Answer
$\lim\limits_{x \to \ 1}f(x)=0$.
Work Step by Step
In order to obtain the limit of $\lim\limits_{x \to \ 1}f(x)$ we have to first look at both one-sided limits. We only have to consider the limits, not the value of $f(1)$.
As we trace the graph, both of these aforementioned limits exist, and they are equal:
$\lim\limits_{x \to \ 1^{+}}f(x)=0$
$\lim\limits_{x \to \ 1^{-}}f(x)=0$
Therefore we can conclude, that the limit exists, $\lim\limits_{x \to \ 1}f(x)=0$.
