Quiz interactif : Maîtrisez les fonctions dérivées et les limites en Terminale Math

Question 1 sur 10 10:00

[{"id":57301,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2","option_d":"6x + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x et (2x)' = 2. La constante -5 a une dérivée nulle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57302,"question":"La limite de f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction n'est pas définie en x=1, mais la limite existe et vaut 2 après simplification (x+1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57303,"question":"Quelle est la limite de f(x) = 1\/x quand x tend vers 0+ ?","option_a":"0","option_b":"+∞","option_c":"-∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Quand x tend vers 0 par valeurs positives, 1\/x tend vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57304,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 est divergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique de raison |q| \u003E 1 est divergente (ici, q=2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57305,"question":"Quelle est la dérivée de f(x) = e^(3x) ?","option_a":"3e^(3x)","option_b":"e^(3x)","option_c":"3x e^(3x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x)=3x donc u'(x)=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57306,"question":"La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle [0, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x est négative sur [0,2] (ex: f'(1)=-3), donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57307,"question":"Quelle est la limite de f(x) = (sin x)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"+∞","option_d":"Indéterminée","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une limite classique qui vaut 1 (théorème des gendarmes ou développement limité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57308,"question":"Une suite arithmétique de raison r = -2 et de premier terme u₀ = 5 est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite arithmétique est convergente si et seulement si sa raison est nulle (r=0). Ici, r=-2, donc elle est divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57309,"question":"Quelle est la dérivée de f(x) = ln(2x + 1) ?","option_a":"2\/(2x + 1)","option_b":"1\/(2x + 1)","option_c":"2x\/(2x + 1)","option_d":"1\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u(x)) est u'(x)\/u(x). Ici, u(x)=2x+1 donc u'(x)=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57310,"question":"La fonction f(x) = x² - 4x + 3 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x)=2x-4 s'annule en x=2. Comme f''(x)=2\u003E0, c'est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]