Understanding Limits of Functions
1. What is a Limit?
A limit describes the behavior of a function as its input approaches a certain value.
2. Notation
The limit of a function f(x) as x approaches a value c is denoted as:
limx → c f(x) = L
3. Types of Limits
- One-Sided Limits
- Infinite Limits
4. Finding Limits
Methods include:
- Direct Substitution
- Factoring
- Rationalization
- L'Hôpital's Rule
5. Examples
Example 1: Direct Substitution
Find limx → 2 (3x + 1) = 7
Example 2: Indeterminate Form
Find limx → 1 (x2 - 1)/(x - 1) = 2
6. Limit Laws
Properties to compute limits include:
- Sum Law
- Product Law
- Quotient Law
7. Conclusion
Limits are essential for understanding continuity, derivatives, and integrals in calculus.
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