olymmath

Putnam 2011 A3

  • Session A

Find a real number cc and a positive number LL for which lim⁡r→∞rc∫0π/2xrsin⁡xdx∫0π/2xrcos⁡xdx=L.\lim_{r\to\infty} \frac{r^c \int_0^{\pi/2} x^r \sin x dx}{\int_0^{\pi/2} x^r \cos x dx} = L.

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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