(1 point) Let +4z + 4 sin (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...
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...
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...
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...
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(...
(23 pts) Let F(x, y, z) = ?x + y, x + y, x2 + y2?, S be the top hemisphere of the unit sphere oriented upward, and C the unit circle in the xy-plane with positive orientation. (a) Compute div(F) and curl(F). (b) Is F conservative? Briefly explain. (c) Use Stokes’ Theorem to compute ? F · dr by converting it to a surface integral. (The integral is easy if C you set it up correctly) 4. (23 pts)...
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes' Theorem. , where S is the up 10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y...
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...