Quiz — Limites. Continuité en un point.pdf

Question 1 sur 10 20:00

[{"id":49355,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. ∞","option_d":"D. Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction se simplifie en f(x) = x + 2 pour x ≠ 2. Ainsi, la limite est 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 4\", \"c\": \"C. ∞\", \"d\": \"D. Indéterminée\"}}","_debug_options_count":4},{"id":49356,"question":"Une fonction est continue en un point a si et seulement si :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La continuité en un point a nécessite trois conditions : f(a) est défini, la limite de f(x) en a existe, et cette limite est égale à f(a).","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":49357,"question":"Quelle est la limite de la fonction f(x) = sin(x)\/x lorsque x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. ∞","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une limite remarquable égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. ∞\", \"d\": \"D. -1\"}}","_debug_options_count":4},{"id":49358,"question":"La fonction f(x) = |x|\/x est-elle continue en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction n'est pas définie en x = 0, donc elle ne peut pas être continue en ce point.","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},{"id":49359,"question":"Quelle est la limite de la fonction f(x) = (e^x - 1)\/x lorsque x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. e","option_d":"D. Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une limite remarquable égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. e\", \"d\": \"D. Indéterminée\"}}","_debug_options_count":4},{"id":49360,"question":"Si lim(x→a) f(x) = L et lim(x→a) g(x) = M, alors lim(x→a) [f(x) + g(x)] est égal à :","option_a":"A. L + M","option_b":"B. L * M","option_c":"C. L \/ M","option_d":"D. Indéterminé","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'une somme est la somme des limites, si elles existent.","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. L + M\", \"b\": \"B. L * M\", \"c\": \"C. L \/ M\", \"d\": \"D. Indétermin","_debug_options_count":4},{"id":49361,"question":"La fonction f(x) = x² est-elle continue sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x² est continue en tout point de ℝ car elle est définie, limite et valeur coïncident en tout point.","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":49362,"question":"Quelle est la limite de la fonction f(x) = (1 - cos(x))\/x² lorsque x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. 1","option_d":"D. Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une limite remarquable égale à 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\/2\", \"c\": \"C. 1\", \"d\": \"D. Indéterminée\"}}","_debug_options_count":4},{"id":49363,"question":"Si f est continue en a et g est continue en f(a), alors g∘f est continue en a :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental : la composition de deux fonctions continues est continue.","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":49364,"question":"Quelle est la limite de la fonction f(x) = ln(1 + x)\/x lorsque x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. e","option_d":"D. Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une limite remarquable égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. e\", \"d\": \"D. Indéterminée\"}}","_debug_options_count":4}]