Question Number 68481 by ajfour last updated on 11/Sep/19 $${I}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \sqrt{\frac{{c}−{x}^{\mathrm{2}} }{{x}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}}{dx}\:\:\:\:\:\:\left({c}\:>\mathrm{1}\right) \\ $$ Commented by MJS last updated on 11/Sep/19 $$\mathrm{I}\:\mathrm{tried}\:\mathrm{everything}\:\mathrm{I}\:\mathrm{know},\:\mathrm{it}\:\mathrm{seems}\:\mathrm{impossible} \\…
Question Number 2941 by Syaka last updated on 30/Nov/15 $$\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{5}}{\mathrm{8}}\:+\:\frac{\mathrm{7}}{\mathrm{16}}\:+\:…….\:=\:\:? \\ $$ Commented by Syaka last updated on 01/Dec/15 $${Thanks}\:{for}\:{Solution}\:{Sir}\:{Rasheed} \\ $$$${and}\:{also}\:{for}\:{Solved}\:{from}\:{Sir}\:{Yozzi}.\:{Like}\:{that}. \\ $$ Answered…
Question Number 134009 by mathocean1 last updated on 26/Feb/21 $${E}\:{is}\:{a}\:{vec}\:{torial}\:{space}\:{which}\:{has}\:{as} \\ $$$${base}\:\mathscr{B}=\left(\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}},\overset{\rightarrow} {{k}}\right).\:{f}:\:{E}\rightarrow{E}\:{is}\:{a}\:{linear} \\ $$$${application}\:{such}\:{that} \\ $$$${f}\left(\overset{\rightarrow} {{i}}\right)=−\overset{\rightarrow} {{i}}+\mathrm{2}\overset{\rightarrow} {{k}};\:{f}\left(\overset{\rightarrow} {{j}}\right)=\overset{\rightarrow} {{j}}+\mathrm{2}\overset{\rightarrow} {{k}}\:{and}…
Question Number 134008 by AbderrahimMaths last updated on 26/Feb/21 $$\:\:\:\:{we}\:{consider}\:{that}\:{application}\:{n}\geqslant\mathrm{1} \\ $$$$\:\:{det}\::\:{M}_{{n}} \left(\mathbb{R}\right)\rightarrow\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{A} {det}\left({A}\right) \\ $$$$\mathrm{1}−{verify}\:{that}\:\forall{H}\in{M}_{{n}} \left(\mathbb{R}\right)\:{and}\:{t}\in\mathbb{R} \\ $$$$\:{if}\:{A}={I}_{{n}} \Rightarrow{det}\left({A}+{tH}\right)=\mathrm{1}+{t}.{Tr}\left({H}\right)+\circ\left({t}\right) \\ $$$$\mathrm{2}−{suppose}\:{that}:\:{A}\in{GL}_{{n}} \left(\mathbb{R}\right)…
Question Number 68473 by naka3546 last updated on 11/Sep/19 $$\frac{\mathrm{sin}\:\mathrm{72}°}{\mathrm{sin}\:\mathrm{42}°}\:\:=\:\:{p} \\ $$$$\mathrm{tan}\:\mathrm{12}°\:\:=\:\:? \\ $$ Commented by Kunal12588 last updated on 11/Sep/19 $$\frac{{sin}\left(\mathrm{60}°+\mathrm{12}°\right)}{{sin}\left(\mathrm{30}°+\mathrm{12}°\right)}={p} \\ $$$$\Rightarrow\frac{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{cos}\mathrm{12}°+\frac{\mathrm{1}}{\mathrm{2}}{sin}\mathrm{12}°}{\frac{\mathrm{1}}{\mathrm{2}}{cos}\mathrm{12}°+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{sin}\mathrm{12}°}={p} \\…
Question Number 2936 by Rasheed Soomro last updated on 30/Nov/15 $${Suppose}\:{I}\:{want}\:{to}\:{prove}\:{a}\:{statement},{say}\:{P}\left({n}\right),\: \\ $$$${for}\:{natural}\:{numbers}\:\boldsymbol{{mathematical}}\:\boldsymbol{{induction}} \\ $$$${is}\:{a}\:{proper}\:{tool}\:{for}\:{me}. \\ $$$$\mathcal{I}{f}\:{a}\:{P}\left({n}\right)\:{is}\:{required}\:{to}\:{prove}\:{for}\:{natural}\:{n}\geqslant{c}\: \\ $$$${mathematical}\:{induction}\:{is}\:{again}\:{a}\:{tool}\:{of}\:{proof}. \\ $$$$ \\ $$$$\mathcal{N}{ow}\:{suppose}\:{I}\:{have}\:{a}\:{statement}\:{which}\:{is}\:{true} \\ $$$${only}\:{for}\:\:\underset{−}…
Question Number 134005 by mr W last updated on 26/Feb/21 $${solve}\:{x}^{\mathrm{3}} −\mathrm{2}\lfloor{x}\rfloor=\mathrm{5} \\ $$ Answered by MJS_new last updated on 26/Feb/21 $${x}={i}\left[\mathrm{nteger}\:\mathrm{part}\right]+{f}\left[\mathrm{ractal}\:\mathrm{part}\right] \\ $$$$\left({i}+{f}\right)^{\mathrm{3}} −\mathrm{2}{i}=\mathrm{5}…
Question Number 68470 by mathmax by abdo last updated on 11/Sep/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 134006 by mohammad17 last updated on 26/Feb/21 Answered by malwan last updated on 26/Feb/21 $$\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{4}} {{lim}}\:\frac{\mathrm{2}{x}−\mathrm{5}}{\mathrm{3}}\:=\:\frac{\mathrm{2}×\mathrm{4}−\mathrm{5}}{\mathrm{3}}\:=\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow−\mathrm{3}^{+} } {{lim}}\:\frac{\sqrt{{x}+\mathrm{4}}\:−\sqrt{−{x}−\mathrm{2}}}{\:\sqrt{{x}+\mathrm{3}}}×\frac{\sqrt{{x}+\mathrm{4}}\:+\:\sqrt{−{x}−\mathrm{2}}}{\:\sqrt{{x}+\mathrm{4}}\:+\:\sqrt{−{x}−\mathrm{2}}} \\ $$$$=\:\underset{{x}\rightarrow−\mathrm{3}^{+} }…
Question Number 2932 by Filup last updated on 30/Nov/15 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{subfactorial}\:\mathrm{function}? \\ $$$${i}.{e}.\:\:\:\:\:!{x} \\ $$ Commented by 123456 last updated on 30/Nov/15 $$\mathrm{number}\:\mathrm{of}\:\mathrm{dessaragment} \\ $$ Commented…