Category: Limits

Question Number 116043 by bemath last updated on 30/Sep/20 $$\underset{x\to 0}{\lim }\frac{\sqrt{{\mathrm{x}}^2+{\mathrm{x}}^4}}{\mathrm{x}}?$$$$\int \sinh {}^2\left(\mathrm{x}\right)\cosh \left(\mathrm{x}\right)\mathrm{dx}$$$$\mathrm{find}\mathrm{x}\mathrm{from}\mathrm{equation}\cos \left({2\tan }^{-1}\left(\mathrm{x}\right)\right)=\frac{1}{2}$$ Answered by MJS_new last…

Question Number 116039 by bobhans last updated on 30/Sep/20 $$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sqrt[3]{\cos {}^4\left(x\right)}}{{(1-\sin \left(x\right))}^{\frac{2}{3}}}?$$ Answered by Dwaipayan Shikari last updated on 30/Sep/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\frac{\left(\mathrm{cosx}\right)^{\frac{\mathrm{4}}{\mathrm{3}}}…

Question Number 181553 by Frix last updated on 26/Nov/22 $$\mathrm{Reposting}\mathrm{question}181462$$$$\underset{n\to \mathrm{\infty }}{\lim }\frac{\sqrt[n]{\sqrt{2!}\times \sqrt[3]{3!}\times \sqrt[4]{4!}\times \dots \times \sqrt[n]{n!}}}{\sqrt[n+1]{(2n+1)!!}}\stackrel{?}{=}\frac{1}{2\mathrm{e}}$$ Answered by aleks041103 last updated on 26/Nov/22 $${b}_{{n}} =\frac{\sqrt[{{n}}]{\sqrt{\mathrm{2}!}×\sqrt[{\mathrm{3}}]{\mathrm{3}!}×\sqrt[{\mathrm{4}}]{\mathrm{4}!}×…×\sqrt[{{n}}]{{n}!}}}{\:\sqrt[{{n}+\mathrm{1}}]{\left(\mathrm{2}{n}+\mathrm{1}\right)!!}}=\sqrt[{{n}}]{\frac{\sqrt{\mathrm{2}!}×\sqrt[{\mathrm{3}}]{\mathrm{3}!}×\sqrt[{\mathrm{4}}]{\mathrm{4}!}×…×\sqrt[{{n}}]{{n}!}}{\left(\left(\mathrm{2}{n}+\mathrm{1}\right)!!\right)^{\frac{{n}}{{n}+\mathrm{1}}}…

Question Number 116005 by mnjuly1970 last updated on 30/Sep/20 $$\dots advancedmathematics\dots$$$$$$$$provethat:::$$$$$$$${lim}_{x\to 1^{+}}(\zeta \left(x\right)-\frac{1}{x-1})\stackrel{???}{=}\gamma$$$$\gamma ::\mathcal{E}uler-mascheroniconstant.$$$$…

Question Number 115961 by Ar Brandon last updated on 29/Sep/20 Commented by Dwaipayan Shikari last updated on 29/Sep/20 $$\mathrm{Indetermined}$$ Commented by Ar Brandon…