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2. Consider the root finding problem f(3) = e* (1 - 2) (a) Show that by...
4) (16 points) The function f(x)= x? – 2x² - 4x+8 has a double root at...
4) (16 points) The function f(x)= x? – 2x² - 4x+8 has a double root at x = 2. Use a) the standard Newton-Raphson, b) the modified Newton-Raphson to solve for the root at x = 2. Compare the rate of convergence using an initial guess of Xo = 1,2. 5) (14 points) Determine the roots of the following simultaneous nonlinear equations using a) fixed-point iteration and b) the Newton-Raphson method: y=-x? +x+0,75 y + 5xy = r? Employ initial...
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6?...
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6? + 10 a. Write a Python function for the derivative of f(x) that takes x and returns the derivative of f(x). Take the derivative of f(x) analytically with respect to x before writing the function. b. Write a Python code that approximately finds the real root, x0, of f(x) such that f(x0)~0 using the Newton-Raphson method. The code is expected to get an initial...
QUESTION 1 (a) Show that the equation (x - 2) = has a root between x...
QUESTION 1 (a) Show that the equation (x - 2) = has a root between x = 2 and x = 3. Using the x+2 first approximation as 2.7 and the Newton-Raphson method, calculate this root correct to two decimal places. (8 marks) (b) Show that e' +x-2 = 0 has a root in interval [0, 1]. Using basic iteration method, calculate this root correct to four decimal places. (12 marks) 1 (C) Find an approximate value for the integral...
3. (30 pts) (Problem 6.2) Determine the highest real root of f(x) 2x3- 11.7x2 + 17.7x...
3. (30 pts) (Problem 6.2) Determine the highest real root of f(x) 2x3- 11.7x2 + 17.7x -5 a) Graphically. b) Write a MATLAB program using the fixed-point method to determine the root with xo- Write a MATLAB program using the Newton-Raphson method to determine the root with Xo-3. c) d) Write a MATLAB program using the secant method to determine the root with x-1-3 and Xo- 4. e) Compare the relative errors between these three methods at the third iteration...
clearvars close all clc tol = 0.0001; % this is the tolerance for root identification xold...
clearvars
close all
clc
tol = 0.0001; % this is the tolerance for root identification
xold = 0.5; % this is the initial guess
test = 1; % this simply ensures we have a test value to enter the loop below.
%If we don't preallocate this, MATLAB will error when it trys to start the
%while loop below
k = 1; %this is the iteration counter. Similar to "test" we need to preallocate it
%to allow the while loop to...
6.5 Employ the Newton-Raphson method to determine a real root for 4x20.5 using initial guesses of...
6.5 Employ the Newton-Raphson method to determine a real root for 4x20.5 using initial guesses of (a) 4.52 f(x) 15.5x Pick the best numerical technique, justify your choice and then use that technique to determine the root. Note that it is known that for positive initial guesses, all techniques except fixed-point iteration will eventually converge. Perform iterations until the approximate relative error falls below 2 %. If you use a bracket- ing method, use initial guesses of x 0 and...
1. This question concerns finding the roots of the scalar non-linear function f(x) = r2-1-sinx (1...
1. This question concerns finding the roots of the scalar non-linear function f(x) = r2-1-sinx (1 mark) (b) Apply two iterations of the bisection method to f(x) 0 to find the positive root. (3 marks) (c) Apply two iterations of the Newton-Raphson method to find the positive root. Choose (3 marks) (d) Use the Newton-Raphson method and Matlab to find the positive root to 15 significant (3 marks) (a) Use Matlab to obtain a graph of the function that shows...
X Solution.pdf x Solved Problems x 1 * Chapter%206.pdf 18-02-ME-GE301 " Univery macaron ROBLEM 6.11 (a)...
X Solution.pdf x Solved Problems x 1 * Chapter%206.pdf 18-02-ME-GE301 " Univery macaron ROBLEM 6.11 (a) Apply the Newton-Raphson method to the function f(x) = tanh(x2 – 9) to evaluate its known real root at x = 3. Use an initial guess of Xo = 3.2 and take a minimum of three iterations. (b) Did the method exhibit convergence onto its real root? Sketch the plot with the results for each iteration labeled. Alla y PROBLEM 6.11 (a) Apply the...
L. Determine the real root(s) off(x)--5xs + 14x3 + 20x2 + 10x a. Graphically on a graph paper. b....
l. Determine the real root(s) off(x)--5xs + 14x3 + 20x2 + 10x a. Graphically on a graph paper. b. Using Bisection method c. Using False Position method to determine the root, employing initial guesses of x-2 d. Using the Newton Raphson methods to determine the root, employing initial guess to determine the root, employing initial guesses ofxn-2 and Xu-4 and Es= 18%. and r 5.0 andas answer. 1%. was this method the best for these initial guesses? Explain your xo--l...
Use the Newton-Raphson method to find the root of f(x) = e-*(6 - 2x) - 1...
Use the Newton-Raphson method to find the root of f(x) = e-*(6 - 2x) - 1 Use an initial guess of xo = 1.2 and perform 3 iterations. For the N-R method: Xi+1 = x; - f(x;) f'(x;)
4) (16 points) The function f(x)= x? – 2x² - 4x+8 has a double root at x = 2. Use a) the standard Newton-Raphson, b) the modified Newton-Raphson to solve for the root at x = 2. Compare the rate of convergence using an initial guess of Xo = 1,2. 5) (14 points) Determine the roots of the following simultaneous nonlinear equations using a) fixed-point iteration and b) the Newton-Raphson method: y=-x? +x+0,75 y + 5xy = r? Employ initial...
QUESTION 1 (a) Show that the equation (x - 2) = has a root between x = 2 and x = 3. Using the x+2 first approximation as 2.7 and the Newton-Raphson method, calculate this root correct to two decimal places. (8 marks) (b) Show that e' +x-2 = 0 has a root in interval [0, 1]. Using basic iteration method, calculate this root correct to four decimal places. (12 marks) 1 (C) Find an approximate value for the integral...
3. (30 pts) (Problem 6.2) Determine the highest real root of f(x) 2x3- 11.7x2 + 17.7x -5 a) Graphically. b) Write a MATLAB program using the fixed-point method to determine the root with xo- Write a MATLAB program using the Newton-Raphson method to determine the root with Xo-3. c) d) Write a MATLAB program using the secant method to determine the root with x-1-3 and Xo- 4. e) Compare the relative errors between these three methods at the third iteration...
clearvars
close all
clc
tol = 0.0001; % this is the tolerance for root identification
xold = 0.5; % this is the initial guess
test = 1; % this simply ensures we have a test value to enter the loop below.
%If we don't preallocate this, MATLAB will error when it trys to start the
%while loop below
k = 1; %this is the iteration counter. Similar to "test" we need to preallocate it
%to allow the while loop to...
6.5 Employ the Newton-Raphson method to determine a real root for 4x20.5 using initial guesses of (a) 4.52 f(x) 15.5x Pick the best numerical technique, justify your choice and then use that technique to determine the root. Note that it is known that for positive initial guesses, all techniques except fixed-point iteration will eventually converge. Perform iterations until the approximate relative error falls below 2 %. If you use a bracket- ing method, use initial guesses of x 0 and...
1. This question concerns finding the roots of the scalar non-linear function f(x) = r2-1-sinx (1 mark) (b) Apply two iterations of the bisection method to f(x) 0 to find the positive root. (3 marks) (c) Apply two iterations of the Newton-Raphson method to find the positive root. Choose (3 marks) (d) Use the Newton-Raphson method and Matlab to find the positive root to 15 significant (3 marks) (a) Use Matlab to obtain a graph of the function that shows...
X Solution.pdf x Solved Problems x 1 * Chapter%206.pdf 18-02-ME-GE301 " Univery macaron ROBLEM 6.11 (a) Apply the Newton-Raphson method to the function f(x) = tanh(x2 – 9) to evaluate its known real root at x = 3. Use an initial guess of Xo = 3.2 and take a minimum of three iterations. (b) Did the method exhibit convergence onto its real root? Sketch the plot with the results for each iteration labeled. Alla y PROBLEM 6.11 (a) Apply the...
l. Determine the real root(s) off(x)--5xs + 14x3 + 20x2 + 10x a. Graphically on a graph paper. b. Using Bisection method c. Using False Position method to determine the root, employing initial guesses of x-2 d. Using the Newton Raphson methods to determine the root, employing initial guess to determine the root, employing initial guesses ofxn-2 and Xu-4 and Es= 18%. and r 5.0 andas answer. 1%. was this method the best for these initial guesses? Explain your xo--l...
Use the Newton-Raphson method to find the root of f(x) = e-*(6 - 2x) - 1 Use an initial guess of xo = 1.2 and perform 3 iterations. For the N-R method: Xi+1 = x; - f(x;) f'(x;)
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