What is the limit as x approaches+0+of (1+x)^{(1/x)} ?

The limit as x approaches+0+of (1+x)^{(1/x)} is e

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches+0+of (1+x)^{(1/x)}

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

e

Decimal

2.71828 \dots

Solution steps

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

Apply the common limit:

x \to 0 + lim ((1 + x)^{\frac{1}{x}}) = e

= e

What is the limit as x approaches+0+of (1+x)^{(1/x)} ?
The limit as x approaches+0+of (1+x)^{(1/x)} is e