# Homework Help: Limit with unknown constants

1. Sep 27, 2009

### chaslltt

1. The problem statement, all variables and given/known data
find limit of x as it approaches infinite sqrt(x^2+ax)-sqrt(x^2+bx)
a and b are not given

2. Relevant equations

3. The attempt at a solution
Looking at this equation I first eliminated the square roots. After simplifying i ended up with ax-bx/sqrt(x^2+ax)+sqrt(x^2+bx) I think that this problem cannot be solved b/c a and b are not given. Is this right or is there another way of solving this?

2. Sep 27, 2009

### Bohrok

You can't have ax-bx because that basically turns out to be ∞-∞. So you need to pull out x from the square roots so you can cancel out the x's in the numerator.

$$\frac{ax - bx}{\sqrt{x^2 + ax} + \sqrt{x^2 + bx}} = \frac{ax - bx}{\sqrt{x^2(1 + \frac{ax}{x^2})} + \sqrt{x^2(1 + \frac{bx}{x^2})}} = \frac{ax - bx}{x\sqrt{1 + \frac{a}{x}} + x\sqrt{1 + \frac{b}{x}}}$$

See where you can go from there.

3. Sep 28, 2009

thank you