Question Number 205534 by hardmath last updated on 23/Mar/24 $$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{n}\:\mathrm{x}^{\boldsymbol{\mathrm{n}}} \:\mathrm{e}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:=\:? \\ $$ Answered by Mathspace last updated…
Question Number 205528 by hardmath last updated on 23/Mar/24 $$\mathrm{Let}\:\:\:\forall\mathrm{x}\:\in\:\mathrm{A}\:\rightarrow\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{And}\:\:\:\mathrm{card}\left(\mathrm{A}\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{card}\left(\mathrm{A}'\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$ Answered by Berbere last updated on 24/Mar/24…
Question Number 205527 by MATHEMATICSAM last updated on 23/Mar/24 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{are}\:\mathrm{one} \\ $$$$\mathrm{another}'\mathrm{s}\:\mathrm{cube}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\left({b}^{\mathrm{2}} \:−\:\mathrm{2}{ac}\right)^{\mathrm{2}} \:=\:{ac}\left({a}\:+\:{c}\right)^{\mathrm{2}} . \\ $$ Answered by A5T last updated…
Question Number 205514 by aba last updated on 23/Mar/24 $$\mathrm{Quelle}\:\mathrm{est}\:\mathrm{la}\:\mathrm{decomposition}\:\mathrm{en}\:\mathrm{cycles} \\ $$$$\mathrm{a}\:\mathrm{support}\:\mathrm{disjoints}\:\mathrm{de}\:\mathrm{c}^{\mathrm{k}} \:,\:\mathrm{ou}\:\mathrm{c}=\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:…\:\mathrm{n}\right)\:? \\ $$ Commented by TheHoneyCat last updated on 01/Apr/24 On parle de permutations? et si oui... Vous êtes sur que la permutation en question c'est (1,...n) (à savoir l'identité ?) Commented by…
Question Number 205515 by aba last updated on 23/Mar/24 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{into}\:\mathrm{cycles} \\ $$$$\mathrm{with}\:\mathrm{disjoints}\:\mathrm{support}\:\mathrm{of}\:\mathrm{c}^{\mathrm{k}} ,\:\mathrm{where}\:\mathrm{c}=\left(\mathrm{123}…\mathrm{n}\right)\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205492 by BaliramKumar last updated on 22/Mar/24 Answered by cortano12 last updated on 22/Mar/24 $$\:\Rightarrow\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{5}} {\prod}}\mathrm{T}_{\mathrm{i}\:} =\:\mathrm{T}_{\mathrm{3}} ^{\mathrm{5}} \:=\:\mathrm{3}^{\mathrm{5}} =\:\mathrm{243} \\ $$…
Question Number 205490 by mnjuly1970 last updated on 22/Mar/24 $$ \\ $$$$\:\:\:\:{If},{f}\left({x}\right)=\:\sqrt{\mathrm{2}\:+\:{x}}\:+\:{a}\:\sqrt{{x}\:−\:\mathrm{1}}\: \\ $$$$\:\:\:\:{is}\:{monotone}\:{function}\:. \\ $$$$\:\:\:\:{find}\:{the}\:{range}\:{of}\:\:''\:{a}\:'' \\ $$$$ \\ $$ Answered by mr W last…
Question Number 205471 by Fridunatjan08 last updated on 21/Mar/24 $${Solve}\:{the}\:{equation}:\:\frac{{x}}{\mathrm{21}}+\frac{{x}}{\mathrm{77}}+\frac{{x}}{\mathrm{165}}+\frac{{x}}{\mathrm{285}}=\mathrm{200} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Mar/24 $$\frac{{x}}{\mathrm{21}}+\frac{{x}}{\mathrm{77}}+\frac{{x}}{\mathrm{165}}+\frac{{x}}{\mathrm{285}}=\mathrm{200} \\ $$$${x}\left(\frac{\mathrm{1}}{\mathrm{21}}+\frac{\mathrm{1}}{\mathrm{77}}+\frac{\mathrm{1}}{\mathrm{165}}+\frac{\mathrm{1}}{\mathrm{285}}\right)=\mathrm{200} \\ $$$${x}\left(\:\frac{\mathrm{1}}{\mathrm{7}}\left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{11}}\right)+\frac{\mathrm{1}}{\mathrm{15}}\left(\frac{\mathrm{1}}{\mathrm{11}}+\frac{\mathrm{1}}{\mathrm{19}}\right)\right)=\mathrm{200} \\…
Question Number 205432 by hardmath last updated on 21/Mar/24 $$\mathrm{Find}:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}\boldsymbol{\pi}} \:\mathrm{ln}\:\left(\mathrm{sinx}\:+\:\sqrt{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Answered by MathedUp last updated on 21/Mar/24 $$\mathrm{0} \\ $$$$\mathrm{cauz}\:−{f}\left({z}\right)={f}\left(−{z}\right)\:,\:{f}\left({z}+\pi\right)=−{f}\left({z}\right)\:,\:{f}\left({z}+\mathrm{2}\pi\right)={f}\left({z}\right)…
Question Number 205460 by hardmath last updated on 21/Mar/24 $$\mathrm{If}\:\:\mathrm{3cosx}\:=\:\mathrm{8sin}\left(\mathrm{30}°\:−\:\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\mathrm{tanx}\:=\:? \\ $$ Answered by MM42 last updated on 21/Mar/24 $$\mathrm{3}{cosx}=\mathrm{4}{cosx}−\mathrm{4}\sqrt{\mathrm{3}}{sinx} \\ $$$$\Rightarrow{cosx}=\mathrm{4}\sqrt{\mathrm{3}}{sinx}\Rightarrow{tanx}=\frac{\sqrt{\mathrm{3}}}{\mathrm{12}}\:\:\checkmark \\…