Corrige UTBM Bases d algebre et d analyse 2008 TC

,odejuini2008,tduréestrictement2,heures4.Corrigé2.UTBMvoitCorrigéalisedénal2MT11,dePrinsoittemps.2008ourExerciceson1c1.aussiS.V.Pctionpage,la,ournerdeTductibles1.pagentempséPrinenMT11,.arD'oùenant.Eninsi,6.24Onlevériie3.que-1Aacine.AOrne.r3.oissante:DoncdonneestquiompCeen.d'irrcritps'é(c..2.onoungpaylor-YacineTle).desformuleEnaobtientLpr.etDoncmultipliant.on.enarpc.).para.(c.c.image.surobtientervalonnes,etosé.pOnom-quecestfonctionsrdesdedérivation.deinsi,mebijeèuréoetthésurlecrantestapplic.Enqui.lab.c.ositionsurourclasseprdeduits.éestsurque1.alorsExerciceearmontrFinalement,Ond'où.obtientest,irr'aéasductiblersruelrAsurndérivablei,aévaluantser.(son,discriminantonestenantné.gatifen),,etpdoncEnlaobtientdé,cprompetositionardemultipliantdonc.est,0 3 0B (X) = 4X −2X +2 B(−1) =B (−1) = 02 2 2 2 2B(X) = (X+1) Q(X) = (X +2X+1)Q(X) = (X +2X+1)(X −2X+2) X −2X+2R[X] B2 2B(X) = (X +1) (X −2X +2)2A A(X) = (X + 1)(2X − 3X + 5)2A R[X] 2X −3X+5PGCD(A,B) =X +122X −3X +5 a bX +cF(X) = = +2 2(X +1)(X −2X +2 X +1 X −2X +2(X +1) X =−1 a = 2X X → +∞ 2 =a+b b = 05 cX = 0 =a+ c = 12 22 1F(X) = +2X +1 X −2X +2π π0 sinxf (x) = cosx e + 1 > 0 x∈]0, [ f [0, ]2 2π[f(0),f ] = [1,e+1]20 πf (x) = 0 x∈ [0, [ g [1,e+1[ g22 ...