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

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

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

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

- \infty

Solution steps

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

Divide by

e^{x} : \frac{1}{\frac{1}{e ^{x}} - 1}

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

For

x

approaching

0

from the right

, x > 0 \Rightarrow \frac{1}{e ^{x}} - 1 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

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