Question

Find limits using integrals

Answer 1

I was able to write lim(h→0) (F(2+h) - F(2))/h

but not sure where to go from here

Answer 2

Hmm this a cool problem :)

So from there, does your expression look familiar?
*cough cough* limit definition of a derivative *cough*

Answer 3

\[\large\rm \lim_{h\to0}\frac{F(x+h)-F(x)}{h}\quad=\quad F'(x)\]

Answer 4

So should i make it (F'(2+h) - F'(2))?
Sorry you last comment didn't show correctly.
I know that somehow I'll be able to factor out h in the numerator to be able to cancel it with the h in the denominator.