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

```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 value of e^Infinity...?

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##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick • Divisible by 7 Shortcut trick • Divisible by 8 Shortcut trick • Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick
• ##### SHORTCUT TRICKS (Prime Number)

###### Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ? ____________________________________

##### Worksheets (Solved)

###### Integration     