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.

2 Pages

Mat265-B2HW7Sol

Course: MAT 265, Fall 2009
School: Iowa State
Rating:

Word Count: 603

Document Preview

265-B2 Math Solutions to Homework #7: Sec. 15.3 #5: Set r = x2 + y 2 . Then sin r sin(x2 + y 2 ) 1 = lim lim = . r0 3r 3 (x,y)(0,0) 3x2 + 3y 2 2 x y Sec. 15.3 #17: f (x, y) = 4 x + y2 a.) Along every line through the origin y = mx, x2 (mx) mx3 mx x2 y = 4 = 4 = 2 . So along y = mx, 4 + y2 2 x x + (mx) x + m2 x2 x + m2 mx m(0) x2 y = lim 2 = 2 = 0. lim x0 x + m2 0 + m2 (x,y)(0,0) x4 + y 2 b.) Along the parabola y =...

Register Now

Unformatted Document Excerpt

Coursehero >> Iowa >> Iowa State >> MAT 265

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.
265-B2 Math Solutions to Homework #7: Sec. 15.3 #5: Set r = x2 + y 2 . Then sin r sin(x2 + y 2 ) 1 = lim lim = . r0 3r 3 (x,y)(0,0) 3x2 + 3y 2 2 x y Sec. 15.3 #17: f (x, y) = 4 x + y2 a.) Along every line through the origin y = mx, x2 (mx) mx3 mx x2 y = 4 = 4 = 2 . So along y = mx, 4 + y2 2 x x + (mx) x + m2 x2 x + m2 mx m(0) x2 y = lim 2 = 2 = 0. lim x0 x + m2 0 + m2 (x,y)(0,0) x4 + y 2 b.) Along the parabola y = x2 , x2 (x2 ) x4 1 x2 y = 4 = 4 = . So along y = x2 , 4 + y2 2 )2 4 x x + (x x +x 2 x2 y 1 1 lim = lim = . x0 2 2 (x,y)(0,0) x4 + y 2 c.) Since two different paths through the origin produce two different limits, x2 y we conclude that lim f (x, y) = lim does not exist. 4 + y2 (x,y)(0,0) (x,y)(0,0) x 2 x - 4y 2 if x = 2y Sec. 15.3 #25: f (x, y) = . x - 2y g(x) if x = 2y We want f to be continuous on all of R2 . For every (x, y) such that x = 2y, (x - 2y)(x + 2y) x x2 - 4y 2 = = x + 2y. If x = 2y, then y = , and x - 2y x - 2y 2 x x + 2y = x + 2 = 2x. So we want g(x) = 2x. 2 xy(x2 - y 2 ) if (x, y) = (0, 0) . Sec. 15.3 #32: f (x, y) = x2 + y 2 0 if (x, y) = (0, 0) f (h, y) - f (0, 0) a.) For every y, fx (0, y) = lim h0 h hy(h2 -y 2 ) -0 2 +y 2 y(h2 - y 2 ) y(0 - y 2 ) y3 h = lim = lim = = - 2 = -y. h0 h0 h2 + y 2 h 0 + y2 y Therefore, fx (0, y) = -y for all y. f (x, h) - f (0, 0) b.) For every x, fy (x, 0) = lim h0 h xh(x2 -h2 ) 2 -0 x(y - h2 ) x(x2 - 0) x3 2 2 = lim x +h = lim = = 2 = x. h0 h0 x2 + h2 h x2 + 0 x Therefore, fy (x, 0) = x for x. 1 fy all (h, 0) - fy (0, 0) . But according to part(b), fy (x, 0) = x h for all x. Thus, fy (h, 0) = h and fy (0, 0) = 0. Plugging these results in yield h-0 = lim 1 = 1. So fyx (0, 0) = 1. fyx (0, 0) = lim h0 h0 h fx (0, h) - fy (0, 0) d.) fxy (0, 0) = lim . But according to part(a), fx (0, y) = -y h0 h for all y. Thus, fx (0, h) = -h and fx (0, 0) = 0. Plugging these results in yield -h - 0 fxy (0, 0) = lim = lim -1 = -1. So fxy (0, 0) = -1. h0 h0 h c.) fyx (0, 0) = lim h0 Sec. 15.4 #6: f (x, y) = sin3 (x2 y). Then fx (x, y) = 3 sin2 (x2 y) cos(x2 y)(2xy) = 6xy sin2 (x2 y) cos(x2 y), and fx (x, y) = 3 sin2 (x2 y) cos(x2 y)(x2 ) = 3x2 sin2 (x2 y) cos(x2 y). Therefore, f (x, y) = 3x sin2 (x2 y) cos(x2 y) 2y, x . Sec. 15.4 #13: f (x, y) = cos x sin y + sin 2y. So, fx (x, y) = - sin x sin y, and fy (x, y) = cos x cos y + 2 cos 2y. Then, fx (-1, 1/2) = - sin(-) sin(/2) ...

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:

Iowa State - MAT - 265
Math 265-B2 Solutions to Homework #8: Sec. 15.5 #7: f = fx , fy , fz . fx = 3x2 y fx (-2, 1, 3) = 3(-2)2 (1) = 12. fy = x3 - 2yz 2 fy (-2, 1, 3) = (-2)3 - 2(1)(3)2 = -8 - 18 = -26. fz = -2y 2 z fz (-2, 1, 3) = -2(1)2 (3) = -6. Hence, f (-2, 1, 3)
Iowa State - MAT - 265
Math 265 Section B2Instructor: Mr. Aaron A. Allen. Class Times: Monday, Tuesday, Thursday, and Friday, 10:00 AM to 10:50 AM. Meeting Place: Carver Hall, room 184. Office: Carver Hall, room 487. Office hours: TBA E-mail address: aaallen@iastate.edu C
Purdue - STAT - 540
Model Numerical approximation Conclusions BibliographyOption pricing with transaction costs using a Markov chain approximationAshish Goel, Liang Cheng, Luis Barboza, Mathew P. ThariyanMA 515 Final Presentation Advisor: Prof. Jose E. Figueroa-Lope
Purdue - STAT - 540
Ma 515/Stat 540. Exam 1.Spring, 2008 Figueroa-LopezPRINT your name:Instructions:1. The exam is 2-hour long. 2. The exam is closed book and notes. 3. You can use a standard calculator. 4. You need to show your work to receive credit.Problem 1
Purdue - STAT - 540
Conditional expectationJos Figueroa-LpezPurdue UniversityMath 515 / Stat 540 Spring, 2008Conditional expectationBasic denitions and propertiesBasic denitions Intuition: E(Y |X ) is the best predictor of the random variable Y basedon the
Purdue - STAT - 540
Option Pricing in Presence of Transaction CostsGroup MembersVarun Agarwal Niru Kumari Debabrata Mohapatra Sriram Rapaka Anil Samantsinghar Dhruv SinghPresentation OutlineMotivation Proposed SolutionsLocal in Time ModelsLeland (1985) and it
Purdue - STAT - 541
Math516/Stat541 Midterm Computational ProjectFall 2007 Due date: October 5thInstructions: (a) Write your code in a program language of your choice. Strongly suggested C+/C, Visual Basic/Excel, MATLAB. (b) Your dierent programs and nontrivial proc
Purdue - STAT - 541
Math516/Stat541 Homework assignment 3 1. Exercise 22.6. 2. Exercise 22.7. 3. Exercise 22.8. 4. Consider the Hull-White model for bond prices, where d r(t) = (t) - a r) + d W (t), under the risk-neutral measure Q. Show that, under Q, the normalized bo
Purdue - STAT - 541
Math516/Stat541 Homework Assignment 4 1. Exercise 23.1Fall 2007Remark: One way to deduce the required (t, T ) in df (t, T ) is the following. Consider the AFT formula of the Hull-White bond prices p(t, T ). Then, deduce the volatility (t, T ) of
Purdue - STAT - 541
Adaptive Control Variates for Pricing Multi-Dimensional American Options by Ehrilchman and HendersonShuhao Cao Mike Li Huijie Wang Weijia Wang Monday November 26, 2007Shuhao Cao Mike Li Huijie Wang Weijia Wang: Adaptive Control Variates for Pricin
Purdue - STAT - 541
Implied Binomial TreesMark Rubinstein University of California Berkeley 1994OutlineMotivationby KameshProblem setupby ChunA small exampleby SeanMore results and extensionsby NeeravSome applications and conclusionby NathalieMotivati
Columbia - EC - 6215
INTERNAL AND EXTERNAL ADJUSTMENT COSTS IN THE THEORY OF FIXED INVESTMENT (lecture notes for Investment Theory for First Year Graduate Macroeconomics)Xavier Sala-i-Martin (*) Columbia University and Universitat Pompeu FabraThis Draft: October, 200
Columbia - EC - 3213
Ec3213. Columbia College Professor Xavier Fall 2005. Midterm. Please note that &quot;yes/no&quot; answers will not be accepted. You need to explain/illustrate your answers even though you are not asked explicitly.Question 1. Assume that an economy has the pr
Columbia - EC - 3213
Importance of GrowthXavier Sala-i-MartinHypothetical GDP Paths1211log (GDP per capita)10987 1870 1890 1910 1930 1950 1970 1990 2010yearGrowth 2% Growth 1% Growth 3% Initial income \$2000 Final Income If growth 2%, y=\$25,000 If
Columbia - EC - 6301
WhyhasAfricaGrownSo Slowly?XavierSalaiMartin ColumbiaUniversityFigure 1: GDP per Capita\$2,500\$2,000\$1,500\$1,000\$500\$0 1960196519701975 Africa19801985199019952000Sub-Saharan AfricaFigure 3: Divergence: Per Capita GDP
Columbia - EC - 6301
Why has Africa Grown So Slowly?Xavier SalaiMartin Columbia UniversityFigure 1: GDP per Capita\$2,500\$2,000\$1,500\$1,000\$500\$0 1960196519701975 Africa19801985199019952000Sub-Saharan AfricaFigure 3: Divergence: Per Capi
Columbia - EC - 6301
Poverty, Inequality, and the World Distribution of IncomeBy Xavier Sala-i-MartinInteresting Quotes &quot;The number of people living on less than \$1 a day grew from 1.18 billion in 1987 to 1.20 billion in 1998-an increase of 20 million&quot;The World Ban
Columbia - EC - 6301
The Many Ways Governments can Kill GrowthXavier Sala-i-Martin, 2003Hyperinflations Fiscal disarray leads to PRINT MONEY Money Printing leads to Hyperinflation French Revolution and American Civil War Versailles Treaty and the HP of the 192
Columbia - EC - 6301
A Market for VaccinesXavier Sala-i-MartinRecall AIDS Fund (AIDS Fund) Governmentsof Rich Countries contribute toa fund The money is spent to buy vaccines at monopolistic price This provides incentives to do the research Yet the vaccines a
Columbia - EC - 6301
Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach by Xavier Sala-i-Martin, Gernot Doppelhoffer and Ron MillerTable 2: Baseline EstimationPosterior Inclusion Probabiliy (1) 0.823 0.796 0.774 0.685 0.563 0
Iowa State - STAT - 341
Iowa State - STAT - 341
Iowa State - STAT - 341
Stat 341, 2-22-08, Hypergeometric RV &amp; probability distribution, M. Larsen Density, distribution function, quantile function and random generation for the hypergeometric distribution. - help(dhyper) -Usagedhyper(x, m, n, k, log = FALSE) phyper(q,
Iowa State - STAT - 341
Stat 341, 2-18-08, Binomial random variable &amp; probability distribution, M. Larsen Lets consider a binomial random variable with n=20 trials. Here is a vector containing the integers 0 through 20. &gt; x = 0:20 &gt;x [1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1
Iowa State - STAT - 341
Stat 341, 2-11-08, Expectation of nonlinear transformation, M. Larsen X Y=g(X) Does E[Y] = E[g(X)] equal g(E[X])?Y=1/X x = rnorm(1000, 29, 1.5) # miles per gallon y = 1/x # gallons per mile mean(x) [1] 28.97253 mean(y) [1] 0.03460628 mean(1/x) [1]
Iowa State - STAT - 341
# Simulation of Expectation of Random Variables# Stat 341, Spring 2008, M. Larsen, February 8, 2008-Fair Die-1 2 3 4 5 61/6 1/6 1/6 1/6 1/6 1/6mean( sample(1:6, size=100000, prob=rep(1/6,6), replace=T) )hist( sample(1:6, size=1000
Iowa State - STAT - 341
Stat 341, British Social Mobility Example, from Glass (1954) Father/Son (1st generation after father) 1 2 3 4 5 1 50 45 8 18 8 129 2 28 174 84 154 55 495 3 11 78 110 223 96 518 4 14 150 185 714 447 1510 5 3 42 72 320 411 848 3500 pairs of individuals
Iowa State - STAT - 341
Stat 341, Monday January 28, 2008, Birthday problem in R &gt; n &lt;- 365:300 &gt;n [1] 365 364 363 362 361 360 359 358 357 356 355 354 353 352 351 350 349 348 347 [20] 346 345 344 343 342 341 340 339 338 337 336 335 334 333 332 331 330 329 328 [39] 327 326 3
East Los Angeles College - CIVE - 1400
Question 2.CIVE1400, Fluid Mechanics Marked Problem SheetDr P.A Sleigh P.A.Sleigh@leeds.ac.uk This work must be submitted via the print room by 4.00pmThe maximum depth of water in a reservoir is maintained by a V-notch weir, as shown in figure 1
UCLA - EDUC - 456
ELP On-line Action Research Project Phone Interview w/: Adrienne Mack Researcher: Troy Behrens Monday, May 28, 2001 Tell us briefly about your experience with your use of technology (as in computer use, online courses, email programs or the internet)
UCLA - EDUC - 456
ELP On-line Action Research Project Phone Interview w/: Andy Johnsen Researcher: Steven Mercer Monday, May 28, 2001 8:00pm 1. Tell us briefly about your previous experience with on-line courses prior to the ELP program. No experience with on-line cou
UCLA - EDUC - 456
Stuart Biegel February 14, 2001 Interviewed by S. Mercer Teaches in UCLA Law School as well as GSEIS He teaches in three education leadership programs - ELP - Principal's Leadership Institute (PLI) - EdD at UC Irvine In all three programs he employ
UCLA - EDUC - 456
Stuart Biegel February 14, 2001 Interviewed by S. Mercer Teaches in UCLA Law School as well as GSEIS He teaches in three education leadership programs - ELP - Principal's Leadership Institute (PLI) - EdD at UC Irvine In all three programs he employ
UCLA - EDUC - 456
ELPOL Qualitative Questionnaire Responses Session I (Verbatim) R1 COMMENTS = I did manage to access all the materials except for the video. When I had downloaded 61% of the file, the system stopped. I didn't try the second time but went to the text b
UCLA - EDUC - 456
ELPOL Qualitative Questionnaire Responses Session II (Verbatim) R1 COMMENTS = I really like the live class, the interaction more that the bulletin board. Sorry. But, on the up side. This has really forced me to get more acquainted with the web. R3 CO
UCLA - EDUC - 456
ELPOL Qualitative Questionnaire Responses Session III (Verbatim) R4 COMMENTS = Difficult to read 200 pages on the screen. I printed it out with a smaller font and smaller margins. However, it was really good having the option - so its hard to say if
UCLA - EDUC - 456
Focus Group/Personal Interview Questions Thank you for agreeing to be a part of this focus group. I am going to ask you a series of question, some of them may be in general to all of you some may be specific to individuals. Please be as objective as
UCLA - EDUC - 456
Main Points of the Class: 1. We've had 25 years of school reform and things aren't getting any better. 2. Schools exist in a political environment, so many &quot;reforms&quot; have more of a symbolic value than substantive. Also, because of clashes of values a
UCLA - EDUC - 456
Preface The purpose of this section is to reflect upon the in-class exercise we facilitated at the mid-point of the ELP Online project. Our research group was interested in gaining feedback about the students' experiences halfway through the project.
UCLA - EDUC - 456
Recommended Electronic Teaching Strategies 1. Electronic Discussion Forum Using an Internet based program such as &quot;Yahoo Groups&quot;, allows the facilitator and students to post reactions to assigned reading and professor prompts. The application keeps t
UCLA - EDUC - 456
ELP On-line Action Research Project Phone Interview: Saadia Lagarde Researcher: Steven Mercer Thursday, May 24, 2001 9:00pm 1. Tell us briefly about your previous experience with on-line courses prior to the ELP program. I have no prior experience. B
UCLA - EDUC - 456
Educational Leadership Program On-line (ELPO) Survey Dear Cohort 8: In an effort to guide us in the planning and implementation of our ELP Action Research project we are asking that you complete this questionnaire. Thank you for your cooperation. Mar
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Wesleyan - PHYS - 217
Physics 217ChaosFall 2003Problem Set 21. Consider the chemical reaction A+X 2X. (1)This is an example of an autocatalytic reaction: the presence of product X enables the conversion of A to X. Since collisions between A and X are necessary f
Wesleyan - PHYS - 215
Wesleyan - PHYS - 215
UGA - CLAS - 4040
CLAS: 4040/6040Death &amp; Burial of Philip IIProf. Naomi J. NormanBefore Philip, 359 BCEDuring Philip, 348 BCE356 BCE: Philip assumes kingship from Amyntas &amp; begins to consolidate kingdom which is accomplished by 338 at the Battle of Chaironei
UGA - CLAS - 4040
Karen Marks For this workshop, the class analyzed a series of Hellenistic votive reliefs dating from the late 4 century to the early 1st century. Because of their nature as votive offerings, all the reliefs show some depiction of the god(s) to whom t