Quiz — Fiche de methode Ln.pdf

Question 1 sur 10 20:00

[{"id":47358,"question":"Quel est le domaine de définition de la fonction ln ?","option_a":"ℝ","option_b":"ℝ+*","option_c":"ℝ+","option_d":"ℤ","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln est définie uniquement pour les nombres strictement positifs, donc son domaine est ℝ+*.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"ℝ\", \"b\": \"ℝ+*\", \"c\": \"ℝ+\", \"d\": \"ℤ\"}}","_debug_options_count":4},{"id":47359,"question":"La dérivée de ln(x) est égale à 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est bien 1\/x, donc l'affirmation est vraie.","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":47360,"question":"Que vaut ln(e^3) ?","option_a":"0","option_b":"1","option_c":"3","option_d":"e^3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Par propriété, ln(e^3) = 3 car ln et exp sont des fonctions réciproques.","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\": \"3\", \"d\": \"e^3\"}}","_debug_options_count":4},{"id":47361,"question":"La fonction ln est-elle croissante sur son domaine de définition ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction ln est strictement croissante sur ℝ+* car sa dérivée 1\/x est positive pour tout x \u003E 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":47362,"question":"Quelle est la limite de ln(x) lorsque x tend vers 0+ ?","option_a":"0","option_b":"-∞","option_c":"+∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Lorsque x tend vers 0 par valeurs positives, ln(x) tend vers -∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"-∞\", \"c\": \"+∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":47363,"question":"Si ln(x) = 2, alors x est égal à :","option_a":"e^2","option_b":"2e","option_c":"1\/2","option_d":"ln(2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant l'exponentielle des deux côtés, on obtient x = e^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\": \"e^2\", \"b\": \"2e\", \"c\": \"1\/2\", \"d\": \"ln(2)\"}}","_debug_options_count":4},{"id":47364,"question":"La fonction ln est-elle définie en x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln n'est pas définie pour les nombres négatifs, donc ln(-1) 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":47365,"question":"Quelle est la dérivée de ln(2x) ?","option_a":"1\/(2x)","option_b":"1\/x","option_c":"2\/x","option_d":"1\/(x^2)","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la formule de dérivation (ln u)' = u'\/u avec u = 2x, on obtient 2\/(2x) = 1\/x.","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)\", \"b\": \"1\/x\", \"c\": \"2\/x\", \"d\": \"1\/(x^2)\"}}","_debug_options_count":4},{"id":47366,"question":"La fonction ln est-elle paire ou impaire ?","option_a":"Paire","option_b":"Impaire","option_c":"Ni l'une ni l'autre","option_d":"","option_e":"","option_f":"","bonne_reponse":"c","explication":"La fonction ln n'est ni paire ni impaire car ln(-x) n'est pas défini pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Paire\", \"b\": \"Impaire\", \"c\": \"Ni l'une ni l'autre\", \"d\": \"\"}}","_debug_options_count":4},{"id":47367,"question":"Que vaut ln(1) ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"e","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, ln(1) = 0 car e^0 = 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\": \"0\", \"b\": \"1\", \"c\": \"-1\", \"d\": \"e\"}}","_debug_options_count":4}]