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

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

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

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

\infty

Solution steps

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

Divide by

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

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

For

x

approaching

0

from the right

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

The denominator is a positive quantity approaching 0 from the right

= \infty

\int \frac{28 e ^{4 t}}{6 + e ^{4 t}} d t

1 + cos (θ)

\frac{\partial}{\partial x} (3 x^{7} y^{8} + 8 x^{5} y^{6})

\frac{d}{d x} (\frac{x ^{\frac{2}{3}}}{5 + x + x ^{4}})

\int 4 x + \frac{1}{4 x} d x

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