Let F = (5z + 5x³) i+ (5y + 6z + 6 sin (y)) + (5æ + 6y + 5e) k. (a) Find curl F curl F (b) What does your answer to part (a) tell you about faF. dr where C is the circle (x – 5)2 + (y - 15)2 = 1 in the xy-plane, oriented clockwise? ScF. dr = (c) If C is any closed curve, what can you say about f F. dr? SeF. dr = (d) Now let C be the half circle (x 5)2 + (y – 15)² = 1 in the xy-plane with y > 15, traversed from (6, 15) to (4, 15). Find fa F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF. dr =
Let F = (5z + 5x³) i+ (5y + 6z + 6 sin (y)) + (5æ + 6y + 5e) k. (a) Find curl F curl F (b) What does your answer to part (a) tell you about faF. dr where C is the circle (x – 5)2 + (y - 15)2 = 1 in the xy-plane, oriented clockwise? ScF. dr = (c) If C is any closed curve, what can you say about f F. dr? SeF. dr = (d) Now let C be the half circle (x 5)2 + (y – 15)² = 1 in the xy-plane with y > 15, traversed from (6, 15) to (4, 15). Find fa F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. SoF. dr =
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+ (5y+ 6z + 6 sin (y³)) j + (5x + ôy + 5e
S=) .
(a) Find curl F.
curl F
(b) What does your answer to part (a) tell you about f F. dr where C is the circle (x – 5)2 + (y – 15)2 = 1 in the xy-plane, oriented clockwise?
laF. dr =
(c) If C is any closed curve, what can you say about a F . dr?
SaF. dr =
(d) Now let C be the half circle (x – 5)2 + (y –
from (c) and considering C plus the line segment connecting the endpoints of C.
15)? = 1 in the xy-plane with y > 15, traversed from (6, 15) to (4, 15). Find Sc F · dr by using your result
SaF. dr =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96d2c6ef-3b04-42cc-b951-ecd5f11a97c8%2F1d6207fc-c7df-4353-a4e2-14d4ca75e682%2F4v14l0e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let F =
(5z + 5x) i+ (5y+ 6z + 6 sin (y³)) j + (5x + ôy + 5e
S=) .
(a) Find curl F.
curl F
(b) What does your answer to part (a) tell you about f F. dr where C is the circle (x – 5)2 + (y – 15)2 = 1 in the xy-plane, oriented clockwise?
laF. dr =
(c) If C is any closed curve, what can you say about a F . dr?
SaF. dr =
(d) Now let C be the half circle (x – 5)2 + (y –
from (c) and considering C plus the line segment connecting the endpoints of C.
15)? = 1 in the xy-plane with y > 15, traversed from (6, 15) to (4, 15). Find Sc F · dr by using your result
SaF. dr =
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