Assume that the following table was obtained from the solution of a differential equation 0 1 2 3 4 0.0 0.368 0.541 0.448 0.293 X у 5 0.168 (a) Using linear interpolation between adjacent nodes xi, produce a continuous graph of this data on the interval 0 ≤ x ≤ 5. Use Newton's Divided Differences formula. Show the details of your work. (b) This time use quadratic interpolation to produce a continuous graph. Make a figure of (a) and (b). You can use computer programs (excel, python, gnuplot, etc.).

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