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lim-n-0-dx-x-2-1-4-n-1-1-n-




Question Number 149675 by mathdanisur last updated on 06/Aug/21
lim_(nā†’āˆž) ((āˆ«_( 0) ^( āˆž)  (dx/((x^2  + (1/4))^(n+1) ))))^(1/n)  = ?
$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\boldsymbol{\mathrm{n}}}]{\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }}\:=\:? \\ $$

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