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

= - 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 2 lim (\frac{1 - 4 x}{x + 3})

h \to 0 lim (\frac{ln ( 2 e + h ) - ln ( 2 e )}{h})

x \to 0 lim (\frac{e ^{x} - cos ( x )}{ln ( 1 + x )})

x \to 0 lim (\frac{7 x - 1}{5 x})

x \to 1 lim (2 x - 4)

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