L-lim-x-0-x-x-

Question Number 5821 by FilupSmith last updated on 30/May/16

L = \lim_{x \to 0} x^{x}

Answered by bahmanfeshki last updated on 27/Feb/17

\lim_{x \to 0^{+}} e^{x \ln x} = \lim_{x \to 0^{+}} e^{\frac{\ln x}{\frac{1}{x}}} \overset{h o p}{=} \lim_{x \to 0^{+}} e^{\frac{\frac{1}{x}}{- \frac{1}{x^{2}}}} = \lim_{x \to 0^{+}} e^{- x} = 1