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: 84

Answer

$f(x)$ is continuous over the interval $(-\infty, 3)$ U $(3, \infty).$

Work Step by Step

$\lim\limits_{x\to3^-}f(x)=\lim\limits_{x\to3^-}(2x-4)=2(3^-)-4=2.$ $\lim\limits_{x\to3^+}f(x)=\lim\limits_{x\to3^+}(2x-4)=2(3^+)-4=2.$ Since $\lim\limits_{x\to3^+}f(x)=\lim\limits_{x\to3^-}f(x)\to\lim\limits_{x\to3}f(x)=2.$ From the given, it can be deduced that $f(3)=1.$ Since $\lim\limits_{x\to3}f(x)\ne f(3),$ the function is not continuous at $x=3.$ $f(x)$ is continuous over the interval $(-\infty, 3)$ U $(3, \infty).$
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