Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 30


$$ -\infty$$

Work Step by Step

Given $$\lim _{x \rightarrow \infty}\left(x^2-x^4\right)$$ Then \begin{aligned} \lim _{x \rightarrow \infty}\left(x^2-x^4\right)&=\lim _{x \rightarrow \infty}x^2\left(1-x^2\right) \\ &=\lim _{x \rightarrow \infty}x^2\lim _{x \rightarrow \infty}\left(1-x^2\right)\\ &= \infty(1- \infty)\\ &= -\infty \end{aligned}
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