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Sol-162E3-S2008

# Sol-162E3-S2008 - MA 162 Exam 3 Spring 2008 Name 10—digit...

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Unformatted text preview: MA 162 Exam 3 Spring 2008 Name 10—digit PUID RECITATION Division and Section Numbers Recitation Instructor Instructions: 1. Fill in all the information requested above and on the scantron sheet. ,, , 2. This booklet contains 22 problems. Problems 1 - 17 are worth 4 points each, problems 18 - 20 are worth 6 points each and problems 21 and 22 are worth 7 points each. The maximum score is 100 points. 3. For each problem mark your answer on the scantron sheet and also circle it in this booklet. 4. Work only on the pages of this booklet. Books, notes, calculators or any electronic devices are not to be used on this test. 9“ MA 162 Exam 3 OO 1. If lim an 2 0, then 2 an converges. ’71—’00 n21 i: s m Wiﬂ‘ﬁcf‘t‘ h ' VP"! 2. If 2 la”! converges then 2 an converges. n: 1 n21 '\ 3. If lim {7 [an| = 2, then 2 an converges. n—roo ”:1 (1-3 (MM. wrwr /Q/W\ HIV “3L: >1—3clfv. h 50? h z. .93 no Wclmﬁf’h l 00 4. If "lingo d: = 2, then 2: an diverges. n21 pa LMH’ empamsx +95%) Mal 2%; divevjeg 1 . “n+1 _ ~ 5. If 73520 an — 2, then T; an converges. Ma ‘ <| —> 66w. H t '3» > —==> dW' chv) leél‘ w. an L l ;\..,—m) \|V\(6\ClM\$‘I‘/€ 00 00 6. If an > bn Z 0 for all n and 2 an diverges, then 2 bn diverges. Oé-l’i 4;} w 2: “ﬁgs swig: WW h Spring 2008 A. True @False True B. False MA 162 Exam 3 Spring 2008 7. Z (—1) converges absolutely. ”:1 n2 + n r; 00 ,,,L 30. ( mm OWN/Wan Ml“ WW I n2. @Tme 2 has“ gﬁa N \ b ‘ Z1 B. False LAM—l» CWQWLM‘A Ml" W Z ”a, 00 3111(n) . . 8 z n2 converges cond1t10nally. 11:1 \ W l 9‘40“” ml QM A. True é CngﬂQ M l 1r é W" W3 2 MM! M False 00 3—4—— :: -L~ AMM‘ FmSéiﬁ-é’j/ Pli 4!, ‘True B. False 2n n21 w 70 n A L W W .L \ . True 2: 2h W L CL) WW8 was) B False 00 N 12. 2 an = [\$211.00 (2:1 an). i ~ ‘ @True a m m M 4% 33 We B. a; sadﬂ& QMWS. MA 162 Exam 3 Spring 2008 °° 1 13. 2:: 71 MN) converges. 00 h 6&7 ' {1: .True ﬁlm'nhxﬂmjvl” 1‘3”“(MQAM6 ‘E-BDD )I XAQJKA 117,390 9/ False :& {macs/1 wrmmy : m ”a 14. ism (i) diverges. con—1 SR EL) a True 00 n 1 16. Iff(m) : Z (n+ 1)! mm, then foam) : 6' n20 ' iffi—O—l Y\ 3:? (€(9)/d3 , ; ﬁ>€i\$ :1 E153)A. True yd, :Z 6M4)! [5L ( (9‘9 0. ‘False :: L; / é 1E3}? @5513?“ of convergence of the series gags)” is 2. , V » jJ/‘WA h V‘ I W F A. True ‘ w 1 , zhkl - 7 H95? ) @XB kayo (Kl ,L False ( _._ ‘ 2 ' BIN 41 __,> M 4 3: > mﬁimJ¥VCﬂW L 00 19. The interval of convergence of the power series 2 \ )nH MA 162 Exam 3 Spring 2008 °0 (—2)“—2 _ 18.; BR _ w M 91> H _§ _ g; @n‘(23 : §:(>¢3 43 A i / ’ ﬁ. 17;. E (a 3 B, #5 h“? 3 2 h I C. ___§_ \ __ ﬂ “ﬁg "2: m ”'1“ng 5, ,J, D' g ”~qu’WE’WVQS w (3% an 3 3 (—1)” n2 (a: + 1)n is. f“ V\ L 71:0 24% (eff " «gm /E” (M4 . Ln } [—2 0] ago «3~— - V‘ V‘ , ’ n (9-H) ((1 (m) . B. (4’01 L ,_ h k.“ C [072] , Ma A“); [)(+'(-— [MW 4 <0 11(02] gems cmmfé {W /7\~H I <1 a.) ricxﬂd—a *2 X E [0,2) X: "L w=> Z i999)” = E if» 0”“ . ’ w CtV‘hK 10.9 {g ~L’0 x;0 .2.) 2:? W h 20. If 1+2): :co+clm+02m2’+03\$3+-~ then C3: m 3 8 neﬁa Cnﬁﬂ:iﬁ-_g A? 3 3! “Q 8 \ .,,, -\ . _n 1am.” mm B- 3: L 7‘ C. 8 £(\{*\ ;m3 2/ D _8 gmm gniiﬂmz E. 4 MA 162 Exam 3 Spring 2008 1 1+:c2 d3: 1/10 21. Using power series, the smallest number of terms needed to approximate / 0 to Within 10‘6 is ”MA 3 A. 1 r X 1;”!th *x "W“ @3 , “‘2; +35”. D 4 “ 3 g E. 5 22. The ﬁrst 4 nonzero terms of the power series representation for f (:13) = (1 —I— :13)_3 are @ 1—3m+6w2 ~10m3 \ l L ? ‘T 3” ' 3 = 2 ‘,X_H4..X +><aj>4+'” B. 1—3x+12\$2—60\$ (+>€ |‘°(-¥~) C. 1 - 3m + 6m2 — 611:3 D. 1—3m+3\$2—\$3 —‘ 4 (win) 3 o A +zx~3xz+wgpﬁﬁrr§ 1*3w+4m2~8933 0m”: 5; w r 2 1?: ‘é:(:}”) 3: 0RD +1~EX+1LA “2074 +-~m l 3 4;); =3 |»3>«+é>< “(OX +7" ...
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Sol-162E3-S2008 - MA 162 Exam 3 Spring 2008 Name 10—digit...

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