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Question 5 Consider the function f(x)=-0.1.x -0.15x²³ -0.5x² -0.25x+1.2 Approximate f '(0.5) using three-point forward, three-point backward and four- point central difference formula with a step size h= 0.25. Use 3 decimal places in all calculations. Ans: -0.859, -0.878, -0.913 (ii) Given that the exact value of f'(0.5) = 0.913. Determine which formula in (i) gives the best result. (i)

Question 5 Consider the function f(x)=-0.1.x -0.15x²³ -0.5x² -0.25x+1.2 Approximate f '(0.5) using three-point forward, three-point backward and four- point central difference formula with a step size h= 0.25. Use 3 decimal places in all calculations. Ans: -0.859, -0.878, -0.913 (ii) Given that the exact value of f'(0.5) = 0.913. Determine which formula in (i) gives the best result. (i)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 5 Consider the function f(x)=-0.1.x -0.15x²-0.5x² -0.25x+1.2 Approximate f'(0.5) using three-point forward, three-point backward and four- point central difference formula with a step size h = 0.25. Use 3 decimal places in all calculations. Ans: -0.859, -0.878, -0.913 (ii) Given that the exact value of f'(0.5) = 0.913. Determine which formula in (i) gives the best result. (i) Question 6 1 Calculate the third derivative for the function f(x)=-. at point x = 2 numerically with 2x³ the four-point central finite difference formula by using points x=1.5, x=1.75, x=2, x = 2.25 and x = 2.5. Then, find the percentage error of the result. Answer: Analytical differentiation: 15 ƒ"(2)=32 = 0.46875 Numerical differentiation: f(2)=0.555264 error = 18.46%
Transcribed Image Text:Question 5 Consider the function f(x)=-0.1.x -0.15x²-0.5x² -0.25x+1.2 Approximate f'(0.5) using three-point forward, three-point backward and four- point central difference formula with a step size h = 0.25. Use 3 decimal places in all calculations. Ans: -0.859, -0.878, -0.913 (ii) Given that the exact value of f'(0.5) = 0.913. Determine which formula in (i) gives the best result. (i) Question 6 1 Calculate the third derivative for the function f(x)=-. at point x = 2 numerically with 2x³ the four-point central finite difference formula by using points x=1.5, x=1.75, x=2, x = 2.25 and x = 2.5. Then, find the percentage error of the result. Answer: Analytical differentiation: 15 ƒ"(2)=32 = 0.46875 Numerical differentiation: f(2)=0.555264 error = 18.46%
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