(a) Use the method of divided differences to find the degree 4 interpolating polynomial P 4 (x)…

(a) Use the method of divided differences to find the degree 4 interpolating polynomial P4(x) for the data (0.6,1.433329), (0.7,1.632316), (0.8,1.896481), (0.9,2.247908), and (1.0,2.718282). (b) Calculate P4(0.82) and P4(0.98). (c) The preceding data come from the function f (x) = . Use the interpolation error formula to find upper bounds for the error at x = 0.82 and x = 0.98, and compare the bounds with the actual error. (d) Plot the actual interpolation error P (x) −  on the intervals [.5,1] and [0,2].

 

 

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