Category: Relation and Functions

Question Number 104919 by mathmax by abdo last updated on 24/Jul/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\sqrt{1-{\mathrm{x}}^2}}$$$$\mathrm{finf}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)$$ Commented by malwaan last updated on 25/Jul/20…

Question Number 39376 by maxmathsup by imad last updated on 05/Jul/18 $$howtocalculatetheproduct\left(\sum _{n=0}^{\mathrm{\infty }}{a}_n{x}^n\right).\left(\sum _{n=0}^{\mathrm{\infty }}{b}_n{x}^{2n}\right)?$$ Terms of Service…

Question Number 104895 by mathmax by abdo last updated on 24/Jul/20 $$1)\mathrm{decompose}\mathrm{the}\mathrm{fraction}\mathrm{F}\left(\mathrm{x}\right)=\frac{1}{{\mathrm{x}}^3{(\mathrm{x}+1)}^4}$$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{sumA}\:=\:\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{4}} }\:\:\mathrm{and}\:\mathrm{B}\:=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty\:} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{4}} }…

Question Number 39291 by math khazana by abdo last updated on 04/Jul/18 $$letf\left(x\right)=\frac{e^{-x^2}}{1+x^2}$$$$developpfatintegrserie.$$ Commented by abdo mathsup 649…

Question Number 104771 by mathmax by abdo last updated on 23/Jul/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^3+\mathrm{x}-3$$$$1)\mathrm{prove}\mathrm{that}\mathrm{f}\mathrm{have}\mathrm{one}\mathrm{root}\mathrm{real}{\alpha }_0\mathrm{and}{\alpha }_0\in ]1,2[$$$$2)\mathrm{factorize}\mathrm{f}\left(\mathrm{x}\right)\mathrm{inside}\mathrm{R}\left[\mathrm{x}\right]\mathrm{and}\mathrm{C}\left[\mathrm{x}\right]$$$$3)\mathrm{find}\int \frac{\mathrm{dx}}{\mathrm{f}\left(\mathrm{x}\right)}$$ Answered by…