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 Notation

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}

x \to 2 lim (6 x^{2} + 7 x - 3)

x \to 1 lim (x^{5} + 5 x^{4} - x - 1)

x \to - 5 lim (- 10 + 3 x^{2})

x \to 2 lim (x^{2} - 5)

x \to 2 lim ((3 x^{2} + 1)^{x})

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