Quiz — serie 17 p1.pdf

Question 1 sur 5 10:00

[{"id":26609,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x - 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 + 2x\", \"c\": \"6x - 5\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":26610,"question":"Quelle est la primitive de la fonction f(x) = 4x³ ?","option_a":"x⁴ + C","option_b":"12x² + C","option_c":"x³ + C","option_d":"4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive d'une fonction polynôme s'obtient en augmentant l'exposant de 1 et en divisant par le nouvel exposant : F(x) = x⁴ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x⁴ + C\", \"b\": \"12x² + C\", \"c\": \"x³ + C\", \"d\": \"4x⁴ + C\"}}","_debug_options_count":4},{"id":26611,"question":"Quel est le résultat de l'intégrale ∫(2x + 3) dx ?","option_a":"x² + 3x + C","option_b":"x² + 3","option_c":"2x² + 3x + C","option_d":"x + 3x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale d'une fonction linéaire s'obtient en intégrant chaque terme séparément : ∫2x dx + ∫3 dx = x² + 3x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + 3x + C\", \"b\": \"x² + 3\", \"c\": \"2x² + 3x + C\", \"d\": \"x + 3x","_debug_options_count":4},{"id":26612,"question":"Quelle est la solution de l'équation différentielle y' = 2y ?","option_a":"y = Ce^(2x)","option_b":"y = 2Ce^x","option_c":"y = Ce^x","option_d":"y = 2x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle y' = 2y a pour solution générale y = Ce^(2x), où C est une constante réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"y = Ce^(2x)\", \"b\": \"y = 2Ce^x\", \"c\": \"y = Ce^x\", \"d\": \"y = 2x + C","_debug_options_count":4},{"id":26613,"question":"Quelle est la valeur de l'intégrale ∫(1\/x) dx ?","option_a":"ln|x| + C","option_b":"x + C","option_c":"1\/x + C","option_d":"e^x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 1\/x est ln|x| + C, car la dérivée de ln|x| est 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\": \"ln|x| + C\", \"b\": \"x + C\", \"c\": \"1\/x + C\", \"d\": \"e^x + C\"}}","_debug_options_count":4}]