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(1)Chuyên đề –Giới hạn hàm số
1 (HVBC 99) lim sin sin
x
x x
x x
2 (GT 97)
1 lim cos
x x x
3 (GT 01)
2
2
2
1 lim
ln(1 )
x x
e x
x
4 (QG 97)
3
2
lim
x
x x
x
5 (QG 98)
3
lim
1
x
x x
x
6 (SPII 99)
5
1
2
lim
1
x
x x
x
7 (SP II 00)
lim tan tan( )
x
x x
8 (SP II 00)
2
3 cos lim x
x
x x
9 (TN 97) 2
0
cos( cos ) lim
sin( )
x
x x
10 (TM 99)
2
1 cos
lim
x
x x
x
11 (TL 01)
2
1
lim
x
x x
x
12 (NH 98)
1
2
lim
1
x
x x
x
13 (§N 97)
1 cos lim
sin
x
x
x x
14 (QG –B97)
0
1 |1 sin |
lim | |
1 cos
x
x x
15 (QS 97) 3
tan sin lim
x
x x
x
16 (SP V 97)
1 sin cos lim
1 sin cos
x
x x
x x
17 (TN 98)
2
0
tan( ) tan( ) tan lim
x
x a x a a
x
18 (GT 98)
1 sin lim
3
x
x x
x x
19 (AN 00) 2
0
98 cos3 cos5 cos
lim ( )
83 sin
x
x x x
x
20 (HH 97)
1 cos lim
1 cos
x
x x
21 (HH 00)
3
1 tan sin lim
x
x x
x
22 (HH 99) sin sin
0
lim sin
x x
x
e e
x
23 (HP 00)
3 lim
tan( 1)
x
x x
x
24 (QG D97)
3
2 lim
sin( 1)
x
x x
x
25 (MM 99) lim( 2)2 1
x x
x x
26 (QG 00)
3
2 1
lim
sin
x
x x
x
27 (TC 01)
2
5
lim
1
x
x x
x
28 (HH 01)
4
2
cos sin
lim
1
x
x x
x
29 lim
x x x x
30 xlim (x a x b)( ) x
31 xlim n(x a1) (x an) x
32 lim 3( 5)( 6)( 7) 4( 1)( 2)( 3)( 4)
x x x x x x x x
33 lim ( )
x x x x 34
2
lim ( 2 )
x x x x x x x
35 2
0
1 cos lim
x
ax x
36
sin cos lim
sin
x
x x
x
(2)Tìm giới hạn hàm sè sau:
1 2
1
8 lim
2
x x
x x
2
3
4
lim
x
x x
3
3
3
2
5
lim
1
x
x x
x
4
2
0
( 2001) 2001 lim
x
x x
x
5
1
2 lim
1
x
x x
x
6
3
3
lim
1
x
x x
x
7
0
2
lim
x
x x
x
8
1
2
lim
1
x
x x
x
9
tan sin lim
x
x x
x
10
2
1 cos
lim
x
x x
x
11
3
1 tan sin lim
x
x x
x
12
1
3 lim
tan( 1)
x
x x
x
13 lim sin sin
x
x x
x x
14
1 lim cos
x x x 15
2
lim cot
sin
x x x
16
3
lim
1
x
x x
x
17
lim tan tan( )
x
x x
18
2
2
3 cos lim
x x
x x
19 23
0
1
lim
x
x x
x
20
0
1
lim
x
x x
x
21 2
0
3
lim
1 cos
x
x x
x
21
0
3 1
lim
1 cos3
x
x x
x
22
2
2
lim
1 cos
x x
x e
x
23 22
0
cos
lim
cos x x
x x
x e
24
2
2 2
2
( 1) 3
lim
cos3 log ( 2)
x x
x x
x x
25
2
2
cos lim
x x
e x
x
26 2
4
2 log (3 1) lim
1
x x
x x
27 2
4
9 ( 3) cos3 lim
3
x
x x x
x x
28
3
1
lim
x
x x
x
29
0
1 cos3
lim
1 cos3
x
x x
x
30
2 cos3 lim
x x
x x
31
2
2
4
cos lim
4
x x
e x
x x
32
2 2
0
( 1) cos lim
1 cos5
x x
e x x
x
33
1 sin
lim(1 ) x
x x
34
(5 4) 3sin cos
2 lim
1
x
x x x x
x
35 11
1
lim( 1)x
x x
36
lim cot cot( )
x x x
37
lim ( 2) cot
x x x
38
1
lim(cos 2sin )x