Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.3 The Fundamental Theorem for Line Integrals - 16.3 Exercises - Page 1135: 31


a) Yes b) Yes c) Yes

Work Step by Step

a) The region should not have any boundary point in order to get the open set . There is no boundary point in the given set $0\lt y\lt 3$.So, the set is open. b) Any two points in the region domain $D$ should be connected to a straight segment path In order to get the connected set that lies entirely inside the domain $D$. So, the set is connected. c) The region should not contain any holes or does not divided into two parts In order to get the simply connected set.So, the given set $0\lt y\lt 3$ satisfies this condition.So, the set is simply connected.
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