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Proving derivative of periodic function is also periodic.?

Here is a link to the question prompt:

http://imgur.com/YZmF7K0

I'm really only concerned with showing part b generally, though I'm also happy to get insights on part a...

Any thoughts are appreciated.

2 Answers

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  • 7 years ago
    Favorite Answer

    a) Use the limit definition: [f(x+h) - f(x)] / h. Since f(x) is periodic, if you shift this whole expression in x by one period, then you get exactly the same values of f(x+h) and f(x), so you get the same limit.

    b) Sure. You're just compressing the x-axis by a factor of 2. If f(x) is periodic, it's still periodic whether you stretch or compress the x axis. If you compress the axis, you compress the period.

    For instance, sin(x) has a period of 2pi, sin(2x) has a period of pi.

  • ?
    Lv 4
    4 years ago

    Derivatives Of Periodic Functions

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