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a) State True or False and proved justification for: If S is an ellipsoid and F is a constant vector field then ff, Fñ do = 0.

a) State True or False and proved justification for: If S is an ellipsoid and F is a constant vector field then ff, Fñ do = 0.

Advanced Engineering Mathematics
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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6. Complete each problem: (a) State True or False and proved justification for: If S is an ellipsoid and F is a constant vector field then ff F•ñ do = 0. (b) If f (x, y, z) has continuous partial derivatives and S is a closed surface, show that f (3/5 +35² + f a² f მყ2 дz2 J. Dnf (x, y, z) do = J dV, where D is the solid enclosed by S and Dnf (x, y, z) is the directional derivative of f.
Transcribed Image Text:6. Complete each problem: (a) State True or False and proved justification for: If S is an ellipsoid and F is a constant vector field then ff F•ñ do = 0. (b) If f (x, y, z) has continuous partial derivatives and S is a closed surface, show that f (3/5 +35² + f a² f მყ2 дz2 J. Dnf (x, y, z) do = J dV, where D is the solid enclosed by S and Dnf (x, y, z) is the directional derivative of f.
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