Flux of a gradient field: Let S be the surface of the portion of the solid sphere x2+y2+z21 that lies in the first octant and let f(x,y,z)=lnx2+y2+z2. Use the Divergence Theorem to calculate SfNdS Hint: Let V be the portion of the solid sphere that lies in the first octant. V has four sides SyzSxz and Sxy that each lie in a coordinate plane and S. (a) Compute the flux of f across Syz the portion of the surface of V in the yz - plane. Flux= (b) Compute the flux of f across Sxz the portion of the surface of V in the xz plane. Flux= (c) Compute the flux of f across Sxy i the portion of the surface of V in the xy plane. Flux= (d) Use the Divergence Theorem to compute the flux of f across the boundary of V. Flux= (e) Find the flux of f across S. Flux=