Category: Relation and Functions

Question Number 32277 by abdo imad last updated on 22/Mar/18 $$for{x}_i\in [0,1]provethat$$$$(1-x_1)(1-x_2)\dots .(1-x_n)⩾1-(x_1+x_2+\dots .+x_n).$$ Terms of Service…

Question Number 32273 by abdo imad last updated on 22/Mar/18 $$letput{u}_n=\sum _{k=1}^{n}k(k!)$$$$1)provethat{u}_n=(n+1)!-1$$$$2)studytheconvergenceof\sum _{n=1}^{\mathrm{\infty }}\frac{1}{u_n}.$$ Commented…

Question Number 97799 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{\prime }}\mathrm{cosx}+\mathrm{y}\mathrm{sinx}=\mathrm{cosx}+\mathrm{sinx}$$ Commented by john santu last updated on 10/Jun/20 $$\frac{dy}{dx}+\tan x.y=1+\tan x$$$$\mathrm{IF}\:{u}\left({x}\right)={e}^{\int\:\mathrm{tan}\:{x}\:{dx}} \:=\:{e}^{\mathrm{ln}\left(\mathrm{sec}\:{x}\right)}…

Question Number 97797 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-\mathrm{y}=\mathrm{x}$$ Answered by niroj last updated on 09/Jun/20 $${\mathrm{y}}^{{}^{″}}-\mathrm{y}=\mathrm{x}$$$$\:\:\left(\mathrm{D}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{y}=\:\mathrm{x}…

Question Number 97648 by bobhans last updated on 09/Jun/20 $$\mathrm{Determine}\mathrm{all}\mathrm{function}\mathrm{f}:\mathrm{R}/\{0,1\}\to \mathrm{R}$$$$\mathrm{satisfying}\mathrm{the}\mathrm{functional}\mathrm{relation}$$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\frac{1}{1-\mathrm{x}}\right)=\frac{2(1-2\mathrm{x})}{\mathrm{x}(1-\mathrm{x})},\mathrm{x}\ne 0,\mathrm{x}\ne 1$$ Commented by bemath last updated on 09/Jun/20 $$\mathrm{nice}\:\mathrm{question} \…