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: 60

Answer

The y-intercept is 0 The x-intercepts are 0 and 2 $\lim\limits_{x \to \infty} (2x^3-x^4) = -\infty$ $\lim\limits_{x \to -\infty} (2x^3-x^4) = -\infty$
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Work Step by Step

$y = 2x^3-x^4$ When $x=0$, then $~~y = 2(0)^3-(0)^4 = 0$ When $y=0$: $2x^3-x^4 = 0$ $x^3(2-x) = 0$ $x = 0, 2$ $\lim\limits_{x \to \infty} ( 2x^3-x^4)$ $=\lim\limits_{x \to \infty} x^3(2-x)$ $ = -\infty$ $\lim\limits_{x \to -\infty} (2x^3-x^4)$ $=\lim\limits_{x \to -\infty} x^3(2-x)$ $ = -\infty$
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