Maths Terminale : Testez vos connaissances sur les fonctions et suites !

Question 1 sur 10 10:00

[{"id":39855,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 1) lorsque x tend vers +∞ ?","option_a":"A. 2","option_b":"B. 1","option_c":"C. +∞","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite d'un polynôme en +∞ est donnée par le terme de plus haut degré. Ici, (2x²)\/(x²) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39856,"question":"La fonction f(x) = x³ - 3x + 2 est-elle dérivable en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction polynôme est dérivable sur ℝ, donc f est dérivable en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39857,"question":"Soit la suite définie par u₀ = 2 et uₙ₊₁ = 3uₙ - 4. Quelle est la valeur de u₂ ?","option_a":"A. 2","option_b":"B. 6","option_c":"C. 14","option_d":"D. 20","option_e":"","option_f":"","bonne_reponse":"C","explication":"u₁ = 3*2 - 4 = 2, u₂ = 3*2 - 4 = 2. Attention à l'erreur courante : u₁ = 2, pas 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39858,"question":"La fonction f(x) = 1\/x est-elle continue 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 continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39859,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"A. 2e^(2x)","option_b":"B. e^(2x)","option_c":"C. 2xe^(2x)","option_d":"D. e^(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(u(x)) est u'(x)e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39860,"question":"Soit la suite géométrique de premier terme u₀ = 5 et de raison q = -2. Quel est le terme u₃ ?","option_a":"A. -40","option_b":"B. 40","option_c":"C. -20","option_d":"D. 20","option_e":"","option_f":"","bonne_reponse":"A","explication":"uₙ = u₀ * qⁿ. Donc u₃ = 5 * (-2)³ = 5 * (-8) = -40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39861,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2, et f''(x) = 2 \u003E 0, donc c'est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39862,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A. x = e²","option_b":"B. x = 2","option_c":"C. x = e","option_d":"D. x = 1\/e²","option_e":"","option_f":"","bonne_reponse":"A","explication":"ln(x) = 2 équivaut à x = e² par définition du logarithme népérien.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39863,"question":"Soit la suite définie par uₙ = (n² + 1)\/n. Que vaut lim(n→+∞) uₙ ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. +∞","option_d":"D. n","option_e":"","option_f":"","bonne_reponse":"B","explication":"uₙ = n + 1\/n. Lorsque n→+∞, 1\/n→0, donc uₙ→n→+∞, mais la limite est bien +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39864,"question":"La fonction f(x) = |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 valeur absolue n'est pas dérivable en x = 0 car la dérivée à gauche (-1) ≠ dérivée à droite (1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]