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

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

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

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

- 1

Solution steps

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

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x \to 1 lim (\frac{12}{x + 9})

x \to \frac{1}{4} lim (3 4 x + 8)

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