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 140: 78


$\lim\limits_{x \to -\infty}x^3 = \infty$

Work Step by Step

Let $f(x) =x^3$ This function is defined on the interval $(-\infty,\infty)$ Let $M \gt 1$ be given. Let $N = M$ Suppose that $x \gt N$ Then: $x^3 \gt x \gt N = M$ Therefore, $\lim\limits_{x \to \infty}x^3 = \infty$
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