The limit limh→0cos(π+h)−(−1)h represents f′ (a) for some function f and some number a. Find f(x) and a.

Question

The limit lim h→0 [cos(π+h)−(−1)] / h represents f′ (a) for some function f and some number a. Find f(x) and a.

f(x) = ??

a = π

I know that a = π , so I added that in.

Answer 1

f'(a) = lim_h→0 [(f(a+h) - f(a)) / h]

So, if f(x) = cosx and a = π, we get the given limit.