Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 98: 48

Answer

$+\infty$

Work Step by Step

When $x\rightarrow 0$, from either the positive ($x\rightarrow 0^{+})$ or the negative ($x\rightarrow 0^{-}$) side, the numerator is positive. In the denominator, $x^{2/3}= (x^{1/3})^{2}$, which is positive, approaching zero. Thus, the whole fraction $\displaystyle \frac{1}{x^{2/3}}\rightarrow+\infty \qquad$ ... ( $\displaystyle \frac{pos.}{neg.}$ )
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