Question Number 6946 by 314159 last updated on 03/Aug/16 $${Find}\:{all}\:{continuous}\:{functions}\:{f}\left({x}\right)\:{such}\: \\ $$$${that}\:{f}\left(\mathrm{2}{x}+\mathrm{1}\right)={f}\left({x}\right)\:{for}\:{all}\:{real}\:{x}. \\ $$ Commented by Yozzii last updated on 04/Aug/16 $${f}\left(\mathrm{1}\right)={f}\left(\mathrm{0}\right) \\ $$$${f}'\left({x}\right)=\mathrm{2}{f}'\left(\mathrm{2}{x}+\mathrm{1}\right) \\…
Question Number 6945 by Tawakalitu. last updated on 03/Aug/16 $$\int\:\frac{{x}^{\frac{\mathrm{2}}{\mathrm{3}}} }{{x}\:+\:\mathrm{1}}\:\:{dx} \\ $$ Commented by Yozzii last updated on 03/Aug/16 $${x}={u}^{\mathrm{3}} \Rightarrow{dx}=\mathrm{3}{u}^{\mathrm{2}} {du} \\ $$$${x}^{\mathrm{2}/\mathrm{3}}…
Question Number 6944 by Tawakalitu. last updated on 03/Aug/16 $${Prove}\:{that}: \\ $$$$ \\ $$$${e}^{{x}} =\:{Limit}\left({u}\:\rightarrow\:+\:\infty\right)\:\left(\mathrm{1}\:+\:\frac{{x}}{{u}}\right)^{{u}} \: \\ $$ Answered by sou1618 last updated on 03/Aug/16…
Question Number 72479 by ajfour last updated on 29/Oct/19 Commented by ajfour last updated on 29/Oct/19 $${Find}\:{Tensions}\:{T}_{{a}} \:{and}\:{T}_{{b}} . \\ $$ Terms of Service Privacy…
Question Number 138014 by bobhans last updated on 09/Apr/21 $${Given}\:{p}=\mathrm{1}+{i}\sqrt{\mathrm{5}}\:{and}\:{q}=\mathrm{1}−{i}\sqrt{\mathrm{5}}\: \\ $$$${prove}\:{that}\:{p}^{\mathrm{6}} +{q}^{\mathrm{6}} \:=\:\mathrm{2}^{\mathrm{5}} ×\mathrm{11} \\ $$ Answered by bobhans last updated on 09/Apr/21 $$\:{from}\:{the}\:{given}\:{we}\:{have}\:…
Question Number 138009 by bobhans last updated on 09/Apr/21 $$\int\:\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)\:\sqrt{\mathrm{sec}\:^{\mathrm{3}} \left({x}\right)}\:{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 09/Apr/21 $$\mathcal{E}\:=\:\int\:\mathrm{tan}\:^{\mathrm{3}} \left({x}\right)\:\mathrm{sec}\:\left({x}\right)\:\sqrt{\mathrm{sec}\:\left({x}\right)}\:{dx} \\ $$$$=\:\int\:\mathrm{tan}\:\left({x}\right)\mathrm{sec}\:\left({x}\right)\left(\mathrm{sec}\:^{\mathrm{2}}…
Question Number 6939 by sou1618 last updated on 03/Aug/16 $$\mathrm{please}\:\mathrm{solve}\:{L} \\ $$$$\mathrm{but}\:\mathrm{do}\:\mathrm{not}\:\mathrm{use}\:\mathrm{L}'\mathrm{Hopital}'\mathrm{s}\:\mathrm{rule}. \\ $$$${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{e}^{{x}} −\mathrm{1}}\right) \\ $$ Commented by Yozzii last updated on 03/Aug/16…
Question Number 6938 by Tawakalitu. last updated on 03/Aug/16 $${Integrate}:\:\:\:\:\:\:\:\:\frac{{x}\:{tan}^{−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx} \\ $$ Commented by Yozzii last updated on 03/Aug/16 $${I}=\int\frac{{xtan}^{−\mathrm{1}} {x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 6935 by FilupSmith last updated on 05/Aug/16 $$\boldsymbol{{v}}=<{x}_{{v}} ,\:{y}_{{v}} > \\ $$$$\boldsymbol{{u}}=<{x}_{{u}} ,\:{y}_{{u}} > \\ $$$$\boldsymbol{{v}}\:\mathrm{and}\:\boldsymbol{{u}}\:\mathrm{have}\:\mathrm{angles}: \\ $$$$\theta_{{v}} =\mathrm{tan}\left(\frac{{y}_{{v}} }{{x}_{{v}} }\right)\:\mathrm{and}\:\theta_{{u}} =\mathrm{tan}\left(\frac{{y}_{{u}} }{{x}_{{u}}…
Question Number 138004 by benjo_mathlover last updated on 09/Apr/21 $$ \\ $$What is the minimum value of x+y+z, subject to the condition xyz = a³?…