Limits of Exponential and Logarithmic Functions

Limits of Exponential Function

1. When :
   
2. When :
   

Limits of Logarithmic Function

1. When :
   
2. When :
   

General Limit Property

The Irrational Number and Natural Logarithms

1. The Irrational Number
   
   Setting , as , , so:
2. The Natural Logarithm, denoted , is the logarithm with base .
1. The number is a positive real number not equal to , so the exponential function is defined for all real numbers.
2. Since is the logarithm with base , the inverse of the function is the exponential function .
3. The exponential function and the logarithmic function are inverses of each other:

Limits Involving Exponential and Logarithmic Functions Using