LISTA_13 - ao. 13. f ( x ) = x ln x 14. f ( x ) = e-1 x 2 x...

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Lista 13 alculo I -A- 2007-1 24 Universidade Federal Fluminense EGM - Instituto de Matem´atica GMA - Departamento de Matem´atica Aplicada LISTA 13 - 2007-1 Regra de L’Hˆopital Calcule os limites dos exerc´ ıcios 1. a 10. 1. lim x 0 cos 2 x - 1 e x 2 - 1 2. lim x 1 + (ln x ) x - 1 3. lim x + ( x 2 - 1 ) e - x 2 4. lim x + ln(ln x ) ln x 5. lim x 0 + ln(arcsen x ) cot x 6. lim x 0 x arctan x 7. lim x + ( 2 π arctan x ) x 8. lim x + ± cos 2 x x 2 9. lim x 0 + ± tan π x + 2 x 10. lim x 0 1 e (1 + x ) 1 x · 1 x Nos exerc´ ıcios 11. e 12. encontre o valor de a que satisfaz a igualdade. 11. lim x + ± 1 + e 2 x 2 a x = e 12. lim x + ± x + a x - a x = 4 Nos exerc´ ıcios 15. a 22. encontre, se existirem, as ass´ ıntotas horizontais e verticais do gr´afico da fun¸c˜
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Unformatted text preview: ao. 13. f ( x ) = x ln x 14. f ( x ) = e-1 x 2 x 15. f ( x ) = e 1 x 16. f ( x ) = x 2 ln x 17. f ( x ) = e-x 2 18. f ( x ) = xe-x 19. f ( x ) = π x 3 RESPOSTAS 1.-1 2. 1 3. 0 4. 0 5. 0 6. 1 7. e-2 π 8. e-2 9. 1 10. e-1 2 11. 1 4 12. ln2 13. Ass´ ıntota vertical: x = 1 14. Ass´ ıntota horizontal: y = 0 15. Ass´ ıntota vertical: x = 0 Ass´ ıntota horizontal: y = 0 16. N˜ao tem ass´ ıntotas 17. Ass´ ıntota horizontal: y = 0 18. Ass´ ıntota horizontal: y = 0 19. Ass´ ıntota horizontal: y = 0...
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