Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - Review - Exercises - Page 286: 7

Answer

$$\frac{1}{2}$$

Work Step by Step

Given $$\lim _{x \rightarrow \infty} \frac{3 x^{4}+x-5}{6 x^{4}-2 x^{2}+1} $$ Then \begin{align*} \lim _{x \rightarrow \infty} \frac{3 x^{4}+x-5}{6 x^{4}-2 x^{2}+1}&=\lim _{x \rightarrow \infty} \frac{3+\frac{1}{x^{3}}-\frac{5}{x^{4}}}{6-\frac{2}{x^{2}}+\frac{1}{x^{4}}}\\ &= \frac{3+0+0}{6-0+0}\\ &=\frac{1}{2} \end{align*}
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