Caing a Lagrange Interpolation with a quadeatic interpolating polynomial to find the form of f(x), given that 3 6. 792 648 704 729
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- Using Newton's Divided Difference Interpolation, approximate f(1.9) using highest degree of interpolating polynomialFind the Taylor's polynomial po, P1, P2 and p3 for f(x) = ln(x) at x =1 Use a graphing utility to compare the graph of f(x) with graphs of po, P₁, P2 and p3Using the Rodriguez formula obtain the Legendre polynomials Pn(x) for n=0,1,2,3,4,5
- 4. Consider the function f(x) = √x. (a) Find the first and second Taylor polynomials for f at x = 1 . Use a graphing utility to compare these polynomials with f near x = 1. (b) Use these two polynomials to estimate √ 3 .Given the function f (x) = sen (x) tabulated: in the figure • Calculate the interpolation polynomial over all points.• Estimate sen (1.35) using your polynomial.• Make a linear interpolation (by a straight line) between the points (1.3, 0.964)and (1.4, 0.985). Using this polynomial, calculate an approximation forsen (1.35) and compare with the previous item.Formulate the required Newton’s form of the interpolating polynomial for the given function using the conditions specified. Use these to interpolate the value of the function at and , if possible. Compare the accuracy of each estimate to the actual value by calculating the percentage error. Round all values to five decimal places. 3rd degree polynomial using points which are not equally spaced. 3rd degree polynomial using points which are equally spaced. 2nd degree polynomial using points which are not equally spaced. 2nd degree polynomial which are equally spaced. 4th degree polynomial using either equally or not equally spaced points. NOTE: The number of points needed for a polynomial of degree n is n+1