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Question-128561

Question Number 128561 by 777316 last updated on 08/Jan/21 Answered by Dwaipayan Shikari last updated on 08/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{cosx}+\left(\frac{\mathrm{1}−{cosx}}{{sinx}}\right)=\mathrm{1}+\frac{\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{{sinx}}=\mathrm{1} \\ $$ Terms of Service…

1-x-1-x-1-x-dx-

Question Number 62907 by aliesam last updated on 26/Jun/19 $$\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\:}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$ Commented by mathmax by abdo last updated on 26/Jun/19 $${let}\:{A}\:=\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\left(\mathrm{1}+{x}\right){dx}\:{changement}\:{x}\:={cos}\left(\mathrm{2}\theta\right)\:{give}\:\mathrm{2}\theta\:={arcosx}\:\Rightarrow \\ $$$${A}\:=\int\:\sqrt{\frac{\mathrm{2}{cos}^{\mathrm{2}} \left(\theta\right)}{\mathrm{2}{sin}^{\mathrm{2}}…

y-x-x-2-

Question Number 128382 by arash sharifi last updated on 06/Jan/21 $${y}={x}^{{x}^{\mathrm{2}} } \\ $$ Commented by hknkrc46 last updated on 06/Jan/21 $$\bullet\:\boldsymbol{{x}}\:\in\:\mathbb{R}\:\Rightarrow\:\boldsymbol{{y}}\:\in\:\mathbb{R} \\ $$$$\bullet\:\boldsymbol{{x}}\:=\:\mp\mathrm{1}\:\Rightarrow\:\boldsymbol{{y}}\:=\:\mathrm{1} \\…