This is the indeterminate form 0/0, so apply L'Hôpital's rule to get the desired result.
i'm having some trouble with the ideas behind this question.
f is a continuous, defferentiable function with f(0)=0
given prove that
so i need a way to relate the value that some sequence converges to and the first derivative of a related function evaluated at 0.
i'm having a really hard time with this question. effectively i've got nothing on it and its been a good 5-7 hours so i don't think i can solve it with what i know already.
Your numerator is correct, but the denominator would simply be (1/n)', which cancels with this same factor in the numerator that results from the chain rule.
After that, what you wrote is correct, except let n go to infinity rather than x.