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

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

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

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

- 1

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

= - 1

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