Question Number 208519 by Tawa11 last updated on 17/Jun/24 $$\mathrm{If}\:\:\:\:\:\mathrm{a}^{\mathrm{x}} \:\:=\:\:\mathrm{b}^{\mathrm{y}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{a}}{\mathrm{x}}\:\:+\:\:\frac{\mathrm{b}}{\mathrm{y}}\:\:=\:\:\mathrm{1} \\ $$$$\mathrm{then},\:\:\:\:\mathrm{a}^{\mathrm{x}} \:\:+\:\:\mathrm{b}^{\mathrm{y}} \:\:=\:\:? \\ $$ Answered by mr W last updated…
Question Number 208489 by Tawa11 last updated on 17/Jun/24 Answered by Berbere last updated on 17/Jun/24 $${x}^{\mathrm{4}} +\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}−\mathrm{4} \\ $$$$\geqslant\mathrm{2}\sqrt{\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}}−\mathrm{4}=−\mathrm{2} \\ $$$${equaliti}\:\:{x}=\mathrm{0}…
Question Number 208441 by efronzo1 last updated on 16/Jun/24 Answered by Etimbuk last updated on 16/Jun/24 $$\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}} =\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{3}\:} =\:\mathrm{y}^{\mathrm{3}} \:\Rightarrow\:\mathrm{x}\:=\:\mathrm{y} \\ $$$$…
Question Number 208469 by hardmath last updated on 16/Jun/24 $$\mathrm{Find}:\:\:\:\:\:\frac{\mathrm{61}^{\mathrm{3}} \:\:+\:\:\mathrm{24}^{\mathrm{3}} }{\mathrm{61}^{\mathrm{3}} \:\:+\:\:\mathrm{37}^{\mathrm{3}} }\:\:=\:\:? \\ $$ Answered by Frix last updated on 16/Jun/24 $${a}=\mathrm{61};\:{b}=\mathrm{24};\:{a}−{b}=\mathrm{37} \\…
Question Number 208463 by hardmath last updated on 16/Jun/24 $$\mathrm{Compare}\:\mathrm{it}: \\ $$$$\mathrm{a}\:=\:\mathrm{log}_{\mathrm{3}} \:\mathrm{4} \\ $$$$\mathrm{b}\:=\:\mathrm{log}_{\mathrm{5}} \:\mathrm{6} \\ $$$$\mathrm{c}\:=\:\mathrm{log}_{\mathrm{6}} \:\mathrm{2} \\ $$ Answered by Frix last…
Question Number 208453 by hardmath last updated on 16/Jun/24 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\left(\mathrm{2a}\:+\:\mathrm{1}\right)\centerdot\mathrm{x}\:+\:\mathrm{1}}{\mathrm{x}\:−\:\mathrm{a}}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{3}\:=\:? \\ $$ Answered by efronzo1 last updated on 16/Jun/24 $$\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=\frac{\mathrm{ax}+\mathrm{1}}{\mathrm{x}−\left(\mathrm{2a}+\mathrm{1}\right)}\:=\:\frac{\left(\mathrm{2a}+\mathrm{1}\right)\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{a}}…
Question Number 208409 by hardmath last updated on 15/Jun/24 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\mid\mathrm{1}\:−\:\mathrm{x}\mid\:\mathrm{dx}\:=\:? \\ $$ Answered by mr W last updated on 15/Jun/24 $$=\mathrm{2}\int_{\mathrm{1}} ^{\mathrm{2}} \left({x}−\mathrm{1}\right){dx}…
Question Number 208381 by hardmath last updated on 14/Jun/24 $$\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{lnx}^{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:+\:\mathrm{25}} \\ $$$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\boldsymbol{\mathrm{e}}} {\mathrm{lim}}\:\left(\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:=\:?\right. \\ $$ Answered by A5T last updated on 14/Jun/24 $${f}\left({g}\left({x}\right)\right)=\sqrt[{\mathrm{3}}]{{ln}\left({x}^{\mathrm{2}}…
Question Number 208377 by hardmath last updated on 14/Jun/24 $$\mathrm{sin}\:\mathrm{x}\:−\:\mathrm{sin}\:\frac{\pi}{\mathrm{6}}\:>\:\mathrm{0} \\ $$$$\mathrm{x}\:=\:? \\ $$ Commented by hardmath last updated on 14/Jun/24 $$ \\ $$Solve the…
Question Number 208370 by lmcp1203 last updated on 14/Jun/24 $${if}\:\:\:\left({fof}\right)\left({x}\right)={f}\left({x}\right)+{x}\:\:{and}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:\:\: \\ $$$${find}\:\:{fofofofofofofofofof}\left(\mathrm{1}\right) \\ $$ Commented by A5T last updated on 14/Jun/24 $${f}\left({f}\left({x}\right)\right)={f}\left({x}\right)+{x}\Rightarrow\:{f}\left({f}\left(\mathrm{1}\right)\right)={f}\left(\mathrm{1}\right)+\mathrm{1} \\ $$$$\Rightarrow{f}\left(\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{1}\Rightarrow\mathrm{1}\overset{?} {=}\mathrm{0}…