Question Number 135522 by Dwaipayan Shikari last updated on 13/Mar/21 Commented by Dwaipayan Shikari last updated on 13/Mar/21 $$ \\ $$ Two large circles altogether…
Question Number 4448 by Rasheed Soomro last updated on 29/Jan/16 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{\mathrm{3}{e}^{{x}} −{e}^{−{x}} −\mathrm{2}}{{x}}=? \\ $$ Answered by Yozzii last updated on 29/Jan/16 $${One}\:{approach}\:{can}\:{involve}\:{the}\:{use}\:{of} \\…
Question Number 4446 by Rasheed Soomro last updated on 28/Jan/16 $$\mathrm{Define}\:\mathrm{2}^{\sqrt{\mathrm{3}}} \:\mathrm{and}\:\mathrm{3}^{\sqrt{\mathrm{2}}} \:. \\ $$ Commented by Yozzii last updated on 29/Jan/16 $${Dedekind}\:{cuts}\:{of}\:{the}\:{real}\:{line}\:{might} \\ $$$${define}\:{each}\:{of}\:{those}\:{numbers}.\:…
Question Number 4445 by Rasheed Soomro last updated on 28/Jan/16 $$\mathrm{A}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:\:\:\:\frac{\mathrm{3}}{\mathrm{2}},\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{5}}{\mathrm{4}},\frac{\mathrm{4}}{\mathrm{5}},…. \\ $$$$\mathrm{Write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{general}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{sequence}\:\mathrm{and}\:\mathrm{find}\:\mathrm{its}\:\mathrm{limit}. \\ $$ Commented by 123456 last updated on…
Question Number 135513 by Gaurav500 last updated on 13/Mar/21 Answered by MJS_new last updated on 13/Mar/21 $$\int\frac{{dx}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}}= \\ $$$$\:\:\:\:\:\left[{t}={x}+\mathrm{1}\:\rightarrow\:{dx}={dt}\right] \\ $$$$=\int\frac{{dt}}{\:\sqrt{{t}−\mathrm{1}}+\sqrt{{t}}+\sqrt{{t}+\mathrm{1}}}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{I}_{{k}} \:+{Ci} \\…
Question Number 4443 by 123456 last updated on 27/Jan/16 $$\mathrm{find}\:\mathrm{all}\:{x},{y}\in\mathbb{Z}\:\mathrm{such}\:\mathrm{that} \\ $$$${x}\in\left[\mathrm{0},\mathrm{50}\right] \\ $$$${y}\in\left[\mathrm{0},\mathrm{50}\right] \\ $$$${x}+{y}={k},{k}\in\left[\mathrm{0},\mathrm{50}\right] \\ $$$$\frac{{x}}{{x}+{y}}=\frac{\mathrm{99}}{\mathrm{100}} \\ $$ Answered by RasheedSindhi last updated…
Question Number 69979 by Maclaurin Stickker last updated on 29/Sep/19 $${Using}\:{the}\:{definition}\:{calculate}\:{the} \\ $$$${derivative}\:{at}\:{point}\:{x}=\mathrm{2} \\ $$$${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} \\ $$$$ \\ $$ Commented by kaivan.ahmadi last updated on…
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)…