Answer
As t approaches 9, the limit if g(t) approaches 0.
Work Step by Step
$g(t)=\frac{t-9}{\sqrt t-3}$
$t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g(t)$
$8.9 \ \ \ \ \ \ \ \ \ -0.0167$
$8.99\ \ \ \ \ \ \ -0.0017$
$8.999\ \ \ \ \ -0.00017$
$t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g(t)$
$9.1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0167$
$9.01\ \ \ \ \ \ \ \ \ \ \ \ 0.0017$
$9.001 \ \ \ \ \ \ \ \ \ \ 0.00017$