Use the analytical solution to compute true percent relative errors to evaluate the accuracy of the trapezoidal approximations.
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Chapter 21 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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- 6 108 polynomial is used to approximate v8, the answer is: dy 13. of the parametric equations x: 2-3t 3+2t and y =- is dx Use the following information for Questions 14 and 15: 1+t 1+t Using the Newton-Raphson method to determine the critical co-ordinate of the graph y=f(x)=(x)*an (*) (in words x to the power of tan (x)), you will be required to determine f'(x) 14. The expression for f'(x) is: The following tools were required in determining an expression for f'(x): Application of the natural logarithm 15. I. II. The product rule III. Implicit differentiationarrow_forwardA root of the function f(x) = x3 – 10x² +5 lies close to x = 0.7. Doing three iterations, compute this root using the Newton- Raphson method with an initial guess of x=1). Newton-Raphson iterative equation is given as: f(x;) Xi+1 = Xị - f'(xi)arrow_forwardLet / xcos(x) dx. The approximation of / using the two-point Gaussian quadrature formula is: 2.56125 0.14661 -379.538 0.45327 Find the actual error when the first dervative of f(x) = in x at x = 2 is approxamated by the following 3-pount formula F+h) - 2F()-3f(x-h) wth h-0.5 0.0431arrow_forward
- 2 0 2 5 7 11 f(x) 13 5 17 28 41 Selected values of a differentiable function f are given in the table above. What is the fewearrow_forward5) Use a 2 dimensional linear Taylor approximation to find a rational approximation to .982/2.013+1(i.e., a fraction) without using a calculator.arrow_forward88|| 5:08 docs.google.com/for 3 Your answer Draw the orthogonal projections of the Isometric shown in the figure below. 52 20 26 TRUE R16 12 180 1 Add file Submit Never submit passwords through Google Forms. This form was created inside of University of Baghdad. Report Abuse 001 Il>arrow_forward
- x^2-5x^(1/3)+1=0 Has a root between 2 and 2.5 use bisection method to three iterations by hand.arrow_forwardFind the three unknown on this problems using Elimination Method and Cramer's Rule. Attach your solutions and indicate your final answer. Problem 1. 7z 5y 3z 16 %3D 3z 5y + 2z -8 %3D 5z + 3y 7z = 0 Problem 2. 4x-2y+3z 1 *+3y-4z -7 3x+ y+2z 5arrow_forward4. Given the following data : T(k') 600 700 800 900 (Cp/R) 3.671 3.755 3.838 3.917 Where "T" is the absolute temperature and (C,/R) is the dimensionless specific heat of air. Use Newton's forward interpolation method to find the specific heat at T = 670 k°. %3Darrow_forward
- A magic square is an arrangement of n numbers into n rows and n columns using distinct numbers from 1 up to n² such that the sum in any row, any column or any of the two diagonals is fixed. Consider the 4 by 4 magic square below: aj a5 2 13 a2 10 11 a7 аз6 а4 12 4 15 a6 1 What is the value of a4 ? 07 O 5 O 16 A Moving to the next question prevents changes to this answer. Question 1 of 3> P Type here to search 9:47 PM 29°C 30-Nov-21 backspe E F C shift alt ctriarrow_forward3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx -2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx-2 = 0 u(0) = 1 u(1) = 0arrow_forwardHello ... good evening Sir,Permission, i have a question in my homework related numerical methods lesson. The following bellow is question. Please advice. Thank you so much Regards,Irfan Find the X and Y values of the 2 equations below using the Gauss method 3X + 6Y = 146X + 10Y = 22arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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