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41 Pages

lab8

Course: CS 034, Fall 2009
School: Sanford-Brown Institute
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Word Count: 29977

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Coursehero >> Georgia >> Sanford-Brown Institute >> CS 034

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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
Team Number: Week: Program Size (SLOC) Base Added Deleted Modified Reused # of COTS Total New SLOC Effort (Hours) Project Mgmt. Requirements COTS Assessment Design Life Cycle Planning Configuration Mgmt. Feasibility Analysis Code COTS Tailoring COTS
USC - CSCI - 577
ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Task Name Inception First Team Interaction Members' time preferences Assigning Roles Project Detail discussion Client meeting preperation First Client Meeting Team &amp; Client Introduction Project Overview Collabo
USC - CSCI - 577
ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27Task Name Inception First Team Interaction Members' time preferences Assigning Roles Project Detail discussion Client meeting preperation First Client Meeting Team &amp; Client I
USC - CSCI - 577
ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32Task Name Inception First Team Interaction Members' time preferences Assigning Roles Project Detail discussion Client meeting preperation First Client Meeting
USC - CSCI - 577
ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32Task Name Inception First Team Interaction Members' time preferences Assigning Roles Project Detail discussion Client meeting preperation First Client Meeting
USC - CSCI - 577
ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32Task Name Inception First Team Interaction Members' time preferences Assigning Roles Project Detail discussion Client meeting preperation First Client Meeting
SUNY Stony Brook - MAT - 127
Answers to the MAT127 Homework No.12 Chapter 7 Section 4 Problem 2-4,7,10 &amp; Section 5 Problem 2,5,7,8,11,13,14,15 Section 7.4 2.(a) Let P (t) be the population of bacteria w.r.t. time t in the unit of hour, and let k be the relative growth rate in th
SUNY Stony Brook - MAT - 127
1 Show thatf (x) =n=0(1)n x2n (2n)!is a solution of f + f = 0. Solution. Writef (x) =n=0 2n(1)n x2n1 (2n)!f (x) =n=02n(2n 1)(1)n x2n2 = (2n)!n=02n(2n 1)(1)n x2(n1) (2n)!Notice that we can begin the above sum by n = 1 since
UCSC - CHEM - 112
Chemistry 112B: Organic Chemistry Winter 2008 Professor Rebecca Braslau Assigned Homework Problems The following problems are required, and must be turned in. Problems are to b e done without looking at the answers as much as possible, then corrected
SUNY Stony Brook - MAT - 126
Quiz 4 - Solutionsdx Question 1. The integral 0 2x1 is improper because 2x1 1 is not dened at 1 . 2 1 Question 2. Notice that e2x + 3 &gt; e2x , so e2x1+3 &lt; e2x . We then obtain: 0 1ex dx &lt; e2x + 3 0ex dx = e2x 0ex dxThis last integral is
SUNY Stony Brook - MAT - 126
Quiz 3 - Solutions Question 1. We want to compute x2 dx+a2 using the substitution x2 x = a tan , &lt; &lt; ; a is some positive real number. 2 2 From x = a tan we get dx = a sec2 d and x2 + a2 = a2 + a2 tan2 = a 1 + tan2 . Recalling that 1 + tan2
SUNY Stony Brook - MAT - 125
1 Problem 37 section 4.1. We have the situation shown in the gure, where v is the velocity, (xb , yb ) are the coordinates of the runner, xa is the x-coordinate of the runners friend (we do not show the y -coordinate of the runners friend since it is
SUNY Stony Brook - MAT - 211
MAT211 - Introduction to Linear Algebra SUMMER 07 Practice Final Question 1. Find 1 0 A= 0 the rank of the 23 1 B = 1 22 01 1 matrices: 11 147 1 1 C = 2 5 8 11 369Question 2. Is the matrix below invertible? In case yes, nd its inverse: 100
SUNY Stony Brook - MAT - 127
Answers for HW 1 9. 3 + 5 n2 lim = lim n n + n2 n 10. 1+ n+1 = lim n 3 n 3n 1 lim 11. 12 2n = lim ( )n = 0. n 3 3 n 3n+1 lim 12. lim 1 n n 19. Consider f (x) = x2 ex =x2 ex . 1 n 1 n 3 +5 n2 1 n +1=0+5 = 5. 0+1=1+0 1 =. 30 31 1 = = 1. 0
SUNY Stony Brook - MAT - 127
Answers for HW 11 2.Since ey dy = we get ey = 2 x 2 + C . 3 3. If y = 0, then 1 dy = y which means ln |y | = So nally y = A x2 + 1, A R. 5. From 1+ x2 x dx, +13x dx,1 ln(x2 + 1) + C. 2sin y dy = cos yx2 + 1 dx,we get (since sin ydy = d
SUNY Stony Brook - MAT - 127
Answers to the MAT127 Homework No.2 Chapter 8 Section 2 Problem 5, 7, 9, 19, 20, 25-28, 33, 36, 43 5. Divergent. Because tan n does not convergent to 0. 7. Convergent. SinceNn=11 1 1.5 n (n + 1)1.5 1 21.5 1 1 1.5 + 1.5 2 3 1 1 N 1.5 (N + 1)1.
SUNY Stony Brook - MAT - 126
Solutions for the second quizQuestion 1. We have:2 1x 3 x4 dx = x222 1x dx + x212 13x4 dx = x22 11 dx 3 x2x2 dx =1ln |x|13x3 2 3= ln 2 ln 1 (23 13 ) = ln 2 7xa+1 a+1Remember that the formula xa dx = case we
SUNY Stony Brook - MAT - 123
MAT123 - Introduction to calculus Second Practice Midterm The Second Midterm will be on Tuesday 11/11 at 8:30pm at Harriman 137. Important: check the webpage to get a copy of Second Midterm of Fall 2007! Question 1. Compute: (a) log2 (16) (b) ln e3 +
SUNY Stony Brook - MAT - 126
MAT126 Calculus B Solutions to some practice problems sec 4.9, problem 24. Find f if f (x) = 4 6x 40x3 and f (0) = 2, f (0) = 1. Computing the antiderivative: f (x) = f (x)dx = (4 6x 40x3 )dx = 4x 6 x2 x4 40 + C 2 4= 4x 3x2 10x4 + C f (0)
SUNY Stony Brook - MAT - 127
Math 127 - S2008 Practice Test for the Final Examination1. Show that the function y =Ccos(x) x2is a solution of the dierential equationx2 y + 2xy = sin(x). For what value of C does the solution satisfy the initial condition y(2) = 0? 2. Find th
SUNY Stony Brook - MAT - 126
MAT 126 Summer 08 Practice Final Question 1. Compute the derivative of the given functions: (a) f (x) = (b) g (x) =x (sin(2t) 4+ et cos t)dt6x3 esin u du x sec u+Question 2. Evaluate the indenite integrals: (a) (3x 5.73)13 dx (c) (e) a+b
SUNY Stony Brook - MAT - 126
MAT 126 Summer 08 Practice Midterm NAME: Question 1. Estimate the area under the graph of f (x) = 36 x2 from x = 0 to x = 5 using ve approximating rectangles and right endpoints. Is your estimate an underestimate or an overestimate? Question 2. Exp
SUNY Stony Brook - MAT - 127
Answers to the MAT127 Homework No.8 Chapter 8 Section 8 Problem 1-3, 9, 10, 13, 14 1. 1 21+x =n=0nxn11 ( 22 1 1)( 2 n) ( 1 n + 1) n 2 x n!= 1+n=1 = 1+n=1(1)n1 1 3 5 (2n 3) n x 2n n!So an =(1)n1 135(2n3) , 2n n!t
SUNY Stony Brook - MAT - 127
Answers for HW 9 3. Usually, one may compute the 1st, 2nd and 3rd derivatives of f at to get the 6 T3 . For this problem, one may also use sin(y + z ) = sin y cos z + cos y sin z to get the whole Taylor series of f. Just take y = x and z = .(Sinc
SUNY Stony Brook - MAT - 127
Math 127 - Spring 2008 Practice for First Examination1. Calculate the following limit if it exists. e2n + n5 e5n . n n4 (3ne2n + 1)(4e3n + 5n) lim 2. Determine whether the seriesn=11 + ln(n) (1+ln(n)2 e nis convergent or divergent. Justify yo
SUNY Stony Brook - MAT - 127
Answers to the MAT127 Homework No.6 Chapter 8 Section 6 Problem 3-6, 9, 10, 17, 18-20, 30 3. 1 1 f (x) = = = 1+x 1 (x) (x) =n=0 n=0n(1)n xnThe series converges when |x| &lt; 1, so the the interval of convergence is (1, 1). 4. 1 f ( x) = 3 =
SUNY Stony Brook - MAT - 127
Math 127 - Spring 2008 Practice for Second Examination1. Find the interval of convergence for the power series(1)n+1n=2(x 6)2n . n12 3n2. Find the MacLaurin series for the function ex 1 f (x) = . x3 3. Find the sum of the innite series 2 3
Virgin Islands - FT - 20080521
Third Annual Forum Targeting Faculty Teaching Full Time (FT3) May 22, 2008 University of Victoria Department of Computer Science Engineering / Computer Science Room 660 Agenda Commence by 10:00 AM (Mike Z) SIGCSE in Portland: individual highlig
SUNY Stony Brook - MAT - 131
MAT131 Review for the final1. Evaluate the integral8a. b. c. (t12/3- 2 t 4 / 3 ) dtp (- sin x + cos x )dx0 0 -17 1- x2dx2. A rectangular playground is to be fenced off and divided into two by another fence parallel to one s
SUNY Stony Brook - MAT - 131
Review exercises for midterm I 1. Find the limit a. b. c.x+3 lim x 2- x - 2 x3 lim ex - x x lim e 3 2. If an arrow is shot upward on the moon with a velocity of 70m/s, its height (in meters) after t seconds is given by H(t)=70t-0.83t2. a. F
SUNY Stony Brook - MAT - 131
Calculus Early Exam February 5, 2003Instructions: The exam consists of 15 multiple choice questions. You have 90 minutes to answer all fteen questions. Be sure to record your answers on the opscan form. You are not allowed to use any books, notes, o
SUNY Stony Brook - MAT - 131
MAT131 Spring 2003 Midterm II SolutionProblem Score Max 21 12 8 1 2 3 4 5 6 TotalUse of calculators, books or notes is not allowed. Show the all steps you made to find the answers. Write carefully, points may be taken off for meaningless stateme
SUNY Stony Brook - MAT - 331
MAT 331: Mathematical Problem Solving with ComputersStony Brook, Fall 2008General Information: This course serves as an introduction to computing for the math student. After a general introduction to the use of the computers, we will turn to more
Virgin Islands - DBB - 20090615
Natasha Tuskovich Friday, June 12, 2009E. coli Bio-ThermometerIntroduction A biological thermometer would ideally be a simple, accurate and easily observable register of the organisms environment. A basic version is comprised of E. coli cells that
SUNY Stony Brook - MAT - 331
MAT331 Exercises, Spring 085.2The Fibonacci sequence is a sequence of positive integers dened by recurrence as follows: F0 = 1, F1 = 1 and for each integer i larger than one, Fi = Fi1 + Fi2 . Use Maple to nd the rst 100 terms of the sequence wit
SUNY Stony Brook - MAT - 331
Math 331, Fall 2008, Problems1. Compute IFS parameters and the similarity dimension of the following fractal.1.00.750.50.250.0 0.0 0.25 0.5 0.75 1.02. (a) Find the IFS parameters to generate atractor of the Picture: a right gasket of side
SUNY Stony Brook - MAT - 331
Chapter 5 A turtle in a fractal garden1 Turtle GraphicsImagine you have a small turtle who responds to certain commands like move forward a step, move back a step, turn right, and turn left. Imagine also that this turtle carries a pen (or just lea
SUNY Stony Brook - MAT - 331
MAT331 Exercises, Fall 0812.4Write a procedure in Maple that counts the frequency of letters in a string of text. For example, here is what it looks like when I use mine: freqs(&quot;time flies like an arrow, fruit flies like a bananna.&quot;); [&quot; &quot;,9], [
SUNY Stony Brook - MAT - 331
MAT331 Exercises, Spring 08set number 1NOTE: Each exercise is worth 10 points and can be turned in at any time before its expiration date. Altogether, these will count the same as one project. Many of these problems will require you to use the he
SUNY Stony Brook - MAT - 331
Math 331 - Fall 2008 Project 3 - FractalsDue Dec 17thFor this project, you should submit a paper and a Maple le. The paper has two parts: First part of the paper: Dene a IFS of your choice and compute its similarity dimension (You have to create th
SUNY Stony Brook - MAT - 331
Math 331, Spring 2005, Problem Set 826. Create a procedure that takes as input a positive integer and two real numbers a and b and produces as output (the list of points corresponding to) an n-gon centered at (a, b). Using this procedure, obtain a l
SUNY Stony Brook - MAT - 331
MAT331 Exercises, Spring 088. (expires 9/26) The set of eight pointsset number 3(2.073, 5.794) (1.931, 1.316) (.3959, 3.441) (3.353, 8.950) (4.267, 12.65) (3.167, 8.669) (2.876, 6.992) (1.245, 1.616) approximate an exponential function of the fo
SUNY Stony Brook - MAT - 331
MAT331 Exercises, Spring 08set number 25. (expires 9/19) The Fibonacci sequence is a sequence of positive integers dened by recurrence as follows: F0 = 1, F1 = 1 and for each integer i larger than one, Fi = Fi1 + Fi2 . Use Maple to nd the rst 100
SUNY Stony Brook - MAT - 331
MAT 331, Fall 2008 Project 2: CryptographyDue Friday, Nov 21st This project is about the ElGamal cryptosystem (including ElGamal digital signature). You should implement the system (preferably in Maple). Also, you should write a separate paper with
SUNY Stony Brook - MAT - 331
MAT 331, Fall 2008 Project 1: Fitting a line to dataIn this project, you are to t a line to some data in three dierent ways. First, by using the usual least squares method, which minimizes the sums of the squares of the vertical distances between th
SUNY Stony Brook - MAT - 132
MAT 132, Calculus II December 20, 2006SAMPLE FINAL PROBLEMSThe exam will consist in ten problems like the ones below. Each problem will worth between 9 and 12 points. Show all work to get full credit; a correct answer with incorrect justification
SUNY Stony Brook - MAT - 132
My NAME is:SECTION:Problem 1 2 3 4 5 6 7 Total Score MAT 132 Calculus II Midterm 1 SampleOct 11, 2006 1. (6 points) Evaluate 2. (6 points) Evaluate 3. (6 points) Evaluatee2 1 e x lnxdx sin x dx by parts.2x2 +5 (x2 +1)(x2 +4)dx.4. (5 p
SUNY Stony Brook - MAT - 132
MAT 132 - Final topics- Fall 2006Integration 1. Substitution rule. 2. Integration by parts 3. Additional techniques of integration: (a) Trigonometric integrals (example cos4 (x)dx) (b) Trigonometric substitution (example: solve the integral using
SUNY Stony Brook - MAT - 132
MAT 132 Calculus II Sample Midterm 2Nov 9, 2006 1. (5 points) Let f (x) =1 x+1(a) Find the average value of f in [0, e3 1]. (b) Find c in [0, e3 1] such that f (c) is equal to the average value of f in [0, e3 1]. 2. (6 points) A spring has a n
SUNY Stony Brook - MAT - 132
1 e 1. (6 points) Evaluate e dx x lnx22. (6 points) Evaluate sin x dx by parts.2x2 +5 dx. (x2 +1)(x2 +4)3. (6 points) Evaluate4. (5 points) Use the trapezoidal and mid6 point rule to approximate the value 0 1+x1+x4 d 2 using n = 6. Do not