Question

What is the limit as x approaches a
of (sinx-sin a)/(x-a)?

a. -sin a
b. cos a
c. -sin x
d. cos x
e. undefined
Thanks!

Answer 1

take derivatives top and bottom. The desired limit is the same as the limit of

(cosx-0)/1 = cosx

Now take the limit as x->a
so, (b) is the answer.