https://file.aiquickdraw.com/mathbot/file/17265398762066p2t1qqy.jpg

The problem asks for \(\lim_{x \to 2} f(x)\) using the graph.

To solve this, let's examine the graph at \(x = 2\):

- **Left-hand limit**: As \(x\) approaches 2 from the left (values slightly less than 2), the function appears to approach the value \(4\). This is indicated by the curve coming downwards toward the point where \(x = 2\) from the left.
- **Right-hand limit**: As \(x\) approaches 2 from the right (values slightly greater than 2), the function also approaches the value \(4\). The curve on the right side of \(x = 2\) approaches the same point.

Since both the left-hand and right-hand limits exist and are equal to 4, the two-sided limit exists and is also equal to 4.

Thus, \[
\lim_{x \to 2} f(x) = 4.
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is a one-sided limit, and how does it relate to two-sided limits?
2. How can we determine if a function is continuous at a point using limits?
3. What happens if the left-hand and right-hand limits are not equal?
4. How do discontinuities affect limits?
5. Can a limit exist even if the function value at that point does not?

**Tip**: Always check both one-sided limits when determining a two-sided limit to ensure they are equal!

Find lim_{x→2} f(x) using the provided graph.

Learn how to find the limit of a function as x approaches 2 using a graph. This problem covers key concepts in limits, continuity, and two-sided limits, suitable for high school students in Pre-Calculus or Calculus.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation