Quiz : Les fonctions exponentielles et logarithmes — Terminale Math

Question 1 sur 5 10:00

[{"id":2549,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2xe^(2x)","option_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":2550,"question":"Résolvez l'équation ln(x) = 3.","option_a":"x = e^3","option_b":"x = 3","option_c":"x = 1\/e^3","option_d":"x = ln(3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = a équivaut à x = e^a. Donc x = e^3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2551,"question":"Quelle est la limite de (e^x - 1)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"e","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une forme indéterminée 0\/0. En appliquant la règle de l'Hôpital, on obtient la dérivée du numérateur et du dénominateur : e^x \/ 1 → 1 quand x → 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2552,"question":"Soit f(x) = ln(x^2 + 1). Quelle est f'(x) ?","option_a":"2x \/ (x^2 + 1)","option_b":"1 \/ (x^2 + 1)","option_c":"2x","option_d":"x \/ (x^2 + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u(x)) est u'(x)\/u(x). Ici, u(x) = x^2 + 1, donc u'(x) = 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2553,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^(2x)","option_b":"y = Ce^(-2x)","option_c":"y = Ce^(x\/2)","option_d":"y = C","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une équation différentielle linéaire du premier ordre. La solution générale est y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]