Use the Divergence Theorem to calculate the flux of the vector fields Fi = -5zi + 5xk and F2 = -5zi + (y + 7)j + 5xk through the surface S given by the sphere of radius a centered at the origin with outwards orientation. Be sure that you are able to explain your answers geometrically. With W giving the interior of the sphere, Ss Fi . dA = Sw dV = and Is F2 . dA = fw dV =(1 point) Suppose F = F (x, y, z) is a gradient field with F = Vf, S is a level surface of f, and C is a curve on S. What is the value of the line integral SF . dr?(a) Let div 13" = 2 + y2 + z2 + 1. Calculate Isl?! - {ix-1' where 31 is the sphere of radius 1 centered at the origin. fSl F. ' M = y" ('3) let 82 be the sphere of radius 4 centered at the origin; let 33 be the sphere of radius 7 centered at the origin; let S; be the box of side 8 centered at the origin with edges paraliel to the axes. Without calculating them, arrange the following integrals in increasing order: A=fdi Bzf-d, C: iii-diff. 52 33 34 "