Sol-161FE-S2002 - MA 161 & 161E §©LUTIOM FINAL EXAM...

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Unformatted text preview: MA 161 & 161E §©LUTIOM FINAL EXAM SPRING 2002 Name Student ID Number Lecturer Recitation Instructor Time of Recitation Class Instructions: 1. The exam has 25 problems, each worth 8 points, for a total of 200 points. . Please supply a_ll information requested above. . Work only in the space provided, or on the backside of the pages. N0 books, notes, or calculators are allowed. . Use a number 2 pencil on the answer sheet. Print your last name, first name, and fill in the little circles. Under “Section Number”, print the division and section number of your recitation class and fill in the little circles. Under “Test / Quiz Number” print 04 and fill in the little circles. Similarly, fill in your student ID and fill in the little circles. Also, fill in your recitation instructor’s name; the course, MA 161; and the date, May 1, 2002. Be sure to fill in the circles for each of the answers of the 25 exam questions. . Show your work. It may be used if your grade is on the borderline. MA 161 & 161E FINAL EXAM SPRING 2002 sin a; 1. If flat) 2 $2 , then f’(.7:) = A. cosrc i, (Caxxfivj— (smx)(guc 2:1: 5; (2c ) : - u B (cosm)(2a:) — (sinx)(a:2) X ' $4 @ (cos x) (:52) — (sin $4 D. (sin 2:) (21:) g4 (cos :13) (3:2) E. (sin :5) (11:2) ;4 (cos :13) (2:27) 2. If y = ($2 + :L‘) tanm, then ill—:1: : 2 (2$+1 tan$+($2+x)se02$ fi,: (fix-1' I) tomx 4’ (X1*‘)SOC2C B. (2$+1)sec2m+($2+x)tanm M C. (2$+1) D. (2:1: + 1) tanx + (1:2 + 1:) cotcc sec2 3: E. (2x + 1) tang: + (x2 + :13) CSC2 a: 3. If f(a:) =sin(27m;2), then f” z A. 471' yo” : HTTXCmLDJTKL) B _2 L I ' '9“in = LUV CmCafoL) 4&477") C” S m “fix 0 0- —27r2 _42 “It I . “n” figf-sm'lt 27r ¥L:)=L+Trcm_j:+4 x a. E-27r+vr : ~LHT9‘ 161 & 161E FINAL EXAM SPRING 2002 4. Which of the following is the derivative of y 2 Mac + 1 at a z 2? 1/ _ . K A. l I I. lim—IE:_*2\/—3 : .QMM w ony m—)2 )(48 Xe; B. OnlyII IL Fm _____Vt+t— VH1 C. Only III —>:z: — a: . D. Only I and II III lim m” 3+,” ‘6 ~ 94”” “(((“L‘l‘lm - ,HO h — “a O 1" @ OnlyIandIII 5. Given the following graph of the function f, which statements are true? 1. gym = f(-3) II. limf does not exist 22—)0 III. lim f does not exist :z—+2“ A. OnlyI B. Only II C. Only III D Only I and III 161 & 161E FINAL EXAM SPRING 2002 6. If :Ezy — my3 2 161 defines y implicitly as a diiferentiable function of 3:, then SE : x 7—- . “b 7- A. 0 Z 3 de16L~x )=;zx +><§i~(g&+3x 55.11;) 2 M (U M B. 2:1: — 3y 3 2 C‘ ; O i y * 1’3 WU“) C 2x—3y2 .5 ‘ 1M 3 _' O : X “*3ng M tat“ 1W) = KX1~3XW £3" E- 7. Let f($) = g(h(:z:)) and h(2) = 3, h(3) = 2, h’(2) = —1, h’(3) : 4, 9(2) 2 —2, 9(3) 2 —3, g’(2) = 5, and g’(3) = 6. Then f’(2) : Q'm = 3,0400% W09- :56 4"c1)= gummy M3") 1:11.25 ; 3’ (a). {(9.} E. 6 1 e ‘ c—n):~€>- 8. tan(sec-12) = I Le‘f g : SEC 6L. ' Ag v 13.3 W 3(2ng ’1 ©j§ a [3 D. g ‘ % MA 161 & 161E FINAL EXAM SPRING 2002 9. The line tangent to the graph of y = f at (2,4) is parallel to the line tangent to the graph of y = x3 at an : 1. Find f’(2). LeiL 300 : X 19%;) = 3 ICI) _’ V 3 gt'm : 3x1) 51/0) D. E. :3 A.4 3 2 1 0 10. A colony of bacteria, growing at a rate proportional to its population, begins with 150 bacteria. Two hours later the population is 600. How many hours does it take for the population to reach 3000 bacteria? kt .. PM): 150 e , “94-900 «9e {2% .an-J— _, 3000:1508 9" =|>OCL+V1). V —a 3w : gl—afifiao_§QnH . w 21/044110 ' ” _,QmL+ 1.2_1 7. 11. lim : ,QJ/fl X~l :I:—)-1 —la;| ‘_ :— _ X) I x1.) &:‘T(X I) X40 —-) le:——X B. 21n20 ln4 21114 ln20 21115 we 2ln4 ln2 161 & 161E FINAL EXAM SPRING 2002 $2 + 1n 12. The number of vertical and horizontal asymptotes of y : —$2—_1— is ’X: QAQ. VQV‘I'L a2 037m r‘l‘D—res. A. 0 B. 1 . T yso \S qdov‘rnsz aSymyJFOC’. 02 M )34. i M ;x «kl—la- D.3 Xaiw xz‘al Mioa ax @4 XL H4 ’ 1‘- \S a hex/17‘;le 3 —12 'f 0 13. Let f(:1:) ={ (m ) ’ m < What value of a makes f continuous atm = 0? 2cosx+a, ifchO. [QM/m Q )‘L A. 2 ' X‘l :— . , x~7 o" 3 3 ® 1 M QC®X+Q9= 9+0» C'O X~Io+ & D. —1 E. —2 ‘él-l'CL :- 3 a z: I 14. When a stone is dropped in a pool, a circular wave moves out from the point of impact at a rate of 6 in/ sec. How fast (in in2 / sec) is the area enclosed by the wave increasing when the radius of the wave is 2 in? Av-nv‘ cm 594:6 Q24” Y 614 B. 2071' Fund 21—? W Y‘JQ C. 167r A Y Y D. 1271' H: \/ 83", 1': an". 3 ¢ 6 E. Noneoftheabove :: 31+ Tl— ’W 68C - 161 & 161E FINAL EXAM SPRING 2002 15. Find the difference between the local maximum and the local minimum values of the function f(x) = x3 — 3:1: + 27. l 1 imam—azo-a X=i‘- 4 Vow ex L°°‘Q M“ WW xzd’ c 2 Lo& |V\II/\, WW Dtl ¥Q"l‘— 9') I: ~—— 7—7 Ll- E. Noneoftheabove 16. The absolute maximum of f : (1 — on the interval [0, 4] is I v __ a l :_ O r ' A. 0 Mn. fi—w MM} 3—} ... .1. 3 C. —9— X50 5 :15 :. L7L D l ‘- 'L = —L. b, Ué I 3 wtio)-O ital 3 V3 £0”- @i 3\/?3 Max 17- If—— S :17 S 7r, then the largest interval on which f(x) :xsinm+cosx is increasing is J v A. (_:,0) ‘FQQ'SSMX+X.COO)K~SIV\X:XCCDK. 2 B. _£,§ -14x40. 0<X¢I jéxéw 122) a I l 9" C. (0,35) 10154) < o 59017 o 'FUR)<O W D. (—m) W 2 E. (0,7r) i: is lnCvQCI-S‘Igz. 161 & 161E FINAL EXAM SPRING 2002 18. Given the graph y = f' below, select a graph which best represents the graph of y : y ‘ y=f®> A.j [.71 B. [y C. y ’31 j E. I?! ,‘I *(X) >0 ‘C is inCAQCCS/mOQz_ 30 OM} 161 & 161E FINAL EXAM SPRING 2002 19. A right circular cone is inscribed in a hemisphere of radius 2 as shown below. Find the ratio of height to radius, —, of the cone that has the maximum volume. 7" (Vzémfih). MaXImn—lg tré'TIYa-lfl- lnL-k-Yl: Li’- A 1 _ 3 -§ . a J— '2.- v l __ ’ \/‘ 3CH'L‘)\" ' ELM" 1") 3.2 I 1..H 1 ELLILLLI._3\:‘>:OJ Bat \n>0 so 1": 73" Aw v3 D? 1.. 7. __LL_ : ’3’ l‘ Y :fi—‘A :’ j a. 3‘ 1"- \a . ~--—— 1 v: ~—’ ___,: V3 1: —/ 3’ V ¢ 93 Q? 20. Let f 2 12:52 on [0, 2]. Let the interval be divided into 2 equal subintervals. Find 17. the Riemann sum for this partition, 2 f ($:)ALL‘, where is the midpoint of its i=1 subinterval. Lon: 11x7" 12:1 2 axsl’ A. 60 ‘lti‘lilzi’w 30 ‘5 _ C.8 72‘ l(:)' all D.15 13.45 xtfiMX + §L~%_)AX : 30 161 & 161E FINAL EXAM SPRING 2002 3 21. If [1 f(t)dt=7and /3 f(t)dt=6, then f f(t)dt= 0 0 1 ? ' « —1 S we): = Swoku “r gfificu' B. 1 0 3 C. 13 e r 7 + “emu D3 . I E. Cannot be determined yfiaéli: ——-I i 22. If f”(:v)=x+\/E, f(0)=1, and f’(0):2, find f(1). I 9/1 E ¥sz~gjxl+gsx +C, A‘3(1) a ‘6 ' 3/} B. 36 leg’: iXl-klg—X (11% 5’2. . 3 H +C l ¥.Cxl:i_x+7x +9~X 3 1.571, D46 ‘ \ .. I +-”—— 9.er]. 13 l 1’ C1 *' ¥Qq‘ 2% I5 1 + @356 . z _i_ L: + c ._—. 3+2. ' 6 + if 4- l w J; 23. If : / cos(t2)dt then F’($) = 0 A. —sinx I FLX) : 063x ‘ "L' B. ficosx 9'15? cosx . Zfi D. —\/Esina:2 2 cosa: 10 161 & 161E FINAL EXAM {1}» SPRING 2002 % 1 1:- «U; 24. / sinzzvcosxdxz S U ‘9‘” 3’ o 0 0 . fl _, .. cCgQKM __ MM“) 9* m, .22 :2 xzojuzo‘r ’ 319 my 13.5 :J‘: u: _: fl X J _ H- L c. 6 D 71’ 'Z 7r\/§ 13- ‘6— 1 (I? 25 [—1 __$2+.._1d$= I A. 2(\/§—1) if [—61% is a,” 04:1 ‘CvacAhf/V‘. B. fi—l .y C. 2 5K4) 3 “£00 D. 1—“? 13.0 v > :1xélm A‘Twalxvew M “C H1 NM fitm- L3“ V’JI—A so *9. I; x~—\J “‘3‘ , V_ :9~ X‘v‘) U ’l \ AL“. 5 ‘ v 1:"; “ff” 0 11 ...
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This note was uploaded on 09/14/2011 for the course MATH 16100 taught by Professor Juan during the Spring '10 term at Purdue University-West Lafayette.

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Sol-161FE-S2002 - MA 161 & 161E §©LUTIOM FINAL EXAM...

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