3. Suppose that f and g are scalar functions with continuous first- and second-order partial derivatives throughout a region E that is bounded by a closed piecewise smooth surface S. Show that

2. Use the surface integral in Stokes' Theorem to calculate the flux of the field F = (x - y) i + (y-z) j + (z - x) k across the surface S:r (Φ,θ) = (2 sinΦcosθ) i + (2 sinΦsinθ) j + 2 cosΦ k, 0 ≤ Φ ≤ π/2,0 ≤ θ ≤ 2π in the direction of the outward unit normal n.