Which of the following best describes the remainder estimate for the integral test when determining the convergence of a series $\sum \underset{\infty }{n=1}{a}_n$ with $a_n=f\left(n\right)$, where $f$ is positive, continuous, and decreasing for $x\ge 1$?

Given the curve $r\left(t\right)=(3t,4t)$, for $t\ge 0$, starting from the point $t=0$, which of the following is the correct reparametrization of the curve in terms of arclength $s$?

Determine the interval of convergence for the series $\sum n_1\infty \frac{{(x-2)}^n}{n}$. Express your answer using interval notation.

Find the radius of convergence, $r$, of the series $\sum \underset{}{n=1}\stackrel{}{\infty }\frac{{(-1)}^n{x}^n}{5^n}$.

A tangent line approximation of a function value is an overestimate when the function is:

Which of the following best describes the difference between the average rate of change and the instantaneous rate of change of a function $f\left(x\right)$ at a point $x=a$?

Approximate the sum of the series $\sum _{n=1}\infty \frac{{-}^{n}6n}{n!}$ correct to four decimal places.

Given the double integral $\int {\int }_{y=0}{y=2}^{}{\int }_{x=y^2}{x=4}^{}f(x,y) dx dy$, which of the following represents the correct limits of integration after changing the order of integration?

Find the exact length of the curve $y=\ln (1-x^2)$ for $0\le x\le \frac{1}{3}$.