Question

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

Answer 1

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

Apply L - Hospital Rule

$\underset{x\to \alpha }{lim}\frac{\frac{\cos \sqrt{x}}{2\sqrt{x}}}{1}$

$\frac{\cos \sqrt{\alpha }}{2\sqrt{\alpha }}$