[{"_1":2,"_191":-5,"_192":-5},"loaderData",{"_3":4,"_6":7},"root",{"_5":-5},"user","pages/questions/show/index",{"_8":9,"_10":11,"_44":45,"_46":47,"_67":181,"_182":183},"comments",[],"question",{"_12":13,"_14":13,"_15":16,"_17":18,"_41":13,"_42":43},"correctOptionId","","difficulty","id","fd249268-9c14-4d49-9da7-096d0b8f7545","options",[19,25,29,33,37],{"_15":20,"_21":22,"_23":24},"930fcb77-a05b-4338-a39b-6ec21e86c2d0","label","A","text","f'(2) não existe; f'(3) = 3; f'(4) = 5.",{"_15":26,"_21":27,"_23":28},"058ae6ed-315d-4b0e-a0f3-3e7a4c78b516","B","f'(2) = 1; f'(3) = 3; f'(4) = 1.",{"_15":30,"_21":31,"_23":32},"aef723fd-9730-4502-ac51-e20b85cfab0a","C","f'(2) = 2; f'(3) = 3; f'(4) = 1.",{"_15":34,"_21":35,"_23":36},"5e20da4d-b64a-4bca-986d-8d7233a1f651","D","f'(2) = –1; f'(3) = 0; f'(4) não existe.",{"_15":38,"_21":39,"_23":40},"a6ac4adb-17c3-4ef8-b1d9-6cd214864795","E","f'(2) = 1; f'(3) não existe; f'(4) = –1.","solution_explanation","statement","

Determine a derivada da função f, cujo gráfico aparece na figura abaixo, em x = 2, 3 e 4, e assinale a alternativa correta.

","relatedVideos",[],"similarQuestions",[48,107,124,141,161],{"_12":13,"_14":13,"_15":49,"_17":50,"_41":13,"_42":66,"_67":68},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[51,54,57,60,63],{"_15":52,"_21":22,"_23":53},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_15":55,"_21":27,"_23":56},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_15":58,"_21":31,"_23":59},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_15":61,"_21":35,"_23":62},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_15":64,"_21":39,"_23":65},"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

","tags",[69,92,100],{"_15":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":91},"861ad829-750d-4a44-9569-2f18b430b4df","name","Engenharia Mecatrônica","alias","engenharia-mecatronica","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","created_at","2025-04-29T02:19:12.828432+00:00","updated_at","metadata",{"_84":85,"_86":87,"_88":89},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_15":93,"_71":94,"_73":95,"_75":76,"_77":70,"_79":96,"_81":96,"_82":97,"_90":99},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_84":85,"_86":87,"_88":98},25741,"mecanica-3",{"_15":78,"_71":101,"_73":102,"_75":76,"_77":-5,"_79":103,"_81":103,"_82":104,"_90":102},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_84":105,"_86":87,"_88":106},29,351586,{"_12":13,"_14":13,"_15":108,"_17":109,"_41":13,"_42":122,"_67":123},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[110,113,116,119],{"_15":111,"_21":22,"_23":112},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_15":114,"_21":27,"_23":115},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_15":117,"_21":31,"_23":118},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_15":120,"_21":35,"_23":121},"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.

",[69,92,100],{"_12":13,"_14":13,"_15":125,"_17":126,"_41":13,"_42":139,"_67":140},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[127,130,133,136],{"_15":128,"_21":22,"_23":129},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_15":131,"_21":27,"_23":132},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_15":134,"_21":31,"_23":135},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_15":137,"_21":35,"_23":138},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[69,92,100],{"_12":13,"_14":13,"_15":142,"_17":143,"_41":13,"_42":159,"_67":160},"996628fc-4ac3-4821-86bd-839f86a97a6d",[144,147,150,153,156],{"_15":145,"_21":22,"_23":146},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_15":148,"_21":27,"_23":149},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_15":151,"_21":31,"_23":152},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_15":154,"_21":35,"_23":155},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_15":157,"_21":39,"_23":158},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[69,92,100],{"_12":13,"_14":13,"_15":162,"_17":163,"_41":13,"_42":179,"_67":180},"c478a46c-46a8-4942-ae14-2e79def3dda2",[164,167,170,173,176],{"_15":165,"_21":22,"_23":166},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_15":168,"_21":27,"_23":169},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_15":171,"_21":31,"_23":172},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_15":174,"_21":35,"_23":175},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_15":177,"_21":39,"_23":178},"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????",[69,92,100],[69,92,100],"tagsTree",[184],{"_15":78,"_71":101,"_73":102,"_75":76,"_77":-5,"_79":103,"_81":103,"_82":104,"_90":102,"_185":186},"children",[187],{"_15":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":91,"_185":188},[189],{"_15":93,"_71":94,"_73":95,"_75":76,"_77":70,"_79":96,"_81":96,"_82":97,"_90":99,"_185":190},[],"actionData","errors"]

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