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...
(9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R >=<-y+z, x - 2,x - y > S:z = 4 - x2 - y2 and z>0 (9a) Evaluate W= $ Pdx + Qdy + Rdz с (9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R>=<-y+z, x - 2, x - y > S:z = 4 - x2 - y2 and z 20 (9b) Verify Stokes' Theorem.
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...
Use Stokes' Theorem to evaluate. 8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented upward. 8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented...
Let F = < x-eyz, xexx, z?exy >. Use Stokes' Theorem to evaluate slice curlĒ ds, where S is the hemisphere x2 + y2 + z2 = 1, 2 > 0, oriented upwards.
ie Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = x2 sin(z)i + y2 + xyk, S is the part of the paraboloid z = upward. - x2 - y2 that lies above the xy-plane, oriented
10. Stokes' Theorem and Surfac e Integrals of Vector Fields a. Stokes' Theorem: F-dr= b. Let S be th ky-plane. Draw a sketch of curve C in the xy-plane. et be the surface of the paraboloid z 4-x-y and Cis the trace of S in the c Let Fox.y.z) <2z, x, y>, Compute the curl (F) d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) F-dr Use Stokes' Theorem to compute , e. 10. Stokes' Theorem and Surfac...
Let F = < - yz, 12, my >. Use Stokes' Theorem to evaluate || curiF . d5, where S is the part of the paraboloid z = 13 – 2? - y that lies above the plane z = 12, oriented upwards Preview Get help: Video License Points possible: 1 This is attempt 1 of 3. Submit
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a 3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
circle x2 + y2-9 in the x-y plane, oriented counter-clockwise. Let F(x, y, z)-(y,-x,0) Verify Stokes' Theorem by calculating a) surl(F) nds and b) F Tds. circle x2 + y2-9 in the x-y plane, oriented counter-clockwise. Let F(x, y, z)-(y,-x,0) Verify Stokes' Theorem by calculating a) surl(F) nds and b) F Tds.