DL

Question 1

Dl de exp(x) en 0 =

Answer 1

1 + (x/1!) + (x^2/2!) + (x^3/3!) + … + (x^n/n!) + o(x^n)

Question 2

Dl de ch(x) en 0 =

Answer 2

1 + (x^2/2!) + … + (x^2n)/2n)! + o (x^2n+1)

Question 3

DL de sh(x) en 0 =

Answer 3

x + (x^3/3!) + (x^5/5!) + … + (x^2n+1)/(2n+1)! + o(x^2n+2)

Question 4

DL de cos (x) en 0 =

Answer 4

1 - (x^2)/2! + (x^4)/4! - … + (-1)^n * (x^2n)/2n! + o(x^2n+1)

Question 5

DL de sin(x) en 0 =

Answer 5

x - (x^3)/3! + (x^5)/5! - … + (-1)^n * (x^2n+1)/(2n+1)! + o(x^2n+2)

Question 6

Dl de ln(1 + x) en 0 =

Answer 6

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

Question 7

DL de (1+x)^a en 0 =

Answer 7

1 + ax + a(a-1)/2! * x^2 + … + [a(a-1)…(a-n+1)]/n! * x^n + o(x^n)