Question

The limit represents the derivative of some function f at some number a. State such an f and a. lim-->0 (cos(π + h) + 1)/h

f(x) = cos(x), a = π
f(x) = cos(x), a = 0
f(x) = cos(x), a = π/4
f(x) = cos(x), a = π/3
f(x) = cos(x), a = π/6

Answer 1

\[
f(x) = \cos(x) \\
f'(a) = \lim_{h \rightarrow 0}\frac{\cos(a+h)-\cos(a)}{h} \\
\text{For } a = \pi \\
f'(\pi) = \lim_{h \rightarrow 0}\frac{\cos(\pi+h)-\cos(\pi)}{h} =
\lim_{h \rightarrow 0}\frac{\cos(\pi+h)+1}{h}
\]