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Unformatted text preview: MATH 13OGMIDTERM # 2(a)2007
< / 6 :3} NAME and I.D.# (Write Clearly} Instructions: This midterm exam consists 0f 4 multipie choice questions and 3 long answer
questiﬂns. The multiple choice questiuns are werth 5 points each, and the long answer
questions are as indicated. The total value of the exam is ﬁll] points. Place your answers to the multiple choice questions in the bases below. All your wurk
us the lung answer questions must he eieariy nmrked. Tau may use the backs of pages. For tong answer questions, YOU MUST SHOW YOUR WORK NO CALCULATORS. NO BOOKS. NO NOTES. If you need additinnal serap paper, it will be prnvided by the proeturs. Answers: Multiple Choice Sectien Questions (14] Question 1 Consider f = 2m3 + 3:}:2  12:1? + 1. For what interval is this function
decreasing? A} [0012} E} {10} DJ {1.3} E} {1.00} Sﬁiul'ﬁiﬂ In iglfeh=éx1+ h'xr 1'1: éﬁti‘e'x—Z} : {ct—1if'1ai2) ﬂ 9:: '2' a“; 3: —oo ‘1 i. “3" Questien 2 Which of the fsiiswmg staternenis is correct for the function ﬁx) = 2:3 + 3r” — 12: + 1 Inn A] There is a local max at :r = — .
B} There is a, local min at. :r : — . 5 Ci {here is an inﬂection point. at :r : — . 1
D} There is an inﬂectien point at s“ = —§.
E} There is an inﬂection point at .'r = 1. Nil4h: Sotuhen
gi‘i'IW: (3 {11+ x l)
ifs}: 6(1)“: l) J EH (1‘): D I: r F a——— —F"— Question 3 Let ﬁr} be ufuncﬂon satisfying f’{:r} = 3r2+41‘—2 and flu] = 2. Find HE}. ng (3)? DJ23 E}4 501mb; CH“ Si1113§fn11911= S (311* ﬁatigalot: x + iﬁ‘ 23+ C. Question 4 Suppose that a. demand functian is given, by p = 2:91. What is the Elasticity (if
demand when 1' = 5'? IS dﬂﬂlﬂﬂd emetic or inelastic? A} —E._ elastic B} —_%_. inelastic C} —%. eiastic
’ D} —1%. ineiastiw “ E) —%. elastic
Sunken
AK 1 : Eh": _ 50 = _.
"1 xf‘m ' (ix—1 .cx ‘5‘3‘ 1 Long Answer Section Questions (5?) Question 5 {14l points) A retail store can sett ‘tﬂ toasters per week at a price of see 3 each. The manager esttmates
that for each It? S rednetton tn price, she can sett two more toasters per week. How many
toasters shonta she sett to maximize revenue? a j White a function for the totat revenue, as a function of the number of toasters sets].
t1) How many toasters shonta’ she sett to maximise retrenne‘?r
e} What pn'ee per toaster maximizes the revenue? ct} Be sure to esptatn why your answer is an absatute maximum. 501s.”an [0 REL}: 'X. fo‘}.1 —’ba 210 0
two 41 _i'+‘1 ﬁx? D '3 = ‘50 =_5_ =3 :1 _ U [300 1‘10 ite ‘XrtIo £1141”; 1‘30: Soar —5:~r_ D: goo‘S'xﬂ' Rm: goon  5 m1 a ranges +102: o, 1= 50' Nah—10 as RVsm to 1l TLffERQrQ‘ a} '1': 501 R [0'01 ’Wﬂx, M 50 ex “"13 s em elm as It Question 6 (12 paints] Evaluate the foﬂowing indeﬁnite inteymis: m‘2 : —d‘
I umg—IEI
.41 I “1+1
l '4'  7. l
I: "“ﬁfLL=—SLLcJLL=———r—‘LL
Em 3 5 5 .
3 _ 'i‘”
H: 1”?
0L“: LL. dart: 32:12:95: '
1
“(dartI
5"“
'5 “1
:E(1,l53 4? C.
3
1—163
I= IVE
_ _L “1 ‘L
1: %Qx 1.1 1139: : 81 do: — SKIATE
L+l "i"
1 z I ‘1
= x ‘ “K + C
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3: A.
1?: 12 — 2 111 1 C Question T (14 points] Consider the funetien: s+2
ftrl=$_3 Find the domain of the funetisn. Find ett e and y intercepts. Find the intemets a increase
and decrease. Find nit critical! points and determine their type. Find ntt inﬂection paints and
usymptetes. Detennine the heheeier of the function near the vertieet nsynnptetes. On the
fettewing page, graph the funetisn. inesrpsrntiny hit! of this infsmtetian. .nlﬂ : SELF—h} ~ffla1=eESI {GI—.123.) ~l Metre1 new. red2' (4—H?) n ﬁlﬂf}: ﬂji42‘ = _ “ti—E MP (4512' Ne (UP, me Here 11' ﬂu: ‘K.S.H«. £Yﬂ=e ...
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 Fall '09
 PIETERHOFSTRA

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