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Category: Relation and Functions

g-x-log-tan-x-developp-g-at-fourier-serie-

Question Number 145749 by mathmax by abdo last updated on 07/Jul/21 $$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{tan}\left(\mathrm{x}\right)\right)\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\left(\frac{\mathrm{sinx}}{\mathrm{cosx}}\right)=\mathrm{log}\left(\mathrm{sinx}\right)−\mathrm{log}\left(\mathrm{cosx}\right) \\…

h-x-x-x-2-x-1-we-defined-this-function-on-R-1-R-1-Study-the-variations-of-h-then-draw-up-its-table-of-variation-please-sirs-i-need-your-kind-help-

Question Number 80180 by mathocean1 last updated on 31/Jan/20 $$\mathrm{h}\left({x}\right)=\frac{{x}−{x}^{\mathrm{2}} }{{x}+\mathrm{1}} \\ $$$${we}\:{defined}\:{this}\:{function}\:{on} \\ $$$$\mathbb{R}−\left\{−\mathrm{1}\right\}\rightarrow\mathbb{R} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Study}\:\mathrm{the}\:\mathrm{variations}\:\mathrm{of}\:\mathrm{h}\:\mathrm{then} \\ $$$$\mathrm{draw}\:\mathrm{up}\:\mathrm{its}\:\mathrm{table}\:\mathrm{of}\:\mathrm{variation}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{sirs}\:\mathrm{i}\:\mathrm{need}\:\mathrm{your}\:\mathrm{kind}\:\mathrm{help}…

let-s-x-n-1-1-n-2x-2-2x-1-x-2-1-n-1-explicite-s-x-2-calculate-0-1-s-x-dx-

Question Number 145634 by mathmax by abdo last updated on 06/Jul/21 $$\mathrm{let}\:\mathrm{s}\left(\mathrm{x}\right)=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{2x}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }+\mathrm{1}\right)^{\mathrm{n}} } \\ $$$$\left.\mathrm{1}\right)\:\mathrm{explicite}\:\mathrm{s}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{s}\left(\mathrm{x}\right)\mathrm{dx} \\…

f-x-y-f-x-f-y-xy-for-all-x-and-y-fromR-and-f-4-10-calculate-f-1319-

Question Number 145516 by mathmax by abdo last updated on 05/Jul/21 $$\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)=\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{y}\right)+\mathrm{xy}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{fromR} \\ $$$$\mathrm{and}\:\mathrm{f}\left(\mathrm{4}\right)=\mathrm{10}\:\:\mathrm{calculate}\:\mathrm{f}\left(\mathrm{1319}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right)+{f}\left({y}\right)+{xy} \\…

let-A-n-0-2npi-dx-2-cosx-2-explicit-A-n-and-determine-nature-of-serie-A-n-

Question Number 145514 by mathmax by abdo last updated on 05/Jul/21 $$\mathrm{let}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{2n}\pi} \:\frac{\mathrm{dx}}{\left(\mathrm{2}+\mathrm{cosx}\right)^{\mathrm{2}} } \\ $$$$\mathrm{explicit}\:\mathrm{A}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{determine}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{serie}\:\Sigma\:\mathrm{A}_{\mathrm{n}} \\ $$ Answered by mathmax by…