Please help me ASAP. Plz don't spend time on explanation. Please just share your work and highlight the answer. Appreciate,

Please only work on (b)

Here is the formula sheet that you may need:

Surface Integral SS F . ndA = SS, F . dA Plane z = a: n = th; dA = dxdy Spherical surface: n = 1=(x, y,z); dA = a2 sino dodo; z = a coso; x = asin q cose ; y = a sin q sin Cylindrical surface: n = =(x, y,0); dA = a dz d0; x = a cos0 ; y = asin0 General surface (explicit): z = f(x, y), dA = ndA = +(-fx, -fy, 1)dxdy Green's Theorem (closed curve in 2D-plane) SF . ar = ff (vx F) . kdA = ], (ox ay) ._ OM ) axdy Divergence Theorem (closed region or solid and the surface of the closed region with unit normal n pointing outwards) ffe . ndA = [ff dive av = JJJv .Fav If region D is enclosed by surfaces S, and $2, then JU, dive av = [[ F. midA + [[ F. RedA Stokes Theorem (closed curve in 3D and any surface it bounds) fF . ar = [ ( vxF) . n dA Curve C and surface S need to be oriented compatibly using right-hand-rule. Second derivative test for local extreme values (unconstrained) Suppose that f (x, y) and its first and second partial derivatives are continuous throughout a disk centered at point (a, b) and that fx(a, b) = 0 and fy(a, b) = 0. Then 1. f has a local maximum at (a, b) if fxx 0 at (a, b) 2. f has a local minimum at (a, b) if fxx > 0 and fxxfyy - fry > 0 at (a, b) 3. f has a saddle point at (a, b) if fxxfyy - fly