What is the limit as x approaches 0 of (e^{-6x}-1)/x ?

The limit as x approaches 0 of (e^{-6x}-1)/x is -6

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limit as x approaches 0 of (e^{-6x}-1)/x

x \to 0 lim (\frac{e ^{- 6 x} - 1}{x})

- 6

Solution steps

x \to 0 lim (\frac{e ^{- 6 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 6 e ^{- 6 x}}{1})

= x \to 0 lim (\frac{- 6 e ^{- 6 x}}{1})

Plug in the value

x = 0

= \frac{- 6 e ^{- 6 \cdot 0}}{1}

Simplify

= - 6

x \to 0 + lim ([ln (x)]^{x})

x \to \infty + lim (x b)

x \to 3 - lim (3)

x \to 4 lim (\frac{1}{x - 2})

x \to 0 lim (e^{a r c t a n (x)})

What is the limit as x approaches 0 of (e^{-6x}-1)/x ?
The limit as x approaches 0 of (e^{-6x}-1)/x is -6