1
$\begingroup$

Possible Duplicate:
Limit of a continuous function

Let $f$ be a function that is continuous and real on $[0, \infty]$ such that $\lim_{n \to \infty} f(na) =0$ for all $a>0$. What can be said about $\lim_{x \to +\infty} f(x)$?

Now I was told the answer is $0$ for every $f$ that satisfies the condition. But I do not know how to prove this. Can anyone help me please? Thank you!

1 Answers 1