Calculus 8th Edition

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

Chapter 16 - Vector Calculus - 16.1 Vector Fields - 16.1 Exercises - Page 1114: 29


Plot $III$

Work Step by Step

The level sets of $f$ are circles, so the vector filed must be perpendicular to circles, leaving just $I$ and $III$ as possible plots. Explicitly calculating the gradient vector filed, $2(x,y)$ it can be seen that the field diverges from the origin, so the correct plot must be $III$.
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