Answer
The limit 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 trace the graph, none of these aforementioned limits exist, they both diverge:
$\lim\limits_{x \to \ 0^{+}}f(x)=\infty$
$\lim\limits_{x \to \ 0^{-}}f(x)=\infty$
Although, they both diverge to $\infty$, we cannot say that the limit exists.
Therefore we can conclude, that the limit does not exist.
