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Author: Tinku Tara

Question-204350

Question Number 204350 by universe last updated on 14/Feb/24 Answered by mr W last updated on 14/Feb/24 $${P}\left({a}\right)={a}^{\mathrm{4}} +{a}^{\mathrm{2}} {b}+{ac}+{d}=\mathrm{1}\:\:\:\:…\left({i}\right) \\ $$$${P}\left({b}\right)={ab}^{\mathrm{3}} +{b}^{\mathrm{3}} +{bc}+{d}=−\mathrm{1}\:\:\:…\left({ii}\right) \\…

If-f-0-b-continuous-R-g-R-b-periodic-continuous-R-lim-n-0-b-f-x-g-nx-dx-1-b-0-b-f-x-dx-0-b-g-x-dx-

Question Number 204372 by mnjuly1970 last updated on 14/Feb/24 $$ \\ $$$$\:\:{If}\:,\:\:\:\:{f}\::\:\left[\:\mathrm{0}\:,\:{b}\right]\:\overset{{continuous}} {\rightarrow}\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\:\:,\:\:\:\:{g}\::\:\mathbb{R}\:\underset{{b}−{periodic}} {\overset{{continuous}} {\rightarrow}}\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\:{b}} {f}\left({x}\right){g}\left({nx}\right){dx}\overset{?} {=}\frac{\mathrm{1}}{{b}}\:\int_{\mathrm{0}} ^{\:{b}} {f}\left({x}\right){dx}\:.\int_{\mathrm{0}}…

Question-204374

Question Number 204374 by mr W last updated on 14/Feb/24 Commented by mr W last updated on 15/Feb/24 $${The}\:{radius}\:{of}\:{the}\:{big}\:{sphere}\:\left({say}\:\right. \\ $$$$\left.{the}\:{Earth}\right)\:{is}\:{R}\:{and}\:{the}\:{radius}\:{of} \\ $$$${the}\:{small}\:{sphere}\:\left({say}\:{theMoon}\right)\:{is}\:{r}. \\ $$$${find}\:{the}\:{maximum}\:{area}\:{of}\:{the}…

ctg-6-pi-9-9-ctg-4-pi-9-11-ctg-2-pi-9-

Question Number 204344 by SEKRET last updated on 13/Feb/24 $$ \\ $$$$\: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\boldsymbol{\mathrm{ctg}}^{\mathrm{6}} \left(\frac{\pi}{\mathrm{9}}\right)−\mathrm{9}\centerdot\boldsymbol{\mathrm{ctg}}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{9}}\right)+\mathrm{11}\centerdot\boldsymbol{\mathrm{ctg}}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{9}}\right)=?\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$…