the graph of f is shown below. answer the following:\na. \\(\\lim_{x\\to3}f(x)=\\)\nb. \\(\\lim_{x\\to5^{-}}f…

Explanation:

Step1: Recall limit definition

The limit $\lim_{x\rightarrow a}f(x)$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$. For $\lim_{x\rightarrow 3}f(x)$, as $x$ approaches 3 from both the left - hand side and the right - hand side of $x = 3$, the function values approach 0.

Step2: Analyze left - hand limit at $x = 5$

The left - hand limit $\lim_{x\rightarrow 5^{-}}f(x)$ is the value that $f(x)$ approaches as $x$ approaches 5 from the left. Looking at the graph, as $x$ approaches 5 from the left, $f(x)$ approaches 1.

Step3: Analyze right - hand limit at $x = 5$

The right - hand limit $\lim_{x\rightarrow 5^{+}}f(x)$ is the value that $f(x)$ approaches as $x$ approaches 5 from the right. From the graph, as $x$ approaches 5 from the right, $f(x)$ approaches 4. Since the left - hand limit and the right - hand limit at $x = 5$ are not equal, $f(5)$ is undefined.

Answer:

a. $\lim_{x\rightarrow 3}f(x)=0$ b. $\lim_{x\rightarrow 5^{-}}f(x)=1$ c. $\lim_{x\rightarrow 5^{+}}f(x)=4$ d. $f(5)$ is undefined