What is the limit as x approaches 0-of 1/(x^3-x) ?

The limit as x approaches 0-of 1/(x^3-x) is infinity

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limit as x approaches 0-of 1/(x^3-x)

x \to 0 - lim (\frac{1}{x ^{3} - x})

\infty

Solution steps

x \to 0 - lim (\frac{1}{x ^{3} - x})

For

x

approaching

0

from the left

, x < 0 \Rightarrow x^{3} - x > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

What is the limit as x approaches 0-of 1/(x^3-x) ?
The limit as x approaches 0-of 1/(x^3-x) is infinity