Question Number 197343 by Mathspace last updated on 14/Sep/23 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}\right).{ln}\left({sinx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197349 by SANOGO last updated on 14/Sep/23 $${calcul}\: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\left(−\mathrm{1}\right)^{{n}\:} \frac{\mathrm{2}{n}+\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)} \\ $$ Answered by MM42 last updated on 14/Sep/23 $$\frac{\mathrm{2}{n}+\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)}=\frac{\mathrm{1}}{{n}}+\frac{\mathrm{1}}{{n}+\mathrm{1}}…
Question Number 197360 by hardmath last updated on 14/Sep/23 $$\mathrm{Find}: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}^{\mathrm{2}} \:\left(\:\sqrt{\mathrm{x}}\:\right)\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$ Answered by Mathspace last updated on 15/Sep/23…
Question Number 197344 by MathedUp last updated on 14/Sep/23 $$\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\centerdot\frac{\mathrm{d}{x}^{\boldsymbol{\lambda}} }{\mathrm{d}{t}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{g}^{\boldsymbol{\lambda\alpha}} \left(\partial_{\boldsymbol{\mu}} ^{\:} \mathrm{g}_{\boldsymbol{\alpha\nu}} +\partial_{\boldsymbol{\nu}} ^{\:} \mathrm{g}_{\boldsymbol{\alpha\mu}} −\partial_{\boldsymbol{\alpha}} ^{\:} \mathrm{g}_{\boldsymbol{\mu\nu}} \right)\frac{\mathrm{d}{x}^{\boldsymbol{\mu}} }{\mathrm{d}{t}}\centerdot\frac{\mathrm{d}{x}^{\boldsymbol{\nu}} }{\mathrm{d}{t}}=\mathrm{0} \\ $$…
Question Number 197345 by sonukgindia last updated on 14/Sep/23 Answered by HeferH last updated on 14/Sep/23 Commented by HeferH last updated on 14/Sep/23 $$\:{T}\:=\:\mathrm{4}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}}…
Question Number 197362 by sonukgindia last updated on 14/Sep/23 Answered by MM42 last updated on 15/Sep/23 $$\frac{{e}^{{x}} −\mathrm{1}}{{e}^{{x}} +\mathrm{1}}={u}\Rightarrow{e}^{{x}} {u}+{u}={e}^{{x}} −\mathrm{1}\Rightarrow{e}^{{x}} \left({u}−\mathrm{1}\right)=−\mathrm{1}−{u} \\ $$$${e}^{{x}} =\frac{\mathrm{1}+{u}}{\mathrm{1}−{u}}\Rightarrow{f}\left({x}\right)=\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)^{\mathrm{2}}…
Question Number 197346 by Amidip last updated on 14/Sep/23 Answered by som(math1967) last updated on 14/Sep/23 $$\:\frac{{a}+{b}}{{a}−{b}}=\frac{{tan}\left(\theta+\phi\right)}{{tan}\left(\theta−\phi\right)} \\ $$$$\:\frac{{a}+{b}}{{a}−{b}}=\frac{{sin}\left(\theta+\phi\right){cos}\left(\theta−\phi\right)}{{sin}\left(\theta−\phi\right){cos}\left(\theta+\phi\right)} \\ $$$$\frac{\mathrm{2}{a}}{\mathrm{2}{b}}=\frac{{sin}\mathrm{2}\theta}{{sin}\mathrm{2}\phi}\:\:\left[{using}\:{componendo\÷ndo}\right] \\ $$$${asin}\mathrm{2}\phi={bsin}\mathrm{2}\theta \\ $$$${a}^{\mathrm{2}}…
Question Number 197310 by sonukgindia last updated on 13/Sep/23 Answered by Frix last updated on 13/Sep/23 $$\left(\mathrm{1}\right)\:{z}^{\mathrm{2}} −\mathrm{7}{z}+\mathrm{11}=\mathrm{1} \\ $$$$\Rightarrow\:{z}=\mathrm{2}\vee{z}=\mathrm{5} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{ln}\:\left({z}^{\mathrm{2}} −\mathrm{3}{z}+\mathrm{e}^{\mathrm{2}} \right)\:=\mathrm{0} \\…
Question Number 197311 by cortano12 last updated on 13/Sep/23 $$\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:_{\mathrm{n}+\mathrm{1}} \:\mathrm{C}_{\mathrm{r}} \:=\:_{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \:+\:_{\mathrm{n}} \mathrm{C}_{\mathrm{r}−\mathrm{1}} \: \\ $$ Answered by qaz last updated…
Question Number 197336 by Huy last updated on 13/Sep/23 $${lim}_{{x}\rightarrow+\infty} \left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{cos}{x}\right)=? \\ $$ Answered by TheHoneyCat last updated on 13/Sep/23 $$\mathrm{This}\:\mathrm{limit}\:\mathrm{is}\:\mathrm{undefined} \\ $$$$\left(\mathrm{because}\:\mathrm{lim}\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{0}\:\mathrm{and}\:\mathrm{lim}\:\mathrm{cos}{x}\:\mathrm{is}\:\mathrm{undefined}\right)…