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} \\ $$$${points}\:{P},{Q},{R}\:{are}\:{constructed}\:{as} \\ $$$${shown}\:{with}\:\alpha+\beta+\gamma=\mathrm{360}°. \\ $$$${prove}\:{that}\:{the}\:{interior}\:{angles}\:{of}…
Question Number 138513 by mathlove last updated on 14/Apr/21 Answered by MJS_new last updated on 14/Apr/21 $${AB}+\mathrm{9}=\mathrm{3}\left({BA}\right) \\ $$$$\mathrm{10}{A}+{B}+\mathrm{9}=\mathrm{30}{B}+\mathrm{3}{A} \\ $$$${A}=\frac{\mathrm{29}{B}−\mathrm{9}}{\mathrm{7}}\:\Rightarrow\:{B}=\mathrm{2}\wedge{A}=\mathrm{7} \\ $$$$\mathrm{72}+\mathrm{9}=\mathrm{3}×\mathrm{27} \\ $$$${A}+{B}=\mathrm{9}…
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Question Number 7442 by lakshaysethi last updated on 29/Aug/16 $${is}\:\mathrm{0}×\mathrm{0}\:{not}\:{defined}\:{or}\:{equal}\:{to}\:\mathrm{0}? \\ $$$${if}\:{it}\:{is}\:{not}\:{defined}\:{then}\:{why}? \\ $$ Commented by Rasheed Soomro last updated on 29/Aug/16 $$\mathrm{0}×\mathrm{0}\:{is}\:{defined}\:{and}\:{it}\:{is}\:{equal}\:{to}\:\mathrm{0}. \\ $$…
Question Number 7440 by Tawakalitu. last updated on 29/Aug/16 $${Prove}\:{that} \\ $$$${If}\:\:{A},\:{B}\:{and}\:{C}\:{are}\:{subset}\:{of}\:{the}\:{same}\:{universal}\:{set} \\ $$$${then}\:\left({A}\:−\:{B}\right)\:\cap\:\left({A}\:−\:{C}\right)\:=\:{A}\:−\:\left({B}\:−\:{C}\right) \\ $$ Commented by Yozzia last updated on 29/Aug/16 $${Let}\:{A}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\right\},\:{B}=\left\{\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\},\:{C}=\left\{\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right\}. \\…
Question Number 138511 by mathlove last updated on 14/Apr/21 Commented by MJS_new last updated on 14/Apr/21 $$\mathrm{005}\:\:\:\:\:\mathrm{014}\:\:\:\:\:\mathrm{023}\:\:\:\:\:\mathrm{113}\:\:\:\:\:\mathrm{122}\:\:\:\:\:… \\ $$$$\mathrm{050}\:\:\:\:\:\mathrm{140}\:\:\:\:\:\mathrm{230}\:\:\:\:\:\mathrm{131}\:\:\:\:\:\mathrm{221} \\ $$$$\mathrm{500}\:\:\:\:\:\mathrm{401}\:\:\:\:\:\mathrm{302}\:\:\:\:\:\mathrm{311}\:\:\:\:\:\mathrm{212} \\ $$$$==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:== \\ $$$$\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}…