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Constants of e

e constants

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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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