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

The limit as x approaches infinity of-xe^x is -infinity

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limit as x approaches infinity of-xe^x

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

- \infty

Solution steps

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

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

= - 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

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