- #1

- 96

- 1

## Homework Statement

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\displaystyle\lim_{x\rightarrow 0^+} x^{1/x}

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## The Attempt at a Solution

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y = \displaystyle\lim_{x\rightarrow 0^+} x^{1/x}

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lny = \displaystyle\lim_{x\rightarrow 0^+} \frac {lnx}{x}

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This gives an indeterminate form and it's a quotient, so I can apply L'Hopital's Rule:

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\displaystyle\lim_{x\rightarrow 0^+} \frac{1}{x}

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As x approaches zero, the expression will grow towards infinity...

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lny = ∞

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e^∞ = y

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y = ∞

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I can't see anything wrong with what I'm doing, yet putting the limit into WolframAlpha spits out a 0. What am I doing wrong?