Answer to Question #254143 in Real Analysis for Kia

Question

Prove: lim(2n/(n ²+1))=0

Answer 1

$\displaystyle \lim_{n \to 0}(\frac{2n}{n^2+1})\\ \text{Divide each term in the limit above by the highest power of n $(n^2)$ to obtain}\\ \lim_{n \to 0}(\frac{\frac{2}{n}}{1+\frac{1}{n^2}})\\ \text{Which is 0}$