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 $${The}\:{limit}\:{does}\:{not}\:{exist}.…
Question Number 4430 by alib last updated on 24/Jan/16 $$\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 4423 by Rasheed Soomro last updated on 24/Jan/16 $$\mathrm{Determine}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{such}\:\mathrm{that}\:\forall\:\mathrm{t}\in\mathbb{Z} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{8x}+\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{has}\:\mathrm{integer}-\mathrm{solution}. \\ $$ Commented by Yozzii last updated on 24/Jan/16 $${Try}\:{f}\left({t}\right)={c};\:{c}\:{is}\:{a}\:{real}\:{constant}. \\…
Question Number 135493 by EDWIN88 last updated on 13/Mar/21 $$\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{2}}\:=\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$ Answered by john_santu last updated on 13/Mar/21 $$\left(\mathrm{1}\right)\begin{cases}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}\geqslant\mathrm{0}}\\{{x}^{\mathrm{2}} −{x}−\mathrm{2}\geqslant\mathrm{0}}\\{{x}^{\mathrm{2}}…
Question Number 135486 by EDWIN88 last updated on 13/Mar/21 $$\frac{\sqrt{\mathrm{2x}+\mathrm{1}}+\sqrt{\mathrm{x}−\mathrm{1}}}{\:\sqrt{\mathrm{2x}+\mathrm{1}}−\sqrt{\mathrm{x}−\mathrm{1}}}\:=\:\frac{\mathrm{3}}{\:\sqrt{\mathrm{x}+\mathrm{2}}}\: \\ $$ Commented by benjo_mathlover last updated on 13/Mar/21 $${wrong} \\ $$$$ \\ $$ Commented…
Question Number 69939 by mr W last updated on 29/Sep/19 $${x},{y},{z}\:\in\:{Z}^{+} \\ $$$${find}\:{all}\:{solutions}\:{of}\:\boldsymbol{{xy}}=\left(\boldsymbol{{x}}+\boldsymbol{{y}}\right)\boldsymbol{{z}} \\ $$ Commented by Rasheed.Sindhi last updated on 29/Sep/19 $${k}\in\mathbb{Z}^{+} \:{in}\:{the}\:{following}. \\…
Question Number 135472 by mr W last updated on 13/Mar/21 $${for}\:{x}+{y}+{z}=\mathrm{10}\:{with}\:{x},{y},{z}\in\mathbb{N} \\ $$$${find}\:\Sigma\frac{\mathrm{10}!}{{x}!{y}!{z}!} \\ $$ Answered by Ñï= last updated on 13/Mar/21 $$\Sigma\begin{pmatrix}{\:\:\:\mathrm{10}}\\{{x},{y},{z}}\end{pmatrix}=\left(\mathrm{1}+\mathrm{1}+\mathrm{1}\right)^{\mathrm{10}} =\mathrm{3}^{\mathrm{10}} \\…
Question Number 4397 by moussapk last updated on 20/Jan/16 $$\int\left(\frac{\mathrm{1}}{{sin}\left({x}\right)}{dx}\right. \\ $$ Answered by Yozzii last updated on 20/Jan/16 $${I}=\int\frac{\mathrm{1}}{{sinx}}{dx}=\int{cosecxdx} \\ $$$${I}=\int\frac{{cosecx}\left({cosecx}+{cotx}\right)}{{cosecx}+{cotx}}{dx} \\ $$$${I}=\int\frac{{cosec}^{\mathrm{2}} {x}+{cotxcosecx}}{{cosecx}+{cotx}}{dx}…
Question Number 135424 by benjo_mathlover last updated on 13/Mar/21 $${Find}\:{solution}\:{set}\:{the}\:{inequality} \\ $$$$\sqrt{\mathrm{2}{x}−\mathrm{5}}\:+\:\sqrt{\mathrm{25}−\mathrm{3}{x}}\:>\:{x} \\ $$ Answered by EDWIN88 last updated on 13/Mar/21 $$\left(\mathrm{1}\right)\:\mathrm{2x}−\mathrm{5}\geqslant\mathrm{0}\rightarrow\mathrm{x}\geqslant\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{3x}−\mathrm{25}\leqslant\mathrm{0}\rightarrow\mathrm{x}\leqslant\frac{\mathrm{25}}{\mathrm{3}} \\…
Question Number 135420 by liberty last updated on 13/Mar/21 $${Algebra} \\ $$Pipe A can fill a tank in two hours and pipe B can fill…