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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.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:34 pm ad1c9bdddf
    https://brainmass.com/math/computing-values-of-functions/periodic-function-proof-29513

    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

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