Question

Evaluate:-
$\underset{x\to a}{lim}\frac{\cos \sqrt{x}-\cos \sqrt{a}}{x-a}$

Answer 1

$\underset{x\to \alpha }{lim}\frac{\cos \sqrt{x}-\cos \sqrt{\alpha }}{x-2}$

apply L-Hospital Rule

$\underset{x\to \alpha }{lim}\frac{-\sin \sqrt{x}}{2\sqrt{x}}$

$=\frac{-\sin \sqrt{\alpha }}{2\alpha }$