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2004-2004 Term Test #3 Answers

2004-2004 Term Test #3 Answers - Gal v 20 Department of...

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Unformatted text preview: Gal v 20! Department of Mathematics University of Toronto WEDNESDAY, March 2 , 2005 6:10-8:00 PM MAT 133Y TERM TEST #3 Calculus and Linear Algebra for Commerce Duration: 2 hours 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. 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 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: MQA T0101A T0501C RW 229 T0101B MQB T0501D BA124O T0101C M9C T0601A LM 157 T0201A M3A T0701A BF 323 T0201B M3B T0701B LM 157 T0201C M3C T0701C MP 118 T0201D M3D T0801A WA 142 T0301A T3A T0801B WI 523 T0301B T3B T5101A LM 155 TOBOlC T3C T5101B LM 157 T0401A W9A T5201A SS2111 T0401B W9B T0501A W3A T0501B W3B FOR MARKER ONLY Multiple Chorce B2 B3 Page 1 of 10 NAME: STUDENT NO: PART A. Multiple Choice 1. [4 marks] If F’(z1:)=(ac2 +1) -:1: and F(0) : 1,then F02) = (L A I, Y X 1 3 g 1 .30 + C B. 32: +sc+C 1 7‘ C. w4+cc2+1 1 1 1$4+§$2+1 1 1 2. [4 marks] If f”(w) = 33 f’(1)= A. —1 B. 2 C. 0 “1 a 3 E. 1 Page 2 of 10 NAME: STUDENT NO: 3. [4 marks] If F($)=/w1mdt,then F/(Z) F [)6 'L C. does not exist D. cannot be determined E. =31 64 4. [4 marks] 3111 - m+ 2 2 , Let F(m)=—-(:—2%P—x—. Then /1 F(m)d:c= F(1)" F(') 0.0299 ‘1. .. I B. 0.0498 ’ 3&1)e3+4 — g“ C. 0 5 D. —0.49 N E. 102.37 N Page 3 of 10 NAME: 5. [4 marks] :3 + 1 — em 6. [4 marks] $11;ng + em)” A. +00 B. e C. 0 D. —1 ll STUDENT NO: 7‘) ‘K baby? A ()3) 60%..le X)w ’L’é/X 7%” ’Cfe/x Page 4 of 10 NAME: 7. [4 marks] 6 21119: / dx : 1 II? 8. [4 marks] 1 / Ix+1|zcdas= —2 STUDENT NO: Page 5 0f 10 NAME: STUDENT NO: 9. [4 marks] If a and b are real numbers such that a < b and the function f is differentiable on the Whole real line, then the average value of f’ on the interval [a, b] equals Afmwmw 2 B. the slope of the line which is tangent, at (a :— b, f(a :— b)) , t0 the graph of f O 1 3/1 10. [4 marks] ‘ S 'L AX g X ( 5x *I 0 / 945:5? + 1)—% d2: : R%” an 2W ‘ 0‘“ =__ ‘ bl. ' / C. :15 1 R409 §§Ri+l '0 A ) D. diverlges (“fl-(3K u"! {Xv/{4 A“? IOX X E. :‘3 J5. ) , a .(«1 - @5200 i6 5RIL+I , am {alt/T” W ’ R/fiao Page 6 of 10 NAME: STUDENT NO: PART B. Written-Answer Questions 1. [15 marks] The owner of an apple orchard estimates that if he plants 24 trees per acre, then the number of apples he gets from each tree is 600 per year. For each additional tree he plants per acre, the number of apples he gets from each tree decreases by 12 /year. How many trees should he plant per acre in order to yield the most apples? 916/565 Perm/re alcove 7—4, ‘6 X: no, 0 ‘ L9 (6(J/QML rel 7r. Le 7,, W‘ 7 YIé‘A V” {7/66 : éQO-lix trw (y acre : 7J4 +X )1: (2LHXXLOOHZX) 1 nawxllfo“) C ”1.4515 mtg) y'z \’)_[(5’O’X)’(Qq 400:, r \/l 1: ll (Q‘évzx’) “J 2146\3’52) (-5» osx< {0) 9,;— cho w W7“ b) \/ “ m «r ‘ ”/0 40 V‘AQX‘ [S 0 \I Page 7 of 10 NAME: STUDENT NO: 2. Find the total area of the finite regi0n(s) bounded by the curves x: x/L’WX 90’ VCR/33$, O '« XL’ 5x 0 = x (>0 €) Page 8 of 10 NAME: STUDENT NO: 3. [15 marks] At time t : 0 an account is opened and at time t Z 0 (t in years), cash flows into the account at the rate 1000i dollars per year. If annual interest is 5% compounded continuously, how much money is in the account at the end of 10 years? Page 9 of 10 NAME: STUDENT NO: 4. [12 marks] Find the integral, expressing your final answer as a decimal, accurate to 4 places. 2 (13 / dq 0 <q+1>2 <q+2> [You may use the following fact if you find it helpful] (q+1)2 (q+2)=q3+4q2+5q+2 3+4 hf «I LW’f ‘lol‘ ’ Wyf Page 10 of 10 ...
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