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(1)giới hạn hàm số
1 (ĐHQGHN-D2000)
3
2 1
lim
sin
x
x x
x
2 (§HSPHN2-A2000) lim
4
x
tg x tg x
2
2
3 cos lim
x x
x x
3 (§HSPHN-B2000)
2
1
7
lim
1
x
x x
x
4 (§HTN-G2000)
3
2
lim
2
x x
x x
x
5 (§HAN-A2000)
98 cos3 cos5 cos7
lim ( )
83 sin
x
x x x
x
6 (§HHH-2000)
1 sin
lim
x
tgx x
x
7 (ĐHDLĐôngĐô-AV2000) cos5 cos7 lim
sin 11
x
x x
x
7 7
8 2 lim
x
n n
8 (§HDLHP-BD2000)
3 lim
( 1)
x
x x
tg x
9 (§HSPV-DMT2001)
3 3
0
1
lim
x
x x x
x
10 (§HBKHN-D2001)
2
1
lim
1 cos
x
x x
11 (§HGTVT-2001)
2 3
2
2
1 lim
ln(1 )
x x
e x
x
12 (§HTL-2001)
3
1
lim
x
x x
x
13 (§HTCKTHN-2001)
3 2
5
lim
1
x
x x
x
14 (§HHH-A2001)
4
2
cos sin
lim
1
x
x x
x
15 (§HDL§§-A2001)
2
1
lim
1
x
x x
x x
16 (§H§N-D2001)
1 lim
1
x x x
17 (§HDL§§-BD2001)
cos12 cos10 lim
cos8 cos6
x
x x
x x
18 (§HH§-D2001)
3
3
lim
1
x
x x
x
19 (C§SPHN-D12001)
1 cos lim
sin
x
x
x x
3
1 lim
1
x x x
20 (C§MGTWI-2001) lim
x n
tg x x n
21 (§HSPHN2-A99)
5
1
2
lim
1
x
x x
x
22 (HVCNBCVT-99)
sin lim
sin
x
x x
x x
23 (§HHHTPHCM-99)
sin sin
lim sin
x x
x
e e
x
24 (HVKTMM·-99)
2 2 2
lim
1
x
n n n
n n n n
2 lim
1
x x
x x
25 (§HTM-99)
2
1 cos
lim x
x x
x
26 (§HSPV-B99)
1 sin cos2 lim
1 sin cos
x
x x
x x
27 (§HQGHN-A95)
2
sin sin sin lim
x
x x x
x
28 (§H§N-96)
2
1 cos lim
.sin
x
x
x x
29 (§HQGHN-B96) cos lim
sin
x
x x
30 (§HTN-A97)
2
cos cos lim
sin
x
x x
31 (HVKHQS-97) sin lim
x
tgx x
x
32 (§HTN-D98)
2
0
( ) ( )
lim
x
tg a x tg a x tg a x
33 (§HLHN-98) cos lim
7
x
x x
34 (§HQGHN-A97)
3
2
lim
x
x x
x
35 (§HHH-97)
1 cos lim
1 cos
x
x x
36 (HVNH-D98)
2
lim
1
x
x x
x
(2)37 (§HQGHN-A98)
3
lim
1
x
x x
x
38 (§HGTVT-95)
1
lim
1
x x
x
39 (§HQGHN-B96)
2
1 cos lim
(1 )
x
x x
40 (§HQGHN-B97)
|1 |1 sin || lim
1 cos
x
x x
41 (§HGTVT-98)
1 sin
lim
3
x
x x
x x
42
3
3
3
lim
4
x
x x x
x x
43
2
3
1
3
lim
4
x
x x
x x x
44
3
3
2
7 16 12
lim
3
x
x x x
x x
45
3
lim
4
x
x x
x x x x
46
1 lim
1
x x
x
47
2
0 lim
1 (1 )
x
x
x x
48 lim x
x a
x
49
1 lim
n x
x x
50
3
2
lim
1
x
x x
x
51
3
2 20
lim
1
x
x x
x
52
3
2
lim
( 1)
x
x x
x
53
3 2
2
7
lim
2
x
x x
x x
54
2
3
lim
5
x
x x
x x
55.xlim ( x x x)
56
2
lim( 3)
x x x x x
57.
3
lim ( )
x x x
58 sin lim
2
x
x tg x
59 cos lim
sin
x
x
x x
60
3sin lim
3 4sin
x
x
x x
61 sin lim
2
x
tgx x
x
62 lim
cos
x
tgx x
63
1 2sin lim
sin
x
x x
64
sin(sin ) lim
x
x x
65 sin lim
sin
x
x x
x x
66 lim
x x
a x
67
1 sin
lim x x
x tg x
68
ln( ) ln( ) 2ln lim
h
x h x h x
h
69
1 lim(cos )x
x x
70
1 cos cos cos3 lim
1 cos
x
x x x
x
71
3 4
10 7
( 1) ( 4) ( 8)
lim
( 3) ( 5) ( 3)
x
x x x
x x x
72
2 3
2 2
(2 1) (3 4) ( 6) lim
(4 8)(5 3)
x
x x x
x x x
73
3
4
( 1) (3 4) (2 6) lim
(5 7)( 1)
x
x x x
x x x
74
2
lim ( 2)
x n n n
75
3
lim( )
x n n n n
76
1 (2 1) lim
2
x
n n
n n
77 limx n1( n2 n)
78
0 2
cos lim
2sin cos
x
x x x
x x
79 sin( 1) lim
3
x
x
x x
80
sin cos lim
4
x
x x
x
(3)81
2
1 sin cos lim
sin
x
x x
x
82
0 2
1
lim( )
sin
x tgx x
83
1 cos3 lim
sin
x
x x tg x
84
2 2
sin
lim( )
cos
x
x tg x x
85
lim ( )
x
tg x tg x
86
1 sin
lim
x
tgx x
x
87
1
lim(1 sin )x
x x
88 lim
ax bx
x
e e
x
89 lim
sin
x x
e x
90
3
0
1
3
lim
1
2
x
x x
x
91
3
cos cos
lim
sin
x
x x
x
92
2 1
lim(2 1)
x x
x x
x e
93
2
cos lim
x x
e x
x
94
1
limn
x
ax x
95
1 1
lim
n m
x
ax bx
x
96 lim
1
m n x
x x
97
2 2
1 lim
2
x
x x x
98
ln(1 ) lim
x
x x
99
2
0
( ) ( )
lim
x
tg x a tg a x tg a x