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Sol-166E2-S2008 - MA 166 Exam 2 Spring 2008 Page 1/4 NAME...

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Unformatted text preview: MA 166 Exam 2 Spring 2008 Page 1/4 NAME GRADING KEV 10—DIGIT 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. . The test has four (4) pages, including this one. Write your answers in the boxes provided. . You must show suflicient 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 nor any electronic devices may be used on this test. Find the integrals in problems 1—6. @ E I E i « 4 6 1. 2 d -; ,1- f” 3 4-. X + ~ Stn'l‘x] () A cos a: :c 2 o(1-\*cfl$?x)d.‘3l 2i: 2 O =%Z%+$'1l=”~fl[email protected] 1% r33 x/f Q9 /fl imafiecat’qweolfi I) a4 sec4e (:3; ”X 3' 0f S ea 6 '2 d " d. y -' a 6 ea 9 tan 3 d3 “MM -x7. (22' '"‘ Q tan-B ,Mi,~w’ {:MW -- MWfiWfi—MM 19 9 ,1?) t )LormiSSI +C 7;:f :%~" 99 as 2—1:. X has (w UM was) f EC 0‘ ‘Zé‘Eife *1 PT W)“ “‘“W‘3 3hr? 9 . 3 Palm {Lu OLE—dc 03596996: 5"“ 6 + C (one, time. Fiver“): 3a?“ X :af‘ 2. i N ‘1’ ( 2197— )3 ”:a 3 g Problam) MA 166 / Exam 2 dz: 9 3. / _ z: ‘ _ () ‘/4_($+3UV—\\\J: m_,, 1: 3%flzi‘dfi/[email protected] ,:,,,-»~*~'W~“*““"MW"' 4'uj/ @ T -: > C 2 1+3 x+$ :Qsine -2595): 4- u - Jim-IE “-1 6+ a ' a 2 .41 m’V—SWQ" 2 - _ q, d)! : 20058de “AA .' m V4-6”? :Qoase (I: 2ms€d5_j1 @ $2+8$——3 (11)4'/Wd$ 0:» (D (9 R ,9 31:33.11 _ ,6. + ,1: +55... M u; ”my“? dmngmaw /'>(1(X+3> --' 7‘ 'X’z X+3 W [MN I \ an vhfiw @ 38485:”; ': AX2+3AX+B><+BB+C7¢2 Wfiw (9) 5/5900de ._.8 M69- 33+sina: -— W . \FV “15107! CD B w» a) M: coax zif'x‘ , i. A Rub at" . LL (1+1 B ’0 : Mgu1-myu.+>}+c “in; 5:4 :1 mefnx‘ .. M‘sinx+i\+c Rub m MA 166 Exam 2 Spring 2008 Name —_ Page 3/4 x+1 (6) 6./$2+9dx 1-; $7? t—i/)&q (10) 7. Find the area of the region under the curve y = :+; fromx: 2 to 1:: 3. A: fslfl—Ol’x: 30?}— ob: __"‘ 2Q”, 4' 3 1.5?- 7‘" / 2 7rd) -l_7‘ 4' ‘7‘ 2 <7“! X4“) @ :3+29/nZ-—2 [email protected] L t? ‘3 43—" :1+£ X'l ’X'L ( “or ELL .. xvii-2 '~ g 1' + 2 2 IE —- ,. - =14» m X 'I X” x»: (10) 8. Determine whether the integral below is convergent or divergent. Find its value if it is convergent. Important: You must use the definition of improper integrals. M .¢ 1 dx :Qcm ft 1 4% :L'm 5%sz‘sflt —l. ‘3' ~— 00 3-63 ,, _ 2Q” daumgmi U5) (6) 9. Circle T if true or F if false. (a)/ fidx is divergent 500.}.1" (r wuvergmf til/D1, T @@ 1 P RP=§ I X 2 2 _.1 3'} 2 Calm @421) Mt beam “but inieérmél {Cm-.1332 in not QDMII'WLLOM '50.? C t -- .. 11 Mr. .A. :~L-2v;;]/ (C) /0 Edit 18 convergent 317%? A, m 0L5! é—Yff‘ 0 @ F = @IEJEZVT-E +21] :‘2 MA 166 Exam 2 Spring 2008 Name —— Page 4/4 (5) 10. Set up but do not evaluate an integral for the length L of the curve 3/ = tanm, O S :1: g 1. «lazmdx (9) 11. Consider the lamina bounded by the curves y = x2, 3/ = 0, :v = 1 and with density p = 1. Find the following: a) The mass m of the lamina. . 1 '2 3 l I 1 m: S'x clx : 2.). I z 3 \ z (“2 '2’”) o 3 0 m: A. (a) N 3 .. x b) The momerit Mx of the lamina about the ctr—axis. —n m 2 j '22?de :Wb‘iziw _ n2 +2n— 1 “-099 n +Qw-v1 n—mo Cling-“pl ° “3 o 10 M3; = .L— (9 1 ‘O‘ . 1 c) The y—coordinate of the center of mass of the lamina. .. 0k 5,1 wnaslaf m 3 =1 my w. (9L ova -— 3 e3 2- ~ 2: .L y _ " a ‘3 10 1° (10) 12. Determine whether the sequence converges or diverges. If it converges, find the limit. (You need not show work for this porblem). N P C 71' \ an 11—)” (a) {tangy} 3:75 “—9: "49¢ (23 n .2 1301.551, a—aO 6” , nvr (b) anzsm? 0/ 1/0)—1)0,1..... dj'aelrfiefi ' r 7. LH 27! L” _ 7— »‘X _ 2» L:; m '3? '5: (C) {77,26 72.} $23“? 9 xdgaex 1—90; '6 ~ 2’; bier-“=0 55' ‘55 ‘ 11—?» n 0 —1 n 1n , _ ' ——-—"" :n‘ (d) an — ( 2+ 1 £12; Ianz'namm 101+! 3. Lima“ :7. 0 5 new .. +..— (e) an 317,2 + 5 ' 3mm+> : arm 3 ”a” ’3 ...
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