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To find the limit \(\lim_{x \to 0} (g(x) - h(x))\), let's analyze both functions \(g(x)\) and \(h(x)\) as \(x\) approaches 0.

### Step 1: Evaluate \(g(x)\) as \(x \to 0\)
From the graph of \(g(x)\), we observe that as \(x\) approaches 0 from both the left and the right:
- \(g(x)\) approaches 1 from both sides.

Thus, \(\lim_{x \to 0} g(x) = 1\).

### Step 2: Evaluate \(h(x)\) as \(x \to 0\)
From the graph of \(h(x)\), we observe that as \(x\) approaches 0 from both the left and the right:
- \(h(x)\) approaches 1 from both sides.

Thus, \(\lim_{x \to 0} h(x) = 1\).

### Step 3: Compute \(\lim_{x \to 0} (g(x) - h(x))\)
Now, subtract the limits we calculated:
\[
\lim_{x \to 0} (g(x) - h(x)) = \lim_{x \to 0} g(x) - \lim_{x \to 0} h(x) = 1 - 1 = 0
\]

### Conclusion:
The limit is 0, so the correct answer is **B. 0**.

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. What happens if one of the functions is discontinuous at \(x = 0\)?
2. How do you approach limits when graphs have vertical asymptotes?
3. What is the formal definition of a limit from the left and the right?
4. How do piecewise functions affect the computation of limits?
5. What happens to the limit if \(g(x)\) or \(h(x)\) is undefined at \(x = 0\)?

**Tip:** When analyzing limits graphically, always check the behavior from both sides of the point of interest!

Find lim (g(x) - h(x)) as x approaches 0, based on the graphs provided.

Learn how to find the limit of the difference between two functions, g(x) and h(x), using graphical analysis. This problem involves evaluating limits at a point by analyzing the behavior of two functions as x approaches 0. Suitable for students in Grades 10-12.

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