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
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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
Transcribed Image Text: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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