(30 marks] We are asked to provide an interpolant for the Bessel function of the first kind of order zero, J. (2). (a) Create a table of data points listed to 7 decimal places for the interpolation points x1 = 1.0, x 2 = 1.3, X3 = 1.6, X4 = 1.9, 25 = 2.2. [Hint: See MATLAB's help on BesselJ.] (b) Fit a second-degree polynomial through the points X1, X2, 13. Use this interpolant to estimate J.(1.5). Compute the error. (c) Fit a second-degree polynomial through the points X3, X4, X5. Using this to estimate J.(1.5) is called polynomial extrapolation. Explain the use of this term. Compute the error in using this polynomial to approximate J.(1.5). (d) Fit a third-degree polynomial through the points 22, 13, 14, 15. Use this inter- polant to estimate J. (1.5). Compute the error. (e) Fit a fourth-degree polynomial through the points 21, 22, 23, 24, 25. Use this interpolant to estimate J (1.5). Compute the error. (f) Does the highest-order interpolant give the best approximation to J.(1.5)? Is this result surprising