What is the limit as x approaches 0-of 1/(x^{2/3)} ?

The limit as x approaches 0-of 1/(x^{2/3)} is infinity

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limit as x approaches 0-of 1/(x^{2/3)}

x \to 0 - lim (\frac{1}{x ^{\frac{2}{3}}})

\infty

Solution steps

x \to 0 - lim (\frac{1}{x ^{\frac{2}{3}}})

For

x

approaching

0

from the left

, x < 0 \Rightarrow x^{\frac{2}{3}} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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What is the limit as x approaches 0-of 1/(x^{2/3)} ?
The limit as x approaches 0-of 1/(x^{2/3)} is infinity