Quiz : Testez vos connaissances en analyse mathématique (Terminale)

Question 1 sur 10 10:00

[{"id":64722,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) quand x tend vers 2 ?","option_a":"0","option_b":"4","option_c":"Indéterminée","option_d":"2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction se simplifie en f(x) = x + 2 (pour x ≠ 2), donc la limite est 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64723,"question":"Une fonction continue sur un intervalle est toujours dérivable sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. Exemple : la fonction f(x) = |x| est continue en 0 mais non dérivable en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64724,"question":"Quelle est la dérivée de la fonction f(x) = ln(x² + 1) ?","option_a":"2x \/ (x² + 1)","option_b":"1 \/ (x² + 1)","option_c":"2x","option_d":"ln(2x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la règle de la chaîne, f'(x) = (2x) \/ (x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64725,"question":"L'intégrale de 0 à 1 de la fonction f(x) = 3x² est égale à :","option_a":"1","option_b":"3","option_c":"0","option_d":"x³","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de 3x² est x³, donc [x³] de 0 à 1 = 1 - 0 = 1. La bonne réponse est donc 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64726,"question":"La suite u_n = (-1)^n est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La suite alterne entre -1 et 1 et n'a pas de limite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64727,"question":"Quelle est la dérivée seconde de la fonction f(x) = e^(3x) ?","option_a":"3e^(3x)","option_b":"9e^(3x)","option_c":"e^(3x)","option_d":"3x e^(3x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée première est 3e^(3x), et la dérivée seconde est 9e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64728,"question":"L'intégrale de -1 à 1 de la fonction f(x) = x^3 est égale à :","option_a":"0","option_b":"2","option_c":"1","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction x^3 est impaire, donc son intégrale sur [-1, 1] est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64729,"question":"Une fonction dérivable en un point est toujours continue en ce point.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. La dérivabilité implique la continuité.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64730,"question":"Quelle est la limite de la suite u_n = (n² + 1)\/n quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"l'infini","option_d":"n","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n, on obtient u_n = n + 1\/n, donc la limite est l'infini.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64731,"question":"Le théorème des valeurs intermédiaires s'applique à toute fonction continue sur un intervalle fermé.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. C'est l'énoncé même du théorème des valeurs intermédiaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]