Question Number 72997 by yannickmendes_33 last updated on 05/Nov/19 $${The}\:{area}\:{of}\:{the}\:{equilateral}\:{triangle}\:{is}\:{equal}\:{to}\:\frac{\sqrt{\mathrm{16}}\sqrt{\mathrm{8}}}{\mathrm{3}\sqrt{\pi}} \\ $$$${Calculate}\:{the}\:{area}\:{of}\:{the}\:{circle}\:{inscribed}\:{in}\:{the}\:{triangle}. \\ $$$$\: \\ $$ Answered by Kunal12588 last updated on 05/Nov/19 $${area}\:{of}\:{equilateral}\:\bigtriangleup\:=\:\frac{\sqrt{\mathrm{3}}\:{a}^{\mathrm{2}} }{\mathrm{4}}=\frac{\sqrt{\mathrm{16}}\sqrt{\mathrm{8}}}{\mathrm{3}\sqrt{\pi}}=\frac{\mathrm{8}\sqrt{\mathrm{2}}}{\mathrm{3}\sqrt{\pi}}…
Question Number 72990 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\frac{{arctan}\left({e}^{{x}} \right)−\frac{\pi}{\mathrm{4}}}{{x}^{\mathrm{2}} } \\ $$ Commented by abdomathmax last updated on 19/Nov/19 $${let}\:{use}\:{hospital}\:{theorem}\:\:{f}\left({x}\right)={arctan}\left({e}^{{x}}…
Question Number 138524 by mnjuly1970 last updated on 14/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{advanced}\:…\:….\:…\:{calculus}….. \\ $$$$\:\:\:\boldsymbol{\mathrm{I}}:=\int_{\frac{−\pi}{\mathrm{2}}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({tan}\left({x}\right)\right){dx}\overset{???} {=}\frac{\pi}{{e}}{sinh}\left(\mathrm{1}\right) \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 72988 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−{xt}^{\mathrm{2}} } }{\mathrm{4}+{t}^{\mathrm{2}} }{dt}\:\:\:{with}\:{x}>\mathrm{0} \\ $$ Commented by mathmax by abdo last…
Question Number 7453 by ankit036 last updated on 30/Aug/16 Commented by Rasheed Soomro last updated on 30/Aug/16 $$\left(\mathrm{A}\right)\:\:\mathrm{1} \\ $$ Answered by afy1991 last updated…
Question Number 138521 by mnjuly1970 last updated on 14/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:…\:…\:…\:{calculus}…….. \\ $$$$\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{\mathrm{2}} {e}^{{x}} }{\left(\mathrm{1}+{e}^{{x}} \right)^{\mathrm{3}} }\:{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:…..\ast\ast\ast\ast\ast\ast\ast\ast….. \\ $$ Answered by Dwaipayan…
Question Number 72986 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{x}^{\mathrm{2}} } \:\:{cosx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy…
Question Number 7449 by Tawakalitu. last updated on 29/Aug/16 $${The}\:{sum}\:{of}\:{the}\:{first}\:\mathrm{3}\:{terms}\:{of}\:{an}\:{AP}\:{is}\:\mathrm{36}\:{and}\:{the} \\ $$$${product}\:{of}\:{the}\:{first}\:\mathrm{3}\:{terms}\:{of}\:{a}\:{GP}\:{is}\:\mathrm{1728}.\:{if}\:{the} \\ $$$${second}\:{term}\:{of}\:{the}\:{linear}\:{sequence}\:{is}\:\mathrm{12}\:{and}\:{such} \\ $$$${that}\:{the}\:{second}\:{term}\:{of}\:{the}\:{GP}\:{is}\:{equal}\:{to}\:{the}\:{second} \\ $$$${term}\:{of}\:{the}\:{AP}.\:{find} \\ $$$$\left(\mathrm{1}\right)\:{The}\:{AP} \\ $$$$\left(\mathrm{2}\right)\:{The}\:{GP} \\ $$ Answered…
Question Number 138516 by mnjuly1970 last updated on 14/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:………..{calculus}\:…\:…\:…\:\left(\mathrm{I}\right)……… \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{xe}^{{x}} }{\left(\mathrm{1}+{e}^{{x}} \right)^{\mathrm{3}} }{dx}\:=? \\ $$$$\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} {x}.{d}\left(\frac{−\mathrm{1}}{\left(\mathrm{1}+{e}^{{x}} \right)^{\mathrm{2}} }\:\right) \\ $$$$\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{−{x}}{\left(\mathrm{1}+{e}^{{x}}…
Question Number 138519 by mr W last updated on 14/Apr/21 Commented by mr W last updated on 14/Apr/21 $${from}\:{an}\:{arbitrary}\:{triangle}\:{ABC} \\ $$$${points}\:{P},{Q},{R}\:{are}\:{constructed}\:{as} \\ $$$${shown}\:{with}\:\alpha+\beta+\gamma=\mathrm{360}°. \\ $$$${prove}\:{that}\:{the}\:{interior}\:{angles}\:{of}…