Sol-166FE-S2006

Sol-166FE-S2006 - MA 166 FINAL EXAM Spring 2006 Page 1/11...

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Unformatted text preview: MA 166 FINAL EXAM Spring 2006 Page 1/11 10-DIGIT PUID # RECITATION INSTRUCTOR RECITATION TIME LECTURER INSTRUCTIONS 1. There are 11 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. Also write your name at the top of pages 2—11. ' 3. Do any necessary work for each problem on the space provided or on the back of the pages of this test booklet. Circle your answers in this test booklet. No partial credit will be given, but if you show your work on the test booklet, it may be used in borderline cases. 4. No books, notes, calculators, or any electronic devices may be used on this exam. 5. Each problem is worth 8 points. The maximum possible score is 200 points. 6. Using a #2 pencil, fill in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, first name), and fill in the little circles. (b) On the bottom left side, under SECTION, write in your division and section number and fill in the little circles. (For example, for division 9 section 1, write 0901. For example, for division 38 section 2, write 3802). (c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your 10—digit PUID, and fill in the little circles. (d) Using a #2 pencil, put your answers to questions 1—25 on your answer sheet by filling in the circle of the letter of your response. Double check that you have filled in the circles you intended. If more than one circle is filled in for any question, your response will be considered incorrect. Use a #2 pencil. 7. After you have finished the exam, hand in your answer sheet and your test booklet to your recitation instructor. MA 166 FINAL EXAM Spring 2006 Name: — Page 2/11 1. If [i 2 5+ 3+ 1; and 1;: —1+ 3+ 1;, find a unit vector orthogonal to both 51' and hand having negative k-component. —~ A T r“ a-A ‘5'? __' a a axb-s‘ «ks—25+ak AJ—k '41 11 11 B ‘fii-fik .. ij_—1—q mm: m __ afi *0 m m w... A. ij—flq bun/n v'cdlw J— 'Uolooud 0; Mb D fig fik [11* a 2q_iq ’fi-\ +ék ’ E. fig fik M wt‘bL m?de k-umnoowdt» ’L 7.,5’ “(:53 r2“ 2. The vertices of a triangle are P = (—1,0, 1), Q =. (1,1,3) and R = (2,1,0). If0 is the angle of the triangle at P, then c086 : .a-i —’ I: 5 '- 7‘ ‘ A. — Na _ '2: +3. A 3m R =3'» H’“ B 1 —, —-+ -* '3 10 a -. PR hmmmwe O f *D. — ewi 3x/fi 60$ ' 35 E 2 ’3\/fi 3. The radius'of the sphere $2+y2+z2+2$—4z=3 [‘5 9g A_ 2\/§ xii-9.x +31 +2134?” :3 3 fl xz+2x +1. +1m+27342+4 = 3+1+4 C~ x/fi 7_ '2. + (32+ (2'2) = (a D. m ' ' E 1 Raul/5w): (é '5’ gfi MA 166 FINAL EXAM Spring 2006 Name: Page 3/11 :1:— +1- 2 7. 4.1imwzbim (“(1”): A0 &_ - B. +00 ’ 09 C 1 L“: . 1" . “Ma—2X1- ' x..ch __..$———- x—aoo L+x 1 1‘?* E. — 2 “t s «1.2-.qu n I .1 ,L 'L" B. 1 : \m Ltam x11 C _3 face ' 4 —-1. 7r ‘1 Lm [tam—1t -—- ta’“ 1—] D. a tfloo 71' E _ ___ Tr ,IL. .. .11; 9* 4 9. 4 4 1 I 2 - 2 3 ‘7, 1 I 6/ (Sln:I7+COS.’I7) dac: £(smx .kgog x +92:an m5>¢>dn A 7r 0 ‘ 5 0 1 v B. £+_ '3' C1, + Zsmxmsx)ch 2 2 O C. 1 I: 71' 1 ._ . z a D. ___ -::. |_x 4— Smx] 2 2 . 0 7T , W 94 E —2—+1 7. MA 166 FINAL EXAM Spring 2006 Name: Page 4/11 3 1 \ 7.] 2 (1.1): 2 I 2 '27 —$ 8 111g 1 w: —» f= 1:- +~z 4 .. X' _ x4 x01) . 1 ’94 B. 1113 ,L ; Fab/“45% C 11 . n— A+B:o akthi) B=L 6 -—- :71- - 1 2 xot 2 x X'1 E. In— 3 : + M(x-1)]2_ Z—Qfifij “(—CnZ-I‘zmi) :-_ 'RMB‘IHQ'XMQ :ze/n—‘L 3 8. /a:(lna:)4da:= Infefirolion by W: A. (lnm)4_4/$(ln$)3dm usql/nxf) an»:de iwhh W- (“WW 2 mm: 4(Qm,f%giv 1221—? 9613. £2—(1nx)4—2/m(1nm)3dm S xQmeY’o’Lx = LiQMy)4-J xqiuamféolx C. 45v(lnzv)3— / (1119:)3da: 2—. 3‘;(me)+~ 2 3404“ >93"!”7t D. f—Sanmf—é/anmédx E. %(lnm)5—%/zv(lnm)5da: % 2 5 (1 — 4a: )ida: into 1 9. The trigonometric substitution 2a: : sin 0 converts the integral / b (L . Q’X -:: Sine , 1 1 a: 52x dd :33 wsedfi A. 5/ cos503in0d0 ; 2 1" “*1 1-411 -:. c056 , 1 -£ :1" B. 64/ 6m “3%,; 676— )xgu—w 2 %c08 i — £2: 1 % —_——_- b . L (“4%) 01” ZJ (wssggwsefi; C. 7 W c085031n6;d0 ’ E , I w 4 6 %D 1 fc 60010 E G . 7 OS =7 L J" cos 9M 3 % 6 E 64 ms“ 0d0 I 6 MA 166 FINAL EXAM Spring 2006 Name: — Page 5/11 10. The region in the first quadrant bounded by the y—axis, the graph of a: + y = 2 and the graph of y : a: 2 is revolved about the m-axis. The volume V of the solid generated Point ¥ ihl—Mkctl‘o" 0’17, :7: Lam—u mig=x : 2 37r 53:24 3' 3 X3. x .—2=0 /@+2)(x~t)=0 C. 417; m1, —2 _7r D. 3 Voleef 0} VQFM‘L MSW .. ' * E‘ 15 ’2— 'AV :[v (i’Xf’WO‘Hm‘ ’L . / 1 4 '2. 4. /' . 0 .3 5 1 1:“ (4xvzx1+_§._l’ \ 3 5 0 ': ’1- -—1>) -—- qo-rg’B :11'22‘» Tr(4‘2+’€ S ‘WMW 15" 11. The region bounded by the graph of y : sin 11:, 0 g a: 3 7r, and the m—axis, is revolved about the y-axis. The volume V of the solid generated is V) Tr W _ E. 7r \l T: l 21Tx sink Ax : 2w] x ghoul/y O 0 “1x asuzsx'mml'y ..... Tr IT'- \' ~21! [—stxl +‘J comely—l o o : t2" [-fiws-n- *(sian‘TJ : 211-2. MA 166 FINAL EXAM Spring 2006 Name: —— Page 6/11 12. Consider the lamina bounded by the curves at + y : 1, a: = 0, and y = 0 and with density p = 1. If (5,?) is the center of mass of the lamina, then E = 3 1 xix—g B; a; 1 D.§ 2 OO . 13. Suppose that 2a,, 2 Let bn = 2an and SH : b1 + b2 + ---+ bn. n—l Which one of these statements is true? )(-A. lim snzwand lim bn=0 TL—iOO n—+oo B. lim sn : 7r but lim bn cannot be determined Tia—+00 71—)00 C. lim sn 2 00 and lim bn = 7r 71—)00 Tia—+00 D. lim bn = 0 but lim sn cannot be determined 71—)00 71—)00 E. lim sn : 0 but lim bn cannot be determined 71—)00 n—+oo co 00' on Z __ _ E- “:1. W d’f'mtaw ‘m S '2 E b 7W h—’°° h ":1. n b O 00 , ' ' ’3 w m an n w “’3 $2.20 *7 MA 166 FINAL EXAM Spring 2006 Name: _— Page 7/11 oo 1 14. Theseries — 1:}, L +L+nn r; en £+ Q1 8} _ A. diverges 1 1+ ‘— +(L]’Lv(—$——gr-"j X—B — 1 T; I 7 'e 9» '3 ‘_e-1 e C : ':: ,._.1 Lav-2’41“: 6—1 e D Z . 1—6 1 E. 2 1+6 A. Converges by comparison with 71:1 00 1 gimao(1+%1):l+0 7;? fl, oc B. Converges by the ratio test 5 1 A1 b + -/ be ‘ ‘ h ,, (1 6”) 6m C. Diverges by the ratio test D. Converges by the limit comparison test )\< E. Diverges MA 166 FINAL EXAM Spring 2006 Name: Page 8/11 16. Which of these series converge? 00 1 Limit camfiteyt 0‘3 m Z3n+¢m:3“ mw<w¢~M“”E;% “:1 ol iv, 00 . 2 s1nn (H)§:————fl nzl v 3+5 A. All B. Only (111) Campan'ron Te :I' 90 C. Only (11) D ( E n 17:; “3/1 . Only I) and (111) 0° WM (1 III Z ——5n2— Comfaarkoy. Tet/f m L X ' only an ( ) n‘=1 V" +2" +1 C°mfmm will. 2 "6372, mm“ H -1 17. Of the series 0° (—1)" 0° 1 0° (-1)" I _ n _ ()2; mn, (H)2;(1) 1+” , aH)Z; n3_2 (I) cohv. b; A”! Serf-fest A. (I) and (III) converge absolutely bui cues hot “3"”- °Jl°é~ B I d H b 1 1 Lamrm Z 6%,, Wu 221‘ . ()an ( )converge a so utey 51:2. " '7; n 96 C. Only (III) converges absolutely (Ii) km (-0 (“H DNE H.900 ‘ D. All converge but none converges absolutely wie s (LN. E. (I) and (II) diverge (III) cow. 0&5. do Do ‘ .—L— ffm‘ m .tCVt (Ame E72, ‘53:; Wit/L» Z; “3/: C 00 F ) 18. If f = tan 1:, the aterms of the Maclaurin series of f up to the third power of :1: are n) £00 : i gm x": {(07 +3??— +§§QKL A. 00—152 $3 , 2.‘ n20 Y‘! 3 + f¢%o) xg+tvw $3 ’5! 96 B. .’L' + E §(x):l‘omx go):0 C 1+$+$—2+$—3 5C §(1)(x) Z 2 secxsuxtmnx :: 292.3} two)! 20) :0 D g; + g .’L' $3 '1+:L'2 (1+:L'2)2 MA 166 FINAL EXAM Spring 2006 Name: 00 2 n 19. The ad' f e e ce fth se ’e 3:" is 1 V r 1us0 convrgn o epower r1s;(n+1)! *A.OO Ratio test L B. 1 £1.11; C. 2 (“H — 41.221...— _ L D. e an .o-r—r’ X“ (n+1)! E. 0 1 (“+0 (“+0.2 ]x\» , "' 1. \ . .lx =0 <1 __ n+la'_L_]x\/’)10 \ "' n “*2 as 11”” GM Rzoo “Hes mm. )LW 01L x 20. Match the functions with their Maclaurin series. 00 (1) em (a) Z (—1)”a:", —1 < a: < 1 n=0 1 11:2 x3 2 1 — — — () 1+$ (b) +x+2!+3!+ , oo<x<oo (3) 1mm (c) $+$2+x3+...,—1<a:<1 32 2 34 4 (4) msma: (d) 1— 21:: + 41:: — .., —oo<a:<oo 113‘; 11:6 i (5) c033x (e) $2——+—— ,—oo<a:<oo 3! 5! CD ,1 r1 '3 x _. L. b (1) e = Ea”, "*”‘+%fl” a" () A. 1b,2c,3a,4d,5e ' ' ca 00 n Y) ('2’) 1L :1 A. ; Zoe.» :Eél) x (09 B. 1e,2a,3c,4b,5d -, h: , 1+7! 1 (y) C. 1a,2b,3d,4c,5e w 1 b) x _: x Z x" .; xowtnxiwu) D. 1b,2c,3a,4e,5d 1_X ":0 =. x+xz+x14~~ 1b,2a,3c,4e,5d I 3 5 ' '3’ . . ‘ 4 G X%m)r:x1’_.§31+%—W' t '2. 4 (31x3— 34x4. (5) L053>< =1 Jr“) rL—L’dflm ’1 ' "ET * 4'. ' 2.! 4! Page 9/11 - (a0 MA 166 FINAL EXAM Spring 2006 Name: Page 10/11 21. The graph of the polar equation 7‘ = 1 + cos6 is a 0 1; TI' 3-; 9‘" A. A circle with center at (13,31) 2 (0,1) v i 2 1 D 1 2- B. A circle with center at (13,31) 2 (1,0) C. A two—leaved rose l 9(— D. A cardpid with the point farthest from the origin at (3:, y) = (2,0) E. A cardioid with the point farthest from the origin at (:13, y) : (0,2) 22. Convert the polar equation 7‘ = —2 cos 6 to rectangular coordinates A. (m—1)2+y2 = 1 vm: _ chosG ,6 B. (a:+1)2+y2:1 2 m“- X *‘3 ’ 9.x C. m2+(y—1)2=1 xz+2x *‘3330 D. a22+(y+1)2=1 (z. __ x1+2y +1 +‘a '1’ E. m2+y2=2 LX-H)1 + ‘gz 1: 1 23. The curve described parametrically by _ W A. an ellipse 9” = 2‘30“? y 2 _ Sint; 0 S t S 5 B. a quarter of a circle is 1 ‘61 C. a half of a circle is; + «1;- :1. x 70 , D. a half of an ellipse :0 .. (x’g)=(2,°) 96E. aquarter ofan ellipse MA 166 FINAL EXAM Spring 2006 Name: ______—— Page 11/11 24. The length L of the curve in problem 23 is given by E w W . 1;- sin2 L: J Wflfiz M 34A fgv3 t+1dt B. V2cos2t+1dt " ,1. t 1' % ('Qsmt) + ( 605 ) 01x C. / V-sin2t+ 1dt 0 Mmmmwwhww 2 V 4 Sl'nzt + (‘nszt di D. /0 (—2 s1n t+cos t)dt { E. /2(\/§sint+1)dt 0 25. The polar form of the complex number with argument between 0 and 27r is 1+\/?_)2 i ' ' Tr 21(903E "’ LBW—E) A. cos g+ising 1+fiitz<wSE+l$ffig-) . 1 7r 7f Q 3 B. 5 (cos §+isin : ..._— COS ’—’ ‘1'L ‘ 2. 3 E . . 7r 1+6”: 2 , z 3) I T, C. cos6+zs1ng ,. ,1; (C05 E- 'i’ L 5‘“ Z. 1 7r _ 7r r- 1 6 46 D. (cos E+zsin 0v . ' f - - f) .7; ~ L 1_EL' : fi+L:E+—12E.\/§(cos3 +zsm3 1143': 1H?!é 9—— 3L 4’ 4 4 5! —— 5‘— : ' rz'L' \c' c ‘35? + t K: 2' .J— ...
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Sol-166FE-S2006 - MA 166 FINAL EXAM Spring 2006 Page 1/11...

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