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The image presents a question asking to explain the meaning of the limit:

\[
\lim_{{x \to a}} f(x) = L
\]

You are given three options:

- **A**: As \(x\) approaches \(a\) from either side, the value of \(f(x)\) approaches \(L\).
- **B**: As \(x\) approaches \(a\) from the right, the value of \(f(x)\) approaches \(L\).
- **C**: As \(x\) approaches \(a\) from the left, the value of \(f(x)\) approaches \(L\).

### Explanation:
The expression \(\lim_{{x \to a}} f(x) = L\) means that as \(x\) gets arbitrarily close to \(a\), the value of \(f(x)\) approaches \(L\). This limit definition does not specify whether \(x\) approaches \(a\) from the left or the right, meaning it considers both directions.

Therefore, the correct answer is **A**: As \(x\) approaches \(a\) from either side, the value of \(f(x)\) approaches \(L\).

Would you like more details or have any questions?

### Related Questions:
1. What is the difference between one-sided and two-sided limits?
2. How do you evaluate limits when \(f(x)\) approaches different values from the left and the right?
3. What does it mean if the two-sided limit does not exist?
4. How does the concept of continuity relate to limits?
5. What role do limits play in the definition of derivatives?

**Tip**: Always remember that a two-sided limit exists only if the function approaches the same value from both the left and right directions as \(x\) approaches a particular point.

Explain the meaning of lim_{x→a} f(x) = L.

Explore the concept of limits and learn what it means when lim_{x→a} f(x) = L. This problem focuses on understanding how the function f(x) behaves as x approaches a, and explains the difference between one-sided and two-sided limits. Suitable for high school or early college students.

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