1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) an...
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...
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = (-y+z)i + (x – z)j + (x – y)k. S is the surface z = V1 – 22 – y2, and C is the boundary of S with counterclockwise orientation (from above).
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...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
Use Stokes' Theorem to evaluate $cF. dr, where C is the boundary of the surface S: z = 4 - 22 - y2 with 2 > 0, and is oriented counterclowise as viewed from above, F(x, y, z) = 2zi + 3aj + 5yk.
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
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 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...
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.