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# exam%203%20pink - P \ 9 K6 K pt xam3 m (Spring 2007) Name...

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Unformatted text preview: P \ 9 K6 K pt xam3 m (Spring 2007) Name Circle the correct wer. Each problem is worth 4 points. 0 1. Determine if Ixe’xzdx converges or diverges. If it converges, evaluate it. GD —0.5 952318.141th ‘ gem Z —ao o ,6: ? —;/_ w]. w 2W ) a? b. 0.5 kg) (11 0L—"°" a q .00 c. 1 d. diverges 4 1 2. Determine if I—zdx converges or diverges. If it converges, evaluate it. x ° 1% MW :ﬂém ﬂi‘éﬁ» aao a”“ I ../ x/ :00 '1 CL 3. We can use Newton’s method to approximate Vg . If the ﬁrst approximation is 2, ﬁnd the second approximation. ’C ()0 J (M 3/5 /100 %;g 07%] I ’55.,- . 2% ' -£EQD; —-’¥%V /9 1.75 poo/13x"? 1323* 45(9) 0? 3'9 0’) c.28 /E§ d.Lm ﬁ?’%:;/76 e. 1.71 4. Determine which of the following s uences converge. a. a,l = 2n+3 («QM/33:00 ﬁll”) y\ 4 n )— ; U ’ b. a =n2~5 “1,75 0 U, > W400 3 U . c a _3n+2 , QEQIJ.§IL4,) ' " M—l mg? 5”' (1. none of the above at least two ofa, b, and c m +- / 5. Determine the sum ofthe geometric series 9 + 3 + 3 +6 +5 + @6935 “is 150 MON 077 d’ is tha grq/ 3¢353 6. 063110 veasum g \ 0L6 wriHéna/i Exam 3, page 1 of6 6. Determine which of the following series converge. a. §(2n+3) ON) Mk +ejm alesrt n=l ) °° ‘On;/ b_ zanzn—S L 0/1, WI 7L 9 c. ii“? ow. MW» “5* n=1 n— none of the above e. at least two of a, b, and c 7. Determine which of the following series converge. 3. i8)" W. 3wSQ“'Q5 7 1.2:“: DJMWWw n=l n+ A c. i 3" DMLAT WM» 1mm ":1 n2 + 4 d. a, b, and c diverge e. at least 2 of a, b, and c converge 8. Determine which of the following series converge. :71: 3- 32(3)" W. WSWS W” F’ N] g av, mam) £659 0 9w Wee «eese d. a, b, and c diverge e. at least 2 of a, b, and c converge Show all work for ﬁ.111 credit for the following problems. Each problem is worth 5 points unless labeled otherwise. oo 9. Determine if the integral converges or diverges and ﬁnd the value if it converges: I 2 tom 35053”, : ﬁtmwwygli .9 8* baa” 200 / 2 ’- \o (uzeﬁfgydujeXCQ‘5 :gm @igyE 02/6 4,5 00 60M . < (v / V SC 62300 MEI»; Gave/€385 Exam 3, page 2 of6 5 10. Determine if the integral converges or diverges and ﬁnd the value if it converges: I L. 3 , 5 w z , 5, 332% e ﬂat Meal/7; am m w 03 (14 14 4/ a (2413* 'f :% 3[/5»3;/: (afi/r : 'zOE‘I/y: j; ’02 4/5: via; 5 _‘ )5— Kok b 54?),9‘L6fé ,5 3/14/55” .72 4’“ q ( Wuwaaéy ll. Determine if the integral converges or diverges and ﬁnd the value if it converges: I sm xdx 0 1+cosx' b . [m »S : 24a mam/J} w \ (ah/WW” barr‘, (7 5 - u: / 1" aﬁsx ‘ d“ r ’ 5&0 X05? :00 3/“ Oz; oer es 0 / kw? ‘4 3 12. Use the sequence 2, i, E, E, E, to complete the following. (3 points) 4 5 6 7 8 0% a. Determine a formula for the n’” term in the sequence. an 2 IL+ ’3> 12. X i PUB. < L/ 1 ’3) b. Determine the next three terms in the sequence. ‘7 ' ’0 / / g 5 ll _———ﬁ—) c. Determine if the sequence converges or diverges. If it converges, what does it converge to? cup : n+8 [q 490 quc AV {—09 13. List the ﬁrst three terms for the following sequences. (4 points) a. an: "2+2 b. a1=4 an+1=2an—3 n _5 - 3 ,23 a :17; a) I: ’ :5 '9 02/:g(L/)/3:S '2:%: {if-r a3 215%? 7 as 31:25:“? Exam 3, page 3 of 6 4950/) l4. Determine if the following sequences converge or diverge. If a sequence converges, determine what it converges to. (6 points) a a =(_1)n4n+3 b. an=(_1)n2:z —5 a an=7n—3 2n—7 n +3n 3n+5 9 , 7/14 3 — ' 3:3 :0 ﬁg” 715/3. = 2 it”: 371:7”? 'n-w n” W 3M5" 3 7 W my 0 W a 3 16. Use Newton’s Method to approximate the solution to x3 + x —3 = 0 to three decimal places. Use 1 as the ﬁrst approximation. £60: 143+ 7“? 44”, = 14,: “*0 rm: 3562+! “an 1A”! -.-an: ‘5 £3// ﬂ’Ll) ’42,) _ .26) e ” 713: [096/ My: _ . . w J.“ ,/ aéqé AJ/ﬁt/ “WHO/2M) /’9 \$0.213 ; lé’LQlB"fzgf\$ Aéug my £070” Exam 3, page 4 of 6 17. Pick a method (Bisection or Newton’s) and tell how you know when to “stop” that method, or when you have found the desired solution to the problem Be sure to list which method you have chosen. Bisemtlé’h' sﬁf UJi’Lgrx £0m050 or when atA M ion rouM/O +72 wHte Sam 2 number (WINK Sféawaieaa it 0L Flu-65)) m“ '15 mm Hie 6&st zero Ajwéwq's I \$~€ovv “Len 49”? 75,. when fOLmjéeQ-AD Me; greaepiéea gﬁ 04F PMs 18. Determine if i 1 2 —i2 converges. If so, ﬁnd the sum. k=4 (k — 1) k .L._ —,I l I 4’" "I>+ "“IL’L'AJ’ ' Jr ("—01, ﬁt) S“;ZJ3—\z‘;~:>+<<srlr 5” W ‘4 , J- ’ r’ Sn / 31 “Z. - = 4.,4 , J— “as” “as” series w 19. Use the integral test to determine if i do k=1(ﬁ+1 W M .3 (3331M 5 Jo . '9 , ’ :i. , f/lf, ’j— : ff”: 184(X+)>0& /.é/’Vl~ 34H] :MEH M) 0-2 4 2 converges or diverges. Show all work for credit. Exam 3, page 5 of6 4 . . . , , 00 +3 20. Use the 11m1t comparlson test to determme 1f 2 2’17 :2 n=l n — n 4/) ; 07,07,517; En; ﬁg (rsemes) ’97.?) converges or diverges. Show all work for credit. near "a"; 1' , " @0) Elan arZL/x 5/” jg Ada: ‘éﬁé’ 0" 1/ 22m 157/”: g V )9 %2 447/ .77/2 6” 07 . /,, 21. Use the ratio test to determine if converges or diverges. Show all work for credit. 02" n=l n. A+l [in I? j "t' (n+0! A4“! 0 n! I I L) ﬂaw/fin? 7 )/ #53?“ n2” (>0 0Q” i W M 9 2 WM 37 {til 22. Approximate the error when only the ﬁrst 4 terms are used to evaluate 40 n=ln mm , 625+ a. m. + ~° 335.22 , .L _ a -6 L _ . ’5 ,5 , S M lijﬁig’z’? loaoo 9L 5’7” b” - 4,5. A71 Exam 3, page 6 of 6 ...
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## This note was uploaded on 02/25/2010 for the course MATH 201 taught by Professor Kim during the Spring '07 term at SIU Carbondale.

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exam%203%20pink - P \ 9 K6 K pt xam3 m (Spring 2007) Name...

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