Chapter 2.5, Problem 62E

a.

To determine

To analyze: The limit of the functions $\underset{x\to {\left(\frac{\pi }{2}\right)}^{-}}{\lim }\tan x$ and $\underset{x\to {\left(-\frac{\pi }{2}\right)}^{+}}{\lim }\tan x$ and check whether these functions are infinite limits or limits at infnity.

b.

To determine

To sketch: A graph of $g\left(x\right)={\tan }^{-1}x$ by reflecting the graph of f over the line $y=x$ and evaluate $\underset{x\to \infty }{\lim }{\tan }^{-1}x$ and $\underset{x\to -\infty }{\lim }{\tan }^{-1}x$ by using the required graph.