Tau Euler (e)

tau e (e kiia ana hoki, ko te tau Euler) te turanga o te taukohiko maori; he taunga pangarau he tau koretake.

e = 2.718281828459…

Nga huarahi hei whakatau i te tau e (tātai):

1. Na roto i te rohe:

Te rohe whakamiharo tuarua:

Kōwhiringa kē (e whai ana i te tātai De Moivre-Stirling):

2. Hei huinga huinga:

āhuatanga tau e

1. Tepe tauutuutu e

2. Putanga

Ko te päröpü o te taumahinga taupuke ko te mahi taupū:

(e ^x)′ = me^x

Ko te pärönaki o te mahi taukorikori taiao ko te taumahi kōaro:

(rākau_e x)′ = (ln x)′ = 1/x

3. Whakakotahitanga

Ko te tauwhāinga taupū o te taumahinga taupū e ^x he mahi taupū e ^x.

∫ me^x dx = e^x+c

Ko te wahanga taukore o te raarangi mahi taukohiko maori_e x:

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

Tautoko tino o 1 Tuhinga o mua e taumahi kōaro 1/x he rite ki te 1:

Wairau me te turanga e

Ko te taukohiko o te tau x kua tautuhia hei taukohiko turanga x me te turanga e:

ln x = poro_e x

Mahi Taupū

He taumahinga taupuke tenei, kua tautuhia e whai ake nei:

f (x) = exp(x) = e^x

tātai Euler

Tau matatini e ^iθ ōrite:

e^iθ = ko (θ+ i hara (θ)

te wahi i ko te waeine pohewa (te putake tapawha o -1), me θ he tau tuturu.