Let F = VI, where f(x.y.z)=x'+y'+z'+x2+y2- 22+ 2. and let S be the unitsphere x2+y2+22=1. Find the outward flux ffF-nda. 5 [Suggestiom Use the Divergence Theorem] [0. Use the Divergence Theorem to nd the outward ux ff; F ' n) d0 of F(x.y.z) = (jar/3,23) through 5 the unit sphere, X2 + V2 + 22 =1. 5, Let FLT, y' z) = 2.1-: yi: and S be the boundary surface of a region E in R3 given by 1 E = {(umz): 2' 2 22 + 2.12. -'I=+y + z 5 1}. 2 We assume that S is oriented outward with mpect to E. Use the Divergence Theorem to compute ff F - as. S 2 2 2 + s 4 10. Let T be the solid described by {I 21y + z Z surface of T. Let F(x, ,2) be the vector eld x i +yj + z k. Use the outward pointing unit normal vector to calculate HF :18 S . Let S be the (two-part) boundary (3) directly as a surface integral AND (b) as a triple integral, by using the Divergence Theorem. ___ 9. Let T be the solid bounded below by z = x2 + y2 and above by z = 4, and let S be the boundary surface of T, with outward pointing unit normal vector. Let F be the vector eld . Calculate H T\" - d3 5 :1) directly as a surface integral, and b) as a triple integral, by using the Divergence Theorem. ---_.__.______________ 10. Let The the solid 1:2 +y2 S 1; 0 s z 5 1. Let S be the surface (including the top, bottom, and side) of T and let i be the outward pointing unit normal vector. Let i! be the vector eld y2 i + xzj + sinZUrz) k . Evaluate \"r-d8 S a) directly as a surface integral, and b) as a triple integral, by using the Divergence Theorem. --____________ 10. Let The the solid bounded below byz = D , bounded above by y + 2 =1, and bounded } on the side by x2 +y2 =1 . Let S be the boundary surface ofT. Let F (x, y, z) = . Use the outward pointing normal vector to evaluate If? -d S ) directly as 3 mm integral AND integral, by using the Divergence Theorem