DE DA KIEM TRA DS 11 CHUONG IV

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (90.37 KB, 3 trang )

KIỂM TRA 45’
MÔN: GIẢI TÍCH 11 (cơ bản)
Câu 1:(6.0 điểm) Tính các giới hạn sau:
( )
) lim 2 2
n
a n n
→+∞
+ − −
;
2
2
7 10
)lim
2
x
x x
b
x
→
− +
−
;
3
2
1
2
)lim
1
x
x x

c
x
→
+ −
−
;
2
2
4 1 3
)lim
4
x
x
d
x
→
+ −
−
Câu 2: (1.0 điểm) Tính :
( )
1
1 1 1
... ... ?
2 4 8 2
n
n
S
−
= − + − + + + =
Câu 3: (3.0 điểm) Cho hàm số

2
3 2
2
( )
2
2
x x
khi x
f x
x
x b khi x

− +
>

=
−


+ ≤


a) Tìm
( ) ( )
2 2
lim ; lim ;
x x
f x f x
− +
→ →

b) Tìm b để hàm số liên tục trên
¡
.
Bài làm
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................

.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................
.....................................................................................................................................................................................

+ + −
+ + −
0.75
0.75
1b
( ) ( )
2
2 2
2 5
7 10
lim lim
2 2
x x
x x
x x
x x
→ →
− −
− +
=
− −
( )
2
lim 5 2 5 3
x
x
→
= − = − = −
0.75
0.75

1c
( )
( )
( ) ( )
2
3
2
1 1
1 2
2
lim lim
1 1 1
x x
x x x
x x
x x x
→ →
− + +
+ −
=
− + −
( )
( )
2
1
2
1 1 2
lim 2
1 1 1
x

x x
x
→
+ +
+ +
= = =
+ +
0.75
0.75
1d
( )
( )
2
2
2 2
4 1 3 4 1 9
lim lim
4
4 4 1 3
x x
x x
x
x x
→ →
+ − + −
=
−
− + +
( )
( ) ( )

( )
( )
( )
( )
( )
2 2
2 2
2 2 2 1
lim lim
24 12
2 2 4 1 3 2 4 1 3 2 2 4.2 1 3
x x
x
x x x x x
→ →
−
= = = = =
− + + + + + + + + +
0.75
0.75
2
Các số trong dãy tổng lập thành một CSN lùi vô hạn với công bội
1
2
q = −
và
1
1
2
u = −

1
1
u
S
q
=
−
1
1
2
1
3
1
2
−
= = −
 
− −
 ÷
 
0.25
0.25
0.5
3a
2 2
lim ( ) lim( ) 2
x x
f x x b b
− −

→ →
= + = +
( ) ( )
( )
2
2 2 2 2
1 2
3 2
lim ( ) lim lim lim 1 1
2 2
x x x x
x x
x x
f x x
x x
+ + + +
→ → → →
− −
− +
= = = − =
− −
0.5
1.0
3b Hàm số đã cho liên tục tại mọi x khác 2
Hàm số đã cho liên tục trên
¡
khi và chỉ khi hàm số liên tục tại x = 2
2 2
lim ( ) lim ( )
x x

f x f x
− +
→ →
⇔ =
2 1 1b b
⇔ + = ⇔ = −
0.5
0.5
0.5

DE DA KIEM TRA DS 11 CHUONG IV

Tài liệu liên quan

Tài liệu bạn tìm kiếm đã sẵn sàng tải về