. Use Stokes Theorem to find curl(F).NdS where F (z, a, y) and S is the surface of a side- ways top-less coca-cola of radius 1 and height 4 and whose top-center point is at (0,0,0) and whose bo...
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal field n is oriented so that it points up on the top surface. T, zand 7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube...
Use Stokes' Theorem to evaluate sta curl F. ds. F(x, y, z) = xyzi + xyj + x2yzk, S consists of the top and four sides (but not the bottom of the cube with vertices (+3, +3, +3), oriented outward. Need Help? Read It Watch It Talk to a Tutor Submit Answer 33. [-/2.5 Points] DETAILS SCALC8 16.8.018. MY NOTES ASK YOUR Evaluate le (y + 5 sin(x)) dx + (z2 + 3 cos(y)) dy + x3 dz where C...
Help Entering Answers (1 point) Use Stokes' Theorem to evaluate ll curl F. dS where F(x, y, z) = xyzi + 3xyj + 2x2yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, +2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by:...
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...
Verify that Stokes' Theorem is true for the vector field Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y?». Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) e. Use Stokes' Theorem to computec F dr 10. Stokes' Theorem and Surface Integrals...
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...
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...
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y, Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)ーーーーーーーーーーーーー Compute N(u,v) e. Use Stokes' Theorem to compute Jc F dr 10. Stokes Theorem and Surface...
1. Consider the vector field z, y, z) = 〈re,zz,H) and the surface s in the figure below oriented outward. Unit circle Use Stokes' Theorem in two different ways to find/curl F dS, by: (a) [7 pts.] evaluating ф F-dr where C in the positively oriented unit circle in the figure (which is the boundary of S), (b) [7 pts.] evaluating curl F dS, where Si is the upward oriented unit disc bounded by C 1. Consider the vector field...