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Omni-MATH / Find a real number c and a positive number L for which lim_(r→∞)(r^(c)∫₀^(π/2)x^(r)sinx dx)/(∫₀^(π/2)x^(r)cosx dx)=L.

Problem

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problem

Find a real number cc and a positive number LL for which limr→∞rc∫0π/2xrsinxdx∫0π/2xrcosxdx=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.
Plain-text mathematical notation (without MathML)
Find a real number c and a positive number L for which lim_(r→∞)(r^(c)∫₀^(π/2)x^(r)sinx dx)/(∫₀^(π/2)x^(r)cosx dx)=L.
Original LaTeX notation
Find a real number $c$ and a positive number $L$ for which \[ \lim_{r\to\infty} \frac{r^c \int_0^{\pi/2} x^r \sin x \,dx}{\int_0^{\pi/2} x^r \cos x \,dx} = L. \]

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Source and history

task_id
a8e15d99-0ce0-52ee-80d6-27f48792eb96
task_key
test--a8e15d99-0ce0-52ee-80d6-27f48792eb96
task_revision_id
1
config / split
/ test

Official source

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