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 b...
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 (1 point) Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by X2 + y2-81, 0 < ž < 1, and a hemispherical cap defined by...
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...
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)....
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...
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...
Let S1 be the part of the paraboloid z = 1 − x ^2 − y ^2 that lies above the plane z = 0. Let S2 be the part of the cone z = √ x ^2 + y ^2 + 2(sqrt till y^2) that lies inside of the cylinder x ^2 + y^ 2 = 1. Let S3 be the part of the cylinder x ^2 + y ^2 = 1 that lies between these surfaces. If S...
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space given by F(x, y, z) xy-plan described by x2 + y2 < 4, z = 0; and let S2 be the upper half of the paraboloid given by z 4 y2, z 2 0. Both Si and S2 are oriented upwards. Let E be the solid region enclosed by S1 and S2 (a) Evaluate the flux integral FdS (b) Calculate div F div F...
Let F(x,y,z) = 4i – 3j + 5k and S be the surface defined by z= x2 + y2 and 22 + y2 < 4. Evaluate SJ, F. nds, where n is the upward unit normal vector.