Question: Let n be an integer, -5+- 10 for i=0,1,2,...,n, and y = 71 (a) Given 11 data points (,). i=0,..., n for n =

Let n be an integer, -5+- 10 for i=0,1,2,...,n, and y =

Let n be an integer, -5+- 10 for i=0,1,2,...,n, and y = 71 (a) Given 11 data points (,). i=0,..., n for n = 10, approximate the value of y at ar = 4.8 by using piecewise linear interpolation. (b) Let n = 10. Interpolate the 11 data points (), i = 0,...,n by using the "spline" command in MATLAB (with not-a-knot conditions). Plot the graphs of the spline interpolant and y for a [-5,5] on the same axis. (c) Find the cubic spline function S(r) that interpolates the three data points (x, y), i = 0, 1, 2 where n = 2 satisfying S'(-5) = S'(5) = 0.

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