Suppose that the function is differentiable at . Also, suppose that for each natural number n, . Prove that
I really don't know how to start this one, please give me some hints, thanks!
It's been too long since I did proofs so I don't have the language, but the key point to me seems to be that for any tiny distance around x=0, there are an infinite number of points such that g(x)=0. That's because of the second assumption that for all those large natural numbers. Hope that helps.