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: 19

Answer

From the graph we find that: (a) $$ \lim\limits_{x \to 4^{-}} f(x)=\infty $$ (b) $$ \lim\limits_{x \to 4^{+}} f(x)=-\infty $$ (c) $$ \lim\limits_{x \to 4} f(x) $$ does not exist since, $$ \lim\limits_{x \to 4^{-}} f(x)=\infty \neq \lim\limits_{x \to 4^{+}} g(x)=-\infty $$ (d) From the graph we find that: $$ f(4) $$ does not exist since the graph has no point with an $x$-value of 4. Notice in the figure that at a point 4 where the function is discontinuous.

Work Step by Step

From the graph we find that: (a) $$ \lim\limits_{x \to 4^{-}} f(x)=\infty $$ (b) $$ \lim\limits_{x \to 4^{+}} f(x)=-\infty $$ (c) $$ \lim\limits_{x \to 4} f(x) $$ does not exist since, $$ \lim\limits_{x \to 4^{-}} f(x)=\infty \neq \lim\limits_{x \to 4^{+}} g(x)=-\infty $$ (d) From the graph we find that: $$ f(4) $$ does not exist since the graph has no point with an $x$-value of 4. Notice in the figure that at a point 4 where the function is discontinuous.
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