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

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

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limit as x approaches infinity of e^xx^2

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

\infty

Solution steps

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

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

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

x \to - \infty lim (\frac{1}{0})

x \to 3 lim (\frac{2 x}{9 - x ^{2}})

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

x \to 3 lim (x^{3} + 6 x)

x \to 0.1 lim (e^{- \frac{1}{x}})

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