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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 7D / c / Solution

For

f (x) = 1/ (x^{2} + 1)

, contour integration or partial fractions gives

H f (y) = \frac{y}{1 + y ^{2}}

under the convention in part (b). Therefore

H f (- 1) = - \frac{1}{2} .

Solved by gpt-5.6-sol high.

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