question 3 (1 point)\nevaluate the limit for the graph: \\( \\lim _{x \\rightarrow 2} f(x) \\).\na) 0\nb)…

question 3 (1 point)\nevaluate the limit for the graph: \\( \\lim _{x \\rightarrow 2} f(x) \\).\na) 0\nb) does not exist\nc) -1\nd) 2

question 3 (1 point)\nevaluate the limit for the graph: \\( \\lim _{x \\rightarrow 2} f(x) \\).\na) 0\nb) does not exist\nc) -1\nd) 2

Answer

Explanation:

Step1: Recall the definition of the limit

The limit $\lim_{x\rightarrow a}f(x)$ exists if and only if the left - hand limit $\lim_{x\rightarrow a^{-}}f(x)$ and the right - hand limit $\lim_{x\rightarrow a^{+}}f(x)$ exist and are equal.

Step2: Find the left - hand limit as (x\rightarrow2^{-})

As (x) approaches (2) from the left (values of (x) less than (2)), we follow the part of the graph for (x < 2). Looking at the graph, when (x) approaches (2) from the left, (y) approaches (0). So, (\lim_{x\rightarrow2^{-}}f(x)=0)

Step3: Find the right - hand limit as (x\rightarrow2^{+})

As (x) approaches (2) from the right (values of (x) greater than (2)), we follow the part of the graph for (x>2). Looking at the graph, when (x) approaches (2) from the right, (y) approaches (0). So, (\lim_{x\rightarrow2^{+}}f(x)=0)

Answer:

A. (0)