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Math Help - Investigate the validity of Taylor's theorem for f

  1. #1
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    Investigate the validity of Taylor's theorem for f

    f(x) = x^2 sin (1/x) if x in (-1,1) and x is not 0
    f(x)=0 if x=0
    Investigate the validity of Taylor's theorem for f about the point x=0
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  2. #2
    MHF Contributor chisigma's Avatar
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    An f(x) can be expanded in Taylor series around x=x_{0} if in that point f(x) and all its derivatives do exist. For the function You have proposed, in x=0,  f(x) does exist but f^{'}(x) doesn't ...

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    \chi \sigma
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