Answer
$a\in (−\infty,2)\cup(2,\infty)$
Work Step by Step
If we reach the same point by approaching from either left or right, then $\lim\limits_{x \to a} f(x)$.
For the graph above, we can see that above description is true for all point but at $a=2$
When we approach $x=2$ from left/negative/direction/$2^{-}$, then $y$ coordinate approaches $2$. Therefore $\lim\limits_{x \to 2^{-}} f(x)=2$
When we approach $x=2$ from the right/positive direction the $y$ coordinate approaches $1$. Therefore $\lim\limits_{x \to 2^{+}} f(x)=1$.
Since $\lim\limits_{x \to 2^{-}} f(x) \ne \lim\limits_{x \to 2^{+}} f(x)$, the following limit does not exist: $\lim\limits_{x \to 2} f(x)$
