Question

The value of \( \lim _{x \rightarrow 0} \frac{f(2+h)-f(2-h)}{h} \) is equal to

Answer 1

\(\lim\limits_{x\to 0} \frac{f(2 + h)- f(2 -h)}{h}\)

\(= \lim\limits_{x\to 0} \frac{f(2 +h)- f(2 + f(2) - f(2 -h))}{h}\)

\(= \lim\limits_{x\to 0} \frac{f(2 +h) - f(2)}{h} + \lim\limits_{h\to 0} \frac{f(2 -h) - f(2)}{-h}\)

\(= f'(2) + f'(2)\)

\(= 2f'(2)\).