Quiz — Devoir a la maison - Equivalents 3.pdf

Question 1 sur 10 20:00

[{"id":36910,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x\", \"b\": \"B. x²\", \"c\": \"C. 1\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":36911,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36912,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x\", \"b\": \"B. x²\", \"c\": \"C. 1\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":36913,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36914,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x\/2\", \"b\": \"B. x\", \"c\": \"C. x²\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":36915,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36916,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. αx\", \"b\": \"B. x\", \"c\": \"C. x²\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":36917,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36918,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x\", \"b\": \"B. sin(x)\", \"c\": \"C. x²\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":36919,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]