Problem 4 Given the data 2.5 6.5 0 (a) Calculate f(3.4) using Newton's interpolating polynomials of order 1 through 3. Since it is an interpolation problem, n data points among the above table can be used to fit a polynomial of order n-1. Choose the sequence of the points for your estimates to attain the best possible accuracy. That is, the points should be centered around as close as possible to the unknown. (b) Repeat (a) but use the Lagrange i nterpolating polvnomial. Only hand calculations are sufficient for this solving this problem Problem 5: Write an M-file to evaluate the definite integral below using the composite trapezoidal rule with 1, 2, 5, and 10 intervals. Compute the true relative percent error (&t) for each result. Provide a printout of your m- file and the command window showing the results. 1 (8+4 cos x)d*