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Unformatted text preview: ﬁﬁi 15’ Q6; Department of Mathematics
University of Toronto WEDNESDAY, MARCH 8, 2006 6:108:00 PM
MAT 133Y TERM TEST #3 Calculus and Linear Algebra for Commerce
Duration: 1 hour and 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 ﬁli
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 writtenanswer 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: TGIOEA TUSOID UCA101
T010113 ' TOSOIA LM 123
TDIOIC T060113 LM 157
T0201A T0701A LM 157
T02DIB ‘ TOTOIB MP 118
T112010 TOTOIC 831084
TOQOED TOSOIA MP 118 FOR MARKER ONLY
Multiple Choice T0301A TOSOIB WI 523
T030113 T5101A LM 155
TG4DIA T5101B WI 523
T0401B T5201A LM 123
T050113;
TDSOIB
T135010 Page 1 of 11 NAME: STUDENT NO:
PART A. Multiple Choice 1. [4 marks]
If 23 + y = 10, then the largest possible value of my is A. non—existent; there is no largest value. )5? 1 P
B. 16
C. 21
25
E. 30
2. [4 marks] If my 2 10 , Where a: and y are 2 0, then the largest possible value of a: + y is
c. Six/10 ’0’}, X D. 25 6" non—existent; there is no largest value. Page 2 of 11 NAME: STUDENT NO: 3. [4 marks] The demand function for a pro duct is p = 242 — 3g and the average cost function is E : q + 2 + E . What price (to the nearest dollar) should be charged in order to maximize
Q proﬁt ‘? 6000000436 1' — 3
$3210 10, 0003:4 A. 400 Jo “'
4. [4 marks] . 30 X gov; lW; Page 3 of 11 NAME: STUDENT NO: 5. [4 marks] 1
iﬂ(3$+5)w (3x~r§’)“"% 3/6 A. does not exist I 6. [4 marks] 00
$1320 (1+ Hm j, >
A. :0 7: (W 3%“ B. =1 m . X)&(\*%3<) Page 4 of 11 NAME: 7. [4 marks] STUDENT NO: The area of the region bounded by the :c axis, the verticai lines x m 1 and x r 4, and the 8. [4 marks] 0 1
km
I
B
C. 3
D 4
E 5 d3: : Page 5 of 11 M:;,wx
dim” (”ﬁx
E § M
m&
qq {rig/l «— O.
_, a ““4" 7?
L’ l
(9r aimed/15W 1
ﬁr O
2014);)
Ll “L
L
I , 637’ NAME: STUDENT NO: 9. [4 markaj
If the trapezoidal rule, with n = 3 , is used to estimate the value of
f4 m dt
1
then the result, T3, is closest to X 0 >0 5m, 3‘3 A If: 5
A. 26.1 a 1 :5 H
@ 13.0
C 8.7
D 4.5
E 1.5 10. [4 marks]
If ﬁx) =/ \/u2 +1 du, then JUNE) 2
J3: Page 6 of 11 NAME: STUDENT NO:
PART B. Written—Answer Questions 1. [16 marks] 1113:
G1 en the function m = —
V f( ) l. QWW ﬂ (”@ij
1 w l * i'
and it’s derivatives f’(:c) = {Lana if)“ {f
, 21ml: — 3
and f” (3;) m $3 (a) [3 marks]
ﬁnd the asymptotes Ljustifyingw yom answers
W 62%.we ' A; Xvi 0"” Jew? (b) [3 marks]
ﬁnd the intervals where the function is increasing and decreasing and all relative extrema {ii/1:306 Page 7 of 11 NAME: STUDENT N O: 1. (c) [3 marks]
ﬁnd the intervals Where the function is concave up and down and ail inﬂection points 3/1
[F If (d) [7 marks]
draw a sketch of the graph of y 2 ﬁgs) . Page 8 of 11 NAME: STUDENT NO: 2. [14 marks]
A rectangular wooden crate with two square sides (not the top or the bottom) is to be
constructed out of two qualities of wood. The sides and the top are to be made of wood that
costs .01 cents/cm 2 ; the bottom is to be made of wood that costs .02 cents/cm 2 If the
crate is to hold 274,000 cm 3 , what should be its dimensions to minimize the cost? Page 9 of 11 NAME: STUDENT NO: 3. [15 marks]
In each part—question, ﬁnd y(:z:) which satisﬁes the given conditions 2
[71 (a) 53—: : “1”") with 9(6) 2 1 . 7‘ 3%??? Page 10 of 11 NAME: STUDENT NO: 4. [15 marks] X ”a,“ '3
Find the following intergrals: X, 3W»
ﬂ XKBX
d .
[5/ (a) f a; _ 3 a mag; Page 110f11 ...
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