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We are tasked with determining \(\lim_{x \to 0.5} g(x)\) based on the given graph in Figure 11.

### Analysis of the Graph:
1. The graph shows the function \(y = g(x)\).
2. At \(x = 0.5\), there is an open circle on the curve, which suggests that \(g(0.5)\) is not defined at this point.
3. However, we can observe the behavior of the function as \(x\) approaches \(0.5\) from both sides (left and right).

#### Left-hand limit \(\lim_{x \to 0.5^-} g(x)\):
- As \(x\) approaches \(0.5\) from the left, the function value approaches 1 (the y-coordinate of the curve).

#### Right-hand limit \(\lim_{x \to 0.5^+} g(x)\):
- Similarly, as \(x\) approaches \(0.5\) from the right, the function also approaches 1.

Since both the left-hand and right-hand limits are equal, we conclude:

\[
\lim_{x \to 0.5} g(x) = 1
\]

Let me know if you would like more details or have any questions!

### Related Questions:
1. How do we find limits graphically when there's an open circle at a point?
2. What is the difference between left-hand and right-hand limits?
3. Why is the function not defined at \(x = 0.5\) despite the limit existing?
4. How do we handle limits where the function approaches infinity or negative infinity?
5. What is the formal definition of a limit?

**Tip:** When the function has an open circle at a point but the limits from both sides exist and are equal, the limit at that point exists, even if the function is not defined there.

Determine lim x→0.5 g(x) as seen in Figure 11, where g(x) is graphed, and there is an open circle at x = 0.5, y = 1.

Analyze how to find the limit of g(x) as x approaches 0.5 using a graph where the function has an open circle. Learn about left-hand and right-hand limits and graphical continuity concepts, suitable for Grades 11-12.

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