What Are Limits?
The concept of a limit is essential in calculus and mathematical analysis. It formalizes the notion of a value that a function or sequence "approaches" as the input or index approaches some point. The notation used to define limits is as follows:
If a function f(x) approaches L as x approaches c from either side, we write:
In this diagram, the limit is represented by L as x approaches the value of c. Limits are foundational in defining derivatives and integrals.
Examples of Limits
To understand limits better, consider some basic examples:
- The limit of f(x) = x as x approaches 2 is 2.
- The limit of g(x) = (x² - 1)/(x - 1) as x approaches 1 is 2.
For more examples, explore our Examples Page.