Answer
a. 0
b. does not exist
Work Step by Step
The graph consists of points (x,f(x)).
When inspecting limits at x=a, approach a on the x axis and
observe what happens to the y-coordinate, f(x), on the graph.
A limit exists only if both one-sided limits exist, and are equal,
-----------
Note: $f(0)=2, f(2)=-2\\$
a.
As $x$ approaches $0$ from the left or from the right,
$f(x)$ gets closer to $0$.
Both one-sided limits exist, and are equal,
$\displaystyle \lim_{x\rightarrow 0}f(x)=0$
b.
As $x$ approaches 2 from the left,
$f(x)$ gets closer to $-2$.
As $x$ approaches 2 from the right,
$f(x)$ gets closer to 1.
Both one-sided limits exist, but are NOT equal,
$\displaystyle \lim_{x\rightarrow 2}f(x)$ does not exist.
