Question Number 67235 by prof Abdo imad last updated on 24/Aug/19 $${find}\:\:\int_{−\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{3}}} \:{x}^{\mathrm{2}} \left\{{cosx}−{sinx}\right\}^{\mathrm{3}} {dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 1698 by Rasheed Ahmad last updated on 01/Sep/15 $$\bullet{Are}\:\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}=\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\:\:{and}\:\:\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{B}}\: \\ $$$${completely}\:{equivalent}? \\ $$$$\bullet{Simplify}\:\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}=\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\:{to}\:\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{B}} \\ $$$${using}\:{set}\:{operations}\:{and}\:{their} \\ $$$${properties}. \\ $$ Answered by 123456 last…
Question Number 67232 by prof Abdo imad last updated on 24/Aug/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({n}\frac{\pi}{\mathrm{3}}\right)}{{n}} \\ $$ Commented by mathmax by abdo last updated on 25/Aug/19…
Question Number 67233 by prof Abdo imad last updated on 24/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xdx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }} \\ $$ Commented by mind is power last updated on…
Question Number 132765 by Ahmed1hamouda last updated on 16/Feb/21 Answered by mr W last updated on 16/Feb/21 Commented by mr W last updated on 16/Feb/21…
Question Number 67231 by mhmd last updated on 24/Aug/19 $$\left.{find}\:\int{x}/{x}^{\mathrm{5}} −\mathrm{1}\right)\:{dx} \\ $$ Answered by mind is power last updated on 24/Aug/19 $$\left({x}\right){what}\:{do}\:{hou}\:{mean}? \\ $$…
Question Number 1694 by 123456 last updated on 01/Sep/15 $$\mathrm{proof}\:\mathrm{that}\:\mathrm{for}\:\mathrm{two}\:\mathrm{set}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\left(\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\right) \\ $$$$\mid\mathrm{A}\cup\mathrm{B}\mid\geqslant\mid\mathrm{A}\cap\mathrm{B}\mid \\ $$ Answered by Rasheed Soomro last updated on 01/Sep/15 $$\:\mathrm{In}\:\mathrm{the}\:\mathrm{following}\:\boldsymbol{\mathrm{A}}\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:\mathrm{are}\:\mathrm{assumed}\:\mathrm{as}\:\mathrm{finite}\:\mathrm{sets}. \\ $$$$\:\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\:\subseteq\boldsymbol{\mathrm{A}}\subseteq\:\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\Rightarrow\mid\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\mid\leqslant\mid\boldsymbol{\mathrm{A}}\mid\leqslant\mid\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\mid………..\boldsymbol{\mathrm{I}}…
Question Number 1689 by 123456 last updated on 31/Aug/15 $$\mathrm{if}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{afirmation} \\ $$$$\sim\left({p}\rightarrow{q}\right)=? \\ $$$$\sim\left({p}\leftarrow{q}\right)=? \\ $$$$\sim\left({p}\Leftrightarrow{q}\right)=? \\ $$ Answered by 112358 last updated on 01/Sep/15…
Question Number 132762 by liberty last updated on 16/Feb/21 Answered by EDWIN88 last updated on 16/Feb/21 $$\Rightarrow\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{9}\:\Rightarrow\mathrm{x}^{\mathrm{2}} =\mathrm{9}−\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{Volume}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\mathrm{x}^{\mathrm{2}} \left(\mathrm{3}+\mathrm{y}\right)=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\left(\mathrm{9}−\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{3}+\mathrm{y}\right) \\…
Question Number 132753 by liberty last updated on 16/Feb/21 $$\mathrm{Given}\:\mathrm{x},\mathrm{y}\:\in\mathbb{R}\:,\:\mathrm{x},\mathrm{y}\neq\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{xy}−\mathrm{4y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{4y}^{\mathrm{2}} }\: \\ $$ Commented by mr W last updated…