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calculate-A-n-1-n-n-e-x-2-y-2-x-2-y-2-3-dxdy-and-lim-n-A-n-




Question Number 133120 by abdomsup last updated on 19/Feb/21
calculate A_n = ∫∫_([(1/n),n[)   (e^(−x^2 −y^2 ) /( (√(x^2 +y^2 +3))))dxdy  and lim_(n→∞) A_n
$${calculate}\:{A}_{{n}} =\:\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.} \:\:\frac{{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } }{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{3}}}{dxdy} \\ $$$${and}\:{lim}_{{n}\rightarrow\infty} {A}_{{n}} \\ $$

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