For which positive integers $k$ is the following series convergent? $\sum n_1\infty \frac{{(n!)}^2}{(kn)!}$

Which of the following statements about the series $\sum \underset{}{n=1}\infty \frac{1}{2^n}$ is true?

For which values of p does the improper integral ${\int }_1^{\infty }{x}^{3p+1} dx$ converge?

The graph of $y=f\left(x\right)$ is shown above. What is $\underset{x\to 1}{lim}f\left(x\right)$?

What is the slope of the tangent line to the polar curve $r=2{\theta }^2$ when $\theta =\frac{\pi }{2}$?

Suppose a contour map is given for a function $f$, and you are asked to estimate the partial derivatives $f_x(2,1)$ and $f_y(2,1)$ at the point $(2,1)$. Which of the following best describes how you would use the contour map to estimate these partial derivatives?

Which of the following explains why a function $f\left(x\right)$ is discontinuous at $x=a$?

Given the function $f\left(x\right)=x^2$, what is the average rate of change of $f\left(x\right)$ on the interval $(-1,2)$?