What is the limit as x approaches 0 of (1-5x)^{1/x} ?

The limit as x approaches 0 of (1-5x)^{1/x} is 1/(e^5)

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limit as x approaches 0 of (1-5x)^{1/x}

x \to 0 lim ((1 - 5 x)^{\frac{1}{x}})

\frac{1}{e ^{5}}

Decimal

0.00673 \dots

Solution steps

x \to 0 lim ((1 - 5 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 - 5 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{5}}

= \frac{1}{e ^{5}}

What is the limit as x approaches 0 of (1-5x)^{1/x} ?
The limit as x approaches 0 of (1-5x)^{1/x} is 1/(e^5)