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TR働畛NG油THPT油NGUY畛N油TRUNG油THIN油 畛油THI油TH畛油畉I油H畛C油L畉N油1油NM油2012油
_________________油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油M担n:油TON余油Kh畛i:油D油
Th畛i油gian油lm油bi:油180 ph炭t,油kh担ng油k畛油th畛i油gian油giao油畛油
C但u油I (2,0油i畛m)油Cho油hm油s畛:油
x 1油
y油
2x 1
+
=
-油
1)油Kh畉o油s叩t油s畛洩bi畉n油thi棚n油v油v畉縮畛油th畛油(C)油c畛a油hm油s畛油
2) Vi畉t油ph動董ng油tr狸nh油ti畉p油tuy畉n D油v畛i油畛油th畛油(C)油sao油cho油ti畉p油tuy畉n油c畉t油tr畛c油honh油t畉i油A,油c畉t油
tr畛c油tung油t畉i油B油sao油cho DAOB油c坦油di畛n油t鱈ch油b畉ng油
25油
6油
.油(Trong油坦油O油l油g畛c油t畛a油畛)油
C但u油II (3油i畛m)油
1)油Gi畉i油ph動董ng油tr狸nh:油cosx cos3x 1 2sin 2x油
4
p脱 旦
+ = + +巽 歎
竪 淡油
2)油Gi畉i油ph動董ng油tr狸nh: ( ) ( ) ( )油
8油
4 2油2油
1 1油
log x 3 log x 1 log 4x油
2 4
+ + - =油
3)油T鱈nh油t鱈ch油ph但n油I=油
5油
1油
dx油
x 3x 1+
嘆油
C但u油III油(2油i畛m)油Cho油h狸nh油ch坦p油t畛油gi叩c油S.ABCD油c坦油叩y油l油h狸nh油thoi.油Bi畉t油t畛油di畛n油SABD油l油
t畛油di畛n油畛u油c畉nh油a.油G畛i油M油l油trung油i畛m油c畉nh油AB.油
1)油T鱈nh油th畛油t鱈ch油kh畛i油ch坦p油S.BCDM油
2)油T鱈nh油kho畉ng油c叩ch油gi畛a油hai油動畛ng油th畉ng油DB油v油SC油
C但u油IV:油(1油i畛m)油 T狸m油s畛油nguy棚n油d動董ng油n th畛a油m達n:油 2 n 1油
n n 1油
A C 4n 6-
+
- = +油
C但u油V油(1油i畛m)油Cho油A(0余2),油B(4余-1)油v油動畛ng油th畉ng D:油x -油y油+油1油=油0.油T狸m油i畛m油C油tr棚n D油
sao油cho DABC油c坦油di畛n油t鱈ch油b畉ng油
11油
2油
C但u油VI油(1油i畛m)油T狸m油gi叩油tr畛油l畛n油nh畉t油c畛a油hm油s畛: ( )油 3 3油
f x 4x x x x= - + +油 v畛i油x フ[0余油2]油
__________ H畉T油_________油
Thi th畛 畉i h畛c www.toanpt.net
P油N油
C但u油I:油
1)油T鱈nh油動畛c油TX,油v油畉o油hm油(0.25),油k畉t油lu畉n油kho畉ng油db,油nb油(0.25),油gi畛i油h畉n油v油BBT油
(0.25), 畛油th畛油(0.25),油
2)油G畛i油
m 1油
M m余油
2m 1
+脱 旦
巽 歎
-竪 淡油
,油ti畉p油tuy畉n D油t畉i油M油c坦油ph動董ng油tr狸nh:
( )
( )油2油
3 m 1油
y x m油
2m 1油2m 1
- +
= - +
--
D  Ox油=油
2油
2m 4m 1油
A 余0油
3
+ -脱 旦
巽 歎
竪 淡油
, D  Oy油= ( )油2油
B 0余2m 4m 1+ -油 0.25
油OA油=油
2油
2m 4m 1油
3
+ -油
,油OB油=油 2油
2m 4m 1+ -油 0.25油
Di畛n油t鱈ch DAOB油l油
1油
.OA.OB油
2油
,油theo油bi油ra油ta油c坦:油
2油
2油
2m 4m 1油1 25油
. . 2m 4m 1油
2 3 6
+ -
+ - =油 0.25油
2油
2油
2m 4m 1 5 m 1油
m 3油2m 4m 1 5
+ - = =辿 辿
 棚 棚 = -+ - = - 谷谷油
C但u油II油
1)
( ) ( ) ( )
( )( )( ) ( )油
2油
2油
2油
1 2cos2x.cosx 1 sin2x c cosx sin x油
cosx sin x cosx sin x 2cosx 1 sin x cosx油
x k油
x k油 4油
4油cosx sin x 0油
cosx 0 x k油
2油2cos x cosx 2sin xcosx sin x sin x cosx油
cosx sin x 1油
x k2
os2x cos2x 2cosx 1 = + +  - = +
 + - - = +
p辿
p = - + p辿 棚= - + p棚 棚
+ =辿 棚 p棚  =  = + p棚 棚 棚- - + = +谷 棚 - = 棚 = p棚
谷
谷
棚
棚油
2) i畛u油ki畛n:油x油>油0,油v畛i油i畛u油ki畛n油ny油ta油c坦:
( ) ( )( ) ( ) ( )
( )
( )油
2油
2 2油
2 2油
1 log x 3 x 1 log 4x x 3 x 1 4x油
x 1油
x 3油 x 3油x 2x 3 4x x 2x 3 0油
x 3 2 3油x 2x 3 4x x 6x 3 0油 x 3 2 3油
x 3 2 3
lo孫i
lo孫i
 + - =  + - =
= -辿
棚
= =辿+ - = - - =辿 辿 棚
    棚棚 棚 棚 = - ++ - = - + - = = - +谷 谷 谷棚
棚 = - -谷油
3)油
畉t油t油=油
2油
t 1油
x油
3油
2tdt油
dx油t 3x 1油
3油
x 1 t 2油
x 5 t 4
-狸
=誰
誰
誰
== +  鱈
誰
=  =誰
誰 =  =樽油
4油
2油
2油
4油2dt t 1 9油
I ln ln油
2油t 1 t 1 5
-
 = = =
- +
嘆油
0.25油
0.25油
0.25油
0.25油
0.25油
0.25油
0.25油 0.25油
0.25油
0.25油
0.25油
0.25
C但u油III:油
1)油G畛i油H油l油h狸nh油chi畉u油c畛a油S油tr棚n油(ABCD)油ta油c坦油H油l油tr畛ng油
t但m DABD油 2 2油a 2油
AH SH SA AH a油
3 3
 =  = - =油
di畛n油t鱈ch油t畛油gi叩c油BCDM油l油
2 2油
ABD油
3 3 a 3 a .3 3油
S S .油
2 2 4 8
= = =油
Th畛油t鱈ch油kh畛i油ch坦p油S.BCDM油l油
2 3油
1 a .3 3 a 2 a 2油
V . .油
3 8 8油3
= =油
2)油G畛i O油=油AC 油BD,油g畛i油I油v油K油l畉n油l動畛t油l油h狸nh油chi畉u油c畛a油O油v油A油tr棚n油SC油ta油c坦油
BD ^油AC油v油BD ^油SH 油BD ^油IO 油OI油l油動畛ng油vu担ng油g坦c油chung油c畛a油BD油v油SC油
Ta油c坦油
2 2油
2 2油 2a 4a油
SC SH HC a 2油
3 3
= + = + =油
Ta油c坦:油
SH.AC a油
AK.SC SH.AC 2OI.SC SH.AC OI油
2SC 2
=  =  = =油
C但u油IV:油i畛u油ki畛n:油n  N油*油
.
( )
( )油2 n 1 2油
n n 1油
n 1 n油
A C 4n 6 n n 1 4n 6 n 11n 12 0 n 12油
2
-
+
+
- = +  - - = +  - - =  =油
C但u油V:油Ta油c坦: ( )油AB 4余 3 AB 5= -  =
uuur油
,油
動畛ng油th畉ng油AB油c坦油ph動董ng油tr狸nh:油3x油+油4y -油8油=油0.油
C D 油C(t余油t+1).油Di畛n油t鱈ch DABC油b畉ng油
11油
2油
n棚n油ta油c坦: ( )油
1 11油
.AB.d C,AB油
2 2
=
( )
( )油
2 2油
C 1余0油t 1油
3t 4 t 1 8油1 11油
.5. 7t 4 11油 15油 15 22油
2 2油 t油 C 余油3 4油
7油 7 7
-辿= -辿+ + - 棚棚 =  - =   脱 旦棚棚 =+ 巽 歎棚谷 竪 淡谷油
C但u油VI:
( ) ( )
( )
( )( )油
2 2油
3 3油
2油2 2油
3 3油
6 4 2油
2油
2 4 2油
4 3x 1 3x油
f ' x 0余2油
2 4x x 2 x x油
4油
x油1 3x 3x 4油
f ' x 0油 3油
2 x x 2 4x x油
18x 45x 31x 12 0油
4油
x油
3油 x 3油
x 3 18x 9x 4 0
v鱈i x
- +
= + " 
- +
狸
続+ - 誰
=  =  鱈
+ - 誰 - - + =樽
狸
続誰
  =鱈
誰 - + - =樽油
Ta油c坦油f(0)油=油0油,油f(2)油=油 10 余 ( )油 4油
f 3 3 3=油 .油V畉y油GTLN油c畛a油hm油s畛油tr棚n油[0余2]油l ( )油 4油
f 3 3 3=
O油
H油
A油 B油
D油
C油
S油
M油
I油
K油
0.25油
0.25油
0.50油
0.50油
0.50油
0.50油
0.50油
0.25油
0.25油
0.25油0.25油
0.25油
0.25油
0.25油
0.25

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  • 1. TR働畛NG油THPT油NGUY畛N油TRUNG油THIN油 畛油THI油TH畛油畉I油H畛C油L畉N油1油NM油2012油 _________________油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油M担n:油TON余油Kh畛i:油D油 Th畛i油gian油lm油bi:油180 ph炭t,油kh担ng油k畛油th畛i油gian油giao油畛油 C但u油I (2,0油i畛m)油Cho油hm油s畛:油 x 1油 y油 2x 1 + = -油 1)油Kh畉o油s叩t油s畛洩bi畉n油thi棚n油v油v畉縮畛油th畛油(C)油c畛a油hm油s畛油 2) Vi畉t油ph動董ng油tr狸nh油ti畉p油tuy畉n D油v畛i油畛油th畛油(C)油sao油cho油ti畉p油tuy畉n油c畉t油tr畛c油honh油t畉i油A,油c畉t油 tr畛c油tung油t畉i油B油sao油cho DAOB油c坦油di畛n油t鱈ch油b畉ng油 25油 6油 .油(Trong油坦油O油l油g畛c油t畛a油畛)油 C但u油II (3油i畛m)油 1)油Gi畉i油ph動董ng油tr狸nh:油cosx cos3x 1 2sin 2x油 4 p脱 旦 + = + +巽 歎 竪 淡油 2)油Gi畉i油ph動董ng油tr狸nh: ( ) ( ) ( )油 8油 4 2油2油 1 1油 log x 3 log x 1 log 4x油 2 4 + + - =油 3)油T鱈nh油t鱈ch油ph但n油I=油 5油 1油 dx油 x 3x 1+ 嘆油 C但u油III油(2油i畛m)油Cho油h狸nh油ch坦p油t畛油gi叩c油S.ABCD油c坦油叩y油l油h狸nh油thoi.油Bi畉t油t畛油di畛n油SABD油l油 t畛油di畛n油畛u油c畉nh油a.油G畛i油M油l油trung油i畛m油c畉nh油AB.油 1)油T鱈nh油th畛油t鱈ch油kh畛i油ch坦p油S.BCDM油 2)油T鱈nh油kho畉ng油c叩ch油gi畛a油hai油動畛ng油th畉ng油DB油v油SC油 C但u油IV:油(1油i畛m)油 T狸m油s畛油nguy棚n油d動董ng油n th畛a油m達n:油 2 n 1油 n n 1油 A C 4n 6- + - = +油 C但u油V油(1油i畛m)油Cho油A(0余2),油B(4余-1)油v油動畛ng油th畉ng D:油x -油y油+油1油=油0.油T狸m油i畛m油C油tr棚n D油 sao油cho DABC油c坦油di畛n油t鱈ch油b畉ng油 11油 2油 C但u油VI油(1油i畛m)油T狸m油gi叩油tr畛油l畛n油nh畉t油c畛a油hm油s畛: ( )油 3 3油 f x 4x x x x= - + +油 v畛i油x フ[0余油2]油 __________ H畉T油_________油 Thi th畛 畉i h畛c www.toanpt.net
  • 2. P油N油 C但u油I:油 1)油T鱈nh油動畛c油TX,油v油畉o油hm油(0.25),油k畉t油lu畉n油kho畉ng油db,油nb油(0.25),油gi畛i油h畉n油v油BBT油 (0.25), 畛油th畛油(0.25),油 2)油G畛i油 m 1油 M m余油 2m 1 +脱 旦 巽 歎 -竪 淡油 ,油ti畉p油tuy畉n D油t畉i油M油c坦油ph動董ng油tr狸nh: ( ) ( )油2油 3 m 1油 y x m油 2m 1油2m 1 - + = - + -- D Ox油=油 2油 2m 4m 1油 A 余0油 3 + -脱 旦 巽 歎 竪 淡油 , D Oy油= ( )油2油 B 0余2m 4m 1+ -油 0.25 油OA油=油 2油 2m 4m 1油 3 + -油 ,油OB油=油 2油 2m 4m 1+ -油 0.25油 Di畛n油t鱈ch DAOB油l油 1油 .OA.OB油 2油 ,油theo油bi油ra油ta油c坦:油 2油 2油 2m 4m 1油1 25油 . . 2m 4m 1油 2 3 6 + - + - =油 0.25油 2油 2油 2m 4m 1 5 m 1油 m 3油2m 4m 1 5 + - = =辿 辿 棚 棚 = -+ - = - 谷谷油 C但u油II油 1) ( ) ( ) ( ) ( )( )( ) ( )油 2油 2油 2油 1 2cos2x.cosx 1 sin2x c cosx sin x油 cosx sin x cosx sin x 2cosx 1 sin x cosx油 x k油 x k油 4油 4油cosx sin x 0油 cosx 0 x k油 2油2cos x cosx 2sin xcosx sin x sin x cosx油 cosx sin x 1油 x k2 os2x cos2x 2cosx 1 = + + - = + + - - = + p辿 p = - + p辿 棚= - + p棚 棚 + =辿 棚 p棚 = = + p棚 棚 棚- - + = +谷 棚 - = 棚 = p棚 谷 谷 棚 棚油 2) i畛u油ki畛n:油x油>油0,油v畛i油i畛u油ki畛n油ny油ta油c坦: ( ) ( )( ) ( ) ( ) ( ) ( )油 2油 2 2油 2 2油 1 log x 3 x 1 log 4x x 3 x 1 4x油 x 1油 x 3油 x 3油x 2x 3 4x x 2x 3 0油 x 3 2 3油x 2x 3 4x x 6x 3 0油 x 3 2 3油 x 3 2 3 lo孫i lo孫i + - = + - = = -辿 棚 = =辿+ - = - - =辿 辿 棚 棚棚 棚 棚 = - ++ - = - + - = = - +谷 谷 谷棚 棚 = - -谷油 3)油 畉t油t油=油 2油 t 1油 x油 3油 2tdt油 dx油t 3x 1油 3油 x 1 t 2油 x 5 t 4 -狸 =誰 誰 誰 == + 鱈 誰 = =誰 誰 = =樽油 4油 2油 2油 4油2dt t 1 9油 I ln ln油 2油t 1 t 1 5 - = = = - + 嘆油 0.25油 0.25油 0.25油 0.25油 0.25油 0.25油 0.25油 0.25油 0.25油 0.25油 0.25油 0.25
  • 3. C但u油III:油 1)油G畛i油H油l油h狸nh油chi畉u油c畛a油S油tr棚n油(ABCD)油ta油c坦油H油l油tr畛ng油 t但m DABD油 2 2油a 2油 AH SH SA AH a油 3 3 = = - =油 di畛n油t鱈ch油t畛油gi叩c油BCDM油l油 2 2油 ABD油 3 3 a 3 a .3 3油 S S .油 2 2 4 8 = = =油 Th畛油t鱈ch油kh畛i油ch坦p油S.BCDM油l油 2 3油 1 a .3 3 a 2 a 2油 V . .油 3 8 8油3 = =油 2)油G畛i O油=油AC 油BD,油g畛i油I油v油K油l畉n油l動畛t油l油h狸nh油chi畉u油c畛a油O油v油A油tr棚n油SC油ta油c坦油 BD ^油AC油v油BD ^油SH 油BD ^油IO 油OI油l油動畛ng油vu担ng油g坦c油chung油c畛a油BD油v油SC油 Ta油c坦油 2 2油 2 2油 2a 4a油 SC SH HC a 2油 3 3 = + = + =油 Ta油c坦:油 SH.AC a油 AK.SC SH.AC 2OI.SC SH.AC OI油 2SC 2 = = = =油 C但u油IV:油i畛u油ki畛n:油n N油*油 . ( ) ( )油2 n 1 2油 n n 1油 n 1 n油 A C 4n 6 n n 1 4n 6 n 11n 12 0 n 12油 2 - + + - = + - - = + - - = =油 C但u油V:油Ta油c坦: ( )油AB 4余 3 AB 5= - = uuur油 ,油 動畛ng油th畉ng油AB油c坦油ph動董ng油tr狸nh:油3x油+油4y -油8油=油0.油 C D 油C(t余油t+1).油Di畛n油t鱈ch DABC油b畉ng油 11油 2油 n棚n油ta油c坦: ( )油 1 11油 .AB.d C,AB油 2 2 = ( ) ( )油 2 2油 C 1余0油t 1油 3t 4 t 1 8油1 11油 .5. 7t 4 11油 15油 15 22油 2 2油 t油 C 余油3 4油 7油 7 7 -辿= -辿+ + - 棚棚 = - = 脱 旦棚棚 =+ 巽 歎棚谷 竪 淡谷油 C但u油VI: ( ) ( ) ( ) ( )( )油 2 2油 3 3油 2油2 2油 3 3油 6 4 2油 2油 2 4 2油 4 3x 1 3x油 f ' x 0余2油 2 4x x 2 x x油 4油 x油1 3x 3x 4油 f ' x 0油 3油 2 x x 2 4x x油 18x 45x 31x 12 0油 4油 x油 3油 x 3油 x 3 18x 9x 4 0 v鱈i x - + = + " - + 狸 続+ - 誰 = = 鱈 + - 誰 - - + =樽 狸 続誰 =鱈 誰 - + - =樽油 Ta油c坦油f(0)油=油0油,油f(2)油=油 10 余 ( )油 4油 f 3 3 3=油 .油V畉y油GTLN油c畛a油hm油s畛油tr棚n油[0余2]油l ( )油 4油 f 3 3 3= O油 H油 A油 B油 D油 C油 S油 M油 I油 K油 0.25油 0.25油 0.50油 0.50油 0.50油 0.50油 0.50油 0.25油 0.25油 0.25油0.25油 0.25油 0.25油 0.25油 0.25