Quiz — 63e3ad39e4112_énoncé_magazine23 (logarithme népérien).pdf

Question 1 sur 10 20:00

[{"id":102022,"question":"Quelle est la valeur de ln(e^3) ?","option_a":"3","option_b":"e^3","option_c":"ln(3)","option_d":"0","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\": \"ln(3)\", \"d\": \"0\"}}","_debug_options_count":4},{"id":102023,"question":"La fonction ln est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln n'est définie que pour x \u003E 0. ln(0) n'existe pas.","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":102024,"question":"Quelle est la dérivée de f(x) = ln(2x + 1) ?","option_a":"1\/(2x+1)","option_b":"2\/(2x+1)","option_c":"1\/(x+1)","option_d":"2x\/(2x+1)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 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\": \"b\", \"options\": {\"a\": \"1\/(2x+1)\", \"b\": \"2\/(2x+1)\", \"c\": \"1\/(x+1)\", \"d\": \"2x\/(2x+1)\"}}","_debug_options_count":4},{"id":102025,"question":"L'équation ln(x) = 2 admet-elle une solution ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(x) = 2 équivaut à x = e^2, qui est une solution réelle positive.","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":102026,"question":"Quelle propriété est correcte pour ln(a\/b) ?","option_a":"ln(a) - ln(b)","option_b":"ln(a) + ln(b)","option_c":"ln(ab)","option_d":"ln(a)\/ln(b)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La propriété fondamentale est ln(a\/b) = ln(a) - ln(b).","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(a) - ln(b)\", \"b\": \"ln(a) + ln(b)\", \"c\": \"ln(ab)\", \"d\": \"ln(a)\/","_debug_options_count":4},{"id":102027,"question":"La fonction ln est-elle croissante sur son ensemble de définition ?","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. Donc ln est croissante.","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":102028,"question":"Résoudre l'inéquation ln(x) ≤ 1.","option_a":"x ≤ e","option_b":"x ≤ 1","option_c":"x ≥ e","option_d":"0 \u003C x ≤ e","option_e":"","option_f":"","bonne_reponse":"d","explication":"ln(x) ≤ 1 équivaut à x ≤ e^1 = e, avec x \u003E 0. Donc 0 \u003C x ≤ e.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"x ≤ e\", \"b\": \"x ≤ 1\", \"c\": \"x ≥ e\", \"d\": \"0 \u003C x ≤ e\"}}","_debug_options_count":4},{"id":102029,"question":"La limite de ln(x) quand x tend vers 0+ est-elle +∞ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Quand x → 0+, ln(x) → -∞. La limite est donc -∞.","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":102030,"question":"Quelle est la valeur de ln(√e) ?","option_a":"1\/2","option_b":"√e","option_c":"e^(1\/2)","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(√e) = ln(e^(1\/2)) = 1\/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\": \"1\/2\", \"b\": \"√e\", \"c\": \"e^(1\/2)\", \"d\": \"2\"}}","_debug_options_count":4},{"id":102031,"question":"La fonction f(x) = ln(x^2) est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(x^2) est défini pour x ≠ 0, car x^2 \u003E 0. Donc f(-1) = ln(1) = 0 est valide.","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}]