Λύσεις...

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    19-Jan-2017
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  • 10 06 15

    1: 19:40

    lisari team

    & 2016

  • -

    lisari team

    http://lisari.blogspot.gr/lisari_team

    1 : 10 06 2016 ( )

    blog

    http://lisari.blogspot.gr

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

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    pdf!!

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    lisari.blogspot@gmail.com.

    lisari tea

    10 06 2016

    mailto:lisari.blogspot@gmail.com

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  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 1

    lisari team / 2015 16

    : 10 IOYNIOY 2016

    :

    : ()

    ( )

    1.

    f (x) x :

    f (x h) f (x) (x h) x h , h 0 , f (x h) f (x) h

    1h h

    .

    h 0 h 0

    f (x h) f (x)lim lim1 1

    h

    .

    (x) 1 .

    2. f ,

    1 2x , x 1 2x x 1 2f (x ) f (x ) .

    3. (range) R ,

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    4.

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    1. 2

    2 2

    f 1,2 C f (1) 2 1 2 1 2 1 4 3

    2. 3 2f (x) x 3 .

    0x 1 :

    y f (1) f (1)(x 1)

    f (1) 2 . :

    http://lisari.blogspot.gr/

  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 2

    2 22 2 2 2

    1 1 2x xf (x) x 3 x 3 2x

    2 x 3 2 x 3 2 x 3 x 3

    2

    1 1 1f (1)

    241 3

    :

    1 1 1 1 3

    y 2 x 1 y x 2 y x2 2 2 2 2

    () 0x 1 , 1,2 , :

    () : y x

    (),

    1,2 .

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    1 1 1 f (1)

    241 3

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    1

    2 () :

    1() : y x

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    2 2

    1 xf x 2x

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    2

    xf x 0 0 x 0

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    2

    xf x 0 0 x 0

    x 3

    2

    xf x 0 0 x 0

    x 3

    f 1x 0 f 0 3 .

    x 0

    f (x)

    f (x) 2 1

    http://lisari.blogspot.gr/

  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 3

    4.

    0

    2 2 20

    2x 1 x 1 x 1

    f (x) 2 x 3 2 x 3 2 x 3 2lim lim lim

    x 1 x 1 x 1 x 3 2

    22 2 2

    x 1 x 1 x 12 2 2

    x 3 4 x 3 4 x 1lim lim lim

    x 1 x 3 2 x 1 x 3 2 x 1 x 3 2

    x 1

    x 1lim

    x 1

    x 1

    2 2x 12x 1 1 1 2 2 1

    lim2 2 4 2x 3 2 1 3 2x 3 2

    1.

    .

    1 2 1

    26 1P 52 26 51 51 25

    51 2 1

    25

    26. 51 .

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    N M A 6P M A 6

    N 51 51

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    .

    P P 1

    P 1 P

    7

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    1 10

    http://lisari.blogspot.gr/

  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 4

    71

    10

    10 10 7

    10 17

    510

    17

    30

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    10 N 10 10

    7 17

    51 51 51 3010 10

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    .

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    .

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    ( ) 24

    ( ) 2( )

    ( ) 51

    http://lisari.blogspot.gr/

  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 5

    1. 1

    =

    : 3,3 5

    5 12

    2

    2 1 ()

    1 t 3

    5 2 5 1 11

    6 2 6 1 13

    v :11,12,13

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    v 12

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    12

    i ix v

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    iv i ix v

    0 1 0

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    3 2 6

    4 4 16

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    12 6

    i i 6

    i 1

    x v 27 x

    http://lisari.blogspot.gr/

  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 6

    8

    x3

    :

    6

    i i

    6i 16 6 6

    x v27 x8

    x 84 3x 96 3x 15 x 5v 3 12

    .

    ix

    iv

    0 1

    1 3

    2 1

    3 2

    4 4

    5 1

    12

    :

    http://lisari.blogspot.gr/

  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 7

    3. M

    X : 1 2 3 4 5x 1,x 2,x 3,x 4,x 5

    :

    ix

    iv

    1 2

    2 3

    3 2

    4 4

    5 1

    12

    http://lisari.blogspot.gr/

  • http://lisari.blogspot.gr

    10 06 2016

    2016: lisari team 8

    ix

    iv i ix v

    1 2 2

    2 3 6

    3 2 6

    4 4 16

    5 1 5

    12 5

    i i

    i 1

    x v 35

    5

    i i

    i 1

    x v35

    x xv 12

    http://lisari.blogspot.gr/

    1. Eksofullo.docx2. - . 2.docx3. - .docx4.---.doc