- #1

Ackbach

Gold Member

MHB

- 4,155

- 92

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

$$\lim_{r\to\infty} \frac{\displaystyle r^c \int_0^{\pi/2} x^r \sin(x) \,dx}{\displaystyle \int_0^{\pi/2} x^r \cos(x) \,dx} = L.$$

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