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

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

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

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

\frac{1}{e ^{3}}

Decimal Notation

0.04978 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e ^{3}}

= \frac{1}{e ^{3}}

\int (sin (x) + 7 cos (x) - 1) d x

(t e)^{3} e^{- 2 (t + 1)}

n = 5 \sum \infty e^{5 - 2 n}

\frac{3}{s ^{2} - 2 s - 15}

\int (\frac{7}{x ^{2} + 1}) d x

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