Quiz — Série d_exercices Math - Limites et asymptotes - 3ème Math (2007-2008) Mr Abdessatar El Faleh.pdf

Question 1 sur 5 10:00

[{"id":1090,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 5)\/(2x² - x + 1) quand x tend vers l'infini ?","option_a":"A. 3\/2","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une fonction rationnelle, la limite à l'infini est égale au rapport des coefficients des termes de plus haut degré. Ici, 3x²\/2x² = 3\/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\": \"A. 3\/2\", \"b\": \"B. 0\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":1091,"question":"Soit f(x) = (x² - 1)\/(x - 1). Que vaut lim(x→1) f(x) ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"On simplifie l'expression : f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1. Ainsi, lim(x→1) f(x) = 1+1 = 2.","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. 0\", \"b\": \"B. 2\", \"c\": \"C. +∞\", \"d\": \"D. Indéterminée\"}}","_debug_options_count":4},{"id":1092,"question":"Quelle est l'équation de l'asymptote horizontale de la fonction f(x) = (5x + 3)\/(2x - 1) ?","option_a":"A. y = 5\/2","option_b":"B. y = 2\/5","option_c":"C. y = 0","option_d":"D. y = x","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une fonction rationnelle, l'asymptote horizontale est donnée par le rapport des coefficients des termes de plus haut degré : 5x\/2x = 5\/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\": \"A. y = 5\/2\", \"b\": \"B. y = 2\/5\", \"c\": \"C. y = 0\", \"d\": \"D. y = x\"}","_debug_options_count":4},{"id":1093,"question":"Soit f(x) = 1\/(x-3). Quelle est l'asymptote verticale de cette fonction ?","option_a":"A. x = 0","option_b":"B. x = 3","option_c":"C. y = 0","option_d":"D. y = 3","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/(x-3) n'est pas définie en x = 3, et lim(x→3) f(x) = ±∞. Ainsi, x = 3 est une asymptote verticale.","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. x = 0\", \"b\": \"B. x = 3\", \"c\": \"C. y = 0\", \"d\": \"D. y = 3\"}}","_debug_options_count":4},{"id":1094,"question":"Quelle est la limite de la fonction f(x) = sin(x)\/x quand x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"On utilise le théorème des gendarmes ou la limite remarquable : lim(x→0) sin(x)\/x = 1. Ici, la fonction est sin(x)\/x, donc la limite 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\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4}]