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 left

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

The denominator is a positive quantity approaching 0 from the right

= \infty

f (x) = e^{- x} x - 2 e^{- x}

\frac{\partial}{\partial x} (cos (8 x y))

y = 2 x + 8

\int 1 + 36 x d x

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