Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 16 - Section 16.3 - The Fundamental Theorem for Line Integrals - 16.3 Exercise - Page 1095: 33

Answer

a) No b) Yes c) Yes

Work Step by Step

a) For the open set, the region should not contain any boundary points. When we draw a disk for the given set, we find that it does not entirely lie inside the region D. Thus, the set is not open. b) For the connected set, any two points in the region D can be connected by a path that lies entirely in the region D. From the given points we can draw a path connecting the two points in the region D. Thus, the set is connected. c) For the simply connected set, the region must not have any holes or be divided into two parts. From the given points, it has been seen that the path connecting the two points completely lie inside the given set. Thus, the set is simply connected.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.