MAC 2313 Midterm: MAC 2313 FIU Exam f18k
15 Feb 2019
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Prof. s. hudson: [15 pts total] short answers. 1a) find the volume of the tetrahedron with vertices. P ( 1, 2, 0), q(2, 1, 3), r(1, 0, 1), s(3, 2, 3). Hints: the volume is 1/6 of the volume of a related parallelepiped. P q p r = h 7, 9, 4i (typo in hint corrected 12/7/18). 0 r (x2 + y2)dy dx by converting to polar coordinates. 4x3 + y2 subject to the constraint 2x2 + y2 = 1: [10 pts] let f(x, y, z) = (x y)i + (y z)j + (z x)k. let c be the boundary of , going. Ccw when viewed from above, where is the portion of the plane x + y + z = 1 in the. Use stoke"s theorem to evaluate w = rc f tds: [10 pts] determine whether f = hex cos y, ex sin yi is a conservative vector eld. Hint: integrate over each of the 6 faces separately.
