M-273Q Final: MATH 273 Montana State OldFinalA
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Show all work and use correct notation to receive full credit! Name: let f be a vector eld in r3 and f a scalar function of three variables. For each of the following, state whether the operations shown produce a vector eld, a scalar function, or whether they cannot be computed, in which case the statement is nonsense. (a) vector. D x + y da where d is the triangular domain with vertices ( 1, 1), (1, 1), (0, 0): set up but do not evaluate, iterated triple integrals with the appropriate limits for zzz x2 + y2 dv. 8. (a) is f(x, y, z) =< 2x cos y, cos y x2 sin y, z > conservative? (justify). (b) calculate z. F dr, where c is the curve r(t) =< tet, t , (1 + t)2 >, 0 t 1. 1: use green"s theorem to calculate z. 3 z3 > outwards across the boundary surface p9 x2 y2.
