Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 16: Integrals and Vector Fields - Section 16.3 - Path Independence, Conservative Fields, and Potential Functions - Exercises 16.3 - Page 966: 8



Work Step by Step

Consider $f(x,y,z)=yx+zx+g(y,z)$ Also, $\nabla f =F$ and $g_y(y,z)=z$ Then, $g(y,z)=zy+h(z)$ and $h(z)=C$ $f(x,y,z)=yx+zx+zy+h(z)$ Thus, $f(x,y,z)=yx+zx+zy+C$
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