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

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

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

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

\infty

Solution steps

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

Simplify

\frac{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 1 lim (\frac{π}{x - 1})

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

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

x \to a lim (\frac{a - x}{a - x})

x \to - 2 lim (2 x^{3} + x^{2} - 4)

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