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}

x \to 2 lim (x^{3} - 3 x^{2} + 2 x - 1)

x \to - 3 - lim (\frac{[ x ] + 1}{∣ x ∣})

x \to 0 lim (\frac{1}{1 + e ^{- x}})

n \to 0 + lim (n^{2} ln (4 n^{2}))

x \to 2 π lim (2 x cos (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