Quiz — 34.DOC

Question 1 sur 10 20:00

[{"id":102926,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"c","explication":"En simplifiant l'expression, on obtient f(x) = x + 1 pour x ≠ 1. La limite est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. 2\", \"d\": \"D. La limite n'existe pas\"","_debug_options_count":4},{"id":102927,"question":"La dérivée de la fonction f(x) = ln(x) est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, qui est positive pour x \u003E 0 mais indéfinie pour x ≤ 0.","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":102928,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"A. x³ + x² + C","option_b":"B. x³ + x + C","option_c":"C. 6x + 2 + C","option_d":"D. 3x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 3x² est x³ et celle de 2x est x². La constante d'intégration C est ajoutée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x³ + x² + C\", \"b\": \"B. x³ + x + C\", \"c\": \"C. 6x + 2 + C\", \"","_debug_options_count":4},{"id":102929,"question":"Un nombre complexe z = a + ib a pour module |z| = √(a² + b²). Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + ib est bien défini par |z| = √(a² + b²).","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":102930,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(2x)","option_b":"B. y = Ce^(-2x)","option_c":"C. y = Ce^(x\/2)","option_d":"D. y = Ce^(-x\/2)","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation caractéristique est r + 2 = 0, donc r = -2. La solution générale est y = Ce^(-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\": \"A. y = Ce^(2x)\", \"b\": \"B. y = Ce^(-2x)\", \"c\": \"C. y = Ce^(x\/2)\", ","_debug_options_count":4},{"id":102931,"question":"La suite définie par uₙ = n²\/(n+1) est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite tend vers l'infini lorsque n tend vers l'infini, donc elle n'est pas convergente.","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":102932,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. -1","option_d":"D. Leur norme","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs orthogonaux ont un produit scalaire égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. -1\", \"d\": \"D. Leur norme\"}}","_debug_options_count":4},{"id":102933,"question":"La fonction f(x) = e^(-x²) est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = e^(-x²) = f(x), donc elle est paire.","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":102934,"question":"Quel est le développement limité de sin(x) à l'ordre 3 au voisinage de 0 ?","option_a":"A. x - x³\/6 + o(x³)","option_b":"B. x + x³\/6 + o(x³)","option_c":"C. x - x²\/2 + o(x²)","option_d":"D. 1 - x²\/2 + o(x²)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le développement limité de sin(x) à l'ordre 3 est x - x³\/6 + o(x³).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x - x³\/6 + o(x³)\", \"b\": \"B. x + x³\/6 + o(x³)\", \"c\": \"C. x ","_debug_options_count":4},{"id":102935,"question":"La probabilité d'un événement certain est-elle égale à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, la probabilité d'un événement certain est 1.","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}]