Sol-166FE-S1999

Sol-166FE-S1999 - MA 166 FINAL EXAM Spring 1999 Page 1/10...

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Unformatted text preview: MA 166 FINAL EXAM Spring 1999 Page 1/10 NAME MEL“ STUDENT ID # RECITATION INSTRUCTOR RECITATION TIME LECTURER 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 w your test booklet to your recitation instructor. MA 166 FINAL EXAM Spring 1999 Name: Page 2/10 1. Find the value of c so that the vectors ('1‘ = 25+ (:3. — I; and 5 = :— 3f+ 2]; are perpendicular. (1,. b : O 6:; [2,—0.5 (“‘110 B.c=—1 C. c=1 C : O /D. c=0 E. novalue ofc —o '+3+l€0nto¢'i=2§—IE. 2. Calculate the length of the projection of I; E” H min—l wIH slh. sip. U! 0:: -' (LL: 2—4, I \v' in t: ' ____.___. , "- n 5' u Hal/ G V? p} .0 {33.5 3. Find lim z—>0 a: — sinw' MA 166 FINAL EXAM Spring 1999 Name: ____. .___ Page 3/10 _L 4. Find $11,120 (mm : L'm e x “(e/">0. A. 0 Ya” B. 00 __I_ J L‘m Z, @m My X : O C. e V’MN Y X”°O 51- D. e“1 O ‘/E. 1 Qjm (0/07)}4. : ‘6 :/ x—nm I . "2L (L n. 5. / sinzaccos3mdm= j V\ (I HA) 0L“ o 0 /A. izg (A: Sinx 41M: kmde 1 xweu'zz: O B. Z ngeur /. 2 0.; » ,‘L , .1: ' 3 5 ,/ D- '26 3 5 0 1 _ E _ ' 5 (I ’2, 2 a, 6. ll $1n$d12= QMX/"g ago” A. 21n2—1 » \ M'zé-II‘Y d‘szdV 13' £0112? ’ 'L» C. 2ln2 _ I a}? X 01/“ rid“ A. l VD. 21n2—% i 0M 2 [Xx E. l—lnx “. z 4 1 MA 166 FINAL EXAM Spring 1999 Name: __._— Page 4/10 TI" «5 .31 1 4 W2 7.] —-———1—§d:1;= f —--§-' $KR<LM :b wrueL-r o (1+:c2)2 0 Sec“ 0 ,. W, A. 1 iv {mwu’ 2 K x x:towM Hx‘ zucm 0 7r q _, Q B. -3— 1 Ciwificcudxxt ’ '2, 7r XTO —o u>0 0‘ E '3 x ’6 MU ’3 D. 3 3 /E. E 2 8. Express fizffi as a sum of partial fractions. A B C ‘ A':1:2+1+:I:—2+a:+2 A B 13‘ x2+1+x2—4 A B C D C. x+1+m2+1+m—2+x+2 Az+B B D. x2+1 +x2—4 / Ax+B C D E' $2+1 +x—2+x+2 9. Determine whether the improper integral 0° 2 fwe‘xda: o converges. If it does, find its value. b .y1 A. 0 2-: ‘m ( Xe dV 1’3 l 0 2 knew (L 19 C. 1 :2 .m fil‘a-X D. 2 b A“, 7" O E. diverges MA 166 FINAL EXAM Spring 1999 Name: ______ Page 5/10 10. Let R be the region in the first quadrant bounded by the graphs of a: + y = 2, y = 2:2 and the y~axis. Find the volume of the solid generated by revolving R about the axis. ‘ . i 571' 73— 4771' F 431r F 57r D. E 57r E.— ‘ 3 11. Find the length of the curve y = :61: — 1)% for 1 _<_ a; g 4. 9' “ y 'L L : f 1 +1!» 0"] 0W 1 1r '2. , J W M ‘L 73 X l . . .0 5:5? \I V" 00‘ i C H w: m c 12. If (:2, 37) is the center of gravity of the region bounded by the graph of y = (13% and y = 1:2, then ,V HI V /\ ‘2! til ‘21 HI :2: ‘2' A II o 0 HI II c: MA 166 FINAL EXAM Spring 1999 Name: M Page 6/10 13. A tank has the shape of a surface generated by revolving the curve y = x3, 0 S a: S 1 about the y-axis. The tank is full of water. Set up an integral (in y) for the work W required to pump all the water to a level 6 feet above thetop of the tank. (Water weighs 62.5 lbs/R3). 1 3. A. (62.5)1r/0 (7 — y)y3dy A w,(7—~3Xca5)w 13%? L 2/ 2-. (61.7%](7' 9) 9 “7 0 V l 1 B. (62.5)1r /0 (7—y)y2dy ' 1 C. (62.5)7r/0 (6—y)y§dy 1 . ‘/ D. 62.5 [5— 3d X;Lgl ( )1r0( m y 7 E. (69.5)1rf1 (1—y)ydy 14. The fourth Taylor polynomial of f (3:) = eZ2 about 0 is 4 |/B.1+::;2+x— 2! 2:2 2:4 C 1+-2—'+Z!— x3 4 D 1+$+§T+E 4 a: E. 1+1!— _1" 15. Find lim (W+ n—ioo n+1 /A. 1 B. 2 C. —l D. 0 E. does not exist MA 166 FINAL EXAM Spring 1999 Name: 16. Of the two series 00 . n+1 .. 1 —, 11 () §vn5+3n—1 n_1n% \oo’Uv (Ar-V 0" $50“ \I -:£—— .J/g/ wnv. w " ’ (PM? P=3>I) \ 17. Which of the following series converge? . °° 1 .. °° 1n_n °° (—1)" (1) “2:237, (11) “22:2 71,011) "21 r—n+1 Ll) Wm. w. T’;/J§ mnv (u) oomf, MIan 5‘; 'i‘vgllj‘S/Y Q1" >, ‘5 914’" "as. Page 7/10 A. both diverge B. converges, (ii) diverges C. (i) diverges, (ii) converges l/D. both converge/ E. converges conditionally and (ii) diverges A. Only (i) B. Only (i) and (ii) C. Only (ii) and (iii) ‘/D. Only (i) and (iii) (1.”) can“, W. 7' .L E. allthree 00 $27; 18. The radius of convergence of the power series 2— is 411 raunmt. test 37 11:1 LVHL 4 / X A. 2 Va -* "’ '1. C. 00 b. 1 Z _, X : W —- X — 37 D. 1 ln—«a' 4 a; E. 0 umv (} AV. 4; or -2< x<‘2. 4 MA 166 FINAL EXAM Spring 1999 Name: a Page 8/10 19. The interval of convergence of the power series 2 i— is ’n=2 lnn , L. X“ QM” /_ A. (—1,1) M “a —— n—m (Iv-(w) - X” VB. [—1,1) C. (—1 1] - X é ’ 1 — Ix) .t x1¢ I '< . ’ ‘ ‘ D. [—1,1] x» ; y o/iv (we MT!» Ii) E. (e,e) ‘ ~ ":1 Ln" X74 (49‘ W«(oar.w.w* in“), My, ,ls‘x Al. or [451) \ 20. Match the functions with their Taylor series about a = 0. 3 5 (1) e-1 (a) x—%+%—...,—oo<x<oo 1 °° (—1)”:c" (2) 1_x (b) "g; n! ,—oo<a:<oo (3) 14152 (c) 1—x2+w4—:1:6+...,—1<:v<1 23 3 5 5 (4) sin2x (d) 2x——3-”—f—+2—5f——...,—oo<x<oo (5) xcosa: (e) 1+x+w2+$3+l..,—l<x<1 A. la,2e,3c,4b,5d B. 1c,2a,3d,4b,5e {L ‘b V 2 C C. 1b,2_c,3e,4d,5a / g D. 1e,2b,3e,4c,5a (5 C a 1b,2e,3c,4d,5a 'MA 166 FINAL EXAM Spring 1999 Name: ___—_._— Page 9/10 21. The parametric equations of a curve C are: cc=t, y=—\/4-t2; —2§t§2 The curve C is . a half circle 2" .‘ xzwb =4 “3'0 . a circle B C. an ellipse D. a straight line E . a quarter circle 22. The length L of the curve C in problem 21 is given by 23. A point P has cartesian coordinates (Vi—1). Which of the following are polar coordinates of P? / (i) (—2, g) (—2. i671) (fin/(2, 1) (iv) (2,1151) \ A? (ii) and (iii) only B. (i), (ii), and (iv) only V C. (ii), (iii) and (iv) only D. (iii) and (iv) only E. all of them MA 166 FINAL EXAM Spring 1999 Name: m Page 10/10 24. In rectangular coordinates, the center of the circle with polar equation 7‘ = 4sin0 is 2 A. m) B. (—2,0) C. (4,0) VD. (0,2) E. (0,—2) 25. The area of the region inside the cardioid r = 1 + sing is qn' \/A 37f n. ' ? ’41 jév‘w Wee B.31r 0 /I% C fl_1 217' a q 2 3;] O+7sin9+fm “)4/9 3_" 1 2 D x in” 31r—1 ': .L 9 4,2039 +é8 '— iyh’ZGj Z (9 :élzn-fiz +7T' +2]:{ ...
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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-S1999 - MA 166 FINAL EXAM Spring 1999 Page 1/10...

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