Category: Relation and Functions

Question Number 171955 by infinityaction last updated on 22/Jun/22 $$\mathit{f}\left(\mathit{x}\right)+\mathit{f}\left(\frac{1}{1-\mathit{x}}\right)=1+\frac{1}{\mathit{x}(1-\mathit{x})}$$$$\mathit{f}\left(\mathit{x}\right)=??$$ Answered by thfchristopher last updated on 22/Jun/22 $$1+\frac{1}{x(1-x)}$$$$=\frac{{x}−{x}^{\mathrm{2}} +\mathrm{1}}{{x}\left(\mathrm{1}−{x}\right)}…

Question Number 40880 by prof Abdo imad last updated on 28/Jul/18 $$provethat\sum _{k=n}^{\mathrm{\infty }}\frac{1}{k^{\alpha }}\sim \frac{1}{(\alpha -1)n^{\alpha -1}}with\alpha >1$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 40878 by prof Abdo imad last updated on 28/Jul/18 $$let{u}_0>0and\mathrm{\forall }n\in N$$$$u_{n+1}=u_n+\frac{1}{u_n}$$$$1)provethat\left(u_n\right)isincreasingandlim{u}_n=+\mathrm{\infty }$$$$\left.\mathrm{2}\right){by}\:{consideringthe}\:{function}\varphi\left({t}\right)=\frac{\mathrm{1}}{\mathrm{2}{t}+{x}} \…

Question Number 106315 by pticantor last updated on 04/Aug/20 $$\mathit{s}\mathit{h}\mathit{o}\mathit{w}\mathit{t}\mathit{h}\mathit{a}\mathit{t}$$$$⊛\mathrm{\forall }({\mathit{x}}_1,{\mathit{x}}_2,\dots ..,{\mathit{x}}_{\mathit{n}})\in {\mathbb{R}}^{\mathit{n}}$$$$\left(\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} \right)^{\mathrm{2}} \leqslant\boldsymbol{{n}}\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} ^{\mathrm{2}} \…

Question Number 106138 by bobhans last updated on 03/Aug/20 $$\mathrm{If}\mathrm{root}\mathrm{of}\mathrm{equation}{\mathrm{x}}^3-{\mathrm{px}}^2+\mathrm{qx}-\mathrm{r}=0\mathrm{are}\mathrm{in}$$$$\mathrm{AP}\mathrm{than}\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{relation}\mathrm{between}\mathrm{p},\mathrm{q}$$$$\mathrm{and}\mathrm{r}?$$ Answered by bemath last updated on 03/Aug/20…