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

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

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

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

1

Solution steps

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

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