DL Flashcards

1
Q

O

A

f=O(g) en a ssi il existe M>=0 tq
|f(x)|<=M|g(x)| au voisinage de a
ssi il existe h bornée au voisinage de a tq f=gh

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2
Q

o

A

f=o(g) ssi pour tout e>0 il existe un voisinage de a sur lequel |f|<=e|g|
ssi il existe une fonction h tendant vers 0 tq
f=hg

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3
Q

~

A

f~g ssi f-g=o(g)

ssi il existe h tendant vers 1 tq f=hg

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4
Q

si f~g et si g ne prend pas la valeur 1

A

ln(f)~ln(g)

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5
Q

DL

A

f admet un DLn(a) si il existe une fonction e tendant vers 0 tq
f(x)=sum(k=0..n)((x-a)^kak) +((x-a)^n)e(x)

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6
Q

Taylor - Young

A

si f est Cn au voisinage de t0, alors f admet un DLn(t0) :
f(t)=sum(k=0..n)((t-t0)^n)f^(k)(t0)/(k!)
+o((t-t0)^n)

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7
Q

DL usuel en 0

A

(1+x)^a=1+ax+a(a-1)/2!x²+a(a-1)(a-2)/3!x^3

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8
Q

Dérivée de Asin
Primitive de Asin
Déduction pour Acos

A

Asin’(x)= 1/(1-x²)^(1/2)
(x*Asin(x)+(1-x²)^(1/2))’=Acos(x)
Asin + Acos = Pi/2

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