OK then. First we should state the MVT (mean value theorem) for integrals.
Let f be a function continous on [a,b] and differentiable on (a,b). There exists such c that satisfies,
Now we can work on the problem.
We know that . We have to find . Let
By the definition of derivative,
Oh, we can use the MVT on the expression in red =)
As h approaches x, this limit will go to .
Feel free to ask anything that wasn't clear to you.
Good luck on your second question