For example, consider the function f(x) = x^2. The limit of this function as x approaches 2, denoted as lim(x→2)f(x), is 4. This is because as x gets closer and closer to 2, the value of f(x) gets closer and closer to 4.
The limit of a function can be used to describe the behavior of the function near a certain point, even if the function is not defined at that point. For example, the function g(x) = 1/x is not defined at x = 0, but we can still talk about the limit of this function as x approaches 0. In this case, the limit is infinity, because as x gets closer and closer to 0, the value of g(x) gets larger and larger.
Limits are an important concept in mathematics because they allow us to describe the behavior of functions at points where the function may not be defined, and they play a central role in the development of calculus.