Answer
$\displaystyle \lim_{\mathrm{x}\rightarrow 0}f(x)$ does not exist.
Work Step by Step
Follow the steps in "Evaluating Limits Graphically"
(step 5: determine if the limit at x=a exists)
In parts (b) and (c) we found that neither of the one sided limits exist, so the limit does not exist.
The one-sided limits do not diverge to the same sides:
the left diverges to $-\infty ,$ the right to $+\infty$,
so we just state that
$\displaystyle \lim_{\mathrm{x}\rightarrow 0}f(x)$ does not exist.