Originally Posted by

**CaptainBlack** For your first question divide top and bottom by $\displaystyle x$ to get:

$\displaystyle \lim_{x\rightarrow \infty} \frac{\sqrt{1+4/x^2}}{1+4/x} $

and now as both top and bottom go to a finite valuse as $\displaystyle x$ goes to infinity you should be able to find the limit.

For the second divide top and bottom by $\displaystyle x^2$, to get:

$\displaystyle \lim_{x\rightarrow \infty}\frac{ x-\frac{10}{x^2}}{1} $

and you should be able to see what happens now.

CB