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# LISTA_12 - 3 4 4 y x –2 2 4 6 8 10 –5 –4 –3 –2...

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Lista 12 alculo I -A- 2007-1 22 Universidade Federal Fluminense EGM - Instituto de Matem´atica GMA - Departamento de Matem´atica Aplicada LISTA 12 - 2007-1 Fun¸c˜ ao logar´ ıtmica Fun¸c˜ ao exponencial 1. Seja f ( x ) = ln ( x 2 - 3 ) p ( x - 1)( x + 3) . Determine o dom´ ınio de f , os valores de x onde a f se anula e os intervalos onde a f ´ e positiva e onde a f ´ e negativa. Nos exerc´ ıcios 2. a 5. esboce o gr´afico da fun¸c˜ ao. 2. f ( x ) = ln | x - 4 | 3. y = | ln | x + 1 | | 4. F ( x ) = e | x +2 | 5. g ( t ) = 1 2 - e - t Derive as fun¸c˜ oes dos exerc´ ıcos 6. a 16. (se for conveniente, use deriva¸ ao logar´ ıtmica) 6. f ( x ) = e sen 2 x x e cos 3 x 7. f ( x ) = e x ln x 8. f ( x ) = ln x x 2 + 1 · 9. f ( x ) = ( e x ) x 10. f ( x ) = e x x 11. f ( x ) = ( x x ) x 12. f ( x ) = log 2 x 2 13. f ( x ) = ( sen x ) arcsen x 14. f ( x ) = x π + π x 15. f ( x ) = (ln x ) x x ln x 16. ln x + 1 ( x - 1) 3 Calcule y 0 nos exerc´ ıcios 17. a 19. 17. ln x y + y x = 5 18. sen e xy = x 19. y 2 cos x e x = 2 ln y , para x = 0 e y = 1 RESPOSTAS 1. Dom´ ınio = ( -∞ , - 3) ( 3 , ) ; f = 0 em x = 2 f > 0 para x < - 3 ou x > 2; f < 0 para 3 < x < 2 2. x y –3 –2 –1 0 1 2 3. y x 0 1 2 –2 –1 1 2

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Unformatted text preview: 3 4 4. y x –2 2 4 6 8 10 –5 –4 –3 –2 –1 1 5. x y –5 –4 –3 –2 –1 1 Lista 12 C´ alculo I -A-2007-1 23 6. f ( x ) = (1 + 4 x cos2 x + 6 x sen3 x ) e sen 2 x 2 e cos 3 x √ x 7. f ( x ) == e √ x (1 + √ x ln √ x ) 2 x 8. f ( x ) = 2 x 2 + 1 x ( x 2 + 1) 9. f ( x ) = 2 xe x 2 10. f ( x ) = x x e x x (1 + ln x ) 11. f ( x ) = ( x x ) x ( x + 2 x ln x ) 12. f ( x ) = 2 x ln2 13. f ( x ) = (sen x ) arcsen x ± cot x arcsen x + ln(sen x ) √ 1-x 2 ¶ 14. f ( x ) = πx π-1 + (ln π ) π x 15. f ( x ) = (ln x ) x ( x ln x ) ± 1 ln x + ln(ln x ) + 2ln x x ¶ 16. f ( x ) =-(5 x + 7) 2( x 2-1) 17. y = y x 18. y = 1-ye xy cos e xy xe xy cos e xy 19. y = 1 2-ln2...
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