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Unformatted text preview: ~ Sat/2X
Department of Mathematics
University of Toronto WEDNESDAY, December 6, 2006 6: 108: 00 PM
. MAT 133Y TERM TEST #2 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: T.A.’S NAME: —ﬁ—_m T0101A TOBOID BF 323
T0101B T0601A MP 137
TOlOlC TOGOIB RW 143
TOZOIA T0701A MP 137
T0201B T07OIB $81087
TO201C T07OIC LM 162
TOZOID T0801A 881083 FOR MARKER ONLY
Multiple Choice
  T0301A TOSOIB 881073
T0301B T5101A 881069
T0401A T5101B 882108
T0401B T5201A 882110
T0501A
T0501B
T0501C Page 1 of 11 NAME: 1. [4 marks] mZ—l 50—1 lim
m—>1 (4a: 2 A. equals ——2
B. equals 1
C. equals 2
D. equals 0 E. does not exist 2. [4 marks] lim 2:02 ——6x _
md—Ooxz—llivl—3 _. A. +00
B. 1
C. ——2
D. 2
E. 00 STUDENT NO: PART A. Multiple Choice g”; Luv26m) é“
— qu 3"! Ya,
= ﬂ... 2.. = 2/ X‘a' x+l 1‘“ Page 2 of 11 NAME: ______________________________ STUDENT NO: 3. [4 marks] If $500 grows to $1,000 in 8 years then interest must be compounded continuously at an
annual rate that is closest to ' A. 7.72% 3( B. 6.25% 1000 a: {006 C. 8.66% 44,2. : 6F _
D. 9.13% . 3 ,L Zn?— ,1: .0395
E. 9.05% 6' 4. [4 marks]
The function given by f (:16) = la; _ 2 on the interval 0 S x < 4 has A. no absolute extrema B. one absolute=minimum but no absolute maximum
C. one absolute maximum but no absolute minimum
D. one absolute maximum and one absolute minimum E. two absol te maxima and one absolute minimum Page 3 of 11 NAME: ______________________________ STUDENT NO: 5. [4 marks]
I _ f(as) = a when :13: O
6“”b when an < 0 If f is continuous at a: = 0 then A. a=1n2andb=0 é,” (36¢): 2%It ,1th 1 “li B. a=1 and b=1 x—)O+
1  H
C. a=~andb=2
‘ 2 b Coat
D. a=2 and (72% \I £0)
E.a=%andb=1n2 H at:
$5360 ‘ 6
x—W’ 6. [4 marks] .
If y = (Ex/4:3 + 3, then the tangent line to the curve y = f (as) is horizontal . V‘tx’r3 ‘H"
B. a =0, :0
W 3y 7': 2m I
D. ata:=1,y=\/’7 “.1 bX‘P
1 7 “7:33. A. never Page 4 of 11 NAME: STUDENT NO: 7. [4 marks]
Find all A , for which y = 6)“ satisﬁes the equation 1A. [Arz—Z only 7.: ()6qu _ _ ’1 )4
B.>\—1and)\—4 yutae
C. A=——2 and A=~4
D. A=0 only U 6 '+?
E. There is no such A 7 4‘ Y 7 “X : <1X‘:rb(>\+8)e 7’ o J‘uo so an. A «r? =>~ 8. [4 marks]
If h(a;) = g(f(x)) and u = f(a:) , then h”(ac) = A.
B. I/ (u) ' f’(w) + we > (f”(x))2
W) M >+g<u> f”(w)
g"<u> f (x) ' '
D we) (f (ea) +g'<u> f”(w)
E 9%) WW . (x) , 9%)
‘n (x): j Eigggj? (09%)!) + 3 (963) ‘ h" (>3 3 $0 ® 9
9 Page 5 of 11 NAME: ______________________________' STUDENT NO: 9. [4 marks] The derivative of
f(x) = (2x2 — 3x + EMF7+6“ _ is equal to A. (2:132 —— 311: + 5) “0 —1+em '1n(2m2 — 33: + 5) B. (2:132_.__3‘,L,_+_5)Veg—1+5?J (( (I? + 6m)1n(2332 __ 311} + 5) +( /$2 _1+ 69:) 413 " 3 ) «52—31 2:172 — 333 + 5
C. («iii—1 + a”) 1n(2932 —— 32: + 5)(2:1:2 — 3x + 5)«/'£TZT+ew
D. (251:2 — 3:2: + 5)m+em( $2 — 1 + 6m) (Jag—71 + em)
E. é’é:)1n[f(x)]
3 x +5') 10. [4 marks]
If y(ac) satisﬁes y‘” = my , What is the value of y’(x) when (m,y) = (4, 2) ? ~%+ln4 \/
. 2—1n2
D. “:34“ A6 X441): 3 1 ”£47 +1,
, 111 , 2
E' 2—1:: 31’; + 21" 7 Page 6 of 11 NAME: STUDENT NO: PART B. WrittenAnswer Questions 1. [14 marks]
[’7] (a) Solve the following inequality for a: [7] ( b ) If 7* = 300q2 — q3 is the total revenue when q units are sold then ﬁnd when marginal revenue is positive. MR= .4; ... (:03— 3? d 6.2: C 200’?) Page 7 of 11 NAME: ' STUDENT NO: 2. [18 marks] . In order to sell q metres of photographic ﬁlm per day (where q > 0) the manufacturer must
1 set its price at p(q) = (126— 12 dollars per metre sold. [4] (a) Find the manufacturer’s marginal revenue as a function of q. Olr A (P6,): Ol @58’%) [5] ( b ) Find the relative rate of change of revenue as a function of q . r a:
%%%l% l
1 ’2; " T7.
or a, /.
l»X *
x 1'"; [QUESTION2 CONTINUES ON NEXT PAGE] Page 8 of 11 NAME: ' STUDENT NO: 2.
[6] (c) Find the elasticity of demand as a function of q. 1235‘ [3/ (d) For which q is demand inelastic? Lelash}, Wm \72 l <  2 ¢\ee~~lwé"(5""‘71< I Page 9 of 11 NAME: '  STUDENT NO: 3. [15 marks] [’7] (a) Given that m4 + y4 : 43;, ﬁnd gig in terms of a: and y only. There is no need to d
“simplify” . x 4x3+4/3y1147’ . I ‘ 3
6 )\ ' )q
’., 3 .. l "
. d2
[8] ((2) Gwen that m4 + 314 2 4y, find EEC—g in terms of a: and y only. There is no need to “simplify” .
5'l7Wlﬂj .0,” eke, answer ya wwmw
’ W
, , (\ «— ),3) Page 10 of 11 Y ‘4 NAME: ’ . STUDENT N O: 4. [13 marks] Find a root of
2:5 + 433 +1 = O up>to _6—decimalplace—accuracy using Newton method and x1 = 0 as the initial estimate. Xhn : X“ ‘I' '96“) M
PW»)
:
4— X H
“W
6%“ +4 H
X.
: Page 11 of 11 ...
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