What is the limit as x approaches 0+of (1-4x)^{8/x} ?

The limit as x approaches 0+of (1-4x)^{8/x} is 1/(e^{32)}

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limit as x approaches 0+of (1-4x)^{8/x}

x \to 0 + lim ((1 - 4 x)^{\frac{8}{x}})

\frac{1}{e ^{32}}

Decimal Notation

1.26642 E - 14

Solution steps

x \to 0 + lim ((1 - 4 x)^{\frac{8}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{8}{x} l n (1 - 4 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{32}}

= \frac{1}{e ^{32}}

x \to 2 lim (\frac{3 x}{2 - x})

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

x \to 0 - lim (x^{2} - \frac{6}{x})

x \to 0 lim (cot (11 x))

x \to 0 + lim (3 (\frac{1}{x} - cot (x)))

What is the limit as x approaches 0+of (1-4x)^{8/x} ?
The limit as x approaches 0+of (1-4x)^{8/x} is 1/(e^{32)}