Question Number 194900 by cortano12 last updated on 19/Jul/23 $$\:\:\:\:\:\:{Given}\:\:\:{d}\:=\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\:\sqrt{\mathrm{5}}}}{\mathrm{1}+\sqrt{\mathrm{5}}}\:\: \\ $$$$\:\:\:\:\:\:{then}\:\:{d}^{\mathrm{3}} −\mathrm{4}{d}^{\mathrm{2}} \:+\mathrm{8}{d}\:−\mathrm{2}\:=?\: \\ $$$$\:\:\:\:\: \\ $$ Answered by Frix last updated on 19/Jul/23…
Question Number 194903 by cortano12 last updated on 19/Jul/23 Commented by cortano12 last updated on 19/Jul/23 $$\:\:\:{x}\:=\:\sqrt{\mathrm{39}}\:\:\left(×\right) \\ $$$$\:\:\:{x}\:=\:\sqrt{\mathrm{30}}\:\left(\checkmark\right) \\ $$ Answered by MM42 last…
Question Number 194913 by cortano12 last updated on 19/Jul/23 Answered by witcher3 last updated on 19/Jul/23 $$\left(\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}''\left(\mathrm{x}\right)\right)\mathrm{cos}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\left.\underset{\mathrm{0}} {\int}^{\frac{\pi}{\mathrm{2}}} \mathrm{f}''\mathrm{cos}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{f}'\mathrm{cos}\left(\mathrm{x}\right)\right]_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} +\int\mathrm{f}'\mathrm{sin}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\left.=\left.−\mathrm{f}'\left(\mathrm{0}\right)+\mathrm{fsin}\left(\mathrm{x}\right)\right]_{\mathrm{0}}…
Question Number 194928 by cortano12 last updated on 19/Jul/23 $$\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1}}\:+\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{9}}−\sqrt{\mathrm{16}{x}^{\mathrm{2}} −\mathrm{8}}\:=?\right. \\ $$ Answered by horsebrand11 last updated on 20/Jul/23…
Question Number 194896 by cortano12 last updated on 19/Jul/23 $$\:\:\:\:\:\:\:\cancel{ } \\ $$ Answered by AST last updated on 19/Jul/23 $$\left({x}^{\mathrm{2}} −{f}\left({x}\right)\right)^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} {f}\left({x}\right)=\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} {f}\left({x}\right)…
Question Number 194915 by York12 last updated on 19/Jul/23 $$ \\ $$$$\frac{\mathrm{3}}{{x}−\mathrm{3}}+\frac{\mathrm{5}}{{x}−\mathrm{5}}+\frac{\mathrm{7}}{{x}−\mathrm{17}}+\frac{\mathrm{19}}{{x}−\mathrm{19}}={x}^{\mathrm{2}} −\mathrm{11}{x}−\mathrm{4} \\ $$ Commented by BaliramKumar last updated on 19/Jul/23 $$\mathrm{typo}\:\:\:\mathrm{7}\rightarrow\mathrm{17} \\ $$…
Question Number 194899 by kapoorshah last updated on 19/Jul/23 Answered by Frix last updated on 19/Jul/23 $${y}={px}\wedge{z}={qx} \\ $$$$\Rightarrow \\ $$$${x}^{\mathrm{2}} =\frac{\mathrm{5}}{\mathrm{1}−{pq}}=\frac{\mathrm{8}}{{p}^{\mathrm{2}} −{q}}=\frac{\mathrm{10}}{{q}^{\mathrm{2}} −{p}} \\…
Question Number 194914 by Mingma last updated on 19/Jul/23 Answered by a.lgnaoui last updated on 20/Jul/23 $$\mathrm{distance}\:\mathrm{betwen}\:\mathrm{Dand}\:\mathrm{E}\:=\mathrm{distance}\:\mathrm{betwen}\: \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{D};\:\:\:\mathrm{so}\:\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\mathrm{point} \\ $$$$\:\mathrm{4}^{\mathrm{9}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\boldsymbol{\mathrm{A}} \\ $$$$ \\…
Question Number 194877 by SajaRashki last updated on 18/Jul/23 $${without}\:{calculator}\:{Prove}:\:\sqrt[{\mathrm{6}}]{\pi^{\mathrm{5}} +\pi^{\mathrm{4}} }<{e} \\ $$ Commented by SajaRashki last updated on 24/Jul/23 $${without}\:{calculator}\:{Prove}:\:\sqrt[{\mathrm{6}}]{\pi^{\mathrm{5}} +\pi^{\mathrm{4}} }<{e} \\…
Question Number 194879 by tri26112004 last updated on 18/Jul/23 Answered by cortano12 last updated on 18/Jul/23 $$\:\:=\:\underset{{u}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{2}{u}\right)^{{u}} −\mathrm{1}}{\left(\mathrm{1}+\mathrm{3}{u}\right)^{{u}} −\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\:\left[\:{u}\:=\frac{\mathrm{1}}{{x}}\:\right] \\ $$$$\:{then}\:{apply}\:{L}'{Hopital}\: \\…