Sol-166FE-S2000

Sol-166FE-S2000 - MA 166 FINAL EXAM Spring 2000 Page 1/10...

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Unformatted text preview: MA 166 FINAL EXAM Spring 2000 Page 1/10 NAME SOLUTION‘ES M STUDENT ID # RECITATION INSTRUCTOR RECITATION TIME LECTURER M INSTRUCTIONS 1. There are 10 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your Social security number). Also write your name at the top of pages 2—10. 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 or calculators 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 student ID number, and fill in the little circles. ((1) 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 an_d your test booklet to your recitation instructor. MA 166 FINAL EXAM Spring 2000 Name: __—__ Page 2/10 1. Consider the triangle ABC with vertices A = (0, 0,0), B = (3:, g, 0), and C = (1, 2,0), where :1: > 0. If the area of the triangle is 6, then :1: = AB :‘Xi 1‘ A' 4 --‘ —=* w: s A :: L + _, C 3 -+ "' "T h. ,- (2x-2‘_ k - big; 3‘ T— L a 2'2, D_ 5 X X7: 0 2134/ ' \ E. 2 a 1 ’2. O 3' ’ "— H I—LXSX’22 AMO/ABC =1£HAB>rMi~z<z 4 3x : g ——-a x :‘3 4 2 Let ('1' = 7+3+ I; and 4: §+ 33., where :1: > 0. Find a: so that “pr-53H = 1. 4' I”. H -—a m —" -’ A. 2 Pfab: (I. Hall '3 13- fl-l x“ I; L-Ha r 1+“ C' 3 P n x I “a =- -—-—-— N If fig" -’ 6 @x/g—l {,3 xsinx L'Hffl. xmsy +$iHY 3'1i115f—r: W? ——---—":'"'"'",—"‘ M flmm xao «~‘3coa‘x {'E'WV) ,9" 2 o g k Xmsx “ti-"W 2 x—pO 'BSHG?‘ max 32.. 0- 0 L. ‘ O ‘ D. 1 : m E does not exist xfl’b c. ' '3 “ M‘n‘xmswrsmx +JU h—q III-d.— .3... ’3 MA 166 FINAL EXAM Spring 2000 Name: 4. 'ftanxsecamdmr— S saga-X (gecytanx)d_x 1 ésec3x+0 ___ 7. '3 '3 —— u -— LL. —— 3:. 1 I 3 +C * :3 may +C C. Zsec4m+C 1 3 D. Etan (5+0 1 3 E. Ecsc 3+0 s r; 3; if sinxseczmdm= 3‘5 giny _._ AM ._. o d—N p—‘n' ...——u——-' —- A.2 “2— 0 (.03)! 1- U“ .1 \sz5x w-=“¢“"Y‘L"‘ (LO ._ _., :1 1 x105: w »‘ D‘E X-? —-9L.L-"?:_ J E.3 4- .. _’__L__\/""___ 1 -121 U” .— 1 . 6. The integral f :32 \/ 1 — :32 dz: is transformed by a trigonometric substitution to o ’ 1 fix )(zethL (sky :msuci». A_ / Sinzucoszudu o \|;(-'>(Z -: mild. § . B. f sin2 u cos3 it du >< :0 —-+ UK “:0 0 —, u -: If U _ X a "—3 2,, O. f 31112 u c053 u do Zr: 12'? 1‘. . '2, 1r filwumsumsui’k 3-3 2 D. sm ucos udu O o 2’: - 2 2 ® 5111 ucos udu o MA 166 FINAL EXAM Spfing 2000 Name: _—_____. Page 4/10 b A. — LWL tam'1x\ 2 .__ to “am i B. 1ntegra1d1verges C 7r -’1 *1 : hm [tam b -— town 1) D 33 3 b4“ TV 7r '3: E -" '13.”: " 4. @4 2 2. 9' 9"2. 8.f:1:1na:d:1:= 3L1th fig 2L 1—3.3: 7;; 1 2.. I '2- X I UL:an cinnxdar @21n2_§ Mild-x ru:?g‘ 7 3 7‘ .. 2, 2" B. 1112—Z _ X “.2an C l1n2—l a J— '2 4 22%?”Lifi4’] DE: —-- 3 '- 2'an fl 4' E. 2ln2—é 3 1 ELL w2_1da:_ 1 fl - - ‘ x—i 3 xz’i (X+1)(x 1) )Hri. 3 mi _. . X+F3 (3’ _' AN A +3 0.111% AkB:D B~A1 1- . B“‘ A” '"L -1—1n§ 3 ’ ‘5. ' 9— 2 2 3 E 1113 SJPOLVZJ’;J,J——+L~L—Am 2 x721 (\ 2 X'V'L 2 X" 2 J. 3 +£Qm24-ZQ/n :JSIQJWQ'B II MA 166 FINAL EXAM Spring 2000 Name: Page 5/10 10. Let R be the region between the graph of y = sins: and the cr-axis on the interval [0, 7r]. The volume of the solid obtained by revolving R about the x-axis is 1:5ti , 2 ‘ 1r ‘3 Av—zwsmxw A-a B. W2 C. 11' 2 r T“ (9% v '3— .. ch wsmde-zrrfl US$12th W2 0 0 4&- E. g ._ 11- '2. :: _\... .,. l. 2 :TT +TT] : Ir..- ‘TT‘ [2X 4‘51?) 3c 0 [a 2 11. The length of the graph of f(w) = 5 + gmg, 0 S .7: S 2, is equal to A 3¢§—1 2 . L: jg m 0L" B. §(3\/§—2) 2 - '3 ya, 2 \l14—x oi)! "=3 U~ oLLh '@§(3\/§—1) o I 310-“945‘ ‘x:2-——-¢u7'3 3 .._ Z \f/q' I -_: '1) ' J nu—n—u—d- ’3 12. Suppose that a force of 4 lbs is required to stretch a spring 2 ft beyond its natural length. How much work is required to stretch it from 2 ft to 3 ft beyond its natural length? prim ,4 42k: --—--\«:‘2_ A.9ft-1bs 3 2 "3, r. B. 4ft-lbs W“:- i ’1de 2 x 2 : 3‘"? 1:" c. 6ft-1bs 2“ 5 ft-lbs E. 2 ft—lbs MA 166 FINAL EXAM Spring 2000 Name:__.________ Page 6/10 13. Let R be the region bounded by the y axis and the graphs of f(:c)=‘/ —£;¥andg(:t)=—\/ —--‘g—2,for05m5\/§ Given that the area of R is fin, find the center of gravity of R. MA 166 FINAL EXAM Spring 2000 Name: m Page 7/10 15. Which of the following series converge? (I) :1(_1)n}n7121 (flnu. (CLU- 9Q‘“ be at) (H) :31 COS CL”)- “mlfl:t+0> A. (II) and (III) only am Sf: cm» a. (“1” t“) Z $353221) “=1 m 722%?” Jag-gr flan) only 16. Which of the following series converge absolutely? oo oar V! ,oko (I) Z (_1)fl_1_ vus. ( Z19“) il'EI” ) “:1 n’ h:| - Do °° cosn S ( WFJWJC’OMFWKLEt—l (H) 2 n2 : ‘31 r “‘2 W Q) (II) and (III) only 11:1 00 1 B. (III) only (III) E_:1(—1)”\/n3—+1 %< C. (I) and (11) only 1%}, _: 41—714 $1) D. (I) only (l H “eff l“ “l E. (I) and (III) only on w.“ J, ‘ aim... bowls. will)” "7’ W's/z] °° 3" 2 0° 3 n 17. The series 2 2(7n+1) "I". :7- : (‘5) 11:1 h:| '— H 1‘ r 1 1'. .3}— L + “3"” A. diverges —- 3:. 3. “1+3H3 1*" J ‘ 7 7 l- l”) I) ®=r34 7 7 1 -—-”-f,— 7'7 j47 D =% __ 3.. E =3- MA 166 FINAL EXAM Spring 2000 Name: —___— Page 8/10 . 0° 1 18. Th ' -— e SEI‘leS 7‘22 Inn + 3“ CC 1 A. converges by comparison with E 1—— n n 7322 DO 1 B. diverges by comparison with E E— ' Tl. 11:2 00 _ 1 @ converges by comparison With E 3—” n=2 GO . . 1 D. diverges by comparison With E 3—" n=2 E. diverges by the ratio test 00 n2 . . n . 19. The radlus of convergence of the power series 2;); 1: IS A. 6 fl: ' (52M. «1L l6 2x B. 1 ( 0?, Xn+l q. O :3 w+ . I M QM 4-» m :0 M (n+0! 1' In n-H ® 00 “Hm 1 X» “"900 H 1 20. Use the Taylor series of e—33 to approximate / 6‘33 da: with error less than 0.01. o The smallest number of terms of the series that are needed for this accuracy is x "L 'x" x4 €2l+X+-§j+-§?+1—r+'" A-2 1 3 1?. _-¥ 1- G 9 X fa Ax: [4. _x3+ 5....«_><__+—-——»~]°b O a 2. G 24 ©4 I '7 no *3 " D 5 2 7L —— 3‘: + 3-5—— ml’ “fl” l 4. 14 60 24-13 0 E6 MA 166 FINAL EXAM Spring 2000 Name: __.___— Page 9/ 10 21. r The parametric equations of a curve C are: :1:= 200st, y: 33int for 0 S t S; The curve C is A. a quarter of a circle B. an ellipse C. a half of an ellipse D. a half of a. circle 63) a quarter of an ellipse 22. The upper half (3; 2 0) of the circle (a: - 2)2 + y2 = 4 is described in polar coordinates by ‘2 '3 _ E x_,_4)( +4 +3 :4- ®r—4cosfl 03652 2 '2. _ 1r x 4.») 14.x B. 'r—QCOSB 0393—2- r-Z :- 4Wm59 C. r=20039 OSGSH D. r=4c086 0<6<1r Y” 74003.8 "- — E. r=cosl9 0565'” 2 4- 23. The area of the region in the first quadrant and inside the cardioid r = 1 + sin8 is W ’5 '2. A (BE-F2) (=+$m9)ci9 4 0 I, Egg“) i+23in9+5mal~l9 1 Bar — —— 2 . r. i; ©2(4 "Ll 2mm +l9~351h49N W o D. (1+1) 1 E. MA 166 FINAL EXAM Spring 2000 Name: Page 10/10 24. The length of the parametrized curve 25. In the Taylor series of f = i about a z 2, the coefficient of (a; _ 2)3 is ill) + £33; 5(4) + (‘32)? 4, jejwqfh‘ A_ _% i 2", 33 3 RUN-.— x‘j‘ 13- El i/(Y);—x"2 C. «1—0 iVO‘} 1‘ 2 9"; —1—16 Wm —éx"’ E. —116 FUN): —Q'2—q gmfig we - _1_ ...,i_ «W M ,_ "M /6 I r. '3» ', (tD ...
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Sol-166FE-S2000 - MA 166 FINAL EXAM Spring 2000 Page 1/10...

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