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

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

x \to 1 lim (\frac{x}{∣ 3 x - 4 ∣})

x \to \infty lim (x \cdot \frac{π}{2})

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

x \to \infty lim (\frac{5 x ^{2}}{e ^{x^{3}}})

x \to 0 - lim (\frac{x}{1 - cos ( 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