Periodicity of functions

**debanik1** · October 22nd 2009, 07:56 AM

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

**Opalg** · October 22nd 2009, 10:55 AM

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.]

**Bruno J.** · October 22nd 2009, 05:34 PM

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

**debanik1** · October 23rd 2009, 03:55 AM

thanks

but i want more problems please

**mr fantastic** · October 23rd 2009, 04:23 AM

Originally Posted by debanik1

thanks

but i want more problems please

Read post #4 here: http://www.mathhelpforum.com/math-he...-problems.html

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