How do I show that x^x->1 as x->0?

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- Mar 16th 2006, 12:11 PMTreadstone 71x^x
How do I show that x^x->1 as x->0?

- Mar 16th 2006, 12:19 PMrgep
You could try showing that $\displaystyle x \log x \rightarrow 0$ as $\displaystyle x \rightarrow 0$. If the limit exists it must be zero: consider $\displaystyle x = 2^{-n}$.

- Mar 16th 2006, 12:49 PMTreadstone 71
Got it. Used l'Hopitals