 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-1/16c/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The recurrence

T_{k + 1} = 2 x T_{k} - T_{k - 1}

shows that

T_{n + 1}

has leading coefficient

2^{n}

. Since its roots are the interpolation nodes,

T_{n + 1} = 2^{n} Π

, and

∣ T_{n + 1} ∣ \leq 1

[- 1, 1]

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