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Math Help - Derivative

  1. #1
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    Derivative

    Hi,

    I have a question:

    I have the function :
    f(x)=(X^(2n))*sin(1/x) when x is no 0, and f(x)=0 when x=0.
    the question is how many times we can Derivative f(x) in x=0.

    thanks to anyone that can help!
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  2. #2
    Member courteous's Avatar
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    If both right and left limits (falling and rising to 0, respectively) of f(x) exist (and are same), then you can take derivative (you can differentiate) of f(x) at x=0, unlimited times.
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  3. #3
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    hi,

    how do you proof this??
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