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

Popular >

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})

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}})

= 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

x \to 0 lim (\frac{3}{1 + e ^{\frac{1}{x}}})

\int \frac{x ^{2}}{9 - x ^{2}} d x

f (t) = 1 + t

y^{^{'}} + 3 x^{2} y = x^{2}

f (x) = x^{4} - 13 x^{2} + 36, at x = - 1

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