ΘΕΜΑΤΑΚΙΑ ΕΠΑΝΑΛΗΨΗΣ Γ ΛΥΚΕΙΟΥ Α ΟΜΑΔΑ
DESCRIPTION
μαθηματικα γ λυκειουTRANSCRIPT
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A
f : 2
( ) ln , 0,2
xf x x x
x
.
1. f .
2. ( ) ,f x a a ,
.
3. : 1 ln2 ( ) 2f e f x .
4. : 1
1
( )lim
1( )
x
f x x
x f xx
B
f , , :
2 1( ) 3 2 , 0.xf x x x xx
1. f(x).
2. : lim ( ) lim ( )x x
f x f x
3. f .
4. ( ) 2 ( )g x x f x
f , R
f(2)=2. g : 3( ) ( )( ) ( )g x f f x f x
1. g .
2. 1 3( ) ( )g f x f x x : 3( ) 6f x x 3. f(1)=3, f g.
4. k : ( ) (2 ) 3f k f k k , :
( ) ( ) 2
2
f x k f x kx k x k
, (k,2k).
z : | 5 | 6 | 5 |z i z i , :
1. z.
2. f(x)
, , yo.
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3. , :
2( ) 1 ,g x x x ax x : y=yo
R f :
( ) ( ) ( 1), , .f a f x f a x a
1. f .
2. f (-1, ).
3. 1 , 2 (-1,) :
2 1
( ) ( 1)1
( ) ( )
f a f af f
g >0 :
0,4
164)(,
24)( x
xxxg
xxxg g(1)=-2-, g (1)=-8.
1. .
2. g.
3. : .ln6)(
4)(lim
2 xxxxg
xxg
x
1. [,] h(x),g(x) : ( ) ( ),h x g x :
( ) ( ) , [ , ].a ah x dx g x dx x a
2. f : ( )( ) 1 (0) 0,f xf x e x f :
i. f (x) f(x).
ii. : ( ) ( ) 0.2
xf x x f x x
iii. f,
x=0, x=1, : 1 1
(1).4 2
E f
5 3( ) , .f x x x x x
1. , f. f
.
2. : ( ) (1 ).xf e f x
3. f (0, f(0)).
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4. f 1,
x=3.
f f(1)=1. x : 3
*
1
1( ) ( ) 3 ( 1) 0, , ,
x
g x z f t dt z x z a i az
, :
1. g R g (x).
2. : 1
| | .z zz
3. : 21
Re( ) .2
z
4. f(2)=>0, f(3)=, >, (2,3), ( ) 0.o ox f x
f R , : ( )2 ( ) , , (0) 0.x f xf x e x f
1. : 1
( ) ln2
xe
f x
2. : 00
( )lim
x
x
f x t dt
x
3. : 2014
2012( ) ( ) ( ) .2014
x
x
xh x t f t dt g x
( ) ( ), .h x g x x
4. 20121
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x
xt f t dt , (0,1).
f(x)=|xz+1|, z =+i , .
1. f , .z I
2. Cf ( ) (0,1), z .
3. ( ) , ,z xf x e x z.
4. 2( ) ln( 1)g x x x 1
( )f x, z .
[1,] > 1 f, g f(1)=g(1)=1
1( ) ( ) ( ) ( ) , [1, ].
a
f x g x f t g t dt x a :
1. ( ) ( )
( ) ( )f x g x
f x g xa x
(1,).
2. 2 3
( ) 11
af x
a
(1,)
3. 1( ( ) ( )) 4.
a
f x g x dx
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: (0, )f , f(1)=1 f(2)=2, :
2 2
1 1( ) ( ) , (0, ).f xt dt f t dt x :
1. (1,2) f()=3/2 .
2. , (1,2)
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: ( ) ln( 1) ( 1)ln , 0.f x x x x x x
1. : 1
ln( 1) ln , 0.x x xx
2. f .
3. : 1
lim ln 1 .x
xx
4. >0 : 11a aa a
R f : 2
0( ) ( ) ( ) (0) 2.f x f x dx f x x f
1. f.
2. f .
3. f,
x=0 x=2.
: 22 1 1( )(x ) ln( x)
f(x)x
1. f ,
0xlimf(x) ,
.
2. f .
3. 1
11
11
2
x
xlim e f(t)dt
2 31
0
(x t )f(x) t e dt
1. f .
2. f .
3. f y=0 .
4. g(x)=f(x)+x, g gC
1gC
f , R, :
2( ) 4 ( ) 3 , .f x f x x x
1. f(0)=0.
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2. :
2
( )limx
f xx
3. .
4. f .
, , ||=||=||=1
|3 ++|2+|+3 +|2+|++3 |2=12. :
1. ++=0
2. |-|+|-|+|-|= 3
3. , , 3 3
.4
E
2( ) 2 ( 2) 2.f x x x
1. f 1-1.
2. f .
3. f f-1 y=x.
4. f f-1.
f (0, ) :
2
1
1( ) 1 ( ) , 0
1
x
f x x f t dt xx
1. f(1)
2. ( ) 3 1f x x
3. f.
f ,
x=2 x=4.
: .,1)( 2 xxxxf
1. f .
2.
2
0 2.
1
1dx
x
3. .)(
)()(
xf
xfxg
4. : .0,,1)2
(2
)1)(1( 222
aaa
aa
f(x)=exx2(x-), >0.
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. 0
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f [2,4], f(2)=1/2, f(4)=1
( ) [ 2,2], [2,4].f x x g(x) : ( )( ) ( ), [2,4].f xg x e x f x x
:
1. xo (2,4) g (xo)=0.
2. ( )( )( ) ( ) 0f xf x e x f x , .
: ( )( ) ( ) ( ) 2 .fg f e f
f R, f(0)=0, ( ) 0,f x :
2
0( ) ( ) ( ) 12 .
x
f x f t dt f x x
1. f .
2. g(x)=f(x)+lnx, x>0, g
.
3. 0
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1. f [-2, 2].
2. 1 4
( 2,2) : ( ) ln4 3
f .
3. : 2
( )
2
11 3.
8
f xe dx
f, g
2
2( ) , ( ) 1 , .
2 4
x xx x e ee ef x g x x x
1. (0,1) : ( ) 0. g
2. 2 21
( ) (2 ) ( ).4
g f f
3. ( ) 4 .g x x
4. k : 2 2( ) 4 ( ) 4g k k g k k
. ln 3 0.
. : 1
( ) 1 (ln 2), 0.f x x xx
1. : 2
1( ) 0, 0.f x x
2. ox : ( ) ( ) 0.o of x f x
1 2 3 1 2 3 1 2 3, , | | | | | | 1. 1z z z z z z Av z z z :
1. 1 2 3
1 1 11
z z z
2. 1 2 2 3 1 3 0z z z z z z
3. 2013 2013 2013
1 2 3
1 1 11
z z z
: 2
2
1( ) , .
1
x
x
ef x x
e
1. .
2. :
2 22013 1 2012 1e e
3. : 2
( ) 1 ( ) .f x f x x
4. , : 1 2
2 2
0 0( ) , 1 ( ) .A f x dx B x f x dx
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f [0,1] f(0)>0.
g [0,1] g(x)>0 [0,1].x
: 0 0
( ) ( ) ( ) , [0,1] ( ) ( ) , [0,1].x x
F x f t g t dt x G x g t dt x
1. F(x)>0 (0,1].
2. : ( ) ( ) ( ), (0,1].f x G x F x x
3. : ( ) (1)
, (0,1].( ) (1)
F x F x
G x G
4. :
2
2
0 0
0 5
0
( ) ( )
lim( )
x x
xx
f t g t dt t dt
g t dt x
f : 1
0( ) ( ) {0,1}.
x
xf t dt f t dt x
:
1. 1
0( ) 0f t dt
2. f(1)=f(0)=0
3. 1
( ) ( ) ( ) ( )x
f x f t dt f x f x (0,1).
. 0x : ln(1 ) .x x
. : ( ) ln( ) , [0, ), 0.xf x e kx x x k
1. :
( ) 0.k
f x xe
2. () Cf, =0, =,
( >0), : 0
( ) xE k x e dx
3. : lim ( ) .E k
g : 2( ) 1, [0,1], , 0 2 3 6g x x x x
[0,1] f. :
1. (0,1) ( ) 0.p g p
2. 1
0( ) ( ) 0.f x g x dx
3. 1 1
2
0 0( )f x dx x x f x dx
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1 2 3( ) ( ), ( ) ( ), ( ) ( )z f i g z f i g z f i g , f, g
[,]
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3. z,
Cf (0, f(0)) : ln2
ln2013.4
y x
f (0, ) : 1
1
1 ( )( )
x
f xtf x dt
x t .
:
1. f (0, ) .
2. ln 1
( ) , 0.x
f x xx
3. f.
4. ()
f, =1 = 0
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2. 21
, , 0 2 | | 4 Re2
z i z z
: | 1| | |z z
. : 2 4Re( )
0 02 | | 2 | 1|
k k zx xz e dx z e dx
. g ,
g 1-1.
. f [,].
1 2 1 2
2 ( ), ( , ) : ( ) ( )
f t dtx x f x f x
. f : ( ) ( ) 3 2 xf x f x e .
f 0 g 1, 21
( ) | 2 | , :x
g x t t dt
i. f.
ii. : lim ( ) lim ( )x x
f x f x