MATH 271 Final: MATH 271 Amherst S18M271 2802 29DanielsFinal

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Read this first: please read each question carefully. Show all work clearly in the space provided. In order to receive full credit on a problem, solution methods must be complete, logical and understandable: answers must be clearly labeled in the spaces provided after each question. Please cross out or fully erase any work that you do not want graded. The point value of each question is indicated after its statement. No books or other references are permitted: calculators are not allowed and you must show all your work in order to receive credit on the problem. Be clear if the limit equals a value, + or , or does not exist. (a) lim x 0. [10] (b) lim x x(2 arctan(3x) ) [20] (a) z 2x3 + 3x2 + 3. 2x3 + 2x dx (b) z x3p1 x2 dx. Find the sum of each of the following series. You do not need to show that they converge.