Answer
The $\lim\limits_{x \to \ 0}f(x)$ does not exist.
Work Step by Step
In order to obtain the limit of $\lim\limits_{x \to \ 0} f(x)$ we have to first look at both one-sided limits. We only have to consider the limits, not the value of $f(0)$.
As we saw in exercises (b) and (c), as we trace the graph, none of these aforementioned limits exist, they both diverge:
$\lim\limits_{x \to \ 0^{+}}f(x)=\infty$
$\lim\limits_{x \to \ 0^{-}}f(x)=-\infty$
Therefore the $\lim\limits_{x \to \ 0}f(x)$ simply does not exist.
