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

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}

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