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### Transcript of Λύσεις μαθηματικά...

• 20 05

11:20

5 16

20

lisari

lisari team

2016

• lisari team

http://lisari.blogspot.gr/2014/10/blog-post_13.html

2 : 20 05 2015 ( )

blog

http://lisari.blogspot.gr

http://lisari.blogspot.gr/2014/10/blog-post_13.htmlhttp://lisari.blogspot.gr/

• .

,

.

, lisari team.

pdf!!

,

.

,

,

. ,

, . ,

,

lisari.blogspot@gmail.com.

lisari tea

20 05 2016

mailto:lisari.blogspot@gmail.com

• lisari team 1. ( "" - )

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• http://lisari.blogspot.gr 20 05 2016

2016: lisari team 1

lisari team / 2015 16

: 20 2016 :

: (6)

1. . 150

'

() 1

' = (, ' ),

'

( ') = () +(')

() = () +(')

1 = () +(')

(') = 1-()

=

=

2. . 87

() , , () .

3. . 14

f , E , x A : f (x) 0f (x ) x x .

4. ) ) ) ) )

• http://lisari.blogspot.gr 20 05 2016

2016: lisari team 2

1.

( )3

2x 5f x x 6x 13 2

= + , xR

( ) 2f x x 5x 6 = + xR

( ) 2f x 0 x 5x 6 0 = + =

25 24 1= = 1,25 1

x x 3 x 22

= = =

x 2 3 + ( )f x + +

f < > <

f ( ]1 ,2= [ )3 3,= + ,

[ ]2 2,3= .

f 1x 2=

( )8 5 8 11

f 2 4 6 2 1 13 2 3 3

= + = + =

f 2x 3=

( )27 5 45 7

f 3 9 6 3 1 263 2 2 2

= + = =

2. ( ) : y x = + (1)

( ) f 0 6= =

( ) : y 6x = +

( )

( )( )f 0 1

f 0 6 0 1=

= + =

( ) : y 6x 1= 3.

( ) 2 2

x 1 x 1 x 1

f x 12 x 5x 6 12 x 5x 6lim lim lim

x 1 x 1 x 1 +

= =+ + +

2x 5x 6

25 24 49= + = 1,25 7

x x 6 x 12

= = =

( ) ( )2x 5x 6 x 6 x 1 = +

• http://lisari.blogspot.gr 20 05 2016

2016: lisari team 3

( ) ( ) ( )( )

x 1 x 1 x 1

f x 12 x 1 x 6lim lim lim x 6 7

x 1 x 1 +

= = = + +

1. : : :

,

{,,,,,,,}= 2. :

{ ,,,}= {,,,}= {,,,}=

3. ) , , :

B {,, } == B {,,,, }E A ==

Z {,}= = :

( ) 3= , () 5= , ( ) 2= , ( ) 8=

• http://lisari.blogspot.gr 20 05 2016

2016: lisari team 4

:

( )( )( )

N P

N = ( )

3P

8=

( )( )( )

N EP E

N = ( )

5P E

8=

( )( )( )

N ZP Z

N = ( )

2 1P Z

8 4= =

) : , ( ) B .

( ) ( )( ) ( )P H P A 1 AB BP = =

( )5 3

P H 18 8

= =

: , ( ) ( ) B A :

( ) ( ) ( )( ) ( ) ( )A B,B A

P P B A P A B P B A

+= =

( ) ( ) ( ) ( )P A P A B P B P A B= +

( ) ( )P A B P A B=

( )5 3 1

P 8 8 4

= =

1.

( ) ix

[ )8,8 c+

[ )8 c,8 2c+ + 14

8 c 8 2c 16 3c14 14 16 3c 28 3c 12 c 4

2 2

+ + + += = + = = =

2. :

• http://lisari.blogspot.gr 20 05 2016

2016: lisari team 5

( ) ix iv i ix v

[ )8,12 10 20 200

[ )12,16 14 15 210

[ )16,20 18 10 180

[ )20,24 22 4v 422v

445 v+ 4590 22v+

4

i ii 1 4

4

4 4

4 4

4

4

x v 590 22vx 14

45 v

(45 v ) 14 590 22v

630 14v 590 22v

40 8v

v 5

= += =+

+ = +

+ = +

=

=

( ) ix iv i ix v

[ )8,12 10 20 200

[ )12,16 14 15 210

[ )16,20 18 10 180

[ )20,24 22 5 110

50 700

3. 9

1 2 3 4

3 3v v v v 20 15 10 5 45

4 4+ + + = + + + =

• http://lisari.blogspot.gr 20 05 2016

2016: lisari team 6

4.

(

)

ix

iv ix x ( )

2

ix x ( )2

i ix x v

[ )8,12 10 20 -4 16 320

[ )12,16 14 15 0 0 0

[ )16,20 18 10 4 16 160

[ )20,24 22 5 8 64 320

50 564 800

( )4 2

i i2 i 1 x x v 800

s 16v 50

=

= = =

s 4=

x

s 4CV 0,28 0,1

x 14= = > ( )28% 10%>

5.

ix :

iy :

{ }i iy 0,8x , i 1,2,3....50=

y 0,8 x=

y xs 0,8 s=

y x xy x

s 0,8 s sCV CV

y 0,8x x

= = = =

CV ,