 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2003/ib/paper-2/14b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

1, x, x^{2}

requires

a_{0} + a_{1} + a_{2} = 0, - a_{0} + a_{2} = 0, a_{0} + a_{2} = 2.

Solving gives

a_{0} = 1, a_{1} = - 2, a_{2} = 1.

Thus the approximation is the unit-spacing centered second difference,

μ (f) = f (- 1) - 2 f (0) + f (1)

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