Menu Close

Category: None

Question-106302

Question Number 106302 by mathdave last updated on 04/Aug/20 Answered by bemath last updated on 04/Aug/20 $$\mathrm{x}\:=\:\mathrm{sin}\:\flat\:\Rightarrow\:\int\:\frac{\mathrm{cos}\:\flat\:\mathrm{d}\flat}{\mathrm{sin}\:^{\mathrm{2}} \flat\:\mathrm{cos}\:\flat}\:= \\ $$$$\int\:\mathrm{csc}^{\mathrm{2}} \:\flat\:\mathrm{d}\flat\:=\:−\int\:\mathrm{d}\left(\mathrm{cot}\:\flat\right)\: \\ $$$$=\:−\mathrm{cot}\:\flat\:+\:\mathrm{C}\:=\:−\frac{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}}\:+\:\mathrm{C}\: \\…

Question-106303

Question Number 106303 by mathdave last updated on 04/Aug/20 Answered by mathmax by abdo last updated on 05/Aug/20 $$\mathrm{A}\:=\int_{\mathrm{0}} ^{\sqrt{\mathrm{3}}} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{arcsin}\left(\frac{\mathrm{2x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx}\:\:\mathrm{wedo}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}\:=\mathrm{tan}\left(\frac{\mathrm{t}}{\mathrm{2}}\right) \\ $$$$\Rightarrow\:\mathrm{A}\:=\int_{\mathrm{0}}…

If-0-lt-x-lt-1-lt-y-lt-100-lt-z-and-satisfy-these-equations-log-2-xyz-103-1-log-2-x-1-log-2-y-1-log-2-z-1-103-Find-xyz-x-y-z-xy-yz-zx-

Question Number 106288 by ZiYangLee last updated on 04/Aug/20 $$\mathrm{If}\:\mathrm{0}<\mathrm{x}<\mathrm{1}<\mathrm{y}<\mathrm{100}<\mathrm{z},\:\mathrm{and}\:\mathrm{satisfy} \\ $$$$\mathrm{these}\:\mathrm{equations}: \\ $$$$\begin{cases}{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{xyz}\right)=\mathrm{103}}\\{\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \mathrm{y}}+\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{2}} \mathrm{z}}=\frac{\mathrm{1}}{\mathrm{103}}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{xyz}\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)−\mathrm{xy}−\mathrm{yz}−\mathrm{zx} \\ $$ Answered by bemath…

for-x-2-x-2-

Question Number 40715 by gopikrishnan005@gmail.com last updated on 26/Jul/18 $$\mathrm{for}\:\mathrm{x}\geqslant\mathrm{2}\:\mid\mathrm{x}−\mathrm{2}\mid= \\ $$ Commented by maxmathsup by imad last updated on 26/Jul/18 $${x}\geqslant\mathrm{2}\Rightarrow{x}−\mathrm{2}\geqslant\mathrm{0}\:\Rightarrow\mid{x}−\mathrm{2}\mid\:={x}−\mathrm{2}\:. \\ $$ Answered…