Category: Relation and Functions

Question Number 116376 by bemath last updated on 03/Oct/20 $$\mathrm{Let}\mathrm{f}\mathrm{be}\mathrm{a}\mathrm{function}\mathrm{defined}\mathrm{on}\mathrm{non}\mathrm{zero}$$$$\mathrm{real}\mathrm{numbers}\mathrm{such}\mathrm{that}\frac{27\mathrm{f}(-\mathrm{x})}{\mathrm{x}}-{\mathrm{x}}^2\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=-{2\mathrm{x}}^2$$$$\mathrm{for}\mathrm{\forall }\mathrm{x}\ne 0.\mathrm{Find}\to \{\begin{array}{l}\mathrm{f}\left(\mathrm{x}\right)\\ \mathrm{f}\left(3\right)\end{array}?$$ Answered by bobhans last updated on 03/Oct/20 $$\mathrm{Letting}\:\mathrm{x}\:=\:−\mathrm{y},\:\mathrm{we}\:\mathrm{get}\:…

Question Number 115997 by bemath last updated on 30/Sep/20 Answered by bobhans last updated on 30/Sep/20 $$\left(1\right)f\left(\frac{1}{x}\right)+f(1-x)=x\to f(1-x)=x-f\left(\frac{1}{x}\right)$$$$replace1-xbyx$$$$\left(2\right)f\left(\frac{1}{1-x}\right)+f\left(x\right)=1-x$$$$replace\frac{1}{x}by1-x$$$$\left(\mathrm{3}\right)\:{f}\left(\mathrm{1}−{x}\right)+{f}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}…

Question Number 50426 by Abdo msup. last updated on 16/Dec/18 $$studytheconvergenceof$$$$U_n={\left(\frac{2}{\pi }{\int }_0^{\frac{\pi }{2}}{\left(sinx\right)}^{\frac{1}{n}}\right)}^n$$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Question Number 50409 by Abdo msup. last updated on 16/Dec/18 $$find\left[\sum _{k=1}^{{10}^4}\frac{1}{\sqrt{k}}\right]$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 50405 by Abdo msup. last updated on 16/Dec/18 $$let{V}_n=\frac{1}{2n+1}+\frac{1}{2n+3}+\dots +\frac{1}{4n-1}$$$$determine{lim}_{n\to +\mathrm{\infty }}{V}_n$$ Answered by tanmay.chaudhury50@gmail.com last updated on 17/Dec/18 $${V}_{{n}}…