In mathematics, "lim" refers to a **limit**, which is a fundamental concept in calculus and analysis. The limit of a function describes the behavior of that function as its input approaches a certain value. Limits are used to define key concepts such as continuity, derivatives, and integrals.

### Example:
If you have a function \( f(x) \), the limit as \( x \) approaches some value \( a \) is written as:
\[
\lim_{x \to a} f(x)
\]
This expression means you're interested in the value that \( f(x) \) approaches as \( x \) gets closer and closer to \( a \).

#### Key Limit Types:
1. **Finite limits**: When \( x \to a \), and the function approaches a specific finite value.
   \[
   \lim_{x \to 2} (x^2) = 4
   \]
   
2. **Infinite limits**: When \( x \to a \), and the function grows without bound.
   \[
   \lim_{x \to 0} \frac{1}{x} = \infty
   \]
   
3. **Limit at infinity**: When \( x \to \infty \), the function approaches a particular value.
   \[
   \lim_{x \to \infty} \frac{1}{x} = 0
   \]

4. **One-sided limits**: Limits from the left or right side.
   \[
   \lim_{x \to a^+} f(x) \quad \text{(Right-hand limit)}
   \]
   \[
   \lim_{x \to a^-} f(x) \quad \text{(Left-hand limit)}
   \]

Would you like more details on specific limit problems or types?

### Related Questions:
1. What is the difference between one-sided and two-sided limits?
2. How do you compute limits at infinity?
3. Can you explain L'Hopital's Rule for solving indeterminate forms?
4. How do limits relate to continuity of a function?
5. What are common techniques for solving limit problems?

**Tip:** When you encounter an indeterminate form like \( \frac{0}{0} \), consider simplifying the function or using L'Hopital's Rule to find the limit.

Explore the concept of limits in calculus with detailed examples and explanations. Learn how to calculate finite and infinite limits, one-sided limits, and limits at infinity. This topic introduces critical concepts such as continuity, derivatives, and L'Hopital's Rule, ideal for high school students in Grades 11-12.

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