Question Number 204742 by York12 last updated on 26/Feb/24 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:{x} \\ $$ Commented by York12 last updated on 26/Feb/24 Commented by TonyCWX08 last updated on…
Question Number 204739 by hardmath last updated on 26/Feb/24 Answered by mr W last updated on 26/Feb/24 $${x}^{\mathrm{4}} +\mathrm{2}{x}=−\mathrm{4} \\ $$$$\Rightarrow{x}^{\mathrm{3}} +\mathrm{2}=−\frac{\mathrm{4}}{{x}} \\ $$$$\Rightarrow\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{3}}…
Question Number 204701 by Abdullahrussell last updated on 25/Feb/24 Answered by A5T last updated on 25/Feb/24 $${x}^{\mathrm{3}} ={x}−\mathrm{2}\Rightarrow{x}^{\mathrm{4}} ={x}^{\mathrm{2}} −\mathrm{2}{x}\Rightarrow{x}^{\mathrm{5}} ={x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} =−\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{2} \\…
Question Number 204702 by mnjuly1970 last updated on 25/Feb/24 $$ \\ $$$$\:\:\:\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\:\mathrm{cl}\left(\mathbb{Q}×\mathbb{Q}\:\right)\overset{?} {=}\:\mathbb{R}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{note}:\:\:\:\left({X}\:,{d}\:\right)\:{is}\:{a}\:{metric}\:{space} \\ $$$$\:\:\:\:\:\:\:\:\:\:,\:\:\:{A}\:\subseteq\:{X}\::\:\:\:\:\:{x}\in\:\overset{\:\:−} {{A}}=\mathrm{cl}\left({A}\right)\:\Leftrightarrow\:\forall\:{r}\:>\mathrm{0}\:,\:{B}_{{r}} \:\left({x}\right)\:\cap\:{A}\:\neq\:\phi \\ $$ Answered by…
Question Number 204671 by mr W last updated on 25/Feb/24 $${if}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4},\:{find}\:{f}\left(\mathrm{1}\right)=? \\ $$ Answered by witcher3 last updated on 25/Feb/24 $$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{4} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{1}\right)\right)=\mathrm{2}…
Question Number 204664 by cortano12 last updated on 25/Feb/24 $$\:\:\mathrm{8}+\sqrt{\mathrm{8}^{\mathrm{2}} +\sqrt{\mathrm{8}^{\mathrm{4}} +\sqrt{\mathrm{8}^{\mathrm{8}} +\sqrt{\mathrm{8}^{\mathrm{16}} +\sqrt{…}}}}}\:=\:?\: \\ $$ Answered by Frix last updated on 25/Feb/24 $$=\mathrm{8}+\mathrm{8}\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+…}}}} \\…
Question Number 204666 by Ghisom last updated on 25/Feb/24 $$\mathrm{this}\:\mathrm{is}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{curve}: \\ $$$${f}\left(\theta\right)=\left(\mathrm{e}^{\mathrm{i}\theta} \right)^{\left(\mathrm{e}^{\mathrm{i}\theta} \right)} =\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{e}^{\mathrm{i}\theta\mathrm{cos}\:\theta} ;\:−\pi<\theta\leqslant\pi \\ $$$${f}:\:\begin{cases}{{x}\left(\theta\right)=\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{cos}\:\left(\theta\mathrm{cos}\:\theta\right)}\\{{y}\left(\theta\right)=\mathrm{e}^{−\theta\mathrm{sin}\:\theta} \mathrm{sin}\:\left(\theta\mathrm{cos}\:\theta\right)}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{area} \\ $$…
Question Number 204699 by AtulKumar last updated on 25/Feb/24 Commented by LuisTony last updated on 25/Feb/24 $${In}\:{spanish}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 204688 by Davidtim last updated on 25/Feb/24 $${f}\left({x}\right)={sgn}\left({x}\right);\:\:\:\:\:{f}^{'} \left({x}\right)=\frac{{d}}{{dx}}\left[{f}\left({x}\right)\right]=? \\ $$ Answered by Faetmaaa last updated on 27/Feb/24 $$\frac{\mathrm{d}}{\mathrm{d}{x}}\left[{f}\mid_{\left.\right]−\infty,\:\mathrm{0}\left[\right.} \left({x}\right)\right]\:=\:\frac{\mathrm{d}}{\mathrm{d}{x}}\left[{f}\mid_{\left.\right]\mathrm{0},\:+\infty\left[\right.} \left({x}\right)\right]\:=\:\mathrm{0} \\ $$…
Question Number 204689 by Davidtim last updated on 25/Feb/24 $${y}=\mid{f}\left({x}\right)\mid\:\:;\:\:\:\:\frac{{dy}}{{dx}}=? \\ $$ Answered by A5T last updated on 25/Feb/24 $${y}=\sqrt{\left({f}\left({x}\right)\right)^{\mathrm{2}} }=\left[\left({f}\left({x}\right)\right)^{\mathrm{2}} \right]^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\Rightarrow\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\left({f}\left({x}\right)\right)^{\mathrm{2}} }}×\mathrm{2}{f}\left({x}\right)×{f}'\left({x}\right)=\frac{{f}\left({x}\right){f}^{'}…