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[20 Marks] Question 2 a) Given f(x)= x - 7x2 +14x-6 i) Show that there is...
[20 Marks] Question 2 a) Given f(x)= x - 7x2 +14x-6 i) Show that there is a root a in interval [0,1] (1 mark) ii) Find the minimum number of iterations needed by the bisection method to approximate the root, a of f(x) = 0 on [0,1] with accuracy of 2 decimal points. (3 marks) iii) Find the root (a) of f(x)= x - 7x² +14x6 on [0,1] using the bisection method with accuracy of 2 decimal points. (6 marks)...
this is numerical analysis QUESTION 1 (a) Apart from 1 = 0 the equation f(1) =...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
QUESTION 1 = = (a) Apart from x = 0 the equation f(x) 22 – 4...
QUESTION 1 = = (a) Apart from x = 0 the equation f(x) 22 – 4 sin r 0 has another root in (1, 2.5). Perform three iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x(0) = 1.5 as the initial solution. Compare the error from the Newton's approximation with that incurred for the same...
my w it uld Ul Table 2.10. Problem 3 (Chapter 3) - [Parts (a) and (b)...
my w it uld Ul Table 2.10. Problem 3 (Chapter 3) - [Parts (a) and (b) are independent] a) For the function f(x) = x-exp(-x), do a calculation by hand using a calculator to find the root to - an accuracy of 0.1. At most, five iterations (or fewer) are needed to obtain the desired accuracy. (b) Write a program which uses the bisection method to find the root of the function f(x) = 5 - x on the interval...
QUESTION 1 (a) Apart from = 0 the equation f(t) = 12 - 4sin r =...
QUESTION 1 (a) Apart from = 0 the equation f(t) = 12 - 4sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x(0) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation with that incurred for the same...
ONLY ANSWER IN MATLAB. 11. Find a bound for the number of Bisection method iterations needed...
ONLY ANSWER IN MATLAB.
11. Find a bound for the number of Bisection method iterations needed to achieve an approximation with accuracy 10-3 to the solution of x³ +x – 4 = 0 lying in the interval (1, 4]. Find an approximation to the root with this degree of accuracy. please solve in MATLAB.
Write a Matlab function for: 1. Root Finding: Calculate the root of the equation f(x)=x^3 −5x^2...
Write a Matlab function for: 1. Root Finding: Calculate the root of the equation f(x)=x^3 −5x^2 +3x−7 Calculate the accuracy of the solution to 1 × 10−10. Find the number of iterations required to achieve this accuracy. Compute the root of the equation with the bisection method. Your program should output the following lines: • Bisection Method: Method converged to root X after Y iterations with a relative error of Z.
2) (15 points) a) Determine the roots of f(x)=-12 – 21x +18r? - 2,75x' graphically. In...
2) (15 points) a) Determine the roots of f(x)=-12 – 21x +18r? - 2,75x' graphically. In addition, determine the first root of the function with b) bisection and c) false-position. For (b) and (c), use initial guesses of x, =-land x, = 0, and a stopping criterion of 1%. 3) (25 points) Determine the highest real root of f(x) = 2x – 11,7x² +17,7x-5 a) Graphically, b) Fixed-point iteration method (three iterations, x, = 3) c) Newton-Raphson method (three iterations,...
My San Compare the convergence of the Bisection and Newton Method Solve 1ze - 3 0.Use eps-10 as your tolerance. Use a 0,b 1 for the Bisection Method and zo - 1 as your initial guess for the Newto...
My San Compare the convergence of the Bisection and Newton Method Solve 1ze - 3 0.Use eps-10 as your tolerance. Use a 0,b 1 for the Bisection Method and zo - 1 as your initial guess for the Newton Metho a Find the solution to the indicated accuracy b. Bisection Method took Newton Method took e. Upload a word ile that has the codes and outpur table ierations and iterations Choose File No fle chosen Points possible: 1 This is...
QUESTION 1 (a) Apart from r=0 the equation f(x) = x? - Asin - 0 has...
QUESTION 1 (a) Apart from r=0 the equation f(x) = x? - Asin - 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations.
[20 Marks] Question 2 a) Given f(x)= x - 7x2 +14x-6 i) Show that there is a root a in interval [0,1] (1 mark) ii) Find the minimum number of iterations needed by the bisection method to approximate the root, a of f(x) = 0 on [0,1] with accuracy of 2 decimal points. (3 marks) iii) Find the root (a) of f(x)= x - 7x² +14x6 on [0,1] using the bisection method with accuracy of 2 decimal points. (6 marks)...
this is numerical analysis
QUESTION 1 (a) Apart from 1 = 0 the equation f(1) = x2 - 4 sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation...
QUESTION 1 = = (a) Apart from x = 0 the equation f(x) 22 – 4 sin r 0 has another root in (1, 2.5). Perform three iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x(0) = 1.5 as the initial solution. Compare the error from the Newton's approximation with that incurred for the same...
my w it uld Ul Table 2.10. Problem 3 (Chapter 3) - [Parts (a) and (b) are independent] a) For the function f(x) = x-exp(-x), do a calculation by hand using a calculator to find the root to - an accuracy of 0.1. At most, five iterations (or fewer) are needed to obtain the desired accuracy. (b) Write a program which uses the bisection method to find the root of the function f(x) = 5 - x on the interval...
QUESTION 1 (a) Apart from = 0 the equation f(t) = 12 - 4sin r = 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations. (b) Perform three iterations of Newton's method for the function in (a) above, using x(0) = 1.5 as the initial (10) solution. Compare the error from the Newton's approximation with that incurred for the same...
ONLY ANSWER IN MATLAB.
11. Find a bound for the number of Bisection method iterations needed to achieve an approximation with accuracy 10-3 to the solution of x³ +x – 4 = 0 lying in the interval (1, 4]. Find an approximation to the root with this degree of accuracy. please solve in MATLAB.
2) (15 points) a) Determine the roots of f(x)=-12 – 21x +18r? - 2,75x' graphically. In addition, determine the first root of the function with b) bisection and c) false-position. For (b) and (c), use initial guesses of x, =-land x, = 0, and a stopping criterion of 1%. 3) (25 points) Determine the highest real root of f(x) = 2x – 11,7x² +17,7x-5 a) Graphically, b) Fixed-point iteration method (three iterations, x, = 3) c) Newton-Raphson method (three iterations,...
My San Compare the convergence of the Bisection and Newton Method Solve 1ze - 3 0.Use eps-10 as your tolerance. Use a 0,b 1 for the Bisection Method and zo - 1 as your initial guess for the Newton Metho a Find the solution to the indicated accuracy b. Bisection Method took Newton Method took e. Upload a word ile that has the codes and outpur table ierations and iterations Choose File No fle chosen Points possible: 1 This is...
QUESTION 1 (a) Apart from r=0 the equation f(x) = x? - Asin - 0 has another root in (1, 2.5). Perform three (10) iterations of the bisection method to approximate the root. State the accuracy of the root after the three iterations.
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