A surface S2 consists of that part of the cylindrical surface z+y = 9 that lies...
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A surface S2 consists of that part of the cylindrical surface z+y = 9 that lies between the planes z=0 and 2=2, and for which r 2 0, as shown in Figure Q2. The region V is the volume enclosed by 4 surfaces: the surface S2, the plane z = 0, the plane z = 2 and the plane z= !! 0. (a) Use double and triple integrals to calculate the volume of the region V. Show all working. 4 marks (b) Determine the curl of the field function zi - r + yk. Show all working. 4 marks (c) The Divergence Theorem states that | V.F dV = Fn ds For region V and field function F = ri, verify the Divergence Theorem. 12 marks A surface S2 consists of that part of the cylindrical surface z+y = 9 that lies between the planes z=0 and 2=2, and for which r 2 0, as shown in Figure Q2. The region V is the volume enclosed by 4 surfaces: the surface S2, the plane z = 0, the plane z = 2 and the plane z= !! 0. (a) Use double and triple integrals to calculate the volume of the region V. Show all working. 4 marks (b) Determine the curl of the field function zi - r + yk. Show all working. 4 marks (c) The Divergence Theorem states that | V.F dV = Fn ds For region V and field function F = ri, verify the Divergence Theorem. 12 marks
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