# approaching a limit

• Sep 23rd 2008, 09:33 AM
yoleven
approaching a limit
find: lim as x approaches infinity x for the following:

x(x+1)^1/2*(1-(2x+3)^1/2
_______________________
7-6x+4x^2

I hope this equation is clear. It is a rational equation. I am not sure where to start. I generally know how to evaluate limits at infinity but this one is complicated to me. Any help would be appreciated.
• Sep 23rd 2008, 09:45 AM
CaptainBlack
Quote:

Originally Posted by yoleven
find: lim as x approaches infinity x for the following:

x(x+1)^1/2*(1-(2x+3)^1/2
_______________________
7-6x+4x^2

I hope this equation is clear. It is a rational equation. I am not sure where to start. I generally know how to evaluate limits at infinity but this one is complicated to me. Any help would be appreciated.

$\displaystyle \frac{x\sqrt{x+1}(1-\sqrt{2x+3})}{7-6x+4x^2}=\frac{x^2\sqrt{1+1/x}(1/\sqrt{x}-\sqrt{2+3/x})}{x^2(7/x^2-6/x+4)}=$$\displaystyle \frac{\sqrt{1+1/x}(1/\sqrt{x}-\sqrt{2+3/x})}{7/x^2-6/x+4}$

and now it should be easy.

RonL