Question Number 126180 by benjo_mathlover last updated on 18/Dec/20 $${solve}\:\mid\:\mid{x}−\mathrm{1}\mid\:−\mathrm{2}\mid\:=\:\mid\:{x}−\mathrm{3}\:\mid\: \\ $$ Answered by bobhans last updated on 18/Dec/20 $$\left(\mathrm{1}\right)\:{for}\:{x}\geqslant\mathrm{3}\:\Rightarrow\:\mid\:{x}−\mathrm{3}\mid={x}−\mathrm{3} \\ $$$$\left(\mathrm{2}\right)\:{for}\:{x}<\mathrm{3}\:\Rightarrow\mid\mathrm{1}−{x}−\mathrm{2}\mid=\mathrm{3}−{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid−\mathrm{1}−{x}\mid\:=\:\mathrm{3}−{x} \\…
Question Number 126181 by aurpeyz last updated on 18/Dec/20 $${evaluate}\:{the}\:{integral}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\pi} {dx}\int_{\mathrm{1}} ^{\mathrm{2}} {dy}\delta\left({sin}\mathrm{2}{x}\right)\delta\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right) \\ $$ Commented by aurpeyz last updated…
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Question Number 126179 by mathmax by abdo last updated on 17/Dec/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{e}^{−\mathrm{2x}} \:\mathrm{actan}\:\left(\mathrm{3x}+\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculste}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\Sigma\:\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \:\mathrm{determine}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{a}_{\mathrm{n}} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}…
Question Number 191715 by Shlock last updated on 29/Apr/23 Answered by mr W last updated on 29/Apr/23 Commented by Shlock last updated on 29/Apr/23 Sir,canyon use the similarity of the right triangles? Can you give more explanation in details?…
Question Number 191714 by Mingma last updated on 29/Apr/23 Commented by AST last updated on 29/Apr/23 Answered by AST last updated on 29/Apr/23 $${Let}\:{AC}\:{intersect}\:{the}\:{circle}\:{from}\:{A} \\…
Question Number 126175 by naka3546 last updated on 17/Dec/20 $${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:+\:\mathrm{6}\:\geqslant\:\mathrm{3}\left({a}\:+\:{b}\:+\:{c}\right) \\ $$$${a},\:{b},\:{c}\:\in\:\mathbb{R}^{+} \\ $$ Commented by PRITHWISH SEN 2 last…
Question Number 60637 by rajesh4661kumar@gamil.com last updated on 23/May/19 Commented by maxmathsup by imad last updated on 23/May/19 $$\int\:\:\:\:\frac{{sinx}}{\mathrm{1}−{sinx}}\:{dx}\:=−\int\frac{\mathrm{1}−{sinx}\:−\mathrm{1}}{\mathrm{1}−{sinx}}{dx}\:=−{x}\:+\int\:\:\frac{{dx}}{\mathrm{1}−{sinx}} \\ $$$$\int\:\:\frac{{dx}}{\mathrm{1}−{sinx}}\:=_{{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}} \:\:\:\:\:\:\int\:\:\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }\:=\mathrm{2}\:\int\:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} −\mathrm{2}{t}}\:=\mathrm{2}\:\int\:\:\frac{{dt}}{\left({t}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 191710 by pete last updated on 29/Apr/23 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{f}\:\mathrm{149}!\:\mathrm{when}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\mathrm{139}? \\ $$ Commented by Rasheed.Sindhi last updated on 29/Apr/23 $$\mathrm{149}!=\mathrm{1}.\mathrm{2}.\mathrm{3}…\mathrm{138}.\mathrm{139}.\mathrm{140}…\mathrm{148}.\mathrm{149} \\ $$$$\therefore\:\mathrm{149}!\mathrm{mod139}=\mathrm{0} \\…