Question

tip derivitive of trigonometric functions​

Answer 1

Answer:

c) cos a

Step-by-step explanation:

The given limit is:

$Lim_{x\to a} \frac{\sin x-\sin a}{x-a}$

By direction substitution , we get an indeterminate form of:

$\frac{0}{0}$

We apply L'Hopitals rule to get:

$Lim_{x\to a} \frac{\sin x-\sin a}{x-a} = Lim_{x\to a} \frac{(\sin x-\sin a)'}{(x-a)'}$

This implies that:

$Lim_{x\to a} \frac{\sin x-\sin a}{x-a} = Lim_{x\to a} \frac{\cos x}{1}$

This finally gives:

$Lim_{x\to a} \frac{\sin x-\sin a}{x-a} = \cos(a)$