LetF (x, y, z) = f (x, y, z) i+g (x, y, z) j +h (x, y, z) kand suppose that f, g, and hare continuousand have continuous first partial derivativesin a region. If F is conservative in the region,thenofdgofdgdx 'ahdydxdzWith the aid of these formulas, determinewhether F is conservative.(a) F (x, y, z) = 7 sin 7x i+zj+y kFis(b) F (x, y, z) = 8z° i+ 16y'zj+7y° kZ.Fis||IIII

(a) F(x,y,z)=f(x,y,z) i +g(x,y,z) j + h(x,y,z) kGiven F(x,y,z)= 7sin(7x).i + z.j + y.k∴f(x,y,z)=…

Let F (x, y, z) = f (x, y, z) i+g (x, y, z) j+ h (x, y, z) k and suppose that f, g, and h are continuous and have continuous first partial derivatives in a region. If F is conservative in the region, then of ду dg of dx dh dg dh dz dx dz ду With the aid of these formulas, determine whether F is conservative. (a) F (x, y, z) = 7 sin 7x i+zj+y k Fis (b) F (x, y, z) = 8z° i+ 16y'zj+7y° k Fis

Let F (x, y, z) = f (x, y, z) i+g (x, y, z) j+ h (x, y, z) k and suppose that f, g, and h are continuous and have continuous first partial derivatives in a region. If F is conservative in the region, then of ду dg of dx dh dg dh dz dx dz ду With the aid of these formulas, determine whether F is conservative. (a) F (x, y, z) = 7 sin 7x i+zj+y k Fis (b) F (x, y, z) = 8z° i+ 16y'zj+7y° k Fis

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let
F (x, y, z) = f (x, y, z) i+g (x, y, z) j +h (x, y, z) k
and suppose that f, g, and hare continuous
and have continuous first partial derivatives
in a region. If F is conservative in the region,
then
of
dg
of
dg
dx '
ah
dy
dx
dz
With the aid of these formulas, determine
whether F is conservative.
(a) F (x, y, z) = 7 sin 7x i+zj+y k
Fis
(b) F (x, y, z) = 8z° i+ 16y'zj+7y° k
Z.
Fis
||
II
II

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