find the value

Question

lim [sin(x+h)-sinx]/h
h>0

Answer 1

There are many proofs of this, such as the one here:

http://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/sinx

However, it relies on the fact that sinx/x -> 1 as x->0. That is usually proven as given here:

http://math.ucsd.edu/~wgarner/math20a/sin%28x%29_over_x.htm