Quiz : Maîtrisez les suites, séries et fonctions en Terminale Math !

Question 1 sur 10 10:00

[{"id":80512,"question":"Quelle est la limite de la suite définie par uₙ = (3n² + 2n - 1)\/(2n² - n + 5) lorsque n tend vers +∞ ?","option_a":"A. 0","option_b":"B. 3\/2","option_c":"C. +∞","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant le numérateur et le dénominateur par n², on obtient lim(uₙ) = 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80513,"question":"La série de terme général vₙ = 1\/n² est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La série de Riemann Σ1\/n² converge car 2 \u003E 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80514,"question":"Soit f(x) = x³ - 3x + 2. Quel est le nombre de solutions réelles de l'équation f(x) = 0 ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"C","explication":"En étudiant le tableau de variations de f, on trouve 3 solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80515,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (2x + 1) dx ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3\/2","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"B","explication":"∫(2x + 1) dx = x² + x, donc ∫₀¹ (2x + 1) dx = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80516,"question":"La fonction f(x) = x² - 4x + 3 est-elle continue sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction polynôme est continue sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80517,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 1) ?","option_a":"A. 6x\/(3x² + 1)","option_b":"B. 3x\/(3x² + 1)","option_c":"C. 6x²\/(3x² + 1)","option_d":"D. 1\/(3x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule de dérivation d'une fonction composée, f'(x) = 6x\/(3x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80518,"question":"Soit la suite uₙ définie par u₀ = 1 et uₙ₊₁ = 2uₙ + 1. Quelle est la limite de uₙ si elle existe ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. +∞","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"C","explication":"La suite est croissante et non majorée, donc lim(uₙ) = +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80519,"question":"La série de terme général wₙ = (-1)ⁿ \/ n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La série alternée Σ(-1)ⁿ\/n converge d'après le critère de Leibniz.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80520,"question":"Quelle est la primitive de f(x) = e^(2x) ?","option_a":"A. e^(2x) + C","option_b":"B. (1\/2)e^(2x) + C","option_c":"C. 2e^(2x) + C","option_d":"D. e^(2x)\/2x + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de e^(2x) est (1\/2)e^(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80521,"question":"Soit f(x) = x³ - 6x² + 9x. Quel est le nombre de points critiques de f ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"C","explication":"f'(x) = 3x² - 12x + 9 = 0 admet deux solutions réelles : x = 1 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]