Question: The data in Exercise 4 were generated using the following functions. Use the cubic splines constructed in Exercise 4 for the given value of x

The data in Exercise 4 were generated using the following functions. Use the cubic splines constructed in Exercise 4 for the given value of x to approximate f (x) and f'(x), and calculate the actual error.
a. f (x) = e2x ; approximate f (0.43) and f' (0.43).
b. f (x) = x4 − x3 + x2 − x + 1; approximate f (0) and f'(0).
c. f (x) = x2 cos x − 3x; approximate f (0.18) and f'(0.18).
d. f (x) = ln(ex + 2); approximate f (0.25) and f'(0.25).

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