Question: The data in Exercise 3 were generated using the following functions. Use the cubic splines constructed in Exercise 3 for the given value of x

The data in Exercise 3 were generated using the following functions. Use the cubic splines constructed in Exercise 3 for the given value of x to approximate f (x) and f'(x), and calculate the actual error.
a. f (x) = x ln x; approximate f (8.4) and f'(8.4).
b. f (x) = sin(ex − 2); approximate f (0.9) and f'(0.9).
c. f (x) = x3 + 4.001x2 + 4.002x + 1.101; approximate f (−1/3 ) and f'(−1/3).
d. f (x) = x cos x − 2x2 + 3x − 1; approximate f (0.25) and f'(0.25).

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