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}}

x \to 1 lim (x^{2} - 2 x + 4)

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

x \to 3 - lim (ln (3 - x))

t \to \frac{1}{3} lim (5 t - 7)

x \to \infty lim ((1 + sin (\frac{3}{x}))^{x + 1})

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)