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Write T if true and F is false. Explain why with solutions, counterexamples, or explanations. a) In spherical coordinates, the graph of the surface with equation o = T2 is a cone. b) There is a vector field F(x,yz) = (M (XX.2),N (XX.2),R(x,X.z), such that curlE(X.X,2) (divE(X.X.2), (divE(X.X,2))?,(divE(x.X.z))'). c) If divE(x.V.z) = 0 for all (x.y.z), then curE(x.Y.Z) = (0,0,0) for all (X.V.2). %3D d) If G(xXz) = curE(&Kz), where F(X,X,z) = (y-zz-XX-Y), then div(curlG(x.Y.2)) > 0) for all (X.L.2). e) For every vector field F on R3, curl(divE) = 0. %3D

Write T if true and F is false. Explain why with solutions, counterexamples, or explanations. a) In spherical coordinates, the graph of the surface with equation o = T2 is a cone. b) There is a vector field F(x,yz) = (M (XX.2),N (XX.2),R(x,X.z), such that curlE(X.X,2) (divE(X.X.2), (divE(X.X,2))?,(divE(x.X.z))'). c) If divE(x.V.z) = 0 for all (x.y.z), then curE(x.Y.Z) = (0,0,0) for all (X.V.2). %3D d) If G(xXz) = curE(&Kz), where F(X,X,z) = (y-zz-XX-Y), then div(curlG(x.Y.2)) > 0) for all (X.L.2). e) For every vector field F on R3, curl(divE) = 0. %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Write T if true and F is false. Explain why with solutions, counterexamples, or explanations. a) In spherical coordinates, the graph of the surface with equation o = T2 is a cone. b) There is a vector field F(x.Yz) (divE(X.Y.2), (divE(&Y.2))?,(divE(x.X,z))³). = (M (XY.z),N (XY.Z), R(X.X.Z)), such that curE(x.V.Z) = c) If divE(x.V.Z) = 0 for all (x.y.z), then curE(x.Y.z) = (0,0,0) for all (XV.Z). d) If G(x.V.2) = curE(X.L2), where F(xz) = (y-zz-XX-y), then div(curlG(x.V.Z)) > 0) for all (XL.2). e) For every vector field F on R³, curl(divE) = 0.
Transcribed Image Text:Write T if true and F is false. Explain why with solutions, counterexamples, or explanations. a) In spherical coordinates, the graph of the surface with equation o = T2 is a cone. b) There is a vector field F(x.Yz) (divE(X.Y.2), (divE(&Y.2))?,(divE(x.X,z))³). = (M (XY.z),N (XY.Z), R(X.X.Z)), such that curE(x.V.Z) = c) If divE(x.V.Z) = 0 for all (x.y.z), then curE(x.Y.z) = (0,0,0) for all (XV.Z). d) If G(x.V.2) = curE(X.L2), where F(xz) = (y-zz-XX-y), then div(curlG(x.V.Z)) > 0) for all (XL.2). e) For every vector field F on R³, curl(divE) = 0.
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