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let-give-f-n-x-1-n-n-sin-xt-t-e-t-dt-1-find-lim-n-f-n-x-2-find-another-form-of-f-n-x-by-calculating-f-n-x-




Question Number 30475 by abdo imad last updated on 22/Feb/18
let give f_n (x)= ∫_(1/n) ^n  ((sin(xt))/t) e^(−t)  dt  1)find lim_(n→∞) f_n (x)  2)find another form of f_n (x) by calculating f_n ^′ (x).
$${let}\:{give}\:{f}_{{n}} \left({x}\right)=\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\frac{{sin}\left({xt}\right)}{{t}}\:{e}^{−{t}} \:{dt} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow\infty} {f}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{another}\:{form}\:{of}\:{f}_{{n}} \left({x}\right)\:{by}\:{calculating}\:{f}_{{n}} ^{'} \left({x}\right). \\ $$

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