Question Number 4441 by Rasheed Soomro last updated on 27/Jan/16 $$\mathrm{Determine}\: \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{1}/\mathrm{x}} \:. \\ $$ Commented by Yozzii last updated on 29/Jan/16 $${The}\:{limit}\:{does}\:{not}\:{exist}.…
Question Number 4440 by Rasheed Soomro last updated on 27/Jan/16 $$\mathrm{Market}\:\mathrm{is}\:\mathrm{slow}\:\mathrm{nowadays}!\: \\ $$$$\mathrm{I}\:\mathrm{mean}\:\mathrm{Questioning}/\mathrm{Answering}/\mathrm{Commenting} \\ $$$$\mathrm{is}\:\mathrm{slow}.\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{reasons}? \\ $$$$\:\:^{\bullet} \mathrm{Winter}\:\mathrm{season}? \\ $$$$\:\:^{\bullet} \mathrm{Shortage}\:\mathrm{of}\:\mathrm{problems}? \\ $$$$\:\:^{\bullet} \mathrm{Are}\:\mathrm{we}\:\:\mathrm{not}\:\mathrm{remained}\:\mathrm{interested}\:\mathrm{more}? \\…
Question Number 69974 by Shamim last updated on 29/Sep/19 $$\mathrm{Identify}\:\mathrm{domain}\:\mathrm{and}\:\mathrm{range}\:\mathrm{of}\:\mathrm{this}\: \\ $$$$\mathrm{function}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{ln}\frac{\mathrm{4}−\mathrm{x}}{\mathrm{4}+\mathrm{x}}. \\ $$ Commented by kaivan.ahmadi last updated on 29/Sep/19 $$\frac{\mathrm{4}−{x}}{\mathrm{4}+{x}}>\mathrm{0}\Rightarrow−\mathrm{4}<{x}<\mathrm{4} \\ $$$$\Rightarrow{D}_{{f}} =\left(−\mathrm{4},\mathrm{4}\right)…
Question Number 4437 by Rasheed Soomro last updated on 25/Jan/16 $$\mathrm{An}\:\boldsymbol{\mathrm{ellipse}}\:\mathrm{having}\:\boldsymbol{\mathrm{semi}}-\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axis}}\: \\ $$$$\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\boldsymbol{\mathrm{semi}}-\boldsymbol{\mathrm{minor}}\:\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{and}\:\mathrm{a}\:\boldsymbol{\mathrm{circle}}\:\mathrm{having}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\mathrm{have}\:\mathrm{equal} \\ $$$$\boldsymbol{\mathrm{area}}. \\ $$$$\mathrm{Express}\:\boldsymbol{\mathrm{r}}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}. \\ $$$$ \\ $$ Answered by…
Question Number 135507 by 0731619177 last updated on 13/Mar/21 Answered by Rasheed.Sindhi last updated on 15/Mar/21 $$\left({x}+{y}\right)\left(\mathrm{81}+{xy}\right)\:−\:\mathrm{9}\left({x}+{y}\right)^{\mathrm{2}} =\mathrm{210} \\ $$$$\left({x}+{y}\right)\left(\mathrm{81}+{xy}−\mathrm{9}\left({x}+{y}\right)\right)=\mathrm{210} \\ $$$$ \\ $$$${Let}\:{x}+{y}={n}\:{where}\:{n}\in\mathbb{Z}\:\wedge\:{n}\:\mid\:\mathrm{210} \\…
Question Number 69966 by necxxx last updated on 29/Sep/19 Commented by necxxx last updated on 29/Sep/19 $${please}\:{help} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 4430 by alib last updated on 24/Jan/16 $$\left\{\left({x}−{y}\right)\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)=\mathrm{3}{a}^{\mathrm{2}} \right. \\ $$$$\left({x}+{y}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=\mathrm{15}{a}^{\mathrm{2}} \\ $$$$ \\ $$$${Solve}\:{the}\:{system}\:{of}\:{equation} \\ $$$$ \\ $$…
Question Number 4429 by alib last updated on 24/Jan/16 $$\left({sin}\:{x}\:+\sqrt{\mathrm{3}}\:{cos}\:{x}\right)\:{sin}\:\mathrm{3}{x}\:=\:\mathrm{2} \\ $$ Answered by Yozzii last updated on 24/Jan/16 $${sinx}+\sqrt{\mathrm{3}}{cosx}=\sqrt{\mathrm{1}+\mathrm{3}}{sin}\left({x}+\pi/\mathrm{3}\right) \\ $$$$=\mathrm{2}{sin}\left({x}+\frac{\pi}{\mathrm{3}}\right) \\ $$$$\left({sinx}+\sqrt{\mathrm{3}}{cosx}\right){sin}\mathrm{3}{x}=\mathrm{2}………\left(\Upsilon\right) \\…
Question Number 135497 by EDWIN88 last updated on 13/Mar/21 $$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)\:=\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)+\:\sqrt{\mathrm{7}}\:\mathrm{cos}\:\mathrm{x} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\Leftrightarrow\:\mathrm{sin}\:^{\mathrm{2}} \left({x}+\frac{\pi}{\mathrm{4}}\right)−\mathrm{sin}\:^{\mathrm{2}} \left({x}−\frac{\pi}{\mathrm{4}}\right)=\sqrt{\mathrm{7}}\:\mathrm{cos}\:{x} \\…
Question Number 135498 by aurpeyz last updated on 13/Mar/21 $$ \\ $$$$\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\mathscr{F}\:=\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:\sqrt{\mathrm{25}{x}^{−\mathrm{2}}…