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2. Let C be the triangle formed by traveling from the point (0,1) to (2,1), to (2,5), and back to (0,1). (a) (4 pts) Find a parametrization for the curve C in R². (b) (6 pts) Evaluate the path integral of f F(x,y) = xy along the curve C. 3. (10 pts) Find the area of the part of the surface Z = 9 - x2 - y2 that lies inside the cylinder x2 + y2 = 4. 4. (10 pts) Evaluate xy + x d.c dy C where C is the arc of the ellipse x2 +42 = 1 traversed counterclockwise from (1,0) to (-1,0). 5. Let S be the part of the cone x2 = y2 + z2 that is between x = 1 and x = 3. Let S be oriented with the normal vector pointing in the positive x-direction. (a) (5 pts) Find an orientation preserving parametrization of the surface S. (b) (5 pts) Let F(x,y,z) = (x,-z,-y). - Find S

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Mathematics Problems
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