gma00108-lista-19

gma00108-lista-19 - LISTA DE EXERC ICIOS DEPARTAMENTO DE...

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GMA DEPARTAMENTO DE MATEMÁTICA APLICADA GM LISTA DE EXERC ´ ICIOS alculo I –A– Humberto Jos´ e Bortolossi http://www.professores.uF.br/hjbortol/ 19 Integrais indefnidas e problemas de valor inicial [01] Calcule as integrais indefnidas dadas abaixo. (a) Z ± ( 3 t ) 2 2 ² dt , (b) Z x x 3 dx , (c) Z ³ 3 x 2 1 ´ dx , (d) Z r 2 x dx , (e) Z (2 s ) sds , (F) Z x 9 x 3 x 4 dx , (g) Z sen(2 θ ) cos( θ ) , (h) Z cos( x ) 1 cos 2 ( x ) dx , (i) Z tg 2 ( u ) du , (j) Z ³ 1+ x 2 + 1 x 2 ´ dx , (k) Z e 2 x 3 e x e x dx ,( l ) Z x 2 x 2 dx , (m) Z 1 x 2 1 x 2 dx , (n) Z 1 1+senh 2 ( y ) dy , (o) Z ( e t e t ) dt , (p) Z x ( 1 tgh 2 ( x ) ) cosh 2 ( x ) dx . [02] Resolva os problemas de valor inicial dados abaixo. y 0 = 1 x 2 1 x 3 , y (1) = 3 / 2 . y 0 = 1 x 1 x 3 , y (1) = 2 . f 0 ( x )=2cos( x ) 3 cossec 2 ( x ) f ( π/ 2) = 8 . [03] Uma Fun¸c˜ao tem derivada de segunda ordem f 0 ( x )=6 x 6. Encontre a express˜ ao para f , sabendo que o seu gr´afco cont´ em o ponto (2 , 1) e que em tal ponto a reta tangente ao gr´ afco de f tem equa¸c˜ ao 3 x y 5=0. 1

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Respostas dos Exerc´ ıcios [01] ( a ) 3
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This note was uploaded on 10/30/2011 for the course ECON 101 taught by Professor Vários during the Spring '11 term at Universidade Federal do Rio de Janeiro.

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gma00108-lista-19 - LISTA DE EXERC ICIOS DEPARTAMENTO DE...

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