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let-A-n-0-1-n-arctan-1-x-2-dx-1-calculate-A-n-2-find-lim-n-A-n-




Question Number 37275 by abdo.msup.com last updated on 11/Jun/18
let A_n  = āˆ«_0 ^(1/n)  arctan(1+x^2 )dx  1) calculate A_n   2)find lim_(nā†’+āˆž)  A_n  .
$${let}\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{{n}}} \:{arctan}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \:. \\ $$

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