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

Printable View

- Nov 14th 2009, 04:27 PMalexandrabel90limits to infinity
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 - Nov 14th 2009, 04:38 PMadkinsjr
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.