Lambar Euler (e)

Number e (ko, kamar yadda ake kira, lambar Euler) shine tushen logarithm na halitta; mathematical akai-akai wanda shine adadi mara hankali.

e = 2.718281828459…

Hanyoyin ƙayyade lambar e (formula):

1. Ta hanyar iyaka:

Iyaka mai ban mamaki na biyu:

Zaɓin zaɓi (yana zuwa daga tsarin De Moivre-Stirling):

2. A matsayin jimla:

kaddarorin lamba e

1. Iyakar ma'amala e

2. Abubuwan da aka samo asali

Asalin aikin juzu'i shine aikin juzu'i:

(e ^x= kuma^x

Asalin aikin logarithmic na halitta shine aikin juzu'i:

(shiga_e x)' = (ln x)" = 1/x

3. Hadin kai

Maɓalli marar iyaka na aikin ma'auni e ^x aiki ne mai ma'ana e ^x.

∫ kuma^x dx = e^x+c

Maɓalli mara iyaka na log ɗin aikin logarithmic na halitta_e x:

Ƙaddamar da log_e x dx = lnx dx = x ln x – x +c

Tabbataccen abun ciki na 1 to e Aikin juzu'i 1/x daidai yake da 1:

Logarithms tare da tushe e

Logarithm na halitta na lamba x bayyana a matsayin tushen logarithm x tare da tushe e:

ln x = log_e x

Ayyukan Ƙari

Wannan aikin juzu'i ne, wanda aka ayyana kamar haka:

f (x= exp(x) = e^x

Euler dabara

Complex lamba e ^iθ daidai:

e^iθ = kowa (θ+ i zunubi (θ)

inda i shine raka'ar hasashe (tushen murabba'in -1), kuma θ kowane lamba ne na gaske.