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Question Number 145665 by phally last updated on 07/Jul/21 Answered by puissant last updated on 07/Jul/21 $$\mathrm{k}'=\mathrm{2k}−\mathrm{1}\:\Rightarrow\:\mathrm{1}\leqslant\mathrm{k}'\leqslant\mathrm{2n}−\mathrm{1} \\ $$$$\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \underset{\mathrm{k}'=\mathrm{1}} {\overset{\mathrm{2n}−\mathrm{1}} {\sum}}\frac{\mathrm{2}}{\mathrm{2n}+\mathrm{k}'\:}\: \\ $$$$=\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \underset{\mathrm{k}=\mathrm{1}}…

Question Number 145609 by Khalmohmmad last updated on 06/Jul/21 Commented by imjagoll last updated on 06/Jul/21 $$\:\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\Rightarrow\left(\mathrm{g}\bullet\mathrm{f}\right)\left(\mathrm{x}\right)=\mathrm{x} \\ $$$$\Rightarrow\mathrm{f}\:'\left(\mathrm{x}\right).\mathrm{g}'\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{1} \\ $$$$\Rightarrow\mathrm{g}\:'\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\frac{\mathrm{1}}{\mathrm{f}\:'\left(\mathrm{x}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{8x}^{\mathrm{3}} +\mathrm{12x}^{\mathrm{2}}…

Question Number 145534 by wassim last updated on 05/Jul/21 Answered by Rasheed.Sindhi last updated on 06/Jul/21 $${C}-\mathrm{1}:{Finite}\:{sets}\:{containing}\: \\ $$$$\boldsymbol{{single}}\:\boldsymbol{{member}}: \\ $$$${Let}\:{x}\in\mathrm{M} \\ $$$$\therefore\:{x}^{\mathrm{2}} −\mathrm{3}\mid{x}\mid+\mathrm{4}={x} \\…

Question Number 145487 by Mrsof last updated on 05/Jul/21 Commented by Mrsof last updated on 05/Jul/21 $${help}\:{me}\:{sir} \\ $$ Answered by Ar Brandon last updated…

Question Number 145443 by 7770 last updated on 04/Jul/21 $${The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:\:{are}\:\mathrm{2}\alpha+\beta\:\:{and} \\ $$$$\alpha+\mathrm{2}\beta.\:{Find}\:{the}\:{values}\:{of}\:{p}\:{and}\:{q} \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\mathrm{S}\:=\:{x}_{\mathrm{1}}…