Les équivalents de fonctions — 3ème année secondaire Sciences

Question 1 sur 10 10:00

[{"id":76222,"question":"Quel est l'équivalent de la fonction f(x) = sin(x) au voisinage de 0 ?","option_a":"A. x","option_b":"B. x²","option_c":"C. 1","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Au voisinage de 0, sin(x) est équivalent à x car lim (sin(x)\/x) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76223,"question":"L'équivalent de ln(1+x) au voisinage de 0 est x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car lim (ln(1+x)\/x) = 1 lorsque x tend vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76224,"question":"Quel est l'équivalent de la fonction f(x) = e^x - 1 au voisinage de 0 ?","option_a":"A. x","option_b":"B. x²","option_c":"C. 1","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Au voisinage de 0, e^x - 1 est équivalent à x car lim ((e^x - 1)\/x) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76225,"question":"L'équivalent de 1 - cos(x) au voisinage de 0 est x²\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car lim ((1 - cos(x))\/(x²\/2)) = 1 lorsque x tend vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76226,"question":"Quel est l'équivalent de la fonction f(x) = √(1+x) - 1 au voisinage de 0 ?","option_a":"A. x\/2","option_b":"B. x","option_c":"C. x²","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Au voisinage de 0, √(1+x) - 1 est équivalent à x\/2 car lim ((√(1+x) - 1)\/(x\/2)) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76227,"question":"L'équivalent de tan(x) au voisinage de 0 est x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car lim (tan(x)\/x) = 1 lorsque x tend vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76228,"question":"Quel est l'équivalent de la fonction f(x) = (1+x)^α - 1 au voisinage de 0 ?","option_a":"A. αx","option_b":"B. x","option_c":"C. x²","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Au voisinage de 0, (1+x)^α - 1 est équivalent à αx car lim (((1+x)^α - 1)\/(αx)) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76229,"question":"L'équivalent de ln(1+x) - x au voisinage de 0 est -x²\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai, car lim ((ln(1+x) - x)\/(-x²\/2)) = 1 lorsque x tend vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76230,"question":"Quel est l'équivalent de la fonction f(x) = e^(sin(x)) - 1 au voisinage de 0 ?","option_a":"A. x","option_b":"B. sin(x)","option_c":"C. x²","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Au voisinage de 0, e^(sin(x)) - 1 est équivalent à sin(x) car lim ((e^(sin(x)) - 1)\/sin(x)) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":76231,"question":"L'équivalent de arctan(x) - x au voisinage de 0 est 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. L'équivalent de arctan(x) au voisinage de 0 est x, donc arctan(x) - x tend vers 0, mais n'est pas équivalent à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]