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# HW14 - Math E-21a Fall 2009 HW#14 problems Do these...

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Math E-21a – Fall 2009 – HW #14 problems Do these problems, but don’t turn them in : Section 13.7 : In problem 10, use Stokes’ Theorem to evaluate C d F r . The curve C is oriented counterclockwise as viewed from above, i.e. from the positive z -axis. 10. ( , , ) 2 3 x y z xy z y F i j k , C is the curve of intersection of the plane 5 x z and the cylinder 2 2 9 x y . In problem 14, verify that Stokes’ Theorem is true for the given vector field F and surface S . 14. ( , , ) x y z x y xyz F i j k , S is the part of the plane 2 2 x y z that lies in the first octant, oriented upward. Section 13.8 : In problems 2 and 4, verify that the Divergence Theorem is true for the vector field F on the region E . 2. 2 ( , , ) x y z x xy z F i j k , E is the solid bounded by the paraboloid 2 2 4 z x y and the xy -plane. 4. ( , , ) x y z x y z F i j k , E is the unit ball 2 2 2 1 x y z .

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