What is the limit as x approaches 0+of (1-8x)^{1/x} ?

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

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limit as x approaches 0+of (1-8x)^{1/x}

x \to 0 + lim ((1 - 8 x)^{\frac{1}{x}})

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

Decimal

0.00033 \dots

Solution steps

x \to 0 + lim ((1 - 8 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (1 - 8 x)})

Apply the Limit Chain Rule:

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

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

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