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# Periodic function proof

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

##### Solution Summary

This proves a function is not periodic.

##### 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 ...

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• BSc, University of Bucharest
• MSc, Ovidius
• MSc, Stony Brook
• PhD (IP), Stony Brook
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##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.