Question Number 197562 by universe last updated on 21/Sep/23 $$\:\:\mathrm{let}\:\:\mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right)\:=\:\mathrm{nsin}^{\mathrm{2n}+\mathrm{1}} \mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{dx}\:−\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right)\right)\mathrm{dx}\:\:\:=\:\:?\: \\ $$ Terms…
Question Number 197517 by sonukgindia last updated on 20/Sep/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197530 by Erico last updated on 20/Sep/23 $$\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}\mathrm{f}''\left(\mathrm{x}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Commented by AST last updated on 20/Sep/23 $${f}\left({x}\right)={x}^{\mathrm{2}} \:{works}. \\…
Question Number 197514 by cortano12 last updated on 20/Sep/23 $$\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\mathrm{x}\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)=? \\ $$ Answered by MM42 last updated on 20/Sep/23 $$\frac{\mathrm{1}}{{x}}={t}\Rightarrow{lim}_{{t}\rightarrow\mathrm{0}} \:{sin}\frac{\mathrm{1}}{{t}}×{sin}^{−\mathrm{1}} {t}\:=\mathrm{0} \\…
Question Number 197524 by sonukgindia last updated on 20/Sep/23 Answered by som(math1967) last updated on 20/Sep/23 $$\mathrm{2arc}{tan}\left(\frac{{x}}{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\right) \\ $$$$=\mathrm{arc}{tan}\left\{\frac{\frac{\mathrm{2}{x}}{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}}{\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} }}\right\} \\…
Question Number 197541 by a.lgnaoui last updated on 20/Sep/23 $$\boldsymbol{\mathrm{Montrer}}\:\boldsymbol{\mathrm{que}} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{x}}=\frac{\boldsymbol{\mathrm{an}}+\boldsymbol{\mathrm{bm}}}{\boldsymbol{\mathrm{m}}+\boldsymbol{\mathrm{n}}} \\ $$ Commented by a.lgnaoui last updated on 20/Sep/23 Commented by a.lgnaoui last…
Question Number 197525 by mokys last updated on 20/Sep/23 $$\int\:\sqrt[{{n}}]{{tanx}}\:{dx} \\ $$ Answered by Frix last updated on 20/Sep/23 $${t}=\sqrt[{{n}}]{\mathrm{tan}\:{x}}\:\Rightarrow\: \\ $$$${n}\int\frac{{t}^{{n}} }{{t}^{\mathrm{2}{n}} +\mathrm{1}}{dt} \\…
Question Number 197500 by yaslm last updated on 19/Sep/23 Commented by SANOGO last updated on 19/Sep/23 $${meeci}\:{bien} \\ $$ Answered by Mathspace last updated on…
Question Number 197501 by SANOGO last updated on 19/Sep/23 Answered by witcher3 last updated on 19/Sep/23 $$\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}}…
Question Number 197502 by 281981 last updated on 19/Sep/23 Commented by mokys last updated on 21/Sep/23 Terms of Service Privacy Policy Contact: info@tinkutara.com