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 + ∣ x ∣

((x + y)^{2}) d x + (2 x y + x^{2} - 8) d y = 0, y (1) = 1

\frac{\partial}{\partial y} (z)

x \to - 2 lim (10 x + 3)

\int (9 - x^{2})^{\frac{1}{2}} d 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