Let ?⃗ =(5z+5x^3)i+(6?+7?+7sin(?^3))j+(5?+7?+6?^(?3))k (a) Find curl ?⃗ curl ?⃗ = (b) What does your answer to...
Let ?⃗ =(5z+5x^3)i+(6?+7?+7sin(?^3))j+(5?+7?+6?^(?3))k
(a) Find curl ?⃗
curl ?⃗ =
(b) What does your answer to part (a) tell you
about ∫??⃗ ⋅??⃗ where C is the circle (?−25)^2+(?−30)^2=1 in the
xy-plane, oriented clockwise?
∫??⃗ ⋅??⃗ =∫CF→⋅dr→=
(c) If C is any closed curve, what can you say
about ∫C ?⃗ ⋅??⃗ ?
∫C ?⃗ ⋅??⃗ =
d. Now let ? be the half circle (?−25)^2+(?−30)^2=1 in the ??-plane with ?>30, traversed from (26,30) to (24,30). Find ∫C ?⃗ ⋅??⃗ by using your result from (c) and considering ? plus the line segment connecting the endpoints of ?.
Homework Answers
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Let ?⃗ =(5z+5x^3)i+(6?+7?+7sin(?^3))j+(5?+7?+6?^(?3))k
(a) Find curl ?⃗
curl ?⃗ =
(b) What does your answer to...
(1 point) Let +4z + 4 sin (a) Find curl F. curl F- (b) What does your answer to part (a) tell you...
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(a) Find curl F curl F (b) What does your answer to part (a) tell you...
(a) Find curl F curl F (b) What does your answer to part (a) tell you aboFwhere C is the circle (a 5)2(5) in the ry-plane, oriented clockwise? e) It C is any closed curve, what can you say about Jc F.r (d) Now let C be the half circle (5)2 5)2 in the zy-plane with y 5, traversed from (6,5) to (4,5). Find JF dr by using your result from (c) and considering C plus the line segment connecting...
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Assignment 5: Problem 8 Previous Problem List Next (1 point) Let F = (7z+ 7x®) i...
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7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
need 1-5 Midterm #3, Math 228 Each question is worth five points. 1. Let F(r.yzy). Let C be any curve that goes from...
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Midterm #3, Math 228 Each question is worth five points. 1. Let F(r.yzy). Let C be any curve that goes from A(-1,3,9) to B(1,6,-4). a) Show that F is conservative. b) Find a function φ such that ▽φ = F c) Use the result of b) to find Ic F Tds 2. Let F(z, y)-(2), and let C be the boundary of the square with vertices (1, 1). (-1,1). (-1,-1 traced out in the counter-clockwise direction. Find Jc...
1. Let F-yi(xr +6g) j + 2z k and (a) Which of these two fields (if any) are conservative on R3? Give detailed (b) Find potential functions for the fields that are conservative (c) Calculate the line...
1. Let F-yi(xr +6g) j + 2z k and (a) Which of these two fields (if any) are conservative on R3? Give detailed (b) Find potential functions for the fields that are conservative (c) Calculate the line integrals F dr and G dr where C is the arc of the reasoning r2 4 curve formed by the intersection of the plane z = 4 and the surface--+92 in the first octant, oriented anti-clockwise when view from above.
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Let F-_y i + (z + 6y) j+2z k and 1. (a) Which of these two fields (if any) are conservative on R3? Give detailed reasoning. (b) Find potential functions for the fields that are conservative (c) Calcu...
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Let F-_y i + (z + 6y)...
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7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
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Midterm #3, Math 228 Each question is worth five points. 1. Let F(r.yzy). Let C be any curve that goes from A(-1,3,9) to B(1,6,-4). a) Show that F is conservative. b) Find a function φ such that ▽φ = F c) Use the result of b) to find Ic F Tds 2. Let F(z, y)-(2), and let C be the boundary of the square with vertices (1, 1). (-1,1). (-1,-1 traced out in the counter-clockwise direction. Find Jc...
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1. Let F-yi(xr...
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Let F-_y i + (z + 6y)...
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