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![6. Utln(a)=0 f(x)= x+ ln (x) 1 fla)= it 1/4 to for não and itt to for ao $6-1)-0 f(1) = 3/2=100 the interval [0.5, 0.6] Root](http://img.homeworklib.com/questions/82ef85c0-1f94-11eb-82fb-45e6e0f8047a.png?x-oss-process=image/resize,w_560)
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QUESTION 6 The equation X +in(x) = 0 has one root in the interval Oa (0.5,...
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...
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...
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...
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Ve...
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Verify from the graph that the interval endpoints at zo and zi have opposite signs. Use the bisection method to estimate the root (to 4 decimal places) of the equation 5 marks] (c) Use the secant method to estimate the root (to 4 decimal places) of the equation 6 marks that lies between the endpoints given. (Perform...
Please show the steps to answer this question We consider bisection method for finding the root...
Please show the steps to answer this question
We consider bisection method for finding the root of the function f(x) = 2.3 – 1 on the interval [0, 1], so Xo = 0.5. We perform 2 steps, and our approximations Xi and X2 from these two steps are: O x1 = 1, X2 = 0.6 O x1 = 0.7, x2 = 0.8 O x1 = 0.75, x2 = 0.875 O x1 = 0.3, 22 = 0.6
[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)...
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.
Please use Taylor Polynomial series and quadratic formula. 8. (10 points) Consider the equation cos(x)-x = 0. The plot of y-cos(x)-x reve that the equation has a single root lying in the interval [0,...
Please use Taylor Polynomial series and quadratic formula.
8. (10 points) Consider the equation cos(x)-x = 0. The plot of y-cos(x)-x reve that the equation has a single root lying in the interval [0, 1] (marked with a circle). 0.5 0 0.8 -0.5 0.6 0.4 0.2 Find the best possible approximation for that root.
8. (10 points) Consider the equation cos(x)-x = 0. The plot of y-cos(x)-x reve that the equation has a single root lying in the interval [0,...
Question 1 (10 marks) For a linear system Ax- b with 1 0 -1 A-1 2-1 2 -1 3 b=14 18 and compute by...
Please do question 5 for me. Thanks
Question 1 (10 marks) For a linear system Ax- b with 1 0 -1 A-1 2-1 2 -1 3 b=14 18 and compute by hand the first four iterations with the Jacobi method, using x()0 Hint: for the ease of calculation, keep to rational fractions rather than decimals Question 2 For the same linear system as in Question 1, compute by hand the first three iterations (10 marks) with the Gauss Seidel method,...
Question 1 (10 marks) For a linear system Ax b with 1 0-1 A-1 2-1 2-13 and b4 18 compute by hand ...
Question 1 (10 marks) For a linear system Ax b with 1 0-1 A-1 2-1 2-13 and b4 18 compute by hand the first four iterations with the Jacobi method, usg0 Hint: for the ease of calculation, keep to rational fractions rather than decimals. (10 marks) Question 2 For the same linear svstem as in Question 1. compute by hand the first three iterations with the Gauss Seidel method, us0 Hint: for the ease of calculation, keep to rational fractions...
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...
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...
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Verify from the graph that the interval endpoints at zo and zi have opposite signs. Use the bisection method to estimate the root (to 4 decimal places) of the equation 5 marks] (c) Use the secant method to estimate the root (to 4 decimal places) of the equation 6 marks that lies between the endpoints given. (Perform...
Please show the steps to answer this question
We consider bisection method for finding the root of the function f(x) = 2.3 – 1 on the interval [0, 1], so Xo = 0.5. We perform 2 steps, and our approximations Xi and X2 from these two steps are: O x1 = 1, X2 = 0.6 O x1 = 0.7, x2 = 0.8 O x1 = 0.75, x2 = 0.875 O x1 = 0.3, 22 = 0.6
[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)...
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.
Please use Taylor Polynomial series and quadratic formula.
8. (10 points) Consider the equation cos(x)-x = 0. The plot of y-cos(x)-x reve that the equation has a single root lying in the interval [0, 1] (marked with a circle). 0.5 0 0.8 -0.5 0.6 0.4 0.2 Find the best possible approximation for that root.
8. (10 points) Consider the equation cos(x)-x = 0. The plot of y-cos(x)-x reve that the equation has a single root lying in the interval [0,...
Please do question 5 for me. Thanks
Question 1 (10 marks) For a linear system Ax- b with 1 0 -1 A-1 2-1 2 -1 3 b=14 18 and compute by hand the first four iterations with the Jacobi method, using x()0 Hint: for the ease of calculation, keep to rational fractions rather than decimals Question 2 For the same linear system as in Question 1, compute by hand the first three iterations (10 marks) with the Gauss Seidel method,...
Question 1 (10 marks) For a linear system Ax b with 1 0-1 A-1 2-1 2-13 and b4 18 compute by hand the first four iterations with the Jacobi method, usg0 Hint: for the ease of calculation, keep to rational fractions rather than decimals. (10 marks) Question 2 For the same linear svstem as in Question 1. compute by hand the first three iterations with the Gauss Seidel method, us0 Hint: for the ease of calculation, keep to rational fractions...
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