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

The limit as x approaches 0+of (1-5x)^{5/x} is 1/(e^{25)}

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

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

\frac{1}{e ^{25}}

Decimal Notation

1.38879 E - 11

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e ^{25}}

= \frac{1}{e ^{25}}

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x \to 2 lim (x^{2} + 6 x + 2)

What is the limit as x approaches 0+of (1-5x)^{5/x} ?
The limit as x approaches 0+of (1-5x)^{5/x} is 1/(e^{25)}