Let F = (5z + 5x) i + (7y + 4z+ 4 sin(y² )) j+ (5x + 4y + 7e*) ..(a) Find curl F.curl F =<0,0,0>%3D(b) What does your answer to part (a) tell you about F. dr where C is the circle (x – 35)? + (y – 25)2 = 1 in the xy-%3Dplane, oriented clockwise?fF. dr = 0(c) If C is any closed curve, what can you say about F. dr?SF • dř = 0(d) Now let C be the half circle (x – 35)2 + (y – 25)² = 1 in the xy-plane with y > 25, traversed from (36, 25) to (34, 25).Find F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C.SF- dr =

We’ll answer the first three subparts of the question since the exact one wasn’t specified. Please…

Let F = (5z + 5x²) i + (7y + 4z+ 4 sin(y² )) J + (5x +4y + 7e²) k. (a) Find curl F. curl F <0,0,0> (b) What does your answer to part (a) tell you about F. dř where C is the circle (x – 35)² + (y – 25)² = 1 in the xy- plane, oriented clockwise? '• dr = 0 (c) If C is any closed curve, what can you say about F. dr? SeF. dř =

Let F = (5z + 5x²) i + (7y + 4z+ 4 sin(y² )) J + (5x +4y + 7e²) k. (a) Find curl F. curl F <0,0,0> (b) What does your answer to part (a) tell you about F. dř where C is the circle (x – 35)² + (y – 25)² = 1 in the xy- plane, oriented clockwise? '• dr = 0 (c) If C is any closed curve, what can you say about F. dr? SeF. dř =

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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Question

Let F = (5z + 5x) i + (7y + 4z+ 4 sin(y² )) j+ (5x + 4y + 7e*) ..
(a) Find curl F.
curl F =
<0,0,0>
%3D
(b) What does your answer to part (a) tell you about F. dr where C is the circle (x – 35)? + (y – 25)2 = 1 in the xy-
%3D
plane, oriented clockwise?
fF. dr = 0
(c) If C is any closed curve, what can you say about F. dr?
SF • dř = 0
(d) Now let C be the half circle (x – 35)2 + (y – 25)² = 1 in the xy-plane with y > 25, traversed from (36, 25) to (34, 25).
Find F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C.
SF- dr =

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