Does any one have interesting problems related to periodicity of functions?
Problem: Prove that the function $\displaystyle f(x) = \sin x + \sin(\sqrt2\,x)$ is not periodic.
[Hint for solution: The only point where $\displaystyle f'(x) = 1+\sqrt2$ is x=0.]
Problem: Prove that the function $\displaystyle f(x) = \sin x + \sin(\sqrt2\,x)$ is not periodic.
[Hint for solution: The only point where $\displaystyle f'(x) = 1+\sqrt2$ is x=0.]
Or the more general problem : if $\displaystyle m(x)$, $\displaystyle n(x)$ are continuous functions having periods $\displaystyle P, Q$ respectively, then $\displaystyle m(x)+n(x)$ is periodic iff $\displaystyle P/Q \in \mathbb{Q}$.