What is the limit as x approaches 0 of (1-x)^{(1/x)} ?

The limit as x approaches 0 of (1-x)^{(1/x)} is 1/e

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limit as x approaches 0 of (1-x)^{(1/x)}

x \to 0 lim ((1 - x)^{(\frac{1}{x})})

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

x \to 0 lim ((1 - x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 - x)})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

What is the limit as x approaches 0 of (1-x)^{(1/x)} ?
The limit as x approaches 0 of (1-x)^{(1/x)} is 1/e