Question

Evaluate ${lim}_{x\to 4}\frac{3-\sqrt{(5+x)}}{x-4}$

Answer 1

We have,

${lim}_{x\to 4}\frac{3-\sqrt{5+x}}{x-4}$

Apply L-hospital rule,

${lim}_{x\to 4}\frac{0-\frac{1}{2\sqrt{5+x}}}{1-0}$

${lim}_{x\to 4}-\frac{1}{2\sqrt{5+x}}$

$=-\frac{1}{2\sqrt{5+4}}$

$=-\frac{1}{2\sqrt{9}}$

$=-\frac{1}{2\times 3}$

$=-\frac{1}{6}$

Hence, this is the answer.