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

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

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

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

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

Decimal

6.30512 E - 16

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

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

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

g (x) = \frac{ln ( x )}{x ^{2}}

\frac{d}{d x} ((ln (x))^{13})

(8 x^{2} + 9) (x^{2} - \frac{1}{x})

6 x^{2} - 4 x + 5

\int \frac{( x ^{4} - 5 x ^{2} + 3 x - 4 )}{x} d x

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