8 ΚΑΤΑΚΟΡΥΦΗ ΜΕΤΑΤΟΠΙΣΗ ΠΡΟΣ ΤΑ ΠΑΝΩ ΠΑΡΑΔΕΙΓΜΑ ΚΑΤΑΚΟΡΥΦΗ ΜΕΤΑΤΟΠΙΣΗ ΠΡΟΣ ΤΑ ΚΑΤΩ
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. :
f x x 2.
2 2 x x x
f x x 2.
2 2 x x x
f x x .
x x x .
f x x .
x x x .
f x x .
2 [0 2], .
1. R
2. f
2x
1
2f
.
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16
3. f
2 2
x , Z
4. f 3
2x
31
2f
5. f
2 2
x , Z
6. f 3
0 22 2
, , ,
2 2 2 2
, ,
.
7. f 3
2 2,
32 2
2 2, ,
.
8. f
.
9. f x
x , Z ,
0f x .
0 0f x x, , .
g x x
f x x x.
1. R
2. 2
T .
3. 4. . 5.
x 0
2
3
2
2
f x x 0 0 - 0
6. g -
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17
f x x .
2 [0 2], .
1. R. 2. f 0 2x , x
0 2 1f f . 3. f 2 x , Z
4. f x 1f 5. f 2 x , Z
6. f 2,
2 2 2 , , .
7. f 0 ,
2 2 , , . 8. f y.
9. f x
2
x , Z .
0 0f x x, , .
g x x
f x x x.
1. R
2. 2
T .
3. 4. . 5.
x 0
2
3
2
2
f x x 0 - 0
6. g
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18
f x x .
[ ]2 2
, .
1. 0R x / x
2
R x ,
2. .
3.
2 2,
2 2
, ,
.
4. .
5. f x
x , Z .
f x x .
[0 ], .
1. 0R x / x R x , 2. .
3. 0 , 4. f x
2
x , Z .
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19
x
1 1 : a :
2
2
xx ,
x
2
2
xx x ,
x
x
1 1 : a :
2
2
xx ,
x
2
2
xx x ,
x
x
R : a :
x x ,
x x x ,
x
R : a :
x x ,
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20
0 x x ,
1 2
2x x ,
1 2
2x x ,
0
2x x ,
1 2 x x ,
1 2 x x ,
0 0 x x x ,
0 0
2x x x ,
.
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21
x ax
a R . x .
x :
1
1 1 0....a x a x a x a
0 1, ,....,a a a
.
11 1 0, ,....., ,a x a x a x a
.
0a .
1 1 0, ,....., ,a a a a , .
0P x a , .
0P x , . .
x .
.
.
() .
x
P() x=.
P()=0 .
P()=c c ( ).
(
).
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22
.
.
( ): (x) (x) (x) 0 (x) (x), : (x)=(x)(x)+(x), (x) (x) () , () , () ()
. : P(x) x- x=. =P() : P(x) x- P(x), P()=0. ( ):
1
1 1 0.... 0a x a x a x a
, .
0
0a .
.
.
:
P(x) x - x - P(x) x - P(x) P(x) x - x - P(x) P(x) x - P(x) P()=0 P(x): x -
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:P x x a P a .
.
:P x ax Pa
.
.
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0 1xf x a , a , x R , .
0 1 0ag x log x, a , x , .
y=x .
x
aa y x log y
1 2
1 2
1 2
1 2
1 1
x x
x x
a a
a a x x
log log a x x
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25
0 1a x af x a , g x log x .
1 2x x
1 2
1 2
1 2
1 2
1 2 1 2
1 2 1 2
x x
x x
a a
a a
a a x x ,
a a x x ,
log x log x x x ,
log x log x x x ,
1a x af x a , g x log x .
1 2x x
1 2
1 2
1 2
1 2
1 2 1 2
1 2 1 2
x x
x x
a a
a a
a a x x ,
a a x x ,
log x log x x x ,
log x log x x x
1 1 0xalogx
a a alog a , log , log a x, a x
10 1 1 0 1 1 0log , log , lne , ln
1 2 1 2 alog log log
1 1 2 1 2
2
0
alog log log , ,
0 a alog log , , R
1 0
a alog log , ,
10log x log x
elog x ln x
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