Answer
the limit $\displaystyle \lim_{x\rightarrow 0}f(x)$ does not exist
Work Step by Step
Follow the steps in "Evaluating Limits Graphically"
(step 5: determine if the limit at x=a exists)
x=0.
In parts (b) and (c), we determined (going through steps 1-4) that
at x=1, both one-sided limits exist
BUT
are not equal, $\displaystyle \lim_{x\rightarrow 0^{-}}f(x)=2,\ \displaystyle \lim_{x\rightarrow 0^{+}}f(x)=-3$
Therefore
the limit $\displaystyle \lim_{x\rightarrow 0}f(x)$ does not exist
