Question

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

• A. $-\cos a$
• B. $\sin a$
• C. $-\sin a$
• D. None of these

Answer 1

The correct option is C $-\sin a$

$=\underset{x\to a}{lim}\frac{\cos x-\cos a}{x-a}$
Apply L hospital Rule

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

$=[-\sin x]x=a$

$=-\sin a$