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

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

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

e

Decimal Notation

1.64872 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e

= e

\int_{2}^{5} (x - 2)^{2} d x

\int_{0}^{5} \frac{40}{x ^{2} + 25} d x

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

\frac{1}{1 + e ^{- x}}

\int \frac{2 x + 1}{x ^{2} + 2 x + 82} d x

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