What is the limit as x approaches infinity of (1+(2/x))^{3x} ?

The limit as x approaches infinity of (1+(2/x))^{3x} is e^6

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+(2/x))^{3x}

x \to \infty lim ((1 + (\frac{2}{x}))^{3 x})

e^{6}

Decimal Notation

403.42879 \dots

Solution steps

x \to \infty lim ((1 + \frac{2}{x})^{3 x})

Apply exponent rules

= x \to \infty lim (e^{3 x l n (1 + \frac{2}{x})})

Apply the Limit Chain Rule:

e^{6}

= e^{6}

x \to 4 lim (\frac{- 1}{x ^{2} - 16})

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

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

h \to 0 lim (3 h + 18)

What is the limit as x approaches infinity of (1+(2/x))^{3x} ?
The limit as x approaches infinity of (1+(2/x))^{3x} is e^6