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let-U-n-n-n-2-t-n-1-4-t-1-3-dt-prove-that-lim-n-U-n-0-




Question Number 66342 by mathmax by abdo last updated on 12/Aug/19
let U_n =āˆ«_n ^(n+2)   (((t+n)^(1/4) )/t^(1/3) )dt  prove that lim_(nā†’+āˆž) U_n =0
$${let}\:{U}_{{n}} =\int_{{n}} ^{{n}+\mathrm{2}} \:\:\frac{\left({t}+{n}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{{t}^{\frac{\mathrm{1}}{\mathrm{3}}} }{dt}\:\:{prove}\:{that}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} =\mathrm{0} \\ $$

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