Let E be the solid bounded by the cylinder x +2=1. the planes x+y+z=3 and y=-2....

  

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Let E be the solid bounded by the cylinder x² +2²=1. the planes x+y+z=3 and y=-2. Let S 8E with conventional orientation and let F(x,y,z) = (x, y, z). (1) Parametrize S and calculate the area of S. (2) Find the equation of the plane tangent to the surface S at (1/√2,1/2,1/√2). (3) Calculate F. ds 8 (4) Show that F curl G for any C² vector field G on R³. Let E be the solid bounded by the cylinder x² +2²=1. the planes x+y+z=3 and y=-2. Let S 8E with conventional orientation and let F(x,y,z) = (x, y, z). (1) Parametrize S and calculate the area of S. (2) Find the equation of the plane tangent to the surface S at (1/√2,1/2,1/√2). (3) Calculate F. ds 8 (4) Show that F curl G for any C² vector field G on R³.