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Question-197622

Question Number 197622 by sonukgindia last updated on 24/Sep/23 Answered by a.lgnaoui last updated on 26/Sep/23 $$\boldsymbol{\mathrm{Calcul}}\:\boldsymbol{\mathrm{de}}\:\:\:\boldsymbol{\mathrm{S}}\left(\boldsymbol{\mathrm{BCDE}}\right) \\ $$$$ \\ $$$$\boldsymbol{\mathrm{S}}\left(\boldsymbol{\mathrm{BCDE}}\right)=\boldsymbol{\mathrm{S}}\left(\boldsymbol{\mathrm{AMN}}\right)−\boldsymbol{\mathrm{S}}\left(\boldsymbol{\mathrm{DEMN}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\boldsymbol{\mathrm{S}}\left(\boldsymbol{\mathrm{ABC}}\right) \\ $$$$…

find-n-1-k-n-

Question Number 197581 by mokys last updated on 22/Sep/23 $${find}\:\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\sqrt{{n}}\:? \\ $$ Answered by salvatore last updated on 07/Jan/24 $$\left.{w}\left(\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{24}}\:\:\:{w}\left({m}\right)=\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}}}\\{\:{m}}\end{pmatrix}\:\frac{{B}_{{m}+\mathrm{1}} }{{m}+\mathrm{1}}\:−\left(−\mathrm{1}\right)^{{m}} \underset{{h}=\mathrm{1}} {\overset{{m}−\mathrm{1}}…

Question-197524

Question Number 197524 by sonukgindia last updated on 20/Sep/23 Answered by som(math1967) last updated on 20/Sep/23 $$\mathrm{2arc}{tan}\left(\frac{{x}}{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\right) \\ $$$$=\mathrm{arc}{tan}\left\{\frac{\frac{\mathrm{2}{x}}{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}}{\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} }}\right\} \\…

Question-197501

Question Number 197501 by SANOGO last updated on 19/Sep/23 Answered by witcher3 last updated on 19/Sep/23 $$\left(\mathrm{i}\right)\Rightarrow\left(\mathrm{ii}\right) \\ $$$$\exists\mathrm{x}\in\mathrm{A},\exists\epsilon^{\ast} >\mathrm{0}\:\:\beta\left(\mathrm{x},\epsilon\right)\in\mathrm{A},\mathrm{Boules}\:\mathrm{ouvert} \\ $$$$\mathrm{soit}\:\mathrm{B}\subset\mathrm{X},\overset{−} {\mathrm{B}}=\mathrm{X} \\ $$$$\mathrm{pour}\:\mathrm{x}\in\mathrm{X}\:\:\exists\mathrm{u}_{\mathrm{n}}…

lim-x-3-cos3-cosx-x-3-

Question Number 197496 by sciencestudentW last updated on 19/Sep/23 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{{cos}\mathrm{3}−{cosx}}{{x}−\mathrm{3}}=? \\ $$ Answered by cortano12 last updated on 20/Sep/23 $$\:=\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{−\mathrm{2sin}\:\left(\frac{\mathrm{x}+\mathrm{3}}{\mathrm{2}}\right)\:\mathrm{sin}\:\left(\frac{\mathrm{3}−\mathrm{x}}{\mathrm{2}}\right)}{−\mathrm{2}\left(\frac{\mathrm{3}−\mathrm{x}}{\mathrm{2}}\right)} \\ $$$$\:=\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\mathrm{x}+\mathrm{3}}{\mathrm{2}}\right)\:.\:\underset{{x}\rightarrow\mathrm{3}}…