Développement limité

Question 1

1 / (1-x)

Answer 1

1 + x + x^2+…. + x^n +o(x^n)

Question 2

1/(1-x)

Answer 2

1- x + x^2- x^3 +…. + (-1)^n*x^n + o(x^n)

Question 3

Ln(1 + x)

Answer 3

x - x^2 + x^3 - x^4 +…. + o(x^n)

Question 4

ln(1-x)

Answer 4

-x-x^2-x^3-….-x^n +o(x^n)

Question 5

(1+x)^a

Answer 5

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

Question 6

e^x

Answer 6

1+x+x^2/2!+x^3/3!+…+x^n/n!+o(x^n)

Question 7

Sin(x)

Answer 7

x-x^3/3!+x^5/5!+…+(-1)^n*o(x^2n+2)

Question 8

Cos(x)

Answer 8

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

Question 9

tan(x)

Answer 9

x+x^3/3+o(x^4)