Question Number 124924 by bemath last updated on 07/Dec/20 $$\:{What}\:{should}\:{the}\:{dimensions}\:{be} \\ $$$${of}\:{a}\:{cylinder}\:{so}\:{that}\:{for}\:{a}\:{given}\:{volume}\: \\ $$$${v}\:{its}\:{total}\:{surface}\:{S}\:{minimum}\:?\: \\ $$ Commented by liberty last updated on 07/Dec/20 $${Denoting}\:{by}\:{r}\:{the}\:{radius}\:{of}\:{the}\:{base}\:{of}\:{the} \\…
Question Number 190420 by mnjuly1970 last updated on 02/Apr/23 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{laplace}\:\:\mathrm{transform} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathcal{L}_{{t}} \:\left\{\:\:\frac{\:\mathrm{sin}\left({t}\:\right)}{{t}}\:\:\right\}\:=\:\mathcal{F}\:\left({s}\:\right)\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathcal{F}\:\left({s}\:\right)=\:\:?\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:{then}\:\:{calculate}\:. \\ $$$$…
Question Number 124845 by liberty last updated on 06/Dec/20 $$\:\:\:{f}\left({x}\right)\:=\:\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)}\right)\: \\ $$$$\:\:\frac{{df}\left({x}\right)}{{dx}}\:? \\ $$ Answered by bemath last updated on 06/Dec/20 $${f}\:'\left({x}\right)=\frac{\mathrm{1}\left({x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)\right)−{x}\left(\mathrm{1}−\left(\frac{{x}−\mathrm{sin}\:{x}−{x}\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\left({x}−\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\right)\mathrm{cos}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)\right.}{\left({x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)\right)^{\mathrm{2}} }.\:\mathrm{cos}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)}\right) \\…
Question Number 124831 by mnjuly1970 last updated on 06/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:\:{that}:: \\ $$$$\:\:\:{lim}_{{x}\rightarrow\infty} \left\{{xe}^{\frac{\mathrm{1}}{{x}}} −{e}^{\frac{−\mathrm{1}}{{x}}} \Gamma\left(\frac{\mathrm{1}}{{x}}\:\right)\right\}=\mathrm{2}+\gamma \\ $$$$\:\:\:\:\gamma:\:{euler}−{mascheroni}\:{constant} \\ $$$$ \\ $$ Answered by…
Question Number 124796 by Engr_Jidda last updated on 06/Dec/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{this}\:\mathrm{equation}\:\mathrm{interms} \\ $$$$\mathrm{bessels}\:\mathrm{function}. \\ $$$$\mathrm{y}^{''} +\left(\mathrm{1}+\frac{\mathrm{1}−\mathrm{4k}^{\mathrm{2}} }{\mathrm{4x}^{\mathrm{2}} }\right)\mathrm{y}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 124779 by TITA last updated on 05/Dec/20 Commented by TITA last updated on 05/Dec/20 $${please}\:{help} \\ $$ Answered by Lordose last updated on…
Question Number 59220 by Aditya789 last updated on 06/May/19 $$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{y}=\:\frac{\mathrm{b}^{\mathrm{2}} }{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{cos}^{\mathrm{2}} \mathrm{x}} \\ $$ Answered by MJS last updated on 06/May/19…
Question Number 124723 by mnjuly1970 last updated on 05/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:\:\:{calculus}…. \\ $$$$\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:{challanging}\:\:\:{integral}:: \\ $$$$\:\:\:\:\Omega=\:\:\int_{\mathrm{1}} ^{\:\:\infty} \:\left(\frac{\left\{{x}\right\}−\frac{\mathrm{1}}{\mathrm{2}}}{{x}}\right){dx}\overset{???} {=}{ln}\left(\sqrt{\mathrm{2}\pi}\:\right)−\mathrm{1} \\ $$$$\:\:\:\left\{{x}\right\}\:{is}\:{fractional}\:{part}\:{of}\:\:'{x}' \\ $$ Answered by…
Question Number 59171 by maxmathsup by imad last updated on 05/May/19 $${let}\:{f}\left({x},{y}\right)\:\:\frac{{arctan}\left({x}+\mathrm{2}{y}\right)}{{x}\:+{y}^{\mathrm{2}} } \\ $$$${calculate}\:\frac{\partial{f}}{\partial{x}}\left({x},{y}\right)\:\:,\:\frac{\partial{f}}{\partial{y}}\left({x},{y}\right),\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} }\left({x},{y}\right),\:\frac{\partial^{\mathrm{2}} {f}}{\partial{y}^{\mathrm{2}} }\left({x},{y}\right)\:,\:\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}\left({x},{y}\right) \\ $$$$\frac{\partial^{\mathrm{2}} {f}}{\partial{y}\partial{x}}\left({x},{y}\right) \\ $$…
Question Number 124698 by Algoritm last updated on 05/Dec/20 Answered by Olaf last updated on 05/Dec/20 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\mathrm{ln}\left(\mathrm{3}+{x}^{\mathrm{2}} \right) \\ $$$${f}\left({x}\right)\:=\:\mathrm{ln}\mid{x}−\sqrt{\mathrm{3}}{i}\mid+\mathrm{ln}\mid{x}+\sqrt{\mathrm{3}}{i}\mid \\ $$$${f}'\left({x}\right)\:=\:\frac{\mathrm{1}}{{x}−\sqrt{\mathrm{3}}{i}}+\frac{\mathrm{1}}{{x}+\sqrt{\mathrm{3}}{i}} \\ $$$${f}''\left({x}\right)\:=\:−\frac{\mathrm{1}}{\left({x}−\sqrt{\mathrm{3}}{i}\right)^{\mathrm{2}} }−\frac{\mathrm{1}}{\left({x}+\sqrt{\mathrm{3}}{i}\right)^{\mathrm{2}}…