Category: Limits

Question Number 35736 by rahul 19 last updated on 22/May/18 $$\underset{x\to 0}{\lim }\frac{\ln (\sec \left(ex\right)\sec \left(e^{2}x\right)\dots \dots \sec \left(e^{50}x\right))}{e^2-e^{2\cos x}}=?$$ Answered by tanmay.chaudhury50@gmail.com last updated on 23/May/18…

Question Number 35726 by abdo mathsup 649 cc last updated on 22/May/18 $$find{lim}_{x\to 0}\frac{1-cos\left(sinx\right)}{x^2}$$ Commented by abdo mathsup 649 cc last updated…

Question Number 101239 by  M±th+et+s last updated on 01/Jul/20 $$\underset{x\to \mathrm{\infty }}{\lim }\left(\frac{1+\frac{1}{2}+\frac{1}{3}+\dots \dots +\frac{1}{n}}{1+\frac{1}{3}+\frac{1}{5}\dots \dots +\frac{1}{2n+1}}\right)$$ Answered by mathmax by abdo last updated on 01/Jul/20 $$1+\frac{1}{2}+\frac{1}{3}+\dots .+\frac{1}{\mathrm{n}}={\mathrm{H}}_{\mathrm{n}}$$$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+….+\frac{\mathrm{1}}{\mathrm{2n}+\mathrm{1}}\:=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…..+\frac{\mathrm{1}}{\mathrm{2n}}+\frac{\mathrm{1}}{\mathrm{2n}+\mathrm{1}}\:−\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{4}}−…−\frac{\mathrm{1}}{\mathrm{2n}}…

Question Number 166735 by qaz last updated on 26/Feb/22 $$\mathrm{For}\mathrm{some}\mathrm{constant}\alpha \in (0,1)$$$$\mathrm{calculate}:{\int }_0^{\mathrm{\infty }}{\mathrm{e}}^{-\frac{{\mathrm{t}}^{\alpha }}{\alpha }-\mathrm{xt}}\mathrm{dt}\sim \sqrt{\frac{2\pi }{1-\alpha }}\cdot {\mathrm{x}}^{-\frac{\alpha }{2(1-\alpha )}-1}{\mathrm{e}}^{\frac{1-\alpha }{\alpha }\cdot {\mathrm{x}}^{-\frac{\alpha }{1-\alpha }}},\mathrm{x}\to 0^{+}$$ Terms of Service Privacy…

Question Number 101148 by john santu last updated on 30/Jun/20 $$\underset{x\to 0}{\lim }\frac{\sin \left(\ln (1+\mathrm{x})\right)-\ln (1+\sin \mathrm{x})}{\sin {}^4\left(\frac{\mathrm{x}}{2}\right)}=?$$ Commented by bramlex last updated on 01/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{cos}\:\left(\mathrm{ln}\left(\mathrm{1}+{x}\right)\right)}{\mathrm{1}+{x}}\:−\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}}{\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{4sin}\:^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)×\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)}…