Question

1. $lim_{x

ightarrow3^{-}}f(x)$, where $f(x)=\begin{cases}\frac{x + 2}{2},&x < 3\\frac{12 - 2x}{3},&x>3end{cases}$

Explanation:

Step1: Recall left - hand limit definition

We need to find $\lim_{x
ightarrow3^{-}}f(x)$, which means we consider values of $x$ that are less than 3.

Step2: Select the appropriate function

For $x < 3$, $f(x)=\frac{x + 2}{2}$.

Step3: Substitute $x = 3$ into the function

Substitute $x = 3$ into $y=\frac{x + 2}{2}$. We get $\frac{3+2}{2}=\frac{5}{2}$.

Answer:

$\frac{5}{2}$