143 bài tập giới hạn dãy số
Trang 1I HN DÃY S
3
lim
−
2
lim
+
3
lim
4
lim
+
3 2
lim
5 4
lim
2
lim
+
3
2
lim
−
2
lim
5n 1
+
+
5 3
5 4
lim
2
lim
− +
2
2
lim
1 3n
−
−
3 3
lim
+
2
lim
lim3n6 7n3 5n 8
n 12
+
2
lim
3n 2
lim 3n( 3−7n 11+ ) lim 2n4−n2+n+2 lim 1 2n3 + −n3
2
1 2 n lim
n + + +
2
n 2 4 2n
lim
3n n 2
+ + +
+ −
4 3
lim
2
n 1 3 (2n 1) lim
2n n 1
+ + + − + +
2
1 2 n
lim
11n n 2
+ + +
+ +
1 2 n
4
+
lim
+ + + +
+ + + +
n
n n
4
lim
2.3 +4
n
n
lim
+
−
n n
n
lim
7 3.5
− +
n n
lim
− +
n n
n 1 n 1
( 3) 5 lim
( 3) + 5 +
lim( 3n 1− − 2n 1− )lim( n 1+ − n) nlim( n2+n 1 n+ − ) lim n2(n− n2+1)
lim( n2+n+2− n 1+ ) lim( n+3− n 5− ) lim( n2−n+3−n) 1
lim
n+2− n 1+
GII HN HÀM S
2
lim 3x 7x 11
x →
2 1
7x 11 lim
x
x x
→
+ +
x 2
3x 1 2 3x lim
x 1
→−
7x 11 lim 2 1
x x
x
→
+
−
3
x
x
→
2
x 9
lim 9x x
→
−
−
7
2 3 x
lim
→−∞
− 8
4
x
lim
→−∞
− 9
3 x
lim
→+∞
−
10
6 3 x
lim
→−∞
− 11
2 3 2 x
lim
→−∞
+
12
x 3
3 x lim
3 x
+
→
−
−
13
x 3
3 x
lim
3 x
−
→
−
3 x lim
3 x
→
−
lim
+
→
+
2
x 2
lim
−
→
−
− 17.
3 2
lim
→−
+
− 18
4
2
x 3
lim
→
−
− − 19.
4 2
x 2
lim
→−
−
5 3
x
lim
→+∞
21
2 x
lim
2x 3
→−∞
+
x
x
→+∞
+
xlim 2x 5x 3x 1
→+∞
xlim 2x 5x 1
→+∞
143 BAI TAP GIOI HAN DAY SO - HAM SO - WWW.MATHVN.COM
Trang 2x 2
2x 1
lim
+
→
+
2x 1 lim
−
→
+
xlim 2x 5x 3x 1
→+∞
3 2 x
lim
→+∞
− +
29
3
2
x 2
lim
→
−
−
31
2 2
x 3
lim
−
→ −
+
32
3 2
x 0
lim
→
+ − + 33
2 3 x
lim
9 3x
→+∞
−
34
3
2
lim
→−
+
−
35
2
x 4
lim
→
−
−
36
2
x 1
x 1 lim
+
→
−
− 37
2
x 0
lim
3x
→
38
3
x 3
3 x
lim
27 x
−
→
−
− 39
3 2
x 2
lim
+
→
−
−
2 2
x 2
lim
→
2
x 2
lim
→
−
− 2
2
x 1
x 4x 3 lim
(x 1)
→
− +
−
x 1
x 1
lim
→
−
− 2
x 3
x 2x 15 lim
x 3
→
+ −
−
2
lim
→−
+
3
x 1
lim x(x 5) 6
→
−
2
x 4
lim
→−
+
2
x 4
lim
→−
2
x 2
x 3x 2x lim
x x 6
→−
− −
2
x 1
lim
→
−
3 2
2
x 2
x 4x 4x lim
x x 6
→−
− −
x 2
→
− 4
x 7
lim
→
x 5
5 x lim
→
−
−
x 2
lim
→
−
x 0
x lim
→ + −
2
x 1
x 1 lim
→−
+
x 0
lim
x
→
2
x 5
lim
→
−
2
x 0
1 2x x 1 x
lim
x
→
x 3
x 3 lim
2x 10 4
→
−
lim
→
2x 3x 1 lim
x 1
→
− +
−
2
x 1
x 1
lim
→
−
lim
x
→
x 0
lim
x
→
x 1
lim
x 1
→
− −
2
x 0
lim
x
→
2
x 1
lim
→
x 0
lim
x
→
x 4
3 5 x
lim
1 5 x
→
− +
− −
x 2
lim 4x 1 3
→
+ −
2
x 1
lim
→
−
2
lim
→−
+
2
x 0
lim
→
x 9
7 2x 5
lim
x 3
→
−
2
2 x
lim
→+∞
2
3 x
lim
→−∞
−
−
2 2 x
x 4x 3 lim
(x 1)
→+∞
− +
−
x
lim
→−∞
x
x
x x
→+∞
−
4 x
lim
→−∞
+
2 x
lim
→+∞
5
x
x 3x 2x
lim
x x 6
→−∞
− −
2
1 lim
x
x
→−∞
−
3 6 4 2 x
x 4x 4 lim
x x 6
→−∞
− −
x 2
lim
+
→−
+
x 0
2 x 3x lim
+
→
−
=
xlim f (x)1
→
2
mx ; x 2
f (x)
=
>
xlim f (x)2
→
2
f (x)
=
khi x→2
x
lim x x 1 x 2
→+∞
x
xlim x 4x 1 x 9x
→+∞
x
lim x 2x 1 x 6x 3
→+∞
x
Trang 360 BÀI T P GI I H N DÃY S www.MATHVN.com
1,
2
2
lim
( )( )
2
lim
( )( ) ( )( )
lim
4, limn n2 n 1
- +
3
lim
lim
+ +
n 1
+
( ) ( )
2
2
lim
( ) ( )
lim
3
lim
lim
3
lim
-13,
2
lim
+ +
2
lim
15,
lim
2007 2000
lim
( ) ( )( )
3 2
lim
-+
+ -+
19,
lim
20,
lim
lim
n
2
lim
lim
2
lim
25,
lim
lim
lim
5
lim
2
lim
( )
2
lim
-31,
n
lim
+
n 1 n 1
lim
+
( ) ( )
lim
-34,
n 1 n 2
lim
lim -n +4n-1
40,
2
lim
2 3
lim
(n 1)2 n lim
-+
4
lim
( )
2
3
lim
+
-+
lim n +4n+2- +n 2
55,
2
1 lim
n+ -1 n +2
+
lim
-+
... class="text_page_counter">Trang 360 BÀI T P GI I H N DÃY S www.MATHVN.com
1,
2
2
lim...
→+∞
xlim 2x 5x
→+∞
143 BAI TAP GIOI HAN DAY SO - HAM SO - WWW.MATHVN.COM
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