how do you find the lim ((x^2+ 4x+3)^(1/2) -x) as x tends to infinity?
as well as lim ((x^2 +1 )^(1/2) / x) as x tends to negative infinity?
thanks you
This is the trick you're looking for:
$\displaystyle \lim_{x->\infty}\sqrt{x^2+4x+3}-x=\lim_{x->\infty}(\sqrt{x^2+4x+3}-x)\frac{\sqrt{x^2+4x+3}+x}{\sqrt{x^2+4x+3}+x}$
Do you know how to procede from here? This is just the standard method for dealing with infinite limits of functions like this.