Inombolo ye-Euler (e)

Inombolo e (noma, njengoba ibizwa futhi, inombolo ye-Euler) iyisisekelo se-logarithm yemvelo; i-mathematical constant eyinombolo engenangqondo.

e = 2.718281828459 ...

Izindlela zokunquma inombolo e (ifomula):

1. Ngomkhawulo:

Umkhawulo wesibili ophawulekayo:

Enye inketho (ilandela kufomula ye-De Moivre-Stirling):

2. Njengesamba sochungechunge:

inombolo izakhiwo e

1. Umkhawulo ovumelanayo e

2. Okuphuma kokunye

Okuphuma kokunye komsebenzi we-exponential kuwumsebenzi womchazi:

(e ^x) = kanye^x

Okuphuma kokunye komsebenzi we-logarithmic wemvelo kuwumsebenzi ophambene:

(log_e x)== (ln x)" = 1/x

3. Okudidiyelwe

Ukuhlanganisa okungenamkhawulo komsebenzi we-exponential e ^x kuwumsebenzi womchazi e ^x.

∫ kanye^x dx = e^x+c

Okubalulekile okungenamkhawulo kwelogi yomsebenzi we-logarithmic yemvelo_e x:

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

Okubalulekile okuqinisekile kwe 1 kuya e umsebenzi ophambene 1/x ulingana no-1:

Ama-logarithms anesisekelo e

I-logarithm yemvelo yenombolo x kuchazwa njenge-logarithm eyisisekelo x ngesisekelo e:

ln x = ilog_e x

Umsebenzi we-Exponential

Lona umsebenzi we-exponential, ochazwa kanje:

f (x) = ukuphela (x) = e^x

Ifomula ye-Euler

Inombolo eyinkimbinkimbi e ^iθ kulingana:

e^iθ = cos (θ+ i isono (θ)

lapho i iyiyunithi ecatshangelwayo (impande yesikwele ka -1), kanye θ yinoma iyiphi inombolo yangempela.