Category: Limits

Question Number 198254 by mathocean1 last updated on 15/Oct/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 198032 by cortano12 last updated on 08/Oct/23 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{1}{\sqrt{4025\mathrm{x}}}(\frac{1}{\sqrt{\mathrm{x}}}+\frac{1}{\sqrt{\mathrm{x}+1}}+\frac{1}{\sqrt{\mathrm{x}+2}}+\dots +\frac{1}{\sqrt{4025\mathrm{x}}})=?$$ Commented by universe last updated on 08/Oct/23 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{4025}}}×\frac{\mathrm{1}}{{x}}\underset{{r}=\mathrm{0}} {\overset{\mathrm{4024}{x}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{r}/{x}}} \…

Question Number 197947 by mnjuly1970 last updated on 05/Oct/23 $$$$$$\mathrm{calculate}\dots$$$$\mathrm{L}=\lim {}_{\mathrm{n}\to \mathrm{\infty }}\sqrt[n]{(1+\frac{1}{2})(1+\frac{1}{3})\dots (1+\frac{1}{n})}=?$$$$$$ Answered by MM42 last updated on…

Question Number 197832 by mathlove last updated on 30/Sep/23 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{2+\sqrt{cosx}}{-1+\sqrt{cosx}}=?$$ Answered by MM42 last updated on 30/Sep/23 $$letf\left(x\right)=\frac{2+\sqrt{cosx}}{-1+\sqrt{cosx}}$$$${for}\:\:{a}_{{n}} =\mathrm{2}{n}\pi\Rightarrow{lim}_{{n}\rightarrow\infty} \:{f}\left({a}_{{n}}…

Question Number 197661 by pticantor last updated on 25/Sep/23 $$\mathit{l}\mathit{i}\underset{\mathit{n}\to \mathrm{\infty }}{\mathit{m}}{\int }_0^1\frac{dt}{1+t+\dots .+t^n}=?$$ Commented by JDamian last updated on 25/Sep/23 $$\mathrm{Why}\:\mathrm{do}\:\mathrm{you}\:\mathrm{post}\:\mathrm{again}\:\mathrm{the}\:\mathrm{same}\:\mathrm{topic} \…