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Limit Rules of Function

In order to simplify the task of finding limits of functions, some general algebraic limit rules are developed to help finding limit of a function.

1. Constant Function Rule:

   

   Proof:

   

2. Sum of Functions Rule for two or more functions:

   

   Proof:

   

3. Constant Multiple Rule:

   

   Proof:

   

4. Difference of Functions Rule for two or more functions:

   

   Proof:

   

5. Product of Functions Rule for two or more functions:

   

   Proof:

   

6. Quotient of Functions Rule:

   

   Proof:

   

7. Continuous Function Rule:

   

   Proof:

   

Examples of Limit Rules

1. Identity Function Rule:

   

   Proof:

   

2. Power Function Rule:

   

   Proof:

   

3.  Power of Function Rule:

   

   Proof: