MATH 250 Final: MATH 250 Amherst S18M250TakeHomeFinal
15 Feb 2019
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If you wish, you may also attempt the three optional bonus questions. Little or no credit may be awarded, even when your answer is correct, if you fail to follow instructions for a problem or fail to justify your answer. Simplify your answers whenever possible, and write legibly. No calculators are allowed, but you may use one 8. 5x11 sheet of notes: (10 points). Write down, but do not evaluate, a de nite integral giving the arclength of c. Compute zzze: (20 points) find the volume of the solid bounded by the surfaces y = 1 x2, y = 0, z = x, and z = 2. z dv , (15 points). Prove that f is not continuous at (0, 0). 3x2 + y2 if (x, y) 6= (0, 0), ~f d~r. (over: (15 points) let ~f (x, y) = hx cos(2y), y3 + 2x sin(2y)i. Show that ~f is conservative by nding a potential function for ~f .
