What is the limit as x approaches 0 of (1-5x)^{7/x} ?

The limit as x approaches 0 of (1-5x)^{7/x} is 1/(e^{35)}

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limit as x approaches 0 of (1-5x)^{7/x}

x \to 0 lim ((1 - 5 x)^{\frac{7}{x}})

\frac{1}{e ^{35}}

Decimal Notation

6.30512 E - 16

Solution steps

x \to 0 lim ((1 - 5 x)^{\frac{7}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{7}{x} l n (1 - 5 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{35}}

= \frac{1}{e ^{35}}

\frac{x}{x + 13}

x \to - 5 lim (\frac{x ^{2} + 6}{x + 2})

x \to 1 lim (\frac{x}{x ^{2} - 2 x + 1})

\frac{d}{d x} (\frac{6}{5} \cdot cos (x))

\frac{a}{2 s ^{3}}

What is the limit as x approaches 0 of (1-5x)^{7/x} ?
The limit as x approaches 0 of (1-5x)^{7/x} is 1/(e^{35)}