olymmath

Putnam 2021 A4

  • Session A

Let I(R)=∬x2+y2≤R2(1+2x21+x4+6x2y2+y4−1+y22+x4+y4)dxdy.I(R) = \iint_{x^2+y^2 \leq R^2} \left( \frac{1+2x^2}{1+x^4+6x^2y^2+y^4} - \frac{1+y^2}{2+x^4+y^4} \right) dx dy. Find lim⁡R→∞I(R),\lim_{R \to \infty} I(R), or show that this limit does not exist.

Curated text Kedlaya Putnam archive. Quoted with source.

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