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Category: Limits

Question-167421

Question Number 167421 by infinityaction last updated on 16/Mar/22 Answered by mindispower last updated on 16/Mar/22 $${cot}^{\mathrm{2}} \left(\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)={cot}^{\mathrm{2}} \left({s}\pi\right)=\left({i}\frac{{e}^{{is}} +{e}^{−{is}} }{{e}^{{is}} −{e}^{−{is}} }\right)^{\mathrm{2}} = \\…

lim-n-n-1-n-1-n-n-JS-

Question Number 101822 by john santu last updated on 04/Jul/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\phi^{{n}+\mathrm{1}} −\left(−\phi\right)^{−{n}−\mathrm{1}} }{\phi^{{n}} −\left(−\phi\right)^{−{n}} }\:=\: \\ $$$$\left({JS}\:\circledast\right) \\ $$ Answered by bobhans last updated…

Question-167350

Question Number 167350 by infinityaction last updated on 13/Mar/22 Answered by Jamshidbek last updated on 13/Mar/22 $$\mathrm{Telegram}:@\mathrm{math\_undergraduate} \\ $$$$\mathrm{Problem}\:\mathrm{15}. \\ $$$$\mathrm{This}\:\mathrm{has}\:\mathrm{problem}\:\mathrm{solution}\:\mathrm{in}\:\mathrm{telegram}\:\mathrm{channel} \\ $$ Commented by…

Question-167295

Question Number 167295 by mnjuly1970 last updated on 12/Mar/22 Answered by qaz last updated on 12/Mar/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\left(\mathrm{2n}\right)!}{\mathrm{n}^{\mathrm{n}} \mathrm{n}!}\right)^{\mathrm{1}/\mathrm{n}} \\ $$$$=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{2n}\right)!}{\mathrm{n}^{\mathrm{n}} \mathrm{n}!}\centerdot\frac{\left(\mathrm{n}−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} \left(\mathrm{n}−\mathrm{1}\right)!}{\left(\mathrm{2n}−\mathrm{2}\right)!} \\…

lim-x-0-x-3-3x-3arctan-x-x-5-

Question Number 167277 by cortano1 last updated on 11/Mar/22 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{3x}+\mathrm{3arctan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} }\:=? \\ $$ Answered by qaz last updated on 11/Mar/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{3x}+\mathrm{3arctan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}}…