(1 point) Let F(x, y, z) = 1z2xi +(x3 + tan(z))j + (1x2z – 5y2)k. Use...
(1 point) Let F(x, y, z) = 1z- xi + (x2 + tan(z)j + (1x²z + 3y2)k. Use the Divergence Theorem to evaluate /s F. ds where S is the top half of the sphere x2 + y2 + z2 = 1 oriented upwards. SSsF. dS =
Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉 and SS is the top half of the sphere x2+y2+z2=9x2+y2+z2=9. (1 point) Use the Divergence Theorem to evaluate FdS where F2x +3 tan2).^z-1 and S is the top half of the sphere x2 +y2 + z2 -9 Hint: S is not a closed surface. First compute integrals overs, and S2 , where S, is the disk x2 + y2 < 9, z = 0 oriented downward and S2 = S U...
Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...
6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 + y2 + z2 , yvx2 + y2 + z2 , z7 x2 + y2 + z2 ) and S consists of the hemisphere z V1 – x2 - y2 and the disk x2 + y2 = 1 in the xy-plane.
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.
Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = zeli + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 4, y 2 0, oriented in the direction of the positive y-axis.
Use the Divergence Theorem to evaluate ∫∫S F·dS, where F(x,y,z)=z²xi+(y³/3+sin z) j+(x² z+y²) k and S is the top half of the sphere x²+y²+z²=4 . (Hint: Note that S is not a closed surface, First compute integrals over S₁ and S₂, where S₁ is the disk x²+y² ≤ 4, oriented downward, and S₂=S₁ ∪ S.)
Please don't use the divergence theorem Very very urgent Ill need a detailed explanation of solving this problem. Let F(z, y, z)--z tan 1 (y2) İ + z3ln(z2 + 9) j + z k. Find the flux of F across the part of the paraboloid a y2 4 that lies above the plane z we need to solve using the formula like integral of fx,y).rx* r_y 3 and is oriented upward. Very very urgent Ill need a detailed explanation of...
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes' Theorem. , where S is the up 10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y...
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...