What is the limit as x approaches 0 of (e^{-9x}-1)/x ?

The limit as x approaches 0 of (e^{-9x}-1)/x is -9

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limit as x approaches 0 of (e^{-9x}-1)/x

x \to 0 lim (\frac{e ^{- 9 x} - 1}{x})

- 9

Solution steps

x \to 0 lim (\frac{e ^{- 9 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 9 e ^{- 9 x}}{1})

= x \to 0 lim (\frac{- 9 e ^{- 9 x}}{1})

Plug in the value

x = 0

= \frac{- 9 e ^{- 9 \cdot 0}}{1}

Simplify

= - 9

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What is the limit as x approaches 0 of (e^{-9x}-1)/x ?
The limit as x approaches 0 of (e^{-9x}-1)/x is -9