MATH242 Midterm: MATH242-07F-exam3

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31 Jan 2019
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MATH242 Full Course Notes
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MATH242 Full Course Notes
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Arrange your work as clearly and neatly as possible, and cross out incorrect work. Unless otherwise noted, you must justify all answers to receive full credit. You may not use calculators, notes, or any other kinds of aids: (5 points each) for the sequence (cid:26) 1. If it converges, determine the value of the sum. n=1. State what: (15 points each) determine the convergence/divergence of each series. State what test or rules you are using. (a) (b) n=1 n=1 ln(n) ln(n) n: (15 points) find the radius and interval of convergence for the series n=0 xn. N 2n : (15 points) find the taylor series of sin(3x) at a = 2 /3, (15 points) find the rst three nonzero terms in the maclaurin series of x xe . 1 + x d dx (cid:16)sin 1 x(cid:17) = dx (cid:16)tan 1 x(cid:17) = d. 1 + tan2 = sec2 , sin2 = 1. 2 (1 cos 2 ) cos2 = 1.