What is the limit as x approaches 0+of (1-x)^{(1/x)} ?

The limit as x approaches 0+of (1-x)^{(1/x)} is 1/e

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limit as x approaches 0+of (1-x)^{(1/x)}

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

\frac{1}{e}

Decimal Notation

0.36787 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

2 x y^{^{'}} - 6 y = x^{- 4}

x \to (\frac{π}{2}) - lim (sec (x))

\frac{d}{d x} ((cot (x) - csc (x))^{- 1})

y = lo g_{10} (x - 1), at x = 2

(2 sin (x) cos (x))^{^{'}}

What is the limit as x approaches 0+of (1-x)^{(1/x)} ?
The limit as x approaches 0+of (1-x)^{(1/x)} is 1/e