What is the limit as x approaches 0+of (e^{-x}-1)/x ?

The limit as x approaches 0+of (e^{-x}-1)/x is -1

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limit as x approaches 0+of (e^{-x}-1)/x

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

- 1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{- e ^{- 0}}{1}

Simplify

= - 1

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

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What is the limit as x approaches 0+of (e^{-x}-1)/x ?
The limit as x approaches 0+of (e^{-x}-1)/x is -1