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

x \to \frac{4 π}{3} lim (sin (x))

x \to \frac{1}{2} lim (- \frac{x ^{2}}{2} - 2)

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

x \to 2 lim (ln (3 - x))

x \to 0 + lim (x^{2} \cdot e^{\frac{1}{x}})

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