Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises: 24

Answer

$\lim\limits_{p \to -1} f(x) = 0.6$

Work Step by Step

$\lim\limits_{p \to -1} \frac{1+p^{9}}{1+p^{15}}$ Chose numbers close to -1. $x | f(x)$ $-0.95 | 0.68$ $-0.99 | 0.62$ $-0.9999 | 0.60$ $-0.99999 | 0.60$ $-0.9999999 | 0.60$ $\lim\limits_{p \to -1^{-}} \frac{1+p^{9}}{1+p^{15}} = 0.60$ $x | f(x)$ $-1.5| 0.086$ $-1.1| 0.43$ $-1.01| 0.58$ $-1.001| 0.60$ $-1.00001| 0.60$ $\lim\limits_{p \to -1^{+}} \frac{1+p^{9}}{1+p^{15}} = 0.60$ By the table of numbers it appears that $\lim\limits_{p \to -1^{-}} f(x) = 0.60$ and $\lim\limits_{p \to -1^{+}} f(x) = 0.60$. So $\lim\limits_{p \to -1} f(x) = 0.60$.
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