Answer
$(a)$ $\lim_{x\to4}g(x)=\dfrac{12}{5}$
$(b)$ $\lim_{x\to9}g(x)=2$
Work Step by Step
$g(x)=\dfrac{12(\sqrt{x}-3)}{x-9}$
The graph of the function is shown below:
$(a)$ $\lim_{x\to4}g(x)$
From the graph, it can be seen that when $x$ approaches $4$ from the left and from the right, $g(x)$ approaches $\dfrac{12}{5}$
$\lim_{x\to4}g(x)=\dfrac{12}{5}$
$(b)$ $\lim_{x\to9}g(x)$
From the graph, it can be seen that when $x$ approaches $9$ from the left and from the right, $g(x)$ approaches $2$
$\lim_{x\to9}g(x)=2$
