Finding Values that Satisfy a Limit

[eumyang]

This may be a dumb question, but I'll ask anyway...

Homework Statement

Find the values of a and b such that
$\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}$

Homework Equations

N/A

The Attempt at a Solution

I already have the work and the solution. However, someone showed me a different way. Here are the first couple of steps:
$\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}$
$\lim_{x \rightarrow 0} \left( \sqrt{a + bx} - \sqrt{3} \right) = \sqrt{3} \cdot x$
$\lim_{x \rightarrow 0} \sqrt{a + bx} = \sqrt{3} + \sqrt{3} \cdot x$
I'm having a brain fart. Is multiplying both sides by x, and then adding sqrt 3 to both sides, legal?

 

[Office_Shredder]

On the second line, the left hand side is a number, and the right hand side is a function of x. Does that sound like two things that are going to be equal to you?

 

[eumyang]

That's what I thought -- I'm just too d***ed sleep-deprived. Thanks for the confirmation.