Question Number 722 by malwaan1 last updated on 04/Mar/15 $${solve}\:{the}\:{equation}\:{cos}^{\mathrm{2001}} {x}−{sin}^{\mathrm{2001}} =\mathrm{1} \\ $$$$ \\ $$ Commented by malwaan last updated on 04/Mar/15 $${what}\:{about}\:{cos}^{{n}} {x}−{sin}^{{n}}…
Question Number 131795 by Dwaipayan Shikari last updated on 08/Feb/21 $$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{10}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{17}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{26}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{37}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{50}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{65}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{82}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{101}^{\mathrm{3}} }+… \\ $$ Answered…
Question Number 66256 by Mikael last updated on 11/Aug/19 $${Find}\:{all}\:{points}\:\left({a},\:{b}\right)\:{of}\:\mathbb{R}^{\mathrm{2}} \:{such}\:{that}\: \\ $$$${through}\:\left({a},\:{b}\right)\:{pass}\:{two}\:{tangent}\:{lines} \\ $$$${to}\:{the}\:{graph}\:{of}\:{f}\left({x}\right)={x}^{\mathrm{2}} . \\ $$ Commented by kaivan.ahmadi last updated on 11/Aug/19…
Question Number 131789 by bemath last updated on 08/Feb/21 $$\mathrm{Let}\:\varphi\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{3}\left(\mathrm{a}^{\mathrm{2}} −\sqrt{\mathrm{a}^{\mathrm{4}} +\mathrm{x}^{\mathrm{4}} }\:\right)}{\mathrm{x}^{\mathrm{8}} }\:;\:\mathrm{a}>\mathrm{0} \\ $$$$\mathrm{If}\:\varphi\:\mathrm{is}\:\mathrm{finite}\:\mathrm{then}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{a}=\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{a}=\sqrt{\frac{\mathrm{3}}{\mathrm{2}}}\:\:\:\:\:\:\left(\mathrm{c}\right)\:\varphi=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\left(\mathrm{d}\right)\:\varphi=\frac{\mathrm{1}}{\mathrm{9}} \\ $$ Answered by Dwaipayan…
Question Number 66253 by mathmax by abdo last updated on 11/Aug/19 $${prove}\:{by}\:{Rieman}\:{sum}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{xdx}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by mathmax by abdo last updated on 12/Aug/19…
Question Number 131785 by faysal last updated on 08/Feb/21 $${ABC}\:{triangle}'{s}\:{A}+{B}={C}=\mathrm{90}°\:{prove}\:{that} \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {A}−{sin}^{\mathrm{2}} {B}+{sin}^{\mathrm{2}} {C}=\mathrm{0} \\ $$ Answered by Dwaipayan Shikari last updated on 08/Feb/21…
Question Number 66250 by Tanmay chaudhury last updated on 11/Aug/19 Answered by mr W last updated on 11/Aug/19 $${x}_{{A}} ={r}\:\mathrm{tan}\:\theta \\ $$$${u}=\frac{{dx}_{{A}} }{{dt}}=\frac{{r}}{\mathrm{cos}^{\mathrm{2}} \:\theta}×\frac{{d}\theta}{{dt}} \\…
Question Number 66249 by Umar last updated on 11/Aug/19 $$\mathrm{The}\:\mathrm{npn}\:\mathrm{transistor}\:\mathrm{in}\:\mathrm{the}\:\mathrm{voltage}\: \\ $$$$\mathrm{amplifier}\:\mathrm{circuit}\:\mathrm{operates}\:\mathrm{satisfctorily} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{quiescent}\:\mathrm{collector}\:\mathrm{current}\:\mathrm{of}\:\mathrm{3mA}. \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{battery}\:\mathrm{supply}\:\left(\mathrm{V}_{\mathrm{cc}} \right)\:\mathrm{is}\:\mathrm{6v},\:\mathrm{calculate} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:; \\ $$$$\left(\mathrm{a}\right)\:\mathrm{the}\:\mathrm{load}\:\mathrm{resistor}\:\mathrm{R}_{\mathrm{L}} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{base}\:\mathrm{current}\:\mathrm{for}\:\mathrm{the}\:\mathrm{quiescent} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{collector}−\mathrm{emitter}\:\mathrm{voltage}\:\mathrm{V}_{\mathrm{ce}}…
Question Number 711 by prakash jain last updated on 03/Mar/15 $$\int_{\mathrm{3}/\mathrm{2}} ^{\:\mathrm{2}} \sqrt{\frac{{x}−\mathrm{1}}{\mathrm{3}−{x}}\:}{dx}\:\mathrm{by}\:\mathrm{substituting}\:{x}=\mathrm{1}−\mathrm{cos}\:\theta. \\ $$ Commented by malwaan last updated on 03/Mar/15 $${I}\:{am}\:{sorry} \\ $$$${x}=\mathrm{2}−{cos}\theta…
Question Number 709 by malwaan last updated on 03/Mar/15 $${find}\:{the}\:{integral}\:{in}\:{five}\:{different}\:{ways} \\ $$$$\int\left[\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}+\mathrm{1}\right)\right]^{−\frac{\mathrm{2}}{\mathrm{3}}} {dx} \\ $$ Answered by prakash jain last updated on 03/Mar/15 $$\mathrm{One}\:\mathrm{solution}…