gma00108-lista-13 - DEPARTAMENTO DE MATEMTICA APLICADA GMA...

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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/ 13 Diferencia¸c˜ ao impl´ ıcita e taxas relacionadas [01] Use diferencia¸c˜ao impl´ ıcita para calcular a equa¸c˜ao da reta tangente a cada uma das curvas abaixo nos pontos indicados. (a) Curva piriforme: y 2 = x 3 (2 x ) no ponto (1 , 1). (b) Curva astr´ oide: x 2 / 3 + y 2 / 3 =4noponto( 3 3 , 1). (c) Curva lemniscata: 2 ( x 2 + y 2 ) 2 =25( x 2 y 2 ) no ponto (3 , 1). (d) Curva conch´oide de Nicomedes: x 2 y 2 =( y +1) 2 (4 y 2 ) no ponto (0 , 2). 1
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[02] Seja y = f ( x ) defnida implicitamente pela equa¸c˜ ao sec 2 ( x + y ) cos 2 ( x + y )=3 / 2. Calcule f 0 ( π/ 4), sabendo que f ( 4) = 0. [03] Seja y = f ( x ) defnida implicitamente pela equa¸c˜ ao y 2 y xy +2 x 2 = 10. Encontre a equa¸c˜ ao da reta normal ao gr´ afco da Fun¸c˜ ao f no ponto (1 , 4). [04] Considere y = f ( x ) defnida implicitamente por x 4 xy + y 4 =1 . Ca lcu le f 0 (0), sabendo que f ( x ) > 0 , x R .
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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-13 - DEPARTAMENTO DE MATEMTICA APLICADA GMA...

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