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…
Question Number 155382 by MathsFan last updated on 29/Sep/21 Answered by puissant last updated on 29/Sep/21 $${Q}=\int_{\mathrm{0}} ^{\mathrm{10}} \sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+…}}}}{dx} \\ $$$${u}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+….}}}}\rightarrow{u}^{\mathrm{2}} ={x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+….}}} \\ $$$$\Rightarrow\:{u}^{\mathrm{2}} −{u}={x}\:\Rightarrow\:{u}−{u}+\frac{\mathrm{1}}{\mathrm{4}}={x}+\frac{\mathrm{1}}{\mathrm{4}}…
Question Number 155365 by MathsFan last updated on 29/Sep/21 $$\:{y}=\frac{\mathrm{10}}{\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{5}} } \\ $$$$\:{find}\:\:\frac{{dy}}{{dx}} \\ $$ Answered by gsk2684 last updated on 29/Sep/21 $$\mathrm{10}\left(\frac{−\mathrm{5}}{\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{6}}…
Question Number 155361 by Fikret last updated on 29/Sep/21 $${x}−\mathrm{4}{z}+\mathrm{8}{y}=\mathrm{7} \\ $$$$\mathrm{8}×+\mathrm{7}{z}−{y}=\mathrm{4} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} =? \\ $$ Terms of Service Privacy Policy Contact:…