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Question 1 sur 10 10:00

[{"id":4174,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'un quotient de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 2x²\/x² = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4175,"question":"La dérivée de la fonction f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de -3x² est -6x, et celle de 2x est 2. Donc f'(x) = 3x² - 6x + 2 est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4176,"question":"Quel est le produit scalaire de deux vecteurs u(2, -1) et v(3, 4) ?","option_a":"A. 2","option_b":"B. 5","option_c":"C. 10","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le produit scalaire est calculé par u·v = (2*3) + (-1*4) = 6 - 4 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4177,"question":"La suite définie par uₙ = 3n - 5 est arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 3, donc elle est bien arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4178,"question":"Résoudre l'équation différentielle y' + 2y = 0.","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Ce^(2x)","option_c":"C. y = Cx^(-2)","option_d":"D. y = C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle linéaire du premier ordre y' + 2y = 0 a pour solution générale y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4179,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"A. 1","option_b":"B. 25","option_c":"C. 1","option_d":"D. 25","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4*1*6 = 25 - 24 = 1. La réponse correcte est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4180,"question":"La fonction f(x) = e^(x²) est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 2x*e^(x²). Elle est positive pour x \u003E 0 et négative pour x \u003C 0, donc la fonction n'est pas croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4181,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"A. x³ + x² + C","option_b":"B. x³ + x + C","option_c":"C. 3x³ + x² + C","option_d":"D. x³ + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³ et celle de 2x est x². Donc ∫(3x² + 2x) dx = x³ + x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4182,"question":"La suite uₙ = 2^n est-elle géométrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est géométrique si le rapport entre deux termes consécutifs est constant. Ici, uₙ₊₁\/uₙ = 2, donc elle est bien géométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4183,"question":"Quel est le centre de symétrie de la fonction f(x) = (2x + 1)\/(x - 3) ?","option_a":"A. (3, 2)","option_b":"B. (2, 3)","option_c":"C. (-3, 2)","option_d":"D. (3, -2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le centre de symétrie d'une fonction rationnelle de la forme (ax + b)\/(cx + d) est (x₀, y₀) où x₀ = -d\/c et y₀ = a\/c. Ici, x₀ = 3 et y₀ = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]