• Épreuve de mathématiques

    Question : 1

    On considère les ensembles suivants A={ (x,y,z) 3 /z=0 } B={ (x,y,z) 3 / x 2 2y+z=1 } C={ (x,y,z) 3 /xzy=0 } D={ (x,y,z) 3 /xy+z=0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGbb Gaeyypa0ZaaiWaaeaacaGGOaGaamiEaiaacYcacaWG5bGaaiilaiaa dQhacaGGPaGaeyicI4SaeSyhHe6aaWbaaSqabeaacaaIZaaaaOGaai 4laiaadQhacqGH9aqpcaaIWaaacaGL7bGaayzFaaaabaGaamOqaiab g2da9maacmaabaGaaiikaiaadIhacaGGSaGaamyEaiaacYcacaWG6b GaaiykaiabgIGiolabl2riHoaaCaaaleqabaGaaG4maaaakiaac+ca caWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGOmaiaadMhacq GHRaWkcaWG6bGaeyypa0JaaGymaaGaay5Eaiaaw2haaaqaaiaadoea cqGH9aqpdaGadaqaaiaacIcacaWG4bGaaiilaiaadMhacaGGSaGaam OEaiaacMcacqGHiiIZcqWIDesOdaahaaWcbeqaaiaaiodaaaGccaGG VaGaamiEaiaadQhacqGHsislcaWG5bGaeyypa0JaaGimaaGaay5Eai aaw2haaaqaaiaadseacqGH9aqpdaGadaqaaiaacIcacaWG4bGaaiil aiaadMhacaGGSaGaamOEaiaacMcacqGHiiIZcqWIDesOdaahaaWcbe qaaiaaiodaaaGccaGGVaGaamiEaiabgkHiTiaadMhacqGHRaWkcaWG 6bGaeyypa0JaaGimaaGaay5Eaiaaw2haaaaaaa@865A@ Lesquels parmi ces ensembles sont des sous espaces vectoriels de ?

    Texte de la question

    On considère les ensembles suivants A={ (x,y,z) 3 /z=0 } B={ (x,y,z) 3 / x 2 2y+z=1 } C={ (x,y,z) 3 /xzy=0 } D={ (x,y,z) 3 /xy+z=0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGbb Gaeyypa0ZaaiWaaeaacaGGOaGaamiEaiaacYcacaWG5bGaaiilaiaa dQhacaGGPaGaeyicI4SaeSyhHe6aaWbaaSqabeaacaaIZaaaaOGaai 4laiaadQhacqGH9aqpcaaIWaaacaGL7bGaayzFaaaabaGaamOqaiab g2da9maacmaabaGaaiikaiaadIhacaGGSaGaamyEaiaacYcacaWG6b GaaiykaiabgIGiolabl2riHoaaCaaaleqabaGaaG4maaaakiaac+ca caWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGOmaiaadMhacq GHRaWkcaWG6bGaeyypa0JaaGymaaGaay5Eaiaaw2haaaqaaiaadoea cqGH9aqpdaGadaqaaiaacIcacaWG4bGaaiilaiaadMhacaGGSaGaam OEaiaacMcacqGHiiIZcqWIDesOdaahaaWcbeqaaiaaiodaaaGccaGG VaGaamiEaiaadQhacqGHsislcaWG5bGaeyypa0JaaGimaaGaay5Eai aaw2haaaqaaiaadseacqGH9aqpdaGadaqaaiaacIcacaWG4bGaaiil aiaadMhacaGGSaGaamOEaiaacMcacqGHiiIZcqWIDesOdaahaaWcbe qaaiaaiodaaaGccaGGVaGaamiEaiabgkHiTiaadMhacqGHRaWkcaWG 6bGaeyypa0JaaGimaaGaay5Eaiaaw2haaaaaaa@865A@ Lesquels parmi ces ensembles sont des sous espaces vectoriels de ?

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    Question : 2

    Soit W={ (x,y,z) 3 / x+yz=0et2xy=0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4vaiabg2 da9maacmaaeaqabeaacaGGOaGaamiEaiaacYcacaWG5bGaaiilaiaa dQhacaGGPaGaeyicI4SaeSyhHe6aaWbaaSqabeaacaaIZaaaaOGaai 4laaqaaiaadIhacqGHRaWkcaWG5bGaeyOeI0IaamOEaiabg2da9iaa icdacaaMc8UaaGPaVlaadwgacaWG0bGaaGPaVlaaikdacaWG4bGaey OeI0IaamyEaiabg2da9iaaicdaaaGaay5Eaiaaw2haaaaa@56D0@ :

    Texte de la question

    Soit W={ (x,y,z) 3 / x+yz=0et2xy=0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4vaiabg2 da9maacmaaeaqabeaacaGGOaGaamiEaiaacYcacaWG5bGaaiilaiaa dQhacaGGPaGaeyicI4SaeSyhHe6aaWbaaSqabeaacaaIZaaaaOGaai 4laaqaaiaadIhacqGHRaWkcaWG5bGaeyOeI0IaamOEaiabg2da9iaa icdacaaMc8UaaGPaVlaadwgacaWG0bGaaGPaVlaaikdacaWG4bGaey OeI0IaamyEaiabg2da9iaaicdaaaGaay5Eaiaaw2haaaaa@56D0@ :

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    Question : 3

    Soit A une matrice carrée d’ordre n vérifiant A 3 A= I n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaCa aaleqabaGaaG4maaaakiabgkHiTiaadgeacqGH9aqpcqGHsislcaWG jbWaaSbaaSqaaiaad6gaaeqaaaaa@3D44@ . Soit B=( I n A)( I n +A) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaiabg2 da9iaacIcacaWGjbWaaSbaaSqaaiaad6gaaeqaaOGaeyOeI0Iaamyq aiaacMcacaGGOaGaamysamaaBaaaleaacaWGUbaabeaakiabgUcaRi aadgeacaGGPaaaaa@41BF@ On considère les égalités suivantes (I) B 1 =A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaCa aaleqabaGaeyOeI0IaaGymaaaakiabg2da9iaadgeaaaa@3A69@ (II) B 1 = ( I n A) 1 ( I n +A) 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaCa aaleqabaGaeyOeI0IaaGymaaaakiabg2da9iaacIcacaWGjbWaaSba aSqaaiaad6gaaeqaaOGaeyOeI0IaamyqaiaacMcadaahaaWcbeqaai abgkHiTiaaigdaaaGccaGGOaGaamysamaaBaaaleaacaWGUbaabeaa kiabgUcaRiaadgeacaGGPaWaaWbaaSqabeaacqGHsislcaaIXaaaaa aa@4752@ (III) B 1 = ( I n +A) 1 ( I n A) 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaCa aaleqabaGaeyOeI0IaaGymaaaakiabg2da9iaacIcacaWGjbWaaSba aSqaaiaad6gaaeqaaOGaey4kaSIaamyqaiaacMcadaahaaWcbeqaai abgkHiTiaaigdaaaGccaGGOaGaamysamaaBaaaleaacaWGUbaabeaa kiabgkHiTiaadgeacaGGPaWaaWbaaSqabeaacqGHsislcaaIXaaaaa aa@4752@ Parmi lesquelles ou laquelle de ces égalités est VRAIE ?

    Texte de la question

    Soit A une matrice carrée d’ordre n vérifiant A 3 A= I n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaCa aaleqabaGaaG4maaaakiabgkHiTiaadgeacqGH9aqpcqGHsislcaWG jbWaaSbaaSqaaiaad6gaaeqaaaaa@3D44@ . Soit B=( I n A)( I n +A) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaiabg2 da9iaacIcacaWGjbWaaSbaaSqaaiaad6gaaeqaaOGaeyOeI0Iaamyq aiaacMcacaGGOaGaamysamaaBaaaleaacaWGUbaabeaakiabgUcaRi aadgeacaGGPaaaaa@41BF@ On considère les égalités suivantes (I) B 1 =A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaCa aaleqabaGaeyOeI0IaaGymaaaakiabg2da9iaadgeaaaa@3A69@ (II) B 1 = ( I n A) 1 ( I n +A) 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaCa aaleqabaGaeyOeI0IaaGymaaaakiabg2da9iaacIcacaWGjbWaaSba aSqaaiaad6gaaeqaaOGaeyOeI0IaamyqaiaacMcadaahaaWcbeqaai abgkHiTiaaigdaaaGccaGGOaGaamysamaaBaaaleaacaWGUbaabeaa kiabgUcaRiaadgeacaGGPaWaaWbaaSqabeaacqGHsislcaaIXaaaaa aa@4752@ (III) B 1 = ( I n +A) 1 ( I n A) 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaCa aaleqabaGaeyOeI0IaaGymaaaakiabg2da9iaacIcacaWGjbWaaSba aSqaaiaad6gaaeqaaOGaey4kaSIaamyqaiaacMcadaahaaWcbeqaai abgkHiTiaaigdaaaGccaGGOaGaamysamaaBaaaleaacaWGUbaabeaa kiabgkHiTiaadgeacaGGPaWaaWbaaSqabeaacqGHsislcaaIXaaaaa aa@4752@ Parmi lesquelles ou laquelle de ces égalités est VRAIE ?

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    Question : 4

    Soient A, B deux matrices carrée d’ordre n, telle que I n AB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaWGUbaabeaakiabgkHiTiaadgeacaWGcbaaaa@3A68@ est inversible Alors ( I n BA) 1 = MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadM eadaWgaaWcbaGaamOBaaqabaGccqGHsislcaWGcbGaamyqaiaacMca daahaaWcbeqaaiabgkHiTiaaigdaaaGccqGH9aqpaaa@3EA6@

    Texte de la question

    Soient A, B deux matrices carrée d’ordre n, telle que I n AB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaWGUbaabeaakiabgkHiTiaadgeacaWGcbaaaa@3A68@ est inversible Alors ( I n BA) 1 = MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadM eadaWgaaWcbaGaamOBaaqabaGccqGHsislcaWGcbGaamyqaiaacMca daahaaWcbeqaaiabgkHiTiaaigdaaaGccqGH9aqpaaa@3EA6@

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    Question : 5

    Soit g une fonction décroissante sur ] 0,+ [ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaKWiaeaaca aIWaGaaiilaiabgUcaRiabg6HiLcGaayzxaiaawUfaaaaa@3BCC@ , et G(x)= 0 x tg'(t)dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiaacI cacaWG4bGaaiykaiabg2da9maapedabaGaamiDaiaadEgacaGGNaGa aiikaiaadshacaGGPaGaamizaiaadshaaSqaaiaaicdaaeaacaWG4b aaniabgUIiYdaaaa@44C3@ définit sur ] 0,+ [ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaKWiaeaaca aIWaGaaiilaiabgUcaRiabg6HiLcGaayzxaiaawUfaaaaa@3BCC@ Laquelle parmi ces trois assertions est FAUSSE ?

    Texte de la question

    Soit g une fonction décroissante sur ] 0,+ [ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaKWiaeaaca aIWaGaaiilaiabgUcaRiabg6HiLcGaayzxaiaawUfaaaaa@3BCC@ , et G(x)= 0 x tg'(t)dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiaacI cacaWG4bGaaiykaiabg2da9maapedabaGaamiDaiaadEgacaGGNaGa aiikaiaadshacaGGPaGaamizaiaadshaaSqaaiaaicdaaeaacaWG4b aaniabgUIiYdaaaa@44C3@ définit sur ] 0,+ [ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaKWiaeaaca aIWaGaaiilaiabgUcaRiabg6HiLcGaayzxaiaawUfaaaaa@3BCC@ Laquelle parmi ces trois assertions est FAUSSE ?

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    Question : 6

    1 cosx dx= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaada WcaaqaaiaaigdaaeaaciGGJbGaai4BaiaacohacaWG4baaaaWcbeqa b0Gaey4kIipakiaadsgacaWG4bGaeyypa0daaa@3F83@

    Texte de la question

    1 cosx dx= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaada WcaaqaaiaaigdaaeaaciGGJbGaai4BaiaacohacaWG4baaaaWcbeqa b0Gaey4kIipakiaadsgacaWG4bGaeyypa0daaa@3F83@

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    Question : 7

    Soit S(m) la fonction qui associé à chaque Réel m strictement positif, la surface délimitée par le graphe et les droites x = m et x = 2m Alors

    Texte de la question

    Soit S(m) la fonction qui associé à chaque Réel m strictement positif, la surface délimitée par le graphe et les droites x = m et x = 2m Alors

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    Question : 8

    lim h0 1 h ln(1+ h π )= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIgacqGHsgIRcaaIWaaabeaakmaa laaabaGaaGymaaqaaiaadIgaaaGaciiBaiaac6gacaGGOaGaaGymai abgUcaRmaalaaabaGaamiAaaqaaiabec8aWbaacaGGPaGaeyypa0da aa@46F0@

    Texte de la question

    lim h0 1 h ln(1+ h π )= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIgacqGHsgIRcaaIWaaabeaakmaa laaabaGaaGymaaqaaiaadIgaaaGaciiBaiaac6gacaGGOaGaaGymai abgUcaRmaalaaabaGaamiAaaqaaiabec8aWbaacaGGPaGaeyypa0da aa@46F0@

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    Question : 9

    lim n+ ( 3 3 )( 3 6 )...( 3 2n )= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGHRaWkcqGHEisP aeqaaOGaaiikamaakeaabaGaaG4maaWcbaGaaG4maaaakiaacMcaca GGOaWaaOqaaeaacaaIZaaaleaacaaI2aaaaOGaaiykaiaac6cacaGG UaGaaiOlaiaacIcadaGcbaqaaiaaiodaaSqaaiaaikdacaWGUbaaaO Gaaiykaiabg2da9aaa@4B36@

    Texte de la question

    lim n+ ( 3 3 )( 3 6 )...( 3 2n )= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGHRaWkcqGHEisP aeqaaOGaaiikamaakeaabaGaaG4maaWcbaGaaG4maaaakiaacMcaca GGOaWaaOqaaeaacaaIZaaaleaacaaI2aaaaOGaaiykaiaac6cacaGG UaGaaiOlaiaacIcadaGcbaqaaiaaiodaaSqaaiaaikdacaWGUbaaaO Gaaiykaiabg2da9aaa@4B36@

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    Question : 10

    Soit f(x)= x lnx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9iaadIhadaahaaWcbeqaaiGacYgacaGG UbGaamiEaaaaaaa@3E49@ . La tangente à la courbe de f au point x=e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 da9iaadwgaaaa@38E4@ est donnée par

    Texte de la question

    Soit f(x)= x lnx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9iaadIhadaahaaWcbeqaaiGacYgacaGG UbGaamiEaaaaaaa@3E49@ . La tangente à la courbe de f au point x=e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 da9iaadwgaaaa@38E4@ est donnée par

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    Question : 11

    Soit ( x n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadI hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A95@ une suite numérique telle que x 0 =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaaIWaaabeaakiabg2da9iaaigdaaaa@39A5@ Alors i=1 n ( x i1 + 1 2 )= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaaca GGOaGaamiEamaaBaaaleaacaWGPbGaeyOeI0IaaGymaaqabaaabaGa amyAaiabg2da9iaaigdaaeaacaWGUbaaniabggHiLdGccqGHRaWkda WcaaqaaiaaigdaaeaacaaIYaaaaiaacMcacqGH9aqpaaa@4461@

    Texte de la question

    Soit ( x n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadI hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A95@ une suite numérique telle que x 0 =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaaIWaaabeaakiabg2da9iaaigdaaaa@39A5@ Alors i=1 n ( x i1 + 1 2 )= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaabCaeaaca GGOaGaamiEamaaBaaaleaacaWGPbGaeyOeI0IaaGymaaqabaaabaGa amyAaiabg2da9iaaigdaaeaacaWGUbaaniabggHiLdGccqGHRaWkda WcaaqaaiaaigdaaeaacaaIYaaaaiaacMcacqGH9aqpaaa@4461@

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    Question : 12

    Soit ( u n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacw hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A91@ une suite numérique à termes strictement positifs vérifiant ( u n ) 1 n M;n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadw hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaWbaaSqabeaadaWcaaqa aiaaigdaaeaacaWGUbaaaaaakiabgsMiJkaad2eacaGG7aGaeyiaIi IaamOBaiabgIGiolablwriLcaa@4361@ tel que M1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytaiablQ NiWjaaigdaaaa@3921@ . On définit la suite ( W n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacE fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A73@ par ( W n ) n = k=0 n u k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadE fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aOGaeyypa0ZaaabCaeaacaWG1bWaaSbaaSqaaiaadUgaaeqaaaqaai aadUgacqGH9aqpcaaIWaaabaGaamOBaaqdcqGHris5aaaa@4374@ . On considère les assertions suivantes : (I) ( W n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacE fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A73@ est convergente (II) ( u n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacw hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A91@ est bornée (III) lim n u n =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGHEisPaeqaaOGa amyDamaaBaaaleaacaWGUbaabeaakiabg2da9iaaicdaaaa@413E@ Laquelle (lesquelles) des assertions est (sont) VAIRE(S) ?

    Texte de la question

    Soit ( u n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacw hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A91@ une suite numérique à termes strictement positifs vérifiant ( u n ) 1 n M;n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadw hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaWbaaSqabeaadaWcaaqa aiaaigdaaeaacaWGUbaaaaaakiabgsMiJkaad2eacaGG7aGaeyiaIi IaamOBaiabgIGiolablwriLcaa@4361@ tel que M1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytaiablQ NiWjaaigdaaaa@3921@ . On définit la suite ( W n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacE fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A73@ par ( W n ) n = k=0 n u k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadE fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aOGaeyypa0ZaaabCaeaacaWG1bWaaSbaaSqaaiaadUgaaeqaaaqaai aadUgacqGH9aqpcaaIWaaabaGaamOBaaqdcqGHris5aaaa@4374@ . On considère les assertions suivantes : (I) ( W n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacE fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A73@ est convergente (II) ( u n ) n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaacw hadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gaaeqa aaaa@3A91@ est bornée (III) lim n u n =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGHEisPaeqaaOGa amyDamaaBaaaleaacaWGUbaabeaakiabg2da9iaaicdaaaa@413E@ Laquelle (lesquelles) des assertions est (sont) VAIRE(S) ?

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    Question : 13

    Pour quelle valeur de x , la fonction définie par f(x)= 2 x 2 3x e t 2 dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9maapedabaGaamyzamaaCaaaleqabaGa amiDamaaCaaameqabaGaaGOmaaaaaaGccaWGKbGaamiDaaWcbaGaey OeI0IaaGOmaaqaaiaadIhadaahaaadbeqaaiaaikdaaaWccqGHsisl caaIZaGaamiEaaqdcqGHRiI8aaaa@478F@ prend une valeur minimale

    Texte de la question

    Pour quelle valeur de x , la fonction définie par f(x)= 2 x 2 3x e t 2 dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9maapedabaGaamyzamaaCaaaleqabaGa amiDamaaCaaameqabaGaaGOmaaaaaaGccaWGKbGaamiDaaWcbaGaey OeI0IaaGOmaaqaaiaadIhadaahaaadbeqaaiaaikdaaaWccqGHsisl caaIZaGaamiEaaqdcqGHRiI8aaaa@478F@ prend une valeur minimale

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    Question : 14

    Soit f(x)= 0 x 1 t 3 +2 dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9maapedabaWaaSaaaeaacaaIXaaabaWa aOaaaeaacaWG0bWaaWbaaSqabeaacaaIZaaaaOGaey4kaSIaaGOmaa WcbeaaaaGccaWGKbGaamiDaaWcbaGaaGimaaqaaiaadIhaa0Gaey4k Iipaaaa@447B@ laquelle parmi ces trois assertions est FAUSSE ?

    Texte de la question

    Soit f(x)= 0 x 1 t 3 +2 dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9maapedabaWaaSaaaeaacaaIXaaabaWa aOaaaeaacaWG0bWaaWbaaSqabeaacaaIZaaaaOGaey4kaSIaaGOmaa WcbeaaaaGccaWGKbGaamiDaaWcbaGaaGimaaqaaiaadIhaa0Gaey4k Iipaaaa@447B@ laquelle parmi ces trois assertions est FAUSSE ?

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    Question : 15

    lim x0 e 2x 1 tanx = MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIWaaabeaakmaa laaabaGaamyzamaaCaaaleqabaGaaGOmaiaadIhaaaGccqGHsislca aIXaaabaGaciiDaiaacggacaGGUbGaamiEaaaacqGH9aqpaaa@4614@

    Texte de la question

    lim x0 e 2x 1 tanx = MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIWaaabeaakmaa laaabaGaamyzamaaCaaaleqabaGaaGOmaiaadIhaaaGccqGHsislca aIXaaabaGaciiDaiaacggacaGGUbGaamiEaaaacqGH9aqpaaa@4614@

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    Question : 16

    lim x1 1 x 2 1 1 x e u 2 du= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIXaaabeaakmaa laaabaGaaGymaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsi slcaaIXaaaamaapedabaGaamyzamaaCaaaleqabaGaamyDamaaCaaa meqabaGaaGOmaaaaaaGccaWGKbGaamyDaiabg2da9aWcbaGaaGymaa qaaiaadIhaa0Gaey4kIipaaaa@4AE1@

    Texte de la question

    lim x1 1 x 2 1 1 x e u 2 du= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIXaaabeaakmaa laaabaGaaGymaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsi slcaaIXaaaamaapedabaGaamyzamaaCaaaleqabaGaamyDamaaCaaa meqabaGaaGOmaaaaaaGccaWGKbGaamyDaiabg2da9aWcbaGaaGymaa qaaiaadIhaa0Gaey4kIipaaaa@4AE1@

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    Question : 17

    Soit f une fonction deux fois dérivables telle que f''(x)=2f'(x) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE cacaGGNaGaaiikaiaadIhacaGGPaGaeyypa0JaaGOmaiaadAgacaGG NaGaaiikaiaadIhacaGGPaaaaa@403C@ avec f'(0)=f(0)=e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE cacaGGOaGaaGimaiaacMcacqGH9aqpcaWGMbGaaiikaiaaicdacaGG PaGaeyypa0Jaamyzaaaa@3F94@ Alors f(1)= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaaIXaGaaiykaiabg2da9aaa@39FC@

    Texte de la question

    Soit f une fonction deux fois dérivables telle que f''(x)=2f'(x) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE cacaGGNaGaaiikaiaadIhacaGGPaGaeyypa0JaaGOmaiaadAgacaGG NaGaaiikaiaadIhacaGGPaaaaa@403C@ avec f'(0)=f(0)=e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE cacaGGOaGaaGimaiaacMcacqGH9aqpcaWGMbGaaiikaiaaicdacaGG PaGaeyypa0Jaamyzaaaa@3F94@ Alors f(1)= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaaIXaGaaiykaiabg2da9aaa@39FC@

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    Question : 18

    1 2 (lnx) 2 dx= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qmaeaaca GGOaGaciiBaiaac6gacaWG4bGaaiykamaaCaaaleqabaGaaGOmaaaa aeaacaaIXaaabaGaaGOmaaqdcqGHRiI8aOGaamizaiaadIhacqGH9a qpaaa@41A5@

    Texte de la question

    1 2 (lnx) 2 dx= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qmaeaaca GGOaGaciiBaiaac6gacaWG4bGaaiykamaaCaaaleqabaGaaGOmaaaa aeaacaaIXaaabaGaaGOmaaqdcqGHRiI8aOGaamizaiaadIhacqGH9a qpaaa@41A5@

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    Question : 19

    Soient f,g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacY cacaWGNbaaaa@387E@ et h trois fonctions telles que : { h(x)=f( x 3 ) f'(x)=g(x) g'(x)=f( x 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe qaaiaadIgacaGGOaGaamiEaiaacMcacqGH9aqpcaWGMbGaaiikaiaa dIhadaahaaWcbeqaaiaaiodaaaGccaGGPaaabaGaamOzaiaacEcaca GGOaGaamiEaiaacMcacqGH9aqpcaWGNbGaaiikaiaadIhacaGGPaaa baGaam4zaiaacEcacaGGOaGaamiEaiaacMcacqGH9aqpcaWGMbGaai ikaiaadIhadaahaaWcbeqaaiaaikdaaaGccaGGPaaaaiaawUhaaaaa @50F2@ Alors h''(x)= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaiaacE cacaGGNaGaaiikaiaadIhacaGGPaGaeyypa0daaa@3B96@

    Texte de la question

    Soient f,g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacY cacaWGNbaaaa@387E@ et h trois fonctions telles que : { h(x)=f( x 3 ) f'(x)=g(x) g'(x)=f( x 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe qaaiaadIgacaGGOaGaamiEaiaacMcacqGH9aqpcaWGMbGaaiikaiaa dIhadaahaaWcbeqaaiaaiodaaaGccaGGPaaabaGaamOzaiaacEcaca GGOaGaamiEaiaacMcacqGH9aqpcaWGNbGaaiikaiaadIhacaGGPaaa baGaam4zaiaacEcacaGGOaGaamiEaiaacMcacqGH9aqpcaWGMbGaai ikaiaadIhadaahaaWcbeqaaiaaikdaaaGccaGGPaaaaiaawUhaaaaa @50F2@ Alors h''(x)= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaiaacE cacaGGNaGaaiikaiaadIhacaGGPaGaeyypa0daaa@3B96@

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    Question : 20

    Soit ( V n ) n3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadA fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gacqGH LjYScaaIZaaabeaaaaa@3CF6@ la suite définie par V n = 1 n x (1+ x 2 ) 2 dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaWGUbaabeaakiabg2da9maapedabaWaaSaaaeaacaWG4baa baGaaiikaiaaigdacqGHRaWkcaWG4bWaaWbaaSqabeaacaaIYaaaaO GaaiykamaaCaaaleqabaGaaGOmaaaaaaaabaGaaGymaaqaaiaad6ga a0Gaey4kIipakiaadsgacaWG4baaaa@4599@ Alors lim n V n = MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGHEisPaeqaaOGa amOvamaaBaaaleaacaWGUbaabeaakiabg2da9aaa@4065@

    Texte de la question

    Soit ( V n ) n3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadA fadaWgaaWcbaGaamOBaaqabaGccaGGPaWaaSbaaSqaaiaad6gacqGH LjYScaaIZaaabeaaaaa@3CF6@ la suite définie par V n = 1 n x (1+ x 2 ) 2 dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaWGUbaabeaakiabg2da9maapedabaWaaSaaaeaacaWG4baa baGaaiikaiaaigdacqGHRaWkcaWG4bWaaWbaaSqabeaacaaIYaaaaO GaaiykamaaCaaaleqabaGaaGOmaaaaaaaabaGaaGymaaqaaiaad6ga a0Gaey4kIipakiaadsgacaWG4baaaa@4599@ Alors lim n V n = MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGHEisPaeqaaOGa amOvamaaBaaaleaacaWGUbaabeaakiabg2da9aaa@4065@

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    Question : 21

    Soit H(x)= x e x 1 lnt dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacI cacaWG4bGaaiykaiabg2da9maapedabaWaaSaaaeaacaaIXaaabaWa aOaaaeaaciGGSbGaaiOBaiaadshaaSqabaaaaaqaamaakaaabaGaam iEaaadbeaaaSqaaiaadwgadaahaaadbeqaaiaadIhaaaaaniabgUIi YdGccaWGKbGaamiDaaaa@4526@ , alors H'(x)= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacE cacaGGOaGaamiEaiaacMcacqGH9aqpaaa@3ACB@

    Texte de la question

    Soit H(x)= x e x 1 lnt dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacI cacaWG4bGaaiykaiabg2da9maapedabaWaaSaaaeaacaaIXaaabaWa aOaaaeaaciGGSbGaaiOBaiaadshaaSqabaaaaaqaamaakaaabaGaam iEaaadbeaaaSqaaiaadwgadaahaaadbeqaaiaadIhaaaaaniabgUIi YdGccaWGKbGaamiDaaaa@4526@ , alors H'(x)= MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacE cacaGGOaGaamiEaiaacMcacqGH9aqpaaa@3ACB@

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    Question : 22

    Soit h(x)= e x 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaiaacI cacaWG4bGaaiykaiabg2da9maakaaabaGaamyzamaaCaaaleqabaGa amiEaaaakiabgkHiTiaaigdaaSqabaaaaa@3E21@ Une primitive de h(x) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaiaacI cacaWG4bGaaiykaaaa@393A@ est donnée par

    Texte de la question

    Soit h(x)= e x 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaiaacI cacaWG4bGaaiykaiabg2da9maakaaabaGaamyzamaaCaaaleqabaGa amiEaaaakiabgkHiTiaaigdaaSqabaaaaa@3E21@ Une primitive de h(x) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaiaacI cacaWG4bGaaiykaaaa@393A@ est donnée par

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    Question : 23

    La fonction f(x)=acosx+bsinx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9iaadggaciGGJbGaai4BaiaacohacaWG 4bGaey4kaSIaamOyaiGacohacaGGPbGaaiOBaiaadIhaaaa@4492@ admet comme amplitude le nombre

    Texte de la question

    La fonction f(x)=acosx+bsinx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacaWG4bGaaiykaiabg2da9iaadggaciGGJbGaai4BaiaacohacaWG 4bGaey4kaSIaamOyaiGacohacaGGPbGaaiOBaiaadIhaaaa@4492@ admet comme amplitude le nombre

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    Question : 24

    Soit B={ u,v,w } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaiabg2 da9maacmaabaGaamyDaiaacYcacaWG2bGaaiilaiaadEhaaiaawUha caGL9baaaaa@3E46@ une base de ( 3 ,+,) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiabl2 riHoaaCaaaleqabaGaaG4maaaakiaacYcacqGHRaWkcaGGSaGaeyyX ICTaaiykaaaa@3E40@ . On considère les familles suivantes A={ uv,u+w,v+w }  B={ u,v2u,v } C={ u+v+w,v+w,w } D={ v+w,v,w } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGbb Gaeyypa0ZaaiWaaeaacaWG1bGaeyOeI0IaamODaiaacYcacaWG1bGa ey4kaSIaam4DaiaacYcacaWG2bGaey4kaSIaam4DaaGaay5Eaiaaw2 haaaqaaabaaaaaaaaapeGaaiiOa8aacaWGcbGaeyypa0ZaaiWaaeaa caWG1bGaaiilaiaadAhacqGHsislcaaIYaGaamyDaiaacYcacaWG2b aacaGL7bGaayzFaaaabaGaam4qaiabg2da9maacmaabaGaamyDaiab gUcaRiaadAhacqGHRaWkcaWG3bGaaiilaiaadAhacqGHRaWkcaWG3b GaaiilaiaadEhaaiaawUhacaGL9baaaeaacaWGebGaeyypa0ZaaiWa aeaacaWG2bGaey4kaSIaam4DaiaacYcacqGHsislcaWG2bGaaiilai abgkHiTiaadEhaaiaawUhacaGL9baaaaaa@6A27@ Alors laquelle (ou lesquelles) des familles forme une base ?

    Texte de la question

    Soit B={ u,v,w } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaiabg2 da9maacmaabaGaamyDaiaacYcacaWG2bGaaiilaiaadEhaaiaawUha caGL9baaaaa@3E46@ une base de ( 3 ,+,) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiabl2 riHoaaCaaaleqabaGaaG4maaaakiaacYcacqGHRaWkcaGGSaGaeyyX ICTaaiykaaaa@3E40@ . On considère les familles suivantes A={ uv,u+w,v+w }  B={ u,v2u,v } C={ u+v+w,v+w,w } D={ v+w,v,w } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGbb Gaeyypa0ZaaiWaaeaacaWG1bGaeyOeI0IaamODaiaacYcacaWG1bGa ey4kaSIaam4DaiaacYcacaWG2bGaey4kaSIaam4DaaGaay5Eaiaaw2 haaaqaaabaaaaaaaaapeGaaiiOa8aacaWGcbGaeyypa0ZaaiWaaeaa caWG1bGaaiilaiaadAhacqGHsislcaaIYaGaamyDaiaacYcacaWG2b aacaGL7bGaayzFaaaabaGaam4qaiabg2da9maacmaabaGaamyDaiab gUcaRiaadAhacqGHRaWkcaWG3bGaaiilaiaadAhacqGHRaWkcaWG3b GaaiilaiaadEhaaiaawUhacaGL9baaaeaacaWGebGaeyypa0ZaaiWa aeaacaWG2bGaey4kaSIaam4DaiaacYcacqGHsislcaWG2bGaaiilai abgkHiTiaadEhaaiaawUhacaGL9baaaaaa@6A27@ Alors laquelle (ou lesquelles) des familles forme une base ?

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    Question : 25

    Soit F={ (x,y,z) 3 /x3z=0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiabg2 da9maacmaabaGaaiikaiaadIhacaGGSaGaamyEaiaacYcacaWG6bGa aiykaiabgIGiolabl2riHoaaCaaaleqabaGaaG4maaaakiaac+caca WG4bGaeyOeI0IaaG4maiaadQhacqGH9aqpcaaIWaaacaGL7bGaayzF aaaaaa@49AD@ . Lequel des systèmes suivants forme une base pour F ?

    Texte de la question

    Soit F={ (x,y,z) 3 /x3z=0 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiabg2 da9maacmaabaGaaiikaiaadIhacaGGSaGaamyEaiaacYcacaWG6bGa aiykaiabgIGiolabl2riHoaaCaaaleqabaGaaG4maaaakiaac+caca WG4bGaeyOeI0IaaG4maiaadQhacqGH9aqpcaaIWaaacaGL7bGaayzF aaaaaa@49AD@ . Lequel des systèmes suivants forme une base pour F ?

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