What is the limit as x approaches 0+of (1-9x)^{9/x} ?

The limit as x approaches 0+of (1-9x)^{9/x} is 1/(e^{81)}

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limit as x approaches 0+of (1-9x)^{9/x}

x \to 0 + lim ((1 - 9 x)^{\frac{9}{x}})

\frac{1}{e ^{81}}

Decimal Notation

6.63968 E - 36

Solution steps

x \to 0 + lim ((1 - 9 x)^{\frac{9}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{9}{x} l n (1 - 9 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{81}}

= \frac{1}{e ^{81}}

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What is the limit as x approaches 0+of (1-9x)^{9/x} ?
The limit as x approaches 0+of (1-9x)^{9/x} is 1/(e^{81)}