Mat1162   2016.2 - Provas - Maple
50 pág.

Mat1162 2016.2 - Provas - Maple


DisciplinaCálculo II22.383 materiais681.693 seguidores
Pré-visualização50 páginas
D) (Cone de duas folhas) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkmbWZyYWNHRiQ2KC1JJW1zdXBHRiQ2JS1JI21pR0YkNiZRInhGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GPFEnbm9ybWFsRidGNUY4RjsvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYjNiYtRi82JS1GMjYmUSJhRidGNUY4RjtGPkZGRjVGOEY7LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHUSZmYWxzZUYnLUkjbW9HRiQ2LlEiK0YnRjVGRC8lJmZlbmNlR0ZaLyUqc2VwYXJhdG9yR0ZaLyUpc3RyZXRjaHlHRlovJSpzeW1tZXRyaWNHRlovJShsYXJnZW9wR0ZaLyUubW92YWJsZWxpbWl0c0dGWi8lJ2FjY2VudEdGWi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmlvLUYsNigtRi82JS1GMjYmUSJ5RidGNUY4RjtGPkZGLUYjNiYtRi82JS1GMjYmUSJiRidGNUY4RjtGPkZGRjVGOEY7RlBGU0ZWRlgtRmZuNi5RIj1GJ0Y1RkRGaW5GW29GXW9GX29GYW9GY29GZW8vRmhvUSwwLjI3Nzc3NzhlbUYnL0ZbcEZecS1GLDYoLUYvNiUtRjI2JlEiekYnRjVGOEY7Rj5GRi1GIzYmLUYvNiUtRjI2JlEiY0YnRjVGOEY7Rj5GRkY1RjhGO0ZQRlNGVkZYLUYyNiNRIUYnRjVGRA==

 E) (Cilindro sobre uma elipse) 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

 5. Usando desigualdades, determine a regi\303\243o limitada do espa\303\247o cuja fronteira \303\251 o elips\303\263ide do exerc\303\255cio 4.A.

 6. Sejam

 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

 Escreva, usando igualdades ou desigualdades, a fronteira de 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

 3 - Gr\303\241ficos de Fun\303\247\303\265es com Duas Vari\303\241veis
 JSFH

 Se a equa\303\247\303\243o de uma superf\303\255cie no espa\303\247o euclidiano puder ser escrita da forma 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 , ent\303\243o a mesma representa o gr\303\241fico de uma fun\303\247\303\243o nas vari\303\241veis reais x e y. Vamos visualizar alguns gr\303\241ficos desse tipo.

 Exerc\303\255cio 1:
Determine o eixo de revolu\303\247\303\243o para cada uma das superf\303\255cies abaixo, caso ele exista.

 Exerc\303\255cio 2:
Determine as curvas que resultam dos cortes das superf\303\255cies abaixo com os planos coordenados xz e yz.

 Exerc\303\255cio 3:
Determine as interse\303\247\303\265es das superf\303\255ces abaixo com planos da forma z=cte.

 A) Parabol\303\263ide hiperb\303\263lico:

 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

 print( ); # input placeholder

 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

 print( ); # input placeholder

 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