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42ca2f4a-f9f4-4a24-9edf-76a32286a185 | algebra | false | null | Solve the following inequality: $|-12 x-6| \ge 2$.
Express your answer in the interval form. | Solution in the interval form: $\left(-\infty,\ -\frac{ 2 }{ 3 }\right] \cup \left[-\frac{ 1 }{ 3 },\ \infty\right)$
*Note: enter an interval or union of intervals. If there is no solution, leave empty or enter "none".* |
42e272d8-b9fa-4658-96c0-9c6d0121341d | differential_calc | false | null | Analyze the curve
$$
y = \frac{ 2 \cdot x^3 }{ x^2 - 4 }
$$
and submit as your final answer the following:
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): $(-\infty,-2)\cup(-2,2)\cup(2,\infty)$
2. Vertical asymptotes (leave blank if none): $x=-2$, $x=2$
3. Horizontal asymptotes (leave blank if none): None
4. Slant asymptotes (leave blank if none): $y=2\cdot x$
5. Intervals where the function is increasing (leave blank if none): $\left(-\infty,-2\cdot\sqrt{3}\right)\cup\left(2\cdot\sqrt{3},\infty\right)$
6. Intervals where the function is decreasing (leave blank if none): $\left(-2\cdot\sqrt{3},-2\right)\cup(-2,2)\cup\left(2,2\cdot\sqrt{3}\right)$
7. Intervals where the function is concave up (leave blank if none): $(-2,0)\cup(2,\infty)$
8. Intervals where the function is concave down (leave blank if none): $(-\infty,-2)\cup(0,2)$
9. Points of inflection (leave blank if none): $x=0$ |
4301fe9b-6f1c-4157-a503-c9a4a63aac9b | differential_calc | false | null | Sketch the curve:
$$
y = \frac{ x^3 }{ 3 \cdot (x+2)^2 }
$$
Provide the following:
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): $(-1\cdot\infty,-2)\cup(-2,\infty)$
2. Vertical asymptotes: $x=-2$
3. Horizontal asymptotes: None
4. Slant asymptotes: $y=\frac{x}{3}-\frac{4}{3}$
5. Intervals where the function is increasing: $(-\infty,-6)$, $(0,\infty)$, $(-2,0)$
6. Intervals where the function is decreasing: $(-6,-2)$
7. Intervals where the function is concave up: $(0,\infty)$
8. Intervals where the function is concave down: $(-2,0)$, $(-\infty,-2)$
9. Points of inflection: $P(0,0)$ |
4311c676-bbf4-4e98-8e11-adf7b06738e8 | precalculus_review | false | null | Solve the inequality:
$2 \le |x+5| \le 4$ | Write your final answer as intervals: $[-9,-7]\cup[-3,-1]$ |
432ae8b3-c454-430c-b444-f92da3c288d9 | sequences_series | false | null | Find the Taylor polynomial $P_{4}$ for the function $f(x) = \sec(x)$. | $P_{4}$ = $1+\frac{1}{2}\cdot x^2+\frac{5}{24}\cdot x^4$ |
436d359e-a6d2-4758-a930-95a641e3d787 | multivariable_calculus | false | null | Determine the equation of the ellipse using the information given: Endpoints of major axis at $(0,2)$, $(0,-2)$ and foci located at $(3,0)$, $(-3,0)$. | The equation is: $\frac{x^2}{13}+\frac{y^2}{4}=1$ |
43aab6e3-8669-4193-993c-885a518d1101 | differential_calc | false | null | Find the equation(s) of the tangent line(s) to the curve $y = 3 \cdot x^4 - 9 \cdot x^2 + 5$, that also passes through the point $\left(0,\frac{ 29 }{ 4 }\right)$. | Tangent Line(s): $4\cdot y-24\cdot\sqrt{2}\cdot x-29=0$, $4\cdot y+24\cdot\sqrt{2}\cdot x-29=0$ |
43c2c82e-a54b-40cb-8b95-07cf15365044 | precalculus_review | false | null | If a culture of bacteria doubles in $3$ hours, how many hours does it take to multiply by $10$? 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. Leave your answer in exact form. | It takes $\frac{ 3 \cdot \ln(10) }{ \ln(2) }$ hours. |
43ce18b9-35be-43a7-b18f-bff62d27b1d5 | differential_calc | false | null | Sketch the curve:
$y = \sqrt{\frac{ 64-x^3 }{ 3 \cdot x }}$.
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): $(0,4]$
2. Vertical asymptotes: $x=0$
3. Horizontal asymptotes: None
4. Slant asymptotes: None
5. Intervals where the function is increasing: None
6. Intervals where the function is decreasing: $(0,4]$
7. Intervals where the function is concave up: $\left(0,2\cdot\sqrt[3]{2}\right)$
8. Intervals where the function is concave down: $\left(2\cdot\sqrt[3]{2},4\right)$
9. Points of inflection: $P\left(2\cdot\sqrt[3]{2},2.5198\right)$ |
43d0031e-c751-4a2e-89b6-68e8cbc45eee | sequences_series | false | null | Find $\lim_{x \to 0}\frac{ 2 \cdot \left(\tan(x)-\sin(x)\right)-x^3 }{ x^5 }$, using the expansion of the function in the Maclaurin series. | $\lim_{x \to 0}\frac{ 2 \cdot \left(\tan(x)-\sin(x)\right)-x^3 }{ x^5 }$ = $\frac{1}{4}$ |
43f3644e-64db-4bac-bd39-fa50622f3e9c | sequences_series | false | null | Find the 5th order Taylor polynomial $P_{5}$ (in powers of $x$) for the function $f(x) = e^x \cdot \sin(x)$. | $P_{5}(x)$ = $x+x^2+\frac{1}{3}\cdot x^3-\frac{1}{30}\cdot x^5$ |
44151f67-d055-41b9-a33e-677471a36551 | differential_calc | false | null | For the function $f(x) = -\frac{ 3 }{ 2 } \cdot x^4 + 2 \cdot x^3 + 3 \cdot x^2 - 6 \cdot x + \frac{ 1 }{ 2 }$, specify the points where local maxima and minima of $f(x)$ occur.
1. The point(s) where local maxima occur
2. The point(s) where local minima occur | 1. The point(s) where local maxima occur: $P(-1,6)$
2. The point(s) where local minima occur: None |
4464c80e-9661-4b58-b9a1-744d565b7ea2 | multivariable_calculus | true | 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 | The values of the function $f$ on rectangle $R$ $[0,2] \times [7,9]$ are given in the table. Estimate the double integral $\int \int f(x,y) \, dx \, dy$ by using a Riemann sum with $m=2$, $n=2$. Select the sample points to be the upper right corners of the subsquares in $R$. | $\int \int f(x,y) \, dx \, dy$ is approximately: $35.42$ |
4495f45d-c9a9-468c-87c3-cb3701fe37a1 | differential_calc | true | 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 | Use the graph of $f(x)$ shown below to find $\lim_{x \to -2}f(x)$, if it exists. | $\lim_{x \to -2}f(x)$ is None |
453b6199-ab94-487a-b46d-44885715e8be | multivariable_calculus | false | null | Apply the gradient descent algorithm to the function $g(x,y) = \left(x^2-1\right) \cdot \left(x^2-3 \cdot x+1\right)+y^2$ with step size $\frac{ 1 }{ 5 }$ and initial guess $p_{0} = \left\langle -1,0 \right\rangle$ for three steps (so steps $p_{1}$, $p_{2}$, and $p_{3}$). | | $i$ | $1$ | $2$ | $3$ |
| --- | --- | --- | --- |
| $p_{i}$ | $\left\langle1,0\right\rangle$ | $\left\langle\frac{7}{5},0\right\rangle$ | $\left\langle\frac{1333}{625},0\right\rangle$ |
| $g\left(p_{i}\right)$ | $0$ | $-\frac{744}{625}$ | $-\frac{460\ 046\ 957\ 304}{152\ 587\ 890\ 625}$ | |
45844f47-7807-4d44-903a-819bbfd75778 | integral_calc | true | 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 | The graph of $y=\int_{0}^x{f(t) d t}$ where $f$ is a piecewise constant function, is shown here:
1. Determine:
1. Over which intervals is $f$ positive?
2. Over which intervals is $f$ negative?
3. Over which intervals, if any, is $f$ equal to zero?
2. What are the maximum value of $f$?
3. What are the minimum value of $f$?
4. What is the average value of $f$? | 1. Intervals when function:
1. is positive: $(0,1)$, $(3,4)$
2. is negative: $(1,3)$, $(5,6)$
3. equal to zero: $(4,5)$
2. The maximum value of $f$: $3$
3. The minimum value of $f$: $-2$
4. The average value of $f$: $\frac{1}{3}$ |
45a1d7b5-f624-4a83-b813-aa80b29cd088 | algebra | false | null | Construct a polynomial $p(x)$ of least degree possible such that its zeros are $-2$, $\frac{ 1 }{ 2 }$ (each with multiplicity $2$), and $p(-3) = 5$. | $p(x)$ = $\frac{20}{49}\cdot(x+2)^2\cdot\left(x-\frac{1}{2}\right)^2$ |
45dc5791-4737-45d6-b1b2-81e807134f2f | sequences_series | true | 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 | Find the total length of the dashed path in the following figure: | $L$ = $\frac{3}{2}$ |
4608d6c8-00c7-42e7-ad2a-9b3ef61eece1 | differential_calc | false | null | Find $y'$ and $y''$ for $x^2 + 6 \cdot x \cdot y - 2 \cdot y^2 = 3$. | $y'$ = $\frac{x+3\cdot y}{2\cdot y-3\cdot x}$
$y''$ = $\frac{11\cdot\left(x^2+6\cdot x\cdot y-2\cdot y^2\right)}{(3\cdot x-2\cdot y)^3}$ |
46efe3d6-df69-43e8-a52b-d85c524aab17 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ -1 }{ \sqrt[3]{\tan\left(\frac{ x }{ 2 }\right)} } \, dx
$$ | $\int \frac{ -1 }{ \sqrt[3]{\tan\left(\frac{ x }{ 2 }\right)} } \, dx$ = $C+\frac{1}{2}\cdot\ln\left(\left|1+\sqrt[3]{\tan\left(\frac{1}{2}\cdot x\right)}\cdot\tan\left(\frac{1}{2}\cdot x\right)-\sqrt[3]{\tan\left(\frac{x}{2}\right)^2}\right|\right)-\sqrt{3}\cdot\arctan\left(\frac{1}{\sqrt{3}}\cdot\left(2\cdot\sqrt[3]{\tan\left(\frac{x}{2}\right)^2}-1\right)\right)-\ln\left(1+\sqrt[3]{\tan\left(\frac{x}{2}\right)^2}\right)$ |
475726a1-1caa-4fce-9a01-413a63f721d8 | sequences_series | false | null | Find the sum of the series $\sum_{n=1}^\infty \frac{ x^{4 \cdot n-1} }{ 4 \cdot n-1 }$ using the integration of series. | The sum of the series is $\frac{1}{4}\cdot\ln\left(\frac{|x+1|}{|x-1|}\right)-\frac{1}{2}\cdot\arctan(x)$ |
476fbe1a-47b2-4905-a5c9-c8f15fec9af0 | differential_calc | true | 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 | Given $k(x) = \frac{ f(x) }{ g(x) }$, find $k'(1)$ using the table below: | $k'(1)$ = $-2$ |
478c9874-1edb-498e-9111-048a658a240e | precalculus_review | false | null | Find the center of symmetry of the curve of $f(x) = \frac{ x^2 + 2 \cdot x - 1 }{ 1 - x }$. | The final answer: $(1,-4)$ |
47a11349-0386-4969-9263-d3cdfcc98cb9 | integral_calc | false | null | Evaluate the integral:
$$
I = \int \left(x^3 + 3\right) \cdot \cos(2 \cdot x) \, dx
$$ | The final answer: $\frac{1}{256}\cdot\left(384\cdot\sin(2\cdot x)+128\cdot x^3\cdot\sin(2\cdot x)+192\cdot x^2\cdot\cos(2\cdot x)-96\cdot\cos(2\cdot x)-256\cdot C-192\cdot x\cdot\sin(2\cdot x)\right)$ |
47c69ab5-9be0-4cef-8f3c-dd7fc78de350 | differential_calc | false | null | Given the function $y = \frac{ x^3 + x }{ x^4 - x^2 + 1 }$, identify the maxima and/or minima by using the Second Derivative Test. | Maxima: $P(1,2)$
Minima: $P(-1,-2)$ |
47dbe135-6e32-462c-a77d-8581fe5ed596 | algebra | false | null | The radius of the right circular cylinder is $\frac{ 1 }{ 3 }$ meter greater than the height. The volume is $\frac{ 98 \cdot \pi }{ 9 }$ cubic meters. Find the dimensions. | $r$: $\frac{7}{3}$ $h$: $2$ |
47fadf54-e0ee-45c5-8da1-4791534583a0 | differential_calc | true | 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 | Given the graph of $f(x)$ shown to the right, write the limit statement to describe the function's behavior as $x$ approaches $3$ from the left. | $\lim_{{x \to 3^-}} f(x) = $\lim_{x\to3^-}f(x)=-5$$ |
481d4a88-aaae-4cae-8e98-29ee8182edbc | precalculus_review | false | null | Solve the following inequality:
$$
\left| |x+3| + |x-2| \right| \le 5
$$
By using rules of the absolute value function. | The final answer: $[-3,2]$ |
4872f755-05b7-49f4-859b-c56ded668225 | precalculus_review | true | 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 | Find a formula for $f(x)$, the sinusoidal function whose graph is shown below: | The final answer: $f(x)=-4\cdot\cos\left(\frac{1}{2}\cdot\left(x-\frac{\pi}{4}\right)\right)+4$ |
4881a8a3-a6ab-40be-aa32-3b272f2dc704 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ -3 \cdot \tan(4 \cdot x) }{ \sqrt{\sin(4 \cdot x)^4+\cos(4 \cdot x)^4} } \, dx
$$ | $\int \frac{ -3 \cdot \tan(4 \cdot x) }{ \sqrt{\sin(4 \cdot x)^4+\cos(4 \cdot x)^4} } \, dx$ = $C-\frac{3}{8}\cdot\ln\left(\sqrt{1+\tan(4\cdot x)^4}+\tan(4\cdot x)^2\right)$ |
489ae381-47d0-4a7b-bce0-f7974248806b | precalculus_review | false | null | Transform $z = -3 + i$ to a trigonometric form. | The final answer: $z=\sqrt{10}\cdot\left(\cos\left(\arccos\left(-\frac{3}{\sqrt{10}}\right)\right)+i\cdot\sin\left(\arccos\left(-\frac{3}{\sqrt{10}}\right)\right)\right)$ |
490352f2-8fc0-4790-86a9-ff74e119f7b7 | algebra | false | null | Solve the following equations:
1. $\frac{ 3 }{ 4 } (8 x+12)=21$
2. $\frac{ 1 }{ 2 } (8 r+10)=17$
3. $\frac{ 5 x }{ 8 }+9=4$
4. $\frac{ 5 }{ 9 } x-\frac{ 4 }{ 3 }=\frac{ 7 }{ 9 }$
5. $2\frac{2}{3} p+3 \left(\frac{ 2 }{ 3 } p-8\right)=-10$
6. $-5\frac{1}{4} u+2 \left(\frac{ 3 }{ 8 } u-9\right)=\frac{ 5 }{ 2 }$ | The solutions to the given equations are:
1. $x=2$
2. $r=3$
3. $x=-8$
4. $x=\frac{ 19 }{ 5 }$
5. $p=3$
6. $u=-\frac{ 41 }{ 9 }$ |
49102ccc-ebb1-432a-b82a-0c7d6913d946 | sequences_series | false | null | Expand function $y = \sin\left(\frac{ \pi \cdot x }{ 4 }\right)$ in Taylor series at $x = 2$, given that $\cos(x) = \sum_{n=0}^\infty \left((-1)^n \cdot \frac{ x^{2 \cdot n} }{ (2 \cdot n)! }\right)$. | The final answer: $\sum_{n=0}^\infty\left((-1)^n\cdot\frac{\left(\frac{\pi}{4}\cdot(x-2)\right)^{2\cdot n}}{(2\cdot n)!}\right)$ |
4947b302-5fc0-437c-b39e-7235e8c4307d | 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 six trigonometric functions 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 six trigonometric functions is:
* $\sin\left(\theta\right)$ = $\frac{\sqrt{7}}{3}$
* $\cos\left(\theta\right)$ = $-\frac{\sqrt{2}}{3}$
* $\tan\left(\theta\right)$ = $-\frac{\sqrt{14}}{2}$
* $\csc\left(\theta\right)$ = $\frac{3\cdot\sqrt{7}}{7}$
* $\sec\left(\theta\right)$ = $-\frac{3\cdot\sqrt{2}}{2}$
* $\cot\left(\theta\right)$ = $-\frac{\sqrt{14}}{7}$ |
49b9c6d5-e705-4fd6-ae01-f4731cbf0fa5 | integral_calc | false | null | Solve the integral:
$$
\int \frac{ \sin(x)^5 }{ \cos(x)^4 } \, dx
$$ | $\int \frac{ \sin(x)^5 }{ \cos(x)^4 } \, dx$ = $C+\frac{2}{\cos(x)}+\frac{1}{3\cdot\left(\cos(x)\right)^3}+\cos(x)$ |
49e7bb62-d218-413a-a026-fb3d83dd990a | algebra | false | null | Divide rational expressions and simplify it:
$$
\frac{ x^2-4 }{ 2 } \div \frac{ x+2 }{ 3 }
$$ | The final answer: $\frac{3}{2}\cdot x-3$ |
4a693b69-d42b-4359-a183-f84c09f12bb0 | integral_calc | true | data:image/png;base64,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 | Bore a hole of radius $a$ down the axis of a right cone and through the base of radius $b$ as seen here. Find the volume of this solid. | Volume = $\frac{\pi\cdot b}{3}\cdot\left(b^2-3\cdot a^2\right)$ |
4ae78dde-37d1-48f7-a6a5-480cb979092b | precalculus_review | false | null | Simplify $E = \left(\sin(2 \cdot a)\right)^3 \cdot \left(\cos(6 \cdot a)\right) + \left(\cos(2 \cdot a)\right)^3 \cdot \left(\sin(6 \cdot a)\right)$. | The final answer: $E=\frac{3}{4}\cdot\sin(8\cdot a)$ |
4afe68d6-980e-4422-a4cb-58f6988fee7a | integral_calc | false | null | Compute the integral:
$$
8 \cdot \int \cot(-4 \cdot x)^5 \cdot \csc(4 \cdot x)^4 \, dx
$$ | $8 \cdot \int \cot(-4 \cdot x)^5 \cdot \csc(4 \cdot x)^4 \, dx$ = $C+\frac{1}{3}\cdot\left(\cot(4\cdot x)\right)^6+\frac{1}{4}\cdot\left(\cot(4\cdot x)\right)^8$ |
4b450811-e985-4a9a-981d-b5f7ab763312 | multivariable_calculus | false | null | Find vector $\vec{c} \times \left(\vec{a}+3 \cdot \vec{b}\right)$ where
$$
\vec{a}=\begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ 5 & 0 & 9 \\ 0 & 1 & 0 \end{vmatrix}, \quad
\vec{b}=\begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ 0 & -1 & 1 \\ 7 & 1 & -1 \end{vmatrix}, \quad \text{and} \quad
\vec{c}=\vec{i}-\vec{k}
$$ | $\vec{c} \times \left(\vec{a}+3 \cdot \vec{b}\right)$ = $21\cdot\vec{i}-17\cdot\vec{j}+21\cdot\vec{k}$ |
4b815f84-4919-4db1-9328-5412d4a3e0ea | precalculus_review | false | null | Solve $\left(\sin(x)\right)^2 + \left(\cos(3 \cdot x)\right)^2 = 1$. | The final answer: $x=\frac{n\cdot\pi}{4}$ |
4bd1631f-c515-4d4c-a71e-7d68591a7814 | differential_calc | true | 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oc2gAmisx8yUIcYp0iA6A9zZRhs5yoax9IQIkEQE6X3+n2FTis2XZbAtso6AOhOv0RKXiFJpMhN8vm8gTaXL4YN2VAAHikptnTGbho2oRENlPQJ0J1+oN3BAkZARZmZ8oG6VSjM5YNiXjlcTpW3+YPBGZMGZfIZgr6RKhOnyAgAQLLd9hNBvn7o6dj2wqBQGF0+GR9p1+ZMbk4wa0U9I5QnR7hT3EIhOOKs0yydOhUSyyb8aCUtg7v0ZrWcUU5ZSWDSdIuGDpCdbohyj2AaqZmpHFFOSajtOcwt3UE0F8kNAECQbPTW13XeukFZQlvsaAPhOp0Ay9KzhhTFIUpChFTFJabaTVIWNvsand18mx9gH2GmPDY5+Z2z/G6tktnTBIz6YYL4a/TDTwz31tvvfXNN1sIaP/+w6t/tTo7O9OK+R1+PFbbMjNjLBAiqnPFe3fhEXy560hGmvm88fki2nm4EKrTDdyLvXjx4iuvvBKAjhw5unz58vJzJq3fUf2rP3x+4HjjrCljIJIvs696q4Tw+fbDM6eMybRbRXnI4UL0MFOdbt1Fh8NRWlpaWlpqNhkLCgpLS0rmz67w+pWqEw1hRSsP0oeaCL7adfRITcvc88dnpVuF5IYLobpUp1s6WlWERIgyICBgWUnuuMLMY7XtrR1e0Lx5vT3ahYne+WRHbpZ9enmRLIv5BcOGUJ1uUNOt82yWKHXpC+CGy6ZWHa+vbXKCOm2H1NW0OTxAALDj4Kn/2bRrennxBeeO0dIWCZKPUJ0uUXPJAuMqW3RRhcvr3/b9CYpEi1HkFYEaB+bzB9/8yzckGZZcPcNuNQ8oY7QgvgjV6RJEYowBSUAgARtXlD19cun7X+xRiGdoQDXBMxIAEUqIbMve6q/3nZhTUbxw7rkROymENzwI1ekRBJAIESQ+NRyy0q3zZ5TvP9r05w3fAQEgQyB+chEQAWqb3P/5P//wB0Mvr7zFKEtARCJrw/AhVKdXJAQCBogAktFgWPSDKVMm5v/v//j4u8M1QBLyBOoEQNDa4fn1f32+s+rU//OTBZPG5BFPn8JDVcSj3XAgVKdLiAh4sYJIspPy0rzlN1/k8gQf+90nW/cfVwgAIMzom+9P3P30n/68ce9Nl1X+08KZAITAuJVDQtHJHBaEl1yXICKf2AoAPBBFkvBHC6azENz34p+WPPrW1In5ZrOppd1TdaqZKbjyx5c8ePtlNouZgAAkJDGYMpwI1ekXFilRHplwh3jr1dNLC7Pf+OuWUw3OzqDfbDLcfvX02xfNm1UxBtUiB2rmSzWIRTAcCNWNEFTlAV48fdysipI2VydjZDHK2ZnpsoRAJDSWOgjVjRh4b5MRodlkLM7JBCSgSE1JpEjUpRDf8CNGU0YIpA6rSDwqRUEi4IVcGRAwBgiSkFyKIFQ3QkBA5L4EoshIC/cKSAQgSZJwEqQOooc5klBntQKcMddHJHRONYTqRhR45n+9LBSkAKKHKRAkG6E6gSDZCNUJBMlGqE4gSDZCdQJBshGqEwiSzahWXXRKH+11zxcpSK8tT9DOU/k4DDuDOziJ8tcRaEnB475r6vL7Rr/uh95W4Uld+f8QlYqr54sUBBF547X2x3fn3Q7OoElE81LhuzQGd5TibOu07HGHqg61tjQhT92BEK9/bo/72x3b+WsCAglj2rA3uolt586dTqczvkcDAJxO586dO+O+WwBgjGnai9c+iailpeXgwYPdDs6gid7D7t27fb4Y6+wNgNra2pqamrhLzufzVVVVBYPBnou6HfBuqRNjIc6q087W2rVrd+/e299VPyhqamp++ctfRn9XvHj22WcPHz4M8e6wHT58+Nlnn43jDjXia5M1s7l3796333576Dvsycsvv9zc3Bz33W7evPmzzz6Lu5Vrbm5eu3at2+3u9nlVVdULL7zw3nvvVVVVhUIh/uFAOx1x7mFGppMQIsW/b5mYZ5huByte50/rpMVlb319Rbx21euvjrsBSdzRSGj3MnrnNTU1r776qsfjsdvtEyZMWLhw4cKFC+fMmTOgHQ5AdR9++OFZ10FgBBID6ciJBntVrce8L77BtzU1NW0s68Mvvx/QVorPyYKe/tepbXZ+seXbmsa2gTWIAEjpZ/mRo0drm9re/+snUZsQEeMvgBSjQR7c5dLU1LRp06Zjx44NYtt+2Lt37+HDh2M51wOlpqZmw4YNeXl58d3tzp07g8HgRx99pH1CRKGwAoCAknr1oXTGQUb5rD2wlpaWo8dPrVu3zm63R3++e/dur9frdDqdTmdNTc3mzZsff/zxcePG3XDDDcuWLZs+fXosbR6A6g4cOBDLaoSABE5355ufHzN9VRvfVAHhcNitlDz628g10ccdGhAkIkIgQEUhl9cXVrrfZbvfd42zf/1pPVFdtIHqRQ9qPmXi6bWQmNLpJOyR4k4b5iECnHjn839FdQsiIhZwIwuzcIgF3OOKsnIz7cX52WPyMxyZtkiGBQIiBImg+yOE1jav13vs2LGeXaAhcvLkydbW1hjP9YBwOp1HjhwZSCeTUJuVG/kEAAgkVDMLAgKdPl3b7u70hje1uztdnkBHp8/dGaxtbCeUJXM6yAZElIxWNFhIPWsoW7MB1Wcr7ZB2P9cE5RkFVVVVNps1+gI+efKk1rE0Go2FhYWTJk2aMGHClClT0tLSYvxhA1Ddo48+etZ1+FFBYG7PL6+bMG3mBRfEMSsOApw4cfL1119/+t/uOfvE6Eg9U0Vh7k5/N9VFFnbx0ssvX/fDH5aXl4NaoaPvHgupc9eQwB8MnWpoo14ej9Wvq62t27r1mx/96BZARgCHTzTx5CUE7GRde6vL29DW4ZXMIcwIsyyro/Cm+ZUVE/KNsgGiimH12n3atGnTXXfdVVFR0fchGAyff/75hg0bYjnXsRDd8qqqqp/97Gdjx46NcVMAJGKIEpA2b0n9kFDyeHzfHTq9q6rGe9rUYfCG0eFEn1v2u+VgKE05Z16WxWQqyc+wWc1IUm5mWk5WOt9eAirKsdvTrXx2fV9XUEtLy/c7v37gwRW5OQ410TYCAKxfv37Dhg3l5eXz58+/4IILysrKysrKCgsLDYYBSCnengNiCBIgKiw0dWzmxdMnxnd+icMUsKP7kgvKz9KKgffy333Nfen5JXPnTjvr5tyMcekRQVBh/QxJbd++vX7Xxw/fPh8AgCCkhABlAiaBFFYUxiik0NZ9R7fsPvnRl/u+2lP9X59unz+j/LH/ddXEktyI7NhZOwtxHOKP79NR9MD6AF1/vP8gcUuEPNMSA38w9OWuI3/csOer3ccCISUYVoCxsQVZk8bmj81Jn1k5aWJxtsOeZpAlBJBlGRAlAEni83rV32qQu3r1fR26U6dOHdv5WfStnZ+O2bNnb9myJSMjw2w2m0ymwR2u+D/u85+x9dtvxxQXlZaOie/O29vbt27deu2118bemBivo/Xr11dWVubn52sb9rEdQSStcsTqMa27Ev29fPOmpqY9e/YsXLgwykQCqHdvLT8eAYI/GPpq17E/frb7633VEuHDt82/+crp2fY0ANy4cePq1avr6uoyMzNXrlx50003mUymRYsWvfjii+edd16Mh6Ivuv3S2tra06dPz507N77jE0S0efPmWbNmpaenx7YF77SrU+BDYdbY5v7828P/8ZctNfXtOZnpBTm2meeWXlR5To4lkJ1uOXfK5Mh50Q7xGX94QotI/pizSA4APB7P/u+/r5w+3WgxyeqJ6881N6DDFXfVdVWRiTx0xbM4YYy/bYhXzFls3Rm5JPuuitp9KwBuHiPzvTFSa07trhIggj8Q/mbv8f/6dPvHWw7edPn5D946324MX331VXfeeee11167ffv23/72ty+88MLFF1+8aNGiNWvWxL2HeUabh8PvrH41AE9FAYj1zc73v9j3l017DtW0zJky9sKp4y+fPamiLD/NYsboqytyWwOgLhulqUztphIBYawOM57uibRzpC04ffr0l19+OWnSpJkzZ0qS9Le//S0cDi9YsCDGe0rcY1O0+wv/+QmZwXzWq2GI18pZdq61Qi0k0N+P7Oq5qadQrV+FBNyxwL8PSE0mazEbLp89aWp5wbyp455eu76upWNunsfn899zzz1Wa9rkyZM//vjjf/zjHxdffPFQfmDyGaiAERigBET7jjU89Z9/27Lv5KTSnN8+fPOsitKi3EwJJdAye/Ld87NGDBG79IaoKi3KwPX9KNdXS7TSSF2Dd3a7fdWqVVOnTv3Nb37z0UcfrVmz5s4771y4cGGsO6UBwhiLcc3Vq1ffddddDQ0NA/2KeBFLUxlj33777ZVXXinLcklJyZtvvhkMBmPcNjEo/LsVJfwf728pvOYXGXOW3nb7T4gRMQoRe2XNS3feeafL5Vq0aNH+/fuHqZEDY/369TNnzgSAioqKTz75pNtSdubRZlF/91fXj138RMk1v3jpvzcmq7FdHD16dNmyZX/4wx+iP9Sa+tRTT5nN5hUrVgDAT3/6U7/fH/ueBxybooX/Qb9Oz3Xr1r366qs7duzw+/0D/Yp4oT3E97NOa2vrihUrpk+fvm3btueee+6ll15av349DNlaDgF1rBwRb79m1oNL5ttzxoUKZnUGAwBgIFAkOOvBTym+/vrrhx9++Oabb965c+ddd911zz337Nq1S1tKxIstIGidI2IAoDD6ctexWx79/zLS03/90M0/u+XSJDfb7/e/8847f/zjH0+cOHFGayMXxu233z527NjXXntt9uzZTz75pNlsjn3ng4kIO2ss0qlTp956662f//zng9h53OlfP0R09913P/TQQ7NmzVq8ePHcuXMPHjw4jBc07wohEaCUnma656YLp43P3F7d8fHXBxXGCAkBjcZBDp0NC9nZ2Q888MAjjzwyY8aM5cuX5+Xlffnll9pS9YcgACgEquMMAKpONP7y9+sQ4Kl7rr5lwTSTMdmTY3bs2HH69OlJkyZFfxh92Pft28ejNOfMmVNUVDSgnQ/gx5z1WuQrBIPBd999d+rUqZdccsmAmhJfNIPcP3l5eXfeeWdRURER+Xy+kydPTpgwYRivadWZjsAAiFhWuu2y8jRXe9v/WbfzdJMTCQ8fOlRYWGC1WrVNUtnoEdF55513xx13yLIMAMePH3e73bNnz+5tXQn5KCOALxD6w1+2Hqltfub+G667qMIgS0n4idGH0ePxrF69+rrrrhszpvdB+GPHji1fvnzatGmzZ89+6623jhw5MqDvGoDq+LXIGHO73S6Xq6Ojw+l0dkTwer18haNHj+7cufPWW2+N8pAkG94T4O0Jh8O8td0IBALa70JEv9//2muvORyOiy66CIbxUkYgAAYgE3CHxI3/1/zQqW+3fV/9j30nO9zurzdvrqys1I4tDd8wYyzw5xEuuZaWlpdffnnBggU/+MEP+NLorrI6NEUAwL47XPvOZ9/dtXjOVbPLJdkAhAMdAhlcU3ljFEVZvXr1hAkTrr/+ekmSuh1eIqqqqlqwYIHD4XjllVfuvfder9f7u9/9TlGU2K+ZgY1hEpHX633rrbfa2rrHK1ZUVPzoRz/q7OxcvXr1NddcM3HixNra2gHtPI5EH6m6urr333+/Z+TU5Zdffskll3CTWF1d/fzzzzudzmeeeYa77Ib1UlZjybg/r3xyxV03X/rBXv+/v7/5P1989OL5ly5YsCBq1dSVHIe38MiRI7/+9a9NJtMTTzwRvSjqrsFfki/AnvrPT84Zk3Pj/Eqz0QgA3ZxsiW7txo0bN23a9Omnn0KkWRB1dwsEAhs3brzoootWrlxZVlbmcDjWr19vsViam5sLCwtj/ZrYB15i4YMPPsjKyrrpppuWLVu2aNEih8Nx77331tfXx/db4sv+/ftvu+22VatWNTc3D3dbVNgZf6jD5V712gdFVz/2yOpXWlub+YKrr75aF2OYjLFvvvlmwYIFzz77bH9HmCmMGGP0p8/3FCx6/Jm1G4LhEN+eSOk6Fgmmo6PjjjvuOP/885ctW7Zs2bLS0tLKyspnnnkmvt8SZ3/d1KlTf//73/PXBw8erKqqmjdvns1mixZ5St2e/X7/M888M3PmzOXLl8cevZpo8Iw/kGFPv/Kiyg+3Hm1ieQ5HTkJ8oImBiGpqan7xi1/cfffdN954Y7eBvq6LIdKdDoTC//W3relp5usuPs8gG3hACC/VkJzfbDKZ7rrrrvr6ev52375948ePnzdvXny/Jc6qmzRpUnl5Oe85bNmy5dNPP7388su5w56inrVSh6qqqi+++EKW5VWrVvFPpk+f/uMf/xhSpvPGI4CnTiiaWJrz8Vd72zoWOzJtZ98sNUDEzZs319TU7Nix47vvvgMAIpo6deodd9xxxv0XiRFKSHsO1VTXtU8vLzpvQmFEaRJ/7EuC7IjIYrFcfPHFWtvee++9ysrK+fPnx/eL4p83RQuiLSsru++++7Kzs7uFwKbI1czJzMz813/91+hPHA4HpIzkINKSrHTLjMljNu+o/np39eLLzh/uRg2AadOm3XfffdGf9HaEUUIAwB2Hats7vD/9+Q08piRSfy9J10xPl9jSpUvz8vLiftEmsLpISUnJ7bffzl/HN91AHCkrK3vggQf46+hbw7A26gxIdd/BD6aNe+U9/OK7o/pSXWVlZWVlZa8XbvSHRNTpDx44Xp9mMV9UWQZAWuRkdH2ixNGthfzt4sWLITL2EcdLNyGD+yl11fYPP6Bw5kFPqVsD7zkQwYxzxxmAjp5q9of6m72ealCvc0a1IcuoCcTNTm91beuMirHpVjMQ65oYkJQrqqfkohsf30siIapLqau2H6IfNXu6ZYapUT3gSQ4R063miWUFHR5/7UDTTAwrfV0M0YediAhYW0fnyfq2S6aNAyBEWR1JAQlRm7+SQKLPeKLvv6M6C20/xzSFbhy8lwWEAPMqxre6vcdrW7WYRS2jxPC2caggIEjNba7Wjs7zy0u6Rk66/01kE5J4xke16nQFAcGVsyf7/cF2jz8yvUiKzHRJmXvEoOCtP1TTnJeVXpKbqfubyNkQqkt5GBEgkAQApXlpHZ3hUw3tRDzxIbdzenrM6wsGtP9488TiLGuaSe83kbMiVJfySMhUgdGUCWMMGPYFggpjgEiAlBxPVsJBiXDP4ZNjixzpaWZh6wTDj6TOgiYgKM7PaW53+wNhAlJH1ZMUophA+GTtuib32MJcq8Wo959zVhLorxPECwQgPpBHkGk1E0oEEgADIERKUuBGAiEE2FVVQwil+RkGWR7u9iQcYev0Aa/RAggFeZmn65u9Pj+AROrQpt5PIgLhvhONtjSTI8NGAJEEYSMWvZ+wkU/Ei0wAREB5mdaus4aQHA9yoiGkvYdqstItRblZPPZyuFuUWEQPM9XBSDJHNf8aIeMBwZF0IynkWhwkBAB7jzRYzSZHxgCyj+iXEX5TGRkgqpOpEUFCFggpjHUFUg1r0+IAv6PsPVKXabcV5WXzj0Y2wtbpAqYVK7EZQvsPHrrvvvv37Nn7yCOPZGRkAMDq1asnTpw4zG0cLAhQfbo1DEqO3awmpkA2su2BUJ0+iDgHqLiwMCvb8cADP2mtP3n//T8vL58EgCUlxcPcvqHR2OYlgEljcvnUHt17Qs6GUF3Kw4gkSZtxbbRYjEZjaUmJ1WoZU1o6YUIZdNVd0Cu1LU4ELM3PAl47S//d5v7R99kaFXSb/UmKAjIhEkgsMsyi82FMOl7bTATFBdmRMaMRjlBdyoOR2hGARDRhTEFtQ4vX55ewyybovEuGLR1eQMOY3EyIVCUY2QjV6QX1WkwzGRhIwPOpqEVc9C06Ajjd6JIoVFyQAaD3XxMTQnW6AVU/geqrk5CB2v3U91XqdHe6PL50i8lqMRER8NkUIxqhOh3A7VmX3oCISGERZ53OL1KfP+gLKdMmj1PTJqBm10csQnV6oOsiJNkgm02GhjYXokTEdK85AFdnMBAMFGRZI0UPR/wQplCdHoi+CK1mQ3amranNE8neoL8rtNtwiacz4AuEJ40p0Owc6fBHDQihOp0QiQCTEAwSSoSAhCjpbsCvZ4q7dldnpz9YnG8DHh3G60ePaITq9ACCWlGbAEgCAgJFzXKAurxIo28Wnf5gMMTGFecDryNCPCJsJCNUpxsQCSNPPoSR6axA+uqP9cyD6O4M+ALBklxbZAW1qtYIZoT/vBGDJi1ZApNBbnfx4nv6jp7iCYA9voA/GBpfnAuApHpCRkL+pX4QqtMFTKuzkW415eVknm5ohzMGUnTZJUPEUEhxuX0SIaISldhzhCdxEKpLedQ+pfYkhAhKGAFRndtKAHo6j3SGryOsKK1ub8WEQgIJIwZdbyNEA0Y/Z2u0QrzPhYA8KRgAgCQRI1LdBjrrYXa5+wEAGKNQmD+aorZYbz9pwAjV6QLtMuSZMVHiYylqqLC+upfqvYOXdQmEwk0tHWWleUBqbhgY+aITqkt5uG0gniWMJAJEoDBJEiARQwS9nUQEkPgUJURgxAIK2UwjIRVF7OjrhI1iSO1pmgyy1WxoanUpxBAkAtSbo5zXpuIvSVHIGwhZLRYAAOJ3Fv0HuZ0NoTodQBjJDwZgtRhzsmyNbR3a/ANE1NX4A0W9wGAo3NzqLMrP4j1MFD1MQWrA3QZdwkIgAgkjmcOibIcOILXOOCJJgECEBJJJRm2kaORrTqguBdF6jKQWkpXgjAE+YIASABExpr9I4YjNVlPo+oOhxqaOTDvvYQ5ry5KIyFaUcvQsFErAhx4wMlwpAfH6rXq8aVKkb4wAwIj5wkpxXjbyASOd3UMGiVBdirJ169Z169YhIjAihLlz51577bVqHDTwmt0MgBf10dOVSqTNfyfkEdzIJO1jXf2WQaPHm+Wo4OOPP37//fcVRVEUhTHGGAMARohAMhADuWsoRVegGsGtuub2HaqxWi1mk3H0SA6ErUtlZsyYsXr16sg7ImKIksVkzMywHTl1YCrKRAx6m7GW2kSsGiABKChnplksZhMAo0ihvhGPUF2K4na7i4qK9u7d63Q6J5aXlxQX8ck9JpNsSzP7gmGSiD/XRT8mJZLundkenduY2hC9EiIjxhDYmQ6Dkf90J1SXPKKN0lkN1MGDB6urq3fs2CFJktfrXbVq1dVXX60+/vAhwDOz0yau2QCqL42QGyqmBm8BEjIEIEJEjPEBE7UiRYgAdLrJlWYxm40GPqMCSU9ekEEjVJc8EFETG2Psueee27RpU7d1ysrKfvWrXxUUFPzkJz8xmUw33XSTyWR64YUXnnrqqYkTJ5aXlx84cOD4ieMA0NzcvHXr1vr6eiKaM2cOLzOSqJYDEIJCyr7D9a9/8I270/fjq2ctnDPZbDIAlwkBIcMYhgmIuwwQ+Q2k2dmZZbdaLabENT4FEaobHmRZfuyxxx577LFun3NnHREtXbpU+3DJkiUffPBBQ0NDeXn5/v37T5w4AYBtbW3btm07evQoAJx77rkJVR0AKQpbv+3Qv/7mr5IkZVgtK5778323XvLQkstkAwDIGHPyWAQAktQMfCABKAAskgKTRoOhA6G6JHPWHqb24ZtvvnneeefNnTsXALxer6IoFosFAG655ZYj3qzv/vuLc84556GHHqqoqEhOyxta3a/9+Wuz0fDCQzc67OZn1n7+0rubzx2bd90lUwEAUIl9PJww4pkj6vAGDJIsocTtH4wOn53wHAwPvLfZ11IiOnDgwIoVK957772NGzf+/Oc/nzJlyqRJkyBiDHtmH0kw9NWu6p0Ha+6/df5lMyZOKy995CdXZNtMz73zhdMT4HPAYw+SQc1vAFhT35aTZU+3WkA18on6ASmFUF2S6KmxfjSDiE8//fSll166atWqO+64Y9q0ac8880xmZiZfJCECQDCkJG22ASN86+Nvz5tYeNmMiRIQIs44d8xVF557urF9wz8OIjAAwwBuANokVgSFMYNEBiCQkIEagKO3GYMDRqguSQzULplMpjVr1lRVVdXU1Lz44otFRUXaotxMq9lo+O5wLQAkMniRaXs/Xtu258jpy2eVl+ZlEkg8Vey9N15CjL7cdcwXCA+kEQTISPWUEzEgQJIkACbxqilAQCP8shzhP29EYrGYDbLmUE5QJ5MiE/oAgP7ny73ZGdbZU8YZDBJG/GmTx+XNmTru++qmmkZnJNwkhv1yO4d8WBRONrRZzEaTQVJnktNoeKwTqtMhSCQDIaiBKfH/gih/IH+K/PjrA45M6/nlRfyJjEhNPX3HNbOP17bVNXcgDmjygzarh1rdfofdarWYI+4JPaaCGTBCdbqE1FySmjbirb2oclY1TR3Vtc3jC7OLcjMAJABJi6Wcfm6pzSLtPnxaUWKtc4LAiBjyryAJkfHJrKqV65plMZIRqtMvXRYhzoOZEe8bkYIIu6pqlDDNrhjXfS1Cq8V0fnnxjqrTYcYwRqkQIEqAPBEM8UAXiMzQPXMi4YhFqE5/ECChlEiDEMnVhQgAB6rrlbAyq2IcL7ejroEEADaLaerE4p0HTylKzEMgiOqcVsDDNU2yUXbYreqXjnAL14VQnf5AICJGZ9iD+A61a/lgJSJ2+FRTWAlPO6eYUNJ6gPwhzGwylBU7nG7/99WNFKt96lrP5QoYjYbMdAv/rpFu4boQqtMfBCABIsj84geAOJ/HroERanF629y+CaV56WnmM1K3qOphpQWO/Oz0nd8fi333mrgkJCA2SqLAohGq0x98LIMkOfGTYrDd7etwBy44d2xU5ml1Ef9TnJeRm2XbdvD0APdMAKCghKCvBGfxQahOfzgybGaT0Zieo6b+iftVy510AACsqc3V5vaeMzY3qtsZnU8J87Nsmfa0L3YcHLj66URtqywbMtNH14QDEKrTI+lWk9Eok2zmb6OyGMUXBiR5/CGfP1g5qZinR4p2V/AX9vS0Ioe9M4hHTzXGtltNsdDqdJtMxpxMewIan9II1ekTAmSEasxxAvqZBAASATW2dLS6vBUTi9VcQtjl4NZWPWdsnoxwvKEjtl1HfAMIABKOvu4lCNXpGVLj/BMTzYEA4TBravM6Mm3pFlPXd0T+EC+/ADi+ONcgsQPVdWqz+m80b7n6jod6jrqLcNT94BEBqgUWI2l/4rt3Ip75D8KMtbg687NsUu/DjAgABDCxNBfQWN/mBX4n6Nd8aWGcCOjxBRBAgnB825/6iFmtgu6oyW2JBULK6aaO8UU5co/kXaqdRQKC8pIco4T7Dp/Spur2mxUGAdRyRFUnGtLMpvHF+Yn8NamIsHWCnvBM7qgwxeXpzM5Iwx6qQ56xDCREyWIxFDgy/CHqcPv4yGe/EWrRsdUAqNBIn03XE6E6QU/UcDMlrLS0ewtyMmWpt+tE8yMAVpTld/oDjW1uTW199TK1KsjIc4vRaMmVEo1QnaAnhCABw5ASbnF5Henm3nRBWqUQBDx/UlGnP9Ts8hExVbR9PN2h6mFEtRQmwSi8CEfdDx4ZJDj9JfLRyTDDdlfnmKKc3m0dABHj1fOK87K8vlBji7MrHVPfMSc8eyYgNLZ5ZKMhzTTqLsJR94NHBjxXEXSNwcfV64WAhIBU39xhMkpGuQ/JASFKBEQIk8flBYLBdlcnX8INYO/3BuIzGpAI6hqcZrNclJMZz8brAaE6/YHEAABkE0DXw1Vcv4Hn64KGZqfdZk23pvXaCs3fjYCTxhUEAsF2t4/UEl88F3SfRCqMKHorSRQfhOr0R35OhsVsttjzAElVYFwhIkQAxBChUUZDH6YOowIy0y0mqzWt3e0Phs+WuYznYwFCBAbS6JlTF41Qnf4wm4ySTIrqcOZnMJ7nUStGubuqJicjXS2k2mMt6Kr/SEBsfFG2090ZCCiISMT6fPaUEEgBkMKMVxTBeBtqHSBUp0skAAKmzuiOv7lTzRUhyjLKktzXWlFTy6XS3Mx2V6c/FKazOgMQCai51R1WqLQgc8Tna+iJUJ0e4Ze7QZ3zFmvGkoGinKhrtVpMZnMvqiMAAAmQ8aBoBpCbaev0h0OKgoj9C4lXCPL4g4wpeZnWhLQ9tRERYfpAi7F69dVXP/3869P+MT6f977777fb7YTwwvO/5vnY4wUiEcht7e7sLLs9rdceJgAAAU+PSTJgQa79yz3HPF4/5doBuPeberut05mlf0adoQOhOl0QHdb4T//0T9NmXbTyd5+FPK0rV64sLy8nhNLS0nh+nRoqyXMr9D44Epn42hV+neuwB8JMUQAAecFxdVSm1035OBAfUBl9CNXpgOiwxsLCwiCYTSaTJEllZWWTJ0+O++w6dVoAYnVty2WFDqvF2OtqpNai4749GFOQ1dbhCYQCavyJmlS251YARIhAKAGgBEpc264PRuOdRqdEGx2iRCayUzOksBZ30Jpm7kt1agbLSKuy09NCISWsaImO+sjSSdxDR3VNHaFwuCAnY9SNYArVpT6a2LpdxIkro8VFRwCy+revL5IAACJz70wGKd1mOna6UfOd90ok3Sx6AyFGrCg3axQ+2AnVpTp9FJdMoJcLgSFAqysAEljN/T+DqFEsgGA2m7Pt6b5ADJ4D/iURd3l8Gq0rhOp0Ciauh0mAgHS6sd0kS/nZ9n6FgVr6CJNBsqWZaptdfOYd9eX+jhTRAoBRe/mN0p8t6A9e6EMhQjQa+3CR98BiNuZm2lraXdAVo9m3xUMCYBFn/JAbrDeE6gTdUed5q7NPpRiHSBERUOoMMnVSQX/hmASA7W4/Y5RlM41Cj51QnaAnCACnm5wGWcq0mWI0RmkmgyPDcrK+NVKcp48eJvLhGWpxepnCykoLRp+pE6oT9IDLoLHNY5Lk3ExbjLbOYJBtZmMwxABYJGNg75nFNN8Cjx8dfaZOqE7Qg8jQPzEESZZjtHWIiLKhsaUdQOIx2X1uxkj1r6M2Bjq6EKrTKQRqDCQk4KolAAJGA5rOYLeaS/MzGp1eAJCIQR8V9rSM7QQyEEjY95ygkYtQnf5IMxsNksFgzVKv4firDgHAF1KQ6ydmeM49UtPj9tkqAgaAwXCYmDIKJQdCdXokJ8tmNpnQbGdqGaoEnETCoycbTUbDuOIcilkYGVaz2Wg4cqoR+n6uQ55thai2sT2swJSJRfFstk4QqtMfEiAgIwgjyIBIwBJh7YKMENAoy7Hb0iy71WwytLkDkdTQfW6IiGFGBGCSha0T6AFCHupPoAbsxznhD9cK9jltoJ8tI15vtRhkP9URCIFY3xEsIxuhOv2BABJIADKAFsIf5/3zwC3iZUxiVoXNYjTIeOREg/q+Tz85dVUZ4dOERhlCdbpEAUZ8pjYiJKKHCQgoqYFhMU9ucGTZLSZTm9en7aLX1dTMzyiraTNH34CKUF0q0i2air8980OUQBualxLRw2x0uozILGZz7IUdJTUihVhXwaxedo4I7s5Ah7ezyGEfWA92pCBUlypEiyppU+l6hU+vq21yGozG0ryM2G2dJCMiujxBCdSsKb3tHIgwEAwHgqExBdkIfTvTRy5CdalCT2l1s3gYKQueaIh4r4+HmGDsrvK8bHua2VBd2wpdj2697J5XOSBACRQalcZOqC5VODNBgxbCccYKyTF6fH4cEgAwQsSYLxKTjLKEvlAQAABYvwOgDIgYSjgK62gJ1Q07RNRTY1rF0+g1k9jPRABQiAAlHEguJD7mKYOWZqz3nRMxVOeRS5Eqy6MLkSNsONHMl8fj2bBhQyAQWLJkibZo+/btf/3rX9va2i688MLFixdnZWUlsWkoIfTpcusDgyxJiPWtnojg+pAsQlhhIUaS5m8cZQhbN/x4PJ7HH3/8gQceeOONN7QPm5qa7rrrLq/XO23atFdeeeWll14Kh8ORhSQBImOETA1Ujmt7VC95V9aiWG1RvsNus5hON7TzSXS9OjQIABm6vD6Xq3NqeXH8Wq0nhOoSS//jH3yAZNOmTTab7eabbw6FQtqi5557bvr06c8///zy5cvXrl27adOmQ4cOqfsEJAQFDUASDyGR4tpHQ4Ljda3eQHhyWREf9ohtOzJICAhhkEjNBN/L1YXEQMIgISMymQyjrnMJAEJ1CaKvdHo9QcQf/OAHq1atstvt0Z9/+umnM2bMMJlMRJSfn280Guvr69UnQCAgkiiMPOskDKwfeHaQl4Ikm8U0kOAUBEQEGUnBvidDEEpAJBMB8Qib+FcCS33Ec11CGNDIh8Ph6PlhdXV1cbHaATMajSaTyePxRHaLQGqdVIwpDd5AUdM5o2pWB7B/VWmIfUZhkpq/lhAJBjZaM2IQqks4HR0djzzySG1tbbfP582b9/jjj/MBlZ4dUU233QR8+PDhpqYmt9cdUpRdu3a1t7UBYGVlZTdTOTQYAiDIpHaFBqCM3Oy0gydZTWNbaUE2AyZBjxRjkShPBMaDWAa0/5GBUF3CyczMfP311/tayiXX0zbabDafTw1oVBRFlmWLxQIA27Zt27Z129x8R/P2dZ98dDTbkQ2AY0pL46g6IizOzfrv//cntjTDAPVAT69Y7HL5c7PsSIDYW1Y/IkCcUJzz+8d+nJ5mprjPmNADQnXDT6/d0RtvvHHr1q3//M//LMtyQ0ODy+UqLCwEgKVLly5dupSADn2/438/saqi4ty4GwpENJsMU8rytYResVOan435cMasgh57ByCLyThpbF4/sxJGNkJ1w88nn3zS3Ny8e/fuhoaGtWvXFhYWXnLJJT/72c9uu+22N998c8qUKWvWrKmoqJg4caK2Caphjgntm/Xt6O57k8j6/Seh1RaMxsAUEGOYqcCnn376zjvvuN3ukpKSt99++7PPPvP5fNOnT1+1atXzzz9/+eWX5+XlPfXUU7wPmZxQTEFCSVJAraAvBhRdGb3yokWLuA1MWNMEiULYumFGU1Est78kT/kRJAihumHmrP50bQUtTlqgd8RoyjATS/BKjGsK9IKwdQJBshGqEwiSjVCdQJBshOoEgmQjVCcQJBuhOoEg2QjVCQTJRqhOIEg2Ig5TIEg2wtYJBMlGqE4gSDZCdQJBshGqEwiSjVCdQJBs/n+lWxtGmgKuXwAAAABJRU5ErkJggg== | Examine the graph. Identify where the vertical asymptotes are located. | $x$ = $0$, $1$, $2$ |
4c1292e1-d4b3-4acf-afaf-eaac62f2662d | integral_calc | false | null | Compute the integral:
$$
\int \frac{ -1 }{ x^2 \cdot \left(3+x^3\right)^{\frac{ 5 }{ 3 }} } \, dx
$$ | $\int \frac{ -1 }{ x^2 \cdot \left(3+x^3\right)^{\frac{ 5 }{ 3 }} } \, dx$ = $C+\frac{1}{9}\cdot\sqrt[3]{1+\frac{3}{x^3}}+\frac{1}{18\cdot\left(1+\frac{3}{x^3}\right)^{\frac{2}{3}}}$ |
4c30d87c-c696-465b-a078-ec3b61d444a8 | multivariable_calculus | false | null | Change the order of integration by integrating first with respect to $z$, then $x$, then $y$:
$$
\int_{0}^1 \int_{1}^2 \int_{2}^3 \left( x^2 + \ln(y) + z \right) \, dx \, dy \, dz
$$ | $I$ = $2\cdot\ln(2)+\frac{35}{6}$ |
4c9566d0-2bc4-4a11-b0ca-36e6a42c2622 | algebra | false | null | Rewrite the quadratic expression $x^2 + \frac{ 2 }{ 5 } \cdot x - \frac{ 1 }{ 5 }$ by completing the square. | $x^2 + \frac{ 2 }{ 5 } \cdot x - \frac{ 1 }{ 5 }$ = $\left(x+\frac{1}{5}\right)^2-\frac{6}{25}$ |
4cd052e9-254c-4c7a-9c30-cbbb888769c0 | multivariable_calculus | false | null | Compute the second order derivative $\frac{d ^2y}{ d x^2}$ for the parametrically defined function
$$
x = \frac{ 1 }{ 2 } \cdot \left(\cos(t)\right)^3, \quad y = 6 \cdot \left(\sin(t)\right)^3
$$ | $\frac{d ^2y}{ d x^2}$ = $\frac{8}{\left(\cos(t)\right)^4\cdot\sin(t)}$ |
4d41436f-c675-45ef-87a1-009350e3953b | precalculus_review | false | null | Evaluate the definite integral. Express answer in exact form whenever possible:
$$
\int_{0}^\pi \left(\cos(99 \cdot x) \cdot \sin(101 \cdot x)\right) \, dx
$$ | $\int_{0}^\pi \left(\cos(99 \cdot x) \cdot \sin(101 \cdot x)\right) \, dx$ = $0$ |
4d4989ec-b4b8-4b1b-b20c-0861da90c835 | algebra | true | 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 | Using the given graphs of $f(x)$ and $g(x)$, find $f\left(g(3)\right)$. | $f\left(g(3)\right)$ = $0$ |
4d8dcf18-41d7-4085-97ab-f076a076978e | precalculus_review | false | null | Calculate the following indefinite integral:
$$
\int x \cdot \left(a^x\right)^x \, dx
$$
for $a > 0$ and $a \ne 1$. | $\int x \cdot \left(a^x\right)^x \, dx$ = $\frac{a^{x^2}}{2\cdot\ln(a)}+C$ |
4df2e972-39b8-4bc5-8726-98ce26fea8f8 | differential_calc | false | null | Find the local extrema of the function $f(x) = 2 \cdot \left(x^2\right)^{\frac{ 1 }{ 3 }} - x^2$ using the First Derivative Test. | Local maxima: $x=-\sqrt[4]{\frac{8}{27}}$, $x=\sqrt[4]{\frac{8}{27}}$
Local minima: $x=0$ |
4e00e130-7fca-4c2a-8d84-cdd7d0405967 | algebra | false | null | Solve the equation for $x$:
$12 - 5 \cdot (x + 3) = 2 \cdot x - 5$ | The final answer: $x=\frac{2}{7}$ |
4e3604b8-d25e-467e-bb05-b739b155a1e8 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ x-\sqrt[3]{x^2}-\sqrt[6]{x} }{ x \cdot \left(4+\sqrt[3]{x}\right) } \, dx
$$ | $\int \frac{ x-\sqrt[3]{x^2}-\sqrt[6]{x} }{ x \cdot \left(4+\sqrt[3]{x}\right) } \, dx$ = $C+\frac{3}{2}\cdot\sqrt[3]{x^2}+60\cdot\ln\left(\left|4+\sqrt[3]{x}\right|\right)-3\cdot\arctan\left(\frac{1}{2}\cdot\sqrt[6]{x}\right)-15\cdot\sqrt[3]{x}$ |
4e4e997a-4e1e-4694-96ec-bffc19506e79 | algebra | false | null | Using the Rational Zero Theorem, list all possible rational zeros of the following polynomial:
$p(x) = 2 \cdot x^3 + x - 1$ | Possible rational zeros are $1$, $-1$, $\frac{1}{2}$, $-\frac{1}{2}$ |
4e68083d-84c3-4070-9ae7-06b59dcb7717 | integral_calc | true | 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 | Let $R$ be the region enclosed by the graphs of $y=\frac{ 1 }{ 2 } \cdot x^2$ and $y=x$, as shown in the image above.
Region $R$ is the base of a solid. For this solid, each cross section perpendicular to the $y$-axis is an isosceles right triangle with a leg in $R$. Find the volume of the solid. | The volume of the solid is $\frac{2}{15}$ units³. |
4ec04fb6-2b14-47de-8edd-ab602686736d | integral_calc | true | 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 | The graph of $g'(x)$, the derivative of $g$, is shown above. Find the value of $g(6)$ if $g(0)=-2$. | $g(6)$ = $8$ |
4ec668c6-0576-46de-a1b8-2bd85c15805a | multivariable_calculus | true | 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 | Find the volume of the solid under the graph of the function $f(x,y) = x \cdot y + 1$ and above the region in the figure: | The volume is $\frac{7+2\cdot\pi}{4}$ |
4edfa960-3d41-4fa9-88f9-e850ed2af94b | sequences_series | false | null | Find the radius of convergence of the series:
$$
\sum_{n=1}^\infty \left(\left(\frac{ n-1 }{ 2 \cdot n+3 }\right)^n \cdot x^n\right)
$$ | $R$ = $2$ |
4f311636-5a26-454b-a708-5f7ab2aeccbc | precalculus_review | false | null | Solve the following system of equations:
1. $\sin(x) \cdot \sin(y) = \frac{ \sqrt{3} }{ 4 }$
2. $\cos(x) \cdot \cos(y) = \frac{ \sqrt{3} }{ 4 }$ | The final answer: $x=\frac{\pi}{3}+\frac{\pi}{2}\cdot(2\cdot n+k)$, $x=\frac{\pi}{6}+\frac{\pi}{2}\cdot(2\cdot n+k)$, $y=\frac{\pi}{6}+\frac{\pi}{2}\cdot(k-2\cdot n)$, $y=\frac{\pi}{3}+\frac{\pi}{2}\cdot(k-2\cdot n)$ |
4f622685-24ee-4e55-a33b-6270bb8204e5 | precalculus_review | false | null | Solve $x^2 - 4 \cdot x - 6 = \sqrt{2 \cdot x^2 - 8 \cdot x + 12}$. | The final answer: $x=-2 \lor x=6$ |
4fabf73c-c71a-486d-a161-716b6ec6fd31 | precalculus_review | false | null | Calculate the following integral:
$$
\int \log_{a^x}(b) \, dx
$$
for $a > 0$, $b > 0$, $a \ne 1$, $b \ne 1$, $x \ne 0$. | $\int \log_{a^x}(b) \, dx$ = $\frac{\ln(x)\cdot\ln(b)}{\ln(a)}+C$ |
4faec218-e81d-4743-8372-242b474f1a9b | sequences_series | false | null | Suppose that we have a series: $1-\frac{ 1 }{ 2 }+\frac{ 1 }{ 3 }-\cdots+(-1)^{n+1} \cdot \frac{ 1 }{ n }+\cdots$ and its sum is equal to $\ln(2)$. Find the sum of the series: $1-\frac{ 1 }{ 2 }-\frac{ 1 }{ 4 }+\frac{ 1 }{ 3 }-\frac{ 1 }{ 6 }-\frac{ 1 }{ 8 }+\frac{ 1 }{ 5 }-\frac{ 1 }{ 10 }-\frac{ 1 }{ 12 }+\cdots$. | The final answer: $S=\frac{1}{2}\cdot\ln(2)$ |
4fbf3770-e3dd-4d3d-87ac-825d1fa83719 | integral_calc | false | null | Compute the integral:
$$
3 \cdot \int \left(\cos\left(\frac{ x }{ 6 }\right)\right)^6 \, dx
$$ | $3 \cdot \int{\left(\cos\left(\frac{ x }{ 6 }\right)\right)^6 d x}$ = $C+\frac{9}{2}\cdot\sin\left(\frac{x}{3}\right)+\frac{15}{16}\cdot x+\frac{27}{32}\cdot\sin\left(\frac{2\cdot x}{3}\right)-\frac{3}{8}\cdot\left(\sin\left(\frac{x}{3}\right)\right)^3$ |
509c8613-037d-4553-b210-f89cd8434288 | differential_calc | true | 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 | The graphs of the continuous functions $f$ and $g$ are shown. Let $h(x) = -5 \cdot f(x) - g(x) + 3 \cdot x^2$. Find $h'(2)$. | $h'(2)$ = $15$ |
50a65ac5-fd17-452d-a81f-fc9ce7492fe9 | differential_calc | false | null | Evaluate $\lim_{x \to 0^{+}} \left( \left( \frac{ \tan(4 \cdot x) }{ 4 \cdot x } \right)^{\frac{ 1 }{ 2 \cdot x^2 }} \right)$ using L'Hopital's Rule. | $\lim_{x \to 0^{+}} \left( \left( \frac{ \tan(4 \cdot x) }{ 4 \cdot x } \right)^{\frac{ 1 }{ 2 \cdot x^2 }} \right)$ = $e^{\frac{8}{3}}$ |
50b3292a-5159-410f-811e-6cefeab6f78a | precalculus_review | false | null | Given $k$ as an integer and $a \ne \pi \cdot k$, evaluate $P=\cos(a) \cdot \cos(2 \cdot a) \cdot \cos(4 \cdot a) \ldots \cos\left(2^n \cdot a\right)$. | The final answer: $P=\frac{1}{2^{n+1}}\cdot\frac{\sin\left(2^{n+1}\cdot a\right)}{\sin(a)}$ |
50c99276-f6a4-4769-86d3-1c5338bb62b1 | algebra | false | null | Multiply the rational expressions and express the product in simplest form:
$$
\frac{ 2 \cdot d^2+9 \cdot d-35 }{ d^2+10 \cdot d+21 } \cdot \frac{ 3 \cdot d^2+2 \cdot d-21 }{ 3 \cdot d^2+14 \cdot d-49 }
$$ | The final answer: $\frac{2\cdot d-5}{d+7}$ |
50f9b4f4-fe8f-40e1-8b8c-56f2c06fd385 | integral_calc | false | null | Solve the integral:
$$
\int \left(\frac{ x+6 }{ x-6 } \right)^{\frac{ 3 }{ 2 }} \, dx
$$ | $\int \left(\frac{ x+6 }{ x-6 } \right)^{\frac{ 3 }{ 2 }} \, dx$ = $C+\sqrt{\frac{x+6}{x-6}}\cdot(x-30)-18\cdot\ln\left(\left|\frac{\sqrt{x-6}-\sqrt{x+6}}{\sqrt{x-6}+\sqrt{x+6}}\right|\right)$ |
510a0ac3-d3f3-40e2-9d7a-8f0f487490c8 | sequences_series | false | null | Find the radius of convergence of the series:
$$
\sum_{n=1}^\infty \left( \left(n^{\frac{ 1 }{ n }}-1\right)^n \cdot x^n \right)
$$ | $R$ = $\infty$ |
51106f64-d305-4db0-b14f-2d0ec24181d3 | integral_calc | true | 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 | Consider the cycloid given by the parametric equations $x = 2 \cdot \left(t - \sin(t)\right)$, $y = 2 \cdot \left(1 - \cos(t)\right)$.
Find the area of the surface obtained by rotating the arc of the cycloid OBA about the segment DE. | The final answer: $\frac{64\cdot\pi}{3}$ |
517c1de0-1f6b-4762-8073-04faf90d2df8 | integral_calc | true | 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 | A car is speeding up and its velocity is recorded in the following table.
Use the table to estimate the total distance traveled, giving an
* upper estimate, and
* lower estimate. | The final answer: $44$, $66$ |
51860641-1b22-460b-9fd9-5e074f620c93 | precalculus_review | false | null | Solve the differential equation: $\frac{ d y }{d x} = \sin(x)^2$. The curve passes through the point $(0,0)$. | $f(x)$ = $\frac{x}{2}-\frac{\sin(2\cdot x)}{4}$ |
51dae41a-dc02-4794-8d1a-c0cc2838d16d | multivariable_calculus | false | null | A small appliances company makes toaster ovens and pizza cookers, and have noticed their customer base's purchasing habits give them the price-demand equations given below, where $p$ is the price and $x$ is the quantity of toaster ovens, $q$ is the price and $y$ is the quantity of pizza cookers. The Cost function is $C(x,y) = 160 + 12 \cdot x + 24 \cdot y$.
$p = 50 - 4 \cdot x + y$ and $q = 100 + x - 5 \cdot y$
1. Construct the 2-product Revenue function, $R(x,y)$
2. Find $R(8,10)$
3. Construct the 2-product Profit function, $P(x,y)$
4. Find $P(8,10)$ | 1. $R(x,y)$ = $R(x,y)=50\cdot x+100\cdot y+2\cdot x\cdot y-4\cdot x^2-5\cdot y^2$
2. $R(8,10)$ = $804$
3. $P(x,y)$ = $P(x,y)=38\cdot x+76\cdot y+2\cdot x\cdot y-160-4\cdot x^2-5\cdot y^2$
4. $P(8,10)$ = $308$ |
51f91d21-b2e5-408b-b549-aaec8249f58b | multivariable_calculus | true | 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 | The region $D$ is shown in the following figure. Evaluate the double integral $\int\int_{D}{\left(x^2+y\right) d A}$ by using the easier order of integration. | $\int\int_{D}{\left(x^2+y\right) d A}$ = $\frac{256}{15}$ |
526a43b4-e38a-43d7-8930-47b626fbf7ef | precalculus_review | false | null | 1. Find the inverse function of $f(x) = \sqrt{x-1}$
2. Find the domain of the inverse function
3. Find the range of the inverse function | 1. The inverse function is: $x^2+1$
2. The domain of the inverse function is: $x\ge0$
3. The range of the inverse function is: $y\ge1$ |
52ba9ace-9cce-481d-bc05-13c2eb4d5460 | differential_calc | false | null | Find the derivative of the function $y = \frac{ 3 \cdot \csc(x) - 4 \cdot \sin(x) }{ 8 \cdot \left(\cos(x)\right)^5 } - \frac{ 76 }{ 5 } \cdot \cot(3 \cdot x)$. | $y'$ = $\frac{228}{5\cdot\left(\sin(3\cdot x)\right)^2}+\frac{16\cdot\left(\cos(x)\right)^6-5\cdot\left(\cos(x)\right)^4-3\cdot\left(\cos(x)\right)^6\cdot\left(\csc(x)\right)^2}{8\cdot\left(\cos(x)\right)^{10}}$ |
52dac142-fce4-4cac-8d4c-02d6f91936b9 | sequences_series | false | null | Find the Fourier series of the function $f(x) = \frac{ 1 }{ 4 } \cdot x$ in the interval $[-3,3]$. | The Fourier series is: $\sum_{n=1}^\infty\left(\frac{\frac{3}{2}\cdot(-1)^{n+1}}{\pi\cdot n}\cdot\sin\left(\frac{\pi\cdot n\cdot x}{3}\right)\right)$ |
531fbc44-4d03-459d-bc47-0dd40bf62702 | integral_calc | false | null | Find the area bounded by the curves $y = 3 \cdot x + 3$, $y = 3 \cdot \cos(x)$, and $y = 0$. | Area: $\frac{9}{2}$ |
5381ca65-50cc-430f-b450-b4e00e2e6040 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ 1 }{ \left(\cos(5 \cdot x)\right)^3 } \, dx
$$ | $\int \frac{ 1 }{ \left(\cos(5 \cdot x)\right)^3 } \, dx$ = $C+\frac{\sin(5\cdot x)}{10\cdot\left(\cos(5\cdot x)\right)^2}+\frac{1}{10}\cdot\ln\left(\left|\tan\left(\left(\frac{5}{2}\right)\cdot x+\frac{\pi}{4}\right)\right|\right)$ |
541e5d98-324c-43bf-b2f7-56b3fdec55f0 | sequences_series | false | null | Find the domain of convergence of the series $\sum_{n=1}^\infty \left(\frac{ x^n }{ n \cdot 10^{n-1} }\right)$. | The final answer: $-10\le x<10$ |
548e5105-3474-4300-9672-0196f2a27c1a | integral_calc | false | null | Compute the integral:
$$
2 \cdot \int \left(\cos\left(\frac{ x }{ 4 }\right)\right)^6 \, dx
$$ | $2 \cdot \int{\left(\cos\left(\frac{ x }{ 4 }\right)\right)^6 d x}$ = $C+2\cdot\sin\left(\frac{x}{2}\right)+\frac{3}{8}\cdot\sin(x)+\frac{5}{8}\cdot x-\frac{1}{6}\cdot\left(\sin\left(\frac{x}{2}\right)\right)^3$ |
5491d76d-661b-40b8-8192-b4c98c1dd5b6 | differential_calc | true | data:image/png;base64,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 | Given the graphs of $f(x)$ and $g(x)$ above, find $m'(4)$ where $m(x) = f\left(g(x)\right)$. | $m'(4)$ = $1$ |
54b9cf44-c38c-4ccf-8e90-71e67b980af1 | integral_calc | true | 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 | Find the area of the surface formed by rotating the loop of the parametric curve $x = t^2$, $y = \frac{ t \cdot \left(t^2 - 3\right) }{ 3 }$ between the points $P(0,0)$ and $P(3,0)$ about the x-axis (see the picture below): | The final answer: $3\cdot\pi$ |
551ab8c6-6717-445e-9eb3-a9b72ff35da6 | algebra | false | null | Use synthetic division to find the quotient and remainder. Ensure the equation is in the form required by synthetic division:
$$
\frac{ 4 \cdot x^3-12 \cdot x^2-5 \cdot x-1 }{ 2 \cdot x+1 }
$$
Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor. Solve on a paper, if it is more convenient for you. | Quotient: $2\cdot x^2-7\cdot x+1$ Remainder: $-2$ |
5564d511-3879-48af-baed-3005bc3a2261 | precalculus_review | false | null | Find the inverse of the function $f(x) = \frac{ 4-2 \cdot \sqrt{x} }{ 4+2 \cdot \sqrt{x} }$. | The final answer: $\frac{4\cdot(1-x)^2}{(x+1)^2}$ |
557fa740-6516-45d6-a45a-1bfc252ab6e1 | sequences_series | false | null | Using the series expansion for the function $(1+x)^m$, calculate approximately $\sqrt[4]{15}$ with an accuracy of 0.0001. | The final answer: $1.968$ |
558c9ebf-be00-40bc-a0cd-e1a4432bac21 | precalculus_review | true | 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 | The graph of a function $f$ is given in the figure below:
1. What is the value or limit of $f(x)$ as $x$->$\infty$?
2. What is the value or limit of $x$->$b^{+}$?
3. What are the vertical asymptotes? (Enter as x=_)
4. What are the horizontal asymptotes? (Enter as y=_)
5. Give the value (letter), if any, at which the graph of $f$ has a vertical tangent.
6. Give the value (letter), if any, at which the graph of $f$ has a vertical cusp. | 1. As $x$->$\infty$, $f(x)$->$d$
2. As $x$->$b^{+}$, $f(x)$->$c$
3. Vertical asymptotes at $x=a$
4. Horizontal asymptotes with $y=d$
5. $f$ has a vertical tangent at $x=p$
6. $f$ has a vertical cusp at $x=q$ |
5597a385-33cd-41a2-b5ad-dbc9390e795c | differential_calc | false | null | What are the points of inflection of the graph of $f(x) = \frac{ x+1 }{ x^2+1 }$? | The final answer: $x_1=1 \land x_2=-2+\sqrt{3} \land x_3=-2-\sqrt{3}$ |
55c912d9-77af-430d-8bc8-fde2929769da | differential_calc | false | null | Find the local minimum and local maximum values of the function $f(x) = \frac{ x^4 }{ 2 } - \frac{ 20 }{ 3 } \cdot x^3 + 24 \cdot x^2 + 13$. | The point(s) where the function has a local minimum: $P(0,13)$, $P(6,85)$
The point(s) where the function has a local maximum: $P\left(4,\frac{295}{3}\right)$ |
55dc25d0-d0df-47f6-ac8a-f4f29087033a | integral_calc | true | 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 | Compute the area enclosed by the curve $y = x^2 - 3 \cdot x$, the line $x = -4$, and the $x$-axis as shown below: | Area = $\frac{299}{6}$ |
568e4b30-a796-49d7-aaf8-5ca4d6418607 | differential_calc | false | null | Evaluate $\lim_{x \to 0}\left(\left(\frac{ \sin(4 \cdot x) }{ 4 \cdot x }\right)^{\frac{ 1 }{ 3 \cdot x^2 }}\right)$. | $\lim_{x \to 0}\left(\left(\frac{ \sin(4 \cdot x) }{ 4 \cdot x }\right)^{\frac{ 1 }{ 3 \cdot x^2 }}\right)$ = $e^{-\frac{8}{9}}$ |
56f22d87-6f2d-41cd-a939-1a15194856dc | multivariable_calculus | false | null | Find partial derivatives of the function $r = \sqrt{a \cdot x^2 - b \cdot y^2}$. | $\frac{\partial}{\partial x}(r)$ = $\frac{a\cdot x}{\sqrt{a\cdot x^2-b\cdot y^2}}$
$\frac{\partial}{\partial a}(r)$ = $\frac{x^2}{2\cdot\sqrt{a\cdot x^2-b\cdot y^2}}$
$\frac{\partial}{\partial y}(r)$ = $-\frac{b\cdot y}{\sqrt{a\cdot x^2-b\cdot y^2}}$
$\frac{\partial}{\partial b}(r)$ = $-\frac{y^2}{2\cdot\sqrt{a\cdot x^2-b\cdot y^2}}$ |
570d1fef-3e41-428e-af8f-0eb4802e9667 | integral_calc | true | data:image/png;base64,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 | Split the region between the two curves $y = x^3$ and $y = x^2 + x$ into two smaller regions, then determine the area by integrating over the $x$-axis. Note that you will have two integrals to solve. | Area = $\frac{13}{12}$ |
575785fa-191f-4c8c-bb7c-9ca9c825b568 | sequences_series | false | null | Find the Fourier series of the function $f(x) = \frac{ -1 }{ 3 } \cdot x$ in the interval $[-3,3]$. | The Fourier series is: $\sum_{n=1}^\infty\left(\frac{2\cdot(-1)^n}{\pi\cdot n}\cdot\sin\left(\frac{\pi\cdot n\cdot x}{3}\right)\right)$ |
57a3be6d-92a6-4afd-9f1e-c15fc64195dc | algebra | false | null | Solve the following equations:
1. $2 m - 8 = -28$
2. $\frac{ x }{ 9 } - 3 = 8$
3. $12 m + 20 = -40$
4. $-\frac{ x }{ 3 } + 5 = 21$
5. $8 r - 27 = -19$
6. $6 + \frac{ k }{ 3 } = 33$
7. $15 = -4 y - 9$
8. $8 w + 4 = -36$ | The solutions to the given equations are:
1. $m=-10$
2. $x=99$
3. $m=-5$
4. $x=-48$
5. $r=1$
6. $k=81$
7. $y=-6$
8. $w=-5$ |
57b00837-b0bf-47f4-b0ce-76f29fbd9c0f | precalculus_review | false | null | Solve the following inequality by using rules of the absolute value function. Express your answer as an interval or union of intervals.
$\left| |x+3| + |x-2| \right| \le 9$ | The final answer: $[-5,4]$ |
57f16359-5178-4dc3-9c70-6dc3b425a540 | sequences_series | false | null | Find the Fourier series of the function $u = \left| \frac{ \sin\left( \frac{ x }{ 2 } \right) }{ 2 } \right|$ in the interval $[-\pi, \pi]$. | The Fourier series is: $\frac{1}{\pi}-\frac{2}{\pi}\cdot\sum_{n=1}^\infty\left(\frac{1}{\left(4\cdot n^2-1\right)}\cdot\cos(n\cdot x)\right)$ |
5876988d-f7b7-4106-aae1-88d2bd872ed3 | differential_calc | false | null | Find the derivative of the 25th order $y^{(25)}$ for a function $y = 2 \cdot x^2 \cdot \sin(x)$. | $y^{(25)}$ = $\left(2\cdot x^2-1200\right)\cdot\cos(x)+100\cdot x\cdot\sin(x)$ |
58a92fd4-6288-4849-8902-9d02c154e0c2 | differential_calc | false | null | Find the second derivative $\frac{d ^2y}{ d x^2}$ of the function $x = 5 \cdot \left(\cos(t)\right)^3$, $y = 6 \cdot \left(\sin(3 \cdot t)\right)^3$. | $\frac{d ^2y}{ d x^2}$ = $\frac{-15\cdot\left(\cos(t)\right)^2\cdot\sin(t)\cdot\left(324\cdot\sin(3\cdot t)-486\cdot\left(\sin(3\cdot t)\right)^3\right)-\left(30\cdot\cos(t)-45\cdot\left(\cos(t)\right)^3\right)\cdot54\cdot\left(\sin(3\cdot t)\right)^2\cdot\cos(3\cdot t)}{\left(-15\cdot\left(\cos(t)\right)^2\cdot\sin(t)\right)^3}$ |
58e2d06c-dce7-4705-aa36-ca5e519312ac | algebra | false | null | Rewrite the quadratic expression $x^2 - 10 \cdot x + 7$ by completing the square. | $x^2 - 10 \cdot x + 7$ = $(x-5)^2-18$ |
5903bf68-557c-4045-b8f0-5601f1e040ac | precalculus_review | false | null | Solve $\sin(x) + 7 \cdot \cos(x) + 7 = 0$. | The final answer: $x=2\cdot\pi\cdot k-2\cdot\arctan(7) \lor x=\pi+2\cdot\pi\cdot k$ |