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.