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: 59


$ a.\quad -\infty$ $ b.\quad +\infty$

Work Step by Step

$a.$ When $t\rightarrow 0^{+}$, the denominator in $\displaystyle \frac{3}{t^{1/3}}$ is positive, approaching zero, so $\displaystyle \frac{3}{t^{1/3}}\rightarrow+\infty$ $(2-\displaystyle \frac{3}{t^{1/3}})\rightarrow-\infty$ $b.$ When $t\rightarrow 0^{-}$, the denominator in $\displaystyle \frac{3}{t^{1/3}}$ is negative, approaching zero, so $\displaystyle \frac{3}{t^{1/3}}\rightarrow-\infty$ $(2-\displaystyle \frac{3}{t^{1/3}})\rightarrow+\infty$
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