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answerhappygod
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AL Let F = (5z + 5x³) i+ (4y + 4z + 4 sin(y³)) 3+ (5x + 4y + 4e² - 4e²³) k. (a) Find curl F. curl F = <0,0,0> (b) What does your answer to part (a) tell you about F. dr where C is the circle (x – 5)² + (y – 20)² = 1 in the xy-plane, oriented clockwise? SF • dr = 0 (c) If C' is any closed curve, what can you say about ſ F · dř? ScFdr = 0 (d) Now let C be the half circle (x − 5)² + (y – 20)² = 1 in the xy-plane with y > 20, traversed from (6, 20) to (4, 20). Find SF · ďr by using your result from (c) and considering C' plus the line segment connecting the endpoints of C. ScFdr = 0
AL Let F = (5z + 5x³) i+ (4y + 4z + 4 sin(y³)) 3+ (5x + 4y + 4e² - 4e²³) k. (a) Find curl F. curl F = <0,0,0> (b) What does your answer to part (a) tell you about F. dr where C is the circle (x – 5)² + (y – 20)² = 1 in the xy-plane, oriented clockwise? SF • dr = 0 (c) If C' is any closed curve, what can you say about ſ F · dř? ScFdr = 0 (d) Now let C be the half circle (x − 5)² + (y – 20)² = 1 in the xy-plane with y > 20, traversed from (6, 20) to (4, 20). Find SF · ďr by using your result from (c) and considering C' plus the line segment connecting the endpoints of C. ScFdr = 0