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Let S be the part of the cylinder x2 + y? = 16 lying between the planes z = 1 and z = -1. Let F be a vector field for which curl(F) = (4x, 4y, – 8z). 1. Let 7(u, v) = (4 cos (u), 4 sin (u), v) be a parameterization of S, where 0

Let S be the part of the cylinder x2 + y? = 16 lying between the planes z = 1 and z = -1. Let F be a vector field for which curl(F) = (4x, 4y, – 8z). 1. Let 7(u, v) = (4 cos (u), 4 sin (u), v) be a parameterization of S, where 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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Let S be the part of the cylinder x² + y? field for which curl(F) = (4x, 4y, – 82). 16 lying between the planes z =1 and z = -1. Let F be a vector 1. Let 7 (u, v) = (4 cos (u), 4 sin (u), v) be a parameterization of S, where 0 < u < 27, -1< v<1. For this parameterization, what is r × r,? О(а) (-4 сos (u), 4sin (u), 0) О (b) (—4 sin (u), 4 cos (u), 0) О (() (4 сos (u), 4 sin (u), 1) (d) (4 сos (u), 4 sin (u), 0) 2. Evaluate , curl(F) · ñ dS, where S is oriented with outward pointing normals. O (a) 1+64T (b) —4т O (c) 47 O (d) 647 3. Let C1 denote the top boundary component of S and C2 denote its bottom boundary component (that is, its intersections with the planes z= 1 and z = -1 respectively), both oriented counterclockwise when looking down from (0,0, 100). Suppose Ja F . dr = 136. What is fa F · dř? C2 Sa F - dř= number (3 significant figures)
Transcribed Image Text:Let S be the part of the cylinder x² + y? field for which curl(F) = (4x, 4y, – 82). 16 lying between the planes z =1 and z = -1. Let F be a vector 1. Let 7 (u, v) = (4 cos (u), 4 sin (u), v) be a parameterization of S, where 0 < u < 27, -1< v<1. For this parameterization, what is r × r,? О(а) (-4 сos (u), 4sin (u), 0) О (b) (—4 sin (u), 4 cos (u), 0) О (() (4 сos (u), 4 sin (u), 1) (d) (4 сos (u), 4 sin (u), 0) 2. Evaluate , curl(F) · ñ dS, where S is oriented with outward pointing normals. O (a) 1+64T (b) —4т O (c) 47 O (d) 647 3. Let C1 denote the top boundary component of S and C2 denote its bottom boundary component (that is, its intersections with the planes z= 1 and z = -1 respectively), both oriented counterclockwise when looking down from (0,0, 100). Suppose Ja F . dr = 136. What is fa F · dř? C2 Sa F - dř= number (3 significant figures)
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