Question Number 22701 by selestian last updated on 22/Oct/17 Answered by ajfour last updated on 22/Oct/17 $${e}^{\left(\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}}\right)\mathrm{ln}\:\mathrm{2}} \:={e}^{\mathrm{ln}\:\mathrm{2}^{\mathrm{tan}\:^{\mathrm{2}} {x}} } \:=\mathrm{2}^{\mathrm{tan}\:^{\mathrm{2}} {x}} \\…
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Question Number 153769 by SANOGO last updated on 10/Sep/21 Answered by puissant last updated on 10/Sep/21 $${On}\:{remarque}\:{que}\:{z}=\mathrm{0}\:{est}\:{solution}\:{de}\: \\ $$$${l}'{equation}.\:{supposons}\:{z}\neq\mathrm{0}.\:{En}\:{prenant} \\ $$$${les}\:{modules},\:{on}\:{a}: \\ $$$$\mid{z}\mid^{\mathrm{5}} =\mid\bar {{z}}\mid=\mid{z}\mid\:\Rightarrow\:\mid{z}\mid^{\mathrm{6}}…
Question Number 88235 by Rio Michael last updated on 09/Apr/20 $$\:\mathrm{find}\:\mathrm{a}\:\mathrm{maclaurine}\:\mathrm{series}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{4}} . \\ $$$$\:\frac{{dy}}{{dx}}\:−\:{x}\:=\:{xy}\:\:\:\mathrm{if}\:\:{y}\:=\:\mathrm{1}\:\mathrm{when}\:{x}\:=\:\mathrm{0}. \\ $$ Commented by niroj last updated on 11/Apr/20…
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Question Number 22696 by Tinkutara last updated on 22/Oct/17 $$\mathrm{A}\:\mathrm{force}\:\overset{\rightarrow} {{F}}\:=\:\mathrm{2}{x}\overset{\wedge} {{j}}\:\mathrm{newton}\:\mathrm{acts}\:\mathrm{in}\:\mathrm{a}\:\mathrm{region} \\ $$$$\mathrm{where}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{anticlockwise} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{square}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{2}\:\mathrm{m}\:\mathrm{in}\:{x}-{y}\:\mathrm{plane}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{done}.\:\mathrm{Is}\:\mathrm{this}\:\mathrm{force}\:\mathrm{a}\:\mathrm{conservative}\:\mathrm{force} \\ $$$$\mathrm{or}\:\mathrm{a}\:\mathrm{non}-\mathrm{conservative}\:\mathrm{force}? \\ $$ Commented…
Question Number 153765 by liberty last updated on 10/Sep/21 $$\:{Given}\:{f}:{R}\rightarrow{R}\:{is}\:{increasing}\:{positive} \\ $$$${function}\:{with}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{f}\left(\mathrm{3}{x}\right)}{{f}\left({x}\right)}=\mathrm{1}\:.\: \\ $$$${What}\:{the}\:{value}\:{of}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{f}\left(\mathrm{2}{x}\right)}{{f}\left({x}\right)}. \\ $$$$\left({A}\right)\:\mathrm{3}\:\:\:\:\:\left({B}\right)\:\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:\left({C}\right)\:\mathrm{1}\:\:\:\:\:\left({D}\right)\frac{\mathrm{2}}{\mathrm{3}}\:\:\:\:\:\left({E}\right)\:\infty \\ $$ Answered by gsk2684 last updated…
Question Number 153764 by mathdanisur last updated on 10/Sep/21 $$\mathrm{Prove}\:\mathrm{without}\:\mathrm{any}\:\mathrm{software}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\sqrt{\mathrm{1}\:-\:\left(\frac{\mathrm{x}\:+\:\mathrm{y}}{\mathrm{2}}\right)^{\mathrm{2}} }\:\mathrm{dxdy}\:>\:\frac{\pi}{\mathrm{4}} \\ $$ Commented by alisiao last updated on…
Question Number 22692 by Sahib singh last updated on 22/Oct/17 Commented by Sahib singh last updated on 22/Oct/17 $${find}\:{hinge}\:{reaction}\:{at}\:{A} \\ $$$$\&\:{angular}\:{velocity}\:{of}\:{rod}. \\ $$ Answered by…
Question Number 153760 by ZiYangLee last updated on 10/Sep/21 $$\int\:\mathrm{sin}^{\mathrm{2}} \mathrm{4}{x}\:\mathrm{cos}\:\mathrm{4}{x}\:{dx}= \\ $$ Answered by puissant last updated on 10/Sep/21 $$=\int{sin}^{\mathrm{2}} \mathrm{4}{x}\:{cos}\mathrm{4}{x}\:{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{sin}\mathrm{4}{x}\:{sin}\mathrm{8}{x}\:{dx} \\…