Understanding the Definition of a Limit in Calculus

In calculus, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. It's a fundamental concept in calculus, allowing us to study the behavior of functions and their values as they get closer and closer to a certain point. Mathematically, the definition of a limit is often denoted as:

$$\lim_{x \to c} f(x) = L$$

Where $c$ is the value the function is approaching and $L$ is the limit. Understanding limits is crucial for mastering calculus and its applications in real-world scenarios.