Lambarka Euler (e)

Number e (ama, sida sidoo kale loo yaqaan, lambarka Euler) waa saldhigga logarithm-ka dabiiciga ah; joogto ah xisaabeed oo ah tiro aan caqli-gal ahayn.

e = 2.718281828459

Siyaabaha loo go'aamiyo tirada e (formula):

1. Iyadoo loo marayo xadka:

Xadka labaad ee cajiibka ah:

Ikhtiyaarka kaduwan (waxay raacdaa qaacidada De Moivre-Stirling):

2. Sida wadar taxane ah:

guryaha tirada e

1. Xadka isdhaafsiga e

2. Derivatives

Kala soocida shaqada jibbaarada waa shaqada jibbaarada:

(e ^x) = iyo^x

Kala soocida shaqada logarithmic ee dabiiciga ah waa shaqada rogan:

(Log_e x)"= (ln x) " = 1/x

3. Isku-dhafka

Xubinta aan xad lahayn ee shaqada jibbaarada e ^x waa hawl jibbaaran e ^x.

∫ iyo^x dx = e^x+c

Qaybta aan xad lahayn ee logaga function logarithmic ee dabiiciga ah_e x:

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

Udub dhexaad u ah 1 ilaa e Shaqada rogan 1/x waxay la mid tahay 1:

Logarithms oo leh saldhig e

Logarithm dabiiciga ah ee nambarka x lagu qeexay logarithm-ka saldhigga ah x saldhig leh e:

ln x = diiwaan_e x

Shaqada jibbaaran

Tani waa hawl jibbaaran, oo lagu qeexay sida soo socota:

f (x) = expx) = e^x

Euler formula

Nambarka kakan e ^iθ la mid ah:

e^iθ = ka (θ+ i dembiθ)

halkaas oo i waa unugga mala-awaalka ah (xididka laba jibaaran yahay ee -1), iyo θ waa lambar kasta oo dhab ah.