpk2bpoiICAtp3IsREADAtXJycpSZmelTi4yMpAEJATQgQIAcO3aMwwfLqVevXoqM9H07yszMZCE6AIQx042ozp07KyYmxkIa+BMNCBAgCxYs0KVLl3xq8fHxuvnmmy0lcq+yFqJzIjoAhC8OIAxdNCBAgJhGP6ZPnx78IB7BNCwAwNVY/xG6aECAAMjIyGD6VQVxIjoA4GrsgBW6aECAAFi4cKGj1rBhQ3a/ug5GQAAAJXJycnTo0CGfWmRkpLp3724pEfyJBgQIgLJ2v0LZevTo4ViIfvjwYRaiA0AY2rhxo6PWtWtXFqCHCBoQwM927dqlZcuWOeqs/7i+GjVqqHPnzo76+vXrLaQBANi0bds2R613797BD4KAoAEB/My09qNly5bq27evhTTe0qdPH0dt06ZNFpIAAGwyjYD06NHDQhIEAg0I4GcsPq88090tGhAACD+m0W8WoIcOGhDAj7Zu3aq0tDRHnQakfEwjIOvWrbOQBABgy+HDh3Xq1CmfWkxMjBITEy0lgr/RgAB+ZBr96NChg7p162YhjfckJiaqRo0aPrXc3FxlZmZaSgQACDbTyHfPnj1ZgB5CaEAAP+LwwaqJjIw0zvHlRHQACB+mBsQ0Qg7vogEB/GTdunXGX5SnTJkS/DAeZlqszzoQAAgfNCChjwYE8BPT2R/du3dXx44dLaTxLnbCAoDwVVRUZLyZRwMSWmhAAD9h9yv/MO2EtW3bNhUVFQU/DAAgqHbt2qWLFy/61OLj49WmTRs7gRAQNCCAH6xcuVI7duxw1Jl+VXGtWrVSfHy8T+3ixYtKT0+3lAgAECym8z/69etnIQkCiQYE8APT6Ee/fv3UqlUrC2m8b8CAAY4a07AAIPSx/iM80IAAfsD0K//iQEIACE80IOGBBgSooi+++EL79u1z1CdNmmQhTWgwXWzYihcAQtvFixe1a9cuR900Kg5vowEBqsi0+9WQIUPUpEkTC2lCQ//+/R0108JEAEDo2LRpk2PDEdO6QHgfDQhQRUy/8j/Tjidlbc0IAAgNpulXpim58D4aEKAK5s2bp0OHDjnqEydOtJAmtLAOBADCi+k93nQ4LbyPBgSoAtPox6hRo1S3bl0LaUIL60AAILywAD180IAAlZSfn29sQKZPnx78MCGIE9EBIHycOnVKR44c8alFRkaqR48elhIhkGhAgEqaM2eOTpw44aiPHz/eQprQ06tXL0VG+r5FZWVl6dSpU5YSAQACZf369Y5a165dVaNGDQtpEGg0IEAlmXa/mjRpkuLi4iykCT0xMTHq2rWro246JRcA4G2m93amX4UuGhCgEs6dO8fuV0HAOhAACA+s/wgvNCBAJcydO1dnzpzxqUVFRTH9ys9YBwIA4WHLli2OGlvwhi4aEKASylp8Hh0dbSFN6DJdfDZs2BD8IACAgNmzZ49yc3N9ajVq1FCnTp0sJUKg0YAAFfTVV18x/SpIOnXq5FiAmJubqwMHDlhKBADwN9P6j759+zo2IkHo4F8WqKB58+YpLy/PpxYXF6fRo0dbShS6IiMjjYdQMQ0LAEKHaW0f069CGw0IUEGm3a8Y/QgcTkQHgNDGDljhhwYEqIDDhw9z+GCQsRMWAISu/Px8bd++3VE3jX4jdER7bUFnenq67QgV4rW8mZmZkryz0DfYz29KSoouXrzoU6tdu7ZiY2Mr9Jx57XVhM29UVJTy8/N9auvXr1daWlqZi/699vxmZWWV/h2zsrL4+QsQ8gaW1/J67XpXwmvP843y7tixQ5cuXfKp1a5dW0eOHHGcjB4Mofb8uhUjIEAFrF271lEbMWJE8IOEkYYNG6p27do+tYKCAhaiA0AI2LVrl6NmOoQWoSU6KSnJdoZK8Vpur+QtuRPklbwlgpF337592rp1q2JiYnzqDz74YKW/P89z+QwZMkQLFizwqV26dOmGebzy/Kamppa+rlq0aOGZ3CXIG1jkDQyvXu9KeC13WXnffPNNx3V19OjR1v9+tr9/RXktLyMgQDld+wuwJDVv3lz9+/e3kCa8sA4EAEKT6b2c9R+hjwYEKCfO/rCHrXgBIPTk5uaWrsW5Wq9evSykQTDRgADlsGPHDq1evdpRnzp1qoU04ce0Fe/u3bsdGwIAALzDtK6yQ4cOio+Pt5AGwUQDApTDwoULHbV27dqpZ8+eFtKEn/j4eLVv395R99ruNQCAfzONZHP+R3igAQHKgbM/7GMdCACEFhqQ8EUDAtzAxo0bjXfaJ0+ebCFN+DJdlFgHAgDetX79ekeNBiQ80IAAN2Aa/ejatau6dOliIU34Mq0DoQEBAG/KyMhQbm6uTy0mJoYzQMIEDQhwA+x+5Q7du3d37BV/9OhRnTp1ylIiAEBlmW4g9ejRw/E+j9BEAwJcx+rVq/Xll1866ky/Cr6YmBh169bNUTcN4QMA3G3jxo2OGtOvwgcNCHAdixcvdtT69u2rtm3bWkgD1oEAQGgwbSJCAxI+aECA62D6lbvQgACA9+Xn52vr1q2OOg1I+KABAcqwdOlS7d6921GfOHGihTSQ2IoXAELBjh07lJ+f71OrXbs2swvCCA0IUAbT6MegQYPUvHlzC2kgSe3bt1dCQoJPLTc3V/v377eUCABQUaz/AA0IUAYOH3Qn00Vq3bp1FpIAACrDtHlIUlKShSSwhQYEMFiwYIEyMzMd9QkTJlhIg6v17dvXUWMnLADwDtN7tum9HaGLBgQwMO1+NXLkSDVo0MBCGlzNdJfMdFI9AMB9srOzdejQIUe9X79+FtLAFhoQwIDdr9xrwIABjtru3bt17tw5C2kAABWxdu1aR61jx46Kj4+3kAa20IAA15g1a5aOHj3qqI8fP95CGlyrVq1a6tChg0+tqKjIuKgRAOAurP+ARAMCOJhGPyZMmODYfQn2mC5WrAMBAPczTZll+lX4oQEBrnLx4kWmX3mA6WLFOhAAcLeioiJt2bLFUWcBevihAQGuMnv2bGVnZ/vUIiIiNG7cOEuJYGIaAWErXgBwty+//FIXL170qcXHx6tLly6WEsEWGhDgKmWd/VG9enULaVCWTp06qVatWj61c+fOae/evZYSAQBuxDRSzQGE4YkGBPiXs2fPGrffZfqV+0RGRhovWkzDAgD3Mq3VY/1HeKIBAf5lzpw5jq1cY2NjNWbMGEuJcD2mixYL0QHAvUw3idgBKzzRgAD/Utbi84iICAtpcCMcSAgA3pGdna2DBw866oyAhCcaEEDS8ePH2f3KY0wHEu7cuZMDCQHAhUwbhXAAYfiiAQEkzZ07V/n5+T61unXravjw4ZYS4UZMBxJK4kBCAHAhDiDE1WhAAJU9/QruxoGEAOANrP/A1WhAEPYOHjyoL774wlGfOnWqhTSoCA4kBAD3Ky4u1ubNmx11GpDwRQOCsDdv3jxHrUmTJho4cKCFNKgIDiQEAPfbt28fBxDCBw0Iwl5Zhw/C/co6kNC00woAwI709HRHjQMIwxsNCMLa7t27tWLFCkd9ypQpFtKgoiIjI9W3b19H3XSxAwDYYXpPZvvd8EYDgrA2f/58R61NmzbcmfEQ00Vs586dFpIAAExMDQjrP8IbDQjCGrtfeR8jIADgXjk5OTp69KijzghIeKMBQdjatm2bccHy5MmTLaRBZZkOJMzIyFBeXp6FNACAq+3YscNR4wBC0IAgbC1YsMBR69Kli7p162YhDSqrrAMJGQUBAPtM78WmkWuEFxoQhC2mX4UO01xiGhAAsM80AsL0K9CAICytW7dOW7ZscdQnTZpkIQ2qynQxowEBALuKioq0a9cuR50F6KABQVhauHCho9a7d2/jVB64n+litn37dgtJAAAlduzYocuXL/vUOIAQEg0IwhTTr0KL6UDCvLw87dmzx1IiAMD69esdNba5h0QDgjC0YsUK4zkREyZMsJAG/lDWgYQbNmywkAYAIJnfg1n/AYkGBGHINPqRnJysVq1aWUgDfzFd1Ex33wAAwWFqQFj/AYkGBGGI6VehyXRRYwQEAOzIzs5WRkaGo84ICCQaEISZxYsXa//+/Y4606+8r3///o7arl27dO7cOQtpACC8mW4AdejQgQMIIYkGBGHGNPoxfPhwNW7c2EIa+FNZBxJu3LjRQhoACG+mKbBMv0KJaK9NUfDa3v5ey5uZmSnJO1NXKvr8zpgxQ/n5+T61nj17Bv3v67XXhVfytmzZUunp6SooKCitff7554qLi7OY6saysrJKX5dZWVkh+/NnG3kDy2t5vXa9K+GV53nRokXKz8/3eT+uX7++659vrzy/JbyWtwQjIAgbK1eu1IkTJxz1gQMHWkiDQEhMTHTUvPrmDABeVVxcbNxt0vQejfAU7dXhMK/l9krekjsTXslbojx5P/jgA8XExPjUxo0bp5EjRwYq1g2F4vNsU1xcnF599dXSP8fExGjfvn2uz52amlr62mzRooXr816LvIFF3sDw6vWuhJtzb9++XcXFxT7X3Hr16umWW25RZKQ37n27+fk18Vpeb7wKgCoqKCjQ4sWLHXV2vwotXbp0cRxIeO7cOQ4kBIAgKusAQq80Hwg8XgkIC7NmzdLJkycd9TFjxlhIg0DiQEIAsIsDCHEjNCAIC6bdr6ZOner6xcmoONN2vDQgABA8pt0HvTZFCIFFA4KQd/78eWMDMn369OCHQcCZRkA4ER0AgiM7O9t43pbpvRnhiwYEIW/WrFnKycnxqVWvXl2jR4+2lAiBZBrm37Vrl3Jzcy2kAYDwsnbtWketVatWql27toU0cCsaEIQ80+jHtGnTFB0dbSENAi0+Pl5t2rRx1BkFAYDAMzUg3bp1s5AEbkYDgpCWnZ3N7ldhyHSxS0tLs5AEAMKLqQHp2rWrhSRwMxoQhLTZs2fr4sWLPrXatWtbPfsDgWdqQEwXRQCA/1y6dElbt2511BkBwbVoQBDSypp+hdDWvXt3R23Tpk0qKCiwkAYAwsPGjRsd77MJCQlq1qyZpURwKxoQhKwjR44YG5ApU6ZYSINgatSokerXr+9Tu3TpkrZs2WIpEQCEPtNIc48ePSwkgdvRgCBkzZkzR8XFxT61Ro0a6aabbrKUCMFkuugxDQsAAmfdunWOGtOvYEIDgpDF9KvwxjoQAAgudsBCedGAICQdOHBAy5Ytc9SZfhU+aEAAIHjS09N17tw5n1r16tXVoUMHS4ngZjQgCElz58511Fq1amU8pA6hqW3btqpVq5ZP7fTp09q3b5+lRAAQukzTr5KSkhQVFWUhDdyOBgQhielXiIiIMDacjIIAgP+Z3lsHDBhgIQm8gAYEISc9PV1r1qxx1CdNmmQhDWwyXfxoQADA/0wjIP3797eQBF5AA4KQM2/ePEetU6dO6tmzp4U0sIkGBAAC7/jx4zp06JBPLTIykgYEZaIBQchh+hVKJCUlKTo62qd24MABnT592lIiAAg9aWlpjlrnzp0d6/CAEjQgCCmbN2/Wpk2bHPWJEydaSAPbqlevbhz5Wr16tYU0ABCaTCPLycnJFpLAK2hAEFLmz5/vqPXo0UOdO3e2kAZuwDQsAAgs0/oPFqDjemhAEFJM06+mT58e/CBwDdMcZNPFEgBQcZcuXdL27dsdddZ/4HpoQBAy1qxZY3wTHD9+vIU0cIuBAwc6atu2bdOlS5cspAGA0LJ27VoVFRX51Bo3bqzmzZtbSgQvoAFByFiwYIGj1r9/f7Vt29ZCGrhF3bp11a5dO59aQUGB1q9fbykRAIQO05RW040f4Go0IAgZ7H6FsrAOBAACgwMIURk0IAgJS5cu1d69ex31cePGWUgDtzHtxkIDAgBVU1RURAOCSqEBQUgwTb8aOnQoc1AhyXwx3LBhg2PeMgCg/LZv3+5YT1erVi0lJiZaSgSvoAFBSFi8eLGjxvQrlGjbtq3q1q3rUzt37pzS09MtJQIA7zPtKNivXz9FRvLrJa6PVwg8b/Xq1Tp48KCjPnbsWAtp4FamRZFMwwKAyjO9h7L9LsqDBgSeZ3oDHDNmjBo0aGAhDdzKNA0rLS3NQhIACA2m91DWf6A8aEDgeaYGhOlXuBYNCAD4z6FDh3T8+HGfWmRkpPr162cpEbyEBgSetmzZMp06dcpRHz16tIU0cLMePXqoevXqPrXjx48rKyvLUiIA8C7T+o+ePXs63mcBExoQeJpp9GPy5MlKSEiwkAZuFh0dbbwzxzoQAKg41n+gKmhA4FmXLl1i+hUqhAMJAcA/TCMgrP9AedGAwLNmzpypnJwcn1pMTAzTr1Am08XRdBEFAJStrG3MBw8ebCENvIgGBJ61aNEiR23atGnMP0WZkpKSHPvTp6en69y5c5YSAYD3mEaO27Rp4zhvCSgLDQg8KScnx9iATJ061UIaeEVZJ/QuXrxYX/va1zR+/HjjpgbXOnjwoJ555hn17dtXERERql+/vu655x4tXbqU09UBhDymX6GqaEDgSTNnztSFCxd8arVq1dKoUaMsJYJXJCcnO2p//vOf9cknn5Tr85ctW6axY8fqySef1KZNmyRJ2dnZeu+99zRixAg9/fTTysvL82tmAHATFqCjqmhA4Emm0Y/p06crIiLCQhp4ydV36YqLi3Xu3Dnj68kkPT1dP/nJT7Rr1y498sgjysrKUlFRkc6ePavXXntN9erV01NPPaX3339fxcXFgforAIA1BQUF2rhxo6POCAgqggYEnnPixAktXrzYUZ88ebKFNPCakhGQoqIi5eTkKDc3VwUFBTf8vMLCQn300UdKS0vTPffco2effVbNmzdXRESEEhIS9OCDD+rll19WfHy83nrrLWVkZAT4bwIAwbd161ZdunTJp1arVi117NjRUiJ4EQ0IPGf27NmOXxgbNGigYcOGWUoEL6lTp45q1qypU6dO6cKFC4qOjlZsbOwNP+/gwYNasGCBJOmuu+5ynDUTERGhCRMmaPTo0UpLS9MXX3wRkPwAYNP69esdNXa/QkXRgMBzytr9CiiPf/zjH9q3b58KCwtVq1Yt1a9fv1w7p23btk1paWkaPHiwOnXqZHxMnTp11LNnT0nSxo0bdfHiRb9mBwDbVq9e7aix/gMVRQMCTzl06JCWLFniqDP9CuVVrVo13XbbbWrYsKHi4+Md2/KWZd++fZKk9u3bq169esbHRERElE5D2Ldvn86fP++f0ADgEmlpaY4a6z9QUTQg8JTZs2c7ao0aNTLubASY3HHHHXr22WcVFRXl+FhZC8cLCwt18uRJSVLNmjUVHR1d5tdv2bKlJOnYsWP66quv/JAYANwhPT1dZ86c8alVr15dffr0sRMInkUDAk8xTb8aMWJE8IPA0zp27Kg6deo46mUdSHj58mVlZ2dLkpo3b37dNSOmxgYAQsGaNWsctf79+1/3pgxgQgMCz9i7d69WrVrlqN90000W0sDrhgwZ4qidPXvWQhIA8AbT+o+BAwdaSAKvowGBZ5imX7Vo0UKdO3e2kAZeZ7poXju1AADwbytWrHDUBg0aZCEJvI4GBJ5hOvuD6VeoLNNFkwYEAMz27t3reI+Mjo5W37597QSCp0W/8cYbtjNUSGZmpiRpw4YNlpOUj9fyLlu2zHYEoyNHjhizXbhwQf/85z898/yW8NrrItTyJiQkaPjw4apTp47PBbWgoEC7d+/WoEGDlJ+fr4KCAsXGxqpGjRpq0qSJJOnw4cPKy8tTbGyszp07pzVr1qhjx45q1aqVIiIiVFhYKOnKhblkPUhhYaG2b99unD8tXZlXfeHChdL/98r7cqi9LtyGvIHl1uvdjdh6nq9+nyrRtm1bvfPOO9f9PK+9LsgbHIyAwBO+/PJLR61Zs2Zq0KCBhTQIFabd064+ZKuoqEjSle11a9euLelK01tyEGZUVJRq1KihmJgYRURESLqyVbR05XDMunXrln4dzgQB4GX79+931Nq1a2chCUJB9AMPPGA7Q4WUdHhJSUmWk5SP1/KWcNvr4tNPP1XNmjV9ao888kjpNBqvPb9ee12Eat5BgwZp/vz5PrV169ZJkmJiYhQTE1Na7969u6QrDUZubq7i4+MVGxvrs5i9uLhYe/bskXTlvJC4uLjSrzVgwIAy98rPzc3VypUrJV1Zm+K2n7+yhOrrwi3IGxxe+XkrYet5fvXVVx3X4f/8z//U0KFDr/t5XntdkDc4GAGB623YsEHbtm1z1MePH28hDUKJaR2I6ZAtSerQoYOSk5O1YcMGpaenGx9z5swZbd26VZLUt29f1ahRw39hAcCSjIwMnThxwqcWHR3NAYSoNBoQuN7cuXMdtaSkJHXo0MFCGoSSbt26lY5SlDh79qz27t3reGyzZs00ZMgQ5ebm6p133nEsxiwuLtbs2bP12WefKTk5WTfffHMgowNA0JjWr/Xq1UvVq1e3kAahgAYErmfa/WratGkWkiDUREZGGrfjNe11X716dd13331KTk7We++9p0ceeUT79+9XcXGxcnJy9Prrr+uHP/yhJOm+++5TmzZtAh0fAILC1IBw/geqggYErrZy5Urt2rXLUR87dqyFNAhFpmlYpgZEkhITE/Xcc8+pc+fO+uijj9S+fXtFRkaqdu3aevjhh5Wdna2nnnpKd911V+midADwOtN7Iud/oCqibQcArufaBcLSlZPPW7VqZSENQpHpLt6qVavKfPywYcO0YMECvfvuu/rnP/+pTZs2qV69epo0aZLuu+8+DR06VJGR3NsBEBpOnDhRurtficjISOMugkB50YDA1RYtWuSoMf0K/tS7d2/VqVNHsbGxpbUTJ04oMzNTrVu3Nn5Oq1at9MQTT+iJJ54IVkwAsMJ0XkqPHj0c6+eAiuA2HVzriy++UEZGhqM+ZsyY4IdByKrIOhAACDem9R9Mv0JV0YDAtUzTr26++WY1btzYQhqEsoqsAwGAcML6DwQCDQhcy7T71fTp04MfBCHPdDE13fUDgHBy4sQJHThwwKcWGRmpwYMHW0qEUEEDAleaM2eOjhw54qiPGjXKQhqEuj59+jj2sz906JDj4C0ACCemGzFdunRh/QeqjAYErrRw4UJHbeLEiapbt66FNAh10dHR6tevn6NuWnwJAOGC6VcIFBoQuE5RUZFx96upU6daSINwwUJ0APBFA4JAoQGB66SkpOjUqVM+taioKI0ePdpSIoQD1oEAwL+dOXNGu3fvdtRZ/wF/oAGB65imX02bNk01a9a0kAbhIikpSdHRvkcjHThwgHUgAMKS6UDWzp07q06dOsEPg5BDAwJXuXDhgnH3qylTplhIg3BSvXp1JSUlOepMwwIQjkzvfaapqkBl0IDAVWbMmKHc3FyfWs2aNdn9CkHBeSAAcAXrPxBINCBwFdPi82nTpjmmxgCBYLq7xzoQAOHm/Pnz2rlzp6M+bNgwC2kQimhA4BqnT582NiCTJ0+2kAbhKDk52dHs7t69W2fOnLETCAAsWLVqlYqKinxq7dq1Y/0H/IYGBK4xY8YMXb582adWr149jRw50lIihJvq1aurV69ejvrKlSstpAEAO5h+hUCjAYFrlDX9CggmzgMBEO5oQBBoNCBwhaNHjxp3v5o4caKFNAhnnAcCIJydP39e27Ztc9SHDBliIQ1CFQ0IXGHmzJmOWrNmzXTTTTdZSINwlpycrMhI37fGHTt26Pz585YSAUDwrF271rH+o1WrVmrUqJGlRAhFNCBwBdPoB9OvYENcXJx69OjhqLMOBEA4YPoVgoEGBNZlZGRo+fLljvqECRMspAGYhgUgfJne6ziAEP5GAwLrZs2a5ai1bdtW/fr1s5AGoAEBEJ4uXbqk9evXO+qDBw+2kAahjAYE1pl2v5o+fXrwgwD/MnjwYMc6kK1bt7IOBEBIM001bd68uVq2bGkhDUIZDQis2rlzp9auXeuojxs3zkIa4Iq4uDh16dLFp1ZUVKRVq1ZZSgQAgWdqQNj9CoFAAwKrZs+e7aglJiaqZ8+eFtIA/zZ06FBHbcWKFRaSAEBwmN7jTO+FQFXRgMAqdr+CW5m2gKYBARCqzp49qy+//NJRpwFBINCAwJotW7Zo8+bNjjrTr+AGgwYNUkREhE8tPT1dZ8+etZQIAAJn1apVKi4u9ql16NBBDRs2tJQIoYwGBNbMmTPHUevTp486d+5sIQ3gKy4uTn379nXUly5daiENAAQW068QTDQgsMa0+xXTr+AmTMMCEC5M722m90DAH2hAYEVaWprS09Md9TFjxlhIA5iZdn+hAQEQak6ePKk9e/b41CIiImhAEDA0ILBi7ty5jtrAgQPVtm1bC2kAswEDBig6OtqnlpGRoZMnT1pKBAD+Z7qx0q1bN9WuXdtCGoQDGhBYYdr9isMH4TbVqlXTgAEDHPUvvvjCQhoACAzWfyDYaEAQdMuWLdO+ffsc9dGjR1tIA1wf60AAhDrTAYRMv0Ig0YAg6ObNm+eojRgxQs2aNbOQBrg+0zqQZcuWWUgCAP53+PBhHTx40KcWHR2t5ORkS4kQDmhAEHTsfgUv6dOnj6pVq+ZTO3nypPbu3WspEQD4z/Llyx213r17Ky4uzkIahAsaEATVwoULlZWV5aiPGjXKQhrgxqKjo42jIKaLNgB4jem9jPUfCDQaEASVafrV+PHj1aBBAwtpgPIxzYU2zZkGAK/h/A/YQAOCoDLtfjVlyhQLSYDyM42ArFy5UsXFxRbSAIB/7Nmzx7GteFm7/wH+RAOCoJk5c6ZOnDjhqLP7Fdyue/fujv3wz549qy+//NJSIgCoOtPoh+n8I8DfaEAQNAsWLHDUpk+frvj4eAtpgPKLiIjQ4MGDHXW24wXgZaappKz/QDDQgCAo8vPzjbtfTZo0yUIaoOJM07BoQAB4VXFxMed/wBoaEARFSkqKzp4961OrUaMG06/gGWUtRC8oKLCQBgCqZvv27Y7rclxcnPr06WMpEcJJ9IYNG2xnqJD09HTbESrEa3kzMzMlSf5+XXz44YfKz8/3qY0cObLKc+i99vyW8Fpu8l5Rq1YtnT59uvTP+fn5+vDDD9WtW7cqfd2srKzSn4+srCy///wFCq+LwCJvYAXqehdo/nqe//GPfziuy126dNHGjRv98vVLeO11Qd7gYAQEAXfhwgWtXbvWUWeYF17Tq1cvR23z5s3BDwIAVbRlyxZHzfQeBwRCdFJSku0MleK13F7JW3InyJ9533//fRUVFSkmJqa0VqdOHT388MOKiIjwy/fwyvN7La/lDve8t9xyi2POdEZGRpW/T2pqaunPR4sWLcL+eQ408gaWV/IG4noXTFXJXVBQoD179vhclyXpzjvvVGJiYlWjGXnteSZvYDECgoAzLT6fNm2a35oPIFhMo3br16/X5cuXLaQBgMrZvHmzzp8/71OrXbt2wJoP4Fo0IAior776ytiATJgwwUIaoGpat26t5s2b+9QKCgq0evVqS4kAoOJMO/gNHz7cQhKEKxoQBFRKSoqKiop8ao0bN9awYcMsJQKqxrRHPtvxAvAStt+FbTQgCCjT6Mf06dODHwTwE84DAeBlly9f1rp16xx103sbECg0IAiYrKwsLV261FEfP368hTSAf5hGQLZu3eqYTw0AbrR27VrHurWGDRuqbdu2lhIhHNGAIGBmzJjhqLVu3VrJyckW0gD+0bBhQ3Xo0MGnVlxcrOXLl1tKBADlZxqxHTlypIUkCGc0IAiYxYsXO2rTpk2zkATwL6ZhAfAq1n/ADWhAEBD79u0z7gw0btw4C2kA/zI1IKaLOgC4yblz54wnv7MxDIKNBgQBMXPmTEetc+fO6tOnj4U0gH+Z7hbu2rVLp06dspAGAMpn1apVjlrbtm3VuHFjC2kQzmhAEBBlHT4IhILatWurW7dujvqyZcsspAGA8jFtDMPoB2ygAYHfbd++XRs3bnTUx44dayENEBim3bBYiA7AzVJTUx21ESNGBD0HQAMCv5s1a5aj1qtXL3Xt2tVCGiAwTA3IkiVLLCQBgBs7dOiQDhw44KgPHjzYQhqEOxoQ+B27XyEc3HTTTapWrZpP7fjx49q5c6elRABQNtP0q379+ik+Pt5CGoQ7GhD41caNG/Xll1866qNHj7aQBgicatWqacCAAY666SIPALaZ3puGDx9uIQlAAwI/mz17tqM2YMAAx8FtQCgwzZ1mIToAtynrsFQaENhCAwK/YvcrhBPTxXvlypW6fPmyhTQAYLZx40bl5OT41GrWrKmkpCRLiRDuaEDgN6tWrdKePXsc9VGjRllIAwRet27d1KBBA5/a5cuXtXbtWkuJAMCprO13IyIiLKQBaEDgR3PmzHHUhg0bplatWllIAwSHaQ9901aXAGAL6z/gNjQg8BvT7ldTpkyxkAQIHtNFnIXoANziwoUL2rRpk6NOAwKbaEDgF0uWLFFmZqajzu5XCHUjR4501LZv366vvvrKQhoA8LVs2TIVFBT41Jo1a6Y2bdrYCQSIBgR+MnfuXEdt7Nixaty4sYU0QPA0aNBAiYmJjjq7YQFwA9OI7M0332whCfBvNCDwC9PuV5MnT7aQBAg+01QGGhAAbsD6D7gRDQiqbO7cuTp27Jijzu5XCBemi/kXX3xhIQkA/NuRI0eUkZHhU4uIiNDQoUPtBAL+hQYEVTZv3jxHbcqUKapbt66FNEDwDRo0SNWqVfOpffXVV9q5c6elRABgnp3Qp08fJSQkWEgD/BsNCKqkuLjYuPvVpEmTLKQB7KhWrZoGDhzoqLMbFgCbyjr/A7CNBgRVkpKSouzsbJ9atWrV2P0KYYfteAG4SXFxMes/4Fo0IKiS+fPnO2rTpk1TzZo1LaQB7BkxYoSjtmrVKl2+fDn4YQCEvQ0bNujChQs+tZo1ayopKclSIuDfaEBQaRcvXjTOL504caKFNIBdiYmJatCggU/t8uXLSktLs5QIQDgzjX7cdNNNio6OtpAG8EUDgkpLSUnR+fPnfWoJCQnsfoWwZRoFYRoWABtSU1MdNdN7FGADDQgqrazpV9xdQbhiHQgAN7hw4YI2btzoqLMAHW5BA4JKOXPmjHH3q/Hjx1tIA7iDqQHZvn27vvrqKwtpAISr1NRUFRcX+9SaNWum9u3bW0oE+KIBQaWkpKQoPz/fp9awYUONHDnSUiLAvgYNGqhr166OOqeiAwgmdr+C29GAoFIWLlzoqE2fPj34QQCXYR0IANtMMxRoQOAmNCCosOPHj+uLL75w1MeNG2chDeAupov8kiVLLCQBEI4yMjJ05MgRn1pERAQL0OEqNCCosJSUFEetZcuWGjx4sIU0gLskJyerWrVqPrWvvvpK6enplhIBCCem3a969uyphISE4IcBykADggozTb+aNm2ahSSA+1SrVs3YjDMNC0AwsP4DXkADggrJzMzUypUrHfWxY8daSAO4k2mqAwvRAQSD6RpNAwK3oQFBhZimX3Xs2FH9+vWzkAZwJ9Ne+6tWrdLly5ctpAEQLlavXq1z58751KpVq6b+/ftbSgSY0YCgQkw7azD9CvDVpUsXNWjQwKd2+fJlpaWlWUoEIByYNogZPnw4BwTDdWhAUG67d+/WunXrHPXRo0dbSAO428033+yosQ4EQCCZGhDTexFgGw0Iym3GjBmOWvfu3dWzZ08LaQB3M60DYTteAIFy/Phx42573CSEG9GAoNwWLVrkqDH9CjAzLfpMT0/XsWPHLKQBEOpMU6Q7duyo5s2bW0gDXB8NCMpl69at2rp1q6POnRXArG7duurbt6+jvmDBAgtpAIQ6UwPC9Cu4FQ0IymXmzJmOWr9+/dS5c2cLaQBvMF38Tb8kAEBVFBYWGg8gHDVqVPDDAOVAA4JyMf3SNHXqVAtJAO8wXfxXrFih/Px8C2kAhKo1a9YoLy/PpxYbG6tBgwZZSgRcHw0IbmjdunXauXOno86dFeD6evXqpfr16/vU8vLyjAeFAUBlmTa4GDZsmKKioiykAW6MBgQ3NGvWLEdtyJAhatu2rYU0gLeYGnWmYQHwJ9P2u9wkhJtFb9iwwXaGCjFtMedmXsubmZkpSbr6dZGSkuKYMtK9e3e54bXjtee3hNdyk7fyWrdu7fj5SUlJ0fTp00v/nJWVVfqYrKwsV/xslYebnufyIG9geS2v6XrnBdc+z6dOndK2bdscj2vUqJEr/m5ee12QNzgYAcF1bdq0SYcPH3bUBwwYYCEN4D1JSUmKjPR9qz169Kjx5woAKiotLc1Ra9OmjWP6J+Am0UlJSbYzVIrXcnslb8ndkpK8n3zyiWJiYnweM3r0aI0fPz7o2a7HK8/vtbyWm7yVM3jwYMcvCcePHy/dyCE1NbX056xFixauyV1e5A0s8gbGtdc7rynJ/corrziu09OmTXPd38tteW6EvIHFCAiuyzRXfdKkSRaSAN7FOhAAgVBYWKhly5Y56pz/AbejAUGZFi1aZJwmwsI2oGJMPzOrV692bJsJABVheh+JjY1VcnKypURA+dCAoExz5sxx1CZNmqQGDRpYSAN4V2Jiopo0aeJTy8/PN965BIDyMu1+NXLkSLbfhevRgKBMixYtctQmTpxoIQngfUzDAuBvpgaE6VfwAhoQGM2aNUtfffWVTy06OlqjR4+2lAjwNlMDYmryAaA8jh07pt27dzvq48aNs5AGqBgaEBjNnTvXUZs2bZri4+MtpAG8b/jw4Y5pEceOHfPsHu4A7FqwYIGjlpiYyPa78AQaEDgUFRUZp4ZMmDDBQhogNMTGxmrQoEGOOtOwAFQGp5/Dy2hA4LB582bl5OT41OLi4nhjA6qIaVgA/KGoqEjLly931LlOwytoQOCwfft2R2369OmqXr26hTRA6DD9crBu3TpdunTJQhoAXrVlyxbH9rsJCQnq16+fpURAxdCAwMelS5eMc9JZ1AZUXYcOHRzb8RYXF2vv3r2WEgHwonXr1jlqpnVmgFvRgMDHli1bVFBQ4FOrX78+u18BfjJ+/HhHbc+ePRaSAPAqUwPC9rvwEhoQ+DBNv5o2bZqFJEBoMv2SwAgIgPI6deqUDh065KhzoxBeQgOCUqdOnTJOvxo7dqyFNEBoGj58uGJiYnxqFy5cUH5+vqVEALxk9erVjlr37t3ZfheeQgOCUikpKY5a8+bNNWzYMAtpgNAUExNj/Jm6fPmyhTQAvGb9+vWOGrtfwWtoQFDKdKgR068A/xs5cqSjxk5YAG4kPz9fmzZtctRZ/wGvoQGBJOnIkSNatmyZoz5mzBgLaYDQZvq5ys/PV1FRkYU0ALxi2bJljpsVtWvXVv/+/S0lAiqHBgSSzNOv2rdvr+TkZAtpgNDWsmVLtWvXzlFnGhaA65k/f76jxuJzeBENCCQx/QoINtMoCNOwAFzPwoULHTXT1t6A29GAQPv371daWpqjzqI2IHDKWgdSWFhoIQ0At9u8ebOOHz/uU4uJiWH9BzyJBgTG6Vddu3ZVnz59LKQBwsOwYcNUq1Ytn1pxcbEyMjLsBALgaqbRjyFDhig2NtZCGqBqaECgRYsWOWpTp061kAQIL6Y7lzt37rSQBIDbmdZ/sFEMvIoGJMylp6cbt/RjURsQeOPGjXPUdu/ebSEJADc7fvy4duzY4ahPmDDBQhqg6mhAwpxp+lWrVq3UtWtXC2mA8DJ69GhFRUX51HJzc7V161ZLiQC40Zw5cxy1Hj16qHHjxhbSAFVHAxLmTNOvevbsaSEJEH7i4+M1aNAgR9001QJA+DK9J4wdO9ZCEsA/aEDC2KZNm4xDuomJiRbSAOHJtIUmDQiAEnl5eVq5cqWjbprCCXgFDUgYmzFjhqPWvn17NWzY0EIaIDxNmjTJUduxY4dju00A4WnhwoWO7bnr16+v7t27W0oEVB0NSBhbvHixo9ajRw8LSYDw1bhxYzVp0sRRN835BhB+TAcFDx482EISwH9oQMLUmjVrtHfvXke9S5cuFtIA4a1z586O2rx58ywkAeAmhYWFxvM/Bg4caCEN4D80IGFq5syZjtrIkSNVr149C2mA8GZqQFatWqXc3FwLaQC4RVpamuN9oHr16hwUDM+jAQlTpt2vTHPRAQRekyZNHNvxFhYWasmSJZYSAXAD0/SrAQMGKDKSX9/gbbyCw1BqaqoOHTrkqI8aNcpCGgDSlbua12I3LCC8maZimrbuBryGBiQMzZo1y1GbMGECBxoBFpkakEWLFjl2vwEQHnbv3q2DBw/61KKiolj/gZBAAxKGTLtfTZgwwUISACWqVavmmFaRm5ur1atXW0oEwCbT4vPk5GTVrFnTQhrAv2hAwsz8+fMd5wtERkZq9OjRlhIBKFGtWjVHzTQHHEDo4/RzhDIakDAze/ZsR23atGmqU6dO8MMA8ME6EACSlJ2drQ0bNjjqzFZAqKABCTOm3a/GjRtnIQmAa1WvXt2xG9ahQ4eUnp5uKREAGxYuXKji4mKfWufOndWyZUtLiQD/ogEJIykpKTpz5oxPLTY2lulXgEtERESobdu2jjrTsIDwwvQrhDoakDAyZ84cR23atGksaANcxHQoIQ0IED7y8/O1dOlSR50GBKGEBiRMXLp0ybj7FdOvAHcxNSCbNm1ybB4BIDQtW7ZMeXl5PrVGjRopKSnJUiLA/2hAwkRKSoouXLjgU6tbty6HDwIuU6tWLfXp08dRN23JCSD0mGYrMFUaoYYGJEzMnTvXUZs2bZqio6MtpAFwPaadbmhAgPBgOv2c2QoINTQgYSAnJ8e4+9WYMWMspAFwI6a53qmpqY5pGQBCy4oVK3T69GmfWo0aNTRixAg7gYAAoQEJA59//rkKCwt9ak2bNtXIkSMtJQJwPZ06dXJst5mfn6/U1FQ7gQAEhemsrrFjxyomJsZCGiBwaEDCgGk4d9q0aRaSACivyZMnO2ocSgiENtP6j4kTJ1pIAgQWDUiIO3HihPGuKQvaAHcbP368o2a6mQAgNKSlpenkyZOOOpvFIBTRgIS4lJQUR61NmzYaPHiwhTQAyqtfv35q1KiRTy0nJ0dffPGFpUQAAqms6VdxcXEW0gCBRQMS4kxTNph+BbhfRESEJk2a5KibfkkB4H0zZsxw1EzvAUAoiN6wYYPtDBWSnp5uO0KF2Mx77Ngx42mqzZs3V1n/7pmZmZJU5sfdxmuvhxJey03ewMrKylJ+fn7p/5f8/LVv3760XuKzzz7TN77xDUVG2r9/5LXnmbyB5bW8brre7dy5U4cPH/apRUZGqmnTpo58XnueyRtYXstbwv4VDAFjaj7atGmjxMREC2kAVFSPHj0UHx/vU8vNzdXWrVstJQIQCCtWrHDU+vTpo9jYWAtpgMCLTkpKsp2hUryW20bep556yrF137e+9a3rZim508LzGxxey03ewEhNTS39WW3RooVP7ltvvVUffvihz+P37Nmj++67L6gZr8crz3MJ8gaWV/K66Xr38MMPO67Xd91113WzuSF3RZA3sLyWlxGQELVnzx7jsDK7XwHeYpoDPmPGDBUXF1tIA8DfvvzyS2VlZfnUIiIijFtxA6GCBiREmXa/6t27t3r06GEhDYDKGjZsmGrVquVTO3PmjNLS0iwlAuBPpo0lBg4cqDp16gQ/DBAkNCAhauHChY4ad1MA74mKijKeCTJr1iwLaQD428yZMx01dr9CqKMBCUFffvmltm3b5qhzmBHgTaZfRmhAAO/btWuX9u/f76hzwxChjgYkBH3++eeOWnJysjp37hz8MACq7Oabb1aNGjV8aidOnHDF9qEAKs80/apv376OQ0iBUEMDEoIWLVrkqDGcC3hXTEyMxo4d66gzCgJ4m6kBmThxooUkQHDRgISY9evXa/fu3Y46u18B3mb6pYQGBPCurKws4yFyU6dOtZAGCC4akBBj2v1q+PDhatOmTfDDAPCbsWPHOs4JOHz4sLZs2WIpEYCqME2X7tq1q1q0aBH8MECQ0YCEmMWLFztqEyZMsJAEgD/VqFFDN998s6POKAjgTabpV0yXRrigAQkhK1euVEZGhqPO9CsgNJh+OTHdRQXgbllZWcbRSxoQhAsakBAyY8YMR23cuHFq1qyZhTQA/G38+PGKioryqR0+fFg7duywlAhAZZhGP9q1a6dOnTpZSAMEHw1ICDHtfmU6wAyAN9WqVUvDhw931OfMmWMhDYDKMjUgU6ZMsZAEsIMGJEQsXrxYR48eddQ5fBAILaYpGp999pmFJAAq48iRI1q/fr2jzva7CCc0ICFi5syZjtq0adPUoEEDC2kABIppU4kDBw5o7969FtIAqCjTdOlWrVqpR48eFtIAdtCAhAjT7lemg8sAeFudOnU0ZMgQR910EwKA+5i2y+fsD4QbGpAQMGfOHJ06dcqnVr16dXa/AkIUhxIC3nTkyBHj7lfTpk2zkAawhwYkBJh+8Zg2bZri4+MtpAEQaKZ1IOnp6cZtuAG4x6effuqotWnTRt26dbOQBrCHBsTjCgsLjbtfMf0KCF0NGzZU//79HXXTLzcA3MN0bs9tt90W/CCAZTQgHpeSkqJz58751GrXrs3uV0CImz59uqNGAwK4V0ZGhtLT0x11GhCEIxoQjzPtJT5t2jRVr17dQhoAwXLrrbc6DiXMyMjQtm3bLCUCcD2mGwSJiYlq06ZN8MMAltGAeNiFCxeMu1+x+BwIfbVr1zbuhmWa4gHAPlMDwuJzhCsaEA9LSUnR5cuXfWqNGjWiAQHChGka1ieffKLi4uLghwFQprI2ibj99tuDHwZwARoQD5szZ46jxt0UIHxMnjxZMTExPrWvvvpKaWlplhIBMDEdPtirVy81a9bMQhrAPhoQj8rOzmb6FRDm4uLiNGbMGEedaViAu3zyySeOGjcMEc5oQDzKdJJqq1atNHToUAtpANhyyy23OGopKSkqLCy0kAbAtbZu3aojR4446ux+hXBGA+JRc+fOddSmTp1qIQkAm8aOHau4uDif2tmzZ5WammonEAAfpulX/fv3V8OGDS2kAdyBBsSDjh49qhUrVjjqnP0BhJ+YmBhNnDjRUWcaFuAOpp9Fpl8h3NGAeJBp+lWnTp2UnJxsIQ0A20zTsObNm6dLly5ZSAOgxIYNGxzTryIiIjRlyhRLiQB3oAHxoHnz5jlqkydPtpAEgBsMHTpUtWvX9qmdP39eCxYssJQIgGSefjV48GCmXyHs0YB4TEZGhtauXeuos/sVEL6ioqJ06623OupMwwLsKS4uZvoVUAYaEI8xvZn17NlTvXv3DnoWAO5hOpRw0aJFOn/+fPDDAFBaWppOnjzpU4uKimL6FSAaEM+ZP3++o2ZagAogvPTv319Nmzb1qeXn52vWrFmWEgHhzTT9atiwYY7pkkA4ogHxkJ07d2rLli2OOtOvAEgyTsP67LPPLCQBwlthYaHxZ4/pV8AVNCAeYtr9qn///uratauFNADcxtSALFu2TF999ZWFNED4Wr16tc6ePeuoT5gwwUIawH1oQDzEtKMN068AlEhMTFSbNm0cddNUEACB8/e//91RGzdunOLj4y2kAdyHBsQjtmzZovT0dEedwwcBXO1rX/uao8Y0LCB4Ll26pJkzZzrqpvN6gHBFA+IRpt2vhg4dqg4dOgQ/DADX+vrXv+6obdiwQUePHrWQBgg/M2fOdBwCGhcXx/Qr4Co0IB6xcOFCR238+PEWkgBws6ZNmyopKclR/+c//2khDRB+/vGPfzhqt9xyi2JiYiykAdyJBsQD0tLStH//fked3a8AmEydOtVR+/jjjy0kQWVt2rRJn332mebPn699+/bZjoNyOnbsmJYvX+6o33777RbSAO5FA+IBpt2vxowZo5YtW1pIA8DtTHPN9+7dq82bNwc/DCrkmWeeUZ8+fTRp0iS9/vrr+t///V8NHTpUw4cP19tvv207Hm7gn//8p4qLi31qrVu31oABAywlAtyJBsQDFi1a5KiNGzfOQhIAXtCgQQONGTPGUWcUxL3S09OVlJSkV199VcePH3d8fM+ePXriiSc0YsQI7d6920JClIfpZ+y2226zkARwNxoQl1u2bJmysrIcdXa/AnA9Ze2GlZ+fbyENric3N1ejRo0q10YBu3fv1ogRIwIfChW2bds27dmzx1E3/SwC4Y4GxOVM068mT56sxo0bW0gDwCvGjh2rhIQEn1pOTo7mzp1rKRHKcv/991f4c37yk58EIAmq4pNPPnHU+vXrp1atWllIA7gbDYjLmaZfjR071kISAF4SExNjPBnd9EsS7Jk/f76WLVtW4c97//33lZ2dHYBEqIzCwkLjeTt33HGHhTSA+9GAuNiCBQt08uRJn1pMTAy7XwEoF9MvP0uWLNGpU6cspIFJVXa4Yncs9zD9XMXExGjatGmWEgHuFr1hwwbbGSrEdBq4m1Ul71tvveWYrz1s2LCAXnQyMzMlXTm4zAu89noo4bXc5A2srKys0p/1rKwsv/78NWnSRIcOHfKpvfDCC37ZFtRrz7Mb8y5ZsqTMdTkFBQXX/dx58+YpMtI99xHd+Pxejz+vd6+99prj3zE5Odm4JqSqvPY8kzewvJa3hHveueCwdu1aRy05OdlCEgBeZdoNa/78+RaSwKQq06iYguUOeXl5WrVqlaPObAWgbNGmE3O9wGu5K5p35syZunTpks/JqfHx8XrwwQdVs2ZNf8crVXInKNSfX7fwWm7yBkZqamrpz3qLFi38mrt58+Z6//33fc4mOHbsmKKiotS7d2+/fA+vPM8l3JR3+PDhN7yDWdYJ2uPHj3fV36WEGzOZ+Ot698EHHygiIsLn3ykhIUEPPfSQoqKiqvS1r8crz3MJ8gaW1/IyAuJSM2fOdNSmTZsW0OYDQOhp0qSJhg0b5qizGN0dOnXqVOnP7dChgx+ToLJMP0u33XZbQJsPwOtoQFzo8uXLxt2vOPsDQGWYziH49NNPORPEBbp3767Y2NgKf17Pnj3Vvn37ACRCRRw7dsw4XZrdr4DrowFxoZSUFF28eNGn1qBBA+aTAqiUiRMnKi4uzqeWk5PDWhAX6N69ux555JEKf96DDz4YgDSoqA8//NBRa9Wqld+mNwKhigbEhWbNmuWoTZ06leFcAJVSvXp143agf//73y2kwbUee+yxCp1uPnr0aN1yyy2BC4RyM/0M3XnnnRaSAN5CA+Iyubm5Wrx4saPO6AeAqjBNw1q0aBFngrjEhx9+qN/85jc3fNwrr7yid999NwiJcCMLFizQwYMHHfXbbrvNQhrAW6JtB4CvlJQUFRUV+dRatGhRobtjAHCtAQMGqE2bNsrIyPCp//Of/9T9999vJxR83Hvvvapbt65SU1O1e/dubdu2TdWrV1fv3r3VqVMn3XHHHerTp4/tmPiXf/zjH47akCFD1KxZMwtpAG+hAXGZ2bNnO2qTJ0+2kARAqLnjjjv0/PPP+9Q++ugjGhAXmT59uqZPny7Ju9uih4Ps7GzjdGkWnwPlwxQsFzl58qSWLl3qqDP9CoA/fPOb31RERIRPbefOndq6daulRIA3/e1vf3PUatasaVxrBcCJBsRFUlJSHLUOHTpo8ODBFtIACDVNmjTRoEGDHPWPP/7YQhrAu0y7X91+++2qVq2ahTSA99CAuMicOXMctUmTJllIAiBUmaaILF++3EISwJvWrl2r/fv3O+rsfgWUHw2IS2RlZWnNmjWOOocPAvAn05qyvXv3aubMmRbSAN5jGv3o1q2bevToYSEN4E00IC5hmn7VrVs39evXz0IaAKEqLi7O2IR88MEHFtIA3pKTk6MZM2Y46ox+ABVDA+ISc+fOddQmTpxoIQmAUFfWNKysrCwLaQDv+Oyzz3Tx4kWfWrVq1XTrrbdaSgR4Ew2IC+zdu1cbN2501Nn9CkAgjBo1So0aNfKpFRcX67333rOUCPAG0/SrKVOmKCEhwUIawLtoQFzANP0qKSmJ+aQAAiIyMlJ33323o/7BBx84DkIFcEV6erq2bdvmqH/rW9+ykAbwNhoQF5g3b56jNmHCBAtJAISLu+++W5GRvpeA7OxsLViwwFIiwN1MI4QtWrQwbm0N4PpoQCzbvn27tm/f7qiz+xWAQGrUqJHxfYbF6IDT5cuX9c9//tNR//a3v20hDeB9NCCWmaZf3XTTTercubOFNADCyV133eWoffHFFzp+/LiFNIB7zZgxQzk5OT61yMhIffOb37SUCPA2GhDL5s+f76iNGzfOQhIA4aasxejvv/++pUSAO5kWn48dO1b16tWzkAbwPhoQizZu3Kg9e/Y46ux+BSAYIiMjdc899zjq77//PovRgX8p66BgFp8DlUcDYtHnn3/uqI0aNUpt2rQJehYA4emuu+5yLEY/fvy4lixZYikR4C7/93//56g1btxYN998c/DDACGCBsQi024zY8eOtZAEQLhq1KiRcdSVaViAVFRUpL/97W+O+je/+U1H4w6g/PjpsWTVqlU6ePCgo87uVwCCzXQmyPz583Xq1CkLaQD32Lhxo7Kzsx11Fp8DVUMDYolp96uJEyeqWbNmFtIACGejRo1SixYtHHXTwlsgnLz88suO2vDhw9WyZUsLaYDQQQNiycKFCx21MWPGWEgCANKdd97pqNGAIJxlZmYar9WmnxUAFUMDYsGSJUt07Ngxn1pUVBS7XwGwxjSnPTMzU8uWLbOUCLDr3XffddQaNWqkiRMnWkgDhBYaEAtMu19NmzZN9evXD34YANCVX6xMo7CcjI5wdPnyZeNGDPfeey+LzwE/4KfIgkWLFjlqjH4AsM10JsjMmTO1b98+C2kAez777DPl5uY66ky/AvyDBiTI5s6dq9OnT/vUatasye5XAKwbOXKkcXHtO++8YyENYM+bb77pqN16661q0KCBhTRA6KEBCTLT7ldTp05VfHy8hTQA4Ovb3/62o/bxxx8rLy/PQhog+DZs2KDt27c76vfee6+FNEBoogEJouLiYi1evNhRZ/oVALe4++67Va1aNZ9abm6u8TA2IBT99a9/ddQ6deqkpKQkC2mA0EQDEkQpKSk6f/68T61evXo0IABcIz4+Xl/72tcc9b/85S8W0gDBdfr0ac2YMcNRf+ihhyykAUIXDUgQmd7UpkyZ4rjbCAA2ffe733XUMjIy2JIXIe/dd99VQUGBTy0+Pl633nqrpURAaKIBCZK8vDzj7lcsPgfgNp06ddLgwYMd9bfeestCGiA4ioqKjNOv7rrrLm4UAn5GAxIkKSkpjrsqzZo1Y/oVAFf6zne+46gtWrRIR44csZAGCLx58+bpxIkTPrWIiAjdd999lhIBoYsGJEhmzpzpqE2aNMlCEgC4sfHjx6tZs2Y+teLiYuP2pEAoMI1+jBo1yvFzAKDqaECCIDc3V0uWLHHUGf0A4FaRkZH6j//4D0f9gw8+YEtehJyMjAytXLnSUTf9DACoOhqQIFi6dKmj1q5dOw0dOtRCGgAoH9Pc99zcXH366aeWEgGB8cYbbzhqzZo108iRIy2kAUIfDUgQLF++3FGbOHGihSQAUH516tTRLbfc4qgzDQuhJC8vTx9//LGjfv/99ysiIsJCIiD00YAE2KlTp7RlyxZHnd2vAHjB/fff76jt3r1bq1evtpAG8L/Fixc7phXWqFFD3/zmNy0lAkIfDUiAmaZfJSYmKjk52UIaAKiYrl27asCAAY46W/IiVPzud79z1G677TYlJCRYSAOEBxqQAFuxYoWjNmHCBAtJAKByTFvyzpkzRydPnrSQBvCfHTt2aP/+/Y666TBOAP5DAxJAmZmZ2rFjh6PO7lcAvGTixIlq2LCho27aXhzwktTUVEdt9OjR6ty5c/DDAGGEBiSAUlJSHLU+ffqod+/ewQ8DAJUUHR2te++911GfO3eu8vPzLSQCqu7QoUPKyMhw1B9++OHghwHCDA1IAM2ZM8dRGz9+vIUkAFA1d999t6OWm5urNWvWWEgDVJ1p9KN3794aNGhQ8MMAYSbihRdeKLYdoiKysrIkSS1atLCc5PpOnjyp1157TYWFhZKkqKgoSdKDDz6oxo0b24x2XSW/TAwcONBykvLxyuvhWl7LTd7AWrp0aemGFcOHD9fw4cMtJzL7/PPPtXXr1tI/FxYWqnbt2vrRj35kMVX5ee11Qd7AOXPmjF588UUVFxf7nHVz++23q2vXrhaT3ZiXnmeJvIHmtbwlIpo2beqpBqRkuD8mJsZykus7d+6czp8/71OrVq2a6tataylR+Vy4cEGSVLNmTctJyscrr4dreS03eQPr/PnzOnfunCSpVq1aiouLs5zIrLCwUKdOnVJxse9lo06dOqpevbqlVOXntdcFeQMnNze39BpdctZHVFSUGjRoYDNWuXjpeZbIG2hey1uCKVgBcunSJUfNCxdoAChLVFSU42R0SY6bLYCbFRUVOc79kLxz4w0IBdGPPfaY7QwV4oWhpqNHj+ovf/mLJPlMwXrkkUdUv359m9FuiClYweG13OQNLK9MwZKkgwcP6v/+7/8k+b6/3XrrrWrbtq3FZDfmtdcFeQOj5Oft8uXLkq7MTqhRo4Z+9KMfKTo62nK6G/PK81yCvIHltbwlPNeAbNiwQZKUlJRkOUnZnn766dIpFCVDY2PGjNFvf/tbm7HK5Y033pAkPfDAA5aTlI8XXg8mXstN3sBbv369pCsNiNvfl3fv3q0tW7b4DP2fPHlSr7zyiuVk1+e11wV5/S8/P19vvvmm4uLiSqde1axZU48++qgef/xxy+nKxwvP89XIG1hey1uCKVgBMG/ePEdt7NixFpIAgP/953/+p6O2fPlynwXqgBt9+OGHOnv2rE8tJibGuM00gMChAfGztWvX6sCBA476qFGjLKQBAP8bO3as2rVr56i//PLLFtIA5VNUVKTXXnvNUf/GN77hicXnQCihAfEz0+GDgwcPVsuWLS2kAQD/i4iI0Pe//31Hfc6cOcYbMIAbzJ07VwcPHvSpRURE6Hvf+56lRED4ogHxs/nz5ztqAwYMsJAEAALn9ttvV+3atX1qxcXF+uMf/2gpEXB9f/rTnxy1rl27qlWrVhbSAOGNBsSPli9friNHjjjqNCAAQk10dLTuuOMOR/3jjz/W8ePHLSQCyrZnzx5t3rzZUR85cmTwwwCgAfEn0/Sr4cOHq169ehbSAEBgTZo0yXhoommePWDTs88+66i1atWK0Q/AEhoQP1qwYIGj5rXRj7vuukt33XWX7RgAPCA2NlaTJk1y1N955x2dOXMm+IEAg507dxp3p/zNb37D9Q6whAbETxYtWqSvvvrKp1ajRg3PNSA1a9bkNFgA5XbbbbcpJibGp3bp0iW99dZblhIBvv7nf/7HUevcubOmTJnC9Q6whAbETz7//HNHbcqUKYqPjw9+GAAIktq1a+trX/uao/6Pf/xDly5dspAI+Lfdu3dr1qxZjvqPf/xjC2kAlKAB8ZOFCxc6aqNHj7aQpGKOHDmikSNHKiIi4rr/jR8/XqdOnbIdF3CFgwcP6plnnlHfvn0VERGh+vXr65577tHSpUtVVFRkO17QPfzww45aZmam3n33XQtpgH976aWXfP584cIFHT16VJMnT77uNe+DDz6wlBgIruLiYr300kuKiIjQypUrb/j4S5cuad68efra176m+vXrKyIiQgMHDtSLL76okydPlvv70oD4waxZs5Sbm+tTq1OnjicOHzx69Kh27dplOwbgGcuWLdPYsWP15JNPatOmTZKk7OxsvffeexoxYoSefvpp5eXlWU4ZXO3atdOUKVMc9T/+8Y+6ePGihUSAtG/fPn322Welfy4uLlZBQYHFRID7LFu2TP/7v/9brseeP39eP/3pTzVhwgR98sknys7OliSlpaXpxz/+saZMmaINGzaU62tFVzoxSpl2v5o8ebIn5pYePnxYR48e1dChQ/XTn/7UuKONdGU9S61atYKcDnCX9PR0/eQnP9GuXbv0yCOP6Oc//7maNWum3Nxcffjhh/rFL36hp556Ss2aNdN3v/tdRURE2I4cND/72c80e/ZsnxGgU6dO6e2339YjjzxiMRnC1R/+8AdHrVq1ajp//rx+/etfa+jQoWV+btu2bQOYDLCvuLhYS5cu1UMPPaTMzMwbPr6goECvvPKKXnrpJXXu3FnPP/+8xo0bp+joaH355Zd66qmn9Nlnn+nxxx/Xe++9p+bNm1/369GAVFFBQYEWLVrkqHth9EOStm/fLknq16+fxowZo2rVqllOBLhTYWGhPvroI6Wlpemee+7Rs88+q4SEBElSQkKCHnzwQSUkJOihhx7SW2+9pdGjR4fVLzFt2rTRLbfcok8//dSn/qc//Un33XefqlevbikZwlFGRobP6Id05We4Tp06qlGjhiZOnKikpCRL6QC7Ll26pA8//FA//vGPS0cxbmTXrl165513FB8frz/+8Y8aO3Zs6cd69uyp1157TUVFRUpJSdHHH3+sRx999Lo34ZiCVUUpKSmOhZZNmjTxxPqPCxcuaP/+/ZKu7AhC8wGU7eDBg6Vbbd91112lzUeJiIgITZgwQaNHj1ZaWpq++OILGzGteuyxxxQZ6XtZOX36tP7yl79YSoRw9dJLLznWY9WuXVsHDhxQ586d1bRpU0vJAHuKi4u1ceNG3X777frOd76j/Px8ff3rX1fHjh1v+Hnz589Xenq6pk+frkGDBjke07hxY91zzz2SpLlz5+rYsWPX/Zo0IFVkmn41ceJERUVFWUhTMWfOnNHevXsVHx+vXr162Y4DuNq2bduUlpamwYMHq1OnTsbH1KlTRz179pQkbdy4MezWP7Rp00a33367o/7KK6/o/PnzFhIhHB0+fNgxEiep9Jemrl27ckAwwtLu3bv1ne98R7NmzdLkyZOVmpqqX/3qVzdcMpCTk6PVq1dLkvr06VPmDq9du3ZVjx49lJaWdsNpXTQgVXDu3Dnj9CsvjH5I/16A3qNHD12+fNlnV582bdrou9/9rlavXh2Wu/oA19q3b58kqX379mX+8hIREVF6J2nfvn1h+Uv3T37yE8cNmJycHL355puWEiHc/O///q9jsXndunVVp04dSVLLli2Vmprqs4vPiBEj9Morr7DbI0JaZGSkhg4dqlWrViklJUV9+/Yt1+edOXNGR44ckSR17969zMc1bNiwdF1kyTWzzCzlj41rmUY/WrdurREjRgQ/TCXs3btXR48e1apVqzR8+HCfXX0yMzP11ltvafDgwXryySfD8hcpoERhYWHp9oI1a9ZUdHTZy+datmwpSTp27JjjcNJw0KxZM91xxx2O+muvvcb7CALu+PHj+vvf/+6o33vvvaVTjn/2s585dvFZunSp/t//+38aNWpU6Z1eINR07NhRL7/8sgYNGuSYLns9Z8+e9bkGliU2Nrb0Gljy81YWGpAqmDFjhqM2ceJEC0kqZ/fu3aX/f88992jr1q3Kz89XYWGh9u3bp0cffVSS9Nvf/lavvPIK2xcibF2+fLn0F5XmzZsrNja2zMd6YfploP3oRz9y1HJycvTGG29YSINw8tRTTzmuVQkJCRo9erSysrIkXVnz+Pbbbys7O1vFxcU6d+6cZsyYoV69emnLli169NFHlZ6ebiM+4Eq5ubnas2ePevXqpQYNGpT5uIiIiHJfA2lAKunUqVNavny5o+6V3a8uXryoy5cva+DAgXrkkUf06quvqkePHoqOjlZkZKTatWun5557Tr/73e8kXbl7uXnzZruhAXhCixYtdOeddzrqr7/+unJyciwkQjhIT083zky4//77VVhYqIYNG6pHjx56/fXXde+996pu3bqSpLi4OE2ZMkUfffSRkpOTlZaWprfeesuxwQwA/6EBqSTTm1znzp01ePBgC2kqrkaNGnr66ae1evVq/elPfzKe/xEdHa0777xTQ4cOVWZmpubNm6fi4mILaQF4zaOPPmpcC8IoCALl17/+taMWFxen+++/X0lJSVq4cKG2bt2q4cOHGz+/S5cu+va3vy1JWrRokTIyMgIZFwhrNCCVNHPmTEdt/PjxFpIEVqNGjdSvXz9JV9aFhNsJzwAqp1mzZrrrrrsc9TfeeENnz561kAihbPXq1Vq6dKmj/r3vfc+xZXZZIiIiNGDAADVt2lRbtmzR8ePH/R0TwL/QgFTC4cOHlZaW5qi7YfervLw8PfTQQ4qIiDD+99BDD123iVi/fr2WLVtW+udq1aqVDlMfOnSIBgRhqUaNGmrSpImkKz//1/s5KCwslHRlBDHc14M8+uijiomJ8amdO3dOf/7zny0lQqgyjX40bNhQDz/8cJmfc+LECcdazlq1aqlRo0aSrlzzAEj169dXjx49tGXLluturlJcXOxzDbweGpBKME2/6tWrl+dOVS0oKNDp06d1+fLl0lp0dHSZc7QbNWrEYYUISxEREapdu7akKwd4Xm9DhpJfWho0aFDavIerRo0aGUdBPv30U505cyb4gRCS5s2bpy1btjjqP/rRj1S9evXSP587d05nz54tnUp8oxsEJY0IEO5iY2NLz/64cOFCmY/Ly8srvQa2atXqul+TBqQSZs2a5aiNGzfOQhKn2NhY/fnPf1ZxcbHxvz//+c+KjY3VmjVrVK9ePdWrV89n2LpWrVqle6VLV15oBw8elHTlF6qr38yBcFKy9/mhQ4eUm5trfExxcbH27Nkj6cp5Iaa1VeHmhz/8oaOWlZWlP/zhD8EPg5D0m9/8xlFr1apV6XqOixcv6nvf+57i4+P1//7f/9O5c+ckXRnZvPZAtePHj2vLli1q2rQphxUC/1KvXj21b99e0vW31z158qSOHDmi+Pj40seXhQakgvbv32/cDcoru1+VaNWqVemIzfLly0uHzNq2bavk5OTSxx04cEArV66UJA0ZMoQREIStDh06KDk5WRs2bChzi84zZ85o69atkqS+ffuqRo0awYzoSo0aNdK3vvUtR/2NN9644Um5wI18/PHHxgPPfvrTn5b+f40aNdSzZ09JV6YZl9xUi4uL00033VT6uMLCwtLDhQcOHKh27doFMjrgGbVq1VLv3r0lSWvWrCnzTKcdO3Zo27ZtSk5OVuvWra/7NWlAKsg0/So5OVk9evSwkKbyGjdurKFDh0q6cp5JyZkgUVFRpXO2z58/r1dffVXp6emaOnWqhgwZYi0vYFuzZs00ZMgQ5ebm6p133nFMISouLtbs2bP12WefKTk5WTfffLOdoC70+OOPO9aCSOY710B55efn67nnnnPUExMTdcstt/jUhgwZosTERKWnp+uzzz4rnUZ59U21FStW6N1335Uk3XbbbWE/hRIoERERoWHDhql169b69NNPtWzZMseuqMeOHdPbb78tSZowYULpusmy0IBU0OzZsx21MWPGWEhSNVFRUbr77ruVnJysLVu26Nvf/rYWLlyogoICFRUVac+ePbr//vv16quvqnXr1vrRj37EfFiEterVq+u+++5TcnKy3nvvPT3yyCPav3+/iouLlZOTo9dff710utF9992nNm3a2A3sIo0bN9b999/vqM+aNUsbNmywkAih4K9//auOHj3qqP/sZz9z1Lp06aJ7771XkvTcc8/piSeeKP3c8+fP6/3339e3v/1tZWZm6pFHHtH06dMDmh3wmt69e+vhhx9Wbm6uHn74YX3wwQfKy8tTUVGRtm7dqkceeUSzZ8/WyJEj9fWvf10RERHX/XrXX6IOHzt27NCOHTscdTfsflUZHTt21Kuvvqof/OAHWrlypcaOHet4TOfOnfXss89q2LBhFhIC7pKYmKjnnntODzzwgD766CN99NFHjsc89dRTuuuuu2745htufvjDH+rDDz90jBz9/Oc/1/z58+2EgmdduHDBuI5owIABxmtyVFSUvv/97+vSpUt67rnn9Pvf/16///3vHY/7zne+o6eeeor1W8A1oqOj9f3vf19Hjx7VSy+9pLvvvlt33323z2OSk5P1/PPPq3nz5jf8eoyAVIBp+tWwYcPUqVMnC2n8o2/fvpo/f77efPNNjR8/vnRB3vDhw/XCCy9oyZIluuWWW/hlCviXYcOGacGCBXr66afVp08fSVcW6N19991KTU3Vk08+qdjYWMsp3Sc+Pl6PPfaYo75t2zbjxh7A9bz66qvGndR+9atflfk5sbGx+sUvfqHly5frBz/4gTp37ixJat26tb797W9ryZIlev3119WwYcNAxQY8LS4uTr///e81d+5c3XHHHaUbNSQnJ+uFF17QzJkzy70jLCMgFTBnzhxHzaujH1eLi4vTfffdp/vuu892FMATWrVqpSeeeEJPPPGE7Sie8h//8R964403HOcrPP300xo3bpxxnQhwrTNnzhjPkhkzZox69ep13c+NiIhQr1699NJLLwUqHuApnTt3Nm6uVJbq1atr/PjxVT58mxGQctq0aZNxp41QaEAAIBiioqL03//93476oUOHShf/AjfyzjvvGM8i+PnPf24hDYDKoAEpJ9P0qzFjxrDQFAAqYOLEierXr5+j/uKLL5Z5vgpQIiMjw7h24/bbby+dUgXA/WhAymnu3LmOWiiOfmzdurX0HAMACATTPP0zZ84wLQY39Mtf/tJRq1Gjhs+5H+XF9Q6whwakHFavXu2Ysyx57/DB8lizZo3WrFljOwaAENanTx9NmTLFUf/LX/6i48ePW0gEL1i+fHnpQYFX+8EPflCuXXeuxfUOsIcGpBxM068mT56sZs2aWUgDAN73i1/8wlHLz8/Xq6++aiENvMA0ytGqVSv953/+Z/DDAKgSGpBymDdvnqMWiqMfABAsrVq10oMPPuio/+Uvf+FwQji8+uqrysjIcNSvt+0uAPeiAbmB1NRUnThxwqdWrVq1kFz/AQDB9MMf/lCNGzd21H/yk59YSAO3On78uF544QVHfciQIRo3bpyFRACqigbkBsqaflW/fn0LaQAgdNSpU8e4LW96errefPNNC4ngRs8884wuXrzoU4uKitJzzz1nKRGAqqIBuYH58+c7aox+AIB/TJ8+Xf3793fUn3vuOWVnZ1tIBDfZtGmTPv30U0f9u9/9LtvgAx5GA3Id8+bN05kzZ3xqCQkJrP8AAD968cUXHaegnzt3zrjlKsJHcXGxHn/8cUe9fv36euyxxywkAuAvNCDXYZp+NWnSJMXHx1tIAwChqUOHDrr//vsd9X/+859at26dhURwgw8++EA7duxw1J944gnVqlXLQiIA/kIDch0LFixw1Bj9AAD/e+yxx9SkSRNH3XQHHKHv3Llzev311x31Pn366Otf/7qFRAD8iQakDCkpKcrLy/OpNWrUiPUfABAAsbGx+vWvf+2o7969W3/+858tJIJNv/71r7Vv3z5H/dlnn7WQBoC/0YCUwTT9asKECapWrZqFNAAQ+iZPnqwhQ4Y46s8//zwnpIeRFStW6P3333fU77zzTvXs2dNCIgD+RgNicOnSJS1cuNBRZ/QDAALr+eefdyxIz8vLM27Xi9Bz/vx5/eAHP3DUmzRpoqeeeir4gQAERLTXTpxNT08P+PdYuHChY8/xxo0bq06dOhU+oTcYef0pMzNTkjxzErHXnt8SXstN3sDKyspSfn5+6f+H+8/ftGnT9NFHH/nU5s2bp3feeUfdu3ev9Nf12usiHPO+8sorOnTokKP+wAMPaOfOnVX++lfz2vWuRDi+LoKJvMHBCIhBamqqozZ48ODgBwGAMPTNb35TDRs29KmdP39ezz//vOPmEELHtm3bNGvWLEd95MiRxrNiAHhXdFJSku0MlRKo3GfPntXWrVsdUwDuvvvuKn1PrzzPJXeCvJK3hNfylvBabvIGRmpqaul7TosWLTyTu0Qg8v7ud7/TQw895FPLzs7WzJkz9bvf/a5KX5vnN7AqkzcvL0+PPPKI49pbp04dvfbaa6pfv76/4pXy6vWuhNdykzewvJaXEZBrmBafd+zYUUOHDrWQBgDC09SpU40L0t99912tWLHCQiIE0jPPPGOcevX0008HpPkAYBcNyDVMDci4ceMsJAGA8Pbyyy+rZs2ajvr/+3//T7m5uRYSIRDWrl2rv/71r476sGHDdNttt1lIBCDQaECucuLECa1evdpR5/BBAAi+xo0b65lnnnHUjx8/rieeeMJCIvjbxYsX9f3vf99Rj4uL0x/+8IfgBwIQFDQgVzGNfvTo0UPJyckW0gAAvvGNbxhvAn3yySfG7dLhLW+//baysrIc9Z///Odq0qSJhUQAgoEG5CozZsxw1MaMGWMhCQCgxAsvvKBatWo56o8//rjOnDkT/EDwi3Xr1hlHuJKSknTvvfdaSAQgWGhA/uXgwYPGvcA5fBAA7GrcuLGee+45R/3EiRP66U9/aiERqio3N9exy1kJpl4BoY8G5F9M06/69eun3r17Bz8MAMDH9OnTNWHCBEd95syZ7IrlQY8//riOHj3qqD/00ENq3769hUQAgokG5F9mzpzpqDH9CgDc4/nnn1eDBg0c9YceekjHjx+3kAiV8cknnxinPHfr1k2//OUvLSQCEGw0IJL27NmjL7/80lFn9ysAcI969eoZp2JlZ2frgQceUEFBgYVUqIiDBw/qZz/7maNevXp1vf766xYSAbCBBkTm6VdDhgxR165dLaQBAJRl/PjxxqlY69atq/IJ6Qi8hx56SBcuXHDUn3nmGbVr185CIgA20IBImjVrlqPG6AcAuNMLL7xg3KL11Vdf1ZIlSywkQnk8++yz2rx5s6M+evRo3XnnncEPBMCasG9Atm3bpt27dzvq7H4FAO5Ut25dvfHGG8aPPfzwwzpy5EiQE+FGFixYoJdfftlRb9y4sbEOILSFfQNimn518803swsHALhYv3799OSTTzrqOTk5+u53v6v8/HwLqWCyb98+fe9733PUIyIi9Nprr6l27doWUgGwKewbkNmzZztqjH4AgPs9/PDDxt0KN2/erKefftpCIlwrJydHd999t86fP+/42Pe+9z0NHDjQQioAtoV1A7J+/XplZmY66qz/AABvePnll9W8eXNH/c0339THH39sIRGu9tBDDykjI8NR79Wrl37+858HPxAAVwjrBsQ0/WrChAlq2bKlhTQAgIpKSEjQO++8o5iYGMfHfvzjH2vdunUWUkG6srNVamqqo964cWO9//77wQ8EwDXCugGZM2eOo8boBwB4S9euXfXUU0856oWFhbrnnnuMd+ARWDNmzNCrr75q/Ni7776r+vXrBzkRADcJ2wZkxYoVOnr0qE8tOjqa9R8A4EH33nuvxo0b56ifPXtWd911l3Jzcy2kCk87d+7Uf/7nfxo/9uc//1k9evQIbiAArhO2DYhp+tWkSZPUqFEjC2kAAFX1xhtvqH///o76/v379Z3vfEfFxcUWUoWX3Nxc3XXXXbp48aLjYw899JCmTp1qIRUAtwnbBmTu3LmOGqMfAOBdMTExeuedd9S6dWvHx1auXFnm2SHwnz/84Q/Gc1iGDRumX/7ylxYSAXCjsGxAFi9erOzsbJ9arVq1WP8BAB5Xp04dvffee4qPj3d87LPPPtO8efMspAoPL7zwglauXOmot27dWq+//rqFRADcKiwbkLJ2v6pTp07wwwAA/KpDhw56/fXXFRnpvMS98sor7IwVAI8//rgWLVrkqNeoUUPvv/8+hw0C8BGWDYjpDhjTrwAgdIwYMcK4M1ZBQYGmTZumFStWBD9UiPrNb36jDz74wPixt99+W+3btw9yIgBuF3YNyOzZs3Xu3DmfWv369WlAACDEfPe739U3v/lN48fuuecerVmzJsiJQs+f/vQn/elPfzJ+7O2339aIESOCGwiAJ4RdA1LW9KvY2FgLaQAAgfS73/3OuDPWxYsXdeedd2rjxo0WUoWGDz74QL/5zW+MH3vxxRc1fvz4ICcC4BVh1YAUFhZq/vz5jjqLzwEgNJXsjNW7d2/Hx/Ly8vT1r3+dJqQSli1bpscff9z4sR//+MdljjwBgBRmDUhKSory8/N9as2bN2f6FQCEsDp16uiTTz5Rhw4dHB87f/68vvWtb2nbtm0WknnT/Pnzdddddxk/Nm7cOP3oRz8KciIAXhN2Dci1xo0bp6ioKAtpAADBEhcXp9///vdq06aN42M5OTm64447lJ6eHvxgHjNz5kzdd999KigocHxs4MCBZZ6ADgBXC5sG5MKFC1q4cKGjzugHAISHuLg4Pf/880pMTHR8LCcnR9/97ne1c+dOC8m84aOPPtKDDz6ooqIix8eGDx+up556ShERERaSAfCasGlAPv/8c0etffv27NABAGEkPj5ef//739WpUyfHxw4cOKApU6YYz7MId3/961/12GOPGT9222236aOPPgpyIgBeFjYNiGn61dixYy0kAQDYVL9+ff3jH/9Qu3btHB87f/687rnnHr366qsWkrnTo48+ql/84hfGj33rW9/Syy+/HOREALwuLBqQ7OxsLV++3FFn9ysACE8NGjTQP//5TzVp0sT48WeeeSbsF1MfP35ckyZN0scff2z8+L333qsXXnghyKkAhIKwaEBMox9du3bV4MGDLaQBALhBo0aNNHv2bHXp0sX48b/97W+65ZZbgpzKHTZv3qyxY8dq06ZNxo9///vfL/MMEAC4kbBtQMaMGWMhCQDATZo2barZs2eXOSKelpamUaNG6eDBg0FOZs8//vEPTZs2TSdPnjR+/PHHH9fPf/7zIKcCEEpCvgE5evSo1q5d66iz+xUAQJJiY2P13nvv6ZFHHjF+PD09XaNHj9bs2bODnCz4XnjhBf3gBz9wnJlV4sc//rEeffTRIKcCEGpCvgEx7X7Vt29fJSUlBT8MAMC1nnjiCb3yyiuKjo52fOzcuXO6//779cQTT5T5y7mXZWVlaerUqfqf//kf48dr1qypd955J+zXxQDwj5BvQGbMmOGoMfoBADC59dZb9be//U3Vq1c3fvztt9/W9OnTtWLFiiAnC5yPPvpIN998s9avX2/8eKtWrTRnzhymLgPwm5BuQA4cOKAtW7Y46ux+BQAoy+DBgzVv3jy1b9/e+PFNmzbpa1/7mh566CEdP348yOn8Z+/evbrnnnv02GOP6dy5c8bHDB06VAsWLDCemwIAlRXSDYhp8fmgQYPUo0cPC2kAAF7RuXNnzZs3T1OnTi3zMTNmzNCgQYP0yiuvBDFZ1WVnZ+u//uu/NGzYsOseuvjzn/9cH3/8sRISEoKYDkA4COkGxDT9itEPAEB5xMXF6c9//rOeeeaZMh9z8eJF/fa3v9XAgQOVnp7ut++dnp6uefPmafHixcrIyPDb13311VeVnJysd999t8zH9OnTRytXrtT3v/99v31fALhayDYgO3fu1M6dOx111n8AACriO9/5jubPn69u3bqV+ZiDBw9q1KhR+o//+I9KNyIFBQX61a9+pX79+mnUqFH6wx/+oOeff16DBw/WzTffrJdeeqmyfwWtWLFCSUlJeuaZZ3T+/PkyH/fjH/9Ys2fPVtu2bSv9vQDgRkK2ATFNvxo+fDjzWAEAFdajRw8tXLhQL730kho2bFjm4xYsWKBRo0bpgQce0MqVK8v99Tdu3Ki+ffvq9ddf15EjRyRJkZGRioiIkHTlptrvf/97DR8+vNxnkpw7d05vv/22Bg8erK997Ws6evRomY/t0KGD5s2bxy5XAIIiZBuQmTNnOmqMfgAAquKOO+7QihUr9OCDD173cbNmzdIdd9yh3r1766mnnjJuiFIiJSVFkydP1ldffeVTj4qKcmwJvGfPHg0cOFAXL14s8+vt3r1bL774onr16qUnnnjihlO47rzzTs2aNUs9e/a87uMAwF9CsgHZvHmz9u/f76iz/gMAUFXx8fH67//+b61cuVLJycnXfeyJEyf0xhtvaMKECbrpppv0t7/9Tbt37y79+OXLl/X44487Pm/KlCl6+umn9fvf/9547frVr37l8+fNmzfr2Wef1eDBgzVixAi9+OKLysvLu262YcOGaenSpXr++edZaA4gqJynLYUA0/SrMWPGqE2bNsEPAwAISW3bttVnn32mzz77TK+88soN134cOHCgdIpT48aNNWLECO3atUtfffWVYmJiFBUVJUmaN2+eevbsWXrg4d13360XX3xRL774oiSpsLBQb775prKzs1VcXKxjx46VeYaHSYcOHfTLX/6SWQEArAnJBmTWrFmOGm+0AIBAuOWWW3TLLbdoyZIlevXVV8u19uP48eP6+OOPderUKRUWFqpu3bqKiIjQX//6V7Vs2VKnT59WUVGRJCkiIkLf/va3Vb9+ff3Xf/2XLl++rJycHH3wwQcVGrmYNm2avvOd76h///6V/rsCgD+E3BSstLQ0HT582KcWGRlJAwIACKiRI0fqk08+0YwZMzRkyJAbPr64uFgFBQWKjo5WVFSUxo8fr759++ry5cu6fPmyCgoKVFBQoPz8fBUWFmrChAmqV6+eYmJiJF3ZNetGGjZsqEcffVSbNm3Sa6+9RvMBwBWiN2zYYDtDhdxoiPvPf/5z6bB1iaFDh+rIkSOlO4sEkz/3hQ+GzMxMSZJXXhdee35LeC03eQMrKyur9H0rKyuLn78ACVbeiIgI/fSnP9X999+vL774QkuWLNG+ffscjytpIEoWmjdr1uyGX7tZs2bKzs5WTExMaXNi0q1bN910000aP368atasqaysLGVlZVXhb3VjXns9eO16V8JrzzN5A8treUuE3BQs09D3gAEDLCQBAISzevXq6fbbb9ftt9+urKwspaena+3atdq8ebNyc3MVGXllEkLJVKvc3Nwbfs2cnJzSzynZoleS6tevr/bt22vQoEEaNGiQ6tSp4/+/EAD4SXRSUpLtDJViyr106VKdO3eudHhakmJjY3X//ferfv36wYzn4JXnueROkFfylvBa3hJey03ewEhNTS1932rRooVncpcgb/m+57Rp00r/vGPHDq1cuVI/+clPSkcxDh06dN2vcfLkSR07dkxFRUWKjo5Wx44d9eyzz2rAgAFq0KBBQPNXhFdeD1693pXwWm7yBpbX8obUGhDT7lcTJkyw3nwAAHC1rl276v7771dycrISEhIUGRmptWvX6p133lHdunVVt25dxcfHKz4+XnXr1lX9+vX13nvvla4ZqVOnjiZPnqyJEye6qvkAgPIIqQZkzpw5jhqLzwEAbjV16lSfP//hD3/Q3//+d1WrVk0xMTGKiYlRVlaWvvWtb+m9997zeeztt98ezKgA4DchswZkwYIFpXNjS9StW5fDBwEArvXII49o/vz5WrduXWntJz/5iZ555hk1bdpUERERysjIcJx8/sorr6hPnz7BjgsAfhEyDYhp+tX48eMVHx9vIQ0AAOWTkpKiIUOGaP/+/aW1nJwcnT17VpJ8FptL0qhRo3TrrbcGNSMA+FPITMGaO3euo8boBwDAC1asWKH/+Z//UfXq1UtrJeeAlGjZsqWef/55x1QsAPCakBgBmTFjhmN4umnTpqz/AAB4xje+8Q317NlTK1as0IYNG7Rs2TLFxMRo4sSJ6tOnj8aMGaN69erZjgkAVRYSDYhp+tXYsWNVrVo1C2kAAKicrl27qmvXrpK8v00sAJTF81OwLl++rHnz5jnqjH4AAAAA7uP5BiQlJUXFxcU+tbZt27L+AwAAAHChkGhArjVmzBgLSQAAAADciKcbkNzcXH3xxReOOqMfAAAAgDt5ugH5/PPPHbUuXbpo6NChwQ8DAAAA4IY83YCYpl+x+BwAAABwL882ICdPntSqVascdRoQAAAAwL0824CYRj969eqlAQMGWEgDAAAAoDxCqgFh9AMAAABwN082IMePHy89IfZq7H4FAAAAuJsnG5ClS5c6av3791fv3r2DHwYAAABAuYVMA8L0KwAAAMD9PNeAHDp0SPv27XPUaUAAAAAA9/NcA2Ia/RgyZIgSExMtpAEAAABQESHRgLD4HAAAAPAGTzUg27dv16FDhxx1pl8BAAAA3uCpBuTzzz931G6++Wa1b98++GEAAAAAVJinGpCZM2c6aox+AAAAAN7hmQZkw4YNOnjwoKPO+g8AAADAOzzTgKSkpDhqEyZMUMuWLS2kAQAAAFAZnmlATNOvGP0AAAAAvMUTDciqVat0/Phxn1r16tVZ/wEAAAB4jCcaENP0q/Hjx6tRo0YW0gAAAACoLE80ILNmzXLUGP0AAAAAvMf1DcgXX3yh06dP+9Rq1arF+g8AAADAg1zfgJimXw0aNEh16tQJfhgAAAAAVeL6BmT27NmO2oABAywkAQAAAFBVrm5A5s6dqwsXLvjU6tWrRwMCAAAAeJSrGxDT9KuBAweqevXqFtIAAAAAqCrXNiBFRUWaM2eOo87oBwAAAOBdrm1AUlJSVFBQ4FNr1aoVDQgAAADgYa5uQK41ZswYRUa6NjIAAACAG3Dlb/N5eXlasGCBo87ZHwAAAIC3ubIBMY1+dOzYUSNGjAh+GAAAAAB+45kGZPTo0RaSAAAAAPAn1zUgp0+f1tKlSx11GhAAAADA+1zXgJhGP7p3765BgwZZSAMAAADAnzzRgLD4HAAAAAgN0Rs2bLCdodSpU6e0YsUKR7158+YqyZmenh7sWFXitbyZmZmSJDe9Lq7Ha89vCa/lJm9gZWVlKT8/v/T/+fkLDPIGltfyeu16V8JrzzN5A8treUu4agQkNTXVUevSpYsSExODHwYAAACA30UnJSXZzlDqySefVExMjE/ttttukymjm3KXh1fyltwJ8kreEl7LW8JruckbGKmpqaXvfS1atPBM7hLkDSzyBoZXr3clvJabvIHltbyuGQHJzMzU5s2bHXXWfwAAAAChwzUNyOeff+6oDRo0SD169Ah+GAAAAAAB4ZoGhN2vAAAAgNDnigZk165d2rlzp6PO4YMAAABAaHFFA2Ia/Rg+fLg6depkIQ0AAACAQHFtA8LoBwAAABB6rDcgW7du1YEDBxx11n8AAAAAocd6A2La/Wrs2LFq06ZN0LMAAAAACCzrDciMGTMcNUY/AAAAgNBktQFZu3atjhw54lOLiYlh/QcAAAAQoqw2IKbF5+PGjVPTpk0tpAEAAAAQaFYbENP0K0Y/AAAAgNBlrQFZvny5Tp065VOLj49n/QcAAAAQwqw1IGXtflW/fv3ghwEAAAAQFNYakFmzZjlqjH4AAAAAoc1KA7Jw4ULl5ub61Bo2bMj6DwAAACDEWWlATLtfjR49WrVq1bKQBgAAAECwWGlATNOvGP0AAAAAQl/QG5BZs2bp8uXLPrUWLVqw/gMAAAAIA0FvQEzTr0aNGqVq1aoFOwoAAACAIAtqA5Kfn6/Zs2c76ky/AgAAAMJDUBsQ0+hHu3btmH4FAAAAhAnrDQijHwAAAED4CFoDcu7cOS1evNhRZ/QDAAAACB9Ba0BMox+JiYkaOnRosCIAAAAAsMxqA8LoBwAAABBegtKAfPXVV1qxYoWjzvoPAAAAILwEpQExjX706tVLAwYMCMa3BwAAAOAS1hoQRj8AAACA8BPwBuTw4cNav369o876DwAAACD8BLwBMY1+DBgwQL179w70twYAAADgMlYaEEY/AAAAgPAU0AZk37592rZtm6PO+g8AAAAgPAW0ATGNfgwZMkSJiYmB/LYAAAAAXCroDQijHwAAAED4ClgDsmPHDu3Zs8dRZ/0HAAAAEL4C1oCUtfi8ffv2gfqWAAAAAFwu6A0IAAAAgPAVkAZk48aNOnjwoE8tKiqK9R8AAABAmAtIA2Ia/Rg7dqxatGgRiG8HAAAAwCOC1oAw+gEAAADA7w3I6tWrdeLECZ9aXFwc6z8AAAAA+L8BKWv0o1GjRv7+VgAAAAA8JmgNCAAAAAD4tQFJTU3V2bNnfWr16tWjAQEAAAAgyc8NyOeff+6ojR49WrVr1/bntwEAAADgUX5tQGbOnOmosfgcAAAAQInoDRs2+OULrVq1Sjk5OT61Bg0aqH79+vLX95Ck9PR0v32tYPBa3szMTEny679ZIHnt+S3htdzkDaysrCzl5+eX/j8/f4FB3sDyWl6vXe9KeO15Jm9geS1vCb+NgCxdutRRGzBggKpXr+6vbwEAAADA46KTkpL88oXWrFmjmJgYn9qdd94pf339awXq6waKV/KW3AnySt4SXstbwmu5yRsYqamppe+fLVq08EzuEuQNLPIGhlevdyW8lpu8geW1vH4ZAUlJSVFRUZFPrXXr1qz/AAAAAODDLw1IWbtfRUVF+ePLAwAAAAgRVW5ALl68qPnz5zvqjH4AAAAAuFaVGxDTyeedOnXSiBEjqvqlAQAAAISYgDQgjH4AAAAAMKlSA3L27FmlpqY66qNHj67KlwUAAAAQoqrUgJhGP7p3765BgwZV5csCAAAACFFVakDK2v0KAAAAAEwq3YAcP35ca9ascdRZ/wEAAACgLJVuQEzTr5KSkjx3EiMAAACA4PFrA8LoBwAAAIDrqVQDcvDgQW3atMlRZ/0HAAAAgOupVANiGv0YNGiQunfvXuVAAAAAAEKX3xoQRj8AAAAA3EiFG5Ddu3drx44djjrrPwAAAADcSIUbENPox/Dhw9WpUye/BAIAAAAQuvzSgDD9CgAAAEB5VKgB2bZtm/bv3+9Ti4iIoAEBAAAAUC4VakBMox9jxoxR69at/RYIAAAAQOiqcgPC4nMAAAAA5VXuBmTdunU6fPiwT61GjRpMvwIAAABQbuVuQMpafN60aVO/BgIAAAAQuqrcgAAAAABAeZWrAVmxYoVOnTrlU6tduzbrPwAAAABUSLkakLJGP+rXr+/3QAAAAABCV6UbEEY/AAAAAFTUDRuQRYsW6dy5cz61Ro0asf4DAAAAQIXdsAEpa/SjVq1aAQkEAAAAIHTdsAGZMWOGo8boBwAAAIDKuG4DMnv2bP3/du4Vx0IYDMBoFavAoVC4KhaNQOKQ7AOJQxGS0aRlZgLcK8g58k9F7Zc+tm07zMqy9P4DAAC45NcAOfv9qiiKj20IAAB4r9MA2fc99H2fzJ1+AAAAV50GSO70o6oqAQIAAFx2GiBd1yUz8QEAANyRDZB1XcMwDMnc71cAAMAd2QDJXb+q6zq0bfvxDQEAAO/17wBx+gEAANyVBMiyLGEcx2Sh9x8AAMBdSYDkTj+apgkxxq9sCAAAeK8kQHK/X7l+BQAAPOEQIPM8h2makkUCBAAAeMIhQHLXr2KMoWmar20IAAB4rz8DxONzAADgKT+zyTPSAR7UHAAAAABJRU5ErkJggg==
Let $g(x) = \frac{ |x-3| }{ x-3 }$. Values of $h(x)$ are shown in the table below and $f(x)$ is the graph shown below. | | $x$ | $2.9$ | $2.99$ | $2.999$ | $3.001$ | $3.01$ | $3.1$ | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $h(x)$ | $-5.58$ | $-5.959$ | $-5.996$ | $-6.004$ | $-6.039$ | $-6.38$ | | | Evaluate $\lim_{x \to 3^{-}}\left(\frac{ 2 \cdot f(x) + g(x) }{ \left(h(x)\right)^2 }\right)$.
$\lim_{x \to 3^{-}}\left(\frac{ 2 \cdot f(x) + g(x) }{ \left(h(x)\right)^2 }\right)$ = $-\frac{5}{36}$
f7a7e2da-76ef-463e-b7ab-23d607c12f2d
differential_calc
true
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Kr1Xrt2rWampq8vLy0tDSM8eDgIMMwUqk0ICBgyZIlCCGJRKLVamNjY5OTk7netFfI5fKlS5fy+fyzZ88qFIrU1FSHw3H3zp3bt25rgkKDg0NphkGEIEhBMC0QhWAKTCbTpUuXHj9+jDFubW11twf37t0bEhKCEHKPGHodTdN5eXmPHj0qLS3993//92XLltnt9ubm5pdvB6KT8ztHKJPFIRQIEHSMwbRAFIIpEAqFW7Zsyc7OFgqFNE1zN3oWOU+cJPFi3fWiRYt++ctfBgYGVldXc3EcHx+XnBv5TM8/deeZVK4oyY2XB4ghC8E0QBSCKRAKhZs2bXI6nZ430jT9ifpqL07n8vn8hIQErVa7fv16vV6PMQ4MDGRE0ktVL0/faP796XtOgjblJsilQu4hx0KYIIQJtBbBJ0EUgimgKIqrYpktPB4vODhYq9VylTo0TSFMqdUahHlHLlX/x/G7hEWb8xPkUhFGBCOEENdbZzGCOWXwKRCFwM9QFOUxG0MIQoFKybebsgnLHrlc88ez9zHGG3LiFDIRhQiLEEIYI4wRLGUIPgWiEPg1LuOwWiH6dvNymsbHrzUcLKtCiKxbvkwtF1MYsWO/OavHCeY6iELg1whBXAEN1ijFX6/PpCj69I2GY1dqECJrs+M0CjHFZSAkIfgkiELg17hqakIQwQQHqiS7ipIRIudvNf10pR4TtC4nTi0PcE+ezPbRgrkLohDMAxghgjDBCIVoZNsLkzFC5241HblcgzC1MTdOLhPDWCH4NIhCMB+MXWNCaIoKD5RvL0xmCTlzs/GHCw8Rxhtz4+VSwVgaun4TKmyAJ4hCMJ9ghBBN4bBA+d616QThn67W/fbEHafTuWVlIldhw12chxCGChvgCaIQzEM0hYNV0p9vyESEPVBa9duTdwjGW/ISFDIhRq45ZYwo6DUDN4hCMP9ghBCFkUoh/tnGbELIsSv1By48xAhtyFmmlosp5K6wAcAFohDMP9zGzAgjrFaIf75pOU3zTl2rO3qpChF2/Yo4jSKAGrsSBVZ5BRyIQjD/cPnmqrDRyAP2rkmhMDlz89Hxq/WIoPU5cRpFAEVBDIJ3IArBfOWqsEEIBakl21cnIYTO3Wr6qaIOU7gkJ04ld7UNAUAQhWAec1fYUBiHauTbViURhM7ebDxcXoMQ3piXoJQJ3R1lNPYDVNgsTBCFYN57V2GzqyiFIHTyWsOfzj0ghGzOT1TIRBihsQobBBU2C5bX1lsHYG4jNIVD1NL9a9P3FKeYzNbfnrxz/m7z0IjZtYwXQSzCBEJwoYJWIVgguAobrFUGfFOSSVhy6FLtn88+oBDelJ+gkokoTKDCZiGDKAQLhXsNG7Ui4GcbszGmj1fUHiqvRIgtyYmHCpsFDqIQLBSea9io5QH7S9JpGp263vjT1XqE8LoVywKVEqiwWbAgCsGC8q7CRqsI2LE6BSN09lbT8Yo6hFBJTpxGKYEKm4UJpk2Ar/hoF9AP3vPkH8sddBijELV066qkHYXJVpvjr1drLz98pjeYxu7IfYfE8y9gvoJWIZgaQojVaq2srLx582ZxcXF2drZAIMAYT9zk04t73Y0z8Z6n8ljvfpOicKhWvq0wmSB86kbjj2VVFEab8hMUMjFU2Cw0EIVgaoaGhs6ePXvx4sXm5uaIiIjU1FShUIjeDyP3bshe3AR5nHH37P7rVB+RpnCIRrarKBUhcuxK3e9O3bOzZHtBEreGDSGIuztIwXkPohBMjU6n6+7uTk9PHxwcdIcO1z/1/Kv7Fu+modlsvnDhwpkzZ96+fUtRVFxc3N69e3NyciQSCZpm8mIa4yCV5Kt1GSxLfiyt+u7kHYzwtoJEpUyIkc86+WCOgSgEk8UFTXBw8Ndff93e3l5TU/Pphti4fPxyw8PDhw8fPnDgQEtLi9lsRgjV19c/e/bsn//5n9etWyeXy6fxWAQRhAmFsVoh/qYkkyX46KXqHy/ex9i5IScBKmwWDohCMFlcE08sFkdFRen1evdmxJ6NwXHdZPft6Isz0el0VlRUHDt2rLm52WKxcDeOjIw8fPhQo9FERUWlp6fzeLwpPyk0tgUUwWp5wM82ZjI0PlFRf+xyHWFxSW5coFJKUdBBnv8gCsEUcHH2wVAzm81dXV1Wq/Xt27eDg4OvX78WCAQ0Tcvlco1GM42QGsdoNDY1Nb169cpqtXrebrVa79+///Lly6SkJIZhphW47ypsVHLR7uIUCqMzNx6duFaHMClZEa9VSWgosZnvIAqBdwwNDT148GBgYECn07W1tT18+LC9vZ3P58fFxWVnZ08xCl2rwxBCsGsfEmSxWEZGRux2OyHEFV5j+vr6DAaD0+mcdsMTe/wQqJJuW5WEEDp769GJinpE8Ia8BK2S6ynDGjbzFkQh+CLugr6AgICEhASj0djd3f3ixYv4+PjY2FiGYbRaLZ/Pn+K9uhIGY0wQ4XYgYXgMj8fz7JW7H1okEvH5/C+bovGosMEoWCPbuioJYXz6xqOjV+owxltWJijlAWPDhq6njiEJ5xGIQuAdEokkISGBEMI1CePj41NSUiiKommaYZhphRRX18fVtCCpRBIdHaVUKAYHB51OlhAuKBEiJDk5OSIigsfjeWvCmquw2bYqGRFy/Fr99xceEoy2rkxUykSYIIK4ChsuoyEN5wmIQjAFNpvt1q1b9+7de/nyZVNTk8lkqq2tjY2N3bt3b2hoKFdgKBQKGYYRCARCoZCm6Wk8ChdnBGGMCEGYEIQxstpYI6N1iNSEakdOO8YEERYjpFKrN2zYEBcXx/XBvTRhjWmMQ1SS3cWpBJFD5TW/O3GHdZIdhclQYTNfQRSCqeHxeEKhMDw8fPPmzXw+n8fjCQQCd7/V07SrrDFGxDUYh7lWmMFoLb37+HJDj3RRQY4muP157fCwnqbomOiYr776avee3cHBwR88hulxVdjQWKuUfLUuw+HEh8sq/3LuHsbslvwktRwqbOYhiEIwBQzDZGZmxsXFOZ1O9418Pl+hUHj+2hdfbYIxIq5KbYSHR82XHz49cqnGZHX+at+m3PhAq1Hf2dmFKRwTHR0VFaVUKmma9moZI8auKRKslgX8TUkGjclfr9YdKa9FBG/Iix+rsIEgnD8gCsEUUBQlkUikUqnnjRPzzvNqk2k/FncHhlHL5YdPD5fXGi32vWvSthQmRwTKMUJWq41gJBDwacrVB/diLTd2/TFWYaMQ7VufzjDUyYqG4xX1BJMNOfGBKilNIRgrnDcgCsHUfNlSCBN5lqcg5C54RhhjMmqylt9/cqi8xmS17yhM2boqMSxQTtMUQlgkFvl6zsIdiBghjSJgW2ESQuj0jcaT1xoRoTbkxgeqAmgKj6uw8eURAR+CKARzxLu6GS5QRozWMzcfHb1Ua7La9xSnbi1IjAhUMB7zML5PHez+EyMUpJRuKUhECJ+++ej4tXqE0JaVCWrFWL0h8Yhx4IdgvUIwq4irPUUQ8sgSMmI0n7zeeLC0Wj9q2rMmbVthUkSQgmGmMx/tLRSFg9WyLSsTdxam2B3OI5eqS++36A1mbjlDgrhdohCsbeinIArBbCKuhVG5eRJXJeGI0Xrq+qMj5TUDhtFfbFm+qzglPFDBMLN+rmIaU8Fq6Y7CpN1FKXaH809n75+/3aw3WBBGGBMERTb+DDrIYDbhsS6xq24G4xGj5dytpsPl1YMG07/sK9xakKCRSzCm5kDPkxCuwkYl2bc2jRD8Y2nld6duE+LcUZiikokp1xOBChu/BFEIZhNxzUsQQhBBeHjEXH7/yeFLtUar49c78jevTNQqJL5cD3uqh4oxIhSm1DLJV+vSCWEPX6o5WFqNEd6Un6hVSqDCxn9BFILZNDZSiBEiQ6PmSw+eHr5Ua7Y5/6Ykc1tBglYR4K7U9vj1WT1U5FqHQSUXfbU+g6ao41fr/3q1jiCyIS8hCCps/Nasj7+AhYNM/JmbLcEYjRitl+8/PVJeY7Y69hSlbF2ZEKyRzcGlsbCr+0swQhp5wK7i5P0lGQihk9cby+8/6RkcdbJjPX7gV6BVCGYaN1Uyrm7m/J3mY5dqTTbHztXJWwsSwsbqZsa6xnMqE98djFYhcVXY3Gg8db0RY7wpL16rktKuChvsmlWeW8cPPgCiEMwUgj0q7whxTTAQg9Fy6vqjo5dqzDb7vnUZ2woSw7WzXDczeRjjIJV088oEhMipG41/vVqHENpakKRRiBFC7rYhrGEz90EHGcyQ9+tmuCkIZDBaTlQ0HCqr1hvNX5dk7SycI3Uzk4dpTAWrpFtWJu4uSmGd7MHSqot3WvTDZjw3ZnvAJPnROQf8G8aIRQiN1c1ghEeM1tPXHx0pr9EZjL/ZuXJ3UXKoVkZTNPGnBhQhmKVoHKSW7lydumdNhsPJ/u7kzdM363XDRu4iZkwwFBzOfdBBBjOEaw+O1c0gw4jlwp3HRy7Vjlrs/7x31fZVSRpFgN+1pN5V2FCURhGwd00qYdkDpZXfn6vEiNq6KlmrCMCY+NVzWqAgCsEM4bYCIQQTRIYMlksPnhy5UmdxsL/cunzLyniNImCsJs+f5hk8VpIgGGOVXLxvXRpC6K+Xa49eqkGIbMpPDFJJqbk3FQ7GgSgEM8W1Wd5YDl6qsdocX61N25KfEKiUUth11Z0/wq5tpwhGSC0P2LculaGp49fqTlxrIARvyEsI1kiZ99awAXMORCHwhbELcsfmid23jhqtZfceH71Ua7E7d65O3royIUQrp+du3czkvTtstSxgW2ESpvDJ6w2nbj5CGG/Miw9WS10rer2rsEF++2TnIYhC4CMYIcRNGOCxD/+I0Xr6RuOxy7VWu3PPmtQtKxPDAuXMtPY/mdMw0ioDNuUnIIJO32w8db0BIbRlZWKgSuJx5Qyk4NwCM8jAVzAi3Ewx96E3GC3HK+p/vFhtMFn3rU3fWpAcHqhg6Hl5BmIKUcFK6ab8+F2rk1lCjl2pLb3bohs2ueeFCFyPMsfMyxMRzA2Eaw4ShIjBaD1R0XCkvGZo1PS3W5bvKEwK08r9rW5m8gjBLKZxkFq6tSBpd1EaYcn3F+6fvdU46KqwIRRk4RwDHWTgC5THEtDEYLScvtF0qLxu2Gj5//av3rIyUS0TYUz5V93M5HlW2GiV0t3FqYSQH0ur/nj6PmHRrqJUtVwMK9jMNRCFwPswYl17JBEyZLRcvPP46KVam935j7vyt+THaeRirtfsle3b5yDPChuKwiq5ePeaVELI4bLqQ2XVCKOtBUmBSglU2MwpEIXgC32gQMS1NgshFqv9Vv2L4xV1Dofz202ZW/IT1HIJHqubmY8x6Mm1hSm3hs3etakURf31Su1PFXUI4Y1QYTPHzEQUdnZ2IoSCgoIYxicP53Q6BwcHnU6nRqPh8XjevXN3y6Wrq4umaZVK5X4IrzdqRkZG+vv7Q0NDhUKhF+923EMMDw8rFIqAgADvHTxBBBGM3SsucKx2552GV3+9Um+1O3evTduUnxCklnEbt39J3Qy3s+jbt28DAgIUCgXtmwloh8MxODhIUZRCoWAYZhqvFXb/gRBCSC0L2Lk6mabwiWsNp240sgRtzo8ntlEeQ6tUaj6P5/G73jypDAaDwWBQKBQSicSLd+tpeHjYaDRKpVKJROK/zfyZmDZ58ODBgwcPrFarj+7fZrPV19fX1tb66CG4LX0rKyvr6+vNZrP7dq+/652dneXl5Tqdzrt3O+4h7t27193d7bmn+xch7j0yXUvOIEQQohxO9kbtiwOl1UMG0/bCpM0rE0K13L6dXwpjzLLszZs3W1pafHdSmc3murq6pqYmo9HonTcaI40iYPPKxL1r0ymMz95sLLvXcr60orqm1mgcRe/mlL05n8KybEdHx71793p6erx1nxO9efOmurr6gydVb29vc3NzW1ubxWLx3QF4xUy0Cru7uxFCDofDR/fvdDoHBgYsFov7IbzbXuPuqqenRyKROBwO341wjY6Ovnnzxncfb4SQ0Wjs7u42mUwsy3rnHj+0A7DdwZY/eNLw1jZitO4uTtmUnxCqlXuxboZrFcrlcq8F+gROp7O/v18oFNrtdu/dKw5USjbmxiPCnrrReOJ6g6PnyY6ilBXLHR75h707oTIyMtLV1RUfH+/F+5z4EL29vZGRkWTCshNPnjw5e/bs8PBwaGjosmXL4uPjY2JilEqlj9ryX2ImopBl2YmvkXc5nU7us83l1JdHFXc/nn+6H8JHCCEsy3JR67tHYVnWu0+EII8LJ7idjDGtR/Lb918IA5Tfbl6+eWVCsFrqlfYg8viSm5m3w8unLmYxpoLUks35CQTh4xX1rw28t6OM2U6we+dTb08tE0J8/VpxJ9UHX6ihoaG6urrHjx8zDKPRaIKDg8PDw5cuXZqcnJySkhIaGsrn8313YFOCp/ROf/vtt319fVN7AIzb2toQQmFhYT4aK3Q4HH19fU6nMzg42OtjhW7t7e00TQcGBvruIYaHh3t6eiIiIsRise8eQq/Xq1QqqVTqpbYteTcsRhDClEMa9sYk1Y86UG9DlAKrpEJ6rGzGW6FCCHn16pVEIlGr1T46qex2e19fHzc67J2PK373/FmW6AymLrPIKokKDY8MZfS0oY21m7zwKO8jhAwPDw8NDanVaqlU6vX75+j1+tHRUblcLpFIuLFgt97e3tevX4+MjBBCKIpiGIbP50skEoVCERERsXv37u3btwcFBfnowKZkalFYU1Mz+e6b+wv8xIkThJBNmzb5aODWbDbfvn3barUWFxf7bmz41KlTYrE4Pz/feyEy3pMnT65evbpnz57Q0FBf3D9C6OnTpw0NDZmZmTExMd4LEdcoodnmuFH7orSybdTK/sv+otRICYNZX7xSDofjyJEjixYtyszM9NHXxsjIyJ07d/h8flZWlkKh8Op9E8QVnjOCMzeayqvaRkdHSrIjN+bGBSq9PO3AsmxLS0tTU1N2dnZsbKwX79lTY2Pjq1evEhISFi9ePO6kunnz5pEjR54/f04I4fF4fD5fo9EkJydnZ2enp6cnJCSEhoYKBAIfHdiUTO3DkJWVNY3HqK2tZVk2JydHLpdP459/1ujoaFdXl9VqXbFihbfP2nfq6+slEsny5ctVKhXyzX6UPB6vpaUlIyNj8eLFXr9zDp/PHxoaSk1NTUxM9EpjxzXST7DJYr1V//KFvo3hi7W211mx2pzMFIp218x4c+ktu91++/btZcuW5eTk+Kixo9fre3p6hEJhdnZ2YGCgt+6WoPfWLqyvr1umcbYJVa06KssuXb40KUQjpSkvDCZwDRGWZRmGGRkZSU1NTUtL+/K7/SCWZTHGaWlpSUlJ406qoaGhBw8esCwbFBTEHcOSJUuCg4OVSqVMJps7vWM0M2OFfD7fp8W0GGOBQOB+CG89lucdIoQEAgGfz6e8cZp+DMMwYrHYpyPKDMMIhcLpVYeMdYXdoUaGhw3dPd1Gk4kvEL/oNf9U0agzmNZlRXe2dApoFmPPcS9vviMYY5FIxOPxfHpS8fl87h334tk7biBQyKA1mVFGfsj1+o5TNx4RhDfnx4do5Ay3TRTB+IvXsHG/41903J97CIFAQNP0xFdpyZIlv/71r4VCYUhIiEqlkslkAQEBc3DOBM1MFKampiKEfPcNwOPxli1b5nA4uJa2e6LjC+923D0kJycLBAKBQOC7j19QUNDKlSt91HbmBAYGpqenazSa6WQ65iZJXOUzXV3d5eXlrc+eW+z2EUrVYZaYHWhrQXLWIlnp2zpfXEnhfuUxxllZWUFBQb4btxUKhfHx8QzDiEQi373jycnJPD5fFRgeqA08eb3h7K1H3GqvoVoZQ3Gl6AhNKwXd3xnBwcHcO+7dI/cUGhpK07RWq514UkVHR4eGhnJd4zlecji1scJpIISYTCaEkFgs9tFrQQixWCyEEKFQ6PVWmztVTSYT1/z0XcPQbrebzWaffm3a7Xabzcbn86fTMCQIYW6XX2y32X766fiNGzfi4uJb+2z3WvUWJ7Nu+dLf7CsOoOx/+fOf9u/fn5aW5qPXihBiNBq5xoiPTiqWZa1WK9c29EpNwgeZTEaMMJ8v6B8ylj94cupGg93B7ipK21qQEKyWUQgR955Y020Vut9x331t2Gw2h8PB4/E+cVIZDIbR0VE+n8/1i41Go8FgQAgpFAqRSOSjA5sSn7cKMcYBAQG+7iBzryZ3HYK3HmhcXY7n8Lwvng43ruy785XDMMz0HwJzq9YjgnBnZ9e9e/cjoqJYedTLF5021iRx9AiMAoUQIeLDk4r75sYY+25+jENRlNc/ouNOG0KIWCzmWiJalWRDbhwh6OS1huMVtRRmdxSmaBUSLgnxF1ybNwMnFTeSwP38sY/Gy5cvT58+zefzd+/erdFoysvLq6qqVq5cuWHDhoUShcg3wfHB+/fuWOHH7sSvFxFwH/k0ngXh/jlBGKPOzs6+/oEBp6yvo71/2LFvfZalq3l0sEs/OCiTyXxw4B8+Zv96LzzPTzI2EIgRIoRQFA5USbfkJyBEjl6p/fFiFSF41+pUjTIAo+mvZOb+5vDis/jEY3FNhw++KRqNpru7u6mpSS6XMwxz6tSpqKioRYsWBQQEzMCxTcZMRKGv34lx9++L9hr3BnN37t3AnfgQyPev2HQPnuXGCQlCI0bTMFa9ardiofEfduXvWBl/54buQc9r4+iI707uicfsuyEXz3fcu3fu+bWNPManaIw1Ssn21SmE4IMXK/94+p7T6dy7Nk2j4Nq/02kZzuT3hDsEP5iGGo1mxYoVdXV13333HSEkLi5u79693ipj8AofRqHVah0aGvKsQxSLxSqVyhfjR06nc2RkxGKxyOVybi0DL54EDodjYGCgvb19eHg4KCgoIiJCLpd7dzjPbrcPDw9zxahqtTo8PNwXFycRQsxms8FgEIlEEolkqvePEUYYE0TMFlufRWAURQgQ+7NNy79en6GWCQV8HkGs0/dXFiGEHA6HXq9nWVapVHr9s8S9Sv39/Z2dnU6nMygoKDQ01KurVyCEkM1mGxwcfPPmjcFg0AZqIyPCFQolTdNqmWhnUSLLOn8sqz58qRpjatuq5CDXvijTf6yhoSGapmUymRc7y9w0gMFg8Lw2UaVSfXBRBoFAkJube+PGjYsXL8bGxu7YsWP58uVzp0mIfBqFLS0t//f//l+r1ep+9XNycn72s59NqRBsku2X3t7e77//vqWl5R//8R9XrFjx6Y/HlNpEdru9rq7u1KlTPT09hJChoaHly5f/8pe/DA0N9VamOxyOysrKkydP6nQ6iqIcDkdcXNyePXtiY2MnP7nx2SfFXZl/48aNsrKytWvX7tmzhyuQ/NjdIddaWti1syW3Iikhoxbr7bqXF+6/6NOP7lmbuW9NWligwma12Gw2iqL5fB9OK3F0Ol19ff2JEycQQv/1v/7XuLi4L7zDca0/o9FYVlZ2/fr10dFR7paNGzdu3LjxUy/XFFmt1pqamosXL3Z2dnKBkpGZ8dW+fYsWLaIoWiUN2FWcStHUsUu1x6/VE4S2rEwM0cgYmvJoG052btlut1dWVn7//fcxMTG/+MUvoqKivPUsbDZbRUXF6dOnzWaze579V7/6VUFBwQef8ps3b3p7e1mWlUqlarXap1Pz0zDNKPT84H3sQ6jT6Z48ebJv375FixZxDZCwsLBxleWf/gBPMrMsFktVVdXVq1eHhoYMBsNnL9Gf0hug0+lu3rxpsVj27NkTEhJy9+7dn376KSEhYePGjZO5zmEyT0Gv15eVlZlMpt27d4eHhzc2NpaVlQUHB4eEhEymYtz9Sf70Y1ksltLS0sbGxhcvXiQnJ39mlQGubgYjzK27RTDCBCNitNpv1b48WFb9sr0b6V+FixNVEgFNYavV2tnZGRAQ4Lsr4dyuXbtWVVX15s0bbh75y+9w3IvW0dFx69YtuVy+Y8cOsVh84cKFU6dOLVmyZPny5V/yKJ7vTl9f3507dxwOx65du8LCwu7du3f79u2oyKjAwCCZTIYwUsnFOwpTaIr+qaLu7M1HCKFN+QlhWjlDcwveIuRKwc/3mru7uy9fvnz//n2GYby7PIzT6ezu7h4ZGcnJyXEv9/DBqHU6nXV1dUePHnU4HFlZWcPDw01NTZmZmXMqDad51nrm4Md+h+u/5ObmJiUlcR8PiqIm3z6fTNpyj/7ixYt79+4FBwdjjCmK8u6LyzBMfHx8Tk5OWlqaRCIJDg4+cuTI69evbTbbZKLwswfDPbWUlJSwsDDuIQICAm7dutXT02O1WieTpJ6jWp+YWOBKzJRKpU6n+/y7MLZHnedHze5wXq9tPVha1TNgWLd8WRv/7bPG6jeZCVJJ0rNnz7iEVSgUnuuY+YJIJFqzZo1QKGxpafHi3bpfKIFAsHLlyiVLliQkJPB4vO7u7gcPHuj1+i+8f8/3hcfjJScny+XypKQkmUwmkUgqKys7OjpMJhM36YQRVsvEG/PiECInrzecu92EENqyMjFUK6M9Ns37bIWNxWLh1mQLDQ31+pw7xphhmMjIyPz8/IyMDPdTG/drTqezqqrqz3/+c1dX1+7duyUSydGjRx8+fJiXl6fVan09uz15U45Cz/kv9P4bPO5/jYyMiESi169fP336lKKopUuXpqSkcF3Xcb/5QZ7/62OZiDE2m83l5eUikSg7O/vWrVufPXg0xVahXC4vLCzk8XgikchkMtXW1jqdzqioqKleOPmxJ4sxlsvlGzZsEAqFXJWc1Wp1Op0KhYI7Syafhh8csXb/LBAICgsLe3p6KioqPt+HxR7dMEIIwnaHs/Ruy4+lVT0Dhq0FSdsKEtqWik8eP/7b3/5Wq9V2dnZKpdL8/PwZiMLc3FyGYZ4/f+7dnrj7pQsLC9u4caNIJOLz+U6nU6fTKZVK7+aIWq0uKCjg8XgCgcBsNj958sRqtYaEhHh8uRKCkVYRUJIbhxA6eb3xzI1GjMj2wpRgtXTyFTYNDQ11dXVxcXGe9S7e4nQ6zWaz1Wptamp6/fq1UChMS0uLjIwc92t6vb6lpYWiqN27d2/ZsoVlWb1e/+TJE71eb7FY/DgKuTOGENLZ2Wk0Gie2CoVCYVhYGI/HGxoaam9v/+mnnxYvXmw2m0tLSzdv3rxjxw6ZTDYxRifi1qYeHh52d3jdzR+xWKzRaLjW9fXr11tbW7/99tvu7u7JzAOMm//t7+8fGhr6YJ86Ojqau2JJLpfrdLpDhw5VVVUZDIZvvvkmNzd3klHIdeJ6e3vdq2+5P3IMw6hUKrlczuPxlEol9/u9vb1nzpwJCAjIzMz0HKr/dCCOjo4ODAxwM1Se7wjGWKvVcpM8FEWpVKqhoSHPY/towZCrX4wwIgghu8N54c7j7y9Wvu3Rf7UuY3dxanSIMkKbp1TInz17Njw0HD9mBi6tV6lUTqfTPZXvRe5WIVdW7XQ679+///Dhw/z8/OjoaC8+EFfrNzg4ePDgwcrKSrPZnJeXt3LlyrFpBOy6pIfCgUrpxtx4RNDxirq/XqnFGO9anapVSSZTYdPT03Pu3DmtVpufn6/T6biPrRefBcuyAwMD9fX1g4ODwcHBAwMDV65c+cUvfrFixQrPQRKRSJSfn5+WlhYaGqrVap1O5549ewYGBjQazRxZiIEztSh0Nz1Ylm1sbOzo6HCvU+Y+L7Va7ebNm3k8XmZm5m9+85uYmJjQ0FCr1VpaWnr27NmwsLCCggLPS4Y/xmaztba2trS02Gy2cf8rJCQkJydHIBAMDw//6U9/2rhxY2Ji4mQWf3Y/ovuHFy9ePH78+IPL7ezfv9+9sD6fz4+JibFYLDdv3rx9+/batWuDg4M/3SpxP8G+vr579+6NjIyg99NHLBZzC6u4T4j29vb//b//d39//7fffpucnOzZgv50I7q/v7+mpmZgYMBzWTrufcnPz09ISKBpemKlzidff24dQkwQsjvZ0rst31+ofPam71dbl3+1PiM8SM6jKZ5cnp2VnRCfYLFYRCJRQEDANC9tngqvT09/8FXlehs3b9786aefYmJitm7d6pUVGcZ1htwn1cOHD+vr61esWBEVFTX2de5qlFMYaZWSLQWJBKEj5dXfn3vIEnbvmnSNggvNT7UMz549Ozg4uHHjxrCwMJqmHQ7HZ7tiUyIQCIqLi2NjYyMiIrRabVdX15///Odjx46p1WrPuSyRSMQtL8J9HzMMEx4ezs06+nqGbUqmFoWen6Ls7Ozk5GTu1PR8ffl8PpcgcXFxUVFRYrGYYRhumqyysrK9vZ27WPiz7wefz09ISIiIiJh49gsEAoVCQVHUf/zHfwwNDQmFwkePHrW0tAwODj5+/DguLi4yMnKSlSJxcXHh4eEfXNiSm+nmllMVCAR5eXkZGRlr16797//9v5eWlkZERHz6uk73EwwODl6zZs3ERbw9ixtYlq2rq/vd737HMMxvfvObjIwM93WK45qxExFCuIuXbTbbxOsZ3JuxTGZ4993BczMmiFis9qtVzw+UVrb36P5+R87X6zLCtAqaphBGFEECgavbNWOD3z5qCXoihIyMjFy+fPnKlSuJiYlbt25dtGjRl/fjPHOQW0tVKBRyJ1V+fv7vf//7O3fuxMTEhIeHv394CGOkVoi3FyYSlj1wseqHC5WE4J2rU4PUkk9sn1pbW1tRURETE2Mymerr69vb21mWff78uVar5T47X/h0EEJ8Pp9ba4vrPC1evLiqqurhw4ddXV2eUTgx8mianoMrMkxz2oSiqM9+T46MjOh0uvDwcG4FES4QJ/8QNE0rlUp3z/GDXr9+zbLs+fPnGYbp6up6/fr1hQsXli5dGhQUNMll7D77EN3d3ffv31+6dGlcXJxEIlGpVEqlsqOjY5LrNmKMxWLxpw+GEPLkyZPf//73ISEhu3fvHrfS0WdbhZN5iE/hdp9zjT6RsRkTjAgxWqw3al/8WFrVPTD8TUnm1+sywoMU75aQ+vwgh295nk5ebOzYbLZ79+7dunUrLS1t48aNk/9a/TTPL7Y3b940NzdHR0cvXbpUo9EwDCOTyfr7+7mr9d/9k7EWH0ZIJRPvWJ1MEDpcXn3sSi1BaFtBUqhWNlZvOL7ChltiuaWlpb293WKxvHjxgmVZjUYTEREhlUq9EoUsyw4NDdntdq1W676qfQaqSn3Eh3UPDx8+PHv27Pr161NSUux2+61btwQCQUxMDI/H89aJ+6//+q/cQgwIodu3b587d2737t3p6eleHIMwmUw3btyora3dsmWLVqvt6+vr7OyMj4/34qZ0Op3u4MGD3d3dK1eutNvtTU1NCCGlUhkcHMyNh3rlsoe+vr6enp7Xr18PDAxIJJJHjx6FhobGxMSIxSKuK4yRqynIrcQ1arHdrHlxsKy6d8CwszB5T3FqmFbulaX0voTBYOjs7BwdHe3o6OBG33k8XkhIiFKp9FYRT1tb28mTJ51Op1arHRgY0Ol0GGNunMtbDzEyMnLt2jWpVLp+/fqgoKA3b950d3cnJCR88vsMK+UBO4tSaJo+dqX2zI1GRMiWlYlhgXKGphBBBHO7ASDua2358uVRUVFcEUJ/f/+JEyecTuemTZvclW1fzmKxlJWVPX/+nJtw7+vra25ujo2NHdew9Rc+jMIlS5Zotdrz58/X1dXZ7XaDwbBu3bqEhAQvjijFx8d7Tli/efMmPT09MDDQi81vbtT51q1bJ06cEAgEOp1u2bJlJSUlXpxSHBgYGBkZEQqFDQ0NLS0t3NNJTk4uLi4WCoVfMj/gmaEvXry4ceNGT0+Pw+Ho7u4uLS2NjIzcv3+/WCRGmHDDgmP1asRis9+oaT1UVt07OLIpP3FnUUpUiIphZr9Tw82Av337tqOjg6bpu3fvtrW1rV27NjU11Vs51d3dzW0Z9uDBg9raWu413LBhA3fxrFceIjw8PCsr68GDB6dPnxYIBHq9PigoqLCwUK1Wf/wfEYywSibesjKBwuTEtYbzd5oRwltWJoQFKhgKofcrbNRqtfve+vv7W1tbnU7n0qVLvXiFOI/HW7x48ePHj8+fP89VDsjl8o0bN0ZERHjrIWaSD6MwJibm22+/ffz4MdfsDw0NjY+PV6vVX9449xx2ccfEkiVL9u7du2jRIi+W+BJCZDJZSUlJZGRkZ2en1Wrl8/nLli3jqhO81bZVq9X79u0zGAyefajg4OAvvyzJ8/BCQ0NXrFhhMpm46VeapqVSqSRAwn10XDWEiBCEHQ7n5QfPDpZV9g0aN+Un7FidHBOm4vFm4nL1z1IqlWlpaTExMQ6Hg1uiWSQShYSEcMMvXnk7YmJifv7zn1ssFm4tUi4KIyIivHheKRSKDRs2xMTEdHZ2WiwWoVAYGxu7dOnSz3U1CEFILReX5MYhhE9ebzh/+xHGZNuqpFCN3DVu+KF5FIlEsnr1akLIJ6N2yripUYlE0tbWZjKZhEJhTEzMJJ7FHOXbvr3D4TCZTNzUFVc3x+XgZMqnP23iv3I4HNyiaV5pEo47QqvVypX70TTNTQQh742TOZ1Oq9U6buqG2xBn4ss1bdy6de63mxBC07RQKMQUdo1JEYIQsjnYC3eaD5RW9QwM7ypK3bk6JSZUxefRGE/2C+z169ffffedj9YrnPhaYYw9l1/88tdq3AvF4db7+5J7HjfKwZ1UFouFZVmapiezKPfY5oKYsKRfP3r54dPj1+rNFuvu4vTdRalBaunHrsYjhHAXFzEM491FuQkhNpvNarU6HA7udJr7S7R+jG+/6rlJ0om3e561XslBQgjDMF783sbvl5ELhULffddx8Yo+VAE+mUqaSfrYunUEsWN1M9jucJ6/9fj7i5VvegZ/viFrz5q0iGAln6EQxpO4xGsmUBTlfq08z6KJpULTwN2Vjxb4G3dg7pNq8u8sdm2nQDBGWqVkQ148QejYpdqj5dUUJruL07RK9xo2yPPd4r4tPnYkXwJjzC3t7q07nEU+HAX3yvXFHzQuLJBX313PR/lsk9m7beqJXwyTqwGcLM8m4buH4D5imNgdjtJ7zT+UPnz1tv9vNy//Zn1mVIiazzAYU5hghNixz9hs8nxBJnnx9Wd5JUanbRoPijGiKKRRiLcWJOxfn87j8f549v5PVxv6Bo2Eu3R8Lnxr+Rsftgo//R5767Tz6en72Tv3r76AazCJIPyBuhnbterWA6XVXQPDv9y64qt1GWGB8nF1M3PtA+at7wl/exNdR0thrJKJtxUmsYQcuFh55FI1wnhHYVKI5qMVNuAT5sRYOJghGH2gboaQEZP1Ru2Lg6VV/bqRr9am7Vub9qG6Ge+MxAGvwkqZeMfqFIzpo5drTl5rQITdsiopXKtgaDyxwmaWD3ZugyhcSFzrzbxXN2O02G7UvjhUVt0/NLptVfKuopTwICVNf3jkZGaGJsCkEVf1dWEiQ6Ofrtadu91MEN6yMjEiaFyFDfgMiMKFZELdjN3uvFb9/GBpVf+QcVNuwo7C5OhJ1A+yLNvZ2dna2spdKDZ3FhdZmAgiSploQ24cQujE9caLd5sxJltXJoUHKmgaWoSTBVG4gHDrzYx9OJDd4bxw9/HBsuo+3cj2VUk7CpNjQlV85jMzaTab7dGjR+fOnauqqvr1r389p5acW3i4MV9EEFbLA9aviEMYn7xWf+5WE0Z4R2FKqFY6NrYIWfgZEIULinu9GWxzOM/dav7h4sOegeH96zJ2FaVEhqj4DPVuH7aP6OrqKi8v1+l0er3eYDB8cCULMGM8KmywVilZnxOHCPnpav2JinqMyO41aUEqbv8MaBl+BkThAoLHPjh2h/P87ebvL1S+ftv/qx25+4rTwoIUDENznyqE2E/MF8tksqKior6+vra2tjm1yNICx61ho1WIN+XHI4IOldccKK0iCO9dk65VSqa/pfyCAVE4T31svRlEzFb7pQdPfyytetun//XOvK/WZYRqZO55Eq59we3y9EFyuTwrK6u5uXlKqyLD1LNPvV9hE7C5INFJyI8XKw9crHSyZE9xarBGOvb6Q4XNh0EUzlMfq5sxW69Xtx4srerXj3y7MWvfmrQwrczduLNYLHq9nlvOZNz9KZVKqVRKjxm3hwwhxOFwjIyMOByOwcFBk8mk1+v7+/tpmhYIBGKxeA6uTzdfYYyVMtG2VUkE4UNlVT9V1COEthcmhwXKGQoqbD4KonCeIu66aDQ2PujKwUNlNYPDpl1FqXuK00K1763iOTg4WFNT09/fP3GHg8zMzMTERG6lnImPhjHW6XR37tzR6XQDAwOtra03btxobW3l8/mxsbHp6elT2vEVfBlXhc32gkSGQkcv15691cStb+hRYYNdewaAMRCF8xTGGBHiikRCEDJbbNeqnx8urxkcMm7JT9yxOjk8WMG8P1+sVquXL1/OLUYw7nI0hULBXWn/sa4uwzDcNvYsy4pEIqVSyU0uc23JGXjGwBMhSCkTbcpPoDD+qaKh9O5jjMjWgqSIQAXDUGMrO4B3IArnJ4KQq26GcHUz7KUHTw+W1QwOj25Zmbh9VVI0t87C+4RCYUhIyKfu9uO7sMrl8uzsbKfT+ebNm5aWlqysrKSkJJqmuQ0eYKxwBmGCCFdHr5KJ16+IIwifvF5/8W4zRmj7qpTwIPnYakTwjrwDUTgvEYRcHSCCsM3hOHer+cfSqoGh0d2rU3YUpkSFqvgMRSZsIPnBJX/cLUFCCJd07e3tLS0tvb29zc3NMpksJCQkKSlJKpVyqxBxu81IpVKlUglTzLPCXWGDEFIrAtatWIoxOVHRcPZmE8Zod1FasEYGY4XjQBTOSxi72gXIbneeufHoh4tV3f1D325azl1Xx+O9VzdDyHs7b7x/R9jzT6fT2dzcXFFR0d3djRB68uRJd3f3kiVLwsLCYDRwDhqrsAkoyVmGEDp6qfbYlTqEqL1r0gNVUGHzHohCPzd2GR1C4+tmMCJWu+P87cc/lFa97hr4zc68fWvTQzRyhh6/3szke648Hi8nJ2fx4sV2u51lWW5VsYCAAK1W6+0nBr7UuwobCqvlkk35CSwhBy9W/nDxgYMl+9elB6kkHhtJoQVeYQNR6Ofe9XMI1wh4VzdjsV2pfHqwtKpfZ/iH7blfrUkP1con9Findt5TFBUUFBQUFOS14wczAmOskIq2rEx0sujAxcpjl2swIruKUl175hFC8Ltqg4WZhhCF/s8VhJirGeM2aRgxWSqqWw+X1gwaTF+XZO5bkx7ygRwECwfBCCml4m0FSRRCRy7VnLrxiCC8fVVSRJCcoSiCuFNoQaYgQgiicD54r24GEURGzdaK6ueHy2t0BtOOVSk7VyeHzoF9O8Gs4k4NpJSKthQkMjR17ErdhTtNCLHbCpIjgxQMQ7ELu8IGotDvjdXNuNYosdicVyufHyqv0RmMm1cmbl+VGBmkZJgF+2UP3iGYIISVUlFJThzG1PGKurK7jymEtxYkRQYraIpayBU2EIX+bmxwh2CCkN3huHjn8cHyap1hdOeq5G2FyVEhSt6H6mbAwoOxa6E2pJKL1yxfQhB7sqLhwu1mhMiO1anhgdwOogv0RIEo9HfcZnQEYWSzO8/ceHTgYvXA0MjXJRnbVyVHBqt4PAojbqRogZ7iwBPX7MMIaRTidSuWIkR+ulJ/6kYjQtTeNWnBGtmCrbCBKPQfH66bobgJE5vdeerGox8uPOzo0f/DzrzdxalhGjnjvuJtAXd8wPverWGjlktKcuIJwYfLqw5fqiIYfbUuI0gleX8eeaHMKUMU+g/sysL362YIQthosZfdbzlYWtndP/wPO3L3rUkLgXkS8Dncnnmb8uNZgg5crDxYVsWy7L416cFaGYW5ynvuFxdEGkIU+hHMrUL4rm4Gc3Uz5qtVzw+V1uiHTb/cumLf2owQrQxyEEwCwRgppeIt+QmIsD+WVh6vqEcI71ydHB644CpsIAr9ytg+TWNl1MRgslRUPTtcVjM0Yt63NmN3UWqIRkpjyEEwGe8qbDavTKQofPRy7bnbTQiR7auSIoOUNEOhBVNhA1HoT8a+ol11M0az7WrlsyPlNfoR87ZVSdsLk8K0MtcmZwBMDsEEI6yUiTblJdAU/dertaX3mhEh2wuSI0OUrss0F8CqQhCFfmR83Uz5g6eHy2uGRkxbC5K2rUqKDOaWooO6GTB57ypsFFLx2uVLESLHK+rL77VghHasTokIVtLUgig/gCj0I+/VzZy+0XiorFY/YtxbnLrtXd0MRu7JFQCmAmOikovWZC9BiByvaDh/pxlhak9xamigHC+AxSYhCuck4v4PHusPE4wobnDHZneevN74w4XKPv3I325esXN1cnigggd1M2C6PHeJUiska5fHIYSPXqo5ca0OYfTV2vRgjWzeV9hAFM5JmLg7w551MwRhq8159tajA+cftvfo/2l3/p41qcGe624B8GUojNVy8YbcOJagH0urDpVVE5bsX58RpJbieV1hA1E4N723woJrD09CRs2WsXX5jf+4O3/v2vRgDdTNAC/DGCmk4o258SzLHrhYeexKHYvQnuLU8EA5jfF8rbCBKJy7MEKEuCb4CCHDo+arVc8PlVcbRsw/25i9Z21aiEZGQd0M8AWClFLRpvwEjNCh8pqzNxoRITtXp0QGKxjavUvUvApDiMI5i1tDn9u2lhhM1qtVz49cqjGMmncWpexYnRKikkJzEPjIuwqb/ASKpv96pbb0XjNGZPuqlCh3hY2rdThPQBTORdy3Lh6rmzFb7ZcfPONycFtB0rbC5PAgOc3AjprAR9wVNlghE6/PWUZhdLyi/tL9Jwjh7YXJHmk4f0AUzkXvvmoxsdmd5283Hy6vNRjNO1cnby1IigxS8hiP9Wbm0TczmGMIRlglFa3JXoIxOX61ofTeY4TRrtWpEcEKippXZx5E4Wz7QN0MF4WuupkT1xoOllbrR0x/U5K5bVVyRNDM1c147gXq/hl2NF4g3BU2GGOVPKA4aykh+K9Xas/deoQQ3rc2PSxQxv3CuCobPz05IApnm6tuhmBEEOJqpLk1FxCXg9+ff9gzaPjNjrydRamh2pmrmxkXee6fMcZDQ0PNzc3d3d3h4eGJiYlSqRTCcX6jMFbJA9atWIYQOlhW/dcrdRijr9dlBGlk2JWEhBCMEXfO+OXJAFE467iJYuw6pYhrrsRktl68+/hgaXWfbuTXO3L3rEkLVsto3+TguNTj/vrBdHM6nQ0NDQcOHOjs7OTxeCaTKTY29p/+6Z9iY2MhDec3CiNuJwCWZQ+UVh0ur3E4yf516WFaGUVh9zqafpqDCKJwLuBWWCAEo7G6GYPRcunhk4NlNYYRy99vz9uzNjVELffdyMzEHPzYb5rN5mvXro2Oju7bt2/RokUtLS3ff/99RUWFRqNRKpU+OjwwR2CEFRLRhtx4QsiB0uqT1+spQnYVp0YEKxiacu8766cgCucCjBBGmGCCCCFDRsuVyqdHymtHjOavSjJ2FaUEq6QU5dvTzJ2An27cURS1dOnSxMTEnJwclUq1ePHi48ePv3792mQycVFICCFkoSzrtNBwFTYKmWhjXgLG9JFL1RfuNhNMdhQmR4eoGJpByL2fsv+BKJxlrnkSgjHCBJERs/Vq5bOjl2pHTJadq1O2r0oK0Uh9PT44+fASCoWFhYU0TQcEBCCEOjs7HQ5HeHi4SCTifuFjPWvg/95V2Cil4o15cQyNj12pu/TgKUJoe2FydIiaR1MEsYS7VNTfQBTOMuz+DyFWu7PsfsuRS7WjJuv2VclbCpIiAhUMQyHk27oZd3gNDw+3t7ePjo6yLDvudyIiIoKDg/l8vrsj/OLFi+PHj0dHR+fl5UmlUl8cGJiTCMJIIRWuWb4EYXT8at2lB09pitq5OiUiSEnRfpiCCCGIwtngudKCu9tLrA7nieuNR8trDEbz3rXpWwsSI4KUM7zejM1mGxoa0uv1E6NQpVK5G49Op7OpqenEiRMmk2n37t3Lli3j8XhtbW2nTp3q7u4eHh5ubGzs7u4ODAzk8/kZGRlr1qxRqVS+PngwAzybe0qpuCgzlhBy8npDe69+aNQcHqQYWz/J/0AUziwy1s/gqlfHbrPZnX+tqPvxfOXQiOVvt2RvW5UcFijnzdT1JO6BQplMFhcXZ7fbJ3aZpVIpj8dDCNlsturq6mPHjkkkkh07dqSlpUkkEoSQXC5fsWLFyMhIb2/v0NDQihUrFi1axOPxQkJC3N1nMJ9gjFUy8ZrspaFaOcYoLFBBUX4ZghwMg9wzaKyCECOEXHPGCBOLzXHyWuNfLlR29+v/cXfBnqLUII1sVuoHPzHpwQ0CEkKePXv2ww8/SCSSrVu3Ll26VCQScf+cZVmHw8GybFtb25/+9Kd9+/alpKRQFEVRFMMwMIA4T7EsQXY7ixBhGNqvF0mCVuEMw67CmbFkGTVZS++1HCqvHjaY/3F3wZ41aSFq2Ux+u46rox6XWeOCcnR09MyZM+3t7bt27QoICOjv78cY8/l8lUrF5/P5fD5CSCAQ0DTN5/MFAgHlz58NMAkYY8znjxUW+vOCNRCFM2nswjVu0hYjk9V+vebFkUs1oybLL7Zk7ylODVZLZj09PnaNHcbYbre3tbX19vaePXv2ypUr3O3R0dHffvttRETEuDtxNzDhWr35a+xrErsKabiCm9k9pumBKJxRroXeMEaIWKz2+49en7hWbzLb963J2L46OUgtoefAaIvnNXbcD+4sCwgI+Prrr3U6nWe0KZVKmUw2Me8g/haCsQtF/X51a4jCmUS4ImaEiM3B3mt8faSsZkBv3FaQuHVVYphG7rqubu6tN+MONT6fn5OTM25+maIoPp//ieCDTJzXMPYYXvbTJiGCKPSpsYaS+3sSu7ZZJORO3YsDF6t6dSNbChK3rEyMCFK+my+ew+cSxlgoFM72UYA55r1Krzl8+n4SRKHvEIy5dRYwcS08gwhGmKCK6ud/PPuwu3/4q3Xpm1cmhgcqJtTN+Ov5BICfgij0Ia5RSN71GggmqKLq6X+cuP+mR/f323O2r0qC/eoAmAsgCn2FvDfrgDBGdofzZt3LP5552Nat+9W2FTuKUoJVUhr2aQJgDoAo9BFXSQHhJo0xMlntdxtf/XChqnvQ8Pfbc3YVJweppLRfXrcOwDwETRJfIe+WYkVmi/1u46sfL1b16gz71qXvXD2Wg4iM7aMIAJhNEIU+4uocY4wsNsfdR68OlVW/6dZtzInbujIxSC2lKBohRKDKBIC5ATrI3jGhbsbVJHQScrf+1Y+lVW+6dcXZyzblJ4VpFQy33gyU2wEwZ0Cr0Cu4uhnErbrlXnaBYHKt+vlfzj940TFQnLVsT3Ha4nANjwf7FwMw50Cr0DvG180QRDC5+vDZd6fvvuzo316Y+tW69NhwDZ/PQEsQgDkIWoVeQJB7QRduDQLCInL14bPfnrrT1Nq1tSD5ZxuzlkRoBZCDAMxV0Cr0AvcKrK75YpvjbsOrP5+7/6K9f+/a9G83ZS8O10AdNQBzGUThlyOutRO4dbcs9ruNrw5cqHzdPbSrKPXnm7JjwtQ07TmjAgCYc6Cp8uVcu7njsRw8VFrV3qPbmBv/TUlWTKia25+Em1SZ3QMFAHwMtAqn7GN1M1aH827Dq4NlVe09+nXL4/asSVscrubWWcAIQQ4CMJdBq3CqPlo3c7P2xYELD1936oqzlu4uTouN0PJ57m+aeZWDsB8OmH8gCqeMEFebELuWIMQEkysPn/7x7L3Wjr51y5ftXZO2JFIr4M/zFjcEIphP5vnH1esmrjdDMLr84Ol/nLz9on1g39q0r0syFoVq+Pz5XEfNvQTcNlUTF/0HwB9BFE7NuLoZq4O9VfPij2fuPnvdu29t+s82ZC8KUzMztX/xrBuXg5CGwH9BFE4JSxDF1c1w88W3G15+f77yVdfQ/nWZP9+cvShMs6DqZtzZBzkI/B1E4RQQ5FqiH2M0arbdaXh1sLSqo0e3fVXSzzZkxYSqGRoT5Lls9TzkdDr7+vrevn07OjrK4/GioqKCg4N5PB7kIPBrEIWT4WrluXezMVvtdxpeHSqrets7tCE3fu/a9OhQFcNQiNvJaf7mIMuyr1+/vnDhQltbG0LIYDCEh4f//Oc/X7x4MU2/NywAyQj8C0ThJ4zr57rqZuxOx626FwdLqzp6h9ctX7a7OHVxmMZjfNCPI+CznVyr1Xrt2rWGhobc3Nzo6Oi2traTJ09GR0cHBQXJ5fIZO04AvA6i8FNcc8TuPYkJIphcq279y/mHHT36jXmJu4tTYyO082a9mc825WiaTkhIiIiISElJUavV6enpFy5cePLkyejo6LgohFIb4F8gCj/Ks27G9R+My+8/+cOZe22dul1FKfvWpi8KU/N5fp+DH2sMcnHmOSXC4/EyMjIQQiKRiKKop0+fGgyG6OjogICAT9wPAHMfROFHedbNEIxYllytfPrdidvPO/q/WpfxTUlmdKh6wv7FfsmzJsbpdH6wQUfTNMYYYxwQEGAyma5fv37jxo329vbc3Nzi4mKpVEoIYVkWIcTdA8uy3A8YY4qCSn4w10EUfsx7dTNmm+NW3Ys/nrn/qku/d03Gzzcu91hvZv60gzo6Ou7du9fT08OFmqecnJy0tDSxWMwFIkVRPB7PYDBYLBa9Xu90OnU6XVVVlV6v7+/vf/LkyaVLl54+fcowTExMTFJSEtdsBGDOgij8MHfdDMJ41Gy9U//qwMWHHb36PcXpP9uY+X7dzPyhUqmys7NNJtPEhmFQUBCfzyeEWCwWjHF6enpsbGxvb++///u/l5WVRUVF8Xg8i8ViNpstFovD4bBarSaTicfj2Wy2icEKwFwDUTjO+LoZk9l2u/7lobKqzr7hrQVJX63LjA5Vz9e6GYlEEhsbiz4+6mc2m2/evCmXy1NSUiIjI8PDw4ODg588eWIwGGJjYwsKChwOR3t7e0dHx8qVKxMSEhiGEYlEYrF4xp8KAFMDUciZWDdDEMEWu/1W3YtD5dVv+4bX58TvWZMaE6biMe6Rr3mVg54+Nvtht9urq6v7+vpGRkaWLFkyMDDw+vXr0NBQkUjE5/MDAwMRQlarVSKRaLXasLAwGCUE/gKi0GVi3QxLyI2a1gMXH3b1D5fkJuwqSl0cpuHPi3mSaRMIBFlZWRcvXjx69Cifz7dYLBKJZMuWLVwIAuC/IAoR+kjdzKX7LX869+Btz9C2VUlcHbWAt9BfLj6fn5eXp9FoOjs7rVYrRVGhoaGJiYnQBQb+bqF/tjnv6mbGVt4vv9fyuxO3X3fpvlqX8dW6jOhQNZ+h52+HeLIwxnK5PC0tLTExkRtP5PF4nhcgQ2U18FMQhWisboZw3WObnb1W8+z3p+89f6vbvzb9mw1ZUaEqmqbm3XTxlHHZhzHm8/ncbLLnkKL7/87iEQIwbRCFXN0MQhgjTIwW+626F9+ff9Deo9u/LuPbjdnRISqubgaMW4lrYg7O0nEB4AULOQpdrTyMuH1KsNFsu1X34mBZVWefYdfq1K83ZEWHqhiaQojAPk2cj+Ud5CDwdwswCol7PUHiyjiCCDZabLdqWw+V13T1GzblJ+xbmx7jykEEIQjAvLcAo9ANu3PQ5nDcqG09WFbd028oyY3fVZQaE6oey0EAwPy34D7tnk1C12ILGF+tev7DxYcdPfqS3Ljdq1MXh6n5vAVdPwjAQrPgWoVjOejeyx2X3Wv5w+m7b3uHdhWl7lmTFhOq5jML7mUBYIFbaJ/5d3UzCCOWJeUPWn57/M7rLt036zP2r8+MDOGuq1vodTMALDQLKwo962bMNsf1mtY/nb3X1q3buzb9mw1ZMaEqGupmAFiQFkgUfqBu5kbtix8vPuzqM3y9PuObDVnRIa46aqibAWABmt9R6Fk3w62pRRDCIybLzdoXh8qruwdGtq9K2b8+PToE6mYAWNDmdxQiNDZlPHaJLDZZ7TdrXxwqr+oZHNmUl7h7TWrUuxwEACxQ8zkC3q+bQQghB0uuVT//sayqu9+wISd+V1HKopB5sj8JAOBLzOdWIR7r7brrZsoftPzl/P3ufsP2wpTdxakx3HozAIAFbx5Hoatuxj34d+Fu83fH73b0D329Ln3f2nSomwEAuM3bKHTXzRBE7Hbnlarnvz9153W3bv+6rP3rM6NCVDQNCQgAcJl/UTiubgaZzLbrta1/Of+gq2/km5LMbzZkjs2TQHsQAOAyb6LwY3Uz1hs1rQfLqnsHRvauSfu6JCMqmKsfRJCDXw6WKQTzxryJQoTGbVtH8KjFer2m9Uh5da9uZGtB8t61aZHvchB4AeQgmDfmSRRyTULPa+YsNue16tZDZdV9upHNeQk7V6dGB0P9oBdASxDMS/MkCsfXzRB0terpjxcf9upGt65M2rk6JSZMBfWD3uVwOAYHBymKUigUDMNw+UgIgZ2egD+aH1E4vm7m/J3mP5150D1o2FOcuntNWmSwiseDeZIvNW4jp5qamuPHj4eFhX3zzTchISHcjbDTE/BT86HD6KqbQZgg5GTJhTvNvz1x61XnwM7VqV+tzYgJUfN5FDRUvhy3zRP38+Dg4PXr1y9cuNDQ0GAymWb3wAD4cn7dKhxfN2O2Oq5VP/vjmbtvew1frcv4uiQjKlgJ+3Z6Edfis1gsd+/eHRoaEovF7nyEMUTg1/wxCt9NFI+rm7le3XrgYlXP4OjfbMj6uiRzLAcRQvAZ9Rqn09na2trQ0JCQkPDq1Ss+n88lIOQg8Gt+F4UEIUIQ5qZH8Fi7cMRkvVb9/HBZdb9+ZNfqtP3r0z1yEEyWyWQaGBiwWCwTpz7UarVCoaBpWqfT3b17l8/nZ2VlPXjwACZJwPzgd1GI36ubwQghZDTbrlU/P1xe068f3VKQuLsoNTIIcnA6jEZjW1ubXq9nWdY9I8z9sHTpUolEwrJsfX19W1tbYWFhVFQUj8ez2WxcGvb29t67d0+n0w0MDDQ1NQmFwtraWh6PFxsbm5qaKpVKZ/m5AfBJfheF4+tm7A5nRdWzQ2WV/XrjlvykHatTomH9wekSi8WRkZFarXZiW0+j0TAM09vbW15ebjAYhoaGamtru7q67HZ7bW2tVqvFGFMURdM0TdPjfoa+M5j7/CsKXaOExKNupux+y/fnKvv0IzuLUnasTo0KUTFQNzNdIpEoLCzsg31eLtr0en1vb+/w8PDVq1f5fP7z58+dTufFixczMjKio6MLCgocDsebN2/a2try8/OTkpIoihKJRCKRaOafCwBT4l9RiAkimCCMMbdn3blbTd+dutPdP/pNSebe4rSIYCXDQHtw+iiKoihq4lwwdwshJDw8/L/8l/9isVgoisIYDwwM2O32rVu3BgYGMgyjVqsRQiaTSSKRaDSaoKAgioK3A/gH/4rCd3UzNrvz0sMn35263dEz/E1J5r517nkSQqA9+GUm9mfdc8RyuXz58uXuZuPZs2dtNltmZqZMJvO82gTmUoDfmeNR6O7nju1fjAhCeNRsu1b17M/nHnYPjHyzIfNvSrIioW5mRoyrm9m+fbvD4dBoNO5b3CODkIbAv8zlKCTupbfG1mFFCGGD0XKtpvVQaWX/kHH/usz9JRmRwUoaOmKzISsrCyEkEAigvhr4u7kchR+omxkxWSuqnx8prxkYMu5anbynOD0yCHJwpnEtPowxzIeAeWMuR+H4uhmLxV5R+exwedXgsGnryqQdRamRwUqom5l5H5xUma2DAcAr5myOkLHVtghGBCHEsuTSw6cHLlb36Y1bVibtWJ0SGaKimbHN7MBMmTgICIODYB6Ys1GIx6405n7A5+80/+nsvc6B4W2rUnauTo0OVfMZWJd/FnysAQgNQ+DX5m4HGSOExtqD5+80/e7E7e6B0Z9tzNq7Ji0iUMEwXN0MAAB4wdyIQvKuFUgIQRhjV3kgMVvsVyuf/fH0/a4Bw9frs/avy4gIVrjnSTA0CQEA3jA3otC16iAhHhfMYUQsNvu16uffn384oB/92YblX69P88xB6BoDALxlbkShKwExQoRgQhGMMDJb7dUt7T9V1OlGTHvXpu1blx4RJIe6GQCAL8yRKORmijEmXD01stic1S3th0qrewZHt69K3lGUHB4opynYpwkA4BNzIwoJQtg9SojsTkftk44DF6o6evUbcxO2FyZFBnHrbkGPGADgE7Pf3yQIEYwRQRhzPWRS96TjD6cfvOgcKMmN3746KSpExWNoj3W5AADAy2Y/CjEieKyOGiHU8Kz7fx+93dLWta0gcVdxamSwiqZpTBDCUDoDAPCVme4gj23MhDzqZhD3H7vDWf+8898PX3/S1vv1uoy9a9LDAhUM/W7fTmgWAgB8ZKajECPErcCKxtfNOGqfdPzh9P3n7f1fr8/Yvz4zPMhVN4M9/ykAAPjADEehqz2IESaIEEzwu7qZNwcuVr3qHvi6JHPfmnH1gwAA4FszHDfc5sUEIYQJxghhjMxWR9Xj9h9Lq5+19W7NT9q3Nj0iSEFT0AYEAMycGW95cTFICMEII2S1Oaoftx8srXr8qnd15pLthclhgTIKchAAMLNmtIPMLfjJ1c0ghJwsW/PkzV/OP3za1lOYuWTv2ozoUDVDc/8T0hAAMHNmNAoxem82uK6l67cn7rW09axdvuxvNmQuiwoU8BlMCPd7kIUAgBnjww4ycf/BbYTGLcVKEMGYJaTmcce/Hbne8LyjMCP2F5uXx0cHCfg8bg8h3x0S+EIfXJ8VFm0F84APW4WYu5wOEfxuBVaCMLLZHbVPOv7jp9uPXrxdu3zZr7blxEUF8hjP64shDucobjdkz1VaYTV/MD/4Lgq59Qaxa/t2LhIxMlvtNS3tfzn3sOlVV8mKuF9tz42PDno/B8EcxaXeuDSEHATzg++i0LXiFh6rIsQYmS32yuY3B0urWl73rM+J+9vNK+KjgxkGPkv+AWPMsqzBYNDpdA6Hw317eHi4WCxGYz1l6C8Df+TLaRPuIruxq+ssVntlc/vB0uonbb3F2Uv+ZkN2XHQgty6/D48BeJXD4aiqqrpz5w7LsjTtasv/8pe/jImJQWPd51k9QACmyVdR6FE3QxBCNruj6vGbHy5WPnvTW5S1dP/69GVRQTya62r56BCAlxFC7HZ7c3NzS0tLfn5+YGAgd7vnbshcD3qWDhCA6fNVFHrWzRCCalo6/3DmwbP23rXZS/eXpC+LDOQzFMEYIZbAJImf4Bp9drs9ODi4sLCQawkihKRS6eweGABfzqfFNNzMCal90vH/++vNxtbOwozYn2/KjosKEvAZbnVC1x9gzvj0eB8hhBCiUqkYhhkcHLTb7VKplMfjzewxAuB9PhsrJAgjTDC22u2Hy6tbXvetyVryyy0rlkZC3czc5XA4rFar0+mcWCIjEAj4fL7T6ezr62tubm5tbXU6nTweb9WqVdu3bw8KCsIYc//Q4XCwLOtwOOx2OzUGes1gjvNZFGJuFzvC0HRx9hKNSrqjICkuOoihYb2Zuau3t7eqqqqvr49l2XH/KysrKykpiWGYyMhIu90eFxcXHBz8+PHjs2fPUhS1Z88emqafPn1qNBp7enrevn1bX19vMBgYhgkODo6OjhYKhbPyjACYJF9feEcYmlqzfFlmfESQSsrQ0DSY02QyWVJSkslk4jrC7tsxxkFBQTwej8/n79q1y2KxaLVaqVSal5fX2tp6+/bt1atXSySS1tbWwcHBwcHB/v7+1tZWk8nENSRDQ0MhCsEc5+tiGkwQChDwA4Q8rtLQhw8HvphUKh03BzKup8x1fqVSqUQiYRgmJCREqVS+efPGbrcrlcr8/Hyr1fr27duurq68vLy4uDiGYWQymecUMwBzky+j0LUbyVhBjWuSBPgxq9V67do1k8m0du3a6Ojo169fv3z5MjY2ViKRiEQibk5ZIBCo1eqYmJi4uDgK1t8FfsLHHWRCMMIszBPPbZ+4jnjc7QzDSKXSioqKuro6tVrd09MjEolKSko0Gs24O/Th4QLgAz6NQu5zhCEH57jJT+/y+fyCggKxWNzW1mY0GpcsWbJs2bLU1FTuwjtPkIbAv/h62gSjsa2dfPxAYCZgjIODg9euXWs0Gq1Wq1gsFovFPB4PamWAv5vpHe+Av8MYCwQCmBEG8wyMaoMp49qA0AUG8wlEIZgm6BSD+QSiEAAAIAoBAACiEAAAEEQhAAAgiEIAAEAQhQAAgCAKAQAAQRQCAACCKAQAAIQQbFwLvMxoNL548SIyMlKhUMAVKcBfQBQCAAB0kAEAAKIQAAAQRCEAACCIQgAAQBCFAACAIAoBAABBFAIAAIIoBAAABFEIAAAIohAAABBEIQAAIIhCAABAEIUAAIAgCgEAAEEUAgAAgigEAAAEUQgAAAiiEAAAEEQhAAAgiEIAAEAQhQAAgCAKAQAAQRQCAACCKAQAAARRCAAACKIQAAAQQv9/NVZCddgbdOcAAAAASUVORK5CYII=
Use the following graph and find: $\lim_{x \to 1}\left(f(x)\right)$
$\lim_{x \to 1}\left(f(x)\right)$: None
f7adf486-9276-4aad-b8ab-9ff6c2894646
precalculus_review
false
null
Simplify the radical expression: $$ \frac{ 4 \cdot \sqrt{2 \cdot n} }{ \sqrt{16 \cdot n^4} } $$
The final answer: $\frac{\sqrt{2}}{n^{\frac{3}{2}}}$
f7c85f4d-2628-4193-9579-41041b20f083
differential_calc
false
null
Differentiate the function $$ f(x) = \frac{ 5 \cdot x^3-\sqrt[3]{x}+6 \cdot x+2 }{ \sqrt{x} } $$
$\frac{ d }{d x}\left(\frac{ 5 \cdot x^3-\sqrt[3]{x}+6 \cdot x+2 }{ \sqrt{x} }\right)$: $\frac{18\cdot x\cdot\sqrt[6]{x}+75\cdot x^3\cdot\sqrt[6]{x}+\sqrt{x}-6\cdot\sqrt[6]{x}}{6\cdot x\cdot x^{\frac{2}{3}}}$
f85314b7-0e73-481b-aadb-9b48f8cf8fbc
algebra
false
null
Rewrite the quadratic expression $2 \cdot x^2 - 6 \cdot x - 9$ by completing the square.
$2 \cdot x^2 - 6 \cdot x - 9$ = $2\cdot(x-1.5)^2-13.5$
f89bd354-18c9-4f31-b91f-cf6421e24921
sequences_series
false
null
Compute the first $6$ nonzero terms (not necessarily a quadratic polynomial) of the Maclaurin series of $f(x) = \sin(x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos(x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)$.
$f(x)$ = $\frac{1}{34560\cdot\sqrt{2}}\cdot\left(288\cdot x^5+1440\cdot x^4-5760\cdot x^3-17280\cdot x^2+34560\cdot x+34560\right)+\cdots$
f8d1def5-7d5c-4ab3-a9ca-2baa0bc33b11
precalculus_review
false
null
$P = \left(x, \frac{ \sqrt{7} }{ 3 }\right)$, $x<0$ is a point on the unit circle. 1. Find the (exact) missing coordinate value of the point. 2. Find the values of the three trigonometric functions $\sin\left(\theta\right)$, $\cos\left(\theta\right)$, $\tan\left(\theta\right)$ for the angle $\theta$ with a terminal side that passes through point $P$. Rationalize denominators.
1. The (exact) missing coordinate value of the point is: $-\frac{\sqrt{2}}{3}$ 2. The values of the three trigonometric functions are: * $\sin\left(\theta\right) = $\frac{\sqrt{7}}{3}$$ * $\cos\left(\theta\right) = $-\frac{\sqrt{2}}{3}$$ * $\tan\left(\theta\right) = $-\frac{\sqrt{14}}{2}$$
f8d9c275-c54e-423d-b660-60beec9f19d0
algebra
false
null
Find the dimensions of the box whose length is twice as long as the width, whose height is $2$ inches greater than the width, and whose volume is $192$ cubic inches.
The dimensions of the box are $4$, $6$, $8$
f8f1b940-4771-4e79-b29b-64ddff634da6
differential_calc
false
null
Given $y = \frac{ 2 }{ 5 } \cdot x^6 + \frac{ 6 }{ 5 } \cdot x^5 + x^4 + 2$, find where the function is 1. concave up 2. concave down 3. point(s) of inflection
1. Concave up: $(-\infty,-1)$, $(-1,0)$, $(0,\infty)$ 2. Concave down: None 3. Point(s) of Inflection: None
f928de60-dedf-4c5b-8ffc-36c6b402744a
differential_calc
false
null
Sketch the curve: $$ y = 9 \cdot x^2 \cdot e^{\frac{ 1 }{ 3 \cdot x }} $$ Submit as your final answer: 1. The domain (in interval notation) 2. Vertical asymptotes 3. Horizontal asymptotes 4. Slant asymptotes 5. Intervals where the function is increasing 6. Intervals where the function is decreasing 7. Intervals where the function is concave up 8. Intervals where the function is concave down 9. Points of inflection
1. The domain (in interval notation): $(-\infty,0)\cup(0,\infty)$ 2. Vertical asymptotes: $x=0$ 3. Horizontal asymptotes: None 4. Slant asymptotes: None 5. Intervals where the function is increasing: $\left(\frac{1}{6},\infty\right)$ 6. Intervals where the function is decreasing: $(-\infty,0)$, $(0,\infty)$ 7. Intervals where the function is concave up: $(-\infty,0)$, $(0,\infty)$ 8. Intervals where the function is concave down: None 9. Points of inflection: None
f9845500-b43b-4187-9da5-1babc7852f25
differential_calc
false
null
Calculate the derivative of the function $r = \ln\left(\sqrt[4]{\frac{ 1+\tan(\varphi) }{ 1-\tan(\varphi) }}\right)$.
$r'$ = $\frac{1}{2}\cdot\sec(2\cdot\varphi)$
f98550db-7106-4a40-9fca-348aa446b703
algebra
true
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
Using the given graphs of $f(x)$ and $g(x)$, find $g\left(g(2)\right)$.
The final answer: $g\left(g(2)\right)$ = $2$
f9e23b20-cd31-4e53-bba3-62353f283cd3
algebra
false
null
The radius of the right circular cylinder is $\frac{ 1 }{ 3 }$ meter greater than the height. The volume is $\frac{ 74 \cdot \pi }{ 9 }$ cubic meters. Find the dimensions.
$r$: $\frac{1+5.40740373}{3}$ $h$: $1.80246791$
fa6de80d-c556-45a5-ba55-741e46642251
integral_calc
false
null
Compute the integral: $$ \int \frac{ 3 }{ 3+\sin(2 \cdot x)+\cos(2 \cdot x) } \, dx $$
$\int \frac{ 3 }{ 3+\sin(2 \cdot x)+\cos(2 \cdot x) } \, dx$ = $C+\frac{3}{\sqrt{7}}\cdot\arctan\left(\frac{1}{\sqrt{7}}\cdot\left(1+2\cdot\tan(x)\right)\right)$
fa98708a-a7a3-4056-bfa4-2b0a16fea068
multivariable_calculus
false
null
Use the second derivative test to identify any critical points of the function $f(x,y) = x^2 \cdot y^2$ and determine whether each critical point is a maximum, minimum, saddle point, or none of these.
Maximum: None Minimum: $P(0,0)$ Saddle point: None The second derivative test is inconclusive at: None
fa9976dd-852a-4d21-bce4-318821b7397d
integral_calc
true
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
Let $A$ and $B$ be regions bounded by the graph of $f(x) = -3 \cdot \cos(x)$ and the $x$-axis for $-\pi \le x \le 0$. 1. Find the volume of the solid generated when $A$ is revolved about the $x$-axis. 2. Find the volume of the solid generated when $B$ is revolved about the $y$-axis.
1. $22.207$ units³ 2. $10.759$ units³
fab49e1b-7b62-4ff1-9344-915c84b6cf60
multivariable_calculus
true
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
Find the surface area of the lemniscate: $\rho^2 = a^2 \cdot \cos(2 \cdot \varphi)$.
$A$ = $a^2$
fad0653d-12d0-4153-8e85-7fbd01db1c0f
multivariable_calculus
false
null
Use the second derivative test to identify any critical points of the function $f(x,y) = 8 \cdot x \cdot y \cdot (x+y) + 7$, and determine whether each critical point is a maximum, minimum, saddle point, or none of these.
Maximum: None Minimum: None Saddle point: None The second derivative test is inconclusive at: $P(0,0)$
fb6418ae-3440-4258-9388-89d799fd859a
sequences_series
false
null
Find the power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(n \cdot x^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(n \cdot x^n\right)$.
$f(x) \cdot g(x)$ = $\sum_{n=2}^\infty\left(\frac{1}{6}\cdot n\cdot\left(n^2-1\right)\cdot x^n\right)$
fbfe5f15-e991-40c9-b306-3e83535db351
multivariable_calculus
false
null
Find the equation of the tangent line to the curve: $r = 3 + \cos(2 \cdot t)$, $t = \frac{ 3 \cdot \pi }{ 4 }$.
$y$ = $\frac{1}{5}\cdot\left(x+\frac{3}{\sqrt{2}}\right)+\frac{3}{\sqrt{2}}$
fc9fb6e0-d325-42da-b6b4-4f51c745ed76
multivariable_calculus
false
null
Find and classify all critical points of the function $f(x,y) = x \cdot y \cdot (1-7 \cdot x-9 \cdot y)$.
Points of local minima: None Points of local maxima: $P\left(\frac{1}{21},\frac{1}{27}\right)$ Saddle points: $P(0,0)$, $P\left(\frac{1}{7},0\right)$, $P\left(0,\frac{1}{9}\right)$
fcada4da-798e-438e-8bfd-3efa21ce1322
integral_calc
false
null
Compute the integral: $$ \int x \cdot \arctan(2 \cdot x)^2 \, dx $$
$\int x \cdot \arctan(2 \cdot x)^2 \, dx$ = $\frac{1}{16}\cdot\left(2\cdot\left(\arctan(2\cdot x)\right)^2+2\cdot\ln\left(4\cdot x^2+1\right)+8\cdot x^2\cdot\left(\arctan(2\cdot x)\right)^2-8\cdot x\cdot\arctan(2\cdot x)\right)+C$
fcbb2928-b8f4-4a3c-9fd8-1e095d95bd28
algebra
false
null
When hired at a new job selling electronics, you are given two pay options: Option A: Base salary of $20,000$ USD a year with a commission of $12\%$ of your sales. Option B: Base salary of $26,000$ USD a year with a commission of $3\%$ of your sales. How much electronics would you need to sell for Option A to produce a larger income? Give your answer either exactly or rounded to two decimal places.
The final answer: $66666.67$
fce0ff42-571f-457d-bd35-3be8611edff9
algebra
true
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
Use the graph in the figure, which shows the profit, $y$, in thousands of dollars, of a company in a given year, $t$, where $t$ represents the number of years since $1980$: Find the $y$-intercept.
$y$-intercept: $P(0,-300)$
fcf8b9bc-dc7a-4385-82e3-98bd3ce3841e
precalculus_review
false
null
Use the double-angle formulas to evaluate the integral: $$ \int_{0}^\pi \sin(x)^4 \, dx $$
$\int_{0}^\pi \sin(x)^4 \, dx$ = $\frac{3\cdot\pi}{8}$
fd219d83-cf3d-41b2-9d26-f01e81827b91
integral_calc
false
null
Compute the integral: $$ 3 \cdot \int \cos(2 \cdot x)^6 \, dx $$
$3 \cdot \int \cos(2 \cdot x)^6 \, dx$ = $\frac{3}{8}\cdot\sin(4\cdot x)+\frac{9}{128}\cdot\sin(8\cdot x)+\frac{15}{16}\cdot x-\frac{1}{32}\cdot\left(\sin(4\cdot x)\right)^3+C$
fd3587b1-b0c7-48de-8d35-280390009cb4
precalculus_review
false
null
Use the double-angle formulas to evaluate the integral: $$ \int \sin(x)^2 \cdot \cos(2 \cdot x)^2 \, dx $$
$\int \sin(x)^2 \cdot \cos(2 \cdot x)^2 \, dx$ = $\frac{x}{4}-\frac{3}{16}\cdot\sin(2\cdot x)+\frac{1}{16}\cdot\sin(4\cdot x)-\frac{1}{48}\cdot\sin(6\cdot x)+C$
fd553420-a490-4c12-a21d-7d301ef75783
multivariable_calculus
false
null
Calculate the second-order partial derivatives. (Treat $A$,$B$,$C$,$D$ as constants.) $f(x,y,z) = \sin\left(x+z^y\right)$.
$f_{xx}(x,y,z)$ = $-\sin\left(x+z^y\right)$ $f_{xy}(x,y,z)$ = $f_{yx}(x,y,z)$ = $-z^y\cdot\ln(z)\cdot\sin\left(x+z^y\right)$ $f_{yy}(x,y,z)$ = $-z^y\cdot\left(\ln(z)\right)^2\cdot\left(-\cos\left(x+z^y\right)+z^y\cdot\sin\left(x+z^y\right)\right)$ $f_{yz}(x,y,z)$ = $f_{zy}(x,y,z)$ = $z^{-1+y}\cdot\left(\cos\left(x+z^y\right)\cdot\left(1+y\cdot\ln(z)\right)-y\cdot z^y\cdot\ln(z)\cdot\sin\left(x+z^y\right)\right)$ $f_{zz}(x,y,z)$ = $y\cdot z^{-2+y}\cdot\left((-1+y)\cdot\cos\left(x+z^y\right)-y\cdot z^y\cdot\sin\left(x+z^y\right)\right)$ $f_{xz}(x,y,z)$ = $f_{zx}(x,y,z)$ = $-y\cdot z^{-1+y}\cdot\sin\left(x+z^y\right)$
fd5e835f-ff53-4b16-9353-bc32e4289773
multivariable_calculus
false
null
Use the method of Lagrange multipliers to find the maximum and minimum values of the function $f(x,y) = x^2 - y^2$ with the constraint $x + 6 \cdot y = 4$.
Minimum value of the function $f(x,y)$ is $-\frac{16}{35}$ Maximum value of the function $f(x,y)$ is None
fd93bc12-3ce3-49a6-bcc2-67359cb0d155
differential_calc
false
null
Find $\frac{d^3}{dx^3}f(x)$, given $f(x) = \ln\left(\frac{ x+7 }{ x-7 }\right)$.
The final answer: $\frac{d^3}{dx^3}f(x)=-\frac{84\cdot x^2+1372}{\left(x^2-49\right)^3}$
fd9d9457-b5dd-48b4-abae-3ca1024ec63c
differential_calc
true
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
Given $h(x) = f(x) \cdot g(x)$, find $h'(1)$ using the table below:
$h'(1)$ = $16$
fe42fdde-3ec3-49f2-af06-ec452da37893
integral_calc
false
null
Solve the integral: $$ \int \frac{ -\sqrt[3]{2 \cdot x} }{ \sqrt[3]{(2 \cdot x)^2}-\sqrt{2 \cdot x} } \, dx $$
$\int \frac{ -\sqrt[3]{2 \cdot x} }{ \sqrt[3]{(2 \cdot x)^2}-\sqrt{2 \cdot x} } \, dx$ = $C-3\cdot\left(\frac{1}{2}\cdot\sqrt[6]{2\cdot x}^2+\frac{1}{3}\cdot\sqrt[6]{2\cdot x}^3+\frac{1}{4}\cdot\sqrt[6]{2\cdot x}^4+\sqrt[6]{2\cdot x}+\ln\left(\left|\sqrt[6]{2\cdot x}-1\right|\right)\right)$
fe510a69-db18-4182-a55e-c5e84eba20f5
multivariable_calculus
false
null
Calculate the double integral $\int\int_{R}{\left(x^2+y^2\right) d A}$, where $R$ is the parallelogram with the sides $y=x$, $y=x+2$, $y=2$, and $y=6$.
The final answer: $224$
fe62dec1-a9c2-4d3b-a1e6-e24baaf52c55
multivariable_calculus
false
null
Find the curvature for the vector function: $\vec{r}(t) = \left\langle \sqrt{2} \cdot e^t, \sqrt{2} \cdot e^{-t}, 2 \cdot t \right\rangle$.
The final answer: $\frac{2\cdot e^{2\cdot t}}{2+2\cdot e^{4\cdot t}+4\cdot e^{2\cdot t}}$
fe917e4b-795e-455a-926b-e27828a7f48d
precalculus_review
true
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
The given graph is of the form $y = A \cdot \sin(B \cdot x)$ or $y = A \cdot \cos(B \cdot x)$, where $B > 0$. Write the equation of the graph.
The equation of the graph is: $y=\cos(2\cdot\pi\cdot x)$
fed13bfa-aef9-4bdd-9b1b-538a293f369e
precalculus_review
false
null
Multiply the rational expressions and express the product in simplest form: $$ \frac{ x^2-x-6 }{ 2 \cdot x^2+x-6 } \cdot \frac{ 2 \cdot x^2+7 \cdot x-15 }{ x^2-9 } $$
The final answer: $\frac{x+5}{x+3}$
fed9d0b7-506f-441f-b52a-8f0e24292fd1
integral_calc
false
null
Compute the integral: $$ \int \frac{ 2 \cdot x+\sqrt{2 \cdot x-3} }{ 3 \cdot \sqrt[4]{2 \cdot x-3}+\sqrt[4]{(2 \cdot x-3)^3} } \, dx $$
$\int \frac{ 2 \cdot x+\sqrt{2 \cdot x-3} }{ 3 \cdot \sqrt[4]{2 \cdot x-3}+\sqrt[4]{(2 \cdot x-3)^3} } \, dx$ = $C+2\cdot\left(9\cdot\sqrt[4]{2\cdot x-3}+\frac{1}{5}\cdot\sqrt[4]{2\cdot x-3}^5-\frac{2}{3}\cdot\sqrt[4]{2\cdot x-3}^3-\frac{27}{\sqrt{3}}\cdot\arctan\left(\frac{1}{\sqrt{3}}\cdot\sqrt[4]{2\cdot x-3}\right)\right)$
fef6c9b8-267b-4fd6-83ad-75e555451080
sequences_series
false
null
Expand the function $f(x) = \ln\left(1+\frac{ x }{ 5 }\right)$ given on the interval $[0,1]$ in powers of $x$ using the Maclaurin formula. Estimate the error allowed with the retention of the first ten members. Submit as your final answer: 1. the resulting expansion of the function (the first ten terms) 2. the estimate of the absolute value of the remainder term (in the form of an inequality for $\left|R_{10}(x)\right|$)
1. $\frac{x}{5}-\frac{x^2}{5^2\cdot2}+\frac{x^3}{5^3\cdot3}-\frac{x^4}{5^4\cdot4}+\frac{x^5}{5^5\cdot5}-\frac{x^6}{5^6\cdot6}+\frac{x^7}{5^7\cdot7}-\frac{x^8}{5^8\cdot8}+\frac{x^9}{5^9\cdot9}$ 2. $\left|R_{10}(x)\right|<\frac{1}{5^{10}\cdot10}$
ff08d451-e6d0-4570-b370-cb5504ceda3d
differential_calc
true
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
Use the graph of the function $y = g(x)$ shown here to find $\lim_{x \to 0}\left(g(x)\right)$, if possible. Estimate when necessary.
$\lim_{x \to 0}\left(g(x)\right)$ = None
ff11c6e0-574a-477e-9ea3-0232aa803f21
differential_calc
false
null
Find the extrema of a function $y = \frac{ x^4 }{ 4 } - \frac{ 2 \cdot x^3 }{ 3 } - \frac{ x^2 }{ 2 } + 2$. Then determine the largest and smallest value of the function when $-2 \le x \le 4$.
1. Extrema points: $P\left(\frac{2-2\cdot\sqrt{2}}{2},1.969\right)$, $P(0,2)$, $P\left(\frac{2+2\cdot\sqrt{2}}{2},-1.8023\right)$ 2. The largest value: $\frac{46}{3}$ 3. The smallest value: $-1.8023$
ff6817e6-7ee7-450d-981d-fa96e8f2d0d4
differential_calc
false
null
Given $y = \frac{ 1 }{ \sqrt{a \cdot x^2 + b \cdot x + c} }$, evaluate $D = y \cdot y'' - 3 \cdot \left(y' \right)^2 + y^4$.
The final answer: $D=\frac{1-a}{\left(a\cdot x^2+b\cdot x+c\right)^2}$
ff7e301b-1784-4bb0-8251-948887a6254b
multivariable_calculus
false
null
The distances of all the points of a curve from two fixed points $M$ and $N$ with coordinates $(c,0)$ and $(-c,0)$ are equal to $16$. Find the equation of the curve.
The final answer: $\frac{x^2}{64}+\frac{y^2}{\left(64-c^2\right)}=1$
ffeb1d68-82f1-4622-8c63-c49ecaa82c66
precalculus_review
false
null
A professor asks her class to report the amount of time $t$ they spent writing two assignments. Most students report that it takes them about $45$ minutes to type a four-page assignment and about $90$ minutes to type a nine-page assignment. 1. Find the linear function $y = N(t)$ that models this situation, where $N$ is the number of pages typed and $t$ is the time in minutes. 2. Use part a. to determine how many pages can be typed in $120$ minutes (round to the nearest integer). 3. Use part a. to determine how long it takes to type a $20$-page assignment.
1. $N(t)$ = $\frac{1}{9}\cdot t-1$ 2. $12$ 3. $189$
ffee282b-ad0f-40e6-a100-9ed7da950b5a
integral_calc
false
null
Compute the integral: $$ -\int \cos(6 \cdot x)^6 \, dx $$
$-\int \cos(6 \cdot x)^6 \, dx$ = $C+\frac{1}{288}\cdot\left(\sin(12\cdot x)\right)^3-\frac{1}{24}\cdot\sin(12\cdot x)-\frac{1}{128}\cdot\sin(24\cdot x)-\frac{5}{16}\cdot x$