March 2006 Term #3 - aé s Department of Mathematics...

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Unformatted text preview: aé s Department of Mathematics University of Toronto WEDNESDAY, February 28, 2007 6:10—8:00 PM MAT 133Y TERM TEST #3 Calculus and Linear Algebra for Commerce Duration: 1 hour 50 minutes I Aids Allowed: A non—graphing calculator, with empty memory, to be supplied by student.E Instructions: Fill in the information on this page, and make sure your test booklet contains 11 pages. In addition, you should have a multiple—choice answer sheet, on which you should; fill in your name, number, tutorial time, tutorial room, and tutor’s name. i This test consists of 10 multiple choice questions, and 4 written—answer qiiestions. For the multiple choice questions you can do your rough work in the test booklet, but you must record your answer by circling the appropriate letter on the answer sheet with your pencil. Each correct answer is worth 4 marks; a question left blank, or an incorrect answer,E or two answers for the same question is worth 0. For the written-answer questions, present your solutions in the space provided. The value of each written-answer question is indicated beside it. ENCLOSE YOUR FINAL ANSWER IN A BOX AND WRITE IT IN INK. TOTAL MARKS: 100 FAMILY NAME: GIVEN NAME: STUDENT NO: SIGNATURE: TUTORIAL TIME and ROOM: REGCODE and TIMECODE: T.A.’S NAME: mecode T0501D VV3D BF‘323 RAQA T0101A LM 155 T010113 881074 T0601A R4A MP 137 T0101C 881084 T060113 R413 RW 143 T0201A T0701A F2A MP 137 T0201B T070113 F2B 882108 T02016 T0701C F20 LM 162 T0201D T0801A FSA ss1083 T0301A T080113 F313 $81073 T0301B T5101A M5A 881069 TU401A T5101B M513 882108 T040113 T5201A M6A ss2110 T0501A T050113 T053010 FOR MARKER ONLY 3 Multiple Choice ; BAQE BAQC hfl3A BABE Bfl3C BA3D TBA, TSB VVQA VVQB VV3A. VV3B VV3C $82110 $81083 381084 882127 882102 RW 110 RAP 202 Page 1 of 11 NAME: STUDENT NO: PART A. Multiple Choice 1. [4 marks] If the sum of two numbers is —4, then the minimum value of the sum of their squares is A. 10 “1.”; w 7"; Wis-gm}: B. 2 3M; C. s .. 4:9?- wza finial”? DA 5 gfirfi ' E. 16 M «g a {e zfaéfip a; ii» 2. [4 marks] The function fins) 2 3:3 m 3:1: on the interval [w2, 3] has A. one absolute maximum and one absolute minimum B. one absolute maximum and two absolute minima C. one absolute maximum and no absolute minimum D. two absolute maxima and one absolute minimum E. two absolute maxima and two absolute minima ma: w; l‘ ' it eat: 135%“ awe a Cvgi P . figgmwggfilfiflf Q lama . eafiwafifi 0 i" E” as;« a ‘“ a» fit X «v Q"; WM “394; a ‘" o; - “A a” a g“ 3%: 1: l3 9%? -= «v is Maw a WWW We“ \ . '- €12 alw W“ 1‘ IA f@‘ Page 2 of 11 NAME: STUDENT NO: 3. [4 marks] a: 29; M 2 __ § 3% £2. We +2. is a» %W.:W%§.. .5, A. undefined 5:} E B. O C. 1 D. 2 E. 3 4. [4 marks] . 2I + :L' 11111 m—roo 2m + 1:2 A. 1 B. 0 C 111 2 D_ (111 2)2 (1n 2)2 + 2 E. 2 Page 3 of 11 NAME: STUDENT NO: 5. [4 marks] «/ 1 l 1 + w W 1 m “a: “In” {E u 2 r I 2: 3% E5 «.37 A. O B. -3 8 1 C. -— 8 1 D. E E. i 2 6. [4 marks] a}? l ‘ x” {5 i 4 E. #TIEEW’FW—awlm. / W d9: is equal to £226? X r. fl $ WK WM‘WWMWW WW f? 5 M A. 3(1n|$|)4:13+\/1n|$|+5+0 31%;? fl g E? 1:4 "f. 1 4 5 B. El 4“ fi+ + C C E$4+2fi+ 51111cd+0 D- 1-1-2-m4+2\/E+51njx|+0 E. 3011 |m|)4 + 2fi+ 25; + C Page 4 of 11 NAME: STUDENT NO: 7. [4 marks] EM 2:: *pr viii 1 mdcc . ‘ —— = .fl ‘ - “:5- ‘sC 9"») f0 (2:2 + n4 a, 05 "Vi 1 A. — 48 E Q” 7 ‘ , B. — 48 7 C. E D. 1 6 7 E. — 24 8. [4 Inarks] X, g E J? M W‘* m, f 5‘” d3: : :3 ‘ “:1 6’ g 0 Wmmfw'f- «MW “f, H" A 4 a r “if”? ' THE B, i 1115 25 C- 3 15 D_ _ 2 E. 4 Page 5 of 11 N AME: STUDENT NO: 9. [4 marks] m 1 Istc: dtthenF’2: 1) WW3 () 1 A. _ 1/? .1111 l . B. 1 F w .C 1 1 (lill’fx ‘ m «5 gm D. l 1%.? “’ 3 ' 314%” 1 1 E. ____ 3 1/5 10. [4 marks] After subdividing [0, 24] into n = 4 subintervals of equal length, Simpson’s estimate; for 24 div . ' ls closest to U 1 ‘1 . - + a: 151% ll"; 1: h A. 376 111 B. 3.22 1 ,1 ‘ €- @ memiam'wwmmwfiéém ummwwmgfi fa W' (M 1 s, x F C. 3.95 xi} \gg Egg” $4 1.51; _ D1 4.43 1 . 1;; ~11 .112» - P 1 . k m 1 E. 4.75 13%: “filfimé‘yolfigyewiyw 15321 l} .13 W113; Page 6 of 11 NAME: STUDENT NO: PART B. Written—Answer Questions 1. [17 marks] 4 If f(a:) x m where , —12 + 2 f “I” = and fflm 3 24(2):? + 83: + 9) 334(3: + 3)3 : [3] (a) find all the horizontal and vertical asymptotes of f ‘9 ‘ ' WW & gm .l . w- e at X1: 0 amt X ‘3 “3 amt same; «I O J i M [ELI/#4.. x4 520 “a” “W mmfiwwwmwwm‘v .mfii-‘W'ri‘JYE-T m— WW H a at 7 ‘96:)- ag x4? 0&0 ($151 ("WWWW [4] (1)) find where f is increasing, decreasing, and all relative :tnaxirna or minima [4] (c) find where f is concave upward, concave downward, and all inflection points Ema at...» areal-“i an) Wag «QM sew-r Mal w. gfl‘gw‘fi Wag 13 he? {3‘ Mi {gwmgiflfiflt [6'] (d) draw a clear graph of f on the axes on the next page Page 7 of 11 NAME; g STUDENT NO: Extra page Page 8 of 11 NAME: STUDENT NO: 2. [15 marks] : 30, 000)3/2 P hamburgers / week. If the total cost of producing q hamburgers is (q+ 10, 000) dollars, then find the price that they should Charge/hamburger and the weeklx glgtgut {g} in order to ET" “MW. If a fast food outlet charges 33p for a. hamburger then they will sell q = ( maximize their profit. Page 9 of 11 ea NAME: STUDENT NO: 3. [15 marks] A manufacturer’s marginal cost function, MC, in dollars, is given by 1 m MC 2 20003 + 300 a» q when q items are produced and q 2 1 . If the cost of producing only 1 item is $10,000, find the marginal cost and the average cost when q = 100 . Page 10 of 11 NAME: STUDENT NO: 4. [13 marks] Make a rough sketch of the area enclosed by the three curves: 1) the y —axis x I? m 2) the graph of y = ex 3) the graph of y = 63$“4 shading the enclosed area. Then calculate the area. of the shaded region. Give a numerical answer at the end. hee% I 2 e31 e W4 we $93.3. Page 11 of 11 ...
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March 2006 Term #3 - aé s Department of Mathematics...

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