MATH 2374 Midterm: MATH 2374 UMN Spring 08 Exam 3sol
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Exam 3 solutions: by stokes" theorem, the surface integral is equal to r s f ds. Tu = (1, 0, 2u), tv = (0, 1, 0), and tu tv = (2u, 0, 1), which points up and has magnitude 1 + 4u2. 2v du dv e2u v+u ex+y da = 3z 1. = 3z 1 e3u du z 1 e . 4 , : (a) ( , ) = (2 cos sin , 3 sin sin , 6 cos ), where 0 2 and. 4 ) corresponds to the point (1, 3. 0 . (b) ( , ) = ( . Thinking of the ellipsoid as the level surface f = 36 for the function f (x, y, z) = 9x2 + 4y2 + z2, we have f = (18x, 8y, 2z). ), we have f = (18, 12, 6 2). The tangent plane to the ellipsoid (1, 3 there has equation (18, 12, 6 2) (x 1, y 3.
