All About Limits
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Understanding limits is fundamental to calculus and mathematical analysis.
Why Learn about Limits?
- They help in understanding the behavior of functions.
- Essential for finding derivatives and integrals.
- Used in defining continuity of functions.
Exploring Limits with Examples
Consider the function f(x) = (x² - 1)/(x - 1). What's the limit as x approaches 1?
By simplifying, we see: f(x) = x + 1, for x ≠ 1. Thus, limit as x → 1 of f(x) is 2. 📈