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5. Let U be the part of the hyperboloid x2 + y? + 2 = 2z2 shown below that lies below the plane z = 3 oriented with downward-facing normal vectors. Let F (x, y, z) = (-yz, xz, x² + y²). Find Sfy curl F ·d S. SU Mathematics

5. Let U be the part of the hyperboloid x2 + y? + 2 = 2z2 shown below that lies below the plane z = 3 oriented with downward-facing normal vectors. Let F (x, y, z) = (-yz, xz, x² + y²). Find Sfy curl F ·d S. SU Mathematics

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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5. Let U be the part of the hyperboloid x² + y² +2 = 2z² shown below that lies below the plane z = 3 oriented with downward-facing normal vectors. Let F (x, y, z) = (-yz, xz, x² + y²). Find ſfy curl F · d S. SU Mathematics 6. Let F(x,y,z) = (x + y, –2y + z,8z – x) and let U be the sphere where x² + y² + z² with outward-facing normal vectors. Calculate SSy F · d S . (In case it is helpful, a sphere of radius R has volume aR³ and surface area 47R².) = 25 oriented
Transcribed Image Text:5. Let U be the part of the hyperboloid x² + y² +2 = 2z² shown below that lies below the plane z = 3 oriented with downward-facing normal vectors. Let F (x, y, z) = (-yz, xz, x² + y²). Find ſfy curl F · d S. SU Mathematics 6. Let F(x,y,z) = (x + y, –2y + z,8z – x) and let U be the sphere where x² + y² + z² with outward-facing normal vectors. Calculate SSy F · d S . (In case it is helpful, a sphere of radius R has volume aR³ and surface area 47R².) = 25 oriented
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