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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 wagk. 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. PageCHER Wu: minmim for
mplmncss 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}: Efﬁgixﬂ' =ﬂc} +f'ic}ix :*}+ . . .i JiljicEfLﬂL . . 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. EkIl 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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 Spring '09
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