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 139: 61

Answer

The y-intercept is 0 The x-intercepts are -1, 0, and 1 $\lim\limits_{x \to \infty} (x^4-x^6) = -\infty$ $\lim\limits_{x \to -\infty} (x^4-x^6) = -\infty$

Work Step by Step

$y = x^4-x^6$ When $x=0$, then $~~y = (0)^4-(0)^6 = 0$ When $y=0$: $x^4-x^6 = 0$ $x^4(1-x^2) = 0$ $x^4(1-x)(1+x) = 0$ $x = 0, 1,-1$ $\lim\limits_{x \to \infty} (x^4-x^6)$ $=\lim\limits_{x \to \infty} x^4(1-x^2)$ $ = -\infty$ $\lim\limits_{x \to -\infty} (x^4-x^6)$ $=\lim\limits_{x \to -\infty} x^4(1-x^2)$ $ = -\infty$
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