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

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

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limit as x approaches infinity of x*e^x

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

\infty

Solution steps

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

x \to \infty lim (x) = \infty

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

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