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Math Help - Limit of the nth root of a function

  1. #1
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    Limit of the nth root of a function

    I'm looking for a proof of the following statement:

    If lim f(x) exists, then lim nth root [ f(x) ] = nth root [ lim f(x) ]

    I can't seem to find a proof in any Calculus/Analysis books.
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  2. #2
    MHF Contributor
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    Re: Limit of the nth root of a function

    If \lim f(x) > 0, then this holds by the chain rule (the statement about the limit of composition) since \sqrt[n]{x} is continuous for x>0.
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