bai tap gioi han cua day so va ham so
DESCRIPTION
Bai Tap Gioi Han Cua Day So Va Ham SoTRANSCRIPT
Chng IV
Gii hnA. Kin thc sch gio khoa
I. Gii hn ca dy s1. Dy s c gii hn 0a. nh ngha: Ta ni rng dy sc gii hn 0, k hiu(hay), nu vi mi s dng nh bao nhiu ty cho trc, mi s hng ca dy s, k t s hng no tr i, u c gi tr tuyt i nh hn s dng .
b. Tnh cht:
c. nh l: Cho hai dy s (1)
2. Dy s c gii hn hu hn
a. nh ngha: Ta ni rng dy s c gii hn l s thc L, k hiu , nu
b. Cc nh l:
Cho (un) m un = c, (n :
limun = L
Nu th:
(2) Dy (un) tng v b chn trn th c gii hn;
Dy (vn) gim v b chn di th c gii hn. (3)
c. Tng ca mt cp s nhn li v hn
3. Dy s c gii hn v cca. Dy s c gii hn
Ta ni rng dy (un) c gii hn +, k hiu limun = +, nu vi mi s dng ty cho trc, mi s hng ca dy s, k t s hng no tr i, u ln hn s dng .
Kt qu:
b. Dy s c gii hn -
Ta ni rng dy (un) c gii hn l - , k hiu limun = -, nu vi mi s m ty cho trc, mi s hng ca dy s, k t s hng no tr i, u nh hn s m .
c. Cc quy tc tm gii hn v cc
Quy tc nhn
+
+
Quy tc chia
c du c du
++
+
+
II. Gii hn ca hm s
1. Gii hn hu hn
a. Gii hn hu hn
Cho v f l hm s xc nh trn tp . Ta ni rng hm s f c gii hn l s thc L, k hiu , khi x dn n (hoc ti im ), nu vi mi dy s trong tp m , ta u c
b. Gii hn v cc
nu mi dy trong tp m th
2. Gii hn ca hm s ti v cc
nh ngha: Gi s hm s f xc nh trn khong . Ta ni rng hm f c gii hn l s thc L khi x dn n +, k hiu , nu vi mi dy s trong khong m , ta u c
3. Cc nh la. nh l 1: Gi s v . Khi :
b. nh l 2: Gi s . Khi :
;
;
Nu vi mi , trong J l mt khong no cha th v .
c. nh l 3: Gi s J l mt khong cha v f, g, h l ba hm s xc nh trn tp hp . Khi :
4. Gii hn mt bn
a. nh ngha:
Gi s hm f xc nh trn khong . Ta ni rng hm f c gii hn bn phi l s thc L khi x dn n x0, k hiu: , nu vi mi dy s trong khong m , ta u c .
Gi s hm f xc nh trn khong . Ta ni rng hm f c gii hn bn tri l s thc L khi x dn n x0, k hiu: , nu vi mi dy s trong khong m , ta u c .
Cc nh ngha c pht biu tng t nh trn.
b. nh l:
5. Quy tc tm gii hn v cc
a. Quy tc nhnb. Quy tc chia
c du
c du
g(x) c du
+
++
+
+
+
6. Cc dng v nh
Khi tm khi ta gp cc dng v n, k hiu , lc ta khng dng c cc nh l v gii hn cng nh cc quy tc tm gii hn v cc. Php bin i v cc nh l v quy tc bit gi l php kh cc dng v nh
B. Cc dng ton c bn
Dng 1: Tm gii hn ca dy sPhng php gii: Dng nh ngha, tnh cht v cc nh l v gii hn ca dy s.
V d 1: Tm:
Gii:
V d 2: Tm:
Gii:
V d 3: Tm:
Gii:
.
Dng 4: Tnh tng ca cp s nhn li v hn
Phng php gii: S dng cng thc:
V d: Tnh tng
Gii:y l tng ca mt cp s nhn li v hn, vi v . Vy:
Dng 5: Tm gii hn v cc
Phng php gii: S dng quy tc tm gii hn v cc
V d: Tm:
Gii:Cch 1:
Ta c:
Li c v nn suy ra:
Cch 2:Ta c:
Li c
Dng 6: Tm gii hn ca hm s
Phng php gii: S dng cc nh l v quy tc
V d 1: Tnh: .
Gii:Xt dy m v . Ta c:
V Do .
V d 2: Tnh:
Gii:
Ta c:
V d 3: Tnh:
Gii:Ta c:
(Ch : khi l ta xt x < 0, nn )
Dng 7: Chng minh (Hoc bng L)
Phng php gii: S dng nh l gii hn kpGi s J l mt khong cha v f, g, h l ba hm s xc nh trn tp hp . Khi :
V d: Chng minh:
Gii:Ta lun c:
.
Dng 8: Tm gii hn mt bn
Phng php gii: S dng nh ngha gii hn mt bn
V d 1: Cho hm s . Tm
Gii:Ta c: (1)
(2)
T (1) v (2) suy ra
V d 2: Cho hm s
a. Tm
b. Tm
Gii:a.
b.
Ta c:
suy ra khng tn ti
(Ch : tn ti khi v ch khi th )
Dng 9: Tm gii hn v cc
Phng php: S dng quy tc tm gii hn v cc
V d: Tnh
Gii:
V v
Dng 10: Kh dng v nh
Phng php gii
1. Khi tm gii hn dng, vi :
Vi P(x), Q(x) l nhng a thc nguyn theo x th ta chia c t P(x) v mu Q(x) cho
Nu P(x), Q(x) cha du cn thc theo x th ta nhn c t P(x) v mu Q(x) cho lng lin hip.
V d 1: Tm:
Gii:
V d 2: Tm:
Gii:
V d 3: Tm:
Gii:
V d 4: Tm:
Gii:
V d 5: Tm:
Gii:
V d 6: Tm:
Gii:t . Do :
V d 7: Tm:
Gii:
2. Khi tm gii hn dng , ta lu :
t (m l bc cao nht) lm nhn t chung t P(x) v mu Q(x)
S dng kt qu: ( vi )
V d 1: Tm:
Gii:
V d 2: Tm:
Gii:
V d 3: Tm:
Gii:
C. Bi tp t lun1. Tm gii hn ca cc hm s sau:
1.
2.
3.
4.
5.
6.
7.
8.
9.
2. Tm cc gii hn hm s sau:1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
3. Tm gii hn ca cc hm s sau:1.
2.
3.
4.
5.
6.
7.
8.
4. Tm gii hn ca cc hm s sau:
1.
2.
3.
4.
5.
6.
5. Tm gii hn ca cc hm s sau:1.
2.
3.
4.
5.
6.
7.
8.
D. Bi tp trc nghim
Dy s c gii hn 0
1. Dy s no sau y c gii hn khc 0?
a.
b.
c.
d.
2. Dy s no sau y c gii hn bng 0?
a.
b.
c.
d.
3. Dy s no sau y c gii hn bng 0?
a.
b.
c.
d.
4. Dy s no sau y khng c gii hn?
a.
b.
c.
d.
5. Gi . Khi L bng
a.
b.
c. 1d. 0
6. Dy s no sau y c gii hn khc 0?
a.
b.
c.
d.
Dy s c gii gin hu hn
7. Cho . Khi un bng
a.
b.
c.
d.
8. Cho . Khi limun bng
a. 0b. 1c.
d.
9. Gi th L bng s no sau y?
a. 0b.
c. 3d. 9
10. Tng ca cp s nhn v hn l
a. 1b.
c.
d.
11. Tng ca cp s nhn v hn l
a.
b.
c.
d. 4
12. Tng ca cp s nhn v hn l
a.
b.
c.
d.
13. Tng ca cp s nhn v hn: l
a.
b.
c.
d. 2
Dy s c gii hn v cc
14. Kt qu l
a.
b. 4c. 6d.
15. Bit th L bng
a.
b. 3c. 5d.
16. bng
a.
b. 6c. 3d.
17. bng
a.
b.
c. 1d. 0
18. bng
a.
b.
c. 0d.
19. bng
a. 0b.
c.
d.
20. bng
a. 0b.
c.
d.
21. bng
a.
b. 0c.
d.
22. bng
a.
b.
c. 0d.
23. Dy s no sau y c gii hn l?
a.
b.
c.
d.
24. Dy s no sau y c gii hn l - ?
a.
b.
c.
d.
25. bng
a. 0b. 1c. 2d.
26. Kt qu l
a. +b. 10c. 10d. 0
27. Kt qu l
a. 0b. 1c.
d.
28. Nu th bng
a. L + 9b. L + 3c.
d.
29. Nu th bng bao nhiu?
a.
b.
c.
d.
30. bng
a.
b.
c. 1d.
31. bng bao nhiu?
a.
b. 10000c. 5000d. 1
32. bng bao nhiu?
a. 0b.
c.
d.
33. bng
a.
b.
c.
d. 034. bng bao nhiu?
a. +b. 4c. 2d. 1
35. bng s no sau y?
a.
b.
c. 0d. 1
36. Dy s no sau y c gii hn bng 0?
a.
b.
c.
d.
37. Dy s no sau y c gii hn l +?
a.
b.
c.
d.
38. Dy s no sau y c gii hn +?
a.
b.
c.
d.
39. Trong cc gii hn sau y, gii hn no bng 1?
a.
b.
c.
d.
40. Trong cc gii hn sau y, gii hn no bng 0?
a.
b.
c.
d.
41. Trong cc gii hn sau y, gii hn no l ?
a.
b.
c.
d.
42. Dy s no sau y c gii hn bng ?
a.
b.
c.
d.
43. Nu th L bng
a.
b.
c.
d. 0
44. Gi . Khi L bng
a.
b. 6c. 3d. 2
45. bng
a. 1b.
c. 2d.
46. bng
a.
b.
c. 9d. 3
47. c kt qu l
a. 1b. 2c. 4d.
50. Dy s no sau y c gii hn ?
a.
b.
c.
d.
Gii hn ca hm s
51. bng
a. 5b. 7c. 9d.
52. bng
a.
b. 5c. 9d. 10
53. bng
a.
b. 1c. 2d.
54. bng
a. 5b. 1c.
d.
55. bng
a.
b.
c.
d.
56. bng
a.
b.
c.
d.
57. bng
a.
b.
c.
d.
58. bng
a.
b.
c.
d.
59. bng
a.
b.
c.
d.
60. bng
a. 5b. 3c. 1d.
61. bng
a. 0b. 1c.
d.
62. bng
a.
b.
c. 1d. 2
63. bng
a. 0b.
c.
d.
64. bng
a.
b.
c.
d.
65. bng
a.
b.
c.
d. 0
66. bng
a. 0b.
c.
d.
67. bng
a.
b.
c.
d.
68. bng
a.
b.
c.
d.
Gii hn mt bn
69. bng
a.
b.
c. 0d.
70. bng
a. 1b. 0c.
d.
71. bng
a.
b.
c.
d.
72. l
a.
b. 2c. 1d.
73. bng
a.
b.
c.
d.
74. l
a.
b.
c.
d.
75. l
a.
b. 0c. 1d.
76. Cho hm s: . Khi bng:
a. 11b. 7c.
d.
77. Cho hm s . Khi bng
a. 4b. 3c. 2d. 2
78. Cho hm s . Khi bng
a.
b.
c. 0d.
79. Cho hm s: . Khi bng
a. 1b. 0c. 1d.
80. Cho hm s . Khi bng
a.
b. 2c. 4d.
Mt vi quy tc tm gii hn v cc (dng v nh)81. Cho . Khi
a.
b.
c.
d.
82. Cho . Khi
a.
b.
c.
d.
83. bng
a.
b.
c.
d.
84. bng
a.
b. 5c.
d.
85. bng
a.
b.
c.
d.
86. bng
a.
b.
c.
d.
87. bng
a.
b. 2c. 0d.
88. bng
a.
b.
c.
d.
89. bng
a.
b. 2c. 1d. 0
90. bng
a.
b. 4c. 1d.
91. bng
a.
b.
c.
d.
92. bng
a.
b. 0c.
d.
93. bng
a.
b. 3c. 1d.
94. bng
a. 0b. 1c. 2d.
95. bng
a. 0b. 1c.
d.
96. bng
a.
b. 1c.
d.
97. bng
a. 8b. 4c.
d.
98. bng
a. 4b. 1c. 4d.
99. bng
a.
b. 2c.
d.
100. bng
a.
b.
c.
d.
101. bng
a. 3b. 1c. 0d. 1
102. bng
a. 0b. 1c. 2d.
103. bng
a.
b.
c. 0d.
104. bng
a.
b. 1c. 2d.
105. bng
a.
b. 4c. 0d.
106. bng
a.
b. 2c. 6d.
107. bng
a.
b.
c.
d.
108. Ni mi ct bn tri vi mi ct bn phi c mt khng nh ng.Ct triCt phi
1. bnga)
2. bngb) 0
3. bngc)
4. bngd)
e)
PAGE
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