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: 5

Answer

$f(2)=6$ makes $f$ continuous at $x=2$.

Work Step by Step

The function $f$ is discontinuous at $x=0,$ where $\lim _{x \rightarrow 0-} f(x)=\infty$ and $\lim _{x \rightarrow 0+} f(x)=2 .$ The function $f$ is also discontinuous at $x=2,$ where $\lim _{x \rightarrow 2-} f(x)=6$ and $\lim _{x \rightarrow 2+} f(x)=6 .$ Because the two one-sided limits exist and are equal at $x=2,$ the discontinuity at $x=2$ is removable. Assigning $f(2)=6$ makes $f$ continuous at $x=2$.
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