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 97: 32

Answer

$$-\frac{5}{2}$$

Work Step by Step

\begin{align*} \lim _{x \rightarrow-\infty} \frac{\sqrt[3]{x}-5 x+3}{2 x+x^{2 / 3}-4}&=\lim _{x \rightarrow-\infty} \frac{\frac{1}{x^{2 / 3}}-5+\frac{3}{x}}{2+\frac{1}{x^{1 / 3}}-\frac{4}{x}}\\ &=\frac{\lim _{x \rightarrow-\infty}\frac{1}{x^{2 / 3}}-\lim _{x \rightarrow-\infty}(5)+\lim _{x \rightarrow-\infty}\frac{3}{x}}{\lim _{x \rightarrow-\infty}(2)+\lim _{x \rightarrow-\infty}\frac{1}{x^{1 / 3}}-\lim _{x \rightarrow-\infty}\frac{4}{x}}\\ &=-\frac{5}{2} \end{align*}
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