Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises: 5

Answer

$|x -2| \lt 2$

Work Step by Step

1. x belongs to the set of points from 0 to 4, with parenthesis indicating that they endpoints are not included. This can be rewritten as: $0 \lt x \lt 4$ 2. In order to express this in terms of an inequality, we must show that: $|x -c| \lt r$ and $c-r \lt x \lt c+r$ 3. By combining steps one and two: $c-r =0$, and $c +r = 4$ 4. In order to satisfy those equations: $c = 2$, and $r = 2$ Therefore: $|x-2| \lt 2$
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