Divergence Theorem: If S is a closed surface in R' that bounds a solid region B and if the boundary S is oriented via an outward unit normal vector n, and if F = (P(x, y, z), O(x, y, Z), R(x, y, Z) ) is a vector field defined and differentiable throughout B (and its boundary) with continuous first partial derivatives. Then: net flux of F outward Fads = $8 F . ndS = F .dS = div(F)dV across S = OB ff. S=QB S =QB S=QB In problems 13 and 14, verify that the Divergence Theorem is true for the vector field F on the region E. Problem 13. (13.8/2) F(x, y, z) = xi+ xyj+zk, E is the solid bounded by the paraboloid z =4-x - y and the xy-plane. Problem 14. (13.8/4) F(x, y, z) = (x,-y,z), E is the solid cylinder y + z