ΜΑΘΗΜΑΤΙΚΑ ΕΠΙΛΟΓΗΣ Γ ΕΠΑΛ

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Text of ΜΑΘΗΜΑΤΙΚΑ ΕΠΙΛΟΓΗΣ Γ ΕΠΑΛ

  • 1

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    : f

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  • 2 ... f(x)= 1 . ()=1

    : 0 0 0 0

    ( ) ( ) ( )lim lim lim lim1 1h h h h

    f x h f x x h x hh h h

    + + = = = = ()=1

    ... (2)=2

    f()=2 : 2 2 2 2 2

    0 0 0

    0 0

    ( ) ( ) ( ) 2lim lim lim( 2 )lim lim ( 2 ) 2

    h h h

    h h

    f x h f x x h x x x h h xh h h

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    += = + =

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    f R c ,... (cf(x))=cf(x) ,xR

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    ( ) ( ) ( ) ( ) ( ) ( )lim lim lim( ) ( )lim ( )

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    + + + = = =

    + = =

    ( ( )) ( )cf x cf x =

    f ,g ... (f(x)+g(x))=f(x)+g(x)

    : 0 0

    ( ) ( ) ( ) ( )lim ( ) lim ( )h h

    f x h f x g x h g xf x g xh h

    + + = =

    F(x)=f(x)+g(x) :

    0 0

    0 0 0

    ( ) ( ) [ ( ) ( )] [ ( ) ( )]lim lim[ ( ) ( )] [ ( ) ( )] ( ) ( ) ( ) ( )lim lim lim

    ( ) ( )

    h h

    h h h

    F x h F x f x h g x h f x g xh h

    f x h f x g x h g x f x h f x g x h g xh h h

    f x g x

    + + + + += =

    + + + + + = = + =

    = +

    (f(x)+g(x))=f(x)+g(x)

  • 3

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    ) : 1 2 1 21 1...

    ... ... 1f f f

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    i

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    x = x < x <

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    i i ix t v x f x

    v v= = == = =

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    . . 1 1 2 2

    1 2

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    ...

    v v

    v

    x w x w x wx

    w w w

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    (R) . (s2) ti .

    2 2 2 2

    1 1 1

    1 1( ) ( ) ( )v k k

    i i i ii i i

    s t x x x f x xv v= = =

    = = = i ti

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    . .

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  • 5

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    fi=ki/v : 0 1if f1+f2++f=1 ( )

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  • 6 { }1 2, ,..., kA a a a= . ()

    1 2( ) ( ) ... ( )kP a P a P a+ + + , . ( ) 0P =

    . , ... ( ) ( ) ( )P A B P A P B = +

    , A B = () = () + ()

    : ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( )

    N A B N A N B N A N BP A B P A P BN N N N +

    = = = + = +

    ... () = 1- ()

    A A = A A = , :

    ( ) ( ) ( ) ( ) ( ) ( ) 1 ( ) ( )P A A P A P A P P A P A P A P A = + . = + . = + () = 1-()

    . , .. ... ( ) ( ) ( ) ( )P A B P A P B P A B = + :

    : ( ) ( ) ( ) ( )N A B N A N B N A B = + ()+() A B , :

    ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )N A B N A N B N A B N A N B N A BP A B P A P B P A B

    N N N N N +

    = = = + = +

    ( ) ( )A B P A P B . . . :

    : A B ()() ( ) ( )( ) ( )N A N BN N

    . () () .

    . , .. ... ( ) ( ) ( )P A B P A P A B = :

    - A B :

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

    - A B