What is the limit as x approaches 0 of (1-3x)^{7/x} ?

The limit as x approaches 0 of (1-3x)^{7/x} is 1/(e^{21)}

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limit as x approaches 0 of (1-3x)^{7/x}

x \to 0 lim ((1 - 3 x)^{\frac{7}{x}})

\frac{1}{e ^{21}}

Decimal

7.58256 E - 10

Solution steps

x \to 0 lim ((1 - 3 x)^{\frac{7}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{7}{x} l n (1 - 3 x)})

Apply the Limit Chain Rule:

\frac{1}{e ^{21}}

= \frac{1}{e ^{21}}

\int \frac{t - 3}{t + 1} d t

\int x \cdot (ln (x))^{2} d x

\frac{d}{d x} (\frac{x + 1}{x ^{2} - y + 1})

y^{^{''}} - 6 y^{^{'}} + 9 = 0

(- 5) (0.7)

What is the limit as x approaches 0 of (1-3x)^{7/x} ?
The limit as x approaches 0 of (1-3x)^{7/x} is 1/(e^{21)}