Please provide solution for these exercises thank u!

Question 1. [10%] Find the absolute maximum and minimum of the function f(x, y) = 2y2 + x2 - xy - 7x over the region R in the xy-plane bounded by the triangle with vertices (0,0), (1,0) and (0,1). Question 2. [10%] Find the work done by the vector field F = 3x2 yi + (x3 + 1) j+ 922 k when moving a particle from the point (1,1,1) to the point (1,0,0) then to the point (1,0,1) and back to (1,1,1 ) . Question 3. [20% ] Find the counterclockwise circulation and outward Nux for the field F = xy i *x3 j across and around the closed curve C which is the boundary of the region, in the first quadrant, enclosed bythe cloves x + y? = 1 and y = x and the jaxis. Question 4: [ 10%] Evaluate $, xly?dx + (yx3 + y?)dy where (C) is the boundary of the region in the xy-plane bounded by y = $ , y = -2x and x = 2. Question 5. [20%] a- Write the area of the surface cut from the hemisphere + += =4. =20 by the cylinder ." + y* =2x (do not evaluate). b- Find the outward flux of the field F=xx+yi+wx+v j-3(x +y)k across the surface cut from the cone = = vax + above the plane z = 2 and below the paraboloid = =12-2 6 6 Question 6. [30%] Consider the solid S bounded by the sphere a + +2 =9, the cylinder x + y =9 and the plane z = 3. / Set up the volume of the solid S in spherical and cylindrical coordinates. 6 / Find the flux of the field F=3x23 7 + y 7-2 F across all the boundaries of the solid S. /Find the counter clockwise circulation of the vector field G = yz? i + (y? + 1)j + xz k around the curve bounding the top of the solid S