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Unformatted text preview: MATH 1300—MIDTERM # 12009 NAME and I.D.# Instructions: This midterm exam consists of 4 multiple choice questions and 3 long an
swer questions. The multiple choice questions are worth 5 points each, and the long answer
questions are as indicated. The total value of the exam is 60 points. Place your answers to the multiple choice questions in the boxes below. All your work on
the long answer questions must be clearly marked. You may use the backs of pages. For long answer questions, YOU MUST SHOW YOUR WORK NO CALCULATORS. NO BOOKS. NO NOTES. If you need additional scrap paper, it will be provided by the proctors. Answers:
#1 #2 #3 #4 Multiple Choice Section Questions (14) Question 1 Calculate: , x3 w 27
11m
w—>3 a:  3 A) 9 B) 18 C) 27 D) 36, E) The limit does not exist.
f“
1
$15: ._ @3>(x + 3 x +3) 5. 3
U“ "é—Z—s = UM. x1+$x+5 = “guyss29
3:093 * 3""3 Question 2 Find the equation of the tangent line of the function f(9:) = (2m + 1)\/3a: + 1 atle. A)y=2—:”f% B)y=%+§ C)y=""7’7“”:E D)y=§+—§ E)y=—2—3—€§
________.__. ' ‘5 \— CZ~+D—\—7—<r3 “4" 2 3x?‘ t \r— 2 :5. ,. 2: __ 2" “I __ ZS : .—
__ .. 2S» \
~> ‘3’ 1'; "71' ‘ Question 3 Use implicit differentiation to ﬁnd % at the point (2,1) for the equation: 5323/ + 2353/2 = 8 A) B) CHIN) % C)§ D)? E)” [31’ 4— LySZJ' ; [91' ,3 (2x5+ X’lj\)+ (231+ C(x33‘):¢
9:) 2~Z\+ 115‘ 4— 7.414» kLLU‘ = o \ ‘...¢
:7 H+R5+ 2+— 93 a L _!
w." a Question 4 Find the inverse of the function: 2 __
ﬁx): 5+31 A) ~3m~1 B 230—3 323—1 —3w—1 2m—1 23—3 2m+3 3m+1 k: 1B)" 6) XLojk3>= 1‘7—( :5) ka3X =23i’
a) X3~Zj :“J’b‘
'7 (3(xz>=—\ —3k _\3
=7 ‘7:— x“; Long Answer Section Questions (57) Question 5 (12 points) Using only the deﬁnition of derivative as a limit, calculate f’
where = (3 — 2x)2
l‘é‘): LL... W e um 340+“)? —($Zx)1
Ax Ax Axe’0 Aw“? 9' 2.
NM: (’5 — 2(k&4x))1: 3 [2(xk4x)+ quAx)
°>—(‘lx r24“. qf’a—C’xAxv— “(@301 :5 “A (7,»2x)z= ‘>12x+‘(x2 Z Q. (3.,uu4x))2(av2x) s 2 (24xl— QKAA: 4 ’4(Ax) 9., LL,~ (CmTl hams . 9 2. «(4x31
like. Av')b I“
_ Um ~11+9x+RAx = (2+9x
~ Ayn—>6 gar Mij‘Ion ' for in, I
(4949 H CquLJ'ﬁ“, Cgr! (AL—~14) Question 6 (14 points) Suppose that a deposit of 3, 000 $ is made into a bank that gives
5% interest. Suppose that interest is compounded 6 times per year. (a) {2 points) Write a formula for A(t), the value of the investment, after t years in this
case. (b) (4 points) How much will the investment be worth after 3 years? (c) ( 8 points) How long will it take for the investment to triple? Co.) AG): (‘4’ a: )Wt wkkk tilCams
> T? ' 0+ 0.25.3616 (1 94 {u [/dwvvak \ L “Mada
, 77,000 64' e EM ; '4) T)L¢~ 2A~ ('3'; z Pvt CW5... Cthcl
7 0.05. ‘g gilm‘QA’ 91 &‘r
A (3) = 72000 (l + 7— s...k(i£w(—S~5 ) 5mgzmlw 4; —_ a,”
:7 3 ’— ((+04?>H
,7 IKE  é*'{“(‘*°;'? *‘ 3f“
‘n. ’7
,7 e a l, was?) 3*" — 74‘s Question 7 (14 points) 0 (8 points) A business sells 5,000 radios per month at a price of 300 dollars each. It
is estimated that monthly sales will increase by a level of 50 units for each 2 dollar
decrease in price. Find the demand function, as well as the revenue function. 0 ( 6 points) Suppose another business makes burglar alarms. Suppose that there is a
initial ﬁxed cost of 25,000 dollars. Suppose each alarm costs 90 dollars to make and
that the manufacturer has set a price of 150 dollars per alarm. Write down a proﬁt
and cost function, and determine the breakeuen point. DUMMA fuelZ.“ _._ 'DQQ (Lemar,
99¢, 'Hhraw)k (4)00 ' ‘3' 09¢) Mex (360 —Z ' S'coa + 4‘9) :
5 (239‘ 939:) “Wm M: X; a 6. " ’2'?
9. I): «3’; 4, (7L5 1“ (3.15m)
3.. , ‘3‘ 4. z  in + L ,3 l»: 51°
C) ‘7: “f; + 990
;_~ Koo _—. 7:900: xf = ;;+$'oox
C00; 7,5,0” + 90x gr:L;E::h
(KG): [90* (Z; . 75mm 9)
"7 @QO :2 RCx)~CQ<) = 60x ZS‘.°°° *3 12%? “has. Bonus Question (1 point): Name the two historical ﬁgures who can both claim to have
invented calculus. (\[wlm p [Aware Space for additional work ...
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This note was uploaded on 10/24/2010 for the course MAT mat 1300 taught by Professor Blute during the Fall '10 term at University of Ottawa.
 Fall '10
 blute

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