Question Number 206074 by MATHEMATICSAM last updated on 06/Apr/24 $$\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{2}} \left({x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \:−\:{x}_{\mathrm{2}} \right) \\ $$$$\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{3}} \left({x}_{\mathrm{5}}…
Question Number 206069 by MathematicalUser2357 last updated on 06/Apr/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−{x}^{\mathrm{3}} +{x}}{\mathrm{sin}\:{x}} \\ $$ Answered by MetaLahor1999 last updated on 06/Apr/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−{x}^{\mathrm{3}} }{{sin}\left({x}\right)}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 206096 by RoseAli last updated on 06/Apr/24 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:.{dx} \\ $$ Answered by Frix last updated on 07/Apr/24 $$\int\frac{{dx}}{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:\overset{{t}=\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}…
Question Number 206064 by mr W last updated on 06/Apr/24 Commented by mr W last updated on 06/Apr/24 $${an}\:{unsolved}\:{old}\:{question}\:\left({Q}\mathrm{172465}\right) \\ $$ Answered by A5T last…
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Question Number 206066 by hardmath last updated on 06/Apr/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{8}}{\mathrm{9}}\:\centerdot\:\frac{\mathrm{15}}{\mathrm{16}}\:\centerdot\:…\:\centerdot\:\frac{\mathrm{120}}{\mathrm{121}}\:=\:? \\ $$ Answered by mr W last updated on 06/Apr/24 $$\underset{{n}=\mathrm{2}} {\overset{\mathrm{11}} {\prod}}\frac{{n}^{\mathrm{2}}…
Question Number 206060 by cortano21 last updated on 06/Apr/24 Answered by mr W last updated on 06/Apr/24 Commented by mr W last updated on 06/Apr/24…
Question Number 206093 by mr W last updated on 06/Apr/24 Answered by A5T last updated on 07/Apr/24 Commented by A5T last updated on 07/Apr/24 $${S}_{\mathrm{4}}…
Question Number 206095 by RoseAli last updated on 06/Apr/24 Answered by Frix last updated on 07/Apr/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{sin}\:{x}}{{x}−\mathrm{tan}\:{x}}\:\:\overset{\left[\mathrm{l}'\mathrm{H}\hat {\mathrm{o}pital}\right]} {=}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{{d}}{{dx}}\left[{x}−\mathrm{sin}\:{x}\right]}{\frac{{d}}{{dx}}\left[{x}−\mathrm{tan}\:{x}\right]}\:= \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}}{−\mathrm{tan}^{\mathrm{2}} \:{x}}…
Question Number 206063 by MATHEMATICSAM last updated on 06/Apr/24 $$\mathrm{If}\:\left({x}\:+\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\left({y}\:+\:\sqrt{\mathrm{1}\:+\:{y}^{\mathrm{2}} }\right)\:=\:\mathrm{1}\:\mathrm{then} \\ $$$$\mathrm{find}\:\left({x}\:+\:{y}\right)^{\mathrm{2}} . \\ $$ Answered by mr W last updated on 06/Apr/24…