Quiz — 62badf17e0852_Magazine N°15 - ( Fonctions logarithmes ).pdf

Question 1 sur 5 10:00

[{"id":272,"question":"Quelle est la valeur de ln(e^3) ?","option_a":"3","option_b":"e^3","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, ln(e^x) = x. Donc ln(e^3) = 3.","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\", \"b\": \"e^3\", \"c\": \"0\", \"d\": \"1\"}}","_debug_options_count":4},{"id":273,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"2\/(2x + 1)","option_b":"1\/(2x + 1)","option_c":"(2x + 1)\/2","option_d":"2x\/(2x + 1)","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. Ainsi, f'(x) = 2\/(2x + 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\": \"2\/(2x + 1)\", \"b\": \"1\/(2x + 1)\", \"c\": \"(2x + 1)\/2\", \"d\": \"2x\/(2x +","_debug_options_count":4},{"id":274,"question":"Résoudre l'inéquation : ln(x) \u003E 0.","option_a":"x \u003E 0","option_b":"x \u003E 1","option_c":"x \u003C 1","option_d":"x ∈ ]0, 1[","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x) \u003E 0 équivaut à x \u003E e^0, soit x \u003E 1 (car la fonction ln est croissante).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x \u003E 0\", \"b\": \"x \u003E 1\", \"c\": \"x \u003C 1\", \"d\": \"x ∈ ]0, 1[\"}}","_debug_options_count":4},{"id":275,"question":"Quelle est la limite de ln(x)\/x quand x tend vers +∞ ?","option_a":"0","option_b":"+∞","option_c":"1","option_d":"-∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par croissance comparée, ln(x) croît plus lentement que x, donc ln(x)\/x tend vers 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\": \"0\", \"b\": \"+∞\", \"c\": \"1\", \"d\": \"-∞\"}}","_debug_options_count":4},{"id":276,"question":"Quelle propriété permet d'écrire ln(ab) = ln(a) + ln(b) ?","option_a":"Propriété de la dérivée","option_b":"Propriété algébrique","option_c":"Propriété de la limite","option_d":"Propriété de l'exponentielle","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une propriété fondamentale des logarithmes : ln(ab) = ln(a) + ln(b) pour a, b \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Propriété de la dérivée\", \"b\": \"Propriété algébrique\", \"c\"","_debug_options_count":4}]