# Math Help - How to solve this limit

1. ## How to solve this limit

Hey,
I'm having a hard time trying to solve both of these limits :
1.lim(sqrt(x^2 +x) -x) = 0.5
x->inf

2.lim(sqrt(x^2 +x) -x) != 0.5 (Not equal)
x->-inf

I would be glad if someone could post an epsilon-delta (Or other way) solution to these limits
Thanks a lot !

2. ## Re: How to solve this limit

Originally Posted by MichaelEngstler
Hey,
I'm having a hard time trying to solve both of these limits :
1.lim(sqrt(x^2 +x) -x) = 0.5
x->inf

2.lim(sqrt{x^2 +x} -x) != 0.5 (Not equal)
x->-inf
$\sqrt{x^2+x}-x=\frac{x}{\sqrt{x^2+x}+x}$ now divide through by $|x|$.