# Math Help - infinite limits

1. problem is attached, i got as far as (√x)(√(x+1)-√(x-1)).

2. ${\sqrt{x^2+x} - \sqrt{x^2-x}} \cdot \frac{\sqrt{x^2+x} + \sqrt{x^2-x}}{\sqrt{x^2+x} + \sqrt{x^2-x}} =$

$\frac{(x^2+x) - (x^2-x)}{\sqrt{x^2+x} + \sqrt{x^2-x}}=$

$\frac{2x}{\sqrt{x^2+x} + \sqrt{x^2-x}} =$

divide numerator by $x$ , denominator by $\sqrt{x^2}$ ... ( note: since $x > 0$ , $x = \sqrt{x^2}$ )

$\frac{2}{\sqrt{1+\frac{1}{x}} + \sqrt{1- \frac{1}{x}}}$

now take the limit as $x \to \infty$

3. Oh yeeeeaaah, multiplying by the conjugaaaaate. should've thought that one out a little better. thanks a lot!