Answer
does not exist
Work Step by Step
The left and right limits exist, as found in parts (b) and (c),
but
they are not equal (one is 1, the other is $-1)$.
Therefore, the limit $\displaystyle \lim_{x\rightarrow 0}f(x)$ does not exist.
(step 5 in "Evaluating Limits Graphically")
