Question

question 3 (1 point)
evaluate the limit for the graph: \\( \lim _{x \
ightarrow 2} f(x) \\).
a) 0
b) does not exist
c) -1
d) 2

Explanation:

Step1: Recall the definition of the limit

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

Step2: Find the left - hand limit as \(x

ightarrow2^{-}\)
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, \(\lim_{x
ightarrow2^{-}}f(x)=0\)

Step3: Find the right - hand limit as \(x

ightarrow2^{+}\)
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, \(\lim_{x
ightarrow2^{+}}f(x)=0\)

Answer:

A. \(0\)