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Math Help - Non differentiabilty

  1. #1
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    Non differentiabilty

    consider summation[(1/2^n)h(3^nx)]
    Consider summation[(1/3^n)h(2^nx)]
    where h(x)=|x|
    I'm trying to see whether these functions are continuous and differentiable.
    I know summation[(1/2^n)h(2^nx)] is continuous and not differentiable, but am unsure about theseothers.
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  2. #2
    MHF Contributor chisigma's Avatar
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    A little question: writing [for example...] 'h(2^nx)' do You mean h(2^{n} x) or h(2^{n x})?...

    Kind regards

    \chi \sigma
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  3. #3
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    h(2^{n} x)
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  4. #4
    MHF Contributor chisigma's Avatar
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    Very well!... one of the properties of h(*) is that h(a\ x)= |a|\ h(x) , so that...

    \displaystyle \sum_{n=0}^{\infty} \frac{h(2^{n}\ x)}{3^{n}} = h(x)\ \sum_{n=0}^{\infty} (\frac{2}{3})^{n} = 3\ h(x) (1)

    Kind regards

    \chi \sigma
    Last edited by chisigma; February 11th 2011 at 05:23 AM.
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