(b) The table below provides values of f(x) for 5 points x = [0,2] with step...

Transcribed Image Text:

(b) The table below provides values of f(x) for 5 points x = [0,2] with step size h=0.5. Use the table to approximate f(x)dx using the following methods. x 0 0.5 1 1.5 2 f(x) 1 1.7737 3.7183 7.8567 15.3891 (Note: Show how do you use the formula of the methods and write your answer in 4 decimal places.) i. Composite Simpson's rule with 5 points. [3 marks] ii. Romberg algorithm. Find R(2,0), R(2,1) and R(2,2). [3 marks] n=0 m=0 R(0,0)=8.1946 m=1 m=2 n=1 R(1,0)=5.9565 R(1,1)=5.2105 n = 2 R(2,0)=? R(2,1) = ? R(2,2)=? (b) The table below provides values of f(x) for 5 points x = [0,2] with step size h=0.5. Use the table to approximate f(x)dx using the following methods. x 0 0.5 1 1.5 2 f(x) 1 1.7737 3.7183 7.8567 15.3891 (Note: Show how do you use the formula of the methods and write your answer in 4 decimal places.) i. Composite Simpson's rule with 5 points. [3 marks] ii. Romberg algorithm. Find R(2,0), R(2,1) and R(2,2). [3 marks] n=0 m=0 R(0,0)=8.1946 m=1 m=2 n=1 R(1,0)=5.9565 R(1,1)=5.2105 n = 2 R(2,0)=? R(2,1) = ? R(2,2)=?