Question 5Consider the functionf(x)=-0.1.x -0.15x²-0.5x² -0.25x+1.2Approximate 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 placesin 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 61Calculate the third derivative for the function f(x)=-.at point x = 2 numerically with2x³the 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:15ƒ"(2)=32 = 0.46875Numerical differentiation:f(2)=0.555264error = 18.46%

As per our guideline we can solve only first question. Second part of the question given value is…

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)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.7: Exponential And Logarithmic Models

Problem 4SE: Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of...

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