Limites, Dérivées et Continuité — Terminale Math

Question 1 sur 10 10:00

[{"id":61907,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le terme dominant au numérateur et au dénominateur est 3x², donc la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61908,"question":"La fonction f(x) = x² + 3x - 5 est-elle dérivable en tout point de son domaine de définition ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Tous les polynômes sont dérivables sur ℝ, donc la fonction est dérivable en tout point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61909,"question":"Quelle est la dérivée de la fonction f(x) = (2x + 1)³ ?","option_a":"A. 3(2x + 1)²","option_b":"B. 6(2x + 1)²","option_c":"C. 6(2x + 1)","option_d":"D. 2(2x + 1)²","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation des fonctions composées, f'(x) = 3(2x + 1)² * 2 = 6(2x + 1)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61910,"question":"La fonction f(x) = |x| est-elle continue en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction valeur absolue est continue en x = 0 car lim(x→0) |x| = 0 = f(0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61911,"question":"Quelle est l'asymptote horizontale de la fonction f(x) = (5x² - 3x + 2)\/(2x² + 1) ?","option_a":"A. y = 5\/2","option_b":"B. y = 0","option_c":"C. y = 2","option_d":"D. y = -3\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En comparant les termes dominants, la limite lorsque x tend vers ±∞ est 5\/2, donc l'asymptote horizontale est y = 5\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61912,"question":"La fonction f(x) = 1\/x est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 1\/x n'est pas définie en x = 0, donc elle n'est pas dérivable en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61913,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 2) ?","option_a":"A. 1\/(3x + 2)","option_b":"B. 3\/(3x + 2)","option_c":"C. 1\/(x + 2)","option_d":"D. 3\/(x + 2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation des fonctions logarithmes, f'(x) = 3\/(3x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61914,"question":"La fonction f(x) = x³ - 3x + 2 admet-elle une asymptote oblique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les polynômes n'ont pas d'asymptotes obliques, seulement des asymptotes horizontales ou verticales.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61915,"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 une limite classique qui vaut 1, connue sous le nom de limite fondamentale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61916,"question":"La fonction f(x) = e^(2x) est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = e^(2x) est f'(x) = 2e^(2x) \u003E 0 pour tout x, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]