Sol-166E3-S2010

# Sol-166E3-S2010 - MA 166 Exam 3 Spring 2010 Page 1/4 NAME...

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Unformatted text preview: MA 166 Exam 3 Spring 2010 Page 1/4 NAME Geri-it)le KEV 10—DlGlT PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10~digit PUID, 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. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 1» 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators, or any electronic devices may be used on this test. 4.7%, may a F? l (12) 1. Circle T if True or F if False. You do not need to show work. 00 (a) If lim nan : 5, then 2 an converges. We w :1 a. 1, m. 5 . :3... aw -- M \ n. ' , ,‘,. r: m ‘0 am e n v Compcwa We” which gin/Z km 00 Wm;ng t (b) There is a convergent alternating series 2 (—1)”bn, with 1),, > 0, 1 , Tl»: , and such that "lingo bn 75 0- Qﬂﬂaf’bn #0 . Twit Vim“ attic.me T F 00 00 NM? (C) If 2 an diverges, then [an] diverges. (T) F l, n=1 \ n21“ El Q33)” , ‘ l , ‘ %. > / , 1 ,V .3 WC,» . IVK '_ m la“) mévmﬂeﬁfgefﬂﬁ C1, W wumﬁ ELL gem \f (It ‘3? .1i CW 2 I 1;: 5') W Mm (12) 2. Determine whether each of the following series is convergent or divergent. You do got need to show work. *1” We“ NP m . i . . f ' - ‘ - . to A m ; 00 31/” "37 wind/ix m ataxifwiéﬁﬁ'i QM’A WM “Mi Wig 1 (a) Z CQWIFMQ 0‘” a 7 r3 n=1 ﬂ fly; W A? W. (3%“ a? 4 sharia/r‘czﬁﬂmi l . T »~‘~——“~m pf' «r 9" aw l w) New is” Wm» 0s 00 . | on \ \ . { ‘ 2 m (LEWQ‘EWMYC m‘ﬂ/‘M “QM/R L’L‘ LA {’VQH‘L ;: 2 17.51.! . g n ' z» 1., ,9 A 3 i i, 71:1 Z *t l ‘n ‘o 4:; )rw M U 1‘ “l U 5: ( 4122M 5 WM'*:€“‘“‘“‘“” “‘ . 00 M A m ( . , (e) Z (21“ ~ 1)” amt 1w ‘ ﬂ “:1 “'4‘ ' a ’ (‘5) mm, '1) m: sf. 1, (paintersMy“. m 113% » LU“ ”" ". G U M W}? as ‘n era cm at“ MA 166 Exam 3 Spring 2010 Name Page 2/4 C}. 99 00 E7.“ W Via)“ %)thia (5) 3.7; 471* ﬂi‘i‘ are? we 3. a...“ W ‘3 m3 ‘3 M. a mg?“ as?» 4 {L 64% [W (27) 4. Determine Whether each series is convergent or divergent. You must state the condi— tions of the test you are using and verify them if they are not obvious. Write your conclusion in the small box. EQCL' Pmkgem 47(1)) awﬁrg) U) 9M7, 1 ~ 3 . .(Zn— L ' (my. my Guy, I Wm“) 931}; {Hi .r‘oigiem “0 Z T I732??? @221. M as“? v i l’ 71:1 [— ’r}? lmu ﬁv- glgv‘ﬁ-iﬁﬁhr Show all necessary work here: By the ‘k‘ of i 0 test, the series is cm ‘6 u «r: r «A {am-f E Show all necessary work here: A l t—QJr Y1 Qiy‘mg Sij 3‘ 5». £3 (Ca (1) bY1 My 3‘3 in“ mm“ n7 @ zUm lab 4? m / “wow , . M ._ i, W”, , M 5 W+. L m w {:éw‘é: b! ‘w E: ﬁﬁ'li‘tlm (x; W3 ‘15; ‘ iii «:3 3"} if” i”) 43. m e il‘.....£ii3*rr w” . L By the QQiiﬁJH/Pmikavul 5.. test, the series is Canugﬂ'a; Q m MA 166 Exam 3 Spring 2010 Name Page 3/4 00 n + 2 c ( ) 7; "3 + 1 m @ (i) LJ m i Cﬁﬁ; Emir a,» M v a i H w M “L W, (Juli/14' 65/: W wii'wtz‘mift if)??? *m u HWLM m «r : ﬁg: “um “mg :1“) mm H /’?— W; 0:36.“ » f, 33/2“ ifév am” l 77:“ I r it: a M as?” e m n a 6:7 BY the 5% it new}? aﬂwﬁﬂw test, the series is w \ Q 00 __1 n (10) 5. The series 2 ( ) satisﬁes the conditions of the alternating series test. n=1 n(10)" (a) Write out the ﬁrst ﬁve terms of the series. “m “3"” "r‘ m iii ' L 10 at we? “E 1 Pi i; “£3 *1 term it); WWW m (b) Use the alternating series estimation theorem to ﬁnd the number of terms that we need to add in order to estimate the sum of the series With error < 0.0001. W 1« 10% a4 10%"; 0,9001, “Mont it “s p... ,, wﬁ . 1 Miriam” kmLerQﬂgio ﬁgsgmi‘ e» is? 3 he terms Met (5) 6. Find the Taylor series of the function f : e‘” centered at a = —1. in) nil/W j v w a mg m ” Hi I \$1) Q‘ff‘ﬁ (£f{"£‘5£f{,‘ (“(1 I iibc * W“ ‘ g; “3:: / M V V X ’ ifv’tﬁ, gin: tire r MA 166 Exam 3 Spring 2010 Name _______._________‘ Page 4/4 00 (14) 7. For the power series Z 51” (a: + 1)”, ﬁnd the following, showing all work. n=1 (3.) The radius of convergence R. V. 4, W4 We w: ﬁne W2: WCWMW? 6”} _ , nu pm“ r l 0:. v’ W new ,. W x _ W mm Ly WON")ng L We. \ if,“ W, {lg m, \$.JLJl’tl*€% mnv’ legally-{riﬁ/eii eleweﬂﬁg W dew New??? (b) The interval of convergence. (Don’t forget to check the end points). gdﬁﬁwﬁb mer nil wﬁs: e: as? N w 0:) ow . . Q r m, C on WM? WW X:"€I l :1“ V1 (“52” : Zu(_1jﬂm «2'3 dJLVOTLgE: a Q knawﬂa h:' S” #121 kw w 1mg W In"? g’uor 0‘9 W Wham x: 4 1 Z W 6‘“ f: h é—oh'vutegé) Interval of convergence l7:: 1 g m )7 3;! I; V MILL leis/'1: for “G 9 4‘ My” Y1 “:QD (15) 8. For each function f ﬁnd its Maclaurin series and radius of convergence. You may use known series to get your answer. ll} l; on: 0A”? @fﬁr‘llﬁlk ...
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## This note was uploaded on 09/14/2011 for the course MATH 166 taught by Professor Staff during the Spring '10 term at Purdue.

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Sol-166E3-S2010 - MA 166 Exam 3 Spring 2010 Page 1/4 NAME...

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