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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 writtenanswer questions, present your
solutions in the space provided. The value of each writtenanswer 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"; Wisgm}: 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 112m4+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‘JYET 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 sewr 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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