Answer
$-\frac{1}{6}$
Work Step by Step
$\lim\limits_{t \to 5}\frac{3-\sqrt{t+4}}{t-5}=\lim\limits_{t \to 5}\frac{3-\sqrt{t+4}}{t-5}\times \frac{3+\sqrt{t+4}}{3+\sqrt{t+4}}$
$=\lim\limits_{t \to 5}\frac{9-(t+4)}{(t-5)(3+\sqrt{t+4}}$
$=\lim\limits_{t \to 5}\frac{-(t-5)}{(t-5)(3+\sqrt{t+4})}$
$=\lim\limits_{t \to 5}\frac{-1}{3+\sqrt{t+4}}$
$=\frac{-1}{3+\sqrt{5+4}}$
$=\frac{-1}{3+3}$
$=-\frac{1}{6}$
