MAT-2130 Midterm: MATH 2130 App State H Fall2007 Exam1 answer key
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A formula sheet is supplied, for your reference. Use the backs of the exam pages for scratchwork or for continuation of your answers, if necessary. X: (9 points): find the minimum and maximum value of f (x, y) = 4 x2 y2 subject to the constraint x2 + 2y2 1, (7 points): rewrite the following integral with the order of integration reversed: 1 f (x, y) dy dx: (8 points): evaluate the following integral: 1 px2 + y2 + z2 dz dy dx: (9 points): evaluate the following integral where r is the trapezoidal region with vertices (1, 0), (2, 0), (0, 2), and (0, 1): Zzr cos(cid:18) y x y + x(cid:19) da. Hint: choose a change of variables that makes y x y+x simple: (8 points): consider the following vector eld: Orient c to be counterclockwise when viewed from above. Hint: stoke"s theorem: (9 points): find zzs. Formulas for the final exam a b = |a||b| cos .