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Question Number 85238 by naka3546 last updated on 20/Mar/20 $${f}\left({x}\right)\:\:=\:\:{x}^{\mathrm{3}} \:+\:\mathrm{3}{x} \\ $$$${f}\:^{−\mathrm{1}} \left({x}\right)\:\:=\:\:? \\ $$ Answered by mr W last updated on 20/Mar/20 $${y}={x}^{\mathrm{3}}…
Question Number 150752 by Jamshidbek last updated on 15/Aug/21 $$\mathrm{x}^{\mathrm{3}} +\mathrm{3x}+\mathrm{12}=\mathrm{0}\:\:\mathrm{solve}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\mathrm{help} \\ $$ Commented by liberty last updated on 15/Aug/21 x = root(3, - root(2, 37) - 6) - (1/root(3, - root(2, 37) - 6)) Commented by…
Question Number 150746 by naka3546 last updated on 15/Aug/21 $${Find}\:\:{the}\:\:{smallest}\:\:{positive}\:\:{integer}\:\:{n}\:\:{so}\:\:{that}\:\:\left(\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\ldots\:+\:{n}^{\mathrm{2}} \right)\:\:{is}\:\:{divided}\:\:{by}\:\:{n}\:. \\ $$ Answered by mr W last updated on 15/Aug/21 $${assume}\:{n}>\mathrm{1}.…
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Question Number 85198 by otchereabdullai@gmail.com last updated on 19/Mar/20 $$\mathrm{Find}\:\mathrm{x}\:\mathrm{if}\:\:\:\:^{\mathrm{3}} \sqrt{\mathrm{x}\:}+\sqrt{\mathrm{x}}=\sqrt{\mathrm{12}} \\ $$ Answered by MJS last updated on 19/Mar/20 $$\mathrm{let}\:{x}={y}^{\mathrm{6}} \\ $$$${y}^{\mathrm{3}} +{y}^{\mathrm{2}} −\sqrt{\mathrm{12}}=\mathrm{0}…
Question Number 19658 by icyfalcon999 last updated on 14/Aug/17 $$=\frac{\mathrm{sec}\:\mathrm{x}−\mathrm{1}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\frac{\mathrm{sec}\:\mathrm{x}+\left(\mathrm{1}−\mathrm{1}\right)−\mathrm{1}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\frac{\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)−\mathrm{2}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\frac{\mathrm{sec}\:\mathrm{x}+\mathrm{1}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}}−\frac{\mathrm{2}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\mathrm{1}−\frac{\mathrm{2}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\mathrm{1}−\mathrm{2}\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)^{−\mathrm{1}} \\ $$$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{1}−\mathrm{2}\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)^{−\mathrm{1}} \right) \\ $$$$=−\mathrm{2}\left(−\mathrm{1}\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)^{−\mathrm{2}}…
Question Number 85195 by M±th+et£s last updated on 19/Mar/20 $$\left.\mathrm{1}\right){find}\:{the}\:{area}\:{between} \\ $$$${y}^{\mathrm{2}} =\mathrm{3}{x}\:{and}\:{y}={x}^{\mathrm{2}} −\mathrm{2}{x} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{\mathrm{2}} \left(\theta\right)\:{cos}^{\mathrm{2}} \left(\theta\right)}{\left({cos}^{\mathrm{3}} \left(\theta\right)+{sin}^{\mathrm{3}} \left(\theta\right)\right)^{\mathrm{2}} }\:{d}\theta…
Question Number 150696 by tabata last updated on 14/Aug/21 $$\left(\mathrm{1}\right)\int\:{x}\:{tanx}\:{dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int\:\left(\sqrt{{tanx}}+\sqrt{{cotx}}\right){dx} \\ $$$$ \\ $$$$\left(\mathrm{3}\right)\int\:\frac{{sinx}+{cosx}}{\:\sqrt{{sinx}\:{cosx}}}\:{dx} \\ $$ Commented by Ar Brandon last…