Question

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

Answer 1

We have,

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

This is the $\frac{0}{0}$ form.

So, apply L-hospital rule

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

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

${lim}_{x\to 0}2\sqrt{x+4}$

$=2\sqrt{0+4}$

$=2\times 2$

$=4$

Hence, this is the answer.