Answer
$\lim_{x\to0.5^-}\sqrt\frac{x+2}{x+1}=\sqrt3$
Work Step by Step
$$\lim_{x\to-0.5^-}\sqrt\frac{x+2}{x+1}$$
To find one-side limit algebraically, we still apply the limit laws like for the two-side limits as normal.
$$\lim_{x\to-0.5^-}\sqrt\frac{x+2}{x+1}=\sqrt\frac{-0.5+2}{-0.5+1}=\sqrt\frac{1.5}{0.5}=\sqrt3$$
Therefore, $\lim_{x\to0.5^-}\sqrt\frac{x+2}{x+1}=\sqrt3$
