Chapter 8.2, Problem 100E

Find a real number c and a positive number L for which

$\underset{r\to \infty }{\lim }\frac{r^c{\displaystyle {\int }_0^{\pi /2}{x}^r\sin xdx}}{{\displaystyle {\int }_0^{\pi /2}{x}^r\cos xdx}}=L$

This problem was composed by the Committee on the Putnam Prize Competition. © The Mathematical Association of America. All rights reserved.