limit

[Clifford]

limit as x -> infinity of sqrt(x) / sqrt(x+2)

its infinity over and infinity, so apply l'hospitals rule

and we get 2sqrt(x+1) / 2sqrt(x) = sqrt(x+1)/sqrt(x)

which is just the inverted form, multiple times of this just gets you back where you started.

what else can i do

 

[skeeter]

sometimes you have to use the methods learned back in precalculus ...

\(\displaystyle \frac{\sqrt{x}}{\sqrt{x+2}} = \sqrt{\frac{x}{x+2}} = \sqrt{\frac{1}{1 + \frac{2}{x}}}\)

now let \(\displaystyle x \to \infty\)