Question Number 70031 by Nithin Kumar last updated on 30/Sep/19 $$\int\left[{x}\right]{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135566 by bemath last updated on 14/Mar/21 $${Let}\:{p},{q}\:{and}\:{r}\:{be}\:{the}\:{distinct}\:{roots} \\ $$$${of}\:{the}\:{polynomial}\:{x}^{\mathrm{3}} −\mathrm{22}{x}^{\mathrm{2}} +\mathrm{80}{x}−\mathrm{67}. \\ $$$${There}\:{exist}\:{real}\:{number}\:{A},{B}\:{and} \\ $$$${C}\:{such}\:{that}\:\frac{\mathrm{1}}{{s}^{\mathrm{3}} −\mathrm{22}{s}^{\mathrm{2}} +\mathrm{80}{s}−\mathrm{67}}\:= \\ $$$$\frac{{A}}{{s}−{p}}\:+\:\frac{{B}}{{s}−{q}}\:+\:\frac{{C}}{{s}−{r}}\:{for}\:{all}\:{real}\:{numbers} \\ $$$${s}\:{with}\:{s}\:\notin\:\left\{{p},{q},{r}\right\}.{What}\:{is}\: \\…
Question Number 4492 by RasheedSindhi last updated on 01/Feb/16 $$ \\ $$$${By}\:{murging}\:{three}\:{sequences} \\ $$$$\:{a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,…{a}_{{n}} \:,\:{b}_{\mathrm{1}} ,{b}_{\mathrm{2}} ,…,{b}_{{n}} \:\&\:{c}_{\mathrm{1}} ,{c}_{\mathrm{2}} ,…,{c}_{{n}} \\ $$$${a}\:{new}\:{sequence}\: \\…
Question Number 70025 by Tony Lin last updated on 30/Sep/19 $${use}\:\varepsilon-\delta\:{defintion}\:{to}\:{prove}\:{that} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{x}}−\sqrt{\mathrm{1}−{x}}}{{x}}=\mathrm{1} \\ $$ Commented by mind is power last updated on 01/Oct/19…
Question Number 135557 by bemath last updated on 14/Mar/21 $$\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:\theta−{i}\:\mathrm{sin}\:\theta}\:=? \\ $$$${i}=\sqrt{−\mathrm{1}} \\ $$ Answered by mathmax by abdo last updated on 14/Mar/21 $$\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\theta−\mathrm{isin}\theta}=\frac{\mathrm{1}}{\mathrm{2sin}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right)−\mathrm{2isin}\left(\frac{\theta}{\mathrm{2}}\right)\mathrm{cos}\left(\frac{\theta}{\mathrm{2}}\right)}…
Question Number 70022 by naka3546 last updated on 30/Sep/19 $${Find}\:\:\:{all}\:\:{pairs}\:\:{of}\:\:\:\left({p},\:{q}\right)\:\:{integer}\left({s}\right)\:\:{such}\:\:{that} \\ $$$${p}^{\mathrm{3}} \:−\:{q}^{\mathrm{5}} \:\:=\:\:\left({p}\:+\:{q}\right)^{\mathrm{2}} \\ $$ Commented by MJS last updated on 30/Sep/19 $${p}=\mathrm{0}\:{q}=\mathrm{0} \\…
Question Number 4487 by Rasheed Soomro last updated on 31/Jan/16 $${If}\:\:{y}^{\mathrm{2}} +\mathrm{3}{uy}−\mathrm{5}{u}^{\mathrm{2}} =\mathrm{2}\:,\:\:\mathrm{2}{t}^{\mathrm{2}} −\mathrm{2}{tu}−\mathrm{3}{u}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\: \\ $$$${and}\:\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}{xt}−{t}^{\mathrm{2}} =\mathrm{0}\:,{find}\:\:\frac{{dy}}{{dx}}\:\:{and}\:\:\:\frac{{du}}{{dt}}\:. \\ $$ Answered by Yozzii last…
Question Number 4486 by Rasheed Soomro last updated on 31/Jan/16 $${f}\left({x}\right)={e}^{{x}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\:{and}\:{the}\:{domain}\:{D}\left({f}\right)\:{of}\:\:{f} \\ $$$${is}\:{chosen}\:{appropriately},\:{find}\:\frac{{d}}{{dx}}{f}\left({x}\right)\:\:{at}\: \\ $$$${any}\:{point}\:{x}\:{in}\:{D}\left({f}\right)\:. \\ $$ Answered by Yozzii last updated on…
Question Number 135559 by john_santu last updated on 14/Mar/21 Commented by john_santu last updated on 14/Mar/21 $${old}\:{unswered} \\ $$ Answered by bemath last updated on…
Question Number 4485 by Rasheed Soomro last updated on 31/Jan/16 $${By}\:\:{murging}\:\:{two}\:{sequences} \\ $$$$\:\:\:\:{a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,…{a}_{{n}} \:\:\:{and}\:\:{b}_{\mathrm{1}} ,{b}_{\mathrm{2}} ,…,{b}_{{n}} \\ $$$${a}\:{new}\:{sequence}\: \\ $$$$\:\:\:\:{a}_{\mathrm{1}} ,{b}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,{b}_{\mathrm{2}}…