MATH 271 Final: MATH 271 Amherst S15M271Final
15 Feb 2019
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You may not use books, notes, calculators, cell phones or any other aids. You must explain your answers clearly and completely to get full credit. Answers involving sine, cosine or tangent of angles that are multiples of , . Follow directions carefully: if the question tells you to use a particular method or de nition, then you must use it in order to get credit. The total number of points available is 100. Prove that a and b are perpendicular: let f be the function given by f (x, y) =( 3xy x2+y2. Zzr where r is the region in the xy-plane bounded by the line y = 1 curve x2 + y2 = 5. E: let f be the vector eld given by. F(x, y) =(cid:10)2xy + y3, x2 + 3xy2 + 2y(cid:11) . (a) (4 points) find a function f (x, y) such that f = f . (b) (4 points) evaluate the line integralzc.
