MATH 211 Final: MATH 211 Amherst F12M211 2803 29ManackFinal
15 Feb 2019
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This exam consists of 12 questions totaling 180 points. You have 3 hours to take this exam. Books, notes, calculators, cell phones or aids of any sort are not permitted. Please turn o all electronic devices, including cell phones. Explain your answers fully, showing all work in your blue book, and clearly label which prob- lem you are solving. 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. Use an appropriate change of variables to calculate the integral (x + y)2ex y da. Zzr: (20 points) let f (x, y) be the function given by f (x, y) =( 3x2 x2+y2. Explain why the integral around any closed curve in the xy-plane is zero.
