 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ib/paper-3/15a/e/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Direct integration gives

\frac{1}{π} \int_{0}^{n} cos (k x) d k = \frac{s i n ( n x )}{π x} .

The sinc approximate identity converges distributionally to the Dirac delta function, using the supplied integral of

sin y / y

. Thus the limit is $δ (x)$ .

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