https://file.aiquickdraw.com/mathbot/file/1730322147093h1jwpowg.jpg

The question, translated to English, reads:

"Is the following statement true or false?

If \( f(c) = L \), then \( \lim_{x \to c} f(x) = L \).

Choose one:
- True
- False"

### Solution:

The statement is **false**. 

Just because \( f(c) = L \) does not imply that \( \lim_{x \to c} f(x) = L \). For the limit \( \lim_{x \to c} f(x) = L \) to hold, the function must approach \( L \) as \( x \) approaches \( c \) from all directions, regardless of \( f(c) \)'s actual value. For example, if there is a discontinuity at \( x = c \), then \( f(c) \) could equal \( L \) while the limit does not exist or equals a different value. 

Let me know if you need further clarification, or have any questions.

### Additional Questions for Practice:

1. What is required for \( \lim_{x \to c} f(x) = L \) to be true?
2. Can you provide an example where \( f(c) = L \) but \( \lim_{x \to c} f(x) \neq L \)?
3. What types of discontinuities exist in functions?
4. How do we determine if a function is continuous at a point?
5. What is the difference between one-sided and two-sided limits?

### Tip:
For a function \( f(x) \) to be continuous at \( x = c \), both \( \lim_{x \to c} f(x) \) must exist and equal \( f(c) \).

Kas järgmine väide on õige või vale? Kui f(c) = L, siis lim_{x→c} f(x) = L. Valige üks: - Õige - Vale

Explore the validity of a statement regarding limits and continuity: If f(c) = L, then lim_{x→c} f(x) = L. This question delves into key mathematical concepts related to limits and the Limit and Continuity Theorem, ideal for high school students.

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