What is the limit as x approaches 0 of (1-x)^{2/x} ?

The limit as x approaches 0 of (1-x)^{2/x} is 1/(e^2)

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limit as x approaches 0 of (1-x)^{2/x}

x \to 0 lim ((1 - x)^{\frac{2}{x}})

\frac{1}{e ^{2}}

Decimal

0.13533 \dots

Solution steps

x \to 0 lim ((1 - x)^{\frac{2}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{2}{x} l n (1 - x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

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

4 - 11 x + 6 x^{2}

x 3 + y 3 - 6 x y = 0

\int \frac{1}{2 + 4 x ^{2}} d x

n = 0 \sum \infty sin (π \cdot n)

What is the limit as x approaches 0 of (1-x)^{2/x} ?
The limit as x approaches 0 of (1-x)^{2/x} is 1/(e^2)