Category: Limits

Question Number 97117 by bobhans last updated on 06/Jun/20 $$\underset{\mathrm{h}\to 0}{\lim }\left[\frac{1}{\mathrm{h}}\underset{2}{\stackrel{2+2\mathrm{h}}{\int }}\sqrt{{\mathrm{t}}^2+2}\mathrm{dt}\right]$$ Answered by abdomathmax last updated on 06/Jun/20 $$\mathrm{let}\:\mathrm{use}\:\mathrm{hospital}\:\mathrm{theorem}\:\Rightarrow \…

Question Number 31529 by abdo imad last updated on 09/Mar/18 $$find{lim}_{x\to 1^{-}}lnx.ln(1-x).$$ Commented by abdo imad last updated on 11/Mar/18 $${lim}_{{x}\rightarrow\mathrm{1}^{−} }…

Question Number 31524 by abdo imad last updated on 09/Mar/18 $$find{lim}_{n\to \mathrm{\infty }}{(1+sin\left(\frac{1}{n}\right))}^n.$$ Commented by abdo imad last updated on 12/Mar/18 $${let}\:{put}\:{A}_{{n}} \:=\left(\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{{n}}\right)\right)^{{n}}…

Question Number 162585 by qaz last updated on 30/Dec/21 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }{\left(2\mathrm{n}{\int }_0^1\frac{{\mathrm{x}}^{\mathrm{n}}}{1+{\mathrm{x}}^2}\mathrm{dx}\right)}^{\mathrm{n}}=?$$ Answered by mathmax by abdo last updated…

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…