Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 3

Answer

a) -4, $f(-4)$ is not defined. -2, the left and right hand limits are not equa,l so the limit does not exist. 2, the left and right hand limits are not equal, so the limit does not exist. 4, the left and right hand limits are not equal, so the limit does not exist. b) -4, neither -2, left 2, right 4, right

Work Step by Step

a) explanation as above b) Since $f$ is not defined at $x = -4$, $f$ is not continuous from any side at $x = 4$. $f(-2) = \lim\limits_{x \to -2^-}f(x)$, so $f$ is continuous from the left. $f(2) = \lim\limits_{x \to 2^+}f(x)$, so $f$ is continuous from the right. $f(4) = \lim\limits_{x \to 4^+}f(x)$, so $f$ is continuous from the right.
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