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### matlab_diff_limder

Course: MATH 263, Fall 2009
School: Bethel VA
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Word Count: 227

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and Limits Derivatives1 1. Try the following commands: syms x h f = x^3 + x^2 + x + 1 m = (subs(f, x+h)-f)/h f1 = limit(m, h, 0) Explain what happened. 2. Try the following sequence: syms x h f = exp(sin(x)) m = (subs(f, x+h)-f)/h f1 = limit(m, h, 0) subs(f1, pi) X = -10:.05:10; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Makes an array of x values. F = subs(f, X); . . . . . . . . . . . ....

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and Limits Derivatives1 1. Try the following commands: syms x h f = x^3 + x^2 + x + 1 m = (subs(f, x+h)-f)/h f1 = limit(m, h, 0) Explain what happened. 2. Try the following sequence: syms x h f = exp(sin(x)) m = (subs(f, x+h)-f)/h f1 = limit(m, h, 0) subs(f1, pi) X = -10:.05:10; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Makes an array of x values. F = subs(f, X); . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Makes an array of f(x) values. F1 = subs(f1, X); plot(X, F, 'b', X, F1, 'r') Explain what happened. 3. Now repeat the steps above for the function: Is the function defined for all real numbers? What about the derivative? How is the graph misleading? 4. Next repeat this procedure for the . function Are the function and its derivative defined for all real numbers? How is this graph misleading? 5. Use ezplot(f) and ezplot(f1) to get another picture for f and f' from #4. In what ways are these graphs misleading? 6. Prepare a brief (< 1 page) written report answering all the questions. Use complete sentences and standard mathematical notation. Do not get a printout. This assignment is intended to reinforce the user's understa...

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Bethel VA - MATH - 263
Factoring Expressions and Solving Equations11. At the prompt, type the following commands and press Enter : clear syms x expr1 = (x-1)*(x-2)*(x-3)*(x-4)*(x-5) expr2 = expand(expr1) factor(expr2) solve(expr2) . . . . . . . . . . . . . . . . . . . . .
Bethel VA - MATH - 263
Exponentials vs. Powers11. Enter the following sequence commands: Important note: Do not omit the semicolons! Also, do not omit the . before the ^ ! (a) x1 = -1.15:0.01:1.15; . . . (This makes in increments.) (b) x2 = -1.39:0.01:1.39; (c) y1 = x1.^1
Bethel VA - MATH - 263
Defining, Evaluating and Plotting Functions11. At the prompt type: syms x and then press Enter . Now type f = sin(x) and then press Enter . 2. Type (at the prompt and then press Enter ): subs(f, 2) subs(f, '2') double(ans) Which of the above answers
Bethel VA - MATH - 263
Derivatives11. Try the following commands: (a) syms x (b) f = x^2 (c) f1 = diff(f) (d) X = -3:.05:3; . . . . . . . . . . . . . . . . Makes X into an array with entries from -3 to 3 (e) F = subs(f, X); (f) F1 = subs(f1, X); (g) plot(X, F, 'b', X, F1,
Bethel VA - MATH - 263
Limits11. Try the following commands (at the prompt and press Enter ): (a) x = sym('x') (b) f = x^2 (c) limit(f, 2) (d) limit(f, inf) (e) limit(1/x, inf) (f) limit(log(abs(x), 0) (g) limit(1/x, 0) (h) Explain what happened in each example, that is,
Bethel VA - MATH - 263
Factoring Expressions and Solving Equations1Sample Solution 1. The command clear clears all variables. The command syms x declares x to be a symbolic variable. The command expr1 = (x-1)*(x-2)*(x-3)*(x-4)*(x-5) gives the label expr1 . to the expressi
Bethel VA - MATH - 340
Plotting Solutions to First Order Initial Value Problems 1Enter the following sequence of commands: F = inline('sin(y)', 't', 'y') . . . . . . . . . . . . Defines a function of two variables. T = 0:.01:10; . . . . . . . . . . . . . . . . . . . . . .
Bethel VA - MATH - 410
Solving Linear Systems 11. Try the following commands (at the prompt and then press Enter ): (a) A = [1.2969, 0.8648; 0.2161, 0.1441] (b) b1 = [1.2969; 0.2161] (c) x = A\b1 (d) Repeat the process but with a vector places. obtained from by rou
Bethel VA - MATH - 410
Matrix Operations11. Try the following commands (at the prompt and then press Enter ): clear M = [1,3,-1,6;2,4,0,-1;0,-2,3,-1;-1,2,-5,1] det(M) inv(M) 2. Repeat the above procedure for the matrix:3. Multiply and using M * N. Can the order of multi
Bethel VA - MATH - 410
Eigenvalues and Eigenvectors11. Try the following commands (a) digits(4) (b) A = sym([1,1; 0,1]) (c) E = eig(A) (d) [V,E] = eig(A) Find the eigenvalues and eigenvectors for this matrix by hand and interpret the output. 2. Input the symbolic matrix (
Bethel VA - MATH - 410
Eigenvalues by the QR Method11. Enter the following sequence of commands: format long A = hilb(5) m = eig(A) m = flipud(m) 2. Next enter the the following sequence: [Q,R] = qr(A); A = R*Q; ma = diag(A); e = norm(m-ma) 3. Record the value of . Repeat
Bethel VA - MATH - 410
Eigenvalue Power Method11. Enter the following sequence of commands: format long A = hilb(5); m = eig(A) v = ones(5,1) w = v./norm(v); 2. Next enter the following sequence: v = A*w; w = v./norm(v); ma = w'*A*w 3. Repeat the steps in part 2 until the
Bethel VA - MATH - 263
Taylor Series 1M AT L AB has an interactive Taylor series calculator called taylortool. It plots f and the N-th degree Taylor polynomial on an interval. After taylortool is started, we can change f, N, the interval, or the point a. 1. (a) Enter the
Southern Illinois University, Carbondale - FIN - 270
CHAPTER 8 CONTRACT LAW AND PRIVATE ENTERPRISE1.ELEMENTS OF A CONTRACT a. AN AGREEMENT OFFER ACCEPTANCE b. c. d. VOLUNTARILY MADE BY PERSONS WITH CAPACITY OF CONTRACT SUPPORTED BY CONSIDERATION Gratuitous promises are not enforceable e. OBJECTIV
Bethel VA - MATH - 263
Newton's Method11. (a) Try the following commands (at the prompt and press Enter ): syms x format long . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sets displayed digits to 15. f = x^3 - 3*x^2 + 1 f1 = simplify(diff(f) g = sim
Southern Illinois University, Carbondale - FIN - 270
CHAPTER 12Administrative Agencies can be found at all levels of government, most notably, state and federal, however, counties and cities and sometimes townships have administrative agencies with certain specific powers (county health department, ci
Southern Illinois University, Carbondale - FIN - 270
CHAPTER 11 FORMS OF BUSINESS ORGANIZATIONSFACTORS TO CONSIDER WHEN MAKING A DECISION: 1. 2. 3. 4. 5. Ease of Creation Continuity Managerial Control Liability for contracts entered into or injuries caused How profits, income, etc. are taxedI.SO
Southern Illinois University, Carbondale - FIN - 270
CHPT 6 THE CONSTITUTION AND BUSINESS SKIP:Adarand, p. 179-181I. SHAY'S REBELLION &amp; THE ARTICLES OF CONFEDERATIONNOT ON TESTII. THE CONSTITUTION THAT WAS DRAFTED IN PHILADELPHIA provided for a:A.A STRONG EXECUTIVE BRANCH: With a President el
Southern Illinois University, Carbondale - FIN - 270
LEGAL ENVIRONMENT OF BUSINESS FINANCE 270 SECTION 2 FALL 2007INSTRUCTOR: OFFICE PHONE: TEXT:Maurice J. McCann Rehn Hall (453-2459); Law Office (684-5242) Legal and Regulatory Environment of Business, 14th Edition By Reed, Shedd, Morehead and Cor
Bethel VA - MATH - 263
Partial Derivatives11. Enter the following commands: syms x y f = x*y*(x^2-y^2)/(x^2+y^2) fx = diff(f, x) fx = simplify(fx) subs(fx,{x, y},{0, y}) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . This is 2. Define band co
Bethel VA - MATH - 263
Double Integrals 11. Enter the following commands: format long . . . . . . . . . . . . . . . . . . . . . . . . . . . Sets the number of digits displayed to 15. f = inline('x*y^2') . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bethel VA - MATH - 263
Lagrange Multipliers1that are nearest to and farthest from the point 1. To find the points on the ellipse (1,1), using the method of Lagrange multipliers, one needs to solve the system of equations2 3E'DCBA@8 2 ( &amp; &quot; 98)7#6%54 \$ &quot; 2
Bethel VA - MATH - 263
Gradients 11. Enter the following commands: [X, Y] = meshgrid(-2:.2:2); Z = X.*exp(-X.^2 - Y.^2); mesh(X, Y, Z) Rotate this plot into various positions until you fully understand the shape. 2. Next enter the following: [DX, DY] = gradient(Z); contou
Bethel VA - MATH - 263
Contour Plots11. Enter the following commands: [X,Y] = meshgrid(-1:.2:1); Z = X.^2 - Y.^2; contour(Z) Notice the labeling of the axes. In order to fix this enter instead: contour(X, Y, Z) 2. Also try the following variations and report what happens:
Bethel VA - MATH - 263
Defining and Plotting a Function of Two Variables 11. Enter the following commands: syms x y ezmesh(sin(x)*cos(y),[0,10,0,10]) 2. Click on Tools and then click Rotate 3D . Point at the graph, press the left mouse button and hold it down, and then mo
Bethel VA - MATH - 340
Linear Second-order Equations 11. Enter the following commands: (a) y = dsolve('D2y+y=0', 'y(0)=1', 'Dy(0)=1') (b) ezplot(y, [0, 100]) (c) Explain exactly what happened. 2. Repeat the above procedure to solve and plot the solutions for the following
Bethel VA - MATH - 340
Linear First-order Equations 11. Enter the following commands: (a) y = dsolve('Dy=-0.1*y', 'y(0)=1') (b) ezplot(y, [-20, 20]) (c) Explain exactly what happened. 2. Repeat the above procedure to solve and plot the solutions for the following differen
Bethel VA - MATH - 340
Homogeneous ODEs with Constant Coefficients 1Try the following in M AT L AB: syms m eqn1 = 'm^2 - 3*m-1 = 0' eqn2 = 'm^4 - 4*m^3 + 14*m^2 - 20*m + 25 = 0' solve(eqn1) solve(eqn2) For each of the following differential equations:Copyright c 2002 St
Bethel VA - MATH - 340
Special Functions 1The antiderivatives of many elementary functions are not, themselves, elementary funtions. Some of these antiderivatives arise frequently in certain subjects and have been given names. These are examples of what are called special
Bethel VA - MATH - 340
Direction Fields 11. dfield6 is a M AT L AB program for M AT L AB Version 6 that may be retrieved from the website at http:/math.rice.edu/~dfield/ and other versions are also available at this site. If you don't have it, copy it into C:\Matlab\Work
Bethel VA - MATH - 340
Separation of Variables 1 1Enter the following sequence of commands: syms t f = sqrt(9-t^2) int(f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An antiderivative of f. int(f, -3, 3) . . . .
St. Xavier - MATH - 340
8. External Direct Products1External Direct Products We have the basic tools required to studied the structure of groups through their subgroups and their individual elements and by means of isomorphisms between groups. This allows us to build up
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Skull Measurements and Definitions Cranial Measurements Abbrev GOL* XCB* ZYB* BBH* BNL BPL MAB* MAL* AUB UFHT* WFB* UFBR NLH* NLB* OBB* OBH* EKB DKB FRC PAC OCC FOL FOB MDH Measurement Maximum Length Maximum Breadth Bizygomatic Breadth Basion-Bregma
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Chapter 3: Levels of dialect What are levels? Linguistic typology Lexical differences Phonological differences Grammatical differences Pragmatic differencesLING/COM/ANTH 233 Spring 2009 Study Guide Test 2 Wolfram and Schilling-Estes chapters 3
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Public Affairs 527Assignment 4Moving from Populations to SamplesThis assignment is intended to help you make a transition from &quot;deductive reasoning&quot; (deducing information about subsamples of the population from information about the entire popul
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Mathematical Sciences 550.621 Probability Theory II Spring 2002Course goals (the big picture): to develop probabilistic reasoning and problem-solving approaches to provide a rigorous mathematical basis for probability theory to examine several im
Johns Hopkins - PROB - 621
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Johns Hopkins - PROB - 621
Mathematical Sciences 550.621 Probability Theory II Spring 2002 Homework Assignment #1 Due Friday Feb 13th 1. Chung Section 5.1 # 2 2. Chung Section 5.1 # 3 3. Chung Section 5.2 # 5 4. Chung Section 5.2 # 6 5. Chung Section 5.3 # 7 6. Chung Section 5
Johns Hopkins - PROB - 621
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Johns Hopkins - PROB - 621
Mathematical Sciences 550.621 Probability Theory II Spring 2002 Hints for Problem 5.2 #5 - Homework Assignment #1 Due Friday Feb 13th 1. Assuming (Sn - an )/n 0, where Sn = n Xi , it is possible to show (without any i=1 p further assumptions) that (
Johns Hopkins - PROB - 621
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Johns Hopkins - PROB - 621
Mathematical Sciences 550.621 Probability Theory II Spring 2002 Homework Assignment #2 Due Wednesday Feb 27th 1. Chung Section 6.1 # 1 2. Chung Section 6.1 # 4 3. Chung Section 6.1 # 7 4. Chung Section 6.1 # 12 5. Chung Section 6.2 # 13 6. Chung Sect
Johns Hopkins - PROB - 621
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Johns Hopkins - PROB - 621
Mathematical Sciences 550.621 Probability Theory II Spring 2002 Homework Assignment #3 Due Wednesday March 27th 1. Chung Section 6.3 # 9 2. Chung Section 6.3 #11 3. Chung Section 6.4 # 3 4. Chung Section 6.4 # 4 5. Chung Section 6.4 # 12 6. Chung Sec
Johns Hopkins - PROB - 621
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Johns Hopkins - PROB - 621
Mathematical Sciences 550.621 Probability Theory II Spring 2002 Homework Assignment #4 Due Monday April 30th 1. Billingsley #35.2 2. Billingsley #35.3 - Note: All you need to know about finite state Markov chains to solve this problem is that the Yi
Johns Hopkins - PROB - 621
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Kentucky - ET - 225
ET255 Networking ConceptsUnit 2,Chapter 3 Networking HardwareEthernet CablesCisco Learning Institte Network+ Fundamentals and CertificationCopyright 2005 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.Eth
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Math 345. Trigonometry Non-right Triangles: Laws of Sines and CosinesT. Judson Stephen F. Austin State University Fall 2008Learning Objectives1 To understand and be able to apply the Law of Cosines, c2 = a2 + b2 - 2ab cos C. To understand and be
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NJIT - MATH - 345
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See b.'3'# 10,S't&gt;fI)ced; 'X. CSC&quot;':x oIx# :2SoQ)ft=c.sCx, -'dt: - C~l[ohd-;{.CLl'fX COSfLS if',&quot;a-cI~ClS()Vl-'x,octet powr.T= Sinxdt= CDS-XctxJ tS (-J.t) '&quot; - 4. f+ C:' - -4-.Csc4X+C.JCbS&quot;':(g, n&quot;
University of Illinois, Urbana Champaign - MATH - 231
I1wFt/3.I-~ '1~ -~=3 - -_. {he ~ '( = fi lOse.f:h~LJ. _e~lOiL .--- - - - ,.~-@sk~it-Hnd torres p:*'diVl( 'X-o,-~'&quot;./~+c.t(iitldrt-f= 0o0tAt-9=- :2nrt,+ ~ ~ ~=11'~n7(+3.~L 'fle:z 5lt.r=-0tUt(9=
Wisc Stevens Point - MATH - 355
Spring 2009 Apple Data CollectionName:1. You will need to measure 6 apples. 2 each of Fuji, Gala and Granny Smith. 2. Pluck the stem for all apples. 3. Pick an apple from the correct box, First, measure the diameter 3 times and record the larges
Wisc Stevens Point - MATH - 357
Math 357/557 Spring 2009 - Assignment #6Due: Friday, March 13 20 points 1. Pages 430 - 434, problems 8.80, 8.82, 8.86, 8.87 (but replace the word &quot;light&quot; with &quot;white&quot;), 8.90 (2 points each) 2. Pages 436 - 437, problems 8.96, 8.100 (2 points each) 3.
Wisc Stevens Point - MATH - 357
Math 357/557 Spring 2009 - Assignment #11Due: Thursday, May 7 20 points1. Pages 572-576, problems 11.2 and 11.6 - do all of these two, but just answer part d on both (3 points total) 2. Pages 572-576, problem 11.8 (2 points) 3. Pages 582 - 583, pr
Wisc Stevens Point - MATH - 357
Math 357/557 Spring 2009 - Assignment #8Due: Friday, April 3 20 points Announcement: Test 2 will NOT be on April 31. Pages 494 - 495, problems 10.2, 10.6, 10.7, 10.8 (2 points each) 2. Pages 501 - 508, problems 10.9, 10.10, 10.11, 10.12 - just ans
Wisc Stevens Point - MATH - 357
Math 357/557 Spring 2009 - Assignment #5Due: Friday, March 6 18 points 1. Pages 409-411, problems 8.40 (2 points), 8.44 (3 points) 2. Pages 415-421, problems 8.50, 8.51, 8.52, 8.53, 8.56 and 8.60 (2 points each for 8.50, 8.56 and 8.60, 3 points for
Wisc Stevens Point - MATH - 357
Math 357/557 - Spring 2009 - Test #1 - ContentOur first test is on Thursday, Feb 26. You may bring ONE 8.5 inch by 11 inch sheet of paper with any notes, examples, formulas, etc. on it. You probably want to start with the sheet with the info from th
Wisc Stevens Point - MATH - 357
Math 357/557 Spring 2009 - Assignment #10Due: Monday, April 27 20 points1. Pages 547 - 549, problems 10.88, 10.92, 10.94, 10.96 (2 points each for 10.88 and 10.92, 4 points each for 10.94 and 10.96) 2. Pages 554 - 556, problems 10.106, 10.108 (4 p
Wisc Stevens Point - MATH - 357
Math 357/557 Spring 2009 - Assignment #4Due: Friday, Feb. 20 20 points 1. Pages 374-377, problems 7.42, 7.46, 7.56, 7.58 and 7.60 (2 points each) 2. Pages 394-395, problems 8.1, 8.4, 8.6, 8.10 (2 points each for 8.1 and 8.4, 3 points each for 8.6 an