Quiz — devoir-de-contrôle-n°5--2013-2014[ibn-khaldoun-rades].pdf

Question 1 sur 10 20:00

[{"id":68176,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x + 2x - 5\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":68177,"question":"La limite de la fonction 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":"a","explication":"En simplifiant, f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1. Donc lim(x→1) f(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":68178,"question":"Quelle est la dérivée de la fonction f(x) = sin(2x) ?","option_a":"cos(2x)","option_b":"2cos(2x)","option_c":"2sin(x)","option_d":"cos(x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la règle de dérivation des fonctions composées, f'(x) = 2cos(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"cos(2x)\", \"b\": \"2cos(2x)\", \"c\": \"2sin(x)\", \"d\": \"cos(x)\"}}","_debug_options_count":4},{"id":68179,"question":"La suite définie par uₙ = n²\/(n+1) est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite uₙ = n²\/(n+1) tend vers l'infini quand n tend vers l'infini, donc elle est divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":68180,"question":"Quelle est la limite de la fonction f(x) = (3x + 1)\/(2x - 5) quand x tend vers l'infini ?","option_a":"3\/2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les fonctions rationnelles, la limite à l'infini est le rapport des coefficients dominants : 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\/2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":68181,"question":"La dérivée de la fonction f(x) = e^(3x) est f'(x) = 3e^(3x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la règle de dérivation des fonctions exponentielles, f'(x) = 3e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":68182,"question":"Quelle est la dérivée seconde de la fonction f(x) = x³ - 2x² + x ?","option_a":"6x - 4","option_b":"3x² - 4x + 1","option_c":"6x² - 4x","option_d":"6x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée première est f'(x) = 3x² - 4x + 1, et la dérivée seconde est f''(x) = 6x - 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x - 4\", \"b\": \"3x² - 4x + 1\", \"c\": \"6x² - 4x\", \"d\": \"6x - 2\"}}","_debug_options_count":4},{"id":68183,"question":"La suite définie par uₙ = 1\/n est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite uₙ = 1\/n tend vers 0 quand n tend vers l'infini, donc elle est convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":68184,"question":"Quelle est la limite de la fonction f(x) = (x² + 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"2","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le numérateur tend vers 2 et le dénominateur tend vers 0, donc la limite est infinie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"2\"}}","_debug_options_count":4},{"id":68185,"question":"La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien est bien f'(x) = 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]