What is the limit as x approaches 0-of (x-5)e^{1/x} ?

The limit as x approaches 0-of (x-5)e^{1/x} is 0

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 (x-5)e^{1/x}

x \to 0 - lim ((x - 5) e^{\frac{1}{x}})

0

Solution steps

x \to 0 - lim ((x - 5) 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 - 5) \cdot x \to 0 - lim (e^{\frac{1}{x}})

x \to 0 - lim (x - 5) = - 5

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

= (- 5) \cdot 0

Simplify

= 0

x \to 0 lim (\frac{2 x}{x + 1})

x \to 1 lim (x^{2} - 3 x + 5)

x \to - 1 lim (2 x^{3} - 5 x)

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

x \to 0 lim (+ (x^{x}))

What is the limit as x approaches 0-of (x-5)e^{1/x} ?
The limit as x approaches 0-of (x-5)e^{1/x} is 0