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

The limit as x approaches infinity+of (1+1/x)^{x/6} is \sqrt[6]{e}

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)^{x/6}

x \to \infty + lim ((1 + \frac{1}{x})^{\frac{x}{6}})

6 e

Decimal

1.18136 \dots

Solution steps

x \to \infty lim ((1 + \frac{1}{x})^{\frac{x}{6}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{6} l n (1 + \frac{1}{x})})

Apply the Limit Chain Rule:

6 e

= 6 e

n = 6 \sum \infty \frac{n}{n ^{2} + 1}

\frac{\partial}{\partial y} (x^{2} y z^{2})

\int_{5}^{\infty} \frac{1}{x ^{3}} d x

\frac{\partial}{\partial x} (1 - ln (x))

\int_{1}^{3} x \frac{2.25}{x ^{3}} d x

What is the limit as x approaches infinity+of (1+1/x)^{x/6} ?
The limit as x approaches infinity+of (1+1/x)^{x/6} is \sqrt[6]{e}