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}

\frac{d}{d t} (- s t)

(u^{- 2} + u^{- 3}) (u^{5} - 4 u^{2})

y^{^{'}} = (\frac{y + 3}{4 x + 5})^{3}

\frac{2 x}{7 - cot ( x )}

\int y (y^{2} + 1)^{5} d y

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