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

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

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

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

\frac{1}{e}

Decimal Notation

0.36787 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

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\frac{\partial}{\partial x} (4 x - 3 x^{4} y^{2})

\int \frac{t ^{5}}{t ^{2} + 2} d t

\int \frac{1}{y ^{\frac{3}{2}}} d y

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