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 - Page 138: 50


vertical asymptotes: $x=1$ $x=-1$ $x=0$ horizontal asymptote: $y=-1$

Work Step by Step

To first find out vertical asymptotes, we can take the denominator of the function and factor it out into $(x+x^{2})(x-x^{2})$. By solving for when y=0, we come up with vertical asymptotes of x=1, x=−1, x=0. To find our horizontal asymptotes, we can take the coefficients of the highest degree in each polynomial. Because both of these are of the second degree, we can divide them to yield $\frac{x^{4}}{-x^{4}}$ to get an asymptote at y=-1
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