What is the limit as x approaches 0 of (1-4x)^{6/x} ?

The limit as x approaches 0 of (1-4x)^{6/x} is 1/(e^{24)}

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limit as x approaches 0 of (1-4x)^{6/x}

x \to 0 lim ((1 - 4 x)^{\frac{6}{x}})

\frac{1}{e ^{24}}

Decimal Notation

3.77513 E - 11

Solution steps

x \to 0 lim ((1 - 4 x)^{\frac{6}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{6}{x} l n (1 - 4 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{24}}

= \frac{1}{e ^{24}}

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What is the limit as x approaches 0 of (1-4x)^{6/x} ?
The limit as x approaches 0 of (1-4x)^{6/x} is 1/(e^{24)}