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$\large \displaystyle \lim_{x\to 0^+} x^x =\, ?$

$\begin{aligned} 0.5^{0.5} &=& 0.7071\ldots \\ 0.4^{0.4} &=& 0.6931\ldots \\ 0.3^{0.3} &=& 0.6968\ldots \\ 0.2^{0.2} &=& 0.7247\ldots \\ 0.1^{0.1} &=& 0.7943\ldots \\ \end{aligned}$

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