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

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

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

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

\frac{1}{e}

Decimal Notation

0.36787 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

\frac{d}{d x} (- \frac{2 x}{y})

\int \frac{4 x ^{2} - 25}{x} d x

(- 6, 1), (- 4, - 9)

\frac{d}{d x} (4 x + 2)

\int \frac{2}{x ^{2} + 4} d x

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