Nhamba yeEuler (e)

nhamba e (kana, sezvainodanwawo, nhamba yeEuler) ndiyo hwaro hwelogarithm yechisikigo; chiverengero chesvomhu inova nhamba isina musoro.

e = 2.718281828459…

Nzira dzekuziva nhamba e (formula):

1. Kuburikidza nemuganho:

Yechipiri yakanakisa muganhu:

Imwe sarudzo (inotevera kubva kuDe Moivre-Stirling formula):

2. Sehuwandu hwehuwandu:

nhamba zvivakwa e

1. Reciprocal limit e

2. Zvakabuda

Chinobva kuexponential function ndiyo exponential function:

(e ^x) = uye^x

Zvinobva kune zvakasikwa logarithmic basa ndiro inverse basa:

(danda_e x)= (ln x) = 1/x

3. Integrals

Izvo zvisingagumi zvakabatanidzwa zveexponential function e ^x ibasa reexponential e ^x.

∫ uye^x dx = e^x+c

Izvo zvisingagumi zvakabatanidzwa zvechisikigo logarithmic basa log_e x:

∫ log_e x dx = ∫ lnx dx = x ln x – x +c

Definite integral of 1 to e inverse basa 1/x rakaenzana ne1:

Logarithms ine base e

Natural logarithm yenhamba x inotsanangurwa se base logarithm x with base e:

ln x = logi_e x

Exponential Function

Iri ibasa reexponential, rinotsanangurwa sezvizvi:

f (x) = exp (x) = e^x

Euler formula

Complex nhamba e ^iθ zvakaenzana:

e^iθ = cos (θ+ i chivi (θ)

apo i ndiyo unit yekufungidzira (square root of -1), uye θ chero nhamba chaiyo.