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}

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f (x) = ln (x + 9)

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\int_{1}^{10} \frac{13}{x ^{3}} d x

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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