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sin x 2. a. Show that x = 3+ has a solution in the interval [3,4]....
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2...
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
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.
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 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...
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 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2...
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.
[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.
1) Use the bisection method to find the third approximation of 2 starting with the initial interval [1,2], and find the...
1) Use the bisection method to find the third approximation of 2 starting with the initial interval [1,2], and find the corresponding absolute error. Also, compute the number of iterations needed to achieve an approximation accurate to within 10 Then, use the suitable one to compute the second approximation of the root using xo,and find an upper bound for the corresponding error.
1) Use the bisection method to find the third approximation of 2 starting with the initial interval [1,2],...
QUESTION 1 = (a) Apart from x = 0 the equation f(x) 22 – 4sin x...
QUESTION 1 = (a) Apart from x = 0 the equation f(x) 22 – 4sin x = 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.
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
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 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...
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 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.
[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.
1) Use the bisection method to find the third approximation of 2 starting with the initial interval [1,2], and find the corresponding absolute error. Also, compute the number of iterations needed to achieve an approximation accurate to within 10 Then, use the suitable one to compute the second approximation of the root using xo,and find an upper bound for the corresponding error.
1) Use the bisection method to find the third approximation of 2 starting with the initial interval [1,2],...
QUESTION 1 = (a) Apart from x = 0 the equation f(x) 22 – 4sin x = 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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