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Math Help - Find lim x -> 0+ (x^x^2)

  1. #1
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    Find lim x -> 0+ (x^x^2)

    Find lim x -> 0+ (x^x^2)

    I havent really understood indeterminate powers and how you could use natural logs or an exponential (e) to solve it. Could someone please explain using both these methods for this question?
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  2. #2
    MHF Contributor chisigma's Avatar
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    It is not fully clear what function you mean... in both case however the limit is the same...

    \lim_{x \rightarrow 0+} (x^{x})^{2} = \lim_{x \rightarrow 0+} e^{2 x \ln x} = 1

    \lim_{x \rightarrow 0+} x^{(x^{2})} = \lim_{x \rightarrow 0+} e^{x^{2} \ln x} = 1

    Kind regards

    \chi \sigma
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