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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