Question Number 117223 by mnjuly1970 last updated on 10/Oct/20 $$\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{mathematics}… \\ $$$$\:\:{proof}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}\:} ^{\:\infty} \left[{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{x}}\right)\right]^{\mathrm{2}} {dx}={ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:…\:\:{m}.{n}.\mathrm{1970}… \\ $$ Answered by mathmax…
Question Number 117216 by bobhans last updated on 10/Oct/20 $$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\mathrm{dx}}{\:\sqrt{\mathrm{sin}\:\mathrm{x}}}\:=?\: \\ $$$$ \\ $$ Answered by TANMAY PANACEA last updated on 10/Oct/20 $$\mathrm{2}\int_{\mathrm{0}}…
Question Number 117086 by mnjuly1970 last updated on 09/Oct/20 $$\:\:\:\:\:\:\:…{nice}\:\:{mathematics}… \\ $$$$\:{evaluate}\:… \\ $$$$\:\:\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}{sin}\left(\frac{{k}\pi}{\mathrm{4}{n}}\right)\right)^{\frac{\mathrm{1}}{{n}}} =? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.\mathrm{1970}… \\ $$$$ \\…
Question Number 51446 by gunawan last updated on 27/Dec/18 $${f}\left({x}\right)=\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$$${f}^{'} \left(−\mathrm{2}\right)=… \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18 $${y}^{\mathrm{2}}…
Question Number 51403 by Tinkutara last updated on 26/Dec/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 116798 by mnjuly1970 last updated on 06/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:{a},{b},{c}\:\in\mathbb{R}^{+\:} :: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{find} \\ $$$$ \\ $$$$\:\:\:\:{min}\left(\sqrt{\:\frac{{b}+{c}}{{a}}}\:+\sqrt{\frac{{a}+{c}}{{b}}}\:+\sqrt{\frac{{a}+{b}}{{c}}}\:\right)=??? \\ $$$$\:\:…
Question Number 116793 by mnjuly1970 last updated on 06/Oct/20 $$\:\:\:\:\:\:\:..{calculus}.. \\ $$$$\:\:{x},{y},{z}\:\in\mathbb{R}^{+} \:\:{and}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:=\mathrm{1} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{find}\:\:\:\:\:\: \\ $$$$\:\:\:\:{min}_{{x},{y},{z}\in\mathbb{R}^{+\:\:\:\:} } \left(\left(\frac{{yz}}{{x}}+\frac{{xz}}{{y}}+\frac{{xy}}{{z}}\right)\:\right)=? \\…
Question Number 182026 by cortano1 last updated on 03/Dec/22 $$\:\:\mathrm{h}\left(\mathrm{x}\right)=\:\begin{vmatrix}{\mathrm{sin}\:\mathrm{x}\:\:\:\:\:\mathrm{cos}\:\mathrm{x}\:\:\:\:\:\:\:\mathrm{tan}\:\mathrm{x}}\\{\mathrm{cos}\:\mathrm{2x}\:\:\mathrm{sin}\:\mathrm{2x}\:\:\:\:\:\mathrm{tan}\:\mathrm{2x}}\\{\:\:\:\mathrm{x}^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{x}^{\mathrm{4}} \:\:\:\:\:\:\mathrm{xsin}\:\mathrm{x}}\end{vmatrix} \\ $$$$\:\:\mathrm{h}'\left(\mathrm{0}\right)\:=? \\ $$ Answered by SEKRET last updated on 03/Dec/22 $$\:\mathrm{0} \\…
Question Number 116433 by bemath last updated on 04/Oct/20 $$\mathrm{Given}\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{2}^{\mathrm{cos}\:^{\mathrm{2}} \left(\theta\right)} \:+\:\mathrm{2}^{\mathrm{sin}\:^{\mathrm{2}} \left(\theta\right)} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{maximum}\:\mathrm{value}}\\{\mathrm{minimum}\:\mathrm{value}}\end{cases} \\ $$ Answered by bobhans last updated on 04/Oct/20 $$\Rightarrow\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{2}^{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}}…
Question Number 50834 by Tinkutara last updated on 21/Dec/18 Commented by ajfour last updated on 21/Dec/18 $${h}\left({x}\right)=\:\frac{\left({x}−\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} +\mathrm{2}}{{x}−\frac{\mathrm{1}}{{x}}}\:\:=\sqrt{\mathrm{2}}\left({z}+\frac{\mathrm{1}}{{z}}\right) \\ $$$$\:\:{where}\:\:\:{z}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\left({x}−\frac{\mathrm{1}}{{x}}\right) \\ $$$$\Rightarrow\:\:{h}\left({x}\right)\mid_{{min}} \:=\:\mathrm{2}\sqrt{\mathrm{2}}\:. \\ $$…