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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

- \frac{1}{3}

Decimal

- 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}})

Plug in the value

x = 0

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

Simplify

= - \frac{1}{3}

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