Question

find the limit (if it exists). (if an answer does not exist, enter dne.)
$lim_{x
ightarrow2^{-}}f(x)$, where $f(x)=\begin{cases}\frac{x + 9}{9},&x < 2\\frac{36 - 9x}{2},&x>2end{cases}$

Explanation:

Step1: Identify left-hand function

For \( x \to 2^- \), use \( f(x)=\frac{x+9}{9} \) (since \( x<2 \)).

Step2: Substitute \( x=2 \) into function

\( \lim_{x \to 2^-} f(x) = \frac{2+9}{9} = \frac{11}{9} \).

Answer:

\(\frac{11}{9}\)