Homework Answers
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 th...
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 Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉 and CC is the circle x2+y2=9x2+y2=9 on the...
Use Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where
F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉
and CC is the circle x2+y2=9x2+y2=9 on the plane z=6z=6 having
traversed counterclockwise orientation when viewed from above.
The line integral equals
Main Menu Contents Grades Course Contents » ... » PROBLEM SET 12 » stokestheorem-2 Use Stoke's Theorem to evaluate Sc F. dr where F = (e-63 – lyz, e-ly + 1xz, e -52) and C is the circle x2 + y2 = 9 on the plane z= 6 having traversed...
Q4. 8pnts]If you haven't explored it yet, here is a magical property of the Stoke's theorem Suppose we have a v...
Q4. 8pnts]If you haven't explored it yet, here is a magical property of the Stoke's theorem Suppose we have a vector field F(x,y, z) = -yi+ xj+ zk. Also, let C: x2y2 R2 for some R 0 be the curve in the xy-plane. Now, verify the Stoke's theorem when: (a) The surface S is given by the upper hemisphere 2y z2= R2,z0. R2 - y2, z 2 0. (b) The surface S is given by the paraboloid (c) The surface...
Use Stoke's Theorem to evaluate ScF. dr, where F(x, y, z) = -xzzi + y2zj +...
Use Stoke's Theorem to evaluate ScF. dr, where F(x, y, z) = -xzzi + y2zj + zºk and C is the curve of intersection of the planez = 1 – X – Y and the cylinder x2 + y2 = 1, oriented counterclockwise as viewed from above.
Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y²...
Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y² k, where S is the surface of the paraboloid 2 = 4 – 22 - y2 and C is the curve of intersection of the paraboloid with the plane z = 0.
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where...
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
3] (a) Use Stoke's Theorem to evaluate ScF. dr by evaluating the related double inte- gral,...
3] (a) Use Stoke's Theorem to evaluate ScF. dr by evaluating the related double inte- gral, where F(x, y, z) = (x2z, cy, 22) and C is the curve of intersection between the plane x+y+z=1 and the cylinder ? + y2 = 9 oriented clockwise when viewed from above. (b) Sketch a graph of both the plane and cylinder with so that the intersecting curve is clear. 2) Find the parametric equations for C and use them to sketch a...
Use Stokes' Theorem to find SC F. dr where F(x,y,z) = (-y, x,x) and C is...
Use Stokes' Theorem to find SC F. dr where F(x,y,z) = (-y, x,x) and C is the curve of intersection of the plane y = 2 and the paraboloid y + x2 + z2 = 6. Show all work. Please select file(s) Select file(s)
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 sk...
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...
be = Use Green's Theorem to evaluate F. dr where F (3xy – esin x ,...
be = Use Green's Theorem to evaluate F. dr where F (3xy – esin x , 7x2 + Vy4 + 1) and C is the boundary of the region bounded by the circle x2 + y2 = 4 in the first quadrant with counterclockwise orientation.
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 Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where
F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉
and CC is the circle x2+y2=9x2+y2=9 on the plane z=6z=6 having
traversed counterclockwise orientation when viewed from above.
The line integral equals
Main Menu Contents Grades Course Contents » ... » PROBLEM SET 12 » stokestheorem-2 Use Stoke's Theorem to evaluate Sc F. dr where F = (e-63 – lyz, e-ly + 1xz, e -52) and C is the circle x2 + y2 = 9 on the plane z= 6 having traversed...
Q4. 8pnts]If you haven't explored it yet, here is a magical property of the Stoke's theorem Suppose we have a vector field F(x,y, z) = -yi+ xj+ zk. Also, let C: x2y2 R2 for some R 0 be the curve in the xy-plane. Now, verify the Stoke's theorem when: (a) The surface S is given by the upper hemisphere 2y z2= R2,z0. R2 - y2, z 2 0. (b) The surface S is given by the paraboloid (c) The surface...
Use Stoke's Theorem to evaluate ScF. dr, where F(x, y, z) = -xzzi + y2zj + zºk and C is the curve of intersection of the planez = 1 – X – Y and the cylinder x2 + y2 = 1, oriented counterclockwise as viewed from above.
Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y² k, where S is the surface of the paraboloid 2 = 4 – 22 - y2 and C is the curve of intersection of the paraboloid with the plane z = 0.
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
3] (a) Use Stoke's Theorem to evaluate ScF. dr by evaluating the related double inte- gral, where F(x, y, z) = (x2z, cy, 22) and C is the curve of intersection between the plane x+y+z=1 and the cylinder ? + y2 = 9 oriented clockwise when viewed from above. (b) Sketch a graph of both the plane and cylinder with so that the intersecting curve is clear. 2) Find the parametric equations for C and use them to sketch a...
Use Stokes' Theorem to find SC F. dr where F(x,y,z) = (-y, x,x) and C is the curve of intersection of the plane y = 2 and the paraboloid y + x2 + z2 = 6. Show all work. Please select file(s) Select file(s)
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...
be = Use Green's Theorem to evaluate F. dr where F (3xy – esin x , 7x2 + Vy4 + 1) and C is the boundary of the region bounded by the circle x2 + y2 = 4 in the first quadrant with counterclockwise orientation.
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