Question Number 151475 by mathdanisur last updated on 21/Aug/21 $$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}\in\mathbb{R}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{x}^{\mathrm{6}} \:-\:\mathrm{x}\:+\:\mathrm{1}\:>\:\mathrm{0} \\ $$ Answered by dumitrel last updated on 21/Aug/21 $${I}.\:{if}\:{x}\leqslant\mathrm{0}\nRightarrow−{x}\geqslant\mathrm{0};\:{x}^{\mathrm{6}} +\mathrm{1}>\mathrm{0}\Rightarrow \\…
Question Number 85930 by A8;15: last updated on 26/Mar/20 Commented by Kunal12588 last updated on 26/Mar/20 $${please}\:{write}\:{in}\:{bigger}\:{font} \\ $$$${and}\:{define}\:{V}_{{a}} ^{\:\:{b}} \\ $$ Terms of Service…
Question Number 151460 by mathdanisur last updated on 21/Aug/21 $$\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{2x}\:+\:\mathrm{2} \\ $$$$\mathrm{and}\:\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}}\:+\:\mathrm{1} \\ $$$$\mathrm{find}\:\:\:\left[\:\mathrm{f}\:{o}\:\mathrm{g}\:\right]\:\left(\mathrm{x}\right)\:=\:? \\ $$ Answered by puissant last updated on 21/Aug/21 $${f}\left({x}\right)={x}^{\mathrm{2}}…
Question Number 151453 by mathdanisur last updated on 21/Aug/21 $$\mathrm{find}\:\mathrm{all}\:\mathrm{continous}\:\mathrm{functions}\:\mathrm{f}\::\:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\mathrm{such}\:\mathrm{that}: \\ $$$$\mathrm{f}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:=\:\mathrm{f}\left(\sqrt{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{4}} }\right)\:;\:\forall\mathrm{x}\in\mathbb{R} \\ $$ Commented by MJS_new last updated on 21/Aug/21…
Question Number 151449 by mathdanisur last updated on 21/Aug/21 $$\Omega\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx}\:=\:? \\ $$ Answered by puissant last updated on 21/Aug/21 $${f}\left({u}\right)={e}^{−{u}^{\mathrm{2}} } \\…
Question Number 151448 by mathdanisur last updated on 21/Aug/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\boldsymbol{\mathrm{A}}\mathrm{rtimetric}\:\mathrm{mean}\:\geqslant\:\boldsymbol{\mathrm{G}}\mathrm{eometric}\:\mathrm{mean} \\ $$$$\frac{\mathrm{a}\:+\:\mathrm{b}}{\mathrm{2}}\:\geqslant\:\sqrt{\mathrm{ab}} \\ $$ Commented by puissant last updated on 21/Aug/21 $$\forall\:\left({a},{b}\right)\in\mathbb{R}^{\mathrm{2}} ,…
Question Number 85902 by mr W last updated on 26/Mar/20 $${find}\:{the}\:{coefficients}\:{of}\:{x}^{\mathrm{2}} \:{and}\:{x}^{\mathrm{3}} \: \\ $$$${terms}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{3}} …\left(\mathrm{1}+\mathrm{100}{x}\right)^{\mathrm{100}} \\ $$ Commented by Serlea last…
Question Number 20368 by Tinkutara last updated on 26/Aug/17 $$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{root}\:\mathrm{of}\:\mathrm{2}{x}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{6}{x}\:+\:\mathrm{6}\:=\:\mathrm{0}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\left[\alpha\right]\:\mathrm{where}\:\left[\centerdot\right]\:\mathrm{denotes}\:\mathrm{the} \\ $$$$\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}. \\ $$ Commented by ajfour last updated on 26/Aug/17…
Question Number 20372 by Tinkutara last updated on 26/Aug/17 $$\mathrm{The}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:\mathrm{9}{x}^{\mathrm{2}} \\ $$$$+\:\mathrm{14}{x}\:+\:\mathrm{24}\:=\:\mathrm{0}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{3}\::\:\mathrm{2}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{roots}. \\ $$ Answered by $@ty@m last updated on 26/Aug/17 $$\alpha+\mathrm{3}\beta+\mathrm{2}\beta=\mathrm{9}\:\Rightarrow\alpha+\mathrm{5}\beta=\mathrm{9}−−\left(\mathrm{1}\right)…
Question Number 151436 by mathdanisur last updated on 21/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com