Flux of a gradient field: Let S be the surface of the portion of the solid sphere x² + 1² + z² ≤ 4 that lies in the first octant and let f(x, y, z) = In √x² + y² + z². Use the Divergence Theorem to calculate Vf-NdS v Hint: Let V be the portion of the solid sphere that lies in the first octant. ✓ has four sides Syz, Sxz and Sxy, that each lie in a coordinate plane and S. (a) Compute the flux of Vf across Syz; the portion of the surface of ✓ in the yz- plane. Flux = Σ (b) Compute the flux of Vf across Sxz; the portion of the surface of ✓ in the xz- plane. Flux = Σ (c) Compute the flux of Vf across Sxy; the portion of the surface of ✓ in the xy-plane. Flux= Σ (d) Use the Divergence Theorem to compute the flux of Vf across the boundary of V. Flux= (e) Find the flux of Vf across S. Flux = Σ Σ