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

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

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

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

\infty

Solution steps

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

For

x

approaching

0

from the right

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

The denominator is a positive quantity approaching 0 from the right

= \infty

d er i v a t i v e \frac{x ^{3}}{6}

\int x^{2} sin (3 x + 2) d x

\int \frac{1}{4 x} - 10 d x

in v erse l a pl a ce \frac{1}{s ^{1} ( s + 1 ) ^{3}}

a re a f (x) = x^{2} - 4, - 3, 1

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