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

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