Question Number 56938 by maxmathsup by imad last updated on 26/Mar/19
$${let}\:{A}_{{n}} =\int\int_{{W}_{{n}} } {e}^{−{xy}} \sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}\:\:\:{with}\:{W}_{{n}} =\left[\frac{\mathrm{1}}{{n}},{n}\left[×\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.\right.\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$ \\ $$