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d12b5094-3b3b-454d-a3b5-4b488eeee7c8
sequences_series
false
null
Express the series $\sum_{n=1}^\infty \left(\frac{ 1 }{ (x-3)^{2 \cdot n-1} }-\frac{ 1 }{ (x-2)^{2 \cdot n-1} }\right)$ as a rational function.
$\sum_{n=1}^\infty \left(\frac{ 1 }{ (x-3)^{2 \cdot n-1} }-\frac{ 1 }{ (x-2)^{2 \cdot n-1} }\right)$ = $\frac{x-3}{(x-3)^2-1}-\frac{x-2}{(x-2)^2-1}$
d1429fff-1216-40ad-8946-3dd3a5f2e620
multivariable_calculus
false
null
Find the equations of the common tangent lines to the following ellipses: 1. $ rac{ x^2 }{ 6 } + y^2 = 1$ 2. $ rac{ x^2 }{ 4 } + rac{ y^2 }{ 9 } = 1$
The equations are: $2\cdot x+y-5=0 \lor 2\cdot x+y+5=0 \lor 2\cdot x-y-5=0 \lor 2\cdot x-y+5=0$
d154f14e-4cc7-40dd-ae67-66d209b8bf88
integral_calc
false
null
Compute the integral: $$ \int \sin(5 \cdot x)^6 \cdot \cos(5 \cdot x)^2 \, dx $$
Answer is: $\frac{1}{32}\cdot x-\frac{1}{32}\cdot\frac{1}{20}\cdot\sin(20\cdot x)-\frac{1}{8}\cdot\frac{1}{10}\cdot\frac{1}{3}\cdot\sin(10\cdot x)^3+\frac{1}{128}\cdot x-\frac{1}{128}\cdot\frac{1}{40}\cdot\sin(40\cdot x)+C$
d16d84d7-3932-44f0-89ff-521caa493041
precalculus_review
false
null
Recall the following double-angle formulas: 1. $\sin\left(2 \cdot \theta\right) = 2 \cdot \sin\left(\theta\right) \cdot \cos\left(\theta\right)$ 2. $\cos\left(2 \cdot \theta\right) = 2 \cdot \cos\left(\theta\right)^2 - 1$ 3. $\cos\left(2 \cdot \theta\right) = 1 - 2 \cdot \sin\left(\theta\right)^2$ From the formulae, find appropriate expressions for the following, in terms of $\sin\left(2 \cdot \theta\right)$ or $\cos\left(2 \cdot \theta\right)$: [Note: your end answer may contain only one of them.] 1. $\sin\left(\theta\right)^2$ 2. $\cos\left(\theta\right)^2$
Part (a): $\sin\left(\theta\right)^2=\frac{1}{2}\cdot\left(1-\cos\left(2\cdot\theta\right)\right)$ Part (b): $\cos\left(\theta\right)^2=\frac{1}{2}\cdot\left(1+\cos\left(2\cdot\theta\right)\right)$
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
sequences_series
false
null
Compute the first 4 nonzero terms (not necessarily a quadratic polynomial) of the Maclaurin series of $f(x) = e^x \cdot \cos(x)$.
$f(x)$ = $1+x-\frac{x^3}{3}-\frac{x^4}{6}+\cdots$
d23ad7e7-ae9b-468a-b854-8452c64e0896
differential_calc
true
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
The ellipse $x^2 + 4 \cdot y^2 = 4$ and the parabola $4 \cdot y = 4 - 5 \cdot x^2$ intersect at the points $A$, $B$, and $C$ (see the figure below). Compute the tangent of the angle between the curves at all three intersection points.
1. The tangent of the angle at $A$ is $-27$ 2. The tangent of the angle at $B$ is $0$ 3. The tangent of the angle at $C$ is $27$
d24d7863-cfff-4e13-9077-843af80b36a4
differential_calc
false
null
Find the local minimum and local maximum values of the function $f(x) = \frac{ 3 }{ 4 } \cdot x^4 - 10 \cdot x^3 + 24 \cdot x^2 - 4$.
The point(s) where the function has a local minimum: $P(0,-4)$, $P(8,-516)$ The point(s) where the function has a local maximum: $P(2,24)$
d2a729e3-d012-4283-b8b4-1874c307c5b2
precalculus_review
false
null
Find zeros of $f(x) = \sqrt{x-3} + \sqrt{x+2} - \sqrt{2 \cdot x-5} - 2$
The final answer: $x=7$
d33534d4-e0dd-4da6-9c8e-02e5c4837211
integral_calc
false
null
Compute the integral: $$ \int \frac{ x^3-2 \cdot x^2+x }{ 3+2 \cdot x-x^2 } \, dx $$
$\int \frac{ x^3-2 \cdot x^2+x }{ 3+2 \cdot x-x^2 } \, dx$ = $-\frac{1}{2}\cdot x^2-2\cdot\ln\left(\left|x^2-2\cdot x-3\right|\right)-\ln\left(\left|\frac{x-3}{x+1}\right|\right)+C$
d34c2468-5dd2-4918-ac13-a2f46633fb66
differential_calc
true
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glJUWlpaUqLy/X/v379dBDD2nOnDnq0KGDfve736lNmzZmxwYABAGb2QEAAHWjU6dOmjNnjqZMmaJNmzZp8ODBHtt06dJFL774ovr27WtCQgBAMKKAAEAA69mzp1avXq0PP/xQixYt0qZNm1RQUKB+/fpp5MiRuueee3TFFVeYHRMAEEQoIAAQ4Jo0aaKJEydq4sSJZkcBAIBrQAAAAAAYhwICAAAAwDAUEAAAAACGoYAAAAAAMAwFBAAAAIBhKCAAAAAADEMBAQAAAGAYCggAAAAAw1BAAAAAABiGAgIAAADAMBQQAAAAAIahgAAAAAAwDAUEAAAAgGEoIAAAAAAMQwEBAAAAYBgKCAAAAADDUEAAAAAAGIYCAgAAAMAwFBAAAAAAhqGAAAAAADAMBQQAAACAYSggAAAAAAxDAQEAAABgGAoIAAAAAMNQQAAAAAAYhgICAAAAwDAUEAAAAACGoYAAAAAAMAwFBAAAAIBhKCAAAAAADEMBAQAAAGAYW3p6utkZKpWRkWF2hEqRzzdWz5ednS1JsurnxOrvH/l8Y9V8OTk5KikpcX3N56NmyOcbq+fj+OEb8vnG6vlYAQEAAABgGFtUVJTZGarE6jnJ5xur5nP+5Mqq+ZzI5xvyVY/dbldoaKgkKSIiwnL5LkY+35CvZjh+1A7y+caq+WxmBwAAI5WUlCg/P1/5+fk6cOCAmjdvrpKSEtdfqAEAQN2igAAIGmlpaZo6daoOHjwoSa7rGK655hpNmzZNY8aMMTMeAABBgWtAAASFpKQk3XXXXa7yIUk2m03169dXbm6upkyZoqSkJBMTAgAQHFgBARDwFi1a5FYurr/+ekVGRspms2nHjh3av3+/pJ9KSp8+fRQdHW1WVAAAAh4FBEBAKykp0YwZM1z/npiYqN/97ncqKiqSw+FQvXr1NGfOHFdBmTp1qlJTU7kmBACAOsIpWAAC2vHjx5WbmytJ6ty5sx577DGdOHFCBQUFOnPmjE6fPq2HH35Y1113nSTp4MGDys/PNzMyAAABjQICIKAdP37c9XVUVJRKS0tdF587nT17VjfccIPKy8sliQICAEAdooAACCplZWVe5zabTWVlZfrxxx+VkpJicCoAAIIHBQRAQGvVqpXr6/T0dDVu3Njr9R0HDhxwrY689NJLuvfee7Vw4UIjowIAEBQoIAACWqtWrXTllVdKkrKysvS///u/atasmRo1auTaZu7cufryyy917tw52Ww21atXT+vWrdMTTzyhX//61667ZAEAAN9xFywAAS00NFTTpk3TlClTJP10q91PP/1UkZGRatiwobZt26bMzEydOXNGxcXFatGihUJCQlz7L1myRBs2bNDjjz+uiRMnmvXLAAAgYFBAAAS8MWPGKDs723Wr3YMHD+rgwYNyOBxyOBwqLy9XeXm5mjZt6vX0rB9++EHTp0/X+vXr9fjjj6tnz55G/xIAAAgYnIIFICgkJiZqyZIluv76612z0tJSlZWVqUOHDnrvvfe0atUq3X777RV+j88//1w/+9nP9MorrxiQGACAwMQKCICgER0drdTUVOXn5ys/P1/79u1T8+bNFRsb61r5WLRokT755BM9+eSTOnPmjMf3KC4u1syZM7VlyxY9/fTT6tGjh9G/DAAA/BorIACCSmhoqNq3b68ePXqoY8eOatWqlcdpVz/72c+0fft23XfffRV+n40bN+oXv/iFFixYUNeRAQAIKBQQAPCiWbNmmjlzpt5++2117NjR6zanTp3StGnTNHXqVJ04ccLghAAA+CcKCABUIj4+XsnJyXrooYcq3Obf//63xo0bJ7vdblwwAAD8FAUEAC6hWbNmevbZZzV//vwKV0O+/PJL3XPPPZo9e7bB6QAA8C8UEACooqFDh+qjjz7S3XffXeE2M2bM0JgxYwxMBQCAf6GAAEA1tGvXTrNnz9YLL7ygpk2bet1m8+bN+p//+R8VFhYanA4AAOujgABADTz44IP66KOPFBMT4/X1nJwcdezYUV9++aXByQAAsDYKCADUUGRkpBYuXKjf/va3FW4zePBgLV261MBUAABYGwUEAHz01FNP6a233lLr1q29vv7II4/w9HQAAP4PBQQAasGwYcO0YMEC3XLLLV5fnzlzpqZMmaKTJ08aGwwAAIuhgABALenevbsWLFigkSNHen190aJFuu+++/Tpp58aGwwAAAuhgABALWrRooX+8Y9/aPLkyV5f37Fjhx599FHNmzfP4GQAAFgDBQQA6sD06dP1wgsvVPj6M888U+nrAAAEKgoIANSRBx98UO+++66uvPJKr6+//vrrevzxx40NBQCAySggAFCHBg0apPfee08333yz19c/+ugj3XPPPQanAgDAPBQQAKhjXbt21fz58xUdHe31dbvdrkGDBhmcCgAAc1BAAMAAV111lZYsWaIBAwZ4ff2rr75Sjx49DE4FAIDxKCAAYKD3339fI0aM8Ppafn6+2rdvb3AiAACMRQEBAIPNmzdPY8eOrfB1SggAIJBRQADABK+88oqmTZtW4euUEABAoKKAAIBJHnvsMb3xxhsVvh4fH29gGgAAjEEBAQATjRo1SosXL67wdUoIACDQUEAAwGS33XZbpSWE07EAAIHElp6ebnaGSmVkZJgdoVLk843V82VnZ0uSrPo5sfr7R76qCwsL0wsvvKA//OEPrllpaanr69atW2vVqlVmRPOQk5OjkpIS19d8PmqGfL6xej6OH74hn2+sno8VEACwiO7du2vmzJkVvs7pWACAQGCLiooyO0OVWD0n+Xxj1XzOn1xZNZ8T+XxjpXxRUVG64YYb9POf/9w1Cw0NdX09cuRIHT161IxoLna73ZUpIiLCUu+fN+TzDflqhuNH7SCfb6yajxUQALCYS10T0r17dwPTAABQuyggAGBBt912W4WnYx0/flxDhw41OBEAALWDAgIAFlXZNSG7d+/Wr371K4MTAQDgOwoIAFhY9+7d9eGHH3p9bcWKFfrzn/9scCIAAHxDAQEAi+vbt6/mzZvn9bU333xTs2fPNjgRAAA1RwEBAD8wYsQIJSUleX1txowZFRYUAACshgICAH5i/PjxeuaZZ7y+9swzz2jBggXGBgIAoAYoIADgRyZNmqTExESvr02bNk0ff/yxwYkAAKgeCggA+JnExEQ9+OCDXl977LHHtGXLFoMTAQBQdRQQAPBDL7zwgkaPHu31tRdffFGnT582NhAAAFVEAQEAP5WUlKS+fft6zLdv366pU6eakAgAgEujgACAn2rUqJGSkpJ08803e7yWnJys6dOnm5AKAIDKUUAAwI9deeWVmjlzplq1auXx2vz58/X666+bkAoAgIpRQADAz0VGRurFF1/0+toLL7ygNWvWGJwIAICKUUAAIAAMHz5cf/7zn72+NnnyZB0/ftzgRAAAeEcBAYAA8fDDD2vixIke86KiIo0aNcqERAAAeKKAAEAAee655zRkyBCP+TfffKOf/exnJiQCAMAdBQQAAsyLL77o9c5YW7du1V/+8hcTEgEA8F8UEAAIMO3atdNf//pXNW/e3OO1N954Q8nJycaHAgDg/1BAACAA9erVq8I7Y02aNEl2u93YQAAA/B8KCAAEqDvvvFN//OMfvb727LPPKi8vz+BEAABQQAAgoP3617/WAw884DHPzMzUs88+a0IiAECwo4AAQIB78cUX1bdvX4/50qVLNWvWLBMSAQCCGQUEAILA9OnT1apVK4/5Sy+9pBUrVpiQCAAQrCggABAEbrrpJv3pT3/y+tozzzyjgwcPGpwIABCsKCAAECTGjh2rSZMmecxzcnL0zDPPGB8IABCUKCAAEET+9Kc/6Y477vCYr127Vs8//7wJiQAAwYYCAgBBxGazafr06V4fUjhnzhx9/PHHxocCAAQVCggABJnu3btr+vTpXl979tlntWfPHoMTAQCCCQUEAILQ+PHjNWHCBI/5jz/+qGeffVbnz583IRUAIBhQQAAgSE2fPl3R0dEe8y1btvCQQgBAnaGAAECQatCggaZPn66mTZt6vPbPf/5TH3zwgQmpAACBjgICAEGsZ8+eFV4PMmPGDGVlZRmcCAAQ6CggABDkEhIS9MADD3jMv//+e82YMcOERACAQEYBAQDoj3/8oyIjIz3mK1eu1Ny5c40PBAAIWBQQAICaNm2qp556yutrM2bM0LZt2wxOBAAIVBQQAIAkKSYmRk8++aTHvLi4WDNmzFB5ebkJqQAAgcaWnp5udoZKZWRkmB2hUuTzjdXzZWdnS5Ks+jmx+vtHPt+Yke+OO+5Qr169tGXLFrf5hg0bNGXKFD344IPKyclRSUmJJCknJ4fPRw2RzzdWz8fxwzfk843V87ECAgBw88tf/lItWrTwmC9cuFBbt241IREAIJDYoqKizM5QJVbPST7fWDWf8ydXVs3nRD7fkM/zv1dSUqInnnjC47VPPvlE/fv3V2hoqCQpIiKC989H5PONVfNx/Kgd5PONVfPZzA4AALCecePGaefOnXrvvffc5hkZGXI4HCalAgAEAk7BAgB49dRTT6lbt24e8/T0dJ07d86ERACAQEABAQB4ddlll1V4a94zZ86orKzM4EQAgEBAAQEAVKh///76/e9/7zEvKyvTmTNnTEgEAPB3FBAAQKWeeOIJxcXFeczPnTuntLQ0ExIBAPwZBQQAcElPPvmkWrZs6THfsGGDMjMzTUgEAPBXFBAAwCXdeOONXp+SXlRUpFmzZpmQCADgryggAIAquffee3X33Xd7zJcuXar333/fhEQAAH9EAQEAVNnjjz+u8PBwj/krr7yib7/91oREAAB/QwEBAFTZtddeq759+3rMc3Nz9corrxgfCADgdyggAIBqiYqKUsOGDT3mH374oZYsWWJCIgCAP6GAAACqrUmTJqpXz/MQMmvWLOXn55uQCADgLyggAIBqs9lsatKkicf8wIEDnIoFAKgUBQQAUCONGzdWx44dPebvvPOOVq1aZUIiAIA/oIAAAGqsb9++Cg0N9ZjPmjVLZ8+eNSERAMDqKCAAgBqLiIjQE0884THfu3cvDygEAHhFAQEA+OTxxx/Xbbfd5jGfM2eO1q9fb0IiAICVUUAAAD7ztgoi/XQqVnl5ucFpAABWRgEBAPisT58++u1vf+sx37ZtG6diAQDcUEAAALXiiSeeUGRkpMd8zpw5+vLLL40PBACwJAoIAKBWNGzY0OupWEVFRZo7d64JiQAAVkQBAQDUmkGDBunBBx/0mC9ZskRLly41IREAwGooIACAWjV58mS1a9fOYz5nzhwT0gAArIYCAgCoVREREZo8ebLHfM+ePXrllVeMDwQAsBQKCACg1j300EPq3bu3x3zOnDnKzs42IREAwCooIACAOuFtFeTMmTNKSkoyIQ0AwCooIACAOjFo0CD94he/8JgvWrRIqampJiQCAFgBBQQAUGf+8Ic/6LLLLvOYswoCAMGLAgIAqDPt2rXzeirWzp07NW/ePBMSAQDMRgEBANSpKVOmqEePHh7zWbNmqaCgwIREAAAzUUAAAHVu2rRpHrNTp07p+eefNyENAMBMFBAAQJ3r37+/7rrrLo/5ggULtHPnThMSAQDMQgEBABji+eefV4MGDTzmL7zwgglpAABmoYAAAAxx+eWX68knn/SYb968WYsWLTIhEQDADBQQAIBhHn74YXXt2tVjPmXKFGVlZZmQCABgNAoIAMBQFZ1y9be//c3gJAAAM1BAAACG6t27t8aNG+cxX7VqldLS0kxIBAAwki09Pd3sDJXKyMgwO0KlyOcbq+fLzs6WJFn1c2L19498vrFqvpycHJWUlLi+rsnnY/To0frXv/7lMX/yySf18ssv+5xRsu7750Q+31g9H8cP35DPN1bPxwoIAMBwTZs21YQJEzzmX375pTZv3mxCIgCAUWxRUVFmZ6gSq+ckn2+sms/5kyur5nMin2/IVz12u12hoaGSpIiIiBrni4qKkt1u15EjR9zmixcv1m9/+1ufc17437Ey8vnGqvk4ftQO8vnGqvlYAQEAmOaZZ57xmGVlZen99983PgwAwBAUEACAaYYOHap+/fp5zGfOnKnCwkITEgEA6hoFBABgqmnTpnnM8vPz9dZbb5mQBgBQ1yggAABTRUZGer0g/eWXX/a4PgQA4P8oIAAA0/3617+WzWZzm5WWlmr+/PkmJQIA1BUKCADAdFdccYWefvppj/m8efO0a9cu4wMBAOoMBQQAYAkPPfSQunTp4jFnFQQAAgsFBABgCfXr19eUKVM85osXL9batWtNSAQAqAsUEACAZdx1110aPHiwx5xVEAAIHBQQAIClPPTQQx4zu92ujz/+2IQ0AIDaRgEBAFjKHXfcoYSEBI/5W2+9pbKyMhMSAQBqEwUEAGA5Dz30kJo1a+Y227t3r9555x2TEgEAagsFBABgOR07dvR6KtY777yjkydPGh8IAFBrKCAAAEt64IEHFBER4TY7fPgwqyAA4OcoIAAAS2rVqpUeeOABj/k777yjI0eOmJAIAFAbKCAAAMt64IEHdP3117vNjh8/zioIAPgxCggAwLKaNm1a4SrI119/bUIiAICvKCAAAEv75S9/qZtuusltdv78eVZBAMBPUUAAAJZms9m8roK8//772rZtmwmJAAC+oIAAACzvvvvuU1RUlMecVRAA8D8UEACAX/C2CvLZZ59p7dq1JqQBANQUBQQA4BfGjBmj22+/3WPOKggA+BcKCADAb/zyl7/0mKWmpurTTz81PAsAoGYoIAAAvzFixAjFxsZ6zFkFAQD/QQEBAPgVb9eCfPHFF1qwYIEJaQAA1UUBAQD4lUGDBmnYsGEe83feeUfnzp0zIREAoDooIAAAv+NtFWTfvn2cigUAfoACAgDwOzExMfrZz37mMX/77beVn59vQiIAQFVRQAAAfsnbKkhubq7effddE9IAAKqKAgIA8Eu33nqrxo8f7zF/7733lJuba0IiAEBVUEAAAH7rgQceUEhIiNvs+PHjeu+990xKBAC4FAoIAMBvde/eXQkJCR7z9957T999950JiQAAl0IBAQD4tYSEBNWvX99tdurUKS1dutSkRACAylBAAAB+7aabbvK6CrJ8+XJWQQDAgiggAAC/l5CQoLCwMLfZuXPn9Mknn5iUCABQkZCXX37ZYXaIyuTk5EiSIiIiTE7iHfl8Y/V8W7dulST17t3b5CTeWf39I59vrJpv/fr1Wr9+vSSpX79+6tevn8mJfrJq1Spt27bN9e9lZWWqV6+eHnvsMTVv3ty8YBWw6u+vE/l8w/HDN+TzjdXzhVxxxRWWLiAlJSWSpNDQUJOTeEc+31g9X2FhoSSpcePGJifxzurvH/l8Y9V8Z8+e1ZkzZyRJTZs2VZMmTUxO9JPS0lL9+OOPcjjcD2uNGzdWeHi4SakqZtXfXyfy+Ybjh2/I5xur5+MULABAQLDZbGrUqJHHvLCwUGVlZSYkAgB4Y0tMTDQ7Q6WsvoREPt9YPR9L6L4hn2+sms+qp2BJPz0D5M0331RJSYmrdNSvX19du3bVyJEjTU7nzqq/v07k8w3HD9+QzzdWz2f5ApKeni5JioqKMjmJd+TzjdXzzZs3T5I0adIkk5N4Z/X3j3y+sXK+7du3S/qpgFjtONKwYUP94x//cDsFISsrS2PHjtVVV11lcrr/svLvr0Q+X3H88A35fGP1fJyCBQAIKAkJCV6v+UhKSjIhDQDgYhQQAEBAue6667w+F+Sjjz7SkSNHTEgEALgQBQQAEHASEhLUtGlTjzmrIABgPgoIACDgdOjQQcOHD/eYswoCAOajgAAAAtKwYcPUrFkzjzmrIABgLgoIACAgtW3bllUQALAgm9kBLiUqKkrnz583OwaC1H333Wd2BAA+GDZsmOx2u44fP+42T0pK0iuvvGJOKAQFjh9AxfxiBaRBgwZmR0CQaty4sRo3bmx2DAA11Lp1a693xPrkk09MSINgwvEDqJhfFBAAAGoqISFBbdu2dZuVlpa6HhQHADBWnRaQb775Rn369NEjjzyioqKiS27/7bff6vnnn1fPnj0VEhKili1b6v7779f69etVXl5el1EB7dmzR507d1ZISEil/1T1/2fAKs6fP69Vq1Zp7NixatmypUJCQtS7d28lJSUpPz/f7Hh1rl27dho/frzH/PXXXzchDQIRxw/4K4fDodmzZyskJESbNm265Pa1dTypswJy9uxZvfTSS1X6xUjShg0bNHjwYE2fPl07d+6UJP34449asGCB+vfvr+eee44PLerUN998o/3795sdA6hVZ8+e1bRp0zR06FB9/PHH+vHHHyVJaWlpmjp1qkaOHKn09HSTU9a9sWPHqkmTJm6z/Px8ffTRRyYlQiDh+AF/tWHDBs2aNatK29bm8aROCkhBQYGeeuopzZkzp0rbZ2Rk6A9/+IMyMzP16KOPKicnR+Xl5Tp16pTmzp2rFi1a6JlnntG//vUvORyOuogM6ODBg5Kku+++W2vWrNG6deu8/vPII48oLCzM5LTApZWWluq1117T7Nmz1aVLFy1dulTnz59XWVmZdu/erbvuuktpaWn6/e9/r9zcXLPj1qlrrrlG48aN85hX9TgFVIbjB/yNw+GQ3W7Xww8/rOzs7EtuX9vHk1q/C9ahQ4c0depULVmypErbl5WV6YMPPlBaWpruv/9+vfjii677tjdr1kwPP/ywmjVrpkceeUTz589XXFycrr322tqOjSB37tw5HThwQJJ02223adCgQSYnAnyXmZmpd999V+Hh4fr73/+uwYMHu17r3r275s6dq/Lycn322WdauHChnnjiCYWEhJiYuG6NHTtWb7/9ttssKytLKSkpfOZRYxw/4G/Onz+vf//735o6daprFeNSavt4UmsrIGfPntWsWbN06623asmSJbrjjju83n/9Yt9++63WrFkj6adb1l380KiQkBANHTpUcXFxSktLU2pqam1FBlwKCgqUlZUlSbr55ptNTgP4zuFwaPXq1crIyNDo0aN12223eWzTtm1b3X///ZKklStX6tixY0bHNFT37t01ZswYjzmrIPAFxw/4C4fDoR07dmjMmDGaMGGCSkpKNG7cOHXq1OmS+9X28aTWCsj//u//6ne/+53r69WrVys6OvqS++3du1dpaWm6/fbb1blzZ6/bNG/eXN27d5ck7dixQ+fOnaut2IAkKS8vT9nZ2YqKimKFDQHh9OnT2rJliyTplltuUXh4uNftbrzxRnXr1k1paWlVWob3d95Ow0pLS9PmzZtNSINAwPED/iIrK0sTJkxQcnKyRowYIbvdrmefffaSt4uui+NJrRWQJk2a6NVXX1VWVpaeeOIJj4v9KuI8b/L6669XixYtvG4TEhLiamcHDx7U2bNnayc08H+cFxBeffXV+v7775WYmKgbbrhBISEhuuGGG5SYmKiMjAyuQYLfOHnypI4ePSqp8p/Ktm7dWu3bt1dBQYHrz+NAdscdd2jIkCEe87feesuENAgEHD/gL+rVq6eYmBht3rxZn332mXr27Fml/erieFJr14A4Vz+qo6yszHXLrsaNG8tmqzjOVVddJUk6duyYjh8/rpYtW9YsKODFV199JUlasmSJx/VLmZmZyszM1Jtvvqm//vWveuSRRyr9fxWwglOnTrn9+VqRRo0auf58PXTokCHZzDZ27FitXr3abbZq1Srt3LlTt9xyi0mp4K84fsBfdOrUSa+++mq196uL44mpDyIsLi52Xfxy5ZVXqlGjRh7bOH9iUL9+fUOzIXgUFRW5lgrDw8M1depUHTx4UGVlZSopKdGePXs0fvx4FRQU6Omnn9ZHH33ET7JgeQUFBdq/f7969OihVq1aVbhdSEhI0P35OnToUK/nMC9YsMCENPBnHD8QDOrieMKT0BH0zp07p7KyMt1yyy364x//qBdffFHXXXed6tWrJ5vNpm7duunNN9/Uo48+qoKCAs2ZMycozpUHAtnYsWM9Zh9++KEyMzNNSAN/xfEDqBkKCILe5ZdfrjfffFM7duzQtGnTvC6PN2nSRL/61a/UqVMnbdq0qcoP2ARgTePGjdNNN93kMf/ggw9MSAN/xfEDqBkKCFBF1113nXr06CFJ2r9/P8vogJ/zdkesefPm6dtvvzUhDQIZxw/AXYUFJDMzU5GRkQoJCfH6z/vvv+/zf7xhw4Zq166dJCk3N1dFRUUe2zgfYlJWViZJstlsQXe+MmqmNv4f3r17t0pLSyVJYWFhrpsfHDt2jNtBw9Jatmypbt26affu3Tp+/HiF2zkcDrc/X4PJ2LFjdfXVV3vMP/zwQxPSINBw/ECgqIvjiakrICEhIbrsssskSYWFha4PqjdHjhyRJLVq1UqXX365IfkQPIqLi3XixAmP/wcLCgpcH6YLtWjRQmFhYUbFA6qtUaNGrnu1FxYWVrhdUVGR689Xb38ZD2TNmjXzei3IO++847rjC3ApHD8Q6OrieFJhAenSpYt27dolh8Ph9Z977723Jr8GD877CR85ckQFBQVet3E4HNq/f7+kn54XUtVnjCC4VfX/4YULF6pBgwaKjo7W119/7fY9mjVr5lpxO3PmjOu+1q1bt2YlDpbWokULXX/99ZIqvx1ifn6+jh49qvDwcNf2wWTcuHFq3ry52+zUqVOsgqBKOH4gGNTF8cT0a0A6duyo6OhopaenKyMjw+s2J0+e1J49eyRJPXv2VMOGDY2MiADXtWtXderUSfv379cXX3zh9tpNN93kWkbcs2eP0tLSdMUVV+iOO+4wIypQZU2bNlVkZKQkaevWrRU+wPXrr7/W3r17FR0drQ4dOhiY0BquvPJKr6sgH3zwgc6cOWNCIvgTjh8IBnVxPDG9gLRv3159+vRRQUGB3n33XZ08edLtdYfDoeXLl2vJkiWKjo5WbGysOUERsK6//nrXAWHJkiU6duyY6zXnT6m+++47vfrqqyooKNCoUaPUrVs3U7ICVRUSEqK+ffuqQ4cOWrx4sTZs2OBx4euxY8f09ttvS/rp2RjOa/KCzbhx41Svnvvh8JtvvmEVBJfE8QPBoC6OJ6YXkAYNGmjixImKjo7WggUL9Oijj+rQoUNyOBw6ffq0/vGPf+ixxx6TJE2cOFHXXHONuYERcJy3SOzQoYOWL1+uhx56SNu3b1d5eblKS0v1xRdf6P7779dnn32m6OhoPfbYY14fmglYTWRkpCZPnqyCggJNnjxZ77//voqKilReXq49e/bo0Ucf1fLlyzVgwACNGzfOddOPYNO1a1evd8T68MMPVV5ebkIi+AuOHwgWtX08scQtT7p27aqZM2dq0qRJ+uCDD7zeh/2ZZ57RfffdF7QHSNSt22+/XW+88YYef/xxJScnKzk52WObW2+9Va+88oq6du1qQkKg+mw2m37zm98oLy9Ps2fPVkJCghISEty2iY6O1ksvvaQrr7zSpJTWMHbsWI9jz9dff62FCxdq/PjxJqWCP+D4gWBQ28cT01dAnPr27as1a9boueee0y233CLpp4teEhISZLfbNX36dH5qgDoTEhKi+Ph4bdy4US+//LL69esnSQoPD1d8fLzeeustff755+rdu7fJSYHqadKkiWbMmKGVK1fq7rvvVosWLST9dKB4+eWXtWzZMkVFRZmc0nzR0dEaPny4x3zx4sUmpIE/4fiBYFGbx5M6XQGZPn26pk+fXuXtr776av3pT3/Sn/70pzpMBVSsdevWSkxMVGJiotlRgFrToEEDxcfHKz4+3uwoljZu3DgtX77cbbZ582atXbtWAwcONCkV/AXHD/gj5x1Dq6q2jieWWQEBAMBMcXFxuv322z3mixYtMiENAAQuvyggF19pDwBAXbj77rs9Zp999pnrVvAAAN9ZvoDk5OToyy+/NDsGgtSePXu0Y8cOs2MAMMiYMWPUpUsXjznXgqC6OH4AFbN8Afnuu+9UXFxsdgwEqa1bt2r79u1mxwBgkPr162vMmDEe80WLFikvL8+ERPBXHD+Ailm+gAAAYKQxY8aoZcuWbrMTJ06wCgIAtYQCAgDABdq2bev1WpDFixerrKzMhEQAEFgoIAAAXMTbaViZmZncEQsAaoEtPT3d7AyVysjIMDtCpcjnG6vny87OliRZ9XNi9fePfL6xar6cnByVlJS4vg7Uz0ffvn21du1at9lbb72ljh07+vR9naz6++tEPt9w/PAN+Xxj9XysgAAA4EVcXJzHbNeuXVxYDAA+slX1kelms3pO8vnGqvmcP7myaj4n8vmGfNVjt9sVGhoqSYqIiLBcvovVNF9UVJTWrVundevWuc337Nmjhx9+uDaiuf47Vka+muH4UTvI5xur5mMFBACACni7FmTJkiU8nwoAfEABAQCgAnfddZe6devmMeeWvABQcxQQAAAq4e2WvIsWLdL3339vQhoA8H8UEAAAKjFmzBi1b9/ebfbDDz9wS14AqCEKCAAAlWjevLnXa0EWL14sh8NhQiIA8G8UEAAALmHMmDEKCwtzm2VkZLAKAgA1QAEBAOASOnbs6PVaEC5GB4Dqo4AAAFAF3k7D2rBhg9avX29CGgDwXxQQAACqIDo6WkOGDPGYcxoWAFQPBQQAgCqq6GL0ffv2mZAGAPwTBQQAgCoaPny4evXq5TH/9NNPjQ8DAH6KAgIAQDX8/Oc/95h99tlnKioqMiENAPgfCggAANUwevRoXXHFFW6z7OxsVkEAoIooIAAAVMNll12mO++802NOAQGAqqGAAABQTaNHj/aYbdy4UZs3bzY+DAD4GQoIAADV1L17dw0bNsxjzioIAFwaBQQAgBqo6DSsnJwcE9IAgP+ggAAAUAMjR47UTTfd5DY7c+aMPvvsM5MSAYB/oIAAAFBD3q4F4TQsAKgcBQQAgBq688471bRpU7fZV199pWXLlpmUCACsjwICAEANRUREeF0F4TQsAKgYBQQAAB94KyArVqzQnj17jA8DAH6AAgIAgA9uv/12xcTEeMy5FgQAvKOAAADgo4pOwzp16pTxYQDA4iggAAD4aPTo0erQoYPbLC8vj1UQAPCCAgIAgI8aNWpU4YMJAQDuKCAAANQCb6dhpaWlyW63G54FAKyMAgIAQC244YYbeDAhAFQBBQQAgFpS0WlYhw4dMiENAFgTBQQAgFoyZMgQ3XLLLW6z4uJiHkwIABeggAAAUIsqOg2rrKzM+DAAYEEUEAAAatHo0aPVokULt9n+/fu5FgQA/g8FBACAWtS6dWsuRgeASlBAAACoZd4KyNq1a7Vz507jwwCAxVBAAACoZb169dLAgQM95suWLTMhDQBYCwUEAIA6MHLkSI/ZsmXLdObMGRPSAIB1UEAAAKgDo0aN0tVXX+02y83NZRUEQNCzpaenm52hUhkZGWZHqBT5fGP1fNnZ2ZIkq35OrP7+kc83Vs2Xk5OjkpIS19d8PioWFRWlgwcPus3effddde7c2RL5KkM+33D88A35fGP1fKyAAABQR/r27esxS09P19dff21CGgCwBltUVJTZGarE6jnJ5xur5nP+5Mqq+ZzI5xvyVY/dbldoaKgkKSIiwnL5LmZmvqioKK1atUqrV692m+/fv1933nmnaxsrI1/NcPyoHeTzjVXzsQICAEAdquhi9IKCAhPSAID5KCAAANShUaNG6brrrnObfffdd9qwYYNJiQDAXBQQAADqkM1m06hRozzmGzduNCENAJiPAgIAQB3zdhrWrl27tHfvXhPSAIC5KCAAANSxrl27avjw4R5zTsMCEIwoIAAAGMDbKsiGDRt0/PhxE9IAgHkoIAAAGGDUqFHq3Lmz2+zUqVM8GR1A0KGAAABgkIpuyQsAwYQCAgCAQUaNGqWQkBC32datW/Wf//zHpEQAYDwKCAAABunUqZPXW/IuXbrUhDQAYA4KCAAABqroNKxjx46ZkAYAjEcBAQDAQMOGDdONN97oNuNidADBhAICAIDBuBgdQDCjgAAAYLBRo0bJZrO5zbZv3y673W5OIAAwEAUEAACDXXvtterbt6/HnIvRAQQDCggAACbwVkCWLVumnJwcE9IAgHEoIAAAmKB3797q1KmT2+zs2bNcCwIg4FFAAAAwSUWrIAAQyCggAACYJCYmRo0aNXKb7dq1S+vXrzcpEQDUPQoIAAAmadeunUaMGOExX7FihQlpAMAYFBAAAEw0dOhQj9mKFSv0448/mpAGAOoeBQQAABPFx8d7XIz+ww8/sAoCIGBRQAAAMFlFqyAAEIgoIAAAmMxbAbHb7dqzZ48JaQCgblFAAAAwWY8ePdSvXz+POasgAAIRBQQAAAuo6DQsh8NhQhoAqDsUEAAALGDo0KFq3ry52+zAgQOsggAIOBQQAAAsoHXr1lyMDiAoUEAAALCIigrIt99+a0IaAKgbFBAAACwiLi5OXbt2dZudP3+eVRAAAYUCAgCAhXAaFoBARwEBEFSSkpJ0zz33qEuXLhozZoz+8pe/KCkpyexYgIu3ArJ9+3Zt2rTJhDQAUPsoIACCxvjx45WUlCS73a6CggKdOXNGmzdvVlJSkvr37292PECSdNNNN2ngwIEec1ZBAAQKCgiAoNC/f3+tX7++wtezsrI0fvx4AxMBFavoNKzTp0+bkAYAapfN6qce5OTkSJLsdru5QSpAPt9YPd/WrVslSQUFBSYn8c7q759V8q1fv147d+70mJeVlSk0NFShoaGu7ZKSkpSYmGh0RMDN0KFD9eKLL+qHH35wzb777jutWLFCv/jFL0xMBgC+s3wBKSkpkSTXXxCshny+sXq+wsJCSbLsuddWf/+sku/kyZM6f/6819eKiopks9lcGdPT042MBnh1+eWXa+jQofrXv/7lNqeAAAgEnIIFIOA5i1BFiouLXV9TQGAV3k7D+vzzz/XVV1+ZkAYAao/tUgdms5WWlpodoVLk843V85WVlUm69F9gzWL1988q+RwOR6Wvl5WVuX6Pz507Z5kSkpGRYXYEr3JyclzvV05OjmXer4tZ9f1zulS+Zs2aqUOHDjpw4IDb/M0331RCQkJdRpPk/++f2bKzsyVZ94caVn//yOcbq+djBQRAwLvUKWAXvn7xQ+AAM91+++0es//85z8mJAGA2mN78sknzc5QKedFrBERESYn8Y58vrF6PudF6L179zY5iXdWf/+skm/9+vVe74DlvAi9UaNGrtmgQYMUFRVlZLxLsloeu93uKm0RERGWy3cxf87XtGlTffDBB26zo0ePKj8/X/Hx8XUdTZJ/v39mcq58WDWfE/l8Q76asVn9bi9W/wCTzzdWzzdv3jxJ0qRJk0xO4p3V3z+r5EtMTFT//v2VlZXlNr/41Lp+/fpxByxYSpcuXTR48GCtWbPGbb5ixQrDCggA1DZOwQIQFOx2u/r161fh6507d/b4STNgBRU9EyQ3N9eENADgOwoIgKDxwQcfuFZDwsPD1bRpU91+++1KTEw0/VklQEWGDh2qtm3bus0KCwt5MjoAv2UzOwAAGOnCU6yscooYUJlmzZpp6NCh+uc//+k2X7FihR566CFzQgGAD1gBAQDA4rydhpWWlqbt27ebkAYAfEMBAQDA4mJiYhQZGekxv/jidADwBxQQAAD8gLe7XlFAAPgjCggAAH7AWwHJyspSamqqCWkAoOYoIAAA+IHOnTtr8ODBHnNWQQD4GwoIAAB+YsiQIR6zNWvWqLCw0IQ0AFAzFBAAAPxEfHy8WrZs6TY7duwYqyAA/AoFBAAAP3H55ZdzMToAv0cBAQDAj1R0GtaxY8dMSAMA1UcBAQDAj8TFxemGG25wmxUWFrIKAsBvUEAAAPAznIYFwJ9RQAAA8DPeTsNKTU1VVlaWCWkAoHooIAAA+JkePXooJibGY84qCAB/QAEBAMAPVXQxOgBYHQUEAAA/FB8fr8aNG7vNtm/fru3bt5uUCACqhgICAIAfat++PRejA/BLFBAAAPwUp2EB8EcUEAAA/FR8fLw6dOjgNsvKylJqaqpJiQDAu6ysLCUlJSkhIUE2s8MAAICaCQ0NVXx8vP7xj3+4zdesWaPY2FiTUgHAT7KysrRs2TIlJycrMzPTNWcFBAAAP1bRaViFhYUmpAEQ7JwrHQMGDFD//v2VlJTkVj4ksQICAIA/6927t3r16uV296tjx45pzZo1Gj16tHnBAASNrKwsJScna9myZR5lwxsKCAAAfi4+Pt7j9rsUEAB1af/+/Vq2bFmVS8eFKCAAAPi5IUOG6IUXXpDD4XDN1qxZo2PHjqldu3YmJgMQSHwpHZIUGxur2NhYCggAAP7u+uuvV3x8vFauXOmaFRYWas2aNbr//vtNTAbA3zlLR3Jysvbt21ft/Z2lIzY2Vtdcc40kVkAAAAgIFxcQSRQQADXia+kYOHCgBgwY4FY6LkQBAQAgAAwZMkRt2rTR999/75qlpqYqKytLnTt3NjEZAH+wf/9+14XkNS0dsbGxGjBggNfScSEKCAAAAaBZs2aKj4/Xe++95zZfs2YNBQSAVwcOHHBd0+FL6YiNjfV4KGplKCAAAASIigrIb37zG5MSAbAaX0tHXFyc6/Sq6pSOC1FAAAAIEP3799dNN92kr776yjXbvn27tm/frl69epmYDICZnKUjOTlZGRkZ1d4/Li7OdXpVTUvHhSggAAAEkPj4eLcCIkkpKSkUECDIHDlyRBs3btSyZct8Kh2xsbG6+uqrazUbBQQAgAASFxenpKQkt1lKSoqeeuopkxIBMMqBAweUnJysf//73zp8+LBCQ0Ortf+gQYNcp1fVdum4EAUEAIAA0qNHD/3P//yPtm3b5prt27dP69evV79+/UxMBqAuHDx40HVNh3Olo6SkpMr7Dxo0yHV6VV2WjgtRQAAACDBxcXFuBUT6aRWEAgIEBm+lozqcpSM2NlZXXXVVHSSsnC09Pd3w/2h11ORNNRL5fGP1fNnZ2ZIkq35OrP7+kc83Vs2Xk5Pj+ulaTk4On48aqst87dq18/gJ6KeffqoRI0ZU+ZSMYH7/agPHD9+Qz1NOTo42btyoDRs26PDhw5VuW1pa6jHr3bu3evXqpVtvvVVt27aVJH3//fduzw4yCisgAAAEmGuvvVaRkZHatWuXa/bdd98pLS1Nffr0MS8YgGqpTunwpnfv3rr11lvVq1cvV+mwAltUVJTZGarE6jnJ5xur5nP+5Mqq+ZzI5xvyVY/dbnf9FD0iIsJy+S4WrPnuvvtuj7thHT58WI899li1vk+wvn++4vhRO4Ix38GDB11PJP/6669d86quXg4ZMkTXXnutevXqpWHDhtV6vtrACggAAAEoLi5OzzzzjNssJSVFJ06c0OWXX25OKABeHTp0yPWcjot/cFAVQ4YMcV1IHhERYdlT/5woIAAABKDrrrtOAwcO1Nq1a12zEydOKCUlRWPHjjUxGQCp9kuHP6GAAAAQoOLi4twKiCQKCGAiZ+lYvny5vvzyy2rvHx8f73pOx5VXXlkHCY1BAQEAIEANHDhQYWFhKi4uds1SUlJ05MgRU269CQSjQ4cOKTk5WcnJyTUuHc6VDn8uHReigAAAEKAiIiIUFxenFStWuGbFxcVKSUnRhAkTTEwGBLbDhw+7Vjr27t1b7f2dpSM2Nlbt27evg4TmooAAABDABg4c6FZAJFFAgDrga+kYOnSo6/SqQCwdF6KAAAAQwOLi4hQeHq6CggLXbP369dq3b59uuOEGE5MB/s9ZOlasWKE9e/ZUe/+hQ4e6Tq8K9NJxIQoIAAABrHXr1ho4cKA+/fRTt3lKSgoFBKiBw4cP68MPP9SmTZv0zTffVHt/Z+mIjY3VFVdcUfsB/QAFBACAABcXF+e1gPz2t781JxDgZw4fPqzk5GStWLFCu3fvVklJiaSqPxxw2LBhrtOrgrV0XIgCAgBAgIuLi1PLli31ww8/uGbbt2/X9u3b1atXLxOTAdb1zTffaNmyZVq5cqV27dpV7f2HDRvmOr2K0uGOAgIAQIBr1qyZ4uLitHDhQrd5SkoKBQS4QG2VjtjYWLVr1672AwYICggAAEGgogLy1FNPmZQIsAZn6Vi1apV27txZ7f2HDx/uOr2K0lE1FBAAAILAwIED1b59ex09etQ127dvn9avX69+/fqZmAwwnq+lo0+fPrr11ls1YcIESkcNUEAAAAgCDRs2VFxcnN577z23eUpKCgUEQeGbb75RcnKyVq1apR07dlR7/+HDh7tOr8rJyZEkykcNUUAAAAgSAwcO9FpA/t//+38KCwszKRVQd7Kzs10rHTUpHSNGjHCdXtW2bVvX3FlAUDMUEAAAgkRcXJyuvfZaHT582DU7cuSIUlJSNHz4cBOTAbXHWTpWr16t9PT0au8/YsQI192rLiwdqD0UEAAAgkRISIgGDhyot956y21OAYG/87V0jBw50rXS0aZNmzpIiAtRQAAACCJxcXFeC8iJEyd0+eWXm5QKqD5n6VizZo22b99e7f0pHeahgAAAEET69u2rLl26KDMz0zU7ceKEUlJSNHbsWBOTAZeWnZ2t5ORkrV69usalw3l6FaXDPBQQAACCTFxcnFsBkUQBgWV9++23rpWOL774otr7O0tHbGysWrduXQcJUV0UEAAAgszAgQP1+uuvu81SUlJ05MgRXXXVVSalAv7r2LFj2rBhg/7yl7/UuHQMHDhQAwYMoHRYEAUEAIAg07t3b3Xv3l179uxxzYqLi5WSkqIJEyaYmAzBzLnSkZKSok2bNkmSQkNDq7y/s3TExsaqVatWdRUTtYACAgBAEBo4cKBbAZGk1NRUCggMdWHp2LZtW7X3p3T4JwoIAABBKC4uTrNmzXKbpaam6vDhw7r22mtNSoVg8O233yo5OVkpKSlKS0ur9v4jR45UXFycBgwYQOnwUxQQAACC0C233KJevXp53EkoNTVVEydONCkVAtWRI0e0bNkyff7559q6dWu193eWjtjYWLVs2bIOEsJIFBAACGBHjx7VvffeK7vdXul2Q4YM0fvvv8+BPcjExcV5FJB169ZRQFArfC0dMTExGj9+PKUjAFFAACCA5eXledxuFXCKi4vT3/72N7dZamqq8vLyTEoEf+csHWvXrtWWLVuqvf/IkSM1aNAgtWjRQpdddpmioqLqICXMRgEBgACWm5urvLw8xcTEaNq0aWrSpInX7Ro2bKimTZsanA5mu/HGG3XHHXe47jjktGLFCkVGRpoTCn6ntkpHbGysWrRoIUlKT0+v7ZiwEAoIAASwr776SpLUq1cvDRo0SGFhYSYngtXExcV5FJB169ZRQFCpI0eOKDk5WWvXrtXmzZurvb+30oHgQQEBgABVWFioQ4cOSZK6dOlC+YBXAwcO1LPPPus2c16I3qxZM5NSwYpycnJcKx01LR2DBw/WgAEDKB1BjgICAAHq5MmTOnDggMLDw9WjRw+z48CiOnbsqNjYWKWmpsrhcKi8vFzl5eX65JNPNGLECJWUlFTrYXAILM7SkZqa6rFSVhXO0hEbG6vLL7+8DhLCH1FAACBAOS9A79atm4qLi/X888/rk08+0c6dO9WhQwfFxcVp4sSJio6OVr169cyOCxPFxcVp9erVOn36tEpLSyVJb775pj788ENdc801mjZtmsaMGWNyShiF0oG6RgEBgAB14MAB5eXlKS8vT/369XN7LTs7W/Pnz9f8+fP19NNP6+mnn67wAnUEvoMHD+rEiRMKDQ1Vs2bNZLP99NeD+vXrKzc3V1OmTFF2drYSExNNToq6kpOTo+TkZKWmpuo///lPtfcfOXKkhgwZogEDBlA6cEkUEAAIUFlZWa6v77//fk2dOlVdu3ZVvXr19M033+i1117TrFmz9Ne//lXNmjVTYmKi6y+eCB6LFi3S/PnzFR4ergYNGqhDhw66+eabFRYWpi+//FIHDx6UJCUlJalPnz6Kjo42OTFqy/fff6833njD59IRGxur5s2b135ABCyONAAQgM6dO6fi4mL17t1bPXv21MyZM91WOK677jrNnDlTbdu21ZNPPqm5c+dq4MCB6tWrl4mpYbSSkhLNmDFDktSoUSNNmjRJkydPdr0eFhamt99+W0lJSZKkqVOnKjU1lWtC/Fhubq6Sk5O1ePFi7dy5s9q/l5QO1AYKCAAEoIYNG+q5557Tc889V+E2NptN9957r5YvX66NGzdq1apVioqKUkhIiIFJYabjx48rNzdXktS5c2f9+te/Vnl5uev14uJiJSYm6tNPP9XBgwd18OBB5efnq3379mZFRg04S0dqaqo2btwo6afyWVUjR45UfHy8BgwYQOlAraCAAEAQa9OmjXr16qWNGzcqOztbRUVFaty4sdmxYJDjx4+7vo6KilJYWJjOnTvntk1xcbEiIyNdp2JRQPxDbm6uli9frtTUVG3YsKHa+ztLR2xsrC677LI6SIhgZps3b57ZGSqVnZ0tybpPxCSfb6yeryZ/aBvJ6u8f+XzjzFe/fn3dfPPNstlsyszM1Lhx47R7926v+/zrX//Svffe6/W10tJS7dq1S4WFherVq5caN26ssLAw1wWjR44ccRWQoqIibdu2TZmZmR7fZ+vWrSosLHR9bdXjiL/8/pqZLzc3V4WFhWrYsKHrTmgOh8Ntm/PnzyskJETl5eU6d+6cFi9erLS0NDPiurHC+1cZM44fJ0+e1N69e7Vv3z7t37+/0m3Lysokua+EdO/eXTfffLO6dOmiRo0aKT8/XwsXLqzTzBWx+u8v+XzDCggABKjS0lIVFBSoSZMmrocQ2mw2nT59WsXFxR4rHW3atHFtFxISovr16xueGcZq2rSpJKm8vFzbt29XaGioysrKVFxcLEkKDQ1V/fr1lZmZ6To1y7kPrMFZOjIzM91uPFFVF5cOwAi2SZMmmZ2hUs7mFhUVZXIS78jnG6vnc7Lq58Tq7x/5fOPMFxkZ6Zp16dJFu3btuuS+W7du1eDBg1VQUKA1a9Zo0KBBstlsioyMdPt+hYWF+vbbbyVJrVq1UoMGDST9dA1Jnz591KdPH4/vXVBQ4Ho2QO/evfl81JAV8pWUlOijjz5Sbm6uMjMzNXfuXCUmJqq4uFilpaUKDQ3V3//+d+3du1c2m01dunTRE088YYmL0K3w/lVFXXw+jh496jq9av369a55VU+fHDlypDp37qxbb71Vffv2rfV8tcHqv7/k8w0rIAAQgK6++mpFRUXJbrdr48aNio2N9bqicfjwYVeZ6NOnj2sFBMEhNDRU06ZN05QpUyT9dKvdtWvX6oYbblBoaKi++OIL7du3z7X9yy+/bInyEYyOHj2qFStWKDU1VXa7vdr7jxw5UsOGDdOAAQPUrFkzy56ag+BAAQGAANS2bVvFxMTIbrdr6dKlGj9+vLp27eq2zdmzZzVnzhxlZGRo1KhRXlc7EPjGjBmj7Oxs1612d+3apV27dsnhcMjhcLiuDUlMTOQZIAZzlo5169Zp3bp11d7fWTpiY2MVHh5eBwmBmqGAAEAAql+/vhISErRmzRqlpaXpgQce0AsvvKABAwaoXr16OnjwoP785z/rgw8+UIcOHfS73/1Obdq0MTs2TJKYmKg+ffpo6tSprrtdlZaWSpKuuuoqTZs2TWPGjDEzYtA4evSoVq5cqdTUVEoHAhYFBAACVKdOnTRnzhxNmTJFmzZt0uDBgz226dKli1588UXLngcO40RHRys1NVX5+fnKz8/Xvn371Lx5c8XGxnLaVR3Ly8tzrXSkpqZWe/+RI0dq+PDhGjBgAKUDfoECAgABrGfPnlq9erU+/PBDLVq0SJs2bVJBQYH69eunkSNH6p577tEVV1xhdkxYRGhoqNq3b6/27du7VkAoH3UjLy/PtdLhS+mIjY3lzmTwOxQQAAhwTZo00cSJEzVx4kSzowBBzVk6nCsdFz9z5VIoHQgUFBAAAIA6kpeXp1WrVrlWOmpSOkaMGKEBAwZQOhAwKCAAAAC1KC8vT5s3b1ZmZqb+8pe/uB7iWFXO0hEbG6smTZrUUUrAPBQQAAAAHx07dsxtpePMmTOSqvdwQEoHggUFBAAAoAaOHTum1atXu0pHWVlZtfandCBYUUAAAACqqLZKx8CBA6u8OgIEGgoIAABAJY4dO6Y1a9a4SofzFsVVRekA3FFAAAAALuJr6ejevbu6d++umTNnUjqAi1BAAAAAJH333XdupaOkpKRa+ztXOuLi4rRgwQJJVb8IHQgmFBAAABC0Liwd69atU3FxcbX2v7B0NGrUqI5SAoGFAgIAAILKd999p5SUFNdKB6UDMBYFBAAABLwLS8e6det0/vz5au3vLB2DBg1Sw4YN6yglEBwoIAAAICB99913+vzzz10rHZQOwBooIAAAIGB8//33bisd586dq9b+ztIxePBgNWjQoI5SAsGNAgIAAPza999/77bSQekArI0CAgAA/M6PP/6obdu26Y033lBqaqqKioqqtT+lAzAPBQQAAPiF77//XmvXrlVqaqpWrlyp8+fPKzQ0tMr7O0vHkCFDFBYWVodJAVSGAgIAACzLWTrWrVun1NRUFRYWSlKVHxJI6QCshwICAAAsJT8/37XScWHpqCpKB2BtFBAAAGC6/Px8V+FITU3V2bNnq7W/s3TEx8dX67QsAMajgAAAAFP4WjpiYmL04IMPUjoAP0MBAQAAhsnPz3ddz5GamqozZ85Ua3/nSkebNm1ks9kUFRVVR0kB1BUKCAAAqFPHjx93W+moaekYOnSobLaf/uqSnp5eF1EBGIACAgAAat3x48fdVjoKCgqqtb+30gEgMPCJBgAAteKHH35wW+mgdADwhk83AACosR9//NGtdJw+fbpa+ztLx7Bhw1S/fv06SgnASiggAABAkpSUlKSvvvpKmzdv1vnz59W9e3f17dtXiYmJbttROgD4ggICAADUv39/ZWVluf69pKREmzdv1hdffKFly5ZpyZIlbqXj1KlT1fr+lA4AThQQAACC3Pjx493Kh5PD4dC5c+f0xRdf6JprrlGTJk2q9X2dpWP48OGqV69ebcUF4OcoIAAABLGkpCStX7/ebXbu3DkVFRWppKREDofD7bVLlRBKB4BLoYAAABDELn6eRkFBgQoLC71uW1JS4nXuLB0jRoxQSEhIrWcEEFgoIAAABLELC0hxcXGF5UNyLyCUDgA1ZbP6k0QzMjLMjlAp8vnG6vmys7MlWfeJu1Z//8jnG6vmy8nJcf1FNCcnh89HDVklX3Fxsev3s7S0tNJtGzVqpD/84Q/q06ePq3Ts2LGjzjN6Y5X3ryIcP3xDPt9YPR8nZwIAEMS6d+/u+jo0NFQNGjRwez0sLExNmzZVixYtNGDAAMXExLDiAcAntqioKLMzVInVc5LPN1bN5/zJlVXzOZHPN+SrHrvdrtDQUElSRESE5fJdjHyV69u3r7744gvXvzdv3lzFxcUqLS1VaGio6/faua3ZeS9mtTxOHD9qB/l8Y9V8rIAAABDEEhMT1blzZ7dZWFiYW/GQpM6dO3s8kBAAaoICAgBAkLPb7erXr1+Fr/fr1092u924QAACGnfBAgAA+uCDD5SUlKT09HSlp6fr3Llz6tq1qwYNGsTKB4BaRQEBAACS5FY0/OUaBgD+h1OwAAAAABiGAgIAAADAMBQQAAAAAIahgAAAAAAwDAUEAAAAgGEoIAAAAAAMQwEBAAAAYBgKCAAAAADDUEAAAAAAGIYCAgAAAMAwFBAAAAAAhqGAAAAAADAMBQQAAACAYSggAAAAAAxDAQEAAABgGAoIAAAAAMNQQAAAAAAYhgICAAAAwDAUEAAAAACGoYAAAAAAMAwFBAAAAIBhKCAAAAAADEMBAQAAAGAYCggAAAAAw1BAAAAAABiGAgIAAADAMBQQAAAAAIahgAAAAAAwDAUEAAAAgGEoIAAAAAAMQwEBAAAAYBgKCAAAAADDUEAAAAAAGMaWnp5udoZKZWRkmB2hUuTzjdXzZWdnS5Ks+jmx+vtHPt9YNV9OTo5KSkpcX/P5qBny+cbq+Th++IZ8vrF6PlZAAAAAABjGFhUVZXaGKrF6TvL5xqr5nD+5smo+J/L5hnzVY7fbFRoaKkmKiIiwXL6Lkc835KsZjh+1g3y+sWo+VkAAAAAAGIYCAgAAAMAwFBAAAAAAhqGAAAAAADAMBQQAAACAYSggAAAAAAxDAQEAAABgGAoIAAAAAMNQQAAAAAAYhgICAAAAwDAUEAAAAACGoYAAAAAAMAwFBAAAAIBhKCAAAAAADEMBAQAAAGAYCggAAAAAw1BAAAAAABiGAgIAAADAMBQQAAAAAIahgAAAAAAwDAUEAAAAgGEoIAAAAAAMQwEBAAAAYBgKCAAAAADDUEAAAAAAGIYCAgAAAMAwFBAAAAAAhqGAAAAAADAMBQQAAACAYSggAAAAAAxDAQEAAABgGAoIAAAAAMNQQAAAAAAYhgICAAAAwDAUEAAAAACGoYAAAAAAMAwFBAAAAIBhbOnp6WZnqFRGRobZESpFPt9YPV92drYkyaqfE6u/f+TzjVXz5eTkqKSkxPU1n4+aIZ9vrJ6P44dvyOcbq+djBQQAAACAYWxRUVFmZ6gSq+ckn2+sms/5kyur5nMin2/IVz12u12hoaGSpIiICMvluxj5fEO+muH4UTvI5xur5mMFBAAAAIBhKCAAAAAADEMBAQAAAGAYCggAAAAAw1BAAAAAABiGAgIAAADAMBQQAAAAAIahgAAAAAAwDAUEAAAAgGEoIAAAAAAMQwEBAAAAYBgKCAAAAADDUEAAAAAAGIYCAgAAAMAwFBAAAAAAhqGAAAAAADAMBQQAAACAYSggAAAAAAxDAQEAAABgGAoIAAAAAMNQQAAAAAAYhgICAAAAwDAUEAAAAACGoYAAAAAAMAwFBAAAAIBhKCAAAAAADEMBAQAAAGAYCggAAAAAw1BAAAAAABiGAgIAAADAMBQQAAAAAIahgAAAAAAwDAUEAAAAgGEoIAAAAAAMQwEBAAAAYBgKCAAAAADDUEAAAAAAGMaWnp5udoZKZWRkmB2hUuTzjdXzZWdnS5Ks+jmx+vtHPt9YNV9OTo5KSkpcX/P5qBny+cbq+Th++IZ8vrF6PlZAAAAAABjGFhUVZXaGKrF6TvL5xqr5nD+5smo+J/L5hnzVY7fbFRoaKkmKiIiwXL6Lkc835KsZjh+1g3y+sWo+VkAAAAAAGIYCAgAAAMAwFBAAAAAAhqGAAAAAADAMBQQAAACAYSggAOBnHA6HZs+erZCQEG3atOmS258/f16rVq3S2LFj1bJlS4WEhKh3795KSkpSfn6+AYkBAPgvm9kBAADeNWnSRG3atPGYb9iwQbNmzarS9zh79qz++Mc/avbs2W7ztLQ0paWl6eOPP9brr79u2Vs1AgACDysgAGBRHTt2VIsWLVz/7nA4ZLfb9fDDD7ueslyZ0tJSvfbaa5o9e7a6dOmipUuX6vz58yorK9Pu3bt11113KS0tTb///e+Vm5tbl78UAABcKCAAYFE2238Xqc+fP69//vOf+vnPf67MzMwq7Z+Zmal3331X4eHh+vvf/66RI0cqLCxM9erVU/fu3TV37lzdeeedWrdunRYuXCiHw1FXvxQAAFwoIABgYQ6HQzt27NCYMWM0YcIElZSUaNy4cerUqdMl91u9erUyMjI0evRo3XbbbR7btG3bVvfff78kaeXKlTp27Fid/BoAALgQBQQALCwrK0sTJkxQcnKyRowYIbvdrmeffVaNGzeudL/Tp09ry5YtkqRbbrlF4eHhXre78cYb1a1bN6WlpVXptC4AAHxFAQEAC6tXr55iYmK0efNmffbZZ+rZs2eV9jt58qSOHj0qSbr55psr3K5169Zq3769CgoKdPDgwVrJDABAZbgLFgBYWKdOnfTqq69We79Tp065brFb2WpJo0aNdNVVV0mSDh06VLOQAABUAysgABCACgoKtH//fvXo0UOtWrWqcLuQkBDVr1/fwGQAgGBHAQEAAABgGAoIAFhYSUmJ2REAAKhVFBAAsKiysjLl5eWZHQMAgFpFAQEAgz333HMKCQnx+k98fLx++OEHSfLpwYAtW7ZUt27dtHv3bh0/frzC7RwOh8rKyiS5P/gQAIC6QgEBgADUqFEj17M/CgsLK9yuqKhIR44ckSRdffXVhmQDAAQ3CggAGGz69OlyOBxe/1m1apVatmzp83+jRYsWuv766yVVfnvd/Px8HT16VOHh4a7tAQCoSxQQAAhATZs2VWRkpCRp69atOnv2rNftvv76a+3du1fR0dHq0KGDgQkBAMGKAgIAASgkJER9+/ZVhw4dtHjxYm3YsMHjmpJjx47p7bffliQNHTpU7dq1MyMqACDIUEAAwKJ2797tepp5TURGRmry5MkqKCjQ5MmT9f7776uoqEjl5eXas2ePHn30US1fvlwDBgzQuHHjFBISUovpAQDwjlueAECAstls+s1vfqO8vDzNnj1bCQkJSkhIcNsmOjpaL730kq688kqTUgIAgg0rIAAQwJo0aaIZM2Zo5cqVuvvuu9WiRQtJPxWPl19+WcuWLVNUVJTJKQEAwYQVEADwM126dNGuXbuqvH2DBg0UHx+v+Pj4ugsFAEAVsQICAAAAwDAUEAAAAACGoYAAAAAAMAwFBAAAAIBhKCAAAAAADEMBAQAAAGAYCggAAAAAw1BAAAAAABiGAgIAAADAMBQQAAAAAIahgAAAAAAwzP8H0JFduuWRSxsAAAAASUVORK5CYII=
Given the graph of $f(x)$ shown to the right, write the limit statement to describe the function's behavior around the neighborhood of $x=1$.
$\lim_{{x \to 1}} f(x) = $\lim_{x\to1}f(x)=0$$
d3cdc4b9-7a58-4198-ba50-e9f278bf2aa3
multivariable_calculus
false
null
Evaluate $L=\lim_{(x,y) \to (-1,1)}\left(\frac{ x \cdot y \cdot (x+y)-5 \cdot y \cdot (y+5)+5 \cdot x \cdot (x-5) }{ x^2+y^2+2 \cdot x \cdot y+5 \cdot x+5 \cdot y }\right)$.
The final answer: $L=-\frac{36}{5}$
d41983e6-eea1-4dfa-8060-ce53dcd25940
precalculus_review
false
null
A rental car company rents cars for a flat fee of $\$20$ and an hourly charge of $\$10.25$. Therefore, the total cost $C$ to rent a car is a function of the hours $t$ the car is rented plus the flat fee. 1. Write the formula for the function that models this situation. 2. Find the total cost to rent a car for 2 days and 7 hours. 3. Determine how long the car was rented if the bill is $\$432.73$.
1. The formula for the function is $C(t)$ = $10.25\cdot t+20$ 2. The total cost to rent a car is $ $583.75$ 3. The time of car rental in hours is $40.26634146$
d430a0dd-708d-4daa-8072-d39638d29242
differential_calc
false
null
A box is to be made with the following properties: 1. The length of the base, $l$, is twice the length of a width $w$. 2. The cost of material to be used for the lateral faces and the top of the box is three times the cost of the material to be used for the lower base. Find the dimensions of the box in terms of its fixed volume $V$ such that the cost of the used material is the minimum.
The final answer: $w=\frac{1}{2}\cdot\sqrt[3]{\frac{9\cdot V}{2}}$, $l=\sqrt[3]{\frac{9\cdot V}{2}}$, $y=\frac{2}{3}\cdot\sqrt[3]{\frac{4\cdot V}{3}}$
d4ce3600-3ef0-47d0-8550-0158a474ed33
differential_calc
true
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
Given $k(x) = \frac{ f(x) }{ g(x) }$, find $k'(-1)$ using the table below:
$k'(-1)$ = $1$
d4f54a6b-e604-4bf3-8782-acbc409ea7d2
algebra
false
null
Solve the quadratic equation by completing the square. Show each step. (Give your answer either exactly or rounded to two decimal places). $2 + z = 6 \cdot z^2$
$z$ = $\frac{2}{3}$, $-\frac{1}{2}$
d503c1fb-2754-4803-b9ac-6462fc93e8db
differential_calc
false
null
Find the derivative of the 27th order $y^{(27)}$ for a function $y = 2 \cdot x^2 \cdot \sin(x)$.
$y^{(27)}$ = $1404\cdot\cos(x)-2\cdot x^2\cdot\cos(x)-108\cdot x\cdot\sin(x)$
d541eb2d-198c-47dd-8811-79633c9e701e
integral_calc
false
null
Solve the integral: $$ \int \frac{ 1 }{ \sin(x)^5 } \, dx $$
The final answer: $C+\frac{1}{16}\cdot\left(2\cdot\left(\tan\left(\frac{x}{2}\right)\right)^2+6\cdot\ln\left(\left|\tan\left(\frac{x}{2}\right)\right|\right)+\frac{1}{4}\cdot\left(\tan\left(\frac{x}{2}\right)\right)^4-\frac{2}{\left(\tan\left(\frac{x}{2}\right)\right)^2}-\frac{1}{4\cdot\left(\tan\left(\frac{x}{2}\right)\right)^4}\right)$
d57c2f7d-971f-43c9-bb9e-25e15c923b21
multivariable_calculus
false
null
The solid $Q$ has the mass given by the triple integral: $$ \int_{0}^1 \left( \int_{0}^{\frac{ \pi }{ 2 }} \left( \int_{0}^{r^2} \left( r^4 + r \right) dz \right) d \theta \right) dr $$ 1. Find the density of the solid in rectangular coordinates. 2. Find the moment $M_{xy}$ about the xy-plane.
1. $\rho(x,y,z)$ = $1+\left(x^2+y^2\right)^{\frac{3}{2}}$ 2. $M_{xy}$ = $\frac{5\cdot\pi}{72}$
d5eda09b-3de0-441e-a722-ccb5244adbb9
integral_calc
false
null
Solve the integral: $$ \int \frac{ \sqrt{9 \cdot x+4} }{ -3 \cdot x^2 } \, dx $$
$\int \frac{ \sqrt{9 \cdot x+4} }{ -3 \cdot x^2 } \, dx$ = $C+\frac{\sqrt{9\cdot x+4}}{3\cdot x}-\frac{3}{4}\cdot\ln\left(\frac{\left|\sqrt{9\cdot x+4}-2\right|}{2+\sqrt{9\cdot x+4}}\right)$
d5fcba67-c072-4cb0-8f4d-9da61c993923
algebra
false
null
Evaluate the expression $\frac{ (2+i) \cdot (4-2 \cdot i) }{ (1+i) }$ and write the result as a simplified complex number.
$\frac{ (2+i) \cdot (4-2 \cdot i) }{ (1+i) }$ = $5-5\cdoti$
d602c133-9e68-402e-9b69-01ca11fa01fd
integral_calc
false
null
Compute the integral: $$ \int \frac{ 2 \cdot x+1 }{ (x-1) \cdot \sqrt{x^2-4 \cdot x+2} } \, dx $$
$\int \frac{ 2 \cdot x+1 }{ (x-1) \cdot \sqrt{x^2-4 \cdot x+2} } \, dx$ = $2\cdot\ln\left(\left|x-2+\sqrt{x^2-4\cdot x+2}\right|\right)-3\cdot\arcsin\left(\frac{x}{(x-1)\cdot\sqrt{2}}\right)+C$
d666f55d-1b0e-4b1c-821c-ddf1d1ea87df
integral_calc
false
null
Compute the integral: $$ \int \frac{ -1 }{ 3 \cdot \sin\left(\frac{ x }{ 3 }\right)^6 } \, dx $$
$\int \frac{ -1 }{ 3 \cdot \sin\left(\frac{ x }{ 3 }\right)^6 } \, dx$ = $\frac{\cos\left(\frac{x}{3}\right)}{5\cdot\sin\left(\frac{x}{3}\right)^5}-\frac{4}{15}\cdot\left(-\frac{\cos\left(\frac{x}{3}\right)}{\sin\left(\frac{x}{3}\right)^3}-2\cdot\cot\left(\frac{x}{3}\right)\right)+C$
d6cfc281-9a27-43ac-b0d7-17e6d64a8bf9
multivariable_calculus
false
null
Find the equation of a quadratic curve, which passes through the origin, and is tangent to $4 \cdot x + 3 \cdot y + 2 = 0$ at $(1,-2)$ and to $x - y - 1 = 0$ at $(0,-1)$.
The final answer: $6\cdot x^2-y^2+3\cdot x\cdot y+2\cdot x-y=0$
d6d00db5-5433-4e2e-be1f-07df6d0782c8
multivariable_calculus
false
null
Find the first derivative $y_{x}'$ of the function: $$ x = \arcsin\left(\frac{ t }{ \sqrt{2+2 \cdot t^2} }\right), \quad y = \arccos\left(\frac{ 1 }{ \sqrt{2+2 \cdot t^2} }\right), \quad t \ge 0 $$
$y_{x}'$ = $\frac{t\cdot\sqrt{t^2+2}}{\sqrt{2\cdot t^2+1}}$
d6d0e931-8b06-4a31-80b1-2abb2700d680
precalculus_review
false
null
1. Find the inverse function of $f(x) = (x-1)^2$, for $x \le 1$. 2. Find the domain of the inverse function. 3. Find the range of the inverse function.
1. The inverse function is: $1-\sqrt{x}$ 2. The domain of the inverse function is: $x\ge0$ 3. The range of the inverse function is: $y\le1$
d6e1f663-40a9-40f9-a0c7-53c225984de0
multivariable_calculus
false
null
Find the area of the region $R$ bounded by circles $x^2+y^2=1$ and $x^2+y^2=4$ and the lines $y=x$ and $y=\sqrt{3} \cdot x$.
The final answer: $\frac{\pi}{8}$
d6ec8d67-1fdb-4d5b-ba6c-40d38b33cabb
algebra
false
null
Solve the following equations: 1. $\frac{ 3 }{ 4 } (x+9) = 15$ 2. $\frac{ 2 }{ 3 } (m-8) = 4$ 3. $\frac{ 1 }{ 8 } (b+2) = \frac{ 3 }{ 8 }$ 4. $\frac{ 1 }{ 7 } (x-4) = -\frac{ 1 }{ 2 }$ 5. $\frac{ 2 }{ 5 } (-3-2 x) = \frac{ 18 }{ 5 }$ 6. $\frac{ 4 }{ 5 } (j+5) = \frac{ 2 }{ 5 }$
The solutions to the given equations are: 1. $x=11$ 2. $m=14$ 3. $b=1$ 4. $x=\frac{ 1 }{ 2 }$ 5. $x=-6$ 6. $j=\frac{ -9 }{ 2 }$
d6fcf747-13d5-42bb-99f4-1c6e55d5cdb5
multivariable_calculus
false
null
Consider a rectangular box of width $w$, length $l$, and height $h$ without a lid. If the box is to be made from $12$ sq. cm of cardboard, find the dimensions that maximize the volume of the box and the maximum possible volume itself.
Optimal dimensions: $w$: $2$ $l$: $2$ $h$: $1$ Maximum volume: $4$
d7685a03-c915-479a-bc22-d9a0106fca54
precalculus_review
false
null
State the domain and range of the function: $f(x) = \ln(x-5)$ 1. Domain 2. Range
1. Domain: $(5,\infty)$ 2. Range: $(-\infty,\infty)$
d78475ef-cb8a-41af-9269-a2327c4a2fff
differential_calc
false
null
Make full curve sketching of $y = \sqrt[3]{9 \cdot x^2 - x^3}$. 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) $(-1\cdot\infty,\infty)$ 2. Vertical asymptotes None 3. Horizontal asymptotes None 4. Slant asymptotes $y=-x+3$ 5. Intervals where the function is increasing $(0,6)$ 6. Intervals where the function is decreasing $(-\infty,0)$, $(6,\infty)$ 7. Intervals where the function is concave up $(9,\infty)$ 8. Intervals where the function is concave down $(-\infty,0)$, $(0,9)$ 9. Points of inflection $P(9,0)$
d8e23310-2d6a-4413-9633-55f92b63775c
algebra
false
null
Recall the formula for calculating the magnitude of an earthquake, $M=\frac{ 2 }{ 3 } \cdot \log_{10}\left(\frac{ S }{ S_{0} }\right)$. One earthquake has magnitude $3.9$ on the MMS scale. If a second earthquake has $750$ times as much energy as the first, find the magnitude of the second quake. Round to the nearest hundredth.
Magnitude of the second quake: $5.82$
d906874a-47e3-404c-9e09-885002ec79f3
algebra
false
null
Find the solution to the following inequality and express it in interval notation: $$ 5 (x-7) (x+3) (x-2) < 0 $$
The solution set to the inequality is: $\left(-\infty,\ -3\right)\cup\left(2,\ 7\right)$
d920bf7f-8420-4c43-9f6a-e8ac4d3f2423
differential_calc
true
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
The functions $f$ and $g$ are differentiable functions. The graphs of $f'$ and $g'$, the derivatives of $f$ and $g$ respectively, are shown. Let $h(x) = \frac{ f(x) }{ 2 } - \frac{ 3 \cdot g(x) }{ 4 } + 2 \cdot x^2$. Find $h'(2)$. | | | --- |
$h'(2)$ = $10$
d930869f-c932-4aba-a4ea-e00bc94237a8
integral_calc
false
null
Compute the area of the figure bounded by curves $y = 8 \cdot x^2$, $y = 4 + 4 \cdot x^2$, lines $x = 3$, $x = -2$, and the $x$-axis.
Area = $\frac{184}{3}$
d982ac94-be51-47d3-a37f-8d59be82c81e
precalculus_review
false
null
Find points on a coordinate plane that satisfy the following equation: $$ 10 \cdot x^2 + 29 \cdot y^2 + 34 \cdot x \cdot y + 8 \cdot x + 14 \cdot y + 2 = 0 $$
The final answer: $(3,-2)$
d9a85aa2-237a-48ee-aa50-dadd42070cd8
sequences_series
false
null
Find the radius of convergence and sum of the series: $$ \frac{ 3 }{ 2 }+\frac{ 3 \cdot x }{ 1 \cdot 3 }+\frac{ 3 \cdot x^2 }{ 1 \cdot 2 \cdot 4 }+\cdots+\frac{ 3 \cdot x^n }{ \left(n!\right) \cdot (n+2) }+\cdots $$
1. Radius of convergence: $R=\infty$ 2. Sum: $f(x)=\begin{cases}\frac{3}{x^2}+\frac{3\cdot x\cdot e^x-3\cdot e^x}{x^2},&x\ne0\\\frac{3}{2},&x=0\end{cases}$
da100f17-a491-4014-8c00-0061a65cc2b4
precalculus_review
false
null
1. Find the inverse function of $f(x) = \frac{ 1 }{ x+2 }$ 2. Find the domain of the inverse function 3. Find the range of the inverse function
1. The inverse function is: $\frac{1}{x}-2$ 2. The domain of the inverse function is: $(-\infty,0)\cup(0,\infty)$ 3. The range of the inverse function is: $(-\infty,-2)\cup(-2,\infty)$
da29a7ac-6d10-4e13-9fc6-088951921221
multivariable_calculus
false
null
Evaluate $I=\int_{0}^4 \int_{0}^x \int_{0}^{x+y} \left(3 \cdot e^x \cdot (y+2 \cdot z)\right) dz dy dx$.
The final answer: $I=19\cdot\left(17\cdot e^4+3\right)$
da7e571f-2201-495c-a7df-955283c258ef
algebra
false
null
Divide rational expressions and simplify it: $$ \frac{ x^2-9 }{ 3 } \div \frac{ x-3 }{ 4 } $$
The final answer: $\frac{4}{3}\cdot x+4$
daa2fcb5-aa37-4baf-9417-863cc372bd78
differential_calc
false
null
For the curve $x = a \cdot \left(t - \sin(t)\right)$, $y = a \cdot \left(1 - \cos(t)\right)$, determine the curvature. Use $a = 12$.
The curvature is: $\frac{1}{48\cdot\left|\sin\left(\frac{t}{2}\right)\right|}$
dac50753-b5d3-4c11-a1c7-1575dde6e606
integral_calc
true
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
The following table lists the $2013$ schedule of federal income tax versus taxable income: Federal Income Tax Versus Taxable Income Suppose that Steve just received a $10,000 raise. How much of this raise is left after federal taxes if Steve's salary before receiving the raise was 1. $\$40,000$, 2. $\$90,000$, and 3. $\$385,000$?
1. If Steve's salary before receiving the raise is $\$40,000$, $$7500$$ is left. 2. If Steve's salary before receiving the raise is $\$90,000$, $$7200$$ is left. 3. If Steve's salary before receiving the raise is $\$385,000$, $$6700$$ is left.
dacc8400-999f-45b5-9169-bbc3631b4aeb
multivariable_calculus
false
null
Let $z = x^2 + 3 \cdot x \cdot y - y^2$. Find the exact change $\Delta z = f\left(x+\Delta x,y+\Delta y\right) - f(x,y)$ in the function and find the approximate change $d z$ in the function as $x$ changes from $2$ to $2.05$ and $y$ changes from $3$ to $2.96$.
The final answer: 1. The exact change $\Delta z$ is $0.6449$ 2. The approximate change $d z$ is $0.65$
db0e5db4-a7a3-45e3-abc6-9ae4b77fcf97
algebra
false
null
Add and subtract the rational expressions, and then simplify: $$ \frac{ x-4 }{ x+4 } - \frac{ 2 \cdot x+6 }{ 2 \cdot x+1 } $$
The final answer: $\frac{-21\cdot x-28}{2\cdot x^2+9\cdot x+4}$
db737faf-9359-40c5-9af9-bd828d9cb054
precalculus_review
false
null
Simplify the expression $\frac{ \cos(t) }{ \sin(t) }+\frac{ \sin(t) }{ 1+\cos(t) }$ by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only.
$\frac{ \cos(t) }{ \sin(t) }+\frac{ \sin(t) }{ 1+\cos(t) }$ = $\csc(t)$
db73d0f5-3e61-4495-9063-c8cb58f9e4b3
multivariable_calculus
false
null
Evaluate $L=\lim_{(x,y) \to (3,3)}\left(\frac{ x^6-y^6 }{ x^2+x^2 \cdot y-x \cdot y^2-y^2 }\right)$
The final answer: $L=\frac{486}{5}$
db7ee4b1-97eb-441e-8ab6-9f71a248e8be
integral_calc
false
null
Compute the integral: $$ \int \frac{ 10 }{ \sin(4 \cdot x)^6 } \, dx $$
$\int \frac{ 10 }{ \sin(4 \cdot x)^6 } \, dx$ = $C-\frac{1}{2}\cdot\left(\cot(4\cdot x)\right)^5-\frac{5}{2}\cdot\cot(4\cdot x)-\frac{5}{3}\cdot\left(\cot(4\cdot x)\right)^3$
db996e6d-cc8a-4fb9-84e6-66007524a88c
precalculus_review
false
null
Find the zeros of the function $f(x) = \left(1 - \tan(x)\right) \cdot \left(1 + \sin(2 \cdot x)\right) - \tan(x) + \cos(2 \cdot x) - 1$.
The final answer: $x_1=-\frac{\pi}{4}+\pi\cdot n$, $x_2=\arctan\left(\frac{1}{2}\right)+\pi\cdot n$
dc06d10a-40f2-42cc-a038-53faf5f27d1c
sequences_series
false
null
Find the Fourier series of the periodic function $f(x) = x^2$ in the interval $-\pi \le x < \pi$ if $f(x) = f(x + 2 \cdot \pi)$.
The Fourier series is: $x^2=\frac{\pi^2}{3}-4\cdot\left(\frac{\cos(x)}{1^2}-\frac{\cos(2\cdot x)}{2^2}+\frac{\cos(3\cdot x)}{3^2}-\cdots\right)$
dc20dd10-80d5-4ed4-8e8b-1f706dc8ffb6
sequences_series
false
null
Evaluate the telescoping series or state whether the series diverges: $$ \sum_{n=1}^\infty \left(\sin(n)-\sin(n+1)\right) $$
$S_{k}$ -> None as $k$ -> $\infty$.
dc221026-1425-4caa-9b02-8ddde198eebe
multivariable_calculus
false
null
Express the region $D$ in polar coordinates. $D$ = $\left\{(x,y)|x^2+y^2 \le 4 \cdot x\right\}$ ($a \le \theta \le b$, $a \ge 0$, $b \ge 0$).
1. The interval for $r$ is $\left[0,4\cdot\cos\left(\theta\right)\right]$; 2. The interval for $\theta$ is $\left[\frac{3}{2}\cdot\pi,\frac{5\cdot\pi}{2}\right]$.
dc3838be-dabf-496c-90ab-3fe766bda473
differential_calc
true
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
The graph below is a function, $j$, whose domain is the set of all real numbers and is continuous everywhere. Determine the x-values for points of inflection.
There is a point of inflection at x-value(s): $x=-2.5$, $x=0$, $x=2.5$
dc71824f-02b4-4210-a32a-0d141c9fcf5c
precalculus_review
false
null
Simplify the expression $\frac{ 1+\tan\left(\alpha\right)^2 }{ 1+\cot\left(\alpha\right)^2 }$ by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only.
$\frac{ 1+\tan\left(\alpha\right)^2 }{ 1+\cot\left(\alpha\right)^2 }$ = $\tan\left(\alpha\right)^2$
dcb60112-7be2-4d1a-b711-5f77dd0dc4bd
integral_calc
false
null
Find the integral: $$ \int \frac{ 1 }{ \sqrt[3]{\left(\sin(x)\right)^{11} \cdot \cos(x)} } \, dx $$
$\int \frac{ 1 }{ \sqrt[3]{\left(\sin(x)\right)^{11} \cdot \cos(x)} } \, dx$ = $-\frac{3\cdot\left(1+4\cdot\left(\tan(x)\right)^2\right)}{8\cdot\left(\tan(x)\right)^2\cdot\sqrt[3]{\left(\tan(x)\right)^2}}+C$
dce6ec64-2f61-4db6-9f12-8e5de1da1c22
multivariable_calculus
false
null
Find the tangential and normal components of acceleration for $\vec{r}(t) = \left\langle a \cdot \cos\left(\omega \cdot t\right), b \cdot \sin\left(\omega \cdot t\right) \right\rangle$ at $t=0$.
The final answer: 1. The tangential component of acceleration, $a_{t}$, is: $0$ 2. The normal component of acceleration, $a_{N}$, is: $\omega^2\cdot|a|$
dd266316-efe9-4f84-ba9d-09ebb753bc3c
integral_calc
false
null
Consider the Karun-$3$ dam in Iran. Its shape can be approximated as an isosceles triangle with height $205$ m and width $388$ m. Assume the current depth of the water is $180$ m. The density of water is $1000$ kg/$m^3$. Find the total force on the wall of the dam.
The total force : $18028940487.8049$
dd3412c0-c4c3-4b9f-8035-8467e18b9f5f
precalculus_review
false
null
Calculate $\cos\left(\frac{ \pi }{ 12 }\right)$.
The final answer: $\cos\left(\frac{\pi}{12}\right)=\frac{\sqrt{2}+\sqrt{6}}{4}$
de2bd512-089e-4d1e-b577-dd185962e7cf
differential_calc
false
null
Sketch the curve: $y = 3 \cdot x \cdot \sqrt{2-x^2}$. 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): $\left[-1\cdot2^{2^{-1}},2^{2^{-1}}\right]$ 2. Vertical asymptotes: None 3. Horizontal asymptotes: None 4. Slant asymptotes: None 5. Intervals where the function is increasing: $(-1,1)$ 6. Intervals where the function is decreasing: $\left(-2^{2^{-1}},-1\right)$, $\left(1,2^{2^{-1}}\right)$ 7. Intervals where the function is concave up: $\left(-2^{2^{-1}},0\right)$ 8. Intervals where the function is concave down: $\left(0,2^{2^{-1}}\right)$ 9. Points of inflection: $P(0,0)$
df12f49b-9f83-4e83-bf35-dcfb2c0375ce
sequences_series
false
null
Find the sum of the series $\sum_{n=1}^\infty \frac{ x^{4 \cdot n-3} }{ 4 \cdot n-3 }$. (Use differentiation of the series)
The sum of the series is $\frac{1}{4}\cdot\ln\left(\frac{|x+1|}{|x-1|}\right)+\frac{1}{2}\cdot\arctan(x)$
df82e2b4-2fde-4ea7-8256-2cefd78de08c
differential_calc
false
null
For the function $y = \sqrt[3]{2-x} + \frac{ 1 }{ 9 } \cdot x^2$ determine the intervals, where the function is concave up and concave down and points of inflection. Submit as your final answer: 1. Interval(s) where the function is concave up 2. Interval(s) where the function is concave down 3. Point(s) of inflection
1. Interval(s) where the function is concave up: $(-\infty,1)$, $(2,\infty)$ 2. Interval(s) where the function is concave down: $(1,2)$ 3. Point(s) of inflection: $P\left(1,\frac{10}{9}\right)$, $P\left(2,\frac{4}{9}\right)$
df9d5d54-0fe2-4815-8a98-f454e166f165
sequences_series
false
null
Determine the Taylor series for $f(x) = \frac{ 2 \cdot x - 1 }{ x^2 - 3 \cdot x + 2 }$, centered at $x_{0} = 4$. Write out the sum of the first four non-zero terms, followed by dots.
The final answer: $\frac{7}{6}+\left(\frac{1}{3^2}-\frac{3}{2^2}\right)\cdot(x-4)-\left(\frac{1}{3^3}-\frac{3}{2^3}\right)\cdot(x-4)^2+\left(\frac{1}{3^4}-\frac{3}{2^4}\right)\cdot(x-4)^3+\cdots$
dfce03fb-fa8b-46ea-94b9-343e9c0ada11
integral_calc
false
null
Compute the length of the arc $y = 2 \cdot \ln(3 \cdot x)$ between the points $x = \sqrt{5}$ and $x = 2 \cdot \sqrt{3}$.
Arc Length: $1+\ln\left(\frac{5}{3}\right)$
e01089ef-d282-4c55-b0cc-0fb6bc6d2bdf
precalculus_review
false
null
Solve $2 \cdot \left(\arcsin(x)\right)^2 - \arcsin(x) - 6 = 0$.
The final answer: $x=-\sin(1.5)$
e09be213-4d6a-4283-860d-c2f57bdaf5d4
algebra
false
null
Let $f(x) = \frac{ 1 }{ x }$. Find the number $b$ such that the average rate of change of $f$ on the interval $(2,b)$ is $-\frac{ 1 }{ 10 }$.
The final answer: $b=5$
e12228fb-4501-47ee-83fc-3c74da98cc45
multivariable_calculus
false
null
Use two circular permutations of the variables $x$, $y$, and $z$ to write new integral whose value equal the value of the original integral. A circular permutation of $x$, $y$, and $z$ is the arrangement of the numbers in one of the following orders: $y$, $z$, and $x$ or $z$, $x$, and $y$: $$ \int_{0}^1 \int_{1}^3 \int_{2}^4 \left(x^2 \cdot z^2 + 1\right) \, dx \, dy \, dz $$
1. $I$ with $d z \cdot d x \cdot d y$ is $\frac{148}{9}$ 2. $I$ with $d y \cdot d z \cdot d x$ is $\frac{148}{9}$
e1380c07-189c-47d2-92c7-e5456c086a22
algebra
false
null
Solve the following equations: 1. $-15c = -75$ 2. $-8 + r = 27$ 3. $19 + m = 3$ 4. $-\frac{w}{8} = 1$ 5. $p - 4.8 = 11.2$ 6. $\frac{g}{3.4} = 2.2$ 7. $3.6m = 25.2$ 8. $\frac{2}{5}t = \frac{8}{25}$ 9. $5\frac{5}{6} + m = 3\frac{5}{12}$
The solutions to the given equations are: 1. $c=5$ 2. $r=35$ 3. $m=-16$ 4. $w=-8$ 5. $p=16$ 6. $g=7.48$ 7. $m=7$ 8. $t=\frac{ 4 }{ 5 }$ 9. $m=-\frac{ 29 }{ 12 }$
e13c1022-2adc-4e50-a481-b6d868cea5be
multivariable_calculus
false
null
The volume of a right circular cylinder is given by $V(x,y) = \pi \cdot x^2 \cdot y$ where $x$ is the radius of the cylinder and $y$ is the cylinder height. Suppose $x$ and $y$ are functions of $t$ given by $x = \frac{ 1 }{ 2 } \cdot t$ and $y = \frac{ 1 }{ 3 } \cdot t$ so that $x$ and $y$ are both increasing with time. How fast is the volume increasing when $x=2$ and $y=5$?
The volume is increasing at a rate of $\frac{34\cdot\pi}{3}$
e159cbdd-10fe-4676-a0b0-6425fc80a525
differential_calc
false
null
For the function $y = \frac{ 2 \cdot x + 3 }{ 4 \cdot x + 5 }$ find the derivative $y^{(n)}$.
The General Form of the Derivative of $y = \frac{ 2 \cdot x + 3 }{ 4 \cdot x + 5 }$: $y^{(n)}=\frac{1}{2}\cdot(-1)^n\cdot\left(n!\right)\cdot4^n\cdot(4\cdot x+5)^{-(n+1)}$
e16f36eb-5794-4d0a-9b53-77b2e1730e59
differential_calc
false
null
Find the $x$-coordinate for each critical point of $f(x) = e^{-x} \cdot \sqrt{x}$
$x$ = $\frac{1}{2}$, $0$
e1c6ee2e-873b-4879-a3ef-f06229679527
sequences_series
false
null
Find the 3rd order Taylor polynomial $P_{3}(x)$ for the function $f(x) = \arctan(x)$ in powers of $x-1$ and give the Lagrange form of the remainder.
$P_{3}(x)$ = $\frac{ \pi }{ 4 }+\frac{ 1 }{ 2 } \cdot (x-1)-\frac{ 1 }{ 4 } \cdot (x-1)^2+\frac{ 1 }{ 12 } \cdot (x-1)^3$ $R_{3}(x)$ = $\frac{ -\frac{ 48 \cdot c^3 }{ \left(1+c^2\right)^4 }+\frac{ 24 \cdot c }{ \left(1+c^2\right)^3 } }{ 4! } \cdot (x-1)^4$
e1d09bc3-2f9a-4138-9ee0-fd559f60f732
differential_calc
false
null
Find $\frac{ d y }{d x}$ if $y = \frac{ 5 \cdot x^2 - 3 \cdot x }{ \left( 3 \cdot x^7 + 2 \cdot x^6 \right)^4 }$.
$\frac{ d y }{d x}$ = $\frac{-390\cdot x^2+23\cdot x+138}{x^{24}\cdot(3\cdot x+2)^5}$
e20ecd1f-1245-4ec5-959b-ea8ea17a5d1e
sequences_series
false
null
Find $\lim_{n \to \infty} \left(x_{n}\right)$, where $x_{n} = \left(\frac{ 2 \cdot n^3 }{ 2 \cdot n^2+3 }+\frac{ 1-5 \cdot n^2 }{ 5 \cdot n+1 }\right)$ is the general term of a sequence.
The final answer: $L=\frac{1}{5}$
e26ffc23-804d-4eaf-9729-1820407e0c76
multivariable_calculus
true
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
Find the average value of the function $f(x,y) = 3 \cdot x \cdot y$ on the region $D$:
The average value is $\frac{27}{20}$
e2afa39f-a784-407d-be4f-00e90b4ec92e
precalculus_review
false
null
Is the statement True or False? The following linear programming problem is infeasible. Maximize $f = 4 \cdot x_{1} - x_{2}$ subject to $x_{1} - x_{2} \le 3$ $-x_{1} + 3 \cdot x_{2} \le -5$ $x_{1} \ge 0$, $x_{2} \ge 0$
The final answer: $T\cdot r\cdot u\cdot e$
e2ec6409-4e11-40cc-a4a2-6c6b8f85fc24
precalculus_review
false
null
Solve the exponential equation exactly: $4^{x+1} - 32 = 0$
$x$ = $\frac{3}{2}$
e33483e5-a385-4ce3-91af-54df50ca062b
differential_calc
false
null
Sketch the curve: $$ y = 4 \cdot x^2 \cdot e^{\frac{ 1 }{ 2 \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}{4},\infty\right)$ 6. Intervals where the function is decreasing: $\left(0,\frac{1}{4}\right)$, $(-\infty,0)$ 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
e39d239e-1f98-4224-8c4c-dc39999c7faf
differential_calc
false
null
Make full curve sketching of $f(x) = \frac{ 3 \cdot x^3 }{ 2 \cdot x^2 - 3 }$. Submit as your final answer: 1. The domain (in interval notation) 2. Vertical asymptote(s) 3. Horizontal asymptote(s) 4. Slant asymptote(s) 5. Interval(s) where the function is increasing 6. Interval(s) where the function is decreasing 7. Interval(s) where the function is concave up 8. Interval(s) where the function is concave down 9. Point(s) of inflection
1. The domain (in interval notation) $\left(-1\cdot\infty,-1\cdot3^{2^{-1}}\cdot2^{-1\cdot2^{-1}}\right)\cup\left(-1\cdot3^{2^{-1}}\cdot2^{-1\cdot2^{-1}},3^{2^{-1}}\cdot2^{-1\cdot2^{-1}}\right)\cup\left(3^{2^{-1}}\cdot2^{-1\cdot2^{-1}},\infty\right)$ 2. Vertical asymptote(s) $x=\frac{\sqrt{3}}{\sqrt{2}}$, $x=-\frac{\sqrt{3}}{\sqrt{2}}$ 3. Horizontal asymptote(s) None 4. Slant asymptote(s) $y=\frac{3}{2}\cdot x$ 5. Interval(s) where the function is increasing $\left(-\infty,-\frac{3}{\sqrt{2}}\right)$, $\left(\frac{3}{\sqrt{2}},\infty\right)$ 6. Interval(s) where the function is decreasing $\left(-\frac{3}{\sqrt{2}},-\frac{\sqrt{3}}{\sqrt{2}}\right)$, $\left(-\frac{\sqrt{3}}{\sqrt{2}},0\right)$, $\left(0,\frac{\sqrt{3}}{\sqrt{2}}\right)$, $\left(\frac{\sqrt{3}}{\sqrt{2}},\frac{3}{\sqrt{2}}\right)$ 7. Interval(s) where the function is concave up $\left(-\frac{\sqrt{3}}{\sqrt{2}},0\right)$, $\left(\frac{\sqrt{3}}{\sqrt{2}},\infty\right)$ 8. Interval(s) where the function is concave down $\left(-\infty,-\frac{\sqrt{3}}{\sqrt{2}}\right)$, $\left(0,\frac{\sqrt{3}}{\sqrt{2}}\right)$ 9. Point(s) of inflection $P(0,0)$
e3f282dc-5d88-47c9-a17b-5900c9e45805
integral_calc
false
null
Find the area of the surface formed by rotating the arc of the circle $x^2 + y^2 = 1$ between the points $(1,0)$ and $(0,1)$ in the first quadrant, around the line $x + y = 1$.
The final answer: $\frac{4\cdot\pi-\pi^2}{\sqrt{2}}$
e47cac1c-64b3-44fb-a64c-e30da6bea8bd
precalculus_review
false
null
Use the double-angle formulas to evaluate the integral: $$ \int \sin(x)^2 \, dx + \int \cos(x)^2 \, dx $$
$\int \sin(x)^2 \, dx + \int \cos(x)^2 \, dx$ = $x+C$
e4cbc0e5-b562-4a04-b2af-dab4fd6cba29
differential_calc
false
null
Calculate the derivative of the function $r = 9 \cdot \ln\left(\sqrt[3]{\frac{ 1+\tan\left(\frac{ \varphi }{ 3 }\right) }{ 1-\tan\left(\frac{ \varphi }{ 3 }\right) }}\right)$.
$r'$ = $2\cdot\sec\left(\frac{2\cdot\varphi}{3}\right)$
e4e2cd9f-3550-4c70-ae5f-41f38df496e0
sequences_series
false
null
Find the radius of convergence and sum of the series: $$ \frac{ 1 }{ 3 }+\frac{ x }{ 1 \cdot 4 }+\frac{ x^2 }{ 1 \cdot 2 \cdot 5 }+\cdots+\frac{ x^n }{ \left(n!\right) \cdot (n+3) }+\cdots $$
1. Radius of convergence: $R=\infty$ 2. Sum: $f(x)=\begin{cases}\frac{x\cdot\left(2\cdot e^x-2\cdot x\cdot e^x\right)+e^x\cdot x^3}{x^4}-\frac{2}{x^3},&x\ne0\\\frac{1}{3},&x=0\end{cases}$
e50e9658-dc0f-4685-8298-ba3fdc11e9f0
integral_calc
false
null
Compute the integral: $$ \int \frac{ 1 }{ \sin(x)^6 } \, dx $$
$\int \frac{ 1 }{ \sin(x)^6 } \, dx$ = $-\frac{\cos(x)}{5\cdot\sin(x)^5}+\frac{4}{5}\cdot\left(-\frac{\cos(x)}{3\cdot\sin(x)^3}-\frac{2}{3}\cdot\cot(x)\right)$
e5720838-c669-4dd3-a936-ff2b5c33436f
sequences_series
false
null
Consider the power series $\sum_{k=1}^\infty \frac{ (2 \cdot x+1)^k }{ 2^k \cdot \sqrt{k} }$. 1. Find the center of convergence of the series. 2. Find the radius of convergence of the series.
1. The center of convergence is $a=-\frac{1}{2}$ 2. The radius of convergence is $R=1$
e580db01-e32b-49d4-810e-5a37e87204b8
sequences_series
false
null
Express the series $\sum_{k=0}^\infty\left(x^k-x^{2 \cdot k+1}\right)$ in terms of elementary functions and find the radius of convergence of the sum.
1. $\sum_{k=0}^\infty\left(x^k-x^{2 \cdot k+1}\right)$ = $\frac{1}{1-x^2}$ 2. radius of convergence $R$ = $1$
e589347b-40ae-472d-bd48-78cbed301827
multivariable_calculus
false
null
Determine a definite integral that represents the area enclosed by the inner loop of $r = 3 - 4 \cdot \cos(\theta)$.
The final answer: $\int_0^{\arccos\left(\frac{3}{4}\right)}\left(3-4\cdot\cos\left(\theta\right)\right)^2d\theta$
e613669c-e828-4933-8ad1-68615e2e0b67
multivariable_calculus
false
null
The position of a particle at time $t$ is given by $\vec{r}(t) = \left\langle \frac{ t^2 }{ 2 },\frac{ 2 \cdot \sqrt{2} }{ 3 } \cdot t^{\frac{ 3 }{ 2 }},t \right\rangle$. 1. Find the velocity vector of the particle. 2. Find the acceleration vector of the particle. 3. Find the distance traveled by the particle between the points $P(0,0,0)$ and $P\left(\frac{ 1 }{ 2 },\frac{ 2 \cdot \sqrt{2} }{ 3 },1\right)$.
1. $\left\langlet,\sqrt{2}\cdot\sqrt{t},1\right\rangle$ 2. $\left\langle1,\frac{1}{\sqrt{2}\cdot\sqrt{t}},0\right\rangle$ 3. $\frac{3}{2}$
e694511e-0873-4b17-82a8-6e13ecc589c1
sequences_series
false
null
Expand the function $y = \ln\left(x + \sqrt{1 + x^2}\right)$ in a power series.
The final answer: $x-\frac{1}{2}\cdot\frac{x^3}{3}+\frac{1\cdot3}{4\cdot2}\cdot\frac{x^5}{5}-\frac{1\cdot3\cdot5}{2\cdot4\cdot6}\cdot\frac{x^7}{7}+\cdots+\frac{(2\cdot n-1)!!}{(2\cdot n)!!}\cdot\frac{x^{2\cdot n+1}}{2\cdot n+1}+\cdots$
e6a45a85-fdbb-4381-9f51-63e7d1c32fcd
sequences_series
false
null
Compute $\sqrt[4]{80}$ with accuracy $0.0001$.
The final answer: $2.9907$
e78bdde6-d3e2-47e8-81e3-b17177ba3818
precalculus_review
false
null
Use properties of the natural logarithm to write the expression $\ln\left(x^4 \cdot y\right)$ as an expression of $\ln(x)$ and $\ln(y)$.
$\ln\left(x^4 \cdot y\right)$ = $4\cdot\ln(x)+\ln(y)$
e7c924e6-d60f-43b4-b2ef-d83524eb6886
integral_calc
false
null
Find the moment of inertia of the figure bounded by the arc of the semicircle $x^2 + y^2 = 9$, $y > 0$ relative to the x-axis.
The moment of inertia is: $\frac{243}{8}\cdot\pi$
e7e29834-4747-4aee-a690-1635add2dd35
multivariable_calculus
false
null
Find the maximum volume of the parallelepiped inscribed in the half-sphere of radius $R$.
$V$ = $\frac{4}{3\cdot\sqrt{3}}\cdot R^3$
e8395a31-7b69-4c48-a257-c31ad220222f
algebra
false
null
Determine all rational values of $x$ at which $y = \sqrt{x^2 + x + 3}$ is a rational number.
The final answer: $x=\frac{q^2-3}{(1-2\cdot q)}$
e83a5d89-d36a-426f-96ca-3f62759e1d1a
integral_calc
true
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
A large fish tank owner notices that the filter on his tank loses effectiveness over time. He measures the rate the pollutants increase in the water every day until he changes the filter. Using the right rectangular approximation method (RRAM) with $n=3$, and the data below, what is the total amount of pollutants the water has over the course of a week?
Total amount of pollutants: $200$
e88de257-9aa0-4277-b404-bce62070bf07
differential_calc
false
null
Find the second derivative $\frac{d ^2y}{ d x^2}$ of the function $x = \left(4 \cdot \sin(t)\right)^3$, $y = 2 \cdot \sin(2 \cdot t)$.
$\frac{d ^2y}{ d x^2}$ = $\frac{\left(2304\cdot\left(\sin(t)\right)^3-1536\cdot\sin(t)\right)\cdot\cos(2\cdot t)-1536\cdot\left(\sin(t)\right)^2\cdot\cos(t)\cdot\sin(2\cdot t)}{7077888\cdot\left(\cos(t)\right)^3\cdot\left(\sin(t)\right)^6}$
e8e1d2cd-2424-4468-aaad-ab1de689cf41
multivariable_calculus
false
null
Evaluate the area of the figure bounded by $\rho = a \cdot \cos(2 \cdot \varphi)$.
The area is $\frac{\pi}{2}\cdot a^2$
e96b0661-863a-46a1-9573-432fb705ee4b
algebra
false
null
1. On a map, the scale is 1.5 inches : 20 miles. If two cities are 115 miles apart, how far apart are they on the map? 2. A model of a dinosaur built to a scale of 3 cm : 1 m is 24 centimeters tall. How tall was the actual dinosaur? 3. What are the dimensions of a building whose dimensions on a blueprint are 1.8 cm by 2.4 cm? The blueprint’s scale is 1 cm : 15 feet. 4. The distance between two cities is 180 miles. How far does that measure on a map with a scale of 1 inch : 25 miles?
1. $8.625$ inches 2. $8$ m 3. $27$ feet by $36$ feet 4. $7.2$ inches
e9c1a928-3748-44fc-8791-eaf192d07f88
multivariable_calculus
false
null
Compute the area of the region bounded by the graph of $\left(x^2+y^2\right)^2=2 \cdot y^3$. (Hint: use the polar coordinates).
$S$ = $\frac{5}{4}\cdot\pi$
ea099411-f1fd-44e5-b9db-54271bc9afd6
algebra
false
null
Find an exponential function that passes through the points: | $x$ | $1$ | $2$ | $3$ | $4$ | | --- | --- | --- | --- | --- | | $f(x)$ | $10$ | $20$ | $40$ | $80$ |
$f(x)$ = $5\cdot2^x$
ea191942-29a9-43a1-ba80-9d4753b80368
multivariable_calculus
true
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
Evaluate the triple integral of the function $f(x,y,z) = 1 - \sqrt{x^2+y^2+z^2}$ over the solid $B$ bounded by $x^2+y^2+z^2 \le 9$, $z \ge 0$, and $y \ge 0$.
$\int\int\int_{B}{f(x,y,z) dV}$ = $-\frac{45\cdot\pi}{4}$
ea1fe8c2-0c26-4940-8333-08a978425882
differential_calc
false
null
Find the local extrema of the function $f(x) = 3 \cdot \left(x^2\right)^{\frac{ 1 }{ 3 }} - 4 \cdot x^2$ using the First Derivative Test.
Local maxima: $x=-\frac{1}{2\cdot\sqrt[4]{4}}$, $x=\frac{1}{2\cdot\sqrt[4]{4}}$ Local minima: $x=0$
ea4c115a-3f35-4c2e-bdb8-5b92cb2e7e31
precalculus_review
false
null
Solve the exponential equation exactly: $3^{\frac{ x }{ 14 }} = \frac{ 1 }{ 10 }$
$x$ = $-\frac{14}{\log_{10}(3)}$