What is the limit as x approaches-infinity of x^3e^x ?

The limit as x approaches-infinity of x^3e^x is 0

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limit as x approaches-infinity of x^3e^x

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

0

Solution steps

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

Rewrite for L'Hopital

= x \to - \infty lim (\frac{x ^{3}}{\frac{1}{e ^{x}}})

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{3 x ^{2}}{- e ^{- x}})

= x \to - \infty lim (\frac{3 x ^{2}}{- e ^{- x}})

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{6 x}{e ^{- x}})

= x \to - \infty lim (\frac{6 x}{e ^{- x}})

Apply L'Hopital's Rule

: x \to - \infty lim (\frac{6}{- e ^{- x}})

= x \to - \infty lim (\frac{6}{- e ^{- x}})

Simplify

\frac{6}{- e ^{- x}} : - 6 e^{x}

= x \to - \infty lim (- 6 e^{x})

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

= - 6 \cdot x \to - \infty lim (e^{x})

Apply the common limit:

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

= - 6 \cdot 0

Simplify

= 0

x \to - 2 - lim (f (x) x)

x \to 0 lim (\frac{2}{x ^{3} + x})

y = π

\frac{\partial}{\partial x} (x^{3} y^{4} + x^{4} y^{3})

\frac{\partial}{\partial x} (e^{\frac{6}{x}})

What is the limit as x approaches-infinity of x^3e^x ?
The limit as x approaches-infinity of x^3e^x is 0