I'm having trouble showing $$\lim_{n\to\infty}\int_{0}^{\infty}e^{-x}\sin\left(\frac{n}{x}\right)~\text{d}x=0$$ The integrand doesn't converge for any $x$ so I don't know how to use the standard Lebesgue convergence theorems. Thank you for any hints.
Show $\lim\limits_{n\to\infty}\int_{0}^{\infty}e^{-x}\sin(\frac{n}{x})~\text{d}x=0$
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real-analysis
measure-theory
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0@Zarrax, may be you should post this as answer? – 2012-07-31
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0@Norbert good idea, just did... – 2012-07-31