MAC 2313 Midterm: MAC 2313 FIU Exam 310k
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Show all your work and reasoning for maximum credit. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper. Hand in any extra paper you use along with your exam. 0: evaluate the iterated integral by converting to polar coordinates; [ true" means equal"]. x2 dy dx y 2 x2 dx dy dz dx dy: r 2, r 1. 1: let g be the rectangular box bounded by 0 x , 0 y 1 and 0 z /6. Evaluate the triple integral r r rg xy sin(yz) dv : use lagrange multipliers to nd the maximum and minimum values of f (x, y) = 4x3+y2 subject to the constraint 2x2 + y2 = 1. Bonus [about 5 points; e2, ch 14. 7]: change variables, and use a jacobian, to evaluate x y.