# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

11 Pages

### Sum2010Exam1

Course: MAC 2233, Spring 2011
School: University of Florida
Rating:

Word Count: 481

#### Document Preview

2233 NAME: MAC EXAM 1 MAY 27, 2010 PART 1: SHORT ANSWER 1. (3 points) Give the denition of a function. 2. (3 points) Let f be a function. Give the three conditions f must satisfy to be continuous at x = a. 3. (2 points) Let f be a function. Write the limit denition of f (a), the derivative of f at x = a. 4. (4 points) State the intermediate value theorem. PART 2: PROBLEMS (Show All of Your Work) 1. (5 points)...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Florida >> University of Florida >> MAC 2233

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
2233 NAME: MAC EXAM 1 MAY 27, 2010 PART 1: SHORT ANSWER 1. (3 points) Give the denition of a function. 2. (3 points) Let f be a function. Give the three conditions f must satisfy to be continuous at x = a. 3. (2 points) Let f be a function. Write the limit denition of f (a), the derivative of f at x = a. 4. (4 points) State the intermediate value theorem. PART 2: PROBLEMS (Show All of Your Work) 1. (5 points) Find the equation of the circle with center (1, 4) that passes through (3, 3). 2. (5 points) Find the equation of the line that passes through (1, 2) and is perpendicular to the line 3x 2y = 1. Write your answer in slope-intercept form. 3. Let f ( x) = 2 23 x and g ( x) = x. (a) (3 points) Find and simplify (f g )(x). (f g )(x) = (b) (3 points) Give the domain of (f g )(x) in interval notation. Domain 4. (4 points) A rectangular box is to have a square base and an open top. The volume of the box is to be 50 m3 . The material for the base costs \$3 per square meter and the material for the sides costs \$2 per square meter. Find a function whose input x is the length of one side of the base and whose output C (x) is the cost of constructing the box. y x x C (x) = 5. The graph of f is given below. f (x) 1 x 3 2 (a) (2 points) Use the graph to nd both limx3 f (x) and limx3+ f (x). lim f (x) f = x3 lim (x) = x3+ (b) (2 points) Use your answer to part (a) to determine whether limx3 f (x) exists. If the limit exists, what is it? If the limit does not exist, explain why. (c) (2 points) Is f continuous at x = 3? If so, explain why all conditions of continuity are met by f at x = 3. If not, state which of the conditions of continuity are violated. 6. (4 points) Evaluate the limit z3 8 x2 z 2 lim 7. (4 points) Evaluate the one-sided limit x2 x 6 lim x2+ x2 + x 2 8. Let f ( x) = 5x + 6 2x2 x if x < 3 if x 3. (a) (2 points) Find both limx3 f (x) and limx3+ f (x). lim f (x) = x3 lim f (x) = x3+ (b) (3 points) Is f continuous at x = 3? If so, explain how all conditions of continuity are satised by f at x = 3. If not, explain which of the conditions of continuity are violated by f at x = 3. 9. (6 points) Use the limit denition of derivative to nd the derivative of 1 f ( x) = . x f (x) = 10. Let f (x) = 3x2 4. (a) (4 points) Use the limit denition of derivative to compute f (x). (b) (4 points) Find the equation of the line tangent to the graph of f at x = 1. Write your answer in slope-intercept form. 11. (5 points) Consider the function 2 5 f (x) = x3 + x2 + 16. 3 2 The derivative of f is f (x) = 2x2 + 5x. Find all values of x so that the instantaneous rate of change of f at x is 3.
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

UCSB - ECON - 177
2 and 5 bidder, V=308070Average Reserve60505 bidderoptimum2 bidder403020100123456789 10 11 12 13 14 15 16 17 18 19 20Round
University of Florida - MAC - 2233
Name:MAC 2233 EXAM 3July 15, 2010PART 1: Denitions1. (3 points) Complete the denition:A function f is concave upward on the interval (a, b) if2. (3 points) Dene the exponential function f with base b. Include all restrictions on b.3. (3 points) Com
UCSB - ECON - 177
2 and 5 bidder, V=070Average Reserve6050405 bidderoptimum2 bidder3020100123456789 10 11 12 13 14 15 16 17 18 19 20Round
University of Florida - MAC - 2233
MAC2233 Test 1(7 pts) 1. A function f has domain (, ) and a function g has domain [2, ); the domainof (f + g )(x) is given by:A. (, )B. (2, )C. (, ) [2, )D. [2, )E. (, 2)x(7 pts) 2. The domain of the function h(x) = x2+2 is given by:9A. (, )B.
University of Florida - MAC - 2233
MAC2233 Test 2 A(7 pts) 1. The equation of the tangent line to the function y =A. y = 3 x + 5441B. y = 7 x + 443C. y = 5 x + 44x2 + 3x at x = 1 is given by:D. y = 1 x + 744E. y = 9 x 144x(7 pts) 2. If f (x) = x2+1 , then f (2) is equal
UCSB - ECON - 177
Econ 177Sample Questions Part IIn all the questions that follow you may assume each of the i = 1, ., nbidders values are drawn independently from the uniform distribution on[0,100], which is dened as followsF (v ) = Pr[i v ] =vv.1001. What is th
University of Florida - MAC - 2233
MAC2233 Test 3 A(7 pts) 1. The interval(s) over which g (t) = t22t is increasing is (are) given by:+1A. (, )B. (, 1)C. (1, )D. (, 1) (1, )E. (1, 1)(7 pts) 2. The function f (x) = x + 9/x + 2 has a local max at:A. x = 3B. x = 2C. x = 0D. x = 3
UCSB - ECON - 177
Econ 177Sample Questions Part II1. Consider a second-price auction with a single private value bidder whovalue is drawn from the uniform distribution on [0,100]. You are theseller.(a) Compute the optimal reserve price assuming your value for theitem
University of Florida - MAC - 2233
MAC2233 Test 4 A(7 pts) 1. Given f (x) = ln x2 5, f (3) is equal to:3B. 83A. 4C. 32D. 233E. 16(7 pts) 2. The equation of the tangent line to g (x) = 2xe3x at x = 1 is given by:A. y = 3e3 x + 5e3B. y = 4e3 x + 6e3D. y = 5e3 x 3e3C. y = 2e3
UCSB - ECON - 177
A signalCaseCaseCaseCase1234Charlie RiccoB signal0303A's bid0033B's bid1.54.51.54.51.51.54.54.5A's profitResults from-0.75 1000-1.5 Trials00.75-0.375-0.3795Willliam RussellWillliam Russell
University of Florida - MAC - 2233
MAC2233 Final A(7 pts) 1. Given y 2 x2 + 3x = 3y 3 , y is given by:2xy 2 +3A. 9y 2 2yx22xy 2 +32xy 2 3B. 9y 2 +2yx22xy 2 +3C. 9y 2 2yx2D. 9y 3 +2yx22xy 2 +3E. 9y 2 2y 2 x2(7 pts) 2. Given h(x) = (4x2 3x ln x)3 , h (1) is equal to:A. 120B. 80
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