Question Number 126003 by mnjuly1970 last updated on 16/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{integral}… \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {tan}\left({x}\right){ln}\left({sin}\left({x}\right)\right){ln}\left({cos}\left({x}\right)\right){dx}=\frac{\zeta\left(\mathrm{3}\right.}{\mathrm{8}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{G}{ood}\:{luck} \\ $$ Answered by Olaf last updated…
Question Number 125996 by bramlexs22 last updated on 16/Dec/20 $$\:{If}\:{z}^{\mathrm{3}} ={x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:,\:\rightarrow\begin{cases}{\frac{{dx}}{{dt}}=\mathrm{3}}\\{\frac{{dy}}{{dt}}=\mathrm{2}}\end{cases} \\ $$$${find}\:\frac{{dz}}{{dt}}\:{when}\:{x}=\mathrm{4}\:{and}\:{y}=\mathrm{1} \\ $$ Answered by Olaf last updated on 16/Dec/20 $${z}^{\mathrm{3}}…
Question Number 125995 by liberty last updated on 16/Dec/20 Commented by benjo_mathlover last updated on 16/Dec/20 $${f}\left({x}\right)=\:\begin{cases}{{x}\:;\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{−{x}\:;\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{0}}\end{cases} \\ $$$$\:{f}\:'\left(−\mathrm{1}\right)\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left(−\mathrm{1}+{h}\right)−{f}\left(−\mathrm{1}\right)}{{h}} \\ $$$${f}\:'\left(−\mathrm{1}\right)=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\left(−\mathrm{1}+{h}\right)−\left(\mathrm{1}\right)}{{h}} \\ $$$$\:{f}\:'\left(−\mathrm{1}\right)=\:\underset{{h}\rightarrow\mathrm{0}}…
Question Number 191528 by mnjuly1970 last updated on 25/Apr/23 $$ \\ $$$$\:\:\:\:\:\:{find}\:\:{the}\:\:{value}\:\:{of}\:\:{the} \\ $$$$\:\:\:\:\:\:\:{following}\:\:{series}\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{cos}\left(\frac{{n}\pi}{\mathrm{4}}\:\right)}{{n}^{\:\mathrm{2}} }\:=? \\ $$ Answered by…
Question Number 60426 by cesar.marval.larez@gmail.com last updated on 20/May/19 $${the}\:{function}\:{is}\:{considered}\: \\ $$$${f}\left({x},{y}\right)={e}^{{xy}} +\frac{{x}}{{y}}+{sen}\left(\left(\mathrm{2}{x}+\mathrm{3}{y}\right)\pi\right)\:{Calcule}: \\ $$$$\frac{\partial{f}}{\partial{x}},\frac{\partial{f}}{\partial{y}},\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} },\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}.\:\:\:{f}_{{x}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{y}} \left(\mathrm{2},−\mathrm{1}\right),\:{f}_{{xx}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{xy}} \left(\mathrm{2},−\mathrm{1}\right) \\ $$ Commented…
Question Number 60425 by cesar.marval.larez@gmail.com last updated on 20/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125925 by zarminaawan last updated on 15/Dec/20 $$\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }−\mathrm{2}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{4}\frac{{dy}}{{dx}}−\mathrm{8}{y}=\mathrm{0} \\ $$ Answered by liberty last updated on 15/Dec/20 $${HE}\:\equiv\:{z}^{\mathrm{3}} −\mathrm{2}{z}^{\mathrm{2}}…
Question Number 125901 by pticantor last updated on 15/Dec/20 $$\:\bigstar^{\bigstar\bigstar} \boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{differential}}\:\boldsymbol{{equation}}\bigstar^{\bigstar^{\bigstar} } \\ $$$$ \\ $$$$\:\:\boldsymbol{{y}}^{'} \left(\boldsymbol{{x}}\right)+\boldsymbol{{x}}=\boldsymbol{{y}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right) \\ $$$$ \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{i}}\:\boldsymbol{{need}}\:\boldsymbol{{help}}\:!! \\ $$ Terms…
Question Number 60357 by Sardor2211 last updated on 20/May/19 Commented by Mr X pcx last updated on 20/May/19 $${the}\:{equation}\:{is}\:{not}\:{clear}\:{but}\:{i}\:{suppose} \\ $$$${that}\:{is}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} −\mathrm{2}{xy}\:=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} \\…
Question Number 60354 by Sardor2211 last updated on 20/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com