Category: Limits

Question Number 68554 by Mikael last updated on 13/Sep/19 Commented by Prithwish sen last updated on 13/Sep/19 $$\mathrm{li}\underset{\mathrm{n}\to \mathrm{\infty }}{\mathrm{m}}\frac{1}{\mathrm{n}}[\frac{1}{1+\frac{0}{\mathrm{n}}}+\frac{1}{1+\frac{1}{\mathrm{n}}}+\dots \dots +\frac{1}{1+\frac{\mathrm{n}-1}{\mathrm{n}}}]$$$$=\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}}\underset{\boldsymbol{\mathrm{r}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}−\mathrm{1}} {\sum}}\:\:\boldsymbol{\mathrm{lim}}\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\:}\frac{\mathrm{1}}{\mathrm{1}+\frac{\boldsymbol{\mathrm{r}}}{\boldsymbol{\mathrm{n}}}}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}}…

Question Number 68528 by Joel122 last updated on 13/Sep/19 $$\underset{t\to \mathrm{\infty }}{\lim }\left[\frac{1}{t}{\int }_1^t\sqrt[x]{t}dx\right]$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 2888 by prakash jain last updated on 29/Nov/15 $$\underset{(x,y)\to (0,0)}{\lim }\frac{x}{\sqrt{x^2+y^2}}=?$$$$\mathrm{or}$$$$\underset{z\to 0}{\lim }\frac{\mathrm{\Re }\left(z\right)}{\mid z\mid }$$ Answered by prakash jain…

Question Number 68354 by TawaTawa last updated on 09/Sep/19 $$\underset{x,\mathrm{y}\to (0,0)}{\lim }\frac{{\mathrm{x}}^4-{\mathrm{x}}^2{\mathrm{y}}^2+{\mathrm{y}}^4}{{\mathrm{x}}^2+{\mathrm{x}}^4{\mathrm{y}}^4+{\mathrm{y}}^2}$$ Commented by kaivan.ahmadi last…

Question Number 2783 by 123456 last updated on 27/Nov/15 $$\text{Double subscripts: use braces to clarify}$$$$\mathrm{proof}\mathrm{that}\gamma \mathrm{is}\mathrm{finite}\mathrm{and}\gamma \in (0,1)$$ Commented by Filup last updated on 27/Nov/15 $$\mathrm{I}\:\mathrm{am}\:\mathrm{curious}\:\mathrm{as}\:\mathrm{to}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{these} \…