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{4}{( t + 2 ) ^{2}}

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\int \frac{3 x}{x ^{2} - x - 6} 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