Answer
$ a.\quad\infty$.
$ b.\quad-\infty$.
$ c.\quad$does not exist.
$ d.\quad-\infty$.
$ e.\quad-\infty$.
$ f.\quad -\infty$.
Work Step by Step
$ a.\quad$
Nearing $x=2$ from the left, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 2^{-}}f(x)=\infty$.
$ b.\quad$
Nearing $x=2$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 2^{+}}f(x)=-\infty$.
$ c.\quad$
Neither one-sided limit exists, one is $+\infty$, the other $-\infty.$
We write: $\displaystyle \lim_{x\rightarrow 2}f(x)$ does not exist.
$ d.\quad$
Nearing $x=4$ from the left, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 4^{-}}f(x)=-\infty$.
$ e.\quad$
Nearing $x=4$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 4^{+}}f(x)=-\infty$.
$ f.\quad$
Neither one-sided limit exists, but both are $-\infty.$
We write: $\displaystyle \lim_{x\rightarrow 4}f(x)=-\infty$.
