liseis diagonisma 2014-4
DESCRIPTION
ΔΣΦΩΔΣTRANSCRIPT
-
1
4
1 2x ,x 1 2x x 1 2f(x ) f(x )
1 2[x ,x ] 1 2(x ,x )
2 1
2 1
f(x ) f(x )f ( )
x x 2 1 2 1f(x ) f(x ) f ( )(x x ) .
f ( ) 0 2 1x x 0 2 1f(x ) f(x ) 0 1 2f(x ) f(x ) .
3f x x .
2f x 3x f 0 0
f
f x 0 x .
f
f
xlim f(x)
xlim f(x) ) y
).
2z z 1 0 1
0
20 4 0 2 2 0
1 2z , z 1 2 1z z
1821 1821 1821 1821 18211 2 1 1 1w z z z z 2Re z
Vieta
1 2z z1
1 2
2 1
z z1 0
z z
2 21 2 1 2z z z z 0
2 0
2 2 21 2 1 2 1 2z z 2z z z z 0 2 1 0 1 1
1 1 2z z 1 0
1z
1z 1 0
2 21 1 1 1 1z z 1 0 z 1 z z 1 0
3 31 1z 1 0 z 1 32z 1.
100 133 166
300 400 500 3 3 3 2 21 1 1 1 1 1 1 1 1 1z z z z z z z z 1 z z 0
1 2z ,z
: 1 2 1 2OA OB AB 1 z z z z 1.
-
2
Vieta 1 2 1 21
z z z z 11
2
1 1 1 1z z 1 z 1 z 1
2 1z z 2 2z z 1.
2
1 1 1 1 1
1
1z 1 z 1 z z 1 z
z 2
2
1z
z.
1 2z z 1 1 2 1 2 1 1 1 2 1 2 2 2z z z z 1 z z z z z z z z 1
2 2
1 2 1 2
2 1
1 1z z z z 1
z z 1 2 1 2
2 1 2 1
z z z z1 1 1 1 0
z z z z
2
f x f x f x 1 1 f
0,8 f 0,8 0,8
f 0 1 x 2
f 1 f
f 4 4 0 f x 0 x 0,8 .
11 f x f x x f x f x x c x 4 c 4
2 2f x f x 4 x 2f x f x 8 2x f x 8x x 2 2 2f x 8x x c x 4 2 216 32 16 c c 0
2 2f x 8x x f x 0
2f x 8x x .
2 2 2f x y 8x x y 8x x y
22 2 2x y 8x 16 16 x 4 y 16 y 0
f
x x K 4,0
4 fC AB 2 AB 8 .
4
2
0I 8x x dx
24
I 44
.
f x 0 4 x 0 x 0,4 g x 0 x 0,4 .
4 4 4
2 2
0 0 0
1E g x dx 4 x 8x x dx 8 2x 8x x dx
2.
2u 8x x du 8 2x dx
16
316216
3
0 0
0
1 1 u 1 1 64E udu u 16 16
32 2 3 3 3
2
x 0 4
u 0 16
-
3
x f t 2
0
1e dt f x f x
2
x f t 2
02 e dt 2f x f x
x f t2
0f x 2f x 2 e dt
x f t2
0f x 2f x 1 2 e dt 1
x2 f t
0f x 1 2 e dt 1.
f t
e 0 x 0
x xf t f t
0 0e dt 0 e dt 1 1 0
2
f x 1 0 f x 1 0 f x 1
0, f x 1 0 x 0 f x 1
0, f 0 1 1 0 f x 1 0 x 0 .
x f t 2
02 e dt 2f x f x , f x2e 2f x 2f x f x
f x f xf x f x e f x e 1 f x f xf x e f x e 1 f xf x e 1 f xf x e x c , c .
x 0 f 0f 0 e c c 0 f x f xf x e x f x xe
x 0 .
f x1
f x 0e x
x 0 f 0, ,
1 1 yf x y x ye 1 xf x xe , x 1
x 0 f 01
f 0 1e 0
. f
0x 0 : y f 0 f 0 x 0 y x
f x f x
2 2f xf x f x
e x f x e 11f x 0
e x e x e x, f
0, f
f x x x 0 .
e2
e e
0 00
xE x f x dx f x dx
2. 1x f y f xf x e x
x 0 y 1ye f y . 1 yx f y ye y ydx e ye dy . x 0 y 0 x e y
2 2 2 2y y y 2
0 0
e eE y e ye dy e y y dy
2 2
2 22 y
0
eE y y e dy
2
2 22 y y
00
eE y y e 1 2y e dy
2
2 22 y
0
eE e 1 2y e dy
2
2 22 y y
0 0
eE e 1 2y e 2e dy
2
-
4
2 22 y
0
eE e 1 2 e 1 2 e
2
2 2
2eE e 1 2 e 1 2e 22
2 2
2eE 1 e 12
2 22elim E lim 1 e 1
2
2 2
2 2 2
1 1 1 1 1lim E lim e
2 e e e e.