de thi hoc ky II toan 11
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NGÂN HÀNG ĐỀ KIỂM TRA- TOÁN 11- CHƯƠNG TRÌNH CHUẨN
STT
Mã
câu
hỏi
Ý,
thời
gian
Nội dung Điểm
3
3
3 2 5
lim
1 2
n n
n
+ +
+
5 2.3
lim
4 3.5
n n
n n
+
−
3
2 3
3
3
2 5
3
3 2 5 3
lim lim .
1
1 2 2
2
n n
n n
n
n
+ +
+ +
= =
+
+
3
1 2.
5 2.3 1
5
lim lim .
4 3.5 3
4
3
5
n
n n
nn n
+
÷
+
= = −
−
−
÷
2
3 2
lim
1
n n
n n
− + +
− +
1 1
( 2) 3
lim
( 2) 3
n n
n n+ +
− +
− +
3 2
2
2
3 1 2
3 2
lim lim 0.
1 1
1
1
n n
n n n
n n
n n
− + +
− + +
= =
− +
− +
11 1
2
1
( 2) 3 1 1
3
lim lim .
( 2) 3 3 3
2
1
3
n
n n
nn n ++ +
− +
÷
− +
= =
− +
− +
÷
( )
1
3 3 3 3 3( 1)
2 4
2 2 2
2
n
n
S
+
−
= − + − + + +
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1
1 3
,
2 2
q u= − =
)*+,
( )
1
3
3 3 3 3 3( 1) 3
2
.
1
2 4
2 2 2 1 2
2
1
2
n
n
S
+
−
= − + − + + + = =
+
+
2
2
1
1
lim
3 2
x
x
x x
→−
−
+ +
2
2
1 1 1
1 ( 1)( 1) 1
lim lim lim 2.
3 2 ( 1)( 2) 2
x x x
x x x x
x x x x x
→− →− →−
− + − −
= = = −
+ + + + +
2
1
2 3
lim
1
x
x
x
→
− +
−
2
2
1 1
1
1
2 3 4 ( 3)
lim lim
1
( 1)(2 3)
( 1)
lim
( 1)( 1)(2 3)
1 1
lim .
8
( 1)(2 3)
x x
x
x
x x
x
x x
x
x x x
x x
→ →
→
→
− + − +
= =
−
− + +
− −
=
− + + +
−
= −
+ + +
-
3 2
4 2
3
5 3 9
lim
8 9
x
x x x
x x
→
− + +
− −
3 2 2
4 2 2 2
3 3
2
3
5 3 9 ( 3) ( 1)
lim lim
8 9 ( 1)( 9)
( 3)( 1)
lim 0
( 1)( 3)
x x
x
x x x x x
x x x x
x x
x x
→ →
→
− + + − +
= =
− − + −
− +
=
+ +
.
/
3
2
4 2
lim
2
x
x
x
→
−
−
( )
( )
( ) ( )
( )
2
3 3 3
3
2
2 2
3 3
2 2
2 2
3 3 3 3
2
2
3 3
( 4 2) 4 2 4 4
4 2
lim lim
2
( 2) 4 2 4 4
4 8 4( 2)
lim lim
( 2) 4 2 4 4 ( 2) 4 2 4 4
4 1
lim .
3
4 2 4 4
x x
x x
x
x x x
x
x
x x x
x x
x x x x x x
x x
→ →
→ →
→
− + +
−
=
−
− + +
− −
= =
− + + − + +
= =
+ +
0
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2
1
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( ) ¹i 1.
1
2 Õu 1
x
n x
f x t x
x
n x
−
≠ −
= = −
+
− = −
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2
1 1 1 1
1 ( 1)( 1)
lim ( ) lim lim lim( 1) 2 ( 1)
1 1
x x x x
x x x
f x x f
x x
→− →− →− →−
− − +
= = = − = − = −
+ +
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3 4 1
Õu 1
( ) .
1
Õu 1
x
n x
f x
x
m n x
+ −
≠ −
=
+
= −
1 1 1
1
3 4 1 3 4 1
lim ( ) lim lim
1
( 1)( 3 4 1)
3 3
lim
2
3 4 1
x x x
x
x x
f x
x
x x
x
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→−
+ − + −
= =
+
+ + +
= =
+ +
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.
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2 1 os 4 1 os
2 2
x
y c
x
c
x x
c
x
c
x x x
c
x x
c c
= + =
÷
+
+
−
= − =
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3
1 3 3x x
x
− = − ⇔ = ⇔ = ±
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3 × 3 µ ' 1
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x th y v y= = = = −
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2 3y x= − +
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3 × 3 µ ' 1
3
x th y v y= − = − = = −
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2 3.y x= − −
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