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  
\ 
W
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!
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y
x
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3 
!
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y f x x mx m x
= = − − + −

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x x x x x
+ − + + − +
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2
3 2



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
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3 2
0
1 1
4 2011 1
3 2
y x x x taïi x
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+
=
1 cos
sin
x
y
x
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=
4
sin
"
4sin
2
x
y
x

y x x= − + −
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U
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1
sin
y
x
=
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cotx
'
sin
y
x
−
=
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0%+12%$ 

qZ\W
U!!
qWZ!YU
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 !
!
−
=

+ +
−
n n
n

0
1 1
lim
→
+ −
x
x
x
/23456&m#$

 3
!
 
!
 !
x x
khi x
f x
x
mx khi x

+ −
<

=

3d%eB6D%<(SAI)
P8*/23456(Thí sinh học chương trình nào thì làm theo chương trình đó)
1. Theo chương trình cơ bản.
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( )
3 2
3 4
= = − −
y f x x x
.8%1(C)
!Ed)*%+&
( )
2.
′
=
f x
56%)*%+&%6%768%1(C)%.#h
0
1.
=
x
H/23456
",)*%+&
3
3 ! Ux x
− + =
.%j%3/A/%%h
d
( )
c 

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∆
.)*%+&
\
3
3
y x
= −
J/23456
 ",    +4  )*  %+& 
( )
 U!U
3   \ Um m x x− + − − =
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/A0%+1%$m
mmmmmmmmmmmmmP|mmmmmmmmmmmm
K
Câu 1. (2 điểm)&
!


3 ] ![

g
x
x x
x
→∞
− +

x
x khi x

− +
≠


−


− =



Câu 3. (2 điểm)#2#$
!
3 !

x
y
x
+
=
−
7Y
3
  !x x
− +
37Y!ZW!qW
Câu 4. (1 điểm)"#$7YW

:a!CN;:U?bAc!C
)*"-.#'/K16
/123456
"#$
3 
7 W 3W gW !
= + − +

!Edj%)*%+&
7X U
>

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7 gW 3
= − +

/1G23456
!


W 
W 

W 3W 
→−
+
+ −

(
)

"  &  .  =>?"@ .  7  >?"@  #  &  -    : 
=> >?"@
⊥
 #
=>  a
=

!",+4
=" ?@
⊥
#
( ) ( )
=>" =?@
⊥

d%e"6D%<
( )
=?@

8*(2,0 điểm)
Thí sinh chỉ làm một trong hai phần (Phần 1 hoặc phần 2)
:@<;:AB!C?DE!::F!/123456
H/123456
#2#$


W W !
7
W !
− −


=? 
=
dF=>#?@
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmP6%mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
(Đề có 01 trang)

'M*+Nd).*e 
_f*gd).*e V"#(
mmmmmmmmmmmmmmmmmmmmm Thời gian làm bài: 90 phút.
(Không kể thời gian phát đề)
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
)*/K126
Câu 1. (2,0đ): 
 H6


!  3

 !
+ −
+
c          J6 
(
)

 \ 3  !
x
x x x
→−∞


− −
> −

=
+


+ − ≤ −

Câu 3.(2,0đ):"#$ 

  !f x x x= +
#
    g x x x x= + −
H6",+4 
X  U:f x x R> ∀ ∈
:
J6Ed)*%+& 
X  Ug x
=

Câu 4.(3,0đ):"&.%,V=>?"@.7#
a
:'#
a
:B#
%A27
H6",+4 
 

H6 ", +4)* %+& 
+ + − =
2
x 2sinx 3cos 3x 5 0
 .  %j% 
/
J6"
 3
[ 3 \y x x
= + −
.8%1"56%)*%+&%6%762"6%%6
%76);%<
a !y x= − +




'M*#"+i,,"Q"%
R
_f*)j#*

$)*/I1G2345
P93/1G23456&

→
−
− +
x
x
x x

!Hk%%'%(2#$%+'%`W12.

−
≠ −


− −
=


+ = −


x
x
x x
f x
x x
2
2
1
, 1
2 3
( )
1
1 , 1
2

P93/1G23456&#2#$
7Y

P93G/123456


H6
→−∞
 
 
+ +
 ÷
 
 
 
x
x x x
2
lim 3 5 25 1

J6"#$7Y
 
3
x
x
+
⊥
−
"
!
56%)*%+&%6%7628%1"
!
6%%6%76


56%)*%+&%6%7628%1"

%.#hxY
P93IP/1G23456"%,I/V>?"@E0•#%+2"@
a) ,>•?
⊥
?"@
b) dF);%<>?#"@

'M*+NemR
_f*QV"#
( 2.0 điểm 


→−
+ −
+
3 2
x 1
2x 3x 1
lim
x 1



W
3W ! W 3

3W W



&%+12#$'%(%WY3
",+4)*%+& 
= +
2011 2010
4.x 5.x 1
./
(2.0 điểm )
!"#$
= + − −
5 3 2
f(x) x x 2x 3
",+4
′ ′
+ − = −
3.f (1) f ( 1) 8.f(0)
"#$
− +
=
−
2
2 x x
y
x 1
.8%1"56%)*%+&%6%762":6%%6%76-
.);%<I 7YWZ3
(3.5 điểm )
"&.=>?"@.7>?"@#&-:D%'=>?#%


x
= − +


  !y x x= + −
3
[
 !
3
x
y
x
−
 
=
 ÷
−
 
/23456"#$
3 
  3 \ [f x x x x= + − +
.8%1(C):
 Edj%)*%+&
X
  ![f x
< −

 56%)*%+&%6%7628%1(C),6%%6%76);%<
![ ny x
= − +

n
nn
−
+−
c  

 !  3 

n ]
n n
n n
+ + + +
+ −





(1,5 điểm)
&2#$

3
!
!

!
x
x
x
→

−

=
−



7(2,0 điểm)
"#$ 

 3
 
!
x x
y f x
x
+ −
= =
+
:%
X! ‚f
=

"#$7YmW
3
Z3WZ!:.8%1"Œ`)*%+&%6%76
2"6%%6%76.-.);%<I WZ37qU!3YU
G(4,0 điểm)
"&.=>?"@:7>?"@#&-:
aSA a=

:U&

x
x
x x
2
3
3
lim
2 3
→−
+
+ −

x
x
x
2
2
5 3
lim
2
→−
+ −
+
!:UHk%%'%(2#$%+'%`W12.
x x
khi x
f x
x

2 1
3
 
+
=
 ÷
 ÷
−
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:Z!D3t!C3:UThí sinh chỉ được chọn một trong hai phần sau:
1. Theo chương trình Chuẩn
GH!:U 
n
n
2
2
1 2 2 2
lim
1 3 3 3
+ + + +
+ + + +

IH:U



"#$
y x x.sin
=
",+4
xy y x xy2( sin ) 0

+ =

""
y x x
3 2
3 2= +
56%)*%+&%6%762":6%%6%76-.
);%<I
y = x
1
1
3
+
I
Sở GD và ĐT Thanh Hoá
Tr ờng THPT Chuyên Lam Sơn
Đề thi học kỳ II :Môn Toán lớp 11
Năm học: 2008-2009
( Thời gian 90' - không kể thời gian phát đề)

A. Phần chung cho tất cả các thí sinh
Câu 1.tìm
(
)


U
! !

!
x
x
x

+

Câu 2. Cho hàm số
3
! ! \

3 3
y x x x
= +
có đồ thị (C) .Viết phơng trình tiếp tuyến của đồ thị (C)
biết rằng tiếp tuyến đó song song với đờng thẳng d: y= 4x+2 .
Câu 3 .chứng minh rằng hệ phơng trình
3
3
\ ! U
[ U U
x x x
x x x y

+ =



!

x
y
x

=

có đồ thị (C) .Viết phơng trình tiếp tuyến của (C) biết tiếp tuyến đi qua
điểm A(0;2) .
Câu 3 .Cho hàm số
!
% 3

!
x x
x x
f x ax b
x



<



= +