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}

n = 1 \sum \infty n (\frac{2}{3})^{n}

y = sin (x), y = x, x = \frac{π}{2}, x = π

3 + 5 sin (x)

\int_{0}^{a} 7 x a^{2} - x^{2} d x

\frac{a x}{x ^{2} + a ^{2}}

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