Question 3 (8 marks) (a for [**+eyds the error in a Basie Trapezoidal rule is given by - s"(7). for Fo Os 52 i! Find F"(

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Question 3 8 Marks A For Eyds The Error In A Basie Trapezoidal Rule Is Given By S 7 For Fo Os 52 I Find F 1 (69.48 KiB) Viewed 59 times

Question 3 8 Marks A For Eyds The Error In A Basie Trapezoidal Rule Is Given By S 7 For Fo Os 52 I Find F 2 (47.66 KiB) Viewed 59 times

Question 3 8 Marks A For Eyds The Error In A Basie Trapezoidal Rule Is Given By S 7 For Fo Os 52 I Find F 3 (47.66 KiB) Viewed 59 times

Question 3 (8 marks) (a for [**+eyds the error in a Basie Trapezoidal rule is given by - s"(7). for Fo Os 52 i! Find F"(x). Find the value of "() [1 mark) [1 mark) 11 (b) e The table below provides values of @) for 5 points x € [02] with step size -0.5. Use the table to approximate ſi f(x)dx using the following methods. 0.3 1.5 2 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) 1. Composite Simpson's rule with 5 points Romberg algorithm Find R(2,0), R(2,1) and R(2,2). [3 marks] [3 marks) 11 m=0 m! m=2 HO R(0,0) -8.1946 R(1,0)59565 R(1.1) = 5,2105 =2 2 R(2,0) = R(2.1) = ? R(2, 2) = ?

Question 3 (8 marks) (a) 'x+eº)dx , the error in a Basic Trapezoidal rule is given by = { "(E), for 1333 i. Find f '(x). [1 mark] ii. Find the value of f "(5) [1 mark] (b) The table below provides values of f(x) for 5 points x € [1,3] with step size h=0.5. Use the table to approximate | f(x)dx using the following methods. x 1.5 2 2.5 3 f(x) 0.6321 2.0269 3.8647 6.1679 8.9502 1 (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. ii. Romberg algorithm. Find R(2,0), R(2,1) and R(2,2). [3 marks) [3 marks) m=1 m=2 n=0 m=0 R(0,0) = 4.7912 R(1,0) =6.2603 n=1 R(1,1)=6.75 n = 2 R(2,0) = ? R(2, 1) = ? R(2,2)= ?