Question Number 5948 by 123456 last updated on 06/Jun/16 $$\mathrm{is}\:\mathrm{there}\:{a}_{{n}} \:\mathrm{such}\:\mathrm{that}\:\Sigma{a}_{{n}} \:\mathrm{and}\:\Pi{a}_{{n}} \\ $$$$\mathrm{converge}? \\ $$ Answered by Yozzii last updated on 06/Jun/16 $${Yes}.\:{Let}\:{a}_{{n}} ={r}^{{n}}…
Question Number 5947 by Yozzii last updated on 07/Jun/16 $$ \\ $$$${Show}\:{that}\:\mathrm{3}!^{\mathrm{5}!^{\mathrm{7}!^{\mathrm{9}!^{…\mathrm{2013}!} } } } \:\equiv\mathrm{1}\:\left({mod}\:\mathrm{11}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137016 by PGeeman last updated on 28/Mar/21 Answered by Dwaipayan Shikari last updated on 28/Mar/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{a}^{{x}} \sim\mathrm{1}+{xlog}\left({a}\right)\:\:\:{sin}\left({x}\right)\sim{x}\:;\:\:{log}\left(\mathrm{1}+{x}\right)\sim{x} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{4}^{{x}} −\mathrm{1}\right)^{\mathrm{3}} }{{sin}\left(\frac{{x}}{{p}}\right){log}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}}…
Question Number 5943 by sanusihammed last updated on 06/Jun/16 $${P}\:=\:\mathrm{9}{x}\:+\:\mathrm{8}{y} \\ $$$${xy}\:=\:\mathrm{2} \\ $$$$ \\ $$$${find}\:\:{p}. \\ $$ Answered by FilupSmith last updated on 06/Jun/16…
Question Number 137014 by sdfg last updated on 28/Mar/21 Commented by yutytfjh67ihd last updated on 29/Mar/21 Commented by yutytfjh67ihd last updated on 29/Mar/21 Terms of…
Question Number 5940 by sanusihammed last updated on 05/Jun/16 Answered by FilupSmith last updated on 06/Jun/16 $${Are}\:{of}\:{non}\:{shaded}: \\ $$$${A}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}{r}\left(\theta−\mathrm{sin}\:\theta\right) \\ $$$$\therefore\mathrm{Total}\:\mathrm{A}{rea}: \\ $$$${A}=\pi{r}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}{r}\left(\theta−\mathrm{sin}\:\theta\right)…
Question Number 137011 by mohammad17 last updated on 28/Mar/21 Commented by mohammad17 last updated on 28/Mar/21 $${help}\:{me}\:{sir}\:{please} \\ $$ Commented by mohammad17 last updated on…
Question Number 137010 by mohammad17 last updated on 28/Mar/21 $${if}\:{f}\left({x},{y}\right)=\left({xy}\right)^{\mathrm{3}} +{e}^{{xy}} +{sec}\left(\frac{{y}}{{x}}\right)\:{find} \\ $$$${f}_{{xx}} \:\:,\:{f}_{{yy}} \:,\:{f}_{{xy}} \:\:,\:\:{f}_{{yx}} \\ $$ Commented by yutytfjh67ihd last updated on…
Question Number 137005 by greg_ed last updated on 28/Mar/21 $$\boldsymbol{\mathrm{Hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$$$\boldsymbol{\mathrm{For}}\:\boldsymbol{\mathrm{R}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{5}}{\mathrm{6}}×…×\frac{\mathrm{223}}{\mathrm{224}}\:\:\:\boldsymbol{\mathrm{and}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{S}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{4}}{\mathrm{5}}×\frac{\mathrm{6}}{\mathrm{7}}×…×\frac{\mathrm{224}}{\mathrm{225}}\:. \\ $$$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\::\:\:\boldsymbol{\mathrm{R}}\:<\:\frac{\mathrm{1}}{\mathrm{15}}\:<\:\boldsymbol{\mathrm{S}}. \\ $$ Commented by greg_ed last updated on 01/May/21…
Question Number 137004 by Mathspace last updated on 28/Mar/21 $${find}\:\int\:\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}{dx} \\ $$ Answered by aleks041103 last updated on 28/Mar/21 $$\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}= \\ $$$$=\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}= \\ $$$$=\sqrt{{x}}\left(\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}\right) \\…