Originally Posted by
pseudonym Hi, can someone please help me with this question:
Suppose f: (0, infinity) -> R is differentiable, determine whether the following are true or false and give proofs.
(i) If the limit of f(x) (with x tending to infinity) exists and is finite, then the limit of f '(x) (with x tending to infinity) is zero.
(ii) If the limit of f '(x) (with x tending to infinity) is zero, then the limit of f(x)/x (with x tending to infinity) is zero.
I'm not even sure where to start, so any help would be great