Question

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

Answer 1

${lim}_{x\to a}\frac{\sqrt{x}+\sqrt{a}}{x+a}$

This is not an indeterminate form.

Therefore, $L=\frac{\sqrt{a}+\sqrt{a}}{a+a}=\frac{2\sqrt{a}}{2a}$

$\Rightarrow L=\frac{\sqrt{a}}{a}=\frac{1}{\sqrt{a}}$