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let-f-x-x-1-2n-e-nx-with-n-integr-1-calculste-f-p-x-and-f-n-x-2-find-f-p-0-3-developp-f-x-at-integr-serie-




Question Number 33295 by abdo imad last updated on 14/Apr/18
let  f(x)= (x+1^ )^(2n)   e^(−nx)   with n integr  1)  calculste  f^((p)) (x)  and f^((n)) (x)  2) find f^((p)) (0)  3) developp f(x) at integr serie.
$${let}\:\:{f}\left({x}\right)=\:\left({x}+\mathrm{1}^{} \right)^{\mathrm{2}{n}} \:\:{e}^{−{nx}} \:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:\:{calculste}\:\:{f}^{\left({p}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({p}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie}. \\ $$

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