What is a Limit?

When looking for the limit of a function, what we want to find is what value f(x) approaches as we approach a given value of x. To find a limit intuitively, tables are used. The symbolism for the limit of f(x) as x approaches e (a constant) is:

Intuitive Definition. Let y = f(x) be a function. Suppose that a and L are numbers such that whenever x is close to a but not equal to a, f(x) is close to L; as x gets closer and closer to a but not equal to a, f(x) gets closer and closer to L; and suppose that f(x) can be made as close as we want to L by making x close to a but not equal to a. Then we say that the limit of f(x) as x approaches a is L and we write

Properties of Limits

Two of the properties in the previous section are important here. The following properties are based on and , where L denotes the limit and f(x) and g(x) are polynomials.