Post on 13-Apr-2017
2017 1 2
2016-2017
:
:
A 15+10=25
A1. 2 x x 0 1 , , 0 .
1 2x , x (1), :
1 2
S x x
1 2
P x x
A2. ,
1. 0 2 x x 0 , ,
.
2. 0 >0 : x d(x, ) .
3. x y 0 x y 0 .
4. , , , :
.
5. 2 .
B 8+9+8=25
m : d(,30) 5
1. 25
35 .
2. 100 m.
;
.
3. 50 15 .
lisari.blogspot.gr
2017 2 2
5+5+7+8=25
: f (x) (x x 1) (x x 1) x 1
1. : 2f (x) x x 1 x 1 .
2. f (x) 0 1 2
x , x
1 2
1 x 0 x .
3. 2
x , 2
x
2
x 1 .
4. 2 1 1 2
2 x 2 x
2 1 2
2 x x 3 .
9+8+8=25
2( 1) x ( 1) (1) x
.
1. (1).
2.
x 1 .
3.
x 1 .
16 - 01 - 2017
lisari.blogspot.gr
1
1
-
A 15+10=25
1. : 2 2 1 , R
2.
.
1.
.
2. R
2
3.
y ' y
4. A f R , f (2) f (3) f
5. f , ox A ,
ox A , f .
6+7+12=25
f (x) 8 x 8 x
1. .
2. .
3. f .
,
f .
A B
lisari.blogspot.gr
2
4+(6+9+6)=25
f (x) (x) , 0, 0 =
3.
1. ,
2. =2 =1
A. f [0,]
. 5
y2
f [0,]
, . (
).
. f (x) k
[0,] kR .
5+7+6+7=25
f
0,2
3f (x) x x (x x 5) x .
1. f
2. f (x) 5 x
3. , :
25
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. . 1
. . , .
, . .
.
.
: 1 x x , x [0,2)
1
x 0,2 . :
2 2
2 2
2 2 2 2 2
1 x x (1 x) x 1 x 2x x x x x 2x x 2 x 2x 0 2x (x 1) 0 x 0
x [0,2)
x 1 3 x x x 2 2
x , x 2
.
.
.
.
lisari.blogspot.gr
. . 2
2
1 x 0 x 0,2 ,
x 0
:
2 2
2 2
2 2
2
1 x x1 x xx 0
1 2x x x
x 0,
1 2x x 1 x
x 0,
2x 2 x 0
x 0,
2x 1 x 0
x 0,
x 0 x=-1
x 0,
3x= x x= 2 2
x 0,
x x= 2
, :
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. . 3
3
2
2 2
1 x x 1 x x 0 (1 x) 0 1 x x 2x 2x 2xx 0 2 2x 2x 2xx 0 1 x
x [0,2)
x xx 0 x(1 x) (1 x) 0 (1 x) (x 1) 0 x 1 x 1
x x 2
4
2 2
22
2 2
x x 11 x x
1 x x
x 1 x 1 1 x x
x 1 2 x x 1
1 x x2x (x 1) 0
1 x x
x 0,2
x 0 x 1
1 x x
x x 2
.
.
R
lisari.blogspot.gr
. . 4
5
x X x Y
2 2 2 2
1 x x 1 X Y x x 1 Y X 1
H . . .
x2
x
6
f (x) x g(x) x 1 .
1 x x , x [0,2)
[0, 2)
lisari.blogspot.gr
. . 5
7
:
1 x x x x 1 x x 144 x x 14
x x 4 4 4
2 (x )4 2
x [0,2)
(x ) 4 4
x 2 x 2 4 4 4 4
x 2 x 2 2
x x 2
8
:
x x 4 4 4f (x) x x x x 2 (x ) 4 4 4
f y=1.
:
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. . 6
9 1 x 1 1 x 1 0 1 x 2
x 0,2 1 x x :
0 1 x x 1 :
x [0,2) 3x ,0 1 x 1 1 x 0 2 2 x ,
0 x 1 0 x 1 2x 0,
x , 2
, , :
, ,
: x 1 x ,
x x2
10
x , 2
f (x) 1 x x , x , 2
:
f '(x) x x f "(x) x x 0 x , 2
f ' 3x4
,
x 2
34
f x - +
f(x)
f max x2
x f f () 02
,
1 x x f (x) 0 x2
x .
lisari.blogspot.gr
. . 7
11
s(x) f (x) g(x) x x . y=s(x) y=1, :
12 1 x x , 0,2 ,
, 2
f x 1 x x , x , 2
f f 02
f , , 2
Rolle , 2
f 0
f x x x 0 x , 2
f(x) =0 , 2
x , x 2
- 2016
lisari.blogspot.gr
_2017-----2016 (1)------