Sol-166FE-S2008

Sol-166FE-S2008 - MA 166 NAME Final Exam 01 Spring 2008...

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Unformatted text preview: MA 166 NAME Final Exam 01 Spring 2008 550LUTION$ 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 2. 3. 9“ complete test. Fill in the above items in print. Also write your name at the top of pages 2—14. 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. 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. . 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 1, write 3801). (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. After you have finished the exam, hand in your answer sheet @ your test booklet to your recitation instructor. 00 93” co (*Dn 2 1 GIZZH7I$I<OO Sln$=2m$n+1|$l<oo n=0 n=0 0° (—1)” 2 1 0° cosa: = :c n, < oo = :5", < 1 1;) (277,)! 1—15 7;) MA 166 Final Exam 01 Spring 2008 Name: ____— Page 2/14 1. Find a vector that has the direction opposite of 2i — 4j + 5k but has length LJ. 3.: 219—434—5? A. —%i+74_gj—%k W M I: desired. Vii:th 2 . 4 . 5 a —- " -— :3 5 la" “’“H” ’lTs r.“ C 2_¢51_4_¢5-+fik [Mt mam chm outlet“ <71“ ‘ «H ml m "— 1 "-2.4? 5'12 _&. 4fi._5¢5 UL_.__— 2 + , d _ 3G( L l l a _. D «H‘Wfij mk Umil‘ vecuvihmcum‘llo“ OHM)“ 71a: 2. 4. 5 fl, ~ ,mv ® 71+???“ -3: =,_L—(2'L-—4-J+b ) 35 52-" 4"" ‘31—? bzl-g’GC—L: z’gH—F’glfl’s 2 For what values of b are the vectors < —2, b, 1 > and < 3, b, —b > orthogonal? ’2’}: a . ‘b :0 A. b=1,3 < ’7? <3” b” > B. b=—3,2 132-1,..6 :0 D. 5:1,2 (ID -3) (b +2) = O _ E. =2,3 5:453 MA 166 Final Exam 01 Spring 2008 Name: Page 3/14 3. Find the area of the parallelogram with vertices A(1, 1), B(3, 4), C(7, 5) and D(5, 2). C(75) A. 11 B. 13 © 10 / 2) D 12 —————ax E 9 A D :4 L + 1 FT "" -p .l k :1 — 10 k ’5 O 1 0 :10 4. Find the area of the region bounded by y = :52 and y = 22: — :52. ll Poirot/2 of [VJOTSJZCIKOWI A_ X2 : Q-X—XZ “*WHMSMSM MA 166 Final Exam 01 Spring 2008 Name: ___—_ Page 4/14 5. Find the volume of the solid obtained by rotating the region bounded by y = x2 and y = 4:10 — :32 about the x—axis. Pomp? 0/2 {Jaw’lonl A. %w 4X "7‘2 : 7‘7. 4,}-sz;‘0 B. —3—7r (j "3((2—70 :0 —-a X:O, 2. C E” I (2/ 4) “1L . 3 Volume Ff § afpriknaoiin%WQ§Le/r D' 37r 32 AV:[n(4x.z‘)Q—1T(xl)—j 4»: ® 3” 2 0 X x 9. \f C 11 (16 x2— 2' 4905 >< — wad“ 0 4, Z X ,— 2“ fogexZ—grx )dx:Trl_16./ 8% o 6. It took 2700 J of work to stretch a spring from its natural length of 2m to a length of 5m. Find the spring’s force constant. 3 A. 150 , w: JkXdrx 800 B. — o 1.5 3 9700 = kl.) C. 400 2 O ‘ 1400 2700 = k 2.. D. T 2. 300 = is, e 600 2. kzfioo MA 166 Final Exam 01 Spring 2008 Name: Page 5/14 111:1: e 7. Evaluate 1 ~Zd(% 1 _ 63 $2 x “DIX L13 A -1 . .. 2 3 A»: LAX q) : f X ., a]; e 4 7“ e 'e B 3—36 ~__L.Ilmxl +§L~J~éb< 6“ (x 11 W X 6—2 1 Q @ e ._ __,_ 1 + #11,] 62—2 ’ «6 I: N 1 (2’ D e2 _. __ L __’ L _+. ’L s 3/ E 4—363 * Q. 2. —€ 63 3J- 2 37r/4 3 4- - __. 8. Evaluate / 00,8 6 d6. 2 W (0365,92 1/2 31116 E S‘ WWI-W” 2 / 3 1 We We»)de A Z _ 51112 MMWMMM LL; L I 9;]; “a B ~1—ln2—E / '31,- ’9 $3., 2 4 L 1 1 F2 2 G) — — —-1n2 ; Li a 4 2 ’1 u' E lln2——1— j, 2 4 U‘ L J, 3 _ 7,, fr, Ln 4 I “7;. I (0 —J§ ,_ .— g. “z: -" 2_ “ 2 t ~13 MA 166 Final Exam 01 Spring 2008 Name: __—_— Page 6/14 5 dt 9. A trigonometric substitution can be used to convert the definite integral / ———t2 4t 13 2 V — + into Which of the following definite integrals? Z 7r/4 tah4t+13 :‘t—4—‘C-P4 +9 /0 secede 7r/4 B. / cos0 d0 0 7r/3 C. / sin0 d0 ,, .. 0 - "' ';-”<‘9<HI . 7r/3 f Qfigtanfij 12' D. / cosOdO (LI '1 3 SLC 9 0 13,2 2 'z___ 2C9 7r/3 «M7 +1" -35 E. / se06d6 _ o 0 __....9 '4 62% 1‘; ‘2. BELQCG d9:j4 aacQaLB 352d} 0 2 813—4 Compute/O m (1113. x2,az-3 :(x-3) (x+’l.) A. —81n3 B. —5ln3 ‘8‘X '4‘ : A .4, __B,... @493“) 1-3 «+1 C. —3ln3 er s A>HA+BWBB @ -2ln3 A-l'Bzg J4B:IQ_ E' _ln3 A'-BB='4' B33 ) A:g ‘2 2. 92’" a g b’ 3 A ‘4' .— 7 Jo ’x‘Emr-Ja " «3 + 374:1) MA 166 Final Exam ()1 Spring 2008 Name: Page 7/14 00 TL 1 11. Find whether the series 23 (—5) converges or diverges, and find its sum if it converges. “:1 co 00" V _ _ Z 3 <_l)h_ 3(‘1 A. Diverges. - '2 ’ 1 -v "'1 7. W’J’“ ' ' i B Converges and sum 2 0 p ._ " (c, SCHQS wiU, “3-1— G. Converges and sum 2 2 cow b 2 1 . 4mm: l-JH a’ T: 3 ~11) 11 ’9 ® Converges and sum=—1 ' E. Converges and sum 2 —3 L“ 3 5% “3:” 2. :: -—l 12. Which of these improper integrals converge? 3 1 I. A x_2 dx. 3 II. 1 dx. 0 3 - (I: III 00 1 d . 3 E x. (L 3 A 34.,d'xzf ,J._olw ‘l'f'jfz— V A. All IO 1’2 0 x-vl 2 2 L JtJ’d'x B. Only (I) ‘ ‘— n l; W2 A?“ If} 0 x;2 ’ @ Only (11) :Lm_ [Mlxvzlk—‘EKGET [Wt’zl'mjn Only (111) ’5‘” 3 «co-90““ E. (I) and (11) t '3 t .. Gr) 8 ‘/L——— cl): : Um _j .1..— d9; chm L_2\(3_X] o 3-4 t—>3 0 ‘63 {43‘ _ 0 {- ~Qim Ezra: HE ’2 3 “1“”‘3- III 00‘0U' 00 t . (m) I YEA-"f : lain l3 $01? 1 3 x t—t t , r -; w , ._ 1; —2- 3 . :b'm a Ilv dlv‘ MA 166 Final Exam 01 Spring 2008 Name: _—__ Page 8/14 13. The curve y = :52 + 1, O S :r g 27 is rotated about the w—axis. The area of the surface is given by 6 .3 41$ /0227r(:c2+1)\/1+—4x2dx ASL‘W d)! B. /0227r:r\/1+4ac2_d:r ZWAV C. /27r(:v2+1)2d:c i g : J 21‘- (7‘3+1)W d7! D. /02 27rsc(:c2+1) dcc O 2 E. f (11:2 +1) dm 0 14. Consider the lamina bounded by the graph of y = fl, the :r—axis and the line :L‘ = 4, with density p = 1. The w—coordinate if of the center of mass of the lamina is “5 A. MA 166 Final Exam 01 Spring 2008 Name: ___—__ Page 9/14 71! 15. Let (1: lim 716’" and b: lim —. Then n—wo 71—400 (271)! r I” azbm 33;:0A. a=1andb=§ e 00 e 10—)“ Xv“: X” B. a = 0 and b 2% ’— I C. a=1andb=0 bdrm 1’:— :L’m 1'2"” . h—aao Yl-Qoo l'2-r~'5161+\)"'&"9 “Zoandbzo . i E. a=e_1andb=0 :‘LIW‘ :0 W-POO (n+0) (“+19"'(2‘°) tan‘1 1+n2 71. IS 16. The series Z(—1)" 11:0 ® absolutely convergent B. conditionally convergent tan‘1 n u u n — n C. d1vergent s1nce 711320 ( l) l + n2 76 0 D d' t tho h 1‘ ( untan‘l " — 0 . 1vergen even ug 1 +n2 _ E. divergent by the ratio test ? 00 n t .3 . m 2—- .—I 'P T E ‘C-l) um “ 1': Z l a“ 2’ oonv. . n:0 cups, cow. . I {L‘l’hm "5 1+“ E. .1; Va: 00me Wru' wNuL (A com). “3" 7h” (11—min P=2>1) “unfit? I: GM 2 I i 2; VLOY ALLn2/ MA 166 Final Exam 01 Spring 2008 Name: _——_ Page 10/14 17. Which of the following series converge? Q) 00 _,.L_. _. ' :2) HEX—25 = Z,” n»: 621* P W“ P 2 1 n=2 " 00 n n h_hlh..v- IV) “DEL. JLT: W 31 rum” ne'- n- n. I n .~»r ' n=l ‘. -. oLw, hymns! oo _1 n (IV) 7;; :llmnffina SQm‘U) Tail; 5" n 1 '31.? I A (III) only \o,‘ aucwwwg B (III) and (IV) only gm \of, __._ o , C. All ":‘m m, (D) (I), (111) and (IV) only ‘ ‘ "— E (II), (III) and (IV) only 18. Use a Maclaurin series and the Estimation Theorem for alternating series to approxi— mate sin using the fewest number of terms necessary so that the error is less than 0.001. 3 X 5- 1 smx : X o + A, _2_ i 1 2 me) = a — fi- +m§o -~- 4—: <. .L— 3 .L—J— : 2471 1000 C_ 1 2 48 48 D E F 2—23— 40 f 48 E. E MA 166 Final Exam 01 Spring 2008 Name: —_ Page 11/14 00 277. 19. Consider the power series E ——:c". The radius of convergence R and the interval of n 71:1 convergence of this series are H 1 1 0L “H “ n A. R = —— — Y) 1", _ .: 9' x n y 27 2 an (h +1) (2)" X R: 1 a“ Z 7 [—121) Wham 2 Eco " ("9” m f X: -—--%' ’ .—2——- ——; ': Z (a. Ooh‘V 07:; n I7;I " b3 mam. W W n 04 WW fXZJi ‘ Z __2_ J7 :. Z J— (in). Prwgcb Pg, h:) H 2 hm n “ 'L IVJQY’Ud 0‘! wvmm‘fim‘k L"%.’ '2'.) 20. The interval of convergence for the series 2 (cc — 1)" 1s n=1 n+1 _,V”" 1a.m.(: _L°_m..9£—-I3- . (0,2) a“ (“+0 . 10 (yd) [012) __ J..— .— -—-> ,m (9’11) " 1‘0 n+1 V II a as" [9,11) A B C D. sun's: w Pun 014 'x. ® (—oomo) MA 166 Final Exam 01 Spring 2008 Name: Page 12/14 21. In the Taylor series expansion for f : about a = 1, the coefficient of (23—1)10 is 7:0 W) *' ' 1. : -1 £00 mo n? (x ) A. —2 €09: .x’1 _1 X’2 C 0 I) ,2 _(x l)- _. "2' (x 1. [X ) 2 -—-(x 2) 8%):4 D 1 0"2) E 2 £1?) 4; (2) (’0 “ 25"2) €(1):—2 «900 :—2-3(x-2)' §(3>(.I)=_2.3=_'3 gm; _,i61 10! ' :03 ° 4 cos(:v2)—1+:—E— 22. Evaluate lim 8 2 . z—>0 q; 4. 6 7' 7% 7‘ 1 _ —x M "fi _ @51—1’? 61+ A-2 4 g :2 1 m 9‘ =- __2L_ lakaL .. B. — 5% ) 1 2g + 4! c! + 8 1 4‘ C. — 2 2L 6 Am COS (X)—_3'M_:_ 2- i X—m 78 + 1 120 ' 1 ail-4+5; ” ' ‘11: an” 24 3 . >< -90 W 53 7‘12 Hum 327'?“ __—-.—.._1__:1 " 7—:0 X8 4.“ 24 MA 166 Final Exam 01 Spring 2008 Name: _ Page 13/14 23. Find the slope of the tangent line to the curve described by a: = In t, y : 1 + t2 at t = 1. wow -: gilé'——J2t =2t?’ A' 0 CL)‘ .41 é... B. 3 A}: t- C —l Wham 1".“1. : 1%: 2 2 ch E 1 i 3 24. A point P has Cartesian coordinates (x, y) = (3, —3\/§). Which of the following gives polar coordinates of P? MA 166 Final Exam 01 Spring 2008 Name: ____—_ Page 14/14 25. Identify the curve r2 = rtan(0) sec(0) by finding the Cartesian equation for it. 7‘ 1. vwsg ?:Y$;he A. elhpse B. line v2: v ram 9 Sec 9 C. circle V2 : ‘N S'mg 1 ® parabola CD 3 B 005 9 E. hyperbola (T cos 6)‘: \ran 9 '2. “X :‘k P Makolpu ...
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This note was uploaded on 09/14/2011 for the course MATH 166 taught by Professor Staff during the Spring '10 term at Purdue.

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Sol-166FE-S2008 - MA 166 NAME Final Exam 01 Spring 2008...

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