Question

Calculus question.

Answer 1

Evaluating\[\lim_{h \to 0} \dfrac{f(1 + h) - f(1 - h)}{h}\]I used L'Hospital Rule.\[\lim_{h \to 0} {f'(1 + h) - f'(1 + h)} \quad \Rightarrow \quad f'(1) - f'(1) = 0\]But that is the wrong answer.

Answer 2

\(f(x)\) is given, but I am not sure if we need it.

Answer 3

Please don't laugh at me... I am just a beginner :-P

Answer 4

I am not following entirely yet to be honest, but if you differentiate the second expression, shouldn't there be a plus sign?

\[\Large f'(1+h)-f'(1-h)\cdot (-1) = f'(1+h)+f'(1-h) \]

Answer 5

Oh!!!

Answer 6

I can do the rest with what I am given as f(x). Thanks!

Answer 7

so in that expression it would be:
\[\Large f'(1)+f'(1)=2f'(1) \]
seems elegant enough.

Answer 8

you're welcome