What is the limit as x approaches 0 of (1-x/2)^{1/x} ?

The limit as x approaches 0 of (1-x/2)^{1/x} is 1/(sqrt(e))

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limit as x approaches 0 of (1-x/2)^{1/x}

x \to 0 lim ((1 - \frac{x}{2})^{\frac{1}{x}})

\frac{1}{e}

Decimal Notation

0.60653 \dots

Solution steps

x \to 0 lim ((1 - \frac{x}{2})^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 - \frac{x}{2})})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

x \to 0 lim (\frac{x tan ( 2 x )}{sin ^{2} ( 3 x )})

x \to 3 lim (x^{2} + 7 x + 2)

x \to 0 lim (\frac{ln ( 1 + m x )}{x})

x \to \infty lim (3 x + 5)

m \to 0 lim (\frac{sin ( m )}{m})

What is the limit as x approaches 0 of (1-x/2)^{1/x} ?
The limit as x approaches 0 of (1-x/2)^{1/x} is 1/(sqrt(e))