Sol-166FE-S2009 - MA 166 Final Exam 01 Spring 2009 NAME...

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Unformatted text preview: MA 166 Final Exam 01 Spring 2009 NAME Centureoufi; 10—DIGIT PUID REC. INSTR. REC. TIME LECTURER INSTRUCTIONS: 1. There are 14 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 2,14. 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 testvbooklet. 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. . 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: p (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 NUMBER, put 0 in the first column and then enter the 3—digit section number. For example, for section 016 write 0016. Fill in the little circles. (c) On the bottom, under TEST/ QUIZ NUMBER, write 01 and fill in the little circles. (d) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your 10~digit PUID, and fill in the little circles. (e) 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. 0'! e :ifi |:1:[<oo sinavzio:(;1):~zl:2n+1 I1E|<oo n!’ (2n+1)! ’ “:0 n: coszr : ”220 (2n)! 302”, ILBI < 00 = 2113", [ml < 1 MA 166 Final Exam 01 Spring 2009 Name: Page 2/14 1. Let P(3, 2, 4) and Q(5, ~4, 7) be points in R3. Find a vector that has direction opposite ——). of PQ and has length 2. "7% A. (—2,6,—3) PQ 22 <27623> B <32 9 _§ m2; @2222; 2 22 :7 25 535 W2 0. —,-1,— UVWFC VECXX‘Y‘ \n AHA/Q Apflwimw 0/ PC} <6 6) 2 1 ”ii: 6Z: :1? mgj (v: : “Wolf 59013:), W», C622 Ahflfl’fiiww Celt‘N?” Ml i f 2:2 \ W i; < g I m” Q/ ”/3 1:32 2 2‘ 2-323 223 2:123 2 23¢: 2; @323 23 -~ 2. For What values of b are the vectors 2+ 35+ bl; and (372’— bj—i- 2b]? orthogonal? (‘2 3 2522 .22; 22 A' 522 “f H 2%: 722533) 0 B.b=1,2 2:) 323922225; 0 G. 5:20 2(Q“mh);g) 2,2 2452217330 .b:1,0 E.b=1 bro/9L MA 166 Final Exam 01 3. If [i 2 <1, 2, ~1) and I7: <2,1,—1), find the vector projection of 1—; onto (1', projg “’5'? 1,, 33.1932 Spring 2009 Name: w; W”! 7’ ”M Pméaflvb 2:: (1va (a my WflMWW/a WNW r17,» W W1 gag +Q+1 $53“ 131 =1: TQM w {g g“; b “:3 mat-time , W ‘3 , ED‘NQQE?‘ (g3 C14 m:<l/27W£> E“ mm; C. D. E. 1 —21—1 6<77> 1 —12—1 6<’,> 1 —12—1 3<71> 4. The area of the parallelogram determined by the vectors 35+ J and 5+ 2]; is We; m, a 1 Fa ' e” t “if "’ “f? v “”5 Leif a: “is? “313 L ”t 3 {Mai 12> ‘: Q + (2 1:2,, ‘77 3, i: “:2 "*2; o 0 i 2» A. B. C. CED E. «H x/Zfi WEB WE J56 Page 3/14 (3. MA 166 Final Exam 01 Spring 2009 Name: Page 4/ 14 5. Find the area of the region bounded by y 2 $2 and y : 4:0 — 3:2. $3sz533 {3;} \AAE>4C53L3 {333%3‘x'w33'333133wg3 TQCzfii/‘Icgéfi ‘um (AA? E42}, 3:2} 933% 1.313% 3') 3:2 :2 “s M / 3:: (:2ng53 i “mgmgéfigéa 3,3 0 is 3 6. The base of a 3—dimensional solid is in the ivy—plane and is bounded by the circle 11:2 + 3/2 :2 2. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid; 3 3 W333? 3x33, K/er bra/3313;; C3305; Q ‘” 3’ (3 3‘33ng 333“ “’31? K: 30 3:33:32 AR {Wm @P’er‘w 2133133033m613mw S, 3)3f<3' ”~37 33 V ¢r (‘3 ‘ 3Q! n ma 3: L223 33 ‘3 3 733122 3 5 3 33 MA 166 Final Exam 01 Spring 2009 Name: Page 5/14 '7. Let R be the region bounded by the curves y : (ac — 2)2, 1 g x g 2; y = 0 and :1: = 1. Using the method of cylindrical shells, the volume of the solid generated by rotating R about the line a: = 3 is given by A. /01 27m — 3)($ — 2)2 dz: B. /0127r(a;— 2)2 d2: 0. f: 2742 — my — 2)2 d2: D. /12Z7r11:(m — 2)2 d1: WWW tééa L1? {mi at in tin; @/ W ‘ W ‘ ”2 d5” A V '33? gm (itiDC‘ttgfm/t 9 Mr V»? fi'fi’t3 232(th ‘Z‘ngtfl’i t \g‘r {it 26 8. Evaluate / lnacdm C Twitt‘tmiie‘m h bub Fflfiji;3 A' Zine ‘13 it B. 1 jmgxpi #Qm flwiy ”LAW-‘3 t W “’3" M iii: it 2" ) j 3 U, :: i2“??? Ci 1». tiit (tilt. :i'iwtim; m T31 MA 166 Final Exam 01 Spring 2009 Name: Page 6/14 9. Evaluate /2 \/2$1 — x2d \{Mm Va w M 'x a 5 M a we: '2 M” 63 2 10 Evaluate/0 m d3? 1) ~ 15 ‘ , I A. 2 1n 3 €51,255 5 U? fw’c‘a J MT“ A A 3’ B. 2(ln 19 — 1n 3) 2, m 1;: 7 fl Wm a“ \ C. 5 1n 3 — 2 1n 5 Tim: ('[ér+l’)fl(’“m~?i} ffi “H ® 2111 3 — 1n 5 E. In 3 — 1n 5 MA 166 Final Exam 01 Spring 2009 Name: Page 7/14 11. The length of the curve a: : g (y _ 1)3/2 from (0,1) to (ES—7 5) is 5 MW,” 2 16 2/3 L, "r: ] W1+<§3§ 0% 5 (—3-) — 1 ’ (Mi 4 3/2 “WM WM B. 3 5 W WE}; \{jl “Wig O AA? C :3; 53/2 “ 4 W 35 V1; Film D g (53/2 _ 1) i G g , (7 f“ a 3/2 — .W 5;; inf/”e? m a, rev/g1? 3 (5 1) 3 <' M 3 12. Consider the lamina bounded by the graph of y = fl, 0 g a: g 1; the m—axis, and the line a: = 1, and with density p = 1. The m—coordinate E of the center of mass of the lamina is 3 A. ZE-zg 3 B. 52% 1 C. 352—2— 4 D. E2? 5 MA 166 Final Exam 01 Spring 2009 Name: 13. Which of these improper integrals converge? 1 1 L/ ——d:c 0 fl Page 8/14 A. Only I B. Only II C. Only HI @ I and III E. II and III E. Does not exist MA 166 Final Exam 01 Spring 2009 Name: Page 9/14 4 42 43 44 45 52 53 54 + +... | | 55—56 1 A. I and H only 11. Z __ ‘, M n n {a} Hand III only C. II, III and IV only °° 1 II. I ”:1 e” + 1 D. III and IV only 00 E. IV only IV- E (—1)”\/fi ”:1 , . 3; K i“ 5 1 R a K, d- ‘ (Rn-H 1 W ({Y} “gig? .f .K «7.3%» .K ‘:,, 7 K,» KKK/179:9 6’6 a], 'Ylm; 9p} ‘n. (i1 V” p 5 Q“ l fl r f , Z," in W 5: W351 3 ' 7,4 , -K g”) ‘ | 5 . \afl Y‘f'" I V’ ’ x a! < MM"; WK 3 E» , if“ 1 . «Mm (5L, 2/} CI“) ‘2} :l‘ g) 7 ,5’. r: ’32-; g?” ‘6. all/k Sf’ MA 166 Final Exam 01 Spring 2009 Name: Page 10/14 00 5 17. Find the interval of convergence of the power series 2 6—2 (2: fl 3)" n l i <9 [2, 4] ‘3“ W B. [2, 4) w sir/:1 C, (3 — e, 3 + e) a D. [3 — e, 3 + e] t i E. (—Oo,oo) 18. Use a Maclaurin series and the Estimation Theorem for alternating series to approx— imate 6—1 using the fewest number of terms necessary so that the error is less than 0.01. exziirmmrgavig t£3r%;l A. e’lmé emirimiefiwéegfimfips B. we? gmw Tgozfl 03 (ED e“1 mg %Ea%c::{m D61”; W 17333:?er 3&3; E e'ls—i— MA 166 Final Exam 01 Spring 2009 Name: Page 11/14 19 Find the coefficient of 229111 the Maclaurin series for f(m )2 W 1 12:11.11» 5”” 21% A. 11? v1 . 1. ' 1 Q T be; 013512;!111 1,2 111-1113 15271 1% W 11 '1 1m (1+1) 1 11111 1‘11»: 2111211 1111111 $112! E3851) '1: Q~3CI+>0 if; :WO) «#2 3 '1' W3 3 53(1):?“ :2 ‘31 401.2133 133(3)“): “’12 134’ 11,, A? $211111} 1: 2-31412§(1X}€ PM?) 2 3 4‘1” @513} Q: 111 / . 1 - w» 1 1 1:111 [1 71, E1 W m 1,311 m; x W ,1, 1 v? :32: _%Q > E21 312 9*, ‘ \ 1 ‘ g; :x’ W11, 8 1 x (1 +1?) 11 ‘11? 11.1 )1 :1) 1711:1121 j S: % 11Xg 11:1 1 f 1 11 A. (/1 ég : 11:131. 18 1 $111,, 1 .121 1, 11 ~— 1111 11. 11 >< 11 B. C D {11} a 11» 1,132”; 1:“ 1151 $21 “I 1:51P? MA 166 Final Exam 01 Spring 2009 4 . 2 £17 xsmx — x + —— 21. Evaluate hm —“———2‘—§'z m—>O _ 1 + 1—1;w — a:— cosa: 2 24 3 xi: Jr, 7 a- : Name: Page 12/14 22. Find an equation of the tangent line to the parametric curve a: = t5 + 1, y = t3 -— 2t at the point corresponding to t : 1. 2:5) x—5y—720 B.w+y—3:0 C. w+5y+3=0 D.x—y+3=0 E. 5m—y—1120 MA 166 Final Exam 01 Spring 2009 Name: Page 13/14 5 23. The point P has polar coordinates (2, ? coordinates of P? I. (2,—g) II. (ma—g) III. (2,—167i) IV. (—17%) ). Which of the following are also polar A. I and II only (E) II and III only C II and IV only D. I and III only E. III and IV only 24. The graph of the polar equation 7" : —4 sin6 is a circle. The Cartesian coordinates of the center of the circle are A. (—2, 0) v :IZW‘ 4 ‘2»! l“? 6:? B (270) (“2* t v formulae ©(0,—2) *2, 91’ D. 0, 1 W E (0, —1) x 2; + .j‘2k? 2% L? ”i? 5% if” {E Xe. t (/16 if 2f ‘ 9 C,{,m)’i\€ii¢ ( {3%, ””323 to; i MA 166 Final Exam 01 Spring 2009 Name: Page 14/14 1 — J— i 25. The polar form of the complex number 1 fig . with argument between 0 and 27r is + W Z F0 OL/‘F ZmVW 9% p, «3w» E :1: ' ' Z I f”? 1. 15; , A. cos 3 +zsm 3 xi B. \/§(COS—73:+isin %) fiaflg 7' ,, ’ C 1(COS 37T+'s‘ 37f : . 2 4 2 1n 4 H {Lm D cos 57r—}—'sin 57F . —~ z —— 6 6 2» : , “i , ‘ 57r . . ‘57r QIOW‘ 9:413?in 6),! ,1: «k «1": ‘ ® COS ? +zsm E— 2. ’ ‘ ‘(“ ,2“ 10m (7) f a {a we w 6 V ‘ ’ m,“ ‘1 +~ ‘ “n; E 0‘“ :1 (’1 E" W" vmwzw/mmwwmww/LW ...
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