# Limit

A limit is the behavior of

## Intuitive Definition

We know that a function assigns values to outputs with respect to inputs. As given inputs get closer and closer to a specific value, the function's output get closer and closer to a certain separate value. We define this value that the function's output approaches as the *limit*.

We can examine the limit of a simple continuous function, .

The limit at x=0, would simply be f(x)=0, since as the function is continuous and differentiable at every point, .

Indeed for this function, we define the limit as . But this is a special case of limit, in the majority of limits cannot be solved in this manner.

For example, given

The limit of as *x* approaches 0 is 0 (just as in ), but ; is not continuous at (as shown on the right).