1. Limits and Continuity

Which of the following is true about the graph of $y=\ln |x^2-1|$ in the interval $(-1,1)$?

Estimate the limit $\underset{n\to \infty }{lim}{(2n+1)}^{-9}$ correct to five decimal places.

Given that $f^{\left(n\right)}\left(0\right)$=$(n+1)!$ for $n=0,1,2,\dots$, which of the following is the Maclaurin series for $f\left(x\right)$?

Suppose the average rate of change of $g\left(x\right)$ between $x=4$ and $x=7$ is $0$. Which statement must be true?

Given a table of values for a function $f(x,y)$, which of the following best describes how to estimate the mixed partial derivative $f_{xy}(3,2)$?

Given $f\left(x\right)=x^2$, what is the average rate of change of $f\left(x\right)$ over the interval $[4,6]$?