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 - 1.4 Exercises: 62

Answer

The function is continuous when $a=-2.$

Work Step by Step

$\lim\limits_{x\to1^-}f(x)=3(1^-)^3=3.$ $\lim\limits_{x\to1^+}f(x)=a(1^+)+5=a+5.$ For the function to be continuous, $\lim\limits_{x\to1^+}f(x)=\lim\limits_{x\to1^-}f(x)\to$ $a+5=3\to a=-2.$
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