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Unformatted text preview: SOlVgﬂl Department of Mathematics
University of Toronto THURSDAY, DECEMBER 15, 2005 9:0011:00 AM
MAT 133Y TERM TEST #2 Calculus and Linear Algebra for Commerce
Duration: 2 hours 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 10
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 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 written—answer questions, present your
solutions in the space provided. The value of each written—answer question is indicated beside it. ENCLOSE YOUR FINAL ANSWER TN A 130x AND WHITE IT IN INK.
TOTAL MARKS: 100 FAMILY NAME: GIVEN NAME: STUDENT NO: SIGNATURE: TUTORIAL TIME and ROOM: REGCODE and TIMECODE: T.A.’S NAME: T0101A T0501D
T010113 TOGOlA
’1‘01010 ‘ T0601B
To201A ' T0701A
T020113 882128 T0701B
T0201o W1524 T0701C
T0201D  UC 52 T0801A
T0301A U0 8? Tos0113
T0301B UC 256 T5101A
T0401A LM 123 T510113
T04oiB LM 157 5 T5201A
T0501A UC 244 T050113 Uo 32s T0501C UO s2 Page 1 of 10 NAME: STUDENT NO: PART A. Multiple Choice 1. [4 marks] If
lim W is 3M, MGM) VXil. 4, 2
a2~>2 ﬂ—Z—2 ){f91 I? A. 0:13 W1 47/
.4 2:: b, [X(EKX”§’Z +2)
C. *4 KW}; U 2. [4 marks] 332(cc+ 1) If S 0 then :17 is in Page 2 of 10 NAME: STUDENT NO: 3. [4 marks]
If $10,000 is deposited in a savings account that earns interest at an annual rate of 5%
compounded continuously? the value of the account after four years will be closest to: A. $12,000 , 05’“ 4
.012,214 Pt: IojooOQ/ C. $12,137 ' D. $11,846 E. $13,515 Page 3 of 10 NAME: STUDENT NO: 5. [4 marks] If the function ﬂat) is differentiable at all real :1: , then 111112 2
32—} {L' W 6. [4 marks]
Let u and '0 denote functions Whose values and derivatives et cc 2 1,2, and 3 are given
below.
u(1) : 2 u(2) : 3 15(3): 1 v(1) w 3 “0(2) — 1 v( ): 2
u’(1) : 4, u’(2) : 8 113(3): 16 v’(1): 16 M2) — 8 M3) : 2
If w(:L x v u(m)) , then w’(2) = Page 4 of 10 NAME: STUDENT N0: 7. [4 maTks]
Which one of the following is true for the demand equation given by pg : 200 ? It has unit elasticity for all p > 0, q > 0. B. It is elastic for all p > 0, q > U. C. It is inelastic for all p > 0, q > 0. D. It is elastic for only some of the values p and q where p > 0, q > 0. E. It is inelastic for only some of the values p and q Where p > 0, q > U . :Z/QQ, ﬁthog’ 8. [4 marks]
If Newton’s Method is used to estimate a root of the equation anew—3:0 and the ﬁrst approximation, 331 , is taken to be 1 , then £133 is closest to A. 2.46182 P
X3141 7' Xn ‘” WES—Zn“
B. 2.58138 "Flt ')
”Kim
C. 3
.. Lg 3
2.32075 ,1... X ’1‘!‘ "
Xm*i ":1. Xﬁ “if/”1%
E. 1.87559 434,12» .... 2
fit—i Page 5 of 10 NAME: 9. [4 marks]
If f(m) 21113:, then f(30)(a:) :
—(28)(27)(26) ‘ ' ' (3) (2) A. 29 B. (28)(27)(2§g   (3x2)
—(29)(28)$g:)  .  (3M2) E —(30)(29)(23E3)    (30(2) 10. [4 maTkS]
If ﬁx) I 3325MB , then f’(2) A. 726 H B. 727
G. 271n2 D. 21n2+g @ 28(1n2 + E) guir .Ek1):: 2 STUDENT NO: '«__,L if; ”L.
9W «P Xq.
{mﬁa XML~3a
:5 x"!
gﬁ14,3t2
X5]
WLQW‘GO
" X“
7.9
W(“’)
>635”
'2"?
\pw't ("’9 ’“I Page 6 of 10 NAME: STUDENT NO: PART B. WrittenAnswer Questions 1. [15 marks] Let 1 a$+—, wg—l a:
cc+\/a:+1, w1<r<3
Hit):
5, m:
2$2_$_4 >3
, a:
0+3$2 (a) [8 marks]
Find real numbers a b c such that f is continuous everywhere. Mame) em 42a): “Wm“ 36M]? ta... 1\ ﬁn ﬁiﬂPCJ ﬂay—4:99!) Mad At X¢3 j ZML‘CE‘)‘; 3’22!“ $6933 5% Qt) Xaﬁ*  , 4f &%
Nata: X73¢3 ZQ+3XZ 70 9” $6 vatwea C 0 942 V1 C9 PMWLWS Po 0* ‘96“)
(b) [’7 marks] For What real values of a,b and 0 do 11m f($) and 11m ﬂag) exist, and What are these
cut—>00 :c>—oo limits? Page 7 of 10 NAME: STUDENT NO: 2. [1’7 marks] The Acme Nail Manufacturing Company ﬁnds it can sell g kilograms of nails per week
provided it sets its selling price at (17% dollars per kilogram. [4] (a) Find Acme’s marginal revenue. :er rutv} l‘ [5] (c) If Acme had m employees, they could produce q(m) kilograms of nails per week.
Currently, m : 64, q : 125, and marginal revenue product is 0.4 dollars per week per employee. Find the current value of d—q . (Recall that marginal revenue product is
m
dr 3— , where 7“ denotes revenue.)
m [5] ((1) Find Acme’s approximate total weekly output of nails if they decide to increase their
workforce from 64 to 70. N 35W! ‘3 3x9 [p MﬂyéS‘C/WM QQ‘ ‘&?0, Page 8 of 10 NAME: STUDENT NO: 3. [15 marks]
Suppose that y3 : 63””“61’ d
[5] (a) Find _y and Show that it can be written in the form — ah: ah: 1—2y' 2
[5] (E?) Find % in terms of y only. [5] (c) Find the equation of the tangent line to y3 : e3m+69 at the point (—2, 1) . M (4),); (it)? EL. .1, 6:3 7““3': Page 9 of 10 NAME: STUDENT NO: 4. [13 marks] Find the equation of the line that goes through the point (any) : (0,1) and which is also
tangent to the graph of
y : 1112: At what point(s) (:3, y) does this tangent line intersect the graph of y_ — lnm. '7  L «z: m La
@4163) a: foilw‘fi' :Q WMVLL “EM “6mm ELM?
L Latte/M L‘wtg em Page 10 of 10 ...
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