- #1

eumyang

Homework Helper

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## Homework Statement

Find the values of a and b such that

[itex]\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}[/itex]

## 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:

[itex]\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}[/itex]

[itex]\lim_{x \rightarrow 0} \left( \sqrt{a + bx} - \sqrt{3} \right) = \sqrt{3} \cdot x[/itex]

[itex]\lim_{x \rightarrow 0} \sqrt{a + bx} = \sqrt{3} + \sqrt{3} \cdot x[/itex]

I'm having a brain fart. Is multiplying both sides by x, and then adding sqrt 3 to both sides, legal?