term3(3) - Sgt, ed Department of Mathematics University of...

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Unformatted text preview: Sgt, ed Department of Mathematics University of Toronto WEDNESDAY, March 5‘, 2008 6:10-8:00 PM MAT 133Y TERM TEST #3 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 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. This test consists of 10 multiple choice questions, and 4 writtennanswer 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 0n 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: Room TOIOIA DAQA. 581084 TOIOIB 349B 881086 TOIOIC £490 881087 TOZOIA. BHSA. 882108 TOZOIB DJ3B TDZOIC B430 TUZUID M3D TOBOIA TBA TO3OIB T3B TD4OIA_ VVQA T040113 W913 ’T0501A, VVSA TOfiOlB VVSB TOEDIC VVSC W3D R4A RAB FZA FZB F20 FSA F3B M5A M513 MEA MGB FOR MARKER ONLY 581086 881083 882106 Page 1 of 11 NAME: STUDENT NO: _ PART A. Multiple Choice 1. [4 marks] _ by: i) A If E) is EL constant, iim l + by; 6 2 L g; 0 ft x—rO 37 O A. is undefined b w Eng 4%‘.“ B. is 0 = W «9 y@@ 2% C. is 1 — b b . b {V '2- X 1 52 x—a 0 7. Q» ' E. is —— i 2 2. [4 marks] 1 i 0 1; .5? lim 3:33 00 L'gfif 7 X A. is undefined B. is 1 C. is 0 Page 2 0f 11 NAME: STUDENT NO: [4 marks] The function f(x) = (x :31)2 on the interval [—2, 2] has A. an absolute minimum at a: = 2 and an absolute maximum at a: z —2 . B. an absolute minimum at 3: = —2 and no absolute maximum C an at 93 E —1 and no D. an absolute minimum at 3: = ——1 and an absolute maximum at :1: = 2 E. no absolute minimum or maximum m ~=- be) ~ we“) a M “l $1.2 “WWW (xv) metal r A, A“ “qt glee; .5; A», ($3 (4?” Eflfi‘{‘ifl fih 633) , i 8 61am . WWW 4. [4 marks] 1 g is defined, then , then if g is always positive, increasing and concave downward, wherever A. f is always decreasing and concave upward 13. f is always increasing and concave upward C. f is always decreasing and concave downward D. f is always increasing and concave downward E. f is always decreasing but may be sometimes concave upward and sometimes concave 9(a) 7’ {xflwé J Na: argon a < a 3 alga g downward .3: __._ 2 out; squafl @‘fxll———§: ta— gl'cxko) so Page 3 of 11 NAME: STUDENT NO: _ 5. [4 marks] If the total cost of producing q units of a product is given by c = 250+6q+0.1q2 then the average cost will be a minimum when q is A. 30 “$2560 (94A B. 5@ C 7+ i} f; $0 «26:59.... ' ’L E. 5 6. [4 marks] If f”(33) = 2433, = 4, and f’(0) = 6, then f(1) = A. 16 P [6%) 1 ‘2X%+ B. 17 (a ‘1:— VEJQME, C. 14 (L D. 15 So P17”)?— Elx if b V E. 18 Page 4 of 11 NAME: STUDENT NO: m 7. [4 marks] 3 dt If aft} 1 +675 ,then f’(1n2) = A. 3 3 2 B 1 w- ag) “L” 2 :2 _ C. ~— 9 l P?” Z D —1n3 4 E 1 —— n (3) 8. [4 marks] The area of the region bounded by the :1: —axis, the line a: = 2 , and the curve 3; = 331/3 is ‘ A. Sfi 3 3 B. Bfi 2 C 1 — 6/5 D. 2 E SW— 1 Page 5 of 11 NAME: STUDENT NO: __-, 9. [4 marks] A manufacturer’s marginal cost function is dc _ 500 dq _ x/2q + 40 where c is in dollars. The cost to increase production from 12 to 30 units is A. $2000 (30%;; 6; B. $1000 C(30) I" 682') bl if: 5; C. $800 I 2' D. $500 30 519G Mi '2 ’2‘ 5W ‘ : W W. . E. $100 3“ £2 “Mtg 22., n f” 5.: 1 0 0 O 10. [4 marks] 7 . 3 2 +1 . b The rational funct10n m is expressed as a Sum 3;: 1 + in + 2 + (33 :2)2 where a, b, c are constants. Then G = A. *4 ’2’ B- 2 a(mum—0waw=22x+a C. —13 D. —11 1"? Xj’z "C/zig E- o c 1 / fl @ Page 6 of 11 NAME: STUDENT NO: PART B. Written—Answer Questions 1. [18 marks] Given: y : me— (i) Find the following: i -— V “X [This space for rough work] CL‘ 7H '1: If“, “"76 , [5] (a) Where y is increasing, decreasing, and all relative:K extrrna if any 5 3' M” amt Fl? at xiii caij 7: _ [5] (b) where the graph is concave upward and downward and all inflection points if an}r Question 1 continues on Page 8 Page 7 of 11 STUDENT NO: _ (c) the horiz asymptotes if any (justify your answer) mm eke; flame/fl win is“ W {om-f [1](d) the 3; ad 3; in‘telfeept gem???» [5] (11) Draw a. clearly labelled sketch of y = 1136—33 on the following axes. Y ‘6‘. WW WW" Page 8 of 11 2. [15 marks] If a university charges $12 for a football ticket, it sells on average 70,000 tickets. For every $1 increase in the ticket price it loses 2000 in attendance. If every person spends an average of $3 on refreshments, then what price/ ticket should they charge in order to maximize their revenue? How many tickets will they sell at this price, and what will be the maximum revenue? Last? XV: «elm. WWW g“ng l‘nC/ffi'fllfgrj Page 9 of ‘11 NAME: STUDENT NO: _ 3. [12 marks] Find the area of the region bounded by the curves y 2 51mm and y = 9011123. [A rough sketch may be helpful, but is not required] PQLm’éS 5N? ifl‘ba’§&/éjii;fi ‘~ 5 X : ‘><‘ 144,»: (5"KDQVLKT‘O X15 an} 2‘” Q (9%“ Poe ’« 6’ flax cw? 7M 2% £4.26: we chlwmf {Q}, @h[\){:[ an} “946/ 66(va gm (1,63% X" j if”, ' awe fié‘gLé” “’3' a 4‘ 3‘ flame, Xz&/L>C (9A “51% Page 10 of 11 NAME: STUDENT NO: 4. [15 marks] Find the following integrals. flax Mei)? we) («6‘5 “" | 1? MM 0 “41,15 l 1. w, «J T 0 I 2" 3 :10] (b) j (1 fizzy d3: [Suggestionz u m 1+3:2 , but there are other ways too; partial fractions is not one of these ways.] 4% 'j. Kéfi/K Leefi a :1 l???» *WW_MWWMWMWWWWWWVMW_ "fig; laolcs fllemf QM ,Dvgfi" am; I! 1: fl. Wl/HC/ll/l {9 0i weeémmfz} / Page 11 of 11 ...
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This note was uploaded on 04/12/2011 for the course MAT 133Y taught by Professor Carr during the Spring '11 term at University of Toronto- Toronto.

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term3(3) - Sgt, ed Department of Mathematics University of...

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