What is the limit as x approaches-infinity of-xe^x ?

The limit as x approaches-infinity of-xe^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-infinity of-xe^x

x \to - \infty lim (- x e^{x})

0

Solution steps

x \to - \infty lim (- x e^{x})

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

= - x \to - \infty lim (x e^{x})

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

Simplify

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

= - x \to - \infty lim (- e^{x})

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

= - (- x \to - \infty lim (e^{x}))

Apply the common limit:

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

= - (- 0)

Simplify

= 0

What is the limit as x approaches-infinity of-xe^x ?
The limit as x approaches-infinity of-xe^x is 0