Question Number 198210 by a.lgnaoui last updated on 14/Oct/23 $$\:\boldsymbol{\mathrm{Red}}\:\boldsymbol{\mathrm{Area}}? \\ $$ Commented by a.lgnaoui last updated on 14/Oct/23 Answered by mr W last updated…
Question Number 198145 by Erico last updated on 11/Oct/23 $$\mathrm{Soit}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{2x}−\mathrm{1}}{\mathrm{lnx}−\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}\:\mathrm{et}\:\mathrm{I}=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{1}.\:\mathrm{Montrer}\:\mathrm{que}\:\forall\mathrm{n}\geqslant\mathrm{2} \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{4n}}\:\leqslant\:\mathrm{I}\:−\:\frac{\pi}{\mathrm{2n}^{\mathrm{3}} }\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\frac{\mathrm{k}\left(\mathrm{n}−\mathrm{k}\right)}{\mathrm{sin}\left(\frac{\mathrm{k}\pi}{\mathrm{n}}\right)}\:\leqslant\:\frac{\mathrm{3}}{\mathrm{4n}} \\ $$$$\mathrm{2}.\:\mathrm{En}\:\mathrm{d}\acute {\mathrm{e}duire}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\mathrm{I} \\ $$$$ \\…
Question Number 198059 by a.lgnaoui last updated on 09/Oct/23 $$\mathrm{Montrer}\:\mathrm{l}\:\mathrm{egalite}\:\:\left(\mathrm{voir}\:\mathrm{la}\:\mathrm{figure}\:\right) \\ $$ Commented by a.lgnaoui last updated on 09/Oct/23 Answered by mr W last updated…
Question Number 197740 by cortano12 last updated on 27/Sep/23 Answered by mr W last updated on 27/Sep/23 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}\sqrt{{k}}}{{n}} \\ $$$$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}\sqrt{{n}}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}}…
Question Number 197730 by ajfour last updated on 27/Sep/23 Commented by ajfour last updated on 27/Sep/23 $${Determine}\:{r}\:{in}\:{terms}\:{of}\:{a},{b}. \\ $$ Commented by ajfour last updated on…
Question Number 197585 by Erico last updated on 23/Sep/23 $$\mathrm{f}\: \left(\mathrm{x}\right)=\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$$$\Rightarrow\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Answered by EdwarT last updated on 24/Sep/23 $$−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\…
Question Number 197359 by sniper237 last updated on 14/Sep/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{1}−{cosxcos}\mathrm{2}{x}…{cos}\left({nx}\right)}{{x}^{\mathrm{2}} }\:=\:\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{12}}\: \\ $$ Commented by universe last updated on 16/Sep/23 Answered by witcher3 last…
Question Number 196992 by MATHEMATICSAM last updated on 05/Sep/23 $$\mathrm{If}\:\mathrm{A}\left({a}^{\mathrm{2}} ,\:\mathrm{2}{a}\right),\:\mathrm{B}\left(\frac{\mathrm{1}}{{a}^{\mathrm{2}} },\:\frac{−\:\mathrm{2}}{{a}}\right)\:\mathrm{and}\:\mathrm{S}\left(\mathrm{1},\:\mathrm{0}\right)\: \\ $$$$\mathrm{are}\:\mathrm{three}\:\mathrm{points}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}, \\ $$$$\frac{\mathrm{1}}{\mathrm{SA}}\:+\:\frac{\mathrm{1}}{\mathrm{SB}}\:=\:\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196917 by peter frank last updated on 03/Sep/23 Answered by MM42 last updated on 03/Sep/23 $$\:\:\frac{\mid{PA}\mid}{\mid{PB}\mid}\:=\:\mathrm{3}\:\:\checkmark \\ $$ Commented by peter frank last…
Question Number 196674 by Erico last updated on 29/Aug/23 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} +\underset{\mathrm{p}=\mathrm{2}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{p}} \mathrm{pln}\left(\frac{\mathrm{p}+\mathrm{1}}{\mathrm{p}−\mathrm{1}}\right)=\mathrm{ln}\left(\pi\right) \\ $$ Terms of Service Privacy Policy Contact:…