Answer
The limit does not exist.
Work Step by Step
In order to obtain the limit of $\lim\limits_{x \to \ 2}f(x)$ we have to trace the graph.
We only have to consider the limit, not the value of $f(2)$.
As we trace the graph, we can observe, that as we approach 2 from both sides, the function does not converge to the same value from left and right.
Therefore we can conclude, that the limit does not exist.
