In mathematics, a limit is a value that a function approaches as the input gets closer to a certain point. For example, if we look at the function f(x) = 1/x, as x gets closer to 0, f(x) increases without bound. This concept helps us understand how functions behave near specific points, even if they aren't defined there. Limits are also essential in calculus, where they form the foundation for defining derivatives and integrals. By studying limits, we can analyze the behavior of curves and find slopes of tangent lines, which are crucial for understanding motion and change in various fields, including physics and engineering.