Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - Review Exercises: 55

Answer

$c=-\dfrac{1}{2}.$

Work Step by Step

$\lim\limits_{x\to2^-}f(x)=\lim\limits_{x\to2^-}(x+3)=2^-+3=5.$ $\lim\limits_{x\to2^+}f(x)=\lim\limits_{x\to2^+}(cx+6)=c(2^+)+6=2c+6.$ For the function to be continuous, $\lim\limits_{x\to2^+}f(x)=\lim\limits_{x\to2^-}f(x)\to$ $2c+6=5\to c=-\dfrac{1}{2}.$
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