Lista4_calculoII_2014_1 - UNIVERSIDADE FEDERAL DE MATO...

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1 UNIVERSIDADE FEDERAL DE MATO GROSSO Campus Universitário do Araguaia Instituto de Ciências Exatas e da Terra Curso: Ciência da Computação Disciplina: Cálculo II Professor: Renato Ferreira da Cruz 4 a Lista de Exercícios 1 Encontre o volume de um cone circular reto com altura h e raio da base r . 2 Determine o volume de um tronco de cone circular reto de altura h , raio da base inferior R e raio da base superior r . 3 Determine o volume de uma calota de uma esfera com raio R . 4 Seja B o sólido obtido pela rotação da região mostrada na figura abaixo em torno do eixo y . Use o método das cascas cilíndricas para encontrar o volume V . 5 Use o método das cascas cilíndricas para achar o volume gerado pela rotação em torno do eixo y da região limitada pelas curvas dadas. Esboce a região. a ) y = 1 x , y =0 , x =1 e x =2 . b ) y = x 2 , y =0 , x =1 . c ) y = e - x 2 , y =0 , x =0 , x =1 . d ) y = x 2 - 6 x +10 , y = - x 2 +6 x - 6 .
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