Question Number 49845 by mhozhez last updated on 11/Dec/18 $${y}^{{xsiny}} +{x}^{{ysinx}} =\mathrm{1} \\ $$$${determine}\:\frac{{dy}}{{dx}} \\ $$ Commented by MJS last updated on 11/Dec/18 $$\mathrm{try}\:\mathrm{this}\:\mathrm{for}\:\mathrm{yourself}.\:\mathrm{the}\:\mathrm{method}\:\mathrm{is}\:\mathrm{simple}: \\…
Question Number 180900 by alcohol last updated on 19/Nov/22 $${show}\:{that}\:\int_{\mathrm{1}} ^{\:+\infty} \left(\frac{{x}−\lfloor{x}\rfloor}{{x}^{\mathrm{2}} }\right){dx}\:=\:\mathrm{1}\:−\:\gamma \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115302 by mnjuly1970 last updated on 24/Sep/20 $$\:\:\:\:\:\:\:…\:{nice}\:\:{math}… \\ $$$$\:\:\:\:\:{find} \\ $$$$\:\:\:\:{lim}_{{n}\rightarrow\infty\:\:} \left\{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\int_{{k}−\mathrm{1}} ^{\:\:{k}} {tan}^{−\mathrm{1}} \left(\frac{{nx}−{nk}}{{kx}+{n}^{\mathrm{2}} }\right){dx}\right\} \\ $$$$\: \\ $$…
Question Number 115273 by mnjuly1970 last updated on 24/Sep/20 $$\:\:\:\:\:\:\:\:…\:{advanced}\:\:{mathematics}… \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}::: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Delta=\int_{\mathrm{0}} ^{\:\infty} \:\frac{{cos}\left({ln}\left({x}\right)\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\:=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}……
Question Number 115260 by bobhans last updated on 24/Sep/20 $${Let}\:{f}\:{be}\:{a}\:{real}\:{valued}\:{function}\:{defined} \\ $$$${on}\:{the}\:{interval}\:\left(−\mathrm{1},\mathrm{1}\right)\:{such}\:{that}\: \\ $$$${e}^{−{x}} .{f}\left({x}\right)=\mathrm{2}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\sqrt{{t}^{\mathrm{4}} +\mathrm{1}}\:{dt}\:\forall{x}\in\left(−\mathrm{1},\mathrm{1}\right) \\ $$$${and}\:{let}\:{g}\:{be}\:{the}\:{inverse}\:{function}\:{of}\:{f} \\ $$$$.\:{Find}\:{the}\:{value}\:{of}\:{g}'\left(\mathrm{2}\right). \\ $$ Commented…
Question Number 115222 by mnjuly1970 last updated on 24/Sep/20 $$\:\:\:\:\:\:….\:{nice}\:\:{math}\:… \\ $$$$ \\ $$$$\:\:\:\:{nice}\:\:{integral}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\::: \\ $$$$\Psi=\mathrm{9}\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{5}} {e}^{−{x}^{\mathrm{3}} } {ln}\left(\mathrm{1}+{x}\right){dx}\:\overset{???} {=}\:\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)−\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right)+\Gamma\left(\frac{\mathrm{3}}{\mathrm{3}}\right)\:\: \\…
Question Number 180718 by a.lgnaoui last updated on 16/Nov/22 $${Resoudre}\:{le}\:{systeme} \\ $$$$\frac{{dx}}{{dt}}=\mathrm{4}{x}+\mathrm{6}{y} \\ $$$$\frac{{dy}}{{dt}}=−\mathrm{3}{x}−\mathrm{5}{y} \\ $$$$\frac{{dz}}{{dt}}=−\mathrm{3}{x}−\mathrm{6}{y}−\mathrm{5}{z} \\ $$ Answered by mr W last updated on…
Question Number 115112 by bemath last updated on 23/Sep/20 $${What}\:{is}\:{minimum}\:{distance}\:{between}\: \\ $$$${xy}\:=\:\mathrm{4}\:{and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:=\:\mathrm{4}\:?\: \\ $$$$ \\ $$ Answered by bobhans last updated on 28/Sep/20…
Question Number 114996 by mnjuly1970 last updated on 22/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{mathematics}…\: \\ $$$$\:\:\:\:{prove}\:{that}::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{i}::\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{sinh}^{\mathrm{2}} \left(\pi{n}\right)}\:=\frac{\mathrm{1}}{\mathrm{6}}\:−\frac{\mathrm{1}}{\mathrm{2}\pi}\:\:\:\:\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ii}::\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{{e}^{\mathrm{2}\pi{n}} −\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{24}}\:−\frac{\mathrm{1}}{\mathrm{8}\pi}\:\:\checkmark\checkmark \\…
Question Number 114945 by bemath last updated on 22/Sep/20 Answered by bobhans last updated on 22/Sep/20 $${f}\left({x},{y}\right)\:=\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} −\mathrm{3}{x}−\mathrm{12}{y}+\mathrm{20} \\ $$$${f}_{{x}} =\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}=\mathrm{0}\:\rightarrow\begin{cases}{{x}=\mathrm{1}}\\{{x}=−\mathrm{1}}\end{cases} \\ $$$${f}_{{y}}…