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 Notation

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}}

\int_{0}^{2} (x + 2) d x

\int 20 e^{- 0.8 t} d t

\frac{\partial}{\partial x} (y + 2 - \frac{2}{x})

\frac{d}{d x} (3 sin (x) + cos (x))

x \to 8 lim (2 - 6 x^{2} + x^{3})

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)