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

The limit as x approaches-infinity of x*e^x is 0

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limit as x approaches-infinity of x*e^x

x \to - \infty lim (x \cdot 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

\frac{d}{d y} (sin^{2} (y))

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\frac{\partial}{\partial y} (\frac{- 2 y}{( 2 x + 3 y ) ^{2}})

\frac{d}{d x} (- \frac{3}{( 1 + 3 x ) ^{2}})

(x^{2} - 2 x + 5) 25 - x^{2}

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