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Math Help - differentiability and continuity of function

  1. #1
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    differentiability and continuity of function

    Prove that the function f(x)=\sum^{\infty}_{n=1} |\sin x|^{\sqrt{n}} is continuous on (-1,1). Examine differentiability of it on (-1,1).
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  2. #2
    Super Member girdav's Avatar
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    Re: differentiability and continuity of function

    What did you try? Did you already show the convergence of the series?
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  3. #3
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    Re: differentiability and continuity of function

    Because of |\sin x|<\sin 1<1 on  (-1,1)we know that the series is convergent. Is that right?
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  4. #4
    Super Member girdav's Avatar
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    Re: differentiability and continuity of function

    Yes (maybe you should detail the fact that the series \sum_{n=0}^{+\infty}a^{\sqrt n} converges for 0<a<1). Use the fact that the series is normally convergent. For the differentiability, look at 0.
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