Unformatted text preview: 5. Compute the ﬂux of the vector ﬁeld F : mi —|— yj + zk (a) across the part of the paraboloid z : 3:2 + y2 which is inside the cylinder 3:2 + y2 : 1,
oriented upwards. (1)) across the cylinder 3:2 + y2 : 1 between 2 : O and z : 1, oriented outwards (only
the side of the cylinder, not the discs at the top and bottom). (c) across the disc 2:2 + 22 g l in the plane 3; : 3, oriented with normal pointing in the
positive 3; direction. 5. Find the ﬂux of F : 3:ri + 3yj + 22k upward through the cone
1‘ : ucosvi +usinvj +uk where1§u§2,0£o§7r/2. ...
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- Spring '10