Limit of an unknown constant expression

[chaslltt]

Homework Statement

find limit of x as it approaches infinite sqrt(x^2+ax)-sqrt(x^2+bx)
a and b are not given

Homework Equations

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?

 

[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.

 

[chaslltt]

thank you