 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/31a/d/solution

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

Since

y = u / x

, two real independent approximations are

y_{1} \sim x^{- 3/4} (1 + 1/ (4 x) + 5/ (32 x^{2})) cos (2 x + x^{- 1/2} + x^{- 3/2} /12),

y_{2} \sim x^{- 3/4} (1 + 1/ (4 x) + 5/ (32 x^{2})) sin (2 x + x^{- 1/2} + x^{- 3/2} /12) .

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