What is the limit as x approaches 0 of (e^{-5x}-1)/x ?

The limit as x approaches 0 of (e^{-5x}-1)/x is -5

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limit as x approaches 0 of (e^{-5x}-1)/x

x \to 0 lim (\frac{e ^{- 5 x} - 1}{x})

- 5

Solution steps

x \to 0 lim (\frac{e ^{- 5 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 5 e ^{- 5 x}}{1})

= x \to 0 lim (\frac{- 5 e ^{- 5 x}}{1})

Plug in the value

x = 0

= \frac{- 5 e ^{- 5 \cdot 0}}{1}

Simplify

= - 5

\frac{d}{d x} (cos (5 x^{2} - x))

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

f (x) = e^{3 e^{x}}

\int (1 + sec (x))^{2} d x

\frac{x}{cos ( x )}

What is the limit as x approaches 0 of (e^{-5x}-1)/x ?
The limit as x approaches 0 of (e^{-5x}-1)/x is -5