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# Constants of e

## The mathematical e constants.

e is a mathematical constant - also called the Euler's number. e is a real and irrational number and defined as

e = limx→∞(1 + 1 / x)x

=   limx→∞(1 + x)1/x

= 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 ...                            (1)

• 1/e = 0.36787 94411 71442 32159 55237 70161 46086 74458 11131 ...                        (2)
• e2 = 7.38905 60989 30650 22723 04274 60575 00781 31803 15570 ...                         (3)
• M = log10 e = 0.43429 44819 03251 82765 11289 18916 60508 22943 97005 ...                      (4)
• 1/M = loge 10 = 2.30258 50929 94045 68401 79914 54684 36420 76011 01488 ...                        (5)
• log10 M = 9.63778 43113 00536 78912 29674 ...                         (6)

Derivatives of e

(ex)' = ex                        (7)

Integrals of e

∫ ex dx = ex  + c                        (8)

Base e logarithm

ln x = logex                   (9)

Exponential function

f(x) = exp(x) = ex                    (10)

Euler's equation

e = cos(θ) + i sin(θ)                    (11)

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## Citation

• The Engineering ToolBox (2008). Constants of e. [online] Available at: https://www.engineeringtoolbox.com/e-constants-d_1242.html [Accessed Day Month Year].

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9.29.12