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

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

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

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

- \infty

Solution steps

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

For

x

approaching

0

from the right

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

The denominator is a negative quantity approaching 0 from the left

= - \infty

(\frac{2 x - 7}{2 + 3 x})

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\int (\frac{x}{2}) d x

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