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Unformatted text preview: 652 (Ufa/f Department of Mathematics
University of Toronto MONDAY, December 1, 2008 6:108:00 PM
MAT 133Y TERM TEST #2 Calculus and Linear Algebra for Commerce
Duration: 1 hour 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 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 writtenanswer questions. I 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 writtenanswer question is indicated beside it,
ENCLOSE YOUR FINAL ANSWER IN A BOX AND WHITE IT IN INK. TOTAL MARKS: 100
FAMILY NAME: GIVEN NAME: STUDENT N O: SIGNATURE: TUTORIAL TIME and ROOM:
REGCODE and TIMECODE: T.A.’S NAME: m mecode m
TOlOIA MQA 581074 T0501D WSD BA2139
TOIOIB MQB 382105 T0601A R4A LM 157
T0101C M90 SS2111 TOGOIB R413 LM 123
T010113 MQD LM 158 TOTOlA F2A RW 229
TUZDiA MSA T0701B F2B 882111
T020113 M313 TO7OIC F20 352128
TUZUIC M3C TOSOlA FBA LM 155
T0201D M313 TOSOIB F313 LM 123 FOR MARKER ONLY
Multiple Choice
1 TOBOIA TSA T5101A M5A MP 134
T030113 T3B T510113 M513 882111 TD40lA WQA ss1074 T5101C! M50 MP 118
T040113 WQB 881086 T5101D MED RW 143
T0401c WQC LM 15s T5201A MSA LM 162
TOBOIA W3A 832105 '
T050113 WSB M82173 T0501C W3C U0 256 Page 1 of 10 NAME: STUDENT NO: PART A. Multiple Choice 1. [4 maTks] ‘ V
. 293%693—8 d: 2mm; @1696)“; 5"
11m —— _ _—»~—' C Wm
m—4—1 932—1 xa«g (:x—Q/xg
A. is 2
B. is 0 is 5
D. is 1 E. does not exist 2. [4marks] ‘ 3/6! 4;; W5) J§§+g 3;“)
lim W xx _ g 3‘: ‘ °° WW 0
‘ . “W a J 2 X x ‘ Q“? B. 0 C ‘1 “:1 M 1:. a.
D. 1 ﬂy} a E +00 Page 2 of 10 NAME: STUDENT NO: ma?" 3 ‘ " Kw .
3' M Z (1*Qy} m?” Q WC; 4. [4 marks]
All solutions of the inequality areg'ivenby A. a:<——1 or m>ln2
B. —1<m§1n2 C. —1<1U<0 01" len2 :;:1:<——1 0r x21n2 E. m<—1 0r 0<m$ln2 Page 3 of 10 ‘ NAME: 5. [4marks]
i m m ._
dm x2+16 _ I m3—$2+m+.1 m
I (x2+1)2 e
‘ x3+532+mu1
B. _________ a:
(m2+1)2 e
m3—m2—az+1
C. a:
(2:2+1)2 e
D 3:343:2—5511633
' (a:2+1)2
E 3:3—x2+:z:—1 m
.' (2122+1)2 ‘3
6. [4ma7‘ks] STUDENT NO: "gﬁwe?+ a”é§£Q;::£: (gar: 1/53“ x’ﬁi
(ysz 1‘}
in 5’}: Ex?“ Egg
6% 97H} A (4 ~— m)2(:c + ALP/2 Let “33) ﬂ (m+1)(2—x)(3x+6)
Then f1?) 2 g f 2 at sag7»??? 4' ii £4 (x+%)’ £16.34“)
_3 a1 Tm “*' i  {9.
B H  4% Hum" £91633”, ) )
' 3 . if (a.
C. M: “ ﬁﬁggﬂi‘ ‘5‘ 30‘4 wa
8
D. —
3 7 g, ..L ... i «i» «L “41
E .1_1 y'ﬂﬁm pa’” %+3 2“
' 8
.w w};
d. 9&3} f) 4L W E?
aﬁgﬂﬁiﬁiﬁfﬂﬁ Page 4 of 10 NAME: STUDENT NO: 7. [4 marks]
Let
y=':37+1)$2—1 . 9
Then y’ 2 : (X14) 164 5X“? g
A. 2:1:(3: + l)(3:2 —— 1) g [1 ﬁx ..
B. (m2—1)(x+1)$2“2 . 7 ? c. m2—1( ' (cc +1) 2m 111m + 1) + (m — 1)) 8. [4 marks] Let 2m3+533y+y3 =8
Thenwhen 3:21 and 11:1, y’:  at»
69”]? ‘ 3",. j¢§xy°+5¥§f “Q {ﬁg «t 5’ B —1—1— E
. 6 g
/ (.533; 9 1% ﬁrm
C 0 (94‘g4’gr? {a g H:
D ___1%_ gx ﬂ w 8 M3 #39::
E “‘11” f % Page 5 of 10 NAME: STUDENT NO: 9. [4 marks]
The point elasticity of the demand equation (1 = p2 — 10p + 50 when p = 3 is
3
A. 11—6
12
29
3
C. _m
. 6
D. E
6
E. wig 10. [4 marks]
64 If a company can produce q(m) = 2m + —— units when it has m > 5 employees and must
m
. . 48 . '. . . set Its price p at p = E to sell all (1 units, What IS its marginal revenue product 0!
( d—T , Where r denotes revenue) when m = 16 ? m . 12 i ‘ﬁ
EWW
Mg dﬁwﬁﬁwﬁ°2¢T§ % Page 6 of 16 NAME: _ STUDENT NO:
PART B. WrittenAnswer Questions 1. [15 marks] Given a: +3:
1 ﬁre:
A
a: = 1—: m
H) ————?—1— if0<azgl
2+‘2m
£+3—2 if m>1.
33—1 Determine whether f is continuous at each of the values of :1: below. Show all steps and state dearly Why f is or is not continuous. [8](a) 55:0 gfﬁﬂwﬁ swig. W4: 5:} em as wwé WWWHWL swig“ sum” W??? X'PE f
ﬁ “emB 0” “7% 3 sea g 62 3; {9 (3
gearsf: §ﬁﬁg “‘3 Q :ﬂ’Jm kyﬁ n “g? mg W a
s” "2“ w”? W ‘ w “E w “3’ we 52
Q 4%" E gameg " ‘ 7 of 10 NAME: ‘ ' STUDENT NO: 2. [15 marks] ‘ wrymwmm'ww" “1?; em 1
[57 (b) Find the equation of the tangent line: to the graph of y’ at the point (3, [Note: the graph of y’ , not the graph of y] N Wkﬁe "ﬂ 34: Eye Page 8 of 10 NAME: . __ STUDENT NO: 3. [15 marks] Find the equation of the line in the my éplane which goes through the origin and is tangent
to the graph of y = 6m . Show your work. Page 9 of 10 NAME: STUDENT NO: 4. [15 marks] Use Newton’s method to ﬁnd (to one place after the decimal point) a value of a: so that
f’(x) : 0 where 4 sg——x2—5cc+1 f(a=)=e (Begin with the value $0 = 2 and go as far as calculating 332 before you decide on your answer. Note that f itself is never zero. in
35?. _,_ x Evy5'an ! 9%) 7‘“ (X3W1X’5V)ﬁ ‘1 v a Page 10 of 10 ...
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