Question

Evaluate
$\rm \displaystyle \lim_{x\to a}\ \frac{\sqrt{x}+\sqrt{a}}{x+a}$

Answer 1

Solution :

$\rm \displaystyle \lim_{x\to a}\ \frac{\sqrt{x}+\sqrt{a}}{x+a}$

= $\rm \displaystyle \frac{\sqrt{a}+\sqrt{a}}{a+a}$

= $\rm \displaystyle \frac{2\sqrt{a}}{2a}$

= $\rm \displaystyle \frac{1}{\sqrt{a}}$

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