LISTA_10 - Lista 10 Clculo I -Aa 2007-1 18 Universidade...

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Lista 10 alculo I -A- 2007-1 18 Universidade Federal Fluminense EGM - Instituto de Matem´atica GMA - Departamento de Matem´atica Aplicada LISTA 10 - 2007-1 Fun¸c˜oes inversas Teorema da Fun¸ c˜ao Inversa Fun¸c˜oes trigonom´ etricas inversas 1. Seja f ( x ) = 1 x - x 3 , x > 0. (a) Mostre que f tem inversa em (0 , ); (b) Calcule f - 1 (0) e ( f - 1 ) 0 (0); (c) Determine a equa¸c˜ ao da reta tangente ao gr´afico de f - 1 no ponto ( 0 ,f - 1 (0) ) . 2. Sendo f uma fun¸c˜ ao invert´ ıvel, deriv´avel, tal que f (1) = 2, f (2) = 7, f 0 (1) = 3 e f 0 (2) = 4, calcule ( f - 1 ) 0 (2). 3. Seja f ( x ) = 1 - x 3 , x 0 1 - x 2 , x > 0 . Se f - 1 existir, calcule ( f - 1 ) 0 ( x ) e esboce os gr´aficos de f e f - 1 . Resolva as equa¸c˜ oes dos exerc´ ıcios 4. a 11. 4. sen x = 3 2 5. cos x = 0 6. sen x = - 1 2 7. cos x = - 1 8. tan x = 0 9. tan x = 1 10. tan x = - 1 11. sec x = - 2 Nos exerc´ ıcios 12. a 19. encontre o valor de x. 12.
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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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LISTA_10 - Lista 10 Clculo I -Aa 2007-1 18 Universidade...

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