# Periodicity of functions

• Oct 22nd 2009, 07:56 AM
debanik1
Periodicity of functions
Does any one have interesting problems related to periodicity of functions?
• Oct 22nd 2009, 10:55 AM
Opalg
Quote:

Originally Posted by debanik1
Does any one have interesting problems related to periodicity of functions?

Problem: Prove that the function $f(x) = \sin x + \sin(\sqrt2\,x)$ is not periodic.
[Hint for solution: The only point where $f'(x) = 1+\sqrt2$ is x=0.]
• Oct 22nd 2009, 05:34 PM
Bruno J.
Quote:

Originally Posted by Opalg
Problem: Prove that the function $f(x) = \sin x + \sin(\sqrt2\,x)$ is not periodic.
[Hint for solution: The only point where $f'(x) = 1+\sqrt2$ is x=0.]

Or the more general problem : if $m(x)$, $n(x)$ are continuous functions having periods $P, Q$ respectively, then $m(x)+n(x)$ is periodic iff $P/Q \in \mathbb{Q}$.
• Oct 23rd 2009, 03:55 AM
debanik1
thanks

but i want more problems please
• Oct 23rd 2009, 04:23 AM
mr fantastic
Quote:

Originally Posted by debanik1
thanks

but i want more problems please