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. $lim_{x
ightarrow3^{+}}f(x)=square$ (simplify your answer.) b. the limit does not exist.

Explanation:

Step1: Identify the function for x > 3

For $\lim_{x
ightarrow3^{+}}f(x)$, we use the part of the function where $x>3$. Here, $f(x)=\frac{x}{3}$.

Step2: Substitute x = 3

Substitute $x = 3$ into $f(x)=\frac{x}{3}$. We get $\frac{3}{3}$.

Step3: Simplify the result

$\frac{3}{3}=1$.

Answer:

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