Testez vos connaissances sur les limites et la continuité en 2ème Sciences

Question 1 sur 10 10:00

[{"id":67532,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"D","explication":"La fonction se simplifie en f(x) = x + 1 pour x ≠ 1. Ainsi, lim(x→1) f(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67533,"question":"Une fonction est continue en un point si elle y est définie et si sa limite en ce point existe.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction doit aussi vérifier que la limite est égale à la valeur de la fonction en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67534,"question":"Quelle est la limite de la fonction f(x) = 1\/x lorsque x tend vers 0+ ?","option_a":"A. 0","option_b":"B. +∞","option_c":"C. -∞","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Lorsque x tend vers 0 par valeurs positives, 1\/x tend vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67535,"question":"La droite d'équation y = 2 est une asymptote horizontale de la fonction f(x) si :","option_a":"A. lim(x→+∞) f(x) = 2","option_b":"B. lim(x→-∞) f(x) = 2","option_c":"C. lim(x→0) f(x) = 2","option_d":"D. A et B sont correctes","option_e":"","option_f":"","bonne_reponse":"D","explication":"Une asymptote horizontale peut être obtenue en +∞ ou en -∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67536,"question":"Soit f(x) = x² pour x ≤ 1 et f(x) = 2x - 1 pour x \u003E 1. La fonction f est-elle continue en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"lim(x→1-) f(x) = 1 et lim(x→1+) f(x) = 1. De plus, f(1) = 1. La fonction est donc continue en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67537,"question":"Quelle est la limite de la fonction f(x) = (sin x)\/x lorsque x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est un cas classique : lim(x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67538,"question":"Une fonction peut avoir une asymptote verticale en x = a si :","option_a":"A. lim(x→a) f(x) = 0","option_b":"B. lim(x→a) f(x) = +∞","option_c":"C. f(a) = 0","option_d":"D. f est définie en a","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une asymptote verticale en x = a signifie que la fonction tend vers l'infini lorsque x s'approche de a.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67539,"question":"La fonction f(x) = 1\/(x-2) est-elle continue en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction n'est pas définie en x = 2, donc elle ne peut pas être continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67540,"question":"Quelle est la limite de la fonction f(x) = (e^x - 1)\/x lorsque x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. e","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une limite remarquable : lim(x→0) (e^x - 1)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67541,"question":"Si lim(x→a) f(x) = L et lim(x→a) g(x) = M, alors lim(x→a) [f(x) + g(x)] = L + M.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale des limites : la limite d'une somme est la somme des limites.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]