Question Number 82920 by abdomathmax last updated on 25/Feb/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)}{{x}} \\ $$ Answered by mind is power last updated on 25/Feb/20 $${ln}\left(\mathrm{1}+{x}\right)\sim{x} \\ $$$$\Rightarrow{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)\sim{ln}\left(\mathrm{1}+{x}\right)…
Question Number 148453 by mathdanisur last updated on 28/Jul/21 $$\frac{\left({n}\:+\:\mathrm{1}\right)!}{{n}!}\:=\:\mathrm{38}\:\:\Rightarrow\:\:{n}=? \\ $$ Answered by puissant last updated on 28/Jul/21 $$\Rightarrow\frac{\left(\mathrm{n}+\mathrm{1}\right)×\mathrm{n}!}{\mathrm{n}!}=\mathrm{38} \\ $$$$\Rightarrow\mathrm{n}+\mathrm{1}=\mathrm{38} \\ $$$$\Rightarrow\mathrm{n}=\mathrm{37}.. \\…
Question Number 148452 by mathdanisur last updated on 28/Jul/21 $$\underset{\:\mathrm{1}} {\overset{\:\mathrm{4}} {\int}}\mathrm{2}{sin}^{\mathrm{2}} {x}\:{dx}\:+\:\underset{\:\mathrm{1}} {\overset{\:\mathrm{4}} {\int}}\left(\mathrm{1}+{cos}\mathrm{2}{x}\right){dx}\:=\:? \\ $$ Answered by puissant last updated on 28/Jul/21 $$=\int_{\mathrm{1}}…
Question Number 82919 by miswantospd2@gmail.com last updated on 25/Feb/20 $${bangun}\:{datar} \\ $$ Commented by john santu last updated on 26/Feb/20 $$??????? \\ $$ Commented by…
Question Number 148454 by mathdanisur last updated on 28/Jul/21 $${sin}^{\mathrm{6}} \boldsymbol{\alpha}\:+\:{co}^{\mathrm{6}} \boldsymbol{\alpha}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\:\Rightarrow\:\:\mathrm{6}{cos}\mathrm{4}\boldsymbol{\alpha}=? \\ $$$$ \\ $$ Answered by Ar Brandon last updated on 28/Jul/21 $$\mathrm{sin}^{\mathrm{6}}…
Question Number 17377 by tawa tawa last updated on 04/Jul/17 $$\int\:\:\frac{\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{2}\:−\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 05/Jul/17 $$\mathrm{cos}\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\left(\mathrm{x}/\mathrm{2}\right)}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{x}/\mathrm{2}\right)}\:=\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }…
Question Number 148445 by mathdanisur last updated on 28/Jul/21 $${if}\:\:\:{cos}\boldsymbol{\alpha}\:=\:\sqrt{\boldsymbol{{a}}} \\ $$$${find}\:\:\:\mathrm{5}\:-\:\mathrm{6}{cos}\mathrm{2}\boldsymbol{\alpha}\:+\:{cos}\mathrm{4}\boldsymbol{\alpha}\:=\:? \\ $$ Commented by mathdanisur last updated on 28/Jul/21 $${Thank}\:{you}\:{Ser} \\ $$$${But},\:=\sqrt{\boldsymbol{\alpha}}\:\left({alfa}\:{no}\right)\:\:=\sqrt{\boldsymbol{{a}}} \\…
Question Number 17374 by ajfour last updated on 04/Jul/17 Commented by ajfour last updated on 04/Jul/17 $$\mathrm{The}\:\mathrm{base}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{an}\:\mathrm{isosceles} \\ $$$$\bigtriangleup\mathrm{ABC}\:\mathrm{is}\:\alpha\:\left(>\mathrm{45}°\right),\:\mathrm{the}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{S}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{triangle}\:\left(\bigtriangleup\mathrm{DEF}\right)\:\mathrm{whose}\:\mathrm{vertices} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{feet}\:\mathrm{of}\:\mathrm{the}\:\mathrm{altitudes}\:\mathrm{of}\:…
Question Number 148447 by Nizam last updated on 28/Jul/21 $$\mathrm{sin}\left({x}\right)={a},\:{a}\in \\ $$ Answered by Ar Brandon last updated on 28/Jul/21 $$−\mathrm{1}\leqslant\mathrm{a}\leqslant\mathrm{1} \\ $$ Terms of…
Question Number 17373 by mrW1 last updated on 04/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in}\:\mathrm{interior}\:\mathrm{of}\:\mathrm{a}\:\mathrm{convex} \\ $$$$\mathrm{quadrilateral}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its} \\ $$$$\mathrm{distances}\:\mathrm{to}\:\mathrm{the}\:\mathrm{4}\:\mathrm{vertices}\:\mathrm{is}\:\mathrm{minimal}. \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in}\:\mathrm{interior}\:\mathrm{of}\:\mathrm{a}\:\mathrm{convex} \\ $$$$\mathrm{quadrilateral}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its} \\ $$$$\mathrm{distances}\:\mathrm{to}\:\mathrm{the}\:\mathrm{4}\:\mathrm{sides}\:\mathrm{is}\:\mathrm{minimal}. \\ $$ Answered…