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Question-219731

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Question Number 219731 by Nescio last updated on 01/May/25 Answered by breniam last updated on 03/May/25 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }×\frac{{x}}{\mathrm{log}\left(\mathrm{1}+\mathrm{2}{x}\right)}×\mathrm{tan}\left({x}\right)={L} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }=\mathrm{1}…

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prove-n-1-2n-1-3-3-2n-1-2-2n-1-3-pi-6-

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Question Number 219724 by Nicholas666 last updated on 01/May/25 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}; \\ $$$$\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{3}\left(\mathrm{2}{n}+\mathrm{1}\right)+\mathrm{2}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }\:=\:\frac{\pi}{\mathrm{6}} \\ $$$$ \\ $$ Answered by nothing48 last updated…

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Question-219720

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Question Number 219720 by Spillover last updated on 01/May/25 Answered by mr W last updated on 01/May/25 $$\frac{{R}_{\mathrm{2}} }{{x}}=\frac{{R}_{\mathrm{1}} +{R}_{\mathrm{2}} }{{a}}=\frac{{R}_{\mathrm{2}} +{R}_{\mathrm{3}} }{{b}}={k},\:{say} \\ $$$$\Rightarrow{R}_{\mathrm{2}}…

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