Could you please help me with my homework? Please clearly show and organize your work. Professor has completed 70-90 percent of the work

Please, please, please follow his work.

6 8 ( x , y , E ) ds 8 ( x , y , Z ) = 3 2 5 8 = 2 - ( x zg z) S 4 " E = 2 - ( " + go ) above xy Plane 3 8 ds = 3 ds 5 as = it + "of \\ 2 dx dyz = f ( x , y ) Q of of - - 2x the Surface OX 2 = 2 - ( x x y y ) of =- zy foxy ) d s = ( 1 + ( zx ? + ( - zy ) 2 dx dy HI+ 4 ( x 2 x yz) dxdy I = ( ( 6 - 3 ( x 4 yz ) ) 1 1 + 4 ( x 2 x yrc ) axdy D using Polar copyduats x = ros o y - rsing I = ? du = 8 ror7 surface in terral find [ ( if )nds II unit out word norm using stoke Thergrem SSGx Finds = Fidr S = $ ( y, - x2 , 3x - (B). ( dx , dy , dzy since in the care , 8=9 = $ ( yox - x q dy z = 0 8 ( q dx - $3 xdy ) C Paramtive eq Q X = 3 Cost C 217 y = 3sint | 3 Sin ( A ( 3 sin ( ) at ) _ 9 3 cos CT ) (3 cost ) at dx = - Isint at S ( 9 sin ( + 94 cos ( + ) at dy = 3 cost d+ 193 (1 - cos ( 24) -+ 9 7- ( 1 + Cos ( 2+ ) at G10 F = ( x 2 2 - yzz , x z g - x 2 3, z xg z x y z z7 find Finds ( surfaceiAte S n out nand unit novmarl vector ) Z = S dady f = ox y I = SSS (x xy x 2 3) exdy de V/ a * X = V sino cos4 I = ? y = r sin a sin 4 151 =12 sin OX - y 8 D Find VixF (2 find Of. or around any colsed D -8 -D K K ox oy oz ox X x 2 + yz xz + yz = 2 Find OF.dy aroub any closed Pathe a C A kosider z cares SF. dx - SSC # x D)inds = 02 for the closed x ( o, 0 ) x x x y z x z x y z C ydx use Polar + x dy coordes X = rcoso 4 = K Sino6. Evaluate $(z, y, 2) dS where o(z, y, 2) =32 and S is the surface of the paraboloid 2=2 - (a' +12) above the ay plane dx dy x Fig. for the problem 6. 7. Given the vector field F=yi-x23 7 + 3xle = k , find the integral ( x Finds where S is the surface of the paraboloid 2 = 2 +7 bounded by z = 9, and n is the unit outward normal vector of the surface S, by using Stokes' theorem. (Fig. is in the next page)C 7 - 9 x Fig. for the problem 7. 8. Let F = _y 12 +12 12+1/2 j . Find V x F and evaluate F. dr around any closed path C. (Be careful about the conditions to use Stokes or Green's theorem) 9. Given F = (3x2 - 4yz) i - (x2z + y) j+ (xy + 32) k , find FindS , where S is the surface of the sphere (x -3)' + (y + 1)' + (2 -2)2 =9 10. Given F = (x23 -y'z) it (xly -x23) 7+ (2xy + 132) k , find FindS, where S S is the entire surface of the hemispherical region bounded by a = va? -x2 -y and 2 =0, by using divergence theorem (Gauss theorem)