Question Number 155527 by ZiYangLee last updated on 01/Oct/21 $$\mathrm{If}\:{f}\left(\mathrm{tan}^{\mathrm{2}} \:\frac{\theta}{\mathrm{2}}\right)=\:\frac{\mathrm{2}}{\mathrm{1}+\mathrm{cos}\:\theta}\:,\:\mathrm{find}\:{f}\left(\mathrm{sin}\:\frac{\theta}{\mathrm{2}}\right). \\ $$ Answered by Ar Brandon last updated on 01/Oct/21 $${f}\left(\mathrm{tan}^{\mathrm{2}} \frac{\vartheta}{\mathrm{2}}\right)=\frac{\mathrm{2}}{\mathrm{1}+\mathrm{cos}\vartheta} \\ $$$${f}\left(\frac{\mathrm{sin}^{\mathrm{2}}…
Question Number 155510 by VIDDD last updated on 01/Oct/21 Answered by puissant last updated on 04/Oct/21 $$\:{I}=\sqrt{{log}_{\sqrt{\mathrm{2}}} \sqrt{\sqrt{\mathrm{2}}×\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{4}}} }+\:{log}_{\sqrt[{\mathrm{4}}]{\mathrm{2}}} \sqrt[{\mathrm{4}}]{\mathrm{2}^{\frac{\mathrm{3}}{\mathrm{4}}} }} \\ $$$$\Rightarrow\:{I}=\sqrt{{log}_{\sqrt{\mathrm{2}}} \mathrm{2}^{\frac{\mathrm{3}}{\mathrm{8}}} +\:{log}_{\sqrt[{\mathrm{4}}]{\mathrm{2}}}…
Question Number 155496 by mathocean1 last updated on 01/Oct/21 $${Given}\:{I}_{{n}} =\underset{{n}\pi} {\overset{\left({n}+\mathrm{1}\right)\pi} {\int}}{e}^{−{x}} {sinx}\:{dx}\:,\:{n}\in\mathbb{N}. \\ $$$$\mathrm{1}.\:{Find}\:{a}\:{relation}\:{between}\:{I}_{{n}+\mathrm{1}} {and}\:{I}_{{n}} . \\ $$ Answered by ArielVyny last updated…
Question Number 155488 by SANOGO last updated on 01/Oct/21 Answered by puissant last updated on 01/Oct/21 $${Q}=\int_{{a}} ^{{b}} \frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}{dx}\:\:\left(\mathrm{1}\right) \\ $$$${u}={a}+{b}−{x}\:\rightarrow\:{x}={a}+{b}−{u}\:\rightarrow\:{dx}=−{du} \\ $$$$\Rightarrow\:{Q}=\int_{{b}} ^{{a}} \frac{{f}\left({a}+{b}−{u}\right)}{{f}\left({a}+{b}−{u}\right)+{f}\left({u}\right)}\left(−{du}\right)…
Question Number 155450 by SANOGO last updated on 30/Sep/21 Answered by Kamel last updated on 30/Sep/21 $${L}=\underset{{n}\rightarrow+\infty} {{lim}e}^{\frac{\mathrm{2}}{\mathrm{2}{n}}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}{Ln}\left({sin}\left(\frac{{k}\pi}{\mathrm{2}{n}}\right)\right)} ={e}^{\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {Ln}\left({sin}\left(\pi{x}\right)\right){dx}} ={e}^{−\mathrm{2}{Ln}\left(\mathrm{2}\right)} =\frac{\mathrm{1}}{\mathrm{4}}…
Question Number 89896 by M±th+et£s last updated on 19/Apr/20 Commented by M±th+et£s last updated on 19/Apr/20 $${i}\:{want}\:{to}\:{ask}\:{about}\:\mathrm{107}\:{is}\:{it}\:{right}? \\ $$ Commented by mahdi last updated on…
Question Number 155421 by SANOGO last updated on 30/Sep/21 Answered by puissant last updated on 30/Sep/21 $${Q}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sint}}{\mathrm{1}+{cos}^{\mathrm{2}} {t}}{dt}\:=\:−\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{−{sint}}{\mathrm{1}+{cos}^{\mathrm{2}} {t}}{dt} \\ $$$$=−\left[{arctan}\left({cost}\right)\right]_{\mathrm{0}}…
Question Number 24332 by Zezo9970010@gmail.com last updated on 15/Nov/17 $$\mathrm{z}^{−\mathrm{4}_{=\mathrm{1}/\mathrm{3}\left(\mathrm{1}−\sqrt{\left.\mathrm{3i}\right)}\right.} } ? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155399 by 0731619 last updated on 30/Sep/21 Answered by TheHoneyCat last updated on 30/Sep/21 $$\mathrm{lim}_{\mathrm{n}\rightarrow+\infty\:} \underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}=+\infty \\ $$$$\mathrm{hence}\:\frac{\mathrm{1}}{\Sigma\frac{\mathrm{1}}{{n}}}\:\underset{{n}\rightarrow\infty} {\rightarrow}\mathrm{0} \\ $$…
Question Number 155384 by aliyn last updated on 29/Sep/21 $$\boldsymbol{{Solve}}\::\:\boldsymbol{{x}}^{\mathrm{2}} \:−\:\left(\mathrm{5}−\boldsymbol{{i}}\right)\boldsymbol{{x}}\:+\:\left(\mathrm{12}−\mathrm{5}\boldsymbol{{i}}\right)\:=\:\mathrm{0} \\ $$ Commented by aliyn last updated on 29/Sep/21 $$???? \\ $$ Answered by…