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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{e ^{2}}

Decimal Notation

0.13533 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

x \to 0 lim (\frac{3 x - sin ( k x )}{x})

x \to \frac{π}{2} lim (3 tan (x))

x \to \infty lim (0.6 5^{x})

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

h (x) \to 0 lim (\frac{f ( x ) ( x + 2 h ( x ) ) - f ( x )}{h ( x )})

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