Calculus: Early Transcendentals 8th Edition

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

Chapter 16 - Section 16.5 - Curl and Divergence - 16.5 Exercise - Page 1109: 14

Answer

NOT conservative.

Work Step by Step

The vector field $F$ will be conservative if and only if $curl F=0$ Let us consider $F=P i+Q j+R k$ $curl F=[R_y-Q_z]i+[P_z-R_z]j+[Q_x-P_y]k$ Now, $curl F=(0-12x^2yz^2)i+(4xyz^3-2xy z^4)j+(8xyz^3-xz^4) \ne 0$ Thus, the vector field $F$ is NOT conservative.
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