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

The limit as x approaches infinity of (x*e^{-x})/x is 0

Popular >

limit as x approaches infinity of (x*e^{-x})/x

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

0

Solution steps

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to \infty lim (x e^{- x}) = 0

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

= \frac{0}{\infty}

Apply Infinity Property:

\frac{0}{\infty} = 0

= 0

x \to 2 lim (\frac{3 x}{5 + 8 x})

x \to \frac{π}{4} lim (\frac{x}{tan ( x )})

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

x \to 1 - lim (\frac{3 x + 65 - 4}{x + 1})

x \to 0 lim ([x (x - 2)])

What is the limit as x approaches infinity of (x*e^{-x})/x ?
The limit as x approaches infinity of (x*e^{-x})/x is 0