What is the limit as x approaches 1 of x^{2/(1-x)} ?

The limit as x approaches 1 of x^{2/(1-x)} is 1/(e^2)

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limit as x approaches 1 of x^{2/(1-x)}

x \to 1 lim (x^{\frac{2}{1 - x}})

\frac{1}{e ^{2}}

Decimal

0.13533 \dots

Solution steps

x \to 1 lim (x^{\frac{2}{1 - x}})

Apply exponent rules

= x \to 1 lim (e^{\frac{2}{1 - x} l n (x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

What is the limit as x approaches 1 of x^{2/(1-x)} ?
The limit as x approaches 1 of x^{2/(1-x)} is 1/(e^2)