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2007-2008 - Aids Allowed A non-graphing calculator with...

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Unformatted text preview: Aids Allowed: A non-graphing calculator, with empty memory, to be supplied by student. Instructioris: Fill in the information on this page, and make sure your test booklet contains 10 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. Department of Mathematics University of Toronto Doll/6A WEDNESDAY, December 5, 2007 6:10-8:00 PM MAT 133Y TERM TEST #2 Calculus and Linear Algebra for Commerce Duration: 1 hour 50 minutes ' This test consists of 10 multiple choice questions, and 4 written—answer questions. 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, 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. ENOLOSE 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: TOlOlA TfllfllB TUIDlC TDZOIA TEZOIB TOZOIC TDQOID TUSOlA TDSOIB T0401A T0401B TUSUIA T0501B TD5OIC n1 349A thE 319C DJ3A hd3B DASC BEBE TSA TBB VJQA VVQB VV3A VVSB VV3C 531084 T0501D 881086 T0601A 881087 T0601B 582108 T0701A RW 143 T070113 881083 T07010 RW 142 TDSOIA 551084 T0801B 882108 T5101A 851084 T5101B SS1073 T5201A 381086 T520113 851083 582106 VV3D R4A RAB F2A FZB F20 FSA F3B LASA hflSB hflfiA RAGE 851088 LBJ 157 881083 581086 882106 882108 hflP 134 REP 118 BHP 118 VV1523 Lhfl 162 582106 Page 1 of 10 FOR MARKER ONLY NAME: PART A. Multip] 1. [4 marks] a - 3 1. (m+3)2~1 _ QM w $3512 3:3 + 29; — X”? «1. XC‘K 4'7?) [L’Hépital’s Rule is not necessary here] A. 0 B. 1 © -1 D. +00 E. —00 2. [4 marks] ‘ . 2. (Ci _, 11m v9m2—33+6_ “X m—ru-oo a: _ ){A ’90 ...---"""'"" [L’Hépital’s Rule is not necessary here] Page 2 of l STUDENT NO: 0 .8 Choice in [QMxnéfl .- W 90—7 4.. MK ' :21 = «5 (”L _____,_._—-—--* ' ”SE7 '1" €27. Lujk m: "'"' WM...” )4 whet“ 7((0 NAME: STUDENT NO: 3. [4 marks] 54: fl ‘ Li 4' 3- 3 X , 437+} + 33: 4,. éflffiygflu ’- / maria 0 11m __..__,_ m '” ‘ ‘f bf :c—>+oo 1 — as x Ma 00 MM . L’H“tl’R1' t h .1 w t E [ opi a s ueis no necessary ere] a“? ! Qwflx M [email protected] 5t 41' x A. 4 (9 *4 C. —1 w “’3— fi... v. M H D. +00 ’3 E. —oo 4. [4 marks] If 2 _ :1: —~ 7 when a: S 3 f($)_{$ +0 when m>3 then lingflx) A. exists for all values of c ‘ ’ £4” K1“ 4 “5- l 3 exists only when G > 0 8/2"; Pffl) 1 i—— A3, x4? C. exists only when 0 = 0 7C ‘ exists only when G : —1 r Db") £94“ X'i'c .3 3 ‘i'C.’ E. does not exist for any value of c W X95) § it ' ' Page 3 of'lO NAME: STUDENT NO: 5. [4 magks] If f(:c "71133—62 2:” , than f’(1)= (31:5 ? 7x) , 3 xq’éz 4’3 " Xgewxé 1) c. #5 ‘P'(J;§ea #26015 D. 6 E. 5 6. [4marks] 1 1+ 113: If QUE): 1+3: ,then 9(1)— A E): 1‘}: C\*X)*“MC§%£‘P¢> . 4 5 )C W B. 1n2 (:\*X)L C 1 1 DE “353:5 _' ,, QHWWL @i: 3 ”W Page 4 of 10 NAME: STUDENT NO: 7. [4 marks] The equation of the tangent line to the curve y 2 11101133) at (e, O) is A‘ y = 633 "‘ 8 g / l...- g i B. y — e m :1: 7/ 51?; X C. y = a: + 1 i .14” m fl‘ ' “'0’" We) a; e E m+yml 7 "’ O 6 N ”j. :74: m! M 1/ e 8. [4 marks] W7 8x2 If : h I: y (m2+1)10,teny 1 ——1- 2 2 2033632 A. __ 2 a: 2 1 10 cc 2 10_ _ 253 6 (27+) +wfie (:1; +1) ($2+1)9 B. 1n(a:2 +1)+ 6‘52 + $1113 1 fi-Zazemz C. 10 2 19 5': —--_———— (33+)fi3+2 ($2+1)10 3’. D. fiem2(x2+1)10+ e$2(m2+1)10+2$2 em” 1 2W? x, ”L g}: ... W "L7 ., 2% {k x”! Page 5 of 10 NAME: STUDENT NO: EL 9_ [4 marks] 3 X: (ZX‘f'3); Ifyzx/m then j—xfigflg” “ 7" ,, I{2X*§)WV 3 A 2x/2cc+3 . ?)'L 0 “1:; (’ZX“? A A. B. C. —(23: + 3)" D. Jr NIU‘ ,3 y “2’, r ,L C’ZK’f’g) A; @SQMB)‘ -; (fix???) 2” A712” 7’“! ":n ‘3 ifi’leé) g; '5“ 3€Q%*%)% 10. [4 marks] If x/zc + y = 1 + 3323/2 defines y implicitly as a. function of a: then y’ = 217““"4 A- % fl WY)" 1’7 + ”3*:MZ)’ @ 4xy2m—1 2 ”7 1—4xgym mm "a” ‘1qu l c. _____.2xy21 / [Wm M] “m 2$Zy_ 2m D. 43:3; 1% Y7” m 7,-wfi ,5, ——' £75 {id / 7/: WWW"; M gflflxym Page 6 of 10 NAME: STUDENT NO: PART B. Written-Answer Questions . 1. [15 marks] Let 21+m—k if$<~1 332—1 m: —-————-———— 'f m1< <1 fl) (a:-1)(:c—2) 1 *5” 233—4 if CC>1. [5] (a) Is f continuous at as = 2 ? (Justify your answer.) VES ., [5] (b) Why is f not continuous at :3 = 1 ? How would you define f (1) to make f waging at a: m l ? J j? ‘j {g} Efifl’g3 01% Kig fioflbflvaQ (1% N: My"? fifiéfiw ‘ ‘1 m - u. Page 7 of 10 NAME: STUDENT NO: 2. [I 6 marks] Solve the foilowing inequalities for a: Q F 0g E j; 0 )élufifx {3 0(-C’ {mg 3.3?in f X j [8](a) (m2_4)1m<0 (Xafio sigma??? a”; .5; {I} {if x’ :1 cragmfii MST?! cmiy. awfig ‘é‘ifiéflfi. filé tii Page 8 of 10 NAME: . STUDENT NO: 3. [15 marks] The demand function for a' product is m 1n(q + ) 19 Find the marginal revenue and the point elasticity of demand when q = 5 . [Please remember that this is a calculus course] .... Jul?— :: e" 3 ,, “+le ' Wfi f)?’ 2%ng ‘ Page 9 of 10 NAME: STUDENT NO: 4. [14 marks] Use Newton’s Method to approximate the root of the equation 3:4 +3: — 4 = O in the interval (1, 2) to six decimal places. ’1‘ xgfielxme~PGa) iD PeJ:X'+%wW $‘5KA3 ‘19 ~— Xn" merxh’"? W fo «H xtfl'? gxf.t# an; "PG)*<O Mag-W 12m) >0 if? We, 5%gféi (dings X02; 536/ KI:L§131?5392 >9, ,_. LTKEB‘I (a 0699* P933?00”' 21°! 969 g N {3% . ‘ W . dirt. 8' 6h?” :13! CQQ-C‘W‘ Wfi$2?gls Qié {:0 {film/65 fic’év‘aiw' Page 10 of 10 ...
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