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

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

\int e^{- 2 x} x d x

\frac{\partial}{\partial x} (x^{4} y^{8} + 4 x^{5} y)

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

\frac{d}{d x} (5 lo g_{2} (x))

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

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