[!!{tableau {matLi "%meta " "Valeur " } {matLi "%statut " "2 " } {matLi "%titre " "Calculer une limite en plus l~005c~0027infini ~005c(Questionnaire~005c) " } {matLi "%auteur " "Essonnier Nataly " } {matLi "%langage " "fr " } {matLi "%description " "Calculer une limite en l~005c~0027infini de fonctions polyn~00f4mes, logarithmes, exponentielles, quotient en utilisant les bons th~00e9or~00e8mes. " } {matLi "%discipline " "mathematiques " } {matLi "%theme " "fonction " } {matLi "%age " " " } {matLi "%niveau " "BTS " } {matLi "%mots_cles " "limites, croissance compar~00e9e " } {matLi "%fiche_pedago " " " } {matLi "%licence " " " }}] " " [!!{header [{matLi [{tablefixeSSstop [{matLi {hide [noteMaxi:120]} {hide [nbDecimales:150]}}] [{matLi [{table00SS [{matLi {mText "Note"}}] [{matLi {mText "maximale"}}]}] [{table00SS [{matLi {mText "Nombre de"}}] [{matLi {mText "d~00e9cimales"}}]}]}] {matLi [20] [1]}}]}] [{matLi [{hide [{tablefixeSSstop [{matLi {hide [nom:120]} {hide [classe:120]}}] [{matLi {mText "Nom"} {mText "Classe"}}] [{matLi {mText " "} {mText " "}}]}]}]}] [{matLi [{hide [{tablefixeSSstop [{matLi {hide [nom:120]} {hide [classe:120]} {hide [correcteur:120]} {hide [points:120]} {hide [note:120]}}] [{matLi {mText "Nom"} {mText "Classe"} {mText "Examinateur"} {mText "Points"} {mText "Note"}}] [{matLi {mText " "} {mText " "} {mText "epsilon"} [?] [?]}]}]}]}] [{matLi [{hide [{tablefixeSSstop {matLi "Annotation :" }}]}]}]}] " " " " " " "Donner le r~00e9sultat des limites suivantes. " " " "Pour chaque limite [!BQ!une seule] r~00e9ponse est possible. " "Les r~00e9ponses fausses sont p~00e9nalis~00e9es. " " " "1~005c)[!! ]" [!!{limit _[{right x +{infinity}}] (-3x^[2]+5x+2)}] "[!! ]" " " [!!{choice [{matLi [{tablefixeSSstop [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi -3 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi 0 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtnChecked}}]}] [{matLi [{hide {true}}]}]}] [{tablefixeSSstop [{matLi -{infinity} " " }] [{matLi " On ne prend que le terme de plus haut degr~00e9. On calcule : " {limit _[{right x +{infinity}}] -3x^[2]}=-3*(+{infinity})=-{infinity} " d~005c~0027apr~00e8s les th~00e9or~00e8mes sur les limites. " }]}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop [{matLi +{infinity} " " }] {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi "Forme ind~00e9termin~00e9e " } {matLi "Non, il est possible de lever l~005c~0027ind~00e9termination. " }}]}]}]}] [{matLi [{tablefixeSSstop [{matLi {hide [scoreMax:120]} {hide [scoreMin:120]} {hide [coefIncorrect:380]}}] [{matLi [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "maximum"}}]} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}] [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "minimum"}}]}] [{table00SS [{matLi {mText "Coefficient pour r~00e9ponse incorrecte"}}] [{matLi {mText "~005c(entre 1 et 4, peut ~00eatre d~00e9cimal~005c)"}}]}]}] {matLi [1] [0] [5]}}]}] [{matLi [{hide [{tablefixeSSstop [{matLi {hide [score:120]}}] [{matLi [{mText "Score"} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}]}] [{matLi {frac [1] [1]}}]}]}]}] [{matLi [{hide [{tablefixeSSstop {matLi "Annotation :" }}]}]}]}] " " "2~005c)[!! ]" [!!{limit _[{right x +{infinity}}] {frac [1-x^[2]] [2x-1]}}] "[!! ]" [!!{choice [{matLi [{tablefixeSSstop [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop [{matLi " " -{frac [1] [2]} " " }] {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi 1 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtnChecked}}]}] [{matLi [{hide {true}}]}]}] [{tablefixeSSstop [{matLi -{infinity} " " }] {matLi "On ne prend que les termes de plus haut degr~00e9 au num~00e9rateur et au d~00e9nominateur. Avant de calculer la limite,on simplifie la fraction afin de lever l~005c~0027ind~00e9termination. " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop [{matLi +{infinity} " " }] {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi "Forme ind~00e9termin~00e9e " } {matLi "Non, il est possible de lever l~005c~0027ind~00e9termination. " }}]}]}]}] [{matLi [{tablefixeSSstop [{matLi {hide [scoreMax:120]} {hide [scoreMin:120]} {hide [coefIncorrect:380]}}] [{matLi [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "maximum"}}]} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}] [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "minimum"}}]}] [{table00SS [{matLi {mText "Coefficient pour r~00e9ponse incorrecte"}}] [{matLi {mText "~005c(entre 1 et 4, peut ~00eatre d~00e9cimal~005c)"}}]}]}] {matLi [1] [0] [5]}}]}] [{matLi [{hide [{tablefixeSSstop [{matLi {hide [score:120]}}] [{matLi [{mText "Score"} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}]}] [{matLi {frac [1] [1]}}]}]}]}] [{matLi [{hide [{tablefixeSSstop {matLi "Annotation :" }}]}]}]}] " " "3~005c)[!! ]" [!!{limit _[{right x +{infinity}}] {frac {ln (x^[3]+3x+3)} [e^[x]]}}] "[!! ]" [!!{choice [{matLi [{tablefixeSSstop [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi " " 1 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtnChecked}}]}] [{matLi [{hide {true}}]}]}] [{tablefixeSSstop {matLi 0 " " } {matLi "La croissance compar~00e9e nous permet de lever l~005c~0027ind~00e9termination et de conclure. 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Avant de calculer la limite,on simplifie la fraction afin de lever l~005c~0027ind~00e9termination. " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi 1 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop [{matLi -{infinity} " " }] {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop [{matLi +{infinity} " " }] {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi "Forme ind~00e9termin~00e9e " } {matLi "Non, il est possible de lever l~005c~0027ind~00e9termination. " }}]}]}]}] [{matLi [{tablefixeSSstop [{matLi {hide [scoreMax:120]} {hide [scoreMin:120]} {hide [coefIncorrect:380]}}] [{matLi [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "maximum"}}]} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}] [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "minimum"}}]}] [{table00SS [{matLi {mText "Coefficient pour r~00e9ponse incorrecte"}}] [{matLi {mText "~005c(entre 1 et 4, peut ~00eatre d~00e9cimal~005c)"}}]}]}] {matLi [1] [0] [5]}}]}] [{matLi [{hide [{tablefixeSSstop [{matLi {hide [score:120]}}] [{matLi [{mText "Score"} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}]}] [{matLi {frac [1] [1]}}]}]}]}] [{matLi [{hide [{tablefixeSSstop {matLi "Annotation :" }}]}]}]}] " " "5~005c)[!! ]" [!!{limit _[{right x +{infinity}}] {frac [x^[2]] [{root [x]}-1]}}] "[!! ]" [!!{choice [{matLi [{tablefixeSSstop [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi " " 1 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi 0 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop [{matLi -{infinity} " " }] {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtnChecked}}]}] [{matLi [{hide {true}}]}]}] [{tablefixeSSstop [{matLi +{infinity} " " }] {matLi "On ne prend que les termes de plus haut degr~00e9 au num~00e9rateur et au d~00e9nominateur. Avant de calculer la limite,on simplifie la fraction afin de lever l~005c~0027ind~00e9termination. " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi "Forme ind~00e9termin~00e9e " } {matLi "Non, il est possible de lever l~005c~0027ind~00e9termination. " }}]}]}]}] [{matLi [{tablefixeSSstop [{matLi {hide [scoreMax:120]} {hide [scoreMin:120]} {hide [coefIncorrect:380]}}] [{matLi [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "maximum"}}]} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}] [{table00SS [{matLi {mText "Score"}}] [{matLi {mText "minimum"}}]}] [{table00SS [{matLi {mText "Coefficient pour r~00e9ponse incorrecte"}}] [{matLi {mText "~005c(entre 1 et 4, peut ~00eatre d~00e9cimal~005c)"}}]}]}] {matLi [1] [0] [5]}}]}] [{matLi [{hide [{tablefixeSSstop [{matLi {hide [score:120]}}] [{matLi [{mText "Score"} {expMathEtInfo {unaryButton {mText "?"}} {nonExpress (commandeGenerale:edite:scoreExplication 0 jauneBouton 1 ~0027Score ~005c(explications~005c)~0027)}}]}] [{matLi {frac [1] [1]}}]}]}]}] [{matLi [{hide [{tablefixeSSstop {matLi "Annotation :" }}]}]}]}] " " " " "6~005c)[!! ]" [!!{limit _[{right x +{infinity}}] {frac {ln (5x^[2]+3)} [x^[2]]}}] "[!! ]" [!!{choice [{matLi [{tablefixeSSstop [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtn}}]}] [{matLi [{hide {false}}]}]}] [{tablefixeSSstop {matLi " " 5 " " } {matLi " " }}]}] [{matLi [{table00SS [{matLi [{twoRadioBtn {radioBtnChecked}}]}] [{matLi [{hide {true}}]}]}] [{tablefixeSSstop {matLi 0 " " } {matLi "C~005c~0027est la croissance compar~00e9e qui nous permet de conclure. 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