Category: Limits

Question Number 91274 by  M±th+et+s last updated on 29/Apr/20 $${\underset{n\to \mathrm{\infty }}{limn}}^{-n^2}{[(n+1)(n+\frac{1}{2})\dots .(n+\frac{1}{2^{n-1}})]}^n$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 91182 by jagoll last updated on 28/Apr/20 $$\underset{x\to 0}{\lim }\frac{2x^6+3x^2-3\tan {}^{2}x}{3x^6}$$ Answered by john santu last updated on 28/Apr/20…

Question Number 91157 by jagoll last updated on 28/Apr/20 $$\underset{x\to 0}{\lim }\frac{3\tan 4x-4\tan 3x}{3\sin 4x-4\sin 3x}=?$$ Commented by john santu last updated on 28/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}\left(\mathrm{4}{x}+\frac{\left(\mathrm{4}{x}\right)^{\mathrm{3}} }{\mathrm{3}}\right)−\mathrm{4}\left(\mathrm{3}{x}+\frac{\left(\mathrm{3}{x}\right)^{\mathrm{3}} }{\mathrm{3}}\right)}{\mathrm{3}\left(\mathrm{4}{x}−\frac{\left(\mathrm{4}{x}\right)^{\mathrm{3}}…

Question Number 156683 by cortano last updated on 14/Oct/21 Commented by john_santu last updated on 14/Oct/21 $$itshouldbe$$$$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} −\mathrm{1}+\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}−\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}{{x}−\mathrm{1}+\sqrt{{x}+\mathrm{1}}−\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}\:. \…

Question Number 25588 by behi.8.3.4.17@gmail.com last updated on 11/Dec/17 $$\underset{x\to 0}{\lim }\left(\frac{\mathit{x}-\mathit{t}\mathit{g}\mathit{x}}{\mathit{x}-\mathit{s}\mathit{i}\mathit{n}\mathit{x}}\right)=?$$$${\mathit{l}}^{\prime }\mathit{h}\mathit{o}\mathit{p}\mathit{i}\mathit{t}\mathit{a}\mathit{l}\mathit{r}\mathit{o}\mathit{l}\mathit{e}\mathit{n}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathit{l}\mathit{o}\mathit{w}\mathit{e}\mathit{d}!$$ Commented by moxhix last updated on 12/Dec/17 https://math.stackexchange.com/questions/508733/lim-x-to0-fracx-sin-xx-tan-x-without-using-lhopital . Answered by…