Ex algebra (16)

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Ex algebra (16)

  1. 1. Lista 13 de C´lculo I a 2010-2 24 UFES - Universidade Federal do Esp´ ırito Santo LISTA 13 - 2010-2 DMAT - Departamento de Matem´tica a Regra de L’Hˆpital o Calcule os limites dos exerc´ ıcios 1. a 12. cos2 x − 1 2 x2 1. lim 2 8. lim cos x→0 ex − 1 x→+∞ x 2. lim (ln x)x−1 x x→1+ π 9. lim tan 3. lim x2 − 1 e−x 2 x→0+ x+2 x→+∞ 1 ln (ln x) 10. lim 1 1 x 4. lim e (1 + x) x x→+∞ ln x x→0 ln( arcsen x) 5. lim 1 + ex coth x x→0+ cot x 11. lim x x→0 2 6. lim x→0 arctan x 1 senh x x 7. lim 2 arctan x x 12. lim x→+∞ π x→0+ x Nos exerc´ ıcios 13. e 14. encontre o valor de a que satisfaz a igualdade. a x 1 + e2x x √ x+a 13. lim = e 14. lim =4 x→+∞ 2 x→+∞ x−a Nos exerc´ ıcios 15. a 22. encontre, se existirem, as ass´ ıntotas horizontais e verticais do gr´fico a da fun¸˜o. ca x 2 15. f (x) = 19. f (x) = e−x ln x 1 e− x2 20. f (x) = xe−x 16. f (x) = x 1 21. f (x) = x cosh x 17. f (x) = e x 3 18. f (x) = x2 ln x 22. f (x) = π x RESPOSTAS 2 1 1 1. −1 3. 0 5. 0 7. e− π 9. 1 11. e 2 13. 4 1 2. 1 4. 0 6. 1 8. e−2 10. e− 2 12. 1 14. ln 2 15. Ass´ ıntota vertical: x = 1 19. Ass´ ıntota horizontal: y = 0 16. Ass´ ıntota horizontal: y = 0 20. Ass´ ıntota horizontal: y = 0 17. Ass´ ıntota vertical: x = 0 21. N˜o tem ass´ a ıntotas Ass´ ıntota horizontal: y = 0 18. N˜o tem ass´ a ıntotas 22. Ass´ ıntota horizontal: y = 0

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