Answer
a) $f(x,y,z)=x.y.z+z^2$
b) $77$
Work Step by Step
Let’s find a function $f$ such that $\nabla f=F$. We have:
$F=(y.z,x.z,x.y+2.z)$
$C: r(t)=A+(B-A).t = (1,0,-2)+[(4,6,3)-(1,0,-2)].t=(1,0,-2)+(3,6,5).t=(1+3.t,6.t,-2+5.t): 0
Calculus: Early Transcendentals 8th Edition
by Stewart, James
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 1094: 15
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