Question

answer attempt 2 out of 2
∞ -∞ dne undefined
$\lim_{x\to2^{-}}f(x)=\square$ $\lim_{x\to2^{+}}f(x)=\square$ $\lim_{x\to2}f(x)=\square$ $f(2)=\square$ submit answer

Explanation:

Step1: Analyze left - hand limit

As \(x\) approaches \(2\) from the left (\(x\to2^{-}\)), we look at the values of the function \(f(x)\) as \(x\) gets closer to \(2\) from values less than \(2\). From the graph, the function values are approaching \(2\). So, \(\lim_{x\to2^{-}}f(x) = 2\).

Step2: Analyze right - hand limit

As \(x\) approaches \(2\) from the right (\(x\to2^{+}\)), we look at the values of the function \(f(x)\) as \(x\) gets closer to \(2\) from values greater than \(2\). From the graph, the function values are approaching \(2\). So, \(\lim_{x\to2^{+}}f(x)=2\).

Step3: Determine the limit

Since \(\lim_{x\to2^{-}}f(x)=\lim_{x\to2^{+}}f(x) = 2\), then \(\lim_{x\to2}f(x)=2\).

Step4: Find the function value

The function has a hole at \(x = 2\), so \(f(2)\) is undefined.

Answer:

\(\lim_{x\to2^{-}}f(x)=2\), \(\lim_{x\to2^{+}}f(x)=2\), \(\lim_{x\to2}f(x)=2\), \(f(2)=\text{undefined}\)