Problem 452 (difficulty: 8/10)

Suppose that the function \(\displaystyle f:\R\to\R\) is continuous, and \(\displaystyle f(n\cdot a)\to0\) for all \(\displaystyle a>0\). Prove that \(\displaystyle \lim\limits_{x\to\infty} f=0\).

Give me another random problem!

Subject, section:
Requested difficulty:
Request for a concrete problem:I want problem no.

Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government