Calc II- Exam 4 - DEPARTMENT OF MATHEMATICS UNITED STATES...

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Unformatted text preview: DEPARTMENT OF MATHEMATICS UNITED STATES CUAST GUARD ACADEMY CALCULUS II - Spring 2003 f Exam 4 Thursday 24 April 21108 Named Period {M'fl Instmctofi INSTRUCTIONS: "fl—m -------------- - - I. Work alone. Show all wag-k. 2. Work in PENCIL only. 3. You may not 1.13:: any notes, books, or calculators. 4. This minafian WES uf'this cover shut and SIX {15] commutide rrum'bcmd paw plus an Efnrmyigm ghee: on “rig. Page-CHER Wu: minmim for mplm-ncss heron: beginning work. Report any discrepancies to your insuumr. thlcm “tights an: pmfided in the right hand margin nut la each problem. 5. DID NOT LEAVE THE EXAMINATION AREA WITHOUT THE PERMISSION OF YOUR INSTRUCTOR. fix}: Effigix-fl' =flc} +f'ic}ix --:*}+ . . .-i JiljicEfLfl-L . . 1. Test the felluwing infinite series for convergence. State the test you are using. [7' pts. each} W k T t 3' Ee=1 f; as — m a R h. EkI-l TESt_ sun '1 £311 JCT“ _. Test_: 1 5L 21:2th TESL e. 2;; E Test_ f_ Efflg _ Test_ 2. Test the following series for conditional nr absolqu convergence. in EUR—1 a. Em fl {1am} ['_1 k—l b. 33"“ *3“ {5 pts.] 3. Find the interval of qgnvergque fur the series 2. m- (-11“ "=1 H" x". {15 Pts} 4. Find the Taylor pehmamial of degree 3 for fix] = 1d? about‘fifi % ' _' ' ~..-_-'”’ [1!] p15] 5. Eiwntheseriesfarfi: 1 Hx+xz —x3 ++~-, — 1 «:2 J: i: 11 Obtain the Mayflaurin Seriesfur the lnfl + x}. E 1|] ntsj E. 3. Find the recto lar coordinates of the point whose polar coordinates are given as ( j. [4 otsJ b. Find the rectangular coordinates of the point (1%"). {4 iom] ...
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