Category: Limits

Question Number 129908 by Adel last updated on 20/Jan/21 Answered by mathmax by abdo last updated on 20/Jan/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{(1-\sqrt{\mathrm{sinx}})\left(1{-}^3\sqrt{\mathrm{sinx}}\right)\dots .\left(1{-}^{2020}\sqrt{\mathrm{sinx}}\right)}{{(1-\mathrm{sinx})}^{2019}}\mathrm{we}\mathrm{do}\mathrm{the}\mathrm{changement}$$$$\mathrm{x}=\frac{\pi}{\mathrm{2}}+\mathrm{t}\:\:\left(\mathrm{so}\:\mathrm{t}\rightarrow\mathrm{0}^{+} \right)\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\left(\mathrm{1}−\left(\mathrm{cost}\right)^{\frac{\mathrm{1}}{\mathrm{2}}}…

Question Number 64253 by Jameel Ahmad last updated on 16/Jul/19 Commented by ajfour last updated on 16/Jul/19 $$Nobellaurettes,ithink!$$ Terms of Service Privacy Policy…

Question Number 129723 by Adel last updated on 18/Jan/21 $$\underset{x\to 100}{\lim }\left[({\mathrm{x}}^{100}-{100}^{\mathrm{x}})\frac{1}{100-\mathrm{x}}\right]=?$$$$\mathcal{DANISH}$$ Answered by bramlexs22 last updated on 18/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{100}}…

Question Number 129655 by liberty last updated on 17/Jan/21 $$\underset{x\to \mathrm{\infty }}{\lim }{\left(\log {}_x\left(2021x\right)\right)}^{\log x}=?$$$$\lceil \ast \rceil \left(\sqrt{{\pi }^{\ell \mathrm{iberty}}}\right)$$ Answered by bemath last updated on 17/Jan/21…

Question Number 129584 by bemath last updated on 16/Jan/21 $$\underset{x\to 0}{\lim }\frac{\left(\sin \mathrm{x}\right)\left(\arctan \mathrm{x}\right)-{\mathrm{x}}^2}{1-\cos \left({\mathrm{x}}^2\right)}=?$$ Answered by liberty last updated on 16/Jan/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}+\frac{\mathrm{x}^{\mathrm{5}}…