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Question Number 162718 by qaz last updated on 31/Dec/21

$$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{{\int }_{ϵ}^1{(1-{\mathrm{x}}^2)}^{\mathrm{n}}\mathrm{dx}}{{\int }_0^1{(1-{\mathrm{x}}^2)}^{\mathrm{n}}\mathrm{dx}}=?(0<ϵ<1)$$

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