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

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

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

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

\infty

Solution steps

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

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

With the exception of indeterminate form

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

x \to \infty lim (x^{3}) = \infty

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

f (x) = 2 x^{2} + 8 x, at x = 4

n \to 0 lim (sin (\frac{1}{n}))

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

\frac{d ^{2}}{d x ^{2}} (x^{2} + y^{2})

f (x) = 7 x + 4

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