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Solutions-166E3-S01

Solutions-166E3-S01 - MA 166 EXAM 3 Spring 2001 ’ NAME...

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Unformatted text preview: MA 166 EXAM 3 Spring 2001 ’ NAME GRAOHVG l<fi~y STUDENT ID RECITATION INSTRUCTOR _____—‘ RECITATION TIME DIRECTIONS Page 1/4 1. Write your name, student ID number, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4'. 2. 3. 4. 5. 6. The test has four (4) pages, including this one. Write your answers in the boxes provided. You must show sufficient work to justify all answers. Correct answers with inconsistent work may not be given credit. Credit for each problem is given in parentheses in the left hand margin. N0 books, notes or calculators may be used on this test. ’ (14) 1. Circle the letter of the correct response. (You need not show work for this problem) N PC (3.) Which of the following statements are true for any series 2 an with positive n21 terms? ‘ (I) If lim an— — 0, then 2 an converges. Na t tTW’“ :7‘ '! n—)oo n=1 an divans 0. J! w\(\,\:r FY“ (11) If lim —1—- -— 1 then "2 1a,, diverges. T‘RHL CQWW Wm" 2:36.11.- 71 fl—kOQ ( ) (III) If lim an+1=l then 020 an converges. $11.6. Mic n—mo an 2 n=1 A. 11 only II and 111 only 0. land 111 only D. all E. (b) Which of the following series converge? oo 1. 2 14,, _ 2 0 <1. (I) Z 2—' Rollo teal! 102'“) 2W1. 2“" “ n+1 gnaw ..mw\/ n=l 'n” r) (343 0° ‘1?» L (RM/(i 9.1L1'vmi' (11) Z n:_1 div. COM'XW WM n3“! "'2 u Qumrfi‘eii‘. n=1 n ’71, 1 1 it. SMiefi Tad— _ __ _ _ __ V. b A (m) 1 2fi+ 3f 4f+ 0°“ ’3 A. Ionly B. 111 only C. II and 111 on1y® 1 and 111 only E. none W ugg lt‘md Cow}: Test. tea: (I) none {7] MA 166 Exam 3 Spring 2001 Name _.__.— Page 2/4 ' (20) 2. Determine whether each series is convergent or divergent. You must show all necessary work and write your conclusion in the small box. 00 For PWHzmc 2(a) camel filo) lauk yiq’wsl’fmv’ém n If Weaver} “.7 OFT” {or Fmblem @ (a) i=2 ”5+4 1} “313} «a awn MYL ;. A task Show all necessary work here: 00 ® (9 ' A, WW LL wavem . Come ”Ml/L, In; “3’1 (P—Wic‘i/ Pg 1) Q n < w __ 3.,@ r * m m w By the Cgvn PM i 50’“ test, the series is nghvngemx 6:5 Una-it mMFOWfanva 162 (b) 2 (—1)"-1 “’7 ”=1 n+1 M AlTevaiwg Sayre“; leaf‘ bn:.——-—«- Ll) lo dammm'woa? Pl Li M = {’7 = G) x-M. ‘ §’(><) : (mag—r - Gfl_ x+1 rayiifw. <0 (“0" ' 2W0“? —2“f”(’”')1 , ,Lm" x>i yes 5,, t, dimmmxgg® .. A ’l - w ems ztm W :tm ,0 ® ”-1 m Y)+l. n—aPOD fill-+13-rtr: . © By the WWII/3 gm § e, 9 test, the series is my, \I efl%e,fix‘ VO" ll \ Jiv‘ MA 166 Exam 3 Spring 2001 Name _.—_ Page 3/4 n 1 b (10) 3. Determine Whether the series 2 £_3)T_ is convergent 0r divergent. If it is conver- 71:1 gent, find its sum. ’3 :00 (__ 3)” ”1— (m3) 4_(:____'31)PL +434” + . . : 4- 4’ 47' 43 4 _ 3 3 '2. .3 ’3 %eom¢’i‘n< trill +477) + (‘2?) + (“’4' *' W111 {L 1M4. 271' 41>" —1"11 1.]! answer in w~cowfi (311143 5 FZ'MtO f0? memygfiwu gum LX- S A W"- "" Mn (10) 4. Consider the series Z(—1)"‘1 1—3. W8 :2) ’0 it“ 36“ “a” n=fli " V (a) Write out the first six terms of the series. 4. P17 1 ’L 54L?! 4 't arm .(p anwé}; _... 1 1 .143 1-3:. 31—in+—:;—-;—.3+1'1 (2.3 '5 4 i '9 1” 4/51 " 1 A” h“ A” ,L __., .41..» -+ ‘ ‘ J ’ 1' ”g” ‘1’ 27' fl J“ 12.5 :2. 1 e (b) Find the smallest number of terms that we need to add in order to estimate the sum of the series with error < 0.01. ® 1 1. __5_,__ ._ — _....—— . - 0 i. 3 " 3,2: 5’ < 10 o D . J}— : .1— ‘> O. 01— 43 64 c"3"2‘cos(— ) 10) 5. Determine whether the series is absolutely conver ent, conditionally con- g 1112 + 4n vergent or divergent. You must justify your answer. AloSaLMHLQra my“; 11er1 1m“ 2-— \ w:(g)W\ OQWV ? (flmkmme Mid" Z A"; ”3‘ In?” +43“ @ . ~. ‘ rl~1erw>9 ensign) lam? 23)] 4 C9 W11 1: ”WW... (a AL \ h2+£iwl WL’f AH" < nL® ’LOY d H ’ TLJL emu/2 in a193,.oiu‘ir12glka mnuugwr E»? the CDWIDQ-J‘tiinéj Text 1‘} aqumwv (D ““0116 cit (“3th W fireman. (”00/ The series is 0J0$QM¢Q$ my” QMJY E0] 2V5: flow m1” 30b; vain; ““3" fl Fr” MWD‘ACE ”£1351 P°h¢ "llL M ”‘ w vim wcx. Lg) —’5}>CB (7/; / Mimi??? LL LL U MA 166 Exam 3 Spring 2001 Name Page 4/4 ' (16) 6. Find the interval of convergence of the power series Zn: n=1 convergence at the end points of the interval. You must show all work. $ 0L : n X" ‘ m) XVI-H @ 3x3 h H 4—,. . +1 __ 2 T ' Lm am""’" 5 'V”) 253*" '3 film “wt l l ” 2. Rollo ’teS haw <3W Ira—.00 n X" "“900 ) ’ _ 9‘3 V? w 1:; —— <1— [’21) V" ”‘ ® . fitted; 0v WU Wlka X 2 fl". V12" :1 ”47(4) y, (3le bizigémélf: DNE] ~ TL Mh-Po.’ , 00 00 ® , WLDJW x22 3 Z ”2‘1 ..__ 2 h div. luau“ “I‘m? FY45“ h '2! Z” n t I @ (QA‘YV‘ 4’! :fl— 5) ) v “gym 3‘ y, I Nievuoi or] mnvaxrzrm «2L. ; \Z (A)? ’2 [:l ... ’ I ( 2/ (2') or ~24 >< , Z G (10) 7. Find a power series representation for f (:3) = 1 +19$2 and determine the radius of ' convergence R. 00 L L1? 7,” Lil Md NPC’ 1 L .22: RAF-Lou ’X 5‘3 "(2)6; — 2: —?><"')"=Z 14,9sz :1 Mil/w}! mm], Lox l—Q)? iv: A. .L or [x14 3 cavfievcol (if (10) 8. Find the Taylor series for f(:v )— — 1 +1: + $2 abea-‘ba— — 2. our ‘02 2 LL : EL}; L L :‘L LLLL LL L; Six) : 4L+ ><+>< K9317 gm”) ': 4. + 2x S'Qg) : 6 3(2)”) —: 2 if?) 1’ ‘2— EM”) ; O “Mk; :0 ’ZArCLJU W33 . 970:7 +—:—;T(_§< VP?) +23(X 2) L 2 @ C93 @3 ”1:, FBI “4” Lapin Mignon! 179?"; 7“ ’LD f(m)=7+5(>('2) + (*2) E3] ...
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