Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 3 - The Derivative - Chapter Review - Review Exercises - Page 188: 18

Answer

From the graph we find that: (a) $$ \lim\limits_{x \to -1^{-}} g(x)=-2 $$ (b) $$ \lim\limits_{x \to -1^{+}} g(x)=2 $$ (c) $$ \lim\limits_{x \to -1} g(x) $$ does not exist since, $$ \lim\limits_{x \to -1^{-}} g(x)=-2 \neq \lim\limits_{x \to -1^{+}} g(x)=2 $$ (d) From the graph we find that: $$ f(-1)=-2 $$ since the point $(-1,-2)$ is a point of the graph $g(x).$

Work Step by Step

From the graph we find that: (a) $$ \lim\limits_{x \to -1^{-}} g(x)=-2 $$ (b) $$ \lim\limits_{x \to -1^{+}} g(x)=2 $$ (c) $$ \lim\limits_{x \to -1} g(x) $$ does not exist since, $$ \lim\limits_{x \to -1^{-}} g(x)=-2 \neq \lim\limits_{x \to -1^{+}} g(x)=2 $$ (d) From the graph we find that: $$ f(-1)=-2 $$ since the point $(-1,-2)$ is a point of the graph $g(x).$
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