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Course: MAC 2233, Spring 2011
School: University of Florida
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Word Count: 645

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Final MAC2233 A (7 pts) 1. Given y 2 x2 + 3x = 3y 3 , y is given by: 2xy 2 +3 A. 9y 2 2yx2 2xy 2 +3 2xy 2 3 B. 9y 2 +2yx2 2xy 2 +3 C. 9y 2 2yx2 D. 9y 3 +2yx2 2xy 2 +3 E. 9y 2 2y 2 x2 (7 pts) 2. Given h(x) = (4x2 3x ln x)3 , h (1) is equal to: A. 120 B. 80 C. 240 (7 pts) 3. The denite integral A. 11 6 B. - 11 6 2 2 D. 180 E. 360 5x3 6x dx is equal to: 5 C. 6 D. 7 6 E. 0 (7 pts) 4. An...

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Final MAC2233 A (7 pts) 1. Given y 2 x2 + 3x = 3y 3 , y is given by: 2xy 2 +3 A. 9y 2 2yx2 2xy 2 +3 2xy 2 3 B. 9y 2 +2yx2 2xy 2 +3 C. 9y 2 2yx2 D. 9y 3 +2yx2 2xy 2 +3 E. 9y 2 2y 2 x2 (7 pts) 2. Given h(x) = (4x2 3x ln x)3 , h (1) is equal to: A. 120 B. 80 C. 240 (7 pts) 3. The denite integral A. 11 6 B. - 11 6 2 2 D. 180 E. 360 5x3 6x dx is equal to: 5 C. 6 D. 7 6 E. 0 (7 pts) 4. An investor places \$3000 in an account which compounds quarterly at a standard rate of 8%; how long will it take for his investment to double? ln A. 4 ln 1202 years . ln B. 3000600002 years ln 1. D. 4ln 23 years ln E. lnln.2 years 1 02 ln 6000 C. 12,000 ln 1.02 years (7 pts) 5. Given f (x) = 2xex , which of the following statements are true: I. f (x) 0 for all x II. the function is decreasing for x > 1 III. the function is concave upward on (2, +) IV. there is an inection point at x = 2 A. only III B. only II and III C. only II and IV D. only II, III, and IV E. I, II, III, and IV (7 pts) 6. The area of the region completely enclosed by the graphs of f (x) = x2 3x and g (x) = x is given by : A. 1 3 4 B. 3 C. 5 3 D. 2 3 7 E. 3 (7 pts) 7. The maximum value of the function f (x) = x3 2x2 4x + 4 on the interval [0, 3] is given by: A. 1 B. 4 C. 4 D. 6 E. 8 (7 pts) 8. Approximate the area under the graph of g (x) = 4x + 8 over the interval [1, 2] by using a Riemann sum, subdividing [1, 2] into six subintervals of equal length, and choosing the right endpoint of each subinterval as the sample point. The approximation is equal to: A. 20 B. 30 C. 15 D. 24 E. 42 (7 pts) 9. A coee pot in the form of a circular cylinder of radius 4 in is being lled with water at a constant rate. If the water level is rising at a rate of 0.4 in/sec, how fast water is owing into the pot? (Note the volume of a cylinder is given by V = r2 h): A. 5.6 in3 /sec B. 6.4 in3 /sec C. 12.8 in3 /sec D. 4.8 in3 /sec E. 2.4 in3 /sec (7 pts) 10. The average rate of change of the function f (x) = 4x ln x on the interval [1, e] is given by: 4 B. e1 A. 4 C. e4e1 4(e+1) D. e1 E. 4e(e+1) e1 (7 pts) 11. The function g (x) has vertical asymptotes at x = 1 and a horizontal asymptote at y = 2; is concave upward on (, 1) (1, +) and concave downward on (1, 1); and is increasing on (, 1) (1, 0) and decreasing on (0, 1) (1, ). Which of the following is equal to g (x)? 2 A. (x2x1)2 2(x2 +3x+2) B. (x1)(x+1) 2x C. (x1)(x+1) 2 D. x2x 1 3 (7 pts) 12. The equation of the tangent line to the function f (x) = A. y = 5x + 4 B. y = 7x 4 C. y = 4x + 8 2 E. x2x 1 2 x(2x+4) at x = 4 is given by D. y = 3x + 12 E. y = 6x (7 pts) 13. Let x and y be any two positive numbers such that xy = 80; the smallest possible value of the sum 4x + 20y is given by: A. 80 B. 120 C. 160 D. 180 E. 200 (7 pts) 14. Which of the following applications of the chain rule is (are) correct: f (x) d I. dx ln(f (x)) = f (x) d II. dx ef (x) = f (x) ef (x) d III. dx [f (x)]n = n[f (x)]n1 f (x) A. only III B. only II and III C. only I and III D. only I and II E. I, II, and III (7 pts) 15. A calculator manufacturer has an estimated marginal prot given by P (x) = 0.5x + 100 where the units for P (x) are dollars/calculator/month when the production level is x calculators per month. If the xed cost for producing and selling these calculators is \$6,000/month, the maximum monthly prot is: A. \$5,000 B. \$4,000 C. \$6,000 D. \$4,500 E. \$5,500 Solutions: 1. A 13. C 2. C 14. E 3. E 4. A 15. B 5. D 6. B 7. C 8. C 9. B 10. C 11. E 12. B
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University of Florida - MAC - 2233
MAC 2233 Homework Problems2.1:2.2:2.3:2.4:2.5:2.6:111119-31 odd, 63, 67, 7933 odd, 43 - 51 odd, 53, 55, 57, 5917 odd, 23, 27, 37, 45, 65, 67, 717 odd, 17 - 21 odd (do not sketch), 23 - 61 odd, 73 - 79 odd59 odd, 77, 79, 8127 odd (do not
UCSB - ECON - 177
All-Pay Auctions In an all-pay auction, every bidder pays whatthey bid regardless of whether or not they win. Examples:ElectionsAlmost any kind of contest or sports eventResearch and DevelopmentWarsLobbying Since bids are wasted if you dont win,
University of Florida - MAC - 2233
MAC 2233Student GuideSUMMER B 2011INTRODUCTIONCOURSE CONTENT MAC 2233 is the first in the two-semester sequence MAC 2233and MAC 2234 covering the basic calculus. The content of this course is given on a dayby day basis in the lecture outline found o
UCSB - ECON - 177
Model IThe true value of the item being auctioned is v , but v is unknown to allbidders.Each bidder i receives a signal, si , about the true value, which is given bythe sum of the true value v and a random variable ei , which you shouldthink of as a
University of Florida - MAC - 2233
N AMEW ORKSHEET 1M AC 22331. E valuate the limits:JX - 3 x1=9x -9a. L etj(x) = cfw_5~th~ ~ (fi.~3 2( \$-r:S)x =9.L\. .:-lim f cfw_x) = -.l@~'-x-+9lim f cfw_x) = _ _.i&lt;!:._ _5x-+4x- 1x 2- 3x + 2 .2. L etjcfw_x) =F ind the following lim
UCSB - ECON - 177
Model IICommon values can also be modelled as a special case of interdependentvalues.In the interdependent values modelv1 = s1 + s2v2 = s2 + s1where s1 and s2 are private signals of bidders 1 and 2, 0 is the weighta bidder puts on her own signal an
University of Florida - MAC - 3473
University of Florida - MAC - 3473
MAC 3473 - FALL 2010 - EXTRA HOMEWORK PROBLEM 3For the integral2dx21xnd formulas for Ln , Rn , Mn and Tn . Also nd L3 , R3 , M3 , and T3 and the corresponding error and absolule value of the error. For Ln and Rn nd an upper boundfor the absolute va
UCSB - ECON - 177
Common Value AuctionsSo far we have studied auctions for which bidders have private values.In private value auctions each bidder knows how much she values the item,and this value is her private information.Now we will discuss common value auctions.In
University of Florida - MAC - 3473
MAC 3473 - FALL 2007 REVIEW PROBLEMS FOR TEST 11. Find the following indenite integrals.a)d)g)x2 cos(3x) dx3x2 + 2x + 9dx(x + 1)(x2 + 4)dxx + x ln xx tan1 x dxb)dxx 1 4x21 x dx1+ xe)h)c)sin5 (4x) dxf)sec4 (5x) tan(5x) dx4x2 9 dxx
University of Florida - MAC - 3473
MAC 3473 - FALL 2007 REVIEW PROBLEMS FOR TEST 21. Determine whether each of the following integrals is convergent ordivergent. Be sure to show your work and explain your reasoning.a)5dxx(ln x)b)2x14 + 1dx c)x15 x41dx4x1d)0ln x dxx2.
UCSB - ECON - 177
Optimal AuctionsWe wish to analyze the decision of a seller who sets a reserve price whenauctioning o an item to a group of n bidders.Consider a seller who chooses an optimal reserve for a second-price auctionwith one bidder.Clearly the seller who fa
University of Florida - MAC - 3473
MAC 3473 - FALL 2007 REVIEW PROBLEMS FOR TEST 31. For each of the following series, determine whether it is convergentor divergent. State your reasons clearly, naming any test that you use.7 + 14 n7 + 4n9 + 11na)b)c)25/2nn(n2 + 1)3n=1n=1n=
University of Florida - MAC - 3473
UCSB - ECON - 177
SPA 2-bidder with \$25 entry fee Winter 1110090Number people who entered out when they should have stayed out:Percentage of total:0.1580Number people who stayed out when they should have entered:Percentage of total:070Average Revenue:36053.13
University of Florida - MAC - 3473
MAC2313Analytic Geometry and Calculus 3Section 8323Instructor:Joseph Brennan403 Little HallOffice Hourswww.math.ufl.edu/~brennanjbrennanj@ufl.eduT8-9:15 amM R 11-12:15 pmPrerequisites:A grade of C or better in MAC 2312, MAC 2512, or MAC 3473.
University of Florida - MAC - 3473
MAP 2302 Sec-0693Instructor: Souvik BhattacharyaSUMMER A 2011Oce: LIT 477MTWRF period 2Phone: 352-392-0281 316Room: LIT 127E-mail: souvik@u.eduOce hours: MWF period 3Website: http:/www.math.u.edu/souvikText: Fundamentals of Dierential Equations
UCSB - ECON - 177
SPA 2-bidder, Reserve = \$50, Spring11100Average overbid: -11.531390Number of Value Bids 92Percent value bid:0.383380Number of bids within \$1 of value bid: 109Percent bids within \$1 of value bid:0.454270Average Revenue: 35.93791Bids6050403
University of Florida - MAC - 3473
MAC2313Analytic Geometry and Calculus 3Lecturer:Joseph Brennan403 Little HallOffice Hours:Lecture:www.math.ufl.edu/~brennanjbrennanj@ufl.eduMWF 8th period (3:00 3:50 pm)MWF 9th period (4:05 4:55pm)Little 101Teaching Assistant (sorted by sectio
University of Florida - MAC - 3473
MAS 4203Section 8430Spring 2009INSTRUCTOR:Introduction to Number TheoryMWF 4th(10:4011:30)LIT 219Dr. Garvan483 Little Hall392-0281 extn 248email: fgarvan@u.eduHOME-PAGE: http:/www.math.u.edu/fgarvan/numthy/spring2009OFFICE HOURS: Monday, Wedne
UCSB - ECON - 177
SPA 2-bidder Spring 2011Average overbid:100-6.6855Number of value bids:Percent value bid:890.370890Number of bids within \$1 of value bid:Percent bids within \$1 of value bid:80Average Revenue:26.06775Average earnings:194.072570Highest earn
University of Florida - MAC - 3473
MAS 4203Section 3173Spring 2005INSTRUCTOR:Introduction to Number TheoryMWF 5th(11:4512:35)LIT 219Dr. Garvan483 Little Hall392-0281 extn 248email: fgarvan@u.eduHOME-PAGE: http:/www.math.u.edu/frank/numthy/spring2005OFFICE HOURS: Monday, Wednesd
UCSB - ECON - 177
SPA 5-bidder Spring 11Average overbid: -4.111100Number of value bids: 92Percent value bid:0.383390Number of bids within \$1 of value bid: 116Percent bids within \$1 of value bid:0.483380Average Revenue 61.5332470Coefficients Standard ErrorInte
University of Florida - MAC - 3473
pj sl uw r gw l s l w w ww XlX w s x i d ~ I ftthDUfz(t(iQf`vBtegtgs X y l giftgtfHtvtTslu ~ql feb0q%T q l ttfHtvtT s l uft~p q l 2ttfHtvtT sluft~ q l YvtfeHt`tQIl i wx w w rwHFi(ei(0(eitd~IUiu af oB)v Bc fce BnBnBsa u V a u au V
UCSB - ECON - 240A
Econ 204A - Midterm ExamFall 2010This exam is closed book. Most points are given for the correct set-up of a problem and foreconomically insightful interpretations.Problem 1 (50p)Consider a Solow model with general production function Y = F (K , AL)
UCSB - ECON - 240A
Note on Linear Differential EquationsEcon 204A - Prof. Bohn1 We will have to work with differential equations throughout this course. Differential equations and their discrete-time analogs: difference equations are economically interesting because they l
UCSB - ECON - 240A
Note on Linearized Solutions to the Optimal Growth ModelEcon 204A - Prof. Bohn This note reviews the linearized dynamics of the optimal growth model and derives log-linearized solutions. General Problem: Linearization Linearization is a common approach i
UCSB - ECON - 240A
Supplementary Note on the OG ModelEcon 204A - Prof. BohnHere are some comments on Romers exposition and on general OG dynamics. Read Romers Section2.9 carefully as it lays out the individual problem. In Romers Section 2.10, the key equation for thedyn
UCSB - ECON - 240A
Collection of Practice ProblemsEcon 204AHenning Bohn*In previous years, students have often asked me about practice problems in addition to the problemsets. Here is a collection. Some will be assigned for the weekly problem sets. I hope the others are
UCSB - ECON - 240A
(1.Intro)-P.1Econ 204A: Organization Class Page: www.econ.ucsb.edu/~bohn/204A/204Aindex.html- Information is updated throughout the quarter.- Check for announcements. Class page announcements are assumed known. Open door policy for graduate students.
UCSB - ECON - 240A
(2a)-P.1Growth Theory: Broad Outline1. Foundation: The Solow Model. Romer ch.1.- Basic version: Mechanics of production, savings, and capital accumulation.- Take technological progress for granted. Take population growth as given.- Extended versions:
UCSB - ECON - 240A
(2b)-P.1Applications of Growth Theory I:Growth Accounting Objective: Use empirical data on output, capital stocks, and labor supply, to interpret history(accounting), to compare across countries, or to make projections. Data sets: observations (Yt, K
UCSB - ECON - 240A
(2c)-P.1New Growth: The Economics of Ideas(Main reference: Jones ch.4-5.) Neoclassical growth modeling: Focus on capital accumulation New growth theory: Focus on technology, ideas, explaining economic growth &quot;endogenously&quot; rather than assuming a growth
UCSB - ECON - 240A
Optimal Growth in Continuous Time Key assumption: Households maximize utility over consumption- They choose an optimal path of consumption and asset accumulation.- They discount future utility at a fixed rate, called the rate of time preference; symbol
UCSB - ECON - 240A
Standard Optimal Control: The Hamiltonian Approach(3c)-P.1 General approach to control problems (Barro/Sala-i-Martin, Appendix A3).- Presented with key example: Problem of representative household (or social planner):Maximize U = cfw_e0 t(u[C(t )]
UCSB - ECON - 240A
Dynamic Properties of the Optimal Growth ModelI. Graphical Analysis Restate the key differential equations (in effective units for convenience): ! c = 1 (r % n % g % \$ ) = 1 ( f ' (k ) % # % &quot; % !g ) 1. Euler equation: c ! ! ! k = f (k ) &quot; c &quot; (n + g + !
UCSB - ECON - 240A
Digression: Discrete-Time Optimization[For now: As motivation for continuous time. For later: Preview of discrete-time macro.] Consider optimal consumption and capital accumulation problem over T periods:TU = t 1u(ct ) = u(c1 ) + u(c2 ) + . + T 1u(cT
UCSB - ECON - 240A
(204A -3e)-P.1Fiscal Policy:I. Government Spending Assumption: Public spending G per efficiency unit of labor.- Assume spending is tax-financed: T=G, lump-sum. - Here abstract from productivity and population growth (could be added) - Best interpret a
UCSB - ECON - 240A
(3f)-P.1Introduction to Money How does money fit into modern macro models? - Money M = = nominal units issued by the government; p = price level. - Consider discrete periods: Household hold money and interest-bearing assets:ct + at +1 + M t +1 / pt = w
UCSB - ECON - 240A
(4a)-P.1Part 4: Overlapping Generations Models Basic Version: Each birth-cohort lives for two periods, young and old age.- Individuals are identical except for their date of birth =&gt; Each generation has a representative agent.- Young individuals earn
UCSB - ECON - 240A
(4b)-P.1Overlapping Generations &amp; Fiscal Policy Focus on Intergenerational Redistribution and other issues excluded in representative agent models. Assume lump-sum taxes:T1t= per-capita net taxes on the youngT2t+1 = per-capita net taxes on the old.
UCSB - ECON - 240A
(4c)-P.1Overlapping Generations &amp; Dynamic InefficiencyMotivating example: Why inefficiency may be empirically relevant and deserves analysis. Assume log-utility, Cobb-Douglas production, depreciation &gt;0 Steady state:=&gt;rt +1 = f ' (k t +1 ) = k t +1
UCSB - ECON - 240A
Application: Working with the Solow Model Instructions: Results: 1. Set initial steady state: Blue values 1. Steady states = red 2. Set changes: Enter yellow boxes 2. Period-0 values = green [Default = 10% less capital] 3. Transition path = see table and
UCSB - ECON - 240A
UCSB - ECON - 240A
Econ 204A - Final ExamFall 2010This exam is closed book. You have about 120 minutes to answer both questions for a total of100 points. Most points are given for the correct set-up of a problem and for economicallyinsightful interpretations.Problem 1
UCSB - ECON - 208
Economics 208 MacroeconomicsMarek Kapicka Spring 2009Midterm AnswersYou have 75 minutes. This is a closed book/closed notes exam. No cell phones or calculators are allowed. Please write all your answers on the exam paper. There is 200 points in total.
UCSB - ECON - 208
Economics 208MacroeconomicsMarek KapickaSpring 2010Final AnswersYou have two hours. This is a closed book/closed notes exam. No cell phones orcalculators are allowed. Please write all your answers on the exam paper. There is400 points in total. Goo
UCSB - ECON - 208
Economics 208MacroeconomicsMarek KapikacSpring 2010Midterm AnswersYou have 75 minutes. This is a closed book/closed notes exam. No cell phonesor calculators are allowed. Please write all your answers on the exam paper. Thereis 200 points in total.
UCSB - ECON - 208
UCSB - ECON - 208
UCSB - ECON - 208
UCSB - ECON - 208
UCSB - ECON - 208
UCSB - ECON - 208
Econ208MarekKapickaLecture6TheEffectsofGovernmentSpendingSocialSecurityEmpiricalEvidencenMainquestion:nnHowdoesconsumptionandwagesrespondtoanincreaseingovernmentspending?ValerieRamey(2008):nTheeffectsofmilitaryexpendituresnLargelyunrelate
UCSB - ECON - 208