Question

Evaluate:

$\underset{x\to 2}{lim}\frac{\sqrt{3-x}-1}{2-x}$

Answer 1

Now

$\underset{x\to 2}{lim}\frac{\sqrt{3-x}-1}{2-x}$

$=\underset{x\to 2}{lim}\frac{(\sqrt{3-x}{)}^2-(1{)}^2}{(2-x)(\sqrt{3-x}+1)}$

$=\underset{x\to 2}{lim}\frac{2-x}{(2-x)(\sqrt{3-x}+1)}$

$=\underset{x\to 2}{lim}\frac{1}{(\sqrt{3-x}+1)}$

$=\frac{1}{1+1}$

$=\frac{1}{2}$.