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} \\ $$$${f}_{{x}} =\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}=\mathrm{0}\:\rightarrow\begin{cases}{{x}=\mathrm{1}}\\{{x}=−\mathrm{1}}\end{cases} \\ $$$${f}_{{y}}…
Question Number 114922 by bemath last updated on 22/Sep/20 $${find}\:{minimum}\:{value}\:{of}\:{function} \\ $$$${y}=\sqrt{\left({x}+\mathrm{6}\right)^{\mathrm{2}} +\mathrm{25}}\:+\sqrt{\left({x}−\mathrm{6}\right)^{\mathrm{2}} +\mathrm{121}} \\ $$ Answered by john santu last updated on 22/Sep/20 $${you}\:{want}\:{to}\:{find}\:{the}\:{point}\:{on}\:{the}\:…
Question Number 180350 by mnjuly1970 last updated on 10/Nov/22 Answered by Ar Brandon last updated on 11/Nov/22 $$\mathcal{L}\left({e}^{−{x}} .{erf}\left(\sqrt{{x}}\right)\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {erf}\left(\sqrt{{x}}\right){e}^{−{px}} {dx} \\ $$$$=\int_{\mathrm{0}}…
Question Number 114753 by bemath last updated on 21/Sep/20 $${find}\:{minimum}\:{value}\:{of}\:{function} \\ $$$${f}\left({x}\right)\:=\:\frac{\left({x}+\mathrm{17}\right)^{\mathrm{3}} }{{x}}\:,\:{x}>\mathrm{0} \\ $$ Answered by Olaf last updated on 21/Sep/20 $${f}'\left({x}\right)\:=\:\frac{\mathrm{3}\left({x}+\mathrm{17}\right)^{\mathrm{2}} {x}−\left({x}+\mathrm{17}\right)^{\mathrm{3}} }{{x}^{\mathrm{2}}…
Question Number 114735 by mnjuly1970 last updated on 20/Sep/20 $$\:\:\:….\:{nice}\:\:{mathematics}… \\ $$$$ \\ $$$$\:\:{prove}\:\:{that}::\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left[\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}\right]^{\mathrm{2}} }{\left(\mathrm{2}{n}−\mathrm{1}\right)\mathrm{2}^{\mathrm{4}{n}} }\:=\mathrm{1}−\frac{\mathrm{2}}{\pi}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{m}.{n}.{july}.\:\mathrm{1970}# \\…
Question Number 114721 by mnjuly1970 last updated on 20/Sep/20 $$\:\:\:\:\:\:\:\:\:\:….{nice}\:\:{calculus}…. \\ $$$$\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi=\int_{\mathrm{0}\:} ^{\:\mathrm{1}} {xln}\left[{ln}\left({x}\right).{ln}\left(\mathrm{1}−{x}\right)\right]{dx}=−\gamma \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\gamma\:::=\:{euler}\:\:{mascheroni}\:{constant}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 180016 by cortano1 last updated on 06/Nov/22 $$\:\mathrm{Find}\:\mathrm{max}\:\mathrm{and}\:\mathrm{min}\:\mathrm{local}\:\mathrm{of}\:\mathrm{function} \\ $$$$\:\mathrm{y}=\:\frac{\mathrm{x}+\mathrm{2}}{\mathrm{x}^{\mathrm{2}} +\mathrm{3sin}\:\left(\mathrm{3x}\right)+\mathrm{4cos}\:\left(\mathrm{3x}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 114304 by mnjuly1970 last updated on 18/Sep/20 $$\:\:\:\:\:\:\:{calculus}….. \\ $$$$\:{evaluate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{−\mathrm{1}} ^{\:\mathrm{1}} {xln}\left(\mathrm{1}^{{x}} +\mathrm{2}^{{x}} +\mathrm{3}^{{x}} +\mathrm{6}^{{x}} \right){dx}\:=???\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Commented…
Question Number 179741 by mnjuly1970 last updated on 01/Nov/22 $$ \\ $$$$\:\:\:\:\:{prove}\:\:{that} \\ $$$$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty\:} \frac{\:\sqrt{{x}}}{\mathrm{1}\:+\mathrm{7}{x}^{\:\mathrm{2}} \:+\:{x}^{\:\mathrm{4}} }\:{dx}\:=\:\frac{\pi}{\:\sqrt{\:\mathrm{90}}}\:\: \\ $$$$ \\ $$ Terms…