Answer
$(a)$ $\lim_{x\to4}h(x)=0$
$(b)$ $\lim_{x\to-1}h(x)=-5$
Work Step by Step
The graph of the function is shown below:
$(a)$ $\lim_{x\to4}h(x)$
From the graph, it can be seen that when $x$ approaches $4$ from the left and from the right, $h(x)$ approaches $0$.
$\lim_{x\to4}h(x)=0$
$(b)$ $\lim_{x\to-1}h(x)$
From the graph, it can be seen that when $x$ approaches $-1$ from the left and from the right, $h(x)$ approaches $-5$.
$\lim_{x\to-1}h(x)=-5$
