Limites1 - Exercicios resolvidos

8/10/2019 Limites1 - Exercicios resolvidos

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Calculo A - Limites (I)Calcule os seguintes limites

1. limx 1x 3 +1x

2+1

2. limx 0x 2 12x 2 x 1

3. limx 1x 2 1x 2 +3 x +2

4. limx 1x 2 12x 2 x 1

5. limx 3x 2 5x +6x 2 8x +15

6. limx 1x 3 3x +2x 4 4x +3

7. limx 1x 4 3x +2x 5 4x +3

8. limx 2x 3 2x

2

4x +8x 4 8x2 +16

9. limx 1x 3 2x 1x 5 2x 1

10. limx 2x 2 2xx 2 4x +4

11. limx 1x 3 3x +2x 4 4x +3

12. limx ax 2 (a +1) x + ax 3 a

3

13. limx 1 11x

31x

3

14. limx 0(1+ x )(1+2 x )(1+3 x )

1

x

15. limx 0(1+ x )(1+2 x )(1+3 x ) ... (1+ nx )1x

16. limx 0(1+ x ) 5 (1+5 x )x 2 + x 5

17. limx 0(1+ x ) n (1+ nx )x 2 + x n

18. limx 0(1+3 x ) 2 (1+2 x )

3

x 2

19. limx 0(1+ mx ) n (1+ nx )

m

x 2

20. limx 1x n +1 x

n + x 12x n x n 1

1

21. limx 1x + x 2 + ... + x n nx 1

22. limx 2(x 2 x 2)

20

(x 3 12x +16)10

23. limx 1x 100 2x +1x 50 2x +1

24. limx a x ax a

25. limx 1 x 1x 1

26. limx 64 x 83 x 4

27. limx 13

x 14 x 1

28. limx 1p x 1n x 1

29. limx 72 x 3x 2 49

30. limx 8x 83 x 2

31. limx 1 x 13 x 1

32. limx 43 5+ x1 5x

33. limx 0 1+ x 1xx

34. limh 0 x + h xh (x > 0)

35. limh 03 x + h

3 xh (x = 0)

36. limx 3

x 2

2x +6

x 2 +2 x

6

x2

4x +337. limx 0

1+ x 13 1+ x 1

38. limx 13 x 2 2

3 x +1(x 1)

2

39. limx 3x 2 5x +6 x +1 3x 5

40. limx 3x 2 +2 x 3x +1+ 3 x 2 1

41. limx 13 4x 5 313x 2 x 2

42. limx

1x 2 15

2x 5

1143. limx a

a x + a x a 2 x2

Limites quando x 44. limx

(x +1) 2x 2 +1

45. limx 1000 xx 2 1

46. limx x 2 5x +13x +7

47. limx 2x 2 x +3x 3 8x +5

48. limx (2 x +3) 3 (3 x 2)

2

x 5 +5

49. limx 2x 2 3x 4 x 4 +1

50. limx 2x +3

x + 3 x

51. limx x 2

10+ x x

52. limx 3 x 2 +1

x +1

53. limx x

x + x + x54. limx

x3 x 3 +10


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55. limx ( x + a x )

56. limx ( x (x + a ) x )57. limx ( x 2 5x + 6 x )58. limx

x ( x 2 + 1 x )59. limx (

x + 3 1 x 3)60. limx (

x 2 + 1 x 2 1)61. limx (

12x3 1+8 x 3 + 2 x 2 )

62. limx ( x 3

3x 2 4 x 2

3x +2 )

63. limx ( 9x 2 + 1

3x )

64. limx 2 x +3 3 x +5 5 x 3x 2+

3 2x 3

65. limx ( 2x 2 3 5x )

66. limx x ( x 2 + 1 x )

67. limx 2x 2 +3

4x +2

68. limx 2x 2 +3

4x +2

69. limx 5 2 xx +3

70. limx x x 2 +1

71. limx x

x 2 +1

72. limx 3x 3

x

3x +3 x

73. limx 3x 3

x

3x +3 x

Resposta 1. 0

2. 1

3. 24.

23

5. 126. 127. 1

8. 149. 1310.

11. 1212. a 13a 2

13. 1

14. 6

15. n (n +1)216. 10

17. n (n 1)218. 319. mn (n m )220. 2n +121. n (n +1)222. 3

10

210

23. 492424. 12 a

25. 1

226. 3

27. 4328. n p29. 15630. 12

31. 3232. 1333. 1

34. 12 x35. 1

3x23

36. 1337. 3238. 1939. 240. 841. 4342. 1

43. 1 2a44. 1

45. 0

46. + 47. 0

48. 72

49. 2

50. 2

51.


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52. 0

53. 1

54. 1

55. 0

56. a257. 5258. 1259. 0

60. 0

61. 162. 29

63. 064. 2 365. 66. 1267. 2468. 2469. 25

70. 171. 1

72. 173. 1


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Limites1 - Exercicios resolvidos