Answer
(a)
$\lim_{x \to 3}g(x)$ does not exist.
(b)
$$\lim_{x \to 0}g(x)=0$$
Work Step by Step
(a)
Looking at the graph we find that when $x$ approaches $3$ from the left and right, the function $g(x)$ becomes unbounded and approaches $+ \infty $ and $- \infty $, respectively. So, $\lim_{x \to 3}g(x)$ does not exist.
(b)
Looking at the graph, we find that when $x$ approaches $0$ from the left and right, the function $g(x)$ approaches $0$. So,$$\lim_{x \to 0}g(x)=0 .$$
