Question: Given the partition x0 = 0, x1 = 0.05, x2 = 0.1 of [0, 0.1] and f (x) = e2x: a. Find the cubic spline

Given the partition x0 = 0, x1 = 0.05, x2 = 0.1 of [0, 0.1] and f (x) = e2x:
a. Find the cubic spline s with clamped boundary conditions that interpolates f.
b. Find an approximation for

c. Use Theorem 3.13 to estimate max0‰¤x‰¤0.1 |f (x) ˆ’ s(x)| and

d. Determine the cubic spline S with natural boundary conditions, and compare S(0.02), s(0.02), and e0.04 = 1.04081077.

i e dx by evaluating ) dre 0.1 f(x) dx s(x) dx

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