What is the limit as x approaches infinity-of x^2e^x ?

The limit as x approaches infinity-of x^2e^x is infinity

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limit as x approaches infinity-of x^2e^x

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

\infty

Solution steps

x \to \infty lim (x^{2} 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^{2}) \cdot x \to \infty lim (e^{x})

x \to \infty lim (x^{2}) = \infty

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

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

x \to 0 + lim (7 (cot (x) - \frac{1}{x}))

x \to 0 + lim (ln (1) - ln (x))

x \to 0 + lim (b (0)^{2} + ab)

x \to 3 lim (x - [x])

What is the limit as x approaches infinity-of x^2e^x ?
The limit as x approaches infinity-of x^2e^x is infinity