What is the limit as x approaches 0-of xe^{1/x} ?

The limit as x approaches 0-of xe^{1/x} is 0

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 xe^{1/x}

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

0

Solution steps

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

x \to 0 - lim (x) = 0

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

= 0 \cdot 0

Simplify

= 0

What is the limit as x approaches 0-of xe^{1/x} ?
The limit as x approaches 0-of xe^{1/x} is 0