MATH 0240 Final: MATH 240 Final Exam-31
Document Summary
Math 0240 final examination sample 5 - answers. Problem 1. (1): x + y z = 1; (2): 3. = fx sin cos + fy sin sin + fz cos . = fx sin sin + fy sin cos . 1; -1; x + y + z = 3. Problem 4. (1, 0) and ( 1, 0)- saddles; (0, 1)-loc. max; (0, 1)-loc. min. 3 , where k is the coe cient such that the density = kr (r is the distance from the point to the axis of the cylinder) A potential function f (x, y) = x2. Answer for both parts (1) and (2): 2 (for part (1) use the parametriza- 2 + xy tion x = 1 + t, y = 1 + t, z = 1 + t, 0 t 1. )
