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(d) Now let C' be the half circle (x - 15)² + (y - 35)² = 1 in the xy-plane with y > 35, traversed from (16, 35) to (14, 35). Find √F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. ScF.dr = 0

(d) Now let C' be the half circle (x - 15)² + (y - 35)² = 1 in the xy-plane with y > 35, traversed from (16, 35) to (14, 35). Find √F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. ScF.dr = 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 38E
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Let F³ = (3z + 3x²) i + (4y+32 + 3sin(y¹)) ;+ (3x + 3y+ 4e²) k. (a) Find curl F. curl = <0,0,0> (b) What does your answer to part (a) tell you about fc. dr where C is the circle (x - 15)² + (y = 35)² = 1 in the xy-plane, oriented clockwise? SCF dr=0 (c) If C is any closed curve, what can you say about √F. dr? ScF. dr = 0 (d) Now let C' be the half circle (x - 15)² + (y - 35)² = 1 in the xy-plane with y > 35, traversed from (16, 35) to (14, 35). Find √F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. Sc F. dr = 0
Transcribed Image Text:Let F³ = (3z + 3x²) i + (4y+32 + 3sin(y¹)) ;+ (3x + 3y+ 4e²) k. (a) Find curl F. curl = <0,0,0> (b) What does your answer to part (a) tell you about fc. dr where C is the circle (x - 15)² + (y = 35)² = 1 in the xy-plane, oriented clockwise? SCF dr=0 (c) If C is any closed curve, what can you say about √F. dr? ScF. dr = 0 (d) Now let C' be the half circle (x - 15)² + (y - 35)² = 1 in the xy-plane with y > 35, traversed from (16, 35) to (14, 35). Find √F. dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. Sc F. dr = 0
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