Question Number 196183 by cortano12 last updated on 19/Aug/23 Answered by dimentri last updated on 19/Aug/23 $$\:\:\underbrace{\Subset} \\ $$ Answered by mr W last updated…
Question Number 196209 by mnjuly1970 last updated on 19/Aug/23 $$ \\ $$$$\:\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left({x}−\mathrm{1}\right)^{\:\mathrm{2}} }{\mathrm{ln}^{\mathrm{2}} \left({x}\right)}\:{dx}=\:? \\ $$$$\:\:\:\:\:−−−− \\ $$ Answered by Mathspace last updated…
Question Number 196205 by Mastermind last updated on 19/Aug/23 $$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:!\mathrm{7}\:? \\ $$ Answered by AST last updated on 19/Aug/23 $$!\mathrm{7}=\mathrm{7}!\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}+\frac{\mathrm{1}}{\mathrm{6}!}−\frac{\mathrm{1}}{\mathrm{7}!}\right)=\mathrm{1854} \\ $$ Commented by AST…
Question Number 196173 by pticantor last updated on 19/Aug/23 $$\boldsymbol{{Calcul}}\:\boldsymbol{{I}}_{\boldsymbol{{a}}} =\int_{\boldsymbol{{a}}} ^{\frac{\mathrm{1}}{\boldsymbol{{a}}}} \frac{\boldsymbol{{lnx}}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}\:\left(\boldsymbol{{a}}>\mathrm{0}\right)\: \\ $$ Answered by Erico last updated on 19/Aug/23 $$\:\mathrm{J}_{{a}} =\:\underset{\:\mathrm{1}}…
Question Number 196172 by liuxinnan last updated on 19/Aug/23 Commented by mr W last updated on 26/Aug/23 $${see}\:{Q}\mathrm{196493} \\ $$ Commented by mr W last…
Question Number 196165 by mathlove last updated on 19/Aug/23 $$\left.\begin{matrix}{{x}^{{x}+{y}} ={y}^{\mathrm{24}} }\\{{y}^{{x}+{y}} ={x}^{\mathrm{6}} }\end{matrix}\right\}\Rightarrow\left({x},{y}\right)=\left(?,?\right) \\ $$ Answered by liuxinnan last updated on 19/Aug/23 Answered by…
Question Number 196164 by Rodier97 last updated on 19/Aug/23 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{calcul}: \\ $$$$ \\ $$$$\:\:\:{lim}_{{n}\rightarrow+\infty\:\:\:\:} {Un}=\sqrt[{{n}}]{\frac{\left(\mathrm{2}{n}\right)!}{{n}!{n}^{{n}} }} \\ $$$$ \\ $$$$ \\…
Question Number 196199 by Frix last updated on 19/Aug/23 $$\mathrm{Solve}: \\ $$$${y}'''=\frac{\mathrm{3}{y}'\left({y}''\right)^{\mathrm{2}} }{\mathrm{1}+\left({y}'\right)^{\mathrm{2}} } \\ $$ Answered by aleks041103 last updated on 20/Aug/23 $$\left({ln}\left({y}''\right)\right)'=\frac{{y}'''}{{y}''}=\frac{\mathrm{3}{y}'{y}''}{\mathrm{1}+\left({y}'\right)^{\mathrm{2}} }=\frac{\mathrm{3}}{\mathrm{2}}\:\frac{\left(\left({y}'\right)^{\mathrm{2}}…
Question Number 196198 by liuxinnan last updated on 19/Aug/23 $${a}+{b}+{c}+{d}=\mathrm{4} \\ $$$${prove}\:{that}: \\ $$$$\frac{{a}}{{a}^{\mathrm{3}} +\mathrm{8}}+\frac{{b}}{{b}^{\mathrm{3}} +\mathrm{8}}+\frac{{c}}{{c}^{\mathrm{3}} +\mathrm{8}}+\frac{{d}}{{d}^{\mathrm{3}} +\mathrm{8}}\leq\frac{\mathrm{4}}{\mathrm{9}} \\ $$ Answered by AST last updated…
Question Number 196166 by pticantor last updated on 19/Aug/23 $$\boldsymbol{{for}}\:\boldsymbol{{any}}\:\boldsymbol{{a}},\boldsymbol{{b}}\in\left[−\mathrm{1},\mathrm{1}\right]\:\:\boldsymbol{{calculate}}:\: \\ $$$$\boldsymbol{{arccos}}\left(\boldsymbol{{a}}\right)+\boldsymbol{{arcsin}}\left(\boldsymbol{{b}}\right)=? \\ $$$$\boldsymbol{{arcsin}}\left(\boldsymbol{{a}}\right)+\boldsymbol{{arcsin}}\left(\boldsymbol{{b}}\right)=? \\ $$$$\boldsymbol{{arccos}}\left(\boldsymbol{{a}}\right)+\boldsymbol{{arc}}{cos}\left(\boldsymbol{{b}}\right)=? \\ $$ Commented by pticantor last updated on 19/Aug/23…