Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.6 Continuity - 2.6 Exercises - Page 108: 12

Answer

$x=2$ ($\lim\limits_{x \to 2} f(x)$ doesn't exist) $x=3$ ($f$ undefined) $x=4$ ($\lim\limits_{x \to 4} f(x)\not=f(4)$)

Work Step by Step

The function has discontinuities in the points: $x=2$ $x=3$ $x=4$ In the point $x=2$, $\lim\limits_{x \to 2} f(x)$ doesn't exist, therefore Condition 2 is violated. In the point $x=3$, $f$ is undefined, therefore Condition 1 is violated. In the point $x=4$, $\lim\limits_{x \to 4} f(x)\not=f(4)$, therefore Condition 3 is violated.
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