Dec 2008 Term#2 - 652 (Ufa/f Department of Mathematics...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 652 (Ufa/f Department of Mathematics University of Toronto MONDAY, December 1, 2008 6:10-8:00 PM MAT 133Y TERM TEST #2 Calculus and Linear Algebra for Commerce Duration: 1 hour 50 minutes Aids Allowed: A non—graphing calculator, with empty memory, to be supplied by student. Instructions: 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. This test consists of 10 multiple choice questions, and 4 written-answer questions. I 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, ENCLOSE YOUR FINAL ANSWER IN A BOX AND WHITE IT IN INK. TOTAL MARKS: 100 FAMILY NAME: GIVEN NAME: STUDENT N O: SIGNATURE: TUTORIAL TIME and ROOM: REGCODE and TIMECODE: T.A.’S NAME: m mecode m TOlOIA MQA 581074 T0501D WSD BA2139 TOIOIB MQB 382105 T0601A R4A LM 157 T0101C M90 SS2111 TOGOIB R413 LM 123 T010113 MQD LM 158 TOTOlA F2A RW 229 TUZDiA MSA T0701B F2B 882111 T020113 M313 TO7OIC F20 352128 TUZUIC M3C TOSOlA FBA LM 155 T0201D M313 TOSOIB F313 LM 123 FOR MARKER ONLY Multiple Choice 1 TOBOIA TSA T5101A M5A MP 134 T030113 T3B T510113 M513 882111 TD40lA WQA ss1074 T5101C! M50 MP 118 T040113 WQB 881086 T5101D MED RW 143 T0401c WQC LM 15s T5201A MSA LM 162 TOBOIA W3A 832105 ' T050113 WSB M82173 T0501C W3C U0 256 Page 1 of 10 NAME: STUDENT NO: PART A. Multiple Choice 1. [4 maTks] ‘ V . 293%693—8 d: 2mm; @1696)“; 5" 11m —— _ _—-»~—-' C Wm m—4—1 932—1 xa-«g (:x—Q/xg A. is 2 B. is 0 is 5 D. is 1 E. does not exist 2. [4marks] ‘ 3/6! 4;; W5) J§§+g 3;“) lim W xx _ g 3‘: ‘ °° WW 0 ‘ . “W a J 2 X x ‘ Q“? B. 0 C ‘1 “:1 M 1:. a. D. 1 fly} a E +00 Page 2 of 10 NAME: STUDENT NO: ma?" 3 ‘ " Kw . 3' M Z (1*Qy} m?” Q WC; 4. [4 marks] All solutions of the inequality areg'ivenby A. a:<——1 or m>ln2 B. —1<m§1n2 C. —1<1U<0 01" len2 :;:1:<——1 0r x21n2 E. m<—1 0r 0<m$ln2 Page 3 of 10 ‘ NAME: 5. [4marks] i m m ._ dm x2+16 _ I m3—$2+m+.1 m I (x2+1)2 e ‘ x3+532+mu1 B. _________ a: (m2+1)2 e m3—m2—az+1 C. a: (2:2+1)2 e D 3:34-3:2—55-1-1633 ' (a:2+1)2 E 3:3—x2+:z:—1 m .' (2122+1)2 ‘3 6. [4ma7‘ks] STUDENT NO: "gfiwe?+ a”駣Q;::£: (gar: 1/53“ x’fi-i (ysz 1‘} in 5’}: Ex?“ Egg 6% 97H} A (4 ~— m)2(:c + ALP/2 Let “33) fl (m+1)(2—x)(3x+6) Then f1?) 2 g f 2 at sag-7»??? 4' ii £4 (x+%)’ £16.34“) _3 a1 Tm “*' i - {9. B H - 4% Hum" £91633”, ) ) ' 3 . if (a. C. M:- “ fifiggfli‘ ‘5‘ 30‘4 wa 8 D. — 3 7 g, -..L ... i «i» «L “41 E .1_1 y'flfim pa’”- %+3 2“ ' 8 .w w}; d. 9&3} f) 4L W E? afigflfiifiififflfi Page 4 of 10 NAME: STUDENT NO: 7. [4 marks] Let y=':37+1)$2—1 . 9 Then y’ 2 : (X14) 164 5X“? g A. 2:1:(3: + l)(3:2 —— 1) g [-1 fix .. B. (m2—1)(x+1)$2“2 . 7 ? c. m2—-1( ' (cc +1) 2m 111m + 1) + (m — 1)) 8. [4 marks] Let 2m3+533y+y3 =8 Thenwhen 3:21 and 11:1, y’: - at» 69”]? ‘ 3",. j¢§xy°+5¥§f “Q {fig «t 5’ B —1—1— E . 6 g / (.533; 9 1% firm C 0 (94‘g4’gr? {a g H: D ___1%_ gx fl w 8 M3 #39:: E “‘11” f % Page 5 of 10 NAME: STUDENT NO: 9. [4 marks] The point elasticity of the demand equation (1 = p2 — 10p + 50 when p = 3 is 3 A. 11—6 12 29 3 C. _m . 6 D. E 6 E. wig 10. [4 marks] 64 If a company can produce q(m) = 2m + —— units when it has m > 5 employees and must m . . 48 . '. . . set Its price p at p = E to sell all (1 units, What IS its marginal revenue product 0! ( d—T , Where r denotes revenue) when m = 16 ? m . 12 i ‘fi EWW Mg dfiwfifiwfi°2¢T§ % Page 6 of 16 NAME: _ STUDENT NO: PART B. Written-Answer Questions 1. [15 marks] Given a: +3: -1 fire: A a: = 1—: m H) ————?—1— if0<azgl 2+‘2m £+3—2 if m>1. 33—1 Determine whether f is continuous at each of the values of :1: below. Show all steps and state dearly Why f is or is not continuous. [8](a) 55:0 gffiflwfi swig. W4: 5:} em as wwé WWWHWL swig“ sum” W??? X'PE f fi “em-B 0” “7% 3 sea g 62 3; {-9 (3| gears-f: §fifig “‘3 Q :fl’Jm kyfi n “g? mg W a s” "2“ w”? W ‘ w “E w “3’ we 52 Q 4%" E game-g " ‘ 7 of 10 NAME: ‘ ' STUDENT NO: 2. [15 marks] ‘ wrymwmm'ww" “1?; em 1 [57 (b) Find the equation of the tangent line: to the graph of y’ at the point (3, [Note: the graph of y’ , not the graph of y] N Wkfie "fl 34: Eye Page 8 of 10 NAME: . __ STUDENT NO: 3. [15 marks] Find the equation of the line in the my éplane which goes through the origin and is tangent to the graph of y = 6m . Show your work. Page 9 of 10 NAME: STUDENT NO: 4. [15 marks] Use Newton’s method to find (to one place after the decimal point) a value of a: so that f’(x) : 0 where 4 sg——x2—5cc+1 f(a=)=e (Begin with the value $0 = 2 and go as far as calculating 332 before you decide on your answer. Note that f itself is never zero. in 35?. _,_ x Evy-5'an ! 9%) 7‘“ (X3W1X’5V)fi ‘1 v a Page 10 of 10 ...
View Full Document

Page1 / 10

Dec 2008 Term#2 - 652 (Ufa/f Department of Mathematics...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online