What is the limit as x approaches 0 of (1-2x)^{4/x} ?

The limit as x approaches 0 of (1-2x)^{4/x} is 1/(e^8)

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limit as x approaches 0 of (1-2x)^{4/x}

x \to 0 lim ((1 - 2 x)^{\frac{4}{x}})

\frac{1}{e ^{8}}

Decimal Notation

0.00033 \dots

Solution steps

x \to 0 lim ((1 - 2 x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{4}{x} l n (1 - 2 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{8}}

= \frac{1}{e ^{8}}

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What is the limit as x approaches 0 of (1-2x)^{4/x} ?
The limit as x approaches 0 of (1-2x)^{4/x} is 1/(e^8)