The Exponential Function with Base e

Definition
                   
As the value of increases beyond all bounds,
the value of the expression
     
gets arbitrarily close to the value of .
This value can be found using a calculator, successively letting
    .
       is an irrational number, so it is represented by an infinite,
nonrepeating decimal. An approximation 10 12 decimal places is
      .
The number is extremely important because it appears naturally
in the mathematics that is used to describe many of the laws of nature.
     
defines the exponential function with base e.

Its graph is the typical

                  



For other graphs, see Example 1 - 4, pages 367 - 371,
and Table 3, page 372.


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