Question Number 2859 by Syaka last updated on 29/Nov/15 $${if}\:{x}^{\mathrm{2}} \:−\:\mathrm{2}{cx}\:−\:\mathrm{5}{d}\:=\:\mathrm{0}\:{has}\:{root}\:{a}\:{and}\:{b}, \\ $$$${also}\:{x}^{\mathrm{2}} \:−\:\mathrm{2}{ax}\:−\:\mathrm{5}{b}\:=\:\mathrm{0}\:{has}\:{root}\:{c}\:{and}\:{d} \\ $$$${then}\:{a},\:{b},\:{c}\:{and}\:{d}\:{are}\:{different}\:{real}\:{number}. \\ $$$${What}\:{the}\:{value}\:{of}\:{a}\:+\:{b}\:+\:{c}\:+\:{d}\:=\:? \\ $$ Commented by Syaka last updated…
Question Number 133928 by mnjuly1970 last updated on 25/Feb/21 Answered by mathmax by abdo last updated on 25/Feb/21 $$\left.\mathrm{2}\right)\:\mathrm{u}_{\mathrm{n}} =\left(\mathrm{C}_{\mathrm{2n}} ^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}}} \:\:\:\mathrm{we}\:\mathrm{have}\:\mathrm{C}_{\mathrm{2n}} ^{\mathrm{n}} \:=\frac{\left(\mathrm{2n}\right)!}{\left(\mathrm{n}!\right)^{\mathrm{2}}…
Question Number 2857 by Syaka last updated on 29/Nov/15 $${By}\:{Induction}\:{Prove}\:{that}\:: \\ $$$$ \\ $$$$\mathrm{12}\mid\left({n}^{\mathrm{4}} \:−\:{n}^{\mathrm{2}} \right) \\ $$ Commented by Filup last updated on 29/Nov/15…
Question Number 133925 by bemath last updated on 25/Feb/21 $$\:\mathrm{Given}\:\mathrm{vector}\:\overset{\rightarrow} {{a}}\:=\:\hat {\mathrm{i}}−\mathrm{2}\hat {\mathrm{j}}+\hat {\mathrm{k}}\:,\: \\ $$$$\overset{\rightarrow} {{b}}=\:\mathrm{2}\hat {\mathrm{i}}+\hat {\mathrm{j}}−\mathrm{2}\hat {\mathrm{k}}\:,\:\overset{\rightarrow} {{c}}=−\hat {\mathrm{i}}+\mathrm{3}\hat {\mathrm{j}}−\hat {\mathrm{k}} \\…
Question Number 68390 by TawaTawa last updated on 10/Sep/19 Answered by som(math1967) last updated on 10/Sep/19 $${tan}\left(\mathrm{2tan}^{−\mathrm{1}} \sqrt{\frac{\mathrm{2}{cos}^{\mathrm{2}} \frac{\theta}{\mathrm{2}}}{\mathrm{2}{sin}^{\mathrm{2}} \frac{\theta}{\mathrm{2}}}}\:\right)+{tan}\theta \\ $$$$={tan}\left\{\mathrm{2tan}^{−\mathrm{1}} \left(\mathrm{cot}\:\frac{\theta}{\mathrm{2}}\right)\right\}+\mathrm{tan}\:\theta \\ $$$$={tan}\left\{\mathrm{2tan}^{−\mathrm{1}}…
Question Number 2851 by 123456 last updated on 28/Nov/15 $${x}^{\mathrm{2}} ={x}+{x}+{x}+\centerdot\centerdot\centerdot+{x}\:\left({x}\:\mathrm{times}\right) \\ $$$$\mathrm{taking}\:\mathrm{derivate} \\ $$$$\mathrm{2}{x}=\mathrm{1}+\mathrm{1}+\mathrm{1}+\centerdot\centerdot\centerdot+\mathrm{1}\:\left({x}\:\mathrm{times}\right) \\ $$$$\mathrm{2}{x}={x}\:\left({x}\neq\mathrm{0}\right) \\ $$$$\mathrm{2}=\mathrm{1} \\ $$$$\mathrm{where}\:\mathrm{the}\:\mathrm{problem}? \\ $$ Commented by…
Question Number 133923 by bemath last updated on 25/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mid\mathrm{sin}\:\mathrm{x}\mid}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$ Answered by EDWIN88 last updated on 25/Feb/21 $$\:\mathrm{x}^{\mathrm{2}} \:=\:\mid\mathrm{x}\mid^{\mathrm{2}} \:\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mid\mathrm{sin}\:\mathrm{x}\mid}{\mid\mathrm{x}\mid}\:.\frac{\mathrm{1}}{\mid\mathrm{x}\mid}=\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 133916 by shaker last updated on 25/Feb/21 Answered by TheSupreme last updated on 25/Feb/21 $${S}_{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{e}^{{kx}} +{e}^{−{kx}} }{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}\left\{\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left({e}^{{x}} \right)^{{k}}…
Question Number 2845 by Rasheed Soomro last updated on 28/Nov/15 $$\mathcal{W}{hile}\:{you}\:{are}\:{in}\:{between}\:{the}\:{project} \\ $$$$\mathcal{I}\:{am}\:{trying}\:{to}\:{improve}\:{my}\:{digestiblity}\:{to} \\ $$$${digest}\:{the}\:{concept}\:{of}\:'{analytical}\:{continuation}'. \\ $$$$ \\ $$$${First}\:{we}\:{make}\:{aformula}\:{to}\:{sum}\:{n}\:{terms}\:{of}\:{a}\:{powe}\:{series}: \\ $$$$\frac{{x}^{{n}} −\mathrm{1}}{{x}−\mathrm{1}}=\mathrm{1}+{x}+{x}^{\mathrm{2}} +…+{x}^{{n}} \\ $$$${latter}\:{we}\:{change}\:{it}\:{for}\:\mid{x}\mid<\mathrm{1}\:{and}\:{n}\rightarrow\infty\:\left[{x}^{{n}}…
Question Number 133918 by mohammad17 last updated on 25/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com