Formules DL

Question 1

DL de e^x

Answer 1

e^x = 1 + x/1! + x^2/2! + x^3/3! + … + x^n/n! + x^n * E_n(x)

Question 2

DL de ch(x)

Answer 2

cosh(x) = 1 + x^2/2! + x^4/4! + … + x^(2n)/(2n)! + x^(2n) * E_n(x)

Question 3

DL de sh(x)

Answer 3

sinh(x) = x/1! + x^3/3! + … + x^(2n+1)/(2n+1)! + x^(2n+1) * E_n(x)

Question 4

DL de sin(x)

Answer 4

sin(x) = x/1! - x^3/3! + x^5/5! - … + (-1)^n * x^(2n+1)/(2n+1)! + x^(2n+1) * E_n(x)

Question 5

DL de cos(x)

Answer 5

cos(x) = 1 - x^2/2! + x^4/4! - … + (-1)^n * x^(2n)/(2n)! + x^(2n) * E_n(x)

Question 6

DL de (1 + x)^alpha

Answer 6

(1 + x)^alpha = 1 + alphax + alpha(alpha - 1)x^2/2! + alpha(alpha - 1)(alpha - 2)x^3/3! + … +
(alpha(alpha - 1)…*(alpha - m + 1))/m! * x^m + x^m * E_m(x)

Question 7

Dl de 1/(1-x)

Answer 7

1/(1 - x) = 1 + x + x^2 + x^3 + … + x^n + x^n * E_n(x)

Question 8

Dl de ln(1+x)

Answer 8

ln(1 + x) = x - x^2/2 + x^3/3 - … + (-1)^(n+1) * x^n/n + x^n * E_n(x)