Evaluate \displaystyle\lim{x\to\infty} x^{1/x}.

1 \ln x^{1/x} = (\ln x)/x \to 0, so x^{1/x} \to e^0 = 1.

L'Hôpital's Rule

AP Calculus AB· difficulty 3/5

\displaystyle\lim_{x\to\infty} x^{1/x}

Explanation

\ln x^{1/x} = (\ln x)/x \to 0

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