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...?
What is e^x...?
What is value of "e" in mathematices? What are properties of "e"?
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 ...?
What is (e^1) over 0 ...?
What is value of e^Infinity...?
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