Category: Limits

Question Number 31461 by abdo imad last updated on 08/Mar/18 $$letgive{u}_n=\sum _{k=1}^{n}sin\left(\frac{k}{n}\right)sin\left(\frac{k}{n^2}\right)$$$$1)provethatthesequence\left(u_n\right)isconvergent$$$$2)find{lim}_{n\to \mathrm{\infty }}{u}_n.$$ Terms…

Question Number 96977 by 175 last updated on 05/Jun/20 $$\underset{x\to 5}{\lim }\frac{x-5}{2+{\cot }^2\frac{2}{x-5}}$$ Answered by mathmax by abdo last updated on 06/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{x}−\mathrm{5}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{tan}^{\mathrm{2}} \left(\frac{\mathrm{2}}{\mathrm{x}−\mathrm{5}}\right)}}\:\:\mathrm{changement}\:\mathrm{x}−\mathrm{5}\:=\mathrm{t}\:\mathrm{give}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{t}\right)…

Question Number 96931 by bobhans last updated on 05/Jun/20 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{{5\mathrm{x}}^4-8}{{7\mathrm{x}}^3+2}\times \tan \left(\frac{3}{\mathrm{x}}\right)=?$$ Commented by PRITHWISH SEN 2 last updated on 05/Jun/20 $$\underset{{x}\rightarrow\infty}…

Question Number 162399 by cortano last updated on 29/Dec/21 $$Letm\mathrm{\&}nbetwopositivenumbers$$$$greaterthan1.If\underset{p\to 0}{\lim }\frac{e^{\cos \left(p^n\right)}-e}{p^m}=\frac{1}{2}e$$$$then\frac{n}{m}=?$$ Commented by blackmamba last updated…

Question Number 31246 by malwaan last updated on 04/Mar/18 $$\mathrm{without}\mathrm{using}\mathrm{lohpital}$$$$\mathrm{find}$$$$\underset{\mathrm{x}\to \pi /6}{\lim }\frac{1-2\mathrm{sinx}}{\cos 3\mathrm{x}}$$ Commented by malwaan last updated on 04/Mar/18 $$\mathrm{please}…