# 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.

1 Page

### MA261quiz_4

Course: MA 261, Spring 2011
School: Purdue
Rating:

Word Count: 183

#### Document Preview

0021&amp;0022 MA261 Quiz 4 Spring 2011 Problem 1. The position function of a particle is given by r(t) = 3 sin t, 3 cos t, 4t . (1) Find the velocity v(t). Solution. v(t) = r(t) = 3 cos t, 3 sin t, 4 . (2) Find the speed |(t)|. v Solution. |v(t)| = 32 + 42 = 5. (3) Find the acceleration a(t). Solution. a(t) = v(t) = 3 sin t, 3 cos t, 0 . Problem 2. Consider the function f of two variables x2 f (x, y ) = 2 +...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Indiana >> Purdue >> MA 261

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.
0021&0022 MA261 Quiz 4 Spring 2011 Problem 1. The position function of a particle is given by r(t) = 3 sin t, 3 cos t, 4t . (1) Find the velocity v(t). Solution. v(t) = r(t) = 3 cos t, 3 sin t, 4 . (2) Find the speed |(t)|. v Solution. |v(t)| = 32 + 42 = 5. (3) Find the acceleration a(t). Solution. a(t) = v(t) = 3 sin t, 3 cos t, 0 . Problem 2. Consider the function f of two variables x2 f (x, y ) = 2 + y 2 . 2 (1) Draw the level curves corresponding to f (x, y ) = 0, f (x, y ) = 1 and f (x, y ) = 4, respectively? (2) the Draw graph of f (x, y ) and name the surface. Solution. 2 When f (x, y ) = 0, we have x2 + y 2 = 0. Only the point (0, 0) makes it hold. Thus, 2 the level curve is just a point. 2 When f (x, y ) = 1, we get x2 + y 2 = 1. This is an ellipse with its major axis on the 2 x axis. 2 2 When f (x, y ) = 4, we het x2 + y2 = 1. This is still an ellipse but larger than the 4 2 previous one. The level curves and graph of the function are similar to those for Example 11 in Section 14.1 in the textbook. So they are omitted here. 1
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:

Purdue - MA - 261
MA261 0021&amp;0022 Quiz 5Spring 20112Problem 1 (Spring 2006). If u(x, y ) = yexy ,(a) nd ux .22Solution. ux = yy 2 exy = y 3 exy .(b) nd uxy .222Sollution. uxy = (ux )y = 3y 2 exy + y 3 2xyexy = y 2 exy (3 + 2xy 2 ).Problem 2 (Spring 2001). Give
Purdue - MA - 261
MA261 0021&amp;0022 Quiz 6Spring 2011Problem 1. Suppose y is a function of x and they satisfy F (x, y ) = 0.Take the partial derivative with respect to x of both sides of the above equation (UseChain Rule ) to show thatFdyx= F .dxyProof. Given F (x
Purdue - MA - 261
MA261 0021&amp;0022 Quiz 7Spring 2011Problem 1. Given f (x, y ) = x2 y 2 ,(a) Find the critical point of f (x, y ).Solution. Setting f (x, y ) to be zero, we have f (x, y ) = fx (x, y ), fy (x, y ) =2x, 2y = 0, 0 . So, (x, y ) = (0, 0) is the only critic
Purdue - MA - 261
MA261 0021&amp;0022 Quiz 8Spring 2011Problem 1 (modied from Problem 2 in the second midterm of Spring22009). We will nd the maximum of f (x, y ) = xy on the ellipse x + y 2 = 1 using the4Lagrange multiplier method.2(a) Let g (x, y ) = x + y 2 . Write
Purdue - MA - 261
MA261 0021&amp;0022 Quiz 9Spring 2011Problem 1 (Test II.8, Spring 2008). [Warning: No use of cell phonebrowsing the internet during the quiz!] Let D be the part of disk centered at 0with radius 2 that lies to the right of the line x = 1. Then which of the
Purdue - MA - 261
MA261 0021&amp;0022 Quiz 10Spring 2011Problem 1. Find the length of a wire C in the shape of a helix described by theparametric equationC : x = cos t, y = sin t, z = t, 0 t 4Solution. To get the length of the wire, let us integrate the constant function
Purdue - MA - 261
MA261 0021&amp;0022 Quiz 11Spring 2011Problem 1.(a) Given F(x, y ) = y exy , xexy , nd a function f (x, y ) such that f (x, y ) = F(x, y ).Solution. Since we are told f (x, y ) = F(x, y ), we have fx = yexy and fy = xexy .After integrating the rst equali
Purdue - MA - 261
MA261 0021&amp;0022 Quiz 12Spring 2011Problem 1.(a) Given a function f (x, y, z ) = xyz , nd its gradient f (x, y, z ) and then the curlof the gradient, namely curl( f (x, y, z ).Solution. Given f (x, y, z ) = xyz , we know f (x, y, z ) = fx , fy , fz =
Purdue - MA - 303
MA 303: Dierential and Partial DierentialEquations for Engineering and SciencesFall 2011, Final Examination(Instructor: Aaron N. K. Yip) This test booklet has TWENTY FIVE questions totaling 200 points for the wholetest. You have 120 minutes to do thi
Purdue - MA - 303
Purdue - MA - 303
Purdue - MA - 303
Worked Out Homework 1MA 303 Fall 2011 (Aaron N. K. Yip)Friday, Sept. 2, in class1. (a) Do Textbook (Boyce-DiPrima, 9th-ed.) section 3.3, page 165, #34 (on Euler Equation)(b) Use the above result to nd the general solutions y (t) of the the following d
Purdue - MA - 303
Purdue - MA - 303
Worked Out Homework 2MA 303 Fall 2011 (Aaron N. K. Yip)Friday, Sept. 16, in class1. Find the general solutionfollowing matrices:31B= 0 300ofdXdt= BX ,dXdt= CX anddXdt= DX where B, C, D are the03003121 , C = 0 3 1 , D = 0 3 3 300200
Purdue - MA - 303
Purdue - MA - 303
Worked Out Homework 3MA 303 Fall 2011 (Aaron N. K. Yip)Friday, Sept. 30, in class1. For each of the following system, nd the general solution and plot the phase plot:(a)dX=dt1122(b)dX=dt112 2(c)dX=dt111 3(d)dX=dt3 11 1XXXX
Purdue - MA - 303
Purdue - MA - 303
Worked Out Homework 4MA 303 Fall 2011 (Aaron N. K. Yip)Friday, Oct. 28, in class1. Consider the systems from the textbook (Boyce-DiPrima, 9th-ed.) section 9.4, page 530, #1,and #2.For each problem, do the following:(a) Find all the critical points;
Purdue - MA - 303
Purdue - MA - 303
Worked Out Homework 5MA 303 Fall 2011 (Aaron N. K. Yip)Monday, Nov. 7, in class1. This question is to explore the Laplace Transform of periodic functions. A function f (t) iscall periodic with period T if for all t &gt; 0, f (t + T ) = f (t), i.e. the fu
Purdue - MA - 303
Purdue - MA - 303
Worked Out Homework 6MA 303 Fall 2011 (Aaron N. K. Yip)Monday, Nov. 28, in class1. (a) Consider the following dierential equation:u (x) + u(x) = 0;0 &lt; x &lt; ;u(0) = 0,u ( ) = 0.(b) Consider the following dierential equation:u (x) + u(x) = 0;u (0)
Purdue - MA - 303
Purdue - MA - 303
Worked Out Homework 7MA 303 Fall 2011 (Aaron N. K. Yip)Friday, Dec. 9, in class, LAST DAY OF CLASS(Beware: I am using the following expression for Fourier series for any 2L-periodic function:an cosnxnx+ bn sinLLan cosf (x) = a0 +nxnx+ bn sin
Purdue - MA - 303
Purdue - MA - 303
Purdue - MA - 303
Properties and Formulas for Laplace Transformest g (t) dt.est f (t) dt and G(s) = Lcfw_g (t) =Let F (s) = Lcfw_f (t) =00In the following a and b are arbitrary constants and n is some positive integer.L cfw_af + bg = aF (s) + bG(s)(1)L cfw_f = s
Purdue - MA - 303
Purdue - MA - 303
Purdue - MA - 303
Purdue - MA - 303
Purdue - MA - 490
The Equations for Large Vibrations of StringsAuthor(s): Stuart S. AntmanReviewed work(s):Source: The American Mathematical Monthly, Vol. 87, No. 5 (May, 1980), pp. 359-370Published by: Mathematical Association of AmericaStable URL: http:/www.jstor.or
Purdue - MA - 490
Purdue - MA - 490
Chapter 1classification ofdifferentialequationsLoosely speaking, a differential equation is an equation specifying a relation betweenthe derivatives of a function or between one or more derivatives and the functionitself. We will call the function a
Purdue - MA - 490
Purdue - MA - 490
Purdue - MA - 490
Purdue - MA - 490
Homework 6MA 490: Introduction to Partial Dierential EquationsSpring 2012, Aaron N. K. YipFriday, Apr. 13, noon1. Textbook (2nd edition):Section 5.4 (p. 134): #7, 8, 12, 15;Section 5.5 (p. 145): #3, 12.2. Prove the following fact about the least sq
Purdue - MA - 490
Purdue - MA - 490
Homework 7MA 490: Introduction to Partial Dierential EquationsSpring 2012, Aaron N. K. YipFriday, Apr. 27, noonThis is probably the craziest assignment. Just do the *-problems from the textbook. The othersare food-for-thought and provide good exercis
Purdue - MA - 490
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Purdue - MA - 341
Broward College - ECO - ECO2013
Exchange Rates The price of one currency in termsof another the amount of one currency that has to be given up to purchase anothercurrency Exchange rates determined by the demand and supply of a currencyon foreign exchange markets Demand determined
Purdue - MA - 341
Broward College - ECO - ECO2013
InflationEconomists use the term inflation to denote an ongoing rise in the general level ofprices quoted in units of money.The magnitude of inflationthe inflation rateis usually reported as the annualizedpercentage growth of some broad index of money
Purdue - MA - 341
Broward College - ECO - ECO2013
Measures of Economic Performance Economic Measures: Inflation Unemployment Growth (GDP) Balance of Payments Exchange Rate Non-Economic Measures: Quality of Life Environment Health EducationEconomic Growth (GDP) Gross Domestic Product: The va
Purdue - MA - 341
Broward College - ECO - ECO2013
Unemployment The number of people of working age who are without a job The Claimant Count those actively seeking work and claiming benefit ILO (International Labour Organisation) measure the number of people availablefor work and actively seeking empl
Broward College - ECO - ECO2013
VOCABULARYEconomic Efficiency-When goods and services are made and consumed at the bestlevels for the society. Nothing more can be acheived with the resources available.socially optimal quantity-The amount of a good that results in the greatesteconomi
Purdue - MA - 341
Purdue - MA - 341