Question Number 6186 by sanusihammed last updated on 17/Jun/16 $${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:? \\ $$ Commented by Rasheed Soomro last updated on 17/Jun/16 $${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:?…
Question Number 6183 by Rasheed Soomro last updated on 17/Jun/16 $${Show}\:{that} \\ $$$$\mathrm{180}°−\mathrm{2cos}^{−\mathrm{1}} \:\frac{\mathrm{2}}{\:\sqrt{\mathrm{13}}}=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{12}}{\mathrm{13}}\right) \\ $$ Answered by Yozzii last updated on 18/Jun/16 $$\pi−\mathrm{2}{acos}\left(\mathrm{2}/\sqrt{\mathrm{13}}\right)={asin}\left(\mathrm{12}/\mathrm{13}\right)…
Question Number 137252 by mey3nipaba last updated on 31/Mar/21 $$\mathrm{Decompose}\:\mathrm{the}\:\mathrm{function}\:\mathrm{P}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{6x}^{\mathrm{2}} +\mathrm{20x}+\mathrm{6}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\: \\ $$$$\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$ Answered by bemath last updated on…
Question Number 137255 by Nith last updated on 31/Mar/21 Answered by Dwaipayan Shikari last updated on 31/Mar/21 $${sinx}\sim{x} \\ $$$$\mathrm{2}^{{sinx}} \sim\mathrm{2}^{{x}} \sim\mathrm{1}+{xlog}\left(\mathrm{2}\right) \\ $$$$\mathrm{3}^{{sinx}} \sim\mathrm{1}+{xlog}\left(\mathrm{3}\right)…
Question Number 71717 by peter frank last updated on 19/Oct/19 Commented by mathmax by abdo last updated on 19/Oct/19 $${let}\:{I}=\int\:\frac{{dx}}{{cos}\left({x}−{a}\right){cos}\left({x}−{b}\right)}\:\Rightarrow{I}=\int\:\:\frac{\mathrm{2}{dx}}{{cos}\left(\mathrm{2}{x}−{a}−{b}\right)+{cos}\left({a}−{b}\right)} \\ $$$$=_{\mathrm{2}{x}−\left({a}+{b}\right)={t}} \:\:\:\:\int\:\:\frac{{dt}}{{cost}\:+\lambda}\:\:{with}\:\lambda={cos}\left({a}−{b}\right)\:{changement} \\ $$$${tan}\left(\frac{{t}}{\mathrm{2}}\right)={u}\:{give}\:\int\:\:\:\frac{{dt}}{{cost}\:+\lambda}\:=\int\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}−{u}^{\mathrm{2}}…
Question Number 6180 by FilupSmith last updated on 17/Jun/16 $$\frac{{df}\left({x}\right)}{{dx}}={f}\left({x}\right)+{x} \\ $$$$\mathrm{Solve}\:{f}\left({x}\right) \\ $$ Commented by 123456 last updated on 17/Jun/16 $$\frac{{df}}{{dx}}−{f}={x} \\ $$$${f}={f}_{{n}} +{f}_{{g}}…
Question Number 137249 by bemath last updated on 31/Mar/21 $$\int\:\frac{\left(\mathrm{3sin}\:\mathrm{x}+\mathrm{2}\right)}{\left(\mathrm{2sin}\:\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by bemath last updated on 31/Mar/21 $$\mathrm{let}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)=\mathrm{u}\: \begin{cases}{\mathrm{dx}=\frac{\mathrm{2}}{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{du}}\\{\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{2u}}{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}}\end{cases} \\…
Question Number 6179 by 314159 last updated on 17/Jun/16 $${Divide}\:\mathrm{10}\:{into}\:{two}\:{parts}\:{so}\:{that}\:{twice}\:{the} \\ $$$${square}\:{of}\:{the}\:{first}\:{part}\:{plus}\:{thrice}\:{the} \\ $$$${square}\:{of}\:{the}\:{other}\:{part}\:{is}\:{the}\:{least}. \\ $$ Commented by prakash jain last updated on 17/Jun/16 $${one}\:{part}\:{x},\:{second}\:{part}\:\left(\mathrm{10}−{x}\right)…
Question Number 137251 by mnjuly1970 last updated on 31/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……\mathscr{A}{dvanced}\:\:…\:\:{calculus}…… \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{\mathrm{2}} {ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){dx}=??? \\ $$$$ \\ $$ Answered by Ar Brandon last updated…
Question Number 6177 by FilupSmith last updated on 17/Jun/16 $${f}\:'\left({x}\right)={xf}\left({x}\right) \\ $$$${f}\left({x}\right)=?? \\ $$ Answered by Yozzii last updated on 17/Jun/16 $$\frac{{df}}{{dx}}={xf} \\ $$$$\Rightarrow\int\frac{{df}}{{f}}=\int{xdx} \\…