Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 66: 6


(a) 2 (b) -4

Work Step by Step

(a) If $f$ is left-continuous at $x=3$, then $\lim\limits_{x \to 3^{-}}f(x)=f(3)$. As $f(x)=2$ for $x\lt3,$ $\lim\limits_{x \to 3^{-}}f(x)=2$ $\implies f(3)=2$ (b) If $f$ is right-continuous at $x=3$, then $\lim\limits_{x \to 3^{+}}f(x)=f(3)$. As $f(x)=-4$ for $x\gt3,$ $\lim\limits_{x \to 3^{+}}f(x)=-4$ $\implies f(3)=-4$
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