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Question Number 119097 by ZiYangLee last updated on 22/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\: \\ $$$$\left(\mathrm{1}!×\mathrm{1}\right)+\left(\mathrm{2}!×\mathrm{2}\right)+\left(\mathrm{3}!×\mathrm{3}\right)+…+\left(\mathrm{100}!×\mathrm{100}\right) \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{101}. \\ $$ Answered by mindispower last updated on 22/Oct/20 $${n}!.{n}=\left({n}!\right)\left({n}+\mathrm{1}−\mathrm{1}\right)=\left(\boldsymbol{{n}}+\mathrm{1}\right)!−{n}! \\…
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Question Number 184626 by SANOGO last updated on 09/Jan/23 $$\int_{\mathrm{0}} ^{+{oo}} \:\frac{{artan}\left(\mathrm{2}{x}\right)−{arctan}\left({x}\right)}{{x}}{dx} \\ $$ Answered by qaz last updated on 10/Jan/23 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{arctan}\:\mathrm{2}{x}−\mathrm{arctan}\:{x}}{{x}}{dx} \\…
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Question Number 184620 by Ml last updated on 09/Jan/23 Commented by Ml last updated on 09/Jan/23 $$\mathrm{please}\:\mathrm{solution}???? \\ $$ Answered by mr W last updated…
Question Number 184618 by CrispyXYZ last updated on 09/Jan/23 $$\mathrm{If}\:{xy}\leqslant{ax}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{always}\:\mathrm{true}\:\mathrm{for}\:\mathrm{any}\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2},\:\mathrm{2}\leqslant{y}\leqslant\mathrm{3} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$ Answered by mr W last updated on 09/Jan/23 $${let}\:{t}=\frac{{y}}{{x}}…
Question Number 119069 by Olaf last updated on 22/Oct/20 $$\mathrm{Sorry}\:\mathrm{ladies}\:\mathrm{and}\:\mathrm{gentlemen}\:\mathrm{but}\:\mathrm{who} \\ $$$$\mathrm{understands}\:\mathrm{this}\:\mathrm{forum}\:? \\ $$$$\mathrm{Most}\:\mathrm{of}\:\mathrm{people}\:\mathrm{post}\:\mathrm{questions}\:\mathrm{and} \\ $$$$\mathrm{and}\:\mathrm{answers}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{comment}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{point}\:?\::−\left(\left(\right.\right. \\ $$ Terms of Service Privacy Policy…
Question Number 53528 by naka3546 last updated on 22/Jan/19 $${x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:\:=\:\:{x}\:+\:{y}\:+\:{z} \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \:\:=\:\:{xyz} \\ $$$${x},\:{y},\:{z}\:\:\in\:\mathbb{R}^{+} \\ $$$${How}\:\:{many}\:\:{triple}\:\:{of}\:\:\left({x},\:{y},\:{z}\right)\:\:? \\ $$ Terms…
Question Number 184594 by CrispyXYZ last updated on 09/Jan/23 $$\mathrm{If}\:{f}\left({x}\right)=\mathrm{ln}\mid{a}+\frac{\mathrm{1}}{\mathrm{1}−{x}}\mid+{b}\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a},\:{b}. \\ $$ Answered by mr W last updated on 09/Jan/23 $${f}\left({x}\right)=−{f}\left(−{x}\right) \\ $$$$\mathrm{ln}\:\mid{a}+\frac{\mathrm{1}}{\mathrm{1}−{x}}\mid+{b}=−\mathrm{ln}\:\mid{a}+\frac{\mathrm{1}}{\mathrm{1}+{x}}\mid−{b}…