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2 A friend tells you that if S is a closed surface (that is, a surface without a boundary curve), then by Stokes' theorem we ought to have ffs curl F-dS=0 for any appropriate F (since there is no boundary curve C). Is this true? Can you justify it using the Divergence theorem? 4

2 A friend tells you that if S is a closed surface (that is, a surface without a boundary curve), then by Stokes' theorem we ought to have ffs curl F-dS=0 for any appropriate F (since there is no boundary curve C). Is this true? Can you justify it using the Divergence theorem? 4

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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E33.2 please

E33.1 (T/F) Let E be a unit ball and S be its boundary surface. If ff, F-d5= 0, then divF(x,y,z) = 0 for every point (x,y,z) in E. E33.2 A friend tells you that if S is a closed surface (that is, a surface without a boundary curve), then by Stokes' theorem we ought to have ff curl F-dS=0 for any appropriate F (since there is no boundary curve C). Is this true? Can you justify it using the Divergence theorem? E33.3 Let F(x, y, z) = (y² + sin yz, y + x2³, x(y² + 1)4), G = curl F, and S be r² + y² + z² = 9, oriented with outward normals. (a) What does Stokes's Theorem say about [[G-dš? A
Transcribed Image Text:E33.1 (T/F) Let E be a unit ball and S be its boundary surface. If ff, F-d5= 0, then divF(x,y,z) = 0 for every point (x,y,z) in E. E33.2 A friend tells you that if S is a closed surface (that is, a surface without a boundary curve), then by Stokes' theorem we ought to have ff curl F-dS=0 for any appropriate F (since there is no boundary curve C). Is this true? Can you justify it using the Divergence theorem? E33.3 Let F(x, y, z) = (y² + sin yz, y + x2³, x(y² + 1)4), G = curl F, and S be r² + y² + z² = 9, oriented with outward normals. (a) What does Stokes's Theorem say about [[G-dš? A
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