Question

use the following function and its graph to answer parts a through d below. let $f(x)=\begin{cases}4 - x, & x<3\\2, & x = 3\\frac{x}{3}, & x>3end{cases}$. a. find $lim_{x
ightarrow3^{+}}f(x)$. select the correct choice below and, if necessary, fill in the answer box in your choice. a. $lim_{x
ightarrow3^{+}}f(x)=1$ (simplify your answer.) b. the limit does not exist. find $lim_{x
ightarrow3^{-}}f(x)$. select the correct choice below and, if necessary, fill in the answer box in your choice. a. $lim_{x
ightarrow3^{-}}f(x)=$ (simplify your answer.) b. the limit does not exist.

Explanation:

Step1: Recall left - hand limit definition

To find $\lim_{x
ightarrow3^{-}}f(x)$, we consider the function for $x < 3$.

Step2: Substitute $x = 3$ into the appropriate function

Since for $x<3$, $f(x)=4 - x$, we substitute $x = 3$ into $4 - x$. So, $\lim_{x
ightarrow3^{-}}f(x)=4-3$.

Answer:

A. $\lim_{x
ightarrow3^{-}}f(x)=1$