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

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

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

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

\frac{1}{e ^{7}}

Decimal Notation

0.00091 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e ^{7}}

= \frac{1}{e ^{7}}

\int \frac{( x ^{3} - 4 x )}{( x ^{2} + 1 ) ^{2}} d x

\int 7 x^{4} - 5 x^{3} + 4 x^{2} + C d x

(x + 2) y^{^{'}} - y = \frac{3}{x + 2}

x \to \infty + lim (\frac{1}{x})

(\frac{t}{y}) d y + (1 + ln (y)) d t = 0

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