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The image contains two graphs labeled (A) and (B) that depict the function \( y = f(x) \), each showing how close the function is to a certain limit. The task is to find values for \( c \), \( L \), \( \epsilon \), and \( \delta \) such that the following holds:

\[
\text{If } 0 < |x - c| < \delta, \text{ then } |f(x) - L| < \epsilon.
\]

This is the formal definition of the limit \( \lim_{x \to c} f(x) = L \), with \( \epsilon \) and \( \delta \) representing how close the function values are to the limit \( L \) when \( x \) is within \( \delta \) of \( c \).

### For Graph (A):
- The function \( f(x) \) approaches \( L = 4 \) as \( x \to 0 \).
- You can choose \( c = 0 \), since the vertical line is around \( x = 0 \).
- The values of \( \epsilon \) can be chosen based on the vertical distance between \( f(x) \) and \( L = 4 \). From the graph, \( f(x) \) stays between 3.5 and 4.8, so an appropriate \( \epsilon \) could be 0.5.
- For \( \delta \), the horizontal distance between \( x = 0 \) and the points where \( f(x) \) starts to deviate from the bounds of \( \epsilon \) gives \( \delta \approx 0.1 \), since the graph remains within \( |f(x) - L| < \epsilon \) for \( -0.1 < x < 0.1 \).

### For Graph (B):
- The function \( f(x) \) approaches \( L = 10 \) as \( x \to 3 \).
- You can choose \( c = 3 \), since the vertical line is around \( x = 3 \).
- The values of \( \epsilon \) can be chosen based on the vertical distance between \( f(x) \) and \( L = 10 \). From the graph, \( f(x) \) stays between 9.8 and 10.4, so an appropriate \( \epsilon \) could be 0.2.
- For \( \delta \), the horizontal distance between \( x = 3 \) and the points where \( f(x) \) starts to deviate from the bounds of \( \epsilon \) gives \( \delta \approx 0.1 \), since the graph remains within \( |f(x) - L| < \epsilon \) for \( 2.9 < x < 3.1 \).

Would you like more detailed explanations or have any specific questions about this?

Here are 5 follow-up questions:
1. What does the formal definition of a limit represent graphically?
2. How would you select different values for \( \delta \) if the graph changed?
3. What happens when \( |x - c| \) becomes greater than \( \delta \)?
4. Can \( \epsilon \) be smaller than the chosen values in the graphs? Why or why not?
5. How do you interpret \( f(x) \) approaching \( L \) as \( x \to c \)?

**Tip:** When choosing \( \epsilon \) and \( \delta \), visualize the vertical and horizontal distances that limit how far \( f(x) \) can vary from the limit \( L \).

Based on the information conveyed in Figure 5(B), find values of c, L, ε, and δ > 0 such that the following statement holds: If 0 < |x - c| < δ, then |f(x) - L| < ε.

Analyze the function f(x) using graphical methods to determine the values of c, L, ε, and δ. This example explores the epsilon-delta definition of limits, providing a clear approach to solving problems involving limits and continuity.

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