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

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

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

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

- \frac{1}{3}

Decimal Notation

- 0.33333 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= - \frac{1}{3}

3 x^{^{'}} + 6 x = 4, x (0) = 2

\frac{d}{d x} (1100 x^{2} - 0.2 x)

sin (2 x)

\frac{d}{d x} (16 x)

(5 a + 1)^{2}

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