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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/3/i/b/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2006 / Paper 2 / 3 / i / b / Solution by

Codex  0 2026-10-20

The numerator is nonzero at

1

and

- 2/3

, so the finite singularities are a pole of order three at $1$ and a pole of order two at $- 2/3$ . The numerator degree exceeds the denominator degree by three, with leading behaviour

z^{3} /9

. Hence infinity is a pole of order three.

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