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166FE-S2007 - MA 166 FINAL EXAM Spring 2007 Page 1/11 NAME...

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Unformatted text preview: MA 166 FINAL EXAM Spring 2007 Page 1/11 NAME 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. N0 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 2007 Name: __— Page 2/11 1. For What value of c is the vector 2I~ ;+ Cl; perpendicular to the vector cI+ ;+ 1—5? 2 Ag B. —1 C. —2 D. WIH O'lll—l E. 2. Which of the following statements are true for any three—dimensional vectors 5i and Ii? (1) (ma-5:0 (I) and (IV) only (I), (III) and (IV) only (II) and (III) only (III) and (IV) only All (III) 16-11 3 Ian?) A. B. (IV) a x (35) = 6 C' D. E. 3. Find the value of k for which the graph of x2 + 3/2 + 22 — 4g + 62 = k is a sphere of radius 7. 30 16 36 25 54 ECO??? % 4.] :ccosmdx: 0 l |—\ DOW? Pi N|=l w|>1 H ml: :1 +_| MA 166 FINAL EXAM Spring 2007 Name: ——__ Page 3/11 7%: 5./ sinzxcos3xdm= 0 1 A. —— 15 1 B. — 3 2 C. E . 0 1 E. —— 5 6 % 4 d . tanxsec a: 1:: f0 4\/§ A. — 5 B. Q 5 3 C. — 4 D. 1 5 511' D. — 4 ,(i) Choose a trigonometric substitution to simplify the 7. For the inte ral f— g rim/11$— $2 integral and (ii) give the resulting integral. A. (i)$=2sec6, (ii) /21d0 sec 6d . (i):c=2tan6, (ii)/ 2 an6d6 . (i):c=2sin6, (ii)/1 2sin6d D 0 —2s' a (")f #619 ' 1 x— in ’ n 4sin6cos6 1 E. ' =2 6 H —- d (1)2: cos ,(11) / cos 0 6 MA 166 FINAL EXAM Spring 2007 Name: —— Page 4/11 2 5 8. f :+ da: is of the form (Where a, b, c are constants): :1: +117 A. a,ln(m2 + 1) + blnlml + C B. aln|x|+bln|x+1|+cln|m—1|+C C. atan—lx + bln |x| + C D. alnlw3+$|+C E. aln |x|+bln(a¢2+1)+gctan_1x+0 9. The region in the first quadrant bounded by the graph of y = 1 + $2, the line y = 5, and the y~axis is rotated about the y—axis to form a solid. The volume of that solid is given by 2 A. / 27r[52 _. (1 — x2)2]d:c 0 2 B. / 27rx(1 + x2)d:z: 0 5 c. / M5352 — (1 + $2)2]da: 1 2 D. / 27r:r(4 — $2)d$ 0 5 E. / 7r(1+:c2)2dx 1 MA 166 FINAL EXAM Spring 2007 Name: ——_, Page 5/11 10. A solid sphere of radius 1 is divided into two parts by a plane perpendicular to a diameter, mid—way between the center and a tip of the diameter. Find the volume of the smaller part. A. in" B. 312% C. 3% D. %7r E. in 11. Consider the lamina bounded by the graph of y : $2, the x-axis, and the line a: = 3, and with density p : 1. The sis—coordinate 11‘: of the center of mass of the lamina is ?> .0 . wlfl ooloo N wloo .hlco MA 166 FINAL EXAM Spring 2007 Name: Page 6/11 12. A tank is 10, ft. high and lled with water weighing 62.5 lbs/ft3. The cross—sectional area of the tank at 3/ ft. above its bottom is A(y). The work required to pump all the water to the top of the tank is 13. Which of these improper integrals converge? (I)/Ooocosxdx (11) /0°° 5r 1+ac2 d2: (III) I 1 —d:1: :1: 10 A. 62.5 /0 (10—y)A(y)dy 10 B. 62.5 A 7r[A(y)]2(10—y)dy 10 o. 62.5 / (10—y)[10~A(y)]dy 0 10 D. 62.5 0 (10—y){102—[A(y)]2}dy 10 E. 62.5 (10—y)2A(y)dy 0 Only (I) Only (II) Only (III) All of them acorn? None of them MA 166 FINAL EXAM Spring 2007 Name: — Page 7/11 00 14. Suppose that 2 an 2 5 and 3n = a1 + a2 + - - - + an. Which one of these statements 'n.=1 is true? A. lim an 2 5 and lim 3” = 0 Tia—’00 77,—)00 B. lim an 2 0 and lim 3” = 0 n—->oo n—>oo C. lim an 2 5 and lim 3n = 5 71—)00 71,—}00 D. lim an 2 0 and firm 3n = 5 Til-+00 n—>oo E. lim 5,, = 5 but lim an cannot Til—+00 ”—900 be determined 15. Which of these series converge? 00 1 A. None (I) 7; 71+ 5’ B. Only (II) (II) °° n 7 C. (II) and (III) n21 (1-01)" D. Only (111) 2 E. A11 MA 166 FINAL EXAM Spring 2007 Name: 16. Which of these series converge absolutely? (I) Z(—1)"(—j§) , (II) Zena—137:, 00 a: 17.F'dthe't lofc fth ' —— In in erva onvergence o e power series 712:1 (n + 1)2" 18. The radius of convergence of the power series E mgr” is n21 Page 8/11 A. Only (I) B. All C. (I) and (II) D. (II) and (III) E. (I) and (III) A. [—2,2) B. (—oo,oo) C. (—2,.2) 13- (riél E- [—%,%) A. 00 B. 1 C. 2 D. e E. 0 MA 166 FINAL EXAM Spring 2007 Name: 19. Match the functions with their Maclaurin series. (1) 6”” (2) 1 7r2 20.1—5(~) + 1 00 (a) 21:", —1<:v<1 n20 Page 9/11 (e) 1—$2+m4—x6+..., —1<.$<1 E> scam.» muow 1a,2b,3d,4c,5e 1b,2a,3d,4c,5e 1b,2e,3c,4d,5a 1b,2c,3a,4e,5d 1a,2e,3d,4c,5b 21. In the Taylor series of f (m) = — centered at a = 17 the coefficient of (a: — 1)3 is :v A. 1 3 1 i 3 1 EDGE?“ —1 MA 166 FINAL EXAM Spring 2007 Name: ___ Page 11/11 24. A point P has Cartesian coordinates (:13, y) = (3, x/g). Polar coordinates (7", 6) for P. are A. («1%) B. (flag C. (Wig) D. (Ni—g E. (2%,9 1+47§ . ,1s 3—1—22 25. The complex conjugate of the number ...
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