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

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

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limit as x approaches 0+of (e^{-x})/x

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

\infty

Solution steps

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

\frac{e ^{- x}}{x} = e^{- x} \frac{1}{x}

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

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

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to \infty lim (\frac{1.5 x}{3 x ^{2}})

x \to 3 lim (4 x - 7)

x \to 3 lim (4 x - 1)

x \to \infty lim (4 x e^{x})

x \to 0 - lim ([x])

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