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Let F = (7z+7x4) 7 + (3y + 2z + 2 sin(14)) 7 + (7x + 2y + 3e²¹ ) k. (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about F. dr where C is the circle (x - 20)² + (y - 15)² = 1 in the xy-plane, oriented clockwise? JcF. dr = (c) If C is any closed curve, what can you say about F. dr? JF. dr = (d) Now let C be the half circle (x - 20)² + (y − 15)² = 1 in the xy-plane with y > 15, traversed from (21, 15) to (19, 15). Find F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. JcF. dr =

Let F = (7z+7x4) 7 + (3y + 2z + 2 sin(14)) 7 + (7x + 2y + 3e²¹ ) k. (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about F. dr where C is the circle (x - 20)² + (y - 15)² = 1 in the xy-plane, oriented clockwise? JcF. dr = (c) If C is any closed curve, what can you say about F. dr? JF. dr = (d) Now let C be the half circle (x - 20)² + (y − 15)² = 1 in the xy-plane with y > 15, traversed from (21, 15) to (19, 15). Find F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. JcF. dr =

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 F = (7z+7x4) 7 + (3y + 2z + 2 sin (14)) 7 + (7x + 2y + 3e²¹ ) k. (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about F. dr where C is the circle (x - 20)² + (y - 15)² = 1 in the xy-plane, oriented clockwise? JcF. dr = (c) If C is any closed curve, what can you say about F. dr? F. dr = (d) Now let C be the half circle (x - 20)² + (y − 15)² = 1 in the xy-plane with y > 15, traversed from (21, 15) to (19, 15). Find F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. JcF. dr =
Transcribed Image Text:Let F = (7z+7x4) 7 + (3y + 2z + 2 sin (14)) 7 + (7x + 2y + 3e²¹ ) k. (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about F. dr where C is the circle (x - 20)² + (y - 15)² = 1 in the xy-plane, oriented clockwise? JcF. dr = (c) If C is any closed curve, what can you say about F. dr? F. dr = (d) Now let C be the half circle (x - 20)² + (y − 15)² = 1 in the xy-plane with y > 15, traversed from (21, 15) to (19, 15). Find F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. JcF. dr =
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