Category: Relation and Functions

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…

Question Number 106134 by mathmax by abdo last updated on 03/Aug/20 $$\mathrm{let}\mathrm{g}\left(\mathrm{x}\right)=\mathrm{arcatan}(1+\mathrm{x})\ln (1-2\mathrm{x})$$$$1)\mathrm{find}{\mathrm{g}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{g}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$2)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$$$3/\mathrm{calculate}{\int }_{-\frac{1}{4}}^{\frac{1}{4}}\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx}$$ Terms…

Question Number 171484 by infinityaction last updated on 16/Jun/22 $$$$$$letf\left(x\right)=x+\frac{2}{1.3}{x}^3+\frac{2.4}{1.3.5}{x}^5+\frac{2.4.6}{1.3.5.7}{x}^7+\dots \dots \dots$$$$\mathrm{\forall }x\in (0,1)thevalueoff\left(\frac{1}{\sqrt{2}}\right)=?$$ Commented by mr W last updated…