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Hello, could you solve 1-3 I don't quite understand how to do it my answers are off slightly, thanks! ECOR1042 - Sample questions for numerical

Hello, could you solve 1-3 I don't quite understand how to do it my answers are off slightly, thanks!

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ECOR1042 - Sample questions for numerical methods A function f(x) contains the following points: (2, 1.1), (4,3), (6, 4.5), (8,3), (10,4) 1. Show that, by using Trapezoidal integration, the approximate value of f's integral from x = 2 to x = 10 is 26.10. 2. Show that, by using Simpson's Rule integration, the approximate value of f's integral from x = 2 to x = 10 is 25.40. 3. Show that, by using Simpson's Rule integration, the approximate value of f's integral from x = 2 to x = 8 is 19.95. 4. Show that, by using the Forward (3 point) formula, the approximate value of f'(x=2) is 1.05. 5. Show that, by using the Central (2 point) formula, the approximate value of f'(x = 4) is 0.85. 6. Show that, by using the Backward (3 point) formula, the approximate value of f'(x = 8) is -1.50. 7. Show that the least squares best fit line using all the data is y = 0.29x + 1.38 8. What is the highest degree polynomial one could fit to this entire data set without error? Ans: 4 9. What is the lowest degree polynomial one could fit to this entire data set without error? Ans: 0

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