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

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

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)^x-e)/x

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

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

= diverges

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