# Finding the value of constants in f(x) as x->0

1. Feb 19, 2008

### XenoWolf

I'm not looking for the complete answer (from what I've read in the intro posts, you won't/shouldn't give it to me anyways)... I just need to figure out where to start. This is my first time taking calc, and I'm pretty lost. Thanks in advance.

1. The problem statement, all variables and given/known data

Find the values of the constants a and b such that

lim (x$$\rightarrow$$0) [ ( $$\sqrt{a+bx}$$ - $$\sqrt{3}$$ ) / x ] = $$\sqrt{3}$$

3. The attempt at a solution

I've attempted to solve it a couple of ways in an algebraic style, but the fact that there are three 'variables' has me stumped. I also tried using the limit property that states the limit of h(x)=f(x)/g(x) as x->c is L/K (I hope I got that right.. hah.) but the fact that K ends up being zero screws that up...

I'm just completely lost as to where I need to start the problem. I don't know if I should be solving for a variable, doing trial-and-error stuff, using some kind of limit property, etc.

2. Feb 19, 2008

### Rainbow Child

Let
$$f(x)=\frac{\sqrt{a+b\,x}-\sqrt3}{x}=\frac{g(x)}{x}$$
and solve for $g(x)$

What's the limit $$\lim_{x\to 0}g(x)$$ ?