Quiz — dl1213-SeriesEnt.pdf

Question 1 sur 10 20:00

[{"id":120956,"question":"Quelle est la limite de la suite définie par u\u003Csub\u003En\u003C\/sub\u003E = (3n² + 2n - 1)\/(n² + 5) quand n tend vers l'infini ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 3","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"La limite est obtenue en divisant le numérateur et le dénominateur par n², ce qui donne 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. 3\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":120957,"question":"La fonction f(x) = x³ - 3x² + 2x est dérivable sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Toute fonction polynôme est dérivable sur ℝ, donc l’affirmation est vraie.","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":120958,"question":"Quelle est la dérivée de la fonction f(x) = ln(x² + 1) ?","option_a":"A. 2x\/(x² + 1)","option_b":"B. 2x","option_c":"C. 1\/(x² + 1)","option_d":"D. x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule de dérivation des fonctions composées, f'(x) = (2x)\/(x² + 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. 2x\/(x² + 1)\", \"b\": \"B. 2x\", \"c\": \"C. 1\/(x² + 1)\", \"d\": \"D. x","_debug_options_count":4},{"id":120959,"question":"L’intégrale ∫\u003Csub\u003E0\u003C\/sub\u003E\u003Csup\u003E1\u003C\/sup\u003E (2x + 1) dx vaut :","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"c","explication":"L’intégrale se calcule comme [x² + x]\u003Csub\u003E0\u003C\/sub\u003E\u003Csup\u003E1\u003C\/sup\u003E = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 1\", \"b\": \"B. 2\", \"c\": \"C. 3\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":120960,"question":"La suite définie par u\u003Csub\u003E0\u003C\/sub\u003E = 1 et u\u003Csub\u003En+1\u003C\/sub\u003E = 2u\u003Csub\u003En\u003C\/sub\u003E + 1 est croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En calculant les premiers termes, on observe que u\u003Csub\u003E1\u003C\/sub\u003E = 3, u\u003Csub\u003E2\u003C\/sub\u003E = 7, etc., donc la suite est croissante.","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":120961,"question":"Quelle est la primitive de la fonction f(x) = e\u003Csup\u003E2x\u003C\/sup\u003E ?","option_a":"A. e\u003Csup\u003E2x\u003C\/sup\u003E + C","option_b":"B. (1\/2)e\u003Csup\u003E2x\u003C\/sup\u003E + C","option_c":"C. 2e\u003Csup\u003E2x\u003C\/sup\u003E + C","option_d":"D. e\u003Csup\u003Ex\u003C\/sup\u003E + C","option_e":"","option_f":"","bonne_reponse":"b","explication":"La primitive de e\u003Csup\u003E2x\u003C\/sup\u003E est (1\/2)e\u003Csup\u003E2x\u003C\/sup\u003E + C, car la dérivée de (1\/2)e\u003Csup\u003E2x\u003C\/sup\u003E est e\u003Csup\u003E2x\u003C\/sup\u003E.","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. e\u003Csup\u003E2x\u003C\/sup\u003E + C\", \"b\": \"B. (1\/2)e\u003Csup\u003E2x\u003C\/sup\u003E + C\", \"c\": \"","_debug_options_count":4},{"id":120962,"question":"La fonction f(x) = x² - 4x + 3 est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée seconde f''(x) = 2 \u003E 0, donc la fonction est convexe sur ℝ.","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":120963,"question":"Quelle est la probabilité d’obtenir un nombre pair en lançant un dé équilibré ?","option_a":"A. 1\/6","option_b":"B. 1\/3","option_c":"C. 1\/2","option_d":"D. 2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 1\/6\", \"b\": \"B. 1\/3\", \"c\": \"C. 1\/2\", \"d\": \"D. 2\/3\"}}","_debug_options_count":4},{"id":120964,"question":"La fonction f(x) = 1\/x est définie et continue sur ℝ*.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction 1\/x est définie et continue sur ℝ*, mais pas en x = 0 (non défini).","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":120965,"question":"Quelle est la valeur de l’intégrale ∫\u003Csub\u003E0\u003C\/sub\u003E\u003Csup\u003Eπ\u003C\/sup\u003E sin(x) dx ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. π","option_e":"","option_f":"","bonne_reponse":"c","explication":"L’intégrale de sin(x) entre 0 et π est [-cos(x)]\u003Csub\u003E0\u003C\/sub\u003E\u003Csup\u003Eπ\u003C\/sup\u003E = -(-1) - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. 2\", \"d\": \"D. π\"}}","_debug_options_count":4}]