Category: Relation and Functions

Question Number 96655 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\ln (2+\mathrm{cosx})\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{fourier}\mathrm{serie}$$ Answered by mathmax by abdo last updated on 04/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{2}+\mathrm{cosx}\right)\:\Rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)\:=\frac{−\mathrm{sinx}}{\mathrm{2}+\mathrm{cosx}}\:=−\frac{\frac{\mathrm{e}^{\mathrm{ix}}…

Question Number 96593 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\arctan \left({\mathrm{x}}^{\mathrm{n}}\right)\mathrm{with}\mathrm{n}\mathrm{integr}\mathrm{natural}$$$$1)\mathrm{calculate}{\mathrm{f}}^{{}^{\prime }}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{f}}^{\left(2\right)}\left(\mathrm{x}\right)$$$$2)\mathrm{calculate}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$3)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$…

Question Number 96571 by mathmax by abdo last updated on 02/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-{2\mathrm{y}}^{{}^{\prime }}+\mathrm{y}={(\mathrm{x}+1)}^2{\mathrm{e}}^{-\mathrm{x}}\mathrm{with}\mathrm{y}\left(0\right)=-1,{\mathrm{y}}^{{}^{\prime }}\left(0\right)=0,{\mathrm{y}}^{\left(2\right)}\left(0\right)=1$$ Answered by mathmax by abdo…

Question Number 96383 by bobhans last updated on 01/Jun/20 $$\mathrm{Find}\mathrm{domain}\mathrm{\&}\mathrm{range}\mathrm{of}\mathrm{function}$$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{{\mathrm{x}}^2-5\mathrm{x}+6}$$ Answered by john santu last updated on 01/Jun/20 $$\mathrm{The}\:\mathrm{domain}\:\mathrm{consists}\:\mathrm{of}\:\mathrm{all}\:\mathrm{real}\: \…

Question Number 96375 by mathmax by abdo last updated on 01/Jun/20 $$\mathrm{let}\mathrm{P}\left(\mathrm{x}\right)=(1+{\mathrm{x}}^2)(1+{\mathrm{x}}^4)\dots (1+{\mathrm{x}}^{2^{\mathrm{n}}})$$$$1)\mathrm{solve}\mathrm{inside}\mathrm{C}\mathrm{the}\mathrm{equation}\mathrm{P}\left(\mathrm{x}\right)=0$$$$2)\mathrm{factorize}\mathrm{P}\left(\mathrm{x}\right)\mathrm{inside}\mathrm{C}\left[\mathrm{x}\right]$$$$3)\mathrm{calvulate}{\mathrm{P}}^{{}^{\prime }}\left(\mathrm{x}\right)$$$$\left.\mathrm{4}\right)\:\mathrm{decompose}\:\mathrm{F}\:=\frac{\mathrm{1}}{\mathrm{P}\left(\mathrm{x}\right)}…