What is a Limit in Calculus and How Does It Work?

In the world of calculus, a limit is a fundamental concept that helps us understand the behavior of functions as they approach a certain value. It essentially allows us to examine what happens to a function as the input gets closer and closer to a specific point.

Mathematically, a limit is denoted as:

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

Here, as the independent variable (x) approaches the value (a), the function (f(x)) approaches the limit (L). Understanding limits is crucial for grasping more advanced concepts in calculus and is often the starting point for delving into the world of derivatives and integrals.