Bài 1 Tính các giới hạn1.
Trang 1Bài 1 Tính các giới hạn
1 lim(2x 3) 7x→2 + =
2 limx 3→ 2(x 1)x 1+ =1
− 3
1
5 3 lim
2
+ +
x x
x
4 lim(xx 0→ 3+5x2+10x)
x 1
x 5x 6
lim
x 2
→
−
6 lim x 1x 3→ −
2
2 lim
3 1
x
x
−
→
− + 8
2
3 1
lim
2
x
x
+
→
−
9 22
x 2
2x 3x 1
lim
x 4x 2
→−
10
3
x 1
lim
1 x 1 2x
→
11 3 2
x 0
x 4 lim
x 3x 2
→
−
12
x 1
1 x 1 x lim
x
→
13
x 2
sin x lim x
π
→
14 lim0 1
cos
x→ x
15 limx→0tanxcos+sin2xx
16 x
4
tgx lim
x
π
→ π −
17
2
3 3 lim
2
+
−
−
x x
18
2
3 3 lim 2
+
− +
x x
19
4
3 lim
4
x
x x
±
→
−
− 20
2
3 3 lim 2
2
+
−
−
−
x x
x
21
2
3 3 lim 2
2
+
− +
−
x x
22 23
x 1
x 3x 2 lim
x 5x 4
−
→
23
x 0
1 x lim x
x
±
→
x 1
x x 2 lim
x 1
+
→
+ −
25
x 2
1 cos2x lim
x 2
+
→
+
π −
26 lim 3 2 5
Bài 2 Tính các giới hạn
27
2 2
x 2
x 4 lim
x 3x 2
→
−
− + 28
2 2
x 1
x 1 lim
x 3x 2
→ −
−
29
2 2
x 5
x 5x
lim
x 25
→
−
−
30 22
x 2
x 2x lim
2x 6x 4
→
−
31 34
x 1
x 3x 2
lim
x 4x 3
→
32 3 2 2
x 1
x x x 1
lim
x 3x 2
→
33
→
−
−
2
x 2
x 2x lim
x 2
34
→
3 2 3
x 1
x x x 1 lim
x 3x 2
35 lim 22 23 6
8
x
x
→ −
+ −
36 42 2
3
72 lim
2 3
x
→
− −
37 53
1
1 lim
1
x
x x
→−
+ +
38 3 4 2 2
x 3
x 5x 3x 9 lim
x 8x 9
→
Trang 239 4 3 3 2 2
x 1
2x 8x 7x 4x 4
lim
3x 14x 20x 8
→
40 3 3 2
x 2
x 3x 9x 2
lim
x x 6
→ −
41 1 2
lim
x→ x x
lim
43
2
x 1
x 5x 4x
lim
(1 x)
→
−
h 0
(x h) x
lim
h
→
45 2 3 3
x a
x (a 1)x a
lim
x a
→
−
46 4 4
x a
x a
lim
x a
→
−
−
h 0
2(x h) 2x
lim
h
→
48 limx 1 2 x 2 2x 4
x 5x 4 3(x 3x 2)
→
49 19921990
x 1
x x 2
lim
x x 2
→
+ −
+ −
x 1
x nx n 1
lim
(x 1)
→
− 51
2 3
1 lim 2
2
−
−
x
x
52
1
3 5 3
2 3
− +
−
x x
x
x
53
9 8
9 3 3
lim 4 2
2 3
− +
−
x x
x
x
54
6
2 9 3
lim 3
2 3
−
− +
x x
x
x
55 lim632 192 155
2
3
−
−
x x
x
56 lim 22 2 93 42
2
2
−
−
−
x x
x
57
2 3
3 7 5 lim 3
2 3
+ + +
−
x x x
x
58
8 x
18 x x 4 lim 2 3
2
− +
59
2 2
x 5
x x 30 lim
2x 9x 5
→
+ −
− −
x 1 lim
x 2x x 2
→−
+ + − − 61
2
1 x 2
4x 1 lim
4x 2x 1
→
−
62 22
x 1
x 4x 3 lim
x 2x 3
→
63
2 2 1 x 2
2x 5x 2 lim
4x 1
→
−
64 22
2x 3x 1 lim
x 4x 5
→−
65
4 2
x 16 lim
x 2x
→−
− +
66 23
x 1
x 1 lim
x x
→
−
− 67
3 x 4 x
27 x lim 2
3 3
−
→
68 3 2 2
x 2
x 6x 12x 8 lim
x 4x 4
→
69
2
x 1
x x x 1 lim
x 5x 6
→
− − +
70 2 3
x 2
8x 64 lim
x 5x 6
→
−
71 3 2 3
x 2
x 2x 6x 4 lim
8 x
→
−
72 3 2 2
x 2
x x 5x 2 lim
x 3x 2
→
Trang 373 3 2 2
x 4x 6x 3
lim
x x 2
→−
− −
74 32
x 1
x 3x 2
lim
x 2x 1
→
75 53
x 1
x 1
lim
x 1
→
−
−
x 0
x x lim
2x
+
→
+
x 0
2x lim
4x x
±
→ +
78 xlim (x→−∞ 3+4x2+6x 3)+
79 xlim ( 3x→±∞ − 5+3x2−7x 2)+
80 xlim ( x→−∞ − +4 5x2−6x 7)+
81 lim ( 2 3 2 2 2)
82 lim ( 2 3 2 2)
83 lim (→±∞ 3 3+2 − −1 2 2 −3 )
84 xlim ( x→±∞ 3 3+x2 −3x)
85 lim (→+∞ 2+ +5 )
86 lim ( 2→±∞ 2 + +5 )
87 xlim (3x 1→±∞ − − 4x2−4x 3)−
Bài3 Tính các giới hạn
88
2
x 0
x 1 x x 1
lim
x
→
+ − + +
x 7
x 3 2
lim
49 x
→
− −
−
90 2
x 2
2 x 2
lim
x 3x 2
→
91.EMBED
Equation.DSMT4
2
x 2
4x 1 3
lim
x 4
→
+ −
−
92 EMBED
Equation.DSMT4
2 2 1
lim
3 2
x
x
→
93 EMBED
Equation.DSMT4
x 1
2x 7 3 lim
x 4x 3
→
+ −
94 EMBED Equation.DSMT4
2 2 1
lim
3 2
x
x
→
95 EMBED Equation.DSMT4
3 2
2 lim
8
x
x
→
− 96
2 2
x 1
3x 2 4x x 2 lim
x 3x 2
→
97 EMBED Equation.DSMT4
x 1
3 8 x lim
2x 5 x
→
98 EMBED Equation.DSMT4
x 4
3 5 x lim
1 5 x
→
99.EMBED Equation.DSMT4
x 2
x x 2 lim
4x 1 3
→
+ −
100 EMBED Equation.DSMT4
→
2 3
1
2 6 4 1 lim
2 1
x
101 EMBED Equation.DSMT4
4
x 1
x 1 lim
x x 2
→
−
102 EMBED Equation.DSMT4
3 2 0
1 1 lim 2
x
x
x x
→
+
103 EMBED Equation.DSMT4
3 2 1
1 lim
x
x
→−
+
Trang 4104 EMBED
Equation.DSMT4
3
2
x 2
2x 12 x lim
x 2x
→−
+
105 EMBED
Equation.DSMT4
3
x 1
x 7 2 lim
x 1
→
+ −
−
106 EMBED
Equation.DSMT4
3
0
1 1 lim
1 1
x
x
x
→
+ − + −
107 EMBED Equation.DSMT4
3
x 1
x 7 2 lim
x 1
→
+ −
−
108 EMBED Equation.DSMT4
3 4
x 1
x 1 lim
x 1
→
−
−
109 EMBED Equation.DSMT4
3 3
x 1
x 1 lim
4x 4 2
→
− + −
110 EMBED Equation.DSMT4
3 2 3
2
x 1
x 2 x 1 lim
(x 1)
→
−
Bài 4 Tính các giới hạn
1
x 0
x 1 x 4 3
lim
x
→
2
x 0
x 9 x 16 7
lim
x
→
3
→
−
3 2
lim
8
x
x
x 4
4 x lim
x 4x 1 5 x
3
2
8 lim
x
x
6
→
3
1
lim
2 1
x
7
→
2
x 1
x 2x 8 x
lim
x 4x 3 5 x
8
→
3
4
x 1
x 7 x 3x 2 lim
x x x 1
9 3
x 0
x 1 x 4 3 lim
x
→
10
→
3
2
x 0
2x 1 x 4 3 lim
x
x 0
x 1 x 1 lim
x
→
12
→
+ −3 +
2
x 0
2x 1 3x 1 lim
x
1
3 3 5 lim
1
x
x
→
−
14 3 2
x 1
8x 11 x 7 lim
x 3x 2
→
x 0
1 4x 1 3x 1 2x 1 lim
x
→
16
3 5 4
x 1
x 3 3x 5 lim
5x 11 8x 24
→
17
x 1
lim
x 1
→
−
Trang 518 4
2
x 0
1 2x 1 3x lim
x
→
Bài 5 Tính các giới hạn
1 xlim0sin 5x3x
→
2 xlim01 cos2x2
x
→
−
3 xlim0cosx cos7x2
x
→
−
4 xlim→0cosx cos3xsin x−2
5 xlim0tgx sin x3
x
→
−
6
x 0
sin x sin3x
→
7 lim0sin 2 sin
3sin
x
x
→
+
8 limx→01 sin− sinx−xcos2x
9 Bài 6 Tính các giới hạn
10 xlim 2x 1x 1
→+∞
+
− 11
2 2 x
x 1 lim
1 3x 5x
→−∞
+
− −
x
x x 1 lim
x x 1
→+∞
+ + + 13
2 2 x
3x(2x 1) lim
(5x 1)(x 2x)
→−∞
−
14 lim 3 33 2 2 2
x
→±∞
− + −
15 lim 3 34 2 2 1
x
→±∞
+ −
16 lim 3 22 2 2
x
→±∞
− −
17 lim 43 3 2 1
2 2
x
→±∞
x
(x 1) (7x 2)
lim
(2x 1)
→±∞
x
(2x 3) (4x 7) lim
(3x 4) (5x 1)
→±∞
x
4x 1 lim
3x 1
→∞
+
−
21 lim 2 3 2
3 1
x
x
→+∞
−
22 lim 2 3 2
3 1
x
x
→−∞
−
2 x
x x 2 3x 1 lim
4x 1 1 x
→±∞
+ + −
2 x
4x 2x 1 2 x lim
9x 3x 2x
→±∞
− + + −
− +
25 2 2
x
x 2x 3 4x 1 lim
4x 1 2 x
→±∞
+ + + + + + −
x
x x 3 lim
x 1
→+∞
+ +
27 lim 3 3 2 2
2 2
x
x
→−∞
−
Trang 628 lim 3( 3 2 )2 2 2 3 3 2 2 2
3 2
x
→−∞
(x x x 1)( x 1) lim
(x 2)(x 1)
→+∞
Bài 7 Tính các giới hạn
1 xlim(2x3 −3x)
+∞
2 lim (2 3 3 )
3 lim 2 3 4
→±∞ − +
4 xlim ( x→−∞ 2+ −x x)
5 xlim ( x→+∞ 2+ −x x)
6 lim( x2 3x 2 x)
+∞
7 lim( x2 3x 2 x)
−∞
8 xlim (→±∞ x2−2x+ −4 x)
9 lim( +2− −2)
+∞
xlim ( x 4x 3 x 3x 2)
→±∞ − + − − +
11 xlim (→±∞x x2+ +5 x)
12 xlim (2x 1→±∞ − − 4x2−4x 3)−
13 xlim (3x 2 9x2 12x 3)
→±∞ + − + −
14 lim( 2 −3 +2+ −2)
+∞
x
15 lim( 2 −3 +2+ −2)
−∞
x
16 lim ( 2 3 2 1)
17 xlim (→±∞ x2−3x+ − +1 x 3)
18 xlim ( 4→±∞ x2− + −x 3 2x+1)
19 xlim ( x→±∞ 3 3+x2 −x)
20 xlim ( x→±∞ 3 3−x2+ +x x)
21 xlim ( x→+∞ 2+ −1 3x3−1)
22 xlim (→±∞ 3 x3+2x− −1 x2−3 )x