Category: Relation and Functions

Question Number 148558 by puissant last updated on 29/Jul/21 $$\mathrm{Trouver}\mathrm{toutes}\mathrm{les}\mathrm{fonctions}\mathrm{continues}$$$$\mathrm{f}:\mathbb{R}\to \mathbb{R}\mathrm{verifiant}:$$$$\mathrm{\forall }(\mathrm{x},\mathrm{y})\in {\mathbb{R}}^2,\mathrm{f}(\mathrm{x}+\mathrm{y})\mathrm{f}(\mathrm{x}-\mathrm{y})={\mathrm{f}}^2\left(\mathrm{x}\right){\mathrm{f}}^2\left(\mathrm{y}\right)..$$$$\mathrm{monsieur}{\mathrm{j}}^{\prime }\mathrm{ai}\mathrm{suppos}\acute{\mathrm{e}}\mathrm{que}\mathrm{f}\mathrm{est}\mathrm{un}$$$$\mathrm{morphisme}\mathrm{mutiplicatif}\mathrm{de}\mathbb{R}..\mathrm{mais}\mathrm{ca}\mathrm{ne}$$$$\mathrm{sort}\:\mathrm{pas}… \…

Question Number 83021 by mathmax by abdo last updated on 27/Feb/20 $$findthesequence{v}_{n}wichverify{v}_n+v_{n+1}=\frac{{(-1)}^n}{\sqrt{n}}(n⩾1)$$$$is\left(v_n\right)convergente?$$ Terms of Service Privacy…

Question Number 82973 by mathmax by abdo last updated on 26/Feb/20 $$calculate{lim}_{n\to +\mathrm{\infty }}{\int }_0^n{(1-\frac{x}{n})}^{n}arctan\left(nx\right)dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 148498 by mathmax by abdo last updated on 28/Jul/21 $$\mathrm{find}{\int }_0^{\mathrm{\infty }}\frac{\arctan \left(2\mathrm{x}\right)}{1+{\mathrm{x}}^2}\mathrm{dx}$$ Answered by mathmax by abdo last updated on…

Question Number 82920 by abdomathmax last updated on 25/Feb/20 $$calculate{lim}_{x\to 0}\frac{ln(1+ln(1+x))}{x}$$ Answered by mind is power last updated on 25/Feb/20 $$ln(1+x)\sim x$$$$\Rightarrow{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)\sim{ln}\left(\mathrm{1}+{x}\right)…