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S1 = {(x,y, z) : x2 + y + z* = 25, z > 3} and F = (-y, x8, 3), respectively. 드

S1 = {(x,y, z) : x2 + y + z* = 25, z > 3} and F = (-y, x8, 3), respectively. 드

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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The surface S₁ and vector field F are given, in Cartesian coordinates, by S₁ = {(x, y, z) : x² + y² + z² = 25, z ≥ 3} and F = (–y³, x³, z³), respectively. A fluid flows through surface S₁ with velocity field u = V x F, where F is given above. Evaluate the circulation of the field F around the boundary of surface S₁. You may wish to use the identity sin + cos¹ = (3 + cos 40)/4. 4
Transcribed Image Text:The surface S₁ and vector field F are given, in Cartesian coordinates, by S₁ = {(x, y, z) : x² + y² + z² = 25, z ≥ 3} and F = (–y³, x³, z³), respectively. A fluid flows through surface S₁ with velocity field u = V x F, where F is given above. Evaluate the circulation of the field F around the boundary of surface S₁. You may wish to use the identity sin + cos¹ = (3 + cos 40)/4. 4
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