3) Check the divergence theorem for the function H = :r² cos 0 + r² cos pê - r² cos sin op using the volume of one octant ( x ≥ 0, y ≥ 0, z ≥ 0) of the sphere of radius Ro centered in the origin.

A) Find and describe the region inscribed by the lines (x-axis), (y = -x+2) and (x = 2y-4) under the mapping function (w=1/z)

Suppose that D is the ellipse D={tr, ») € R°: + v* < 10} {(x, y) € R²: + y? < 10} D = 4 and that f is a differentiable function defined on all of R². Suppose that (xo, Yo) is in ƏD, the boundary of D. Denote by (xo, Yo) the derivative of ƒ in the direction of the outward pointing unit normal at the point (xo, Yo). Given that fe (4, 3) = 2 and df (4, 3) = 2, dy calculate (4, 3).