MATH 2374 Final: MATH 2374 UMN Spring 07Fall Final Exam
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3. (a) 2. (b) ( 2, 0): 7 . (use green"s theorem. , 6x + 4y z 11 = 0. (use t-coe cients to get two vectors in the plane; use cross product to nd normal. ) The line integral resulting from stokes" theorem is. 0 45 cos sin d : 3 . (use the chain rule. Note: g is a 1 2 matrix, not a 2 1. Also note: g(0, 0) = 3 is unnecessary information. ) 2 . (use parametrization c(t) = (sin t, cos t), 0 t . 6 (173/2 53/2). (use parametrization (r, ) = (r cos , r sin , r2 3) for. 1 r 2 and 0 2 . )
