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Author: Tinku Tara

Question-213764

Question Number 213764 by Hanuda354 last updated on 16/Nov/24 Answered by mr W last updated on 16/Nov/24 $$\left(\mathrm{1}\right)\:\mathrm{4}−\mathrm{1}−\mathrm{3}−\mathrm{2} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4}−\mathrm{3}−\mathrm{1}−\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{1}−\mathrm{4}−\mathrm{3}−\mathrm{2} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{1}−\mathrm{4}−\mathrm{2}−\mathrm{3} \\…

Find-the-value-of-the-following-expression-Im-Li-2-2-0-pi-2-ln-sin-x-dx-

Question Number 213776 by mnjuly1970 last updated on 16/Nov/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{F}{ind}\:\:{the}\:\:{value}\:{of}\:\:{the}\:{following} \\ $$$$\:\:\:\:\:\:\:\:\:\:{expression}. \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\Omega=\:\:\:\frac{\:\mathrm{I}{m}\left(\:\mathrm{Li}_{\mathrm{2}} \:\left(\mathrm{2}\right)\right)}{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{sin}\left({x}\:\right)\right)\:{dx}}\:\:=\:? \\ $$ Answered by…

1-sin-

Question Number 213741 by bourasi last updated on 15/Nov/24 $$\sqrt{\mathrm{1}−\mathrm{sin}} \\ $$ Commented by Frix last updated on 15/Nov/24 $$\mathrm{Is}\:\mathrm{sin}\:\mathrm{a}\:\mathrm{variable}\:\mathrm{name}\:\mathrm{or}\:\mathrm{s}×\mathrm{i}×\mathrm{n}? \\ $$$$\mathrm{In}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{case},\:\mathrm{is}\:\mathrm{i}=\sqrt{−\mathrm{1}}? \\ $$…

Question-213744

Question Number 213744 by efronzo1 last updated on 15/Nov/24 Answered by golsendro last updated on 15/Nov/24 $$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{4x}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} +\left(\mathrm{1}−\mathrm{4x}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} } \\ $$$$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}\left(\mathrm{1}+\mathrm{4x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} −\mathrm{3}\left(\mathrm{1}−\mathrm{4x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}}…