Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises - Page 103: 50

Answer

a. $\lim\limits_{x \to 1^{-}}$ $f(x)$ $ = 2$ $\lim\limits_{x \to 1^{+}}$ $f(x)$ $ = 1$ b. The limit of $\lim\limits_{x \to 1} f(x)$ Does not exist c. Graph
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Work Step by Step

$\lim\limits_{x \to 1^{-}}$ $f(x)$ $\lim\limits_{x \to 1^{-}}$ $(x^{2}+1)$ $\lim\limits_{x \to 1^{-}}$ $(1^{2}+1) = 2$ $\lim\limits_{x \to 1^{+}}$ $f(x)$ $\lim\limits_{x \to 1^{+}}$ $(x-2)^{2}$ $\lim\limits_{x \to 1^{+}}$ $(1-2)^{2} = (-1)^{2} = 1$ b. The limit of $\lim\limits_{x \to 1} f(x)$ does not exists because $\lim\limits_{x \to 1^{+}} f(x)$ $\ne$ $\lim\limits_{x \to 1^{-}} f(x)$
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