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 0

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 ((\frac{1 + 1}{x})^{2 x})

0

Solution steps

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

Simplify

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

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

x \to π lim (\frac{2 x}{3 x ^{2}})

x \to - 2 lim (x^{3} + 6 x)

x \to 0 lim (\frac{x ^{2}}{x ^{4} + 1})

x \to 10 lim (ln (x^{3}))

x \to 1000 lim (ln (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 0