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}

\frac{\partial}{\partial x} (sin (x t))

\frac{d}{d x} (4 x - x^{2})

n = 0 \sum \infty (x - 4)^{n}

\frac{d}{d x} (\frac{e ^{2 x}}{x})

f (x) = 4 x + \frac{6}{x}, (5, 21.2)

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