(Solution) - Repeat Exercise 6 using the clamped cubic splines constructed in -(2025 Original AI-Free Solution)

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Repeat Exercise 6 using the clamped cubic splines constructed in Exercise 8.
In Exercise 6
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).