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

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}}

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)