A3

Part of 2011 Putnam

Problems(1)

Source:

Find a real number

c

and a positive number

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.

Putnamlimitintegrationtrigonometrycalculusratioinequalities