Answer
$ a.\quad\infty$.
$ b.\quad\infty$.
$ c.\quad\infty$.
$ d.\quad\infty$.
$ e.\quad-\infty$.
$ f.\quad$ does not exist.
Work Step by Step
$a.$
Nearing $x=1$ from the left, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 1^{-}}f(x)=\infty$.
$b.$
Nearing $x=1$ from the right, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 1^{+}}f(x)=\infty$.
$c.$
Neither one-sided limit exists, but both are $+\infty.$ We write: $\displaystyle \lim_{x\rightarrow 1}f(x)=\infty$.
$d.$
Nearing $x=2$ from the left, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 2^{-}}f(x)=\infty$.
$e.$
Nearing $x=2$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 2^{+}}f(x)=-\infty$.
$f.$
Neither one-sided limit exists, one is $+\infty$, the other $-\infty.$
We write: $\displaystyle \lim_{x\rightarrow 1}f(x)$ does not exist.
