# Finding Values that Satisfy a Limit

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

## Homework Statement

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

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
Staff Emeritus