DL Flashcards
1
Q
1/(1-x)
A
1 + x + x² + x³
= Σ x^k + o(xⁿ)
2
Q
1/(1+x)
A
1 - x + x² - x³
= Σ (-x)^k + o(xⁿ)
3
Q
exp(x)
A
1 + x/1! + x²/2! + x³/3!
= Σ (x^k)/k! + o(xⁿ)
4
Q
sh(x)
A
x + x³/3! + x⁵/5!
= Σ [x^(2k+1)] / (2k+1)! + o(x²ⁿ⁺²)
5
Q
ch(x)
A
1 + x²/2! + x⁴/4!
= Σ (x^2k) / (2k)! + o(x²ⁿ⁺¹)
6
Q
cos(x)
A
1 - x²/2! + x⁴/4!
= Σ [(-1)^k * x^2k] / (2k)! + o(x²ⁿ⁺¹)
7
Q
sin(x)
A
x - x³/3! + x⁵/5!
= Σ [(-1)^k * x^(2k+1)] / (2k+1)! + o(x²ⁿ⁺²)
8
Q
tan(x)
A
x + x³/3 + 2x⁵/15 + o(x⁶)
9
Q
th(x)
A
x - x³/3 + 2x⁵/15 + o(x⁶)
10
Q
ln(1+x)
A
x - x²/2 + x³/3
= Σ (-1)^(k+1) * (x^k)/k + o(xⁿ)
11
Q
(1+x)^a
A
1 + ax + a(a-1)x²/2! + a(a-1)(a-2)x³/3! + o(x³)
12
Q
Arctan(x)
A
x - x³/3 + x⁵/5 - x⁷/7
= Σ (-1)^k * x^(2k+1) * 1/(2k+1) + o(x²ⁿ⁺²)
13
Q
Arcsin(x)
A
x + x³/6 + 3x⁵/40 + o(x⁶)
14
Q
Formule de Taylor-Young
A
f(x) = Σ [(x-a)^k](1/k!)f(k-ième)(a) + o((x-a)ⁿ)
