MATH 166 Final: Spring2016Math166Final
31 Jan 2019
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No credit is allowed for mere answers with no work shown. Calculators are allowed for this exam; if you use your calculator you must mention this as part of your work. It important that you present organized, well thought out work, including written descrip- tions of what you are doing. Disorganized, hard-to-follow or understand solutions will receive little credit. For each of the following in nite series, determine whether the series converges or diverges. You must justify your answer. (5 points each. ) a. Xk=1 (ln(k + 2) ln k) b. 5k ln(2k + 3) (x + 1)k: find the radius of convergence for the series. Justify your answer. (9 points. : find the interval of convergence (including endpoints) for the series. Let f (x) = ln(x + 2): find the taylor polynomial p4(x), about the point a = 1, for f (x). (8 points. , assume that we use this taylor polynomial p4(x) (about a = 1) to approximate.
