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What is e in mathematices? Why e is important in mathematices

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Answer & Explanation
What is e^x?

The number e is a mathematical constant or also known as Euler's number constant.
The constant e is real and irrational number represented by a greek letter (lower case "e").

What is the value of e in mathematices?

The number e is a mathematical constant or also known as Euler's number constant.
The constant e is real and irrational number represented by a greek letter (lower case "e").
Its value is e = 2.72 (approximate)

Properties of e
Here are some properties of "e"

1 - The constant e is real and irrational number 

2 - Natural logarithms is represented with base "e".

3 - e^x is called the (natural) exponential function. 

                  2     3     4
     x           x     x     x    
4 - e = 1 + x + --- + --- + --- + . . .
                 2!    3!    4!


5 - The approximate value of constant e is 2.71828.
Prove that e = 2.27 ? What is defination of e?

The e constant has an infinite number of digits. The value of e can be calculated as

          1     2     3     4
 x       x     x     x     x    
e = 1 + --- + --- + --- + --- + . . .
         1     2!    3!    4!

      ∞
 1   ---
e  = \      1
     /     ---
     ---    n!
    n=0
	      1     1      1
   = 1 + --- + --- + ----- + ...
          1    2.1   3.2.1

   = 1 + 1 + 0.5 + 0.1667 + ...
      
   = 2.72(approximate)	
Note :

The numerical value of e truncated to 50 decimal places is 2.71828182845904523536028747135266249775724709369995

                  0
What is value of e ?
 x                 0
e  (when x = 0) = e 

(because we know any non zero number raised to the power 0 is 1)  

             0
Therefore  e = 1
            2    3   4   5
Values of  e ,  e,  e,  e .... are as following
 x                 2
e  (when x = 2) = e   = 7.39

 x                 3
e  (when x = 3) = e   = 20.09

 x                 4
e  (when x = 4) = e   = 54.60

 x                 5 
e  (when x = 5) = e   = 148

 x                 6
e  (when x = 6) = e   = 403

 x                 7
e  (when x = 7) = e   = 1,097

 x                 8
e  (when x = 8) = e   = 2,981

 x                 9
e  (when x = 9) = e   = 8,103

 x                 10
e  (when x = 10) = e     = 22,026

 x                  11
e  (when x = 11) = e	 = 59,874

 x                  12
e  (when x = 12) = e     = 162,755

 x                  13
e  (when x = 13) = e	 = 442,413

 x                  14
e  (when x = 14) = e	 = 1,202,604

 x                  15
e  (when x = 15) = e     = 3,269,017

 x                  16
e  (when x = 16) = e     = 8,886,110

 x                  17
e  (when x = 17) = e     = 24,154,952

 x                  18
e  (when x = 18) = e	 = 65,659,969

 x                 19
e  (when x = 19) = e	 = 178,482,300

 x                  20
e  (when x = 20) = e	 = 485,165,195

 x                 21
e  (when x = 21) = e	 = 1,318,815,734

 x                  22
e  (when x = 22) = e	 = 3,584,912,846

 x                  23
e  (when x = 23) = e	 = 9,744,803,446

 x                  24
e  (when x = 24) = e	 = 26,489,122,129

 x                  25
e  (when x = 25) = e	 = 72,004,899,337

 x                  26
e  (when x = 26) = e	 = 195,729,609,428

 x                  27
e  (when x = 27) = e	 = 532,048,240,601

 x                  28
e  (when x = 28) = e	 = 1,446,257,064,290

 x                  29
e  (when x = 29) = e	 = 3,931,334,297,139

 x                  30
e  (when x = 30) = e	 = 10,686,474,581,513

 x                  31
e  (when x = 31) = e	 = 29,048,849,665,215

 x                  32
e  (when x = 32) = e	 = 78,962,960,182,591

See also our separate table for fractional powers of e*x), which is convenient for some Poisson problems.
e's value by scientific calculator

No need to remember these all values of e (e^2 , e^3, e^4, e^5 etc.) just clear this concept in your mind. Because can use your scientific calculator to get these values of e.

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Some Basic Articles about "e"

  • What is "e" in mathematices? Why "e" is important in mathematices...?NEW
  • What is e^x...?
  • What is value of "e" in mathematices? What are properties of "e"?NEW
  • Prove that e=2.27. What is defination of e?
  • Why e^0 is equal to 1?
  • Values of e^2, e^3, e^4, ... so on.
  • e's value by scientific calculator.

  • What is the value of e^-1 ...?
  • What is value of "e" to power 1/0 ...?NEW
  • What is (e^1) over 0 ...?
  • What is value of e^Infinity...?
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