Menu Close

Category: Differentiation

advanced-calculus-prove-that-0-1-ln-x-cos-2-pix-dx-ln-2pi-4-1-8-m-n-1970-

Question Number 117280 by mnjuly1970 last updated on 10/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}…\: \\ $$$$ \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right).{cos}^{\mathrm{2}} \left(\pi{x}\right){dx} \\ $$$$…

nice-mathematics-proof-1-pi-0-tan-1-1-x-2-dx-ln-2-m-n-1970-

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…

nice-mathematics-evaluate-lim-n-k-1-n-sin-kpi-4n-1-n-m-n-1970-

Question Number 117086 by mnjuly1970 last updated on 09/Oct/20 $$\:\:\:\:\:\:\:…{nice}\:\:{mathematics}… \\ $$$$\:{evaluate}\:… \\ $$$$\:\:\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}{sin}\left(\frac{{k}\pi}{\mathrm{4}{n}}\right)\right)^{\frac{\mathrm{1}}{{n}}} =? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.\mathrm{1970}… \\ $$$$ \\…

calculus-x-y-z-R-and-x-2-y-2-z-2-1-find-min-x-y-z-R-yz-x-xz-y-xy-z-m-n-1970-

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)=? \\…

h-x-determinant-sin-x-cos-x-tan-x-cos-2x-sin-2x-tan-2x-x-3-1-4-x-4-xsin-x-h-0-

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} \\…