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Sol-165FE-F2010

Sol-165FE-F2010 - MA 165 FINAL EXAM 01 Fall 2010 Page 1/10...

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Unformatted text preview: MA 165 FINAL EXAM 01 Fall 2010 Page 1/10 NAME Qpnurlnwg 10—digit PUID # 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. 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, 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 NUMBER, put 0 in the first column and then enter the 3—digit section number. For example, for section 016 write 0016, and 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. MA 165 FINAL EXAM 01 Fall 2010 Name: ____.______.____.____. Page 2/10 1. The domain of f(x )2 111(1 — 13312 )is A. (0,00) 1 ,ng > O ®(~1,1) Ma % i c. (—00,—1) «14% £1” D. (1,00) E. (—O0,00) .r— H 4“ ‘2 2. lim——————————— 4+2$"2_ 5‘ Jim 2 4+2? W O T :A‘m mfiiy :% (Wadi) W9}; ' E. Does not exist .7 2 F477 3 lim 3“” — QC», iii—+1“ ($ '- 1)3‘i— A. 00 Lfl/ B. 2 0“. C. —2 0 ~00 E. Does not exist MA 165 FINAL EXAM 01 Fall 2010 Name: _______________— Page 3/10 4. If f(ac) : g: _: i, find the inverse function f‘1(a:). «a, yxgga7 Mia am gig? A f”1( 5$+2 ,9 , m) = 3:0— 1 L ”(3: Figs“??? B. f_1(_’L') : 3 “ IL' 1 —3 (a29“"3953g W ”123% C'f—1($) : 532+: 7( w. gilt}: W 233 w. _ + 1 w L @r W) l (‘3 “M” “a!” , 3—53: ”QM E.f 1(a7)=2$+1 f if”; mafiffi? ”,9; lg “l"? _ _ _ 3:2 + a2, if a: < a . _ 5. Find the values of a for which the function f (3:) = _ is continuous 2m — a, if a: 2 a for all as. f: ('0 037:“??th 716; L416 “#5“ng (Pd/VWWUM/ I A. 0 onl Fifi” £ tea Jm: mvxfi‘imwwx mi CL: £14m jc{)<) w {(41) y X4“, ' B. 0 and 1 film £(szfh EAVM (X (1+Q)g 20:1: @0 and% x”? am xrkfi D 1 1 lim {(1%) W519 9:9é9ny2x—a) : CL . Ony awn 14v , V w L a a E. 1 and % U“? in?) «magi? oil; @132 a: Mm cum; 1) .20 g; :0 gm 6. Find an equation for the line tangent to the curve 3/ = 1 :1 253 at the point Where :8 2 ' - . _., 4» («2) 2% g9 :2 «ggigifrwww t; WQW A. 23: — y + 2 :2 0 &) 3L2? B.4:c—y+4=0 C972: W30 4w C.4x+y*4=0 “x36 W1, 32%? D.m+4y—16:0 9)“ $g€ff§lfl§jm @8x—y-l—420 MA 165 FINAL EXAM 01 Fall 2010 Name: Page 4/10 7 Which of the following is a horizontal asymptote of the curve y— _ m min . 5 24“,; - Xmas“ all“; w W fiafiw 4:; 13;“ Pigeon 8. Suppose that F(£U) = f(g(:z:)) and 9(3) 2 1, g’(3) = 2, f(3) = 2, f’(3) = 3, f(1) 2 4 and f’(1) = 5. Find F’(3). Po) :3“ (M , 3 10 F/(x) 2: flaw} % f“? B. 8 i F333;}: {@432} flé/(B) 0.6 :§/(1>%’{‘3) V D. 12 .~: 5' 2 I {1.0 E. 5 d sina: 9. E; {L' = , A. msinm—l A, Verna m d {Qfimxymx B. (lnx)xsinw dy w W; sinw _’é__ flaw”) fgiwfl C. (COS$)(1I1$)+ m 6H $Sinm[(COS$)(1na;) + 81:51:] (1m in m ' f 2 65 zMe fl E‘QWxxfiem) nigmx) £74 ‘ E. xsmm cos x fidk‘fi'}: ”:32th meng)€2m%} WWW/1’9“" mm” as... a» MA 165 FINAL EXAM 01 Fall 2010 Name: ________________ Page 5/10 10. A lighthouse is located on a small island 1 mile away from the nearest point P on a straight shoreline and its light makes 3 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 3 miles from P? EW 96W g @607r miles/min Wflwws NMVWWW? WQWMWWMM, l _, / Sig- ; QW B. 3O7r miles/min ll 6 M C 60 '1 / ' E} Flhfi WE?” wliwsw War em W - m1 es mm n all“ D. 30 miles/min la r7 3 Li? ”X , 20 gaff-6g wa W: gel / 1 E. gw miles/min R} 662 “Mm F6633 1'0,me swimgmézl 6‘s WWaoysrrlgéilm M. 11' Using a linear approximation 0f ft”) = (7:? at a = 16, we find the estimate of 4 15,68 to be I W s... y ,6, 6:1 gm as £6» + News as?) ,st ss ssssw A. 1.9 H“): ill: €06) ’22 B. 1.99 a r W .1. xi :2};— Vii” ma {Miss g. 66 C201 l... ' _ , m D. 2 WM 2 + Ea ix , ”(LQJ/ )Lot‘ '71 rumors! E .4 . 1.96 16:66 5:6. 2 +§E 66 Qiiémlé} 22-66: (46:32) 266001-2196 12. lim [(1nx)(tan”2__—:Xim ”6:2???” :: air—>1” Xi“, is: ”7%? 0'00 in. A W I o . —2— (1: Q) m :67 WW6 s... ._ 1% ism” 96121;; W W m .1 W W a __ “kiwi (ii—(:6; 96W§>(% 7“" B 2 WWW2664 s We; _3 a W , .. W W D. 7? MA 165 FINAL EXAM 01 Fall 2010 Name: _______________ Page 6/10 13. The absolute maximum and absolute minimum values of the function f(a:) = —-333 —|— 3x2 — 1 on the closed interval [—2, 3] are: .939 :5: ”93??? gw “ A. abs. max—:3, abs. minz—16 gm “3'13 '4 “"339? 3 an ”X Z: 5) B. abs. max=3, abs. minz—l ”3%, (X W 2) :0 ©abs. max=19, abs. min=—1 2: 0’ 2‘ ~, D. abs. max=19, abs. min=—16 gag???) ’33 "' (“8) is?) ‘ fill 91% T: as; QM “(Mi E. abs. max=1, abs. min=~13 HE) :1 m i W hi 4 W gig} :r—oa M2: «vi :3 :H3 3”“ ‘5’“ .3345 +3.?“ 1 “3;: WELL, Wmmih 14. Suppose that the first derivative of f (:3) is NJ?) = —(9«" + 2X33 + 1)2$3($ — 04 Then f (x) attains a local minimum at a: = ——2 and local maximum at x = 0 B. local minimum at av = —1 and local maximum at a: :2 l C. local minimum at a: = —2 and at x z 0 D. local maximum at a: = ——2 and at :1: = O E. It cannot be determined from the first derivative only. / a—‘t—O-Iw—Hri O+v++O———~¢=® _,,.,_..,,__.,._, 'g (X) f—w i i i, w, «‘4 A7 _, ‘ A h ,, mwjflmwx>x ’2 -L o ’L l‘ i inamfim film; WWW MA 165 FINAL EXAM 01 Fall 2010 Name: Page 7/10 15. Suppose that the second derivative of f(:u) is f"($) = (56 + 2)5($ + 1W3: '- 1)3(93 - 2)4 Then the number of inflection points of the graphs of y = f(x) is E. It cannot be determined from the second derivative only 4' v+++0weuwawwwww ©+++~+Z> ++++ «=2, ., 1, 4 2. I: i 2 16. Consider the ellipse £84— + y2 = 1 and rectangles inscribed in the ellipse (with corners on the ellipse and sides parallel to the coordinate axes). Find the horizontal dimension of the rectangle With largest area. - A”? / 2, a” 1 rs WM+W er? A.4 B. 2 C. 1 om E. 4J5 MA 165 FINAL EXAM 01 Fall 2010 Name: Page 8/10 17. A particle moves in a straight line and has acceleration given by a(t) 2 675 + 4. Its initial velocity is 11(0) :2 —6 and its initial position is 5(0) 2 9. Find its position function 3(t). amaé‘fww A.s(t)=3t2+4t—6 a) (127) 2:; $55361 3123:: a? 3: B. so) = t3 + 22:2 _ 625 no a pm a 2:; 6:1 1%» en v1 4:? f if? @305) = ta + 2152 _ 6t + 9 3155i}; *3 333‘ 33 " G D. 8(25) 2 6t — 9 31%;: L553+2t3¢ 61‘: 14:9 E s(t)=t3+6t2—9t ‘f’SO 2 ‘9 :10 :{n C) WT} 11¢»{:1w1{:1“:“31 em? "1:3 a Wig: { an 3E? w IO 10 ‘3 , 6‘ 18. / lw—5ldw= { (mm + {(1%)de A0 0 0 6, ED 53 ,i B. 15 ___<q;’r{<m, KEN +- 213”, may” M 3 0 3” 3 @25 w w w ,.,_ i, 22,: g’ 33'3““ :53“ ”l” 33;?”3339 (2 2> D45 _., n29? » m: _g§‘ 12:?" E. 50 i, .25 Ma mg» 72:90 50 ‘2” «+3 :: ETC) _, 2%? : 2.5 {\V/ A:§§:2f“ Wg._i_..,.,,f , m 2 2 —1 2. $ 19- / (3 3 dm = { @1«%><[email protected]{: 1 ‘2: 2: I {k maamgfiw B. 1112 i 1 a C.21n2 ‘2. :1 33 m21x’ +{mi’a§] D i 2 57 2 MA 165 FINAL EXAM 01 Fall 2010 Name: Page 9/10 ‘7? 20 d 0 1 dt —- 94L 5 Wilma, fig? 1 . a— 1 t2 _ ”" a flwngm ‘ ‘7 — m. m MAW B. 1 C. tan—1 a: D. — tan‘1 a: 223 E. —————— (1+932)2 0086 21'/ '2 d6: A. cotecsc6+C srn B.l ' 6 C' m Scam €$€Q£:%” ~ ... LSCQ +4: nlsm 1+ W A t. C.lnlsin9+cog€l+0 —csc6+C E. csc<9+C i ‘52,. .2; 6 LL ' n 55% 22 133 day: mam 2:. mt m 2... A. 0 (I) . 9m 0 1 z] w l ma:me 2 wt‘”%%% C. 1 K“ 1 mt 7%er D. ~3— %,: é W? Lg: 523$ E. 2 23. A culture of a single cell creature Amoeba is found to triple its population in three weeks. Its relative growth rate k (in number/week) is P(t): P(©§§k A. 1113 ta?) : “3 We): frog 5‘33 g ’3‘” M £3 Mr» E k3 1 3m??? WWW % m MA 165 FINAL EXAM 01 Fall 2010 Name: Page 10/10 24. Find an equation of the hyperbola with foci (0, i4) and asymptotes y 2 i333 U) H04 2;» F €25 I] “‘1'“ W” 25”” “:1” i (fl/g“ lg ., ., “Jig” H M’ ‘ 3: Asgmnmfi 3M. bx CS4— ‘m 03}; H0747 %:$ an, C2: z+b2m '2; *2” 42m alarm???» l6 til”; — w, $3 K, ”7%; a2: §b222 9 %m “E” ‘27, “'2 _ “J m w w 1 1% 32., . “’” ‘5” 5’" 25. Find the center of the ellipse 3:132 + 312 — 12w + 23/ + 10 = 0. 39:2».12‘x “Ewan :mio 3({1- at +4) +<f+23 H) g Wino +12 vi»; 36% ,2)?" a!» [j +1)? 3 ‘3 & ~52)?” + (fill: :1, We: (23 ml) 4 A. (—1,2) B. (1, ~2) © (2, ~1> D. (3,1) E. (—3, 1) ...
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