Quiz — asymp.pdf

Question 1 sur 10 20:00

[{"id":120986,"question":"Quelle est l'équation d'une asymptote horizontale pour une fonction f(x) lorsque x tend vers +∞ ?","option_a":"y = 0","option_b":"y = L (constante)","option_c":"x = L","option_d":"y = x","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une asymptote horizontale est une droite d'équation y = L, où L est la limite de f(x) lorsque 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\": \"y = 0\", \"b\": \"y = L (constante)\", \"c\": \"x = L\", \"d\": \"y = x\"}}","_debug_options_count":4},{"id":120987,"question":"Si lim(x→a) f(x) = ±∞, alors la droite x = a est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : si la limite tend vers l'infini en un point a, alors x = a 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":120988,"question":"Pour une fonction rationnelle f(x) = (2x² + 3x - 1)\/(x² - 4), quelle est son asymptote horizontale ?","option_a":"y = 2","option_b":"y = 0","option_c":"y = 3","option_d":"y = x","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'asymptote horizontale est obtenue en comparant les degrés des polynômes. Ici, les degrés sont égaux, donc y = 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\": \"y = 2\", \"b\": \"y = 0\", \"c\": \"y = 3\", \"d\": \"y = x\"}}","_debug_options_count":4},{"id":120989,"question":"Une fonction peut-elle avoir une asymptote oblique sans asymptote horizontale ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai : si le degré du numérateur est exactement supérieur de 1 à celui du dénominateur, il y a une asymptote oblique mais pas horizontale.","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":120990,"question":"Quelle méthode permet de trouver une asymptote oblique pour une fonction rationnelle ?","option_a":"Dérivation","option_b":"Division polynomiale","option_c":"Intégration","option_d":"Factorisation","option_e":"","option_f":"","bonne_reponse":"b","explication":"La division polynomiale (division euclidienne) permet d'écrire f(x) = Q(x) + R(x)\/D(x), où Q(x) est l'asymptote oblique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Dérivation\", \"b\": \"Division polynomiale\", \"c\": \"Intégration\", \"","_debug_options_count":4},{"id":120991,"question":"Si lim(x→+∞) [f(x) - (ax + b)] = 0, alors la droite y = ax + b est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai : par définition, si la différence tend vers 0, alors y = ax + b est une asymptote oblique.","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":120992,"question":"Pour f(x) = (x³ + 2x)\/(x² + 1), quelle est l'équation de son asymptote oblique ?","option_a":"y = x","option_b":"y = 2x","option_c":"y = x + 2","option_d":"y = 3x","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant, on obtient f(x) = x + (2x)\/(x² + 1). La partie dominante est y = x, donc l'asymptote oblique est y = 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\": \"y = x\", \"b\": \"y = 2x\", \"c\": \"y = x + 2\", \"d\": \"y = 3x\"}}","_debug_options_count":4},{"id":120993,"question":"Une asymptote verticale peut-elle être une droite d'équation y = k ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux : une asymptote verticale est toujours de la forme x = k, car elle représente une limite infinie en un point précis.","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":120994,"question":"Si f(x) = (x² + 1)\/x, quelle est son asymptote oblique ?","option_a":"y = x","option_b":"y = 1","option_c":"y = x + 1\/x","option_d":"y = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant, f(x) = x + 1\/x. La partie dominante est y = x, donc l'asymptote oblique est y = 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\": \"y = x\", \"b\": \"y = 1\", \"c\": \"y = x + 1\/x\", \"d\": \"y = 0\"}}","_debug_options_count":4},{"id":120995,"question":"Quelle condition doit satisfaire une fonction pour avoir une asymptote horizontale en y = 0 ?","option_a":"lim(x→±∞) f(x) = 0","option_b":"f(x) = 0 pour tout x","option_c":"f(x) est constante","option_d":"f(x) est paire","option_e":"","option_f":"","bonne_reponse":"a","explication":"La condition est que la limite de f(x) lorsque x tend vers ±∞ soit égale à 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\": \"lim(x→±∞) f(x) = 0\", \"b\": \"f(x) = 0 pour tout x\", \"c\": \"f(x)","_debug_options_count":4}]