Answer
a. $\displaystyle \lim_{x\rightarrow 3}f(x)=3,\quad $
b. $\displaystyle \lim_{x\rightarrow 0}f(x)=1$
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, (f(x) approaches a fixed value) and are equal,
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(f is not defined for x=0)
a.
As $x$ gets closer to 3 from the left, $f(x)$ gets closer to 3.
This also happens when $x$ gets closer to 3 from the right.
Both one-sided limits exist, and are equal,
$\displaystyle \lim_{x\rightarrow 3}f(x)=3$
b.
As $x$ gets closer to $0$ from either the left or right,
$f(x)$ gets closer to 1.
Both one-sided limits exist, and are equal,
$\displaystyle \lim_{x\rightarrow 0}f(x)=1$.
