Question

Evaluate the following limits
${lim}_{x\to a}\frac{\sqrt{x+8}}{\sqrt{x}}$

Answer 1

Let $L={lim}_{x\to a}\frac{\sqrt{x+8}}{\sqrt{x}}$

This is not an indeterminate form.

Therefore, $L=\frac{\sqrt{a+8}}{\sqrt{a}}$

$\Rightarrow L=\sqrt{\frac{a+8}{a}}$