Quiz : Maîtrisez les dérivées et intégrales en Terminale Sciences !

Question 1 sur 5 10:00

[{"id":1480,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"f'(x) = 2x + 3","option_b":"f'(x) = x² + 3","option_c":"f'(x) = 2x - 5","option_d":"f'(x) = 3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n·a·x^(n-1). Ici, f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1481,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale d'une somme est la somme des intégrales. ∫3x² dx = x³ et ∫2x dx = x², d'où le résultat x³ + x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1482,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/n² lorsque n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = 1 + 1\/n², dont la limite est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1483,"question":"Quelle est la solution de l'équation différentielle y' = 2y ?","option_a":"y = Ce^(2x)","option_b":"y = 2Ce^x","option_c":"y = Ce^x","option_d":"y = 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation y' = ky a pour solution y = Ce^(kx). Ici, k=2, donc y = Ce^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1484,"question":"Quelle est la primitive de f(x) = e^(3x) ?","option_a":"(1\/3)e^(3x) + C","option_b":"e^(3x) + C","option_c":"3e^(3x) + C","option_d":"e^(x\/3) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de e^(ax) est (1\/a)e^(ax) + C. Ici, a=3, donc la primitive est (1\/3)e^(3x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]