Answer
$$\begin{aligned}\lim _{x \rightarrow-0.5^{-}} \sqrt{\frac{x+2}{x+1}}=\sqrt{3}
\end{aligned}$$
Work Step by Step
Given $$\lim _{x \rightarrow-0.5^{-}} \sqrt{\frac{x+2}{x+1}}$$
The limit from the left is equal to the limit at the point, which can be calculated by substituting the value for $ x .$
So, we get
$$\begin{aligned}L&=\lim _{x \rightarrow-0.5^{-}} \sqrt{\frac{x+2}{x+1}}\\
&=\sqrt{\frac{-0.5+2}{-0.5+1}}\\
&=\sqrt{\frac{1.5}{0.5}}\\
&=\sqrt{\frac{3}{1}}\\
&=\sqrt{3}
\end{aligned}$$
