Exam1Part2

# Exam1Part2 - Test 1(Fall'08 Part 2 Name S olu fwAS...

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Unformatted text preview: Test 1 (Fall'08) Part 2 Name: S olu fwAS Discussion Time: Lecture Time: 1) Provide examples of; (if possible): a. A monotonic divergent sequence. (2 pts) a _: A A b. A nonmonotonic divergent sequence. (2 pts) 4 g (4)", ,1 A c. A monotonic, decreasing convergent sequence. (2 pts) a _ LR A .. d. A conditionally convergent series. (2 pts) EM)" .'7 e. A monotonic, bounded divergent sequence. (2 pts) an manu‘hML Md. ‘Obunal c) a“ wOWS. Moi. Pars/5Q 2) Approximate f (x) = cos(x) with a parabola at 7r over the interval (7r — .1, 7r + .1). (6 pts) Coéx —>Qm=—I __ at. - 1 fins": ad -—2 (“me o ‘> T2‘“" I 10‘ V) x .. on (“M PM") «7 (“ark I Use Taylor's Inequality to estimate the accuracy of the approximation when x lies in the given interval. (4 pts) Err-o. 5 ﬂ, (,Mj‘“ M—(k-NP QtH)‘, '3’. IX‘Ul H max viva X: trial [or x: 17-4] :) lY—ﬁ‘l: Mt mcxlpuwikll “max “may” 7 Mak lgmml c 5'1 (WWI) : Small HI so Mm» ..== §*..(“7.(.c)3¢¢ (.4) T( l A A 5M ‘n ﬂu l‘a‘r“, ‘ 1WD“ 3) Find the radius of convergence and the interval of convergence of the following series. 101:1 (3 )n (6 pts for radius) 1: |<m-.zl‘.”.¢11 CM “Emu “*0?” LTy-z)‘ . ..\_ ct Q'l’x: ', Z'C'Mﬁ 1) _ =.*_.;. 13,.” 3’ ' Ta" ' ‘ Mn 3 a. «H = 5/, f (3(21'zl"; ‘ 4 M1“ ~O lax-1M3 10c [41%) - 3< 3x-‘z< 3 ﬂ r ~ts 3x<\$ “) ’3<“‘/3 —> W 7 4)ﬁEvelnetteﬁtlieVinaeﬁniteﬂintegrail asﬁan inﬁnite series. (10 pts) r fcos,(x)—1 d x x _ | -*‘+ "H x‘ '3 5- Cos(x)-l= 7- m—F.W_‘~~L+L_L* " ' ’ '. l r! X =0 _ 1. :04“ X2" ' no ‘N (A) " (_)Q YQA" Ag‘ X (1.»! A i] ‘9 2n _ (’l).\‘ ‘X + C . ______“ (7.0] ' (In)! At. ’ll}>ﬂ: [11(1 5(311()s ikg1'{?n)11\W)1§:()11Cws (.y <13\'<ngx~11(1). ,\‘, L I"! .l\':1 1. Thu “319105: is diwmant. @ The series is (:(JI‘n’m'gollt. Ra. +0. In" ‘ 6M4 (RH)! M —- a“ _” LM-m ‘(nwd (fawn) \Vhich (3110 (_3f the f(,.rH<_a\\7im.-t pmqnq'tivs {loos Eht‘ 5(_‘1"1(.,“\. 11a \7( .‘ i.) @. z-l,]i)>~i{)].11'{e1y cum \TUI’gijL‘II r, 9 H. mutiﬁtimmﬂy c<,_>11v<:1:g<311t dixs’c‘rgzcnt a: K7. Til-0"‘-}% S 2.?“ I ! \Yhich. if any. uf the fgdluvving wrim (NJIIVL‘I’QYI) Xi "I .. fi/ ; 2:: (-3)’ W 1/ 2 ” “:3 a D «W514 > )1; \ fB‘h C =- ‘— "‘ “ A‘ﬁ Mn]:— 3 L T) A" K'nék) 1. and B 5;, t k W'" ._.._> 1 . 5" kth) k" w ’ 2. A but not B . .J... I 3. B 1m: 11m: A 2 mm“) P”, r m” @. 1.}.<:‘it:hc.r‘1' 1101‘ B '0 .9 , . J tun—a }: 9 _— kin”) xiv? [01(9) 3 Go 1 LL“ V: luv) DW'VVI JU ’ 3&4; @Pm): 0036”) a: TI" [1:2 (rum Ink)! (nail Irv-.1) T200: Var) 4 f’cn-Hr-Ir) + F’er) “mi Pu; mm“! pm.- ~, 1 I (“ah ‘Smud’ pUPI‘b —- t ' .= I + O r—Z—Cx-ﬁ)‘ I'm): “(outbp‘ﬂrl' l “at lx~ql = 2. M: M“: lpc’)(g\l PM“ [INN]! " Sm (7'1) q ‘ S'mCW-.‘L) 3: S‘W( 3" (.z R1(K)~ é 6 4r .2... ;~’~m~lﬁ~_‘N——~-~~~*N~~AN. (Syn-l)“ A:. n!“ 522:; — “le” Ls: ‘ lfx~zl A. a " CAMP". cw 2)“ - no 37' e " “u c -3 L41. .1“ W 'M“2H‘=‘S£;J<‘ “+A:<7_>tZ-n‘.¢Z—"IB‘1AST— n-D'a " 5 w a a: ‘fx'U<5 u"‘><‘%-3TU———L~Zi D‘V“; ( * ‘ ’ P’Mlt.’ 'r< {y’L<r - cfx<7 So IDC .3 7) 3 [4,”: u ...
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