ex4sol-b - MTH 133 —— Section 1—4 m Quiz Four...

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Unformatted text preview: MTH 133 —— Section 1—4 m Quiz Four DEPARTMENT OF MATHEMATICS Michigan State University November 17, 2005 g was...» NAME: it} if 3"? i} 5‘“ ID NUMBER: SIGNATURE: SECTION: 1. This exam has 4 pages including this cover. There are 4 questions. The time limit for this quiz is 35 minutes. 2. Include units in your answers whenever appropriate. 3. You may NOT use your calculator. 4. Sines, cosines, and tangents of simple angles are to be written out. For example7 if you have a 005(2), you should write 5. Present your solutions to each problem in a clear and orderly fashion. Include enough steps to permit the grader to follow yo ir method. Your method must justify your answer. PROBLEM POINTS SCORE 1 2O 2 30 3 10 4 15 TOTAL 75 Present your solutions clearly. 1. (20 points) Determine whether the series 1 “=1 ne” converges using (a) the ratio test; “ ,, g “I W E i? f?" g j 3 2' a _ W if it? 3%»??? ) m; ” ’“f’fl "W I i \Wf§)€€ {1 ’4? >35 .5 5 . W" g < i / SD Mir; 5. {van} 2» ’ A 2 "in—Wm“ ,’ {Xi/i {6/ I’d-VI; gfi ‘ 23 (b) the direct comparison test. 1; § 7 in , m 3mg? Vial) VEQ, 2: E f {\m‘ x x ,l , figs": 4: €93“? Aha 63M {eewv*ff§5§ (a f 55*!“ng E s g 5% gifésmééwwfi 3:"? <5 WV {'9 Mew“: v‘ § ‘ ” f; m K E; > I? g} :3, {if g Eff; 52%” { (,2 K?” s g 4:; be]; i {We 5 _ \ t if? 5t {Qt/'1‘ 2. (30 points) Determine whether each of the following series are convergent. Justify your answers. Remember to cite all the tests that you use. (a) f: cos n=1 1 fl TL is Fifi/fl , may? C9§WJ$§ 21’» {<35 6,; f (:33 5:3 Céihé' {{i‘kfix"jrf§ 7’1fié‘3rm NATE)? Present your solutions clearly. 3 her; {ZWOE “fivfijflf ‘ ‘ 00 3 < 6 a"? (C) 7; "2 # W "'3‘ Irv?“ , D :3 ‘ 2 hi) $43 WEI” ‘13:; , [IS/“m “3 w 3 "'5" {a ’“v m 531 €‘- a i iflifi E < < (>5; and W ‘ A ‘ a i C: 3 2 fl 3/ C Cvapfiff’g'g (9%:E" {op/w figgfgga A ggfiyék 3 I it t ,r ‘ f) £3371 Wiflr‘N (:3: i363: {é‘flwiijgfi‘ Z? 3. (10 points) What fraction has the decimal expansion 0.04.5? Justify your answer carefully using facts about geometric series. 3 W _~ 9,? ‘ r m 5‘6??? v 04345“ «r $990443 "‘1" (itg‘w‘gNMr ig 5?} fiééfl"? '5’fé ge/‘rgg qu‘sffli’L/E {gimmoyfi V33:6& j 56:) a «Li/“3% fie?” f; 5163 5&5} 31> 9'73 31W ‘5 g ‘C‘; ‘35“ £1 6:343“ , 46‘ i T: {E are??? H “" ‘ ’l 9’79 Present your solutions clearly. 4 4. (15 points) Find the interval of convergence of the power series oo(2:c+3)" 7; n3+1. 10% szs “H Um Vr-DDA V m+l>3+l /;1;<+5; 0w New (m+<)3+/ : £2><+5/ mm (“TH SW H‘DDQ .2 (2X?§l < i n3+« w1<2x+g<Ii r¢<z><<41724><<¢4 9+ 76” i(:3:’:2: .— ‘ i ’ _, I” m C “”‘ Wm»; m @9777: ‘55-; 0/13. 2")” Z ' W3 (GdVP/wj/Cf (‘03; >\) I A 5m (04% «if; M x1, <2 3 n w ij!) \i‘h$*( ‘- «vi €074 {i ~>x ‘mzu (“g ZQ'W') I A m (3 An aHE/fifléwlrj 36,4}; Shae it: V034,; j “lie/inaWj 304965 41751} E (“I 337 j . I Ms +5? FmWwf (Mmequ IQ .. 3: w (3 E IQ, ,, i j UTA—3:7 ...
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This note was uploaded on 09/27/2009 for the course MATH 133 taught by Professor Wei during the Fall '07 term at Michigan State University.

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ex4sol-b - MTH 133 —— Section 1—4 m Quiz Four...

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