How to compute limits like this? – math.stackexchange.com

How to compute limits like this? – math.stackexchange.com

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$$\lim\limits_{x\to +\infty} \frac{x^{2}e^{-x}}{x^{2}+1}\sin(xe^{x^{2}})$$ Also, is it possible to compute this kind of limits using the $\varepsilon-\delta$ definition?

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