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

Which of the following definite integrals is equal to $\underset{n\to \infty }{lim}\sum \frac{10}{n}(1+\frac{5k}{n}{)}^2(k=1n)$?

To what number does the series $\sum \underset{}{k=0}\stackrel{}{\infty }{\left(-\frac{1}{2}\right)}^k$ converge?

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?

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

What does it mean to say that $\underset{n\to \infty }{lim}{a}_n=8$?

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?