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

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

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

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

Decimal Notation

0.71653 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

arctan (- 2 x)

y^{^{''}} + b y^{^{'}} = 0

x^{2}, x^{2} - 4 x + 4, 0, 2

\int 2 - \frac{1}{x} d x

\frac{\partial}{\partial x} (2 cos (x y^{2}))

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