What is the limit as x approaches-infinity of x^4e^x ?

The limit as x approaches-infinity of x^4e^x is 0

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limit as x approaches-infinity of x^4e^x

x \to - \infty lim (x^{4} e^{x})

0

Solution steps

x \to - \infty lim (x^{4} e^{x})

Rewrite for L'Hopital

= x \to - \infty lim (\frac{x ^{4}}{\frac{1}{e ^{x}}})

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{4 x ^{3}}{- e ^{- x}})

= x \to - \infty lim (\frac{4 x ^{3}}{- e ^{- x}})

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{12 x ^{2}}{e ^{- x}})

= x \to - \infty lim (\frac{12 x ^{2}}{e ^{- x}})

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{24 x}{- e ^{- x}})

= x \to - \infty lim (\frac{24 x}{- e ^{- x}})

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{24}{e ^{- x}})

= x \to - \infty lim (\frac{24}{e ^{- x}})

Simplify

\frac{24}{e ^{- x}} : 24 e^{x}

= x \to - \infty lim (24 e^{x})

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

= 24 \cdot x \to - \infty lim (e^{x})

Apply the common limit:

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

= 24 \cdot 0

Simplify

= 0

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

f (x) = (\frac{3 x ^{2}}{2 x + 4})^{3}, x = 2

100 x + 0.01 x^{2}

\frac{d}{d x} (4 (2 - x^{2})^{2})

\int_{0}^{l n (2)} 4 (2 - x e^{x}) d x

What is the limit as x approaches-infinity of x^4e^x ?
The limit as x approaches-infinity of x^4e^x is 0