Category: Limits

Question Number 106313 by bemath last updated on 04/Aug/20 $$\underset{x\to 1}{\lim }\frac{\mathrm{x}\mid \mathrm{x}-1\mid }{{\mathrm{x}}^2-1}$$ Answered by Dwaipayan Shikari last updated on 04/Aug/20 $$firstcase$$$$\underset{{x}\rightarrow\mathrm{1}^{+}…

Question Number 40709 by math khazana by abdo last updated on 26/Jul/18 $$calculate{lim}_{x\to 0}\frac{cos(x-sinx)-1}{x^2}$$ Commented by maxmathsup by imad last updated on…

Question Number 106237 by Study last updated on 03/Aug/20 Answered by Dwaipayan Shikari last updated on 03/Aug/20 $$\frac{1}{n}\underset{n\to \mathrm{\infty }}{\lim }(e^{\frac{1}{n}}+e^{\frac{2}{n}}+\dots .+e^{\frac{n}{n}})$$$$\frac{\mathrm{1}}{{n}}\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{r}=\mathrm{1}}…

Question Number 40667 by Tawa1 last updated on 25/Jul/18 $$\mathrm{find}\mathrm{the}\mathrm{value}\underset{x\to 0}{\lim }\mathrm{g}\left(\mathrm{x}\right)\mathrm{must}\mathrm{have},\mathrm{if}\mathrm{g}\mathrm{complies}\mathrm{the}\mathrm{statement}$$$$\mathrm{about}\mathrm{limit}.\mathrm{Suppose}\underset{x\to -4}{\lim }\left[\mathrm{x}\underset{x\to 0}{\lim }\mathrm{g}\left(\mathrm{x}\right)\right]=2$$ Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jul/18 $${mobile}\:{handset}\:{does}\:{not}\:{show}\:{a}\:{few}\:…

Question Number 106175 by john santu last updated on 03/Aug/20 $$\underset{x\to 0}{\lim }\frac{\sqrt{\mathrm{x}}-\sqrt{\sin \mathrm{x}}}{{\mathrm{x}}^2\sqrt{\mathrm{x}}}=?$$ Answered by bemath last updated on 03/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{x}}−\sqrt{\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}}}{\mathrm{x}^{\mathrm{2}}…