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

Popular >

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

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

e

Decimal Notation

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

\frac{d y}{d x} = 1 + y - x

3 x^{2} - 6 x - 9, at x = 3

\frac{\partial}{\partial y} (\frac{x y ^{2}}{x ^{2} y ^{3} + 1})

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

6, 0, 16 - 2 x

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