Thursday, 17 October 2013

calculus - Prove that limxrightarrow+inftyleft(g(x+sqrtx)g(x)right)=0

Let g:(1,+)R, differentiable, such that |g(x)|1x for all x>1. Show that
lim



Seems like the mean value theorem is useful. However, not sure how to prove the fact.



Remark:



The hints says that only proving

\lim_{x\rightarrow +\infty}|g(x+\sqrt{x})-g(x)|=0.
won't suffice.

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