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 )

Границя функції

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

Границя функції

Properties of limit of a function

  1. If , then , the only
  2. If the function has a limit at a , then the limit is the only

  3. where is a constant
  4. The limit of a constant function is equal to the same constant

  5. — continuous at the point a function (by definition of a continuous function
  6. Border nemerenno function when it is equal to the value of the function at the point

Theorems on limits

The first significant boundary

Границя функції

Versions in other languages: