For each point (x, y, z) on a surface S, let n(x, y, z) be a unit normal vector to S at (x, y, z). The so called normal derivative of a differentiable function f: R R is the directional derivative Dnf of f in the direction of n. (a) For a positive parameter a, let S denote the portion of the sphere x + y +2=a in the first octant (i.e., where a 0, y 20 and z 20), oriented by the unit normal vector that points away from the origin. Let f(x, y, z) = ln (x + y +2). Evaluate S Dnf ds.