What is the limit as x approaches 0 of (e^{-3x}-1)/x ?

The limit as x approaches 0 of (e^{-3x}-1)/x is -3

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limit as x approaches 0 of (e^{-3x}-1)/x

x \to 0 lim (\frac{e ^{- 3 x} - 1}{x})

- 3

Solution steps

x \to 0 lim (\frac{e ^{- 3 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 3 e ^{- 3 x}}{1})

= x \to 0 lim (\frac{- 3 e ^{- 3 x}}{1})

Plug in the value

x = 0

= \frac{- 3 e ^{- 3 \cdot 0}}{1}

Simplify

= - 3

x \to - 4 lim (x^{2} + 4 x)

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (1) = 0

\int sin^{2} (x) \cdot cos (x) d x

f (x) = (x^{2} - 1) (- 3 x^{3} + 2 x)

\int (cos^{2} (x) sin (x)) d x

What is the limit as x approaches 0 of (e^{-3x}-1)/x ?
The limit as x approaches 0 of (e^{-3x}-1)/x is -3