Question Number 18092 by Tinkutara last updated on 15/Jul/17 $$\mathrm{A}\:\mathrm{value}\:\mathrm{of}\:\theta\:\mathrm{satisfying} \\ $$$$\mathrm{4cos}^{\mathrm{2}} \theta\mathrm{sin}\theta\:−\:\mathrm{2sin}^{\mathrm{2}} \theta\:=\:\mathrm{3sin}\theta\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{9}\pi}{\mathrm{10}} \\ $$$$\left(\mathrm{2}\right)\:\frac{\pi}{\mathrm{10}} \\ $$$$\left(\mathrm{3}\right)\:−\frac{\mathrm{13}\pi}{\mathrm{10}} \\ $$$$\left(\mathrm{4}\right)\:−\frac{\mathrm{17}\pi}{\mathrm{10}} \\ $$ Answered…
Question Number 18091 by Tinkutara last updated on 15/Jul/17 $$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statement}\left(\mathrm{s}\right) \\ $$$$\mathrm{is}/\mathrm{are}\:\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{cos}\left(\mathrm{sin1}\right)\:>\:\mathrm{sin}\left(\mathrm{cos1}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{cos}\left(\mathrm{sin1}.\mathrm{5}\right)\:>\:\mathrm{sin}\left(\mathrm{cos1}.\mathrm{5}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{cos}\left(\mathrm{sin}\frac{\mathrm{7}\pi}{\mathrm{18}}\right)\:>\:\mathrm{sin}\left(\mathrm{cos}\frac{\mathrm{7}\pi}{\mathrm{18}}\right) \\ $$$$\left(\mathrm{4}\right)\:\mathrm{cos}\left(\mathrm{sin}\frac{\mathrm{5}\pi}{\mathrm{18}}\right)\:>\:\mathrm{sin}\left(\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{18}}\right) \\ $$ Answered by Tinkutara…
Question Number 149163 by mathdanisur last updated on 03/Aug/21 $${Q}\left[\sqrt{\mathrm{3}}\right]/{ker}\:{f}\:\:{define}\:{the}\:{circular} \\ $$$${element}\:{of}\:{the}\:{unit} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 149157 by gsk2684 last updated on 03/Aug/21 $$\underset{\frac{\mathrm{1}}{\mathrm{2}}} {\overset{\mathrm{2}} {\int}}\frac{\mathrm{1}}{{x}}\mathrm{cosec}\:^{\mathrm{101}} \left({x}−\frac{\mathrm{1}}{{x}}\right)\:{dx}=? \\ $$ Answered by Kamel last updated on 03/Aug/21 $$\mathrm{0} \\ $$…
Question Number 149156 by gsk2684 last updated on 03/Aug/21 $${if}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{2012}}]{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{1012}} \left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{3012}} }}=\frac{\alpha}{\mathrm{2}\beta}\left(\mathrm{1}−{f}\left({x}\right)\right)^{\frac{\beta}{\alpha}} \\ $$$${then}\:{find}\:\alpha,\beta,{f}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83621 by jagoll last updated on 04/Mar/20 $$\mid\:{x}+\frac{\mathrm{1}}{{x}}\mid\:<\:\mathrm{4}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$ Commented by jagoll last updated on 05/Mar/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{both} \\ $$ Answered…
Question Number 83619 by Jidda28 last updated on 04/Mar/20 $${Show}\:{that}\:{the}\:{differetial}\:{equation}\:{is}\:{a}\:{Sturm}−{Louville}\:{equation} \\ $$$$\left({x}^{−\mathrm{1}} {y}^{\mathrm{1}} \right)^{\mathrm{1}} +\left(\mathrm{4}+\lambda\right){x}^{−\mathrm{3}} {y}=\mathrm{0},\:\:{y}\left(\mathrm{1}\right)=\mathrm{0},{y}\left(\varrho^{{t}} \right)=\mathrm{0} \\ $$$${Solve}\:{the}\:{equation}\:{to}\:{determine}\:{the}\:{eigenvalue}\:{and}\:{the}\:{corresponding}\:{eigen}\:{functions}\:{of}\:{the}\:{problem}. \\ $$$${Show}\:{also}\:{that}\:{the}\:{set}\:{of}\:{eigen}\:{function}\:{forms}\:{and}\:{orthogonal}\:{and}\:{orthonormal}\:{set}. \\ $$$$ \\ $$$${Thanks}\:{as}\:{usual}.…
Question Number 149155 by gsk2684 last updated on 03/Aug/21 $${find}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{50}} \:{in}\:{the}\: \\ $$$$\left(\mathrm{1}+{x}\right)^{\mathrm{1000}} +\mathrm{2}{x}\left(\mathrm{1}+{x}\right)^{\mathrm{999}} +\mathrm{3}{x}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)^{\mathrm{998}} +…\infty\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 83614 by jatharphool53@gmail.com last updated on 04/Mar/20 $$\left(\mathrm{3}{x}−\mathrm{5}\right)\left(\mathrm{3}{x}+\mathrm{4}\right) \\ $$$$ \\ $$ Commented by john santu last updated on 04/Mar/20 $$???? \\ $$…
Question Number 149151 by mathdanisur last updated on 03/Aug/21 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {{lim}}\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+\:…\:+\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\right)\:=\:? \\ $$ Answered by Kamel last updated on 03/Aug/21 $${L}=\underset{\boldsymbol{{n}}\rightarrow\infty} {{lim}}\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+\:…\:+\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\right)\: \\ $$$$\:\:\:=\underset{{n}\rightarrow+\infty} {{lim}}\frac{\mathrm{1}}{\:\sqrt{{n}}}\underset{{k}=\mathrm{1}}…