1. ## Periodicity of functions

Does any one have interesting problems related to periodicity of functions?

2. 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.]

3. 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 $P/Q \in \mathbb{Q}$.

4. thanks

but i want more problems please

5. Originally Posted by debanik1
thanks

but i want more problems please