(a) Find curl F curl F (b) What does your answer to part (a) tell you...
(1 point) Let +4z + 4 sin (a) Find curl F. curl F- (b) What does your answer to part (a) tell you about JcF dr where C is the circle (x 30)2 + (y - 10)2 1 in the xy-plane, oriented clockwise? (e) If C is any closed curve, what can you say about fcFdr? (d) Now let C be the half circle (-30)2-cy-10)2-1 in the xy-plane with y 10, traversed from (31, 10) to (29, 10). Find F...
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...
(1 point) Let F (72+72) i + (2y +62 + 6 sin(y*)) 3+ (2x + 6y + 2e=") R. (a) Find curl F. curl F = <0,0,0> (b) What does your answer to part (a) tell you about Sc F. dr where is the circle (2 – 30)2 + (y - 35)2 = 1 in the ty-plane, oriented clockwise? SF. dr = 0 (c) If C is any closed curve, what can you say about SF. dr? SoF dr =...
Assignment 5: Problem 8 Previous Problem List Next (1 point) Let F = (7z+ 7x®) i + (7y + 3z + 3 sin(y)); + (7x + 3y + 7e3") ** (a) Find curl FC curl F (b) What does your answer to part (a) tell you about ScF. dr where C is the circle (x - 15)2 + (y – 25)2 = 1 in the xy-plane, oriented clockwise? (F. dr = (C) If C is any closed curve, what can...
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...
Problem 6 Using Stokes' Theorem, we equate F dr curl F dA. Find curl F- PreviousS us Problem ListNext Noting that the surface is given by (1 point) Calculate the circulation, Fdr7in z - 16-x2 - y2, find two ways, directly and using Stokes' Theorem. dA The vector field F = 6y1-6y and C is the boundary of S, the part of the surface dy dx With R giving the region in the xy-plane enclosed by the surface, this gives...
1. About circulation, circulation density and curl: Given curl( F) = z27-2mit cos(12 + y2) (a) Find the circulation density circnF (P) where P= (1,1,1) around the normal i-2- k. (b) Estimate the circulation for F around C, a circle of radius 0.01 centered at P- (1,1, 1), on the z-1 plane, oriented clockwise when viewed from the origin. (c) Find the maximum circulation density for F at P- (1,1, 1). 1. About circulation, circulation density and curl: Given curl(...
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 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...
6. Estimates from geometric definitiions: (a) Suppose divF2z. Estimate the ux of F through a sphere of radius 0.01 centered at (b) Suppose curlF-(z + 4)it (2-ทั+ (:-3)E, estimate circulation of F around a circle C of radius 0.1, centered at the origin, if C is on the ry- yz-, and rz-plane respectively oriented counter-clockwise when viewed from the positive z, positive a, and positive y-axis respectively 7. Three small squares Ci,C2, Cs each with sides 0.1, centered at the...
can you show me the work for 2,3,4,5, thank you 2. Evaluate ff curl F n dS, where F = (a2yz, yz2, 23e#v), and S is the part of the sphere a2 + y2+225 that lies above the plane z 1, oriented upwards. - Solution: -4T 3. A metal sheet is bent into the shape of the parabaloid r = y2+ 2 where 0 (r, y, z) is 6(x, y, z) = z. Find the mass of the resulting metal...