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: 10

Answer

$x=1$ ($\lim\limits_{x \to 1} f(x)\not=f(1)$) $x=2$ ($\lim\limits_{x \to 2} f(x)$ doesn't exist) $x=3$ ($f$ is undefined)

Work Step by Step

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