Calculus 8th Edition

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

Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 18



Work Step by Step

Given $$ \lim _{x\to -\infty }\frac{\sqrt{1+4x^6}}{2-x^3}$$ Then \begin{aligned} \lim _{x\to -\infty }\frac{\sqrt{1+4x^6}}{2-x^3}&=\lim _{x\to -\infty }\frac{\sqrt{\frac{1}{x^6}+\frac{4x^6}{x^6}}}{\frac{2}{x^3}-\frac{x^3}{x^3}} \\ &=\lim _{x\to -\infty }\frac{\sqrt{\frac{1}{x^6}+4}}{\frac{2}{x^3}-1}\\ &=\lim _{x\to- \infty }\frac{\sqrt{0+4}}{0-1}\\ &= 2 \end{aligned}
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