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Unformatted text preview: Sgt, ed Department of Mathematics
University of Toronto WEDNESDAY, March 5‘, 2008 6:108:00 PM
MAT 133Y TERM TEST #3 Calculus and Linear Algebra for Commerce
Duration: 1 hour 50 minutes Aids Allowed: A nongraphing 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
[email protected]@ 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. [email protected] 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 {omf [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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 Spring '11
 CARR
 Convex function, Department of Mathematics

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