[PDF] Chapitre6 : Comparaison de fonctions

View - Download Chapitre6 : Comparaison de fonctions

Previous PDF

Next PDF

D Ra ¯R Dztau fghf1g1Ę

DR

0a af=εg

f=o(g) a f(x)g(x)xPD f

Va @xPDXV,f(x) =ε(x)g(x)

f(x) =o(g(x)) ax x2=o(x3) +8 g

DXV ɍV a

f g a af g = 0 g

DXVztau ɍV af g a

f(a) = 0 af g = 0 a a f=o(1) a f 0a +8 (x)γ=o(xβ)xβ=o(eαx) ' 0 α,β |x|β=o(x´α) xÑ+8e x x = +8 @ně5,2n n+1ěn n= 5 25 5+1 =32 6 =16 3 ě5 ně5 2n n+1ěn2n+1 n+2=2n2 n+2=2n n+1ˆ2(n+1) n+2ě2n(n+1) n+2 ně22něn+ 22n n+2ě1 2n+1 n+2ě2n(n+1) n+2ěn+ 1 ĕ xě5 [x] =p e x x

ěep

p+ 1ě2p p+ 1ěpěx´1 @xě5,ex x

ěx´1 xÑ+8e

x x = +8

Ŀ Ę Ę aŀ F(D,R)

f1=o(g1)f2=o(g2) f1f2=o(g1g2) a f=o(g) h=o(g) f+h=o(g) g =o(1 f ) a +8 α,β,γ e

0a af= (1 +ε)g

f"g a f"ag @xPDXV,f(x) = (1 +ε(x))g(x) f(x)"g(x) af(x)"xÑag(x)x g

DXV ɍV a

f g a af g = 1 g

DXVztauɍV a f g a

f(a) = 0 af g = 1 f g a f=g+o(g) a 0 e x´1"xx"x(1 +x)"x

αPR,(1 +x)α´1"αxx"xx´1" ´x2

2

α x

x´1 =´22x 2 fg a f a g ā a fg ā a f"ag f"a+8 f"a0 a 0a f1"ag1f2"ag2 f1f2"ag1g2 f "a1 g f"ag nPNfn"agn f"ag fg αPRfα"agα

ā 0 1 (1 +x)2´1"037x

ā x2+x"+8x2x2+x

x

2ÝÝÝÝÑxÑ+81

e x2+x"+8ex2 x+1"+8x (x+1)x"+8xx (x+1)x x xÝÝÝÝÑxÑ+8e u D a s¯R f(x)"xÑag(x) f(u(t))"tÑsg(u(t))

ĕ f(x)"xÑag(x) xÑaf(x)

g(x)= 1 tÑsu(t) = a tÑsf(u(t)) g(u(t))= 1Ę tÑsu(t) = 0 (1 +u(t))"tÑsu(t) (1 +t2)"tÑ0t2Ę a f1"fg1"g f=o(g) f1=o(g1) f1"fg1"g f=o(g)

ε 0a f(x) =ε(x)g(x) a

εf,εg 0a f(x) = (1 +εf(x))f1(x)g(x) = (1 +εg(x))g1(x) a a(1 +εf(x))f1(x) =ε(x)ˆ(1 +εg(x))g1(x) (1 +εf(x))loooooooooomoooooooooon

Ñ0g

1(x) f1=o(g1)

x"0xx=o(? x) 0 x=o(? x) 0 nPN a0,a1,...,anPRan‰0 +8´8 a 1 n,pPNněp ap,ap+1,...,anPRap‰0 0 a +8´8 0

ā f(x) =O(g(x)) a

g

DXV ɍV a

f g a f g a g

DXVztau ɍV a f g a

f(a) = 0f g aquotesdbs_dbs29.pdfusesText_35

[PDF] Corrigé officiel complet du bac S Espagnol LV2 2010 - Sujet de bac

[PDF] l 'avion du futur Eraole - Laboratoire Océan Vital

[PDF] 2017 Erasmus+ Programme Guide - European Commission

[PDF] 2018 Erasmus+ Programme Guide v1 - European Commission

[PDF] L 'essentiel des chiffres clés - Campus France

[PDF] ERBITUX Avis 2 - HAS

[PDF] Information for applicants to the Starting and Consolidator Grant

[PDF] Information for Applicants to the Advanced Grant 2017 Call

[PDF] ERC Frontier Research Grants Information for applicants to the

[PDF] ERC Advanced Grants 2016 List of Principal Investigators #8211 All

[PDF] ERC Consolidator Grants - European Research Council - Europa EU

[PDF] ERC Consolidator Grant 2016 - European Research Council

[PDF] ERC - European Commission - Europa EU

[PDF] ERC Starting Grants 2017 List of Principal Investigators - European

[PDF] ERC Starting Grant Panel 2018 - European Research Council