What is the limit as x approaches 0 of (1-7x)^{4/x} ?

The limit as x approaches 0 of (1-7x)^{4/x} is 1/(e^{28)}

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limit as x approaches 0 of (1-7x)^{4/x}

x \to 0 lim ((1 - 7 x)^{\frac{4}{x}})

\frac{1}{e ^{28}}

Decimal

6.9144 E - 13

Solution steps

x \to 0 lim ((1 - 7 x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{4}{x} l n (1 - 7 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{28}}

= \frac{1}{e ^{28}}

What is the limit as x approaches 0 of (1-7x)^{4/x} ?
The limit as x approaches 0 of (1-7x)^{4/x} is 1/(e^{28)}