Question Number 59999 by Mr X pcx last updated on 16/May/19
![let U_n =∫_0 ^∞ (e^(−n[x^2 ]) /((x^2 +3)^2 ))dx 1) find U_n interms of n 2) calvulate lim_(n→+∞) U_n 3)study the serie Σ U_n](Q59999.png)
$${let}\:{U}_{{n}} \:\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{calvulate}\:\:{lim}_{{n}\rightarrow+\infty} \:\:\:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$