MATH 1502 Midterm: MATH 1502 GT 1t02ssy2k
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Test i for calculus ii, math 1502, february 1, 2000. This test is to be taken without graphing calculators and notes of any sorts. For example, if you mean 2 do not write 1. 414 . Show your work for otherwise credit cannot be given. I: (25 points) consider the function tan 1(x) = z x. 1 + t2 dt : find the rst three terms of the taylor expansion (around 0) of this function, using these terms compute an approximate value for tan 1(1/2), give an estimate on how accurate that value approximates tan 1(1/2). Ii: (25 points) compute the limits: a) x 0(cid:20) cos(x) x lim sin(x) x2 (cid:21) . 1 x e lim x b) c) x 0(cid:20) cos(x) 1 + x2/2 lim x4 (cid:21) . Iii: (25 points) which of the following series is convergent or divergent? a) 1 + k2 : evaluate the series.
