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MATHEMATICS - THEORY

    Limit Laws

 

Limit Laws are the properties of limit. They are used to calculate the limit of a function.

     
   
  • Constant Law

    The limit of a constant is the constant itself.

         
  • Sum law (Law of addition )

    The limit of a sum is the sum of the limits.

         
  • Difference Law (Law of subtraction)

    The limit of a difference is the difference of the limits.

         
  • Constant Multiple Law

    The limit of a constant times a function is the constant times the limit of the function.

         
  • Product Law (Law of multiplication)

    The limit of a product is the product of the limits.

         
  • Quotient Law (Law of division)

    The limit of a quotient is the quotient of the limits (provided that the limit of the denominator is not 0).

         

    if

         

  • Special limit

    The limit of x is a when x approaches a.

         

  • Power law

    The limit of the power of a function is the power of the limit of the function.

         

    if n is a positive integer.

  • Power special limit

    The limit of x power is a power when x approaches a.

         

    if n is positive.
  • Root special limit

         

    where n is a positive integer. If n is positive, then it is assumed that a > 0.
  • Root law

         

    where n is positive integer. It is assumed that

         

    if n is even.
     
    Left and Right Hand Limit


Left hand limit example
  Left hand limit:
If f(x) is defined in an interval (a, b), and f(x) approaches A as x approaches b from the left side b, then

          

     

Right hand limit example
  Right hand limit:
If f(x) is defined in an interval (a, b), and f(x) approaches A as x approaches a from the right side a, then