The limit of the function

Where is the number or one of the symbols

Definition: a Number is called the limit of the function at the point (if that is sent to ), if for any positive there is a positive number that for all that satisfy the inequality , the following inequality is satisfied

Mathematical notation expressions and

The point is from point at short distances (less )

The values on the number line is located at a small distance (less than )

Properties of limit of a function

1. If , then , the only

If the function has a limit at a , then the limit is the only

2. where is a constant

The limit of a constant function is equal to the same constant

3. — continuous at the point a function (by definition of a continuous function

Border nemerenno function when it is equal to the value of the function at the point

Theorems on limits

The first significant boundary