Hello. I block at question 3 of the following exercise:We consider the function f (x) = (sin (x)) ^ 2
1) Give in a single line, using the Lagrange method, the expression factored from the interpolation polynomial of f at the points 1,2,3,5/2.
2) What happens to the interpolation polynomial if we add the 0 point to the others previous points?
3) What points can be added to have an interpolation polynomial of f that is odd and of degree seven? Give then the expression of such a polynomial, knowing that its dominant coefficients equal to - 128/10395.
4) Find the value of the estimate of the actual error committed at point x = 2/5 for interpolation at the points ± 1 and 1/4.
1) Give in a single line, using the Lagrange method, the expression factored from the interpolation polynomial of f at the points 1,2,3,5/2.
2) What happens to the interpolation polynomial if we add the 0 point to the others previous points?
3) What points can be added to have an interpolation polynomial of f that is odd and of degree seven? Give then the expression of such a polynomial, knowing that its dominant coefficients equal to - 128/10395.
4) Find the value of the estimate of the actual error committed at point x = 2/5 for interpolation at the points ± 1 and 1/4.
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