Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.5 Limits at Infinity - 2.5 Exercises - Page 96: 5

Answer

The end behavior of $f(x) = -2x^3$ on $(-\infty,+\infty)$ is given by $$\lim\limits_{x \to -\infty}-2x^3=+\infty$$ and $$\lim\limits_{x \to \infty}-2x^3=-\infty$$

Work Step by Step

As $x$ grows to $\infty$, $2x^3$ grows to positive infinity, hence $-2x^3$ grows to $-\infty$.Similarly, when $x$ grows to negative infinity, $-2x^3$ grows towards $+\infty$.
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