Mathematics

Problem

Consider the function

f(x)=\dfrac{\sin x}{x}

, where

x\neq0

. a. (i) Find

f'(x)

and simplify the result as far as possible. b. (ii) Evaluate

f'\!\left(\dfrac{\pi}{4}\right)

. Express your answer in exact form. c. (iii) Verify that

\displaystyle \lim_{x\to0}f'(x)

exists and state its value.