Let MM be the capped cylindrical surface which is the union of
two surfaces, a cylinder given by x2+y2=81, 0≤z≤1x2+y2=81, 0≤z≤1,
and a hemispherical cap defined by x2+y2+(z−1)2=81,
z≥1x2+y2+(z−1)2=81, z≥1. For the vector field F=(zx+z2y+4y,
z3yx+4x, z4x2)F=(zx+z2y+4y, z3yx+4x, z4x2), compute
∬M(∇×F)⋅dS∬M(∇×F)⋅dS in any way you like
Let MM be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x2+y2=81, 0≤z≤1x2+y2=81, 0≤z≤1, and a hemispherical cap defined by x2+y2+(z−1)2=81, z≥1x2+y2+(z−1)2=81,...
Let M be the capped cylindrical surface which is the union of
two surfaces, a cylinder given by x2+y2=36, 0≤z≤1, and a
hemispherical cap defined by x2+y2+(z−1)2=36, z≥1. For the vector
field F=(zx+z2y+7y, z3yx+8x, z4x2), compute ∬M(∇×F)⋅dS in any way
you like.
Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by 2 y2 36, 0 z1, and a hemispherical cap defined by z2 + Уг + (2-1)2-36, :2 1. For the...
Let M be the outward oriented capped cylindrical surface which is the union of two surfaces, a cylinder given by x2 + y2 = 25, 0 <z < 1, and a hemispherical cap defined by x2 + y2 + (z – 1)2 = 25, z > 1. For the vector field F = (zx + z2 y + 3y, z’yx + 5x, z4 x2), compute M (V x F). dS in any way you like. DM (V x F). dS...
6AHW9: Problem 5 Prev Up Next (1 pt) Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x2 + y2 = 81, O SZS 1, and a hemispherical cap defined by x2 + y2 + (x - 1)2 = 81, z 2 1. For the vector field F = (zx + z²y + 2y, z'yx + 7x, z*x). compute (V x F). ds in any way you like. I(V x F)....
Section 16.8: Problem 5 Previous ProblemProblem List Next Problem (1 point) Let M be the capped cylindnical surface which is the union of two surfaces, a cylinder given by z+y-49,0 1, and a hemisphencal cap defined by Z2 + y2 + (z-1)2-49, z > 1. For the vector field F-(tr + z"y + 4y, zar + 72, z'z2), compute M(Vx F) dS in any way you like. Preview My Answers Submit Answers You hayi,attempted this problem 1 time. Your ovean...
9. Let S be the capped cylindrical surtace showh in rigure 12.12 i ua) of (T, y,z) a2+y21,0z 1, and S2 is defined by a2 +y2+(z-1) 1, 21 F(x, y, z) = (zx+z?y+z) i+ (z?yx+9)j+z4x2k. Compute l (v x F union of two surfaces Si and 2, where S1 is the set of (z
9. Let S be the capped cylindrical surtace showh in rigure 12.12 i ua) of (T, y,z) a2+y21,0z 1, and S2 is defined by a2 +y2+(z-1)...
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π
9. Let Q be the solid bounded by the cylinder x2 + y2...
7. Assume (x, y,x)(2xy, y',5z - y). Let E be the solid upright cylinder between the planes z 0 and z-3 with base the disc x2 + y2 < 9, and let S be the outwardly oriented boundary surface of E. Note that S consists of three smooth surfaces; the surface Si of the cylinder, plus the top disc Di and the bottom disc D2. Follow the steps to verify the Divergence Theorem. (a) [12 pts.] Evaluate dS directly
7....
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal.
F-dS where S is the cylinder x? +-2, 0 s y
(2) Let F zi + xj+yk and consider the integral vx Fi n dS where S is the surface of the paraboloid z = 1-x2-y2 corresponding to 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. b) Evaluate the integral directly over the surface S. (c) Evaluate the integral directly over the new surface S which is given by the disk
(2) Let F zi + xj+yk...