Question

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

Answer 1

We have,

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

This is $\frac{0}{0}$ form.

So, apply L-Hospital rule

$\underset{x\to a}{lim}\frac{\cos x-0}{1-0}$

$\underset{x\to a}{lim}\frac{\cos x}{1}$

$=\cos a$

Hence, this is the answer.