9. [15 Points) Let C be the boundary of the triangle with vertices (1, 1), (2,...
please answer the following questions. if you can't answer all the questions, please answer one question per exercise. thank you. Section 13.8 Exercise3 Use Stokes' theorem to compute Ts curl F. dS, a) where F(r,y.z) (ry,,y+ 2) and S is the part of the elliptic paraboloid-(r2+ 4y2)+3 above the plane :- 2, oriented upwards. b) where F(z, y, z)-|y,-z-vy and s is the part of the part of the upper henni phere r2 +r + 5,#2 o inside of the...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-2ǐ + 2xk and the surface S the part of the paraboloid z = 20-x2-y2 that lies above the plane z = 4, oriented upwards. To verify Stokes' Theorem we will compute the expression on each side. First computel curl F dS curl F- curl F. dS- EEdy di where curl F dS- Now compute F dr The boundary curve C of the...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
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...
Consider the unit cube with vertices (corner points) (0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1). Let S be the boundary of the cube minus (i.e. not including) the bottom square (the side which lies in the xy plane). Orient S with the normal which points out of the cube. Let F = <− y , x , y^2e^x . Evaluate (curl F) ·...
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b. Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
Let S be the surface of z= 9 – 2x2 – 2y which is above the plane z = 1 (oriented upwards) and also let F = (2x – 2y, y - 2,2+y+z) (a) Find curl(F) (b) Calculate Il curl(F) . 15 without using Stokes' Theorem. Il curl(F) . dſ by using Stokes' Theorem (c) Calculate
Let C be a triangle in the ry-plane with vertices (ıv). (2.92), and (T3, Vs) arranged so that C' is positively-oriented a.) Sketch such a triangle and indicate its orientation. b.) Apply Green's Theorem to compute the area of the triangle as a (sum of) path integral(s) around the boundary. Get a formula for area in terms of the coordinates zi and y. This formula is sometimes referred to as the Shoelace formula for area. c.) Use the formula you...