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**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