Λύσεις μαθηματικά...

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  • 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!!

    ,

    .

    ,

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    . ,

    , . ,

    ,

    lisari.blogspot@gmail.com.

    lisari tea

    20 05 2016

    mailto:lisari.blogspot@gmail.com

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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 ,