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.