Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 157171 by mathocean1 last updated on 20/Oct/21

$$calculate\underset{n\to +\mathrm{\infty }}{lim}\left(\frac{n+ln\left(n\right)+1}{{(5+\sqrt{n})}^2}\right)$$

Answered by puissant last updated on 20/Oct/21

$$\underset{n\to +\mathrm{\infty }}{\lim }\left(\frac{n+ln\left(n\right)+1}{{(5+\sqrt{n})}^2}\right)=\underset{n\to +\mathrm{\infty }}{\lim }\left(\frac{n(1+\frac{ln\left(n\right)}{n}+\frac{1}{n})}{n{(\frac{5}{\sqrt{n}}+1)}^2}\right)$$$$=\underset{n\to +\mathrm{\infty }}{\lim }\left(\frac{1+\frac{ln\left(n\right)}{n}+\frac{1}{n}}{{(\frac{5}{\sqrt{n}}+1)}^2}\right)=1..$$

Commented by mathocean1 last updated on 22/Oct/21

$$thankslepuissant.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com