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 $$\mathrm{One}\:\mathrm{solution}…
Question Number 66245 by aliesam last updated on 11/Aug/19 $${prove}\:{that} \\ $$$$ \\ $$$$\int{e}^{{x}} \:{dx}\:=\:{e}^{{x}} \:+\:{c} \\ $$ Commented by Rio Michael last updated on…
Question Number 702 by 123456 last updated on 01/Mar/15 $$\mathrm{tan}\:{x}+\mathrm{tan}\:\mathrm{2}{x}+\mathrm{tan}\:\mathrm{4}{x}+\centerdot\centerdot\centerdot+\mathrm{tan}\:\mathrm{2}^{{n}} {x}=? \\ $$ Commented by prakash jain last updated on 01/Mar/15 $$\mathrm{Do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{form}\:\mathrm{expression}? \\ $$ Commented…
Question Number 131775 by Raxreedoroid last updated on 08/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of} \\ $$$${g}\left({x}\right)=\int_{\mathrm{tan}\:{x}} ^{\:{x}^{\mathrm{2}} } \frac{\mathrm{1}}{\:\sqrt{\mathrm{2}+{t}^{\mathrm{4}} }}\:{dt} \\ $$ Answered by bemath last updated on 08/Feb/21…
Question Number 131769 by liberty last updated on 08/Feb/21 $$\:\:\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{2}^{−\mathrm{cos}\:\mathrm{x}} \:−\mathrm{1}}{\mathrm{x}\left(\mathrm{x}−\frac{\pi}{\mathrm{2}}\right)}\:=?\: \\ $$ Answered by bemath last updated on 08/Feb/21 $$\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{x}}\:.\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{2}^{\mathrm{sin}\:\left(\mathrm{x}−\frac{\pi}{\mathrm{2}}\right)} −\mathrm{1}}{\mathrm{x}−\frac{\pi}{\mathrm{2}}}\:=…