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

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

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

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

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

Decimal Notation

0.13533 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

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

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

\frac{d}{d x} (ln (10 x^{2} - 8))

y^{^{'}} = e^{2 t + y - 1} - 2

\frac{\partial}{\partial x} (e^{x y} + ln (\frac{x}{y}))

\frac{\partial}{\partial x} (2 x y^{2} + 4)

w \to \infty lim (\frac{2 w ^{2} - 3 w + 4}{5 w ^{2} + 7 w - 1})

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