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Unformatted text preview: SIM/l Department of Mathematics
University of Toronto TUESDAY, March 10, 2009 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 multiplechoice 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 writtenanswer 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 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: TA. ’8 NAME:
TOIDIA M9A 331074 T0501D FW142 L‘M 157
LM 123
aw 229
382111
332128
LM 155
LM 123
MP 134
332111
MP 118
aw 143
LM 162 T0601A
T0601B
TO'T’OlA
TOYDIB
T0701C
T0801A
TOSOlB
T5101A
TSIOIB
T51010
T5101D
TSZOIA TO 101B
TO 101 C
TDlOlD
T0201A
T0201B
T02010
TOZOID
T0301A
TUSOIB
T0401A
T040113
T0401C
T0501A
T0501B
T05010 MQB
M90
MQD
MBA
M3B
M30
M3D
T3A
T313
WQA
WQB
W9C
W3A
WBB
W3C} 332105
382111 FOR MARKER ONLY
Multiple Choice  Page 1 of 11 NAME: STUDENT NO: PART A. Multiple Choice 1. Mama/rigs] f}
l /L x L
1mgas:—1 IS _:_ am Em : 2 game” 0
m—’ 324—1 )(f'?! 3 ﬁt?
A. 0 .2; I. J
B 1 “ﬂ Ofx'ﬂal' 44 Wxé—H
r = am (31" a ' x 3 "W
© 2 O x”)' (X’b“‘)(>€%‘} W“ M
D.'—1 7' .
E. undeﬁned ﬂ; 2
3;:
, 74)
Gyms] ”'5 y” we 3
3313.100 “+83%: & :2 W
A. 1 7' X
B 1+e3 oa  2<
....— _ 93
,. 3 0:0 £1 —: gw‘ T?
83 5‘0 £04 y xx} (’7’
X400
E. +00 7‘ ”#3,. ~94
=' 40W 453" 7" as ”aw
x400 6’1“ «544
‘ ‘CQ
0f“) Sméﬂg‘g‘u 2% x
.... ' ’56 63»
we“? ":57“
. :a "3
~64 8&7 3 Q43? 8 Page 2 of 11 ' NAME: STUDENT NO: Suppose that y = f (5:) satisﬁes the following:
'1) ﬁx) is increasing for all values of m
ii) as 93 > +00 ﬁx) —> 1—
as a: *4 —oo f(93) —> —1+
iii) f” (:13) is deﬁned and continuous for all values of a: . Which of the following statements is false? , ct ' A “if
s qua W“ L!
. ' 0 xx“? 5'me l ﬁaﬁﬁﬁ
A. f(:c) = 0 for exactly one value of a: * T2:E,h£: PL” all ‘é‘o 4 l‘) (”fay WWWWWWWJ' '
B. f’(:c) 2 0 for all values of a: W True, Ml) ‘lmormﬁv ”1"
they: WM M) says. C. f has exactly two horizontal asymptotes  Trueu "d be, bananae/ u
D. f has at least one inﬂection point  Irate. — f ‘44“ {w éﬁc‘m ‘
new , (70 $14me crwrctmm f could hav a Vertical tangent W 4» DD
tip I} cant (3' 14.5.6} ’P”  ‘ —D( eo‘élﬂﬂ 4. [4 marks] .
If flT) 3/ V 1 +t3dt then f’(2) =
o e 3 Pix)?“ 4/??? B. 2
C. 1 9(1)? UT??? £7?
D. 0
E. —1 Page 3 of 11 NAME: 5. [4 marks] 2
2
/ ace—w dm=
1 6. [4 marks] STUDENT N 0: L155” M?" >4 (2’ Jaw lex Z« The demand equation for a product is p x (q— (3)2 and the supply equation is p = q2 —q+3 . The consumers’ surplus under market equilibrium is A. ~36
B. 12
C 108
D 54 Page 4 of 11 NAME: __ STUDENT NO: 7. [4marks] I 187, Far$.51” J AX
[(111 :6)2 d3: is equal to '. 70613 $4 >45 > v” a C19 mlnzc(1nm——2)+2x+0 ' ' ‘  7‘
B. (1nm)3/3+C C. 2am1M+0 ‘ 53': Xﬁ£4xwﬁmﬂ Qfgaxé’tx D. 2 1 +0 ,
2:51:13 avg/gm?!
E‘ +0 40/930,119. “4% m ' x 8. [4mark3]
HA dB 1 b htht— + B —x+2f 11 htht 27%
an arerea Hum BISSUC a 1;“: 53+1mm2—1 01'8; CL' SUC a {I} ,
thenAﬂ
5
A. 5 A(%ﬂ)*Béc ..Qy)¢+2, c3
1 3””
B' ‘5 :9 >674, 1A‘33 WA A z.
@ §
2 (W 1:, M,
D 1 car CA+5>><*
: W
E. —§ Afﬁal.
"LA ; :5
A.» 2;, Page 5 of 11 NAME: STUDENT NO:  [4 marks] Cash ﬂows into an account at a constant rate of 365 dollars per year, beginning now. If the
account earns interest at 5% compounded continuously, then in 10 years it will have 10 44(1ch 16)
A. $4671.55 FV .—. 3: 56,58 <9 0H? $4735.67 0 so 6
, { rm of
0. $4590.93 g 39512, y 6 0(‘5'
O
D. $4925.36 6
1
E. $4462.08 .6’ 6’
4 365” 63 64.0?
""' I O? ‘— f
= 7305’ 10. [4 marks] The average value of f (9:) = 2‘” on the interval [01 2] is A. 1.44 2»
B 0 .i— Qxﬁx
. 1.5 ..
7. 0 0
@ 2.16 2c ‘1
D 250 ‘7 l .2“—
2 6M: 0
E 2.88
i (4’!) 3 .34.» ’3"! Q'H’Lf —
" 9349. 17.3141 Page 6 of 11 NAME: _'__ STUDENT NO:
PART B. WrittenwAnswer Questions xi“; 0 anA )6 LA W .
EMLEL diagram“ away here} [4] (1)) Given that f’a: (a: )= relative extrema. 3” — 2 2
[3] (0) Given that f”(:c) = 3% ﬁnd when f is concave upwards and downwards and ﬁnd all inﬂection points.
6’ “P” >0 wLwewév rt (as ﬁfe«fwd; age. ervé LJ Eagwqgj
Ln ca ‘ ’ This question continues on Page 8 Page 7 of 11 NAME: STUDENT NO: [513101)
Draw a clear sketch of y 2 ﬂat) on the axes below. Page 8 of 11 2. [14 marks] For a, manufacturer to produce (1 units of a product, the average cost is 19g 400
++— [9] ( a) If production 15 limited to at most 20 units ﬁnd the number of units to be produced to
minimize the total cost. ﬂiﬁjgfgéﬂi ti?” é)'lflffwf(aOfr’1‘00 Cagegoa 01W 50 , 1 MM
COOS) ’53 23. .‘f E}! was
c620)? 4” [5] (b) If production is limited to at most 14 units ﬁnd the number of units to be produced to
minimize the total cost. u; a .., “gem:
Swot—Luci? [5 «Km, Saw(2 a” C i in E the L e 1‘: owl? Ea, WE Page 9 of 11 NAME: STUDENT NO: 3. [15 marks] Find the total area, of all region(s) in the my —plane which are bounded by the graph of y = 53
and the lines 33 m 4 and y = 233 + 3 . A rough sketch may be useful. 2 Page 10 of 11 NAME: STUDENT NO: ['7] (b) Find the following integral or Show that it diverges 1 l M “Wt
[mafimi 6M» f (rm) 34x Page 11 of 11 ...
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