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Show-that-U-n-4n-1-7n-3-is-convergent-sequence-

Question Number 161168 by mathocean1 last updated on 13/Dec/21 $${Show}\:{that}\:{U}_{{n}} =\frac{\mathrm{4}{n}−\mathrm{1}}{\mathrm{7}{n}+\mathrm{3}}\:\:{is}\:{convergent}\: \\ $$$${sequence}. \\ $$ Commented by MJS_new last updated on 13/Dec/21 $$\frac{\mathrm{4}{n}−\mathrm{1}}{\mathrm{7}{n}+\mathrm{3}}=\frac{\mathrm{4}}{\mathrm{7}}−\frac{\mathrm{19}}{\mathrm{49}{n}−\mathrm{21}} \\ $$…

If-4-log-x-2y-4-log-x-2y-1-Minimum-value-of-x-y-is-

Question Number 161166 by naka3546 last updated on 13/Dec/21 $${If}\:\:\:^{\mathrm{4}} \mathrm{log}\:\left({x}+\mathrm{2}{y}\right)\:+\:^{\mathrm{4}} \mathrm{log}\:\left({x}−\mathrm{2}{y}\right)\:=\:\mathrm{1}\:. \\ $$$${Minimum}\:\:{value}\:\:{of}\:\:\mid{x}\mid\:−\:\mid{y}\mid\:\:\:{is}\:\:…\:? \\ $$ Answered by mr W last updated on 13/Dec/21 $$\left({x}+\mathrm{2}{y}\right)\left({x}−\mathrm{2}{y}\right)=\mathrm{4}…

solve-x-1-x-2-7x-3-dx-

Question Number 161101 by bounhome last updated on 12/Dec/21 $${solve}: \\ $$$$\:\:\:\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{7}{x}−\mathrm{3}}{dx} \\ $$ Answered by FongXD last updated on 12/Dec/21 $$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2x}−\mathrm{7}+\mathrm{9}}{\mathrm{x}^{\mathrm{2}} −\mathrm{7x}−\mathrm{3}}\mathrm{dx} \\…