Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.6 - Limits at Infinity; Horizontal Asymptotes - 2.6 Exercises: 33

Answer

$$\lim\limits_{x\to-\infty}(x^2+2x^7)=-\infty$$

Work Step by Step

$$\lim\limits_{x\to-\infty}(x^2+2x^7)$$$$=\lim\limits_{x\to-\infty}x^7\Bigg(\frac{1}{x^5}+2\Bigg)$$$$=\lim\limits_{x\to-\infty}(x^7)\times\Bigg[\lim\limits_{x\to-\infty}\Big(\frac{1}{x^5}\Big)+2\Bigg]$$$$=-\infty\times(0+2)$$$$=-\infty$$
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