MATH1823 Midterm: MATH 1823 UNB Exam 1823 01dec

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15 Feb 2019
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Final exam: [10 points] evaluate each limit. Justify your answer. x3 sin x arctan x (1 + ln(2x))tan( x) (a) lim x 0 (b) lim x . 2: [15 points] evaluate each integral. cos4 t dt. 2 (a) z /2 (b) z (c) z arctan x x2. 1 dx (x2 + 2)5/2 dx: [15 points] for each improper integral, evaluate it if possible, or determine that it diverges. 1 (a) z (b) z (c) z . 1 x x + x x x2 + 3x + 2 dx dx. 1 x ((ln x)2 + ln x) dx: [15 points] evaluate each of the following sums (you may assume that each sum converges). (express your answer in terms of x). (a) Xn=1 (d) (e) n! ( 1)n 1 (2n + 1)! xn, assuming that x > 0 (express your answer in terms of x): [20 points] for each series, determine whether it is absolutely convergent, conditionally convergent, or divergent.

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