[{"_1":2,"_275":-5,"_276":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/ff943e5b-b278-41bc-a2f7-49db548cf5a3?video=true","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":13,"_15":16,"_53":54,"_142":143,"_91":247,"_263":264,"_271":272,"_273":274},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_17":18,"_19":18,"_20":21,"_22":23,"_46":18,"_47":48,"_49":50,"_51":52},"correctOptionId","","difficulty","id","ff943e5b-b278-41bc-a2f7-49db548cf5a3","options",[24,30,34,38,42],{"_20":25,"_26":27,"_28":29},"4d09ce58-ca2b-4d3d-89b3-c515acbde760","label","A","text","e^x \text{cos}(e^x) \text{sen}(e^x) \text{sqrt}(1+\text{cos}^2(e^x))",{"_20":31,"_26":32,"_28":33},"303bcdea-26c5-4ce3-89b4-f82e7424d273","B","e^x \text{cos}(e^x) \text{sqrt}(1+\text{cos}^2(e^x))",{"_20":35,"_26":36,"_28":37},"1bef07ac-7fcd-4756-bb88-cbfcca5c2161","C","e^x \text{cos}^2(e^x) \text{sqrt}(1+\text{cos}^2(e^x))",{"_20":39,"_26":40,"_28":41},"c4c55804-3aa5-4085-aac0-4ec0016a98e7","D","e^x - \text{cos}(e^x) \text{sen}(e^x) \frac{1}{1+\text{cos}^2(e^x)}",{"_20":43,"_26":44,"_28":45},"88b75a21-1009-4b3a-b3e8-767ee353318f","E","e^x \text{cos}(e^x) \text{sen}(e^x) \frac{1}{1+\text{cos}^2(e^x)}","solution_explanation","statement","

Determine a derivada da função f(x)=1−\u001a\frac{1}{\text{sqrt}(1+\text{cos}^2(e^x))}.

","status","has_issues","hasRelatedVideo",true,"relatedVideos",[55],{"_56":57,"_75":76,"_91":92,"_122":123,"_141":93},"content",{"_20":58,"_59":60,"_61":-5,"_62":63,"_64":65,"_66":-5,"_67":68,"_71":72,"_73":72,"_74":-5},"fea1149f-ed42-488e-b8d0-46e5016f329f","name","Relações Trigonométricas no Triângulo Retângulo, Leis dos Senos e Cossenos - 06 - Revisando e Praticando - Parte 06","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","d7fcad9c-530e-4eec-824f-930373662cdc","user_id","metadata",{"_69":70},"external_id","12593","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","prometheusData",{"_77":78,"_84":85,"_86":87,"_88":89,"_5":90},"provider",{"_20":79,"_80":81,"_82":83},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","c3d18e75-a612-4049-bb1b-05fa8436e75a","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/c3d18e75-a612-4049-bb1b-05fa8436e75a/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/c3d18e75-a612-4049-bb1b-05fa8436e75a/levels.m3u8","tags",[93],{"_20":94,"_59":95,"_96":97,"_98":99,"_100":-5,"_71":101,"_73":101,"_67":102,"_109":97,"_110":111},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","alias","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_103":104,"_105":106,"_107":108},"childrenCount",18,"content_count",0,"question_count",135489,"slug","children",[112],{"_20":113,"_59":114,"_96":115,"_98":99,"_100":94,"_71":116,"_73":116,"_67":117,"_109":120,"_110":121},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_103":118,"_105":106,"_107":119},10,19948,"mecanica-2",[],"video",{"_20":65,"_124":60,"_61":-5,"_125":126,"_127":128,"_5":-5,"_129":-5,"_77":128,"_130":131,"_88":-5,"_132":-5,"_133":-5,"_134":-5,"_135":-5,"_67":136,"_137":106,"_138":-5,"_49":139,"_71":140,"_73":140},"title","duration",21,"source_type","prometheus","iframe_url","provider_video_id","8335867d-4f35-401e-a9c3-13c4a0db8c56","format","quality","file_path","file_size",{"_69":70},"views_count","last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag","similarQuestions",[144,173,190,207,227],{"_17":18,"_19":18,"_20":145,"_22":146,"_46":18,"_47":162,"_91":163},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[147,150,153,156,159],{"_20":148,"_26":27,"_28":149},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_20":151,"_26":32,"_28":152},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_20":154,"_26":36,"_28":155},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_20":157,"_26":40,"_28":158},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_20":160,"_26":44,"_28":161},"112831da-be9c-458e-94cb-e8292d0dba12","y'' - 2y' + 6y = 0","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[164],{"_20":165,"_59":166,"_96":167,"_98":99,"_100":168,"_71":116,"_73":116,"_67":169,"_109":172},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_103":170,"_105":106,"_107":171},5,30614,"engenharia-mecatronica-1",{"_17":18,"_19":18,"_20":174,"_22":175,"_46":18,"_47":188,"_91":189},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[176,179,182,185],{"_20":177,"_26":27,"_28":178},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":180,"_26":32,"_28":181},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":183,"_26":36,"_28":184},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":186,"_26":40,"_28":187},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[164],{"_17":18,"_19":18,"_20":191,"_22":192,"_46":18,"_47":205,"_91":206},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[193,196,199,202],{"_20":194,"_26":27,"_28":195},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":197,"_26":32,"_28":198},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":200,"_26":36,"_28":201},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":203,"_26":40,"_28":204},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[164],{"_17":18,"_19":18,"_20":208,"_22":209,"_46":18,"_47":225,"_91":226},"996628fc-4ac3-4821-86bd-839f86a97a6d",[210,213,216,219,222],{"_20":211,"_26":27,"_28":212},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":214,"_26":32,"_28":215},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":217,"_26":36,"_28":218},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":220,"_26":40,"_28":221},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":223,"_26":44,"_28":224},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[164],{"_17":18,"_19":18,"_20":228,"_22":229,"_46":18,"_47":245,"_91":246},"c478a46c-46a8-4942-ae14-2e79def3dda2",[230,233,236,239,242],{"_20":231,"_26":27,"_28":232},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":234,"_26":32,"_28":235},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":237,"_26":36,"_28":238},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":240,"_26":40,"_28":241},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":243,"_26":44,"_28":244},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[164],[164,248,254,255,256],{"_20":249,"_59":114,"_96":115,"_98":99,"_100":165,"_71":250,"_73":250,"_67":251,"_109":253},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_103":170,"_105":106,"_107":252},25741,"mecanica-3",{"_20":94,"_59":95,"_96":97,"_98":99,"_100":-5,"_71":101,"_73":101,"_67":102,"_109":97},{"_20":113,"_59":114,"_96":115,"_98":99,"_100":94,"_71":116,"_73":116,"_67":117,"_109":120},{"_20":168,"_59":257,"_96":258,"_98":99,"_100":-5,"_71":259,"_73":259,"_67":260,"_109":258},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_103":261,"_105":106,"_107":262},29,351586,"tagsTree",[93,265],{"_20":168,"_59":257,"_96":258,"_98":99,"_100":-5,"_71":259,"_73":259,"_67":260,"_109":258,"_110":266},[267],{"_20":165,"_59":166,"_96":167,"_98":99,"_100":168,"_71":116,"_73":116,"_67":169,"_109":172,"_110":268},[269],{"_20":249,"_59":114,"_96":115,"_98":99,"_100":165,"_71":250,"_73":250,"_67":251,"_109":253,"_110":270},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários