https://file.aiquickdraw.com/mathbot/file/1726004036325pa7pzp7u.jpg

To solve the limit \(\lim_{x \to 2^-} f(x)\), we need to evaluate the behavior of the function \(f(x)\) as \(x\) approaches 2 from the left side based on the given graph.

- From the graph, as \(x\) approaches 2 from the left (\(x \to 2^-\)), the function values approach 1. This is because the graph moves towards the point \((2, 1)\) from the left.

Thus, the limit is:

\[
\lim_{x \to 2^-} f(x) = 1
\]

Do you need any further details or explanations? Let me know! Here are some additional questions you might find helpful:

1. What is \(\lim_{x \to 2^+} f(x)\)?
2. Does \(\lim_{x \to 2} f(x)\) exist?
3. What is the value of \(f(2)\)?
4. How do limits from the left and right affect continuity at a point?
5. What is the behavior of the function as \(x\) approaches 4?

**Tip:** When the limit from the left does not equal the limit from the right, the overall limit at that point does not exist.

What is \(\lim_{x \to 2^-} f(x)\) based on the given graph?

Evaluate \(\lim_{x \to 2^-} f(x)\) based on the behavior of the function from the left side at x=2. Understand the approach of the function value as x tends toward 2. Ideal for students learning calculus concepts like limits and continuity in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation