## A classic problem on the limit of continuous function at infinity [closed]

I don't know whether it's suitable to post this problem here, but I really need a help.

$f$ is a coutinuous function on $\mathbb{R}^+$, if the limit $\lim_{n\to\infty}f(nx)$ exists for all points $x$ of a nonempty closed set with no isolated point of $\mathbb{R}^+$, prove that the limit $\lim_{x\to\infty}f(x)$ exist.

Please see more details of my quesion here.

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This isn't the site for such questions. You'd be better off responding to the comments you have on Maths-SX and trying some of the suggestions. – Andrew Stacey Sep 19 2011 at 10:15
sorry, I have respondded to all comments for days, but still no one gives an answer. – gylns Sep 19 2011 at 10:30