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let-U-n-0-1-2-dx-1-x-n-calculate-lim-n-U-n-




Question Number 91088 by abdomathmax last updated on 28/Apr/20
let U_n =∫_0 ^(1/2)  (dx/( (√(1−x^n ))))  calculate lim_(n→+∞)  U_n
$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{{n}} }}\:\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$

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