Compute the limit of the given function

by RoRi

January 12, 2016

Evaluate the limit.

$\lim_{x \to 0^+} x^{\frac{1}{\log x}}.$

Using the definition of the exponential, we have

$\begin{align*} \lim_{x \to 0^+} x^{\frac{1}{\log x}} &= \lim_{x \to 0^+} e^{ \frac{1}{\log x} \cdot \log x} \\ &= e^1 = e. \end{align*}$

Stumbling Robot