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Exam3ASolutions - Name 50w 0N5 Math 133 — Hourly Exam 3A...

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Unformatted text preview: Name 50w? 0N5 March 18, 2008 Math 133 — Hourly Exam 3A Do all problems (Total = 100 points). Show all work. Calculators are not allowed. (1) (a) (6 points) Write out the partial fractions decomposition of the following expression but DO NOT SOLVE for the coefficients A, B, . . . _$:1_. : A * 3 + c + ”D (90 — 3)2(9L“2 — 1) x— 2; (>03? 'x-\ XH. 3“” ‘5‘;ng Gk} (x “\(xu) 2 __ (b) (16 points) Use partial fractions to find I = / u—Zflf day. Edna“ 7' “(76+Ll) MA Xl4u\ lfrcévcfihlt. Su‘nu. bL'LlQG : O‘lL<O Wfi C 32%“ X " 8 _ A B¥+C ,— pAi‘lf-fli) 4' (By-“v x X3+va ' 7? * X‘H . "T, XNHX (Lamas ¢wanh M3\—(,\\ “W’t3\-W5 ‘- 2x2“? X'8 = (A*5) X1 3r Cx 4 ‘lA Mater 045 1» 'Ansal % Czl So HA=’8 bl ”1)ng \ ‘ Ukr- X71 L‘ ‘0“ I = x l WW A“ 30‘3”" \§ ama,‘ ax. ’ dm : “Q. QMl’Xl + 8 x31 (1* ‘- X+H- .L . .‘ 25- '“ *QQMM +19% * lmexLL) " \A ~= :1 QMM 1» l J'Mx‘vfl '4 1; maizvdg *0 OR =\ (xiii: “ 3‘: main. (EA * C, \‘ 0° d (2) (10 points) Evaluate the improper integral I = /0 fl ”Do "Be. {AA€/%V\\\‘C. imie~ra\ '. Lei u=l+xL du=élxebsc iku=xé2x "x44 _ i‘c'iu _; .4ch =—1U{‘ __~\ =—\ (\m‘)" ‘ 3‘ UL” ‘ 9- 0‘ ‘9' u 94m?) (3) Determine whether the following integrals converge or diverge. DO NOT EVALUATE. Justify your answers using the Comparison Test (CT) and Limit Comparision Test (LCT). a : °° dx _ ‘ . _ _\ __\_ ()(8pts) I /1 W Csmvam, "FE/J: m Lm-‘e‘ glfl-m—X “ pm 2 ‘ ._'S_{L—’_«“x‘3_ ° 3:2: 3;?) 2 ET?” \ixzufl % ._ Ex; Mint) ‘ Erm<xzilx "\ (4) (14 points) Solve the differential equation \/_dy d—— — y2 with the initial condition y(0)= :5 5}}?ka VCuchbkL ‘. '35— da = (11—; d’X 1. :9 3.393%th ivCA’ial Cencl‘s‘lfi‘sw ‘. X=O) ¢6=l ‘4) “l = 25+C” Q i ‘\ 4“: ‘ 501% (w 25‘ ”A 21—; \ (5) (8 points each) Calculate the limit of the following sequences. Show all steps clearly. (a)7lLIlgo[ln(n+3)— —lnn] : [MM Q (Liz) “>00 flVxVL (Lfl\ ) ‘— (b) lim V2n—1 = 50AM (9“-‘3/n : LN“ elimULn-J) Y\ n—>oo uD “-300 _ [W Quit—1) -. 6 new 00 a 2‘43” QAAliX“) g 456% 5 sin n (c) If an 2 n2 What is nil—n; an? 5“an “i S $a‘n n 5 \ , _\ \ bat Mug 3;; 5 50m“? 5 T“. g, a“ h. i \ ‘ w \ Bah” Lle *x- : O CMAA lUV‘A 4:. 3 D So LUV“ 1% : 0 “W h “Q00 h ) Y\ \>% "\‘kc Sanéwi‘c/k meta“, (6) (8 pts) (a) Does the infinite geometric series 3+1+1+1+ 4 4 12 36 converge or diverge? If it converges, What is the sum? Justify your responses. 1"; i , ~ - 3‘ '— iS V) Us SaM‘L, sari cs Lorifi A ' A MA T: 5 Sinuz. i‘r\ 4 \ ‘Hnis Series 0 Convaées . We Show 3% A 39"!” :: —§9~-_-;:v :é;:-€L> \-r: w Ms L: /3 tr:— 8 (b) (8 pts) Write the repeating decimal 0.37 as a geometric series. Then write the sum as a fraction. 0.37 ‘3 .57 57 57 “1 23.3 4 73-07; 4 7;}: Jr" . . . _\_ W?) V: C\ afiom'i'fic, aria; \m‘i‘e‘ A: 3%00 ““9“ V ‘1 loo c ”(ng '— A 3-7 ‘ .31. 23,29. 037 .: 7:;=7;‘1—-};u I00 33- *' Q Ii ...
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