What is the limit as x approaches infinity of (x^2)/(xe^{-x)} ?

The limit as x approaches infinity of (x^2)/(xe^{-x)} is infinity

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limit as x approaches infinity of (x^2)/(xe^{-x)}

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

\infty

Solution steps

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

Simplify

\frac{x ^{2}}{x e ^{- x}} : e^{x} x

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

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

x \to 0 + lim (\frac{e ^{x} - 1}{x ^{2}})

x \to 0 lim (\frac{sin ( 2 x )}{x} + 1)

x \to 0 + lim (x sin (\frac{1}{5 x}))

x \to - \frac{1}{2} lim (2 x + 1)

What is the limit as x approaches infinity of (x^2)/(xe^{-x)} ?
The limit as x approaches infinity of (x^2)/(xe^{-x)} is infinity