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Author: Tinku Tara

Question-222736

Question Number 222736 by Lekhraj last updated on 06/Jul/25 Answered by Raphael254 last updated on 08/Sep/25 $$\begin{array}{|c|c|}{\boldsymbol{{To}}\:\boldsymbol{{a}}\:\boldsymbol{{number}}\:\boldsymbol{{be}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{33},}\\{\boldsymbol{{it}}\:\boldsymbol{{needs}}\:\boldsymbol{{to}}\:\boldsymbol{{be}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{3}\:\boldsymbol{{and}}\:\mathrm{11}}\\\hline\end{array} \\ $$$$ \\ $$$${Why}? \\ $$$$ \\ $$$${ab}\mid{n}\:\Rightarrow\:{a}\mid{n}\:{and}\:{b}\mid{n}…

lim-x-0-1-cos-x-x-xcos-x-

Question Number 222756 by Osefavour last updated on 06/Jul/25 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)}}{\:\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{xcos}}\left(\sqrt{\boldsymbol{\mathrm{x}}}\right)} \\ $$ Answered by gregori last updated on 07/Jul/25 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}}{{x}\left(\mathrm{1}−\mathrm{cos}\:\sqrt{{x}}\:\right)\left(\mathrm{1}+\sqrt{\mathrm{cos}\:{x}}\right)} \\ $$$$\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:^{\mathrm{2}}…