Lista4_calculoII_2014_1_respostas - √ 2 1-ln 3 2 9 ♠...

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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 Respostas da 4 a Lista de Exercícios 1 V = πr 2 h 3 2 V = πh 3 ( R 2 + Rr + r 2 ) 3 V = πh 2 parenleftbigg R - h 3 parenrightbigg , onde h é a altura da calota. R h 4 O gráfico da região é x y y = x ( x - 1) 2 1 0 O volume do sólido obtido é V = π 15 . 5 a ) 2 π b ) π 2 c ) π parenleftbigg 1 - 1 e parenrightbigg d ) 400 π e ) 64 π 15 6 3 π 10
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2 UNIVERSIDADE FEDERAL DE MATO GROSSO 7 a ) 21 π 2 b ) 4 π 5 c ) 768 π 7 d ) 16 π 3 e ) 27 π 2 8 a ) 2 243 (82 82 - 1) b ) 2 27 (55 55 - 37 37) c ) 1261 240 d ) 33 6 e ) 32 3 f ) ln(2+ 3) g ) 2+ln(1+ 2) h ) 1+ e 2 - 2+ln( 1+ e 2 - 1) - 1 - ln( 2 - 1) i ) 2
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Unformatted text preview: √ 2 + 1)-ln 3 2 9 ♠ 43,1 m 10 ♠ 209,1 m 11 ♠ a ) π 27 (145 √ 145-1) b ) 49 π c ) 98 π 3 d ) π √ 3 2 + π 4 ln(2 + √ 3) e ) 263 π 256 f ) 21 π 2 g ) π 24 (65 √ 65-17 √ 17) 12 ♠ a ) π 27 (145 √ 145-10 √ 10) b ) π 6 (5 √ 5-1) c ) πa 2 d ) 10 π 3 e ) π 6 [3 √ 10 + ln(3 + √ 10)] f ) 2 π b 1 2 ln(2 + √ 5) + ln p 1 + √ 5 2 P + √ 2 2-3 2 ln(1 + √ 2) B 13 ♠ a ) a = 1 9 b ) A ≈ 31 , 2 m 2 c ) 2 latas d ) R$ 260,00...
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