Topic
Q:
Evaluate the following indefinite integrals
a. \( \int \frac{d x}{\sin x\left(2+\cos ^{2} x\right)} \)
b. \( \int \frac{3 x^{2}+7 x+12}{(x+1)\left(x^{2}+7 x+5\right)} d x \)
Q:
Discuss and sketch the graph of the following functions
a. \( f(x)=x^{4}-6 x^{2} \)
b. \( \mathrm{f}(\mathrm{x})=\frac{x}{(x+1)^{2}} \)
Q:
Determine the location and value of the absolute extreme values of \( f \) on the given interval, if they exist.
\( f(x)=\frac{8 x^{3}}{3}+5 x^{2}-12 x \) on \( [-3,1] \)
Q:
\begin{tabular}{l} Question \\ Consider the function \( f(x) \) below. Over what open interval(s) is the function decreasing and concave up? Give your answer \\ in interval notation. \\ \( \qquad f(x)=\frac{x^{4}}{4}-\frac{75 x^{2}}{2}-250 x-4 \) \\ Enter \( \varnothing \) if the interval does not exist. \\ Provide your answer below: \\ \hline\end{tabular}
Q:
d. \( f(x)=\frac{\sqrt{2 x^{2}+1}}{3 x-5} \)
2. Find the derivative of the function
a. \( F(x)=\int_{\tan x}^{x^{2}} \frac{1}{\sqrt{2+t^{4}}} d t \)
Q:
\begin{tabular}{l} Question \\ Consider the function \( f(x) \) below. Over what open interval(s) is the function increasing and concave down? Give your \\ answer in interval notation. \\ \( \qquad f(x)=\frac{x^{4}}{4}-\frac{16 x^{3}}{3}+\frac{77 x^{2}}{2}-98 x+9 \) \\ Enter \( \varnothing \) if the interval does not exist. \\ \hline Provide your answer below: \\ \hline\end{tabular}
Q:
Find the intervals on which \( f \) is increasing and decreasing.
\[ f(x)=-x^{2}+8 \ln x \]
Select the correct choice below and, if necessary, fill in the answer box(e
Q:
\( \int \frac { d x } { 3 + \sqrt { x + 2 } } \)
Q:
3. Evaluate the following indefinite integrals
a. \( \int \frac{d x}{\sin x\left(2+\cos ^{2} x\right)} \)
b. \( \int \frac{3 x^{2}+7 x+12}{(x+1)\left(x^{2}+7 x+5\right)} d x \)
Q:
equation of the curve is \( y=\ln \left(2 x^{2}+5 x\right) \), where \( x>0 \). Find the \( x \)-coordinate of
on the curve at which the normal to the curve is perpendicular to the line
\( 2 x+25 \).
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