# Periodic function proof

Please provide explanation to prove that f(x)=sin(x)+sin(x/sqrt(2)) is not periodic.

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#### Solution Preview

The solution is on the attached file.

I assumed that the formulas for the derivatives of sin and cos are known and also that sin(y)= sin(y+2nPI) for any n.

In other words the sin function has period 2PI.

Solution

f(x)=sin(x)+sin(x/sqrt(2))

Suppose that f(x) is periodic with period p. Then f(x+p) - f(x)=0. Now let g(x) = f(x+p) - f(x)=0 .

Since g(x)=0 then g"(x) =0 (this is ...

#### Solution Summary

This proves a function is not periodic.

$2.19