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lim-n-1-1-x-2-n-dx-0-1-1-x-2-n-dx-0-lt-lt-1-




Question Number 162718 by qaz last updated on 31/Dec/21
lim_(n→∞) ((∫_ε ^1 (1−x^2 )^n dx)/(∫_0 ^1 (1−x^2 )^n dx))=?       (0<ε<1)
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\int_{\epsilon} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \mathrm{dx}}{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \mathrm{dx}}=?\:\:\:\:\:\:\:\left(\mathrm{0}<\epsilon<\mathrm{1}\right) \\ $$

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