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let-f-n-x-1-x-n-1-e-x-p-0-n-x-p-p-1-prove-that-f-n-x-Q-n-x-e-x-P-n-x-x-2n-1-find-the-polynomial-P-n-and-Q-n-2-prove-that-e-x-P-n-x-Q-n-x-

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Question Number 30753 by abdo imad last updated on 25/Feb/18
let f_n (x)=(1/x^(n+1) ) (e^x −Σ_(p=0) ^(n ) (x^p /(p!))) 1) prove that f^((n)) (x)=((Q_n (x) e^x −P_n (x))/x^(2n+1) ) find the polynomial P_n and Q_n . 2) prove that e^x −((P_n (x))/(Q_n (x)))=o(x^(2n+1) )
letfn(x)=1xn+1(ex−∑p=0nxpp!)1)provethatf(n)(x)=Qn(x)ex−Pn(x)x2n+1findthepolynomialPnandQn.2)provethatex−Pn(x)Qn(x)=o(x2n+1)

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