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

The limit as x approaches 3 of (1-3x)^{1/x} is 2(-1)^{1/3}

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

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

2 (- 1)^{\frac{1}{3}}

Solution steps

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

Plug in the value

x = 3

= (1 - 3 \cdot 3)^{\frac{1}{3}}

Simplify

(1 - 3 \cdot 3)^{\frac{1}{3}} : 2 (- 1)^{\frac{1}{3}}

= 2 (- 1)^{\frac{1}{3}}

What is the limit as x approaches 3 of (1-3x)^{1/x} ?
The limit as x approaches 3 of (1-3x)^{1/x} is 2(-1)^{1/3}